Structurally Complex Reservoirs - Special Publication no 292 (Geological Society Special Publication)

Structurally Complex Reservoirs The Geological Society of London Books Editorial Committee Chief Editor BOB PANKHURS...

Author: S. J. Jolley | D. Barr | J. J. Walsh | R. J. Knipe

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Structurally Complex Reservoirs

The Geological Society of London Books Editorial Committee Chief Editor

BOB PANKHURST (UK) Society Books Editors

JOHN GREGORY (UK) JIM GRIFFITHS (UK) JOHN HOWE (UK) PHIL LEAT (UK) NICK ROBINS (UK) JONATHAN TURNER (UK) Society Books Advisors

MIKE BROWN (USA) ERIC BUFFETAUT (FRANCE ) JONATHAN CRAIG (ITALY )

RETO GIERE´ (GERMANY ) TOM MC CANN (GERMANY ) DOUG STEAD (CANADA ) RANDELL STEPHENSON (NETHERLANDS )

Geological Society books refereeing procedures The Society makes every effort to ensure that the scientific and production quality of its books matches that of its journals. Since 1997, all book proposals have been refereed by specialist reviewers as well as by the Society’s Books Editorial Committee. If the referees identify weaknesses in the proposal, these must be addressed before the proposal is accepted. Once the book is accepted, the Society Book Editors ensure that the volume editors follow strict guidelines on refereeing and quality control. We insist that individual papers can only be accepted after satisfactory review by two independent referees. The questions on the review forms are similar to those for Journal of the Geological Society. The referees’ forms and comments must be available to the Society’s Book Editors on request. Although many of the books result from meetings, the editors are expected to commission papers that were not presented at the meeting to ensure that the book provides a balanced coverage of the subject. Being accepted for presentation at the meeting does not guarantee inclusion in the book. More information about submitting a proposal and producing a book for the Society can be found on its web site: www.geolsoc.org.uk.

It is recommended that reference to all or part of this book should be made in one of the following ways: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) 2007. Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292. DEE , S. J., YIELDING , G., FREEMAN , B. & BRETAN , P. 2007. A comparison between deterministic and stochastic fault seal techniques. In: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 259–270.

GEOLOGICAL SOCIETY SPECIAL PUBLICATION NO. 292

Structurally Complex Reservoirs

EDITED BY

S. J. JOLLEY Shell UK Limited, Aberdeen, UK

D. BARR BP Exploration, Aberdeen, UK

J. J. WALSH University College Dublin, Ireland and

R. J. KNIPE University of Leeds, UK

2007 Published by The Geological Society London

THE GEOLOGICAL SOCIETY The Geological Society of London (GSL) was founded in 1807. It is the oldest national geological society in the world and the largest in Europe. It was incorporated under Royal Charter in 1825 and is Registered Charity 210161. The Society is the UK national learned and professional society for geology with a worldwide Fellowship (FGS) of over 9000. The Society has the power to confer Chartered status on suitably qualified Fellows, and about 2000 of the Fellowship carry the title (CGeol). Chartered Geologists may also obtain the equivalent European title, European Geologist (EurGeol). One fifth of the Society’s fellowship resides outside the UK. To find out more about the Society, log on to www.geolsoc.org.uk. The Geological Society Publishing House (Bath, UK) produces the Society’s international journals and books, and acts as European distributor for selected publications of the American Association of Petroleum Geologists (AAPG), the Indonesian Petroleum Association (IPA), the Geological Society of America (GSA), the Society for Sedimentary Geology (SEPM) and the Geologists’ Association (GA). Joint marketing agreements ensure that GSL Fellows may purchase these societies’ publications at a discount. The Society’s online bookshop (accessible from www.geolsoc.org.uk) offers secure book purchasing with your credit or debit card. To find out about joining the Society and benefiting from substantial discounts on publications of GSL and other societies worldwide, consult www.geolsoc.org.uk, or contact the Fellowship Department at: The Geological Society, Burlington House, Piccadilly, London W1J 0BG: Tel. þ44 (0)20 7434 9944; Fax þ44 (0)20 7439 8975; E-mail: [email protected]. For information about the Society’s meetings, consult Events on www.geolsoc.org.uk. To find out more about the Society’s Corporate Affiliates Scheme, write to [email protected]. Published by The Geological Society from: The Geological Society Publishing House, Unit 7, Brassmill Enterprise Centre, Brassmill Lane, Bath BA1 3JN, UK (Orders: Tel. þ44 (0)1225 445046, Fax þ44 (0)1225 442836) Online bookshop: www.geolsoc.org.uk/bookshop The publishers make no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility for any errors or omissions that may be made. # The Geological Society of London 2007. All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with the provisions of the Copyright Licensing Agency, 90 Tottenham Court Road, London W1P 9HE. Users registered with the Copyright Clearance Center, 27 Congress Street, Salem, MA 01970, USA: the item-fee code for this publication is 0305-8719/07/$15.00. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 978-1-86239-241-0 Typeset by Techset Composition Ltd., Salisbury, UK Printed by MPG Books Ltd, Bodmin, UK Distributors North America For trade and institutional orders: The Geological Society, c/o AIDC, 82 Winter Sport Lane, Williston, VT 05495, USA Orders: Tel þ1 800-972-9892 Fax þ1 802-864-7626 E-mail [email protected] For individual and corporate orders: AAPG Bookstore, PO Box 979, Tulsa, OK 74101-0979, USA Orders: Tel þ1 918-584-2555 Fax þ1 918-560-2652 E-mail [email protected] Website http://bookstore.aapg.org India Affiliated East-West Press Private Ltd, Marketing Division, G-1/16 Ansari Road, Darya Ganj, New Delhi 110 002, India Orders: Tel þ91 11 2327-9113/2326-4180 Fax þ91 11 2326-0538 E-mail [email protected]

Preface This volume was inspired by the Structurally Complex Reservoirs conference held in Burlington House, London between 28th February and 2nd March 2006. We are very grateful to ITF (Industry Technology Facilitator, Aberdeen) and to Duncan Anderson, in particular, for their tremendous efforts in helping us to arrange sponsorship and conference materials for the meeting. The event was sponsored by BG Group, BP, Chevron, ConocoPhillips, Hess, Maersk Oil, Shell, Statoil, Total, and Badleys, Beicip, EarthDecision, RDR, Roxar and Schlumberger: part of their sponsorship also helped to fund the colour production of this volume. We owe a debt of gratitude to all of the authors who wrote and submitted papers to what we think is a unique collection of benchmark papers on the topic of structurally complex reservoirs. We thank them for investing their time and science in this enterprise, and for producing their manuscripts by the deadlines required to guarantee publication in 2007. We also owe a similar debt to all of the referees who devoted their time, effort and expertise to reviewing papers included in this volume: Rolf Ackermann, Mohammed Ameen, Andy Aplin, Wayne Bailey, Tony Batchelor, Mark

Bentley, Stephan Bergbauer, Peter Boult, Peter Bretan, Paul Brockbank, Rob Butler, John Cain, Ben Clennell, Conrad Childs, Gary Couples, Tim Couzens, Steve Dee, David Ferrill, Quentin Fisher, Haakon Fossen, Brett Freeman, Peter Frykman, Alan Gibbs, Richard Gibson, Mark Hempton, Richard Hillis, Bob Holdsworth, Richard Jolly, Greg Jones, Richard Jones, Tor Anders Knai, Hemin Koyi, Bob Krantz, Tron Kristiansen, Gavin Lewis, Richard Lisle, Jingsheng Ma, Laurent Maerten, Gerhard Ma¨kel, Tom Manzocchi, Eddie McAllister, Alan Morris, Steve Naruk, Tim Needham, Jon Olson, Signe Ottesen, David Peacock, Paul Pijush, Peter Rowbotham, Iain Sinclair, Takeo Tanuguchi, Simon Tod, Chris Townsend, Jonathan Turner, Bruno Vendeville, Alastair Welbon, Scott Wilkins, Martha Withjack, Graham Yielding, Bjornar Ystad, Mark Zoback, and other referees who preferred to remain anonymous. We hope readers will find this book both interesting and informative. Steve Jolley, Dave Barr, John Walsh, Rob Knipe, 18 June 2007.

Contents Preface JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. Structurally complex reservoirs: an introduction DOMI´ NGUEZ , R. Structural evolution of the Penguins Cluster, UK northern North Sea WELBON , A. I. F., BROCKBANK , P., BRUNSDEN , D. & OLSEN , T. S. Characterizing and producing from reservoirs in landslides: challenges and opportunities HOFFMAN , K. S. & NEAVE , J. W. The fused fault block approach to fault network modelling TERTOIS , A. L. & MALLET , J. L. Editing faults within tetrahedral volume models in real time KRE´ ZSEK , C., ADAM , J. & GRUJIC , D. Mechanics of fault and expulsion rollover systems developed on passive margins detached on salt: insights from analogue modelling and optical strain monitoring KENDALL , J.-M., FISHER , Q. J., COVEY CRUMP , S., MADDOCK , J., CARTER , A., HALL , S. A., WOOKEY , J., VALCKE , S. L. A., CASEY , M., LLOYD , G. & BEN ISMAIL , W. Seismic anisotropy as an indicator of reservoir quality in siliciclastic rocks WILKINS , S. J. Fracture intensity from geomechanical models: application to the Blue Forest 3D survey, Green River Basin, Wyoming, USA LEWIS , H., HALL , S. A., GUEST , J. & COUPLES , G. D. Kinematically-equivalent but geomechanically-different simulations of fault evolution: the role of loading configurations HALL , S. A. & LEWIS , H. A damage domain approach to integration of geomechanics and seismic anisotropy for fractured reservoir characterization BERGBAUER , S. Testing the predictive capability of curvature analyses FERRILL , D. A., MORRIS , A. P. & SMART , K. J. Stratigraphic control on extensional fault propagation folding: Big Brushy Canyon monocline, Sierra Del Carmen, Texas FISHER , Q. J. & JOLLEY , S. J. Treatment of faults in production simulation models CHILDS , C., WALSH , J. J., MANZOCCHI , T., STRAND , J., NICOL , A., TOMASSO , M., SCHO¨ PFER , M. P. J. & APLIN , A. C. Definition of a fault permeability predictor from outcrop studies of a faulted turbidite sequence, Taranaki, New Zealand DEE , S. J., YIELDING , G., FREEMAN , B. & BRETAN , P. A comparison between deterministic and stochastic fault seal techniques MYERS , R. D., ALLGOOD , A., HJELLBAKK , A., VROLIJK , P. & BRIEDIS , N. Testing fault transmissibility predictions in a structurally dominated reservoir: Ringhorne field, Norway ZIJLSTRA , E. B., REEMST , P. H. M. & FISHER , Q. J. Incorporation of fault properties into production simulation models of Permian reservoirs from the southern North Sea MANZOCCHI , T., WALSH , J. J., TOMASSO , M., STRAND , J., CHILDS , C. & HAUGHTON , P. D. W. Static and dynamic connectivity in bed-scale models of faulted and unfaulted turbidites MA , J., VASZI , A. Z., COUPLES , G. D. & HARRIS , S. D. The link between a heterogeneous model and its flow response: examples from fault damage zones highlighting issues in domain discretization and flow simulation HARRIS , S. D., VASZI , A. Z. & KNIPE , R. J. Three-dimensional upscaling of fault damage zones for reservoir simulation MA¨ KEL , G. H. The modelling of fractured reservoirs: constraints and potential for fracture network geometry and hydraulics analysis MATTHA¨ I , S. K., GEIGER , S., ROBERTS , S. G., PALUSZNY , A., BELAYNEH , M., BURRI , A., MEZENTSEV , A., LU , H., COUMOU , D., DRIESNER , T. & HEINRICH , C. A. Numerical simulation of multi-phase fluid flow in structurally complex reservoirs BARR , D. Conductive faults and sealing fractures in the West Sole gas fields, southern North Sea

vii 1 25 49 75 89 103

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137 159 173 185 203 219 235

259 271 295 309 337

353 375 405

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ZHANG , X., KOUTSABELOULIS , N. C., HEFFER , K. J., MAIN , I. G. & LI , L. Coupled geomechanics –flow modelling at and below a critical stress-state used to investigate common statistical properties of field production data MAIN , I. G., LI , L., HEFFER , K. J., PAPASOULIOTIS , O., LEONARD , T., KOUTSABELOULIS , N. C. & ZHANG , X. The Statistical Reservoir Model: calibrating faults and fractures, and predicting reservoir response to water flood Index

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Structurally complex reservoirs: an introduction S. J. JOLLEY1, D. BARR2, J. J. WALSH3 & R. J. KNIPE4 1

Shell UK Limited, Altens Farm Road, Nigg, Aberdeen AB12 3FY, UK (e-mail: [email protected])

2

BP Exploration, Burnside Drive, Farburn Industrial Estate, Dyce, Aberdeen AB21 7PB, UK 3

Fault Analysis Group, School of Geological Sciences, University College Dublin, Belfield, Dublin 4, Ireland

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Rock Deformation Research Ltd, School of Earth Sciences, University of Leeds, Leeds LS2 9JT, UK Abstract: Structurally complex reservoirs form a distinct class of reservoir, in which fault arrays and fracture networks, in particular, exert an over-riding control on petroleum trapping and production behaviour. With modern exploration and production portfolios commonly held in geologically complex settings, there is an increasing technical challenge to find new prospects and to extract remaining hydrocarbons from these more structurally complex reservoirs. Improved analytical and modelling techniques will enhance our ability to locate connected hydrocarbon volumes and unswept sections of reservoir, and thus help optimize field development, production rates and ultimate recovery. This volume reviews our current understanding and ability to model the complex distribution and behaviour of fault and fracture networks, highlighting their fluid compartmentalizing effects and storage-transmissivity characteristics, and outlining approaches for predicting the dynamic fluid flow and geomechanical behaviour of structurally complex reservoirs. This introductory paper provides an overview of the research status on structurally complex reservoirs and aims to create a context for the collection of papers presented in this volume and, in doing so, an entry point for the reader into the subject. We have focused on the recent progress and outstanding issues in the areas of: (i) structural complexity and fault geometry; (ii) the detection and prediction of faults and fractures; (iii) the compartmentalizing effects of fault systems and complex siliciclastic reservoirs; and (iv) the critical controls that affect fractured reservoirs.

Structurally complex reservoirs form a distinct class of reservoir in which fault arrays and fracture networks, in particular, exert an over-riding control on petroleum trapping and production behaviour (Møller-Pedersen & Koestler 1997; Coward et al. 1998; Jones et al. 1998; McClay 2004; Swennen et al. 2004; Sorkhabi & Tsuji 2005; Lonergan et al. 2007), (e.g. Fig. 1). With ‘easy oil’ becoming scarce, modern exploration and production portfolios are commonly held within geologically complex settings, in which reservoirs of this type are the common form. This means that there is an increasing technical challenge to find new prospects and to extract remaining hydrocarbons from structurally complex reservoirs in mature provinces such as the North Sea. New technologies developed in recent years permit exploration in increasingly hostile environments and economic development and production from some structurally complex discoveries that were previously ‘parked’ decades ago for technology catch-up. Our understanding, detection and ability to model and predict the complex distribution of faults, fracture networks, and other reservoir heterogeneities and their fluid compartmentalizing

effects and storage-transmissivity characteristics, is a critical element in predicting the dynamic fluid flow and geomechanical behaviour of these fields under production conditions. Improved analytical and modelling techniques enhance our ability to locate connected hydrocarbon volumes and unswept sections of reservoir, and ultimately help optimize field development, production rates and ultimate recovery. Geoscientists and engineers are addressing these issues within research institutions and operating asset environments around the world. Although research initiatives on structurally complex reservoirs vary considerably in scope, size and content, their ultimate goal from a practical perspective is to optimize the production of hydrocarbons from reservoirs. The research programmes brokered by the Industry Technology Facilitator (ITF) in the UK are a good example of such initiatives. These were 3-year thematic research collaborations between nine oil companies and over 25 academic and related research institutions in Europe, the USA and Australasia. The research programmes were specifically designed to improve our understanding

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 1–24. DOI: 10.1144/SP292.1 0305-8719/07/$15.00 # The Geological Society of London 2007.

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Fig. 1. Examples of structurally complex reservoirs. (a) Geo-cellular model of an intensely faulted field from the North Sea, in which shallow marine reservoirs are disaggregated into a patchwork of fault blocks. These fault blocks are mostly compartmentalized by sealing faults, and an intra-reservoir shale formation. Most of the fault blocks therefore require a dedicated producer well, and a water injector well to give pressure support to the producer as the block depletes. (b) Models of the fractured Clair reservoir, UKCS (fig. 12 of Barr et al. 2007). On the left are multiple stochastic realizations of a discrete fracture (conductive fault) network. One realization is shown in black and nine others generated using the same method, but with different seed numbers, in cyan. The red realization was made using a different method but with the same seed number as the black realization. On the right is a geo-cellular model showing upscaled effective fracture permeability from one realization.

STRUCTURALLY COMPLEX RESERVOIRS

of the broad range of geoscience and engineering issues associated with production from these complex reservoirs. The results were the catalyst for an international conference (held 28 February – 2 March 2006) and this Special Publication, which brings together a critical mass of papers on related topics. Together they provide the reader with an overview of global research on structurally complex reservoirs. This introductory paper aims to provide context to this collected work (papers cited in bold are those presented in this book) and an entry point into the subject. We have selected a series of sub-themes for this overview, which include: (i) structural complexity and fault geometry; (ii) the detection and prediction of faults and fractures; (iii) the compartmentalizing effects of fault systems and complex siliciclastic reservoirs; and (iv) the critical controls that affect fractured reservoirs. A final section gives a brief comment on future directions and priority areas that emerge from the collected papers.

Structural complexity The past couple of decades have seen the emergence of a variety of significant innovations in the analysis and modelling of structurally complex reservoirs. These developments have been driven mainly by the increased demands of the oil and gas industry and its reservoirs, but have also, crucially, been underpinned by vast improvements in both the quantity and quality of available data. 3D seismic datasets are now common and have been supplemented by a multitude of processing techniques and attribute analyses that facilitate the definition and mapping of structures. Just as 2D seismic has given way to 3D, recent developments in the technology of 4D seismic provide strong indicators that direct imaging of the impact of structures on flow will eventually become an essential tool in optimizing production from many complex reservoirs. Well production data have also increased in both quality and quantity, providing more refined indicators of reservoir production flow and pressure, with the improved constraints arising from horizontal wells and inclined well trajectories, and the general increase in the number of wells available from mature fields in particular. In addition, improved core recovery and improvements in the geological and fluid flow data from reservoirs have been matched by developments in both the capacity and functionality of existing modelling approaches. All these developments have enabled and stimulated both fundamental and applied research on the many technical issues related to the study of structurally complex reservoirs.

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This volume presents a series of papers on the full range of these technical issues. The complete workflow of the reservoir structural geologist is well represented, with papers extending from the detection, mapping and prediction of faults through to fault property modelling and flow modelling of reservoir production. The running order of papers generally tracks this workflow, with the downstream side of it being essentially subdivided into faulted siliciclastic reservoirs and fractured reservoirs. This basic distinction is important, since it focuses the emphasis of studies which address the impacts of structural complexity on reservoir fluid flow. In many siliciclastic reservoirs, the reservoir units which host the hydrocarbons have higher porosities and permeabilities than the faults that transect them. In these circumstances, the faults are detrimental to flow, acting as baffles or barriers within a generally more permeable host rock sedimentary sequence (e.g. Knipe 1993; Downey 1994; Knipe et al. 1997, Yielding et al. 1997; Jones et al. 1998; Manzocchi et al. 1999, 2002; Hesthammer & Fossen 2000; Fisher et al. 2001; Brown 2003; James et al. 2004). Issues such as the primary connectivity of reservoir units will also impact the behaviour of the flow system. In fractured reservoirs, the host rocks (which include limestone, chalks or granite/basement as well as siliciclastic rocks) generally have lower permeabilities than the faults and fractures that transect them (Reiss 1980; Plumb 1994; Nelson 2001; Lonergan et al. 2007). Fluid flow in such reservoirs incorporates the combined effects of pervasive fracture systems, including joints, combined with faults. In these circumstances, the faults will often represent the main flow pathways that tap into the host rock volume which provides the hydrocarbon storage capacity. In a low porosity rock such as granite, storage is primarily in the fracture system but the storage and flow domains may be separate (e.g. with most storage in joints but most flow in conductive faults). In an impermeable but porous rock like some chalks, storage is primarily in the matrix (host rock) but flow is in the fractures. Some siliciclastic fractured reservoirs have a similar split between the flow and storage domains, but in others the matrix permeability is high enough to provide a significant flow contribution, leading to particularly complex behaviour during hydrocarbon recovery. Some fractured limestone reservoirs similarly have zones of high matrix porosity, or of leaching (e.g. palaeokarsts) or secondary porosity (e.g. due to dolomitization). This duality of faults and fractures as flow conduits or barriers is a fundamental property and provides the primary distinction between the two reservoir types. Faults within higher porosity-permeability reservoir units can represent baffles/barriers

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whereas faults in tighter porosity, lower permeability reservoir units, can act as conduits to fluid flow. This duality of behaviour is not drawn on geographical grounds, but can in fact occur on the same structure intersecting different rock sequences, or form on the same structure at different times, when the host rock properties and deformation conditions have changed over geological time. The convenience of defining end-member faulted reservoirs, nevertheless, provides a useful conceptual framework, even if individual reservoirs or faults may sometimes incorporate both types of flow behaviour. For example, faults within fractured reservoirs may act as both seals and conduits over different parts of the fault surface or even at different times during the production history of the field.

Fault geometry Characterization and modelling of individual structurally complex reservoirs, typically begins with the 3D seismic definition and mapping of faults and other structures. Using newly developed modelling tools it is now possible to generate high quality 3D structural ‘framework’ models which can cope with structural complexities, such as intersecting and mutually cross-cutting faults, but also provide a means of examining displacement variations and cross-fault juxtapositions (Badley et al. 1990; Needham et al. 1996; Rutten & Verschuren 2003). These analyses are central elements in many of the studies presented in this volume and are now relatively routinely performed on reservoirs characterized by normal faulting. Geometrical complexities, including those involving cross-cutting and antithetic faults (and related branch-lines), and rapid changes in fault system polarity, present challenges to existing modelling techniques and have led developers to research alternatives which can better represent geological ‘reality’ (e.g. Hoffman & Neave). However, geological modelling is often conducted with the aim of producing geo-cellular models for use in reservoir flow simulation. Thus, it is necessary not just to honour relevant geological complexity at the ‘input’ stage of the 3D structural model, but also at the ‘output’ stage of the simulator grid. The adverse consequences of failing to do so are amply demonstrated in the field examples provided by Fisher & Jolley. Tertois & Mallett show that newly developed methods of tetrahedral volume modelling are capable of modelling such complexly faulted reservoirs, and Mattha¨i et al. describe a hybrid meshing approach which, combined with innovative methods for the discretization of governing

equations, could provide a comprehensive basis for future modelling efforts. Nevertheless, for the foreseeable future, most simulation of structurally complex reservoirs will take place in ‘conventional’ simulators operating on more-or-less regular grids of six-sided cuboid-shaped cells. More sophisticated approaches can and should be used to ‘ground-truth’ such simple models so that we understand the consequences of simplification and where it is or is not acceptable to do so. A recurrent theme in the reservoir modelling of structurally complex reservoirs is that the technical limitations of reservoir modelling packages and the computing hardware which runs them will always be a constraining factor, and that their improvement will always lag behind our technical demands. Interpretation, mapping and visualization tools, by contrast, are now very refined, as are those permitting structural modelling of various types (e.g. displacement analysis, restoration, cross-fault juxtaposition analysis). These tools arise not only from the practical demands of reservoir studies but also from developments arising from research into the geometry and kinematics of faults. Indeed current models for many fundamental aspects of faulting either derive from, or were significantly advanced by, the analysis of seismic data at reservoir scales, including: (i) fault growth models (e.g. Walsh et al. 2002); (ii) polygonal faulting (e.g. Cartwright 1994; Watterson et al. 2000); (iii) salt-related deformation (e.g. Vendeville & Jackson 1992a, b; Jackson 1995); (iv) relays and segment linkage (e.g. Childs et al. 1995); and (v) fault populations (e.g. Yielding et al. 1996; Cowie et al. 1996). There are, of course, many outstanding technical issues relating to the geometry and kinematics of faults, some of which are considered in this volume. Some reservoirs are characterized by very complex fault geometries with different modes of faulting developed at different times and with varying degrees of reactivation. These types of reservoir present a major challenge because although quantitative constraints on normal faults are relatively good, the characteristics of reverse fault systems and strike-slip fault systems, in particular, are less well understood and therefore much less predictable. Similarly, the nature and controls on the reactivation of earlier faults is not well understood, not just on geometrical grounds, but also in terms of flow. Nevertheless, Domı´nguez provides a comprehensive description of structural complexity arising from the interaction of two different fault trends and later fault reactivation in the Penguins field cluster, North Sea. Although this study shows how structurally complex reservoirs can arise from a relatively simple configuration of deformations, careful analysis is capable

STRUCTURALLY COMPLEX RESERVOIRS

of unravelling the structural evolution of the fault arrays. Barr shows that contractional inversion of earlier rift-related normal faults in Southern North Sea gas fields has implications beyond the purely geometrical, with the breaching of earlier seals and creation of conductive fracture networks sometimes having a profound effect on reservoir flow. Many of the studies in this volume have been conducted on reservoirs which include what might be considered relatively conventional tectonic normal fault systems and existing constraints on their geometry, at least in a generic sense, are generally good. High quality reservoir modelling demands the accurate characterization of fault geometries as a prelude to fault seal prediction (e.g. Dee et al.), juxtaposition analysis (e.g. Myers et al.) and fault property characterization and modelling (Fisher & Jolley; Zijlstra et al.), and therefore benefits from existing geometrical constraints. Similarly our current knowledge of the geometry and growth of gravity-slide normal fault systems, related either to the instability of delta slopes or salt, is now quite refined. The analysis and restoration of related structures of both tectonic and gravity-driven fault systems from 3D seismic data has provided excellent constraints on their kinematics (e.g. Jackson 1995). Physical modelling has made a significant contribution to our knowledge of fault array development (e.g. McClay et al. 2002) and the kinematics of gravity-driven fault systems, in particular (e.g. Vendeville & Jackson 1992a,b). The work of Kre´zsek et al. shows how recent technological innovations in imaging and quantifying deformation are capable of defining refined models for the kinematic evolution of margins characterized by salt-related thin-skinned tectonics. We anticipate that similar types of physical modelling studies will provide excellent constraints on the origin, geometry and growth of these types of fault system. Footwall collapse-related landslides are a type of gravity slide system which is less well understood, despite the fact that it is now well established that they dominate the structure of many reservoirs, including some in the North Sea. Although these reservoirs present challenges that are very different from other types of faulted reservoirs, they have not received a great deal of attention. Welbon et al. provide a comprehensive consideration of landslide structures and outline the challenges and opportunities provided by reservoirs in landslides and a new workflow for their characterization. The foregoing discussion highlights some of the technical issues associated with fault systems that have different geometries, origins and multiple event histories. These issues are generally the subjects of the first phase of reservoir characterization, which is mainly conducted by seismic

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interpretation, sometimes supplemented by core analysis. The results of this type of analysis provide the essential backdrop for later phases of the structural geology and flow modelling workflow. This workflow involves a variety of technical components, the selection of which depends on the characteristics and type of reservoir concerned.

Detection and prediction of faults and fractures Fault detection Fault and fracture prediction in the modern exploration and production industry typically begins with 2D or 3D seismic interpretation. The issues and pitfalls involved in representing the geometry of discrete, seismically mappable faults have been discussed in the previous section. In principle, every fault that can be identified on 3D seismic can be mapped in three dimensions and characterized for flow simulation purposes. In practice, of course, inherent limitations of seismic data resolution mean that only the largest faults can be mapped as discrete objects. For example, very high quality seismic may permit faults with throws down to c. 5–10 m (and lengths of hundreds of metres) to be mapped, but a decrease in seismic quality could mean that faults with throws of c. 30–40 m may not be resolvable. In a general sense, the fault system can be subdivided into faults that are large enough to be visible and mappable from offset of reflectors, and the smaller faults that have more subtle seismic signatures that can sometimes be mapped from ‘attribute’ lineations on seismic reflectors (bedding horizons) using various amplitude variation and discontinuity detection techniques. Thus, in the absence of clear reflector offsets, the smaller faults are seen where amplitude becomes dimmed due to net destructive interference of diffracted seismic energy at the fault scarps (see Townsend et al. 1998 for discussion), and where horizon dip and dip azimuth changes sharply. Some of the latter attribute types assume that bedding is approximately planar or gently curved and that lines along which reflector dip changes rapidly are the ‘smeared out’ response to a fault too small to resolve as a discrete object. Others use wavelet correlation techniques to detect a change in seismic character, tracking along a single horizon or in time-slices or a 3D volume. In the first case the discontinuity detected is Horizon A – Fault – Horizon A; and in the second case, Horizon A – Horizon B. Most seismic workstations and many geomodelling software packages have tools such as coherency (Bahorich & Farmer 1995), dip,

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edge-detection or semblance (Marfurt et al. 1998) available; indeed they are routinely used as interpretation aids in the early stages of defining seismically resolvable faults (e.g. Jones & Knipe 1996; Townsend et al. 1998). Care needs to be taken, however, to filter-out erroneous interpretations where seismic quality is sub-optimal, since some ‘semi-automated’ methods are capable of picking noise in addition to ‘real’ faults in the data (Hesthammer et al. 2001). It is a natural extension of this process to use these techniques to define subseismic lineaments. Curvature of seismically mapped surfaces can also serve as an edge detection tool, with hanging wall and footwall cut-offs corresponding to parallel bands of negative and positive curvature respectively (e.g. Murray 1968; Lisle 1994; Stewart & Podolski 1998). It is advisable to filter the input data spatially, to separate gross structural configuration (long wavelength) from faults (short wavelength), and to enhance the signal:noise ratio and resolution at the target wavelength (Bergbauer et al. 2003). Other techniques to enhance the detection of small-scale faulting include shaded illumination, dip-azimuth and directional curvature (extracted along parallel, vertical observation planes). Some techniques are optimally sensitive to faults with particular azimuthal orientations, and care must be taken to ensure that preconceived ideas about the fault trend do not lead to a failure to detect faults with an unanticipated orientation. Practical limitations on the time allocated for interpretation and the requirement to construct a computationally tractable model commonly lead to simplifications or omissions in the final model. Jolley et al. (2007) and Fisher & Jolley have shown how careful thought about the flow implications of a particular simplification can lead to better designed models, given the same data and model size restrictions. They also show that time spent in getting the starting model right is more than repaid by the reduced reservoir engineering effort required to generate a robust, history-matched flow simulation model.

to one which is kinematically self-consistent, by retro-deforming the current geometry to a plausible initial condition and then replicating the current geometry through a plausible forward deformation path. Software implementations of this approach are available in 2D and 3D modelling packages which link fairly seamlessly with seismic interpretation and simulation grid building packages. Typically, these assume that displacement is concentrated on the mappable faults, with intervening fault blocks deforming passively as they are carried on the faults. They also commonly assume constant displacement and slip directions on each fault segment, with discontinuous changes in displacement taking place at fault linkages or branch lines. This model is, of course, a simplification and an alternative view of the fault linkage in a system, which is supported by 3D seismic data and by closely spaced 2D observations in mines and quarries, is that displacement variation along fault planes is the norm and that displacement transfer can be accommodated by deformation of the intervening rock volume. These alternative models for fault linkage, referred to as hard- and softlinkage, may generate a very different level of fault connectivity (Fig. 2; cf. Walsh & Watterson 1991). These two end members will display very different flow behaviour, with Figure 2a being more connected than Figure 2b if the faults are conductive, but less connected if they are sealing. Although there is inherent complexity in the variation of natural fault displacement, mapping measurable displacement components such as fault throw, onto fault-plane-projection ‘Allan’ diagrams (Allan 1989), can provide constraints and quality control checks on the interpretation (Barnett et al. 1987; Badley et al. 1990). A common assumption is that gradual displacement

Fault network geometry Fields with only 2D seismic or outcrop data require much more interpolation and have increased ambiguities around fault geometry and linkage. Rules of thumb often come into play then, perhaps informed by analogue data from fields with 3D seismic, from well-exposed outcrops or from laboratory-scale models and kinematic or geomechanical modelling studies. The balanced crosssection approach (e.g. Dahlstrom 1969; Gibbs 1983) aims to constrain the structural interpretation

Fig. 2. Alternative map interpretations of sparse fault observations, e.g. on 2D seismic lines. (a) A connected (hard-linked) end-member with displacement changing only at fault intersections and a trellis-like fault network. (b) A disconnected (soft-linked) end-member with displacement varying continuously across the fault planes and decreasing to zero at the fault tips.

STRUCTURALLY COMPLEX RESERVOIRS

variation is expected of a simple fault, but abrupt changes in displacement imply the presence of a fault intersection or branch line, even if there is currently no intersecting fault mapped at that location (Badley et al. 1990; Needham et al. 1996; Nicol et al. 2002). Modern seismic and geological interpretation packages typically have some ability to display Allan planes, contoured with appropriate parameters, but the facility is not as widely used as it might be. Even 3D seismic has hidden connectivity issues which can benefit from the same interpretation approach as 2D data. For example, fault planes are rarely imaged directly on seismic cross-sections and have to be interpolated between bedding offsets; and interpretation typically begins on a grid of seed lines with the major faults being embedded in the model early as explicit, manually connected features. However, faults can be isolated features and die out downwards as well as upwards (e.g. Barnett et al. 1987; Walsh & Watterson 1991; Cartwright 1994), or merge into a de´collement surface or ductile zone such as salt or overpressured shale (Cartwright 1994; Jackson 1995; Watterson et al. 2000). Whatever the origin or nature of fault displacement variations, failure to define the geometry and connectivity of faults properly may in fact be one of the main sources of error in the modelling of structurally complex reservoirs, despite the fact that fault mapping now benefits from a variety of supporting techniques. The possibility that fault mapping could unhinge a significant number of reservoir studies may reflect the inherent pressures on geologists and geophysicists, to create the definitive ‘top reservoir map’ rapidly, when a more measured and discriminating 3D mapping approach would represent the best means of defining the basic geometry of faulted reservoirs. Failure to recognize the importance of basic fault mapping in 3D can introduce spurious connections or offsets of stratigraphic models. Even where the reservoir geometry is mapped accurately it is also possible that it is not represented accurately in the 3D simulation grid. However, techniques are available in 3D modelling packages to reproduce important fault-related geometrical features faithfully, such as the 3D variations in fault displacement, the geometries of fault intersections and the presence of fault discontinuities (e.g. relays). If these are not applied consistently, they may introduce unavoidable computational penalties to the model and may compromise later fault property modelling (e.g. some geometrical solutions to so-called ‘Y-fault’ geometries involve severe discretization and aliasing of faults). Hoffman & Neave discuss the advantages and limitations of some 3D fault modelling approaches in common use today.

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Subseismic scale faulting As well as being used to define discrete faults, seismic data, particularly 3D seismic, can be used to detect smaller fault and fracture distributions. Simple seismic attributes responsive to surface roughness at a scale too small to be resolved individually include coherency and its relatives (discrete faults give rise to linear features, whereas background faulting or fracturing generates a broad zone of low coherency) and reflection amplitude (small-scale faulting produces waveform interference and scattering of the seismic energy which dims the amplitude). By their nature these attributes are insensitive to whether the fractures are conductive or sealing. More sophisticated attributes are available with multicomponent and multidirectional seismic acquisition, which allows measurements of seismic anisotropy (Verwest 1994; Bouska & Johnston 2005). A directionally anisotropic seismic response is strongly suggestive of open fractures, because the seismic response of a closed fracture or granulation seam is only subtly different from that of matrix, but that of an open fracture is very different, especially if it is filled by a compressible fluid such as oil or gas. The simplest measure is velocity anisotropy, where seismic rays travelling across an aligned fracture set are slower than those travelling parallel to the fractures (Crampin 1981; Hudson 1981; MacBeth 1995). Multidirectional or orthogonal fracture sets can give rise to an isotropic seismic response, but it may still be possible to infer fracture presence if the velocity is anomalously slow in all azimuths. Obviously that requires a meaningful definition of ‘anomalously low’, and may not be possible where there are large matrix velocity variations due to fluid or lithology effects. Fracture predictions based on seismic anisotropy and coherency-like attributes have been presented by, for example Bloch et al. (2003) and Barr et al. (2007). Calibration against core or image log data is advisable (e.g. Smith & McGarrity 2001) and proof-of-concept may be necessary before committing to a 4C OBC survey. More sophisticated approaches involve shear wave splitting (e.g. Winsterstein 1989; Owen et al. 1998; Maultzsch et al. 2003) and seismic amplitude variation with offset and azimuth (AVOA; Lynn & Thomsen 1990; Hall & Kendall 2003). Kendall et al. show that the magnitude of the seismic response in the Clair field, west of Shetland, depends not only on the fracture anisotropy but also on the matrix anisotropy introduced by bedding and mineral grain alignment. The seismic rays at large source:receiver offset travel at an angle to bedding rather than perpendicular, and therefore ‘see’ a combination of fracture and

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matrix anisotropy. Kendall et al. therefore devoted considerable effort to matrix characterization, as a necessary precursor to seismic fracture prediction. They find an AVOA response between thin-bedded and massive sandstone units which is different in fractured and unfractured cases, even with the same fracture intensity in each unit, and thus they can distinguish between cases where the upper or lower unit is the more fractured. The two end-member geometries in Figure 2 have very different strain distributions between and around the faults. This strain distribution is important because it provides a potential entrypoint to the geomechanical prediction of subseismic faults and fractures, which can enhance or retard flow depending on whether they are more or less conductive than their host rock. Most faults are surrounded by a ‘damage zone’ tens of metres wide, comprising subsidiary faults and fractures (Antonellini & Aydin 1994; McGrath & Davison 1995; Caine et al. 1996; Knipe et al. 1997; Foxford et al. 1998; Beach et al. 1999; Hesthammer et al. 2000; Billi et al. 2003; Berg & Skar 2005). In this context damage refers to a change in the effective bulk properties of the rock caused by a swarm of small-scale structures and may cause flow enhancement or retardation (a drilling or production engineer will often restrict the term damage to flow retardation). In addition, the volumes between the faults have typically suffered volumetric or shear strain, perhaps related to bending during accommodation to the fault surface (e.g. Nicol et al. 2002; see also papers in McClay 2004) or to satisfy compatibility contraints as displacement dies out in a soft-linked fault array (e.g. Fig. 2b, Barnett et al. 1987; see also Hedland 1997; Soliva & Benedicto 2005). There may also be a systematic distribution of subseismic faults related to the large-scale structures. These can have a simple relationship to the major faults (e.g. antithetic in the hanging wall). If their distribution is unpredictable or poorly understood they can be modelled stochastically by assuming or observing a size, frequency relationship such as a fractal or power-law distribution and extrapolating downscale (Childs et al. 1990; Gauthier & Lake 1993; Ma¨kel). There are potential pitfalls in the analysis of such data (Heffer & Bevan 1990; Cowie et al. 1996; Yielding et al. 1996; Belfield 1998) and it is only meaningful within a genetically related range of structures. Subseismic faults might reasonably be extrapolated downscale from seismic faults but in circumstances where mechanical stratigraphy exercises a strong control on the fracturing process, fault or fracture systems may not have fractal geometries and the notion of extrapolation of fault size distributions could be flawed (see Nicol et al. 1996 and Soliva & Benedicto 2005 for discussion). This scenario almost

certainly applies to stratabound joints even in circumstances where they have a component of shear displacement and may display some fractal characteristics (e.g. Odling et al. 1999; Barr). Finally, the mapped fault tip locations are themselves limited by seismic resolution. Where displacement:distance relationships are well defined (e.g. Walsh & Watterson 1987; Cowie & Scholz 1992) it is possible to extrapolate the fault beyond the seismically resolved location to a predicted tip-line, based on the observed rate of displacement loss where it is still seismically observable (Yielding et al. 1996; Rutten & Verschuren 2003). Similarly, the width and internal geometry of fault damage zones has been well characterized in numerous outcrop analogues (Antonellini & Aydin 1994; Hesthammer et al. 2000; Billi et al. 2003; Odling et al. 2005) and can be predicted by selecting the right analogue and control parameters such as fault displacement and host-rock lithology. Once the geometry and petrophysical properties of the small-scale features are defined (see below), their flow implications can be simulated by explicitly modelling the observed fractures or a stochastic representation of them (Heath et al. 1994; Manzocchi et al. 1998; Walsh et al. 1998; Harris et al. 1999, 2003, this volume).

Strain modelling and fracture prediction Perhaps less widely acknowledged is the fact that two identical mapped fault networks can have different bulk strain distributions—although it has long been taught in structural geology textbooks that there are many potential paths to a particular deformed state (e.g. Hobbs et al. 1976, p. 32). If a record of the strain history during progressive deformation is preserved it may be possible to distinguish between alternative deformation paths (e.g. Ramsay 1967 p. 119–120). Lewis et al. demonstrate with a simple example how very different deformation paths resulting in very different internal strain distributions can produce identicalseeming fault and horizon geometries. Structural modelling software is available and under development which tracks the deformation history of the fault blocks (i.e. ‘kinematic restoration’) during the forward modelling step. Such models are nonunique, but they can yield valuable insights into potential subseismic deformation. In some software packages the non-uniqueness is exposed to the user, in that explicit kinematic choices have to be made about the fault-slip and inter-fault deformation mechanism; in that case it should be obvious that a matched result is a possible but not unique solution. But the more automated the process, developed perhaps in the interest of broadening the pool of potential practitioners beyond structural geology specialists, there is a greater risk of users

STRUCTURALLY COMPLEX RESERVOIRS

assuming that the result must be right ‘because the model says so’. Notwithstanding these limitations, considerable effort is currently devoted to developing techniques to predict fracture and small-scale fault distribution at a scale much less than seismic resolution and comparable to that of core or well logs. Typically these will be predictions of the ‘joint-like’ rather than ‘fault-like’ populations. The joint-like population includes shear fractures or granulation seams as well as tension fractures—essentially those features that are small and dispersed enough to form components of an effective medium at the scale of observation, rather than discrete entities. Long-wavelength curvature can be used as a strain predictor (e.g. Stewart & Podolski 1998) with the expectation that outer-arc extensional strains will be associated with open, tensile fractures. Use of this flexural beam model requires the correct choice of mechanical layering and identification of the neutral surface. Fractures would be predicted in synclines below the neutral surface as well as in anticlines above the neutral surface. Caution is advised in interpreting the output maps, as many existing approaches make potentially unacceptable simplifying assumptions (see Bergbauer & Pollard 2003 for review). Combinations of curvature attributes can be used to define a ‘shape curvature’ (Bergbauer et al. 2003), which classifies a mapped surface (at a particular wavelength) into anticlines, synclines, domes, basins etc. Shape curvature may be a predictor of fracture style rather than fracture intensity (e.g. orthogonal v. conjugate v. unidirectional, or shear v. tensile). Bergbauer describes an outcrop example of a fold where curvature shape and magnitude were poor predictors of fracture orientation and intensity but good predictors of fracture style. In this case, fractures developed within the relatively slab-like limbs are passively rotated and propagate along their axes, whereas additional strains at the curved fold hinge have reactivated fractures in shear. Indeed, Ferrill et al. describe the deformation within a monoclinal fault propagation fold, in which they find flexural shearing of well-bedded stratigraphy in the mid-limb has re-worked earlier formed fractures, such that in this case, fracture style is related to dip domain. Both papers emphasize the role of mechanical stratigraphy in governing the underlying deformation processes. Geomechanical models, typically discretized using finite element or boundary element techniques (Crouch & Starfield 1983), go beyond simple curvature. These use elastic (e.g. Wilkins) or more complex, elastic –plastic, constitutive laws to predict the stress and strain distribution between mapped faults. The situation is at its simplest where the structure in question formed as

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a result of a single episode of progressive deformation. In that case it may be acceptable to approximate the driving stress or strain state by that required to deform an initial bedding configuration to the current field geometry. Predicted elastic strains are often scaled, to compensate for the fact that deformation was intermittent with some relaxation of elastic strain and accumulation of permanent strain between increments (e.g. Wilkins). More sophisticated constitutive laws such as the elastic – plastic one used by Lewis et al. attempt to model the progressive evolution of permanent strain through a deformation cycle. Refinements used include variable treatment of fault mechanics (purely frictional v. more complex formulations where some faults are effectively given finite strength) and the introduction of compaction, fluid pressure and gravity effects. An alternative approach where the deformation history is too complex to unravel or represent, is simply to model the present day stress state, treating the reservoir as a relatively homogeneous body of rock dissected by weak faults which locally perturb the far-field stress trajectory; an approach similar to that used in earthquake modelling. Stress perturbations and interactions around faults can be used to predict stress trajectories between faults (from which favoured open fracture orientations can be deduced), or to high-grade as potentially conductive those faults which are closest to a frictional failure criterion. Attempts are now being made to track strain evolution through complex deformation episodes (e.g. Dunbar & Cook 2003; Maerten & Maerten 2006), which in principle allows better control of fracture initiation and subsequent modification. The geomechanical models can be used to help define the displacement history (i.e. geomechanically based structural restoration, e.g. Maerten et al. 2006) or the displacement history can be extracted from a kinematic structural restoration and used as boundary condition inputs to a geomechanical model (e.g. Lewis et al. 2004). The end-point of such modelling is rarely the prediction of individual fracture formation, except for those subseismic faults that are large enough to implement in a 3D reservoir simulation model. More typically, dilational strain is taken as an open fracture indicator and compactional strain as a closed fracture indicator. The magnitude and orientation of the principal stress or strain axes are used to constrain fracture orientation, type and intensity (Ma¨kel; Wilkins). The constraint can either be deterministic, via empirically defined lookup tables or correlations to well data; or stochastic where the geomechanical model outputs are used as constraints on a discrete fracture network which is then upscaled to effective flow properties in a reservoir simulator (e.g. Sabathier

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et al. 1998). An important modelling decision is whether to calibrate directly to static well and seismic observations, or to bypass those and calibrate directly to dynamic, reservoir engineering observations (e.g. Barr). An argument in favour of the latter approach is that the fracture description is a means to an end and that end is populating a reservoir simulation model. Ultimately, the fracture description has to be upscaled to effective cell properties (e.g. Bourbiaux et al. 1997), a step that introduces its own set of assumptions and uncertainties. In addition, the fractures in a vertical well may be unrepresentative even of the surrounding (say) 100 m 100 m grid cell area. A weakness of direct dynamic calibration is that it introduces an empirical step involving poorly defined or understood processes. If the next well fails to match predictions, there is little chance of understanding why, and it will likely be handled by making another poorly understood empirical adjustment. Hall & Lewis attempt to introduce some rigour into this process, by placing seismic and geomechanical attributes on a common descriptive footing, as an effective medium sampled at the target reservoir simulation scale.

Fault compartmentalization Faults transecting siliciclastic reservoirs in which the reservoir units have high porosities and permeabilities generally act as baffles or barriers to flow. In these circumstances, following the 3D mapping of seismically imaged faults and, sometimes, the prediction of subseismic faults, the next major step is definition of fault properties and their incorporation within reservoir models, either as transmissibility multipliers on individual faults, or as upscaled effective permeabilities, in the case of subseismic faults. Here we describe the technical issues and methodologies associated with this phase of the structural geology workflow.

Fault zone properties Natural fault zones are characterized by threedimensionally complex juxtapositions and displaced lenses of host stratigraphy, and modified porosity-permeability variations within the suite of different fault rock products and fracture arrays that the zones usually contain (e.g. Knipe 1993, Childs et al. 1997, this volume; Knipe et al. 1997; Foxford et al. 1998; Fisher & Knipe 1998, 2001; Gibson 1998; Ingram & Urai 1999; Skerlac 1999; Sperrevik et al. 2000; Aydin & Eyal 2002; Jourde et al. 2002; Berg & Skar 2005; Eichhubl et al. 2005; Shipton et al. 2005; van der Zee & Urai 2005). However, there are significant hurdles

to overcome in predicting the distribution of these lithological fragments and fault rock properties within a fault zone, from the often sparse information available to field appraisal and development teams. It is well known that clay content plays a significant role in reducing permeability in fault rocks developed within siliciclastic rocks (e.g. Fisher & Knipe 1998, 2001; Manzocchi et al. 1999; Sperrevik et al. 2002). Consequently algorithms have been developed which attempt to calculate the distribution of average clay content (and therefore the general permeability distribution) within fault zones—from the reservoir properties, clay content and shale bed distributions within the adjacent stratigraphy—at a similar scale to that of a typical simulation model fault (cf. Yielding et al. 1997; Doughty 2003). As discussed by Fisher & Jolley, at the modelling stage many of the predictive algorithms are based on the input of ‘clay contents’ derived from geophysical well log data—and care is therefore needed to account for uncertainties in petrophysical calculation of the ‘shale’ or ‘clay’ content measures (VShale, VClay), and to ensure that these results are compatible with independent measures of clay content (often taken from core samples). The three most commonly used algorithms, developed over a decade ago, use some of the basic processes which entrain clay minerals and discretely bedded shales into a fault zone (Fig. 3). Thus, Shale Gouge Ratio (SGR, Yielding et al. 1997) is based on mechanical mixture of shaley material within a fault gouge, assuming that the resulting fault rock/gouge clay content approximates to the average collective stratigraphic clay content which has been displaced past any given point on the fault. The Clay Smear Potential (CSP, Bouvier et al. 1989; Fulljames et al. 1997) predicts the length continuity of a shale bed plastically smeared into the fault from the fault throw and source shale bed thickness. The Shale Smear Factor (SSF, Lindsay et al. 1993) focuses on predicting the thickness continuity of smears caused by ductile smearing and abrasion of shales and also as a function of throw and source shale bed thickness. In some situations, for example where shale and/or sand beds are relatively thin, it can be argued that clay smears are accounted for within the SGR algorithm, once stratigraphy is upscaled. Where the shale layers are thicker, the smears can become more robust and continuous, such that they preserve stratigraphic compartmentalization despite the faulting but the detail of this is not captured by SGR. Consequently, several proprietary algorithms have developed within the industry as a spin-off from these basic SGR/CSP/SSF forms, mostly in an attempt to integrate them into a harmonic averaging tool for predicting fault zone clay content. Childs et al. provide an important

STRUCTURALLY COMPLEX RESERVOIRS

(a)

Vcl5, Δz5 Vcl4, Δz4

throw

Vcl3, Δz3 Vcl2, Δz2 Vcl1, Δz1

Shale Gouge Ratio

SGR =

Σ (Vcl.Δz) throw

x 100%

(b)

Δz distance

Clay Smear Potential

CSP =

Σ

thickness distance

2

(c)

Δz

throw

Shale Smear Factor

SSF =

throw thickness

Fig. 3. Fault seal algorithms, commonly applied in low/ mid net-to-gross (mixed sand-shale) reservoir stratigraphies. (a) Shale-Gouge-Ratio (SGR; Yielding et al. 1997), (b) Clay-Smear-Potential (CSP; Bouvier et al. 1989; Fulljames et al. 1997), (c) Shale-SmearFactor (SSF; Lindsay et al. 1993). From Jolley et al. (2007), modified from Yielding et al. (1997).

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dataset in this regard, which shows that clay smears can become disengaged from their source layers, to form ‘slugs’ within the fault zone. Their outcrop observations on faulted New Zealand turbidites do not support a systematic arrangement of clay smears in relation to their source beds, and so they have developed a stochastic approach to distribute the smears within the fault planes, which they term the probabilistic Shale Smear Factor (PSSF). An interesting outcome of such a model is to provide effective properties at high throw to bed thickness ratios, which are indeed similar to other approaches, such as SGR. This work therefore provides a rationale for the successful application of these approaches, even though the deformation mechanism which it implicitly assumes may not be correct. Similarly, detailed modelling of fluid flow through a realistic representation of fault damage zones by Harris et al. supports the conclusion that the simpler, commonly used approach of harmonically averaging volume-weighted fault-rock permeability, is a useful first approximation in assessments of the flow impact of subseismic faults (Walsh et al. 1998). The prevailing stress and temperature during deformation also controls the degree of grain breakage (cataclasis) and crystallization of some cementation types, and consequent permeability collapse within the fault zone (Knipe 1989; Zhang et al. 1990; Wong et al. 1997; Chester & Chester 1998; Fisher et al. 2000, 2003). Thus, despite the popular view from the usage of clay-content algorithms in fault seal analysis described above (that low clay content faults developed in sand-rich reservoirs do not seal), under the ‘right’ conditions and geohistories, sealing on a production timescale is also possible in low clay content fault rocks. Where there is a strong palaeotemperature gradient across a field or cluster of fields, this can lead to profound differences in fault compartmentalization and consequent production characteristics (e.g. Hesthammer et al. 2002). However, these low clay content cataclastic seal types can become brittle, damaged and leaky if a field is subsequently deformed under different stress and lower temperature conditions (e.g. Leveille et al. 1997). Barr gives a detailed description of the complex distribution of fault seal compartmentalization, and conductive faults and open fracture systems in the sand-rich aeolian reservoirs of the West Sole gas fields. He shows that sealing lithified cataclasites formed in fault zones during an early rifting phase at high pressures and temperatures with some influence from host sediment facies type on crystallization of certain cementation phases; and that open seal-breaching fracture systems developed during later contractional inversion and fault reactivation at lower pressures and temperatures. In general

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terms the sealing and open structures tend to be mutually exclusive. Although data resolution and a significant element of clustering or selectivity in the reactivation processes introduce technical difficulties, it has nevertheless been possible to use this model to detect reactivation and therefore predict the general distribution of intact and breached seals and/or open fracture networks within the fields.

Static fault seal prediction Exploration projects commonly use a deterministic approach to ‘map’ fault zone properties, such as SGR, within a fault plane and thereby calculate the predicted hydrocarbon columns that can be accumulated and held by sealing faults over geological time (e.g. Yielding 2002). These methods are based on explicit modelling of reservoir and non-reservoir juxtapositions and the sealing properties of fault rocks. However, James et al. (2004) suggest that static fault seals are controlled exclusively by juxtaposition, and they describe a stochastic approach to fault seal analysis, which models variation of stratigraphic stacking across a fault to assess its hydrocarbon retention capacity. An energetic debate has since developed on the conference circuit between proponents of these two radically differing approaches. Dee et al. use the data presented by James et al. (2004), in order to compare and contrast the results that are achieved by these two radically different methods on the same dataset. They compare the stochastic analysis with a standard SGR-based approach and suggest that despite the conceptual differences between the deterministic and stochastic methods, the results are remarkably similar. This study therefore appears to provide another useful validation of a widely applied ‘rule of thumb’.

generally tested by comparing the match between actual historical production data and the simulated production history, the so called ‘history match’. In detail, the fluid flow between adjacent cells in a standard simulation model is expressed by the cell-cell ‘transmissibility’ (a function of the geometry and permeability of the cells). The reduced permeability of an intervening fault is accounted for by correcting the cell – cell transmissibility with a fault transmissibility multiplier, a function of fault rock thickness and permeability (Fig. 4; e.g. Knai & Knipe 1998). However, although the stratigraphic controls on field compartmentalization are routinely addressed within generally accepted geologically-rationalized tools and workflows, it has been an industry-wide experience that the flow retarding effects of the faults are treated in an ad hoc manner by the reservoir engineer, late in the workflow. It is possible to achieve a history match by using the production data to guide manual application of geologically unrealistic faults and fault properties to steer flow and pressures around the model in this way. However, this is likely to be an artificial compensation for other inadequacies and uncertainties in the model, which then become obscured by this activity (Fisher & Jolley). It follows that the more of these trial-and-error amendments there are in a model, the less likely it is that its simulated flow approximates to reality (despite the history match) and consequently the ‘prediction mode’ becomes unreliable. Such structural uncertainty can seriously impact field development planning and production management (e.g. Corrigan 1993; Lia et al. 1997). However, as described below, data, tools and methods have evolved in recent years to permit more valid, systematic incorporation of fault properties within simulation models.

Production fault seal modelling Under production conditions lower permeability fault zones will generally lead to the compartmentalization of pressure distributions, hydrocarbon saturations and contacts across the faults. Fault property modelling under these conditions therefore attempts to define the rate of fluid flow across the faults in order to quantify the connected petroleum volumes that can be accessed by any given well or group of wells. Numerical flow simulation models including the effects of fault properties are now routinely used to guide field development, production management and well planning decisions (e.g. Dake 2001). The reliability of the ‘prediction mode’ of a model is

Fig. 4. Fault transmissibility multiplier (TM) calculation between faulted cells of a simulation model. These calculations differ in detail between simulation software packages and this cartoon (from Jolley et al. 2007, modified after Manzocchi et al. 1999) ignores cell dip terms and assumes net:gross ratios and intersection areas of 1.0.

STRUCTURALLY COMPLEX RESERVOIRS

Incorporating fault properties in production simulation models The fault seal algorithms described above provide the building blocks for inclusion of fault properties within simulation models. For example, Manzocchi et al. (1999, 2002) provided robust methods with which it is possible to invoke these algorithms, to incorporate the flow-retarding effects of faults systematically. Their methods calculate geologically realistic fault transmissibility multipliers from the upscaled model geometry and geo-cellular properties (e.g. stratigraphic distribution of clay, porosity, permeability). Thus, fault rock clay content prediction methods (e.g. SGR/CSP/SSF and other similar algorithms) can be calculated from the reservoir geometries and properties implicit within the geo-cellular cornerpoint grid of a simulation model. The first-order sensitivity of a simulation to structural influence is caused by juxtaposition of flow units and non-flow units across the faults, since this affects the basic ‘plumbing’ within the model. Hoffman & Neave and Tertois & Mallet discuss some of the pitfalls, procedural limitations and potential solutions to the necessary compromises that are made in constructing a 3D fault model from seismic data and the subsequent simulation grid. Thus, geometric flaws introduced at that stage result in inappropriate layer juxtapositions in the cellular model, and also restrict the geologist’s ability to properly represent fault zone properties. Constraints on simulation cell geometry, driven by a desire for simple flow formulae that can be solved by existing technology in a commercially useful timeframe, can introduce compromises in fault representation since it is typically the faults that contribute most geometrical complexity to the model. However the validity of flow simulation models (and therefore the reliability of their results) can be improved vastly through inclusion of geologically realistic faults, integrated with systematically calculated fault zone properties (e.g. Jolley et al. 2007; Fisher & Jolley). In this approach, SGR and/or an SGR/smear algorithm combination can be calculated and used as a proxy for fault rock clay content and integrated with fault rock permeability data to systematically assign fault transmissibility multipliers within simulation models (sensu Manzocchi et al. 1999). Myers et al. provide a case study from a North Sea fluvial reservoir in which the history matches obtained from simulation models are progressively improved by incorporating increasingly realistic fault geometries and stratigraphic architectures. This incremental approach helped to narrow the uncertainty range on fault properties applied to faults in the simulation. Jolley et al. (2007) found that provided a geologically valid model was

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transferred to the simulator, the best history matches were then achieved in a fraction of the usual project time by integrating fault rock property data acquired from drill cores obtained within and close to a given reservoir to calculate the multipliers. This was particularly the case where the sampled fault rocks had experienced a similar stress-temperature (burial) history to that of the study reservoir.

Modelling interaction between faults and stratigraphic complexities Fisher & Jolley review the wide-range of uncertainties associated with the data acquisition and processing, interpretation and modelling phases of the fault property modelling workflow. Additionally, limitations within the generally available modelling technology, force a tension between efforts to capture and preserve the geological information which is critical to fluid storage and flow, and efforts to distil the geology down to more basic elements in order to satisfy a simulation model’s computational memory budget. Care therefore needs to be exercised when characterizing and simplifying stratigraphic details to assign average properties to model cells, as this can disengage continuous depositional features and/or introduce erroneous connections between layers in a model (Myers et al.). For example, it is a common experience that actual flow connectivity within a reservoir is less than that implied by a geo-cellular model of the field. As Fisher & Jolley point out, these effects are frequently assumed to be caused by sealing faults, leading to erroneous ad hoc edits being applied to the structure of the model. There is an alternative, entirely logical explanation for these effects—since the averaging of thin shale beds into a net:gross value for each cell, and the stacking of these cells within the model, can overlook the compartmentalizing effects of relatively thin shale layers between sand bodies, unless these shale layers are explicitly modelled. Despite the obvious interdependence between faults and stratigraphic complexities in controlling compartmentalization, there have been few published attempts to characterize the interplay between these elements directly (e.g. Ainsworth 2006). Manzocchi et al. use a comprehensive suite of faulted and unfaulted models of sheet-like turbidite deposits, to examine the interplay between stratigraphic elements, faulting and fault zone properties using the PSSF method developed by Childs et al. Instead of using the more traditional cellular modelling methods and net:gross ratio to build their models of sand and shale distribution, Manzocchi et al. have developed a bed-scale modelling method which explicitly

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includes a measure of sand body connectivity, known as the amalgamation ratio. Compared to data collected from outcrops of similar turbidite deposits, this method was found to give a far more realistic stratigraphic architecture and interbed connectivity in the models. Describing their results in terms of percolation theory, they found that high net:gross sheet turbidite sequences can be very poorly amalgamated/connected. In those circumstances, the introduction of arrays of subseismic faults (, c. 5 m throw) only reduces the connectivity within models under a rare combination of circumstances and in some situations, the relative influence of faults and stratigraphic elements on flow connectivity in the models were indistinguishable.

Multi-phase flow properties of faults Given the very small pore throats which characterize many fault rocks, water-wet faults (i.e. those having a water film coating all the grain surfaces in the fault rock and thus impinging on its available pore space) have such high water saturations close to the free water level (FWL) of a reservoir that they may have negligible relative permeability to hydrocarbons. At some distance above the FWL the buoyancy force in the hydrocarbon column may be sufficient to overcome the capillary threshold pressure of the fault rock, giving it a finite relative permeability to hydrocarbons, and thus permitting cross-fault flow of oil or gas (for discussion see Fisher et al. 2001; Fisher & Jolley). Traditionally, the multi-phase flow properties of faults have not been included during production simulation modelling, although several key publications have highlighted their importance (e.g. Manzocchi et al. 1998, 2002; Manzocchi 1999; Fisher & Knipe 2001; Rivenæs & Dart 2002; Al-Busafi et al. 2005). A recent innovation in fault handling within reservoir models is the development by Manzocchi et al. (2002) of a method for the inclusion of the two-phase flow properties of faults. Because two-phase properties, unlike single fluid phase properties, cannot be attached to the face of grid blocks in reservoir simulations, this method derives pseudo-relative permeability functions including the fault rock properties in the upstream grid block for cross-fault flow. This method incorporates the saturation and flow rate dependencies of two-phase flow and is a fairly comprehensive treatment of the problem. Zijlstra et al. present flow data from a number of faulted reservoirs suggesting that two-phase flow properties of the faults are important in controlling compartmentalization of fluid production. They support their conclusions by presenting the results of a method for fault property modelling which is easy to

implement and accounts for some of the effects of fault-related single phase and multiphase flow (as described by Manzocchi et al. 1999, 2002).

Upscaling the flow effects of subseismic faults The recognition that subseismic faults could have an impact on flow within siliciclastic reservoirs, has only recently been matched by the development of methods which provide a basis for their incorporation into flow simulation models. Typical approaches involve definition of the upscaled effective properties of subseismically faulted rock volumes, with their eventual implicit inclusion in reservoir simulations. Early work showed that for typical fault densities and geometries (including connectivities), subseismic fault arrays will generally only begin to have a significant impact on flow within reservoirs (i.e. decreasing effective permeabilities by more than c. 20%) when fault rock permeabilities are at least two orders of magnitude below those of the reservoir host rocks (e.g. Manzocchi et al. 1998; Walsh et al. 1998). For less permeable fault rocks, cross-fault flow decreases rapidly with an increase in flow tortuousity, until flow is dominated by the connectivity of sealing faults (Walsh et al. 1998). Analysis of the impact of damage zones surrounding seismically imaged faults reveals similar features, with newly developed methods being capable of exploring the sensitivity of flow to the full range of geometric and scaling parameters associated with damage zones (see Harris et al. and references therein). Harris et al. (1999, 2005, this volume) extend these sensitivity studies into 3D, and make a strong case for the routine definition of damage zone effective properties and their implicit inclusion in reservoir flow simulations. Ma et al. show the extent to which modelling of small fault arrays is sensitive to the modelling methods used, including such issues as discretization and the preservation of fault connectivity. Other issues need to be resolved, such as the multiscaling properties of faults, associated upscaling challenges and the incorporation and displacement of stratigraphic architectures. In that respect, the bed scale modelling of Manzocchi et al. highlights the complex flow sensitivity of faulted sedimentological sequences, a topic which we anticipate will be the subject of future research. Nevertheless, although adoption of associated modelling and upscaling approaches has, hitherto, been relatively slow (with most attention focused on larger seismically imaged faults), recent advances suggest that the incorporation of subseismic faults and damage zones should become relatively routine within the next decade.

STRUCTURALLY COMPLEX RESERVOIRS

Fractured reservoirs Fractured reservoirs form a special class of structurally complex reservoirs in which hydraulically conductive fractures or faults make a significant contribution to, or dominate, subsurface fluid flow. The interaction between the storage domain (typically dominated by matrix lithologies with relatively high pore volume and relatively low permeability) and the flow domain (typically dominated by fractures with relatively low pore volume and relatively high permeability) leads to complex fluid and pressure behaviour. This makes it difficult to predict field performance, even assuming a ‘perfect’ understanding of the nature and distribution of the fractures. The problem is compounded by the fact that fracture properties are generally more difficult to characterize than matrix, whether from core, well-log or seismic observations. Ma¨kel provides a detailed review of the issues which need to be addressed in describing and modelling fractured reservoirs, focusing on analysis, description and calibration of the fracture network; that is, up to the point at which the fracture model is upscaled to a simulation grid and ‘handed off’ to the reservoir engineer. The fractured reservoir papers in this volume supplement a larger collection of papers on this topic, provided in Lonergan et al. (2007). More general reservoir engineering and geological aspects of fractured reservoirs are also covered by, for example, Aguilera (1995) and Nelson (2001).

Types of fractured reservoir Fractured reservoirs are traditionally classified according to the relative contributions of fracture

15

and matrix permeability (e.g. Reiss 1980; Nelson 2001; Allan & Qing Sun 2003; Ma¨kel; Fig. 5). Because of their high conductivity and low pore volume, fractures typically make a large contribution to the flow domain but a small contribution to the storage domain. For a given well or reservoir, a ‘fracture index’ can be defined to represent the magnitude of the fracture v. matrix contribution. For example, the Fracture Productivity Index of Reiss (1980) ratios the well-test Kh (average permeability times the height of the tested interval) to the matrix Kh; it can be assumed that values much larger than unity reflect a significant fracture contribution. This leads to the interesting observation that ‘how fractured’ a field appears depends not just on the conductivity of its fracture network, but also on that of the matrix properties. For example, the West Sole field (Barr) behaves more like a ‘classical’ fractured reservoir than does the Clair field (Barr et al. 2007), despite having an effective fracture permeability an order of magnitude smaller. That is because it has two or three orders of magnitude less matrix permeability. Fractured reservoirs typically have very heterogeneous porosity and permeability distributions (Mattha¨i et al.), which result in characteristic patterns of well performance with most production coming from the best few wells (e.g. Nelson 2001; Barr). The worst wells have failed to intersect connected, conductive fractures and a large financial benefit would flow from an ability to target only the best well locations. In practice that requires a robust pre-drilling description of the effective fracture network, hence much industry and academic attention is focused on that objective.

Fig. 5. Schematic representation of the common subdivision of fractured reservoir types based primarily on matrix character (Nelson 2001; Allan & Qing Sun 2003; fig. 1 of Ma¨kel (this volume).

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Fracture detection and description The recognition of fractures in wells is also dealt with in detail by Ma¨kel. Core is the most definitive source of fracture information and procedures for describing, identifying and classifying them are well established (e.g. Kulander et al. 1990) but it is expensive to acquire and there are some data limitations to consider. Drilling, core recovery and sample preparation and handling can all modify natural fractures or create new fractures which must be screened out of the subsurface description. Purely drilling-induced fractures have characteristic features that make them easy to recognize (Kulander et al. 1990) but more subtle modifications to the geometry or aperture of pre-existing fractures can be harder to recognize. Open fractures are particularly vulnerable to disturbance because they weaken the rock and the most fractured part of a core may be recovered as uninterpretable rubble. Fractures are likely to have larger apertures at surface than in the subsurface, due to the reduction in effective closure stress, and if the fracture faces can be fitted together perfectly they may have had no subsurface aperture. Most fractures described in reservoirs are not simple planar breaks but have irregular faces and are partially propped or bridged by cementing minerals. Such partially cemented fractures may give the best indication of subsurface aperture and if a genetic link can be drawn between cemented and open fractures, and the cement can be shown to have grown in a single phase, vein widths can also provide a useful indicator (e.g. Ma¨kel). In fields produced by depletion drive, the effective stress acting to close a fracture will increase during production and the most hydraulically effective ones may be partially cemented fractures and shear (or shearreactivated) fractures with mismatching walls (e.g. Barr). Borehole image logging tools are available that can detect fractures with varying degrees of success (Ma¨kel). All image logging techniques have their limitations and ultimately benefit from calibration against overlapping core and all suffer to some degree from an inability to detect fractures subparallel to the wellbore (Ma¨kel). For those fractures that can be detected, a sampling correction may be made for the intersection angle between fracture and wellbore (Terzaghi 1965; Ma¨kel). Fractures perpendicular to the well will be overrepresented relative to fractures oblique to the well and this must be corrected in order to model the 3D fracture density in the surrounding reservoir. However, well productivity may be more influenced by the number of fractures intersected (a well drilled perpendicular to fracture strike will be more productive than one drilled parallel to strike)

and uncorrected data may be preferable if that is the objective of the study. Generally, fracture description and prediction or interpolation in the petroleum industry is not carried out in isolation, but combined with integrated reservoir description and simulation modelling. The process of populating and upscaling a fracture model is conceptually similar to that for a matrix model but generally more difficult and less advanced. Techniques include simple interpolation between wells through conventional geostatistical techniques such as kriging (Olarewaju et al. 1997), neural networks (Ouenes & Hartley 2000) and methods which simultaneously incorporate static and dynamic data (Gauthier et al. 2002). Much modern effort is devoted to the construction and analysis of a discrete fracture network (DFN) model, in which a stochastically or (rarely) deterministically generated set of fractures is populated into a map or a 3D volume. Stochastic models are typically conditioned on seismic, geometric or geomechanical inputs (e.g. Bourbiaux et al. 2002; Maerten et al. 2006; Barr et al. 2007). Ma¨kel provides a worked example for a dataset comprising three wells. Traditionally, the fracture model has been built independently of the matrix, which can result in unwanted interactions, e.g. open fractures may be modelled in shales where observation shows they are absent. Most modelling packages now offer some ability to condition the DFN on a layer-cake or geo-cellular matrix model, enabling the modeller to control the effect of mechanical stratigraphy better (the influence of matrix lithology, typically some combination of rock-strength parameters, on fracture initiation and growth). Fracture models are typically built at multiple scales, to represent both discrete conductive faults or ‘fracture corridors’ and small, dispersed fractures or joints. Calibration can be at both the full-field scale and the scale of a well test (e.g. Rawnsley & Wei 2001).

Flow modelling and reservoir simulation The typical situation whereby fractures dominate the flow domain, and matrix the storage domain; means that ideally, fractures and matrix should be kept independent of one another during flow simulation modelling, by use of explicit fracture and matrix cells. The complexity of fracture networks and the sheer number of simulation grid cells required mean that this is rarely done at scales larger than that of a well test, and even then complex models are difficult to represent fully (Basquet et al. 2005). The extreme aspect ratios, low pore volumes and large permeabilities of fractured cells also create computational difficulties for simulators optimized to solve problems

STRUCTURALLY COMPLEX RESERVOIRS

involving more-or-less cuboidal cells having much the same pore volumes and permeabilities in each. In traditional simulators the simplest solution is to upscale the fractures to effective porosity and permeability at the matrix grid-cell size and merge them with the matrix description. That is successful only in the simplest of cases, typically involving single-phase flow in, for example, dry gas fields without an active aquifer. More complex cases are handled by the dual porosity and dual permeability formulations, in which parallel fracture and matrix descriptions are carried in two identical framework grids, with a transfer function controlling flow between the two domains (Warren & Root 1965; Kazemi et al. 1976). The dual porosity approach allows matrix to fracture fluid flow but not the reverse and is suited to cases where matrix permeability is sufficiently low to be neglected. The dual permeability approach allows flow in both directions and is suited to reservoirs with significant matrix permeability, but is much more computationally demanding. The limitations of these approaches are well known (see Mattha¨i et al. for a summary), particularly with respect to multiphase flow, and research is in progress to develop better framework descriptions (unstructured grids based on tetrahedral or polyhedral cells rather than cuboids, e.g. Mattha¨i et al.; Tertois & Mallet) and alternative solver approaches (e.g. Mattha¨i et al.).

Stress-sensitive reservoirs and critically stressed faults Much fractured reservoir description takes a relatively static view of the fracture network and its flowing properties. Geomechanical models are used to predict fracture occurrence much more often than to represent production-induced changes in the fracture network. Where the matrix can be considered unchanging, the elastic response of pre-existing fractures to changing pressure and stress can be measured or modelled (e.g. Jones 1975; Bagheri & Settari 2005). Production-induced fluid pressure changes can do more than just change the aperture of existing fractures by elastic or plastic opening or closing. They can also reactivate preexisting faults and fractures, create new fractures and deform the rock matrix. An extreme example of the latter effect is seen in the Valhall and Ekofisk fields offshore Norway (Agarwal et al. 1997; Zoback & Zinke 2002; Barkved et al. 2003; Toublanc et al. 2005), where overpressured and undercompacted chalk underwent dramatic production-induced changes in porosity and, particularly, permeability. In such stress-sensitive reservoirs it can be difficult to distinguish matrix

17

from fracture response. Zhang et al. describe a scenario in which they simulate the geomechanical response of a faulted and fractured reservoir to hydrocarbon production and water injection. Many fractured reservoirs are geomechanically insensitive (or at least sufficiently so that it can be treated as a second-order effect) or have a sufficiently homogeneous and reversible response that they can be adequately modelled by introducing pressure-sensitive permeability modifiers to the flow simulation model. Others are geomechanically sensitive and require a coupled simulation modelling approach (e.g. Koutsabeloulis & Hope 1998; Maillot et al. 1999; Settari & Walters 1999; Bagheri & Settari 2005). Acute sensitivity to stress or fluid pressure perturbations which are small relative to the total stress state are a characteristic of critically stressed geological systems. In a reservoir context the critically stressed elements are typically faults that are on the verge of frictional slip or failure (e.g. Zhang et al.). In a broader context the same phenomenon is seen with earthquakes, where small stress perturbations can lock or release previously unstable or stable fault segments (Scholz 1990; Harris 1998). Critically stressed faults can be considered to buffer the subsurface stress state; stress cannot be increased substantially without activating some faults and relieving the stress increase. It is not necessary that every fault is critically stressed, only that the system as a whole is locally near failure. Near-critically stressed faults are likely to have slipped in the recent past in response to tectonic and other stress perturbations; as brittle faulting typically causes dilation, such faults may act as fluid conduits (e.g. Barton et al. 1995; Sanderson & Zhang 2004). That forms the basis for some fracture modelling approaches, where the proximity to failure of each mapped fault, and of smaller features such as subseismic faults or an idealized Andersonian joint set, is used as a proxy for fracture conductivity. Microseismic recording of production or hydraulicfracturing induced earthquakes (e.g. Raleigh et al. 1976; Shapiro et al. 1997, 1999; Segall & Fitzgerald 1998; Rutledge et al. 1998, 2004; Maxwell et al. 2006) suggests that some reservoirs are at least close to being critically stressed, although interpretation may be complicated by poro-elastic effects and/or matrix compaction (e.g. Zoback & Zinke 2002). Where there is observational evidence for fault reactivation, the original proximity of the fault to failure can be inferred if the magnitude of the pore pressure perturbation is known (e.g. Raleigh et al. 1976). In other cases independently determined stress and fluid pressure conditions may lie close to the frictional failure envelope for favourably oriented reservoir faults. A critical

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state can be inferred from the stress-buffer argument, although care must be taken to avoid circularity where some of the input parameters were estimated by assuming a critically stressed state. The extent to which reservoirs in general or only certain faults are critically stressed is debated, although it is strongly indicated in cases where in-situ stress or fracture orientations change across them (e.g. Finkbeiner et al. 1997). Heffer et al. (1995) and Heffer (2002) have documented directionality in flow and pressure transmission during water injection in nominally unfractured reservoirs. The direction is consistent with the predicted strike of those faults which were closest to failure, implying that they were already hydraulically conductive or became so as a result of the fluid pressure increase caused by injection. The inclusion or exclusion of such effects in field simulations can have a significant impact on waterflood sweep efficiency; an unrecognized flow directionality will probably mean that most of the injectors are in the wrong place. Critically or near-critically stressed faults can also pose a drilling hazard. Mud losses may occur if the fault is reactivated by drilling mud pressure, which is typically hundreds or thousands of psi higher than formation pressure; and a fault that has previously been reactivated by injection may be associated with a swarm of open fractures which takes losses even if the drilling mud pressure is too low to cause renewed activation. Conversely, such a fault may be responsible for a formation fluid inflow or ‘kick’ if it communicates directly with an active water injector. A bridge between the categorization of structurally complex reservoirs into faulted and fractured types is provided by Main et al. who document the geomechanical response of a conventional faulted reservoir to water injection. Fault behaviour (as barriers or pathways for enhanced flow) changed during field production but in a complex manner related to stress release or transfer along and between faults. It is likely that most of the permeability increases were due to small-scale fracturing, which locally enhanced fluid flow without necessarily forming a widely connected fracture network. In a sense they describe a fractured reservoir, but perhaps one that was not a fractured reservoir prior to water injection and which might never have displayed such behaviour if produced by primary depletion only.

growing understanding and management of structurally complex reservoirs. These include: 1.

2.

3.

4.

5.

6.

7.

Concluding remarks The papers contained in this volume allow the identification of some priority future directions, where continued research and improved application, calibration and validation will add to the

The vital importance of generating robust 3D structural models as a platform for the detailed modelling of complex faulted or fractured reservoirs. Many reservoir studies suffer from the relatively poor quality of basic fault mapping, a shortcoming which is not compensated for by the application of progressively more sophisticated modelling techniques further along the workflow. The importance of applying new methods for the inclusion of fault properties in reservoir models. These methods provide a means of performing geologically refined history matches, and an improved basis for defining fault properties and for production forecasting. The need to develop effective upscaling workflows to ensure inclusion of subseismic structural complexity at the right level of detail in flow simulations. This requirement applies not only to the inclusion of subseismic faults and damage zones, but also to the preservation of features that may be below the resolution of a simulation grid (e.g. relays). The requirement to progress beyond the notion of a single deterministic model, to incorporate the broad range of fault- and structure-related uncertainties. New methods can be used to incorporate uncertainties, but their widespread application may require a change in culture, together with the general acceptance that high quality geologically-refined production forecasting takes time! The importance of improving the links between flow and mechanical feedback processes for the complex stress paths, reactivation of faults and other dynamic fracture damage experienced by reservoirs. Algorithmic improvements in geomechanical simulation (and reductions in computer costs) would extend the range of fields where coupled flow simulation modelling is routinely applied. The introduction of geomechanical rigour into kinematic structural restoration and of kinematic constraints into geomechanical simulations would yield a coupled approach which simplifies both sets of constraints simultaneously with consequential benefits for flow prediction, particularly in fractured reservoirs. Understanding the role of structure in reservoir and fluid behaviour on timescales much longer than production, will yield important insights, primarily in the context of CO2 sequestration. There are lessons to be learned here from the contrasting behaviour of faults and fractures in conventional reservoirs, as observed when

STRUCTURALLY COMPLEX RESERVOIRS

8.

comparing static (exploration) performance with dynamic (production) performance. Cross-learning is available from the mining, toxic and radioactive waste disposal industries, which have had to make similar judgements about the long-term behaviour of fault or stratigraphic seals and fractures. The importance of improving our understanding and ability to model multiphase fluid flow behaviour in both fault-seal and fractured reservoir environments. This will require not just conceptual modelling and computational advance but also laboratory measurements at the limit of current technology and careful calibration against dynamic oil and gas field data. The introduction of a potentially miscible phase in the form of carbon dioxide introduces additional complexity to tertiary recovery and/ or long-term sequestration plans.

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S KERLAC , G. M. 1999. Evaluating top and fault seals. In: B EAUMONT , E. A & F OSTER , N. H. (eds) Handbook of Petroleum Geology: Exploring for Oil and Gas Traps. American Association of Petroleum Geologists. S MITH , R. L. & M C G ARRITY , J. P. 2001. Cracking the fractures – seismic anisotropy in an offshore reservoir. The Leading Edge, 20, 18– 26. S OLIVA , R. & B ENEDICTO , A. 2005. Geometry, scaling relations and spacing of vertically restricted normal faults. Journal of Structural Geology, 27, 317– 325. S ORKHABI , R. & T SUJI , Y. (eds) 2005. Faults, Fluid Flow and Petroleum Traps. American Association of Petroleum Geologists, Memoir, 85. S PERREVIK , S., F ÆRSETH , R. B. & G ABRIELSEN , R. H. 2000. Experiments on clay smear formation along faults. Petroleum Geoscience, 6, 113– 123. S PERREVIK , S., G ILLESPIE , P. A., F ISHER , Q. J., H ALVORSEN , T. & K NIPE , R. J. 2002. Empirical estimation of fault rock properties. In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seal Quantification. Norwegian Petroleum Society, Special Publication 11, 109 –125. S TEWART , S. A & P ODOLSKI , R. 1998. Curvature analysis of gridded geological surfaces. In: C OWARD , M. P., D ALTABAN , T. S. & J OHNSON , H. (eds) Structural Geology in Reservoir Characterization. Geological Society, London, Special Publications, 127, 133–147. S WENNEN , R., R OURE , F. & G RANATH , J. W. (eds) 2004. Deformation, Fluid Flow, and Reservoir Appraisal in Foreland Fold and Thrust Belts. American Association of Petroleum Geologists, Hedberg Series, 1, 1– 2. T ERZAGHI , R. D. 1965. Sources of error in joint surveys. Geotechnique, 15, 287–304. T OWNSEND , C., F IRTH , I. R., W ESTERMAN , R., K IRKEVOLLEN , L., H ARDE , M. & A NDERSEN , T. 1998. Small-scale seismic fault identification and mapping. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. K. (eds) Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 1 –25. T OUBLANC , A., R ENAUD , S., S YLTE , J. E., C LAUSEN , C. K., E IBEN , T. & N A˚ DLAND , G. 2005. Ekofisk Field: fracture permeability evaluation and implementation in the flow model. Petroleum Geoscience, 11, 321– 330. VAN DER Z EE , W. & U RAI , J. L. 2005. Processes of normal fault evolution in a siliciclastic sequence: a case study from Miri, Sarawak, Malaysia. Journal of Structural Geology, 27, 2281–2300. V ENDEVILLE , B. C. & J ACKSON , M. P.A. 1992a. The rise of diapirs during thin-skinned extension. Marine and Petroleum Geology, 9, 331– 353.

V ENDEVILLE , B. C. & J ACKSON , M. P.A. 1992b. The fall of diapirs during thin-skinned extension. Marine and Petroleum Geology, 9, 354–371. V ERWEST , B. J. 1994. Seismic migration in elliptically anisotropic media. Journal of Geophysical Prospecting, 37, 149–166. W ALSH , J. J. & W ATTERSON , J. 1987. Distributions of cumulative displacement and seismic slip on a single normal fault surface. Journal of Structural Geology, 9, 1039–1046. W ALSH , J. J. & W ATTERSON , J. 1991. Geometric and kinematic coherence and scale effects in normal fault systems. In: R OBERTS , A. M., Y IELDING , G. & F REEMAN , B. (eds) The Geometry of Normal Faults. Geological Society, London, Special Publications, 56, 193–203. W ALSH , J. J., W ATTERSON , J., H EATH , A. E. & C HILDS , C. 1998. Representation and scaling of faults in fluid flow models. Petroleum Geoscience, 4, 241–251. W ALSH , J. J., N ICOL , A. & C HILDS , C. 2002. An alternative model for the growth of faults. Journal of Structural Geology, 24, 1669–1675. W ARREN , J. E. & R OOT , P. J. 1963. The behaviour of naturally fractured reservoirs. Society of Petroleum Engineers Journal, September 1963, 245– 255 (SPE426). W ATTERSON , J., W ALSH , J. J., N ICOL , A., N ELL , P. A. R. & B RETAN , P. 2000. Geometry and origin of a polygonal fault system. Journal of the Geological Society, London, 157, 151 –162. W INTERSTEIN , D. F. 1989. Velocity anisotropy terminology for geophysicists. Geophysics, 55, 1070– 1088. W ONG , T.-F., D AVID , C. & Z HU , W. 1997. The transition from brittle faulting to cataclastic flow in porous sandstones: Mechanical deformation. Journal of Geophysical Research, 102,B2, 3009– 3025. Y IELDING , G. 2002. Shale gouge ratio – calibration by geohistory. In: K OESTLER , A. G. & H UNSDALE , R.(eds) Hydrocarbon Seal Quantification. Norwegian Petroleum Society, Special Publication 11, 1–15. Y IELDING , G., N EEDHAM , T. & J ONES , H. 1996. Sampling of fault populations using sub-surface data: a review. Journal of Structural Geology, 18, 135– 146. Y IELDING , G., F REEMAN , B. & N EEDHAM , D. T. 1997. Quantitative fault seal prediction. American Association of Petroleum Geologists Bulletin, 81, 897–917. Z HANG , J., W ONG , T.-F. & D AVIS , D. M. 1990. Micromechanics of pressure-induced grain crushing in porous rocks. Journal of Geophysical Research, 95, 341–352. Z OBACK , M. D. & Z INKE , J. C. 2002. Production-induced normal faulting in the Valhall and Ekofisk oil fields. Pure and Applied Geophysics, 159, 403 –420.

Structural evolution of the Penguins Cluster, UK northern North Sea R. DOMI´NGUEZ Shell UK Ltd, 1 Altens Farm Road, Nigg, Aberdeen AB12 3YF (e-mail: [email protected]) Abstract: The Penguins Cluster is a group of four oil and gas fields in the northern end of the East Shetland Basin. Its structural complexity is caused by the interaction between two or more fault trend populations, fault reactivation and the impact of faulting on the Brent reservoir architecture. This structural picture is further complicated by a NW–SE trending basement lineament interpreted as a Caledonian shear zone. The present day structural configuration is the result of two Mesozoic rifting episodes and their associated thermal subsidence phases. The Permo-Triassic rifting created a number of north– south-trending tilted fault blocks, and was followed by a period of tectonic quiescence until the Middle Jurassic, when a faulting episode coeval with the Brent Group deposition caused footwall rotation, uplift and erosion of the upper Rannoch Formation prior to the deposition of the Etive Formation across the area. The rifting climaxed in the late Jurassic, when the reactivation of pre-existing faults under oblique-slip conditions in the Penguin C Field created small-scale lozenge-shaped transpressional and transtensional fault blocks. The presence of reverse faults in the area is explained with a continuous kinematic model of structural evolution and oblique-slip fault reactivation rather than positive basin inversion.

The Penguins Cluster is a group of four oil and gas fields located at the northern end of the East Shetland Basin (Fig. 1), in Blocks 211/13a and 211/ 14 of the UK northern North Sea, 65 km north of the Brent Field, to which it is tied back (Fig. 2). It was discovered in 1974 by well 211/13-1, which targeted the north–south-trending Penguin Horst, a major Triassic structural feature around which the Penguins Cluster is structured (Fig. 3). The Penguin A field is located in the western flank of the Penguin Horst, with its play being a stratigraphic trap that consists of an up-dip pinchout of the Upper Jurassic Magnus sandstones (Richards et al. 1993; Partington et al. 1993). The Penguin C, D and E fields run from north to south along the eastern flank of the Penguin Horst and share the Brent Group sandstones (Deegan & Scull 1977; Taylor et al. 2003) as their primary reservoir. Here the structural trap is created by a north–south-trend of easterly-tilted Jurassic fault blocks, also known as the Penguins Ridge. Crustal-scale regional cross-sections that pass near the study area based on Yielding et al. 1992 (Fig. 4) reveal a lower section of Triassic and Jurassic tilted fault blocks at a depth of c. 3.0 km overlain by an upper sequence of mostly unfaulted Cretaceous to Cenozoic post-rift sedimentary rocks. The Penguins Cluster is situated on a structurally complex region influenced by two separate structural styles: the Brent Province to the South, mainly affected by north– south-trending faults

related to the opening of the Viking Graben (Badley et al. 1988; Gabrielsen et al. 1999) and the Magnus Province to the NW (De’Ath & Schuyleman 1981; Shepherd et al. 1991) influenced by the opening of the North Atlantic, and mainly affected by NE–SW-trending faults (see Figs 1 & 2). The Penguins Cluster has been on stream since 2003 and, to date, its development has included the drilling of eight sub-horizontal wells aimed at mitigating reservoir compartmentalization caused by the presence of sealing faults and poor intra-reservoir layer connectivity. These wells have sub-horizontal reservoir sections up to 4700 ft long and typically connect two or more fault block compartments. The structural complexity of the Penguins Cluster reservoirs is caused by a combination of four main factors: i) The heavily faulted nature of the producing reservoirs, with fault spacing of less than 100 m in some cases (Penguin D), and the presence of two or more fault trend populations that create intra-field fault block compartments. ii) The sealing nature of some of these faults. Sealing faults have been recognized in Penguin A (different oil compositions sampled at either side of NW –SE-trending faults), Penguin D (oil-bearing reservoir in the north versus a gas accumulation in the south), and Penguin E (different gas– water contact depths logged across faults).

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 25– 48. DOI: 10.1144/SP292.2 0305-8719/07/$15.00 # The Geological Society of London 2007.

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iii) The complex internal Brent reservoir architecture, with thickness changes of the Rannoch Formation and a patchy distribution of the Etive and Tarbert Formations caused by Middle Jurassic faulting and erosion. iv) The presence of small-scale transpressional and transtensional fault blocks that may pose a threat to the drilling of long horizontal wells.

A better understanding of the structural evolution of Penguins and how this fits within the large-scale evolution of the northern North Sea is key for the future development of the Penguins reservoirs and for the exploration and appraisal of near-field prospects. The model of structural evolution presented in this paper aids seismic interpretation by presenting a clear model of structural styles. The study also

' '

Fig. 1. Structural elements map of the North Sea showing the position of the study area in the northern end of the East Shetland Basin. Inset box shows the location of Figure 2. Interpretation of seismic lines A–A0 and B–B0 is shown in Figure 4. Modified from Faerseth (1996).

PENGUINS CLUSTER STRUCTURAL EVOLUTION 20 Km

N Magnus Embayment A C Magnus

Penguins Cluster

D E Don

Tern-Eider Ridge

Beta Murchison

Eider

Tern

Statfjord

Dunlin East Shetland Basin Cormorant

Pelican

Brent Hutton

East Shetland Platform

North Viking Graben Heather Ninian

UK Sector

Fig. 2. Schematic map of the East Shetland Basin showing the location of the Penguins Cluster in relation to the main structural elements and hydrocarbon fields (shaded red). For location see Figure 1.

contributes to reducing the drilling hazards in complex structural areas by predicting the potential location of subseismic flower structures, as well as improving the geological models built in the future by applying a better knowledge of the Brent Group internal reservoir architecture.

Stratigraphy The general stratigraphy of the Penguins area is illustrated in Figure 5. Sedimentary rocks penetrated by wells in Penguins range in age from the Triassic Cormorant Formation sandstones to Cenozoic unconsolidated sediments. Although the base of the Cormorant Formation has not been drilled in Penguins, it is assumed to lie unconformably on a basement of crystalline Caledonian rocks, as encountered in well 211/21-2 of the North Cormorant Field. In the Penguin A field the reservoir consists of Upper Jurassic Magnus Sandstone Member turbidites, absent along the Penguin Ridge. The deltaic and shallow marine Brent Group sandstones (Deegan & Scull 1977; Taylor et al. 2003) form the primary reservoir of the Penguin

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C, D and E fields, targeted by several sub-horizontal wells. The Brent Group rests unconformably over the deep marine Dunlin Group claystones, which form the topseal for the underlying of the Hegre Group. This is made up of the Triassic Cormorant Formation sandstones and the Lower Jurassic Statfjord Formation sandstones, and it constitutes a secondary hydrocarbon reservoir under the Penguin Ridge. The Brent Group is an unconformity-bound sedimentary sequence which varies in thickness between 150 and 300 feet over the Penguins fields. It is divided into four lithostratigraphic formations, with the Ness Formation absent over Penguins. At least one internal unconformity can be identified, at the top of the Rannoch Formation, interpreted as the result of syndepositional fault movements. The base of the Brent Group can be seen to be erosional and unconformable in nature over certain parts of the study area, with its base truncating the underlying Dunlin seismic reflectors. The top Brent is a diachronous unconformity surface, with the overlying Upper Jurassic Heather Formation resting unconformably on top of either the Rannoch, Etive, or Tarbert Formations. The Broom Formation is a non-reservoir quality sandstone package that is 40 feet thick on average. The Rannoch Formation is a shoreface sandstone unit that varies in thickness between 50 feet in 211/14-1s2 and 150 feet thick in 211/14-3. It rests conformably over the Broom Formation, and it can be subdivided into up to eight coarseningupwards shoreface parasequences. The Etive Formation has a patchy distribution over the Penguin C field, only found in the southern and northern ends of the field (PENG-C02 and PENG-C03 wells, respectively), and it is present in all wells drilled to date over the Penguin D and E fields. Interpretation from well data shows that it has a rough tabular shape lying unconformably over the Rannoch Formation, with an average thickness of c. 50 feet and a general trend thickening towards the south, although some degree of erosion at the top of this unit cannot be ruled out. To date, the Ness Formation has not been found in any of the Penguins wells, although it has been identified to the NW of Penguins, in well 211/7-1 of the Magnus area, and is also widespread in the Don Field wells to the south and SW. The Tarbert Formation is a thin veneer of sandstones, up to 15 feet thick, also of patchy distribution encountered when present either at the top of the Rannoch or Etive Formations.

Tectonic history The East Shetland Basin is one of several linked arcuate half-grabens that form the northern North

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Fig. 3. Penguins Cluster Base Cretaceous unconformity depth map in feet. Contour interval is 250 feet. The Base Cretaceous unconformity roughly equates to the top reservoir in the Penguin A (top Magnus Sandstone Member) and C, D & E fields (top Brent Group). The location of seismic lines discussed in the text is shown.

Sea (Lee & Hwang 1993; Odinsen et al. 2000; Coward et al. 2003; Zanella & Coward 2003). Internally, it consists of Jurassic and Triassic tilted fault blocks overlain by Cretaceous and Cenozoic sediments. The East Shetland Basin is an eastfacing rhombic-shaped half graben bounded to the west by the Palaeozoic East Shetland Platform, to the east and south by the Viking Graben, and to the north by the ENE– WSW trending Magnus Embayment (see Figs 1 & 2). The Viking Graben is a NNE– SSW trending Mesozoic rift that represents the northern arm of a Jurassic triple rift system in the North Sea (Yielding 1990).

The northern North Sea is the result of multiple stretching during the Mesozoic, with the two main rifting episodes dated as Permo-Triassic and Jurassic (Badley et al. 1984, 1988; Ziegler 1988; Yielding et al. 1992; Færseth 1996), followed by episodes of passive post-rift thermal subsidence in the early–middle Jurassic, and Cretaceous–Cenozoic, respectively. The underlying basement is Palaeozoic in age and is affected by Caledonian structures formed during the progressive collision of Baltica with Laurentia (Jones et al. 1999). The northern North Sea was affected by east – west (Færseth 1996) or NW–SE (Beach 1987)

PENGUINS CLUSTER STRUCTURAL EVOLUTION

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Fig. 4. Crustal cross-sections of the East Shetland Basin and North Viking Graben, showing approximate location of the study area in Profile A (After Yielding et al. 1992). Location of the lines is shown in Figure 1.

extension that caused the first rifting episode during Permo-Triassic times, followed by tectonic quiescence and post-rift thermal subsidence during the early and middle Jurassic. This Permo-Triassic rifting created a north–south-trending, 180 km wide sedimentary basin (Færseth 1996). Regional seismic lines through the Viking Graben show the Triassic sediments to thicken towards the east, suggesting a relatively deep Triassic basin that had formed in the centre or further east (Færseth 1996) (see Fig. 4). The Permo-Triassic rifting was characterized by north–south-trending faults that form easterly or westerly tilted half grabens. This phase of rifting has been strongly overprinted by late Jurassic extension. There was very little faulting activity during the early to middle Jurassic in the northern North Sea. During this time the area underwent an episode of passive post-rift thermal subsidence during which the Dunlin and Brent Groups were deposited. The second Mesozoic rifting episode affected the northern North Sea during the Jurassic, with the climax of faulting occurring between MidOxfordian to early Kimmeridgian times, and continuing until the early Cretaceous (Rattey & Hayward 1993). There is evidence that faulting may have begun as early as the Middle Jurassic in the northern North Sea (Roberts et al. 1999). This rifting episode developed as a multiple pulses of faulting separated by intervening stages of relative tectonic quiescence; this pattern was a major influence on the nature and architecture of the sediments in the basin (Ravna˚s et al. 2000). Although most authors agree on a rough east– west extension direction for the Jurassic rifting (e.g. Roberts et al. 1990), this structural picture was probably complicated

by slight changes in the extension direction over time. Thus, Thomas & Coward (1995) identified an episode of Oxfordian to Kimmeridgian NW– SE directed extension, followed by a change to NE –SW directed extension during the late Kimmeridgian to early Cretaceous. Overall, the East Shetland Basin was stretched by about 15% during the Jurassic rifting (Roberts et al. 1993). Some authors (Booth et al. 1992; Thomas & Coward 1995) invoke an episode of basin inversion in the East Shetland Basin during the latest Jurassic–early Cretaceous, with strike-slip reactivation of pre-existing structures under a compressional tectonic regime. The tilted fault blocks formed by the Triassic and Jurassic rifting were subsequently eroded by subaerial and shallow-marine processes during the early Cretaceous, and thermal subsidence allowed onlap of sediments onto these eroded blocks, forming the diachronous base Cretaceous unconformity (Zanella & Coward 2003). Following the Jurassic rifting, during the Cretaceous and the Cenozoic, the East Shetland Basin underwent an episode of passive post-rift thermal subsidence, with accumulations of sedimentary rocks up to 4 km thick in the Penguins area.

Structural styles in the Penguins Cluster For discussion purposes, the Penguins Cluster has been subdivided into the following structural areas with characteristic structural styles: the Penguin Horst, the Penguin Lineament, the Penguin Ridge, and the Penguin Basin north and south, as encountered at either side of the Penguin Lineament (Fig. 6).

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R. DOMI´NGUEZ

Fig. 5. Generalized lithostratigraphy of the Penguins Area.

As it is to be expected within its northern North Sea context, the main structural fabric in Penguins has a north– south orientation, as interpreted from time slices (Fig. 6) and fault maps. However, the detailed structural picture is, much more complex, with three other main fault orientation populations identified: west–east, NW–SE and, to a minor extent, NE–SW (see Fig. 3). This diversity in fault trends can be interpreted as derived from the influence of underlying basement

fabrics, the rotation in extension direction during the Jurasssic rifting, and the influence of the NE – SW trending structural grain of the Magnus structural province to the NW.

Penguin Horst The structure of the Penguins Cluster is dominated by the north–south-trending Penguin Horst, a major Triassic structural high some 3 km wide

PENGUINS CLUSTER STRUCTURAL EVOLUTION

31

Fig. 6. (a) Uninterpreted time slice taken through the 3D seismic volume at 3.3 seconds two-way time, and (b) structural interpretation of the time slice showing the structural grain and the main structural areas discussed in the text.

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R. DOMI´NGUEZ

Fig. 7. (a) uninterpreted, and (b) interpreted west to east seismic line across the Penguin A Field, Penguin Horst and Penguin C Field.

PENGUINS CLUSTER STRUCTURAL EVOLUTION

which occurs at about 8500 ft below sea level and contrasts with the neighbouring Penguins Fields structured around it and which occur at depths of around 11000 ft below sea level (see Figs 3 & 6). The Penguin Horst lies on a NE–SW trend of structural highs that can be traced north into the Haltenbanken and Nordland terraces of offshore Norway (Thomas & Coward 1995), and SW into the Tern-Eider Ridge. The Penguin Horst is a striking feature observed in seismic (Fig. 7), which made it the original exploration target for Penguins, discovered by well 211/13-1, drilled on its crest. Figure 7 illustrates that the horst is bounded by normal faults at either side (the West Penguin Fault and East Penguin Fault, respectively), contrasting with previous interpretations of it as either a large-scale positive flower structure (see fig. 12 in Booth et al. 1992) or bounded at either side by compressional positive flower structures (see fig. 14 in Thomas & Coward 1995). The more recent 3D pre-SDM seismic data (1998) was acquired and processed before the field development and has greatly improved the imaging of the Penguins Fields with respect to the previous vintage of 1985, on which the Booth et al. (1992) and Thomas & Coward (1995) interpretations were based. The new level of detail allows for a reinterpretation of previous structural geometries and models, particularly the ‘inverted’ nature of the Penguins Horst. The detailed seismic shown in Figure 7 shows a west –east-trending seismic line and seismic interpretation across the Penguin A field, Penguin Horst, and Penguin C field. This line is similar to those discussed in figure 12 of Booth et al. (1992) and figure 14 of Thomas & Coward (1995). This section is dominated by the presence of the Triassic Penguin Horst which occurs at a depth of c. 2.5 seconds two-way time (TWT), and tagged at a subsea depth of c. 8500 ft by exploration well 211/13-1. The Penguin Horst is a pronounced structural high bounded at either side by steep extensional faults that are poorly imaged deeper than 3.0 seconds two-way time. Internally, it consists of a series of easterly-dipping internal Triassic reflectors that continue across the East Penguin Fault below the Penguin C field. The top of the basement occurs at or around 3.0 seconds TWT, forming a broad antiform of chaotic internal reflectors. The top Triassic, top Dunlin, top Brent and base Cretaceous unconformity seismic reflectors can be picked on the eastern side of the Penguin Horst. The Penguin A field occurs in the hanging wall of the West Penguin Fault, adjacent to the Penguin half graben, which displays a synformal shape. A series of deep reflectors at around 3.5 s TWT and deeper indicate the top of the basement under Penguin A. Above these reflectors the

33

seismic shows an easterly tilt of the Triassic sediments, contrasting with the overlying westerlydipping reflectors at the Upper Jurassic level Humber Group. The sediment thickening against the fault planes of the Humber Group indicates these faults were active at the time of deposition. Seismic and well data indicate the Magnus Sandstone Member to be 600 ft true-vertical thickness (TVT) in the depocentre of the Penguins Basin north (see Fig. 7), thinning into the Penguin A field structural high to about 250 ft TVT (211/ 13-3 well) and eventually pinching out to zero thickness on the edge of the Penguins Horst. These faults also show a much larger throw at top basement level than at Jurassic level, pointing towards a reactivation during the late Jurassic of Triassic structures. The rapid subsidence associated with the late Jurassic fault movement is responsible for the westerly dip observed in the Upper Jurassic seismic reflectors that occur under Penguin A. The Magnus turbiditic sandstones do not occur along the Penguins Ridge, indicating this structural high represented an obstacle to the progradation of turbiditic submarine fans coming from the north and east. The interaction between fault movement and sand deposition caused the thinning and pinchout of the Magnus sands towards the Penguin Horst. Small-scale synthetic faults with small reverse throws on their upper tips can be observed on the hanging wall of larger scale extensional faults off the western flank of the Penguins Horst (see Fig. 7). The reverse nature of these faults can be explained by the rotation of the fault block during the late Jurassic extensional episode and the subsequent steepening of the original normal fault plane. Well and seismic data indicate the base of the Humber Group is unconformable in nature, truncating the Middle Jurassic Brent Group and older Formations. The easterly tilt of the Triassic reflectors, together with the difference in throw observed at top basement level, points to the West Penguin Fault predating in age the East Penguin Fault. The East Penguin Fault probably developed at a later stage to accommodate further extension in the basin. The West Penguin Fault is a major structural feature that can be traced southwards into the Tern-Eider Ridge.

Penguins Lineament The southern end of the Penguin Horst can be illustrated with a west-line through well 211/13a-9s1, at the southern end of the Penguin A field. At this level the Penguin Horst experiences a dramatic reduction in structural height as it encounters a sharp change in structural grain from north–south to NW–SE, as observed mainly in time slices (see Fig. 6) and fault maps (see Fig. 3). At the southern end of the

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R. DOMI´NGUEZ

Penguins Horst the structural fabric swings to the SE and becomes parallel to a NW –SE fault trend that can be traced between the south of the Penguin A field to the NW and the boundary between the Penguin C and D fields to the SE. This structural grain band is interpreted as the shallower expression of an underlying lineament, possibly a basement shear zone or fault system of Caledonian age reactivated in the subsequent Triassic and Jurassic rifting episodes. This basement lineament is observed in time slices as a c. 2 km wide zone of deformation where the Mesozoic stretching resulted in either reactivated older fault planes propagating upwards into the overburden, or as newly-formed faults with a NW –SE trend and therefore an oblique angle to the main west – east extension direction, contrasting with the main north–south structural grain at either side of the lineament. The basement lineament bounds the Penguin A field to the south and the Penguin C field to the SW and south. Several large-scale Jurassic faults in the Penguin A field have a NW–SE trend that intersect a north–south fault population, creating a number of intra-field fault block compartments. At least one of these NW–SE faults is known to be sealing, as demonstrated from two different oil compositions sampled in wells at either side. The southeastern continuation of the basement lineament becomes harder to interpret. Here the lineament seems to run along the boundary between the Penguin C and D fields, although fault maps show this boundary to have a different orientation, created by a NE –SW-trending fault dipping to the south.

Penguins Ridge The Penguins Ridge represents the southern expression of the Penguin Horst across the Penguins Lineament. The Penguin C, D and E fields can be found along this trend. The Penguins Ridge has the same north–south trend as the Penguins Horst, albeit with a much smaller structural relief (1000 feet v. 3500 feet). Its position is some 3 km further SE than the main horst trend across the Penguins Lineament (Fig. 6). This jog in the main structural grain can be explained by the presence of the underlying Caledonian structural fabric that has offset the main locus of faulting either side of it. South of the Penguins Lineament the stretching associated with the Mesozoic rifting was distributed across a number of north–South-trending extensional faults, rather than focusing on a single fault, causing the ridge to be a less pronounced structural feature than the Penguin Horst to the north. It is bounded to the west by a major westerlydipping, north–south-trending fault. Internal

seismic reflectors within this structural high vary from gently easterly-dipping to horizontal (Fig. 8). As in the case of the Penguin Horst, younger faults bound the Penguin Ridge to the east, particularly along the south of the Penguin D field and along the eastern margin of the Penguin E field.

Penguins Basin The Penguins Basin is located west of the Penguins ridge. North of the Penguins Lineament it forms a gentle syncline west of the Penguin A field (see Fig. 7). South of the lineament the basin widens and is composed of a number of easterly-dipping Triassic and Jurassic fault blocks that display a characteristic domino-style and show some degree of thickening of the Upper Jurassic Humber Group against the fault planes. This thickening is a combination of ‘wedging’ in the hanging wall of the faults due to the syn-rift nature of the Humber Group (for further evidence see Figs 7 and 9) with some degree of erosion in the uplifted footwalls. Figure 8 shows a SW –NE trending seismic line and seismic interpretation some 19 km in length which ties the Penguins Basin and the south of the Penguin C field, illustrating the structural styles observed in the Penguins Basin, characterized by a number of westerly-dipping extensional faults with associated minor antithetic faults developed in the hanging walls. The top of the basement occurs at c. 3.75 s TWT over this area, although it is not possible to trace it with confidence due to the poor seismic resolution at this level. Figure 9 shows a staggered seismic line (B– B0 ) some 13 km in length that goes from the Penguin Basin into the southern part of the Penguin D field (west to east), before heading north into the Penguin C field. This line is tied to four exploration wells: 211/13-7, 211/14-1s2, 211/14-3s1(Z) and 211/14-4RE. This geological cross-section has been used as the basis for a palinspastic restoration used to illustrate the structural evolution of Penguins. In the geological cross-section it can be seen that the Penguin D west-bounding fault has accumulated large amounts of throw, estimated in c. 1000 feet from well data. The poor seismic resolution at deeper levels does not allow estimation of the effects of the faulting on the Triassic and deeper levels with a great degree of certainty, although the mapping of an intra-Cormorant Formation seismic reflector and the nature of the intraTriassic seismic reflectors point to a thickening against the fault planes. This geo-seismic section illustrates the syn-rift nature of the Humber Group, eight times thicker in the hanging wall of the main Penguin D bounding fault. The Heather and Kimmeridge Clay formations can be correlated at either side of the fault, and their condensed

PENGUINS CLUSTER STRUCTURAL EVOLUTION

35

Fig. 8. (a) uninterpreted, and (b) interpreted west– east seismic line through the Penguin Basin and the Penguin C South Field, highlighting the main structural elements of the Penguin Basin, and in particular the ‘domino’ nature of the extensional faults.

thickness nature in the footwall indicates the thickness change was mostly driven by the syndepositional movement of the fault, with some smaller degree of footwall erosion in the early Cretaceous. It is also evident from both seismic and well data

that the Dunlin and Brent Groups thicken slightly across the fault into the main Penguins Basin. Most of this thickness difference can be attributed to more accommodation space available in the Penguins Basin during the early to middle Jurassic

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Fig. 9. (a) uninterpreted, and (b) interpreted seismic line between the Penguin Basin, Penguin D and C fields (Penguins Ridge) and tied to wells 211/13-7, 211/14-1s2, 211/14-3s1(z) and 211/14-4RE (see Fig. 3 for location). This interpreted cross-section has been used as the basis for the palinspastic restoration shown on Figure 17.

thermal subsidence that followed the Triassic rifting episode.

Structural evolution Lower Jurassic The early Jurassic was a time of little faulting activity across the northern North Sea, when the

area underwent an episode of passive thermal subsidence following the Triassic rifting during which the Dunlin deep marine shales where deposited. An isochore map of the Dunlin Group over the Penguins and Don Northeast areas (Fig. 10), shows variations in thickness which reflect the underlying main structural elements, with the Dunlin package thinning to less than 300 feet over the structural highs and thickening in the structural

PENGUINS CLUSTER STRUCTURAL EVOLUTION

37

Fig. 10. Thickness in feet of the Dunlin Group in the Penguins Area. This isochore map has been constructed from the thickness in the wells shown. Contour interval every 50 feet.

lows of the Penguins Basin to over twice that thickness. This map was constructed using data from wells that penetrate a full Dunlin stratigraphic sequence (Fig. 11), with all four internal formations. Therefore the changes of thickness cannot be attributed to post-depositional erosion, but are instead interpreted as the result of changes in accommodation space across faults and the effects of remnant late Triassic– early Jurassic palaeotopography, inherited from the Triassic rifting episode. Seismic lines across some major faults such as those shown in Figures 8 and 9 display a thicker Dunlin package in the hanging wall. The overall geometry does not show typical syn-rift wedge geometries against fault planes, suggesting instead a passive, post-kinematic deposition of the Dunlin Group. Fault activity was nonexistent to minor during this period of time, with fault movements perhaps having accommodated

some of the thermal subsidence that followed the Permo-Triassic rifting.

Middle Jurassic Evidence from Penguin D indicates that the initiatial movements of the Jurassic rifting took place as early as the middle Jurassic, coinciding with the Brent Group sandstones deposition, and eventually climaxing during the late Jurassic. The middle Jurassic fault movements had an impact on the deposition and distribution of the internal Brent Group formations, creating at least one intra-Brent unconformity (top Rannoch) in the Penguins area. Figure 12 shows a south– north seismic line and seismic interpretation along the Penguin D field tied to exploration wells 211/14-1s2 and 211/14-3. This line focuses on the Lower to Middle Jurassic

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Fig. 11. Well correlation of the Dunlin Group formations across the Penguins Basin, Penguin D and C fields. See Figure 10 for location of correlation line. Depths are in feet.

intervals (Dunlin and Brent Groups), and illustrates the impact of small-scale intra-field faulting on the Brent reservoir architecture. The base Cretaceous unconformity is a high amplitude reflector that occurs at a depth of around 3 seconds TWT (black loop in the figure). The top Brent has been picked on the red loop immediately underneath. The Dunlin Group is characterized by a series of subparallel seismic reflectors affected by extensional faults. These normal faults have created a depocentre between 211/14-1s2 and 211/14-3 where the Brent Group achieves its maximum thickness. The Brent Group thins progressively southwards, where it has been uplifted due to footwall rotation. A comparison of throw at the base Cretaceous unconformity versus top Dunlin level reveals that these faults were more active during the Middle Jurassic, dying out progressively during the Late Jurassic, where the climax of the extension switched to the large-scale, fieldbounding faults. Figure 13 is a correlation panel of the Brent Group taken from south to north along the Penguin D field wells. It corresponds roughly to the seismic line shown in Figure 12 and it illustrates the Brent reservoir architecture and the impact that the Jurassic faulting had on it. The correlation panel

has been flattened at the top Brent level (effectively top Etive Formation). The Brent Group shows important thickness changes, varying from as little as 150ft true-vertical thickness (TVT) in southern well 211/14-1s2 to 250 ft TVT in northern well 211/14-3. Wells PENG-D01 and PENG-D02 are sub-horizontal development wells which only penetrate the upper section of the Brent Group. The correlation panel shows that the Etive Formation has a relatively constant thickness of around 50 ft TVT, and that the changes in Brent Group thickness are taken up by variations in the Rannoch Formation thickness and the number of internal parasequences this formation can be split up into. Thus, the well with the thinnest Brent section (211/14-1s2), drilled only through the lowermost three Rannoch parasequences, whereas the thicker Brent section of well 211/14-3 consists of a much thicker Rannoch sequence, split up into eight internal parasequences. These thickness and internal reservoir architecture changes are related to the structural position of the wells within the field, with the thinnest Rannoch sequences occuring in the structural highs created by rotated footwalls. This is interpreted as a pulse of fault activity that took place after the Rannoch deposition, creating the top-Rannoch unconformity and leading to fault

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Fig. 12. (a) uninterpreted, and (b) interpreted south– north seismic line along the Penguin D Field. Note the thickening of the Rannoch layers in the downthrown fault blocks. See text for discussion.

block rotation and erosion of the uplifted footwalls before the deposition of a tabular-shaped Etive Formation across the field.

Late Jurassic Although the main extension direction of the Late Jurassic rifting was roughly east –west (Roberts

et al. 1990), alternative orientations, mainly NW– SE and NE –SW, have been proposed by some authors (e.g. Thomas & Coward 1995). The Late Jurassic extension vector must have been directed at an oblique angle to some fault trends, causing the reactivation of these pre-existing fault planes to take place under oblique-slip conditions. Where these faults experienced jogs or bends along their

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Fig. 13. (a) well correlation of Brent Group formations across the Penguins D Field, including the Rannoch Fm shoreface parasequences 1 to 8, flattened at top Brent (top Etive) level. Depths are in feet. (b) Schematic structural interpretation of the log data. See text for discussion.

trend, transpression and transtension took place, as demonstrated by the small-scale flower structures drilled by wells PENG-C01 and PENG-C02. A steep normal fault can be mapped along the main trend of the Penguin C field, running roughly parallel to the top Brent contours, with a NNW–SSE strike orientation (Fig. 14). Detailed mapping of this fault shows two small-scale jogs that occur along its trajectory. A left-stepping jog can be mapped in the central part of the Penguin C field, having created a releasing bend drilled by the sub-horizontal PENG-C01 well, which penetrated a downthrown fault block of Heather shales. The second jog, in the southernmost end of the C field, is a restraining bend that has created a transpressional fault-block of Dunlin shales penetrated by the PENG-C02 well.

Figure 15 shows a NW– SE seismic line and its geological interpretation along the PENG-C01 well trajectory, drilled in the central part of the Penguin C field (see Fig. 14). Whilst drilling a subhorizontal section of Brent Group sandstones, PENG-C01 encountered a c. 300 feet-long section of Upper Jurassic Heather shales, confirmed with biostratigraphic samples, before penetrating again the Brent Group sandstones for the last 1000 feet of the well. The shale section was bounded by faults as confirmed by image logs, and is interpreted as a transtensional ‘pop-down’, or negative flower structure. The small scale of this feature makes it difficult to interpret on seismic, and only one of the faults bounding it can be mapped with confidence. This seismic line also illustrates the unconformable nature of the base of the Brent Group,

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Fig. 14. Penguin C Field top Brent depth structure map. Contour interval is 125 feet. The fault highlighted in red shows two jogs of opposing orientations. This fault was reactivated in the late Jurassic under an oblique-slip extensional regime, causing the jogs to generate a ‘pop-down’ drilled by PENG-C01 and a ‘pop-up’ drilled by PENG-C02. Refer to text for details.

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Fig. 15. (a) uninterpreted, and (b) interpreted seismic line along the PENG-C01 well trajectory. This well drilled through a downthrown fault block composed of Heather shales along the wellpath. See text for discussion. A, motion away from page; T, motion towards page.

seen here truncating a series of underlying Dunlin Group seismic reflectors. Figure 16 shows a SW –NE seismic line and seismic interpretation along the PENG-C02 well trajectory, drilled in the southern part of the Penguin C field and illustrating also the impact of oblique-slip fault movements in the structural evolution of the Penguin C field. PENG-C02 drilled through another intra-Brent shale section, this time dated with biostratigraphic samples as Lower Jurassic Dunlin Group, and also bounded by faults. This feature has been interpreted as a

transpressional ‘pop-up’, or positive flower structure. One of the block-bounding faults can be mapped on seismic with relative confidence, and it can be followed northwards where it ties with the fault drilled through by the PENG-C01 well where the Heather ‘pop-down’ occurred.

Discussion Figure 17 summarizes the Mesozoic structural evolution of the Penguins Cluster using the palinspastic

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Fig. 16. (a) uninterpreted, and (b) interpreted seismic line along the PENG-C02 well trajectory. This well drilled through an upthrown fault block composed of Dunlin shales along the wellpath. See text for discussion. A, motion away from page; T, motion towards page.

restoration of seismic shown in Figure 9 as its basis. Figure 18 summarizes the timing of the main tectonic events in relation to the lithostratigraphy and the unconformities discussed in the text. The present day structural configuration of the Penguins area is the result of two rifting episodes during the Mesozoic (Permo-Triassic and Jurassic) together with their associated phases of thermal relaxation and subsidence. The rifting initiated in

the Permo-Triassic continued in the Middle Jurassic as intermittent pulses of fault activity contemporaneous with the Brent Group deposition, eventually climaxing in the late Jurassic. The faulting was influenced south of Penguin A and the Penguin Horst by a pre-existing NW– SE structural grain inherited from the Caledonian orogeny. The interaction between two subsequent rifting episodes resulted in some cases in the reactivation of

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Fig. 17. Palinspastic restoration applied to the geological cross-section shown on Figure 9. See text for details.

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45

Fig. 18. Generalized stratigraphy of the Penguins Area showing unconformities in red and the tectonic events discussed in the text.

pre-existing faults, leading to oblique-slip transpressional and transtensional fault block movements in the Penguin C field. The structural evolution of the study area during the Triassic is less well understood than the Jurassic evolution due to the poorer resolution of the seismic data at the Triassic depths and the superimposition of the Jurassic deformation on the original Triassic fabric. Triassic fault activity is evident from large-scale faults such as the Penguin West fault, its southern continuation into the Tern-Eider ridge

area to the SW, and the west-bounding fault of the Penguin D and E fields. These are all west-dipping extensional faults against which thickening of the lower part of the Hegre Group, of Triassic age, can be observed in seismic. The Triassic rifting created a structural picture consisting of large-scale easterly-dipping fault blocks against which thickening of the Cormorant Formation occurs. Deposition of the Upper Cormorant and the lowermost Jurassic Statfjord formations took place mostly under thermal subsidence conditions following the

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Triassic rifting episode. Some degree of uplifted fault-block palaeotopography was inherited from the rifting and still existed in the Lower Jurassic (Fig. 17a), either due to the inability of the Hegre Group sedimentation to keep up with the created fault block subsidence, or perhaps due to some degree of fault movement taking up some of the thermal subsidence once the main rifting episode had finished. This is demonstrated by the thickness changes across faults observed in the Dunlin Group claystones (Fig. 17b), as seen on seismic. Well data shows the Dunlin Group to thicken from c. 250 ft TVT along the structural high formed by the Penguins Ridge, to at least 500 ft TVT in the hanging wall of this major fault, into the Penguins Basin. Although the base of the overlying Brent Group can be erosional in some areas, the Dunlin Group thickness changes are depositional and cannot be attributed to erosion, as the correlation of the internal Dunlin formations demonstrates. The deposition of the deep marine Dunlin Group claystones was followed by deposition of the shallower marine and deltaic Brent Group sandstones. Although conformable across much of the area, in some locations the base of the Brent can be seen as being erosional in nature, cutting down and eroding off the uppermost Dunlin Group claystones. Deposition of the lower part of the Brent, the Broom and Rannoch formations, took place mostly under quiescent tectonic conditions when the basin was undergoing thermal subsidence after the Triassic rifting (Fig. 17c). Fault activity was re-established immediately after deposition of the Rannoch Formation, as evidenced by seismic and well data from the Penguin D field. Many of these were newly formed faults in the middle Jurassic as their throw profiles demonstrate. Fault block rotation accompanied the fault movement, causing uplift of the footwalls that were then subjected to subaerial conditions, erosion of the uppermost Rannoch, and peneplanation. This faulting episode resulted in the top Rannoch unconformity. Immediately after, or perhaps coeval with the upper Rannoch erosion, was the deposition of the shallow marine to fluvial Etive Formation across the area (Fig. 17d). Its absence over areas of the Penguin C field is attributed to post-depositional fault movements and erosion. The Jurassic rifting, although initiated during the middle Jurassic, experienced its climax and most of the fault activity during the late Jurassic, as demonstrated by the syn-rift thickening of the late Jurassic-dated Humber Group claystones against major north–south-trending extensional faults (Fig. 17e). Many of these Jurassic faults are reactivated older features, probably Triassic in origin, as demonstrated by the difference in throw observed at different levels. The West Penguin Fault is a clear example, where the interpretation of the top of the

basement shows a much larger throw at top Triassic than at top Jurassic level. The Upper Jurassic Magnus Sandstone Member of the Kimmeridge Clay Formation, the oil reservoir in the Penguin A field, is syn-rift in origin. The provenance of this deep-marine turbiditic fan has been interpreted as being from either the north or the west. This sedimentary package thickens against north–southtrending faults over the Penguin A field (see Fig. 7), demonstrating its syn-rift origin, and it pinches out towards the West Penguin Fault, indicating these faults were moving as the turbiditic sediments tried to ‘climb’ towards the structural highs. The upthrown Penguins Ridge must have acted as a barrier to submarine sediment transport towards the west, where the Magnus Member is absent from all wells in the Penguin C, D and E fields. These submarine fans must have been deflected towards the south by the emerging topography during the late Jurassic, into the Penguin Basin, where it has been encountered as far south into the Penguins Basin as well 211/13-5. The late Jurassic fault activity caused oblique-slip reactivation of some Penguin C faults. Where bends or jogs were encountered along the strike of the fault, as mapped in some of the Penguin C field faults, accommodation problems resulted in transpressional or transtensional fault movements, depending on the relative orientation between the fault strike and the maximum stress vector. These movements created the positive flower structure drilled by the PENG-C02 well, and its strike-related negative flower structure in the central part of the field drilled by PENG-C01. Some authors (Booth et al. 1992; Thomas & Coward 1995) argue that the East Shetland Basin was affected by an episode of basin inversion during the latest Jurassic – early Cretaceous, originating a number of positive flower structures along NE–SW-trending faults. These faults suggest a component of strike-slip during the reactivation of pre-existing structures under a compressional tectonic regime. Booth et al. (1992) interpret the Penguins Horst as an inversion feature, a large-scale ‘pop-up’ developed due to transpressional or compressional movements as a result of strike-slip reactivation of faults during the late Jurassic to earliest Cretaceous (see fig. 12 in Booth et al. 1992). Thomas & Coward (1995), on the other hand, interpret the Penguins Ridge as being delineated with both normal and reverse faults, with positive flower structures, or ‘pop-ups’, developed at either side of the Penguins Horst (see fig. 14 in Thomas & Coward 1995). They argue that inversion may be a consequence of either compression of the basin as a whole, or alternatively, due to transpressional uplift along offset NW–SE systems. These past interpretations are based on 2D seismic

PENGUINS CLUSTER STRUCTURAL EVOLUTION

lines of limited quality. A re-interpretation of more recent, better quality 3D seismic data along the same lines as those used by Thomas & Coward (2005), and Booth et al. (1992) shows the Penguins Horst to be an extensional feature bounded by normal faults on either side which have accumulated throws of at least 2000 feet true-vertical depth at the BCU level. No reverse throws are indicated in the new seismic dataset at either side of the horst, and the previous interpretation of ‘pop-ups’ is here revisited as a series of extensional faults which, in some cases, can be traced down to the top of the basement. The detailed geometry of these faults at depth is uncertain due to deterioration in the seismic quality, and they could also be interpreted as synthetic splays from the main West Penguin Fault, rather than domino-faults. Detailed interpretation of a better quality 3D seismic volume over the Penguins Area shows that the main structural elements that define the Penguins Cluster are extensional in origin, although oblique-slip reactivation of existing normal faults during the late Jurassic has created at least one case of a transpressional flower structure, or ‘pop-up’, in the Penguin C field. Fault activity during the Permo-Triassic and Jurassic rifting episodes reactivated an underlying lineament with a NW –SE trend that runs between the south of the Penguin A field and the boundary between the Penguin C and D fields. This is probably a basement shear zone of Caledonian age that caused the Mesozoic faults overlying it to curve and become subparallel to this NW–SE trend. This basement lineament seems to have accommodated extension in different ways north and south of it. To the north, most of the stretching seems to have focused on one or two major normal faults, originating the Penguins Horst. South of the lineament, the stretching has been distributed among several north–south-trending normal faults. The Penguin Lineament is interpreted as the northwestern expression of the Northern Transfer Zone of the East Shetland Basin described by Lee & Hwang (1993). This is described as a NW–SE trending regional-scale Tornquist lineament that transects the northern area of the East Shetland Basin, and across which basin polarity changes occur. The Jurassic rifting was followed by an episode of thermal relaxation and subsidence of the basin between the Cretaceous and the Cenozoic, with the accummulation of a post-rift megasequence up to c. 3.5 km over Penguins that preserved the late Jurassic palaeotopography from significant erosion. I would like to thank Shell UK Ltd and its partner in the Penguins Cluster, ExxonMobil, for permission to publish this paper. I would also like to thank all of my fellow Penguins team members throughout the years, and in particular K. Fletcher, R. Shelton, D. Bateman and P. Watt.

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References B ADLEY , M. E., E GEBERG , T. & N IPEN , O. 1984. Development of rift basins, illustrated by the structural evolution of the Oseberg feature, Block 30/6, offshore Norway. Journal of the Geological Society, London, 141, 639–649. B ADLEY , M. E., P RICE , J. D., R AMBECH D AHL , C. & A GDESTEIN , T. 1988. The structural evolution of the northern Viking Graben and its bearing upon extensional modes of basin formation. Journal of the Geological Society, London, 145, 455–472. B EACH , A. 1987. A regional model for linked tectonics in north-west Europe. In: B ROOKS , J. & G LENNIE , K. (eds) Petroleum Geology of North West Europe. Graham & Trotman, London, 43– 48. B OOTH , A., S TOCKLEY , F. J. & R OBBINS , J. A. 1992. Late Jurassic Structural Inversion in the North Viking Graben and East Shetland Basin, UK North Sea. Oryx Energy Company Internal Publication. C OWARD , M. P., D EWEY , J. F., H EMPTON , M. & H OLROYD , J. 2003. Tectonic Evolution. In: E VANS , D., G RAHAM , C., A RMOUR , A. & B ATHURST , P. (eds) The Millenium Atlas: Petroleum Geology of the Central and Northern North Sea. Geological Society, London, 17– 33. D E ’A TH , N. G. & S CHUYLEMAN , S. F. 1981. The Geology of the Magnus Oilfied. In: I LLING , L. V. & H OBSON , G. D. (eds) Petroleum Geology of the Continental Shelf of Northwest Europe. Institute of Petroleum, Heyden, London, 342– 351. D EEGAN , C. E. & S CULL , B. J. 1977. A standard lithostratigraphic nomenclature for the Central and Northern North Sea. Institute of Geological Sciences Report 77/25. F ÆRSETH , R. B. 1996. Interaction of Permo-Triassic, and Jurassic extensional fault-blocks during the development of the northern North Sea. Journal of the Geological Society of London, 153, 931– 944. G ABRIELSEN , R. H., O DINSEN , T. & G RUNNALEITTE , I. 1999. Structuring of the North Viking Graben and the Møre Basin; the influence of basement structural grain, and the particular role of the Møre-Trøndelag Fault Complex. Marine and Petroleum Geology, 16, 443– 465. J ONES , G., R ORISON , P., F ROST , R., K NIPE , R. & C OLLERAN , J. 1999. Tectono-stratigraphic development of the southern part of the UKCS Quadrant 15 (eastern Which Ground Graben): implications for the Mesozoic– Tertiary evolution of the Central North Sea Basin. In: F LEET , A. J. & B OLDY , S. A. R. (eds) Petroleum Geology of Northwest Europe: Proceedings of the 5th Conference. Geological Society, London, 133–151. L EE , M. J. & H WANG , Y. J. 1993. Tectonic Evolution and Structural Styles of the East Shetland Basin. In: P ARKER , J. R. (ed.) Petroleum Geology of Northwest Europe: Proceedings of the 4th Conference. Geological Society, London, 1137–1149. O DINSEN , T., R EEMST , P., VAN DER B EEK , P., F ALEIDE , J. I. & G ABRIELSEN , R. H. 2000. Permo-Triassic and Jurassic extension in the northern North Sea: results from tectonostratigraphic forward modeling. In: N ØTTVEDT , A. (ed.) Dynamics of the Norwegian

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Characterizing and producing from reservoirs in landslides: challenges and opportunities A. I. F. WELBON1,2, P. J. BROCKBANK1, D. BRUNSDEN3 & T. S. OLSEN1 1

StatoilHydro, Forusbeen 35, Forushagen, N-4035 Stavanger, Norway

2

BG norge, Løkkeveien 103, Stavanger, Norway (e-mail: [email protected]) 3

Vine Cottage, Chideock, Dorset, England, UK

Abstract: Landslides can consist of rotational slips, translational glide blocks, topples, talus slopes, debris flows, mudslides and compressional toes which can combine in different proportions to form complex landslides. The mass movement can be subaerial or submarine, occur over wide ranges of scale and can vary in rate from creep to catastrophic failure. Complexity of the landslide reflects the controlling factors including the strength of the deforming material and triggering mechanisms such as earthquakes, imposed load, increasing topographic relief and removal of toe material. Processes of landslide deformation include slip on discrete surfaces, distributed shear within the landslide, vertical thinning and lateral spreading through shear, fluidization, porosity collapse and loss of material from the top or toe of the complex. These processes control the quality of the resultant reservoirs. This leads to a greater range of reservoir types than conventional faulted reservoirs, with a proportionate upside and downside potential and difficulty in quantifying uncertainty. This paper uses examples from the literature, outcrops and subsurface datasets (including the Statfjord Field and the Halten Terrace in Norway) to outline the complexity of reservoirs in landslides and the challenges and opportunities in finding and producing them. We present workflows for seismic and subseismic characterization for exploration and reservoir scale based on geomorphological principles. Seismic mapping is achieved by classifying the form of the reflectors (both slip surfaces and the bounding envelope of the landslide) from an atlas of geometric and structural styles and is applied to both the Halten Terrace example and the Statfjord Field. We present a new workflow for reservoir characterization in which integration of structural, biostratigraphic, sedimentological and dynamic data gives key information on process, timing and heterogeneity of the reservoir. For the Statfjord field, important maps of the landslide block stratigraphy derived from a subcrop map and communication maps based on a c. 130 well dataset can be correlated to outcrop analogues and used to develop a predictive tool for landslide reservoir extent and quality, both in this field and others.

Landslides have been documented and studied for centuries (Buckland 1840), generally following onshore events that had catastrophic consequences for local communities (e.g. Frank Slide, Canada 1903). Oil and gas companies have been producing from palaeolandslide complexes (commonly referred to in the industry as ‘slumps’ and ‘degradation complexes’) since shortly after the start of the hydrocarbon industry, but it has only been in the last two decades that seismic imaging technology, together with new integrated techniques, have led to detailed imaging and correct identification of many of these reservoirs. In many hydrocarbon provinces, the presence and magnitude of landslides has been underestimated until late in the development of the fields. In the Tampen Spur area of the North Sea, the number of identified landslide complexes on fields in production has risen from a handful in the late 1990s (Stewart 1997; Underhill et al. 1997; Berger &

Roberts 1999; Hesthammer & Fossen 1999; McLeod & Underhill 1999) to over 20 today. The downslope products of these landslides collect in the hanging wall of fault systems and are now key exploration plays around existing infrastructure. With the advent of high quality 3D seismic data, on many deep-water passive margins landslide products are commonly recognized as the main form of deformation, including the formation of major extensional and compressional landslide systems (Prior & Coleman 1982; Heinio & Davies 2006). Landslides are common on salt diapirs and associated folded sediments. Due to their topographic expression, carbonate reservoirs such as pinnacle reefs are subject to landslide processes on their flanks, and result in modifying the expected recoverable volumes and influencing production strategies to avoid early water breakthrough. Chalk mass movement deposits, synchronous with sedimentation, affect chalk fields in the North Sea.

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 49– 74. DOI: 10.1144/SP292.3 0305-8719/07/$15.00 # The Geological Society of London 2007.

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Development of these reservoirs was commonly postponed whilst other, more conventional, sources were exploited; these sources obeyed established concepts of sequence stratigraphy and basin development and were readily imaged in standard seismic data. With the emphasis of the industry now on the hard to access, non-conventional reservoirs as we enter the second half of the oil age (Campbell & Laherrere 1998; Hall et al. 2003), landslides are a key target both in exploration and production. In this paper we present a review of landslide types and methods for their characterization involving geomorphological analysis of seismic and well data, use of empirical datasets from subsurface landslides and outcrops as analogues, integrated studies which include sedimentology, biostratigraphy, structural geology and the use of production data. We then describe the challenges and opportunities these types of reservoirs present, using examples from various fields.

Landslide type, processes and challenges in identification Landslides have been described (Cruden 1991) as a movement of a mass of rock, earth or debris down a slope. Brunsden (1984) pointed out that these mass movement features do not necessarily have a transport medium (for example rock falls). Thus, landslides can be either subaerial or submarine; indeed on many coastlines today they originate onshore and extend offshore. There are several definitions and classification schemes for landslides (Hutchinson 1968; Varnes 1978; Dikau et al. 1996) which attempt to capture process; this paper follows the classification of Dikau et al. (1996). Landslide processes are varied and often complex. Figure 1 illustrates a series of landslide processes and the resulting morphology of the products. The nature of the process or combination of processes that cause a landslide will control the quality of the resultant hydrocarbon reservoirs. The degree of recovery can be dependent on preservation or enhancement of the original, pre-landslide reservoir character. Thus, landslides (or mass movements) can be classified into eight principle types (Fig. 1). These are slides (rotational and translational) (Fig. 1a, b), topples and falls (Fig. 1c), mudslides and flows (Fig. 1d), lateral spreads (Fig. 1e), and complex landslides (Fig. 1f), extrusions associated with cambering (Fig. 1g) and compressional toes (Fig. 1h) (EPOCH 1993). In addition, they can be further classified on the basis of the material involved, such as rock, debris and soil. Associated with all of these types of landslide can be processes such as creep, extrusion,

fluidization and expulsion of fluids or gas (Seed 1968; Varnes 1978; Varnes et al. 1989). Many of these landslide types can be mapped in seismic, but many fall below seismic resolution. The challenge for the hydrocarbon industry is to map features in seismic data, interpret the process and then predict the range of reservoir type and quality at, and below, seismic resolution. Mass movements are generally triggered through mechanisms such as: loading, removing support from a toe area, increasing pore fluid pressure in the material, or changing the chemistry of the substrate. In addition, in a rift, a thrust belt or on a passive margin, specific types of trigger are common: earthquakes, tsunami loading, loading by creation of topography above regional (footwall uplift, inversion) (Berger & Roberts 1999), glaciations (Bryn et al. 2005), movement on unstable siliceous oozes or salt (density contrast), gasification and increase in pore pressure due to maturation of hydrocarbons (Cobbold et al. 2005). The most common landslides types that can be mapped in seismic, particularly in fault footwalls in rifts and on passive margins, are rotational and translational slides. They are common near the onset of the gravitational collapse (often a back scar) and further downslope are replaced by either compressional toes, mudslides, and debris flows, mixed in with locally derived rock falls from exposed scarps and clifflines. Rotational slides are blocks where movement generally occurs on a spoon-shaped slip surface and the block develops a back tilt as a result (Fig. 1a). Translational slides (or glides, Fig. 1b) form where a block moves on a low angle shear surface with little or no resultant rotation. Rotational slides can be connected to translational slides downslope, in so-called compound failures (Dikau et al. 1996), but commonly, the movement of a translational slide block produces a chasm or ‘graben’ up-dip from the block (Pitts & Brunsden 1987). Rock falls and topples (Fig. 1c) are commonly found at cliff edges or at the foot of steep slopes, and are usually locally derived. Talus slopes develop as a result of the falls, or more generally erosion, of cliff-faces and these become rotated by any subsequent movement of the landslide underneath. This means the original critical taper of the talus slope may not be maintained and the top surface may have a lower dip than expected. As a result, seismic interpretations of falls are rare, often being misinterpreted as debris flows. Toppling failures are common in fractured/jointed rocks and occur at cliff faces. If buttressing material (e.g. rockfalls) prevents major rotation the toppled block may maintain a steep dip. Steep structures will be difficult to image in seismic. Where no buttress exists, the low angle slab of toppled material

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Fig. 1. An atlas of landslide types, partly based on the classification of Dikau et al. 1996. (a) rotational slide; (b) translational slide; (c) topples and rock falls; (d) debris flows and mudslides; (e) lateral spread; (f) complex slides; (g) extrusion and cambering; and (h) compressional toe.

that often undergoes break-up from such a failure will also be hard to image, and again may be incorrectly interpreted as a debris flow or mudslide. Downslope from what are considered ‘intact’ blocks are a series of reworked and mixed rock types (Fig. 1c & d). Dependent on the failure type and process, within a few hundred metres of the onset of a metric to hectometric scale landslide, the original rock type is not recognizable. Breakup occurs as result of the rate of movement and a spreading/shearing process. Reworked sediments are mostly debris and mud flows and slides, lateral spreads and break-up products from toppling failures and rock falls. Mudslides are a mass movement where softened argillaceous to fine sand debris advances on a discrete surface. They are characterized by a source, track and a lobe with lateral shear surfaces and contractional features in the accumulation zone (Brunsden 1984). Debris flows consist

of coarse and fine material in a plastic or fluid medium. Another category of landslide is a lateral spread, (Fig. 1e) which originates from low angle slopes where thixotropic material liquefies and failure results. The original instability can be driven by loading, removal of toe material or chemical changes in, for example, quick clays. Overprinting of landslide processes is common, giving rise to complex slides (Fig. 1f) which can include any combination of landslide types. Examples include translational slides that become rotational as they move from a low angle slip surface to a steep, curved slip surface, and debris flows that become incorporated into rock falls at cliff edges. Additionally, a process that is often overlooked is extrusion and cambering at an emergent, often submarine, cliff face. Loading results in extrusion of ductile rock types causing cambering of the overlying, stiffer rock mass (Fig. 1g).

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Down-dip within the landslide where there is a change in slope, or where buttresses occur such as earlier landslide or fault blocks, a compressional toe can form (Fig. 1h). A common feature in subsurface landslide complexes, given the rapid lateral and down-dip changes in rock type and geometry is the difficulty of imaging the complex. The top of a complex is often a high acoustic impedance layer that is underlain by small, steep, anisotropic blocks and discontinuous layers of material that may contain high porosity, fractured or vuggy rocks. As a result limited return of seismic energy from the complex and scattering of seismic waves is common and therefore processing and seismic imaging is challenging. A surface mapped in seismic data at the top or within the complex may represent a composite of two or more different types of landslide, or a complex slide resulting from overprinting processes. For the purpose of 3D geological model building this means that traditional methods need to be adapted, namely that surfaces from the seismic dataset may have to be split into the component landslide parts, where the thickness, net: gross and porosity reflect the rapid change in landslide type and character.

Outcrop analogues The use of outcrop analogues in the interpretation of landslide structures has been common practice for many years. During work on the Statfjord Field in the North Sea, outcrop analogues were used from the mid-1980s onwards. Outcrops allow examination of processes not seen in seismic, and historical events provide constraint on timing and evolution (Brunsden & Jones 1976; Farrell 1984; Pettinga 1987a, b; Brunsden 1996; Dikau et al. 1996). By using the observations from outcrops to aid in seismic interpretation and by linking to empirical databases of reservoir type and production behaviour, it is possible to narrow the uncertainty range of reservoir types in a landslide complex. Classic exposures of landslides occur along the south coast of Britain, with more than eight thousand recorded (Brunsden & Jones 1976; Brunsden 1996). These are developed within Jurassic and Cretaceous rocks similar to those found in the North Sea and Norwegian Sea. The exposures consist of all the landslide types illustrated in Figure 1 and illustrate the extreme variation of net: gross and thickness possible in a landslide complex. Two exposures of landslides in West Dorset are end members for common types of geomorphological features mappable in seismic data, the

Stonebarrow Hill area and the Black Ven landslide. (Figs 2 & 3). The Stonebarrow Hill landslides are contained within a cuspate back scar that is asymmetric and originates from the erosion of the sea cliff. The asymmetry stems from the landslides detaching at the Jurassic/Cretaceous stratigraphic contact and other bedding slip surfaces which dip 2–38SE, promoting oblique movement downslope (Brunsden 1996). Similar control on the form of slip surfaces is observed in seismic data as a result of regional tectonic tilt, or more commonly, fault related uplift. Pre-existing faults also control landslide geometry, with differential development taking place on either side of the inherited structure, which is also a common feature in seismic datasets. The cuspate form of the slip surfaces is replicated at various scales, down to metres (Fig. 3a), and is also found in seismic data. Where measurable, cuspate slip surfaces, even when near the onset of collapse, generally have significantly higher displacement gradients than those on faults related to crustal stretching (Kim & Sanderson 2004). In other areas, more linear landslip patterns occur where translational glide blocks develop and they can exhibit lower displacement gradients than rift-related faults (Fig. 3b). These aspects can be used as criteria for identification of landslides in the subsurface. Further into the Stonebarrow complex, rotational slides, toppled blocks and translational slide blocks are common, reflecting the increasing influence of a low angle basal slip surface (which is penetrated in boreholes), and resulting in uneven topography of the top of the complex. However, the most important observation from a reservoir prediction point of view is the thinning of the rock mass, driven by loss of material from the top of the blocks (toppling, rock falls), vertical thinning and lateral spreading (see cross-section, Fig. 4). Over a 200– 400 m distance the original stratigraphy thins to 10–20% of the original thickness, a feature that is also common in the subsurface. Further downslope the landslides break up into a series of very narrow (1–5 m wide) blocks separated by open fractures and shear surfaces (Fig. 4, photograph B). Beyond this zone of degradation, which is generally 20– 40 m wide, the blocks break up into debris flows, mudslides, and rock falls, and during heavy rainfall results in run off of these sediments occurs. In the subsurface, these rock types are often referred to as ‘reworked’ sediments. A boundary can be mapped between areas where intact blocks are present and only reworked material exists (Figs 3a & 4), which is a crucial delineator for estimates of reservoir uncertainty and risk in the subsurface. In the region of fault block break-up and beyond are amphitheatre-like areas of landslides with spurs

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Fig. 2. South coast of Britain and the location of the Lyme Regis area. Black Ven is 1 km east of Lyme, and Stonebarrow Hill is 1 km east of Charmouth, both within the indicated area.

of degraded blocks between (Fig. 3a). This area is characterized by both movement towards the eroding sea cliff and oblique movement caused by local topography. The implication for reservoir provenance is clear: it will not always be possible to relate areas of lost material up dip to a downdip equivalent. Across the sea cliff at the southern edge of the landslide complex, the material from uphill moves over to the beach below (C on Fig. 4). This would be equivalent to crossing a fault scarp in a rift or passive margin setting. In addition, rock falls and topples from the cliff mix with the up-dip derived material. Mudslides and debris flows develop into compressional toes in response to under draining on the beach and/or changes in topography. In these exposures high frequency changes in the net: gross and particle size reflect the complex and mixed origin of the material (Fig. 4). In the subsurface this can lead to many surprises: thin, poor quality sands that produce large volumes of

hydrocarbons and local thick sands that deplete rapidly since they connect to small volumes. The Black Ven outcrops to the west of Stonebarrow, immediately East of Lyme Regis, are significantly different. They are characterized by a narrow strip of block slides adjacent to the back scar, faster degradation down-dip than on Stonebarrow and a greater proportion of mudslides (Brunsden 1984). Large landslide events and a higher event frequency reflect a greater rate of cliff retreat in this area of the coast (Brunsden 1996). The whole landslide area is characterized by a stepped profile reflecting the presence of aquicludes at stratigraphic boundaries. The crosssectional area is also smaller, below seismic resolution in typical 3D datasets. Seismic interpreters can often miss the presence of these thin complexes, identifying them as stepped unconformities though they may contain reservoir rocks and provide a migration pathway from source rocks on the flanks into a fault block. A key method for

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Fig. 3. Map view patterns of (a) the Stonebarrow Hill complex, note the cuspate nature of the slip surfaces and the boundary between areas of intact landslide blocks and no landslide blocks; and (b) a linear slip surface pattern associated with a translational slide block developed east of the Stonebarrow complex.

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Fig. 4. A sketch cross-section and photographs of the Stonebarrow Hill landslide showing the evolution of the landslide blocks. (a) The area immediately beneath the onset of landslides; (b) mid-section with progressively thinner fault blocks; (c) lower area showing a local cliff, debris flows and mudslides on the beach. Two landslide events here resulted in the outlined deposits that have significantly different net to gross values. The graph illustrates the net: gross distribution of an equivalent subsurface dataset from the Statfjord East Flank.

identification of these structures is the amphitheatrelike form of the landslide. Since pre-existing heterogeneities and rock types can have a dramatic effect on the form of

landslides it is useful to consider other outcrop examples. In New Zealand, the Waipoapoa landslide in Southern Hawke’s Bay has been described by Pettinga (1987b). In that case, the intersection

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of joint patterns developed in limestone beds controlled the landslide development resulting in a serrated edge to the back scar, but again with an overall cuspate form. Lithology also had a clear effect, as in the Dorset outcrops, controlling the position of the slip surface at the base on the complex. This detachment dips back into the complex indicating the material at the toe moved uphill during translation, driven by the force of the collapsing rock mass at the top of the mountain. Rock type can also prevent the development of the classic cuspate slip surface patterns, particularly when the rock types are cemented or the rate of collapse is slow. The collapse structures in the Canyonlands of Utah (Trudgill & Cartwright 1994) are often used as analogues for extensional faults in rifts, having similar map patterns. These rocks are bounded by slip surfaces which detach in salt and are formed as the result of cutting-down of the Colorado River into the detachment zone and are therefore landslides. Thus they are more akin to translational glide blocks with relatively straight, parallel slip systems linked by breached relay ramps.

Comparison of fault systems and landslides Extensional fault systems related to stretching or shortening in the crust are well studied and understood. Their growth, scaling relationships and seismic geometry, including variation, are documented in detail (Wells & Coppersmith 1994; Cartwright et al. 1995; Walsh et al. 2002). Similar databases exist for thrusts, which may have longer trace lengths (Boyer & Elliott 1982). Slip occurs on a metre scale over large areas of the fault surface during seismic events, and larger slip events occur on larger faults. Growth takes place over hundreds of thousands to millions of years and for rift events can occur over a period of 20 Ma (Jarvis & McKenzie 1980). The geometry of the fault systems is determined by through-going major faults that extend down to the brittle–ductile transition, c. 15 km in the crust (Morley 1995), and fault systems are dominantly planar. Linking occurs via overlap zones that form during fault growth, forming relay ramps and with continued slip, breaching of the ramp occurs. The key controls on the dimensions of faults are the degree of extension, wall rock strength and the mechanical layer thicknesses. These types of fault systems have distinct displacement patterns that reflect growth and linkage. Landslide systems have a geometry that also reflects the process and rate of formation. They develop over minutes to years, but typically hours

to days, through unconstrained movement and have associated strain patterns. Periods of landslide activity can stretch beyond the time interval of the driving mechanism, such as a rift event, which may be 10–20 Ma in duration. Detachment dominated systems prevail where the landslides are coherent (slides, slips) whereas with break-up and formation of incoherent mass movement the translation can either be predominantly at the base or within the landslide. A comparison between landslide blocks and fault blocks is shown in Table 1. Key geometrical differences exist, with landslides being typically curvilinear (cuspate) in map view, occasionally more linear if related to translational glide blocks. Normal fault systems and thrusts exhibit a more linear trend, with a dominant trend perpendicular to the principle stress direction, and a subordinate pattern of linking structures which formed during breaching of relay ramps (Morley 1995). The landslide map form can be asymmetrical, reflecting an oblique dip of the underlying shear surface. Hinge slips develop at the edge of the back scar and generally have relatively high displacement gradients reflecting high movement rates and wall rock strains. Initial map view geometries are cuspate, and with the resulting lateral unloading the map pattern evolves into so called ‘butterfly slips’ as a result of a widening or back stepping of the collapse area (Brunsden 1996). Normal faults in the field and in seismic occur as planar or listric in cross-section, with displacement values increasing with depth reflecting the origin of the failure (crustal stretching) and there is a tendency to map landslide slip surfaces with a similar style and displacement gradient. However, slip surfaces can form initially by compaction across a discontinuity, which leads to decreasing displacement values with depth, and when the landslips move they often form by movement on a planar slip surface which detaches on a stratigraphic boundary. This angular, non-listric geometry is likely to be a common alternative to the classic seismic interpretation of a rotational slip. The lateral extent of landslides can exceed the range for faults (in excess of 300 km), and as a reflection of the strain rate, fault seal properties may also differ. The recovery factors for landslide reservoirs may be higher than the range of fault blocks, as a consequence of the difference in the formation process. Finally, reworked material is associated with landslides and is likely to have a higher proportion of mudslides, debris flows and rockfalls than syn-rift sediments, reflecting the degradation of the fault scarp and the local nature of the sediment input, in contrast to the rift related sediments that may have a higher proportion of footwall derived or far travelled sediments.

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Table 1. A comparison of landslide blocks and faults driven by plate forces Slip surfaces Formation mechanism Rate of formation Range of fault styles Scale (map) Map pattern Associated strain Fault seal potential Recovery factor of blocks Associated features

Faults

Gravitational processes Minutes to 1000s years Listric and planar, detachment dominated 100s kilometres to metres Cuspate or linear Open fractures, small scale faults, or none Yes, but mostly juxtaposition seal From very low to high

Crustal stretching 10 000 to 100 000þ years Dominantly planar but also listric, can reach 15 km depth 100s kilometres to metres Linear, with relay ramps Damage zone around fault dominates

Reworked material

Syntectonic sediments

Characterizing landslides using integrated analogue and subsurface data: an example from the Statfjord field The Statfjord Field is located in the Tampen Spur area of the North Sea (Fig. 5). The structure is a

Yes Moderate to high

rotated extensional fault block with a landslide complex on its eastern flank (Fig. 6). The stratigraphic units on the main field include the Brent and Dunlin Groups and the Statfjord Formation (Kirk 1980; Roberts et al. 1987; Hesthammer et al. 1999). The fault block is approximately

Fig. 5. A location map of the Statfjord Field in the North Sea.

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Fig. 6. A seismic cross-section through the Statfjord field outlining the structural elements, including the Main Field, Main Bounding fault, the East Flank landslide complex, and the hanging wall. (See Fig. 7. for location of profile.)

25 km long and 10 km wide, and the landslide complex, termed the East Flank, is up to 5 km wide (Fig. 7). Although little has been published on this structure, (Roberts et al. 1987; Hesthammer & Fossen 1999) a unique dataset has been collected through the drilling of c. 130 wells during 25 years of production, planning secondary and tertiary recovery mechanisms and through several equity

Fig. 7. A map of the base Cretaceous unconformity, Statfjord Field illustrating the cuspate nature of the landslide complex. (SFA, SFB and SFC refer to platform locations on the Statfjord Field.)

redeterminations. Consequently, this is one of the world’s best studied subsurface landslide datasets. The Statfjord landslide complex developed in response to middle –late Jurassic rifting which spanned the late Callovian –Oxfordian era. Apart from a limited area of erosion in the north and south of the Statfjord fault block, which may have been above wave base, the landslide complex is interpreted to have been submarine, based on the conformable relationship of lower Heather Formation (Bathonian) pre-landslide shales above many landslide blocks and the in-situ Brent Group reservoirs in the main field. Movement continued to a lesser extent in post-Oxfordian times. The triggering mechanisms were likely to include the development of the footwall topography of the Statfjord fault block, earthquakes and associated tsunami loading, changes in fluid pressure and type related to diagenesis/compaction, hydrocarbon maturation and sediment loading. In this analysis, the seismic interpretation and reservoir characterization of the Statfjord East Flank was completed using geomorphological principles where the atlas of geometric and structural styles in Figure 1 was used. The database for the work incorporated well data, biostratigraphic classification of landslide material into ‘intact’ or ‘reworked’ material (from cores, sidewall core and cuttings), and production data (particularly pressure and fluid composition). In the seismic data, the landslide complex consists of the following classic features: cuspate slip surfaces in map view, a rapid thinning downslope and irregular topography at the top of the complex (Figs 7 & 8). In addition the basal slip surface to the complex has a stepped form, backtilted during rotation of the Statfjord fault block. In detail, the geomorphological features identified in the East Flank are rotational slides, translational glide blocks, and reworked material of talus slopes, rock falls, turbidites and mass movement systems. By integrating well, seismic,

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Fig. 8. A cross-section through the Statfjord East Flank based on (a) seismic and (b) a geological model constructed using well data. The East Flank is divided into A, B and C blocks, defined by progressively deeper levels of detachment on the Base of Slope Failure (BSF). Each block has characteristic structural geometries and stratigraphic content.

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sedimentological, biostratigraphic and structural information it is possible to create a cross-section through the landslide complex (Fig. 8). This crosssection is derived from depth converted seismic interpretations of slip surfaces and horizons, supported by horizontal and vertical well data to identify missing/repeated stratigraphy, indicating slip surfaces and unconformities. The cross-section is a generalized representation of the types of landslides found in the East Flank. It includes a stepped underlying slip surface which tends to follow the shale dominated stratigraphic units, this being termed the ‘base of slope failure’. The East Flank is divided into the A, B and C blocks based on the detachment level within the stratigraphy. Rotational slips occur near the back scar, translational glide blocks in the centre of the section and progressively thinner and more deformed landslide blocks are seen downslope before the slipped material becomes broken up into mudslides, debris flows and rockfalls of the reworked Brent complex. The proportion of material lost from the top of the blocks increases downslope, as does the proportion of reworked Brent relative to intact Brent rocks. Local accommodation space created by block topography becomes in filled by rockfalls, mudslides and debris flows. With increasing distance down-dip, the base of slope failure cuts through deeper stratigraphic units which then become part of the landslide complex. Since the main driving mechanism of the landslides is the topography of the major rift fault scarp and this developed episodically over time, there is also an implication in terms of the material incorporated into the landslide complex (Fig. 9). Early in the rift history, where topography on the fault scarp is relatively low, the dominant detachment surfaces are developed within shales of the Ness or lower Brent rocks. With increasing slip on the fault and widening of the footwall uplift zone, the deeper stratigraphic units (Dunlin Group, Statfjord Formation) become part of the complex. The implication for hanging wall sedimentation is that it is likely to be Brent dominated at the base and progressively more influenced by Dunlin and Statfjord rocks as the master fault grows and unroofing progresses. A further implication is that Brent rocks will dominate the hanging wall volumetrically since they form the highest proportion of lost material in the footwall. Based on the extensive database of well data and maps, local detailed seismic interpretation of the East Flank is possible. Two examples are presented in Figure 10. Figure 10a illustrates how stratigraphic and seismic reflector patterns vary from west to east. In the innermost part of the East

Flank, the data indicates rotational slips are present, in the central part there is a thinned layer of low dipping, translational blocks. Further downslope the reflectors actually have a counter regional dip interpreted as either successively deeper eroded blocks, break-up of fault blocks into debris flows or cambering resulting from extrusion of shales in exposed cliff faces at the front of blocks. The interpretation is supported by core data containing thinned and reworked sediments with mixed biostratigraphic assemblages. Figure 10b illustrates a seismic line with an interpretation also supported by well picks in well 33/9-A-7-B. Here a thin block of upper Brent Group stratigraphy has been emplaced on top of older, Dunlin Group rocks and the stratigraphy between is missing. The well data supports the flat reflector interpretation of the Dunlin block, but also indicates the original overlying Brent stratigraphy has been removed, and replaced by a separate Etive block derived from landslides up-dip. As with landslide complexes seen in Dorset and other outcrop analogues, the Statfjord landslide thins down flank. However, in contrast to outcrops, the Statfjord dataset has over 100 wells from an area of c. 20 km 5 km which allow maps of landslide block stratigraphy, thickness and presence of ‘reworked material’ (debris flows, mudslides, talus slopes etc.) to be created. One of the most powerful predictive tools is a subcrop map of the Heather Fm, Draupne Fm, reworked Brent constructed from well logs and seismic information (Fig. 11). This map represents the uppermost stratigraphic unit (generally the first well penetration) of intact blocks of the landslide complex. Changing patterns of stratigraphic units can be used to predict reservoir type down-dip, where well data is sparse. Boundaries between the mapped stratigraphic units are based on the last easternmost occurrence of the relevant well pick and the fault pattern. The map shows that the tops of landslide blocks contain progressively older stratigraphic units down dip, so that Tarbert Fm. is lost first, then Ness and Etive then followed by Rannoch. This pattern is also seen in cross – section (Fig. 8b). Beyond a certain distance down-dip from the onset of landslides, usually 1.5–2 km, there are no more intact Brent landslide blocks left and all wells penetrate Dunlin Gp rocks, directly beneath the Upper Jurassic Heather and Draupne Formations. As the landslide blocks in the East Flank thin and eventually disappear, the thickness of the reworked rocks generally increases but varies rapidly dependent on local topography and accommodation space. After characterizing the landslide complex through geomorphological classification and mapping, it is possible using empirical data from

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Fig. 9. A sketch of the development of the Statfjord East Flank. Footwall uplift of the main bounding fault results in the successive emergence of the Brent, Dunlin and Statfjord rocks. Three stages of detachment development occur as the major shale horizons are exposed. As the footwall uplifts a wider zone becomes unstable, Brent rocks are progressively incorporated into the landslide, as well as deeper rocks. Early emplaced blocks in the hanging wall are of the higher stratigraphic units, progressively older rocks are also incorporated as the complex develops and the proportion of mudslides, debris flows increases with time.

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Fig. 10. Two examples of seismic interpretation in the East Flank. (a) Transition from rotational slides to translational and thinning down slope. (b) On this section in well 33/9-A-7-B Etive rocks are emplaced on the Dunlin Gp rocks, with lower Brent absent, indicating stacked landslide blocks, far-travelled landslides and multiple events (complex slides). (See text for details.)

wells to define trends in net: gross and porosity (Fig. 12). Although observed patterns are very dependent on the stratigraphic unit and lithology, the presented examples are illustrative. Using data from the Brent intact blocks a pattern of increasing then decreasing porosity occurs with distance into the landslide complex in the Etive Fm (Fig. 12a), and generally decreasing porosity is seen in the Rannoch Fm (Fig. 12b). Based on geomorphological observations of block break-up in outcrop and core, the Etive distribution could be interpreted as fracture porosity enhancement as the landslide blocks decrease in size in the middle of the complex, and then reduction occurs as increased mixing of clays and porosity collapse takes place downslope. An interpretation of the Rannoch Fm

results, which was finer grained and more cemented at the time of deformation and of closer proximity to the shale dominated Dunlin, would be that porosity mixing of clays and grain packing dominates the process. A plot of porosity v. distance into the landslide complex for the reworked Brent (Fig. 12c) has the clearest trend, the gradual degradation in rock properties reflecting an increasing mixing of clay and mud downslope as more and more of the Dunlin rocks become incorporated. Similar patterns are also seen in net: gross. Note that the porosity reduction from 0.3 to 0.22 is greater than that expected from compaction processes, which would predict a reduction from 0.27 to 0.23 for sandstones in this depth range (Schlater & Christie 1980).

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Fig. 11. A subcrop map of the Draupne/Heather indicating the uppermost stratigraphic unit in the landside blocks. The green area indicates no intact blocks have been encountered in wells or would be predicted. This map is from 2000; new updates of this map confirm the prediction, with minor discrepancies.

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(Well No. 3, Fig. 13c) has sands with good permeability measured in the well, but after the well was set on production, no significant amounts of hydrocarbons flowed. These responses can be interpreted as the result of penetrating pockets of poor or good reservoir that are in connection with better or worse reservoir whether they be intact blocks or reworked sands. In other words, contrasts between the penetrated stratigraphy and that supplying hydrocarbons to the well are the main control on flow response. Other dynamic and well data can be used to characterize the landslide reservoirs of the East Flank. For example, production and well data collected over more than twenty years has enabled communication patterns to be mapped within the landslide complex (Fig. 14). A study was performed on the rock type that separates the reworked Brent from underlying landslide blocks for all wells in the East Flank. In most wells, particularly those in the outermost part of the landslide complex, the two reservoir sands are separated by shale that is at least 2 m thick (salmon pink areas on the map). This data was then combined with observations of pressure differences between the intact blocks and reworked Brent to see if there was a pressure barrier between the two. The conclusion was that in most areas of the east flank the reworked Brent is not in communication with the underlying landslide blocks and there is no relation between that fact and the presence of compartments in the underlying landslide blocks defined as having restricted or no communication with the Main Field (marked in blue). Fig. 12. Porosity variations in the East Flank with distance into the landslide complex. (a) Etive Fm; (b) Rannoch Fm; (c) Reworked Brent.

Although landslide reservoir characteristics can to some extent be predicted based on outcrop, subsurface and geomorphological analysis, well data indicate that in nature these reservoirs are highly variable in quality and spatial extent, especially if the system is small, and thereby are difficult to predict in detail. This can be illustrated in the reservoir and production characteristics of three wells on Statfjord in the East Flank (Fig. 13), where reworked reservoirs (debris flows, mudslides, etc.) are thought to be in close proximity to intact landslide blocks. All three wells were drilled above the contemporary oil–water contact. Well No.1 (Fig. 13a) has a relatively poor permeability measured from the log suite (2– 200 mD) yet produced oil. Well No. 2 has a very thick sand package with high measured log permeability in the reworked Brent but had poor production characteristics (Fig. 13b). The final well

Regional scale landslides: the Halten Terrace example Where well data is absent or limited the principles of geomorphological analysis can still be used to make predictions about reservoir type and quality. For example, well developed examples of subsurface landslide complexes are present in the Triassic and Jurassic of the Halten Terrace on the midNorway margin (Fig. 15). The structures are developed in Lower –Middle Jurassic pre-rift and Upper Jurassic syn-rift sediments, and formed in response to late Jurassic and early Cretaceous basementinvolved rifting along the Norwegian margin. There are three types of landslide geometry and process found on Halten Terrace that mirror the styles found in outcrop and on the Statfjord field. 1) Simple, unconfined rotational slides and translational glides, produced by gravity gliding. These geometries are related to the translation of a rigid body down a sloping detachment. The deformation occurred during movement

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Fig. 13. Plots of three wells in the Statfjord East Flank illustrating the reservoir quality encountered in the well and production characteristics. (a) Poor measured permeability in the sands, good production; (b) high permeability sands with poor production; (c) good permeability sands which failed to produce.

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Fig. 14. A communication map, typical stratigraphy and pressure development in the Statfjord East Flank. A vertical pressure barrier between intact blocks and reworked sediments is recognized based on dynamic data and identification of shale at the base of the reworked rocks. On the communication map, green areas illustrate contact between landslide blocks and the reworked reservoir, whereas pink areas have no communication. Blue polygons indicate compartments (restricted or no communication) between intact landslide blocks and the main field.

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Fig. 15. A regional depth structure map of the base Cretaceous/top Middle Jurassic on the Halten Terrace, mid-Norway, (note rotation of map). The terrace is defined by two major fault zones, the Klakk and Bremstein Fault systems, which consist of dominantly NNE-striking segments typical of the Jurassic rift trend on this part of the margin. In the eastern parts of the Terrace, however, a number of large fault blocks are bounded by NNW or north-striking faults, which reflect the regional dip of a deeply buried Triassic detachment surface within a major relay ramp in the Klakk Fault system. In this area the dominant structural styles are formed by gravity driven transport rather than continental rifting.

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over low basement topography, usually towards the west and SW. These are the most common landslide structures in the study area. 2) Complex, unconfined deformed slide blocks. These are characterized by the vertical collapse and lateral spreading of a body on a basal shear surface. These structures form more intensely deformed landslide blocks, indicating unconfined movement and higher strain rates over higher basement relief. This landslide type is less common, found only in the western parts of the terrace. 3) Contractional toe-structures where compression and uplift can occur in downslope settings, effectively balancing upslope extension. These structures are recognized only locally. These types of landslide are seen on a smaller scale in the Statfjord Field and in many of the discussed outcrops. The common element to all these three structural styles is the presence of a mechanically weak Triassic evaporitic sequence, which acts as a basal shear or detachment surface and decouples post-salt ‘cover’ geometries from pre-salt ‘basement’ fault systems to differing degrees. From well data it is known that two evaporitic sequences are present in the Ladinian and Carnian (Hollander 1984; Jacobsen & van Veen 1984). Middle–Upper Triassic thickness variations can also be observed in seismic data, and the distribution of landslide structures is closely associated with the depositional distribution of evaporites.

Landslide types on the Halten Terrace Rotational slides on the Halten Terrace are simple rotated fault blocks and graben with little or no internal deformation, formed by gravitational gliding on Triassic evaporite detachments (Fig. 16a). They are usually bounded by planar faults that terminate abruptly within the upper evaporitic section. The base evaporite reflector has little or no relief so that block rotation is taken up by lateral salt movement and the formation of thick salt ‘keels’ beneath the bounding faults. Locally the Jurassic stratigraphy within the fault block has grounded on the base evaporite surface. Translational slides are relatively large horst blocks bounded by detached rotational slides. They form by gravitational gliding and lateral translation on Triassic evaporite detachments (Fig. 16a). The base of the evaporitic section has little or no relief, so that the cover section is the least deformed of all structural styles in the study area. The slide blocks follow the regional dip at Top Upper Salt, so that Top Middle Jurassic is more or less conformable with Top Upper Salt, both of which are often

gently folded. The bounding slip surfaces may be planar or listric, either type terminating in the uppermost evaporites or occasionally lower evaporate section (Fig. 16b). Although the lateral movement of slide blocks is not obvious, it is implied by the adjacent linear collapse graben which form in response to extension both up-dip and down-dip. Some of the largest hydrocarbon discoveries on the Halten Terrace are structures of this type (e.g. Kristin, Tyrihans, Trestakk and Onyx). Semi-regional seismic data suggest structural styles associated with gravity gliding occur in areas with a thick isopachous Upper Salt, low pre-rift basement topography and moderate regional dip at base Upper Salt. The orientation of slip surfaces bounding the slide blocks can also be used to imply regional dip patterns on the basal shear surface at the time of deformation. In western parts of the Halten Terrace and Sklinna Saddle, regional dip at base Upper Salt is to the SW, and dominant slip surface strike/dip is perpendicular/ synthetic to this dip (Fig. 15). Where landslide processes develop on relatively steeply dipping basal detachment slopes, and are unconfined in the downslope direction, the common characteristic is a series of strongly rotated blocks detached on an inclined Triassic evaporite substrate (Fig. 16b). In the upslope domain the blocks are not significantly deformed and are similar to rotational slides and translational glides already described. However, in the downslope direction the blocks become progressively more deformed and thinned through internal shear. It is likely that a full Jurassic section is preserved in the landslide blocks, but reflection character is lost due to small-scale faulting, fracturing and porosity collapse and internal stratigraphy is not recognizable. The most distal blocks exhibit chaotic seismic character and are possibly affected by deformation processes associated with the formation of debris flows, slides and rock falls. As described previously, contractional structures can also be significant elements of gravity driven deformational systems. One excellent example of this is seen in the hanging wall to the large basement-rooted Smørbukk Fault, west of the Smørbukk Field (Fig. 16c). A large anticline can be mapped with a fold axis parallel to the Smørbukk Fault and a trace length of over 25 km (Fig. 15). The fold is best developed within the Lower –Middle Jurassic section, but amplitudes are diminished at base Cretaceous and the top Triassic Salt is also more or less unfolded. The fold is strongly asymmetrical, with a short east-dipping steep limb, and a longer west-dipping limb with lower dips. The western limb passes into a syncline with rotational slides on its western flank. Most of

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Fig. 16. Regional seismic lines from the eastern part of the Halten Terrace illustrating typical geometries in landslide complexes. (a) A profile through the internal, mostly confined, and less deformed part of a landslip complex. The dominant structural styles are rotational and translational slide blocks, gliding over a weakly dipping detachment. (b) A more mature and external part of the same system, characterized by a more steeply dipping detachment, less confinement and a transition from gravity gliding to gravity spreading towards the SW. (c) is a Cross-section through the Smørbukk Field and adjacent hanging wall block. The dominant fault (the Smørbukk Fault) is a basement involved normal fault which generated strong rotation of hanging wall stratigraphy during Jurassic rifting. The resultant steep dips within the Triassic evaporites generated gravitational instability and collapse of the overlying Jurassic stratigraphy, reflected in both up-dip extensional collapse and down-dip compressional uplift above the local regional.

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the fold crest seems to be elevated above a regional defined by the erosional unconformity on the Northern Sklinna High and average elevation for the Smørbukk Field, although positioning the regional? in the Sklinna area is difficult as the degree of truncation is uncertain. However, the geometry is interpreted to be an extensional ‘roll-over’ anticline modified by later gravity-driven compression. As a result of the strong rotation of the hanging-wall block during basement rifting, the entire post-salt stratigraphy became gravitationally unstable and began to move downslope towards the east. This resulted in detached up-dip extensional sliding paired with downslope contractional folding, buttressed by the Smørbukk Fault.

Controls on structural style The landslips on the Halten Terrace were active in the late Jurassic and early Cretaceous (based on growth patterns across fault blocks). This implies initiation during major regional rift-related subsidence, which did not begin until Bathonian time. Accommodation space in graben and rotated hanging walls is generated by down dip gravitational collapse on a basin scale directed towards the Møre-Vøring Basin in the west. Driving mechanisms would be similar to those in the Viking Graben, (e.g. earthquakes and associated tsunami loading, build-up of fault block topography, maturation of hydrocarbons). Present day structural geometries can be linked to tectonic controls at the time of deformation, and these concepts can be used to aid seismic interpretation in areas of poor data, and to predict the type and intensity of deformation within local structures. For the landslide complexes observed on the Halten Terrace, the most important structural controls are the distribution of Triassic evaporites (which impact the degree of linkage between sub-salt ‘basement’ and post-salt ‘cover’ faulting) and the ‘triggering’ of gravity-driven collapse by deep-seated crustal extension determining the dip and orientation of evaporitic substrates beneath the Jurassic sediment pile. Thick-skinned crustal extension in the late Jurassic generated sufficient basement topography to create unstable slopes within the evaporite section, and caused gravity collapse of the cover stratigraphy. Lower strain rates during earlier Jurassic extension do not appear to have been sufficient to trigger any cover deformation or evaporite mobility. Also, since the evaporites were buried to several hundred metres at the time of deformation, they were likely to be immobile and functioned mostly as detachment surfaces. On the Halten Terrace, moderately low syntectonic sediment

accumulation rates (of the Melke and Spekk Formations) mean that sediment loading is unlikely to have driven downslope displacement. The geometry of the basal slope itself and the load of the existing rock mass are likely to have been the most significant factors.

Discussion Landslides in the subsurface are an important set of reservoirs that form an increasing part of the hydrocarbon industry’s exploration and development (E&P) portfolio in deep water passive margins, rifts and collisional belts. A wealth of information from geomorphological observations and research can be used to characterize landslide evolution. The geomorphological understanding combined with data and empirical observations from the subsurface, such as thinning patterns and net: gross statistics provides a tool to predict reservoir quality. Landslides have large ranges of scale from metres to kilometres and within a complex can exhibit highly variable net: gross and permeability. A classification of landslides can be made on the basis of form and material type, in the context of tectonic setting, timing, and depositional environment data derived from structural, biostratigraphic and sedimentological studies. There are several predictive tools that can aid in predicting landslide reservoir type and quality. Seismic mapping is the most important, based on interpreting structures in 3D using geomorphological principles and an atlas of landslide types (Fig. 1). Where well data exist, subcrop maps can be used to map the content of intact landslide blocks and maps can be made of the distribution of reworked material (e.g. debris flows, mudslides, rockfalls). Integrated studies are the key to reservoir characterization, which can include for example biostratigraphic, sedimentological and dynamic studies to classify intact versus reworked sediments, or seismic inversion of the landslide complex to predict net: gross. When the landslide complex has been mapped, an attempt can be made to model the range of thickness or net: gross for new well locations. In the example of the Statfjord East Flank, the geometry of the landslide complex is clear from the form of the Base Cretaceous Unconformity and the multiple detachment levels the Ness Fm, Dunlin Gp and Statford Fm shales. The thinning of the complex is apparent in both seismic and well data and the associated changes in net: gross are documented from a subcrop map (Fig. 11). Reworked sediments are delimited on a communication map (Fig. 14).

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Using these datasets, together with a simplified stratigraphy, an idealized representation of the processes described in this paper can be generated (Fig. 17). The impact of different processes on reservoir distribution and quality can be estimated, and a trend for net: gross and likely reservoir thickness with distance into the landslide constructed. To quantify the processes at work, empirical data from the Statfjord East Flank can be used (see Figs 12 & 13). The example presented shows three processes documented in outcrop: (1) stratigraphic thinning, whilst maintaining net: gross; (2) erosion from the top of the blocks; and (3) break-up and formation of reworked material. Starting with an arbitrary undeformed ‘input’ stratigraphy with a net: gross of 0.5, the thinning model leads to progressively reduced stratigraphic thicknesses within the complex but no decay in net: gross, in line with outcrop and Statfjord observations. In the erosion model all reservoir units are lost by c. 1 km into the complex, and net: gross decreases proportionally. Conversely in the reworked sediment model, thicknesses are controlled by the amount of erosion and break-up of

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the landslide blocks, and by local fault block topography. The result is a pattern of variable but general thickening downslope, with a large range in net: gross. The products of different types of landslides have significantly different implications for hydrocarbon potential. At one extreme the highly complex and variable mix of landslide types found in the Statfjord East Flank have a large impact, both in positive and negative ways. At the other extreme, a large, slowly emplaced translational glide block, such as those seen locally on the Halten Terrace, will have a lesser impact on net: gross and stratigraphic thickness, which may be very similar to the initial undeformed stratigraphy, improving prospectivity. The impact of landslides on fault seal processes and prediction techniques has rarely been discussed in publications. Occasionally fault seal has been considered for large gravitationally driven reverse faults on passive margins or for normal faults that may well be landslide structures (Welbon et al. 1997). The impact of landslides on fault seal is dominated by the likely geometrical and

Fig. 17. A method to predict reservoir ranges based on empirical data and geomorphological process understanding. Using an idealized net to gross input data (0.5) and empirical data on thinning factors, erosion and development of reworked sediments from the Statfjord East Flank, predictions of net to gross and thickness can be made based on end member processes. (See text for details.)

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petrophysical characteristics of slip surfaces, namely the slip rate and displacement gradient, material properties in the slip zone, wall rock and matrix strain, the presence of sand injectites or thief sands within reworked sediments. Geometrical differences between faults and landslide slip surfaces are important, as juxtaposition across the slip surface is likely to be the primary control on across structure flow (Allen 1989). Where high displacement gradients exist on landslide slip surfaces, (higher than faults), then there is a higher likelihood of leakage, given appropriate scales of seal thicknesses (James et al. 2004). With higher strain rates, statistically higher numbers of relay ramps and lenses may exist leading to higher leakage tendencies. Conversely, slow moving translational slide blocks bounded and containing low displacement gradient structures may be more continuous and have fewer leakage points, but may be affected by many open fractures in response to the pull apart process at chasms bounding the slide block. As with faults, the stratigraphic architecture of the reservoir rocks (amalgamation ratio, net: gross) will be key (Bailey et al. 2002; Manzocchi et al. 2007) and landslides developed within reworked sediments will present particular challenges since high variability of net: gross, topography and scale means amalgamation ratio will be variable and difficult to predict. Since slip surfaces in landslides can form under very high strain rates, the materials in the slip zone are likely to have quite different characteristics to faults. One key difference is the fact that faults formed by plate tectonic forces occur by seismic slip, on patches of the fault surface which coalesce, and are followed by creep (Wells & Coppersmith 1994). The landslide slip surface may move entirely by non-seismic creep processes, or have individual movement events at a seismic rate but with much higher slip magnitudes during one event. For example, faults may move up to 20– 30 m in a single seismic event; landslides can often move hundreds of metres, imparting more strain in the slip zone. Another difference is the proportion of injected sands and shales in a landslide versus a fault zone. Both sand and shale injection have been documented for faults but is mostly associated with polygonal fault systems. Based on outcrops and an understanding of process, landslides are likely to have higher proportions of injected fluids along the slip surface since higher strain rates in the wall rocks and underlying material result in sediment remobilization, and detachment dominated slip systems can move laterally, opening up the fault to injection from below, or the infill from sediments at the sea floor above.

The consequences of this are that the traditional algorithms for fault seal (e.g. shale smear factor and shale gouge ratio; Lindsay et al. 1993; Yielding et al. 1997) may not be as generally applicable to landslides and must be used with caution. If possible, local calibration of the fault rocks and displacement gradients must be employed in estimating permeability of the fault zone.

Conclusions Landslides are an increasing component of the hydrocarbon industry’s E&P portfolio, on passive margins, in rifts and on occasion, in mountain belts. Landslide reservoirs are difficult to characterize, having larger ranges of scale and complexity than conventional fault-related reservoirs. In rifts they are often at the limits of seismic detection or poorly imaged because of geological complexity. Landslides have a range of distinct structural styles generally different from fault systems in rifts and this is reflected in reservoir quality. Using an atlas of structural styles, adapted surface mapping techniques, empirical databases and integrated studies it is possible to identify the landslide types and make a prediction of reservoir presence (for example from subcrop maps), thickness and net: gross. To characterize landslide reservoirs effectively, it is necessary to train the subsurface team and have robust data collection and use. Optimally acquired and processed seismic data is important (Ocean Bottom Cable being preferred) as is the acquisition of well data including image log and biostratigraphic information. Traditional techniques of sequence stratigraphy and reservoir characterization and uncertainty modelling do not apply. 3D geological models need to be based on modified workflows that can accommodate the lack of mappable surfaces in seismic, or the fact that single horizons can represent multiple landslide and reservoir types, and capture the rapid change in reservoir properties. Established algorithms of fault seal need to be adapted and the connectivity of the slide surfaces mapped. The focus of the industry in many rifts has been towards characterizing landslides reservoirs on the crest of existing fault block accumulations, which are often the last target of incremental oil recovery studies, but focus now has to switch to the other products of landslides (e.g. the deposits in hanging walls which constitute exploration plays). On passive margins, both extensional and compressional structures are seen, many on a large scale, often associated with salt or mud diapirism. Rates of landslide development in this case control sedimentation and reservoir quality. Again documenting and understanding evolution of

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geometry based on geomorphological principles is important, which will indicate the deep water system depositional slope, as is measurement of the rate of slip surface development which helps in fault seal assessment. Landslide reservoirs are a challenge, reflecting the larger range of uncertainty and risk involved in characterizing and developing them. However, since world wide oil production has exceeded new discoveries since the early 1980s and this situation is likely to perpetuate a high oil price environment, the extra costs of characterizing and exploiting landslides are likely to be offset by the value of the reservoirs. Many people have contributed the understanding of subsurface landslides presented in this paper, in particular the Statfjord landslides. Amongst the pioneers were the original operators in Mobil and their partners and C. Jourdan in Statoil. Others who worked systematically on the East Flank include S. Becker, A. Cullum, H. Fossen, K. Gibbons, J. Hesthammer, S. E. Morterud, P. E. Nielsen and T. Vangsnes. S. Becker and T. Vangsnes are acknowledged for Figure 13 and S. E. Morterud for part of Figure 14. The Halten Terrace interpretations presented here build upon earlier work in Statoil by Ø. S. Kløvjan, M. Larsen, S. Hansen and co-workers, whose contributions to the geological understanding of this region we would also like to acknowledge. The significant contribution of Statoil’s partners is acknowledged they have been vital in building an understanding of subsurface landslides, including C. Kiven and J. Vold.

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C AMPBELL , C. J., H ANSLIEN , S. H., N ELSON , P. H. H., N YSÆTHER , E. & O RMASSEN , E. G. (eds) Geology of the Norwegian Oil and Gas Fields. Graham and Trotman, 319– 340. S CHLATER , J. G. & C HRISTIE , P. A. F. 1980. Continental stretching: An explanation of the post mid-Cretaceous subsidence of the Central North Sea. Journal of Geophysical Research, 85, 3711– 3739. S EED , H. B. 1968. Landslides caused by soil liquifaction. Journal of Soil Mechanics and Foundations Division, 94, 1055– 1122. S TEWART , S. A. 1997. Relationship between basementlinked and gravity-driven fault systems in the UKCS salt basins. Marine and Petroleum Geology, 14, 581–604. T RUDGILL , B. & C ARTWRIGHT , J. 1994. Relay-ramps forms and normal-fault linkages, Canyonlands National Park, Utah. Geological Society of America Bulletin, 106, 1143–1157. U NDERHILL , J. R., S AWYER , M. J., H ODGSON , P., S HALLCROSS , M. D. & G AWTHORPE , R. L. 1997. Implications of fault scarp degradation for Brent group prospectivity, Ninian field Northern North Sea. Bulletin of the American Association of Petroleum Geologists, 81, 999–1022. V ARNES , D. J. 1978. Slope movement: types and processes. In: S CHUSTER , R. L. & K RIZEK , R. J. (eds) Landslide Analysis and Control. Transportation research board special report 176 Washington, D.C. 11–33. V ARNES , D. J., R ADBRUCH -H ALL , D. H. & S AVAGE , W. Z. 1989. Topographic and structural conditions in areas of gravitational spreading in the Western United States. U.S. Geoogical Survey, Professional Paper, 1496, 1 –27. W ALSH , J. J., N ICOL , A. & C HILDS , C. 2002. An alternative model for the growth of faults. Journal of Structural Geology, 24, 1669–1675. W ELBON , A. I., B EACH , A., B ROCKBANK , P. J., F JELD , O., K NOTT , S. D., P EDERSEN , T. & T HOMAS , S. 1997. Fault seal analysis in hydrocarbon exploration and appraisal: examples from offshore mid-Norway. In: M ØLLER -P EDERSON , P. & K OESTLER , A. G. (eds) Hydrocarbon Seals: Importance for Exploration and Production. NPF Special Publication 7. Norwegian Petroleum Society, 125–138. W ELLS , D. L. & C OPPERSMITH , K. J. 1994. New empirical relationships among magnitude, rupture length, rupture width, rupture area and surface displacement, 84, 974–1002. Y IELDING , G., F REEMAN , B. & N EEDHAM , D. T. 1997. Quantitative fault seal prediction. Bulletin of the American Association of Petroleum Geologists, 81, 897–917.

The fused fault block approach to fault network modelling K. S. HOFFMAN1 & J. W. NEAVE2 1

Roxar, Inc., 14701 St Mary’s Lane, Houston, TX 77079 USA (e-mail: [email protected])

2

Roxar, Inc., 2201 Walnut Ave, Suite 240, Fremont, CA 94538 USA

Abstract: Fault network modelling of complex faulted structures, those containing hundreds or even thousands of faults, can be an extremely difficult and time-consuming process. Although techniques for mapping and modelling faulted structures have been in existence for nearly forty years, asset teams still struggle to create correct portrayals of such complex faulted reservoirs due to the limitations of the commonly used techniques. We have developed a new approach to fault network modelling, using a new concept of ‘fused’ fault blocks. The identification of fault– fault intersections is based not on a manually drawn fault network or table of relationships, but rather is derived from the fault surfaces themselves. The calculated intersection lines are then used to truncate faults against each other. Because the truncation information can be stored with the fault model, this process yields a repeatable and easily updatable fault model. The name of our technique ‘fused fault blocks’ refers to the fact that when a section of a fault is removed, the two fault blocks that had been created by the fault are then fused together, forming a single fault block. The resultant fault model can then be used to create a 3D reservoir grid, one in which the fault geometry has not been compromised, and therefore better reflects the actual structure. The speed of the fault-building process ‘seconds or minutes, even for models with hundreds of faults’ also allows multiple interpretations, placing the emphasis of the fault network building on the evaluation of the interpretation and the effects of compartmentalization, and not on the manipulation of software.

One of the primary goals of computer mapping and modelling techniques is to produce a model that is structurally possible, internally consistent, and a viable representation of the interpretation. Twodimensional mapping techniques first became available in the late 1960s and early 1970s; commonly these mapping algorithms did not use standard contouring rules to create the 2D grids and therefore could produce impossible or unreasonable structures. With the advent of 3D computer graphics in the 1980s, mapping and modelling expanded into the 3D world as well. Sophisticated algorithms for distributing petrophysical properties or facies in 3D quickly became indispensable, as these techniques provide better information for reserve calculation and well planning than simple 2D maps. However, the modelling of complex structures continues to be a problem. Several methods have been developed for fault surface and fault network modelling, each of which has advantages and disadvantages. Most methods have practical, if not absolute, limitations to the number of faults that can be incorporated into a model simply due to the size of the resultant model or the complexity of building the network. Many also have limitations as to the types of fault intersections that can be modelled. Exploration and development continues to expand into increasingly complex and risky areas,

where the accuracy of the models becomes more and more important. If the fault network on its own was the final desired result, models with hundreds or thousands of faults could easily be created on a routine basis. Many problems arise in using the fault framework to create the full, layered structural model and in using that complete framework for reservoir gridding and subsequent petrophysical and facies modelling. The fused fault block method of fault network modelling has been developed to address the limitations of current methodologies; to eliminate the restrictions on numbers of faults and types of fault intersections, to increase the speed of the process, and to allow the accuracy of the structural framework to be carried into the reservoir grid. Creating a fault model requires two basic steps: calculating the fault surfaces and calculating truncations. Fault surface modelling is the process of creating a 2D grid surface from a set of input data points. The surfaces are calculated independently of one another, and may cross or intersect each other. Where faults intersect, one fault may be truncated against the other. Calculating these truncations is therefore the process of specifying which fault truncates against the other. Faults are not required to truncate at intersections; faults that do cross, such as X faults, are allowed.

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 75– 87. DOI: 10.1144/SP292.4 0305-8719/07/$15.00 # The Geological Society of London 2007.

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Fault surface modelling The creation of fault surfaces is a straightforward procedure, as it is primarily a question of turning a set of XYZ points into a surface; most of the complexity comes later during the construction of the fault network. Surfaces are generated using either a parametric or a triangulation approach. Parametric surfaces are generally created using B-splines (Akima 1970) in a regular, 2D grid. Discrete smooth interpolation (Mallet 1992) may be used for triangulation. Both methods have advantages and disadvantages.

Single-valued v. multi-valued Most faults are single-valued surfaces, having only one Z value at any given XY location. However, multi-valued faults may be encountered in compressional structures where faults are near vertical (such as flower structures) or where faults have been folded. Triangulation methods are well-suited to model multi-valued surfaces; true three-dimensional shapes such as salt domes or folded faults do not have to be treated as special cases. Many 2D gridding algorithms used to create a parametric surface are based on a grid that is regular and orthogonal in XY space. These grids are by definition single-valued and cannot be used to represent an overturned surface or a completely vertical surface. Methods that use this approach (Belcher 1994) therefore have difficulty with vertical or near-vertical faults and cannot model multivalued fault surfaces. To overcome this limitation, the fault data can be transformed into a space where they are single-valued (Zoraster & Bayer 1993). This method, which is used in the fused fault block technique, determines a plane which best fits the XYZ data, transforms the data so that the best-fit plane is a horizontal surface, and calculates the fault surface using standard parametric gridding techniques in the transformed space. Consider the data shown in Figure 1a. The fault is a single-valued surface with a curved shape. In Figure 1b, a best-fit plane has been calculated for these data (dashed line). A transform function is calculated which rotates this plane so that it becomes horizontal; the data are moved into this transform space (Fig. 1c) and a standard parametric gridding algorithm is used to calculate a surface. The extrapolation of the surface using standard gridding algorithms may be more controlled in this transformed space than in actual XYZ space. Vertical faults thus become ‘horizontal faults’ and are easily modelled; even multi-valued faults can often be transformed into a space where they

Fig. 1. (a) Cross-sectional view of input data points for a fault surface (circles). (b) A plane that approximates the overall trend of the data (dashed line). (c) Data transformed into a space where the best-fit plane is a horizontal surface.

are single-valued. A truly vertical fault is impossible to model using a gridding algorithm that works in XY space, as the fault would never

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extend over even a single grid cell. Faults that are nearly vertical but change dip direction slightly also cannot be modelled in XY space using a gridding algorithm, as the 2D grid is a single-valued surface. The resulting surface would contain spikes (Fig. 2a); the ‘solution’ would be to edit the surface or delete data points and the resulting surface would no longer honour the actual structure. This type of fault can only be modelled using a triangulation method or by transforming the data into a coordinate system where it is a single-valued surface (Fig. 2b). Although a triangulation method would appear to have an advantage in modelling multi-valued fault surfaces, it is computationally expensive and does not provide all of the flexibility of a parametric surface, particularly in interactive modification

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(Segonds et al. 1998). Parametric techniques are standard 2D gridding algorithms, may offer the interpreter a wider choice of algorithms, and may be faster.

Visualization Computer graphics libraries display surfaces as a series of triangles. Surfaces may appear smooth by using Gouraud shading (Gouraud 1971). A triangulated surface may be visualized directly without any further processing. Parametric surfaces are usually triangulated for speed of visualization and also for performing surface– surface intersection calculations. The choice of methodology sometimes becomes a trade-off between the initial steps and the later use. The triangulated surfaces are difficult to modify and lack the type of continuity needed for calculation of derivatives (Charles et al. 1995). They often need to go through a parameterization step in order to build a reservoir grid. The parametric approach needs to go through a triangulation step for visualization, but provides more flexibility in surface manipulation and a more direct workflow to get to a reservoir grid.

Methods used in the fused fault block approach The fused fault block method uses parametric surfaces for the faults. These are created in a transformed space, so that vertical, near-vertical and multi-valued faults can be modelled. Each fault in a model has its own transform function. For visualization purposes, the faults are back-transformed into the actual coordinate space and triangulated. This approach provides the speed and flexibility of the standard parametric technique and also the ability of the triangulation technique to handle multi-valued surfaces.

Fault network modelling

Fig. 2. (a) Cross-sectional view of data points (circles) for a near-vertical fault and the surface that would be generated using an XY-based gridding algorithm. (b) The same data as (a), but a surface generated in a transformed space.

Once the individual fault surfaces are made, they must be joined together into a fault network. The fault network forms the basis for stratigraphic modelling and it is the complete faulted stratigraphic model which is used for reservoir gridding and the subsequent attribute modelling. The most commonly used methods for fault network modelling can be divided into two categories: pillar or node-based methods and binary tree methods. Each of these has its advantages and disadvantages, but neither method can handle the full range of fault intersections or truncations.

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Pillar method At its simplest, a pillar is a line that exists in 3D space. Pillars may be used in several places within the geological modelling process, including fault modelling and reservoir grid building. In a reservoir grid, a pillar is a straight line that ties cells together from the top to the bottom of the grid (Fig. 3). Although some flow simulators do allow curved segments in pillars, they are commonly straight lines. Because a modelling workflow very often includes attribute modelling and flow simulation, pillars are also used to control the shape of the fault surface and the intersections or truncations of faults (Fig. 4). Fault pillars are usually allowed to contain 2, 3, or 5 nodes. Although the use of pillars in fault surface generation ensures that the fault model and the reservoir grid are consistent, it has the disadvantage of sometimes simplifying the fault shape, which can adversely affect detailed geosteering applications, among others, as the faults as represented in the model may not capture important small structural details. Geosteering is a technique, primarily used in horizontal wells, where logging while drilling (LWD) or measurement while drilling (MWD) are used in real time to keep a directional wellbore within a particular formation or reservoir zone. Details such as proximity to faults thus become important, as it may be desired, for example, to keep a wellbore on one side of a fault. If the fault has been moved due to the restrictions of the modelling system, the wellbore could cross the fault and miss the target. Defining fault relationships in a pillar-based method may be done by drawing a sketch that

Fig. 3. Pillars are straight lines in a 3D reservoir grid. Pillars tie together cells from the top to the base of the grid and exist not only along a fault surface but also internal to the grid.

Fig. 4. Pillars along a fault surface. Each pillar has two nodes, one at the top and base of each pillar.

shows the truncation of one fault against another. In some respects, this sketch is similar to the 2D polygons or lines that are used to represent faults on a map, although the network is not required to be associated with a particular horizon. The sketch consists of a series of lines, one for each fault; faults that intersect or cross must share a common node (Fig. 5). Pillars extend from these nodes, and where the faults intersect or cross it is not only the node which must be shared, but also the pillar. The pillar method has several advantages. First, for a small number of faults, it is a very quick and easy method. It is graphical and interactive, and the relationships between the faults are easy to see and clearly defined. Second, the lateral extent of the faults can be changed quickly. It is easy to trim an unwanted portion of a fault (to make it truncate against another fault, for example) by deleting a node. It is also easy to extend a fault to intersect another by moving or adding a node. Some implementations of this method use nodes on 3D polygons to control the intersection and truncation of the faults. Third, because of the interactivity, the geoscientist or modeller can easily alter or

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Fig. 5. A two-dimensional sketch of a fault network. Faults are represented by different line types. Individual nodes are squares; shared nodes are triangles.

change the fault relationships based on soft knowledge without having to create or add any actual data. However, the pillar method also has disadvantages. First, the relationships between the faults are mostly defined in a two-dimensional sense, much like a structural map on one horizon. Once a truncation has been made, it cannot change lower or higher in the section and therefore fault relationships cannot change either in depth or along the length of a fault. Second, the shared node and pillar at the fault intersections can limit the types of intersections that can be modelled. A very low angle intersection, for example, can distort the shape of the shared fault pillar and subsequently the shape of the faults themselves. The third problem is that some types of intersections are treated as special cases. For example a Y-intersection (commonly an antithetic fault truncating against a synthetic fault) requires special construction of the nodes and pillars. The simple example shown in Figure 6 illustrates this problem. This is a simple synthetic/antithetic fault pair, where the darker antithetic fault truncates against the larger synthetic fault. The truncation of the antithetic fault against the synthetic is defined by sharing nodes between the two faults (circles). This requires that the antithetic fault is no longer than the synthetic. The intersections become much more complicated when there are multiple, nested Y-intersections. Lastly, pillars are commonly required to extend from the top to the base of the reservoir and cannot terminate within the reservoir. Some pillar-based methods have attempted to solve this problem by introducing two types of pillars (de

Fig. 6. A pair of synthetic and antithetic faults. Network nodes for the antithetic fault are cubes; shared nodes are circles; and nodes for the synthetic fault only are cylinders.

Jager & Pols 2006) but this adds yet another layer of complexity to the modelling. The ‘solution’ to some of these problems, such as the low angle intersections and Y-intersections, is to move the faults so that the intersections become higher angle or so that the faults do not actually intersect one another. The resulting model is no longer a correct representation of the subsurface, which can impact hydrocarbon volume and recovery calculations, well placement and reservoir simulation. Manual edits of grid cell properties may be necessary, for example, to insert transmissibility multipliers into cells which should have been faulted but are not in the final simulation grid. Calculations that require knowledge of fault information, such as fault seal analysis, are also impacted. The pillar method is not well-suited for models containing hundreds of faults, as the shared pillars cause significant distortion of the surfaces and intersections, and the compromises made by moving the faults have too great an impact on the accuracy of the model.

Binary tree method The term ‘binary tree’ refers to a piecewise approach to identifying fault relationships. In this

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method, a fault divides a volume into hanging-wall and footwall blocks. Faults are added one by one, and each fault must be placed into one of the preceding blocks (hence ‘binary’ as there are only two choices for the placement of the new fault). The new fault forms its own hanging-wall and footwall blocks, which together make up the previous block. This hierarchy looks somewhat like a diagram of a tree, with branches spreading out as more and more faults are added (Fig. 7). Each fault in a model has an explicit relationship to any other fault in the model and the placement in the hierarchy defines the allowable truncations. In the example in Figure 7, Fault 1 is the primary fault; it may truncate any other fault in the model but cannot itself be truncated by any fault. Fault 2 can only be truncated by Fault 1; Fault 4 may be truncated by Fault 2 or Fault 1. The various levels in the hierarchy can, in some ways, be related to the ages of the faults, with the faults at the top being younger, although this is not necessarily a strict age relationship. Manually defining this type of hierarchy can be a difficult task when there are hundreds of faults. Methods of determining the relationships automatically, usually based on the distribution of input data, have been developed, but these solutions must always be checked for erroneous truncations.

The primary advantage of this method is that the intersections are not controlled by pillars: therefore the shape of each fault is independent of the intersecting faults, and intersections such as Y-intersections are no longer a special case. The binary tree method is better suited to models containing hundreds of faults than the pillar method, although even here there are practical limitations to the number of faults that may be incorporated into a model. There are some disadvantages to an explicit binary tree as well. First, the fault relationships are not defined in an interactive, graphical way. Often the relationships are based on a table or a treelike diagram, where editing the relationships is quite difficult. Second, crossing faults are treated as a special case. Because a fault is defined as existing only in the hanging wall or footwall of a previous fault, the crossing fault must be specifically added to both blocks. Potentially, the crossing fault might have to be added in multiple places and it can be difficult to find all of the blocks within a complex tree where the crossing fault needs to be specified. Even methods that build trees automatically cannot always place a crossing fault in all of the correct blocks, especially when there are few data points. Third, non-intersecting faults may interfere with one another. Binary tree methods are generally fault

Fig. 7. Diagram of an explicit binary tree. Each fault subdivides a volume into hanging wall and footwall blocks. Subsequent faults are placed into one of these blocks. A fault may be truncated by any fault preceding it in the tree.

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block based methods; that is the faults create specific fault block volumes bounded by the fault surfaces. Even where faults do not intersect one another, the extrapolated fault surface is used to define the boundaries of the fault block. Fault blocks are extremely useful entities for visualization, volume calculations and other purposes, and the extension of the fault surfaces is a useful and intelligent shortcut to creating the fault block boundaries. The drawback is that a strict binary approach always requires one fault at the beginning of the tree. If the ‘wrong’ fault is chosen as the primary fault in a tree, it could erroneously truncate faults further down in the tree, as shown in Figure 8. Here, if the dashed fault is chosen as the primary fault, the extension of this surface to the west of the solid fault could truncate a valid portion of the solid fault. In a simple model, this problem is easy to diagnose and solve, usually by choosing a different fault as the primary fault. However, in cases where there are hundreds of smaller, subparallel faults with no one fault being an obvious candidate as the primary fault, the problem can be persistent, difficult to find, and only solvable by introducing crossing relationships. The fourth problem is similar: self-truncating faults are impossible to model. The primary fault in a binary tree is that against which all other faults might truncate. The primary fault itself cannot be truncated. Therefore, in a case of self-truncating faults, there will always be part of the primary fault which is incorrectly included in the model. The incorrect overlap can be minimized, but the fact that it

Fig. 8. Non-intersecting faults may erroneously truncate one another when using an explicit binary tree. The dashed fault should actually stop short of the intersection with the solid fault; but if the dashed fault is selected as the primary fault, its extension (used to create fault blocks and shown as a dotted line) may truncate the solid fault.

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exists at all means that additional blocks are created and that subsequent faults might be incorrectly truncated. This Escher-like problem is illustrated in Figure 9. Here, the dotted parts of each of the faults should be truncated. None of these faults can be chosen as the primary, non-truncated fault. Although this triangular problem is quite simplistic, this type of situation can often arise in areas where there are a number of subparallel or en echelon faults. Finally, relationships between faults cannot change along the length of the fault. It is difficult, if not impossible, to create a model where an antithetic fault truncates against a synthetic fault in one part of the model, but where the relationships are reversed in another part of the model.

Methods used in fused fault block approach The fused fault block method is a technique that preserves the advantages of the existing techniques while eliminating (as much as possible) the problems associated with them. This method is based on using parametric surfaces to represent the faults. It also uses an implicit binary tree to define fault relationships. An implicit binary tree differs from the explicit tree described above in that the relationships between the faults are not explicitly defined in a hierarchical diagram or table. The name of the method ‘fused fault block’ refers to the process of joining, or fusing, fault blocks together where appropriate. Two crossing faults, for example, would create four volumes, or fault blocks. If a section of one of the faults is

Fig. 9. Map view of a series of self-truncating faults. Each of these three faults should truncate on one of the other two and in turn be truncated by the remaining fault, a situation which is impossible to model in an explicit binary tree.

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removed, there are only three volumes remaining; two of the original blocks have been merged into one (Fig. 10). Although the concept of ‘fusing’ fault blocks in and of itself is not new technology, the implementation of the method in fault and horizon modelling uses a unique application.

The implicit tree has two major advantages over the explicit tree method. First, faults that do not intersect each other do not need to have any relationship defined (Fig. 11). Non-intersecting faults therefore cannot interfere with one another and cause incorrect truncations. A series

Fig. 10. Derivation of the name of the fused fault block method. (a) Two crossing faults, which create the four fault blocks in (b). (c) One fault has now been truncated against the other; the number of fault blocks has now been reduced to three (d).

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Fig. 11. Two non-intersecting faults. In the fused fault block method, no relationship needs to be defined between these two faults. In an explicit binary tree, one would need to be selected as the primary fault.

of relatively short en echelon faults thus becomes much easier to model as the interpreter is not faced with having to select one of the faults as the primary fault in an explicit tree. The fused fault block method also more fully defines sections of intersecting faults than an explicit tree does, providing more flexibility in defining fault truncations (Fig. 12). Fault truncation specifications for the pillar method are based on eliminating nodes of a fault network line; the binary tree method defines a fault as existing in only one block of a previous fault. Thus each of these methods removes all of a fault on one side or the other of the truncating fault. In the fused fault block method, intersection lines split a fault into areas that are fully defined

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by the intersecting faults. That is, instead of an area of a fault having been defined as existing only in the footwall or hanging wall of the intersecting fault, an area may be defined by its compound relationship to several faults. In the example shown in Figure 12, the yellow-coloured fault in the middle of the model is crossed by three other faults. These intersections define four separate, independent areas of the light-coloured fault. Any one of these four areas may be selected for removal, thus allowing any type of truncation between the faults. The example shown in Figure 12, with the middle section of a fault removed, is no doubt a geologically implausible model. However, the ability to remove any particular section of a fault provides flexibility in defining fault truncations, and has applications to various complex truncations, such as the L-faults discussed below. This technique provides a solution to many of the intersection and truncation problems that exist with the pillar or explicit binary tree methods.

Examples The fused fault block method is not simply a technique for fault modelling. The method is an integral part of horizon modelling. The horizon modelling process uses a fault block based approach to create horizon surfaces from input data. Some modelling methodologies go directly to a 3D grid after creating the fault model (Chambers et al. 1999), but this approach requires making decisions about the grid geometry very early in the modelling process. Different aspects of modelling (facies modelling, rock attribute modelling, or flow simulation, for example) may require different grid

Fig. 12. (a) The yellow fault in the middle of the model is crossed by the three darker faults, creating four sections of the fault surface (A, B, C, D). (b) One of the middle sections has been removed from the fault model. Although removing this particular segment is not geologically reasonable, it illustrates the flexibility of the fault truncation process.

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geometries. In a direct-to-grid approach, the entire horizon model must be rebuilt for each purpose. A second method is to generate parametric surfaces of the horizons. This method can have two variations. One variation creates a single 2D surface for each horizon. Where onlap or truncation due to an unconformity occurs, the surfaces become coincident. This can give rise to problems in the 3D reservoir grid, as grid cells may then become extremely thin or collapse near the truncations. In addition, these surfaces, being single 2D grids, cannot model repeated section. With a fault block based approach, such as that used in our method, the horizons are represented by a patchwork of smaller parametric surfaces. This allows easy modelling of repeated section. The information contained in the fault truncations is used to ensure that the individual parametric surfaces are completely continuous at fault terminations. Our method also does not require that surfaces be coincident in areas of onlap or erosion; the surfaces are instead truncated, which creates a 3D grid without collapsed cells. The fault block based, layered structural model thus provides the basis for creating a reservoir grid. The resultant grid represents the structure more accurately, as shortcuts and compromises in fault intersections and truncations do not have to be made as they often are in other fault modelling methods.

Y-faults The fused fault block method provides a technique to build models of multiple nested Y-faults quickly (Fig. 13a). In this example there are two antithetic faults which truncate against the main synthetic fault, and a smaller synthetic fault that truncates

against one of the antithetic faults. An explicit binary tree method would be able to model these faults, but the pillar method would not be able to include the small synthetic fault, as it creates a Y-on-Y fault situation. In this case, one of the faults would have to be removed from the model, or the surfaces changed so that the faults no longer intersect. Both of these would change the basic structure of the model, and therefore would also change the volumes of the fault blocks. These changes do not have to be made using the fused fault block method, as Y faults are not special cases and have no restrictions on the number of Y intersections. When creating a reservoir grid from a Y-fault model, the faults may be treated as linear pillar faults, or the faults may be regularized as stair-step faults. With Y-fault geometries, it is advisable to treat at least one of the faults as a stair-step fault in order to avoid the problems of collapsed or twisted cells at the fault intersection (Fig. 13b). In this example, the synthetic faults have been treated as stair-step faults and the antithetic faults as pillar faults. All faults could as easily have been treated as stair-step faults if desired.

l faults l faults are just Y-faults turned upside-down, but they are generally treated as even more of a special case than Y-faults when using the pillar approach to fault modelling. This type of fault geometry can also pose problems during horizon modelling, as data for the uppermost horizon in the triangular section of the l will not exist. This type of intersection is not considered to be a special case using the fused fault block method. l faults

Fig. 13. Y-fault model. (a) Fault surfaces showing truncation of two antithetic faults against a main synthetic fault, and a smaller synthetic fault truncating against an antithetic fault. (b) Reservoir grid created from the Y-fault model in (a). Colours represent fault blocks. The synthetic faults have been treated as stair-step faults and the antithetic faults as pillar faults.

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Fig. 14. l fault model. (a) The younger, dark fault in the centre of the model has offset two older faults. The lighter coloured faults on the right side of the model are Y faults and the darker sections at the left are the l faults. (b) Reservoir grid created from fault model in (a). Colours represent fault blocks. The younger fault is a pillar fault and the remaining faults are stair-step.

may often be created where a younger fault has offset a series of older faults (Fig. 14a). These faults could be modelled correctly using an explicit binary tree method, but pillar methods would need to modify the fault surfaces in order to eliminate some of the intersections. The fused fault block method does not require any modifications of the fault surfaces or intersections, and has no limits as to the number of l faults that may be included in a model. As with Y-faults, l faults may be treated as either pillar faults or stair-step faults in the reservoir grid, although to avoid collapsed or twisted cells in the triangular areas, it is advisable to treat some of the faults as stair-step (Fig. 14b). In this example, the younger fault is a pillar fault, and the Y and l faults are stair-step. Because of the dip of the younger fault, the edges of the cells along this fault may pose a problem in flow simulation and the performance might be improved by treating this fault as stair-step as well. Our method allows all possible combinations of fault intersections in the 3D grid: stair-step on stair-step, stairstep on pillar, pillar on stair-step, and pillar on pillar, although the last may not be desirable in certain fault configurations.

Self-truncating faults One of the geometries that is possible in a pillar fault method, but impossible in an explicit binary tree method is a series of self-truncating faults. In an explicit binary tree, one fault must always be selected as the primary fault; this primary fault cannot be truncated by any other fault in the

model. A situation such as that shown in Figure 15, where each of the three faults truncates and is truncated by another fault, would therefore not be possible. The fault geometries would need to be simplified so that one of the intersections is removed, or a small extension beyond the intersection would have to be allowed. Both of these situations could negatively impact the reservoir model, either in terms of fault block volumes or in transmissibility across the faults. The fused fault block method does not require that any fault be selected as the primary. A fault is divided into areas based on the intersections with other faults and these areas may then be manipulated independently of one another. This approach makes it possible to model a series of self-truncating faults correctly. Although this example might appear to be synthetic and unrealistic, crossing conjugate faults have been observed and documented in many locations, and their process of formation has been described by Ferrill et al. (2000).

Changing relationships Faults that change truncation relationships along their length are perhaps some of the most difficult geometries to model correctly. Neither the pillar method nor the explicit binary tree can handle this situation without splitting each fault into at least two separate faults. In an L-type intersection, the truncation relationships between synthetic and antithetic faults can change along the length of the faults (Fig. 16). In one part of the model, the synthetic fault truncates against the antithetic, and in

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Fig. 15. A series of self-truncating faults. (a) Faults prior to truncation. Each fault crosses the other two faults. (b) After truncation. The light-coloured fault at the north end of the model truncates against the dark fault at the east. The dark fault truncates against the medium-coloured fault, which in turn truncates against the light-coloured fault.

another part the opposite relationship is true. In addition, the faults do not exist over the same XY area; the truncated section of the fault is shorter than the truncating section of the other fault. Pillar methods cannot handle such a situation, because one and only one of the faults can be specified as the Y fault, and in this case each fault makes a Y against the other. In addition, a Y fault cannot extend beyond the truncating fault in a pillar-based model, as there must be a common set of pillars in the Y area. An explicit binary tree also has difficulty with this geometry, as a clean truncation between faults can only be accomplished by placing a fault in one of the two blocks created by its predecessor in the tree. Allowing the second fault to cross does not create a clean truncation, and putting a fault into the tree twice can lead to problems with coincident surfaces or sections of faults that do not exactly match. However, this complex situation can be modelled quite easily using the fused fault block technique (Fig. 16). This type of geometry can only be modelled correctly and easily when using a method that fully defines the compound areas of faults and allows them to be manipulated independently.

Conclusions The fused fault block technique for fault network modelling provides a solution to the problems that are inherent in existing methods of fault network modelling. The limitations as to the types of fault intersections that are possible to model have been removed. The fused fault block method can model Y and l faults, which are difficult with the pillar method; it can model self-truncating faults, which are difficult with the explicit binary tree method; and it can model L-shaped intersections, which are difficult or impossible in either the pillar or the explicit binary tree methods. It is now possible to create fault networks of these complex truncations and also to take these networks through to reservoir gridding without having to simplify or alter the fault relationships. Some limitations on reservoir gridding may still remain. With this method, there are no longer any artificial constraints on the simulation grid due to modelling restrictions, but there may be limits to the number of cells that are acceptable for flow simulation. Although advances are continually being made both in hardware and software, there

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Fig. 16. L-shaped intersections. (a) Model viewed from the south, showing the truncation of the light fault against the dark fault and the extension of the dark fault beyond the light fault. (b) Model viewed from the north, showing the truncation of the dark fault against the light fault and the extension of the light fault beyond the dark fault.

are practical limits to the size of a simulation grid. This upscaling is a general problem that applies to almost all simulation grids and is not specific to any one gridding method. The simplicity of building and editing the fault relationships means that models can be updated quickly with new data or even new faults without losing the previously defined fault relationships. In addition, it is possible to test and store different scenarios of fault relationships. The speed of this process places the emphasis of the fault network building on the evaluation of the interpretation and the effects of compartmentalization, and not on manipulation of software. Preserving the true geological structure in the fault network produces more accurate reserve calculations, provides a less risky model for well planning and improves the results used in reservoir simulation. The authors wish to acknowledge the contribution of other members of the team, E. H. Nilsen and E. Sverdrup and would like to thank Roxar AS for permission to publish.

References A KIMA , H. 1970. A new method of interpolation and smooth curve fitting based on local procedures. Journal of the Association for Computing Machinery, 17, 589–602.

B ELCHER , R. C. 1994. Geospatial modelling techniques for understanding internal geometries of complexly faulted reservoirs. Society of Petroleum Engineers Paper, 27543. C HAMBERS , K. T., D E B AUN , D. R., D URLOFSKY , L. J. ET AL . 1999. Geologic modeling, upscaling, and simulation of faulted reservoirs using faulted stratigraphic grids. Society of Petroleum Engineers Paper, 51889. C HARLES , S., D ENY , L., B OMBARDE , S. & M ALLET , J. L. 1995. Toward an interface between triangulated surfaces and parametric representations. Society of Exploration Geophysicists Expanded Abstracts, 14, 1251– 1254. D E J AGER , G. & P OLS , R. J. W. 2006. A fresh look at integrated modelling software. First Break, 24, 75–81. F ERRILL , D. A., M ORRIS , A. P., S TAMATAKOS , J. A. & S IMS , D. W. 2000. Crossing conjugate normal faults. American Association of Petroleum Geologists Bulletin, 84, 1543–1559. G OURAUD , H. 1971. Continuous shading of curved surfaces. IEEE Transactions on Computers, 20, 623–628. M ALLET , J. L. 1992. Discrete smooth interpolation in geometric modelling. Computer Aided Design Journal, 24, 178– 191. S EGONDS , D., B ENNIS , C. & M ALLET , J. L. 1998. 3-D structural modelling: a new approach to interactively modify complex surfaces. Society of Exploration Geophysicists Expanded Abstracts, 17, 707 –709. Z ORASTER , S. & B AYER , S. 1993. Three-dimensional fault modelling from cross-sectional data. American Association of Petroleum Geologists Bulletin, 77, 207.

Editing faults within tetrahedral volume models in real time A. L. TERTOIS & J. L. MALLET Gocad Research Group, ASGA ENSG-INPL/CRPG-CNRS, Rue du Doyen Marcel Roubault - BP 40, 54501 Vandoeuvre-les-Nancy, France (e-mail: [email protected]) Abstract: Accurately positioning faults in a geological model is a major concern because they are responsible for offsets of geological sequences. In the tetrahedral models studied in this paper, faults are discontinuities: faces of tetrahedra on either side of a fault are disconnected. Building tetrahedral models can require a large amount of time, especially when there are many faults. We present a tool for making small, real-time, modifications of faults in tetrahedral models arising from geometrical changes required either by new subsurface data or by new interpretations of existing subsurface data. Fault editing is achieved by moving control points on the fault in the tetrahedral grid and by computing a distortion property over an editable volume relative to the control point and spreading this distortion to neighbouring points using the Discrete Smooth Interpolation technique. The editable volume in which tetrahedron vertices are allowed to move is defined by a given distance to the fault. This approach provides a means of editing faults and fault-related features, such as branch-lines.

Grid building remains one of the main challenges of reservoir modelling. Geometric accuracy must sometimes be overlooked in favour of simple grids, which require fewer computing resources. Generally, reservoirs are modelled as curvilinear grids – Cartesian grids in which the layers of cells are deformed to match horizon and fault geometry. These grids offer a fair compromise between precise geometry and easy computation for property simulation, fluid flow and velocity modelling. However, in some instances, reservoirs are so complex that a curvilinear grid does not reflect the geometry of layers and faults accurately, and sometimes cannot even be constructed without making unacceptable approximations. One option for these complex geometries is to use unstructured and irregular meshes, such as polygonal or tetrahedral grids (Lepage 2002; Pre´vost et al. 2004). The resolution of the mesh can be adapted to the structures to be represented: the mesh is coarse in simple regions and denser where the structures or heterogeneity are more complex. Geological properties are also affected by faults. Some properties, usually related to the geometry of the model, for example distance from a well, may be continuous from one side of the fault to the other. In this case, values on both sides of the fault are identical. Other properties, generally related to rock type, such as porosity, may be continuous before displacement by the fault, but may not be continuous after fault displacement. A method involving vectorial links (Moyen 2005) restores the continuity of the property using fault throw (Fig. 1). Points that were at the same location before faults offset the geological sequences are linked so that property values are equal on both sides of faults. In the first

part of this paper, tetrahedral grid building and volume distortion methods are reviewed. Based on the concepts defined in these methods, a fault editing algorithm is presented in the second part. Finally, examples of consistent geological model editing are explained and illustrated.

Building and editing tetrahedral grids Geological applications based on tetrahedral grids Because their geometry is flexible, tetrahedral meshes have several applications in geology. Tetrahedra can be made to fit the geometry of geological structures and as they are the simplest possible simplexes in three dimensions, tetrahedra are interesting to perform computations on. Velocity modelling. Velocity models play a key role in processing seismic data, especially in preor post-stack time and depth migration, as well as in time-to-depth conversion (Yilmaz 1987). Quantitative interpretation of seismic data uses elastic properties derived from velocities. Comparing the results of velocity modelling with real seismic data for a study area can highlight defects in the velocity model or in the layout and geometry of geological structures. Macy & Smith (1998) use a tetrahedral model in which several regions with different geological attributes are separated by velocity discontinuities. The ray path is calculated in each intersected tetrahedron in turn, using the gradient of the velocity function. Velten (1998) defines tetrahedron columns inside the volume model and

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 89– 101. DOI: 10.1144/SP292.5 0305-8719/07/$15.00 # The Geological Society of London 2007.

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(a)

(b)

Fig. 1. Continuity of properties across a fault. Both sides of the fault are shown apart. Squares in shades of grey represent different values of a geological property. (a) Continuity of a property across a fault. Points that have the same geometrical coordinates also have a common property value. (b) Continuity of a property using fault throw. Points that have the same geometrical coordinates do not have the same property value: for instance point H would have a value between white and light grey. Continuity using fault throw is ensured by vectorial links (dashed grey lines).

computes ray paths using several options for the velocity law inside columns. Three-dimensional restoration. Three-dimensional structural restoration provides strain fields that help validate structural interpretations. Muron developed a restoration method for tetrahedral models based on volume conservation and strain minimization, taking into account mechanical rock properties (Muron 2005). Most other volume restoration methods are not fully three-dimensional: stacks of horizons linked by geological constraints are restored simultaneously (Griffiths et al. 2002). The strain fields generated by three-dimensional restoration can be used as input for fracture simulation in tetrahedral models (Mace´ et al. 2005, 2004). These fractures are modelled using a combination of stochastic methods and geological rules (Cacas et al. 1990; Josnin et al. 2002). Fluid flow modelling. Flow simulation is a key step in understanding the dynamic of an oil or water reservoir. Verma (1996) discusses flow simulation in reservoirs using several types of grids, including Voronoi grids. A Voronoi grid is the dual mesh of a tetrahedral grid. It is obtained by replacing tetrahedra with their barycentres, and linking these points together (Okabe et al. 2000). Voronoi grids are used to model fluid flow in reservoirs using the

finite elements or finite volume methods (Palagi et al. 1993). Two and three-dimensional unstructured cells can be adapted to reservoir heterogeneity (Pre´vost et al. 2004). Streamline-based simulations are an alternative to finite elements and finite volume methods (Matringe et al. 2006) and help assess the accuracy of upscaling in these grids and provide an insight into flow behaviour (Baker et al. 2001; Blunt et al. 1996). Geochron framework. Geometry of geological structures and property modelling can be separated using the Geochron framework (Mallet 2002b, 2004; Mallet et al. 2004). A three-dimensional parameterization with geological considerations such as fault– fault and fault–horizon contacts and sedimentary discontinuity surfaces is computed on a tetrahedral model of the study area. This parameterization associates each node in the tetrahedral grid to its position in the depositional space. If no fault was active during deposition the layers are perfectly flat in the depositional space, so geological properties can be modelled in this space using a fine Cartesian grid. Computing petrophysical properties such as porosity in the depositional space reduces errors introduced by gridding limitations. The parameterization enables mapping high resolution geological properties in the depositional space onto the coarser tetrahedral volume.

FAULT EDITING IN TETRAHEDRAL MODELS

Creating tetrahedral grids There are three main groups of tetrahedral grid creation methods (Owen 1998): octree-based, Delaunay-based and advancing front methods. The most popular meshing methods for geological applications are Delaunay-based. First, interpreters create fault and horizon surfaces from seismic and well data and from geological and regional knowledge (Fig. 2a). Faults represent the structural information in the study area, and partition the subsurface in fault blocks (Fig. 2b). If required, horizon surfaces can be integrated in the model as implicit surfaces. Then, a tetrahedral mesh of the model may be generated using a Delaunay criterion (Lepage 2003). As shown in Figure 2c, faults do not have to extend through the whole tetrahedral volume. Because they are unstructured, tetrahedral volumes can represent complex geometries incorporating, for example, discontinuous faults and fault branching. Rock properties can be stored and visualized directly on the tetrahedral volume or using the Geochron framework (Mallet 2002b, 2004; Mallet et al. 2004), a three-dimensional texture mapping enables

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visualization of properties stored in a regular grid (Fig. 2d). Tetrahedral models in geology can be divided into different fault blocks. Inside a fault block, tetrahedra are all connected, and each tetrahedron shares vertices and faces with its neighbours. A fault is modelled as a topological discontinuity in the volume (Fig. 3a). Tetrahedra on both sides of a fault do not share faces and vertices are duplicated, although the geometrical position of the nodes is the same on both sides. To make property modelling easier on a tetrahedral volume, faces of tetrahedra that are on faults have the same geometry as the triangulated surfaces from which the model was created. In other words, on a fault, three entities have exactly the same shape and location: the triangle of the fault surface and the faces of tetrahedra on both sides of the fault (Fig. 3b).

Model updating New information obtained for a geological volume can make a model obsolete. For instance, a new interpretation of seismic data can show that the

Fig. 2. (a) Seismic and well data with surrounding box. (b) Structural model, with fault network. (c)Tetrahedral volume built from structural model. Faults highlighted in black. (d) 3D texture mapping of porosity simulation on tetrahedral volume. Data courtesy of Schlumberger.

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(a)

(b)

Fig. 3. (a) Fault in a tetrahedral volume. Edges of tetrahedra (grey lines) are constrained by the fault (bold black line). Three geological layers are depicted in this model using a red, white and a green colour. Tetrahedra are not constrained by geological layers: tetrahedron edges can cross these interfaces. (b) Schematic representation of data structures on a fault. Triangle ABC is a triangle of a fault surface. Two tetrahedron faces are associated to this fault triangle: face DEF in tetrahedron DEFG and face HJK in tetrahedron HJKL. Point triplets (A, D, H), (B, E, J) and (C, F, K) have the same coordinates.

geometry of a surface is not accurate, or a new well can provide another data point for the location of a surface. Faults are discontinuities in the grid, hence fault editing requires modification of the geometry and possibly the topology of the tetrahedral mesh. The current way of dealing with this problem is to edit the structural model and build a new tetrahedral volume. However, obtaining a high-quality mesh that conforms to geological structures requires time and effort. Local editing techniques on geological models provide a way of making small adjustments to models without having to go through the whole meshing process. Volume distortion is a very active research field, especially in computer graphics and animation. Freeform deformation (FFD) incorporates a number of techniques for modifying the shapes of objects by the manipulation of control nodes or curves. Barr (1984) introduced a combination of simple objectediting transformations. FFD was made easier to use by Sederberg & Parry (1986), Coquillart (1990) and Chang & Rockwood (1994), who used different kinds of control lattices or curves in order to distort objects. But these methods did not take into account the nature of objects being edited. Hirota et al. (1999) added physical laws to FFD in order to preserve the total volume of objects during geometrical distortion. Borrel & Rappoport (1994) introduced simple constrained deformation (SCODEF). Constraint points possessing a radius of influence and desired distortion determine local B-spline basis functions. The entire space, along with the objects in it, is then distorted according to a linear combination of these

functions, creating bumps in space. Real-time geometrical distortion is possible with this method. Grosse (2002) adapted FFD and SCODEF to geological problems and described a number of solutions for interactive editing of geological models. Caumon et al. (2004) developed tools for editing a geological model in real-time whilst retaining other essential constraints, such as contacts between horizons and fault surfaces. One of the problems faced when modifying the geometry of a set of vertices in a tetrahedral volume is that tetrahedra may flip over. When that occurs, the mesh is no longer valid, because the sign of the algebraic volume of inverted tetrahedra has changed, and because some edges may intersect faces of these tetrahedra. Figure 4 shows an example of tetrahedron inversion where one point is moved through the opposing face of the tetrahedron. Shontz & Vavasis (2003) had to tackle this problem when they modelled the beating of a canine heart using a tetrahedral mesh. They applied geometrical distortion to the triangulated surface bounding the tetrahedral mesh. Then the points inside the volume were moved using linear weighted Laplacian smoothing. A constraint on the function used to deform the boundary of the volume ensured that the mesh did not flip over. They obtained satisfactory results for the canine heart, but the linear weighted Laplacian smoothing could not prevent inversion when the geometrical distortion was large. In conclusion, some of these volume editing methods can be adapted with varying degrees of success to geological models. In FFD methods, control curves are distorted and the object being

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(a)

(b)

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(c)

Fig. 4. Inversion of a tetrahedron. Only point A is moved, points B, C and D are fixed. (a) Tetrahedron before inversion. Point A is moved toward face BCD. Edge AD is hidden. The volume of tetrahedron ABCD is V(ABCD) ¼ (1/ 6)(AC AD). AB, and is here positive. (b) Edges AB, AC and AD are hidden. Point A is moved through face BCD. (c) Edge CD is hidden. V(ABCD) is now negative: the tetrahedron has inverted.

edited is updated accordingly. SCODEF is an interesting method but it creates bumps centred on constrained points, whilst editing fault geometry requires smooth geometrical distortion in the control volume. Our method tries to solve these problems and to provide an intuitive, real-time distortion method adapted to geological problems.

Fault-editing method The fault-editing tool presented here permits small adjustments to fault geometry in real-time. An editable volume around the fault is defined and it is distorted by picking and dragging arbitrary control points. The geometrical distortion of the tetrahedral mesh is instantly visible and editing can be stopped when the new geometry is acceptable. Although the fault-editing tool was developed as a plug-in to the GOCAD software, similar approaches could, in principle, underpin methods implemented in other software systems.

Fault editing Before modifying fault geometries in a tetrahedral model, user-defined control points must be created on the fault which is to be edited and the volume in which the tetrahedron nodes will be allowed to move must be selected. In order to define this volume, a property is computed from the distance from the fault and stored at the nodes of the tetrahedral mesh. This distance property can be adapted to provide different shapes of control volumes. If only the distance from the fault is used, the control volume has boundaries that are parallel to the fault. Using the distance from a point at the centre of the fault will provide a spherical control volume. Any combination of these distance functions can be computed, thus varying the shape of

the control volume. A user-defined threshold value for the distance property defines the editable volume: tetrahedra with property values below this threshold are inside and tetrahedra with property values above the threshold are outside the editable volume and are therefore fixed. A low value enables small changes on a part of the fault, whereas a higher value enables general reshaping of the fault. If the threshold is too low, there will not be enough tetrahedra inside the editable volume to enable fault editing. In order to make the volume selection step easier, visualization tools can also be used to display the distance property on surfaces within a model (e.g. Frank 2006). As a control point is edited, by user-defined dragging inside the control volume, a distortion vector is computed between the starting position of the control point and its current position. This vector V provides distortion direction and magnitude, with the direction W ¼ (1/jVj). V stored for later use and the magnitude computed as a onedimensional property on the control volume. This distortion property is interpolated from the value set by the control point to zero on the borders of the editable volume using the Discrete Smooth Interpolation technique (see below; Mallet 1992, 2002a). This means the distortion varies smoothly from a maximum value at the control point to zero on the borders of the editable volume. Tetrahedra outside the editable volume are not distorted, whereas the vertices of the tetrahedral mesh that are inside the editable volume are moved along W, using the distortion property computed for each vertex. If required, W can be modified so that each vertex is moved in a geologically consistent way. This is of importance when a Geochron parameterization is available: horizons in the tetrahedral mesh are represented by a pseudo-time function. If this function is distorted, so is the geometry of the

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horizons. In order to solve this problem, when a Geochron parameterization is provided, the component of vector W that is normal to the horizons is computed for each vertex and removed. This ensures that the vertices are moved along constant values of the pseudo-time function, thus preserving the geometry of the horizons. Vertices must also be moved in a geometrically consistent way, otherwise tetrahedra could invert. In order to prevent such inversions in the tetrahedral mesh, checks are performed at each step of the distortion. If there are no mesh inversions, editing can proceed and the geometry is updated. If the mesh does invert, the distortion is computed from the distortion vector stored in the previous step and the tool is terminated. Editing is carried out by moving control points around in the selected control volume. When a control point is moved, the editing tool enters a loop in which the distortion property is computed over the control volume and the geometry is updated: these editing steps are shown in Figure 5.

used as a linear solver to compute the distortion function. The tetrahedral mesh provides a finite set of interconnected nodes constituting a linear model. The DSI method minimizes the degree of violation of soft constraints set on the linear model. A constraint is a set of equations linking the nodes in the linear model and translating an idea on how the interpolated property should vary between the nodes that are involved. For instance, one of the basic DSI constraints is the roughness constraint, which states that the interpolated function should vary smoothly from one node of the model to the other. This roughness constraint is translated as a set of coefficients linking neighbouring nodes in the linear model. The DSI problem can be expressed as solving the set of linear equations

Background on Discrete Smooth Interpolation

with Aci a vector containing the coefficients of constraint ci at each node of the linear model, here the tetrahedral mesh. w is the unknown function at the nodes. k is the number of constraints on function w. The goal is to find, for each constraint ci, the

The Discrete Smooth Interpolation (DSI) method, described in detail in Mallet (1992, 2002a), is

Control Point dragged

Atc1 w bc1

(1)

.. . Atck w bck

New Direction Vector

Previous Direction Vector

Update of Constraints on Displacement

Update of Constraints on Displacement

Displacement Interpolation

Displacement Interpolation

No Inversion

Inversion

Geometry Update

Step Backwards

Geometry Update

Fig. 5. Editing loop. As a control point is dragged, the direction vector is computed. This vector is transcribed as constraints on the distortion function, which is then interpolated using DSI. If this distortion invalidates the mesh, the direction vector from the previous editing loop is retrieved, the distortion property is recomputed and the tool is terminated. If the distortion does not invalidate the mesh then the geometry is updated and editing can resume.

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value of w for which the linear combination Atck . w is closest to target value bci. The system of linear equations is solved using a least squares method which minimizes an error criterion computed from the values of the unknown function at the nodes of the tetrahedral mesh. This method has two main features that make it particularly useful for interpolating the distortion function. First, it has proved its robustness in many different problems because it is implemented in the Gocad software. Second, designing new constraints for the DSI method is only a matter of translating mathematical formulae into C þ þ code that can be managed by the software. The mathematical framework of DSI makes it easy to develop new geological constraints as well as geometrical constraints. In addition to the soft constraints described above, which are honoured in a least squares sense, the DSI method can also honour hard constraints such as: Atci w ¼ bci

(2)

Atcj w bcj

Interpolating distortion function The most important step in the editing loop illustrated in Figure 5 is interpolation of the distortion function. This section explains which DSI constraints are set on the distortion function for the interpolation to yield the expected result. Three constraints are set on distortion property w, defined for each node a of the tetrahedral volume V. For a constraint set on the distortion function, Equation 1 can be written as Atci w ¼

X ae V

Aci (a) w (a) bci :

(3)

A distance constraint transfers the distortion of the control points to the volume. Assuming that control point P is located inside tetrahedron T with nodes fa0, a1, a2, a3g, that fg0, g1, g2, g3g, are the barycentric coordinates of P inside T and that the distortion property value at control point P is wp, the DSI constraint associated to control point P can be written as:

A smoothness constraint ensures the gradient of w is constant over the volume, thus propagating the distortion induced by the control points to the editable volume. On the border of the editable volume, a hard constraint specifies that the distortion is zero. The distortion property is constrained to vary smoothly from the value given by the control point to zero on the border of the editable volume by the constant gradient constraint. This constraint was described in (Mallet 2003; Moyen 2005), and it is set on each pair of tetrahedra inside the editable volume having one common face. As a tetrahedral model is edited, tetrahedra must not be flattened or inverted. If that were to happen, tetrahedron edges would cross and algebraic tetrahedron volumes would change signs. A non-inversion constraint for the tetrahedra ensures that they do not invert when pushed against the border of the editable volume or against a tetrahedron pinned by another control point. The distorted tetrahedron T has vertices a0, a1, a2, a3 located at positions x(a0), x(a1), x(a2), x(a3). (vectors x are three-dimensional coordinate vectors, w is the intensity of distortion in direction W. T * is the tetrahedron after distortion). The goal of the non-inversion constraint is to prevent any point from getting on the other side of the opposite face. On a tetrahedron, this amounts to preventing the sign of the algebraic volume from inverting. After distortion, the algebraic volume V (T *) of tetrahedron T * is: 1 V(T ) ¼ ½(x(a1 ) þ w(a1 ) W 6 x(a0 ) w (a0 ) W) (x(a2 ) þ w (a2 ) W x(a0 ) w (a0 ) W) (x(a3 ) þ w (a3 ) W x(a0 ) w (a0 ) W):

(5)

If we define three vectors such that: d1 ¼ x(a1 ) x(a0 ) d2 ¼ x(a2 ) x(a0 ) d3 ¼ x(a3 ) x(a0 );

(6)

equation (5) simplifies to:

Atc w ﬃ bc : Ac (ai ) ¼ gi if i [ f0; 1; 2; 3g Ac (ai ) ¼ 0 if i f0; 1; 2; 3g bc ; ¼ wp

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(4)

6V(T ) ¼ ½(d1 þ (w (a1 ) w (a0 ))W) (d2 þ (w (a2 ) w (a0 ))W) ½d3 þ (w (a3 ) w (a0 ))W :

(7)

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Noting that d1 d2 d3 ¼ 6V(T ) and keeping only first order terms yields: 6V(T ) 6V(T ) þ (w (a2 ) w (a0 )) (d3 d1 ) W þ (w (a1 ) w (a0 )) (d2 d3 ) W þ (w (a3 ) w (a0 )) (d1 d2 ) W: (8) Our goal is to ensure that the sign of V (T *) is the same as the sign of V (T ). One way of achieving this is to constrain w so that: V(T ) V(T ) 0:

(9)

Using equation (8): 0 6V 2 (T ) þ (w (a2 ) w (a0 ))V(T ) (d3 d1 ) W þ (w (a1 ) w (a0 ))V(T ) (d2 d3 ) W þ (w (a3 ) w (a0 ))V(T ) (d1 d2 ) W: (10) In terms of a DSI constraint on w: Ac (a1 ) ¼ V(T ) (d2 d3 ) W Ac (a2 ) ¼ V(T ) (d3 d1 ) W Atc w bc : Ac (a3 ) ¼ V(T ) (d1 d2 ) W Ac (a0 ) ¼ Ac (a1 ) Ac (a2 ) Ac (a3 ) Ac (ai ) ¼ 0 if i f0; 1; 2; 3g (11) bc ¼ 6V 2 (T )(1 1) with 1 [ ½0; 1 : As second-order terms are neglected, bc is chosen as 6V2 (T ) (1 2 1) with 1 0:1. The value of 1 controls how close a tetrahedron can go towards inverting. A low value for 1, such as 0.05 for example, will result in nearly flat tetrahedra. A higher value, such as 0.2, will ensure all tetrahedra keep a certain volume, but will stop editing closer to the starting point. This constraint is installed on all tetrahedra inside the editable volume. The non-inversion constraint has dramatic effects on tetrahedral volumes. In two dimensions, the user can evaluate when triangles will invert and stop before that point. But in three dimensions, it is much more difficult to evaluate the instant when editing goes too far and tetrahedra begin to flip over. The non-inversion constraint stops editing when flipping begins and goes back one

step in the editing to a state where the model is valid.

Consistent editing of geological models In this part, three fault editing examples are shown. The interpreted fault in the first example is not consistent with seismic data for the study area. Its geometry is therefore edited using the fault-editing tool and the result is a better match to the seismic data. In the second example, a single fault is edited while a porosity simulation is mapped on the tetrahedral model. Steps must be taken so that the final model is still geologically valid, so that it honours both the seismic data and the porosity simulation data. In the last example, a fault branch line is edited and it is shown how editing of a fault branch line in a geologically meaningful way is more complicated than editing a single fault.

Adjusting a fault to seismic information After the tetrahedral model was created from interpreted surfaces, fault surfaces within the tetrahedral mesh can be displayed along with seismic data. This can show discrepancies between the seismics and the geometry of the tetrahedral model (Fig. 6b). If this happens, the horizon and fault surfaces used for the creation of the tetrahedral mesh can be edited, and the model can be tessellated again. An alternative time-saving process is to use the fault-editing tool to adjust the geometry of the fault to seismic data. As it is difficult to show a tetrahedral mesh being distorted, only a slice of the model is displayed. Figure 6a shows a global view of the sliced tetrahedral model and the point of view the other images were taken from. Displaying a section in the seismic cube provides a convenient basis for editing, as the user can move control points along a seismic section. Once a control point is set on the fault to be edited (Fig. 7a) it can be dragged until the geometry of the fault matches seismic information (Fig. 7b). The control point is constrained to move along the normal to the fault being edited. The vertices of the tetrahedral mesh are moved along this direction minus the normal to the horizons at each vertex, which is computed from the Geochron parameterization pseudo-time function. This ensures that the pseudo-time function is not distorted, thus preserving horizon geometry. Figure 8 shows superimposed slices of the initial tetrahedral model and of the tetrahedral model after the fault was distorted. The fault geometry is much more consistent with seismic information after editing.

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Fig. 6. A single fault with seismic amplitude, in the same dataset as in Figure 2. (a) Location of displayed fault and seismic slice in the tetrahedral model. The model is cropped along the red line close to the seismic slice in further images. A red arrow shows the point of view of further images. (b) Initial fault geometry (black line) and seismic amplitude. The geometry of the fault does not match seismic information (black arrows). Data courtesy of Schlumberger.

Fig. 7. Single fault editing. (a) Control point for fault editing. The green sphere is a control point positioned on the initial fault prior to editing (shown in yellow). The initial tetrahedral mesh is displayed in black. (b) Final and initial fault geometries (shown in green and black respectively). The control point was dragged towards the right and the geometry of the fault was updated accordingly. The resulting fault in the tetrahedral model matches the seismic data. Data courtesy of Schlumberger.

Fig. 8. Initial and distorted tetrahedral meshes, showing the initial mesh (grey) and fault (yellow), together with the final mesh (black) and fault (pink). Vertices of the tetrahedral mesh were moved along with the edited fault. Data courtesy of Schlumberger.

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Three-dimensional property mapping The three-dimensional mapping in the Geochron model introduces another challenge. In the Geochron framework, geological data are mapped from an image of the depositional space, where horizons are flat, onto a faulted and folded geometry. If a property simulation is mapped to the tetrahedral volume, this simulation can have constraints such as values known from well data. These values must remain constant throughout editing. The texture properties which define the threedimensional mapping on the tetrahedral volume are attached to the vertices of the tetrahedral mesh. As their geometry is independent of the attached texture, the texture properties must be updated in order to avoid distorting the mapping along with the geometry. To achieve this, the texture properties are copied to a background volume before editing begins. As the vertices in the editable volume move, their texture properties are retrieved from the background volume. The vertices move, but the property mapping is not distorted because their texture properties are kept up-to-date. Figure 9a shows a slice in a tetrahedral model with a mapped porosity simulation in which a fault intersects a channel. When the fault is edited, the texture properties are updated so that the channel is not distorted. Not updating the properties distorts the porosity mapping and the channel is stretched on one side of the fault and compressed on the other (Fig. 9b). When the texture properties are updated, the channel keeps its original shape and is transferred in part from one side of the fault to the other (Fig. 9c). If other faults are detected inside the editable volume, the value of the distortion property on their nodes is fixed to zero so that their geometry is not modified.

Editing fault branch lines Editing faults in a geological model is more demanding than just ensuring that the tetrahedra do not flip over. If the object to be edited is not a single fault but a fault branch line, it must be edited in such a way that the main fault does not change shape, so that a secondary fault glides along the main fault without deforming it. When a control point is close to a fault branch line, or even on the branch line, additional constraints ensure that the shape of the main fault is preserved during editing. Branch lines are detected automatically in the initialization phase. If such a line is found inside the editable volume, the normal to the main fault is interpolated as a three-dimensional vector field on the editable volume. If other faults are inside the editable volume, their geometry is fixed. When a control point moves inside the

Fig. 9. Illustration of the editing of a mapped property. A vertical slice in a Geochron model showing colour coded simulated values of porosity and cross-cutting faults (thin black lines). (a) Property mapping before editing, in which a fault intersects a channel. (b) Property mapping after fault editing but without updating texture properties. Fault was translated toward the right from its original position (grey dashed line). Because the texture properties were not updated, the channel has yet to be transformed. (c) Property mapping after editing and including updating of texture properties. Data courtesy of Total.

editable volume, the component of the distortion vector W which is colinear with the normal to the main fault is removed for each vertex (Fig. 10). This ensures vertices only move along the main fault, preserving the general shape of the main fault while editing the secondary fault. Figure 11 shows an example of branch line editing, in which the branch line is straightened out whilst retaining the basic shape of the main fault.

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99

N

W WN (a)

(b)

Fig. 10. Editing points close to the branch line between a main fault (grey) and a secondary fault (white). (a) The initialization step, in which the normal to the main fault (black arrows) is interpolated on the editable volume. This vector is then available for each point of the editable volume. (b) Enlargement of box shown in (a). N is the normal to the main fault. W is the distortion vector retrieved from user editing before projection. WN ¼ W 2 (W . N)N is the distortion vector in which the component along the normal to the main fault has been removed.

Fig. 11. Illustration of branch line editing from two different perspectives. (a) Branch line before editing, showing four control points (red spheres) along its length. (b) Editing branch line in which a selected control point (blue) is allowed to move along a line (grey). (c) Branch line after the editing of four control points, with initial branch line also shown (thick black line). (d) Control points on branch line before editing. (e) Control points during branch line editing. in which selected control points are moved in turn and separately. (f) Control points on branch line after editing, with initial branch line also shown (thick white line). Data courtesy of Total.

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Discussion and conclusions When modelling faulted study areas with tetrahedral meshes, a small geometrical correction to a fault may require a complete rebuild of the model and can be very time-consuming. The fault-editing tool presented in this paper enables direct geometrical adjustments in real-time. The user can control the aspect of the mesh precisely while editing, whereas existing FFD techniques usually involve control lattices or control curves. The magnitude of the editable volume and additional control points can be used to specify precisely which regions of the model can change, and which regions should not be modified. The fault-editing tool also features safety precautions which prevent the introduction of inconsistencies in the model. Tetrahedra are prevented from flipping over and making the mesh invalid. Vertices are moved along the pseudo-time function of the Geochron parameterization, thus preserving horizon geometry on both sides of edited faults. The texture properties for the Geochron parameterization are updated as the model is edited so that texture-mapped properties are not distorted. And finally, fault branch lines are edited in such a way that the secondary fault glides along the main fault, leaving the general shape of the main fault undisturbed. The tool provides graphic feedback fast enough to enable comfortable fault editing. Table 1 gives benchmarks of the tool. The time given for each set of nodes inside the editable volume is the average time spent in one tool loop, from the update of the coordinates of the control point to the graphic update (Fig. 5). The frame rate decreases when the editable volume expands, but a volume with about 700 nodes (about 4200 tetrahedra) can be edited in real-time on standard

Table 1. Tool performance on an Intel Dual Xeon 2.40 GHz - 2.39 GHz 2.00 GB RAM with NVIDIA Quadro4 900 XGL 128 MB running Windows XP Service Pack 2. The editing loop starts with the movement of the control point. The distortion property is smoothly interpolated on the nodes inside the editable volume. Then the geometry of the volume is updated. The loop ends with the graphic update that provides user feedback. The given time is the global time for all these operations. The frame rate is above five frames per second, which provides enough feedback for comfortable editing. Nodes in editable volume 403 705

Average editing loop time (ms)

Frame rate (fps)

124.4 169.8

8.036 5.890

hardware. The frame rate only depends on the number of nodes inside the editable volume: the actual tetrahedral mesh usually is much larger than the sub-volume used for editing (about 50000 tetrahedra for the model tested here). In some cases, larger modifications have to be made to tetrahedral models. A fault may have to be translated over such a distance that keeping existing tetrahedra would lead to tetrahedra of very poor quality. Faults may also have to be added to or removed from the mesh. These changes cannot be made while keeping the same tessellation: if a fault is added to the mesh, a topological discontinuity has to be introduced in the model, and if a fault is removed, this discontinuity has to be sealed. The next step for fast model editing is to develop tools that enable topological changes in tetrahedral models without having to recompute the whole tessellation. This work is part of a Ph.D. sponsored by the Association Scientifique pour la Ge´ologie et ses Applications through the G OCAD consortium. Consortium members are hereby acknowledged. Thanks to EarthDecision for providing the G OCAD development environment. Thanks to T. Frank for visualization tools, R. Moyen for the Geochron parameterization and B. Leflon for the porosity simulation.

References B AKER , R., K UPPE , S., C HUGH , S., B ORA , R., S TOJANOVIC , S. & B ATYCKY , R. 2001. Full-field modeling using streamline-based simulation: Four case studies. Paper SPE 66405, presented at the SPE Reservoir Simulation Symposium, Houston, Texas. B ARR , A. H. 1984. Global and local deformations of solid primitives. In: Proceedings of the 11th Annual Conference an Computer Graphics and Interactive Techniques SIGGRAPH 84. ACM Press, New York, 21–30. B LUNT , M., L IU , K. & T HIELE , M. 1996. A generalized streamline method to predict reservoir flow. Petroleum Geosciences, 2, 259–269. B ORREL , P. & R APPOPORT , A. 1994. Simple constrained deformations for geometric modeling and interactive design. ACM Transaction on Graphics, 13, 137–155. C ACAS , M.-C., L EDOUX , E., DE M ARSILY , G., ET AL . 1990. Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation 2 1. The flow model. Water Resources Research, 26, 479– 489. C AUMON , G., L EPAGE , F., S WORD , C. & M ALLET , J.-L. 2004. Building and editing a sealed geological model. Mathematical Geology, 36, 405– 424. C HANG , Y. & R OCKWOOD , A. P. 1994. A generalized de Casteljau approach to 3D free-form deformation. In: Proceedings of the 21st Annual Conference an Computer Graphics and Interactive Techniques SIGGRAPH 94. ACM Press, New York, 257–260. C OQUILLART , S. 1990. Extended free-form deformation: a sculpturing tool for 3D geometric modeling. Technical

FAULT EDITING IN TETRAHEDRAL MODELS Report RR-1250, Inria, Institut National de Recherche en Informatique et en Automatique. F RANK , T. 2006. Advanced vizualization and modeling of tetrahedral meshes. Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France. G RIFFITHS , P., J ONES , S., S ALTER , N., S CHAEFER , F., O SFIELD , R. & R EISER , H. 2002. A new technique for 3-D flexural-slip restoration. Journal of Structural Geology, 24, 773–782. G ROSSE , O. 2002. Remise en cohe´rence d’un mode`le ge´ologique 3D. Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France. H IROTA , G., L IN , M. C. & M AHESHWARI , R. 1999. Fast volume-preserving free form deformation using multilevel optimization. In: Proceedings of the 5th ACM Symposium on Solid Modeling and Applications 0 SMA 99. ACM Press, New York, 234–245. J OSNIN , J.-Y., J OURDE , H., F´ ENARD , P. & B IDAUX , P. 2002. A three-dimensional model to simulate joint networks in layered rocks. Canadian Journal of Earth Sciences, 39, 1443– 1455. L EPAGE , F. 2002. Triangular and tetrahedral meshes for geological models. In: International Association of Mathematical Geology. IAMG 7th International Conference Proceedings, 15– 20 September. Springer, Berlin, Germany. L EPAGE , F. 2003. Ge´ne´ration de maillages tridimensionnels pour la simulation des phe´nome`nes physiques en ge´osciences. Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France. M ACE´ , L., S OUCHE , L. & M ALLET , J.-L. 2004. 3D fracture characterization based on geomechanics and geologic data uncertainties. In: 9th European Conference on the Mathematics of Oil Recovery (ECMOR). 30 August – 2 September, Cannes, France. EAGE, Houten, The Netherlands. M ACE´ , L., M URON , P. & M ALLET , J. -L. 2005. Integration of fracture data into 3D geomechanical modeling to enhance fractured reservoirs characterization. SPE Paper 95827 presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, U.S.A., 9–12 October, 1 –9. M ACY , B. K. & S MITH , B. A. 1998. 3-D anisotropic ray tracing on a tetrahedral mesh. SEG Technical Program Expanded Abstracts, 1973– 1974. M ALLET , J.-L. 1992. Discrete smooth interpolation in geometric modeling. Computer-Aided Design 24, 4, 178–191. M ALLET , J. -L. 2002a. Geomodeling. Oxford University Press, USA. M ALLET , J.-L. 2002b. Space/time mathematical framework for sedimentary geology. In: Gocad Meeting Proceedings, 24– 25 June 2002, 10–11 June 2003. ASGA, Nancy, France. M ALLET , J.-L. 2003. Constraining a piecewise linear function defined on a 3D complex (Applications to 3D restoration). In: Gocad Meeting Proceedings, 24–25 June 2002, 10–11 June 2003. ASGA, Nancy, France.

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Mechanics of fault and expulsion rollover systems developed on passive margins detached on salt: insights from analogue modelling and optical strain monitoring C. KRE´ZSEK1,2, J. ADAM1 & D. GRUJIC1 1

Dalhousie University, Department of Earth Sciences, Life Sciences Centre, B3H 4J1 Halifax, Nova Scotia, Canada (e-mail: [email protected]) 2 Present address: StatoilHydro, Oil and Energy, Global Exploration, 31 Kjørboveien, N-0246 Oslo, Norway Abstract: Scaled analogue experiments with layered brittle and ductile materials have been used to simulate the development of listric growth-fault and expulsion rollover systems during gravitational spreading of a passive margin sedimentary wedge detached on salt. The experiments were performed with varying sedimentation patterns and rates to simulate different depositional scenarios. Deformation monitoring with 3D optical image correlation techniques was used to quantify the 3D surface evolution and strain history of model structures. Our results indicate that rollover structure kinematics is strongly coupled to sedimentation patterns and rates. Whereas differential loading governs the margin-scale state of stress and extensional spreading in the experiments, more localized feedback between the dynamic depositional systems, fault-controlled subsidence, and salt mobilization control the strain history of local fault structures. This is reflected in the characteristic succession of extensional structures that evolve from symmetrical grabens through early, mature and late (collapsed) basinward listric growth-fault and rollover systems into landward listric growth-fault and rollover systems. A lack of sedimentation enhances reactive diapir rise and passive diapirism, whereas low sedimentation rates favour development of longlived basinward listric growth-fault or expulsion rollover systems. Conversely, high sedimentation rates lead to the development of landward listric growth-fault and rollover systems.

Thin-skinned extension of passive continental margins is controlled by gravity-driven down-slope spreading of the brittle overburden above a viscous (visco-plastic) substratum, such as salt (e.g. Jackson 1995). Down-slope gravitational spreading is induced by the pressure difference DP ¼ P1 2 P2 due to differential sediment loading (Fig. 1). This causes the flow in the viscous substratum and the induced shear causes a drag force at the base of the overburden and triggers extensional failure of the overburden (e.g. Gemmer et al. 2004). The up-dip extension may be accommodated by down-dip shortening (e.g. Burrolet 1975; Jackson & Cramez 1989; Worrall & Snelson 1989; Wu et al. 1990, see fig. 1). Some of the most common structures that develop in the extensional domain are listric growth-fault and rollover systems (e.g. Burrolet 1975; Bally et al. 1981; Shelton 1984; Jackson & Cramez 1989; West 1989; Jackson & Talbot 1991; Xiao & Suppe 1992; Seni 1992; Rowan 1993; Roberts & Yielding 1994; Schuster 1995). Rollover anticlines have been of great interest for oil and gas exploration in salt basins around the world (e.g. Demercian et al. 1993; Diegel et al. 1995; Peel et al. 1995; Cainelli & Mohriak 1999;

Cobbold et al. 2001; Tari et al. 2002; Shimeld 2004) because several play types can be associated with them (e.g. Bally & Tari 2004) (Figs 1 & 2). Thus, a key issue is to understand their structural evolution and mechanics (e.g. Rouby et al. 2000, 2002; Brown et al. 2004). In general, rollover systems may be grouped into two kinematic families: fault rollovers and expulsion rollovers (Fig. 3) (Hossack 1995; Rowan 1993; Ge et al. 1997). Fault rollovers develop because of geometric and space compatibility problems caused by extensional displacement along a listric growth-fault and subsequent down-bending of the hanging wall strata. Listric growth-fault and rollover systems can also be differentiated by the dip of the listric growth-fault relative to the down-slope oriented gravitational spreading direction, into basinward (i.e. down-slope; BLS) or landward (i.e. up slope; LLS) listric growth-fault and rollover systems (Mauduit & Brun 1998). The synsedimentary fault activity is indicated by thickening (i.e. growth) of synkinematic strata toward the listric fault (e.g. Bally et al. 1981). Thus, the kinematics of fault rollover anticlines is closely related to the amount and rate of extension in the overburden. Conversely, expulsion rollovers develop due to salt withdrawal.

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 103–121. DOI: 10.1144/SP292.6 0305-8719/07/$15.00 # The Geological Society of London 2007.

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shelf

basin

P1 P2

Brittle overburden Viscous salt Extension

Contraction

L

KS

L

KS

A A S

S

Fig. 1. Schematic diagram illustrating the effect of differential pressure on the generation of different salt-related structures. Differential pressure (P1 2 P2) in a passive margin wedge (brittle overburden) above a viscous salt (ductile detachment) will trigger flow in the viscous layer and the resulting drag forces will cause extension in the overburden. The up-dip extension may be accommodated by down-dip contraction. Listric growth-fault and rollover systems (here shown as model data) are one of the most characteristic structures that develop in the extensional domain (the scale bar is 1 km) and consist of listric growth-fault (L), salt roller (S), rollover anticline (A) and associated key-stone graben (KS). The white marks represent possible HC play types.

Lateral salt removal (decrease of cross-sectional area, see Fig. 3) forces the progressive sinking of the overburden below the initial regional level (e.g. Schuster 1995; Ge et al. 1997). During lateral salt expulsion, the overburden is passively down-building. Expulsion rollovers do not accommodate any overburden sec

extension but are instead caused by bending due to salt withdrawal (Ge et al. 1997). Although both rollover mechanisms can act together in nature, under certain conditions one of them can dominate. It is not an easy task to discriminate between the different rollover structures and differentiation can only be sec

2km

1.6

1.6

2.0

2.0

2.4

2.4

2.8

pre-salt basement

3.2 pre-salt basement

Oligocene Santonian Turonian Cenomanian

2.8

3.2 Upper Albian Lower Albian Aptian evaporites

Fig. 2. Line drawing of a complex listric growth-fault and rollover from offshore Angola (redrawn based on Rouby et al. 2002, p. 785, fig. 2) that shows an early basinward listric growth phase followed by a late landward listric growth phase.

MECHANICS OF ROLLOVER SYSTEMS

Fault rollover extension “Pinned”

Expulsion rollover no extension “Free” b

a

105

“Pinned”

“Pinned” b

a

Amount of horizontal extension

Amount of salt withdrawal

a

b

a

a

b

a

b

b downbuilding

Overburden Passive diapir Space created by extension or salt withdrawal Fig. 3. Overview of rollover mechanisms, showing how fault rollovers involve extensional faulting of the overburden whilst expulsion rollovers develop due to salt withdrawal.

performed by careful structural restoration (e.g. Seni 1992; Xiao & Suppe 1992; Rowan 1993; Rouby et al. 2000). The kinematic concepts derived from analogue (see review in Jackson 1995) and numerical modelling (e.g. Gemmer et al. 2004) have been proven to be very helpful in understanding and validating the structural evolution of passive margin sedimentary wedges detached on salt. We apply scaled analogue experiments to simulate thin-skinned extension and gravity spreading of a passive margin sedimentary wedge detached on salt. Our aim is to develop an improved understanding of the kinematics and mechanics of fault and salt structures that develop by thin-skinned extensional deformation. This analogue modelling approach with high-resolution strain monitoring enables us quantitatively to assess: (i) the strain history of fault and salt structures; (ii) the role of sedimentation in deformation; and (iii) the changing mechanical conditions during rollover deformation. The experimental results demonstrate that the extensional structures and the margin-scale kinematic segmentation that develop during thin-skinned gravity spreading reflect the mechanical coupling between the ductile and brittle layers.

Modelling technique We use scaled analogue experiments consisting of silica sand and silicone elastomer, and 3D optical deformation analysis (PIV, Particle Imaging Velocimetry; Adam et al. 2005, 2006) to study: (1) the fault mechanisms; (2) the role of sedimentation; and (3) the mechanical coupling between the ductile and brittle layers.

Analogue materials Sifted silica sand (grain size distribution: 0.02– 0.45 mm; angle of internal friction: 348; density: 1.6 g cm23, strain softening c. 10–20%) was used to simulate the non-linear frictional-plastic deformation behaviour of brittle sedimentary rocks (Lohrmann et al. 2003). Coloured silica sand was used as marker horizons for the structural interpretation of the final deformation in model sections. A silicone elastomer (PDMS, polydimethylsiloxane; Wacker Elastomer NA USA; viscosity, 6 104 Pa s; density, 0.99 g cm23) with linear viscous behaviour under experimental strain rates simulates viscous flow of salt sediments under gravitational loading.

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Scaling The models are scaled to allow the quantitative comparison of the model geometry, kinematics and stresses to natural prototypes (e.g. Hubbert 1937; Ramberg 1981; Weijermars et al. 1993; Brun 1999; Costa & Vendeville 2002). The geometric scaling factor l * is 105 deduced from the density and cohesion of the sand material and gravitational acceleration. Therefore, 1 cm in the experiments equals 1 km in nature. Because gravitational acceleration is equal under experiment and natural conditions (i.e. the gravity ratio g* is 1), the stress ratio s * in the brittle overburden is computed using the geometric scaling factor l* and the density ratio r * (rmodel/rprototype ¼ 0.7):

s ¼ l r g ¼ ðlmodel =lprototype Þ ðrmodel =rprototype Þ ¼ 6:96 106 where: lmodel is 1 cm, lprototype is 1 km, rmodel is 1.6 g cm23, rprototype is 2.3 g cm23. The viscosity ratio h* between the model silicone (6 1024 Pa s) and natural salt (c. 1018 Pa s), and the stress ratio s* define the strain ratio 1*: 1 ¼ s =h ¼ 1:16 108 The scaling factor of time t* (i.e. tmodel/tprototype) is inversely proportional to the strain ratio 1*: t ¼ 1=1 1:4 109 Therefore, one hour in our models represents about 140 000 years in nature. The model density ratio of sand and silicone (rsand/rsilicone ¼ 1.61) is greater than the density ratio between sediments and salt in nature for rsalt ¼ 2.2 g cm23) (rsediment/rsalt ¼ 1.05 leading to higher buoyancy forces in the silicone in the model. However, salt mobilization due to buoyancy forces is considered to be minor compared with salt mobilization due to extension of the overburden. As is the case for natural passive margin thin-skinned extensional systems, the salt structures (e.g. reactive and passive diapirs) develop passively due to overburden deformation rather than actively pushing through the overburden due to buoyancy (Vendeville & Jackson 1992).

Experiment setup The 3D experiments were performed on a horizontal rig (120 cm long 90 cm wide). The base of each model consists of a pre-kinematic silicone layer of

1 cm thickness, which represents the initial salt basin with a typical area of 100 65 cm (Fig. 4a). The transparent silicone layer is covered with a thin preexperiment sand layer (c. 0.2 cm) in order to facilitate optical monitoring of the experiment surface. This experimental set up represents a passive margin sedimentary wedge that is prograding over a 80 –100 km wide basin filled with 1km thick evaporites. During the experiment, sand layers were sieved manually with precisely defined time laps and thickness onto the pre-experiment layer to simulate the progradation of a passive margin sedimentary wedge (Fig. 4). The sieving procedure provides homogeneous mechanical conditions (Lohrmann et al. 2003) in the sand layer and allows the structural evolution of the model surface to be linked to specific sedimentation patterns. In order to study the role of sedimentation on the development of the extensional structures in the passive margin sedimentary wedge, we performed experiments with different sedimentation patterns and rates (Table 1), while all other parameters (e.g. thickness and lateral extent of the ductile layer, basement configuration, etc.) were kept constant. Aggradation and progradation were simulated (Models 1 to 4, Fig. 4b, c). Models 1 and 2 (Fig. 4b, Table 1) investigate an aggradation setting where sedimentation was restricted to the initial shelf (i.e. the shelf/slope break was kept fixed). Aggradation was simulated by the incremental deposition of 0.5 cm (Model 1) and 0.25 cm (Model 2) thick sand layers in one-hour time intervals until the final sediment thickness of 4 cm on the shelf was reached. After the shelf build-up, no more sand was added in Model 1 to simulate a long sedimentation condensation interval. In contrast, in Model 2, sedimentation continued after the shelf build-up, but was restricted to active grabens where additional accommodation space was created by extension and/or silicone withdrawal. In Models 3 and 4 sediment aggradation and progradation was simulated. During the shelf build-up, aggradation on the shelf occurred with a rate of 0.12 cm/hour (Model 3) or 0.5 cm/hour (Model 4) coeval with progradation until the shelf succession reached a thickness of 4 cm. After the shelf build-up, sedimentation on the shelf was restricted to active grabens and on the prograding slope area basinward of the shelf –slope break. Progradation consisted of basinward movement of the shelf –slope break at a fixed rate (0.5 cm/hour in Model 3 and 1 cm/hour in Model 4; Table 1) while a constant slope profile was maintained (Fig. 4c). The sedimentation patterns were similar in Models 3 and 4, but Model 4 was performed with higher sedimentation rates. After completion, the experiments were cut perpendicular to the strike of the shelf to generate a set of parallel cross-sections at 5 cm intervals. For the

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107

Fig. 4. Experimental setup for the models presented. (a) Initial silicone basin with 1 cm thick silicone bordered by 3 cm wide sand border. The silicone surface was covered by a thin (c. 0.2 cm) thick pre-experiment sand layer. A height-adjustable guide and rail system was used to model incremental sedimentation with specific patterns and rates. Models 1 to 4 represent different sedimentary scenarios (Table 1). (b) In Models 1 and 2 no progradation is simulated and the shelf is built up by aggradation to 4 cm high with 0.5 cm/hour (Model 1) or 0.25 cm/hour (Model 2) sedimentation rates. After the shelf build up, in Model 1 sedimentation was stopped and in Model 2 sedimentation continued in the active grabens on the shelf and slope. (c) In Models 3 and 4 aggradation was simulated with a rate of 0.12 cm/hour (Model 3) or 0.5 cm/hour (Model 4). Progradation was continuous with a rate of 0.5 cm/hour (Model 3) and 1 cm/hour (Model 4). Aggradation on the shelf was stopped when the sedimentary thickness reached 4 cm. Afterwards the sedimentation on the shelf was restricted to active grabens.

sectioning procedure, the model surface was covered by a thick protective post-experiment sand layer, which removed burial differences and therefore any pressure gradient that would cause further migration of the silicone. Then the model was sprayed with water and finally sectioned and imaged with a digital camera. The section images were digitally edited to aid the structural interpretation. For this paper, we have selected the representative centre sections from the experiments (Fig. 5). Although the post-experiment layer in the central section of Model 4 was too thin to stop diapirism

at the toe of the slope, so that a diapir later pierced the post-experiment layer (Fig. 5d), this late stage diapirism does not impact the syn-experiment extensional structures and can therefore be neglected for the purposes of this study.

Optical strain monitoring 3D optical deformation and surface flow monitoring techniques along with displacement data analysis (PIV) were used to monitor the incremental and total deformation and surface evolution of

Table 1. Experimental setup and parameters Model No.

1 2 3 4

Silicone L W H (cm)

100 100 100 100

65 65 65 65

1 1 1 1

Shelf build up to 4 cm high

Post-shelf build-up

Aggradation (cm/h)

Progradation (cm/h)

Aggradation

Progradation (cm/h)

0.5 0.25 0.12 0.5

None None 0.5 1

None Active grabens Active grabens Active grabens

None None 0.5 1

Duration (hours)

72 56 56 98

Fig. 5. Overview of experiments and extensional evolution. For every experiment, one representative central section is shown together with its associated structural interpretation. The evolution of strain is illustrated as diagrams with incremental horizontal strain and finite horizontal strain v. time (see text for discussion). In all experiments, extensional structures are developed on the shelf and upper slope whereas the deep basin area is characterized by thickened silicone with small-scale buckle folds. Early extensional faults were always planar and evolved coeval with reactive diapir rise. Some of the planar faults, like in Models 2 and 4 were transformed to basinward listric growth-faults (BLS). However, most of them were abandoned early in the experiments (annotated with R). (a) Model 1 ran with high sedimentation rates (0.5 cm/hour) and aggradational sedimentary patterns until 8 hours, with no sedimentation afterwards (Fig. 4, Table 1). Grabens are labelled G1, G2 and G3. (b) Model 2 ran with moderate sedimentation rates (0.25 cm/hour) and aggradational sedimentary patterns until 16 hours. Post-16 hours, the sedimentation continued restricted to active grabens (Fig. 4, Table 1). Basinward listric growth-fault and rollover systems (BLS1 and 2), fault rollovers preserving some early normal faults (R) and keystone grabens (KS) are labelled. (c) Model 3 ran with low sedimentation rates (0.12 cm/hour) and progradational sedimentary patterns (Fig. 4, Table 1). Common extensional faults (R) and expulsion rollovers (ERS1-3) are labelled. (d) Model 4 ran with high sedimentation rates (0.5 cm/hour) and progradational sedimentary patterns. Several early grabens (G1-G3), a basinward listric growth-fault and rollover system (BLS) and a landward listric growth-fault and rollover system (LLS).

Fig. 6. Development of extensional structures in the aggradation (a, b) and progradation (c, d) experiments illustrated by time-series of incremental maximum principal horizontal strain and vertical displacement data. The white lines on the images mark the location of the structural reconstructions. The silicone is black on the structural reconstructions.

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C. KRE´ZSEK ET AL.

the experiments (e.g. Adam et al. 2005, 2006). The monitoring equipment consisted of two computercontrolled high-resolution monochrome CCD cameras that were mounted in a stereo set up over the experiments. Stereo images of the experiment surface taken in intervals of 10 minutes were processed, analysed and cross-correlated using a dedicated image correlation and deformation analysis software adapted for analogue experiments (Strain Master, LaVision#). From successive images, the incremental 3D displacement vector field was calculated with submillimetre accuracy. This 3D incremental displacement field formed the basis for the further analysis of displacement components (e.g. subsidence, vz) and derived strain components (e.g. horizontal strain exx). For additional details of the PIV monitoring method, including technique, computation algorithms, resolution, and accuracy refer to Adam et al. (2005).

Structural and mechanical interpretation The structural interpretation of final model deformation was completed for each section. The integration of the structural model data with the strain data of active faults enabled reliable 3D fault correlation and mechanical analysis of the evolution of the complex fault and expulsion rollover systems. Selected fault and salt structures were restored using conventional balancing techniques (Rowan 1993). Their kinematic evolution was analysed in one-hour intervals using the incremental horizontal strain data (exx) and vertical displacement data (vz). These displacement and strain components yield insights into the accumulation and distribution of incremental strain (e.g. localization of faults) and quantify the incremental vertical movements (e.g. subsidence). The map of the incremental strain data shows extensional faults as linear zones of maximum negative horizontal strain (green), and the hinges of compressional folds appear as trends of maximum positive horizontal strain (blue) (Fig. 6a– d). The negative values of vertical displacement document active subsidence (grabens in blue and magenta colours), whereas the positive values show uplifting areas (passive diapirs and folds in green colours) (Fig. 6a–d). Quantitative analysis of the individual strain history of grabens, fault and expulsion rollover systems (Fig. 5) during the experiment facilitated the study of the characteristic differences and similarities in the kinematic development of these extensional structures. The kinematic analysis shows that distinct combinations of strain and subsidence patterns are characteristic of different extensional structures (e.g. symmetric grabens, listric growthfault and expulsion rollover systems; Fig. 7).

Kinematic development of graben systems In all experiments brittle failure of the sedimentary wedge was caused by flow in the silicone layer arising from the increase in differential load during the shelf build-up. As a result, extensional structures developed on the shelf and the upper slope. The deep basin experienced simultaneous contraction, represented by thickening of the autochthonous silicone and small-scale buckle folding of the thin pre-kinematic sand and silicone layers (Figs 5, 6). All faults terminate in the silicone layer, which therefore functions as the main detachment level. The early extensional evolution in all experiments was very similar. Extension was distributed on the shelf in zones of diffuse strain trending perpendicular to the downslope oriented maximum principal extension direction (Fig. 7a). The strain and subsidence patterns recorded in Model 2 at 5 hours (Figs 6b, 7a) exemplify this configuration. Because of diffuse extension, little or negligible subsidence was observed and the faults and grabens had yet to develop. Early faults developed as strain localized on the edges of the diffuse extensional zones. These faults triggered the formation of symmetrical grabens with a set of conjugate planar normal faults. These early grabens are characterized by symmetrical subsidence patterns with the highest subsidence located centrally (Fig. 7b). Important differences between the experiments occurred in the timing, distribution and frequency of the early extension structures. The finite and incremental strain histories of the early grabens indicate an increase of the incremental strain, but with different strain rates (Fig. 5). Initiation of overburden failure occurred earliest in Model 1, where the first grabens formed after 2 hours. Although Model 1 and 2 had similar aggradational sedimentary patterns, but with different sedimentation rates (Table 1), the early graben systems developed on the outer shelf and upper slope of both models. In Model 1 the first graben system (G1) initiated on the outer shelf. After 5 hours the graben developed into a composite graben system (Fig. 5a) when a second graben system (G2) initiated on the slope (Figs 5a, 6a). In a similar way, in Model 2 the symmetrical graben and basinward listric growth-fault and rollover systems (BLS1, BLS2 and G3 in Figs 5b, 6b) initiated in a basinward breaking sequence. The initial position of the graben systems in both models was similar. However, the one-hour incremental strain rates of the grabens in Model 2 were one order of magnitude lower than those observed in Model 1 (Fig. 5a, b). This is also indicated by the incremental horizontal strain data of Model 2 (Fig. 6b), which was

MECHANICS OF ROLLOVER SYSTEMS

109

Fig. 7. Structural reconstruction overlain by vertical displacement (middle part) and the down-slope oriented principal horizontal strain (upper part) data recorded over one-hour intervals. The combination of these patterns gives important insights into the structural development and constrains the reconstructions of section data. The pattern combinations are characteristic of the development of the following structures: (a) pre-faulting; (b) symmetric simple graben; (c) early basinward listric growth-fault and rollover system; (d) mature basinward listric growth-fault and rollover system; (e) collapse of the rollover anticline; (f) early landward listric growth-fault and rollover system; (g) complex graben; (h) inactive graben with passive diapir; and (i) expulsion rollovers with passive diapir. Note that frequently some compression is indicated near major extensional faults. Compression recorded by the monitoring system adjacent to major extensional faults arises from sediment fall off active fault scarps into the grabens, and therefore does not truly represent tectonic compression of the model.

characterized by narrow graben systems in comparison to Model 1 (Fig. 6a). The progradational sedimentation pattern of Models 3 and 4 differed significantly from the aggradational pattern of Models 1 and 2 (Fig. 4). The positions of the early grabens were similar in Models 3 and 4 (Fig. 6c, d), but different from Models 1 and 2 (Fig. 6a, b). In Models 3 and 4,

the early grabens were located not only on the outer shelf and on the slope as observed in Models 1 and 2, but also occurred on the inner shelf (e.g. ERS1 in Model 3; G1-G3 in Model 4). In general, in Models 3 and 4 more grabens developed on the shelf than in Models 1 and 2. The sedimentation rates were highest in Model 4 and lowest in Model 3 (Table 1), a feature which

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correlates with the larger number of graben systems (i.e. four; Fig. 6d by 5 hours) and the higher strain rates (Fig. 5d) recorded in Model 4. Conversely, Model 3 deformed with the lowest strain rates of all of the models (Fig. 5c). In Model 1, sedimentation ceased after 8 hours with the extension of the graben systems continuing afterwards but with decreasing rates (Figs 5a, 7g). By 11 hours, most of the diapirs pierced the graben floors and emerged to the surface (e.g. Figs 5a, 6a). This initiation of passive diapirism was coeval with the complete cessation of fault activity along the graben shoulders (e.g. Fig. 6a by 11–13 hours; 7 h). After 11 hours, the extension focused entirely on the passive diapirs (Fig. 7h) leading to the continuous widening of the passive diapirs (Fig. 5a). The development of Model 2 was entirely different from the post 8-hours evolution of stagnant Model 1. In Model 2, due to the continuous sedimentation, only the reactive diapir of the graben system G3 was able to actively pierce its graben floor. This most likely occurred because the graben formed on the lower slope, where the overburden was thin (Fig. 5b). In the other grabens (BLS1 and 2), the diapirs never pierced the graben floor. In contrast, after 13 hours, continuous sedimentation transformed the initial symmetrical grabens into basinward listric growth-fault and rollover systems (Fig. 5b). This change is observable as a characteristic subsidence and extensional strain pattern. The subsidence pattern is highly asymmetrical with the location of maximum subsidence shifted toward the listric growth-fault (Fig. 7c), and with new secondary normal faults in the developing hanging wall rollover (key-stone graben in Fig. 7c). These fault and subsidence patterns correlate well with the characteristics of basinward listric growth-fault and rollover systems and are consistent with the structures observed in the model sections. In Model 4, as in Model 2, the graben systems initiated on both the outer shelf and upper slope were rapidly transformed into basinward listric growth-fault and rollover systems (G3 and BLS on Figs 5d, 6d). However, in Model 4 the transformation occurred earlier than in Model 2 (8–9 hours rather than 11 hours). Coeval with the transformation, the extension in the landward part of the Model 4 decreased and the grabens on the inner shelf (G1, G2) became progressively inactive (Figs 5d, 6d). In Model 3, which is characterized by the lowest sedimentation rates of all of the models (Table 1), the transition of the early symmetrical graben systems into basinward listric growth-fault and rollover systems never occurred and the reactive diapirs pierced the central part of the graben floor after

11 hours (Fig. 6c). Similar to Model 1, all faults of the early graben systems became inactive as the diapirs emerged to the surface and further extension was localized along the axis of the passive diapirs. In this progradation scenario with low sedimentation rates, the surface depressions formed by the active grabens in the shelf area were not filled completely during the sedimentation events. Here, a thin layer of sediments (0.12 cm/hour) was supplied to the grabens that covered the top of the passive diapirs. During the subsequent nonsedimentation interval, ongoing extension along the diapir axis formed minor conjugate faults in the thin cover sediments above the diapir. The minor faults bound small grabens, which the incremental vertical displacement data highlight as narrow zones of high subsidence bordered by zones of maximum strain (i.e. faults) (Fig. 6c). However, the evolution of the minor grabens was very short-lived, because the diapirs quickly pierced the new sediment in the graben and emerged again to the surface (Fig. 7i). This cyclic process of diapir burial, minor faulting of the cover and re-emergence of the diapir was observable after every sedimentation event. The total extension accumulated by the conjugate faults above the diapir crest does not account for the finite extension of the grabens because most of the extension was accommodated by the diapirs themselves (Fig. 5c). In Model 1, after 15 hours, a new graben system (G3) started to develop on the inner shelf (Fig. 5a) landward of G1 and G2. By that time, the extension of the composite graben G1 was negligible and only minor in G2. In comparison, the peak strain rate of G3 was about two orders of magnitude smaller than the maximum rates observed for G1 and G2 (Fig. 5a). This suggests that sedimentation had a significant effect on the strain rates, because G3 developed during the non-sedimentation stage. In Models 2 and 3, by contrast, no major structural changes occurred during the late stage of the experiment run. Most of the structures reflect peak incremental strain rates between 15 –20 hours (Fig. 5b, c), after which the strain rates progressively decrease. In Model 4 most of the extension was accumulated by basinward listric growth-fault and rollover systems (BLS in Fig. 5d). During the early evolution (8–9 hours), maximum subsidence was located near the main basinward listric growth-fault and was almost negligible in the incipient keystone grabens (Figs 6d, 7c). This configuration changed between 9–11 hours, when the maximum subsidence progressively shifted from the listric main fault into the keystone graben of the hanging wall rollover (Fig. 7d). The shift of subsidence site was coeval with the decrease in strain rate of the main listric growth-fault. As a result, after 13 hours the

MECHANICS OF ROLLOVER SYSTEMS

subsidence associated with displacement along the main basinward listric growth-fault became almost negligible (Figs 6d, 7e). Thus, ongoing extension in the overburden was not accommodated by the listric main fault but within the keystone grabens. Some planar normal faults of the early reactive diapir stage that were inactive during the basinward listric rollover phase were reactivated in this stage (Fig. 7e). The extension in keystone grabens was controlled by the collapse of the rollover anticline as consequence of the basinward translation of the rafts in the slope area rather than the bending of rollover hanging wall (Figs 6d, 7e). Subsidence in the keystone grabens stopped when one of the landward dipping faults became dominant and developed into the main fault of the newly formed landward listric growth-fault and rollover (Figs 5d, 6d). This transition towards the landward listric growth-fault and rollover is observable in the characteristic asymmetrical subsidence pattern of the hanging wall with the maximum subsidence close to the basinward main fault (Figs 6d, 7f). The rollover collapse and the early phase of the landward fault rollover systems are characterized by the highest incremental extension rates, which decreased progressively during the final stages of the experiments (Fig. 5d).

Listric growth-fault and rollover kinematics Basinward and landward listric growth-fault and rollover systems are characterized by very different kinematic evolutions and contrasting fault mechanisms (Fig. 8). Displacement on the basinward listric growth-faults requires movement of the hanging wall block along the entire fault length including the basal detachment (BB0 ). In the passive margin setting, this is possible if the basinward translation of the hanging wall block is faster in comparison to the footwall block (v2 . v1 and v2 ¼ v3). This requires relatively efficient gliding of the hanging wall block along its basal detachment (Fig. 8a). In contrast, displacement on a landward listric growthfault is possible if the footwall block moves faster than the trailing hanging wall segment (v3 v2). This implies relatively slow (or no) gliding of the hanging wall block (Fig. 8b). Thus, the evolution of landward listric growth-fault and rollover systems, i.e. the growth of the hanging wall block, depends on the basinward translation of its footwall block rather than displacement of the hanging wall (e.g. Mauduit & Brun 1998). Any upslope oriented displacement along the rollover base is only apparent because the segment L0 L00 is merely an ‘old fault trace’ but has not accumulated any true

111

displacement in comparison to the active landward main fault segment (LL0 ) (Fig. 8b). Thin sheet stability analysis (Lehner 2000; Gemmer et al. 2004) shows that the hanging wall movement will be maintained when the horizontal component of the downslope oriented extensional force (FO) triggered by the differential pressure in the overburden is high enough to overcome the horizontal force balance in the ductile layer (FD). The horizontal force balance in the ductile layer is given by: FD ¼ Fp Fc

ð1Þ

where Fc and Fp are forces at the base of the overburden induced by Couette (shear) and Poiseuille (channel) flows of the silicone (i.e. viscous salt substratum) (Fig. 8a). The Couette and Poiseuille forces can be defined as: V ðx2 x1 Þ hc

ð2Þ

hc rgðh1 h2 Þ; 2

ð3Þ

Fc ¼ h

Fp ¼

where h is viscosity of the ductile substratum, r is density of the overburden, g is acceleration due to gravity, V is the horizontal gliding velocity of the overburden; (x2 2 x1) is the length over which Fc is acting; hc silicone thickness; and h1 2 h2 is differential thickness of the overburden. Consider an active basinward listric growthfault and rollover system as part of a margin-scale gravitational spreading system (Fig. 8a). During gravity spreading, most of the accommodation space is generated by the basinward listric growthfault (BB0 ). Therefore, continuous sedimentary loading of the hanging wall block will cause pronounced salt withdrawal beneath the hanging wall block. The thinning of the ductile layer (hc) increases the Couette force and decreases the Poiseuille force (see Eqns 2, 3) which results in increased basal coupling of the hanging wall (FD; Eqn 1). Therefore, in order to maintain displacement along the basinward listric growth-fault (BB0 ), i.e. to overcome the increase of basal coupling, the extensional force FO in the overburden has to increase. The extensional force FO can be achieved by increased differential load due to sedimentation or other external forces (e.g. change of basement tilt; Mauduit et al. 1997). With constant FO, the displacement on basinward listric growthfaults will subsequently decrease in time and will eventually stop due to weld formation beneath the hanging wall rollover.

C. KRE´ZSEK ET AL.

112

Down-slope

Up-slope footwall v1

<

hanging wall v2

=

horst v3

B (a)

K

R

FO R Fc Fp

hc

B’ footwall

hanging wall =

v1

v2

<<

B

v3 L

(b)

K

FO

R Fc L”

L’

hc Fp

Fig. 8. Schematic diagrams showing the kinematics of (a) basinward and (b) landward listric growth-fault and rollover systems. FO, down-slope oriented horizontal component of the gravitational force triggered by the differential load of the overburden; v1 2 v3, horizontal gliding velocities; hc, salt thickness; Fc, Couette flow force; Fp, Poiseuille flow force; K, key-stone graben faults; R, early planar normal faults of the reactive diapir growth stage; BB0 , basinward listric growth-fault; LL0 , landward listric growth-fault; L0 L00 , old inactive fault segment.

Although the weld formation due to restricted high sedimentation slows the basinward translation of the hanging wall rollover, much less sediment is deposited on the basinward horst block (Fig. 8a). Because of only minor salt withdrawal, the efficiency of the basal detachment of the horst block is not affected, and it travels basinward with higher relative velocity than the up-dip hanging wall rollover. This velocity contrast caused by the decreasing gliding velocity of the up-dip rollover (v2) relative to the down-dip horst (v3) creates extension between the two blocks. The extension reactivates pre-existent planar normal faults at the contact of the two blocks that were formed during the early reactive diapir rise (R, Fig. 8a) or triggers keystone graben formation (K, Fig. 8a). This extension creates new space at the transition of the hanging wall rollover and the down-dip horst (Fig. 7). This process triggers the collapse of the rollover anticline and unloading of the salt by

extensional thinning of the overburden generates a reactive diapir. This reactive diapir is later transformed into the salt roller of the newly formed landward listric growth-fault and rollover system. Following the collapse of the hanging wall rollover anticline, extension localizes on a dominant landward listric growth-fault (LL0 , Fig. 7f ). The kinematics of this landward listric growth-fault is entirely dependent on the evolution of the down-dip horst that forms the new footwall block (Fig. 8b). The hanging wall growth of the landward listric fault continues as long as the horizontal component of the extension force FO in the footwall exceeds the horizontal force balance FD in the ductile layer below (Eqn 1). The horizontal component of the extensional force (FO) controls the strain history of individual extensional structures and must be on a high level for a relatively long time in order to transform early symmetrical grabens into basinward and

MECHANICS OF ROLLOVER SYSTEMS

finally landward fault rollover systems. This is illustrated in Model 4 where the graben systems G2 and BLS showed similar strain histories until 10 hours, but then evolved differently (Fig. 5d). After 10 hours, the strain rates of the G2 graben system decreased because the gravitational instability moved progressively basinward with the progradation front (i.e. shelf– slope break). In contrast, the BLS graben system was always located at the shelf –slope break in the proximity of the progradation front and therefore experienced maximum strain rates for a long period of time, which supported the transformation into a landward listric growth-fault and rollover system (LLS, Fig. 5d). The polarity change of the basinward listric growthfault and rollover systems of Model 2 never happened, because the lower sedimentation rates dictated that the gravitational extensional instabilities were not high enough to maintain high strain rates in the experiment.

Sedimentation, strain rates, diapirism and structural evolution Sedimentation and strain rates Models 1 and 2 had similar aggradational sedimentation patterns but different sedimentation rates. Accordingly, their early graben systems initiated in similar positions on the outer shelf and upper slope. However, the strain rates in Model 1 were one order of magnitude higher than those of Model 2, a feature that fits well with the higher early (pre-8 hours) sedimentation rates of Model 1 (0.5 cm/hour) compared to Model 2 (0.25 cm/ hour). The evolution of Models 3 and 4 also suggests a direct correlation between sedimentation and strain rates. Model 4 had the highest sedimentation rates (Table 1), with the high differential pressure due to rapid sediment loading on the shelf causing earlier gravitational instability and failure of the overburden and graben initiation, together with the highest strain rates. Conversely, Model 3 had the lowest sedimentation rates and strain rates, with slower graben evolution arising from the fact that the critical values of differential load necessary to trigger overburden failure were established later.

Sedimentation and diapirism The formation of grabens causes localized thinning of the overburden and differential pressure in the silicone layer such that diapirs start to develop beneath the grabens (reactive diapirism; Vendeville & Jackson 1992). However, the reactive diapirs

113

were preserved only in Model 4 (G1, G2 on Fig. 5d) because the extension in these grabens stopped early in the experiment. In Model 1, the reactive diapirs rose to the surface during the sedimentation phase and were able to pierce the thinned sedimentary cover (active diapirism) after 8 hours and emerge at the surface (passive diapirism) after 11 hours (Fig. 6a). Due to continued extension, the passive diapirs progressively widened and extruded on the graben floors to form canopy systems, which in cross-sectional view are columnar with small overhangs (Fig. 5a). In Model 3, the reactive diapirs managed to pierce the graben floors relatively late in the experiment (Fig. 6c). Their symmetrical triangular shape in cross-sections (Fig. 5c) differs from the columnar diapirs in Model 1 (Fig. 5a). This is a consequence of three interacting factors that essentially control diapirism: (1) the amount of extension; (2) the buoyancy of the uprising silicone; and (3) the strength of the sedimentary cover (Koyi 1996, 1998). Down-bending and rolling of the overburden strata, which onlapped the basinward and landward flanks of the diapir, was coeval with the rise of the triangular diapirs and became important only when the diapirs were in a passive stage. Silicone withdrawal from the diapir flanks generated subsidence and the down-bending of the flanking sediments. Thus, these rim synclines of the diapirs essentially functioned as salt withdrawal minibasins. In Models 2 and 4 most of the early reactive diapirs transformed into roller structures associated with listric growth-fault and rollover systems. In cross-section, the rollers are small-scale triangular shaped asymmetrical diapirs with their shallow dipping flank located beneath the main listric growth-fault (e.g. BLS1, BLS2 in Fig. 5b). As discussed, each experiment can be characterized by a particular type of diapir evolution. The diapirs that developed in experiments with similar sedimentation patterns can be very different (e.g. compare Model 1 v. 2, Model 3 v. 4). Therefore, the sedimentation rate rather than the sedimentation pattern is the most important controlling factor in diapir evolution. Lack of sedimentation triggers extensive passive diapirism and canopy formation. Low sedimentation rates favour well-developed triangular passive diapirs associated with expulsion rollovers. High sedimentation rates prohibit passive diapirism, with early reactive diapirs quickly transformed into roller structures that are associated with listric growth-fault rollover systems.

Sequence of graben initiation Graben initiation stepped basinward in all experiments, with the exception of Graben 3 of Model 1 which formed landward of the earlier graben

114 C. KRE´ZSEK ET AL. Fig. 9. Overview of the relationship between structural evolution and sedimentation rates. In all experiments, the extensional deformation started with symmetrical grabens and associated reactive diapirs. The reactive diapirs developed into passive diapirs in experiments with low sedimentation rates (Model 1 and 3). In cross-section view, the passive diapirs of Model 1 were columnar, whereas in Model 3 triangular associated with expulsion rollovers. In experiments with high sedimentation rates (Models 2 and 4) passive diapirs did not develop and the early symmetrical graben systems were transformed into basinward listric growth-fault and rollover systems. In Model 2 the evolution of basinward listric growth-fault and rollover systems stopped in the mature stage characterized by well developed keystone grabens. In Model 4, the structural evolution continued by transformation of mature basinward listric growth-fault and rollover systems into a landward listric growth-fault and rollover systems. The change of polarity of listric growth-fault systems involved collapse of the basinward listric growth-fault hanging walls. The observed differences in structural evolution are related to sedimentation rates and patterns for identical boundary conditions of the experiments.

MECHANICS OF ROLLOVER SYSTEMS

systems G1 and G2 (Fig. 5a) during the nonsedimentation phase of the experiment (Table 1). Without sedimentation maintaining the slope profile, advanced failure of the outer shelf– upper slope overburden caused the shelf –slope break to retreat landward thereby decreasing the slope angle and hence the differential pressure gradient. This process generated the landward retreat of the highest differential loading instability (Gemmer et al. 2004). This never occurred in the other models where the slope profile was maintained by continuous sedimentation. In Model 2, late sedimentation was focused in the active grabens in the shelf –slope transition and in this way the sedimentation maintained a relatively stable gravitational instability. No new extensional structures developed in the landward shelf area of the experiment. In the progradation experiments (Models 3 and 4), the shelf –slope break always moved basinward, with the gravitational instability continuously prograding basinward and causing a basinward sequence of graben initiation.

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Sedimentation and structural evolution The structural styles and their evolution appear to be strongly influenced by sedimentation rates (Fig. 9), a feature we highlight by plotting the structural developments against sedimentation rate (Fig. 10). Symmetrical grabens with reactive diapirs represented the early stage of extensional deformation in all experiments (Figs 6a–d, 9, 10). In Model 1, the evolution of early grabens ceased after further extension, which allowed passive diapirs to emerge at the surface (Figs 9, 10). Because the passive diapirs became the weakest part of the sedimentary wedge, all extension was focused in the diapirs and fault-related extension ceased (Fig. 6a). In Model 3, with its low sedimentation rate, passive diapirism occurred later and was strongly associated with expulsion rollovers (Figs 5c, 9). In the experiments with higher sedimentation rates, the early graben systems transformed into basinward listric growth-fault and

Node formation sealed grabens

Sedimentation rate

?

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LLS (Model 4) sealed rollovers

Graben with reactive diapir

Basinward listric growthfault rollover system

Passive diapir and expulsion rollovers Passive diapir

BLS (Model 2) ERS (Model 3) sealed diapirs

G (Model 1)

Time Fig. 10. Synthesis of the evolution of salt related structures as a function of sedimentation rates and time. All other parameters are constant and are typical of those of the presented experiments (salt thickness, basin morphology, etc.). Structures that characterize the kinematic domains are shown in the experimental sections (Fig. 5). The grey area represents non-deformation.

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rollover systems (Figs 9, 10). This transformation occurred even faster in Model 4 than in Model 2 (Figs 6b, d, 10) indicating that higher sedimentation favoured rapid transformation. The change of polarity of the listric growth-fault and rollover systems from basinward into landward was observable only in Model 4 (Fig. 5d), which had the highest sedimentation rates. The kinematic sequence of the listric growth-fault and rollover systems indicates that the sedimentation rates strongly influence the velocity of transformation. Because sedimentation efficiently increases salt withdrawal beneath the hanging wall of the basinward listric growth-fault and rollover with increasing basal coupling, higher sedimentation triggers a faster polarity change of growth-fault rollover systems (Fig. 10). With very high sedimentation and progradation rates, the finite extension in the individual graben structures is limited because the rapid thickening of the overburden and basinward migration of the gravitational instability increases the strength of the overburden and decreases the differential load (Fig. 10). The experiments with low sedimentation rates are characterized by symmetrical graben systems (Model 1) and expulsion rollovers (Model 3). In contrast, the experiments with high sedimentation rates (Model 2 and 4) are characterized by listric growth-fault and rollover systems. Thus, under the uniform boundary conditions (e.g. salt thickness, basement morphology, sedimentation patterns) high sedimentation rate is more likely to generate fault rollovers than the low sedimentation rate. The relationship between structural evolution and sedimentation rates shown in Figure 10 reflects the particular boundary conditions of these experiments (Table 1). Besides sedimentation, several other factors affect the structural evolution of passive margin sedimentary wedges detached on salt, for example, initial salt thickness (e.g. Brun et al. 1994; Mauduit & Brun 1998; Brun 1999; Fort et al. 2004), basement configuration (e.g. Ge et al. 1997), and water load (Gemmer et al. 2005). In addition, the mechanical coupling between the brittle and ductile layers has a strong influence on the structural evolution (Brun et al. 1994). A thick pre-kinematic salt layer enhances passive diapirism and expulsion rollover formation, whereas a thin salt layer favours the formation of listric growthfault and rollover systems.

Discussion: comparison with natural systems Early extensional structures in the landward part of many passive margins characterized by thinskinned salt tectonics are represented by

asymmetrical grabens and/or basinward listric growth-fault and rollover systems (Fig. 11). We have observed a similar structural development in the experiments with relatively high sedimentation rates where the symmetrical graben systems were transformed rapidly into asymmetrical fault rollover systems (e.g. Models 2 and 4). Interpreted seismic data indicate that many of the natural early rollover structures developed during a relatively short, but very active, extensional stage (Fig. 11). This is comparable to the early extensional structures of the high sedimentation rate experiments that developed on the inner shelf, but then quickly became inactive (e.g. Model 4). Rapid progradation with high sedimentation rates shifted both the shelf –slope break and the gravitational instability basinward, with the cessation of deformation in the landward part of the experiment. Fault activity in the landward part also decreases because the basinward silicone withdrawal continuously increases the mechanical coupling between the ductile and brittle layers (Eqns 2, 3; Fig. 10). The shear stress below the listric growth-fault and rollover systems therefore increases and the overall strain rates decrease with time. Based on these mechanical concepts derived from the models, a similar history is assumed for the early extensional listric growth-fault and rollover systems in the landward parts of many passive margin basins (e.g. Campos, Northern Santos, Lower Congo basins, Fig. 11). Thin-skinned extension in the shelf and upper slope areas of passive margins may be accommodated by down-dip shortening if a buttress exists in the deep-water basin to trigger contraction. The buttress may be represented by a thick sedimentary overburden (e.g. Gulf of Mexico) or basement high (Santos Basin, offshore Brazil). Without a buttress, extension is dominant in the deep-water part of the passive margin (e.g. northern Scotian Basin). In natural systems, the extensional structures that arise in the deep-water slope and basin are mostly passive diapirs and expulsion rollovers (Fig. 11), which develop under relatively low sedimentation rates. These structures are consistent with the results of Models 1 and 3, where progradation marked by low sedimentation rates on top of the basinward inflated silicone, controls the development of passive diapirs and expulsion rollovers. This is because the combination of low sedimentation rate and thick salt is characterized by weak mechanical coupling between the ductile salt and brittle overburden with low extensional strain rates. In these circumstances, the deep-water extensional structures may be coeval with the listric growth faulting on the landward part of the margins (e.g. Wu et al. 1990; Diegel et al. 1995; Marton et al. 2000; Fort et al. 2004).

Scale

(a) Lower Congo Basin (Angola) 0 1 2 3 4 5 6

E

Basinward listric growth-fault and rollover systems

Landward listric growth-fault and rollover system

Early extensional passive diapirs shortened by late compression

10km

Compressional domain

Fort et al. 2004

W 0 1 2 3 4 5 6

(b) Scotian Basin, Shelburne subbasin (Canada) 0 1 2 3 4 5 6

W

E

0 1 2 3 4 5 6

E

0 1 2 3 4 5 6 7

W

0 1 2 3 4 5 6 7

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Keen et al.1991

(c) Scotian Basin, Sable subbasin (Canada) Basinward listric growth-fault and rollover systems

W

Downbuilding/expulsion

Wade & MacLean 1990

(d) Essaouria Basin (Morocco) 0 1 2 3 4 5

E

Downbuilding/expulsion(extension/passivediapirs) Compressional domain

Tari & Molnar 2006

(e) Santos Basin (Brazil) 0 1 2 3 4 5 6

W

Basinward listric growth-fault and rollover systems

Landward listric growth-fault and rollover systems Cabo Frio

E

0 1 2 3 4 5 6

E

0 1 2 3 4 5 6

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Modica & Brush 2004

MECHANICS OF ROLLOVER SYSTEMS

0 1 2 3 4 5 6 7

(f) Campos Basin (Brazil) 0 1 2 3 4 5 6

W

Basinward listric growth-fault and rollover systems Downbuilding/expulsion

Guardado et al. 1989; Cainelli & Mohriak 1999

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Fig. 11. Natural examples of passive margins detached on salt illustrating principal kinematic domains. Schematic line drawings of interpreted regional seismic sections from (a) offshore Angola (b, c) Atlantic Canada (d) offshore Morocco and (e, f) offshore Brazil; depth is in seconds two-way time. In all cases salt is shown black, and the pre-salt basement is not shown. Most margins indicate an early stage of salt tectonics characterized by landward extension accommodated by basinward shortening (mostly thickening of salt). Early shortening, manifested by folding of deep-basin strata, is evident only on Angolan, Moroccan and Brazilian margins (a, d –f). The extensional domain is characterized by mostly basinward listric growth-fault and rollover systems in the Congo (a), Scotian/Sable (c) and Campos (f) basins. Landward listric growth-fault and rollover systems prevail in the northern Santos Basin (e). Passive diapirs dominate the Scotian/Shelburne (b) and Essaouria (d) basins.

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Some passive margins underlain by salt have experienced even lower sedimentation rates. This is the case for the Shelburne sub-basin of the Scotian margin in eastern Canada (Fig. 11; Keen et al. 1991) or its conjugate margin in offshore Morocco (Fig. 11; Tari & Molnar 2006). In both basins, the extensional structures are mostly symmetrical grabens and seaward leaning diapirs with overhangs and canopies (e.g. Shimeld 2004). The stratigraphic relations observed near the diapirs suggest that the diapir rise was in balance with the low rates of sedimentation until their salt source layers were depleted. Thus, low sedimentation rates support symmetrical graben development and passive diapirism as observed in the Models 1 and 3, but not listric growth-fault and rollover systems. The structural styles of the Shelburne subbasin vary significantly from the Sable sub-basin further to the north, where basinward listric growthfault and rollover systems dominate (Fig. 11; Shimeld 2004). The Sable sub-basin experienced much higher sedimentation rates compared to the Shelburne area due to the progradation of the Sable delta (Wade & MacLean 1990). These features are consistent with the experimental results which demonstrate that, under similar boundary conditions, the development of basinward listric growth-fault and rollover systems require significantly higher sedimentation rates than passive diapirs. Therefore, the increased sediment input from the Sable delta has most likely generated higher extensional strain rates in the Sable area, which favoured the formation of listric growth-fault and rollover systems instead of passive diapirs. One of the most intriguing structures of the Scotian basin is a more than 80 km long basinward listric growth-fault and rollover, known as the Banquereau wedge (Ings & Shimeld 2006) that developed during the Late Jurassic on top of the allochtonous salt nappe seaward of initial salt basin. Similar structures on shale detachments have been reported from the Gulf of Mexico (e.g. Vicksburg Detachment System; Diegel et al. 1995, p. 127, fig. 21). Based on the experimental observations, this type of large-scale basinward listric growth-fault and rollover system would require relatively high sedimentation rates to overcome the increasing shear strength of the basal detachment beneath the hanging wall. Additionally, a mainly aggradational pattern of sedimentation is required to maintain the high gravitational instabilities and to avoid sealing the fault system by faster sediment progradation. Thus, these long-lived systems imply a very sensitive balance between salt thickness, sedimentation rates and patterns. In natural systems, basinward listric growthfault and rollover systems are far more frequent

than landward listric growth-fault and rollover systems. Generally, the evolution of basinward listric growth-fault and rollover systems stops in the early or mature rollover stages and does not reach the late-stage of rollover anticline collapse. In the Gulf of Mexico, most counter-regional (i.e. landward listric) faults are associated with expulsion rollovers (Schuster 1995) and only a few collapsed growth-fault rollover systems are observed (e.g. Diegel et al. 1995, p. 118, fig. 11). However, collapsed basinward listric growth-fault and rollover systems are found in the Western Mediterranean (dos Reis et al. 2005, p. 727, fig. 14) and in the Cabinda Basin, offshore Congo (Rouby et al. 2002, p. 787, fig. 4a). One of the possible reasons for the paucity of landward listric growth-fault and rollover systems is that the change of the polarity of listric growth-faults requires extraordinary high strain rates (e.g. LLS on Fig. 5d) and in many cases, this would require very high sedimentation rates. One of the most frequently cited and strongly debated landward listric growth-fault and rollover system is the Cabo Frio fault system that stretches through the central– northern part of the Santos Basin, offshore Brazil (Fig. 11; Cobbold & Szatmari 1991; Demercian et al. 1993; Mohriak et al. 1995; Szatmari et al. 1996; Ge et al. 1997; Modica & Brush 2004). This part of the Santos Basin differs significantly from the southern part (Modica & Brush 2004) and from the adjacent Campos Basin (Fig. 11; Guardado et al. 1989; Cainelli & Mohriak 1999) where basinward listric growth-fault and rollover systems dominate. In the Santos Basin, most landward listric growth-fault and rollover systems show an early basinward listric phase that clearly predates the initiation of the landward listric growth-fault and rollover (Fig. 11). However, in some other published sections (Mohriak et al. 1995, p. 290, Fig. 14; Modica & Brush 2004, p. 944, fig. 15B) the Cabo Frio fault system seems to be governed by expulsion processes, and thus would more likely be a large scale expulsion rollover. As indicated by the experiments, the evolution of fault and expulsion rollover systems implies very different mechanisms. Therefore, the contrasting styles of evolution seen along the Cabo Frio system may be related to variations in the salt distribution (thick salt would favour the expulsion process) or temporal and spatial variations in sedimentation. Whatever is important, high sedimentation rates during the Late Cretaceous triggered the development of the Cabo Frio system (Meisling et al. 2001; Modica & Brush 2004), whereas the Campos Basin experienced lower sedimentation rates at the same time. Our experimental results support the concept that

MECHANICS OF ROLLOVER SYSTEMS

different sedimentation rates may generate such diverse structures and kinematic sequences as those of the Santos and Campos Basins.

Conclusions Our experimental results demonstrate that sedimentation patterns and rates have a strong influence on the kinematics of extensional structures developed on salt at the passive margins. Early extension is focused on the shelf and the upper slope where high gravitational instabilities exist due to differential sediment loading. Early extensional structures are mostly symmetrical grabens bounded by planar normal faults underlain by reactive diapirs. The experiments described here show that the lack of sedimentation causes low strain rates that favour passive diapirism associated with downbuilding of the overburden. Expulsion rollovers form at slightly higher, but still low, strain and sedimentation rates. Moderate sedimentation rates promote the transformation of symmetrical grabens into basinward listric growth-fault and rollover systems. In such settings, hanging wall growth is associated with thinning of the ductile layer beneath the rollover anticlines. As consequence, the development of basinward listric growth-fault and rollover systems is associated with an increase of brittle –ductile coupling and a decrease in displacement rates on the listric growth-faults. With high sedimentation and progradation rates, basinward listric growth-fault and rollover systems are either sealed or transformed into landward listric growthfault and rollover systems through the collapse of associated hanging wall rollover anticlines. The late-stage structural evolution of listric growth-fault and rollover systems is strongly governed by the position of the structures relative to the shelf-slope break and the zone of high gravitational instability. The kinematic sequence of landward listric growthfault and rollover formation demonstrates that antithetic basal shear is not required for their growth because the landward listric growth-fault is not kinematically connected to a horizontal detachment beneath its hanging wall rollover. The Canadian Foundation of Innovation (CFI) and the Atlantic Innovation Foundation (AIF) financially supported the Analogue Model Deformation Laboratory at Dalhousie University and this study. The authors wish to acknowledge G. Adam, S. King, S. Ballantyne and all students that helped to run the experiments for their steadfast support in the laboratory. The paper benefited from C. Warren’s comments. The authors gratefully acknowledge the critical and very constructive reviews by H. Koyi and J. Walsh that significantly improved the paper.

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Canada. 25th Annual GCSSEPM Foundation Bob F. Perkins Research Conference, Extended Abstract CD, 132 –150. T ARI , G. C., A SHTON , P. R., C OTERILL , K. L. ET AL . 2002. Are West Africa deepwater salt tectonics analogues to the Gulf of Mexico? Oil and Gas Journal, 4, 73–81. V ENDEVILLE , B. C. & J ACKSON , M. P. A. 1992. The rise of diapirs during thin-skinned extension. Marine and Petroleum Geology, 9, 331– 353. W ADE , J. A. & M AC L EAN , B. C. 1990. The geology of the southeastern margin of Canada. In: K EEN , M. J. & W ILLIAMS , G. L. (eds) Geology of Continental Margin of Eastern Canada. Geological Survey of Canada, Geology of Canada, 2, 167–238. W EIJERMARS , R., J ACKSON , M. P. A. & V ENDEVILLE , B. 1993. Rheological and tectonic modeling of salt provinces. Tectonophysics, 217, 143 –174. W EST , D. 1989. Model for salt deformation on deep margin of central Gulf of Mexico Basin. American Association of Petroleum Geologists Bulletin, 73, 1472– 1482. W ORRALL , D. M. & S NELSON , S. 1989. Evolution of the northern Gulf of Mexico, with emphasis on Cenozoic growth-faulting and the role of salt. In: B ALLY , A. W. & P ALMER , A. R. (eds) The Geology of North America – an Overview. Geological Society of America, Boulder, Colorado, A, 97– 138. W U , S., B ALLY , A. W. & C RAMEZ , C. 1990. Allochthonous salt, structure, and stratigraphy of the northeastern Gulf of Mexico; part II, structure. Marine and Petroleum Geology, 7, 334– 370. X IAO , H. & S UPPE , J. 1992. The origin of rollover. American Association of Petroleum Geologists Bulletin, 76, 509– 529.

Seismic anisotropy as an indicator of reservoir quality in siliciclastic rocks J.-M. KENDALL1, Q. J. FISHER2, S. COVEY CRUMP3, J. MADDOCK2, A. CARTER2,4, S. A. HALL3, J. WOOKEY1, S. L. A. VALCKE2,6, M. CASEY2, G. LLOYD2 & W. BEN ISMAIL4 1

Department of Earth Sciences, University of Bristol, Wills Memorial Building, Queen’s Road, Bristol BS8 1RJ, UK (e-mail: [email protected])

2

School of Earth and Environment, Institute of Geophysics and Tectonics, University of Leeds, Leeds LS2 9JT, UK 3

School of Earth, Atmospheric and Environmental Sciences, University of Manchester, Williamson Building, Oxford Road, Manchester M13 9PL 4

CNRS, Laboratoire 3S-R, Grenoble, France

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Now at: StatoilHydro Research Centre, Arkitekt Ebbellsvei 10, Rotvoll, N-7005 Trondheim, Norway

Now at: Faculty of Geosciences, Utrecht University, P.O. Box 80021, 3508 TA Utrecht, The Netherlands Abstract: Improving the accuracy of subsurface imaging is commonly the main incentive for including the effects of anisotropy in seismic processing. However, the anisotropy itself holds valuable information about rock properties and, as such, can be viewed as a seismic attribute. Here we summarize results from an integrated project that explored the potential to use observations of seismic anisotropy to interpret lithological and fluid properties (the SAIL project). Our approach links detailed petrofabric analyses of reservoir rocks, laboratory based measurements of ultrasonic velocities in core samples, and reservoir-scale seismic observations. We present results for the Clair field, a Carboniferous–Devonian reservoir offshore Scotland, west of the Shetland Islands. The reservoir rocks are sandstones that are variable in composition and exhibit anisotropy on three length-scales: the crystal, grain and fracture scale. We have developed a methodology for assessing crystal-preferred-orientation (CPO) using a combination of electron back-scattered diffraction (EBSD), X-ray texture goniometry (XRTG) and image analysis. Modal proportions of individual minerals are measured using quantitative X-ray diffraction (QXRD). These measurements are used to calculate the intrinsic anisotropy due to CPO via Voigt-Reuss-Hill averaging of individual crystal elasticities and their orientations. The intrinsic anisotropy of the rock is controlled by the phyllosilicate content and to a lesser degree the orientation of quartz and feldspar; the latter can serve as a palaeoflow indicator. Our results show remarkable consistency in CPO throughout the reservoir and allow us to construct a mathematical model of reservoir anisotropy. A comparison of CPO-predicted velocities and those derived from laboratory measurements of ultrasonic signals allows the estimation of additional elastic compliance terms due to grain-boundary interactions. The results show that the CPO estimates are good proxies for the intrinsic anisotropy of the clean sandstones. The more micaceous rocks exhibit enhanced anisotropy due to interactions between the phyllosilicate grains. We then compare the lab-scale predictions with reservoir-scale measurements of seismic anisotropy, based on amplitude variation with offset and azimuth (AVOA) analysis and non-hyperbolic moveout. Our mathematical model provides a foundation for interpreting the reservoir-scale seismic data and improving the geological modelling of complex reservoirs. The observed increases in AVOA signal with depth can only be explained with an increase in fracturing beneath the major unit boundaries, rather than a change in intrinsic CPO properties. In general, the style and magnitude of anisotropy in the Clair field appears to be indicative of reservoir quality.

Seismic methods provide the best tools for imaging the architecture of structurally-complex petroleum reservoirs. Equally important is the relationship

between such structure and the litho-stratigraphic properties, stress-state and the fluid response to changes within the reservoir. Recent advances in

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 123–136. DOI: 10.1144/SP292.7 0305-8719/07/$15.00 # The Geological Society of London 2007.

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acquisition and processing have seen the development of a range of seismic techniques for inferring such reservoir properties. These include time-lapse seismic surveys, converted-wave and shear-wave surveys, and passive seismic monitoring, to name a few. Seismologists are now better equipped to image complex structures that are not only heterogeneous but also anisotropic. Whereas seismic heterogeneity refers to spatial variations in velocity, seismic anisotropy refers to variations in velocity with direction of propagation. For example, horizontally travelling P-waves in shales are usually faster than vertically travelling P-waves (e.g. Thomsen 1986). This style of anisotropy is commonly referred to as vertical transverse isotropy (VTI), which is a class of hexagonal symmetry with a vertical symmetry axis and can be described by five independent parameters (e.g. the Thomsen (1986) parameters). In contrast, azimuthal anisotropy can be detected by analysing azimuthal variations in stacking velocities, amplitudes (including those of converted waves), and polarization anomalies. An example of azimuthal anisotropy is horizontal transverse isotropy (HTI), hexagonal symmetry with a horizontal symmetry axis. Another indicator of anisotropy is the propagation of two independent shear-waves that travel at different speeds, which is commonly referred to as shear-wave splitting because the two shear-waves separate as they propagate. A number of methods have been developed for estimating seismic anisotropy using a wide range of seismic data attributes. Commonly, the emphasis is on improving the sharpness of seismic images (Verwest 1989; Bouska & Johnston 2005) or better reconciling variations in depth estimates derived from various datasets (e.g. borehole versus surface seismic data; Banik 1984; Peng & Steenson 2001; Brandsberg-Dahl & Barkved 2002). However, the anisotropy itself is an indicator of a wide range of properties and as such is a seismic attribute that may be influenced by both past and present geological processes. A key challenge with its interpretation is untangling the various contributions to the anisotropy. The SAIL project (seismic anisotropy as an indicator of lithology) was designed to address this issue. This was an ITF (Industry Technology Facilitator UK) coordinated project that was funded by eight oil companies and the UK Department of Trade and Industry (DTI). The aim of the consortium was to investigate the use of observations of seismic anisotropy as an indicator of lithology, fluid properties and rock fracture. It has been long recognized that the Earth is seismically anisotropic on length scales ranging from the crystal to the craton. Most crystals exhibit strong elastic anisotropy, including cubic crystals

such as halite. Crystal preferred orientation (CPO) (or lattice preferred orientation; LPO) within rocks is an effective way of generating anisotropy and it can be caused by depositional processes and subsequent deformation (Silver 1996). Anisotropy will also result from the preferred orientation of shaped inclusions, grain boundaries or layers, and this is often referred to as a shape preferred-orientation (SPO). Such shape fabric and grain orientations are commonly observed in hand specimens and at the outcrop scale. In general, flat disc-shaped inclusions are more effective than elongate cigar-shaped inclusions at generating anisotropy (Kendall 2000). The inclusions can be higher or lower in velocity than the surrounding matrix. For example, aligned fluid-filled ellipsoidal pores or micro-cracks are very effective at generating anisotropy (e.g. Crampin 1994). Furthermore, the periodic layering of materials with contrasting elastic properties will generate transverse isotropy if the seismic wavelength is much longer than the layer thickness (Backus 1962). For example, alternating bands of high and low porosity rock will appear seismically anisotropic. At a larger scale, the preferred alignment of fractures or joint sets will also lead to seismic anisotropy, as long as the fracture spacing is on a smaller length-scale than the dominant seismic wavelength. The seismic wavelength is on the order of 100s of metres for typical reservoir depths, so the fracture spacing must be on the order of less than tens of metres. This article considers the seismic anisotropy in siliciclastic reservoir rocks from the Clair field, which lies west of the Shetland Islands and is the largest petroleum discovery on the UK continental shelf (Ridd 1981; Coney et al. 1993). Although it is one of the largest fields in UK territory, development has only recently started because reservoir heterogeneity has made it difficult to assess accurately future hydrocarbon production based on the results from the discovery and subsequent appraisal wells. As with many fields, fractures seem to increase reservoir connectivity in Clair and should therefore increase production rates (Smith & McGarrity 2001). There is mounting interest in integrating seismic methods, well test data and geological modelling to access fracture density and orientation distribution as well as production behaviour (Barr et al. 2007). A range of seismic techniques are available for measuring anisotropy and potentially fracture orientations/distributions including: shear-wave splitting in VSP data (Winsterstein 1989) and surface seismic data (Gaiser et al. 2001), amplitude variations with offset and azimuth (AVOA) (Lynn & Thomsen 1990; Hall & Kendall 2003), and converted wave amplitude variations with azimuth (Granger et al. 2000).

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In this paper we explore controls on seismic anisotropy over a range of length-scales in the Clair reservoir rocks within the context of the SAIL workflow, which is shown in Figure 1. Our approach links detailed petrofabric analyses of reservoir rocks, laboratory-based measurements of ultrasonic velocities in core samples, and field-scale seismic anisotropy observations. Firstly, detailed petrofabric analysis is used to quantify the modal proportions of minerals and the orientation of individual crystals. This allows the development of a ‘geomathemical’ model of the rocks’ intrinsic

anisotropy due to CPO. This model provides the base to which larger scale anisotropy can be added, for example, that due to oriented fracture sets. The second part of the study involves ultrasonic velocity measurements on core samples. The measurements were carried out for a range of confining pressures, which in turn allowed an assessment of the degree to which the CPO anisotropy could explain the measured anisotropy. Part of the motivation for the velocity measurement was to quantify the degree of additional anisotropy due to grain-scale interactions. For example, more

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Fig. 1. The workflow adopted for the SAIL project. The intrinsic CPO anisotropy (or lattice preferred orientation (LPO)) is determined from petrofabric analyses using quantitative electron back-scattered diffraction (EBSD), X-ray texture goniometry (XRTG) and image analysis. Modal proportions for each mineral are determined using quantitative X-ray diffraction (QXRD). Seismic velocities are measured in the laboratory using ultrasonic transducers. These steps allow the development of a geomathematical model for the intrinsic anisotropy. Longer-wavelength anisotropy can be then added to this model using effective medium modelling. Anisotropic magnetic susceptibility (AMS) is one technique for estimating shape-preferred orientations (SPO) due to aligned cracks and pores. Comparisons of the ultrasonic measurements and the intrinsic anisotropy can be used to estimate stress-induced anisotropy due to aligned cracks and intergranular effects (extrinsic anisotropy). Analysis of field-scale seismic data provides estimates of anisotropy using a variety of techniques (amplitude variation with offset and azimuth (AVOA), shear-wave splitting, and non-hyperbolic moveout). Cumulatively, these results and predictions can be used to help guide interpretations of rock and reservoir properties. RFI (robust fracture interpretation) refers to a related ITF project that considered the link between seismic anisotropy and geomechanical properties of reservoirs.

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compliant material between the harder grains can lead to SPO anisotropy (e.g. Sayers 2002). Finally, a 3D ocean-bottom seismic dataset is analysed using AVOA analysis in an attempt to map out spatial variations in fracture-induced anisotropy. We adopt the methodology of Hall & Kendall (2003) as, like most OBS datasets, the Clair data are sparse in offset and azimuth coverage. This integrated workflow permits evaluation of the degree to which the AVOA is due to fractures as opposed to other competing and more intrinsic mechanisms such as CPO.

Crystal-scale anisotropy A suite of rocks from a range of reservoir depths were collected from core of two wells near the centre of the Clair field. 20 samples were collected to cover the full range of lithologies present. Sample depths ranged from 1660 m to 2200 m. The rocks vary from clean medium-grained sandstones to fine-grained laminated mudstone. In general, the reservoir quality improves as the sandstones become cleaner (less clay-rich) towards the bottom of the reservoir (Coney et al. 1993; Maddock 2006). Mineralogical analysis was carried out using quantitative X-ray diffraction (QXRD) (Hillier

1999). The dominant minerals in the samples are quartz, feldspar, calcite, biotite, muscovite, and fine-grained clays such as illite, kaolinite and smectite. Figure 2 shows an example of variations in the modal proportions of the rock samples that were also used for velocity analysis in the laboratory. Porosity was determined using mercury injection porosimetry and shows that the porosity of the rocks varies from 7% in the mudstones to over 15% in the cleaner sandstone. CPO has been long recognized as an important microstructural control on seismic velocities (e.g. Kaarsberg 1959), but there has been little work that quantifies this effect in sedimentary rocks. A notable exception is the work of Hornby and coworkers (Hornby et al. 1994; Hornby 1998) who used laboratory velocity testing, image analysis and effective medium modelling to understand the elastic properties of shales better. CPO in sedimentary rocks is primarily controlled by gravitational and mechanical compaction. Elongate or platy minerals tend to align and have crystal structure that mimics the grain shape (e.g. clays and micas). Other effects are the diagenetic growth of minerals (Archibald et al. 1996) or depositional alignment due to strong currents (Pettijohn 1975). The characterization of the crystal preferred orientation (CPO) is performed using the methodology developed in the SAIL project (see Valcke

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et al. 2006 and Maddock 2006). Electron backscatter diffraction (EBSD) was used primarily to characterize the orientation of quartz, feldspar and calcite crystals. This technique indexes each crystal and measures their orientations. This is the first time (to the authors’ knowledge) that EBSD has been used for sedimentary rocks. EBSD is less effective with phyllosilicates due their platy nature and the fact that they are often very fine grained. Instead, X-ray texture goniometry (XRTG) (Van der Pluijm et al. 1994) and image analysis can be used to assess CPO in micas and clays. A key difference between EBSD and XRTG image-analysis is that the former produces point measurements for each crystal, whereas the latter measures the bulk aggregate CPO of a particular mineralogy. The EBSD measurements for the quartz and feldspar show remarkably consistent orientations in all of the Clair reservoir rocks. Following Valcke et al. (2006), their orientations are interpreted as palaeoflow indicators and their orientations agree with other independent Clair studies of palaeoflow (Hailwood pers comm.). Such

alignments have been seen in other studies (e.g. Pettijohn 1975; Baas 2000). In contrast, the calcite/ dolomite crystals show a random orientation. This is due to their diagenetic origin; they grow in pore spaces as fluids circulate through the rock. In other studies, calcite commonly shows a preferred orientation when it grows along mica substrata (see Valcke et al. 2006) rather than in pore spaces. Image analyses and XRTG were used to assess CPO in micaceous components of the samples. Figure 3 shows an electron back-scatter atomiccontrast image of a mica-clay rich specimen. These images support assumptions that the mica CPO is due to compaction and has an axial symmetry around a vertical axis. Fine-grained authigenic clays are assumed to be randomly orientated as they are precipitated within the pore spaces of the rock. They are difficult to image and the elasticities of such clays are poorly known (Jakobsen et al. 2003). The elastic constants of Katahara (1996) are used for the fine-grained clays. Initially, we assumed that the pores were spherical in shape and randomly distributed through the rock.

Fig. 3. Back-scatter electron photomicrogaph of a typical Clair sandstone (bottom) and a typical Clair mudstone (top). The sandstone is well-sorted, shows moderate porosity and contains authigenic calcite. In constrast, the mudstone is poorly sorted, shows low porosity and contains well aligned phyllosilicates.

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A geomathematical description of anisotropy The aggregate anisotropy in a rock due to CPO can be estimated given the modal mineralogy, the elastic constants of the minerals and the orientations of the crystals. We use this to produce a ‘geomathematical’ model description of the anisotropy in the Clair reservoir rocks. The EBSD measurements described above are used to assess the anisotropy due to quartz and feldspar CPO. The alignment of micas (muscovite, biotite and chlorite) as assessed using XRTG can be described by a statistical distribution or orientation distribution function. The isotropic elastic properties of the fine clays, calcite and porosity show no coherent preferred orientation, but it is important to include these isotropic components as they dilute the overall CPO anisotropy. These various contributions can be then summed using modal-volume-weighted Voigt-Reuss-Hill (VRH) averaging (Hill 1952). EBSD results define the CPO for each crystal using three Euler angles, which can be then used to rotate the single-crystal elastic constants into a universal coordinate system. Voigt-Reuss-Hill averaging is then used to evaluate the effective anisotropy in a rock due to a given mineralogy (Hill 1952; Mainprice 1990). Finally, the aggregate anisotropy, or elastic constants, of the rock are determined by VRH averaging of each mineral constituent with a QXRD determined weighting for the modal proportion for each mineral. We used a Bingham (1974) distribution to describe the uniaxial probability distribution of the micas, which characterized the strength of the preferred orientation. This in turn can be used to assess the average elastic stiffnesses (Cij) due to mica alignment. Where possible we used EBSD to benchmark these models (Maddock 2006). The contribution to the anisotropy from the micas was then included as part of the volume fraction weighted VRH average for the whole rock. Figure 4 shows the predicted anisotropy due to the micas, quartz and feldspar. These diagrams show lower hemispherical projections of the P-wave velocities and the shear-wave splitting (horizontal wave propagation directions are plotted at the edge of the circle and velocities for vertically propagating waves lie in the centre of the circle). If a rock were composed entirely of micas, the P-wave anisotropy would be over 40% and the maximum amount of shear-wave splitting would be nearly 40%. The mica anisotropy has a VTI symmetry due to the assumption of uniaxial symmetry and the first-arriving shear-wave will be polarized in the horizontal plane. In contrast, the anisotropy due to quartz alignment has an

orthorhombic symmetry and predicts much lower levels of anisotropy (,2% for P-waves and a maximum of nearly 2% shear-wave splitting). Feldspar orientations show very similar symmetry, but higher amounts of anisotropy (almost 7% for P-waves and a maximum of nearly 7% shear-wave splitting). As mentioned, the orientation of the quartz and feldspar appears to be an indicator of palaeoflow and is roughly consistent for all of the rocks sampled throughout the reservoir. Figure 5 shows the combined geomathematical model results for a mica-rich rock and one for a cleaner sandstone. These results include the effects of mica, quartz and feldspar alignment and the diluting effects of the randomly-oriented fine clays, diagenetic calcite, and porosity. It is clear from comparisons with Figure 4 that the anisotropic symmetry in the clean sandstone is dominated by the quartz and feldspar. The more anisotropic mica-rich rock shows a nearly VTI anisotropy indicating the dominant influence of the mica symmetry. Although the overall aggregate amount of anisotropy varies between samples, the strength of anisotropy due to each mineral is consistent (see Maddock 2006 for detail). This means that one only needs to know the volume fractions of each mineral to assess the anisotropy for a particular specimen via the stiffness tensor (i.e. Cij). These results provide a basis for a mathematical model of the intrinsic elasticity of Clair reservoir rocks. The results obtained suggest significant variations in both the magnitude (Fig. 6) and the symmetry of CPO anisotropy throughout the Clair reservoir. The mica content largely dictates the magnitude of the anisotropy in these rocks and there is a transition from VTI to orthorhombic symmetry as the magnitude of the anisotropy decreases towards the bottom of the reservoir. Seismic waves are not very sensitive to the small-scale variations in elastic properties from sample to sample. Therefore for our geomathematical model of the Clair field anisotropy, we determine a single VRH average anisotropy for each of the major lithological units bounded by major seismic reflection horizons (see magnitude variations in Fig. 6 and Unit VI symmetry in Fig. 7). Any interpretation of anisotropy from seismic methods must first account for the contribution from the CPO effect. Using effective medium models (e.g. Hudson 1981), the effects of cracks or fractures can be superimposed on the CPO anisotropy. Figure 7 shows the effect of vertically-aligned fractures on the overall anisotropy from the average rock in Unit VI. A crack density of 0.05 and an aspect ratio of 0.001 is used in the calculation. The magnitude of the

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Fig. 4. Anisotropy due to the alignment of (a) quartz, (b) feldspar, and (c) mica in the Clair specimens. The first column shows P-wave velocities as a function of direction (lower-hemisphere projection). The centre of the hemisphere corresponds to vertical wave propagation, and the perimeter of the hemisphere shows azimuthal variations in horizontal velocities (normally those in the bedding plane). The maximum and minimum P-wave velocity and the P-wave anisotropy (100 (Vmax 2 Vmin)/Vave) are also given below each hemisphere in this column. The second and third columns show variations in shear-wave splitting on a lower-hemisphere projection. Shear-wave splitting is expressed as a percentage and is defined as [100 (Vsfast 2 Vsslow)/Vsave] for a given direction of wave propagation. The maximum and minimum splitting are given below the middle column hemispheres. The ticks on the hemispheres in the right column show the polarizations of the leading (fast) shear-wave for a given direction of wave propagation.

anisotropy does not change significantly. However, the symmetry of the anisotropy is now significantly non-VTI leading to azimuthal variations in the velocities that could produce observable AVOA

effects. In contrast, the VTI symmetry in the uncracked rock will not produce an AVOA signal as there is little azimuthal variation in velocity (and hence reflection coefficient).

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Fig. 5. P-wave anisotropy and shear-wave splitting in (a) a mica-rich sample, where the mica dominates the anisotropy, and (b) a mica-poor sample, where the quartz and feldspar anisotropies dominate. See Figure 4 caption for further explanation of anisotropy plots.

Laboratory velocity measurements and grain-scale anisotropy As described in the previous section, the fine-scale CPO anisotropy can be overprinted by larger-scale SPO anisotropy. For example, alternating beds of high and low porosity sediment or aligned ellipsoidal pores can be effective in generating anisotropy. At a much larger scale, fractures that extend tens of metres and serve as fluid permeability pathways will also be very effective at generating anisotropy in seismic data, as long as the wavelength of the seismic waves is much larger than the spacing between fractures. To address the finer-scale SPO anisotropy, a component of the SAIL project involved laboratory measurements of seismic velocities using ultrasonic transducers. Ultrasonic measurements were made as a function of confining pressure for both P- and S-waves in a purpose-made rig. Grain-scale contributions to the anisotropy can be assessed through differences between the predicted anisotropy due to CPO and the anisotropy

measured in a sample using ultrasonic seismic velocities. Details of this approach are presented in Hall et al. (2007) which draws on the earlier work of Sayers (2002). This methodology allows the determination of crack density tensors that describe the combined effects of multiple populations of microcracks, crack-like porosity and intergranular effects. The results show that the extrinsic intergranular anisotropy in the core samples is strongly related to the intrinsic CPO anisotropy (see Hall et al. 2007). The effect is strongest when the rocks are at room pressure. As confining pressures increase microcracks close. However, even at 50 MPa a substantial residual non-CPO induced anisotropy remains, which is generally aligned with the symmetry of the CPO anisotropy. Furthermore, a strong link is observed between the measured degree of velocity anisotropy and the mica content, which cannot be explained by the CPO effect alone. This residual component could be due to the presence of more compliant material lying between the faces of the stiffer mica grains. This effect can be described in

SEISMIC ANISOTROPY AS AN INDICATOR OF RESERVOIR QUALITY IN SILICICLASTIC ROCKS 131

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terms of microcracks filled with relatively soft material. Figure 8 shows the separated CPO and microcrack components of the velocity anisotropy and the cumulative velocity anisotropy as functions of mica content. The CPO anisotropy increases with mica content, as might be expected. However, the crack-induced anisotropies also show a general increase with mica content, especially for the samples with more HTI symmetries. Furthermore, the two components of the anisotropy are roughly

aligned. Therefore, it appears that the micas not only contribute strongly to the CPO-induced anisotropy, but they also have a strong influence on the grain-scale microcrack anisotropy. In fact, the results suggest that the grain-scale microcracks developed preferentially in planes parallel to the cleavage planes of the flat mica grains.

Fracture-scale anisotropy In 2002, BP acquired a large, 3D 4-component ocean-bottom dataset over an extensive area of the Clair field (Kommedal et al. 2005). A component of the SAIL project involved the analysis of azimuthal variations in P-wave reflection amplitudes using part of this dataset. Vertically-aligned fractures can produce azimuthal variations in AVO (AVOA) (e.g. Ru¨ger 1998). In this context, azimuthal variation in the AVO gradient is approximately elliptical for near offsets; the orientation and ellipticity of the AVO gradient ellipse are useful attributes for fracture characterization. We adopt the methodology of Hall & Kendall (2003) for quantifying the AVOA signal. A notable difference in this study is the use of trim statics, which enable better tracking of events across 3D CMP gathers. The results of the AVOA analysis are shown in Figure 9. In general, the dominant orientation of the major axis of the AVOA ellipse is on average 1388 (with a standard deviation of 46), which agrees with independent estimates of fracture orientations from core analysis and VSP data (Smith & McGarrity 2001; Coney et al. 1993; Barr et al. 2007). Figure 10 shows a ‘quiver plot’ mapping the magnitude and orientation of the AVOA results (see caption) for reflections from the top of Unit V. This plot shows that although the average fracture orientation is roughly NW– SE there is considerable variability in the strength and orientation on a fine scale. Coherent regions of high anisotropy share borders with relatively isotropic regions (i.e. an absence of fractures). An advantage of the AVOA study over borehole-based studies is the added spatial coverage that comes from using surface seismic data. Figure 9 also shows that the mean magnitude of the anisotropy increases from the top of the reservoir (BCU reflection) to the bottom (reflection from the Lewisian basement rock). The CPO anisotropy predicts a VTI symmetry near the top of the reservoir, but in contrast predicts the magnitude of the anisotropy to decrease towards the base of the reservoir. At face value this suggests that the AVOA anisotropy is due to a more extrinsic mechanism and fractures are the likely cause. However, there is some ambiguity inherent in the AVOA

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Fig. 7. (a) VRH-average anisotropy in Unit VI due to CPO. (b) Anisotropy in Unit VI where vertically aligned cracks, oriented in a left-to-right direction across the page, are superimposed on the intrinsic CPO anisotropy. The cracks do not significantly change the magnitude of the anisotropy, only the symmetry of the anisotropy. The uncracked sample has a nearly VTI symmetry, whereas the cracked sample has a nearly orthorhombic symmetry.

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vpx−vpy vpx−vpz vpy−vpz vsxy−vsyz vsxy−vsxz vsyz−vsxz

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Fig. 8. P- and S-wave anisotropy as a function of mica content: (a) anisotropy due to CPO alone (pressure invariant); (b) anisotropy at 45 MPa due solely to crack and intergranular effects, based on the crack densities inverted from the measured velocities (with the CPO anisotropy taken into account) and the Voigt-Reuss-Hill averaged isotropic elasticities (see Hall et al. 2007); (c) the combined effects of CPO and intergranular anisotropy at 45 MPa. Each line corresponds to comparisons of different directions (e.g. vpx 2 vpy is the difference in velocities of P-waves propagating in the x and y directions; vsxy 2 vsxz refers to shear-waves propagating in the x direction and shows the difference in the velocities of those polarized in the y direction versus those polarized in the z direction). The x direction is orientated parallel to the bedding strike.

SEISMIC ANISOTROPY AS AN INDICATOR OF RESERVOIR QUALITY IN SILICICLASTIC ROCKS 133

Fig. 9. A compilation of the AVOA results for reflections from the base-Cretaceous unit (BCU), top of Unit VI, top of Unit V and the Lewisian gneissic basement. The left column shows spatial variations in magnitude of the AVOA anisotropy (the normalized difference between the maximum and minimum AVO gradients). The middle column shows rose diagrams of the inferred fracture orientations. The far right column shows the average magnitude of the AVOA anisotropy for each reflector; note the increase in anisotropy with depth of the reflector.

interpretation as to whether or not the anisotropy increases or decreases across an interface. A means of testing whether or not the predicted VTI anisotropy is coherent at the seismic scale is to estimate anisotropy parameters from nonhyperbolic moveout (Alkhalifah & Rampton 2001; Tsvankin & Thomsen 1994; Van der Baan & Kendall 2002). Unfortunately, the long offset arrivals required for such analysis were unclear in the real data (preliminary analysis using short offset data suggested a decrease in VTI anisotropy towards the bottom of the reservoir, but this deserves further investigation; Rampton pers.comm.). The geomathematical model of the reservoir anisotropy was used to interpret the AVOA results better. The elastic constants are averaged (using

VRH) for a particular geological unit above and below the major interfaces whose reflections were used in the AVOA analysis. Varying levels of vertical fractures are added to the anisotropic units above and below the interface. A reflectivitybased modelling approach (Thomson 1997), which allows fully anisotropic layers, is then used to predict the AVOA response. Figure 11 shows the predicted AVOA magnitude (Hall & Kendall 2003) for the interface between Units V and VI. The strongest AVOA response is observed when the fracturing increases moving downwards from Unit VI to Unit V. In general, the AVOA magnitudes observed with the real data exceed a dimensionless value of 0.2. The CPO þ crack based predictions can only be this large if the fracturing increases below the boundary. The AVOA due to

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Fig. 10. A quiver plot showing spatial variations in the fracture orientation inferred from AVOA analysis of the reflection from the top of Unit V. Strictly speaking, the orientation shows the direction of maximum AVO gradient, which is normally the crack orientation (Hall & Kendall 2003). The length of the ticks is proportional to the magnitude of the anisotropy can be considered as a proxy for crack density. White regions mark areas where the data were not good enough to estimate a reliable AVOA signature.

CPO anisotropy is far too weak to explain the observed signals. As fractures increase permeability within Clair, the identification of an increase in fracturing from Unit VI to Unit V may be used to infer an increase in permeability. In other words, changes in seismic anisotropy derived using AVOA analysis has provided an indication of the distribution of high permeability layers within the Clair reservoir.

Conclusions and future directions The SAIL project has brought together geological analyses, rock physics and geophysical investigations of anisotropy in the Clair field. In the course of this work, the project has considered anisotropy on a range of length scales from the crystalline to the grain to the macro-fracture. The combined analyses of petrofabric, ultrasonic and seismic data has provided a working model for anisotropy, which predicts a decrease in VTI anisotropy and an increase in fracture-induced HTI anisotropy with increasing depth towards the porous clean sandstones. As such, the anisotropy serves as a proxy for reservoir quality. Detailed petrofabric analysis has established rules of thumb for the behaviour of each mineralogy observed in the Clair samples. For example, quartz

Fig. 11. (Top) the predicted AVOA anisotropy for reflections from the top of Unit V. The intrinsic anisotropy in Units V and VI with varying superimposed crack density are included in the calculation. Each column and row indicates the crack density in Unit V and Unit VI, respectively; all numbers should be multiplied by 0.01, thus 2 corresponds to a crack density of 0.02. AVOA anisotropy magnitudes like those observed in the real data only occur when the crack density in the underlying Unit V is much higher than that in the overlying Unit VI. (Bottom) the range of anisotropy (AVOA) magnitudes observed in the real data, inferred from reflections from the interface between Units V and VI.

and feldspar are consistently aligned and serve as a palaeoflow indicator. In contrast, the calcite is random in orientation due to its diagenetic growth in pores. The micas align sub-horizontally and are the most effective minerals in generating CPO anisotropy. The predictable nature of the CPO of these minerals has permitted the development of a

SEISMIC ANISOTROPY AS AN INDICATOR OF RESERVOIR QUALITY IN SILICICLASTIC ROCKS 135

geomathematical model of the intrinsic CPOinduced anisotropy in these polymineral siliciclastic reservoir rocks. We now only need to know the volume fraction of each mineral and the porosity to predict the anisotropy. This geomathematical model has been validated via comparisons with EBSD predictions, ultrasonic measurements, image analysis (see Maddock 2006). In general the CPO anisotropy is appreciable and cannot be dismissed when interpreting anisotropy in seismic data. Larger-scale anisotropy due to macro-fractures or periodic thin layering can be superimposed on the small-scale CPO anisotropy using effective medium theories (e.g. Hudson 1981; Backus 1962; Tandon & Weng 1984). This geomathematical model therefore provides a tool for interpreting estimates of anisotropy from seismic data (e.g. AVOA or shear-wave splitting). Furthermore, it can be used to predict anisotropy parameters that can be used in data processing (e.g. anisotropic depth migration). Comparison with ultrasonic measurements on these samples has enabled the assessment of the additional elastic compliances due to intergranular effects and has allowed the evaluation of the effective anisotropy due to CPO and SPO (cracks, grains) mechanisms. The additional compliance terms are weak in samples with weak anisotropy due to quartz and feldspar. In mica-rich samples there is a significant additional compliance due to microcracks and intergranular material orientated parallel to the mica cleavage planes. Such intergranular effects further enhance the mica-induced CPO anisotropy. Fracture-induced anisotropy at Clair has been analysed using AVOA analysis on part of an OBS dataset. The inferred orientations of the fractures agree with other studies of open fractures in that part of the field. A significant advantage of the AVOA analysis over borehole-confined techniques is that it provides a map of the small-scale spatial variations in the orientation and magnitude of the fractures and hence holds the potential to help guide horizontal drilling for optimal well performance. The AVOA analysis is not sensitive to VTI anisotropy, which should decrease towards the bottom of the reservoir. However, it does suggest that the HTI anisotropy increases towards the bottom of the reservoir. AVOA modelling using this geomathematical model confirms that fracturing must be increasing across the major reservoir interfaces. A workflow has been established for estimating and interpreting anisotropy in fields where core samples are available and 3D wide-azimuth seismic data have been acquired. Additional seismic data would help to constrain the style and cause of anisotropy further (e.g. microseismic data (Teanby et al. 2004) and VSP data (Winterstein

1989)). It remains to be seen whether the rules of thumb established for the Clair field are applicable to other siliciclastic rocks. This work suggests that observations of seismic anisotropy hold much potential for deriving valuable information about reservoir properties. We would like to acknowledge ITF and the sponsors of the SAIL project, Hess, BG Group, BP, Chevron, Kerr-McGee, Shell, Total and the Department of Trade and Industry UK, for funding and constructive input to the project. We thank the Clair partnership (BP, ConocoPhillips, Chevron, Shell and Hess. BG Group and Kerr-McGee) for releasing the data for publication. An anisotropic magnetic susceptibility study done by Er. Hailwood provided helpful constraints on fracturing and paleoflow indicators in the Clair samples. S. Jolley, R. Knipe, D. Barr and D. Anderson are gratefully acknowledged for coordinating this volume. P. Rowbotham and A. Aplin provided constructive reviews that significantly improved the readability of the paper.

References A LKHALIFAH , T. & R AMPTON , D. 2001. Seismic anisotropy in Trinidad: a new tool for lithology determination. The Leading Edge, 20, 420–424. A RCHIBALD , D. D., Q ADRI , S. B. & G ABER , N. P. 1996. Modified calcite deposition due to ultrathin organic films on silicon substrates. Langmuir, 12, 538– 546. B AAS , J. H. 2000. Experimental research on hydraulics and depositional mechanisms of high-density turbidity currents. Final report for TMR Marie Curie Fellowship Programme, pp. 187, European Union, Brussels. B ACKUS , G. 1962. Long-wave elastic anisotropy produced by horizontal layering. Journal of Geophysical Research, 67, 4427–4440. B ANIK , N. C. 1984. Velocity anisotropy of shales and depth estimation in the North Sea basin. Geophysics, 49, 1411–1419. B ARR , D., S AVORY , K. E., F OWLER , S. R., A RMAN , K. & M C G ARRITY , J. P. 2007. Pre-development fracture modelling in the Clair Field, West of Shetland. In: L ONERGAN , L., J OLLY , R. J. H., R AWNSLEY , K. & S ANDERSON , D. J. (eds) Fractured Reservoirs. Geological Society, London, Special Publications, 270, 205– 225. B INGHAM , C. 1974. An anitipodally symmetric distribution of the sphere. Annals of Statistics, 2, 1202– 1225. B OUSKA , J. & J OHNSTON , R. 2005. The first 3D/4-C ocean bottom seismic surveys in the Caspian Sea: Acquisition design and processing strategy. The Leading Edge, 24, 910–921. B RANDSBERG -D AHL , S. & B ARKVED , O. I. 2002. Anisotropic P-Wave Velocity Derived from Deviated Wells at the Valhall Field, 64th Meeting, European Association of Geoscientists and Engineers, Expanded Abstracts, 135. C ONEY , D., F YFE , T., R ETAIL , P. & S MITH , P. 1993. Clair appraisal: the benefits of a co-operative approach. In: P ARKER , J. R. (ed.) Petroleum Geology of Northwest Europe. Proceedings of the 4th conference, Geological Society, London, 1409–1420.

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L YNN , H. B. & T HOMSEN , L. A. 1990. Reflection shearwave data collected near the principal axes of azimuthal anisotropy. Geophysics, 55, 147– 156. M ADDOCK , J. 2006 Seismic anisotropy in siliciclastic sedimentary rocks. Ph.D. Thesis, University of Leeds. M AINPRICE , D. 1990. A Fortran program to calculate seismic anisotropy from the lattice preferred orientation of minerals. Computers and Geosciences, 16, 385–393. P ENG , C. & S TEENSON , K. E. 2001. 3-D prestack depth migration in anisotropic media: A case study at the Lodgepole reef play in North Dakota. The Leading Edge, 20, 524–527. P ETTIJOHN , F. J. 1975. Sedimentary Rocks, 3rd edn. Harper and Row, New York. R IDD , M. F. 1981. Petroleum geology west of the Shetlands. In: I LLING , L. V. & H OBSON , G. D. (eds) Petroleum Geology of the Continental Shelf of NW Europe Institute of Petroleum, Heyden and Son, London, 414 –425. R U¨ GER , A. 1998. Variation of P-wave reflectivity with offset and azimuth in anisotropic media. Geophysics, 63, 935–947. S AYERS , C. M. 2002. Stress-dependent elastic anisotropy of sandstones. Geophysical Prospecting, 50, 85– 95. S ILVER , P. G. 1996. Seismic anisotropy beneath the continents: Probing the depths of geology. Annual Review of Earth and Planetary Sciences, 24, 385–432. S MITH , R. L. & M C G ARRITY , J. P. 2001. Cracking the fractures – seismic anisotropy in an offshore reservoir. The Leading Edge, 20, 18–26. T ANDON , G. P. & W ENG , G. J. 1984. The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites. Polymer Composites, 5, 327–333. T EANBY , N., K ENDALL , J.-M., J ONES , R. H. & B ARKVED , O. I. 2004. Stress-induced temporal variations in seismic anisotropy observed in microseismic data. Geophysical Journal Internationl, 156, 459–466. T HOMSEN , L. A. 1986. Weak elastic anisotropy. Geophysics, 51, 1954–1966. T HOMSON , C. J. 1997. Modelling surface waves in anisotropic structures I. Theory. Physics of the Earth and Planetary Interiors, 103, 195– 206. T SVANKIN , I. & T HOMSEN , L. 1994. Nonhyperbolic reflection moveout in anisotropic media. Geophysics, 59, 1290– 1304. V ALCKE , S. L. A., C ASEY , M., L LOYD , G. E., K ENDALL , J.-M. & & F ISHER , Q. J. 2006. Lattice preferred orientation and seismic anisotropy in sedimentary rocks. Geophysical Journal International, 166, 652–666. V AN DER B AAN , M. & K ENDALL , J.-M. 2002. Estimating anisotropy parameters and traveltimes in the tau-p domain. Geophysics, 67, 1076–1086. V AN DER P LUIJM , B. A., H O , N.-C. & P EACOR , D. R. 1994. High resolution X-ray texture goniometry. Journal of Structural Geology, 16, 1029–1032. V ERWEST , B. J. 1989. Seismic migration in elliptically anisotropic media. Journal of Geophysical Prospecting, 37, 149–166. W INTERSTEIN , D. F. 1989. Velocity anisotropy terminology for geophysicists. Geophysics, 55, 1070– 1088.

Fracture intensity from geomechanical models: application to the Blue Forest 3D survey, Green River Basin, Wyoming, USA S. J. WILKINS Shell International Exploration and Production Inc., 3737 Bellaire Blvd, Houston, TX 77025 (e-mail: [email protected]) Abstract: A geomechanical method is presented for the prediction of subseismic fracture intensity associated with faulting using a boundary element model conditioned from 3D seismic interpretation within the Green River Basin, Wyoming, USA. Seismic data indicate two major phases of deformation: (1) an early phase of approximately ESE-verging contraction accommodated along a NNE– SSW striking system of basement-involved reverse faults and associated drape folds; and (2) a later phase of transtension accommodated by ENE–WSW-trending normal faults that are preferentially located in the hanging wall, above the crest of the drape fold. The models predict different spatial patterns of fracture intensity for each phase of deformation. For D1, enhanced probability for shear failure develops in the upper quadrant of the footwalls along the reverse faults (i.e. forelimb) and the greatest magnitudes occur adjacent to regions with the largest component of observable dip-slip displacement along the faults. During D2, enhanced probability for joint and fault formation occurs along-strike of the normal faults and in a general NE trend. Seismic velocity anisotropy data support the geomechanical predictions for both phases of deformation in that the location and azimuth of large anisotropies correlate with regions of predicted enhancement in joint and fault intensity.

Oil and gas production from low-porosity rocks is most often contingent on the characteristics of the fracture system within the reservoir. Hydraulically conductive fractures may consist of faults (shear displacements parallel to the fracture plane) and joints (opening displacements orthogonal to the fracture plane), although both features may also act as barriers to flow. During initial shear failure, compacted or cemented competent rocks tend to dilate while unconsolidated, highly porous assemblages tend to compact (Paterson & Wong 2005). With increasing strain, fault seal is thought to occur primarily in response to the formation of lowpermeability gouge and/or the entrainment of shale within the fault zone, in addition to secondary mechanisms such as cementation and overpressure within the fault zone. In contrast to the variety of mechanisms leading to the sealing behaviour of faults, the main mechanism for reducing the porosity/ permeability of a joint is cementation (e.g. Laubach et al. 2004). However, in many cases cements are not continuous and instead bridge open portions of the joint surface. It is not yet possible to predict the bridging behaviour of cements, but considerable effort is being devoted towards understanding the linked mechanical– diagenetic burial history of joints (e.g. Noh & Lake 2002; Laubach et al. 2004). Systematic joints are those with spacing approximately proportional to bed thickness in mechanically layered rocks, that exhibit roughly

planar shapes, and have consistent orientations over a large region (Pollard & Aydin 1988; Gross 1993). They are generally inferred to develop in response to some combination of regional tectonic stress and burial/unloading stresses (Engelder & Geiser 1980; Engelder 1985). The periodic spacing arises from the development of a stress ‘shadow’ adjacent to joint surfaces, a region of reduced tension that forms in response to the opening displacement normal to the joint, where subsequent joint nucleation is unfavourable (e.g. Hobbs 1967; Gross et al. 1995; Bai & Pollard 2001). The challenge in low permeability, ‘tight’ reservoirs, is to find areas of increased structural porosity/permeability where the density of permeable fractures is anomalously higher than any background density of systematic joints. This process of mechanical interaction among neighbouring joints leads to joint saturation in mechanically layered rocks, whereby an additional mechanism of deformation must occur to enhance the tensile stress enough to overcome this stress shadow and accommodate subsequent strain. One classic mechanism is folding, whose development is associated with substantial modulations in local stress (relative to the background levels in flat-lying, relatively undeformed rocks) that leads to enhanced fracturing (e.g. Cooke & Pollard 1997; Bergbauer & Pollard 2004). In flat-lying rocks, additional stress is often associated with either the formation of a through-going joint zone

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 137–157. DOI: 10.1144/SP292.8 0305-8719/07/$15.00 # The Geological Society of London 2007.

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that extends beyond the original mechanical boundaries, or the development of a fault zone that perturbs the stress field in adjacent areas and causes additional joints to develop (Jamison & Stearns 1982; Becker & Gross 1996; Davatzes & Aydin 2003). Additional scenarios that lead to high fluid pressures and low effective stresses, such as rapid burial, gas generation or linked fluid flow and structural/stratigraphic trapping, would theoretically result in increased fracture densities. This paper focuses on investigating the mechanism of faulting for inducing high joint densities in the subsurface. Numerous researchers have observed the density of joints to increase adjacent to faults in outcrop and some have performed mechanical models to determine the influence of faulting on enhancing small fault densities (Cooke & Pollard 1997; Maerten et al. 2002; Healy et al. 2004;

Okubo & Schultz 2005) or influencing local joint geometries (Rawnsley et al. 1992; Willemse & Pollard 1998; Bourne & Willemse 2001). However, to the author’s knowledge, a deterministic, mechanically-based model of small fault density in response to faulting has only been attempted by Maerten et al. (2002), and in that study Coloumb shear stress was used as a proxy for relative density. A numerical boundary element model is used to estimate the increase in fracture intensity related to faulting. This technique is applied to the Blue Forest 3D seismic survey within the Green River Basin, Wyoming, USA (Fig. 1). Validation of these fracture intensity models is not currently possible due to the lack of core or borehole images, although seismic velocity anisotropy data provides supportive evidence for the geomechanical predictions.

Fig. 1. Regional and local digital elevation models (a & b) and structure map (c; after Stone 1993) showing the geographical and geological context of the Blue Forest 3D survey within the Green River Basin. See text for details.

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In principle, however, modelled fracture intensity data can then be used to estimate fracture connectivity or similar parameters that are important for characterizing the static reservoir model.

Seismic-scale structural style and evolution within the Blue Forest 3D survey A structural analysis of the Blue Forest 3D seismic survey provides the framework for application of this geomechanical method to model fault-related fracture intensity. Seismic data are interpreted to exhibit two major styles of deformation, each of which affects distinctly different stratigraphic units and provides evidence of cross-cutting relationships for definition of relative timing. The Blue Forest 3D survey is located just east of the Upper Cretaceous (Campanian –Maastrichtian) Moxa Arch (Gries 1983) and outboard of the thin-skinned, North –South trending Wyoming– Idaho fold and thrust belt (Fig. 1) that formed during the Sevier Orogeny (mostly late Cretaceous: Turonian–Paleocene; Wiltschko &

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Dorr 1983; Erslev 1993). The Late Cretaceous (Campanian– Maastrichtian) Rock Springs uplift (Gries 1983), a westward verging basement cored uplift, is east of the survey area and the Wind River uplift and associated Pinedale anticline are to the north (Fig. 1). A contractional phase of deformation is accommodated along an approximately NNE–SSW- striking system of basement-involved reverse faults and associated drape folds in Cretaceous strata (Fig. 2a). Angular unconformities within the folded Upper Cretaceous (Campanian–Maastrichtian) Mesa Verde Formation are observed within the seismic data, and thus record the first episode of structural development that deformed Cretaceous and older strata (Fig. 2a). The flat lying Eocene Fort Union Formation lies unconformably on the slightly SE-dipping Mesa Verde Formation and thus indicates that the early phase of contraction mostly occurred during the late Cretaceous. Assuming dip-slip displacements, this early phase of deformation (D1) accommodates c. ESE verging contraction (Fig. 2a) and is thus kinematically compatible with the continuation of regional east –west contraction throughout the

Fig. 2. Map view and associated traverses of deep (a, Madison Limestone) and shallow (b, Hillard Shale) horizons representative of D1 and D2 structures, respectively. A horizontal shortening axis (112–2928 ¼ e3 ¼ sH [maximum horizontal stress]) during D1 (a) is consistent with SSW-striking, ESE-verging, basement cored reverse faults with dip-slip motion. (b) D2 deformation consists of ENE –WSW-striking normal faults, exhibiting horst and graben geometry, and preferentially located in the hanging wall of the D1 drape fold. Assuming dip-slip displacements and a maximum extension (e1) orthogonal to fault strike, opening-mode joints would strike parallel to the mean strike of the fault system (078– 2588) and sH.

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region that is related to the proximal, thin-skinned Sevier fold and thrust belt located near the present day Wyoming–Idaho border (Fig. 1). This timing of D1 is also synchronous with the development of the Moxa Arch and Rock Springs Uplift (Gries 1983). The approximate ESE –WNW-striking system of fractures expected to develop in response to this phase of deformation (Fig. 3a) is observed throughout the region within outcrop at the basin edges (e.g. Engelder et al. 1997; Hennings et al. 2000; Bergbauer & Pollard 2004; Bellahsen et al. 2006) and within subsurface wells. The second phase of deformation is not as clear in terms of timing and cause, despite the high quality of seismic data. This phase is characterized by the formation of a sometimes en-echelon array of approximately ENE-striking normal faults that

exhibits horst and graben morphology. This later phase of structures (D2) is preferentially located in the hanging-wall crest above the buried reverse faults (Fig. 2b). These faults are observable within the upper Frontier level up to the top Fort Union, but the upper tips are not mappable into younger stratigraphy because the resolution of the seismic data is degraded near the surface (Fig. 2b). If the faults do indeed reach the surface (within the Eocene Green River and Wasatch Formations) then they are at least Eocene or younger, possibly even remaining active today. Alternatively, these faults may have formed during an episode of Paleocene –Early Eocene NE-trending regional contraction, which resolves into a right-lateral shear component along the basement-involved drape fold (Fig. 3b), and would induce transtension

Fig. 3. Schematic representation of deformation at Blue Forest during (a) D1 and (b) D2. Black arrows refer to maximum horizontal stress directions. Thin red lines are joints, black and thick red lines represent faults, yellow shading is sandstone, brown shading is shale, and stippled pattern is basement.

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with NW–SE-trending extension in the above strata. This mechanism would be consistent with a regional counter-clockwise rotation of the maximum horizontal contractional strain from an east –west trend in the Late Cretaceous to north– south in the Eocene, during the last stages of contraction within the Rocky Mountain Foreland (Gries 1983; Craddock & van der Pluijm 1999). In terms of fracture development during D2, the most probable fracture strike would be aligned with the normal faults (ENE). However, regions of increased intensity would be expected to develop adjacent and parallel to the normal faults that are preferentially located above the drape fold (Fig. 3b).

Model configuration and procedure Although analytical elastic solutions are useful for calculating the distribution of stress surrounding a dislocation (i.e. fault) within a medium, complexities associated with real 3D fault geometries and associated slip distributions and mechanical interaction with adjacent structures require the use of numerical models (Pollard & Segall 1987; Bourne & Willemse 2001; Maerten et al. 2002). In this paper, the boundary element method is used for modelling faults as dislocations within the surrounding medium, which invokes a constitutive law (described below) and adheres to an equilibrium of forces between an applied load and the internal deformation so that the sum of forces in any direction and the moment about any point within the model is zero (see Thomas 1993; Bourne & Willemse 2001 and Maerten et al. 2002 for a more detailed discussion). The general approach is, first, to discretize the seismically mapped faults into triangular elements, and use detailed horizon mapping to measure the 3D displacement distributions. Three components of the average regional principal strain are then calculated from transects across the fault system, with directions aligned with the fault system to capture the greatest component of displacement. Bulk material properties of the matrix (Young’s modulus and Poisson’s ratio) are taken from rock mechanics experiments (performed in the Shell Rock Mechanics Lab, Houston, Texas) on core of the reservoir rock of interest. After the model runs, the change in stress–strain is analysed along with realistic in-situ stress conditions to evaluate the potential for brittle fracture with a criterion conditioned by experimental rock mechanics data. Strains are then partitioned into the necessary amount of fractures per grid cell required to accommodate the excess strain (defined later) and thus provide an explicit estimate of the increase in fracture density in response to fault-related stress changes.

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Boundary conditions The boundary element model (BEM) Poly3D (see references in Maerten et al. 2002, 2006) is used for the numerical modelling. It is run either by applying a remote load, in terms of stress or strain, or as prescribed displacements along the fault elements. For example, deformation during a model run may be driven by a regional, threedimensional strain (symmetrical tensor with 6 unique components) applied to the model boundary. The principal strains are calculated from the summations of heaves and throw taken from depth converted seismic interpretations of fault offsets. These strains are then resolved onto the elements of the discretized, traction-free fault surfaces during the model runs. This process neglects any frictional strength the fault may have, which will work against the imposed stress to reduce the net displacements along the modelled fault. Friction will also change the stress directions and magnitudes in the nearby regions relative to the traction-free (frictionless) model (Bourne & Willemse 2001). The frictionless fault assumption is valid when the fault experiences a total stress drop (Bourne & Willemse 2001) and is most likely a better approximation when considering cumulative displacements along a fault. In contrast, the model could be driven by slip along the faults, although by doing so, the context of a regional stress–strain azimuth and the deviations near the faults would be lost because cells adjacent to the faults would only be subject to local stresses in response to fault slip, without regard to any regional driving stress. The resulting slip distribution from models driven by regional strain with traction-free fault elements is often smoother than the explicitly measured distributions that are subject to errors in the structural model. Errors in fault throw distributions could arise from mapping in poor seismic data, but even in the best seismic data, strike-slip components of displacement are difficult to discern. The main advantage in this numerical modelling method is that strike-slip components are free to accumulate, which may be important in regions of complex faulting where the faults experience mechanical interaction. Furthermore, regional average stress or strain values may be used to drive the deformation and evaluate basic trends of fault displacements in data-poor areas. In this paper a model is run for each phase of deformation (D1 and D2). For both phases, the model is run with traction-free fault surfaces that are restricted from dilating and driven by a regional strain. None of the modelled faults reach the Earth’s surface, and the shortest dimension of all the faults is much less than the shortest distance between the fault and the Earth’s surface. Thus a

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whole space, rather than a half-space, is used for both models. In order to use average strain measurements to describe a particular population of faults, it is first necessary to define an average direction of maximum extensional heave or contractional shortening that represents the major horizontal component of strain for the entire population. Because we measure only the dip-slip component of displacement from seismic data, the average directions are perpendicular and parallel to the mean fault strike, while the third component is vertical (i.e. fault throw, thinning during extension and thickening during contraction). Longitudinal strain e is defined as the change (DL) in original line length (Lo) to its final length (Lf ), e¼

DL Lf Lo ¼ : Lo Lf + DL

(1)

A measure of heave or shortening is the horizontal component of extensional or contractional displacement, respectively, and throw is the vertical component of displacement (thinning in extension, thickening in contraction). A geological sign convention is used, where compressive stress is positive and produces a negative extension (i.e. contraction). Conversely, a tensile (negative) stress produces a positive extension (Twiss & Moores 1992, p. 166). Similarly, longitudinal strains are positive for thickening and negative for thinning. The maximum, intermediate, and minimum principle strains are referred to as e1, e2 and e3 (Twiss & Moores 1992). The measured longitudinal strains are averaged across the region, and then rotated into the coordinate reference frame of the numerical model using a right-hand rule coordinate convention (Table 1; x ¼ þve east, y ¼ þve north, and z ¼ þve up). Rotations with multiples other

Table 1. Regional strain boundary conditions

1xx

1xy 1yy

1xz 1yz 1zz

20.01589

0.0057 20.0021

0 0 0.086

0.0016

20.0005 0.0039

0 0 20.023

D1 contraction

D2 extension

than 908 will result in resolved shear strains (exy ¼ eyx, exz ¼ ezx, eyz ¼ ezy) that are also resolved into the x, y, and z coordinate reference frame of the BEM (Table 1). The numerical model incorporates linear elasticity (i.e. Hooke’s law) of the matrix (e.g. Jaeger & Cook 1979), defined by Young’s modulus (E) and Poisson’s ratio (n). The total model output stress and strain consists of two components: eij,total ¼ eij,regional þ eij,local

(2a)

sij,total ¼ sij,regional þ sij,local ,

(2b)

the regional input and the local stress–strain that is modulated in response to faulting. The measured strains from seismic are cumulative, and therefore the corresponding stresses (through Hooke’s law) are larger than the elastic limit that occurs during a single incremental episode of slip. An analysis of the total stress would therefore be unphysical because stress in the crust does not attain such high levels. For example, in the model output, strain in the grid cells that are not influenced by faults would exhibit magnitudes defined by the first term in Equation (2a). For a fault population with an average extensional heave of 100 m, measured over a distance of 2 km, the resulting regional horizontal strain would be 0.053 and the corresponding stress would be 1590 MPa (using a 1D equivalent of Hooke’s law with E ¼ 30 GPa). This stress is greater than c. 15 times the brittle fracture strength of a common sandstone (Lockner 1995). To make the model more realistic, the regional input stresses and strains are removed from the model output before any failure analysis. The remaining local term represents the change in stress and strain related to faulting alone and is hereafter referred to as the excess stress or strain that could be accommodated by the growth of fractures. These values represent modulations from a background, in-situ stress. Thus in order to quantitatively evaluate the excess stress and strain in terms of a failure criterion, the excess values must be added to in-situ stresses that were presumably present during the time of deformation. In this paper, this new state of stress (excess þ in-situ stress) is referred to as the fault-modulated stress regime (FMSR). In-situ stresses are not initially incorporated in the model because the magnitudes of displacement that result from the in-situ stress would be much lower than the cumulative displacements observed on the faults. There are several caveats associated with using the FMSR to analyse the potential for

GEOMECHANICAL FRACTURE PREDICTION

brittle fracture. First, the stress is no longer in equilibrium with adjacent elements and, importantly, the shear driving component of in-situ stress would result in an additional component of slip on any frictionless faults within the model (Bourne & Willemse 2001). Therefore, by adding a nonhydrostatic in-situ stress onto the model results (excess stress) it is implicitly assumed that the faults are locked. Over geological timescales (i.e. millions of years) this is unphysical. However, the in-situ stress magnitudes are simply used as a basis to evaluate the model stress changes against absolute magnitudes of failure strength. For old structures that are no longer active, or those that experienced a protracted history, there will be significant uncertainty in estimating the magnitudes of the in-situ stress field during deformation, whereas for currently active structures the uncertainty is less if adequate subsurface data are available. In this analysis, present-day in-situ stress estimates are used for the youngest phase of extensional deformation (D2). These estimates (Fig. 4) are based on integration of density logs for the overburden pressure, pore-pressure data from Modular Dynamic Tester (MDT) tests, and minimum

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horizontal stress estimates from leak-off test (LOT) and formation integrity test (FIT) data from offset wells Rock Island 4-H, Sidewinder 1-H and Sidewinder 2-H (unpublished proprietary data). Maximum horizontal stress is calibrated from mud-weights in the above wells, and restricted to less than the vertical stress and greater than the minimum horizontal stress (for an extensional environment). Stress gradients (psi) used to model D2 are constructed from the above data (with depth in feet):

s1 ¼ sV ¼ 1:1176 depth 290:52 s2 ¼ sH ¼ 0:5686 depth1:0614

(3)

s3 ¼ sh ¼ 0:1641 depth1:651 Pp ¼ 0:4337 depth where s1, 2, and 3 represent the maximum, intermediate, and minimum principle stresses, respectively, and sV, H, and h represent the vertical, maximum and minimum horizontal stress, respectively. For the earlier contractional phase (D1), the

σ2

σ3

σ

σ

σ

σ

Fig. 4. Present day in-situ stress as a function of depth. These conditions are applied explicitly to D2, whereas for D1 the overburden (minimum principal stress) and pore-pressure are used along with equation (4) to solve for the maximum principal stress.

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same overburden gradient is used, with s1 being constrained by the frictional strength of the crust in a contractional tectonic environment (Engelder 1993, p. 74),

s1 ¼ s3

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 m2s þ 1 þ ms

(4)

where s3 is the vertically oriented minimum principal stress (i.e. overburden), s1 ¼ sH, and * denotes effective stress (s 2 Pp). Here the coefficient of sliding friction (ms) is used, which is generally less than the internal friction that must be overcome in order to nucleate a fault in intact rock without any preexisting weaknesses (e.g. Lockner 1995). For this contractional phase of deformation, the intermediate principal stress is represented by the mean stress (s2 ¼ [s1 þ s3]/2). Present day pore-pressure is assumed to be representative for D1 conditions.

Failure criteria The model output (FMSR ¼ excess þ in-situ stress) is evaluated with the combined Griffith-Coulomb theory for fracture, that incorporates a criterion for both tensile and shear failure (Brace 1960; Paul 1961; McClintock & Walsh 1962; Jaeger & Cook 1979 p. 96 –97, 101 –106). The possibility of transtensional, hybrid shear fracture that is predicted in the tensile regime of the Griffith criterion is neglected for simplicity. The brittle failure criterion employed is thus consistent with the Coulomb criterion for frictional sliding in the compressive field, and the Griffith theory for joint propagation in the tensile field only for the case of zero resolved shear stress. The details of these criteria are presented in the appendix.

Mechanical properties of the Frontier sandstone Triaxial compressive tests were performed on eight core samples from Frontier Formation (2nd Frontier shore face sands) within the adjacent Moxa Arch (Shell Rock Mechanics Lab, Bellaire Technology Center, Houston, Texas). The similarity in tectonic setting and depth imply that the strengths are analogous for the Frontier sandstone within the Blue Forest survey. The samples were deformed until failure with confining pressures ranging between 0 and 5000 psi (34.48 MPa), upon which a Mohr – Coulomb failure analysis was performed to obtain cohesive strength (So) and the coefficient of internal friction (mi). Stress– strain data were analysed to obtain Young’s modulus (E) and Poisson’s ratio (n). Averages were calculated from these data (Table 2) and used in the following analyses.

Table 2. Average mechanical properties of the Frontier sandstone Youngs Modulus (E, GPa) Poisson’s Ratio (n) Cohesion (So, MPa) Internal Friction (mi) Unconfined Compressive Strength (UCS, MPa) Tensile strength (To, MPa)

13.79 0.25 13.36 0.74 61.7 6.9

Fracture density After the model output is evaluated against the shear and tensile failure criteria (appendix equations) the model is repopulated with sufficient fractures to satisfy the excess strain if tensile failure is satisfied. If the shear failure criterion is met then the assumption is made that a fault is nucleated within the cell, and the relative magnitude of Coulomb Failure Stress (CFS, see appendix for explanation) correlates with the probability and/ or density of faults (similar to Maerten et al. 2002). For each grid cell the model output also consists of an excess strain vector, and with knowledge of the model cell dimensions, the heave may be calculated from the excess strain by rearranging equation (1),

heave ¼ DL ¼

elocal Lf 1 + elocal

(5)

where the sign in the denominator is positive for extension or thickening and negative for contraction and shortening, respectively. Joints propagate in the s1 2 s2 plane, normal to s3 (Pollard & Aydin 1988; Engelder 1993) and thus for an extensional regime (with s1 ¼ sV, s2 ¼ sH, s3 ¼ sh, joints are vertical and parallel to s2. However, vertically-oriented joint sets also develop in contractional stress regimes (e.g. Engelder & Geiser 1980; Bourne 2003), often orientated parallel to the maximum direction of compression and shortening (sH ¼ s1) and perpendicular to the minimum horizontal stress (sh ¼ s2). The heave must be calculated in the direction normal to the fracture strike. Therefore, for extensional deformation the heave is calculated in the direction parallel to s3 and the distribution of joint azimuths are indicated from an azimuth map of s2 unit vectors. In contrast, for contractional deformation, the heave is calculated in the direction parallel to s2, and the distribution of joint azimuths are indicated from an azimuth map of s1 unit vectors. Careful attention must be directed towards evaluating the stress and strain directly from the model output if FMSRs are analysed

GEOMECHANICAL FRACTURE PREDICTION

because stress and strain directions may change relative to the model input (see Model results). The heave is accommodated by opening-mode joints (i.e. aperture) in cells where the tensile failure criterion is met, and thus the next issue of concern is to calculate the number of joints necessary to accommodate the total aperture required within the cell. Field observations (Vermilye & Scholz 1995) and theory (Pollard & Segall 1987; Bai et al. 2000; Olson 2003) support a positive correlation between maximum aperture and joint dimensions (length or height), and furthermore joint height is commonly restricted by and thus equivalent to bed thickness (Narr & Suppe 1991; Gross et al. 1995, 1997; Ji & Saruwatari 1998; Bai & Pollard 2000; Underwood et al. 2003). Using bed thickness (T ) as a proxy for joint height therefore provides the means to estimate the maximum aperture accommodated by a single opening-mode joint. Disregarding effects of bed boundaries or differences in elastic properties between adjacent beds and overburden stress (Bai et al. 2000), fracture aperture (A) is a function of driving stress (Ds) and material properties (E and n), A¼

2(1 v2 ) T Ds, E

(6)

where Ds is the effective stress normal to the fracture. In the case of closely spaced joints, mechanical interaction will modulate the driving stress locally, which results in a variation in aperture relative to the idealized model. The tensile fracture strength is used as a first-order estimate of the driving stress. Fracture height (T ) is assumed to be equivalent to bed thickness, and thus conventional log-derived thickness maps can be used as input for calculating the aperture on a bed by bed basis. Equation (6) also implicitly assumes that the stress intensity factor (KIc) varies with fracture length (Olson 2003). This and additional factors listed above thus render equation (6) a first-order approximation. The number of joints/cell is determined from H/A (dividing equation 5 by 6) and an estimate of 1D fracture density ( joints/unit length) can readily be calculated from Joints/unit length ¼

DL (1=length) , To A=T

(7)

where length is the distance of the cell in the direction of the strain that the heave is measured from, the ratio A/T is calculated from equation (6), and To is the observed bed thickness in each cell. These estimates can be compared with

145

observations from either core or borehole image logs, or indirectly from data such as seismic velocity anisotropy.

Model results D1 fracture intensity Regional strain is measured in the directions roughly orthogonal to the average fault strike of D1 reverse faults (i.e. 1108) to measure the maximum shortening (e3, Fig. 2a), as well in the vertical direction to measure the vertical component of strain (e1). The horizontal components are then rotated 208 (counter-clockwise) about the z axis into the coordinate reference frame of the BEM model, which results in non-zero values for the off-diagonal components of the strain tensor (i.e. shear strain) and the intermediate principal strain (Table 1). The regional average contractional heave of c. 700 ft input into the model (1xx ¼ 20.018 ¼ 700/[40000 2 700]) is matched in the output in terms of the maximum dip-slip displacement magnitudes along each of the segments, although the displacement is distributed alongstrike and down-dip as well, just as observed from the seismic data (Fig. 5). The model results, formulated in terms of FMSR, indicate that some regions experience effective tensile stresses below the tensile failure strength estimated for the Frontier sandstone (26.6 MPa, Fig. 6a). However, the maximum principal stress for these cells is too high to permit tensile failure (equation A5 is not satisfied). The shear failure criterion is met in two distinct, but structurally similar regions (Fig. 7) that are consistent with previous calculations of stress change along reverse faults (King et al. 1994). King et al. (1994) demonstrate that the greatest magnitude of shear stress increase is found ahead of the fault tip and in the shallow footwall of the reverse faults (Fig. 8). The symmetrical quadrant of increased shear stress located in the deep quadrant within the hanging wall is not observed at the Frontier horizon, but exists within the model. For the structural configuration at Blue Forest, the upper fault tip projects into the SE-dipping forelimb. The largest magnitudes of CFS (calculated from FMSR, see appendix for explanation) are indeed located in the forelimb of the major drape fold, with maximum magnitudes along the southern segment where displacements are greatest (Fig. 9). The shear failure criterion is also satisfied in a secondary, triangular shaped region in the footwall of the smaller NW-striking reverse fault that is located in the hanging wall of the major reverse fault system. In both cases, the linear region of high

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Fig. 5. View towards SE of main reverse fault system and subsidiary roughly NW-striking reverse fault. Dip-slip component of reverse displacement from D1 model results (scale is saturated at 600 ft). Strike-slip displacements are less than 5% of the maximum dip-slip displacement.

CFS is aligned along-strike of the adjacent reverse fault. In areas where the shear failure criterion is satisfied, the expected strike of the developing faults should parallel the s2 direction (Fig. 9). Importantly, the strike of developing faults is parallel to the major reverse fault. However, the stress vectors are orthogonal to the approximately WNW-trending minor reverse fault in the secondary region of smaller CFS where shear failure is satisfied. This is problematic in that the subsidiary faults should parallel the parent structure. The stress vectors shown (Fig. 9) are calculated from the total model output. To evaluate the stress vectors for the excess stress, the regional input is subtracted from both horizontal components of the stress tensor, and the difference between the minimum and maximum horizontal stress is calculated (Fig. 10). Negative values are indicative of a stress rotation between the horizontal components (i.e. sh becomes sH ). These stress rotations are apparent in the exact locations where stress rotations need be invoked to maintain kinematic compatibility. The large region of predicted stress rotation in the footwall of the Blue Forest structure (Fig. 10) is an artifact of the increased overburden and associated Poisson effects that are not accounted for in the above calculation (but are for the FMSR that includes an in-situ background stress). Importantly, the lack of tensile failure recognized in this model does not imply that a systematic, regional joint set could not have formed under these stress conditions. The homogeneous rheology of the model excludes effects of mechanical stratigraphy, interbedded sedimentary beds with variations in mechanical properties (Corbett et al. 1987; Gross

1995), which may induce a local tension. Under certain conditions, adjacent layers with a contrast in mechanical properties (e.g. E, n) may react differently to the applied load, which creates local tension necessary for joint development even within a fully compressive stress regime that experiences no effective tension (Bourne 2003).

D2 fracture intensity Maximum extensional strain (e1) for D2 normal faults follows the 348–1688 azimuth, orthogonal to the average fault strike for this phase of deformation (Fig. 2b). The horizontal components are then rotated 128 (clockwise) about the z axis into the coordinate reference frame of the BEM, which as for D1, results in non-zero values for the offdiagonal components of the strain tensor (i.e. shear strain) and the intermediate principal strain (Table 1). Although the faults are the result of transtension in a regional contractional environment, the model is driven by extension because of the difficulties in modelling such a complex environment (transtension) with the boundary element method. The strain accommodated during D2 is significantly less than D1, and is distributed throughout the survey on many small faults (Fig. 2b). The results for this phase of deformation, in terms of shear and normal stress derived from FMSR (Fig. 11), indicate that 6.2% of the cells failed in tension and 8.4% failed in shear. The shear criterion is preferentially met ahead of the fault tips, in the regions that experience the greatest increase in shear stress (Figs 8 & 12 see King et al. 1994). Tensile failure is met in the dilational quadrants of the fault, in response to the

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147

Fig. 6. Fault-modulated stress field (compression þve) for (a) D1 contraction and (b) D2 extension. Solid black line at 26.6 MPa represents the estimated tensile strength of the Frontier sandstone determined from rock mechanics experiments; s1 (white diamonds), s2 (black squares) and s3 (grey circles) represent in-situ stress þ excess stress determined from the model. Although s3 exceeds the tensile failure strength during D1, the differential stress is large enough that shear failure is favoured to occur first. However, this is not the case during D2 as numerous cells experience both tensile and shear failure.

predominant reduction of normal stress and secondary reduction in shear stress (Figs 8 & 12). The alternating pattern of NE-trending lobes with tensile and shear failure result from interaction between two adjacent normal fault systems (Fig. 12).

After calculating excess e1 (equation 2) extensional heave in the e1 direction (equation 5), the net sand thickness map (Fig. 13a, derived from well logs in the region) is used to calculate the increase in 1D fracture density (Figs 13d & 14) for

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Fig. 7. Mohr diagram of maximum shear and normal stress calculated from the FMSR for all cells in the model during D1. The shear failure criterion is met in cells that lie above the failure criterion (black circles); the remaining cells are stable (grey crosses). The in-situ stress conditions, with (black stress circle and white diamonds) and without (grey stress circle and grey diamonds) pore-pressure (Pp) are shown for reference. These are the in-situ reference stress states before deformation commences. Model results include pore-pressure.

cells that meet the tensile failure criterion. Excess extension in the e1 direction ranges between c. 0–0.01 (Fig. 13b), which correlates with a heave between 0–12.5 ft cell for the cell dimensions in

this model run (Fig. 13c). Using a net sand thickness map to determine the upper limit of fracture height (50–100 ft) and assuming an aperture:height ratio (A/T ) of 0.0003, results in a calculation of excess

Fig. 8. Cross sectional view of Coulomb Failure Stress (CFS 1023 MPa, tension þve) along a generic reverse fault with a unit slip. The most negative values represent enhanced potential for fault nucleation (dark), more positive values represent stable regions (light). CFS is greatest (most negative) in the dilational quadrants (labeled – ve in inset) of the fault due to the reduction in normal stress and associated increase in the ratio of shear to normal stress.

GEOMECHANICAL FRACTURE PREDICTION

149

Fig. 9. Map view of Coulomb Failure Stress (CFS, compression þve) at Frontier (F1320) level calculated from FMSR. Positive values represent enhanced potential for fault nucleation, negative values represent stable regions. CFS is greatest (most positive) in two distinct regions (also see Fig. 7), each of which correlates with the forelimb within the footwall of the adjacent reverse fault. White contours (interval ¼ 1) represent areas where the shear failure criterion is satisfied (1) and structure contours (black) represent depth to top F1320 which decreases to the east. Black dashes represent s2 stress vectors directly from model output (no FMSR calculated, see text).

Fig. 10. Difference map (at Frontier F1320 level) between excess intermediate horizontal stress and excess maximum horizontal stress (s2 2 781 MPa) 2 (s1 2 502 MPa). Negative values (blue shade) in hanging wall and along drape fold axis indicate areas where the minimum and maximum horizontal stress switch.

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σ

σ

σ

Fig. 11. Mohr diagram of maximum shear and normal stress calculated from the FMSR for all cells in the model during D2. The shear failure criterion is met in cells that lie above the failure criterion (black circles), whereas white diamonds to the left of the failure envelope meet the tensile failure criterion. Remaining cells are stable (grey circles). The in-situ stress conditions, before deformation commences, are displayed for reference (same convention as Fig. 7).

fracture intensity up to c. 0.4 joints/ft (Figs 13d, 14 & 15). However, a mean and median fracture intensity of 0.067 and 0.049 joints/ft is observed in cells that meet the tensile failure criterion (Fig. 15), indicating a median spacing c. 20 ft and an average fracture

spacing ratio (FSR ¼ mean layer thickness/median fracture spacing; Gross 1993) of c. 3.75. An FSR of one is expected for unperturbed, jointed rocks in interbedded mechanical units, whereas higher values are expected when faults or folds perturb the stress field.

Fig. 12. View towards NE of discretized D2 normal faults that mostly displace rocks above the F1320 level. Regions with coloured shading experience tensile failure, while those in grey experience shear failure. Only two faults are displayed for clarity. Black lines are s2 vectors, yellow lines are displacement vectors along the F1320 horizon. Notice that tensile failure is predicted to occur where upwards displacement (and associated reduction in normal stress) is greatest.

GEOMECHANICAL FRACTURE PREDICTION

151

Fig. 13. Map view of D2 model input and results at F1320 interval. (a) Net sand thickness (ft) from logs. (b) Maximum extensional excess strain (C.I. ¼ 0.005) calculated in direction parallel to the e1 vector (black tick). Coloured regions represent areas of extensional excess strain, whereas excess strain does not develop in white areas. (c) Heave (ft/cell) calculated from (b) using equation (5). (d) Excess fracture intensity (joints/ft) in direction of e1.

The elevated FSRs obtained from the model correspond well with the range of FSRs documented in the literature (McQuillan 1973; Ladeira & Price 1981; see Bai & Pollard 2000 for a review), although for many of these studies the structural setting is not well documented. The highest FSR from welldocumented outcrop observations where faults interact with jointed rock is 9.1 (Becker & Gross 1996).

Comparison between geomechanical models and seismic velocity anisotropy Azimuthal anisotropy in P-wave seismic reflection travel times are generally attributed to the presence of open, uncemented fractures in the subsurface (Hudson 1981; Thomsen 1995; Bakulin et al. 2000) because P-waves are retarded from propagating through an open fracture relative to propagating along it. Thus, in rocks exhibiting a fracture-induced anisotropy, the mean direction of the fracture system should theoretically correlate with the azimuth of the fast velocities. However, variations in in-situ stress may also contribute to the azimuthal dependency in velocity (e.g.

Al-Hawas et al. 2003) and regions having orthogonal fracture sets could exhibit no velocity anisotropy if the different sets have similar fracture infilling materials. The geomechanical predictions should be compared with the velocity anisotropy data as a basis for testing the geomechanical predictions and understanding the seismic data better. The results from this study are compared with the velocity anisotropy volume processed by GMG/AXIS (referred to as AZIMTM velocities) for the Blue Forest survey. The azimuthally sorted gathers were collected from the seismic data after normal move out processing and removal of statics in the common depth point domain. These data are then converted to interval velocities (Vint) using a modified Dix equation pertinent to azimuthal anisotropies. Explicit comparison is made between the geomechanical results and a Vint Fast 2 Slow volume, which represents the magnitude of the maximum differences in compressional velocity (Vp) as a function of azimuth (Vfast 2 Vslow) for each bin (5 5 50). Maximum magnitudes of Vint Fast 2 Slow spatially correlate with three structural features

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Fig. 14. Final results for D2 displays regions that experience shear failure (grey), tensile failure (coloured according to fracture intensity with blue low and red high, saturated at 0.4), and stable regions (white). Tick marks represent s2 vectors, which are parallel to e2. Structure contours increase in depth from west to east.

predicted from the geomechanical models (Fig. 16), listed in order of magnitude. 1. 2.

NE-trending normal faults (D2) within the hanging wall of the Blue Forest thrust fault (Fig. 16a). WNW-trending feature of large velocity anisotropy in the footwall of the SSW-verging thrust fault (D1) located in the Blue Forest hanging wall (Fig. 16b).

mean = 0.067

Fig. 15. Histogram of joints per feet in cells that failed via tensile failure during D2.

3.

A NNE –SSW-trending anomaly in the footwall of the Blue Forest thrust, which decreases in amplitude to the NNE (Fig. 16b).

The numerical prediction of a NNE-trending zone of high fault density located in the forelimb of the Blue Forest reverse fault (D1) is represented as a similarly shaped velocity anisotropy anomaly observed slightly east of the expected location. The location of this velocity anisotropy is incorrect and represents an artifact from the anisotropy analysis being performed on unmigrated data. Migration tests indicate that the true location should be in the forelimb of the drape fold, just as predicted from the model, although it is unknown whether the magnitude of the anomaly represents an artifact as well. All other faults within the survey have small enough displacements and associated dips within the folds that they do not suffer from this migration effect. Features 1– 3 correlate with regions of predicted increases in joint and fault density, and imply that these features are fluid-filled and open, maximum horizontal stress is magnified along strike of both joints and faults, or some combination of the two. Forward modelling the velocity anisotropy data from geomechanical model results would perhaps establish the importance of the listed mechanisms.

GEOMECHANICAL FRACTURE PREDICTION

153

Fig. 16. Interval velocity map of fast–slow velocities at (a) 2200 ms (average F1320 level) and (b) 3000 ms ( just below upper fault tip of main fault system). Symbols for reverse (triangles) and normal faults (rectangles) are on the hanging walls. Scale represents velocity difference (ft/sec). (a) Fault traces above the F1320 horizon (black) and below (white) are projected onto the mostly unfaulted (seismically) layer. (b) Fault traces in black intersect the horizon at this level.

Nevertheless, the qualitative correlations recognized here are intriguing in that the velocity anisotropy seems highly dependent on the general structural features observed from seismic interpretation, but more importantly, the patterns of CFS that are associated with these structures. No general velocity anisotropy has been observed throughout the area, despite the probable presence of a regional tectonic set of preliminary roughly east –westtrending joints. This indicates that if present, this set of fractures does not reduce the elastic properties enough to affect the seismic waves. Commonly observed FSR values of c. 1 for regional tectonic sets (see summary in Bai & Pollard 2000), indicate a spacing of c. 75 ft between these structures.

Preliminary attempts have been made to forward model the P-wave velocity anisotropy (Mario Gutierrez, pers. comm. 2004) from the fracture intensity output of these geomechanical models using an idealized penny-shaped fracture model (Hudson 1981) where fracture density, aperture and elastic properties are parameterized in terms of Thomsen’s coefficients (Thomsen 1995). Current research is focused on better understanding the seismic response to natural fractures. Additional (direct) observations are required to confirm these correlations. Explicitly, in-situ stress variations and fracture observations are required. In a well-developed field that contains adequate well control, local stress field variations could be

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derived from a combination of borehole breakout observations, LOT data, RFT or MDT data, density logs and perhaps microseismicity and observations of depletion-induced compaction. Similarly, fracture observations in either core or borehole images (or preferably both) and most importantly those obtained from horizontal and/or highly deviated wells, should be compiled and compared with the predictions. Once any correlations between these features and production data have been established, the methods presented in this paper may be used as a tool for helping to identify appropriate well locations.

Discussion and conclusions A few topics for future consideration were identified from this study. First, the mechanical models do not account for interbed slip, or heterogeneous elastic properties that are observed to influence joint spacing (e.g. Gross et al. 1995; Bai & Pollard 2000; Underwood et al. 2003; Bourne 2003). Variability in mechanical properties within the reservoir interval will act to restrict joint growth at mechanical unit boundaries, which results in a theoretical reduction in aperture and probably a hierarchy of fracture architecture. The latter would be manifest as numerous small joints within single mechanical units and fewer large, through-going joints that span multiple mechanical units and accommodate relatively larger components of strain. Furthermore, predicted joint apertures are based on a fracture mechanics model (Olsen 2003) that does not include mechanical interaction among adjacent joints, which acts to modulate (most likely reduce) the aperture (Bai et al. 2000). Because the model fracture density is based on the aperture/bed thickness scaling relation for isolated joints, the fracture density calculations probably represent minima. In other words, if mechanical interaction among adjacent joints is important in reducing the aperture (relative to the isolated model), then more joints are necessary to accommodate the extensional strain. However, the author is not aware of any detailed field observations of aperture in rocks with high FSR for comparison. The final model output is fracture density, which is probably inferior in its usefulness in characterizing fractured reservoirs relative to parameters such as fracture connectivity and permeability. Nevertheless, permeability can be derived from the former using either simple (e.g. the ‘cubic’ law) or more robust rules that account for the variations in aperture and the influence of loading and FSR on aperture variations (Waite et al. 1999; Bai & Pollard 2001). A discussion of the effects of

fractures on reservoir performance can be found in Nelson (1985). The mechanical model input parameters, such as fault geometry, stress– strain, and rock properties all have important effects on the model output. For D1 deformation, the biggest uncertainty lies in characterizing the in-situ stress at the time of deformation. Although there is a sound physical basis for the use of general stress orientations from the regional structural history and observed seismic-scale fault and slip orientations, the magnitudes of horizontal stress are less certain, and the pore-pressure is assumed to follow a similar gradient as today, which introduces a degree of uncertainty into the results. The frictional strength constraint employed to estimate the maximum horizontal stress provides a maximum differential stress, which in reality may be reduced. In general, a reduction in differential stress would enhance the potential for joint development in some regions rather than faulting for D1. For D2 deformation, the displacements along the faults represent the greatest uncertainty because their displacements are so low and seismic mapping is so difficult. Furthermore, the D1 stress field output and D2 input were treated as separate entities, whereas in reality, the D1 stress field should be input to D2, accounting for any possible changes in overburden, stress orientations, and change in regional tectonics. An additional component of the mechanical modelling that could be improved upon is the inability to incorporate horizontal stress gradients with depth. To circumvent this problem, an in-situ stress field was added to the fault-perturbed stresses (i.e. excess stress) to calculate the FMSR. As a consequence the excess stress that was in equilibrium with surrounding faults after the model run, was taken out of equilibrium. This was done in order to compare the effect of local stress changes against rock strength rather than using a qualitative, relative criterion. Although this effect is probably insignificant, future mechanical modelling should incorporate more realistic in-situ stresses (i.e. with gradients) prior to deformation. Finally, the models presented in this paper are intended to reproduce one component of the deformation – the fault-related fracturing. Additional mechanisms of joint formation (Engelder 1985; Bourne 2003) include far-field tectonic stress, burial, uplift/exhumation, thermal stresses, increase in fluid pressure, diagenesis (which alters rock properties via changes in volume) and hydrocarbon generation (Engelder 2004). The qualitative match between average velocity anisotropy and regions of enhanced fault-related fracturing suggests that these additional mechanisms may be relatively insignificant. However, future

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quantitative forward modelling of the seismic response to fracture density should, provide a quantitative evaluation of the significance of each mechanism.

and s1* is positive and satisfies

Discussions with J. Tabor, J. Busch, S. Naruk, R. Whale, C. Beck-Brake, A. Jackson, M. Gutierrez and J. Soethout helped shape the interpretations and goals of this project. Seismic and well data support from J. Calvache, L. Peirce and F. Doughty are greatly appreciated. GSL editors B. Freeman, L. Maerten and J. Walsh are thanked for their valuable reviews. Earlier reviews and discussions with S. Bourne significantly helped clarify the analysis and strengthen the manuscript. The author thanks Shell International Exploration and Production Inc. and Shell Exploration and Production Co. for permission to publish this work.

where UCS is the unconfined compressive strength. For tensile failure to occur,

Appendix

1 UCS To , s1 . UCS 4So2

1 UCS To s1 , UCS 4So2

s3 Pp ¼ s3 To;

(A1)

where the tensile strength (To) is 0.5So (McClintock & Walsh 1962). So is referred to as the cohesion, and represents the shear strength in absence of any normal stress. For fault nucleation in the compressive regime, the conventional Coulomb criterion in terms of normal (sn) and shear (t) stresses is,

t So þ mi ðsn PpÞ:

(A2)

The coefficient of internal friction (m i) is the shear/ normal stress during failure, which typically ranges from c. 0.6– 1.8, and decreases with increasing confining pressure (Lockner 1995). Internal friction is determined from laboratory tests on intact rock, and is larger than the coefficient of sliding friction along pre-existing discontinuities. Written in terms of the principal stresses, the maximum of equation (A2) becomes (Jaeger & Cook 1979): CFS ¼

ﬃ s1 þ s3 s1 s3 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ m2 þ 1 m; 2 2

(A3)

and shear failure occurs when the Coulomb Failure Stress (CFS) is equal to or exceeds So CFS So;

(A4)

(A6)

must be satisfied in addition to equation (A1). Implicit to equations (A2 2 A3) are that the orientations of the fault planes are not known a priori and the maximum value is found when tan2u ¼ 21/mi, with u representing the angle between s1 and the normal to the fault plane. The cohesion can be estimated from constructing and extrapolating a failure envelope in shear and normal stress space on a conventional Mohr diagram, or rigorously through the relation

Failure criteria The Griffith-Coulomb theory for brittle fracture is used for the analysis of the FMSR output from the model, and follows from treatments by Brace (1960), Jaeger & Cook (1979, p. 96– 97, 101–106), McClintock & Walsh (1962), and Paul (1961). With the convention of compression positive and tension negative, the criterion for the nucleation of joints under tensile failure is,

(A5)

UCS : So ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ m2i þ 1 þ mi 2

(A7)

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Kinematically-equivalent but geomechanically-different simulations of fault evolution: the role of loading configurations H. LEWIS1, S. A. HALL2, J. GUEST1 & G. D. COUPLES1 1

Institute of Petroleum Engineering and ECOSSE Partnership, Heriot-Watt University Edinburgh EH14 4AS, Scotland, UK (e-mail: [email protected]) Also at ECOSSE (Edinburgh Collaborative of Subsurface Science and Engineering), a part of the Edinburgh Research Partnership in Engineering and Mathematics 2

Laboratoire 3S-R, Domaine Universitaire, BP53, 38041 Grenoble Cedex 9, France Abstract: Geomechanical simulations are used to demonstrate the importance of the way that models are loaded. In this paper the development of permanent damage during faulting using frictional-slip models of a reverse fault is investigated. Although the use of different loads and constraints can produce the same faulted geometry (for the same rock type, and at the same burial depth), the models develop very different stress and strain states. Permanent strain magnitudes and distributions between models are quite dissimilar, including the distributions of permanent dilation and compaction. This work demonstrates that boundary loads and boundary constraints are significant factors in determining what stress and deformation states evolve in the simulation model. The examples also illustrate that final (deformed) geometry alone is a very poor basis from which to predict either stress state or open fracture distribution. Bulk finite strain does not allow a prediction of local principal stress directions, magnitudes, or signs, at least in the vicinity of fault damage zones.

For a wide range of subsurface activities it is necessary to predict the types of deformation that exist in subsurface structures, together with their distribution and the associated stress field. Activities can include the planning of wellbore trajectories to avoid or to intersect open fractures or faults, the correct interpretation of well-test data, and the generation of suitable upscaled porosity and permeability values for reservoir flow simulations. Additionally, in oil and gas exploration activities, the timing and location of fault zone sealing or leakage can have a important effect on risking issues such as the identification of migration pathways. In most situations there is a moderately good knowledge of a structural trap’s geometry, presentday regional stress state and the pressures of its contained fluids. Therefore, normally, a first-pass interpretation can be made of rock deformation within the structure. The information sources normally include seismically derived data interpreted to provide seismic velocities and anisotropies, and geological observations, such as identification of fault zone deformation or open fractures in core and downhole logs. Historically, outcrop analogues have also been used to help build a structural interpretation (e.g. Brown & Spang 1978; Jamison 1987). More recently the analysis of seismic data, to quantify seismic velocity anisotropies, has opened up the possibility for mapping

of subsurface properties that might relate to aligned fracturing, but the interpretation of such data is still ambiguous. Two other types of tools are available to help build a reliable picture of the distribution of enhanced and degraded rock permeability and of load-bearing capacity. The first is 2D or 3D kinematic restorations, which can be used to assess the validity of a structural interpretation by ensuring that at least one retrodeformable path exists. The computer-aided implementation of kinematic restoration rules has developed over the last twenty or so years (see for example Gibbs 1983; Fernandez et al. 2004), but the scientific principles have been recognized for nearly a century (Chamberlin 1910; Bucher 1933; Dahlstrom 1969). Although still regarded as somewhat of a specialist task, use of these structural (or more strictly kinematic) restoration tools has seen an increased interest, particularly in oil and gas exploration, for two to three decades. The main disadvantage of using the 2D or 3D kinematic restoration method to predict deformation distribution is its relatively simple representation of rock damage (typically, a strain state). Another issue is that the rules on which the restoration algorithms are based are not always appropriate. The other type of tool for predicting subsurface damage is geomechanical simulation of the stressed and deformed rock volume. Use of this type of tool

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 159–172. DOI: 10.1144/SP292.9 0305-8719/07/$15.00 # The Geological Society of London 2007.

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is both less common and more recent, and, at least for subsurface problems, has most commonly been used to ‘re-stress’ a present-day structure, restoring it to an assumed subsurface stress state by applying boundary stresses, derived from the regional stress field, to the local reservoir. The geomechanical simulations of ‘re-stressed structures’ are capable of providing a better representation of intra-reservoir present-day stress state than kinematic restorations, but they can only predict any damage that may develop in present-day loading, missing out the rock damage associated with all previous stages of the deformation unless that is input explicitly. Lewis et al. (2004) integrate kinematic restorations and geomechanical simulations to create so-called kinematically-informed geomechanics. Their approach involves applying displacements and pinning points or lines derived from the restoration’s movement history to control geomechanical simulations that represent an earlier structural stage. In this way they simulate the stage-by-stage deformation using the displacements believed to have occurred, in the sequence in which they occurred. The resulting simulation models generate changes in rock properties due to permanent strains, as well as changes in stress state. Lewis et al. (2004) illustrate their technique by performing kinematic restorations and then forward geomechanical simulations of a 2D cross-section through the UKCS Clair field (Coney et al. 1993). Maerten & Maerten (2006) use a very similar approach to investigate the sequential deformation of sandbox and natural examples, although their geomechanical simulation method is restricted to the elastic domain. The use of kinematic restorations should reduce the risk of assigning inappropriate loading arrangements for the simulations. However, the translation of ideas from kinematics to simulation input allows choices to be made that can have significant consequences for the simulation result. In this paper we investigate the implications, for the resulting prediction of rock damage and stress state, of making the correct choices of loads and constraints for controlling a simulation model. To do this, we use similar, but subtly different, loading and pinning configurations that still produce the same overall deformed geometry. The types of loads that are available within the simulation code used here are displacement, pressure and force. We describe three representative examples out of about twenty combinations of loading and pinning configurations that are different from one another, but which still produce the same movement along a simple, idealized reverse fault. Fault block movement and shape change is also virtually the same in all cases. However, each model configuration possesses different distributions of

incremental and final stress- and strain-states, together with different distributions of permanent volumetric strains including both dilated (e.g. open fractured) and compacted (sealing) rocks. The work reported here was carried out as part of a study of methods to improve identification of open fractures in the subsurface. In this context, we use the geomechanical simulation outputs to infer possible fracturing (or opening of pre-existing fractures) in places where the permanent strain is dilatant. Open fractures may also be detectable using seismic anisotropy analyses, but that detection is associated with a number of ambiguities. Linking such seismic anisotropy analyses to geomechanical damage prediction can lead to improved fracture identification. Hall et al. (2007) and Hall & Lewis (2007) address the linkage between geomechanical and seismic anisotropy approaches for making open fracture predictions. The subsequent sections of this paper cover the basics of geomechanical simulation and provide an overview of some of the issues associated with using a sophisticated geomechanical simulation tool to model subsurface structure development. The capabilities of the chosen geomechanical simulator are also described, followed by a description of the fault model example and of the general character of the results for the three example loading configurations. Based on these models, preferred ways of operating geomechanical simulation tools can be proposed. The significance of these results is then discussed in terms of their value for predicting open fracturing in the subsurface.

Representing subsurface deformation with a geomechanical simulation All geological structures have a deformation history which is typically multi-stage, as well as having a sedimentation and burial history, and being subject to the present-day stress state. Choosing if the geomechanical simulations will be used to recreate the present-day stress state, or to represent the history of the deformation, is an essential and early part of the model design. Typically, simulations of subsurface structural traps have put the reservoir ‘back into the subsurface’ and use the present-day geometry as an input for the simulation. These ‘back into the subsurface’ simulations typically use stress (or more strictly, traction) loads on the boundaries, and they may involve making some pre-loading geometric compensation for the shape changes that will occur during loading. This method has the advantage of (relative) simplicity, but it has the disadvantage that it cannot infer preexisting patterns of deformed rock properties to be brought in from prior deformation events. Although

GEOMECHANICAL MODEL LOADING/CONSTRAINTS

known or inferred deformed rock zones can be included in the input, this type of simulation does not predict deformation resulting from an earlier stage. Such an approach is limited to the prediction of current day stress and strain states, and in areas of pre-existing rock damage (if known), predicting the changes of, for example, fracture aperture. However, little additional insight can be gained into where any pre-existing damage might be located, or what form such damage is likely to have. The mode employed here is to use geomechanical simulations to evolve the deformation (see also Lewis et al. 2002; Maerten & Maerten 2006; Couples et al. 2007). This method requires the application of loads for one or more previous deformation stages to a geometry representing the chosen starting point in the deformation history. The advantage of this method is that deformed, and so mechanically and petrophysically altered, rock is included in the next stage of the simulation. If the starting point is early enough in the history, more of the final pattern can be discovered via the simulation. The disadvantages are the need for a good starting geometry and suitable loading conditions for each stage, plus the significantly increased complexity of the simulation. For most real subsurface structures, it is currently impractical to represent all deformation from the first structural event and, in practice, only the last one or two stages of the deformation are simulated. Earlier deformation stages can be represented by the appropriate, partially restored, geometry and an imposed pre-stress. This initial model is essentially an early-stage ‘back into the subsurface’ approach, so inevitably suffers from the same problems.

Geomechanical model design and implementation The model chosen for this work is a geometrically simple 608 reverse fault located between two blocks of the well studied Berea Sandstone (Fig. 1). Typically, mechanical simulations in general, and geomechanical simulations in particular, are designed so that the model boundaries are far away from the area of interest so that unwanted boundary effects do not influence the deformation in the area of interest. But here, close boundaries are needed because the purpose is to force the system to respond to the applied loads and constraints. Nearby boundaries, and thus smaller models, are also less costly to build and operate. There are then several motivations for examining a simple and limited system. For this paper, we investigate a small model in which the single planar, pre-existing, frictional fault surface is centrally positioned, and located between two fault

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100 m Fig. 1. Geometry of geomechanical model in its final deformed shape. The two blocks of material were initially adjacent, forming a layer without fault offset. Fault is a pre-existing frictional surface that dips at 608. Model is in 2D in the vertical plane. Original length was 200 m. The block/layer height is 50 m.

blocks that are each long enough to remove the fault region from end effects, but too short for other structures such as folds to develop at the expense of the intended fault displacement. The simulator used in our work is SAVFEMTM, a general-purpose finite element mechanical simulator with some highly specialized geomechanical adaptations (Couples et al. 2007). Most of this software’s characteristics are common to all geomechanical simulators and to most general-purpose mechanical simulators. The basic input data needed for any geomechanical simulation are: the shape and position of each of the various component rock units (the materials); the nature of the interaction of the material blocks, which is specified at their interfaces; a ‘deformation law’ for each material and the associated mechanical-property parameters (potentially including yield limits and post-yield parameters if incorporated in the deformation law); the loads applied to the model; and pinning points or lines that prevent the model from simply translating (pinning could be included under the heading of loads, but we separate it here for emphasis). In addition, SAVFEMTM has certain capabilities designed specifically for subsurface geomechanical problems, described below. The deformation law used in a mechanical simulator can be extremely simple, e.g. an elastic-only law requiring specification of a Young’s modulus and a Poisson’s ratio for isotropic materials, or elastic moduli and directional ratios for anisotropic materials. This type of law is used in many numerical codes that are much simpler to operate than a full-featured geomechanical simulator. However for geomaterials (rocks and soils), more complex laws are often required. For the faulting problem addressed here, an advanced material law is employed that includes yield (failure) and postyield evolution. We use the SAVFEM TM elastic – plastic material model (specifically the general power law material; see Couples et al. 2007), with post-yield strain hardening and softening

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behaviours, and the ability to develop permanent dilation or compaction (Menetrey & William 1993). This material model is capable of generating results that represent an excellent match to laboratory-observed rock deformation behaviour (Couples et al. 2007). SAVFEMTM also has the ability to simulate frictional interfaces. When discontinuities are included in a simulation model, the blocks of material must interact appropriately with their neighbours. The blocks should not interpenetrate, and the interfaces between them need to replicate the physics of the particular interaction. Here, non-welded contacts are treated as idealized frictional surfaces. The interface connections in SAVFEMTM are represented as springs, such that shear or dilational movements are permitted between the blocks (based on the assumed law), but block interpenetration is not permitted (or more correctly, is heavily penalized). All mechanical simulators require that the model be pinned, or constrained, in some way (for static problems). Unconstrained models would simply move and would not deform internally. However, determining pin points, pin lines or pinning planes for subsurface structures is not simple. Their determination is one of the main elements of cross-section balancing and kinematic restoration exercises. Observation of a wide range of kinematic restorations shows that, in practice, pins are widely spaced, with many structures such as large anticlines often not having any internal pins. Therefore, if a geomechanical model aims to represent the structure of interest, plus its nearest pin, the model could need to be enormous. Fortunately SAVFEMTM (like many similar tools) can constrain a model using a specified displacement, and so a much smaller volume can be modelled provided that the displacements along a line or plane can be appropriately specified. It is possible to prescribe both x and y displacement components (e.g. in 2D: 50 m in x and 20 m in y), or to prescribe one component and leave the other free (e.g. 50 m in x and free in y). The simple fault models described in this paper each have a fixed pin line and also use prescribed displacements of both types. The main outputs of the simulator are usually depicted as plots of the components of the stress and strain fields, plastic (permanent) shear strain magnitudes, and vector (trajectory) plots of the maximum and minimum permanent strains and stresses. Examples of these displays are given in the following section.

The fault model The main purpose of this paper is to use geomechanical simulations to show how the same final

deformed geometry, but different stress state and permanent damage distributions, can be produced by using different loading and constraining configurations in otherwise-similar models. We have created simulations of a single reverse fault in a uniform layer of sandstone (Fig. 1) where the fault is represented as a pre-existing frictional plane inclined at 608 to the horizontal. The material description of the rocks represents the well studied Berea sandstone (Coyner 1984; Bernabe & Brace 1990; Hart & Wang 1995; Katz et al. 2000; Wong et al. 2001), whose properties have been characterized in SAVFEMTM. The modelled sandstone layer is 200 m long, 50 m thick (high) and cut by the centrally-located break dipping to the right. The simulation is actually 3D, but a plane strain assumption is made for the third dimension such that variable stresses can develop but out-of-the-plane strains remain constant (and in this case zero). In effect the model is 2D in the vertical plane. A frictional interface with a coefficient of friction of 0.3 is used to separate the two blocks of sandstone across the fault and at the start of the simulation the displacement along the proto-fault is zero. In each loading configuration at least one edge of the model is pinned in the x- and y-directions: in the cases shown here, this is always the left edge of the model. Loads are applied in the form of pressures, forces or displacements at the other edges. The combined loading and pinning arrangements are referred to as the loading configurations. Three different loading configurations are used (Fig. 2; also see section below). Each configuration consists of a different combination of a fixed edge, plus defined displacements, forces or pressures. The total x-direction shortening is 5 m (2.5% horizontal strain), the top of the model is notionally at a burial depth of 500 m and the base at 550 m unless stated otherwise. A hydrostatic fluid pressure gradient is assumed.

The loading configurations The cases investigated here do not represent particular structural events, but all consist of statically admissible sets of conditions that are plausible causes of the fault displacement. The loads are chosen to be different in terms of the work done (or energy input) to the model, both in the absolute value and in their distribution around the model boundary. For example where displacements are replaced by their equivalent forces, the results of the two simulations are identical, as they should be. Case A has 10 MPa pressure applied to the top surface and 11 MPa pressure to the bottom surface, these values representing effective stresses. A displacement of 5 m in the negative x direction is applied to its right vertical edge in a series of

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Case A

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block moves up and to the left, parallel to the fault plane.

Typical result

Case B

Case C

100 m Fig. 2. Schematic diagrams of the loads and constraints applied to Cases A, B and C. Left hand side of the model for each of these cases is pinned, with zero displacement in both x and y directions. The models are shown in their final configurations, which are almost identical. Blue arrows represent boundary pressures (normal tractions), red arrows represent imposed displacements, and green arrows represent applied forces.

increments, whereas the y-displacement of this edge is not constrained. Case B retains the same loading configuration for the left hand fault block. For the right hand block, the upper and lower surfaces are loaded by applied pressures that vary linearly from 10 MPa –110 MPa, and from 11 MPa – 111 MPa, respectively, from the fault to the model edge at the far right end. Case B’s right end is loaded by forces directed in the negative x direction. Case C retains the top and base surface pressures, used in Case A, at 10 MPa and 11 MPa, respectively, but both an x and a y displacement are applied to the right hand edge, such that the right

In spite of there being significant differences between the evolved stress and strain states in the three models, there also is much in common. Therefore the general characteristics are summarized using the results of Case A, and then the differences are discussed. Figure 3 shows the magnitude of the horizontal and vertical stress components, and of the principal stresses, for the central region of the model for Case A. In order to illustrate the details around the fault, the ends are not shown; the mechanical state does not vary much away from the fault zone. The magnitudes of horizontal and vertical strain components, and the magnitude of the effective plastic strain, are shown in Figure 4. The effective plastic strain is a good general scalar approximation to the plastic strain tensor values, and contains both distortional and volumetric strains (Couples et al. 2007); it can be thought of as an equivalent to the octahedral shear stress. There is considerable spatial variation in the values of the stress and strain states, and of the stress and strain components, near the fault plane (Figs 3 & 4). The effective plastic strain plot (Fig. 4d) provides an explanation for these patterns. The rock has yielded adjacent to the fault plane, localizing the deformation. In these simulations, the post-yield behaviour is predominantly strain softening, so that the load-bearing capacity of the rock has decreased and load is necessarily transferred to adjacent rock, pushing that rock closer to yield. In this way the areas of yielded material have grown and the associated stress states reflect this behaviour (Fig. 3). As the rock has strainsoftened, stress has been redistributed from the yielded areas to the still-elastic surrounding material, pushing it nearer to its yield point, and leading to additional yielding in the next load increment. The yielded areas normally have finite, permanent volumetric strain of both compactional and dilational types. The initiation of the localized deformation adjacent to the fault plane appears to occur because of very small jogs in the fault plane (actually in the initially co-located edges of the fault blocks). These tiny jogs occur as a result of round-off of data coordinates that takes place in the finite element mesh generation (because the sine of 608 is an irrational number). The round-off affects the eighth decimal place and so is a trivial geometric distortion, but those small irregularities play a role in causing the initial non-linear feedback that then grows into damage zones. Such irregularities are

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Fig. 3. Calculated mechanical results for Case A. Only the central part of the model is shown. (a) Horizontal stress magnitude. Note the engineering sign convention, with compressional stresses shown as negative values. Horizontal black bar on scale indicates zero. (b) Vertical stress magnitude. (c) Maximum (compressive) principal stress magnitude (geological s1). (d) Minimum principal stress magnitude (geological s3).

very common and, indeed, are probably essential characteristics of natural faults. The numerical model develops a zone of yielded rock surrounding the fault plane (a damage zone) at fault displacements of just a few metres. Beyond

that point in the history, the stress state and the magnitude of the permanent strain both change, but the distribution of permanent deformation changes only slowly. A natural fault probably has many more non-planarities, especially in its early development,

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Fig. 4. Calculated strains for Case A. (a) Horizontal strain magnitude. Colour key shows magnitude of horizontal strain where red is 10% extension and blue is 10% shortening. (b) Vertical strain magnitude. Colour key shows magnitude of vertical strain where red is 10% extension and blue is 10% shortening. (c) Effective plastic strain (deP ¼ ððdePXX2 þ dePYY 2 þ dePZZ 2 þ (dePXY 2 þ dePYZ 2 þ dePZX2 )2 =2 (3(1 þ 212PF ))1=2 Þ, where the P superscript indicates the plastic component of total strain, and the subscripts refer to the usual coordinates. 1PF is the Drucker-Prager flow constant, which gives the dilation/compaction angle. See Couples et al. (2007) for further discussion). Dark blue areas have deformed only elastically. Light blue to red indicates increased magnitude of effective plastic strain. Red ¼ 25% effective plastic strain.

so the geomechanical model may underestimate the complexity of the behaviour of natural fault systems.

The three cases Figure 5 shows a comparison of the effective plastic strain, and the plastic (permanent or anelastic) principal strain tensors, for the three cases shown in Figure 2. That figure also shows the stress trajectories. The distribution of the permanently deformed rock is quite different in each case, as is the magnitude and distribution of the effective plastic strain, even though the deformed shape is almost identical. Horizontal and vertical stress and strain plots also have a similar degree of variation (Figs 3 & 4). The principal stresses are very different for the three cases. If the mechanical descriptions (stress and strain states) for these cases were compared out of the current context (i.e. draw an observation window over the central part of each plot, so that the fault offset is not known), it is unlikely that they would be interpreted as belonging to the same structure.

The magnitude of the effective plastic strain is considerably smaller for Case B than for Case A or Case C. Why? The explanation is likely to be because of the higher mean stresses that occur in Case B, which will suppress the development of dilational yielding, much of the plastic strain being dilational. One way to gain insight into this issue is to run the same models at a deeper simulated depth of burial. In order to consider the role of confining pressure (or mean stress), we have run a suite of otherwise identical simulations representing burial at 1 km (still with a hydrostatic fluid gradient). These simulations (Fig. 6) show the same patterns of deformation as are seen at 500 m burial, although the value of a given stress component is typically, but not always, somewhat larger (more compressive). The range of stress values tends to be somewhat smaller in the simulations representing the 1 km burial than in those representing 500 m burial. For example, the most compressive horizontal stress, 180 MPa, occurs in the shallower simulation, but the maximum is less than 100 MPa in the deeper example. Both the areal extent and the

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Fig. 5. Comparison of the calculated mechanical states in Cases A, B and C. From left to right, the images show: effective plastic strain; principal plastic strains; and principal stresses. Each case is shown at 5 m total shortening (2.5% bulk strain) in the x direction. All effective plastic strain plots use the same colour scale (see caption to Fig. 4). Principal plastic strain plots show the maximum and minimum strains plotted at the centre of each element of the mesh, with line length indicating magnitude, line orientation showing the direction, and line colour indicating extension or contraction. Red lines show a maximum strain that is extensional, and pink lines show a minimum strain that is extensional. Blue lines show a maximum strain that is contractional, and grey lines show a minimum strain that is contractional. Case B line length is scaled to be ten times longer than the line length for Cases A and C. Principal stress plots show the magnitude and orientation of the stress tensors. Line colour for the stress tensors is coded such that blue indicates a maximum principal stress (geological s1) that is compressive, and grey indicates a minimum principal stress that is compressive. Red indicates a maximum principal stress that is tensile, and pink shows a minimum principal stress that is tensile.

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Fig. 6. Horizontal and vertical stress components for Case A loading configuration simulated at burial depths of 500 m (top) and 1000 m (bottom). Note the similarity of patterns, but the variations in magnitudes, and in terms of stress differences. Magnitudes of horizontal stress components vary from 180 MPa compressive to 20 MPa tensile. Magnitudes of vertical stress components vary from 85 MPa compressive to 20 MPa tensile.

magnitude of principal plastic strains are, on average, slightly smaller in the deeper case. These observations are consistent with the well-known increase in yield point that is associated with increasing confining pressure in laboratory tests. The increased rock strength at higher mean stress allows the material to carry more stress without yielding. Thus, the simulation model develops less plastic strain compared to an equivalent lower-mean-stress case, and higher-magnitude stresses develop in the still-elastic material, for the deeper-burial case. What this means is that more of the material remains elastic, and continues to share the load-carrying requirements, so that there is little in the way of concentration of loads (high stresses). When yielding takes place in a work-softening mode (i.e. dilation), the remaining materials must carry a greater share of the load, and hence large stresses that develop when that

happens (i.e. in the shallow-burial cases). These results indicate that, for otherwise similar boundary loads and conditions, the magnitude of the applied boundary pressure affects the magnitude of the stress and strain states that are developed, and the proportion of strain that is permanent. However, those changes in applied pressure have little effect on the patterns of stress and strain that develop, although in detail, these are determined by the feedback that occurs due to yielding. One of the problems in using such simple models is that they are not surrounded by other rock, so that when the fault undergoes displacement, the emerging fault faces are not supported. It is possible to create geomechanical models that are embedded in other rock and so avoid this problem. But that design is more complicated, and the models can become large and complex (and there are interactions with the additional materials that can impact the

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outcome). That situation is no longer at all like the simple, highly constrained models that we seek here. The main consequence of the protruding rock segments is the development of locally anomalous (mainly low-magnitude) stresses: in effect, the boundary loads are attempting to break off the sharp protrusions. These low stresses in those emergent sites do not appear to affect the behaviour of the rest of the model, but their possible effects cannot be demonstrably discounted. These simple simulations are probably not badly skewed because of the artefacts associated with the emergent block tips, so that the main behaviours can be used to assess the role of the loading configurations.

Open fracture prediction The 2D geomechanical simulations produce regions of permanently dilated rock (plastic volume strains indicating a volumetric increase). These dilated regions do not necessarily have macroscopic tensile stresses; in many cases, both principal stresses are compressive, although the values are seldom large. Poro-plasticity theory (Scofield & Wroth 1968; Atkinson & Bransby 1978; Jones & Addis 1986; Wood 1990; Coussy 1995; Cuss et al. 2003) explains the development of dilation in the presence of compressive stresses under certain mean stress and deviatoric stress conditions. In effect, this response is a material characteristic, and is well known in laboratory testing. As a general rule, conditions that result in brittle and transitional permanent deformations in the rock mechanics laboratory can develop dilational strains, and conditions that produce macroscopic ductile deformation can develop compactional strains (see Couples et al. 2007 and references therein). So the development of dilational strains in our simulations, even in the presence of compressional stresses, is exactly as expected for this material. This material characteristic means that stress sign alone is not a good indicator of the presence or absence of open fracturing. However, the direction and sign of the maximum and minimum plastic principal strains can be used to calculate permanent positive (lengthening) or negative (shortening) strain components, and also the dilation or compaction. Open fracture locations and directions can then be estimated on an element by element basis where dilation occurs. This can be done for cumulative strain (all steps), or broken down into increments, which give a better-resolved open fracture prediction. In the absence of a distortional (shear) strain, the principal strains completely describe the dilation, which can be resolved into two orthogonal components, which means that the pattern of open fractures can be derived. By assuming an average

fracture aperture, the fracture spacing can be estimated, or the estimate can assume a fracture intensity and derive the average apertures. However, distortional strain is normally present, and is almost always present in the fault models. Any open fracture prediction must also accommodate the shearing strains, as well as satisfying the permanent dilation or compaction, potentially by invoking shear fractures. The number of permutations that can resolve any particular strain state is large, but there is potential for limiting the solution space by reference to knowledge concerning the way that rocks typically respond. The entirety of the topic of down-scaling the strain is beyond the scope of this paper and is not discussed further here. The three different loading configurations examined here each result in quite different extensional principal strain distributions (Fig. 5). If these distributions were used as input to a fracture prediction, the results would be strongly contrasting for any given algorithm. In real situations, there will very probably be more information available to define the geologically correct (or geologically reasonable) loading configuration such as using kinematically informed geomechanical simulations; see Maerten & Maerten (2006) for examples of that approach. Other data that could help to suggest the correct patterns includes seismic anisotropy studies, used to infer open fracture distributions. Hall & Lewis (2007) and Hall et al. (2007) address the integration of geomechanical prediction of open fracturing and seismic anisotropy detection of open fracturing to produce a more robust fracture identification. By using the geomechanical simulations to predict something that is (partially) observable, it may be possible to gain additional understanding about the loading configuration, and thus the ultimate cause of the structure.

Discussion This paper is focused on showing how different loading configurations, whether taken from kinematic restorations or assumed, can produce very similar structures (i.e. the resulting geometry) that have significantly different stress and strain states, and very different distributions of permanently altered, and particularly dilated (open fractured) rock. In order to assess the relevance of these results, it is necessary to consider whether the processes represented here are likely to have real-world counterparts. First, we address whether the configuration of the intentionally simple models is actually too simple. Then we examine the potential impact of potentially too-simple loading: have we inadvertently forced the simulations to follow some path that they would not normally do under

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a less-restrictive loading arrangement? Although there are certainly some effects that result from the simplifications, we argue that the main points are not due to artefacts. Thus, we are able to develop some guidelines concerning the way that geomechanical simulations should be operated. The single-fault simulations presented in this paper are clearly unrealistic in their use of a preexisting, zero-displacement and undeformed fault plane. Such a starting point will be rare if it exists at all. A pre-existing frictional interface will also change the deformation development from that which will be produced when starting from an undeformed, continuous layer. The pre-existing interface will both ease the initiation of block slippage and will tend to force the fault angle to conform to that of the pre-existing plane. Simulations using a pre-existing frictional interface are very much simpler to run than those with an originally intact layer, but they are of no use unless they usefully represent the behaviour of real faulting systems. Most real fault zones develop both a continuum shear-zone and a discrete slip surface. The three cases reported here go on to develop complex patterns of damage and stress, with abundant evidence of feedback and self-organization. In effect, they develop a fault damage zone. They did not seem to need a prior pattern of damage in order to evolve their complex (but different) patterns. Thus, these simulations are not hampered by having to start with undeformed rock materials. Our models also start with two homogeneous and isotropic blocks of sandstone. A real rock

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would always have more heterogeneity in terms of primary depositional and diagenetic patterns. However, the simulation results reveal that at least Case A and Case C are capable of developing heterogeneity from initial homogeneity. Case B might well have developed additional complexity if that loading had been applied to a multi-layer arrangement, so that yielding in one layer propagated new localized deformations. In general, the simplification of using homogeneous materials does not appear to have a major impact. The next question is whether the models have developed realistically, or whether their responses are overly constrained by the loading configurations. The simulations would not run if the loading constraints were not mechanically valid, so in that sense the loading configurations represent a valid arrangement. But are they realistic for geological structures? The simulations produce a sheared zone adjacent to the slip surface. This zone contains thin strands that have varying amounts of strain, and the zones progressively develop more strain and thicken with continued displacement on the slip surface. These characteristics are very similar to conceptual models of fault damage zone evolution, as inferred from outcrop studies. Similar shear zones develop under experimental conditions in the rock mechanics laboratory in a range of rock types (Logan 2007). Lastly, the shear zones produced from originally intact layers show similar characteristics in terms of approximating the geometric pattern of damage zones (Fig. 7). Thus, we see a strong correspondence between what

Fig. 7. Development of damage zones in originally intact layers. (a) Backscattered SEM image of an experimental model (from Takahashi 2003). This model was deformed under confining pressure, with displacement along pre-cut surfaces in pieces of sandstone causing a shear zone to develop in the thin siltstone. Note how the siltstone has developed a series of thin lozenges of sheared material within the overall damage zone. (b) Composite photomicrograph of another experimental model, deformed by Shin-ichi Uehara in the rock mechanics laboratory at Heriot-Watt University. The sheared material is a Carboniferous mudstone collected from an outcrop exposure near South Queensferry, Scotland. This mudstone was loaded by means of steel blocks slipping along a lubricated pre-cut surface. Note again the development of lozenges of highly sheared material in the damage zone Minor amounts of material were lost in making the thin section. (c) Numerical simulation of the experimental results shown in (b), based on the same geomechanical simulator used to create the other results in this paper. Note, once again, the development of lozenges of highly strained material within the overall shear zone.

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the simulations are doing, and what happens in real materials. So, these loading configurations have been sufficiently permissive to allow the models to respond in a fashion that is as realistic as is the current understanding of the damage zone process. The simulations first develop localized strain in association with minor geometric irregularities on the slip surface. However, the same mesh was used for each case, so there is no inter-model mesh influence. Because the location of these nonplanarities is a result of the mesh generation, any effect can be thought of as a mesh dependence. But this is a different kind of mesh dependence from the effects of different element sizes. Using more and smaller elements has only a minor influence on the stress and strain state developed (results not shown). Using fewer and larger elements likewise has only a minor effect, until very large elements are used, at which point the model will not run. Based on these considerations, we conclude that our approach has not prevented the simulations from behaving in complex and geologically natural ways. It is possible that there are other behaviour modes that have been prevented by this design, but it seems that the models possess patterns that are very like those seen in nature and in experiments. Thus, the outcomes are thought to be sufficiently realistic to enable them to be used to make suggestions about how geomechanical simulations should be operated. So, how does one design good loading configurations? One way is to extract as much understanding as possible from kinematic studies. Lewis et al. (2004) and Maerten & Maerten (2006), illustrate the use of 2D and 3D kinematic restorations to derive displacements and pinning constraints that can be used to set up the loading configurations. The kinematic restorations have the added advantage that they also provide internally consistent prior structural geometries to be used when the simulation does not start from the completely undeformed state. However, the restorations do not produce a unique solution and geological common sense is always in order. That element of common sense should also include an appreciation of the extent to which the assignment of loading configurations can dominate the simulation outcome. One concern with simulations is how they might be evaluated in real-world use. Is it possible to compare the predicted/calculated result with actual stress measurements and to judge the value based on that? Each of the cases described here has the same far-field stress (in locations well away from the damage zone near the slip surface). For a comparison made at those positions, any of

the models is equally acceptable. Even if a stress measurement existed in the fault zone, could the models be distinguished? The authors suspect that this is impossible, due to the short length-scale of the variations in stress state in these models. Matching with actual stress data is probably not a good way to assess the correctness of a simulation outcome. Perhaps a better approach is to compare strain distributions and strain histories. However, even this is not easy to implement. The shape of the model at any deformation stage is associated with a bulk strain value, which can be resolved (using geological knowledge) into different features that comprise that strain. If an outcrop analogue can be studied, the deformation mechanisms operating to achieve the strain in the natural structure provide at least one solution to the inversion problem. If that solution agrees with a simulation model, then the simulation result can be queried to provide information about the mean and deviatoric stresses that cannot be obtained by other methods. Assembling this information into a coherent (and useful) analysis is not simple. Presently, it is only achievable by an experienced geologist, since only small portions of the task can be accomplished using existing software tools. A final comment is warranted. The geomechanical simulations all result in almost identical fault displacements and fault-block movements. This similarity in faulting and fault block translation occurs in spite of each simulation having different loading configurations, and in spite of the different stress and strain states that arise during that deformation sequence. This outcome is not as surprising as it might superficially appear to be. Consider the following. The mechanical loads applied to the boundaries of the geomechanical models have two components. One component represents the effect of burial depth, in the form of a pressure load (in our examples, this was consistent with 500 m to 550 m of burial and assuming a hydrostatic fluid pressure gradient). The other component represents the structural, or tectonic, element of the load. This structural loading is quite different in each case and, in energy terms, the quantity of energy associated with the applied loads is quite different. If this structural loading energy was instead represented by overburden, underburden and side-burden pressures, then the resulting mechanical states would make sense as having occurred at significantly different burial depths. In this context the variation in final stress and strain states is not surprising: more energy input would be expected to produce some combination of different stresses and different permanent strains in the rock.

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Conclusion Multiple geomechanical simulations of a simple faulting problem produce the same final deformed shape, but they reveal major differences in the patterns of evolved stress and strain. This outcome makes it very clear that the final (present) geometry is a very poor indicator of either the present internal stress and strain state (including dilated or compacted rock), or of the historical loads that created the structural feature. Therefore structural shape should not be used as a proxy in stress state interpretation and especially should not be used to predict the directions of local principal stresses, at least in and around significant structures. Geologically correct (or at least geologically reasonable) loading conditions applied to a suitable geomechanical model can contribute significantly to the estimation of the previous and in-situ stress- and strain-states and so to the prediction of the location and orientation of open fractures. This work follows on from geomechanical work completed as part of the RFI and BMFFFS projects. As such it is strictly independent of them but would not exist without them. We would therefore like to thank D. Barr of BP for his continued help and valuable comments throughout our RFI and BMFFFS research. Thanks are also extended the RFI Sponsors (BG Group, BP, ConocoPhillips, Hess, Kerr McGee, Shell, Statoil, Total and the UK Department of Trade and Industry). The Industry Technology Facilitator (ITF) is also acknowledged for establishing the Structurally Complex Reservoirs research programme within which the RFI and BMFFFS project work took place, as well as for their valuable input throughout the course of that research. We also thank both J. Olson and T. Christiansen for insightful reviews that considerably improved the final product.

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M ENETREY , P. & W ILLIAM , K. 1993. A triaxial failure criterion for concrete and its generalisation. Department of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder, CU/SR-93/12. S CHOFIELD , A. N. & W ROTH , C. P. 1968. Critical State Soil Mechanics. McGraw-Hill, New York. T AKAHASHI , M. 2003. Permeability change during experimental fault smearing. Journal of Geophysical Research, 108 (B5), 2234, doi:10.1029/2002JB 001984. W ONG , T.-F., B AUD , P. & K LEIN , E. 2001. Localized failure modes in a compactant porous rock. Geophysical Research Letters, 28, 2521– 2524. W OOD , D. M. 1990. Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press, Cambridge.

A damage domain approach to integration of geomechanics and seismic anisotropy for fractured reservoir characterization S. A. HALL1 & H. LEWIS2 1

Laboratoire 3S-R, Domaine Universitaire, BP53, 38041 Grenoble Cedex 9, France (e-mail: [email protected]) 2

Institute of Petroleum Engineering and ECOSSE, Heriot-Watt University, Edinburgh EH14 4AS, UK

Abstract: The concepts of damage mechanics are proposed as the logical basis for integration of seismic anisotropy based identification and geomechanics based prediction of subsurface fracturing. In such a context a damage tensor can be used to describe the evolution of (anisotropic) degradation of the elastic properties of a rock undergoing deformation. The concepts of damage mechanics are common to both geomechanical and seismic descriptions of rock elasticity but have not previously been connected. In geomechanical simulations of the evolution of geological structures, damage development can be predicted, described and recorded through a single damage tensor representation for each point in the model (with the inclusion of damage by a number of different mechanisms). With appropriate analysis, equivalent information may be determined from anisotropy analysis of seismic reflection data as the seismic wave propagation is sensitive to the total damage. Thus the proposed approaches for parameterization and modelling/analysis, using the damage domain, provide a common quantification of the damage (as detected using seismic data and predicted using geomechanical modelling) that permits integration of the two disciplines. This paper presents the damage-domain theory and linkage between the domains plus practicalities, with respect to both the geomechanical and seismic analyses, with illustration using a simple geomechanical model example.

Delineation and characterization of fracturing is important in the successful exploitation of many hydrocarbon reservoirs as fractures can significantly affect permeability and thus production, e.g. during horizontal drilling or water-flooding. Extensively reported surface observations suggest that fractures often exist in semi-ordered and semiparallel fracture sets and that they can be open under certain deformation histories and in-situ stress states. However, it is difficult to identify, quantify or characterize fracturing in the subsurface, by observation or by inference, especially since there may be significant spatial variations away from points of direct observation, i.e. boreholes (e.g. Hall et al. 2007). A possible means for characterizing subsurface open fracture distributions is through geomechanical modelling of the structural evolution of a reservoir and thus prediction of the positions of likely fracture zones. This in itself represents a significant challenge (e.g. Lewis et al. 2007) and also remains unverified by other data. Therefore, as with many reservoir characterization challenges, there is a need to use some form of remote sensing technique, such as seismic imaging, to provide information on the in-situ properties or conditions.

In particular, seismic anisotropy characterization using seismic reflection data has significant potential for fractured reservoir characterization. If preferentially aligned fracture sets are present in the subsurface at subseismic scale, they may produce seismic anisotropy. Thus, measurements of anisotropy from seismic data may be used to delineate fracturing and investigate their properties. As a result observations of azimuthal anisotropy in seismic reflection data are increasingly being used as a way to characterize fracturing in subsurface hydrocarbon reservoirs. The technique generally involves mapping variations with azimuth (of observation) of seismic reflection travel times or amplitudes (e.g. Lynn & Thomsen 1990; Lynn et al. 1996; Hall 2000; Hall & Kendall 2003; Gray et al. 2002) or shear wave splitting (e.g. Kendall & Kendall 1996; Potters et al. 1999). From these measurements, estimates of the magnitude and principal orientations of the in-situ seismic anisotropy can be derived. The common hypothesis is that these observed anisotropies reflect the in-situ fracturing, e.g. higher magnitude anisotropy indicates a greater degree of fracturing, which could either be a larger number of fractures or increased size of the fractures. However, such

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 173–183. DOI: 10.1144/SP292.10 0305-8719/07/$15.00 # The Geological Society of London 2007.

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interpretations are largely qualitative, ignore other possible causes of anisotropy (e.g. preferred orientation of grains and their contacts; Kendall et al. 2007) and assume a very simple assemblage of fractures. They are also difficult to confirm. Possible confirmation, e.g. of fracture orientation, can be acquired from borehole data, but these data are isolated one dimensional measurements, representing either single points or a series of points in potentially highly variable arrays of fractures. Therefore, although these observations might support the seismic anisotropy measurements, they may (rightly or wrongly) be contradictory solely as a result of the sampling, e.g. if there are widely spaced fractures the borehole might not intersect them, thus not providing a correct impression. Combining the methods of seismic anisotropy observation and geomechanical prediction could provide a better constraint on the most likely in situ fracture distributions. However, this requires a means to combine the two disciplines. Such integration is also of increasing interest in oil and gas production with the advent of time-lapse monitoring of reservoirs and the realization that geomechanical processes are a very important part of the reservoir evolution (e.g. Hall et al. 2005; Barkved et al. 2005; Hatchell & Bourne 2005; Main et al. 2007). Previous methods to link the domains of seismic (anisotropy) analysis and geomechanical modelling have generally been based around laboratory measurements or effective medium modelling. The former generally considers loading tests of laboratory samples (dimensions of centimetres) and measurements of ultrasonic wave velocities (wavelengths of millimetres) during the tests. The analysis then considers comparison of the bulk sample response with the velocity changes measured through the sample to construct empirical relations between the geomechanical evolution and the velocity variations (e.g. Fjaer 1999). Normally such measurements are not truly comparable due to the different spatial sampling of the two methods. Furthermore the observations possible from the laboratory are restricted to the damage type and length-scale that occur up to sample failure and so can not incorporate the effects of damage either at the much larger length-scales of the natural structures or in the form of fractures that are observed in situ. Alternatively, seismic (anisotropy) data can be inverted to derive parameters of idealized, effective-medium representations of the damage, giving parameters such as crack density or aspect ratio. However, this immediately assumes the damage is all of the same character and takes some idealized form. Furthermore, these

idealized forms are, in reality, no closer to the geomechanical model than are the original seismic data values. This paper proposes the use of the ‘damage domain’ as a common domain in which seismic and geomechanical approaches can be integrated on a better physical basis. This approach will provide a quantified analysis of seismic anisotropy data with respect to fracture-induced damage. The paper sets out the philosophy behind the approach and brings together the appropriate theory from each discipline to facilitate development in this multidisciplinary challenge. Initial advances in the application of the concepts are also presented. A rigorous derivation of appropriate damage laws is not the objective of this work and such laws require significant further developments for the case of reservoir fracture-damage evolution at both temporal and spatial geological scales. The background theory of the damage-domain approach is first presented from a mechanics perspective. This involves an explanation of how open fractures are manifest in terms of damage, i.e. how the mechanical characteristics of open fractures can be represented using damage mechanics. This theme is continued through demonstration of the commonality of the damage mechanics concepts for both seismic and geomechanical analyses. Simple model examples of the damage domain approach for open fracture prediction are presented, which is followed by a discussion on how the approach might be employed in practice to quantify seismic anisotropy observations. Open fractures exist at various length scales, but can in general be considered as localized permanent deformation with some degree of dilation or opening. As such they represent a strong discontinuity in displacement. This localized rock damage acts to modify both the flow and mechanical properties of the host medium. If a number of such localized damage features exist with a common alignment they can, together, give rise to anisotropic changes in the rock properties (e.g. seismic velocities and permeability), when regarded at a much larger length scale than the size of the individual damage features. Anisotropy is a continuum concept such that it arises due to the averaging over the domain of observation, such as a seismic wavelength, and individual fractures do not in themselves produce a true anisotropy in permeability or seismic velocities. The development of permanent deformation such as fractures may be described in terms of elasto-plasticity theory where the total strain (1 t) in the deforming medium is represented by the sum of the elastic (1 e) and permanent (plastic, 1 p)

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(a)

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(b)

Fig. 1. Partitioning of strains for: (a) an elasto-plastic model without evolving elastic properties; (b) an elasto-plastic damaging model. In each case the solid diagonal line descending on the right is a hypothetical (ideal) unloading/reloading path, which follows the gradient defined by the current elastic moduli. In (b) the additional dashed, descending line indicates the hypothetical unloading/reloading path if there had been no damage.

strain components (see Fig. 1a): 1 t ¼ 1 e þ 1 p:

(1)

Such an approach might be used to describe yield in laboratory samples. However, application to the development of fracture arrays, as are observed in outcrop and are expected in the subsurface, is not as straightforward. Problems arise since the fractures will be smaller than the geomechanical model element size and so are not represented by yield of the element as a whole. In fact such a representation, at the reservoir scale, is better suited to the modelling of large-scale localizations, such as faults, and associated zones of permanent deformation (e.g. Lewis et al. 2007). Away from the fault region little permanent deformation would be predicted in such models, even though fractures are expected to exist. This is because the ‘failure’ associated with the fracturing seen in situ is at a much smaller scale than the model element size and thus is not captured. An additional problem with standard elasto-plasticity approaches is that they do not predict any evolution of the elastic properties as a result of the permanent deformation. This is not consistent with observations of elastic wave propagation (both in situ seismic and laboratory ultrasonic data), in which fracturing is usually associated with reduced velocities across fracture zones and importantly can lead to the anisotropy that is of interest here. In the context of elasto-plasticity the evolution of the elastic properties with permanent deformation can be incorporated through ‘elasto-plastic coupling’. In such an approach the plastic strain is linked to the evolution of a fabric tensor that is

used to update the (anisotropic) elastic properties (e.g. Gajo et al. 2004). A more general approach, where elastic property (and yield-point) evolution is associated with pre- or post-yield deformation, is provided by continuum damage mechanics. The concepts of continuum damage mechanics are considered to have originated with the paper by Kachanov (1958), although the concepts of damage had been proposed much earlier, e.g. Palmgreen (1924), Miner (1945) and Robinson (1952) (see Lemaitre 1992). The theory has since been developed by various workers, especially in the field of the constitutive modelling of concrete, and good overviews can be found in Lemaitre (1992) and in Jirasek (2004). In damage mechanics the development of strain is assumed to be associated with the opening of cracks or fractures, which act to degrade the stiffness and strength of the medium. This can be represented in terms of a split of the recoverable part of the strain into initial elastic strain (e e) and damage strain (e d) (see Fig. 1b) such that: 1 t ¼ 1 e þ 1 d þ 1 p:

(2)

The damage component of the strain might be further split into various modes of damage depending on level of strain or the ratios of the principal strains. For example, an obvious split for an elastoplastic damage model would be damage that develops before yield, ‘elastic damage’ and damage that occurs after yield, ‘plastic damage’. The former, pre-yield damage, is the most likely to lead to distributed damage with a regularity that could give rise to anisotropy over distances large

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enough to be detected in seismic data. Damage associated with yield at the element scale is likely to be localized in fault zones (when considered at the scale of a hydrocarbon reservoir model). The important issue, when trying to link geomechanical and seismic approaches, is how the damage affects the elastic properties. It can be seen from Figure 1 that the effect of the damage strain is to change the gradient of the unloading leg of the stress –strain curve. The gradient of this unloading is controlled by the evolved elastic properties, which, when considered at the same scale and neglecting frequency dependent fluid movement effects, should be equivalent for both the geomechanical modelling and the elastic wave propagation. In continuum damage mechanics the degradation of the material properties is generally described by the damage parameter, D, which takes values between 0 and 1; 0 being used for a completely intact material and one for a material which is completely degraded. For example the linear elastic stress–strain relationship, sij ¼ Cijkl 1kl , after damage becomes, 0 sij ¼ (1 D)Cijkl 1kl ,

(3)

where sij denotes the stress tensor and e kl the strain tensor (strain-equivalence is assumed such that the effective and nominal strains are equal). In other words the changed elastic properties are described 0 0 0 0 ¼ (1 D)Cijkl so sij ¼ Cijkl 1kl . Here Cijkl by Cijkl is the tensor of elastic properties for the damaged 0 the equivalent tensor for the undamedium and Cijkl 0 can be anisotropic maged medium. Note that Cijkl before the evolution of damage due to the influence of other factors; for example lattice preferred orientation of constituent mineral crystal-axes and the shape preferred orientation of the grains and their contacts that might arise from the processes of sedimentation (e.g. Kendall et al. 2007). The relation given in (3) represents the simplest and most commonly used form of the damage mechanics parameterization with a single damage variable. A more general representation of damage, covering media that are anisotropic or become so as a result of the damage, requires a tensorial description to relate the damaged medium stiffness 0 0 , to the undamaged tensor, Cijkl . This is tensor, Cijkl a linear relation between two fourth-order tensors involving an eighth-order tensor, D8, with 38 elements (Cauvin & Testa 1999). Such a representation is clearly impractical for general use but Cauvin & Testa (1999) show that, based on the principal of strain equivalence and symmetries in D8, this general description can be reduced to

fourth-order tensors such that, 0 0 Cijkl ¼ (Iijrs Dijrs )Crskl ,

ð4Þ

where Iijrs ¼ 12 (dir d js þ dis d jr ) and dij is the Kronnecker delta. Through similar symmetry arguments to those used in the case of the stiffness tensor (e.g. Federov 1968; Hudson 1980), Cauvin & Testa (1999) show that the damage tensor has just 21 independent elements, although it does not possess the full symmetry of Cijkl since Dijkl = Dklij . With increasing symmetry in the damaged system the number of independent elements in the stiffness and damage tensors is reduced. Cauvin & Testa (1999) discuss the symmetry conditions for various cases that are of relevance to geological damage. For example, general transversely isotropic (TI) damage is described by five independent parameters, which reduces to two for the special cases of planar (PTI) or cylindrical (CTI) transverse isotropy. PTI media include those with a single set of rotationally invariant fractures (referred to, in seismic research, as horizontal transverse isotropy, HTI, if the fractures are vertical) or a set of stacked horizontal layers (generally called vertical transverse isotropy, VTI). For the case of HTI damage, only two of the stiffness moduli (those for longitudinal deformation along the x1 direction and for shear in the x1x2 and x1x3 planes) are affected by the damage. Thus there are only two non-zero, independent damage parameters for HTI fracturing and the damage tensor is given, after Cauvin & Testa (1999), (in reduced form) as, 0

DHTI ij

D11 B rb D11 B B rb D11 ¼B B 0 B @ 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 D66 0 0

1 0 0 C C 0 C C, 0 C C 0 A D66

(5)

where rb ¼ (nb =1 nb ) and nb is the Poisson’s ratio of the unfractured rock. The preceding discussion has provided the parameterization to describe the effect of damage on the elastic properties. To utilize this parameterization, within a geomechanical modelling approach, requires a means for prediction of the damage evolution with loading. Damage is essentially a manifestation of a part of the strain in the system and thus is best described as such, i.e. damage is some (non-linear) tensor function of the tensorial strain. However, this is only strictly applicable to monotonic loading. It is generally considered that new damage only occurs after the

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strain passes the previously achieved maximum strain. Reloading or unloading below the previous maximum strain level will be influenced by the previously developed damage but with no creation of new damage (there might also be some elastic changes of the existing damage, e.g. varying aperture; such effects can be addressed, for example, using the approach of Tod (2002) as demonstrated by Hall et al. (2007)). To include this constraint of an evolving ‘damage threshold’, a parameterization is required that records the previously attained maximum strain, e.g. Dijkl ¼ Dijkl (k), where k(t) ¼ max (1(t)) and t is some time function (although this is not necessarily the real time); e.g. Jirasek (2004). This can be generalized to kij for anisotropy. Within such a framework a damage-initiation strain may also be defined (i.e. the level of strain at which damage first starts to evolve). This can be extended to include multiple strain thresholds for different phases of damage evolution and, for example, might be linked to yield criteria to determine the onset of plasticity-induced damage. All the evolved damage, perhaps arising from different mechanisms, can be included in a single parameterization, which is important since the seismic wave propagation will be sensitive to the cumulative effect of all the damage. Damage evolution laws exist for various materials, most evidently in recent years for concrete; Lemaitre (1992), for example, provides a good summary of various damage laws. However, these laws have generally been developed to describe laboratory-scale or small-scale in situ damage in the form of cracks. Thus far there has been no real development of parameterizations for geological scale damage, which will involve cracks and fractures and perhaps the evolution of the former to the latter. Advances in this direction might be facilitated, for example, by developments in seismic-based research into effective medium descriptions of fractured rocks, e.g. Hudson et al. (1996, 1997). The damage mechanics representation outlined above allows description of the degradation of the elastic properties of a rock mass due to the evolution of fractures. Clearly, provided the scale under consideration is similar, this damage parameterization also describes the changes in seismic velocities through the fractured rock mass (since the 0 ); neglecting seismic velocities are functions of Cijkl the influence of frequency-dependent fluid movements. In fact the approach of Schoenberg & Sayers (1995), which is commonly used in seismic modelling and analysis, is based on the same principle of reduction in elastic properties due to the presence of fractures (although the connection to geomechanics and the evolution of

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damage has not before been noted). As such Schoenberg & Sayers (1995) give the elasticity tensor for an HTI fractured rock as, 0

lb ð1 dN Þ Mb ð1 dN Þ lb ð1 dN Þ B l ð1 d Þ M ð1 r 2 d Þ l ð1 r d Þ N b b b N B b b N B 2 B l ð1 d Þ l ð1 r d Þ M ð1 r b N b b N b b dN Þ CijHTI ¼ B B 0 0 0 B B @ 0 0 0 0 0 0 1 0 0 0 C 0 0 0 C C C 0 0 0 C, (6) C 0 mb 0 C C A 0 0 mb ð1 dT Þ 0

0

mb ð1 dT Þ

where Mb ¼ lb þ 2mb , rb ¼ lb =Mb ; nb =1 nb . The terms dN and dT are defined in terms of ‘additional fracture compliances’, ZN and ZT, for rotationally invariant planar cracks or fractures in an isotropic rock whose elastic properties can be described by the Lame´ parameters lb and mb: 0 dN ¼ ZN Mb =1 þ ZN Mb , 1 and 0 dT ¼ ZT mb =1 þ ZT mb , 1. The subscripts N and T refer to normal and tangential, i.e. ZN describes the additional compliance normal to the fractures and ZT relates to the additional shear compliance parallel to the fractures. dN and dT are essentially damage parameters and are equivalent to those in (5); dN ; D11 and dT ; D66 (thus multiplying the isotropic elasticity tensor, Cij0 , by ðI DHTI ij Þ, where I is the appropriate is the damage tensor from identity tensor and DHTI ij (5), gives CijHTI , as in (6)). In the following an example of the approach discussed above is presented using a simple model of damage development. The example given uses geomechanical simulation results adapted from the model presented by Couples (2005) of the evolution of a normal fault structure (see Fig. 2). The example chosen by Couples (2005), and used here with only a change of rock type to sandstone, has a very simple initial geometry to present the approach with minimal complexity. In both cases the model represents a rock (here, sandstone) layer with an initial thickness of 50 m and length 500 m subjected to extension. As a consequence of loading (see Couples (2005) and Fig. 2) a shear zone develops across the initially intact planar sandstone layer. The deformation law that this sandstone follows is very complex, as it is required to simulate the elastic, yielding and potential post-yield strain

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Fig. 2. Schematic of the finite element geomechanical model set-up, which represents an originally intact rock layer between two very stiff elastic layers that are cut by planar, uniformly dipping material discontinuities representing fault planes. Geometry and loading are after Couples (2005). In this work the originally intact layer is sandstone. Note that this figure shows only the central part of the geomechanical model; the full finite element mesh was much larger than this central zone to ensure that edge effects were avoided and that this central zone was loaded appropriately. The global loading, shown here at the margins of the figure for convenience, was: vertical displacement applied to the top; no applied loading at the base but free movement was allowed in the horizontal plane with the constraint of no vertical displacement; normal traction (pressure) applied to the sides.

hardening or softening behaviour of the natural rock. This geomechanical complexity leads to an equivalent complexity in the deformation distribution. The damage evolution, for this example, is calculated from the strains developed in the geomechanical model. Such an approach is perhaps practical for use with commercial geomechanical simulation software, but the damage evolution should be (and will in the future be) integrated into the constitutive law(s) of the simulation. The damage evolution law is described below. A simple damage model is considered with the following characteristics. Damage evolves by the

growth of cracks or fractures due to dilation (damage due to compaction is currently not considered and it is assumed that there are no preexisting cracks or fractures). A proportion of the evolved positive volumetric strain (dilation) is attributed to increasing the damage volume. The cracks/fractures created in the dilation are assumed to always be oriented perpendicular to the direction of maximum extension (following the so-called rotating crack concept). The damage is also assumed to form as open circular cracks such that dN and dT (or D11 and D33) are described by the U11 and U33 parameters of Hudson (1980)

DAMAGE DOMAIN FRACTURE CHARACTERIZATION

(which uses the results of Eshelby 1957) within the framework of Hall (2000) (see also the Appendix of Hall et al. 2007). The cracks are assumed to be in a drained state (i.e. fluids can pass freely in and out of the cracks during loading). The hydro-mechanical effects of the fluids in the cracks could be different for geomechanical and seismic loads and so it may be necessary, in the future, to include some form of ‘fluid influence’ factor. With this description the only free parameter in the model is the aspect ratio of the cracks or fractures (i.e. the ratio of the crack aperture and diameter). Changing this parameter provides a means to describe different types of damage, e.g. damage that evolves during ‘elastic’ loading is likely to involve grain-scale cracks with a larger aspect ratio than long thin fractures that might occur due to ‘plastic’ deformation. For this reason, in the model presented below the damage evolved due to plastic and elastic strains are assumed to have different characteristics. Values of 0.1 and 0.001 have been chosen for the aspect ratios of cracks and fractures respectively. Once the damage has evolved it is assumed to maintain its initial characteristics (e.g. aspect ratio) and the effects of subsequent loading (e.g. elastic opening and closing of the crack apertures), other than the creation of new damage, are not included. Such effects, and the presence of other pre-existing cracks or fractures, can easily be included though a non-linear elastic approach such as that of Tod (2002), as presented by Hall et al. (2007). Figures 3 and 4 show the evolved total, elastic and plastic strains for load steps 5 and 10 of the geomechanical simulation, which equate to 1 m and 2 m total shortening in the horizontal direction. Even at this early stage in the loading, the total

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strains have a large plastic component and are concentrated in the fault zone, although small elastic strains can be seen, both within and away from the fault. Figures 5 to 7 present the evolved damage at these two load steps, calculated as described above, for three different scenarios: (i) only ‘plasticdamage’ evolution in the form of fractures with an aspect ratio of 0.001; (ii) ‘elastic-damage’ and ‘plastic-damage’ both with a crack or fracture aspect ratios of 0.001; (iii) ‘elastic-damage’, with a crack aspect ratio of 0.1, and ‘plastic-damage’, with a fracture aspect ratio of 0.001. The models show greater levels of damage development around the evolving fault, as would be expected and in correspondence to the higher strains. In fact the damage in the fault zone is very high, which would lead to very low seismic velocities (it is likely that there would be little transmission of seismic energy through such regions). Little damage has evolved away from the fault zone, except near where the fault meets the confining blocks. At these points the high level of damage in the layer would lead to large contrast in elastic properties that might be detected in seismic reflection amplitudes. In the model where the evolved damage evolution due to elastic and plastic strains have the same aspect ratio (Fig. 6), additional damage is seen away from the fault zone due to the elastic damage. The magnitude of this damage is small but might be detectable in seismic anisotropy data. In particular shear-wave data might be sensitive to this damage since the value of dT is greater (as it is in general in these models, see below). The model with different damage characteristics for the elastic and plastic components (Fig. 7) shows very similar results to the model

Fig. 3. Maximum and minimum principal strains developed in the geomechanical simulation at load step 5 (total horizontal shortening of 1 m). The total, elastic and plastic components of strain are presented in columns from left to right respectively. The maximum principal (positive, more-dilatational) strains are presented in the first row and the minimum (negative, more-shortening) in the second row. The colour scales show the values of strain as a decimal value (i.e. 1.0 ; 100%). X and Y axis dimensions are metres.

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Fig. 4. Maximum and minimum principal strains developed in the geomechanical simulation at load step 10 (total horizontal shortening of 2 m). Rows and columns are as in Figure 3.

with just plastic damage (Fig. 5). This is because the effect of the higher aspect ratio cracks is much less than the lower aspect ratio fractures and so their contribution to the total damage is insignificant. A key general character of the results is the consistently (and perhaps unreasonably) large value of dT. This arises from the fact that the cracks and fractures are modelled as being open and filled with fluid that is free to move. The damage model might be made more geologically representative by describing more fracture-like damage, e.g. with points of contact along the fracture length; this could be possible using the results of Hudson et al. (1996, 1997). Such a parameterization also allows different types of damage to be described in terms of the fracture spacing for example. The

damage might also be modelled with more representative filling material (described by their bulk and shear moduli). With more realistic models such as these it will be important to improve the definition of the aspect ratio or length and aperture scales of the different types of damage based on actual observations. The commonality of the damage representation for geomechanical and seismic analyses can allow the ‘damage domain’ to be utilised to more directly integrate seismic anisotropy observations and geomechanical predictions of fracturing. Whilst the preceding discussions have outlined a methodology to predict damage in geomechanical simulations, an approach is also required to derive equivalent quantification of the in situ damage

Fig. 5. Evolved damage at load step 5 (left) and 10 (right) for a model with just ‘plastic-damage’ and a fracture aspect ratio of 0.001. Colour bars show the magnitude of the damage: upper plots, dN; lower plots, dT.

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Fig. 6. Evolved damage at load step 5 (left) and 10 (right) for a model with ‘elastic-damage’ and ‘plastic-damage’, both with a crack/fracture aspect ratio of 0.001. Colour bars show the magnitude of the damage: upper plots, dN; lower plots, dT.

from seismic anisotropy data. In the following, this latter issue is briefly discussed and will be presented in more detail in a forthcoming paper. As outlined in the introduction appropriate seismic data (multi-offset and -azimuth or multicomponent data) can be analysed to provide estimates on in situ seismic anisotropy. Such estimates might then be interpreted in terms of fracture

properties. However, such analyses normally have implicit in their approaches a priori assumptions on the nature of the fracturing and the subsequent interpretation is usually based on idealized representations of the damage, giving parameters such as crack density or aspect ratio of ellipsoidal cracks. Schoenberg & Sayers (1995) state that ‘What can be obtained from seismic data is the

Fig. 7. Evolved damage at load step 5 (left) and 10 (right) for a model with ‘elastic-damage’ with a crack aspect ratio of 0.1 and ‘plastic-damage’, both with a fracture aspect ratio of 0.001. Colour bars show the magnitude of the damage: upper plots, dN; lower plots, dT.

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orientation of the dominant set of fractures and some estimate of the fracture compliances relative to the compliance of the complete fractured rock. The estimation of the shape and size distribution is beyond the capability of long wavelength seismic data.’ Thus the most information that can be derived from seismic data about the fracturing is their oriented degrading effect on the elastic properties, i.e. the damage parameters. As such, direct inversion of the damage parameters from seismic data is a more appropriate approach for a number of reasons. First, idealized representation of damage can be largely avoided in the seismic data reduction since fewer assumptions need to be made about the nature of the fractures and their effect on the seismic properties (such assumptions are instead contained within the associated geomechanical model, within which far more appropriate constraint on fracture type is possible). Secondly, since the damage parameters can only take values between 0 and 1, probabilistic approaches can be more easily employed to search the model space (and also to allow the integration of different data types). Finally, the outputs from the inversion are damage parameters that have direct geomechanical relevance and are equivalent to those that can be predicted using the geomechanical simulations, as outlined earlier. Therefore damage inverted from seismic data, using such a direct inversion for damage, could be compared directly to damage predictions using geomechanical simulations in a quantitative statistical way. An alternative approach might be to compare seismic anisotropy signatures (e.g. seismic amplitude variation with offset and azimuth) with equivalents predicted from the simulated damage distributions. However, this approach requires a priori assumptions on the nature of the anisotropy signature in the seismic data analysis (e.g. a cos2f variation in reflection amplitudes with azimuth; see Hall & Kendall 2003), plus yields a quantification in terms of a number of non-physical quantities. The direct damage inversion approach of multioffset and -azimuth seismic data and its potential advantages will be presented in a forthcoming paper. In this associated work the damage inversion approach has been successfully demonstrated for synthetic data examples based on real fracture parameters such that, even with a certain degree of noise, damage parameters can be derived (J. Wookey, pers. comm.). Application to real data is currently hampered by various data processing issues and in particular the acquisition geometries currently used to acquire such data; the same issues also affect more common seismic anisotropy analysis procedures but have not generally been recognized. Therefore additional work is required for the application to real data, which will thus be

followed by development of statistical matching procedures for the data derived damage and simulation results. The key contribution of this paper is the presentation of concepts known and used in mechanics that could be used to address and link seismic anisotropy observations and geomechanical modelling of fractured reservoir evolution. A common link between geomechanical and seismic analyses, with respect to the identification and characterization of open fracture networks, has been proposed based on a damage tensor description of the degradation of elastic properties. The identification of such a link provides a means to combine the two disciplines. Thus this paper represents a starting point for future development of integrated approaches of prediction, by geomechanical modelling of geological structure evolution, and detection, by seismic anisotropy analyses, of fracture damage. Such an approach could provide improved understanding of the current-day open fracture state and thus allow improved prediction, by forward modelling, of geomechanical evolution due to hydrocarbon production (with integrated monitoring by seismic methods). However, to realize this aim requires accurate models for the geomechanical evolution of the reservoir structure. Lewis et al. (2007) addresses some of the issues involved in this challenge. Damage parameterization does not fully avoid the need to use some form of idealized representation of the damage as eventually this is always necessary. However in using the proposed approach, it is not necessary to involve an idealized representation in the seismic data reduction; instead such assumptions are associated with the geomechanical modelling, within which far more appropriate constraint on fracture type is possible. Importantly, the parameterization and approach allow the two disciplines, geomechanical modelling and seismic anisotropy analysis, to be compared in the same framework and thus they may be integrated and the insight from one may be used to support the inferences from the other. Furthermore the parameterization provides a number of advantages for the inversion of seismic data that will be discussed further in a forthcoming paper on the direct damage inversion approach. This work has been carried out in part through the sponsorship of the Robust Fracture Identification (RFI) project at Heriot-Watt University that was brokered by the ITF (Industry Technology Facilitator). The sponsors of the project are acknowledged for their financial support and permission to publish: BG Group, BP, ConocoPhilips, Hess, Kerr-McGee, Shell, Statoil, Total and the UK-DTI. S. Hall was also supported by a Marie Curie Intra-European Individual Fellowship within the 6th European Community Framework Program (project, iGEM) for some of the duration of this work. Thank you

DAMAGE DOMAIN FRACTURE CHARACTERIZATION also to S. Tod and A. Batchelor for their helpful reviews and to D. Barr and co-editors for coordinating this volume.

References B ARKVED , O. I., K RISTIANSEN , T. & F JAER , E. 2005. The 4D seismic response of a compacting reservoir examples from the Valhall field, Norway: In: 75th Annual International Meeting Technical Program, Expanded Abstracts, Society of Exploration Geophysicists, Tulsa. C AUVIN , A. & T ESTA , R. B. 1999. Damage mechanics: basic variables in continuum theories. International Journal of Solids and Structures, 36, 747–761. C OUPLES , G. D. 2005. Seals: the role of geo-mechanics. In: B OULT , P. & K ALDI , J. (eds) Evaluating Fault and Cap Rock Seals. American Association of Petroleum Geologists Hedberg Series, 2, 87– 108. E SHELBY , J. D. 1957. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society of London, A241, 376–396. F EDEROV , F. I. 1968. Theory of elastic waves in crystals. Plenum Press, New York. F JAER , E. 1999. Static and dynamic moduli of weak sandstones. In: A RMADEI , B., K RANZ , R., S COTT , G. & S MEALIE , P. (eds) Rock mechanics for industry. Balkema, Roterdam, 675–681. G AJO , A., B IGONI , D. & M UIR W OOD , D. J. 2004. Multiple shear band development and related instabilities in granular materials. Journal of Mechanics and Physics of Solids, 52, 2683– 2724. G RAY , D., R OBERTS , G. & H EAD , K. 2002. Recent advances in determination of fracture strike and crack density from P-wave seismic data. The Leading Edge, 21, 280. H ALL , S. A. 2000. Rock fracture characterization and seismic anisotropy: application to ocean bottom seismic data. Ph.D. thesis, University of Leeds. H ALL , S. A. & K ENDALL , J-M. 2003. Fracture characterization at Valhall: application of P-wave AVOA analysis to a 3D ocean-bottom data set. Geophysics, 68, 1150–1160. H ALL , S. A., M AC B ETH , C., B ARKVED , O. I. & W ILD , P. 2005. Cross-matching with interpreted warping of 3D streamer and 3D OBC data at Valhall for time-lapse assessment. Geophysical Prospecting, 53, 283–297. H ALL , S. A., L EWIS , H. & M ACLE , X. 2007. Improved seismic identification of inter-fault damage via a linked geomechanics-seismic approach. In: L EWIS , H. & C OUPLES , G. (eds) The Relationship between Damage and Localization. Geological Society, London, Special Publications, 289, 187–207. H ATCHELL , P. & B OURNE , S. J. 2005. Measuring reservoir compaction using time-lapse time-shifts. In: 75th Annual International Meeting Expanded Abstracts Technical Program, Society of Exploration Geophysicists, Tulsa, 2500– 2503. H UDSON , J. A. 1980. Overall properties of a cracked solid. Mathematical Proceedings of the Cambridge Philosophical Society, 88, 371 –384. H UDSON , J. A., L IU , E. & C RAMPIN , S. 1996. Transmission properties of a plane fault. Geophysical Journal International, 125, 559– 566.

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H UDSON , J. A., L IU , E. & C RAMPIN , S. 1997. The mean transmission properties of a fault with imperfect facial contact. Geophysical Journal International, 129, 720– 726. J IRASEK , M. 2004. Non-local damage mechanics with application to concrete. In: V ARDOULAKIS , I. & M IRA , P. (eds) Failure degradation and instabilities. Revue Franc¸aise de Ge´nie Civil, 8, 683– 707. K ACHANOV , L. 1958. Time of the rupture process under creep conditions. Izvestiya Akademiia Nauk SSSR, 8, 26–31. K ENDALL , R. R. & K ENDALL , J-M. 1996. Shear-wave amplitude anomalies in south-central Wyoming. The Leading Edge, 15, 913–920. K ENDALL , J.-M., F ISHER , Q. J., C OVEY C RUMP , S. ET AL . 2007. Seismic anisotropy as an indicator of reservoir quality in siliciclastic rocks. In: J OLLEY , S. J., B ARR , D., W ALSH , J. J. & K NIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 123–136. L EMAITRE , J. 1992. A Course on Damage Mechanics. Springer-Verlag, Berlin. L EWIS , H., H ALL , S. A., G UEST , J. & C OUPLES , G. D. 2007. Kinematically-informed geomechanical simulations of structural evolution: the role of loading configurations. In: J OLLEY , S. J., B ARR , D., W ALSH , J. J. & K NIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 159–172. L YNN , H. B. & T HOMSEN , L. 1990. Reflection shearwave data collected near the principal axes of azimuthal anisotropy. Geophysics, 55, 147–156. L YNN , H. B., S IMON , K. M., B ATES , C. & V AN D OK , R. 1996. Azimuthal anisotropy in P-wave (multiazimuth) data. The Leading Edge, 15, 923 –928. M AIN , I. G., L I , L., H EFFER , K. J., P APASOULIOTIS , O., L EONARD , T., K OUTSABELOULIS , N. C. & Z HANG , X. 2007. The Statistical Reservoir Model: calibrating faults and fractures, and predicting reservoir response to water flood. In: J OLLEY , S. J., B ARR , D., W ALSH , T. J. & K NIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 469– 482. M INER , M. A. 1945. Cumulative damage in fatigue. Journal of Applied Mechanics, Transactions – American Society of Mechanical Engineers, 12, A159– A164. P ALMGREEN , A. 1924. Die Lebensdaner von Kugellagern. Zeitschrift de Vereines Deutsches Ingeniure, 68, 14. P OTTERS , J. H. H. M., G ROENENDAAL , H. J. J., O ATES , S. J., H AKE , J. H. & K ALDEN , A. B. 1999. The 3D shear experiment over the Natih field in Oman. Reservoir geology, data acquisition and anisotropy analysis. Geophysical Prospecting, 47, 637– 662. R OBINSON , E. L. 1952. Effect of temperature variation on the long-time rupture strength of steels. Transactions of American Society of Mechanical Engineers, 74, 777– 781. S CHOENBERG , M. & S AYERS , C. M. 1995. Seismic anisotropy of fractured rock. Geophysics, 60, 204 –211. T OD , S. R. 2002. The effects of stress and fluid pressure on the anisotropy of interconnected cracks. Geophysical Journal International, 149, 149–156.

Testing the predictive capability of curvature analyses S. BERGBAUER BP Exploration, Farburn Industrial Estate, Dyce, Aberdeen AB21 7PB UK (e-mail: [email protected]) Abstract: The curvature of geological surfaces has been used to predict areas of elevated strain, deformation and fracture density. The research presented here tests if and to what extent a geometric measure such as normal surface curvature can be used as a proxy for deformation by comparing field observations with geometric modelling results. This is achieved by first quantifying fracturing in outcrop and then by performing a curvature analysis of the deformed bedding surface. This research suggests that curvature analysis by itself does not allow for the prediction of deformation: fracture density in the Emigrant Gap anticline is unrelated to horizon curvature, and synfolding fractures are aligned with prefolding fractures instead of the directions of principal curvature. Normal surface curvature by itself has only limited value in predicting strain or fracture density; however, surface curvature is a unique descriptor of shape. Describing the geometry of a horizon quantitatively is an essential first step when attempting to compare physical and numerical models with natural surfaces. The tools presented here allow for unique descriptions of three dimensional folded surfaces that are based on the normal surface curvature, and they provide the necessary mathematical rigour and flexibility to allow for descriptions of non-cylindrical folded surfaces.

For over a century, structural geologists have worked on elucidating the mechanisms by which sedimentary strata are deformed during folding (e.g. Gilpin 1883; Cloos 1936; Ramberg 1961; Ramsay 1967; Stearns 1968; Johnson 1977; Davis 1979; Treagus & Treagus 1981; Suppe 1983; Dunne 1986; Ramsay & Huber 1987; Suppe & Medwedeff 1990; Johnson & Fletcher 1994; Bobillo-Ares et al. 2000). A key element of these structural investigations is the quantitative description of the geometrical aspects of folded sedimentary strata. The geometry, taken from field or seismic data, is used to create idealized fold models based on continuum mechanics principles. Results of these model experiments, whether physical or numerical, are compared to the descriptions of natural folds to test hypotheses about the folding mechanisms. This paper challenges various geometrical measures of folds in common use and finds them inadequate to describe the unique spatial variations in fold shape. We argue that an accurate description of the geometry of folded surfaces is a prerequisite to all model studies and point out that modern technological innovations such as LiDAR, GPS, 3D seismic reflection and 3D scanning provide data that warrant a more rigorous approach to the description and subsequent geomechanical analysis of folds. Differential geometry is a mathematical tool for the quantitative description of curves and surfaces (e.g. Struik 1961; Lipschutz 1969; Stoker 1969). Geological structures such as slickenlines, metamorphic lineations, surface intersections, plumose

structures and rib marks, as well as bedding, faults, fractures, metamorphic foliations, sedimentary boundaries and unconformities are inherently three-dimensional and curved, so differential geometry is the appropriate tool for their quantitative description (Chapter 3 in Pollard & Fletscher 2005). Although these structures are commonly described as ‘lineations’ and ‘planes’, and field measurements of trend and plunge or strike and dip imply rectilinear and planar forms, this oversimplified approach to description and data gathering is not sufficient for a rigorous quantitative description. Tools and concepts of differential geometry such as the surface normal vector, tangent vector, and binormal vector, as well as the spatial changes of these quantities as expressed by the concepts of torsion and curvature provide the quantitative rigour. Despite the fact that differential geometry was a well-developed discipline more than one hundred and fifty years ago (e.g. Gauss 1827) when structural geology was in its infancy, it has found only limited application in the quantitative description of geological curves and surfaces. Apart from describing geological surfaces (e.g. Bengtson 1981; Lisle 1992; Lisle & Robinson 1995; Roberts 2001; Bergbauer & Pollard 2003; Bergbauer et al. 2003; Pollard & Fletscher 2005; Mynatt et al. 2007), most publications focused around quantifying the degree of deformation or strain in deformed strata (e.g. Bevis 1986; Ekman 1988; Lisle 1994; Nothard et al. 1996; Samson & Mallet 1997) and predicting fracture orientations and densities in bent strata (e.g. Murray 1968;

From: JOLLEY , S. J., BARR , D. WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 185–202. DOI: 10.1144/SP292.11 0305-8719/07/$15.00 # The Geological Society of London 2007.

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Thomas et al. 1974; Lisle 1994; Fischer & Wilkerson 2000; Hennings et al. 2000). In most cases these investigators have applied their analyses to seek answers regarding the state of deformation, or the degree of fracturing, associated with folded and domed strata. However, results of such analyses have been somewhat ambiguous. Whereas some authors concluded curvature analysis is a valid tool (e.g. Ewy & Hood 1984; Lisle 1994; Hennings et al. 2000) others question its predictive capability (e.g. Schultz-Ela & Yeh 1992; Jamison 1997). For example, Bellahsen et al. (2006) identify four fracture sets from detailed mapping at Sheep Mountain Anticline, Wyoming, and point out that the oldest of these predates folding and strikes oblique to the fold trend; the next younger set correlates in strike with the Laramide compression direction related to folding; the next younger set correlates in strike with the fold trend and is localized in the hinge region; and the youngest set strikes parallel to the oldest set, but is vertical in the dipping beds of the back limb rather than perpendicular to bedding. Of these four sets only the third may be unambiguously associated in terms of fracture density and orientation with the greater curvature of beds in the fold hinge. The most common reason for calculating surface curvature is to predict areas of high fracture density as well as the orientations of fractures that formed during deformation of strata. Murray (1968) found a relationship between fracture permeability and curvature. He argued that fracture porosity is related to the product of bed thickness and curvature, and that fracture permeability is related to the third power of this product. Thomas et al. (1974) proposed an approach, based on thin plate theory, to predict the location of structural discontinuities where maximum principal curvatures are elevated. Despite these early attempts to derive fracture predictions through the relationship of curvature and stress –strain, others have argued for a direct relationship between fracture density and surface curvature (Schultz-Ela & Yeh 1992; Ericsson et al. 1998; Stewart & Podolski 1998). These authors argued that zones of high fracture density should coincide with areas of elevated curvature. Lisle (1994) presented a similar argument relating high Gaussian curvature with areas of high fracture density. Whereas Schultz-Ela & Yeh (1992) concluded that only moderate curvatures correlate well with productive fracture zones, but highest curvature magnitudes do not, Lisle (1994) and Ericsson et al. (1998) argued for the predictive capability of their approaches. Trying to predict the orientation of joints, Fischer & Wilkerson (2000) modelled the temporal evolution of a fold and argued that if joints formed during deformation, they would parallel the direction of minimum

ε bend = –k∗y

Mode I cracks

n e u tr

a l s u rfa c e

y

Fig. 1. Thin plate theory. The pure bending strain (1bend) is linearly related to the surface curvature (k) and the distance from the neutral surface (y). If joints formed due to the pure bending of a layer, they would parallel the axis of zero (minimum) curvature.

curvature. Finally, Hennings et al. (2000) tested a variety of surface attributes extracted from seismic data in their ability to predict the location and intensity of observed fracturing of an exposed Laramide fold. They concluded that the rate of dip change and Gaussian curvature relate best with their fracture density observation. The techniques described above are now widely used in the hydrocarbon industry to predict subseismic fracturing. The theory of pure bending of a thin plate (e.g. Timoshenko & Woinowsky-Krieger 1959) appears to lend some credibility to the idea of a simple relationship between surface curvature and deformation as it relates the bending strain in a thin plate with the product of curvature of the neutral surface and vertical distance from the neutral surface (Fig. 1). However, if applicable to describing the state of deformation of folded strata, assumptions inherent to the thin plate theory need to be applied to the layered strata as well.

Tools from differential geometry for the description of surfaces Natural surfaces may be idealized either by continuous functions, or characterized by samples at points on irregular (geological) or regular (seismic or scanned) grids. In either case, the surface can be defined as: r(x, y) ¼ xex þ yey þ z(x, y)ez ,

(1)

where r is the position vector of every point on the surface, x and y are two independent parameters, z(x, y) is a continuous function or a set of elevation measurements with respect to the x –y parameter

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plane. ex, ey, and ez are the unit vectors in the direction of the Cartesian coordinate system axes, and equation (1) is the parametric form of surfaces considered here. Two partial differential equations, the so-called First and Second Fundamental Forms, uniquely describe the shape of a surface in 3D Euclidean space (Lipschutz 1969, p. 171). The first fundamental form, I, is calculated from the square of an arclength and provides the ‘yard-stick’ on a curved surface; it can be used for the calculation of angles, distances, and areas: 2

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coefficients of the first fundamental form: ez @z ex @z ey @x @y N ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ : axx ayy a2xy

(3b)

Changes in orientation of N with position thereby provide information on the local shape of the surface: II ¼ dr † dN ¼ bxx dx2 þ 2bxy dxdy þ byy dy2 :

2

(4a)

I ¼ dr † dr ¼ axx dx þ 2axy dxdy þ ayy dy : (2a) The coefficients of the first fundamental form (aij) are sometimes referred to as the metric coefficients. These coefficients are calculated from scalar products of the first partial derivatives of the parametric equation (1) for the surface:

Using the parametric equation (1), the coefficients of the second fundamental form are:

bxx ; byy

axx ¼ ayy ¼

@r @r @r @r † , axy ¼ † , and @x @x @x @y @r @r † , @y @y

(2b)

which reduce to scalar quantities that are products of the partial derivatives of the elevation z(x, y):

axx ayy

@z 2 @z @z , and ¼1þ , axy ¼ @x @x @y 2 (2c) @z ¼1þ : @y

The second fundamental form, II, and its coefficients quantify how the unit normal vector N changes orientation on a curved surface. The unit normal vector N to the surface is given by the cross product of two tangent vectors (t x and t y), which describe the tangent plane to the surface at a point, divided by the magnitude of this product (Lipschutz 1969, p. 175). N is defined as: @r @r tx ty @x @y ¼ : N ; tx ty @r @r @x @y

(3a)

The components of the vector N are calculated from the first partial surface derivatives and the

@2r @2r † N, and † N, bxy ; 2 @x @x@y

@2r ; 2 † N, @y

(4b)

which reduce to scalar quantities that are proportional to the second partial derivatives of the elevation z(x, y): @2z 2 @x bxx ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ , axx ayy a2xy @2z @x@y bxy ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ , and axx ayy a2xy

(4c)

@2z @y2 byy ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ , axx ayy a2xy These coefficients are sometimes referred to as the curvature coefficients. Coefficients of the two fundamental forms vary depending on the direction and coordinate system in which they are calculated on the surface. However, the fundamental forms (as opposed to the individual coefficients) are invariant with respect to the choice of parameterization and the coordinate system (Lipschutz 1969, p. 172, 175). Here, the coefficients of the two fundamental forms are calculated at every grid point using a finite difference scheme (e.g. Ames 1992; Bergbauer & Pollard 2003). The only limitations are the precision of the data, the spacing of the sample grid, and the necessity that surface parameterizations be single-valued. Examples of multiple

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values for z(x, y) as in overturned folds or thrust faults can be analysed as separate patches. The two fundamental forms provide a mathematicallysufficient, quantitative description of the shape of the surface at every grid point. In principle, knowledge of the first and second fundamental forms is all that is required to describe a folded surface. Similar to the concepts of stress or strain, which each require six independent quantities (the components) for a complete description of the state at a point, a complete description of a surface at a point requires the six coefficients of the two fundamental forms. Also, similar to the spatial variations of stress or strain in a three-dimensional volume, these coefficients vary depending on the location on the surface in three-dimensional space. Rather than providing renderings of all six stress components throughout a volume, a state of stress is presented more conveniently by providing the three principal magnitudes and their directions. In differential geometry, because of their differential nature, displaying the two fundamental forms themselves is not practical. One could provide maps of the six coefficients; however, for applications that are mainly concerned with describing the shape of a surface, a measure called the normal curvature is generally calculated, and its two principal values and their orientations are mapped onto the surface to convey information on the shape of that surface. From the two fundamental forms, the normal curvature can be calculated (Lipschutz 1969, p. 180): kn ¼

II bxx dx2 þ 2bxy dxdy þ byy dy2 : ¼ axx dx2 þ 2axy dxdy þ ayy dy2 I

(5)

The magnitude of the normal curvature at a point on a surface depends on the direction in which it is calculated, and it varies smoothly with direction according to Euler’s equation from minimum to maximum values at 908 intervals (Lipschutz 1969, p. 196). Thus, a convenient way of representing the normal curvature at any point is by providing the two principal values, Kmin and Kmax, and their directions, which are orthogonal (Lipschutz 1969, p. 181). From the two principal values, the Gaussian (G) and mean (M) curvatures can be calculated at every grid point (Lipschutz 1969, p. 184):

Fig. 2. Six fundamental geometries can be distinguished based on the signs of Gaussian (G) and mean (M) curvatures. Geometries with G ¼ 0 (plane, antiform, synform) are called cylindrical (modified from Roberts 2001).

surfaces (Fig. 2). Apart from discerning areas that are shaped like these six surfaces (plane, antiform, synform, basin, dome, saddle), shape-curvature provides a quantitative method for the discrimination of areas that resemble the cylindrical shapes shown in Figure 2 (G ¼ 0) from non-cylindrical shapes (G = 0). A cylindrical fold is a fold made of a straight line that is moved parallel to itself along a curve in space (Marshak & Mitra 1988, p. 157), and therefore one of the two principal curvature magnitudes and subsequently the Gaussian curvature G of a cylindrical fold is always zero. Although zero Gaussian curvature is a necessary condition of cylindrical folds, not all folds that have zero Gaussian curvature are cylindrical (such as conical folds). In the context of second order surfaces, conical folds would resemble domal or basin-like structures. Shape curvature can be used to calculate the curvature magnitudes that depart from a perfectly cylindrical fold shape, thus allowing for a quantification of ‘non-cylindricity’ of the structure. Moreover, shape-curvature provides information on the local closure direction of the folded surface. This concept in combination with locations of zero dip can be used for the automatic evaluation of hydrocarbon-trapping structures, their spillpoints, and trapped volumes.

G ¼ Kmax † Kmin

(6)

Use of curvature to predict deformation

M ¼ 0:5ðKmax þ Kmin Þ:

(7)

Pure bending of a thin plate

A combination of G and M, which we refer to as shape-curvature, has been used to describe local surface geometries qualitatively (Roberts 2001; Bergbauer et al. 2003). They describe the local surface shape in the context of second-order

Thin plate theory (Fig. 1) relates bed curvature to strain, and strain relates to stress via the elastic properties. Whereas the curvature is the same for all bedding parallel surfaces in that plate, stresses range from tension above to compression below the neutral surface. Since fracturing occurs as a

PREDICTIVE CAPABILITY OF CURVATURE

response to stresses acting across a potential fracture plane, fracture densities are expected to vary significantly across the bent plate. Thin plate theory assumes that the plate only experiences pure bending deformation, that strains are infinitesimal, that the thickness of a mechanical unit is small compared to its lateral extent, that planar cross-sections remain planar during deformation, and that shear strains are negligible. However, strains are generally considered infinitesimal below 1%, thus rendering the applicability of thin plate theory to describe the deformation of most geological folds questionable. Moreover, geological dome structures are often formed by significantly stretching the strata as they are pushed up. The bulk of the strain experienced by strata involved in these folds is therefore not well described by the pure bending of a thin plate. Despite these limitations, several investigators have proposed a direct relationship between deformation (i.e. degree of deformation or strain, fracture density, permeability) and curvature (e.g. Murray 1968; Thomas et al. 1974; Schultz-Ela & Yeh 1992; Ericsson et al. 1998; Stewart & Podolski 1998; Fischer & Wilkerson 2000; Hennings et al. 2000). Fractures are initiated and propagated as a result of stress concentrating at flaws and at fracture tips (Griffith 1924; Anderson 1951; Lawn & Wilshaw 1975; Pollard & Aydin 1988; Willemse & Pollard 1998), hence understanding the stress distribution in deforming strata in space and time is critical. Stresses that arise in strata during fold development are unlikely to be explained by one mechanism alone, such as pure bending. For example, strata that are domed by a rising diapir experience considerable stretching, which is not included in the calculation of pure bending (Jackson & Pollard

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1988). Also, the interaction between deforming layers of different lithologies has the potential to alter the local stress field (e.g. Treagus 1988; Bai & Pollard 2000a, b; McConaughy & Engelder 2001; Wilkins et al. 2001; Young 2001). Moreover, the conditions of the layer boundaries affect the stresses within strata during folding (Cooke & Underwood 2001). If, for example, no beddingparallel slip occurs at interfaces, the entire package acts as a single mechanical unit. If beddingparallel slip develops, or if more ductile interbedded shale or salt layers accommodate significant strain, the stress distribution within the package can be quite complicated. Finally, the stress distribution in the strata changes over time as the structure evolves (Fischer & Wilkerson 2000). Early formed opening fractures, for example, may rotate along with the folding strata, and may be reactivated in shear as the deformation proceeds. These early fractures may perturb the stress field of the fold if they slip or open, and subsequent fracturing may be localized along their tiplines and at bends and steps along their surfaces. Because thin plate theory only accounts for pure bending stresses (thus ignoring plate stretching, layer interactions, or stress perturbations due to heterogeneities such as pre-existing fractures) it is an unsuitable model for investigating fracturing during folding of layered strata. The following curvature analysis of an outcropping bedding surface provides an example of the deformation in a folded surface that is ill described by thin plate theory.

Field observations The Emigrant Gap anticline, located near Casper, Wyoming, is a doubly-plunging anticlinal fold

Fig. 3. Location of the Emigrant Gap anticline, and simplified geological map of parts of Natrona County, WY (from Lageson et al. 1980). Only relevant roads and waterways are shown.

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that parallels the nearby hydrocarbon-producing Pine Mountain – Oil Mountain trend (Stiteler 1954; Cavanaugh 1976; Winn 1986; Hennings et al. 2000; Bergbauer & Pollard 2004). The breached anticline trends approximately NW–SE and is exposed for about 30 km (Fig. 3). The anticline is asymmetrical, with the west flank dipping more sleepy than the east flank. The Emigrant Gap anticline is interpreted to be a forced fold related to Laramide-age movement along the NE-dipping Emigrant Gap thrust (Hennings et al. 2000; Bergbauer & Pollard 2004). The exposed portion of the anticline consists of the Mesozoic Mowry Shale and the Frontier Formation (Fig. 4). These units are part of the Western Interior Cretaceous Basin fill, deposited

in a foreland setting, during the subduction of the Farallon plate under the North American craton and creation of the fold-and-thrust belt of western North America (Kauffman 1984). The Cretaceous strata in Wyoming consist of approximately 1.5 km of mostly siliciclastic sediments derived from both sides of the basin. The Upper Cretaceous stratigraphy for this part of the Casper Arch is summarized in Figure 4b. Mesozoic and older rocks were deformed and uplifted during the Laramide Orogeny (Schmidt et al. 1993). The topographic expression of the Emigrant Gap anticline (Fig. 5a) is shaped by resistant sandstone beds of the Frontier Formation, which consist of a cyclic package of sandstones and shales (Fig. 4b). According to Cavanaugh (1976), each

Fig. 4. Exposed Cretaceous stratigraphy. (a) Photograph along the fold axis looking approximately south showing the exposed stratigraphy and fractures in the A2 sandstone bed. (b) General stratigraphy of the Big Horn Basin Wyoming (modified from Sundell 1986) and detailed stratigraphy of the Frontier Formation (modified from Cavanaugh 1976).

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Fig. 5. (a) Oblique aerial photographs looking north showing exposes sandstone beds and fractures. (b) Close-up of A1 sandstone unit, showing mapped joints (blue) and faults (red).

transgressive–regressive cycle of the Frontier Formation starts with a shale unit, which coarsens upward and is capped by a relatively prominent sandstone bed. These sandstone beds mark the end of each of the five cycles (A1, A2, B, C, D). Bedding-parallel slip probably occurred along the shale units during folding. However, the author found very little evidence for slip along bedding surfaces within the competent sandstones beds. In addition to the five sandstone beds identified by Cavanaugh (1976), two more resistant sandstone beds can be traced around the northern end of the anticline; these represent minor regressive events within one of the major cycles. These two beds are named B2 (B minus) and C2 (C minus) according to their location within the stratigraphy (Fig. 5a). Near the northern termination of the anticline a creek cuts through the entire stratigraphy of the Frontier Formation leaving the lowest sandstone bed (A1) exposed continuously across the fold

hinge. This location is particularly useful for collecting data in three dimensions (Fig. 5b) as the sandstone bed is exposed in map view and cross section allowing for fractures to be traced from the pavement into the cross section. Other beds of the Frontier formation also form extensive pavements on the fold limbs and are even sporadically-exposed around the fold hinge, allowing for extensive data collection (Fig. 4a). From observations on these outcrops, Bergbauer & Pollard (2004) developed a conceptual model describing the deformation of the exposed sandstone layers, which considers the existence of two joint sets prior to folding. This is based on the observation that the same two fracture sets occur in folded and non-folded beds of the Frontier Formation across the field area shown in Figure 3 (see Bergbauer & Pollard (2004) for a more thorough discussion). These prefolding joints introduced anisotropy in the sandstone layers that

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observed in the fold limbs. However, during bending some of these joints were locally reactivated in shear, now seen as minor shear offsets. The observed shear fractures are absent on the fold limbs suggesting a different deformation mechanism. Near the upper and lower tiplines of these inclined shear fractures, tailcracking locally increased fracture intensity above levels observed in the fold limbs. Neither of the two sets of fractures observed on the fold (limbs and hinge) strike parallel or perpendicular to the fold axis.

Curvature analysis of the surface and comparison to fracture model

Fig. 6. Conceptual fracture-fold model for the Emigrant Gap anticline acknowledging the existence of two prefolding joint sets. (a) Prefolding stage: two, almost orthogonal joint sets (J1 and J2) form in flat-lying strata prior to folding. (b) Synfolding stage on the limbs: joints form parallel to the two prefolding joint sets. (c) Synfolding stage on the fold hinge: fracture style depends on the relative orientation of hinge line and prefolding joints. Whereas shear fractures (SF1) and tailcracks form strike-parallel to the J1 joints, mostly joints form subparallel to the J2 set.

influenced the local stress field during folding (Fig. 6). On the fold limbs, this deformation induced further propagation of the existing joints of both sets along strike and also led to infilling of new joints between older joints. This mechanism resulted in two systematic joint sets with fracture densities of approximately four times those observed in non-folded outcrops of the same sandstone bed, regardless of the structural position on the fold. The prefolding joints influenced the local stress field to the extent that new joints propagated subparallel to existing ones, despite the rotation of beds during folding. Because the beds on the fold limbs are only gently curved, this tilting is best described as a nearly rigid body rotation with minor internal deformation. In contrast to the limbs of the anticline, strata located near the fold hinge were significantly bent during folding, leading to an increase in fracture complexity there (Fig. 6). Similar to the limbs, joint sets in the hinge region were also developed further by propagation of early-formed joints and by infilling. This led to a more dense set of subparallel fractures similar in density to joints

To reconstruct the top of the lowest sandstone bed of the Frontier formation numerically the outcrops were sampled in the field (black dots in Fig. 7) using a TrimbleTM Pro XL GPS receiver at intervals not exceeding 100 m (where outcrop permitted). Vertical precisions of 0.5 m to 1.5 m, and horizontal precision of less than 0.7 m were obtained after recording approximately 5 readings at each location, and after real time differentially correcting each position. 2529 point measurements of the northern part of the outcropping sandstone bed were collected. Stereographic projections of 59 poles to bedding measured along this sandstone bed indicate an approximate fold axis of 3458, 048. When viewed along a calculated fold axis (down-plunge view), the top of the sandstone bed defines an anticlinal folded surface with approximately planar limbs and a rounded hinge (Fig. 8). From the GPS data was created a digital model of the surface using gOcadTM and MatlabTM (Fig. 7), despite the limitation that only c. 25% of the intended area of the model is exposed in the field. However, a model of the bedding surface was created to illustrate geometric tools, with the understanding that inferences from the geometric analysis are valid only in regions where data constrains the surface model. Prior to the geometric description the created surface was smoothed using the filter described by Bergbauer et al. (2003). In order to test if normal surface curvature might predict fracture density and fracture orientation, the principal curvatures of the modelled anticlinal bedding surface were calculated and then compared with the observed fracture style and density. Figure 9 shows minimum and maximum curvatures respectively. Minimum principal curvatures range from – 1e23 to 1e3 m21 and are roughly two orders of magnitude smaller in value than the maximum principal curvatures, which range from –1.7e24 to 3.8e3 m21. Colours depicting elevated magnitudes of minimum curvature trend obliquely across the fold axis, which are caused by gentle

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Fig. 7. Oblique view of smoothed model bedding surface. Black dots are GPS data used to create the model. Note that some of the GPS data is located below the surface.

surface undulations observed in outcrop. The directions of minimum curvature, shown as white ticks, generally trend subparallel to the trend of the hinge area, and only change directions significantly across the gentle surface undulations. The maximum principal curvature, which is mostly positive and considerably larger in value than the minimum curvature, is greatest near the crest of the structure. Directions of principal maximum curvature (white ticks) trend approximately perpendicular to the hinge region. This curvature analysis predicts that fracture spacing should be smallest over the hinge of the anticline (where curvature is greatest), and fractures should trend approximately parallel to the fold axis (parallel to the direction of minimum curvature) as indicated in Figure 9c. However, we found that fracture density was approximately constant on the fold. Moreover, fractures strike oblique to the

directions of principal curvature (black lines in Fig. 9c indicate fracture strikes), not following the direction of minimum curvature as predicted by thin plate theory (Fig. 1). Thus, a direct relationship between fracturing and normal surface curvature cannot be established for the bedding surface modelled here. This is not surprising considering that fractures here did not form in a systematic stress field, as predicted by thin plate theory, but in a complex stress field perturbed by the reactivation of prefolding joints and mechanical interactions between beds. This observation should hold true for most geological folds and domes, not only because of the layered nature of geological strata, but also because of rocks generally exhibit heterogeneities on all scales that influence fracture formation (e.g. prefolding fractures, fractures formed early during folding that subsequently reactivate, sedimentological heterogeneities, spatial variations

200 100 0 –100 –500

0

500

1000

Fig. 8. Downplunge view of 2529 GPS points collected on one bedding surface. The fold axis was determined by stereographic projection of 59 poles to bedding (fold axis strike and plunge: 3458/048).

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Fig. 9. See p. 195 for caption.

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in rock properties). Thus, to predict fractures successfully a model that considers heterogeneities of the appropriate scale (i.e. those that have the potential to alter the stress field in which these fractures form) is required.

Use of curvature as a tool for a unique description of folded surfaces Methods In the pursuit of quantitative descriptions of folded surfaces concepts discussed, for example by Turner & Weiss (1963), Fleuty (1964, 1987), Ramsay (1967) and Hudleston (1973) are commonly employed. These authors invoke classification schemes based on stereographic projections of bedding attitudes and cylindrical fold profiles as seen in down-plunge views. From observations largely in metamorphic rocks, Turner & Weiss (1963) provide abundant examples and techniques on the usage of the stereographic projection for fold description. Fleuty (1964, 1987) and Ramsay (1967) focus on establishing ‘unambiguous’ classification schemes for the accurate description of folds using concepts such as crest line, trough line, hinge line, fold axis, dip isogons, and fold tightness. Ramsay (1967) uses the concept of curvature, measured along cross-sections of cylindricallyfolded surfaces, to establish a classification scheme for the relationship of adjacent folded surfaces. Hudleston (1973) establishes a visual approach to classifying fold shapes by providing 30 idealized cross-sectional views of cylindrical and symmetrical folds. These approaches are reviewed in modern textbooks for students of structural geology (e.g. Davis 1984; Suppe 1985; Ramsay & Huber 1987; Marshak & Mitra 1988; Twiss & Moores 1992). A general problem associated with these fold descriptions is the assumption of cylindricity of the folded surfaces. Although a fold might locally contain cylindrical patches, a folded geological horizon is never globally cylindrical. For example, folds do not extend forever, as required by the assumption of cylindricity. This fact is recognized by most structural geologists, and often p-diagrams are used to discriminate patches of local cylindricity

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along the three dimensional fold. A cylindrical fold would have identical cross-sections regardless of where the section is constructed, implying that fold hinge lines, inflections lines, trough lines, and crest lines are straight. Terms such as ‘true profile’, p-diagrams and b –axis all assume the fold to be cylindrical (Lisle & Robinson 1995). Similarly, fold classification schemes that use measures such as the fold tightness (Fleuty 1964), the shape of a fold profile (Hudleston 1973), and the hinge: limb ratio (Ramsay 1967) assume that the fold maintains its shape along trend. When cylindricity of the structure is assumed, it is sufficient to provide one fold profile, to give one measure for bluntness, and to measure one direction for the fold hinge line. These aspects of the fold would then be sufficiently described everywhere, because those measures are constant throughout the fold. The assumption of cylindricity is used for classification schemes because it is a powerful and effective idealization, and because three dimensional data that might challenge such a simplification used to be rare. Moreover, the computational and visualization tools for the analysis and presentation of three-dimensional data were not developed, and subsequently the assumption of cylindricity became a standard for structural analysis. Over the past twenty years this standard has been questioned. Bengtson (1981) suggested that various broad geological structures, such as domes and folds, could be distinguished based on their different ‘bulk’ curvatures. He argued that the overall surface geometry can be extracted from dipmeter data collected at different structural positions. Lisle (1992, 1994), Lisle & Robinson (1995) and Stewart & Podolski (1998) use the sign of Gaussian curvatures calculated over variously curved surfaces to distinguish between elliptical, hyperbolical, and cylindrical surfaces. Such analysis allows for the distinction between surfaces that are shaped like domes or basins (elliptical) and surfaces that are either saddle-like (hyperbolic) or shaped like cylindrical planes, synforms or antiforms. Lisle & Robinson (1995) point out that most existing methods to describe folds are based on the assumption that structures are cylindrically shaped (e.g. Ramsay 1967), and suggest that surface curvature might be a useful tool in describing the

Fig. 9. Principal curvature vectors derived from the normal surface curvature, kn. (a) Magnitude of minimum principal curvature, Kmin, and directions of vector (white ticks). (b) Magnitude and directions (white ticks) of maximum curvature vector (Kmax). White lines are structure contours of the model surface shown in Figure 5. (c) Magnitude of maximum principal curvature, Kmax, directions of minimum curvature (white ticks), and observed fracture directions in outcrop (black lines). If the normal surface curvature were a valid proxy for fracture density and orientation, then fracture spacing should be smallest over the hinge of the anticline, and observed fractures should trend approximately parallel to the white ticks.

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non-cylindrical aspects of folds. Roberts (2001) expands on these concepts by using not only the sign of the Gaussian curvature (G), but also the sign of the mean curvature (M) to distinguish local surface shapes (Fig. 2) as either domes (G . 0, M . 0), bowls (G . 0, M , 0), saddles (G , 0), ridges (G ¼ 0, M . 0), planes (G ¼ 0, M ¼ 0), and synforms (G ¼ 0, M , 0). Bergbauer et al. (2003) refer to this measure as shapecurvature, and suggest this might be useful in the detection of large-scale structural domains (as implied by Reches 1976; Cruikshank & Aydin 1995; Rawnsley et al. 1998). It is because the means of measuring, analysing, and displaying 3D spatial data are now readily available, that it is proposed that the assumption that a folded surface is shaped cylindrically, or symmetrically is now obsolete. All natural folds are non-cylindrical: they do not extend indefinitely along the fold axis without any changes in shape. Researchers who analyse or describe digital models of asymmetrical and non-cylindrical folded surfaces (e.g. Grujic et al. 2002) need tools that go beyond the stereonet and idealized crosssections. Here we explore the usage of differential geometry in providing quantitative measures that avoid assumptions of cylindrical fold shapes, and thus preserve spatial changes in these measures over the entire folded surface. Whereas it is possible to construct a stereographic projection of poles to bedding that is unique (from a given data set of attitudes or maps of strike and dip), the reverse transform (a construction of a surface from the poles to bedding) is not unique, because the spatial information has been lost. Thus, although the bedding surface from the Emigrant Gap anticline, which was constrained by 2529 geographic coordinates (UTM), allows for an infinite number of very similar surfaces that can be constructed from that data, an infinite number of very different surfaces can be constructed from a set of attitude measurements. Possible 3D surfaces that only honour attitude data (and omit the spatial information) might have similar shapes but can significantly differ in their fold amplitudes, their closure direction, their length scales, and even the number of folds in a fold train. Other possible surfaces might be constructed, honouring the same data, by any spatial arrangement of the attitude information, which, in contrast to the bedding surface created from the UTM coordinates, could result in significantly different fold shapes. Thus, representing a folded surface by a stereographic projection of poles to bedding inevitably leads to subjective interpretations of the geometry. A surface description that is based on the first and second fundamental forms of differential

geometry is not only unique, but it is inherently tied to the spatial variations of the surface and does not leave room for a subjective interpretation of the geometry. Thus, particularly for the quantitative comparison of surfaces, in addition to collecting strike and dip measurements in the field, geologists should record and use the geographic coordinates for every sampled point on the structures they are mapping. Meaningful interpretations of geological surfaces can then be presented quantitatively, in light of the sampling theorem (surface coverage), data precision, statistics, and motivation of the analysis. Despite the fact that the first and second fundamental forms fully describe the geometry of a surface, other descriptive measures are normally used for surface descriptions (e.g. strike, dip, hinge and inflection line). As with kn, these measures can be readily derived from the two fundamental forms, but contrary to kn, they do not provide a full description of the shape of a surface. Some of these concepts, such as strike and dip, prove useful for the description of a folded surface, because bedding attitudes constitute a large part of available surface data (e.g. Grujic et al. 2002). The unit normal at a point on a surface is the pole to bedding commonly used for describing surfaces using stereographic projections. The components of the unit normal vector, N, are used to determine the dip and the strike of the surface (Aki & Richards 1980, p. 115): dip ¼ cos1 ðNz Þ

(8)

strike ¼ tan1 ðNy =Nx Þ;

(9)

and

where Nx, Ny, and Nz are the components of N in the ex (north), ey (east), and ez (vertical) directions. Another descriptive term in use that can be derived from the two fundamental forms is the concept of a hinge line. Hinge lines of cylindrical folds, which are straight lines parallel to the fold axis, are defined as lines of maximum curvature (e.g. Marshak & Mitra 1988, p. 214). For threedimensional folded surfaces the concept of hinge lines can be generalized to curves that pass through the loci of greatest values of normal curvature. Thus, they can be calculated analytically and their geometry may depart from that of a straight line. On planar surface patches, the concept of a hinge line has to be replaced by that of a hinge area. Similarly, inflection lines can be derived from the two fundamental forms. Inflection lines on folded cylindrical surfaces are normally thought of as straight lines that pass through points of zero

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curvature measured along the fold profile (e.g. Ramsay 1967, p. 347). This concept also can be generalized for three-dimensional surfaces to curves passing through points across which at least one of the principal curvature values changes sign. Thus, the principal curvatures accurately define the locations of inflection and hinge lines on folded surfaces and therefore a quantitative description of folded surfaces should start with a quantification of the two fundamental forms, from which other measures in common use can readily be derived.

Example of a geometrical description

Fig. 10. Surface attitudes derived from the unit normal vector, N, to the model surface. (a) Bedding dips, and (b) bedding strikes (right hand rule) were calculated at every grid point. White lines are structure contours of the model surface shown in Figure 7.

Figure 10 summarizes some of the traditional geometrical measures of a bedding surface, including a structure contour map (white lines) and colourcoded maps of the strike and dip of bedding, to characterize the surface shape. Bedding dips (Fig. 10a) as large as 358 occur on the west limb of the model surface, and up to 258 on the east limb. The points on the surface at which the dip is close to zero mark the crest of the structure. This is a narrow strip that runs approximately parallel to the y-axis. Figure 10b provides a map of the surface strikes: using the right hand rule (Marshak & Mitra 1988, p. 7), the east limb strikes about 3508, whereas the west limb strikes about 1708. The crest is identified by the approximately 1808 switch of the strike angle. The line of greatest maximum curvatures is defined as the fold hinge (Marshak & Mitra 1988, p. 214), which is shown as the solid black line in Figure 9b. The hinge line of our modelled bedding surface curves in space, and is located to the west of the crest line (dashed black line). Thus, the surface describes a nonsymmetrical fold, and the amount of asymmetry is quantified by the spatial departure between crest and hinge curves. The asymmetry changes along the trend of the anticline, almost vanishing near the northern extremity of the anticline. A second application of the normal curvature, kn, assesses if a folded surface is cylindrical, and provides a measure of the surface’s departure from a cylindrical shape. For a surface to be cylindrical the minimum principal curvature must be zero everywhere, thus forcing the maximum principal curvature to have the same distribution on every cross-section taken perpendicular to the fold axis. Not only is the minimum principal curvature non-zero across the modelled bedding surface (Fig. 9a), the maximum curvature distributions differ from one cross section to another (Fig. 9b). Thus, the modelled surface is not cylindrical, and the magnitudes of the principal curvatures that depart from a cylindrical shape thus quantify that property.

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Discrimination of cylindrical and noncylindrical areas across the modelled bedding surface, and quantification of the non-cylindrical curvatures, can also be achieved using the concept of shape-curvature. Using the colour code of Figure 2 the modelled bedding surface is comprised of domal and saddle-like areas, which reflect the gentle, hinge oblique surface undulations, superimposed on the broader fold shape (Fig. 11a). Thus, the modelled bedding surface does not contain any cylindrically-shaped areas (where G ¼ 0) of significant extent. The quantification of the surface’s departure from cylindrical can be achieved by subsequently setting the smallest values of principal curvatures to zero. Doing so turns areas that minimally depart from one of the cylindrical shapes (shown in Fig. 2), into cylindrically-shaped geometries. This might be helpful in distinguishing areas on surfaces that are significantly non-cylindrical from areas that are quite cylindrical. Thus, a surface can be ‘smoothed’ until the underlying, cylindrical

shape is extracted, and the difference in the magnitudes of the principal curvatures prior to and after extraction of the cylindrical shapes can be used as a measure of the non-cylindrical geometries of the surface. The smallest curvature magnitude across the modelled bedding surface equals 1.5e29 m21 (Fig. 9). Small principal curvatures are located near lines separating different surface shapes, and when principal curvature jkj , 1e25 are set to zero, these areas become shaped like cylindrical antiforms (Fig. 11a). Larger areas of equal cylindrical shapes emerge when principal curvatures of jkj , 5e24 m21 are set to zero, and the surface assumes a roughly antiformal shape (Fig. 11b) with remnants of non-cylindrical areas. Upon setting the threshold value to jkj , 1.5e23 m21 ¼ 0, the entire model surface becomes cylindrical, with two planar limbs and a cylindrical anticline along the fold (Fig. 11c). The surface thus contains approximately five orders of magnitude (from jkj ¼ 1.5e29 to jkj ¼ 5e24 m21) of principal curvatures

Fig. 11. Shape-curvature derived from the normal curvature, kn. Colours indicate the local shape of the surface based on the background colours used in Figure 1. (a) Principal curvature magnitudes below jkj , 1e25 m21, (b) jkj , 5e24 m21, and (c) jkj , 1.5e23 m21 are zeroed out. Five orders of principal curvatures are cancelled before the horizon is approximated by mostly cylindrical surface shapes.

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that depart from a perfectly cylindrical surface shape. If the surface had been sampled on a tighter grid, or smoothed less prior to curvature calculation, the magnitude of smallest curvature contained in the data would have been less than that reported here. However, this would have not changed the curvature threshold value at which the surface turns into cylindrical shapes. The concept of shape-curvature also allows for the determination of the locations of inflection ‘lines’ across the fold. Lines defining areas of equal shape in Figure 11 are inflection lines, because one of the principal curvatures changes its sign across them (in this case it is the minimum curvature, Fig. 9a). Several hinge-line-oblique inflection lines, defined by the gentle surface undulations, are present in Figure 11a. After extracting a purely cylindrical fold shape (Fig. 11c), two inflection lines, trending along the long axis of the model surface, define the transition from the approximately planar limbs to the anticlinal hinge. Moreover, closure direction of the structures can be inferred based on the local shape of the surface: antiforms and domes provide upward closure, synforms and basins are closed downward, and the closure direction for saddle areas depends on the surface shape on either side of the saddle. The three shapecurvature maps indicate that model bedding surface is comprised of either saddle areas and domes (Fig. 11a), or antiforms, domes and planes (Fig. 11b), or planes and antiforms (Fig. 11c). Thus, all three shape-curvature maps confirm the expected upward closure of an anticline. A third application of kn involves the use of shape curvature to distinguish structural domains on surfaces. A structural domain is defined as an area of a rock mass that exhibits a common deformation style. In the absence of significant heterogeneities within the same rock mass, the boundary between two structural domains is often marked by a change in horizon shape. For example, the shape curvature of Figure 11c distinguishes between an antiformal hinge (blue) and two planar limbs (yellow). Our conceptual model (Fig. 6) shows that different deformation styles have been observed between the hinge and the limbs, and that the change in style occurs approximately where the surface changes its shape from an anticlinal hinge to roughly planar limbs. If the shape of a horizon is indeed responsible for producing different structural domains, then a predictive approach can be employed for the non-exposed parts of the fold hinge using the concept of shape curvature: within an area of equal shape, the same fracture style is expected. This implies that for the nonexposed part of the fold hinge, likely a fracture style similar to that observed in outcrops of the hinge would be. Similarly, fracturing along the

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non-exposed fold limbs is expected to be roughly similar to the fractures observed on parts of the exposed fold limbs.

Discussion This analysis assumes that areas of similar surface shape deformed in a similar fashion, and assuming similar rock properties, that this resulted in similar deformation features. For the described bedding surface, the roughly planar areas should have deformed mainly by a rigid body rotation, whereas the areas shaped like an anticline experienced some bending, which resulted in shear reactivation of joints. This similarity analysis is invalid for beds that exhibit significant variability in rock properties. The observed fracture styles in one bed are often significantly different from fracture styles observed in adjacent beds even if the normal curvature is similar. Thus predicting fractures in a bed from observations of fractures in another bed based on this similarity argument is not recommended. Finally, faults that cut through most of the vertical or lateral extent of the fold (such as tear faults or the underlying thrust fault itself) locally create deformation that is not predictable based on this analysis (Hennings et al. 2000). Fitting a surface to the limited GPS coverage shown in Figure 7 is not a unique problem: an infinite number of surfaces can be constructed that more or less honour the 2529 data points. However, normal surface curvatures depend on the surface they are calculated from, so a comparison of the modelled surface with data and observations from the bedding surface is necessary. Furthermore, conclusions about geometry in poorly constrained areas should be viewed with appropriate scepticism. A factor influencing the outcome of the model bedding surface from the Emigrant Gap anticline is the amount of seeds used for surface triangulation in gOcadTM . Triangles were seeded every 70 m along the border of the surface. This distance was chosen based on the sampling distance applied in the field. The target of the sampling procedure in the field was to resolve the broad scale surface shape, as well as the gentle, hinge line oblique surface undulations. The maximum spatial wavelength resolved by a sampling procedure equals twice the sampling spacing (Bracewell 2000). Our choice of maximum sampling distance across the accessible patches of the surface was aimed at resolving surface undulations with wavelengths of approximately 200 m and larger, which requires a minimum sampling interval of 100 m. To avoid further surface aliasing, a slightly smaller seed spacing was chosen for the triangulation than the

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100 m sampling interval employed in the field. Once the surface was triangulated, the choices of re-sampling grid spacing and data interpolation technique (performed with MatlabTM ) only had minor effects on the final surface geometry. These parameters were chosen to maximize the correlation coefficient R2. A final factor influencing the outcome of the modelled surface is the amount of surface smoothing performed prior to curvature calculations. Smoothing is necessary prior to any curvature calculation (Bergbauer & Pollard 2003; Bergbauer et al. 2003). Surface triangulation using gOcadTM produces a rugged surface, full of artificial kinks where adjacent triangles meet. The rugged gOcadTM surface is exported and smoothed using a technique based on the fast Fourier transform (Bergbauer et al. 2003). The surface is smoothed by removing surface wavelengths of 360 m and smaller (frequency filter s ¼ 0.0028 m21). Larger wavelengths were kept, because they apparently describe the surface undulations targeted with the GPS sampling (Fig. 7). Thus, the maximum sampling interval of approximately 100 m in the field successfully sampled these gentle surface undulations.

Conclusions 1.

2.

3.

At the Emigrant Gap anticline, there is no direct link between surface curvature and strike or density of synfolding fractures. Fractures there strike obliquely to either direction of the principal curvatures, and fracture density is roughly constant everywhere on the fold even where the magnitudes of the principal curvatures are large. At the Emigrant Gap anticline, the shape of the horizon controls the deformation style: where the surface is significantly curved and the shape assumes that of an anticline (the hinge of the fold), shear fracturing is widespread. This is in contrast to roughly planar-shaped areas of the horizon (the limbs of the fold) where shear fractures are absent and most fractures formed as joints. A measure called shape-curvature can delineate these differently-shaped areas. Shape curvature can therefore be used to map out structural domains on the anticline. This method for mapping out structural domains should be generally applicable for structures where the shape of the horizon is the dominant factor in controlling deformation. When describing folded surfaces, the first and second fundamental forms provide a tool that uniquely describes their geometry. This is in contrast to common measures such as fold

4.

hinge lines, inflections lines, true profile, tightness, hinge/limb ration, p-diagrams and b-axis etc, which all assume the fold to be cylindrical, and more importantly, are inherently non-unique. These common measures can be derived readily from the two fundamental forms, but not vice versa. It is proposed that where possible any fold description should start with a quantification of the surface in three dimensions. Thus, although measurements of strike and dip of a surface are useful, unambiguous representation of a surface geometry can only be achieved when the geographic coordinates of the data points are also recorded and included in the analysis.

This research was supported by Phillips Petroleum Company, the Stanford Rock Fracture Project, the Stanford McGee foundation, and by NSF EAR-0125935 ‘Strain Accommodation by Fracturing During Folding of Sedimentary Rock’. I would like to thank D. Pollard for his countless contributions to this research. Reviews by R. Lisle, T. Couzens and S. Jolley have improved this manuscript significantly.

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Stratigraphic control on extensional fault propagation folding: Big Brushy Canyon monocline, Sierra Del Carmen, Texas D. A. FERRILL, A. P. MORRIS & K. J. SMART Department of Earth, Material, and Planetary Sciences, Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238, USA (e-mail: [email protected]) Abstract: Mechanical stratigraphy exerts a first-order control on deformation at a range of scales from oilfield-scale structural style to deformation (e.g. fracturing) within an individual reservoir stratum. This paper explores an outcrop example where mechanical stratigraphy in a limestone and shale sequence directly influenced the structural style and distribution of deformation related to the propagation of a ‘seismic-scale’ normal fault that has maximum displacement on the order of 100– 500 m and extends for more than 10 km. A monocline developed in Cretaceous Buda Limestone above tectonically thinned Del Rio Clay and faulted Santa Elena Limestone is here interpreted as an extensional fault propagation fold. Monocline limb dips reach 598. The Del Rio Clay is thinned from approximately 36 m to 1.5 m, whereas the underlying Santa Elena Limestone is offset vertically by approximately 74 m along a steep (approximately 808) normal fault. This large fault displacement of the Santa Elena Limestone is not transferred upward to the Buda Limestone because of ductile flow within the intervening Del Rio Clay. Although upward fault propagation has been inhibited, thinning of the Del Rio Clay and the resultant extreme displacement gradient at the tip of the fault have forced the Buda Limestone into a monoclinal fold. Two competent packstone and grainstone beds, 6 m and 2.7 m thick and separated by 10.5 m of less competent calcareous shale, comprise the Buda Limestone at this location. Deformation features within the competent Buda beds include bed-perpendicular veins that accommodate bed-parallel extension, and bedding plane slip surfaces with an up-dip sense of shear that offset the veins. Deformation is concentrated in the monoclinal limb and not in the monoclinal hinge regions. Consequently, bed-parallel extension and shear strain are associated with monoclinal dip, not with curvature. These results show that for this structure, bed dip is a better proxy for bed-parallel extension and related fracture dilation than is curvature.

This paper describes a case of fault-propagation folding where a mechanically weak layer retards fault propagation, resulting in an appreciable component of folding prior to fault propagation through the folded section. This folding-beforefaulting process partitions the overall throw across the structure into fold- and fault-offset components at a scale and/or dip range outside the capability of seismic reflection data to image and resolve. The fold component of the throw would therefore be masked in the data, resulting in an unrealistic fault juxtaposition of reservoir flow units in standard production geological models derived from it. Furthermore, the folding results in concentrated meso-scale deformation such as extension fracturing and layerparallel slip within the steepening limb during monocline development. This broadens the overall fault damage zone, and can enhance its fault seal capacity if formed under certain physical–chemical conditions (e.g. faulting under high temperature conditions leading to sealing of sand –sand juxtapositions; Fisher & Knipe 1998, 2001). However, if deformation takes place under lower temperature conditions, this has significant implications for the distribution of productive fracture systems (e.g.

Barr 2007; Ma¨kel 2007), for drilling of fracturerelated hazardous zones of fluid pressure loss/gain and well-bore instability, and for permeability architecture in aquifer systems (Ferrill et al. 2004). Seismic reflection imaging of deformed strata can enable predictive computation of foldingrelated strains based on the geometrical characteristics of the interpreted horizons. In this context, curvature of strata is commonly used as a predictor of strain localization and consequent fracturing (e.g. Stewart & Podolski 1998; Ericsson et al. 1998; Hennings et al. 2000; Bergbauer & Pollard 2003; Bergbauer et al. 2003). Normal faulting in single, mechanically strong layers has been the subject of intensive field and laboratory investigation. These analyses suggest that folding prior to or during fault propagation tends to be limited, and most commonly occurs between laterally or vertically overlapping fault tips (e.g. Peacock and Sanderson 1994; Trudgill & Cartwright 1994; Childs et al. 1995; Patton et al. 1998; Ferrill & Morris 2001; Ferrill et al. 2005). However, other studies including field observations (e.g. Sellards & Baker 1934) and analogue modelling (Withjack et al. 1990; Fig. 1) have shown that mechanical

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 203–217. DOI: 10.1144/SP292.12 0305-8719/07/$15.00 # The Geological Society of London 2007.

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exposed across much of central and west Texas, and is part of the West Texas extensional corridor, where extensional deformation has occurred from the Oligocene (?) to the present day associated with the easternmost Basin and Range extension and the southern end of the Rio Grande rift. These same rock strata form important aquifer systems across much of central and west Texas associated with normal faulting in the Balcones Fault system (e.g. Hill 1889; Holt 1956; Arnow 1963; Ferrill et al. 2004). In the study area, a very thick (c. 300 m), mechanically strong limestone (Santa Elena Limestone) is overlain by a very weak clay-rich shale (Del Rio Clay), and a thin (c. 30 m) mechanically-layered limestone unit (Buda Limestone) (Fig. 2c). On the western flank of Big Brushy Canyon, a monocline has developed in the Del Rio Clay (shale) and thin Buda Limestone above a fault in the thick massive Santa Elena Limestone. We investigated the geometry of and internal deformation within the monocline to evaluate the deformation style associated with this structure.

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Fig. 1. Comparison of analogue models of extensional fault propagation folding in a single layer (a) versus a multilayer (b) (after figures 4f and 8f in Withjack et al. 1990). Dashed lines in (a) are initially horizontal passive form lines. Detachment horizons in the multilayer model are simulated by initially horizontal paired acetate sheets.

stratigraphy can strongly influence the style of deformation associated with normal fault propagation. A mechanical multilayer will tend to retard fault propagation in favour of folding, with displacement diminishing upwards and monoclinal folds developing in less competent strata (Sellards & Baker 1934). This paper analyses the nature and distribution of small scale fracture and bedding-plane slip surfaces within a field outcrop example of normal faulting and associated folding in a mechanical multilayer in west Texas, USA (Fig. 2). The fault has a strike length of approximately 10 km and displacement ranging from 0 m at its tip to a maximum of approximately 100 –500 m, and thus would qualify as a ‘seismic scale’ normal fault in petroleum industry terms. The fault is mapped in the Cretaceous carbonate platform sequence that is

Monoclines commonly develop above blind faults where the rate of fault propagation is slow relative to the rate of fault displacement (e.g. Hudson 1955; Beloussov 1959; Sandford 1959; Prucha et al. 1965; Ameen 1988; Hardy & McClay 1999; Willsey et al. 2002; White & Crider 2006). An extensional monocline is characterized by a singlelimbed fault propagation fold, in which layering typically (in originally horizontal layers) dips toward the downthrown side of the normal fault (Fig. 1a & b). Continued fault propagation may cut the monocline limb. Depending on the location of breakthrough, this process will leave panels of rock that dip in the same direction as the fault. These synthetic dip panels may eventually be present in either the hanging wall or footwall, or in both blocks (Ferrill et al. 2005). Analogue modelling using a single clay layer overlying a pre-existing normal fault has shown that fault displacement produces an upwardwidening monocline, with a synclinal axial surface dipping antithetically to the master normal fault, and an anticlinal axial surface that dips in the same direction as the master normal fault (Fig. 1a & b; e.g. Withjack et al. 1990; Jin & Groshong 2006). Upward propagation of a fault in the mechanically strong section produces distributed zones of secondary normal faults between the two monocline axial surfaces (Jin & Groshong 2006). Secondary faults eventually link to develop a through-going normal fault through the clay

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Fig. 2. (a) Map showing location of study area in the Trans-Pecos region of west Texas. (b) Field photograph of monocline in limestone of the Buda Formation, above the clay-rich shales of the Del Rio Clay and Santa Elena Limestone (fault scarp in foreground), Big Brushy Canyon, Sierra Del Carmen, Texas, view is to the south. (c) Stratigraphic column of the Cretaceous stratigraphy exposed at Big Brushy Canyon (modified after St John 1965).

layer (e.g. Withjack et al. 1990). Fault displacement beneath a multilayer containing layer-parallel detachments (simulated using acetate sheets by Withjack et al. 1990) within the deforming clay section also produces an upward-widening monocline above the fault (Fig. 1b). However, in contrast to the single layer models, the multilayer developed

layer-parallel slip along detachment horizons and strata-bound deformation between detachment horizons (Fig. 1b). The acetate sheets prevented propagation of the master fault through the multilayer. This modelling clearly suggested that deformation associated with extensional fault propagation folding is controlled by mechanical stratigraphy

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and dip of the master fault. More recent physical modelling using rock veneers (Patton et al. 1998) and numerical modelling using discrete element code (Finch et al. 2004) both produced results that are in general agreement with the earlier clay modelling.

Big Brushy Canyon monocline, Sierra Del Carmen, Texas The study area lies in the Sierra Del Carmen mountain range within the Black Gap Wildlife Management area adjacent to the eastern margin

Fig. 3. (a) Geological map of study area showing geological units shown as transparent colour overlay on aerial photograph background. Stereonets linked to red dots on map illustrate bedding orientation and poles to fractures measured in the Santa Elena Limestone in the footwall of the fault. Poles to bedding and poles to veins measured in the Buda Limestone (yellow dots on map) within the Big Brushy Canyon monocline are inserted in bottom right corner of figure. (b) Strike-perpendicular cross-section produced by along-strike projection of outcrop geology onto ENE– WSW vertical profile. See (a) for location of profile line.

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Fig. 4. Photographs of outcrop-scale fault zone deformation features in the Brushy Canyon monocline. (a) Oblique view of fault zone and monocline, looking to the SW. (b) Photograph taken looking NW shows fault zone material approximately 1 m thick, composed of fault-parallel and fault-oblique layers coarse blocky to prismatic calcite crystals, and limestone blocks. Geologist wearing orange hat and vest is circled. (c) Large radial prismatic calcite crystals in fault zone indicate fault zone dilation and precipitation of calcite in fault zone during or after fault slip.

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of Big Bend National Park (Fig. 2a). The mountain range was produced by Oligocene and younger extensional fault arrays, with some associated evidence of localized strike-slip and contractional deformation (St John 1965; Moustafa 1988). Cenozoic basin fill comprises conglomerates, sandstones, and shale, and basaltic volcanic units (St John 1965; Maxwell 1968). The pre-Cenozoic strata are part of a regionally extensive carbonatedominated Cretaceous sequence that extends in outcrop from central Texas across west Texas, and these laterally continuous deposits form a well-defined mechanical stratigraphy, that has fundamentally affected the structural development of the region. The topographic relief of the range is controlled by the resistant Cretaceous Santa Elena Limestone, which has been exhumed largely by erosion of the overlying, primarily shale, Del Rio Clay (St John 1965; Maxwell et al. 1967; Maxwell 1968; Maler 1990). Throughout the Sierra Del Carmen, cliffs of the Santa Elena Limestone provide three-dimensional exposures of fault scarps and relay structures. The Big Brushy Canyon monocline explored in this paper is developed in the Del Rio Clay and Buda Limestone, above a steeply dipping fault, the western bounding fault of the Big Brushy Canyon graben as mapped by Moustafa (1988).

Big Brushy Canyon monocline geometry The Big Brushy Canyon monocline is defined by an ENE-dipping panel of beds developed in the Buda Limestone above a steep normal fault (strike: 3348 –3458 and dip: 808), that displaces the massive Santa Elena Limestone by approximately 74 m (Fig. 3). The overlying Del Rio Clay (c. 36 m thick clay-rich calcareous shale; Moustafa 1988) apparently accommodated much of the fault displacement because offset of the Buda Limestone through the monocline is considerably less than displacement of the top of the Santa Elena Limestone across the fault (Figs 2a and 3b). The fault zone (Fig. 4), which is exposed along the footwall scarp in the Santa Elena limestone, is 1.5–3.0 m thick and consists of limestone breccia (Fig. 4b) and massive euhedral calcite, including crowns of radial prismatic calcite crystals tens of centimetres long (Fig. 4c). The Del Rio Clay consists primarily of calcareous clay with abundant limestone nodules towards its stratigraphic top. The resistant exposure of the Buda Limestone that marks the monocline geometry consists of two massive limestone units (lower unit 6 m thick, upper unit 2.7 m thick). These two resistant limestone units consist of beds 1 –2 m thick. Between the two limestone layers of the

Fig. 5. (a) Photograph with locations of veins and layer-parallel slip measurements in key bed of Buda Limestone annotated. (b) Vertical calcite vein in nearly horizontal Buda Limestone crosses shale beds without any bedding-plane offsets. Hammer is 0.38 m long. (c) Thick calcite vein is bent around tips of two bedding-plane slip surfaces. Folding of the vein transfers displacement between bedding-plane slip surfaces. Vein material and host rock are brecciated and have associated uncemented porosity between fragments, indicating that slip and folding of the vein occurred after vein formation. (d) and (e) Network of bedding-plane slip surfaces deflect and offset initially bedding perpendicular vein. Vein medial lines indicated by dashed white lines. Yellow field notebook is 19 cm long.

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Fig. 5. (Continued).

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Buda Limestone, is a recessively weathered, nodular argillaceous limestone section approximately 10.5 m thick. Bedding dips across the monocline range from horizontal ENE of the synclinal axial surface to a maximum measured layer dip in the steepest part of the monocline of 598 (measured along the top of the basal limestone bed of the Buda Limestone). Layering of the Santa Elena Limestone in the footwall of the fault is nearly horizontal, but exhibits steepening dip toward the NW tip of the fault reflecting the displacement gradient and associated upward bowing of the footwall. Fractures in the Santa Elena Limestone occur primarily in two bedding-perpendicular (near vertical) sets: one parallel with fault strike and the other perpendicular to fault strike.

At the top of the footwall scarp, the Santa Elena Limestone is only separated from the Buda Limestone by a thin veneer of highly attenuated (3% of its original thickness) Del Rio Clay. A small outcrop of this thinned calcareous and nodular upper Del Rio Clay has an anastomosing fabric subparallel to stratigraphic layering consisting of irregular layers and of lenticular blocks surrounded by a more clay-rich, thinly laminated calcareous shale. Within the monocline, the Buda Limestone beds are not cut by the master fault (Fig. 5a). Deformation features observable within the monocline consist of extension veins that accommodate layer-parallel extension (Fig. 5b –e), and bedding-plane slip surfaces that offset the veins (Figs 5c –e and 6a– d) and record layer-parallel slip.

Fig. 6. (a) Photograph of host rock brecciation adjacent to folded vein associated with displacement gradient at tip of bedding plane slip surface (see Fig. 5c for position) illustrates uncemented porosity between breccia clasts, indicating that the folding and bedding-plane slip occurred after vein formation. (b) Bedding-plane slip surfaces locally have releasing steps in which calcite veins have filled rhombohedral or lenticular cavities produced by dilation at releasing steps (see Fig. 5e for location). Note 14 cm long felt-tip marker pen for scale. (c) Rhombohedral veins are made up of numerous lenticular (sigmoidal) layers of calcite vein fill, indicating episodic slip and dilation followed by cementation. (d) Photograph showing detail of lenticular vein associated with subtle releasing bend along bedding-plane slip surface.

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Layer extension in the Buda Limestone The resistant massive limestone beds of the Buda Limestone contain thick layer-perpendicular calcite veins (Fig. 5b –e). We conducted a layerparallel scan line survey along a key bed within the upper massive limestone of the Buda Limestone to characterize the veins, quantify the amount of bed-parallel extension that they represent, and quantify their apparent offsets by bedding-parallel slip surfaces as a measure of layer parallel shear. One might assume that vein segments would form independently between bed-parallel slip surfaces, and that although bed-parallel extensions may be consistent from bed to bed, apparent offsets of veins would not reflect bed-parallel slip magnitude. However, several important lines of evidence indicate that the veins or vein fractures were once continuous across the beds and were progressively offset by bed-parallel slip: (1) veins cutting across the entire upper massive limestone of the Buda Limestone are present where the layer is nearly horizontal, providing direct evidence that vein fractures were capable of propagating across the entire mechanical package rather than arresting at minor shale partings within section (Fig. 5b); (2) patterns of vein segments (spacing and thicknesses) consistently match bed-for-bed through the package; (3) deflection of a continuous vein around the tips of bedding plane slip surfaces (Fig. 5c); (4) vein calcite and adjacent host rock are cataclastically deformed where bedding-plane shear is more distributed, for example associated with displacement gradient at the tips of bedding-plane slip surfaces (Figs 5c and 6a); and (5) independent indicators of sense and magnitude of bedding-plane slip, in the form of localized layered vein development at releasing bends along bedding-plane slip surfaces (Fig 6b –d), are consistent with the displacement interpreted from offset vein segments. The layer-perpendicular veins are 5 mm to 0.15 m thick and are generally filled with veinparallel layers of coarse, blocky to prismatic calcite crystals. Fine-grained calcite vein filling is also locally present, and veins commonly display multiple generations of coarse calcite or coarse and fine calcite fill. Veins with medial lines are common (Figs 5e, 6b), and crack-seal textures were not observed in the field. Vein spacings measured parallel to bedding range from ,1 m to approximately 10 m. In addition to the filled aperture, there is commonly a smaller component of unfilled fracture aperture that at depth would generally be fluid filled. Dilation associated with vein filling represents a total of 2% extension parallel to layering (in dip direction). Dilation along vein margins accommodated an additional 0.5% layerparallel extension. Summing these two components,

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mechanical aperture associated with filled and unfilled fracture aperture amounts to 2.5% layer parallel extension along the 33.15 m length of the bed-parallel scan line (Fig. 7a).

Bedding-plane slip in the Buda Limestone Offset of distinctive veins across bedding planes and bed boundaries indicate bedding-plane slip within the two massive limestone layers of the Buda Limestone with a consistent up-dip sense of shear (higher beds moving in the up-dip direction). As noted in the previous section, several pieces of evidence indicate the sense of slip, including sense of deflection of unbroken veins around tips of bedding-plane slip surfaces and veins filling releasing steps along bedding-plane slip surfaces. The slip surfaces are thin zones (,0.01 –0.12 m thick) where shear has been concentrated on

Fig. 7. (a) Cumulative layer elongation versus measured tape distance (see Fig. 5a), with the difference between the cumulative mechanical aperture and cumulative vein thickness values representing the unfilled (open) component of the mechanical aperture. (b) Key bed dip (blue diamonds, scale on left side) and shear strain (g) measured as bed-parallel offset divided by layer thickness (magenta squares, scale on right side), plotted versus measured tape distance.

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bedding planes and thin shale layers. Offset vein fragments are locally present bounded by anastamosing slip surfaces, and lenticular to rhombohedral (in profile) calcite veins are locally present at releasing steps along bedding-plane slip surfaces (Fig. 6b –d). Bedding-plane slip surfaces display slickenlines, anastamosing shear fabrics within shale, and locally attenuated vein material reflecting offset of the bed-perpendicular veins. Beddingplane slip surfaces are traceable on the scale of one to several metres, but several slip surfaces clearly terminate up or down dip, where displacement is transferred to other weak (shaley) bed boundaries. Slip measured parallel to slip direction, along individual bedding planes, offsets veins as much as 0.63 m. Shear strain measurements were made at 14 stations along a single limestone layer in the Buda Limestone exposed in cross-section. Two-dimensional bedding-parallel shear strain, g, (Ramsay 1967) was calculated for each vein measurement station along the bed-parallel traverse by summing the total bedding-plane slip s, and dividing by the total layer thickness t (Table 1; Fig. 7b), such that g ¼ s/t.

Progressive deformation and timing relationships Based on the common occurrence of multiple generations of calcite fill in extensional veins (e.g.

Lee & Wiltschko 2000), we interpret that extension fracture dilation was prolonged and perhaps episodic. This occurred during a transition from conditions suitable for precipitation of coarse calcite fill, to fine calcite fill, to no calcite fill for the latest dilational increments. Coarse calcite is commonly inferred to result from slow precipitation under water saturated conditions (Bathurst 1975), whereas lack of filling of final dilational increments suggest that the rock was not fluid saturated during or after deformation, consistent with progressive erosional exhumation of shallowly buried (,2 km maximum) rocks during extensional deformation. Deformation of veins adjacent to slip surfaces indicates that veins were present at the time of beddingplane slip. Individual veins with consistent mechanical aperture and internal structure can be traced with offset across several (2– 3) bedding-plane slip surfaces. Both extension and shear are greatest where dip is steepest. Close correlation between both layer extension and layer-parallel shear and dips in the monocline limb (Fig. 7a & b) indicates that layer extension and shear are directly related to monocline formation. Based on the various relationships described in this paper, we interpret the following deformation sequence. The primary extension-fracture forming events (initial fracture propagation and dilation) in the Buda Limestone preceded bedding-plane slip, and may have occurred as normal faults were

Table 1. Summary of strain traverse data Station Tape (m)

Bed

Vein

Vein Width (mm)

Total Aperture (mm)

Total Total Bedding Layer Plane Thickness, Slip, s t (cm) (cm)

Shear Strain, g

Strike Dip Strike Dip Material Min Max Min Max M1.1 M1.2 M1.3 M1.4 M1.5 M1.6 M1.7 M1.8 M1.9 M1.10 M1.11 M1.12 M1.13 M1.14

0 0.45 1.25 1.65 11.15 11.15 11.15 12.25 12.25 13.35 15.05 15.05 16.70 16.70 19.45 22.20 24.85 28.40 33.15

348

5

338

25

344

25

351

30

342 331 330 352 343

36 35 37 45 35

155 168 171 132 146 149 334 135 148 131 156 157 156 153 148 159 160 156 161

90 88 80 78 70 83 73 57 65 57 69 65 58 66 64 54 60 63 55

calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite calcite

2 8 2 15 20 20 20 30 8 8 8 8 5 10 55 230 130 170 130 170

28

244

0.1148

42

261

0.1609

80 80 10 50 50 40

90 90 20 60 60 60

80

90

50

306

0.1634

10 50 50 40

20 90 90 60

40 66

306 339

0.1307 0.1947

58

317

0.1830

50 70 20 20 20

60 80 40 40 50

50 70 20 20 20

60 80 40 40 50

55 71 54 69 35

353 340 322 259 298

0.1558 0.2088 0.1677 0.2664 0.1175

EXTENSIONAL FAULT PROPAGATION MONOCLINE

forming in the Santa Elena Limestone below (Fig. 8a). Displacement on the underlying normal fault offset the Santa Elena Limestone, but upward propagation of the fault was accommodated by flow in the Del Rio Clay, which caused tilting of layering and formation of a monocline in the overlying Buda Limestone. This tilting activated slip across thin shale beds between metre-thick massive limestone beds in the Buda Limestone, offsetting early-formed and actively dilating extension fractures (Fig. 8b). Vein material filling the extension fractures indicates precipitation of calcite from solution during and/or after fracture dilation. As fault displacement increased, bedding dips steepened, layer-parallel extension caused continued dilation of layer-perpendicular fractures, and bedding-plane slip continued to offset vein segments with an up-dip sense of shear (Fig. 8c). Localized development of unfilled fracture voids, and unfilled aperture development along offset vein segment margins indicate that layer-parallel extension, and presumably bedding-plane slip, may have continued under dry conditions where calcite deposition was no longer active.

Discussion Distribution of deformation associated with the monocline Analogue modelling by Withjack et al. (1990) suggested that monocline axial surfaces are established early during the deformation, and are fixed with respect to the rock, rather than rock moving through the axial surface or the axial surface sweeping through the rock. The up-dip sense of shear exhibited by the Big Brushy Canyon monocline is consistent with the deformation pattern in the multilayer model of Withjack et al. (1990), and more broadly with flexural slip in contractional folds (c.f. Ramsay 1967; Ferrill & Dunne 1989; Couples et al. 1998 and references therein). This sense of shear contrasts with extensional (down-dip) layerparallel shear seen in imbricate normal fault arrays (Higgs et al. 1991; Ferrill et al. 1998).

Factors that promote monoclinal folding and enable prediction of monocline development We interpret that three major controls led to the formation of the Big Brushy Canyon monocline: (1) upward propagation of an established fault; (2) presence of a sufficiently thick mechanically weak layer to arrest upward propagation of the fault tip; and (3) presence of a thinly bedded and heterolithic layer, capable of distributed bedding parallel shear and localized bedding-plane slip. Without the

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thick, weak Del Rio Clay, a propagating fault would not arrest. Further, a thick, massive and competent limestone in the position of Buda Limestone would be incapable of bedding-plane slip and folding, and being more brittle, would likely fault before a moderate to steep dip developed.

Implications for inference of strain and fracturing from geometric analysis Deformation is concentrated within the monoclinal limb of the Big Brushy Canyon structure rather than in the higher curvature hinge regions. Analysis of layer curvature would be less effective than dip analysis for identifying relatively intensely fractured zones in structures with a similar history of formation. As also advocated by others (e.g. Fischer & Wilkerson 2000), the practice of using layer curvature to predict fracture localization cannot be applied universally.

Implications for fluid communication The Big Brushy Canyon monocline is developed in stratigraphic units that are equivalent to those at the top of the Edwards Aquifer and overlying confining units along the Balcones fault system in south and central Texas (Arnow 1963; Ferrill et al. 2004). Along most of the 390 km long Balcones fault system, the Del Rio Clay consists of clay rich calcareous shale (Maxwell et al. 1967; Maxwell 1968; Moustafa 1988) and is the upper confining layer for the Edwards Group Limestones. Although the Buda Limestone does not have the same regional importance as the Edwards Aquifer, it is locally important as a water-bearing unit (e.g. Holt 1956), and fractures with dissolution enhancement contribute to permeability of this formation (Ferrill & Morris 2003). Consequently, understanding the integrity of the Del Rio Clay confining layer during extensional fault development is essential for aquifer modelling. The behaviour of this confining layer potentially affects recharge, discharge and contamination of the Edwards Aquifer. As explained below, stratigraphic control of structural development also serves as a useful analogue for fault sealing behaviour in carbonate hydrocarbon reservoirs. In the undeformed state, the Del Rio Clay is an effective barrier to vertical fluid movement and it provides the top seal for the confined Edwards Aquifer (e.g. Arnow 1963, in which the Del Rio Clay is referred to as the Grayson Shale). Faults that have less throw than the thickness of the Del Rio Clay will not juxtapose the overlying Buda Limestone with Edwards Aquifer limestones, and will not therefore generate cross-stratal fluid communication in the upper part of the aquifer. The

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Fig. 8. For see caption see p. 215.

D. A. FERRILL ET AL.

EXTENSIONAL FAULT PROPAGATION MONOCLINE

development of shale smear along the fault plane (e.g. Yielding et al. 1997; Aydin & Eyal 2002) may significantly increase displacements required before across-fault fluid communication is developed – more than twice the thickness of the Del Rio Clay in the case of the Big Brushy Canyon monocline. Because of the ability of the Del Rio Clay to decouple deformation in the Buda Limestone from faulting in the Edwards Aquifer limestones at depth, there is strong potential for monocline development prior to faults breaking across the Buda Limestone. Two important implications are: (1) generation of strongly enhanced fracturing in the Buda Limestone and overlying strong brittle layers is likely to occur in monoclines; and (2) ductile deformation and thinning or smear of the Del Rio Clay, as indicated by the fault– monocline relationship at Big Brushy Canyon described here, is likely to occur along fault planes which may continue to provide effective barriers to fluid flow, even along faults where throw exceeds the thickness of the Del Rio Clay.

Conclusions The strong influence of mechanical stratigraphy manifest in the Big Brushy Canyon monocline is likely to be a useful paradigm wherever faults propagate through mechanically strong layers into thick, weaker strata. Faults propagating upward from the massive Santa Elena Limestone are arrested by the less competent Del Rio Clay. The Del Rio Clay is redistributed, causing monoclinal fault propagation folding in the overlying Buda Limestone. Continued displacement on the underlying fault amplifies the monocline, which grows primarily by limb extension and not by hinge migration. Consequently, faulting of the Buda Limestone is preceded by extensional fault propagation folding and monocline formation. Mesoscale deformation in the monocline is represented by bedperpendicular extension veins and bed-parallel slip surfaces (with an up-dip sense of shear) within competent limestone beds of the Buda Formation. Strain is concentrated primarily in areas of steep dip (i.e.

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monocline limbs), rather than in areas of high curvature (i.e. monocline hinges). The geometry and internal deformation observed in the Big Brushy Canyon monocline is consistent with the geometry and deformation patterns produced in multilayer physical models, and contrasts with the deformation style of single layer models. Specifically, within the mechanically weaker section folding and bedding-plane slip precede fault rupture, and ultimate fault rupture through the section results in fault zone localization. Fault damage zone width is established prior to the fault breakthrough. Bed-parallel extension in more competent beds within the mechanically weaker section occurs through the dipping monoclinal panel, and therefore seismic horizon dip attribute analysis would be a better indicator of fracture development than curvature in reservoirs with similar mechanical characteristics to those at Big Brushy Canyon. Conditions that favour development of extensional monoclines include: (1) upward or downward propagation of an established fault; (2) the presence of a sufficiently thick mechanically weak layer to arrest fault propagation; and (3) the presence of a thinly bedded heterolithic layer capable of distributed bedding-parallel shear and/ or bedding-plane slip. Knowledge of lithostratigraphy and seismic imaging in faulted reservoir sections should enable locations of monoclines and faulted monoclines in the subsurface to be inferred. Similar to clay smear processes in faulted clastic sequences, the Big Brushy Canyon monocline illustrates that ductile flow and smear of clay units in carbonate sections is also capable of isolating limestone layers that appear to be juxtaposed based on displacement or throw magnitudes that exceed the thickness of the intervening clay or shale layers. This work was supported by Internal Research and Development projects R9223 and R9665 from Southwest Research Institute. We thank M. Pittman for granting us access to conduct field work in Black Gap Wildlife Management Area. We appreciate the assistance of C. Patton in manuscript preparation. D. Sims and G. Walter provided

Fig. 8. Interpreted synoptic deformation sequence to illustrate the development of the Big Brushy Canyon monocline and the related mesostructures observed in outcrop. (a) Early horizontal extension nucleated bed-perpendicular extension fractures in the Buda Limestone, and steeply-dipping normal faults in the Santa Elena Limestone. (b) Displacement of the Santa Elena Limestone along the normal fault was accommodated by flow in the Del Rio Clay. The overlying Buda Limestone folded to form a monocline, and bedding-plane slip was localized along thin shale partings between metre-thick massive limestone beds in the Buda Limestone, offsetting earlier-formed fractures with an up-dip sense of shear. Fractures dilated to accommodate layer-parallel (dip-parallel) extension, and calcite precipitated from solution to fill fracture porosity to form veins. (c) As fault slip continued, the Del Rio Clay continued to flow and attenuate, monocline dip steepened, and bedding-plane slip and fracture dilation continued. The latest fracture dilation probably occurred in unsaturated conditions, and last increments of fracture dilation was consequently not filled by calcite vein cementation.

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reviews that significantly improved an earlier version of the manuscript. We thank S. Jolley, R. Holdsworth and R. Butler for their constructive reviews that considerably improved the final manuscript.

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Treatment of faults in production simulation models Q. J. FISHER1 & S. J. JOLLEY2 1

Rock Deformation Research Ltd, School of Earth and Environment, University of Leeds, Leeds, LS2 9JT, UK (e-mail: [email protected]) 2

Shell UK Ltd, 1 Altens Farm Road, Nigg, Aberdeen AB12 3FY, UK

Abstract: This paper describes basic ‘rules-of-thumb’ that offer an indication of common uncertainties and pitfalls, as well as the analytical methods, data requirements and work elements required to replicate the impact of faults on fluid flow in production simulation models successfully. The first, and most important, stage in this modelling process is to ensure that an accurate structural interpretation is incorporated into the simulation model. In particular, that all fault linkages and cross-fault juxtapositions are taken from the seismic interpretation into the simulation grid. Fault rocks sometimes reduce the rate of cross-fault flow in which case it is important to account for this reduction in flow within simulation models. This is best achieved if databases of fault rock properties, measured from the field of interest or nearby similar reservoirs, are up-scaled to calculate fault transmissibility multipliers. It is sometimes necessary to consider not just the single-phase permeability but also the capillary pressure and relative permeability characteristics of the fault rocks present. Finally, all the relevant static and dynamic data must be appraised critically. However, the interpretation of such data is usually non-unique and misinterpretations can create errors in the production-related fault seal analysis. Where these basic guidelines are followed, it has been our experience that the project time required to achieve a history match of production data is dramatically reduced. In addition, as the history match is more geologically reasonable, the model is often more reliable for predicting the long-term behaviour of the reservoir. This gives confidence in the model’s forecast to guide development planning and day-to-day field management decisions.

Faults can severely compartmentalize reservoirs resulting in reduced petroleum recovery (e.g. Corrigan 1993). So, to allow better day-to-day decision-making and long-term planning, it is desirable to account accurately for the impact that faults have on fluid flow within production simulation models. Historically, this has been attempted by altering the transmissibility of each fault within the simulation model (using transmissibility multipliers as described later in this paper) on an iterative trial-and-error basis until a history match of the production data has been achieved. Usually, keywords within the simulation model are used to give each fault a single transmissibility multiplier. A problem with such an approach is that history matches are non-unique and so there is a danger that fault transmissibility multipliers are used to compensate for problems within the simulation model that are not actually related to the presence of faults. For example, in our experience, the extent of sedimentary heterogeneity is often underestimated within geological models and this is often compensated for within simulation models by including sealing faults that may not even be visible on seismic data. In such cases, a convincing history match can be achieved by incorporating unrealistic fault geometries and/or fault transmissibility multipliers into the simulation model – but

the results may not be particularly useful for predicting future production behaviour (Dake 2001). In short, results from production simulation models should be viewed with great caution if unrealistic faults and/or fault transmissibility multipliers are needed to achieve a history match of the production data. To the authors’ knowledge, one of the first published attempts to incorporate geologicallyreasonable fault properties into a production simulation model was made by Bentley & Barry (1991). In this semi-quantitative fault seal analysis, conducted on Block IV of the Cormorant Field, North Sea, it was assumed that clay smearing and sand –shale juxtaposition were the most important fault-related mechanisms that restricted fluid flow. Their study mapped variations in the potential of faults to seal by either clay smear or juxtaposition of reservoir against shale. Leakage paths were created on faults at positions with the lowest seal potential by introducing transmissibility between the corresponding grid blocks in the simulation model. If the transmissibility was insufficient for the simulation model results to history match the historic production data, transmissibility was introduced along parts of the fault with the next lowest sealing potential. The method proved to be not only successful in achieving a history match but

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 219–233. DOI: 10.1144/SP292.13 0305-8719/07/$15.00 # The Geological Society of London 2007.

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also provided a calibration of the geologicallybased clay smear model using production data. Since the study of Bentley & Barry (1991), far more data has become available on the structure of faults (e.g. Harris et al. 2003a) and the singlephase permeabilities of fault rocks (e.g. Fisher & Knipe 1998, 2001). Such data has allowed the impact of different fault rock types (e.g. cataclasites, phyllosilicate-framework fault rocks etc.) on fluid flow to be incorporated into production simulation models. In particular, data on fault thickness and permeability has allowed transmissibility multipliers to be calculated, which, when applied to the faces of grid blocks adjacent to faults, take into account the effect that the fault rock has on fluid flow (e.g. Knai & Knipe 1998; Manzocchi et al. 1999; Jolley et al. 2007). More recently, it has been suggested that instead of just considering the single-phase permeability of faults when calculating transmissibility multipliers, it may be also necessary to take into account the capillary pressure and relative permeability of the fault rocks in production simulations models (Fisher & Knipe 2001; Manzocchi et al. 2002; Rivenæs & Dart 2002; Al-Busafi et al. 2005; Al-Hinai et al. 2006; Ziljstra et al. 2007). Several proprietary and commercial software packages are now available to help implement these new workflows and databases. TransGen (Badley Earth Sciences 1999) was the first commercial package to allow the calculation of unique transmissibility multipliers for all neighbour and non-neighbour connections of the faces of gridblocks adjacent to faults within production simulation models. Since then many of the industry-standard software packages used for structural modelling and fault analysis (e.g. TrapTester, Badley GeoScience Ltd) as well as static geocellular (geological reservoir) modelling (e.g. PetrelTM, RMSTM) and production simulation modelling (e.g. EclipseTM), now contain modules that allow transmissibility multipliers to be calculated based on input such as fault rock thickness, fault rock permeability and clay distribution within the reservoir. Despite the advances described above, very few case studies have been published that have demonstrated the capability of these methodologies to predict the fluid flow properties of faults in petroleum reservoirs. Notable exceptions (e.g. Knai & Knipe 1998; Sverdrup et al. 2003; Yielding 2002; Jolley et al. 2007) have found that history matches of production data from petroleum reservoirs in the northern North Sea and Haltenbanken were improved when transmissibility multipliers calculated from realistic fault rock property data (thickness and permeability) were used within production simulation models to account for the impact

of faults on fluid flow. The limited number of published case studies represents a significant omission because it leaves those undertaking fault seal analysis in a production environment with no clear indication of what works and what does not. A particular problem is that there are many methods available to incorporate fault properties into production simulation models yet there are no clear guidelines as to which method to use for a particular reservoir. For example, here we highlight the point that in some reservoirs it may be beneficial to incorporate multiphase flow properties of faults, whereas in other reservoirs accurate simulation model results may be obtained when only single-phase properties are used. Clearly, the geologist’s job is made easier with guidelines for the choice of algorithms used to calculate fault properties, as appropriate to different reservoir types and geological histories. The engineer’s job would also be made easier if guidelines were developed to identify the circumstances in which it is worth making the added effort of incorporating multi-phase flow properties of faults into simulation models. This paper reviews the ground rules and highlights the importance of key elements of production fault seal analysis by discussing recently published examples, where fault seal analysis has been applied to predict how faults affect petroleum production in North Sea reservoirs. In particular we discuss: † the importance of ensuring that a valid structural interpretation is accurately incorporated into the simulation model; † the benefits of obtaining accurate fault rock property data from either the field being simulated or from similar fields in the same reservoir stratigraphy in the region; † how it may sometimes be beneficial to incorporate the multi-phase flow properties of fault rocks into production simulation models; † the dangers of prematurely assigning fault transmissibility multipliers within simulation models based on static data (e.g. differences in crossfault pressures, petroleum–water contacts or fluid compositions); and † how fault seal analysis in a production setting may develop and some of the hurdles that must be overcome to increase its accuracy and allow it to be applied routinely throughout the oil industry.

Incorporating of an accurate structural model In many reservoirs, juxtaposition of reservoir against non-reservoir is by far the most important

FAULTS IN PRODUCTION SIMULATION MODELS

reason for compartmentalization. In these cases, to achieve a reliable production simulation model, it is important to honour cross-fault sand –sand and sand –shale juxtapositions correctly. In effect, this means that particular care should be taken to map faults on seismic data, generate a geologically realistic layering scheme within the geological model and ensure that these are accurately rendered into the production simulation model. To illustrate the importance of incorporating realistic fault geometry into a simulation model, we summarize some results described by Jolley et al. (2007), from the Brent Province of the North Sea. Figure 1a shows a simulation model that was laterally upscaled by a factor of 4 from an originally fine-scale geocellular model (i.e. 25 m 25 m to 100 m 100 m). The resulting fault structures are modified from the original geometrically ‘realistic’ faults to form gross zig-zag shapes that conform to the cell boundaries in an orthogonal grid system. This treatment resulted in a loss of geometrical integrity between the seismic interpretation, static and simulation models. Comparison of the faults picked from the seismic with those included in the simulation model shows a significant discrepancy. In particular, some faults that could not be seen to link on seismic were linked within the simulation model and vice versa. Thus, in this model, the fault geometries and juxtaposition arrangements have been compromised. The simulation could not be history matched despite more than 270 simulation runs

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being conducted in which properties (e.g. permeability distribution, relative permeability curves etc.) were adjusted over a large area of parameter space. In practice, geologically-unrealistic adjustments to the simulation model were attempted to achieve a match of production data such as applying a five-fold increase in the overall reservoir permeability. Steps were taken to correct some of the problems within the simulation model, by building the static geo-cellular model to the cellular dimensions required by the simulation memory budget (i.e. 100 m 100 m), whilst preserving the structural geometries that had been validated previously in the seismic interpretation and framework modelling. In this way, valid fault-horizon geometries were honoured in transfer from the seismic interpretation and framework model through the static model and preserved during transfer into the simulation model (Fig. 1b). The resulting model proved far easier to history match, coming close to a match within 70 simulation runs, including sensitivity analyses before the exercise was terminated. No geologically-unrealistic changes to the reservoir permeability distribution were required. Although it may seem obvious to advise incorporating a realistic fault pattern into a simulation model, this is still far from being standard practice within industry as a whole. The reasons for this are two-fold. First, there is an implicit assumption in most workflows, that faulting is a subordinate

Fig. 1. Top reservoir depth map of a Brent field in which faults identified from the seismic survey (red lines) are shown with those incorporated into the production simulation model (black lines). Blue lines are the well trajectories. (a) Model I: note significant inconsistencies between the faults mapped from seismic and those incorporated into the static and simulation models (white circles). Some faults have been joined within the simulation model, which appear not to be linked within the seismic survey and vice versa. (b) Model II: the geometrical integrity of the fault pattern is preserved between seismic interpretation, static and simulation models. The effect of preserving the fault juxtaposition geometries, is shown by comparing the simulation results from both models (adapted Jolley et al. 2007).

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element of the reservoir geology. The logic behind this is that the reservoir hosts the fluids and it is therefore important to characterize the reservoir layering and its internal flow unit structure. However, given this focus, the ability of the fault system to interrupt the connectivity of the flow units and thereby compartmentalize a field under production is often underestimated at project planning stage. Consequently, structural geology skills and techniques have been under-applied in the building and quality control of the large number of geological and production simulation models currently being used. Second, even where these skills are applied, complex structural geometries sometimes encountered in a reservoir remain difficult to model within many of the standard geological and production simulation modelling tools that are available (cf. Hoffman & Neave 2007). Even relatively simple features such as horizontal branch lines (Y-shaped faults) and intra-reservoir fault tip lines are difficult to represent accurately in most geological models, and even more problematic to transfer through upscaling into a simulation model. In this situation, time set aside within a project to deal with these issues early in the workflow, can improve the quality of the resulting production simulation model.

Incorporating realistic fault rock flow properties Once a reliable structural model has been incorporated into the production simulation model, the next stage is to take into account the impact that fault rocks have on fluid flow. Most attempts to incorporate measured fault rock petrophysical property data into production simulation models follow a similar approach to Manzocchi et al. (1999). In particular, the transmissibility, Tranij, between two grid blocks, i and j, separated by a fault of constant thickness is calculated using:

where tf is the fault rock thickness, and kf is the fault rock permeability. In most production simulation packages it is possible to take into account the presence of fault rock by applying a transmissibility multiplier, TM, to the face of grid blocks adjacent to the fault. The TM is calculated using: TM ¼

TranFij : Tranij

(3)

It can be seen from these equations that to calculate TM values it is necessary to have data on the thickness and permeability of the fault between the grid blocks. The problem is that seismic-scale faults have a highly complex structure in which the principal fault plane, across which most fault displacement is accommodated, is surrounded by a ‘damage zone’ composed of a high density of sub-seismic faults. The approach of Manzocchi et al. (1999), as well as that used in all of the case-studies reviewed in this paper, assumes that this complexity can be represented within the simulation model by the correct choice of an effective thickness and permeability for the fault rock in the grid blocks adjacent to faults. The thickness of fault rocks is usually estimated from empirically derived relationships between fault thickness and fault throw such as those presented by Hull (1988). For example, Manzocchi et al. (1999) suggest using the relationship: t f ¼ d=170

(4)

where d is the fault displacement. In effect, it is assumed that the fault thickness obtained from such relationships is an effective value that takes into account the combined thickness of fault rock through which fluid passes as it flows across the complex fault zone. Clearly, this is an overly simplistic assumption. However, the use of such empirical relationships is partly supported by the results from numerical modelling of single-phase flow through complex fault zones (Harris et al. 2 (1) 2005, 2007). In particular, the numerical results Tranij ¼ suggest that an effective fault rock thickness equal (Li =ki ) þ (Lj =kj ) to around 50% of the total fault thickness (measured where Li and Lj are the cell lengths, ki and kj are the in a perpendicular transect through seismic-scale permeabilities of the undeformed cells. If fault rock faults and their associated damage zones), could of constant thickness is present between the two be used to calculate TM values that take into grid blocks, i and j, the transmissibility between account fluid flow across the main fault plane and the grid blocks across the fault, TranFij, i and j, is through the associated damage zones. In principle, numerical modelling such as that conducted by calculated using: Harris et al. (2005) could use local measures of fault population statistics to calculate specific 2 TranFij ¼ relationships between fault displacement and thick((Li tf )=ki ) þ (2tf =kf ) þ (Lj tf )=kj ness for individual fields. In practice, the large (2) amount of effort needed to make such calculations

FAULTS IN PRODUCTION SIMULATION MODELS

means that simplistic empirical relationships, such as shown in Equation 4, are more often used to estimate fault rock thickness for TM calculations. The effective permeability of fault rock for calculating TM values is usually obtained from empirical relationships between the clay content of faults and their permeability. There are several ‘workhorse’ algorithms available to estimate the clay distribution along a fault. The Clay Smear Potential (CSP; Bouvier et al. 1989), Shale Smear Factor (SSF; Lindsay et al. 1993) and the Shale Gouge Ratio (SGR; Fristad et al. 1997; Yielding et al. 1997) are amongst the most popular. Bouvier et al. (1989) define CSP as: CSP ¼

X T2 D

(5)

where T is the thickness of a shale bed and D is the distance along the fault from the source bed (Fig. 2a). Essentially, the CSP is a measure of the likelihood that a ‘ductile’ clay smear will be continuous along a fault. Lindsay et al. (1993) defined SSF as: SSF ¼

Xt T

throw exceeds the shale thickness by a factor of 7. However, in some situations, outcrop observations do not show a systematic arrangement of clay smears in relation to their source beds, and instead a stochastic approach is used to ‘place’ the smear distributions along the fault planes (e.g. Childs et al. 2007). Subsurface pressure and production data has also been used to calibrate CSP. For example, study of fault sealing in the Cormorant Field described above by Bentley & Barry (1991) found that a CSP of 5 could be used as a ‘rule-of-thumb’ to separate sealing from non-sealing faults. A key limitation of the CSP and SSF algorithms is that they only provide information on the continuity of clay smears, and do not by themselves provide an estimate of the clay content along a fault when the smear is discontinuous. They are also reliant upon the modeller to define and identify the discrete shale layers that are considered as source beds for the smears. SGR is widely used as an alternative (and in conjunction with CSP to ‘infill’ these properties between the smears), because it provides an estimate of the clay content along a fault irrespective of whether or not the clay smear is continuous. Fristad et al. (1997) and Yielding et al. (1997) define SGR as:

(6)

where T is the thickness of a shale bed, t is the fault throw (Fig. 2b). SSF was used to predict the continuity of abrasion-type clay smears in lithified siliciclastic rocks. Outcrop studies are often used to determine values of SSF and/or CSP to discriminate between continuous and discontinuous clay smears. For example, Lindsay et al. (1993) measured SSF along faults in Carboniferous fluvio-deltaic rocks from northern England and concluded that clay smears often become discontinuous when the fault

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P SGR ¼

ðVcl DzÞ 100% t

(7)

where Vcl is the clay or shale fraction in each layer of thickness Dz and t is the fault throw (Fig. 2c). It is possible to combine these algorithms by using CSP to predict the distribution of clay smears and SGR to predict the distribution of other fault rock types (e.g. cataclasites or phyllosilicate-framework fault rocks). All the algorithms used to estimate the clay distribution along faults require information on the

Fig. 2. Diagram illustrating the meaning of algorithms commonly used to estimate the continuity of clay smears or the clay content of fault zones: (a) clay smear potential (CSP); (b) shale smear factor (SSF) (Lindsay et al. 1993); (c) shale gouge ratio (SGR). Based on Yielding et al. (1997).

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clay and fault offset distribution within the reservoir. Usually, the geological or production simulation model is populated with clay values based on wireline log or seismic data; this is often a major uncertainty in fault seal analysis. The offset of grid-blocks within the geological or production simulation models is used to obtain the fault throw. Once the clay distribution along the fault has been estimated, the permeability of the modelled fault rock is then derived using relationships between clay content and fault permeability. Global correlations between fault rock properties and clay content are often used to estimate fault permeability (e.g. Manzocchi et al. 1999; Sperrevik et al. 2002). The fault permeability in such databases is the absolute (i.e. single-phase) value measured from fault rocks collected in outcrop or core, generally from small-scale faults in the damage zones of seismic-scale faults. It is generally assumed that the permeability of these small-scale features can be incorporated directly into Equation 2 to represent the effective permeability of seismic-scale faults. Fisher & Knipe (2001) highlight several reasons why this assumption may be flawed, but also point out that several studies of outcrop analogues have shown that fault rocks in the core of seismic-scale faults have similar permeabilities to the fault rocks within their damage zones. In other words, there is some justification directly incorporating measurements of the permeability of small-scale faults found within core into Equation 2 to calculate the transmissibility between grid blocks on either side of a fault. A problem with using global databases of fault permeability to calculate TM values is that for any given clay content there tends to be a huge scatter in these data. For example, for clay contents of less than 10%, the fault permeability data presented by Sperrevik et al. (2002) vary by nearly eight orders of magnitude due partly to differences in the stress conditions and porosity at the time of faulting as well as the extent of post-faulting diagenesis (Fisher & Knipe 2001). An alternative approach to using these global databases is to measure the flow properties of faults actually contained within core from the field of interest (e.g. Knai & Knipe 1998). If such core is not available for the field of interest or no faults are present within the core, then it is possible to reduce the uncertainty in assigning fault permeability datasets by using data from carefully selected analogues. In this context, a carefully selected analogue is defined as data from a nearby field or fields within the same reservoir units in which faulting occurred at the same time and that has experienced a similar postdeformation diagenetic history (Jolley et al. 2007). The fault thickness, as well as the clay content and permeability of undeformed grid blocks, usually

shows a large variation throughout the simulation model, which means that fault permeability should also vary such that individual TM values need to be calculated for each neighbour and non-neighbour connection across all faults within the model. This contrasts with the traditional trial-and-error method for history matching simulation models, which usually applied a single transmissibility multiplier value for each fault at best, or universally to all faults in a model at worst. To highlight the benefits of incorporating fault rock property data into a simulation model and using a locally derived fault property dataset we summarize an example of a Brent Group reservoir from the Northern North Sea, described in detail by Jolley et al. (2007). In this case, care was taken in the seismic interpretation, structural validation and modelling of the fault system, prior to incorporating fault property data into the simulation model. The faults picked were accurately incorporated into the geological model and their geometries preserved during upscaling to the simulation model. A huge number of simulation runs (.100) were conducted in which fault TM values as well as other variables were altered by trial-and-error, in an attempt to achieve a history match of production data. In spite of this effort, no convincing history match could be obtained. It was then decided to calculate geologically rational fault transmissibility multipliers systematically in the model, at the early stages of the matching process (i.e. at a stage when few if any significant amendments had been applied to the model to improve the history match). The multipliers were calculated from the cellular structure and property grids of the upscaled model, and then incorporated into the simulation runs. Thus, fault thickness was calculated as a function of fault throw explicit within the model, and the clay distribution along faults within the simulation model was estimated using the SGR algorithm described above. This was then used to calculate fault transmissibility multipliers (sensu Manzocchi et al. 1999). Fault permeability was estimated in two ways. First, the fault permeability was estimated using a correlation derived from data amalgamated from published literature sources presented in Manzocchi et al. (1999): 1 log kf ¼ 0:4 4SGR log (d)(1 SGR)5 (8) 4 where d is the fault displacement. Second, fault permeability was taken directly from a correlation between the clay content and the permeability of small-scale faults present in drill cores from this field, and other nearby Brent Group fields that had experienced a similar burial-strain history. In both

FAULTS IN PRODUCTION SIMULATION MODELS

cases, the simulation model provided a far better history match of the production data than had been achieved by changing TM values by trial-and-error, applied uniformly to all faults in the model and on a fault-by-fault basis. Overall, however, the simulation match that used local fault rock property data was significantly better. For example, Figure 3 shows actual field water production data as a function of time as well as the results for three models. The first model was run using traditional juxtaposition analysis and iterative trial-and-error approach to identify a ‘best fit’ TM to apply universally to all faulted cell connections in the model. Restrictions to fluid flow were thus assumed to result largely from the juxtaposition of sediments with contrasting flow properties (i.e. sand against shale). In the second model, fault rock permeability was incorporated using the global relationship represented in Manzocchi et al. (1999), such that a unique TM was calculated for each faulted cell connection in the model. In the third, these unique TMs were calculated based on the empirical relationship between fault rock permeability and clay content values, measured from small-scale faults present in local drill core from this and other Brent Group fields with similar burial-stress histories to the study reservoir. Sophisticated up-scaling techniques were not applied. Instead, the core measurements were used to derive an empirical relationship between clay content and fault permeability. The clay distribution

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along faults within the simulation model was then estimated using the SGR algorithm from which the fault permeability was calculated directly from the empirical correlation between clay content and fault permeability. This fault permeability was then incorporated directly into Equation 2 to calculate the transmissibility between grid blocks on the opposite sides of the faults. Figure 3 shows that the model based on global fault rock properties is an improvement on the model in which a ‘traditional’ juxtaposition approach was used. However, the model using locally derived fault permeabilities provides the best history match.

Considering the multi-phase flow properties of faults Traditionally, the multi-phase flow properties of faults have not been taken into account during production simulation modelling. However, it has recently been suggested that more effort should be devoted to researching the importance of incorporating the multi-phase flow properties of faults in production simulation models (Manzocchi et al. 1998, 2002; Manzocchi 1999; Fisher & Knipe 2001; Rivenæs & Dart 2002; Al-Busafi et al. 2005; Al-Hinai et al. 2006). The small pore throats of many fault rocks means that if they are water-wet then they should have such high water saturations close to the free water level (FWL)

Fig. 3. Cumulative water production history match results for a Brent-type reservoir. Compare the actual history data (black line) with results from the simulation model: without taking into account fault rock property data (red line); and where fault rock properties were estimated from global amalgamated datasets and a locally measured database (blue and green lines respectively). The latter model created the best history match of the production data (adapted from Jolley et al. 2007).

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that they will have negligible relative permeability to hydrocarbons (krh). The fault rocks within this zone will still be permeable to water but, in many situations, the adjacent undeformed reservoir would have a sufficiently low water saturation, and hence low relative permeability to water (krw), that significant cross-fault flow of water would be unlikely. At some distance above the FWL the buoyancy force in the hydrocarbon column may be sufficient to overcome the threshold pressure of the fault rock thereby allowing the fault rock to have a finite relative permeability to hydrocarbons (see Fisher et al. 2001; Al-Busafi et al. 2005; Zijlstra et al. 2007). The results from the first published relative permeability measurements to be conducted on fault rocks (Al-Hinai et al. 2006) indicate that, for buoyancy forces generated by most hydrocarbon columns, the effective permeability of fault rock to petroleum (i.e. the product of absolute and relative permeability) could be two orders of magnitude or more lower than their absolute permeability values. In other words, the transmissibility of faults to petroleum could be over two orders of magnitude lower than the value calculated solely on the single-phase permeability. To the authors’ knowledge, there are very few published accounts of multi-phase flow properties of faults being incorporated into production simulation models. Al-Hinai et al. (2006) and Ziljstra et al. (2007) describe attempts to incorporate the relative permeability and capillary pressure of cataclastic fault rocks into production simulation models of Rotliegend reservoirs in the southern North Sea. Al-Hinai et al. (2006) present a simplified production simulation model of a Rotliegend reservoir in which a 250 bar pressure difference had built up across a fault that juxtaposed reservoir against reservoir. A local grid refinement was used to represent the fault as discrete cells that were given their own relative permeability and capillary pressure curves. Given the relatively sand-rich nature of the reservoir, entrainment of clay into the fault is insufficient to produce the permeability reduction capable of supporting the observed 250 bar cross-fault pressure difference. Faults in the Rotliegend are often cemented by minerals such as anhydrite, siderite and barite (e.g. Fisher & Knipe 2001). However, such cements are not thought to be developed continuously along faults (Fisher & Knipe 1998, 2001) and are not therefore likely to be responsible for such large pressure differences developing during gas production. Instead, modelling suggests that this could only be reproduced realistically if the relative permeability and capillary pressure of the clay-poor fault rock were taken into account. Ziljstra et al. (2007) accounted for the relative permeability characteristics of faults rocks in the production simulation models for two

Rotliegend reservoirs with substantial production history. In both cases, history matches were achieved almost at once, requiring only four or five runs whereas over 100 runs had been made in previous (but unsuccessful) attempts to achieve a match using ‘traditional’ trial-and-error approaches for determining transmissibility multipliers. The non-unique nature of history matches means that these results cannot be taken as unequivocal evidence that the flow properties of the faults had been estimated accurately. However, the results are extremely encouraging in that they offer good physical explanations for two aspects of the production behaviour of these reservoirs. In one reservoir, infill wells often found higher gas pressures when they crossed faults at the flanks of the reservoir whereas gas pressures had tended to equilibrate within the central region. This can be explained in terms of two-phase flow as the capillary entry pressure of faults that are close to the flanks of the reservoir faults is less likely to have been exceeded than faults in the centre of the reservoir. This is simply because the top of the reservoir is closer to the FWL on the flanks, and therefore the buoyancy force in the gas column adjacent to the faults on the flanks is less than can build up in the centre of the field where the gas column is highest (Fig. 4). In a second example presented by Ziljstra et al. (2007), a 20 m differential rise in gas–water contact (GWC) was found to occur across a fault as a result of gas production (Fig. 5a). The rise in GWC is best explained if brine in the aquifer can cross the fault but gas cannot. Again this is easily explained in terms of two-phase flow. The fault in the aquifer does not act as a significant barrier to the flow of brine because only one phase is present and the fault is thin and relatively permeable. However, above the GWC, the gas needs to overcome the capillary entry pressure of the water-wet fault rock before it can flow and even then its flow will be impeded because two phases are present within the pore-space. Incorporation of these effects into the production simulation model was found to provide a good match of the rise in FWL, which was not achieved when multi-phase flow effects were not considered (Fig. 5b). Theory, special core analysis and the results from simulation history matching to production data therefore provide a reasonable indication that in some situations it is crucial to take into account the multi-phase flow properties of faults in simulation models. However, two significant problems need to be overcome before it becomes more common practice. First, there has only been one published study so far in which the relative permeability of fault rocks has been measured (Al-Hinai et al. 2006) and far more data is required to understand the range of properties that they may

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227

Fig. 4. Conceptual model for multi-phase flow across a fault in a petroleum reservoir. (a) The fluid saturations within the reservoir and fault, red for gas, blue for water. (b) The capillary pressure and (c) The relative permeability curves for the fault rock. It is assumed that the fault rock is homogenous throughout the model and that any differences in flow behaviour are due to the balance between capillary and buoyancy forces. The fault has a higher capillary entry pressure than the reservoir. Below the FWL (Zone 1), only brine is present in the undeformed reservoir and the fault rock and therefore TM values can be calculated from the single-phase fault rock permeability values. Close to the FWL (Zone 2), the buoyancy force in the hydrocarbon column is not sufficient to overcome the threshold pressure of the fault. Hence, it has zero relative permeability to hydrocarbon. If the column height is sufficiently high to overcome the capillary entry pressure of the fault (Zone 3) the fault will have a finite relative permeability to gas. The red line marks the height at which the buoyancy force in the gas column is sufficiently high to overcome the capillary entry pressure of the fault rock. It can be seen that faults at the flank of the reservoir are more likely to act as barriers to gas flow because the buoyancy force at the edge of the reservoir is not as high as can be generated in the centre of the reservoir. So the capillary entry pressure of faults in the centre of the field are more likely to be overcome than faults at the flank (adapted from Fisher et al. 2001).

have. Second, although the technology has recently emerged in a few in-house and commercial packages (e.g. TransGen to Badley Earth Sciences 2005), further work is required to develop methods and software functionality, in an industrystandard sense, to allow the routine incorporation of multi-phase flow properties of fault rocks into production simulation models. In terms of generating more data, several joint industry research projects are currently underway to measure the relative permeability of fault rocks. At present, work has been conducted measuring the relative permeability to gas of some low permeability cataclastic faults from PermoTriassic

sandstones from outcrops in the UK (Al-Hinai et al. 2006). However, far more data is required on the relative permeability characteristics of more clay-rich fault rocks, especially to oil. In terms of software implementation, three methods have already been used to incorporate relative permeability and capillary pressure measurements of fault rocks into simulation models. Manzocchi et al. (2002) suggested that pseudofunctions (i.e. pseudo-relative permeability and capillary pressure curves) could be calculated for the grid-cells adjacent to faults that would provide effective flow properties for both the fault rock and its adjacent undeformed sediment. Indeed, the

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Q. J. FISHER & S. J. JOLLEY (b) 70

(a) 8200

60

GWC rise (ft)

TVDSS (ft)

8320 8440 8560 8680

50

Measured Baffle model Tank model

40 30 20 10

2 km

8800

0 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Time (Year)

Fig. 5. (a) Cross section showing the rise of FWL in a compartment within Field B described by Ziljstra et al. (2007). The best explanation for the differential rise in FWL across the fault is for the fault to be acting as more of a barrier to flow in the gas leg than in the aquifer. (b) Comparison of the rise in FWL that was measured with that predicted by a model which does not take into account two-phase flow (Tank Model) with the model in which two-phase flow effects are incorporated (Baffle Model). Clearly, the baffle model provides the better history match.

latest version of the TransGen software (Badley Earth Sciences 2005) contains algorithms to calculate pseudo-relative permeability curves for the grid blocks adjacent to faults, which incorporate the multi-phase flow properties of fault rocks. A key problem with the use of pseudo-functions is that they will vary depending on factors such as fluid flow rate, fault thickness, fault permeability (relative and absolute), host permeability, whether the fault is undergoing drainage or imbibition etc. In effect, this means that different pseudo-functions could be generated for every cell adjacent to a fault within the simulation model. This would generate a huge burden on the memory budget for simulations run within most full-field models unless these are simplified, thus damaging the geological detail and coherence of the models, which we argue should be preserved. It is therefore necessary to limit the number of pseudo-curves incorporated into the model by grouping (Christie 1996; Manzocchi pers. comm. 2005). An alternative approach is to include the fault as a discrete material object (e.g. Al-Busafi et al. 2005), which can be given its own relative permeability and capillary pressure curves. As the cumulative fault rock thickness is usually thin (,1 m) and it has a high permeability contrast with the surrounding sediment, a local grid refinement is required to increase numerical stability in the simulation. Only a small number of faults can be incorporated into a model in this way, before the model size becomes too large. Hence this approach could not be used practically to model large structurally complex reservoirs. However, the approach is ideal for constructing simplified models to test the importance of incorporating multi-phase flow properties into a production simulation model for a given field. Indeed, it would be

worthwhile running sensitivity tests on such simplified models prior to full-field simulation to test the importance of incorporating multi-phase flow properties into the simulation model. This could save a huge amount of time as some modelling has suggested that in many situations it is not necessary to consider the relative permeability of faults in simulation models (Al-Busafi et al. 2005; cf. Jolley et al. 2007). Another pragmatic approach to incorporating the relative permeability and capillary pressure characteristics of faults into some simulation models has been presented by Ziljstra et al. (2007). Their approach divides faults into three zones according to their position relative to the FWL. Transmissibility multipliers for parts of the fault below the FWL are calculated based on the absolute permeability of the fault rock as established through laboratory measurements on faults within core. The fault immediately above the FWL is assumed to be totally sealing to hydrocarbons until its capillary entry pressure is exceeded (i.e. it is given a TM value of 0). The height above the FWL that is made totally sealing is calculated based on the threshold pressure of fault rocks measured by Hg-injection analysis. (Failure to conduct Hg-injection analysis under reservoir stress conditions and uncertainties in converting Hg-injection data into the gas –water system is likely to introduce errors in the calculation of the sealing height.) At greater distances above the FWL, the fault is assumed to allow gas to flow and given a TM value calculated from the gas relative permeability of the fault rock, assuming it to be at irreducible water saturation. In other words, the term kf in Equation 2 is assumed to be the absolute permeability of the fault rock multiplied by its gas relative permeability at irreducible water saturation.

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Ziljstra et al. (2007) used this approach to model the impact of faults on fluid flow within two fault compartmentalized Rotliegend reservoirs from the southern North Sea. The approach is particularly suited to these reservoirs as there are only small changes in FWL during production, therefore the transmissibility multipliers are not expected to change dramatically during production. The history matches in both cases were achieved very rapidly using this new method. It is also relevant that the fault properties used to achieve these history matches were identical to values measured in core. In particular, the geometric average of the fault permeability data and the arithmetic average of the Hg-injection threshold pressures obtained from core samples were the same values used to obtain the history match of the production data.

Critical appraisal of static and dynamic data All of the basic data required to predict the fluid flow properties of faults in the subsurface have large uncertainties: † Structural mapping and fault-horizon modelling derived from seismic data tend to vary significantly depending on factors such as: (i) the vintage of the seismic survey used for the interpretation; (ii) the azimuth at which the seismic data was shot; (iii) the methodology used to process and depth convert or migrate the seismic data; (iv) the skills of the seismic interpreter; and (v) the project time given to perform the interpretation (e.g. Ottesen et al. 2005; Suiter et al. 2005). † There are commonly large uncertainties regarding the distribution of sub-seismic faults (e.g. Ottesen et al. 2005). † There are inherent uncertainties associated with the calculation of net: gross, Vshale and Vclay values from well logs, especially since the methods used are not standardized across the petroleum industry. Consequently, there are related uncertainties in defining discrete sand– shale layering and model property (clay, porositypermeability) grids. † There are uncertainties regarding conceptual models of the broad depositional and local sediment architectures and consequently in the modelling of associated clay and porositypermeability distribution within a reservoir (e.g. Henriquez & Jourdan 1996). † Different algorithms (e.g. various SSF, CSP, SGR), often provide very different estimates of the clay distribution along faults, none of which may be particularly accurate (e.g. Foxford et al. 1998) and need to be used on-merit, as

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appropriate to the distribution of sand –shale within the reservoir being modelled, as well as its burial history. † There could be in excess of an order of magnitude uncertainty regarding the permeability (Fisher & Knipe 2001) and thickness (Manzocchi et al. 1999) of fault rocks. Faced with such wide-ranging uncertainties, it is important to calibrate fault seal methodologies by establishing whether they are consistent with subsurface data (i.e. petroleum distributions, production data etc.). Unfortunately, the interpretation of static and dynamic data is often non-unique (Dake 2001) and therefore great care must be exercised in its use. It is our experience that misinterpretation of static and dynamic data, regarding what it actually reveals about the fluid flow properties of faults, is a common error within the industry. For example, when faced with different petroleum–water contacts across faults it is common practice to presume that the reservoir is compartmentalized as a result of faulting. However, there are other reasons why petroleum– water contacts vary across a field other than fault-related compartmentalization: † Perched water contacts are not uncommon (e.g. Weber 1997). † Active aquifers may result in tilted petroleum– water contacts, especially in low permeability sequences with heavy oil (e.g. Moss et al. 2003). † Cross-fault changes in the capillary entry pressure of sediments may lead to differences in petroleum water contact (e.g. Smith 1966). † Recent tectonic activity may result in a tilted petroleum water contact (Harris et al. 2003b). It is therefore important to establish whether differences in petroleum–water contacts are actually caused by the faults or by other causes. Failure to do so can lead to the false conclusion that faults are far more resistive to fluid flow than is the case. The Pierce Field in the UK North Sea provides an example highlighting the benefits of correctly determining the cause of differences in fluid contacts, and the subsurface uncertainties that are faced in making that definition. Petrophysical well logs from the early development drilling campaigns, were interpreted to show that FWL varied by around 500 m across the field (Fig. 6a). It would have been tempting to attribute these differences to the presence of sealing faults. However, with application of modern sedimentological analysis as well as the determination of the petroleum contact in further wells, it was thought that instead of sealing faults, the FWL could be tilted due to the presence of a hydrodynamic head. Al-Busafi (2005) compared simulation models in which the faults separating wells with different

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Fig. 6. (a) Diagram showing the different gas– and oil– water contacts across the Pierce Field in the central North Sea, UK. (b) The field water production data compared to the results from production simulation models in which faults were treated as totally sealing (Old TM simulation) and results from the simulation model in which fault transmissibility multipliers were calculated (New TM simulation) from core data (adapted from Al-Busafi 2005).

FWLs were treated as sealing, with simulation models where fault transmissibility multipliers were calculated based on realistic fault rock permeability data. The results showed that the models that incorporated realistic fault property data, provided a better history match to production data than the one in which faults were assumed to be sealing (Fig. 6b). The history match of the model that incorporated realistic fault rock properties is still far from perfect because no attempt was made to improve the match by altering other properties within the simulation model (e.g. permeability distribution etc). In addition, with reprocessed seismic data and re-interpretation and modelling work in progress at the time of writing, the mapped and modelled fault architecture is evolving from that perceived and captured in the vintage of models on which Al-Busafi (2005) based his work. A new fault configuration, changes to reservoir sand-body architectures and amalgamation characteristics, and dynamic re-interpretation of petrophysical logs, are all changing the complexion of our understanding of the evolution of petroleum contacts in the field. It is possible that some form of combined tilted-compartment baffled contact arrangement will be resolved, but this remains to be seen. The converse can also occur. In particular, faults may allow cross-fault flow to occur over geological time, and given the right circumstances, rapid flow may occur laterally and vertically within the plane of active fault zones (e.g. Gartrell et al. 2004; Ligtenberg 2005; Wilkins & Naruk 2007). However, the rapid flow rate occurs in pulses and cannot be sustained by these processes, such that

the faults may still prove to be flow barriers during production drawdown. As discussed above, the Brent Province fields described by Jolley et al. (2007) and the Rotliegend fields described by Ziljstra et al. (2007) are all examples where faults have not sealed over geological time but have acted as barriers during production. The evidence used to determine whether or not a reservoir is compartmentalized was reviewed by Smalley et al. (2004). Some measures of compartmentalization, such as differences in the molecularlevel composition of pore fluids can be unreliable if used without care and attention to the fluid types and reservoir geometries and properties, because they take such a long time to equilibrate by diffusion (.10 Ma). Of course, this happens far more quickly if buoyancy-driven convective mixing occurs (e.g. light oil rising through heavy oil in a dipping structure). Thus, although these measures are an indicator of differential charge, they may be misinterpreted to predict compartmentalization under production drawdown, when in fact the fluids may be in mutual communication with the well stock. Data on the fluid flow properties of faults is extremely useful when attempting to appraise static data critically. For example, if large differences in petroleum–water contacts exist across a fault we always attempt to assess whether those differences are consistent with the fault rock properties within the area. If they are not consistent we then attempt to find other explanations for the differences. A particularly important use of fault rock property databases has been in the critical

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appraisal of the meaning of pressure differences in the aquifer. Overall, faults are so thin and have sufficiently high permeability to water that they should allow cross-fault pressure differences in the aquifer to equilibrate rapidly over geological time (e.g. Smalley et al. 2004). Therefore if pressure differences are observed in the aquifer it is necessary to look for other causes than the presence of fault rock in isolation. In general, differences in aquifer pressure are usually caused either by active aquifer drive or the lack of juxtaposition of the reservoir within aquifer across the fault. Information on the fluid flow properties of fault rocks is also useful for the critical appraisal of dynamic data in terms of what it is revealing about the fluid flow behaviour of seismic-scale faults. For example, fault-related barriers to production are most frequently identified when a fault transmissibility multiplier is required to achieve a history match of production data. In many such cases, we have found that fault transmissibility multipliers that have been applied to history match the simulation model correspond to fault rock permeabilities that are several orders of magnitude lower than have ever been measured. In these cases, we suspect that the faults are simply being used to compensate for other inaccuracies in either the reservoir characterization or the simulation model. To identify such situations, it is recommended that where fault transmissibility multipliers are used to achieve a history match, the corresponding fault permeability is compared to global and local databases of fault permeability to establish whether or not they are feasible and realistic. This can be achieved by assuming a fault rock thickness and then rearranging Equation 1, above, to calculate fault permeability.

Conclusions A geologically-rational, evidence-based review has been presented as a guideline for treating faults in production simulation models, as appropriate to the specific geological and fluid characteristics that are particular to a reservoir under study. Examples have been described where this approach has been applied to geometrically robust models of different reservoir types. Far better history matches of production data have been achieved in these cases more quickly than was possible using geometrically weak models and/or by applying ‘universal’ fault transmissibility multipliers by traditional trial-and-error methods. This increases confidence in the reliability of the predictive capabilities of the simulation models. Significant advances have been made in recent years, which now allow geologically-reasonable

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fault seal analyses to be conducted routinely on reservoir modelling projects within operating assets. Based on the case studies discussed in this paper, we would provide the following general advice for anyone wishing to incorporate the effects of faults on fluid flow in production simulation: † Ensure that a geometrically valid structural interpretation is accurately preserved during transfer and incorporation into the static and simulation models. This is best achieved through modelling and validation in conjunction with seismic interpretation, and preserving the geometrical integrity of the resulting static model during upscaling into the simulation model. Thus, it is also recommended that the scale of the geological model grid is set to that which the reservoir engineer will use in the simulator. This ensures that the structural model does not get compromised during upscaling, since the model is transferred without changing cellular dimensions. † Calculate transmissibility multipliers based on realistic flow properties of the fault rocks present within the field. This is best achieved if databases of fault rock properties (permeability and capillary entry pressure) are obtained from the field of interest or local databases measured from similar nearby fields and reservoir units are used. Sophisticated upscaling techniques were not found necessary to improve history matches of production data. Instead, transmissibility multipliers were calculated using: (i) fault thickness values estimated from empirical correlations between fault throw and thickness; and (ii) permeability values measured from the small-scale faults found within the damage zones of larger-scale features. † In some situations, such as high net: gross reservoirs with cataclastic fault rocks, it is important to consider not just the single-phase permeability but also the capillary pressure and relative permeability of the fault rocks present. † Finally, in order to avoid errors being introduced into the production-related fault seal analysis, critical appraisal of all the relevant static and dynamic data is necessary to identify the fluid flow properties of faults within the field of interest. Interpretations of static and dynamic data are often non-unique, so care must be taken in concluding what the data actually reveal about fault-related fluid flow. We would first of all like to express our thanks to Shell and ExxonMobil for approval to publish this manuscript. We also thank our Shell colleagues for their part in helping to test, develop and implement our ideas in ‘live’ asset

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projects. I. Berchenko, H. Dijk, D. Eikmans, M. de Keijzer, I. van der Molen, P. Reemst, W. Wiersema, C. Wood and E. Zijlstra deserve a special mention. Comments from R. Elsinger and J. Marshall, and careful reviews from D. Barr, M. Bentley and P. Bretan helped us to improve this manuscript.

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1998. Structure and content of the Moab fault zone, Utah, USA, and its implications for fault seal prediction. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. J. (eds) Faulting and Fault Sealing in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 87–103. F RISTAD , T., G ROTH , A., Y IELDING , G. & F REEMAN , B. 1997. Quantitative fault seal prediction: a case study from Oseberg Syd. In: M ØLLER -P EDERSON , P. & K OESTLER , A. G. (eds) Hydrocarbon Seals: Importance for Exploration and Production. Norsk Petroleumsforenig, Special Publications, 7, 107–124. G ARTRELL , A., Z HANG , Y., L ISK , M. & D EWHURST , D. 2004. Fault intersections as critical hydrocarbon leakage zones: integrated field study and numerical modelling of an example from the Timor Sea, Australia. Marine and Petroleum Geology, 21, 1165– 1179. H ARRIS , S. D., M C A LLISTER , E., K NIPE , R. J. & O DLING , N. E. 2003a. Predicting the three-dimensional population characteristics of fault zones: a study using stochastic models. Journal of Structural Geology, 25, 1281– 1299. H ARRIS , K., F ILBRANDT , J., H OSSAIN , M. & S HUAILY , H. 2003b. The impact of carbonate-carbonate sealing faults in oilfields of NW Oman. Presented at EAGE Conference ‘Top and Fault Seals: where are we and where do we go?’ Montpellier, September 2003. H ARRIS , S. D., F ISHER , Q. J., V ASZI , A. & W U , K. 2005. Modelling the effects of faults on fluid in petroleum reservoirs: an example of mutiscale-multiphysics simulation. In: I NGHAM , D. B. & P OP , I. (eds) Transport Phenomena in Porous Media, Volume III, 441–476. H ARRIS , S. D., V ASZI , A. & K NIPE , R. J. 2007. Threedimensional upscaling of fault damage zones for reservoir simulation. In: J OLLEY , S. J., B ARR , D., W ALSH , J. J. & K NIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 353–374. H ENRIQUEZ , A. & J OURDAN , C. 1996. Challenges in modelling reservoirs in the North Sea and on the Norwegian shelf. In: G LENNIE , K. & H URST , A. (eds) AD1995: NW Europe’s Hydrocarbon Industry. Geological Society, London, 157– 166. H OFFMAN , K. S. & N EAVE , J. W. 2007. The fused fault block approach to fault network modelling. In: J OLLEY , S. J., B ARR , D., W ALSH , J. J. & K NIPE , R. J.(eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 75–87. H ULL , J. 1988. Thickness – displacement relationships for deformation zones. Journal of Structural Geology, 10, 431–435. J OLLEY , S. J., D IJK , H., L AMENS , J. H., F ISHER , Q. J., M ANZOCCHI , T., E IKMANS , H. & H UANG , Y. 2007. Faulting and fault sealing in production simulation models: Brent Province, northern North Sea. Petroleum Geoscience. 13, 321–340. K NAI , T. A. & K NIPE , R. J. 1998. The impact of faults on fluid flow in the Heidrun Field. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. J. (eds) Faulting and Fault Sealing in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 269– 282. L IGTENBERG , J. H. 2005. Detection of fluid migration pathways in seismic data: implications for fault seal analysis. Basin Research, 17, 141– 153.

FAULTS IN PRODUCTION SIMULATION MODELS L INDSAY , N. G., M URPHY , F. C., W ALSH , J. J. & W ATTERSON , J. 1993. Outcrop studies of shale smears on fault surfaces. In: F LINT , S. T. & B RYANT , A. D. (eds) The Geological Modelling of Hydrocarbon Reservoirs and Outcrop. International Association of Sedimentology, Special Publications, 15, 113–123. M ANZOCCHI , T. 1999. Towards an improved fault representation in two-phase reservoir simulation. EAGE 61st conference and technical exhibition, Helsinki, Finland, 7– 11 June 1999; Volume 1; C– 05. M ANZOCCHI , T., R INGROSE , P. S. & U NDERHILL , J. R. 1998. Flow through fault systems in high porosity sandstones. In: C OWARD , M. P., J OHNSON , H. & D ALTABAN , T. (eds) Structural Geology in Reservoir Characterization. Geological Society, London, Special Publications, 127, 65– 83 M ANZOCCHI , T., W ALSH , J. J., N ELL , P. & Y IELDING , G., 1999. Fault transmissibility multipliers for flow simulation models. Petroleum Geoscience, 5, 53–63. M ANZOCCHI , T., H EATH , A. E., W ALSH , J. J. & C HILDS , C. 2002. The representation of two-phase fault-rock properties in flow simulation models. Petroleum Geoscience, 8, 119 –132. M OSS , B., B ARSON , D., R AKHIT , K., D ENNIS , H. & S WARBRICK , R. 2003. Formation pore pressure and formation waters. In: E VANS , B., G RAHAM , C., A RMOUR , A. & B ATHURST , P. (eds) The Millennium Atlas: Petroleum Geology of the Central and Northern North Sea. Geological Society, London, 317– 329. O TTESEN , S., T OWNSEND , C. & Ø VERLAND , K. M. 2005. Investigating the effect of varying fault geometry and transmissibility on recovery: Using a new workflow for structural uncertainty modelling in a clastic reservoir. In: B OULT , P. & K ALDI , J. (eds) Evaluating Fault and Cap Rock Seals. American Association of Petroleum Geologists, Hedberg Series, 2, 125–136. R IVENÆS , J. C. & D ART , C. 2002. Reservoir compartmentalization by water-saturated faults - Is evaluation possible with todays tools? In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seal Quantification. Norsk Petroleumsforenig, Special Publications, 11, 187– 201. S MALLEY , P. C., E NGLAND , W. A., M UGGERIDGE , A. H., A BACIOGLU , Y. & C AWLEY , S. 2004. Rates of reservoir fluid mixing: implications for interpretation of fluid data. In: C UBITT , J. M., E NGLAND , W. A. & L ARTER , S. (eds) Understanding Petroleum Reservoirs: Towards an Integrated Reservoir Engineering

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Definition of a fault permeability predictor from outcrop studies of a faulted turbidite sequence, Taranaki, New Zealand C. CHILDS1, J. J. WALSH1, T. MANZOCCHI1, J. STRAND1,5, A. NICOL2, M. TOMASSO3,6, ¨ PFER1 & A. C. APLIN4 M. P. J. SCHO 1

Fault Analysis Group, School of Geological Sciences, University College Dublin, Belfield, Dublin 4, Ireland (e-mail: [email protected]) 2

GNS Science, P.O. Box 30368, Lower Hutt, New Zealand

3

Marine and Petroleum Geology Group, School of Geological Sciences, University College Dublin, Belfield, Dublin 4, Ireland

4

School of Civil Engineering and Geosciences, School Office: Cassie Building, University of Newcastle upon Tyne NE1 7RU, UK 5

CSIRO Petroleum, P.O. Box 1130, Bentley, WA 6102, Australia

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Present address: Bureau of Economic Geology, The University of Texas at Austin, University Station, Box X, Austin, Texsas 78713-8924, USA Abstract: Post-depositional normal faults within the turbidite sequence of the Late Miocene Mount Messenger Formation of the Taranaki Basin, New Zealand are characterized by granulation and cataclasis of sands and by the smearing of clay beds. Clay smears maintain continuity for high ratios of fault throw to clay source bed thickness (c. 8), but are highly variable in thickness, and gaps occur at any point between the clay source bed cut-offs at higher ratios. Although cataclastic fault rock permeabilities may be appreciably lower (c. two orders of magnitude) than host rock sandstone permeabilities, the occurrence of continuous clay smears, combined with low clay permeabilities (10s to 100s nD) means that the primary control on fault rock permeability is clay smear continuity. A new permeability predictor, the Probabilistic Shale Smear Factor (PSSF), is developed which incorporates the main characteristics of clay smearing from the Taranaki Basin. The PSSF method calculates fault permeabilities from a simple model of multiple clay smears within fault zones, predicting a more heterogeneous and realistic fault rock structure than other approaches (e.g. Shale Gouge Ratio, SGR). Nevertheless, its averaging effects at higher ratios of fault throw to bed thickness provide a rationale for the application of other fault rock mixing models, e.g. SGR, at appropriate scales.

A large number of parameters are required to define a model of a fault system for the purposes of examining the flow response of a faulted siliciclastic reservoir. These parameters can be divided into those which define the geometrical scaling properties of the fault system and those which define the flow properties of the faults. Fault properties are generally included in reservoir simulators as transmissibility multipliers which modify the potential for flow from one side of a fault to the other (Manzocchi et al. 1999). The calculation of geologically meaningful fault transmissibility multipliers requires predictors of both fault rock thickness and permeability. Fault rock thickness can usually be predicted from the well established positive correlation with fault displacement. Definition of a fault rock permeability predictor is a much more difficult task due to the strongly heterogeneous

and anisotropic nature of fault rocks. Permeability predictors are necessarily based on highly simplified and idealized conceptual models of fault rock which, it is hoped, capture the main controls. Conventional fault permeability predictors vary from those which implicitly assume that fault rocks represent a mixed aggregate of the faulted sequence, with equivalent average permeabilities, such as the Shale Gouge Ratio method (Yielding et al. 1997; Manzocchi et al. 1999; Harris et al. 2002; Sperrevik et al. 2002), to those which provide a simple means of modelling clay smears within fault zones, such as the Shale Smear Factor method (Lindsey et al. 1993). These methods are generally informed by previously published observational and quantitative constraints derived from outcrop studies and by fault permeability measurements from outcrop and subsurface datasets.

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 235–258. DOI: 10.1144/SP292.14 0305-8719/07/$15.00 # The Geological Society of London 2007.

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However, a shortcoming of previous work is that there have been relatively few detailed studies of fault rock distribution within heterogeneous sequences, and these studies rarely consider the full range of issues associated with fault property calculation, from descriptive aspects through to predictive methods. In this paper we present a detailed description of the fault rock distributions associated with normal faults offsetting a poorly lithified, sand– clay turbidite sequence from the Taranaki Basin, North Island, New Zealand. Quantitative constraints from outcrop studies, combined with fault rock permeability measurements, then provide a basis for the development of a novel permeability predictor for faults, referred to as the Probabilistic Shale Smear Factor method. This predictor is compared with existing methods, such as the Shale Gouge Ratio method, and recommendations are made for their application in reservoir modelling. Although the Probabilistic Shale Smear Factor method is developed here for faults offsetting poorly lithified turbidites, its application is not necessarily limited to this setting and it may be applicable to any settings where continuous clay smears are developed.

Geological setting of study area The study area is on the eastern margin of the Taranaki Basin, on the west coast of North Island, New Zealand (Fig. 1). The Taranaki Basin is New Zealand’s only hydrocarbon producing basin and the study area was chosen primarily for its excellent coastal exposures of faulted deep-water turbidites of the upper Miocene Mount Messenger Formation, which is one of the main hydrocarbon reservoir intervals in the Taranaki Basin (Fig. 2). Oil and gas fields producing from the Mount Messenger Fm lie c. 40 km to the SW of the outcrop study area (Fig. 1). A brief outline is given of the geological setting of the study area and descriptions of the outcrop dataset which is the basis for this study. The Taranaki Basin contains Upper Cretaceous and Cenozoic strata with a maximum combined thickness of 9 km (King & Thrasher 1996). The basin originated in the late Cretaceous as a result of extension related to opening of the Tasman Sea and break-up of East Gondwana and since then has had a complex post-Cretaceous development, with several subsidence events related to relative movements of the Australian and Pacific plates (King & Thrasher 1992, 1996). Crustal extension in the last 6 Ma is believed to have risen from back-arc rifting in response to roll-back of the subducting Pacific Plate beneath the North Island. In the northern Taranaki Basin, 1 km– 1.5 km of post-Miocene extension has taken place across a NNE-trending rift (variously referred to as the Turi Fault Zone or the Northern Graben) which is up to about 100 km wide (Fig. 1; Nicol et al.

2005). The upper Miocene Mount Messenger Fm turbidites examined in this study are located within the rift close to its eastern margin (Figs 1 & 2), and are displaced by post-depositional normal faults formed during the most recent phase of crustal extension. The Mount Messenger Fm is continuously exposed for approximately 20 km along a coastal cliff section from Mokau in the north to Pukearuhe in the south (Figs 1 & 2). This coastal section trends NNE –SSW and is up to 200 m high at the White Cliffs. The regional stratigraphic dip is low, averaging 28–58 to the SW. Along the exposure the Mount Messenger has a measured stratigraphic thickness of about 850 m and ranges in age from about 9 Ma –12 Ma (King et al. 1993; King & Thrasher 1996). The rate of coastal erosion is very high (c. 1 m per year, R. Gibbs pers. comm. 2003) so that the outcrop is relatively fresh and large faults (with tens of metres offset) are well exposed. The Mount Messenger Formation represents a westerly prograding, line-sourced turbidite system, so the NNE–SSW outcrop transect passes up through the sequence from basin-floor to slope. The outcrops record a north–south, fining- and shallowing-upwards transect from basin-floor fan, through inner fan, to base-of-slope and lower-slope depositional environments. The sediments themselves comprise interbedded sandstones, siltstones and mudstones, with frequent thin volcaniclastic beds. Initial basin-floor fan deposition is recorded in the exposures around Tongaporutu River (Fig. 2). In both the coastal section and inland exposures, a series of stacked sand-rich fan units are observed. In detail, the mid-fan sediments comprise tabular, massive to thickly bedded sandstones with frequent internal scouring and sand-bed amalgamation. These pass both upwards and laterally into fan-fringe environments characterized by more thinly-bedded sandstones with mudstone interbeds, with sand bodies becoming progressively more isolated within mudstones (e.g. Browne et al. 1996). The inter-fan sediments are represented by bedded to slumped mudstones, with occasional thin sandstone or siltstone beds. Inner-fan canyon-fill sediments are observed in the Waikiekie section (about 3 km south of Tongaporutu; Fig. 2). The lower fill comprises nested, offset-stacked incising channels. Each channel fill typically comprises a basal mudstone-clast lag, overlain by massively bedded sandstone. Moving up through the fill of the canyon, the channels become more isolated, with finer fills, and associated thinly-bedded levee and overbank deposits are present. Base-of-slope sedimentation is recorded at Pukearuhe (Fig. 2) and the southern section of the White Cliffs (,1 km north of Pukearuhe, Fig. 2). This comprises thinly bedded bioturbated sandstones and mudstones, attributed to channel-fill, proximal levee and distal

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Fig. 1. Maps showing the New Zealand plate boundary (inset map), late Miocene and Pliocene to Pleistocene normal faulting in the Taranaki Rift region (stippled area in main map) and the locations of the outcrops and 3D seismic data examined for this study. The main map is modified from King & Thrasher (1996). The locations of cross sections A– A0 (modified from Thrasher et al. 1995) and B– B0 (King & Thrasher 1996) across the northern and southern ends of the rift are shown. Inset map shows locations of active volcanoes (filled triangles); filled arrow shows the relative plate motion vector from DeMets et al. (1994). The Cape Egmont Fault is labelled CEF on cross-section B–B0 (Nicol et al. 2005).

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Fig. 2. Geological map of the Taranaki study area (outlined), together with the main localities referred to in text.

levee sedimentation (Browne & Slatt 2002). The distal levee sediments have sub-parallel bedding which can be correlated over large distances, whereas the bedding frequently changes dip in the proximal levee deposits. The channel scours are of varying size, with the largest in outcrop viewed just south of the Pukearuhe Beach entrance. Faults within the Mount Messenger Fm are postdepositional normal faults which crop out along the entire coastal section and locally inland, most notably the Mokau road section (Fig. 2). The faults have throws (i.e. vertical displacements) of up to 60 m, and fault throws as low as 1 mm can be routinely identified and measured. There are two dominant fault sets striking 005 and 045, each comprising two fault dip directions to define a quadrimodal population of fault orientations (similar to

that described by Reches & Dieterich 1983), with most of the large faults (throw . 10 m) part of the 045 set. Because fault strikes are at a low angle to the general trend of the outcrop, serial sections through individual faults are commonplace. The rare fault kinematic indicators present indicate dip-slip normal movement. The faults are thought to have formed when the sediments were at or close to their maximum burial depth of 1 km–2 km, and there is no evidence in the study area of faulting during deposition of the Mount Messenger Fm.

Structural characterization Structural characterization of the Taranaki study area was directed towards establishing the

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quantitative characteristics of fault systems that are important in the parameterization of faulted reservoir models. Since there are few, if any, quantitative constraints on faults within turbidite sequences, this study examined all of the potentially significant factors including the geometrical properties of the fault system, the internal structure of fault zones and the permeabilities of fault rocks. The fault system was characterized primarily from outcrop studies complemented by analyses of a 3D seismic reflection survey of the Ngatoro and Kaimiro oil and gas fields (Fig. 1). This paper concentrates on one technical aspect: the analysis and modelling of fault rock content and its implications for the definition of fault property algorithms used in reservoir modelling. Quantitative constraints on fault rock content and flow properties were derived from the analysis of fault zones in both 2D (i.e. individual cross-sections) and 3D (i.e. multiple cross-sections) and provide a basis for parameterizing fault properties, such as fault rock thickness and permeability, in reservoir models.

Fault rock types The predominant fault rock types formed in Taranaki are shear bands, i.e. narrow zones of high shear strain. The composition and width of these shear bands varies greatly between different lithologies, defining a spectrum of structures from very narrow (1 mm) clay rich zones developed in fine grained silt and mudstones (Fig. 3a), to deformation bands in porous sandstones that may have widths several times larger than their displacement (Figs 3b, 4e). Since these shear bands are the primary components of both large and small faults, when large faults (displacements of tens of metres) are examined in detail the bulk of the fault rock volume is generally found to be comprised mainly of anastomosing swarms of shear bands (e.g. Figs 3d, 4b, 4c). Fault rock content is strongly heterogeneous reflecting the variations in host rock sequences that are incorporated into the faults (Fig. 4b, c, f ). The main slip surfaces of large faults generally consist of relatively thick (.1 cm), continuous, zones of clay-rich fault rock, either as malleable clay gouge (Fig. 4g) or as amalgamations of relatively harder dark clay layers (Fig. 4b, c); as is discussed in more detail below, these clay layers are formed by smearing of clay-rich source beds along faults. Fault rock mineralogies are the same as those of the host rocks, comprising predominantly quartz, albite, muscovite, biotite and chlorite, with occasional calcite, montmorillonite and zeolite; a mineral assemblage typical of sediments derived from erosion of a low grade metamorphic source area. Montmorillonite, occasionally encountered

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in clay fault rocks, is probably derived from tuff source layers. Shear bands within the coarser (i.e. sand lithologies) (Fig. 5) show a general grain size reduction particularly of the weaker mineralogical components, i.e. feldspars, micas and lithic fragments (see Fig. 5), together with a reduction in the proportion of feldspar and an increase in mica relative to host rock (possibly arising from the breakdown of albite to mica). Similar changes are most likely a feature of clay derived fault rock, though the extent of grain size comminution is very difficult to quantify. Apart from circumstances in which malleable clay fault rocks are generated, and clearly represent clay gouges, the more general term of clay smear has been used, whatever its origin, for entirely clay derived fault rock. In general, breccias are not developed in the faults at Taranaki, reflecting the poor lithification of the sequence at the time of faulting. The only exceptions are thin (typically ,10 cm) quartz cemented siltstone breccia sheets found on some of the largest faults in the area, e.g. at Omahu Pa (Fig. 4d) and Mangapukatea. The presence of these anomalous cemented breccias in otherwise poorly lithified sediments suggests localized flow of deep-sourced brines along larger faults during fault movement.

Fault rock thickness Fault rock thickness was measured as the total thickness encountered on a perpendicular traverse across a fault zone. Measurement of the thickness of fault breccias may be highly subjective due to the often arbitrary and scale-dependent distinction between breccia clasts and undeformed rock; this is not a problem at Taranaki where breccias are rare and, as a consequence, fault rock measurements are far more objective than in most settings. Fault rock thickness relationships at Taranaki differ between facies over the measured scale range of fault throw (Fig. 6). At low throws, fault rock thicknesses are higher in the coarser-grained facies than in the finer grained facies. The massive sandstone facies in particular have large fault rock thicknesses at low throws due to the development of wide deformation bands. At higher throw values the data for the different facies converge (on a log–log plot) so that they are similar at throws .50 cm (Fig. 6). A general positive correlation between fault throw and average fault rock thickness has been reported by a number of authors (Robertson 1983; Hull 1988; Marrett & Allmendinger 1990). In the Taranaki dataset, it has a power-law slope of c. 1 and is most clearly seen when the massive sandstones are excluded. The data define a two order of

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Fig. 3. Selected photographs illustrating some of the common fault rock types encountered in Taranaki. (a) Fault with throw of 1.8 m in siltstones in the White Cliffs (1.5 km north of Pukearuhe; see Fig. 2). The fault comprises thin anastomosing bands of dark fine grained silt– clay. (b) Deformation bands in porous sandstones from Tongaporutu River section stand proud of the outcrop face. The width of these deformation bands can be several times larger than the fault displacement which is generally millimetre scale on individual bands. (c) Fault with throw of c. 60 cm contained within medium bedded sand– clay sequence at Tongaporutu. A continuous clay smear connects the footwall and hanging wall cut-offs of an offset clay unit. The clay smear varies in thickness partly arising from synthetic Riedel shears within the fault zone. (d) A 50 cm wide zone of deformation bands associated with a 5 m throw fault in fine sandstones at Tongaporutu.

magnitude scatter in average thickness at a given throw value and are generally consistent with previously published material for normal faults in siliciclastic sequences. The maximum and minimum observed thicknesses vary over three orders of magnitude with as much as 2.5 orders of magnitude variation observed for individual fault traces. The scatter in these data, on a log–log plot, decreases with increasing throw, a feature which is attributed partly to a decrease in the proportion of fault trace length that is measurable along larger faults.

Shale smearing Outcrops where clay layers are interbedded with sandstones and are offset by faults with throws less

than the sandstone thickness, indicate that clay smears are a crucial component of faults in the study area (Figs 3c, 7a); in these circumstances single smears can be linked to their source layer. Such outcrops at Tongaporutu and Mokau have been used to quantify the continuity of clay smears along fault traces between the footwall and hanging wall cut-offs of clay source layers. Measurements of Shale Smear Factor (SSF, the ratio between fault displacement and apparent source bed thickness i.e. as measured along the fault trace; Lindsay et al. 1993) and clay smear thickness (Fig. 8) demonstrate a decrease in the minimum clay smear thickness with increasing Shale Smear Factor and show that clay smears are generally continuous when the fault displacement

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Fig. 4. Photographs illustrating the range of fault rocks developed within a 30 m – 40 m throw, fault offsetting a sequence of fine sands and silts at Omahu Pa (2 km north of Tongaporutu, see Fig. 2). The 2.5 m wide fault zone dips to the right in (a). There are four main slip surfaces and details of each are shown in (b), (c), (d) and (g) at the locations indicated. The fault zone contains a large lens of fine sandstone (between slip surfaces arrowed d and g, internally deformed by minor antithetic and synthetic slip surfaces (e). This lens is bounded on both sides by slip surfaces comprising mainly clay rich fault rock. (b) Zone of dark grey clay rich bands (upper left to lower right corner of photograph). The slip surface at this location is intersected by synthetic Riedel shears which offset the footwall sandstones and are seen as thin deformation bands each of which is characterized by clay smearing. (c) Anastomosing seams of dark clay rich fault rock transected by minor Riedel shears. (d) Slip surfaces arrowed d (top left to bottom right of photograph) and c (20 cm to the left). The right slip surface comprises a 1 cm thick, dark grey, clay gouge overlain by a layer of quartz cemented siltstone breccia. (e) Dark, clay rich deformation bands within the fine sandstone lens in the centre of the fault zone. (f) Hand sample showing the layered nature of the fault rock, the different layers are derived from different source lithologies. The lighter coloured layers are clay smears derived from mudstone source beds. (g) A 1 cm thick clay gouge (arrowed) overlain by c. 10 cm of foliated siltstone and lenses of strongly cemented siltstone breccia (labelled br). The rectangle outlines the location of the hand sample shown in (f).

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Fig. 5. Hand samples and thin section photographs (plane polarized light) of shear bands in medium grained sandstones from (a) a deformation band (displacement ,1 cm) at Tongaporutu River and (b) a deformation band from within a large displacement fault (c. 12 m throw), c. 500 m south of Tongaporutu. The offset on both deformation bands is small enough that the fault rock is sourced from the adjacent host rock. The host sandstones are immature with a significant proportion of feldspar (c. 10%) and feldspar grains altered to phyllosilicate. There is no clear evidence of reduction in quartz grain size relative to the host sandstones but there is a general grain size reduction together with an increase in the proportion of clay matrix. The brown colour in (a) is due to the presence of haematite. The permeability of the fault rock in (a) is c. 2 mD whereas that of the host rock is in excess of 100 mD.

is less than c. 8 times the apparent source layer thickness. Faults that comprise individual smears derived from single source layers represent a small, though special, subset of the faults studied (e.g. Figs 3c, 7a). In practice, most faults comprise multiple smears arising from different source layers which are offset by multiple slip surfaces (e.g. Fig. 7b). These complexities are compounded by the fact that the thicknesses of even individual smears do not vary in a regular manner along their length. Individual clay smears frequently (c. 50% of those inspected) taper from the clay source bed on one (e.g. Fig. 7a), or very rarely both, sides of the

fault. However, the point of minimum clay smear thickness (or gap in the smear) may occur at any point along the smear. On scales larger than an individual smear, clay smear thicknesses are highly irregular (Figs 3c, 7b, 8b) and the locations of smear breaching are controlled by strain distributions, and slip surfaces, within the fault zone. Shear strains are generally highest at the margins of fault zones so that clay smears are likely to become breached at these locations. Given the numerous slip surfaces and internal complexities of individual fault zones, large numbers of clay smears on metre – decametre scale faults often amalgamate to form highly continuous clay layers (Fig. 7c).

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Interbedded channel levee (C2.3, D2.3) Massive sandstone (B1.1, B2.1) Mudstones with thin siltstones - slumped & bedded (E2.2, F2.1) Multistory channels (B1.1, A2.3) Thick bedded (up to 2m) sandstones (C2.2) Thin bedded sandstones, siltstones and mudstones (C2.3, D2.3) White Cliffs North cycles (C2.3, D2.3) Fig. 6. Mean fault rock thickness versus throw for 420 fault traces. Mean thickness was estimated over the accessible fault trace length which typically extends 4 m from the base of the sea-cliff. The data are subdivided according to facies and the appropriate facies classes of Pickering et al. (1995) are given in brackets.

In addition to clay smearing, in which clay extends somewhere between the footwall and hanging wall location of a given source layer, there are also examples of clay-rich fault rock occurring on parts of faults which have not been bypassed by a clay source layer. The generation mechanism for these clay enriched zones, which is likely to include a contribution from clay injection, is the subject of ongoing work.

Fault rock permeabilities The rocks within the Mount Messenger Fm in Taranaki are very weakly cemented and therefore difficult to core for permeability measurement. Bench mounted cores of hand samples of undeformed sediments provided some samples for Hassler sleeve measurement but not for fault rocks. Most permeability measurements were made using a bench mounted mini-permeameter applied to flat surfaces of hand samples. The lower limit of measurement for both the Hassler sleeve and mini-permeameter is estimated to be c. 0.01 mD, although

measurements lower than c. 0.1 mD should in practice be regarded as maximum values. Lower permeabilities, derived from siltstones and mudstones and their fault rock equivalents, were calculated from mercury injection curves using a mudstone pore space model developed by Yang & Aplin (1998). Comparison between results obtained using this method and those obtained from standard techniques show that this method is accurate to within a factor of three of the true value (Yang & Aplin 2007). Permeability measurements are for fault and host rocks from a range of the facies types encountered within the Mount Messenger Fm. The measured permeabilities lie within the range 6 nD –1500 mD and show a general correlation with grain size (Fig. 9a). The range of permeabilities of the unfaulted sediments within each facies covers up to seven orders of magnitude (for thick bedded sandstone facies), reflecting the lithological heterogeneity within each facies. The measured fault rock permeabilities cover a slightly more limited range, towards the lower end of those of corresponding

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host rocks. Where it is possible to measure the permeability of a host rock and its direct faulted equivalent, the maximum permeability reduction was found to be two orders of magnitude (Fig. 9a). This reduction due to fault processes, i.e. cataclasis, porosity collapse etc., is negligible when compared with the difference in permeability between different lithologies, i.e. sands and clays, within a single facies. The permeability data therefore suggest that the most efficient means of decreasing fault zone permeability is the smearing and incorporation of low permeability lithologies (i.e. clays and siltstones) into fault zones. This conclusion favours the application of shale smear algorithms in fault property modelling (Lindsay et al. 1993; Fulljames et al. 1997; Yielding et al. 1997) a suggestion that will be returned to later in this paper. The phyllosilicate fraction within selected fault and host rocks was measured from SEM and thin section point counting. Although there are significant uncertainties in determining phyllosilicate content (due largely to the fine grained and poorly lithified nature of the rocks) the data demonstrate a decrease in permeability with increasing phyllosilicate content. Fault rock permeabilities decrease by c. 6 orders of magnitude over the range of phyllosilicate content from deformation bands in relatively clean sandstones to clay gouges or smears. Similar negative correlations between phyllosilicate content and permeability have been used to underpin the Shale Gouge Ratio method for attaching properties to faults in flow simulators (Manzocchi et al. 1999). This very significant aspect will be returned to in our consideration of fault parameters for modelling.

Summary – structural characterization The purpose of the outcrop study was to characterize the fault rock content of fault zones within the turbidite sequence of the Taranaki Basin. Several quantitative aspects have been defined that provide important constraints for the definition of models or algorithms for fault property modelling.

Fig. 7. Clay smears in thin to medium bedded turbidites. (a) An example of a clay smear which tapers downwards from the clay rich source rock in the footwall: Awaawaroa, between Mokau and Tongaporutu. Fault displacement is c. 8 cm. (b) Complex clay smear thickness distribution on fault with displacement of 1.2 m, Tongaporutu. Clays are highlighted in blue on inset diagram. (c) Fault strand with continuous clay smear (arrowed) formed by amalgamation of smears derived from several source layers, Awaawaroa. The total fault displacement is in the range 8– 12 m.

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% phyllosilicate Fig. 9. (a) Grain size versus permeability subdivided according to facies and to fault ( ) or host rock (W). Tie lines connect permeability measurements for host rock and fault rock derived directly from those host rocks. (b) Permeability versus percentage phyllosilicate for fault (red) and host rocks (black).

Correlations between fault rock thickness and displacement provide a means of predicting fault rock thickness. Faulting causes a reduction in grain size due to preferential comminution of weaker minerals (feldspars, micas and lithic fragments), causing a maximum observed permeability reduction of two orders of magnitude. Clay smears are a common feature of these fault zones, with smears that are generally continuous when the fault throw is less than eight times the clay source bed thickness. The difference in permeability

between the different lithologies within a sequence is several orders of magnitude larger than the difference in permeability between a fault rock and its parent host rock. The effect of smearing of low permeability rocks, such as clays (which have permeabilities in the nanoDarcy to 100s nanoDarcy range), along a fault therefore has a much greater impact on fault permeability than other fault-related processes (i.e. cataclasis, porosity collapse, etc.). This and other observational data provide support for the application of certain shale smear

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algorithms, such as Shale Smear Factor (Lindsay et al. 1993), in fault property modelling. There is, nevertheless, a negative correlation between the proportion of phyllosilicates in a fault rock and its permeability, a feature that provides some support for the use of the Shale Gouge Ratio algorithm in fault property modelling (Yielding et al. 1997). In the next section, the differences between new and existing fault property algorithms are explored.

Fault property algorithms Two types of parameter are required to define a model of a fault system for the purposes of examining the static connectivity or flow response of a faulted sequence: those that define the geometrical scaling properties of the fault system and those that define the hydraulic properties of the faults. Although the geometrical properties of faults can generally be incorporated explicitly in cellular models, the flow properties of faults are incorporated implicitly as fault transmissibility multipliers. Recently there have been significant advances in the methods used to assign fault transmissibility multipliers. Increasingly, the assignment of transmissibility multipliers is underpinned by geological parameters and methods rather than by ad hoc modifications of multipliers to provide history matches. The generation of geologically derived single phase fault transmissibility multipliers for inclusion in reservoir flow models requires predictors of fault rock thickness, fault rock permeability and the variation in these two parameters over fault surfaces (Manzocchi et al. 1999). As has been found elsewhere (Marrettt & Allmendinger 1990; Knott 1994; Little 1995), and is confirmed by our work in Taranaki, fault rock thickness data can be collected in the field and related primarily to fault displacement with a secondary lithological control. Although there is wide variability in fault rock thickness at a particular throw, an appropriate average thickness can be defined and a predictor, based on fault displacement with (Fig. 6) or without a lithological dependence, can be derived (see Manzocchi et al. 1999). These quantitative definitions therefore provide a means of assigning fault rock thicknesses to faults with varying displacements in flow models. Definition of a meaningful predictor for fault rock permeability is a much more difficult task due to the strongly heterogeneous and anisotropic nature of fault rock. Predictors of fault permeability are necessarily based on simplified and idealized models of fault zone structure. Three permeability predictors are considered based on the idealized fault zone structures shown in Figure 10 (a, b and c). These fault zone structures have been constructed to constrain predictors of

Fig. 10. Idealized fault zone structures implicit in the three fault rock permeability predictors considered in this paper and one additional method. (a) Shale Gouge Ratio method in which wall rocks are mixed to provide a homogeneous fault rock. (b) Simple Shear Zone method where the fault permeability is the thickness weighted harmonic average of the offset wall rocks. (c) Probabilistic Shale Smear Factor method in which initially continuous shale smears become discontinuous with increasing displacement. (d) Clay Smear Potential method where the clay smear thins progressively with distance from the source bed cut-off.

one-dimensional across-fault permeability, i.e. what is the permeability encountered on a line traversing the fault ignoring details of the effect of tortuous flow paths within it. The first of these methods for assigning transmissibility multipliers, the Shale Gouge Ratio method, is perhaps the most conventional method available and was first applied by Manzocchi et al. (1999). We also present two new methods, a Shear Zone method and probabilistic Shale Smear Factor method, both of which can be related to the Shale Gouge Ratio method although they may in fact be more appropriate to the modelling of fault properties in heterogeneous sand –clay sequences, such as the turbidites in the Taranaki Basin. Simplified fault zone structure models including some of those described below (and illustrated in Fig. 10) have already been described. A variety of models in which clay or shale smear thickness decreases with distance from the shale source bed have been proposed (Yielding et al. 1997). Most notable of these is the Clay Smear Potential method (Fig. 10d), in which smear thickness decreases in proportion to the square of the distance to the source bed (Lehner & Pilaar 1997). This method has been applied to estimation of fault seal capacity (Fulljames et al. 1997) and

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permeability prediction (Bentley & Barry 1991). These distance-weighted methods predict a minimum shale smear thickness, and therefore a maximum likelihood of smear disruption, midway between the source layer cut-offs on the footwall and hanging wall sides of a fault. Although smears that taper away from the source layer are common at Taranaki (Fig. 7a), examples of tapering from both source bed cut-offs are extremely rare. Figure 8b shows a plot of clay smear thickness versus distance from the clay source bed, both normalized to the source bed thickness. The data demonstrate that there is no clear relationship between distance from the source bed and smear thickness, and that thicknesses immediately adjacent to the source bed may be as low as those distant from the source bed. We therefore concentrate on fault zone structure models in which fault rock properties do not vary as a function of distance from source layer.

Shale Gouge Ratio permeability predictor The Shale Gouge Ratio (SGR) method is the most widely used permeability predictor and has been applied in a number of published studies (Manzocchi et al. 1999; Childs et al. 2002; Rivenæs & Dart 2002; Sperrevik et al. 2002). It is based on permeability constraints indicating a negative correlation between the phyllosilicate fraction within a fault rock and its permeability (Fig. 9b; Gibson 1998; Sperrevik et al. 2002; this study). The phyllosilicate fraction is equated to SGR, which is the proportion of clay (or shale) within a sequence that has moved past a point on a fault. The SGR can be calculated at any point on a fault surface from a knowledge of the fault displacement and the clay content of the faulted sequence; clay contents can be estimated either by mapping individual clay beds or by modelling Vclay variations. This SGR value is then transformed to a fault rock permeability via a relationship fitted to experimental permeability data such as the data shown in Figure 9b. The precise nature of this relationship varies between studies (Childs et al. 2002; Sperrevik et al. 2002), a feature generally attributed to differences in factors such as the burial depth at the time of faulting and the maximum burial depth. Nevertheless the general perception is that SGR:permeability transformations should follow a negative correlation, perhaps even an approximately linear relationship on a plot of SGR against log-permeability. However previously published data have not been derived from an individual outcrop study area, and although sparse, the Taranaki data are consistent with a straight line or slightly concave upwards curve on Figure 9b. The SGR algorithm implicitly defines a fault rock model in which the host rock lithologies are

mixed together (Fig. 10a), such that a sequence of sands and shales with a net:gross of 80% will, when faulted, produce a homogeneous fault rock with 20% phyllosilicate and an equivalent permeability (derived from a given SGR v. permeability transformation). Since the permeability of a random mixture is the geometric average (e.g. Gutjahr et al. 1978), a linear relationship between SGR and log-permeability, which is equivalent to the geometric average, is consistent with a fault rock model involving perfect mixing. However, a mixing model is not necessarily appropriate in the presence of discrete smears, and two new models that incorporate these are discussed below.

Shear Zone permeability predictor Field observations suggest that the mixing approach embodied in the SGR method may not be appropriate to faults in the Taranaki area. Individual continuous clay smears and anastomosing zones of clay smear provide continuous layers of low permeability rock where net sand content is high and a relatively high permeability would be predicted from the SGR approach. The possibility of low permeability fault rocks (clay smears) derived from relatively low clay content sequences means that SGR cannot be considered a direct proxy for fault rock phyllosilicate content and therefore fault rock permeability. Field observations suggest, by contrast, that the contribution of host rock source layers to fault rock does not, in fact, represent mixing of sand –clay as embodied by the SGR method, and that a more appropriate method would be to attach more significance to the continuity of clay smears. An alternative end member approach to the SGR method is to consider that fault zone structure is a perfect shear zone, with no mixing between faulted units, all of which (clay and sand units) are continuous between the source layer cut-offs (Fig. 10b). In this case the fault rock would comprise an attenuated host rock stratigraphy and, in the absence of fault-related deformation processes (i.e. cataclasis, porosity collapse etc.), the across fault permeability would be the harmonic mean of the clay and sand, weighted according to their relative thickness in the faulted sequence, i.e. the vertical permeability (Kv) of the unfaulted sequence. Here we incorporate the effects of fault processes and the appropriate permeability is the harmonic mean of the sand and clay derived fault rock, weighted according to the thicknesses of their parent wall rocks. This method is likely to provide a relatively low permeability prediction, and is therefore a useful end member predictor, since it does not consider the possibility that clay smears are discontinuous. The method described below does acknowledge

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this likelihood and may well provide the most appropriate fault property predictor for sand – clay sequences.

Probabilistic Shale Smear Factor permeability predictor A more realistic approach to clay smearing than the Shear Zone model described above, is one in which clay smears maintain continuity at relatively low displacements, becoming disrupted as displacement increases (Fig. 10c). Field observations in this and other studies (e.g. Lindsay et al. 1993) suggest that a critical ratio between fault displacement and clay source bed thickness, SSFc, can be defined at which clay smears start to become discontinuous, e.g. the Shale Smear Factor measurements presented in Figure 8a. Such observations form the basis for developing a permeability predictor based on a probabilistic approach to evaluating continuity of clay smears; we refer to this approach as the Probabilistic Shale Smear Factor (PSSF) method. In this article we are not concerned with the precise details of individual realizations of probabilistically placed shale smears (see Manzocchi et al. 2007 for a detailed discussion), but with the average properties of many such realizations. We define PSSF as a fault surface property marking the probability that no smears are present at this position. The fractional number of times many stochastic realizations of smears yield a hole at each location on the fault is therefore approximately equal to the local PSSF value. Central to the PSSF method are the assumptions that the smears are continuous for SSF SSFc, and are placed at a random location between the source shale layers for SSF . SSFc: different placement assumptions generally will result in different hole probabilities even if the same SSFc value is considered. In the following sections we develop a simple application in which these average properties are analytically defined for a single cross-section of a fault. We go on to compare the permeabilities predicted by this method with those of the SGR method and the Shear Zone (SZ) approach, and also to consider when this averaged application of PSSF is appropriate and when the stochastic approach, as implemented by Manzocchi et al. (2007), is required.

Probability calculation In defining the PSSF parameter it is assumed that clay smears are continuous until they reach a critical Shale Smear Factor cut-off value (SSFc) at which they become discontinuous (Fig. 11a). Once a clay smear becomes discontinuous it maintains a constant length which is given by T(SSFc 2 1) and is randomly located between its

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footwall and hanging wall source layer cut-offs. When SSFc is exceeded for a single clay smear, the probability of encountering a gap in that smear at any point between its source layer cut-offs is 1 (T (SSFc 1)=(D T));

(1)

where D is fault displacement and T is the apparent source layer thickness measured along the fault trace. Note that for simplicity in the remaining discussion of PSSF we consider vertical faults offsetting horizontal layering so that D is equal to the throw and T is equal to the true layer thickness. At a particular point on a fault the PSSF or probability of having no smear (i.e. a gap in clay smear) is the product of Equation 1 calculated for each clay layer faulted past that point (Fig. 11b). If the SSF for any of the clay layers is lower than SSFc then the probability of a gap in the smear is zero. The results of calculations using this approach for a rhythmic sand –clay sequence in which all clay layers have the same thickness are illustrated in Figure 12. Probabilities calculated in this way can be expressed either in terms of the likelihood of encountering a gap in the clay smear at a given point on the fault surface (PSSF; Fig. 12) or the lower likelihood that the gap occurs on a window of sand on sand juxtaposition (Fig. 12b). The second of these expressions would be appropriate for estimating reservoir connectivity. The aim is to predict the permeability of the fault surface so that the first expression is appropriate. Expressed in terms of the fault surface, there is always the possibility of a gap in the clay smear once the critical clay smear cut-off is exceeded so that there is always a finite probability of a gap even when the sequence contains 100% clay; this is not the case when only sand on sand juxtapositions are considered. In the formulation below, the probability of encountering a clay smear is taken to be equal along the fault trace length between the upthrown and downthrown source layer cut-offs. This approach could be easily modified to incorporate a probability distribution reflecting, for example, an increased likelihood that a continuous clay smear occurs close to the clay source layer. Fieldwork in the Taranaki area suggests that there is no clear systematic relationship between the proximity to a clay source layer and either the occurrence, or the thickness, of the smear.

Permeability calculation The probability of encountering a gap at any point on the fault trace segment shown in Figure 11b (i.e. PSSF) is the same as the average total hole size (which would be derived from multiple realizations of randomly positioning shale smears in

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SSF = D/T

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Fig. 11. Illustration of the PSSF method. (a) A continuous smear grows until SSF . SSFc, at which point the shale smear breaks and is entrained in the fault at a random position. PSSF is the probability of encountering a gap in this smear at a point between the cutoffs. (b) Schematic cross-section (i) of a rhythmically bedded sand/clay sequence offset by a fault with a throw equal to the thickness of five sand/clay couplets. At any point along the fault trace up to 5 smears may be present (ii) and PSSF is the product of the probabilities of encountering a gap in each individual smear. The smear distribution in (ii) is collapsed to a single discontinuous smear in (iii). PSSF is equivalent to the fractional hole size in (iii) averaged for multiple realizations of the smear placement in (ii).

Fig. 11b) divided by the length of the fault trace segment. This observation is used to convert the probabilities derived above to average across-fault permeabilities. It is assumed that the fault segment length contains gaps in the clay smear equal to the average total hole size, and clay and sand derived fault rock permeabilities are then assigned to the smears and gaps respectively. The average fault rock permeability is then the arithmetic average of the shale and sand derived fault rocks, weighted according to the length of fault trace covered by the two components (Walsh et al. 1998).

PSSF predictions Results of our calculations are shown on plots of probability of a hole in the shale smear (i.e. PSSF) versus the clay fraction of the faulted sequence (Fig. 12). Clearly the probability of a gap increases with decreasing SSFc (Fig. 12a). For a particular SSFc and clay (i.e. shale) fraction, the probability of encountering a gap in the smear increases with the number of beds on which the clay fraction is distributed (Fig. 12c). This is due to overlapping of clay smears reducing the length of clay-covered fault trace. Although the total

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derived from a single thick clay source bed rather than five thin source beds, the total length of clay smear would be the same, but there would be no potential for smear overlap and the probability of generating a gap in the smear would be at a minimum. Where the clay fraction occurs in a single bed then the gap probability is zero at a clay fraction of 1/SSFc. On the log–linear plot of probability versus clay fraction shown in Figure 12c, the relationship for larger numbers of beds is progressively straighter.

Comparison between permeability predictors

Fig. 12. Plots of shale fraction versus probability of a hole in a shale smear (PSSF). (a) PSSF curves for different SSF cut-off values (labelled) for 50 and 5 offset beds. Curves for 50 beds are coloured according to SSF while equivalent curves for five beds are shown black. (b) Curves for 50 offset beds for different SSF cut-offs. Probabilities in this case are calculated for areas of sand on sand juxtaposition (see text). (c) PSSF curves for different numbers of offset beds for shale smear cut-offs of 8 and 5. Curves for SSF ¼ 8 are coloured and labelled according to number of beds, and equivalent curves for SSF ¼ 5 are shown black.

length of smear derived from the faulted sequence is (1 2 SSFc) times the total clay thickness, the proportion of this length which occurs at overlaps of two or more smears, and therefore the probability of a gap, increases with the number of beds. For example if the clay smear in Figure 11b was

Fault rock permeability predictions using the SGR approach are based on a correlation between clay fraction and fault rock permeability. The PSSF approach, by contrast, involves probabilistic predictions of the continuity of clay smears, or more correctly of the presence of lacunae in smears. However, a comparison between the SGR and PSSF methods can be made on a cross-plot of clay fraction and fault rock permeability (Fig. 13). For the purposes of this comparison we have assumed a straight line relationship between SGR and log permeability, representing perfect mixing (grey lines in Fig. 13). The permeability input to the PSSF method is the two end member fault rock permeabilities i.e. those for fault rock derived purely from sand and from clay; in Figure 13(a & b) these are 1 mD and 0.0001 mD respectively. The PSSF curves in Figure 12c are converted to equivalent permeabilities in Figure 13a. The permeability curves are bounded by the clay smear permeability, corresponding to a PSSF of zero, and the sand-derived fault rock permeability, corresponding to a PSSF of one. For large numbers of beds the PSSF derived permeability defines an approximately straight line, the slope of which is dependent on the SSFc (Fig. 13b). It is therefore possible to find a value of SSFc at which the PSSF permeability prediction closely matches the straight-line SGR relationship. For smaller numbers of beds (,10) the nonlinearity of the PSSF relationship means that correspondence between SGR and PSSF cannot be found (Fig. 13a). For typical SSF cut-offs (greater than c. 7) and low bed numbers, the PSSF predicted permeability is lower than the SGR permeability and the difference between the methods increases with decreasing bed number. For large numbers of beds (.10) it is possible to find an SSFc for which both the SGR and PSSF methods predict approximately the same permeabilities. For simple rhythmic sequences this ‘equivalent’ SSFc value is a function only of the

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difference in permeability of the two end member fault rocks. Figure 13c shows PSSF curves based on two sets of end-member permeabilities which each define a fault rock permeability range of four orders of magnitude. The curve shapes for the two permeability cases are identical and the SGR curve is most closely approximated by a SSFc of c. 10. For an increase in permeability range from four to six orders of magnitude, the ‘equivalent’ SSFc increases from c. 10 to 14 (Fig. 13d).

Application to a Taranaki sequence In the previous section we were concerned with a rhythmic sequence where the probability of encountering a hole (i.e. PSSF), and therefore the average predicted permeability, is the same at all points along a fault trace with constant displacement. For non-rhythmic sequences, the probability of encountering a hole will vary along a fault trace, so the averaging technique requires some modification for application to real sequences. Here we illustrate

how the method can be applied to provide an estimate of fault permeability for real sequences. As described above, the probability of there being no clay smear at a point on a fault surface is the product of the probabilities of a gap in each of the individual smears derived from each clay source bed. The permeability at this point is calculated in the same way as described above. For each position on the fault surface, this application calculates the average permeability that would be obtained from multiple realizations of a stochastic smear placement. The following section discusses the circumstances in which such averaging may be appropriate as opposed to those in which an explicit stochastic placement of smears is necessary for capturing the fault permeability heterogeneity. Irrespective of whether averaging is, or is not, appropriate, it is informative to compare the results of this application of the PSSF method with other permeability predictors for a natural sequence. Figure 14 shows ‘triangle’ diagrams (explained in Fig. 14a) contoured for permeability, constructed

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Fig. 14. ‘Triangle’ diagrams of depth versus throw contoured for predicted permeability. The triangle diagram shows the area of juxtaposition of a sequence offset across a notional fault with a throw which varies between zero and that of the sequence as illustrated in the inset to (a). The sequence of sands and shales used to construct the triangle diagrams is shown on the right of the figure: this sequence is equivalent to that found on the southern side of the Tongaporutu River. Permeabilities are in mD (linear scale). Plot (a) is for permeabilities calculated from SGR whereas (b to d) are calculated using the PSSF approach for the different values of SSFc indicated.

for an upward fining sequence within the turbidite sequence recorded at Tongaporutu. The permeability input in this case is a six order of magnitude range from 1 mD for faulted sands through to 1 nD for a pure faulted clay as suggested by the data in Figure 9. The SGR permeability is again predicted using a straight-line relationship between these two end points. Comparison between the SGR based permeability prediction (Fig. 14a) and PSSF results shows the closest correspondence between these methods at an SSFc of c. 12 (Fig. 14c). The similarity of predicted permeabilities is seen in all parts of the sequence from the relatively thickly bedded, high net:gross, base of

the sequence to the finely bedded, low net:gross, top of the sequence. Only at throws equal to a small number of bed thicknesses does the similarity between the predicted permeabilities break down. Figure 15 shows that for fault throws greater than 5 m there is an approximately linear relationship between the PSSF-predicted permeability and clay (i.e. shale) fraction at SSFc ¼ 12. At throws less than 5 m, where only a few beds have moved past a point on a fault, the permeability values drop well below this straight line. The across-fault permeabilities predicted on the basis of the Shear Zone model for the sequence recorded at Tongaporutu are shown in Figure 15.

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Fig. 15. Predicted permeability versus shale fraction plot for the sequence shown in Figure 14. The dots are derived from individual points on the triangle diagram in Figure 14c and are colour coded according to throw. Also shown are PSSF permeability curves for a rhythmically bedded sequence of 50 beds at the indicated SSFc cutoffs, the Shear Zone model (labelled Harmonic mean), and the SGR permeability model (grey).

The predicted permeabilities are calculated from the harmonic mean of the sand and clay derived fault rock permeabilities, weighted according to the thickness of sands and clays that have passed a point on the notional fault. Where the SGR approach to permeability assignment produces estimates of fault permeability close to the upper limit of those predicted by the PSSF application used here, the Shear Zone method provides a curve towards the lower bound of the PSSF data. The PSSF application described here uses a simple approach in which the permeability of a fault containing a continuous clay smear is that of the clay smear and ignores the influence of other fault rock components. This simple approach, when applied to very high values of SSFc, i.e. very thin smears, will lead to unrealistically low predictions of permeability. In the Shear Zone model of fault zone structure, SSFc is effectively infinite but this

model does acknowledge the contribution of non-clay derived fault rocks. This Shear Zone model therefore provides a likely lower bound to permeability predictions derived from the simple PSSF application.

Discussion The curves in Figures 12 & 13 are for probabilities and average permeabilities but give no indication of the validity of these averages or the ranges of values about them. To define the spread of values about the mean we have conducted stochastic modelling of the system illustrated in Figure 11 and discussed in the accompanying text. Modelling results are expressed in terms of the total length of hole in the clay smear, expressed as a fraction of the length of fault trace over which it is measured

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Fig. 16. Plots of the total length of hole in a clay smear as a fraction of fault throw against smear length/ throw for five different numbers of beds (indicated by colour). Curves are shown for the mean hole size (given sufficient realizations, this mean hole size is equal to the fault surface PSSF) and vertical bars are the 5th and 95th percentiles of the distribution. The dashed line is discussed in the text.

(i.e. the sampling window). Results are shown in Figure 16 for cases in which the sampling window is equal to the fault throw. Vertical bars on Figure 16 are the 5th and 95th percentile from 1000 realizations for particular combinations of smear length and number of beds. The curves illustrate the reduction in total hole length with increase in both the number of beds within the throw window (equal to the number of smears and corresponding to an increase in shale fraction) and the length of smears. In addition, the range of hole sizes increases with decreasing number of beds and increasing smear length. There are clearly parts of the curves for which an averaging approach to the calculation of total hole fraction is appropriate, e.g. for 200 beds and a smear length/throw ratio of less than 0.01, and areas where it is inappropriate and large numbers of realizations have a zero hole length e.g. for 200 beds and a smear length/throw ratio greater than 0.02. The dashed curve in Figure 16 connects cases where the population of hole sizes has a coefficient of variation (standard deviation mean) of 0.5; above this curve the coefficient of variation is less than 0.5 and the averaging approach is thought to be appropriate (see below). In the discussion so far we have been concerned with defining situations in which the total hole length, and therefore permeability, can be meaningfully averaged over a length of fault trace equal to the fault throw. In real applications, the length scale on which it is necessary to define permeability variability is likely to be significantly smaller (or potentially larger) than the throw, for example the height of a grid block in a reservoir model. To examine the systematics for fault trace lengths other than the fault throw, hole sizes were measured in fault trace windows of varying length on the

Fig. 17. Contours of (a) mean hole fraction (equivalent to PSSF) as a fraction of the sample window length and (b) coefficient of variation Cv of hole fraction on a plot of window length/throw versus smear length/throw. The mean values and Cv at each point on the plots are calculated for 1000 realizations of a system with 20 offset beds. (c) Curves of Cv ¼ 0.5 calculated for systems with 2, 5, 20, 50 and 200 offset beds. The points labelled X and Y are discussed in the text.

stochastically modelled faults. The results of these analyses, for a system of 20 offset beds, are shown as contours of the mean of fractional hole sizes measured over the fault window (Fig. 17a) and the coefficient of variation (Cv) of these

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fractional hole sizes (Fig. 17b). The data demonstrate that the mean hole fraction within the sample window is independent of window length, however the Cv of hole size is strongly dependent on the window length. As the window length decreases, the Cv increases, and the range of likely hole sizes increases so that the assignment of an average value becomes progressively less representative of the system. This lack of representativeness is most clearly illustrated when most of the realizations have a hole size of zero but the mean is not zero and therefore not representative of the most likely permeability; in these cases the Cv is very high. The situations for which the mean total hole fraction is representative of clay smear distribution on the model fault surface can be defined on the basis of the Cv of fractional hole size. Following Corbett & Jensen (1992), who defined this value as the boundary between homogeneous and heterogeneous systems, Cv ¼ 0.5 is taken as the threshold above which the uncertainty in permeability is considered large enough to warrant stochastic placement, rendering the single, average permeability value calculated with the probabilistic approach too homogeneous. Curves for a Cv of 0.5 for different numbers of beds within a throw window are shown in Figure 17c. These curves demonstrate that the clay smear length/throw ratio at which a Cv of 0.5 is reached is lower for higher numbers of beds (corresponding to a higher shale fraction) because, for a given smear length, the numbers of realizations with a continuous smear will be higher for higher numbers of beds. The use of Figure 17c in determining whether an average or stochastic application of the PSSF approach is appropriate in particular circumstances is illustrated by considering an example of a fault with a throw of 50 m, offsetting a sequence containing twenty 0.2 m thick clay beds. If the window length of interest (e.g. grid cell height) is 5 m, then for an SSFc of 5, the smear length is four times the bed thickness, i.e. 0.8 m. The smear length/throw ratio is 0.016 and the fault plots at the point labelled X in Figure 17c, to the left of the curve for 20 beds and so an averaging approach is appropriate. However, if the SSFc is considered to be 12, then the smear length/throw ratio is 0.03 (point Y on Fig. 17c) and an averaging method is inappropriate. On the face of it, the approaches to fault property prediction in the SGR and PSSF methods are very different. In the SGR method an average property is assigned to all parts of a fault trace between clay source layer cut-offs, whereas in the PSSF method, once the SSFc is exceeded, the fault trace comprises low permeability smears that are punctuated by high permeability gaps. In terms of the predicted permeability of a length of fault trace

between a single pair of source layer cut-offs, the SGR method predicts a smooth increase in permeability with increasing displacement, whereas the PSSF approach predicts a sudden step from the permeability of clay fault rock to that of sandderived fault rock. Nevertheless, despite these apparently stark differences, the results generated from both of these methods may become effectively the same for particular SSFc ranges when the fault throw is several times larger than bed thickness and many shale layers are present in the averaging window. For the Taranaki faults, where the difference in permeability between sand and clay derived fault rocks is up to six orders of magnitude, this equivalence occurs at an SSFc of 12 to 14; this range is higher than, but not dissimilar to, the SSF cut-offs measured at outcrop. The PSSF application described above assumes that once a smear has become discontinuous it stops lengthening; however, it is far more likely that smears will continue to lengthen by shearing with increased fault displacement. It is therefore likely that the effective SSFc which best defines the permeability variation on a fault will be higher than that measured from the clay smear continuity of individual smears seen in outcrop and higher than that which produces similar permeabilities to the SGR approach. If, for instance, shale smears increased their length by 50% due to continued shearing following smear rupture, then an effective SSFc of c. 12 would be appropriate for the Taranaki area and the PSSF prediction of permeability would be very similar to that of the SGR prediction; if continued shearing provided a two-fold increase in smear length then the PSSF prediction would be significantly lower than that of the SGR prediction. The PSSF approach acknowledges the effects of changing correlation lengths on permeability prediction. The method includes the on/off behaviour of clay smears observed in the field when fault displacements are similar to bed thicknesses but also provides an averaged permeability prediction when fault displacements are significantly higher than bed thicknesses. The PSSF method therefore provides a richer permeability predictor than the SGR method providing the opportunity to capture some of the scale-dependent permeability variations associated with faulting.

Conclusions Correlations between fault displacement and fault rock thickness from the Taranaki basin and elsewhere are entirely consistent and provide a means of predicting fault rock thicknesses for fault property modelling. Faulting causes a reduction in grain size providing a maximum observed

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permeability reduction of two orders of magnitude. Clay smears are a common feature of these fault zones, with smears which are generally continuous when the fault throw is less than eight times the clay source bed thickness. Since the difference in permeability between the different lithologies within a sequence is several orders of magnitude larger than the difference in permeability between a fault rock and its parent host rock, the effect of smearing of low permeability rocks, such as clays (which have permeabilities in the nanoDarcy range), along a fault therefore has a much greater impact on fault permeability than other fault-related processes (i.e. cataclasis, porosity collapse, etc.). This and other observational data provide support for the application of certain shale smear algorithms, such as shale smear factor, in fault property modelling. The permeabilities of fault rocks from Taranaki subscribe to approximately straight negative correlations between phyllosilicate content and log fault rock permeability, a correlation which provides support for the application of the Shale Gouge Ratio (SGR) fault rock permeability predictor within upscaled reservoir models in which clay layers are not explicitly modelled. An alternative newly developed fault rock permeability predictor is the Shear Zone (SZ) model, in which fault rock permeabilities are calculated as the harmonic mean of clay and sand derived fault rock, weighted according to the thicknesses of sand and clay in the host rock stratigraphy. This approach provides relatively impermeable faults but nevertheless represents a useful endmember permeability predictor. The predictor which best honours the fault zone structure in Taranaki is believed to be the Probabilistic Shale Smear Factor (PSSF) model. In the PSSF method applied here, fault rock permeabilities are predicted from the probabilities of generating gaps within otherwise continuous smears. PSSF derived permeabilities span the range between the SGR and the SZ methods. In circumstances where more than c. ten beds have been offset across a fault, there is a linear relationship between the permeabilities predicted from the SGR and PSSF methods, indicating a broad equivalence between the two approaches. The PSSF method nevertheless predicts a more heterogeneous and realistic fault rock structure than the SGR approach, and is therefore more consistent with outcrop constraints. Results of one simple application of PSSF to faults in a rhythmically layered sequence, allows circumstances in which it is appropriate to apply a PSSF averaging approach to the estimation of fault permeability, to be distinguished from those when a stochastic approach is required.

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We thank the following companies and their representatives for supporting our ITF brokered FIFT research project entitled ‘Quantitative characteristics of faults and fault zones and their impact on flow within deep water turbidites, onshore New Zealand’: Amerada Hess, BG Energy Holdings, BP Exploration, ConocoPhillips, Kerr-McGee North Sea, Shell, Statoil and Total. We also thank P. Haughton and P. King, our sedimentology partners in the project, and other members of the Fault Analysis Group. We are grateful to M. Arnot at GNS who conducted the permeability measurements using the mini-permeameter and T. Culligan at University College Dublin for thin section preparation. We thank R. Gibson and E. McAllister for their constructive reviews and D. Barr for his editorial handling.

References B ENTLEY , M. R. & B ARRY , J. J. 1991. Representation of fault sealing in a reservoir simulation: Cormorant Block IV, UK North Sea. 66th Annual Technical Conference & Exhibition of the Society of Petroleum Engineers, Dallas, Texas, SPE 22667. 119–126. B ROWNE , G. H. & S LATT , R. M. 2002. Outcrop and behind-outcrop characterization of a late Miocene slope fan system, Mt. Messenger Formation, New Zealand. Bulletin of the American Association of Petroleum Geologists, 86, 841–862. B ROWNE , G. H., M C A LPINE , A. & K ING , P. R. 1996. An outcrop study of bed thickness, continuity and permeability in reservoir facies of the Mt. Messenger Formation, North Taranaki. New Zealand Petroleum Conference Proceedings, 10-13 March 1996, Volume 1. Ministry of Economic Development, Wellington, 154– 163. C HILDS , C., M ANZOCCHI , T., N ELL , P. A. R., W ALSH , J. J., S TRAND , J. A., H EATH , A. E. & L YGREN , T. H. 2002. Geological implications of a large pressure difference across a small fault in the Viking Graben. In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seal Quantification. Norwegian Petroleum Society, Special Publication, 11, 187– 201. C ORBETT , P. W. M. & J ENSEN , J. L. 1992. Estimating mean permeability – how many readings do you need? First Break, 10, 89–94. D E M ETS , G. R. G. & V OGT , P. 1994. Location of the Africa–Australia– India triple junction and motion between the Australian and Indian plates – results from an aeromagnetic investigation of the Central Indian and Carlsberg Ridges. Geophysical Journal International, 119, 893 –930. F ULLJAMES , J. R., Z IJERVELD , L. J. J. & F RANSSEN , R. C. M. W. 1997. Fault seal processes: systematic analysis of fault seals over geological and production time scales. In: M ØLLER -P EDERSEN , P. & K OESTLER , A. G. (eds) Hydrocarbon Seals, Importance for Exploration and Production. Norwegian Petroleum Society, Special Publication, 7, 51–59. G IBSON , R. G. 1998. Physical character and fluid-flow properties of sandstone-derived fault zones. In: C OWARD , M. P., D ALTABAN , T. S. & J OHNSON , H. (eds) Structural Geology in Reservoir

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B ARR , D., W ALSH , J. J. & K NIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 309– 336. M ARRETTT , R. & A LLMENDINGER , R. W. 1990. Kinematic analysis of fault-slip data. Journal of Structural Geology, 12, 973– 986. N ICOL , A., W ALSH , J., B ERRYMAN , K. & N ODDER , S. 2005. Growth of a normal fault by the accumulation of slip over millions of years. Journal of Structural Geology, 27, 327– 342. P ICKERING , K. T., C LARK , J. D., S MITH , R. D. A., H ISCOTT , R. N., R ICCI L UCCI , F. & K ENYON , N. H. 1995. Architectural element analysis of turbidite systems, and selected problems for sand-prone deepwater systems. In: P ICKERING , K. T., H ISCOTT , R. N., K ENYON , N. H., R ICCI L UCCI , F. & S MITH , R. D. A. (eds) Atlas of Deep Water Environments: Architectural Styles in Turbidite Systems. Chapman and Hall, London, 1 –10. R ECHES , Z. & D IETERICH , J. H. 1983. Faulting of rocks in three-dimensional strain fields. 1. Failure of rocks in polyaxial, servo-control experiments. Tectonophysics, 95, 111 –132. R IVENÆS , J. C. & D ART , C. 2002. Reservoir compartmentalisation by water-saturated faults – Is evaluation possible with today’s tools? In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seal Quantification. Norwegian Petroleum Society, Special Publication, 11, 173– 186. R OBERTSON , E. C. 1983. Relationship of fault displacement to gouge and breccia thickness. American Institute of Mining Engineering Transactions, 35, 1426– 1432. S PERREVIK , S., G ILLESPIE , P. A., F ISHER , Q. J., H ALVORSEN , T. & K NIPE , R. J. 2002. Empirical estimation of fault rock properties. In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seal Quantification. Norwegian Petroleum Society, Special Publication, 11, 109– 126. T HRASHER , G. P., K ING , P. R. & C OOK , R. A. 1995. Taranaki Basin Petroleum Atlas. 50 maps plus booklet. Institute of Geological & Nuclear Sciences Ltd, Lower Hutt, New Zealand. W ALSH , J. J., W ATTERSON , J., H EATH , A. E. & C HILDS , C. 1998. Representation and scaling of faults in fluid flow models. Petroleum Geoscience, 4, 241–251. Y ANG , Y. L. & A PLIN , A. C. 1998. Influence of lithology and compaction on the pore size distribution and modelled permeability of some mudstones from the Norwegian Margin. Marine and Petroleum Geology, 15, 163–175. Y ANG , Y. L. & A PLIN , A. C. 2007. Permeability and petrophysical properties of thirty natural mudstones. Journal of Geophysical Research-Solid Earth, 112 (BS), B03206. Y IELDING , G., F REEMAN , B. & N EEDHAM , D. T. 1997. Quantitative fault seal prediction. Bulletin of the American Association of Petroleum Geologists, 81, 897–917.

A comparison between deterministic and stochastic fault seal techniques S. J. DEE1,2, G. YIELDING1, B. FREEMAN1 & P. BRETAN1 1

Badley Geoscience Ltd, North Beck House, North Beck Lane, Hundleby, Spilsby, Lincolnshire, PE23 5NB, UK (e-mail: [email protected]) 2

BP Exploration and Production, Chertsey Road, Sunbury-on-Thames, Middlesex, TW16 7LN, UK

Abstract: Traditionally, the analysis of fault seal has been purely deterministic or a combination of deterministic and stochastic methods. In a deterministic model, prediction of the locations of reservoir overlaps is made from the static model of the reservoir horizon and fault geometry. The principal aim is to map faulted reservoir overlaps and determine their sealing character. This is usually performed using a predictive algorithm such as the shale gouge ratio (SGR) that relates the shale content of the formations that have moved past a point on the fault zone to the sealing capacity of the fault rock. Deterministic fault seal studies are sensitive to the uncertainties associated with mapping of horizons in proximity to faults and the inherent uncertainty in a static fault interpretation in both position and fault zone complexity. Uncertainty in the static structure model can be addressed by convolving uncertainty in throw magnitude with juxtapositions at the fault. However, this does not address the uncertainty in the distribution of reservoirs on either side of the fault. With stochastic models multiple realizations of the stratigraphy can be tested. Stochastic models capture the uncertainty in the position of the reservoir at the fault by allowing multiple realizations of stacking geometries, where the principal assumption is that these stacked reservoir zones are laterally continuous covering the entire likely fill area. Despite the conceptual differences between these two approaches to fault seal analysis, comparison of the predictions they make on the Ling Gu field shows a surprising degree of conformity. The cut-off used to determine the number of sand and shale beds in the stochastic workflow appears to account for seal by fault zone materials, since a conservative cut-off implies fewer sand beds with lower probability of leak and correlates with more shale in the section and higher SGR values.

Understanding fault seal and related trap integrity are key requirements for reliable exploration and production forecasts (Smith 1980; Lindsay et al. 1993; Knipe et al. 1997; Yielding et al. 1997; Manzocchi et al. 1999). Traditionally, fault seal analysis has been purely deterministic or else a combination of deterministic and stochastic methods has been applied (Jones & Hillis 2003). Thus, a quantitative deterministic methodology has been described in a number of previous papers (e.g. Fristad et al. 1997; Yielding et al. 1997; Freeman et al. 1998; Hesthammer & Fossen 2000; Yielding 2002; Bretan et al. 2003; Gibson & Bentham 2003). In this methodology the connections between reservoir units are mapped explicitly at the fault (Allan 1989), and the seal potential of the fault zone material predicted through use of a proxy algorithm such as shale gouge ratio (SGR; Yielding et al. 1997). James et al. (2004) outline an alternative methodology (termed the ‘stochastic multi-fault method’) that analyses the impact of stratigraphic uncertainty on connections between reservoir units across the fault, through stochastic variation of stratigraphic stacking (cf. Bailey et al. 2002).

This paper focuses on a comparison of two published methodologies, one stochastic (James et al. 2004) and one deterministic (Yielding 2002), on the same case study. Do these conceptually different approaches lead to different predictions of fault seal? The objective of this paper is therefore a straight comparison of these two conceptually differing methodologies, and their predictions, as measured against the post-well evaluation of a published dataset from a paper on a stochastic fault seal methodology (James et al. 2004). Although a number of examples are presented in their paper, we have selected the Ling Gu field as the working case study because we could most completely replicate the subsurface geometries for this study.

Methodology Stochastic multi-fault analysis Stochastic models offer the possibility to test multiple realizations of the stratigraphy where there is uncertainty, for example in the number and thickness

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 259–270. DOI: 10.1144/SP292.15 0305-8719/07/$15.00 # The Geological Society of London 2007.

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of sands. In this method, the fault zone composition does not contribute to seal, and it is the first order sand connections across the fault and external spill points that control column heights. A detailed account of the approach is contained in James et al. (2004) and is summarized below. Fault juxtapositions control the connectivity of reservoir flow units and hydrocarbon flows through any reservoir unit contact across the fault. Since the stratigraphy is uncertain, the stochastic multifault method captures the uncertainty in the position of the reservoir through multiple realizations of the stacking geometries. For each realization, the sandon-sand contacts at the fault are computed and compared to spill points defined for the structure. A theoretical contact and hydrocarbon column for each sand is then computed (James et al. 2004). Principal assumptions are that these stacked reservoir zones are laterally continuous covering the entire likely fill area, there are no unconformities, and that the definition of the fault offset at one horizon level adequately models the distribution of displacement on the fault surface. The definition of leak and seal beds is based on a cut-off value applied to the Vshale log. Distributions of leak and seal thickness are determined and average thicknesses and percentages are provided as input for each reservoir package. A Monte Carlo process is then used to create a stacked pattern of leaks and seals for each reservoir package. This is convolved with the simple structural model and the number of realizations where one or more hydrocarbon column(s) encountered at a defined well location, is computed together with the average number of columns, column heights and average and total pay thickness for all the successful cases. It is simple to use alternative structural models with this technique to analyse structural uncertainties, though these must be applied to each stratigraphic interval over which variation occurs (James et al. 2004). Key aspects of the stochastic multi-fault model are the staircasing and the ‘delta-throw’ concepts. The staircasing concept can be applied with (Fig. 1a) or without (Fig. 1b) fault seal contributing to enhanced column heights. In the stochastic multi-fault model all reservoir juxtapositions across a fault are potential leak points, columns are therefore moderated by external spill points or available charge. If faults contribute to seal and can retain hydrocarbons then additional column potential exists in the reservoir sequence (Fig. 1b). The ‘D-throw’ concept (Fig. 2) is based on the observation that, in a thinly bedded reservoir sequence, most sand-on-sand connections are observed in areas where the fault throw is changing more rapidly (James et al. 2004). Thus ‘D-throw’ is defined as the magnitude in the change of throw

Fig. 1. Staircasing at a normal fault. (a) with no fault seal; (b) including a fault seal component at the fault.

Fig. 2. Schematic fault plane juxtaposition diagram (strike projection from the hanging wall) showing the ‘delta throw’ concept (‘D-throw’ after James et al. 2004). A high rate of change of throw gives a high D-throw regardless of absolute throw magnitudes.

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along a specified fault length. Obviously, for cross fault seal analysis, the relative thicknesses of the seal and leak beds together with the D-throw will determine the number of leak points across the faults. Areas of high ‘D-throw’ will have more sand-on-sand connections and increased potential for staircasing (in the stochastic multi-fault method). This useful concept can also be applied in the deterministic fault seal models.

Deterministic fault seal analysis In a simplistic approach, the assumption is that traps are filled down to the shallowest structural spill point. The fault is considered to be sealing everywhere along its length. In reality, where connections exist between reservoir units, there is a potential for across fault leakage. In a deterministic model (Yielding 2002), the location of reservoir overlaps is predicted from the static model of the reservoir horizon and fault geometry. The principal aim is to map faulted reservoir overlaps and determine their sealing character. Fault juxtapositions control the connectivity of reservoir flow units. The fault zone material developed at those juxtapositions controls their capillary and permeability characteristics, and ultimately their static and dynamic seal potential (Watts 1987; Yielding et al. 1997; Fisher & Knipe 1998). This is usually performed using a predictive algorithm such as the shale gouge ratio (SGR; Yielding et al. 1997; Freeman et al. 1998) that relates the shale content of the formations that have moved past a point on the fault zone to the clay content and therefore the sealing capacity of the fault rock (Fig. 3). Fault seal attributes (e.g. SGR) are not a measure of the sealing capacity of the fault: they estimate the relative likelihood of clay gouge or smear being developed at the fault surface (Lehner & Pilaar 1997; Doughty 2003; Koledoye et al. 2003). To use the attributes to predict column height, a relationship (approximate calibration) must be derived. Static seal capacity of the fault system is usually estimated by evaluating: (1) capillary threshold pressures required to breach the fault seal, from a calibration of fault zone clay content to capillary entry pressure (Fisher & Knipe 2001; Sperrevik et al. 2002); and (2) buoyancy pressures generated by the hydrocarbon phase, dependant on the fluid composition (Fisher et al. 2001; Bretan et al. 2003). Leakage of hydrocarbons through a membrane fault seal occurs when the buoyancy pressure generated by the hydrocarbons exceeds the pressure required for hydrocarbons to enter and pass through the largest interconnected pore throat in the seal

Fig. 3. Calculation of the shale gouge ratio (SGR) from the volume of shale (Vshale) for reservoir intervals (cf. Fig. 5).

(capillary threshold pressure). Establishing where the buoyancy pressure equals the fault-zone threshold pressure on a fault surface provides a method for predicting the column height. This method is only applicable for membrane fault seals. Seismic-scale and core-plug data suggest that fault-zone threshold pressures are in the range 0.1 MPa (14.5 psi) to 1 MPa (145 psi) for typical fault-zone compositions (Fisher & Knipe 2001; Bretan et al. 2003). The deterministic analysis described here is not suitable for hydraulic fault seals, permeability seals, heavily cemented fault gouge or cataclastic fault seals (Knipe et al. 1997; Bretan et al. 2003; Brown 2003).

Case study: Ling Gu trap The Ling Gu trap (Fig. 4a) is a simple faulted anticlinal structure with two reservoir intervals, A and B separated by a shaley unit (Fig. 5). The A reservoir is composed of 6 sands and the B reservoir,

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Fig. 4. The Ling Gu trap. (a) A perspective view of the Top A sand depth structure surface. Four main faults (A to D) cut the structure. (b) Observed hydrocarbon column observed in the Ling Gu-1 is retained by faults A and B with potential across fault leak points (1 to 3) and structural spill points (4 and 5). Faults are contoured for throw.

13 sands. Four main faults (A to D) cut the structure (Fig. 4a & b) with normal geometry and fault throw maxima near their centres. Fault B and D are linked along a branchline in the footwall of fault D, and at the intersection the throw on fault B is small. Fault throws are up to a maximum of 50 m, with throw

profiles decreasing towards the fault tips. At maximum throw, both the A sands and B sands are self-juxtaposed (i.e. A sands in the hanging wall juxtaposed against A sands in the footwall). Hanging-wall A sands are nowhere in communication with footwall B sands.

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If a fault rock with capillary seal characteristics is developed within the fault zone then the possibility exists that a hydrocarbon column may be retained at each sand-on-sand juxtaposition (Fig. 6b) with a height proportional to the sealing capacity of the fault zone at each juxtaposition. In deterministic fault seal analysis, the sealing capacity of the fault depends on the clay content of the fault zone (SGR), increasing in clay-rich intervals (e.g. Yielding et al. 1997; Skerlec 1999; Harris et al. 2002; Yielding 2002) and homogenizing with increasing throw (Fig. 6b).

Stochastic multi-fault analysis results

Fig. 5. Volume of shale log (Vshale) for the Ling Gu-1 well.

The Ling Gu-1 well is located 70 m below the crest of the trap (Fig. 4b) and encountered one hydrocarbon-bearing sand in the A interval (i.e. 1 sand out of 6 discrete sands in the interval was hydrocarbon filled) and one in the B interval (1 out of 13). A number of potential hydrocarbon spill points through the fault system are identified on the anticline (Fig. 4b) with external leak points to the east or west (Leaks 4 and 5 respectively) where there is dip leakage. Hydrocarbons are therefore retained by faults A and B (Leaks 2 and 3 respectively; Fig. 4b). Faults D and C cut the section and juxtapose sands at Leaks 1A and 1B, and staircasing on these faults may be an important control on the distribution of contacts. Sequence throw diagrams of the Ling Gu-1 well for both the stochastic multi-fault analysis (Fig. 6a) and deterministic fault seal analysis (Fig. 6b) show that a large number of sand-on-sand juxtapositions are developed at throws up to 50 m for the A sands and at throws up to 100 m for the B sands. In the stochastic multi-fault method these juxtapositions are assumed to be leak points and this suggests that the faults cutting the trap are likely to provide connectivity through staircasing up the stratigraphy and across fault leakage.

Results of the stochastic multi-fault analysis of the Ling Gu trap are reported in detail by James et al. (2004). The analysis presented in this paper focuses on the A sand interval because a top depth structure map was presented in their paper, and differences in closure amplitude and fault geometry probably occur for the B sands (James et al. 2004). Within the A sands only one gas column was encountered in the Ling Gu-1 well within the topmost sand (Fig. 5), with a column height of approximately 78 m (measured from the top of the trap). As hydrocarbons are encountered only in the topmost sands of both the A and B sands, this suggests that staircasing on the low throw portion of fault D in the vicinity of the crest of the trap (Fig. 4b) is controlling the extent of columns retained at the fault. In the stochastic multi-fault analysis method, the assumption that any sand-on-sand juxtaposition across a fault is a leak point, infers that only small columns are likely for sands below the crest of the structure, limited by relatively shallow juxtaposition points. Note that the position of the Ling Gu-1 well is not at the crest of the field, so it is not ideally located for sampling small columns close to the faults.

Deterministic fault seal analysis results In the deterministic analysis, the distribution of low capillary entry pressure (weak) seal points on the fault surface will control the accumulations (Knipe et al. 1997). The distribution of seal potential on the fault can be represented using shale gouge ratio (SGR) derived from mapping the Vshale curve from the Ling Gu-1 well (taken from James et al. 2004) directly onto the hanging wall and footwall of the fault surfaces (Fig. 7a) using the Top A sands depth structure map. The lowest values of SGR occur at sand-on-sand juxtapositions where fault throw deceases towards the mapped tips of faults.

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Fig. 6. Sequence throw diagrams for the Ling Gu-1 well. (a) White areas on the plot highlight potential sand-onsand juxtapositions across a fault. At 50 m throw there are a large number of connections. (b) Sand-on-sand juxtapositions across the fault are now coloured for shale gouge ratio (SGR), a proxy for seal capacity.

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Fig. 7. Perspective view of faults coloured for: (a) shale gouge ratio (SGR); and (b) derived estimate of maximum trappable gas column height.

Using a global fault seal calibration (Yielding 2002) the predicted hydrocarbon columns are relatively small for most overlaps (Fig. 7b), with the smallest column heights corresponding to the lowest values of SGR. Very small columns of around 10 m are predicted where the fault throw

is less than 20 m (red areas on the faults; Fig. 7b) towards the tips of all the mapped faults. Critical sensitivities affecting the calculation of column height are the input Vshale values to the SGR calculation and the hydrocarbon properties assumed (Yielding 2002).

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(2)

Fig. 8. Fault plane diagram (strike projection from the hanging wall) for fault B. Gas –water contacts for the A and B sands are highlighted. At the low throw areas of the fault the sustainable column heights are small.

How does this relate to the observed column in the A & B sands? By mapping the predicted hydrocarbon column heights and thus identifying the weakest point within the trap complex, the critical points are those that have the shallowest hydrocarbon contact depth, and are located highest up on the structure (above the shallowest spill point for the reservoir of interest). By inspection, the critical point on the trap for the A sands is located towards the northern top on Fault B (Fig. 8). The predicted hydrocarbon column height for the A sands is 82 m, reflecting a slight over-estimate (c. 79 m reported in James et al. 2004). In our build of the structural model, based on the interpretation presented in James et al. (2004), the topmost sand-on-sand juxtaposition is shallower than that reported as the contact by about 7 m, so our estimates lie within the uncertainty in the reservoir structure. The predicted hydrocarbon column height for the B sands is around 92 m, a little below those observed of 109 m (Fig. 8). We did not have access to the B surface that is reported by James et al. (2004) to be subtly different, so the discrepancy in the prediction between the two methods cannot be fully validated.

Uncertainties A number of uncertainties exist in both methods: (1) In stochastic multi-fault analysis (James et al. 2004), lateral stratigraphic variation and discontinuity of sands is a key uncertainty. Since the method is essentially a 1D representation of stacking geometries (tabular layers), the

(3)

spatial variation in stratigraphy is not modelled. Although this uncertainty may also be present in the geological model used in deterministic fault seal analysis, it is a true 3D representation of the reservoir stratigraphy and so can accommodate unconformities and other interval variabilities if the data are available to constrain them. Common features of all interpretations of subsurface structure are depth uncertainty in the structural model and geometrical uncertainty (i.e. is the fault-horizon interpretation and linkage correct?). Fault zones in nature are complex (e.g. Bailey et al. 2002) and may be highly segmented, at a range of scales (Hesthammer & Fossen 2000; van der Zee & Urai 2005). Fault zone structures such as relays, singly or doubly breached relays, multiple fault strands and horizon drag, all potentially impact connectivity across the fault (Childs et al. 1997; Hesthammer & Fossen 1997, 2000; Aydin & Eyal 2002; Davatzes & Aydin 2004; Eichhubl et al. 2005). Deterministic fault seal studies are sensitive to the uncertainties associated with mapping of horizons in proximity to faults. Uncertainty in the static structure model can be addressed by convolving uncertainty in throw magnitude with juxtapositions at the fault, such that changing the fault throw may destroy existing overlaps or create new ones. However, this does not address the uncertainty in the distribution of reservoir quality sands on either side of the fault. A fault included within a deterministic fault seal model provides the best estimate of the capillary flow properties across the fault assuming a single fault strand is present at reservoir level (i.e. the method does not account for fluid movement within the plane of the fault).

In the stochastic multi-fault analysis, a Vshale cut-off is used to determine the number of sand and shale beds and their thickness distribution for input into the stochastic model. Sands (below the Vshale cut-off ) are assumed to have no flow resistance and shales are assumed to have infinite capillary resistance. Choice of the Vshale cut-off will clearly affect the proportion of sand in the stacking model and, therefore, the likelihood of sand-on-sand juxtaposition. Vshale estimate is also a critical parameter in the deterministic fault seal method, where it is an input to the determination of the SGR value (Bretan et al. 2003) where variations in the calculation method used (e.g. gamma, neutron density, spontaneous potential) can give different results for the

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same raw log data. A further process-based uncertainty exists for the deterministic methodology: does the SGR method reliably predict the likely properties of the fault zone? Empirical studies (e.g. Foxford et al. 1998; Doughty 2003) have demonstrated a good calibration between outcrop measures and the SGR algorithm; nonetheless uncertainty exists. A further source of uncertainty is the calibration of hydrocarbon column height supported by a particular value of SGR (uncertainties in the hydrocarbon composition, composition of the fault zone, calibration of SGR to buoyancy pressure; see Bretan et al. 2003). Many studies have highlighted the importance of geohistory (see Fisher & Knipe 2001; Sperrevik et al. 2002) whereby fault rocks with the same composition and clay content may have very different seal capacities, particularly at low clay contents. One question raised by James et al. (2004) was whether the Vshale cut-off used to determine leak and seal beds in the stochastic multi-fault model might incidentally account for seal by fault zone materials. Plotting the percentage of leaks in the intervals used in the stochastic multi-fault model against the minimum SGR values observed on each fault shows a clear correlation (Fig. 9) reflecting the decreasing minimum SGR value with increasing sand content of the interval. Onset of fault seal has been observed in the range 15 –30% SGR (Yielding et al. 2002; Gibson & Bentham 2003), corresponding to the transition from leak to

Stochastic multifault analysis leak %

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0.4 0.6 0.8 Minimum SGR (ratio)

seal dominance in the stochastic multi-fault analysis methodology. By varying the Vshale cut-off used to determine the distribution of leak and seal beds in the stochastic multi-fault method there should be a related change in the predictions. The effect of changing Vshale cut-off is to alter the number of leak or seal beds, and their thickness, therefore affecting the prediction of seal potential. For example, using a Vshale cut-off of 0.35 (or 35%) to define leak/seal lithologies (Fig. 10a) results in 6–7 leak beds in the A sands and approximately 15 leak beds in the B sands. Changing the cut-off to 0.5 (or 50%) results in 5 thicker (amalgamated) leak beds in the A sands, increasing the possibility of sand-on-sand connection and decreasing seal potential (Fig. 10b). Using a cut-off of 0.5 results in 15 leak beds in the B sands with greater overall thickness (than those given by the 0.35 cut-off), thus increasing the possibility of sand-on-sand connection and decreasing seal potential. What would be the effect on the inferred results of the stochastic multi-fault method if a Vshale cut-off of 0.5 had been used instead of the one chosen (James et al. 2004)? This would have resulted in more sand-on-sand juxtapositions in the stochastic multi-fault method and in fewer realizations where one or more hydrocarbon columns were encountered. By choosing a relatively low Vshale cut-off as presented in James et al. (2004), the stochastic multi-fault analysis method appears implicitly to incorporate the effects of fault seal due to fault rock properties (Fig. 9), that is it underestimates the true number of sand-on-sand connections as a proxy for the contribution of fault processes to retention of hydrocarbons.

Interpretation ambiguity

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Fig. 9. Correlation between the minimum shale gouge ratio (SGR) values observed on the faults (this paper) and the input leak % values used in the stochastic multi-fault analysis (James et al. 2004).

As the Ling Gu-1 well is located off the crest of the structure close to the gas –water contact (GWC) for the topmost sand (in the A sands), the gas– water contacts in the sands in the crestal part of the accumulation between faults B and C have not been sampled (Fig. 4b). The stochastic multi-fault method predicts these sands are either ‘dry’, have very small hydrocarbon columns or have the same contact as the top A sand. However, this cannot be confirmed or refuted by the observed contacts in the Ling Gu-1 well. The intersection of the hydrocarbon column in the topmost A sand only, does not preclude more extensive columns in the lower sands (Fig. 11). For example, limited hydrocarbon columns retained in sands lower in the section (Fig. 11b), even if they are small additional columns of 5–10 m, would add substantial reserves.

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Fig. 10. Sequence throw diagrams for Vshale cut-offs of (a) 0.35 and (b) 0.5. White areas represent sand-on-sand juxtapositions that are more abundant when a higher Vshale cut-off is used (b).

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References

Fig. 11. Schematic fault plane juxtaposition diagrams (strike projection from the hanging wall) through a trap charged from the footwall. (a) With no fault seal, columns are coincident with sand-on-sand leak points. (b) With fault seal the sand-on-sand overlaps are able to retain limited columns adding to the volume of trapped hydrocarbons.

Conclusions The question posed by this paper is whether the conceptually different deterministic and stochastic approaches lead to different predictions of fault seal. Despite the apparent fundamental difference in the methods, the predicted outcome for the example case study is essentially the same, given the uncertainties in the input petrophysical data. Predicted column heights that can be sustained by overlaps with low SGR values are very small, leading to very limited column heights, permitting staircasing on Fault D and across fault spill from the trap to the east on Fault B (Fig. 4). The distinction between leak and seal beds (based on a Vshale cut-off ) is directly analogous to the Vshale input to the SGR calculation. The cut-off used to determine the number of sand and shale beds in the stochastic workflow appears to account for seal by fault zone materials, since a very conservative cut-off implies fewer sand beds with lower probability of leak and correlates with more shale in the section and higher SGR values. Thanks to ExxonMobil seals experts and colleagues at the Fault Analysis Group at University College, Dublin for discussion of the relative techniques. The comments and suggestions from S. Jolley and reviewers T. Needham and R. Jones are greatly appreciated.

A LLAN , U. S. 1989. Model for hydrocarbon migration and entrapment within faulted structures. American Association of Petroleum Geologists Bulletin, 73, 803– 811. A YDIN , A. & E YAL , Y. 2002. Anatomy of a normal fault with shale smear: Implications for fault seal. American Association of Petroleum Geologists Bulletin, 86, 1367– 1381. B AILEY , W. R., M ANZOCCHI , T., W ALSH , J. J. ET AL . 2002. The effect of faults on the 3D connectivity of reservoir bodies: a case study from the East Pennine Coalfield, UK. Petroleum Geoscience, 8, 263– 277. B RETAN , P., Y IELDING , G. & J ONES , H. 2003. Using calibrated shale gouge ratio to estimate hydrocarbon column heights. American Association of Petroleum Geologists Bulletin, 87, 397–413. B ROWN , A. 2003. Capillary effects on fault-fill sealing. American Association of Petroleum Geologists Bulletin, 87, 381– 395. C HILDS , C., W ALSH , J. J. & W ATTERSON , J. 1997. Complexity in fault zone structure and implications for fault seal prediction. In: M ØLLER -P EDERSEN , P. & K OESTLER , A. G. (eds) Hydrocarbon Seals: Importance for Exploration and Production. Norwegian Petroleum Society, Special Publication, 7, 61–72. D AVATZES , N. C. & A YDIN , A. 2004. Distribution and nature of fault architecture in a layered sandstone and shale sequence: an example from the Moab fault, Utah. In: S ORKHABI , R. & T SUJI , Y. (eds) Faults, Fluid Flow, and Petroleum Traps. American Association of Petroleum Geologists Memoir, 85, 1 –28. D OUGHTY , P. T. 2003. Clay smear seals and fault sealing potential of an exhumed growth fault, Rio Grande Rift, New Mexico. American Association of Petroleum Geologists Bulletin, 87, 427–444. E ICHHUBL , P., D’O NFRO , P. S., A YDIN , A., W ATERS , J. & M C C ARTY , D. K. 2005. Structure, petrophysics, and diagenesis of shale entrained along a normanl fault at Black Diamond Mines, California – Implications for fault seal. American Association of Petroleum Geologists Bulletin, 89, 1113–1137. F ISHER , Q. J. & K NIPE , R. J. 1998. Fault sealing processes in siliciclastic sediments. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. J. (eds) Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 117–134. F ISHER , Q. J. & K NIPE , R. J. 2001. The permeability of faults within siciliclastic petroleum reservoirs of the North Sea and Norwegian Continental Shelf. Marine and Petroleum Geology, 18, 1063– 1081. F ISHER , Q. J., H ARRIS , S. D., M C A LLISTER , E., K NIPE , R. J. & B OLTON , A. J. 2001. Hydrocarbon flow across faults by capillary leakage revisited. Marine and Petroleum Geology, 18, 251– 257. F OXFORD , K. A., W ALSH , J. J., W ATTERSON , J., G ARDEN , I. R., G USCOTT , S. C. & B URLEY , S. D. 1998. Structure and content of the Moab Fault zone, Utah, USA. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. J. (eds) Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 87– 103.

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F REEMAN , B., Y IELDING , G., N EEDHAM , D. T. & B ADLEY , M. E. 1998. Fault seal prediction: the gouge ratio method. In: C OWARD , M. P., D ALTABAN , T. S. & J OHNSON , H. (eds) Structural Geology in Reservoir Characterization. Geological Society, London, Special Publications, 127, 19–25. F RISTAD , T., G ROTH , A., Y IELDING , G. & F REEMAN , B. 1997. Quantitative fault seal prediction: a case study from Oseberg Syd. In: M ØLLER -P EDERSEN , P. & K OESTLER , A. G. (eds) Hydrocarbon Seals: Importance for Exploration and Production. Norwegian Petroleum Society, Special Publication, 7, 107–124. G IBSON , R. G. & B ENTHAM , P. A. 2003. Use of fault-seal analysis in understanding petroleum migration in a complexly faulted anticlinal trap, Columbas Basin, offshore Trinidad. American Association of Petroleum Geologists Bulletin, 87, 465–478. H ARRIS , D., Y IELDING , G., L EVINE , P., M AXWELL , G., R OSE , P. T. & N ELL , P. 2002. Using shale gouge ratio (SGR) to model faults as transmissibility barriers in reservoirs: An example from the Strathspey field, North Sea. Petroleum Geoscience, 8, 167–176. H ESTHAMMER , J. & F OSSEN , H. 1997. The influence of seismic noise in structural interpretation of seismic attribute maps. First Break, 15.6, 209. H ESTHAMMER , J. & F OSSEN , H. 2000. Uncertainties associated with fault sealing analysis. Petroleum Geoscience, 6, 37–47. J AMES , W. R., F AIRCHILD , L. H., N AKAYAMA , G. P., H IPPLER , S. J. & V ROLIJK , P. J. 2004. Fault-seal analysis using a stochastic multi-fault approach. American Association of Petroleum Geologists Bulletin, 88, 885– 904. J ONES , R. M. & H ILLIS , R. R. 2003. An integrated quantitative approach to assessing fault-seal risk. American Association of Petroleum Geologists Bulletin, 87, 507– 524. K NIPE , R. J., F ISHER , Q. J., J ONES , G. ET AL . 1997. Fault seal analysis: Successful methodologies, application and future direction. In: M ØLLER -P EDERSEN , P. & K OESTLER , A. G. (eds) Hydrocarbon Seals. Importance for Exploration and Production. Norwegian Petroleum Society, Special Publication, 7, 15–38. K OLEDOYE , B., A YDIN , A. & M AY , E. 2003. A new process-based methodology for analysis of shale smear along normal faults in the Niger Delta. American Association of Petroleum Geologists Bulletin, 87, 445– 463.

L EHNER , F. K. & P ILAAR , W. F. 1997. The emplacement of clay smears in synsedimentary normal faults: Inferences from field observations near Frechen, Germany. In: M ØLLER -P EDERSEN , P. & K OESTLER , A. G. (eds) Hydrocarbon Seals. Importance for Exploration and Production. Norwegian Petroleum Society, Special Publication, 7, 39– 50. L INDSAY , N. G., M URPHY , F. C., W ALSH , J. J. & W ATTERSON , J. 1993. Outcrop studies of shale smears on fault surfaces. In: F LINT , S. S. & B RYANT , I. D. (eds) The Geological Modelling of Hydrocarbon Reservoirs and Outcrop Analogues. International Association of Sedimentologists Special Publication, 15, 113–123. M ANZOCCHI , T., W ALSH , J. J., N ELL , P. & Y IELDING , G. 1999. Fault transmissibility multipliers for flow simulation models. Petroleum Geoscience, 5, 53–63. S KERLEC , G. M. 1999. Evaluating top and fault seal. In: B EAUMONT , E. A. & F OSTER , N. H. (eds) Exploring for Oil and Gas Traps. AAPG Treatise of Petroleum Geology, Handbook of Petroleum Geology, 10-1–10-94. S MITH , D. A. 1980. Sealing and non-sealing faults in Louisiana Gulf Coast salt basin. American Association of Petroleum Geologists Bulletin, 64, 145 –172. S PERREVIK , S., G ILLESPIE , P. A., F ISHER , Q. J., H ALVORSEN , T. & K NIPE , R. J. 2002. Emirical estimation of fault rock properties. In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seal Quantification. Norwegian Petroleum Society, Special Publication, 11, 109–125. VAN DER Z EE , W. & U RAI , J. 2005. Processes of normal fault evolution in a siliciclastic sequence: a case study from Miri, Sarawak, Malaysia. Journal of Structural Geology, 27, 2281–2300. W ATTS , N. L. 1987. Theoretical aspects of cap-rock and fault seals for single- and two-phase hydrocarbon columns. Marine and Petroleum Geology, 4, 274–307. Y IELDING , G. 2002. Shale Gouge Ratio – Calibration by geohistory. In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seal Quantification. Norwegian Petroleum Society, Special Publication, 11, 2002, 1– 15. Y IELDING , G., F REEMAN , B. & N EEDHAM , D. T. 1997. Quantitative fault seal prediction. American Association of Petroleum Geologists Bulletin, 81, 897–917.

Testing fault transmissibility predictions in a structurally dominated reservoir: Ringhorne field, Norway R. D. MYERS1, A. ALLGOOD1, A. HJELLBAKK2, P. VROLIJK1 & N. BRIEDIS2 1

ExxonMobil Upstream Research Co., 2180 Buffalo Speedway, Houston, TX, 77252-2189, USA (e-mail: [email protected]) 2

ExxonMobil Production Co., P.O. Box 60, 4064 Stavanger, Norway

Abstract: At Ringhorne field, in the North Sea, judicious well placement and high quality 3D seismic data allow good control over stratigraphic and structural frameworks. In particular, two near-horizontal producing wells about 150 m apart on both sides of a critical normal fault are key for deciphering the fault effects on flow. These elements make this field ideal for using production data to constrain a range of process-based fault permeability predictions in a siliciclastic reservoir. A high resolution (50 m 50 m 1.8 m) faulted geological model, constructed in PetrelTM , was used as input to process-based fault permeability predictions. Subsequent multiphase simulation and testing identified critical stratigraphic connections across shale layers and structural connections along a faulted relay around an isolated fault block. The simulations were used systematically as a probe to investigate both these and other controls on production and determine the likely range for permeability of fault zone materials, which are inferred to include deformed shales, sands, and minor cements. This study leverages the most pertinent observations and best constrained interpretations in the field to attempt to extract accurate, quantitative information on fault properties. A range of predicted fault permeability cases, linked to particular fault movement timing scenarios, were tested. The middle case, from a fault timing perspective, was determined to provide the best overall flow simulation match to all actual production information, providing valuable feedback for our process-based fault property prediction approach. Establishing the link between predicted and actual flow, and pressure history in response to critical reservoir plumbing elements, is paramount for evaluating and improving fault permeability predictions.

In reservoir depletion planning the geoscience and engineering focus is typically on predicting subsurface plumbing, which usually incorporates unknown elements of stratigraphy, structure, rock properties and fluid properties. Reservoir fluid data is routinely obtained, usually leaving the permeability structure as the greatest uncertainty. Stratigraphic controls on permeability are well understood and sampled by direct (wells) and indirect (seismic) data collection methods. Fault permeability is relatively poorly understood and often cannot be sampled or measured directly. Inverting subsurface pressures or flow rates from wells is therefore commonly the only recourse for deciphering fault permeability. Even where flow data are available, understanding the role of faults requires deconvolving the effects of all controls on well performance. The geological controls include the fundamental stratigraphic and secondary diagenetic, controlling factors on permeable pathways, and the 3D fault geometry that modifies the stratigraphic connections. In clastic reservoirs these are sand and shale distributions, and related matrix porosity and permeability fields. Few real-world reservoirs allow sufficient control over stratigraphy, rock, and fluid property unknowns to allow reliable determination of fault effects.

The technical need to predict accurately the impact of faults on subsurface flow has been recognized in the petroleum industry for decades (Smith 1966; Nelson 1985). Accurate predictions aid in making wise decisions about how best to utilize subsurface resources, such as in petroleum and groundwater reservoir management, and improve predictions for sequestration, and contaminant mitigation projects. This need has produced several approaches for predicting fault properties, including the distribution and permeability of shaly material (Weber et al. 1978; Lindsay et al. 1993; Yielding et al. 1997; Harris et al. 2002; Holland et al. 2006), cataclastically deformed sands (Engelder 1974; Antonellini & Aydin 1994; Gibson 1998) and combinations of fault rocks (Manzocchi et al. 1999, 2002; Fisher & Knipe 2001; van der Zee & Urai 2005). The petroleum industry lore is riddled with anecdotal information which governs how we interpret the tractability of this problem and how we interpret the effectiveness of any particular technology that purports to solve it. The main reason for these non-scientifically rigorous opinions of the role of faulting is the complicated nature of the problem to be solved. The impact of faults on flow is usually interpreted based on subsurface flow data from wells. This flow information is a convolution

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) 2007. Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 271–294. DOI: 10.1144/SP292.16 0305-8719/07/$15.00 # The Geological Society of London 2007.

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of subsurface parameters that influence pressure and flow rates at wells. The most important parameters governing flow in faulted siliciclastic reservoirs are the geometry, permeability, and capillary properties of reservoir rocks, the fluid properties, the permeability of fault zone materials, and the cross-fault juxtapositions (Smith 1980; Knipe 1997). Other important considerations are the wellbore hydraulics, and the drilling history (i.e. what mud types and weights were used, completion type, deviation geometry, borehole conditions, etc.) since these influence how the well data are interpreted. If all the non-fault related controls on flow are known perfectly then the impact of fault specific properties can be objectively and more rigorously analysed. This is not to say that an interpretation based on such an analysis is unique; there are usually multiple unknowns about the fault component of flow that make it difficult to analyse each element of the fault system systematically and independently. For example, a permeable damage zone may mitigate the effects of limited juxtaposition area of permeable reservoir by allowing along-fault flow through relatively impermeable rocks (Foley et al. 1998; Vrolijk et al. 2005). However, all mitigating factors, such as uncertainty in stratigraphic continuity near faults, are usually poorly known, so it is difficult to isolate any aspect of the fault specific problem, such as permeability of the fault zone material, relative to other effects on flow. These uncertainties highlight that there are two problems with fault permeability prediction schemes. The first is defining a technology that may represent fault properties in the subsurface accurately. The second is obtaining reliable information about that quantity which one wishes to make predictions about. Without reliable truth data, any hypotheses about fault permeability controls are essentially untestable. The result of applying new technology without a rigorously tested validation exercise is a local calibration at best, and an incorrect inference about prediction quality at worst. These issues are avoided by locating one or more well constrained test cases. The objective of this paper is to examine the accuracy of fault transmissibility predictions made using a process-based approach and multiphase flow simulation—under the practical conditions and business drivers of a ‘live’ petroleum reservoir project.

Background The Jurassic Ringhorne field is located in the Norwegian North Sea (Fig. 1). It is an example of a well constrained test case where it is possible to isolate individual aspects of the permeability field and focus on predictions of the permeability-thickness

of fault zone materials developed along an individual fault, more directly than in other published case studies (e.g. Fulljames et al. 1997; Harris 2002). The field is situated on the eastern margin of the Viking Graben, in the same general structural trend as the Jotun, Sleipner, and Balder fields (Fig. 1). The reservoir rocks are Jurassic Statfjord Formation fluvial to shallow marine sandstones, and minor Paleocene Ty Formation deep marine sandstones that overlie Cretaceous chalk. The Ringhorne field was discovered in 1997, and early characterization was based on seismic data that was typical of the time. Interpretations of 3D seismic data indicate potential for multiple internal fault-bound blocks, and early exploration wells were drilled into two of these blocks (Fig. 2). Pressure data collected in the oil and water columns from wells 25/08-11 and 25/08-12A (Fig. 2) confirmed a single field-wide oil–water contact at 1917 m subsea depth prior to production startup at Ringhorne. This contact lies above the depth of local structural spill points associated with flexures, ramps and tips of faults that separate the main fault blocks, thus connections between blocks in the oil leg occur only across faults. This indicates that faults separating reservoir blocks one and two must contain capillary leaks that allow pressure equilibration over geological time. The most recent 3D seismic survey was shot in 2001 with the intention of obtaining the best possible imaging of faults and stratigraphic architectures at the Jurassic levels. The optimized survey achieved relatively high frequency content at the reservoir depth, with nominal one-quarter wavelength fault throw resolution of approximately 13 m vertically (cf. Townsend et al. 1998). The first two production wells were drilled at Ringhorne with the assumption that the larger internal faults would be barriers to flow on a production timescale, requiring secondary pressure support through water injection. These wells are nearly parallel to one another and with subhorizontal completions approximately 150 m apart, on opposite sides of the largest throw, intra-field fault that separates Fault Block 1 (FB1) from Fault Block 2 (Fig. 2). The 25/08-C-6 well in Fault Block 2 (FB2) started production in February 2003, and was followed 50 days later by production startup in the 25/08-C-4 well in FB1. The first 112 days of production were on aquifer drive only, water injection for pressure support started in June of 2003 in FB1 and July 2003 in FB2.

Structure and fault timing Seismic interpretations show that the Ringhorne field is bounded on the east by a large east-dipping

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Fig. 1. (a) Map location of the Jurassic Ringhorne field in the North Sea relative to other oil and gas fields. (b) Oblique 3D view of the base Cretaceous unconformity showing the structural context of Ringhorne field.

normal fault and to the west by several smaller normal faults whose cumulative slip accounts for the horst trap structure (Fig. 3). The northern part of the field contains another intra-field fault that defines Fault Block 3 (Fig. 2). Intra-reservoir faulting is poorly defined north of this bounding fault, principally due to increasing reservoir depth on the NE dipping flank. There is less reservoir in the oil leg in this block and it is therefore of lesser immediate business importance. A production well was drilled into this block late in 2004, but limited production history at the time of this study and relatively poor control over stratigraphic and fault networks in the northern part of the field, preclude using that well data for validation testing. The fault network consists of: a major north – south-trending normal fault with maximum throw

of approximately 200 m; two moderate throw crossfaults with maximum throws of approximately 80 m; an unconnected ‘apron’ of smaller throw faults that partly encircle the structure on the south, west and NW flanks of the horst block; and an additional 12 faults with relatively minor throws (’20 m) interpreted throughout the reservoir (Fig. 4). These faults are interpreted to be discontinuous based on their mapped extent in the 3D seismic volume. In particular, the segment of the field labelled FB1 is only partly fault-bound as mapped because the southern fault contains a relay ramp that connects this block with the main field (discussed below). This segmented fault interpretation plays a significant role in reservoir connectivity and evaluation of the simulation model results relative to predicted fault permeability.

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Fig. 2. Structure contour map at the base reservoir. Green lines are producing wells, blue lines are injection wells. Thin dashed lines are additional wells with production activity in the overlying Ty Formation. Red circles are exploration wells; FB, fault block. Contour interval 20 m.

The trapping structure evolved as part of the preCretaceous break-up of northern Europe from northern North America in pre-Tethys time, but slip on the normal faults in the field continued for some time after as the North Sea basin formed and deepened. The evidence for this multiple slip history is preserved in the present day throw distributions which show dramatic throw changes at a major base Cretaceous unconformity. Fault throws cannot be measured confidently through the high velocity/low impedance Cretaceous chalks. In this interval the throws are linearly interpolated between mapped fault segments above and below the chalk (Fig. 5). This is a well documented, basinwide unconformity that appears to have eroded the upper palaeo fault tips. The majority of slip on most of the seismic-scale faults occurred pre-Cretaceous, presumably during the graben-forming rifting event. There is no measurable growth in sediments across faults in the Late Triassic to Early Jurassic

reservoir interval and mapped braided stream systems that form most of the reservoir rocks are unaffected by faults, suggesting that the faults had no surface expression when the sediments were deposited. However, absence of these syndepositional fault slip indicators does not rule out possible syndepositional fault timing. For example if slip rates were small relative to rates of deposition, there may have been no significant fault scarp and no related stratigraphic influence detectable on seismic scales. Seismic data do provide observations of later slip on the same faults offsetting the Cretaceous chalk, and many of the mapped faults propagated into the shallower section. Some tips are discernable on seismic at least as high as 300 m above the chalk, suggesting significant postCretaceous slip (Fig. 6). A set of polygonal normal faults lie in the shallower shale-rich section, approximately 1000 m above the reservoir interval. Polygonal fault

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Fig. 3. Cross section through the Ringhorne geological model showing 3rd order zonation. Highstand facies generally are shale prone, while lowstand deposits are sand prone. Significant sub-chalk erosion has removed the shallower Jurassic sands in the horst block. The Ringhorne oil–water contact at 1917 m depth is shown as a horizontal line marked OWC.

systems are interpreted to form near the sea floor as sediments compact and de-water (e.g. Cartwright 1996). These faults are mechanically and kinematically independent from the uppermost tips of any of

the faults that cut the reservoir, suggesting that the deeper faults had ceased moving at the time the shallower faults were formed. The height of fault tips above the reservoir, and the lack of mechanical

Fig. 4. Fault network at Ringhorne from 3D seismic (opposing fault sides painted yellow). Most faults are interpreted to be segmented, especially along the west flank. The relay ramp at the south end of FB1 plays a significant role in connectivity and hydrocarbon flow. The scale varies across this oblique view (vertical exaggeration 2:1).

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Fig. 5. Throw verses depth plot for the fault separating FB1 and FB2. All faults that offset the top of the reservoir show similar throw anomalies due to erosion of palaeo-fault tips at the base Cretaceous unconformity. Subsequent slip is recorded by offset of the chalk and younger sediments that overlie the unconformity.

interaction with shallow faults suggest a best estimate of depth of burial of the reservoir during the latest slip to be between 300 m and 1000 m, with a most-likely interpretation of 700 m. However, neither significant syndepositional slip, nor significant recent slip, can be ruled out. Therefore, each of these scenarios must be addressed by a fault permeability prediction, in order to capture the range of fault properties that might exist in the field today.

Stratigraphy Stratigraphy plays an important role in interpreting the impact of faults on flow as continuity of sands up to a fault plane, and subsequent cross-fault juxtapositions, are a requisite for cross-fault flow.

The Statfjord Formation comprises the major reservoir sands at Ringhorne, which are predominantly fluvial braided channel complexes in the deeper section, grading upwards to tidally influenced floodplain and upper shoreface sands (Fig. 7; Husmo et al. 2003). The stratigraphic section is interpreted to record a general southward trending marine transgression over floodplain and braided stream deposits. The disappearance of red beds and appearance of marine dinacysts, coals and possible tidal laminations are clear indicators of a transition from ephemeral to perennial conditions, culminating in a marine flooding event at the top of the reservoir section. The orientation and degree of connectivity, or lateral aggradation, of the stream deposits is based on well correlations and interpretations using the relatively high quality seismic data (Fig. 7). The high data fidelity provides a reasonable level of certainty in the basic stratigraphic breakdown to the level where complexes of channels and associated bar and overbank deposits are combined in a hierarchical fashion. This level of resolution is referred to as a channel complex system (Sprague et al. 2002). Seismic resolution prevents imaging of the limits of the overall Statfjord Formation braided system, or individual channels within the system, and thus some uncertainties exist on the limits of individual fluvial bar sands. To address this uncertainty the individual channels in the geological model are stochastically placed using seismic and well log indicators and object-based modelling of ‘typical’ braided stream bars (Fig. 8). Sand body dimensions and geometries are constrained by seismic interpretations and present day analogues. The braided stream deposits generally have very high porosity and permeability, with measured single-phase core plug permeabilities greater than 3000 mD. In general the sands are well sorted and contain little to no cements. There are two main types of shale in the reservoir: local interfluvial deposits and extensive floodplain deposits. Interfluvial deposits are floodplain sediments that were preserved during the lowstand depositional phase due to bypass of the braided stream systems (i.e. areas where floodplain deposits have been preserved instead of sand). They can be found in any of the sediments dominated by braided channel complexes, within the limits of the field, but are of limited horizontal extent (e.g. the blue areas in Fig. 8). The horizontal producer in FB2 intersected a shale rich interval in the middle of the S7 sand section that is interpreted to be such a deposit. These deposits are generally invisible on seismic data, and are impossible to predict deterministically. More extensive floodplain shales were deposited during the transgressive tract, and lie between the

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Fig. 6. Faults were interpreted only over the reservoir interval. Some tips extend to depths as shallow as 1600 m subsea, or about 300 m shallower than the top of Jurassic reservoirs. There is no observable evidence for syndepositional slip, and the faults tip-out well below a set of shallowly formed polygonal faults at 1000 m depth. A 700 m depth is interpreted for the likely lastest fault slip, with a total range of 300–1000 m.

Fig. 7. Stratigraphic correlations with key wells in each fault block. Seismic data quality allow confident correlations down to 3rd order sequences designated by S1-9. S1-S5 are fluvial dominated, S6 is floodplain/tidal dominated, S7 is fluvial, S8-S9 are floodplain/shoreface. Approximate locations of FB1 and FB2 oil producers used to validate fault permeability predictions are shown by green ellipses.

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Fig. 8. Fluvial reservoir sands are modelled using seismic and modern outcrop analogues. (a) Modern day stream deposits of the Canterbury Plain braid system (provided by Penny Patterson). (b) Stochastic object-based model of a single layer in the S5 interval of the geological model showing an example of channelized sand distribution.

major braided channel complex sets. The transgressive tract floodplain shales were generally laterally continuous, though they may contain sporadic isolated channels sands. These minor sands are isolated and restricted both laterally and vertically. Thus the floodplain shales are generally considered to be intra-reservoir seals on the local fault block scale, particularly near the base of the reservoir section where the channel complexes become more confined.

Fault transmissibility Transmissibility is the volume weighted average permeability of two connected cells or nodes in a flow simulation model, and has units of permeability length. Faults affect the transmissibility by altering connections and interposing fault materials between cross-fault juxtaposed cells. Because there are rarely enough simulation nodes in a model budget to allocate properties to fault zone materials explicitly, most faults are represented in simulation models as discontinuities between offset cells. In these situations the impact of the fault is derived from the geometric effect of changing permeable cell contact areas and cell-to-cell connections. Contact areas are usually

reduced because some permeable cells will have juxtapositions with non-permeable cells across fault planes. Most simulation models can account for these geometric effects explicitly. Outcrop observations show that faults have a finite thickness, often categorized as a high strain core surrounded by a lower strain outer damage zone (Evans 1990; Smith et al. 1990; Caine et al. 1996). The fluid flow effect of the fault zone materials incorporated into the fault core is captured by calculating a multiplier for each cross-fault connection that accounts for the permeability and thickness of this extra material (e.g. Manzocchi et al. 1999). Our approach for calculating fault transmissibility multipliers begins with identification of crossfault sand-on-sand connections in the geological model. A fault zone thickness and permeability are then determined from the throw of the fault and the predicted composition of the fault rock at each connection. The fault zone thickness and permeability are used in the geological model to calculate effective permeability over the length of a model cell. This fault permeability is then upscaled as a model attribute, and transformed to a transmissibility multiplier in the simulation model using simple averaging techniques, similar to the approach described by Manzocchi et al. (1999). The impact of an outer fault damage zone is

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ignored in our transmissibility predictions because its potential impact on fluid flow is considered to be secondary at Ringhorne, due to the high matrix permeability and inferred semi-to-unlithified nature of the sediments when the majority of fault slip occurred. Fault permeability predictions are made for all faults incorporated into the Ringhorne Petrel geological model. This includes all faults mapped in the 3D seismic volume. The predictions use a proprietary calculation of aggregate fault zone permeability that incorporates cataclasis, shale gouge, and diagenetic processes. The distribution of fault permeability varies continuously along a fault surface, depending upon fault throw, juxtaposed sand permeability, and offset stratigraphy. Our approach considers the deformation history in the context of evolving stress state and material properties during progressive burial of sediments. Two main concepts are that effective stresses at the time of faulting, and the stratigraphic stacking, influence the degree and continuity of shale smearing in the fault. Outcrop observations and lab experiments have been used to determine how the permeability of sand-based and shale-based fault zone materials can vary as a function of these influences. Fault permeability is calculated by combining each component and accounting for the geometry of the composite zone, including the frequency and tortuosity of permeable pathways across the shale-rich fraction of the fault. Although the actual component fractions, permeabilities, and continuity at any point along a fault are unknown, and perhaps unknowable, our risking-based permeability model captures the effect of characteristic flow properties of realistic distributions of these unknowns. Our risking scheme associates these distributions to subseismic deformation processes that are controlled, in part, by confining stresses, material property contrasts, fault zone geometry, and stratigraphic architectures. At Ringhorne the faults are predicted to contain tectonized shaly material, sands with a slight amount of cataclasis and possible minor calcite cements. Multiple scenarios are derived that accommodate the ranges in uncertainty in fault zone materials, providing low, mid and high permeability cases that correspond to minimum, most-likely, and maximum reservoir burial depths at the time of latest fault slip (Fig. 9). The dimensions of the fault zone materials are calculated using a transform that relates throw magnitude to thickness based on proprietary and published outcrop measurements (Robertson 1983; Hull 1988; Evans 1990; Childs et al. 1996; Knott et al. 1996; Beach et al. 1997). These generally take the form of an exponential relationship where

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thickness is a function of fault throw or slip. The published data suggest an order of magnitude variation in thickness at a given slip value, with some variability due to differences between specifics of faulting in each outcrop. We use the following transform for the analyses presented here: Thickness ¼ 0:015throw1:01

(1)

The thickness variations for a typical intra-reservoir fault with slip of 1–100 m are on the order of a few metres at most. Typical simulation models have an average node spacing of 50 –100 m, over this distance matrix permeability often varies by an order of magnitude or more. In the context of these cell dimensions and permeability uncertainties, the fault thickness variations are a second order effect, especially when compared to five or more orders of magnitude variation in permeability of faults that contain shale materials (Manzzochi 1999; Crawford et al. 2002). For this reason emphasis is placed on accurately predicting fault permeability. The thickness and permeability of fault zone materials are used together to calculate a fault transmissibility multiplier for each cross-fault connection between permeable sands as represented in the faulted geological model (Fig. 10).

Geological and simulation models The three dimensional stratigraphic and fault framework geometries are integrated in a faulted geological model using Petrel software and industry standard model building approaches. The stratigraphic and fault geometries are honoured explicitly to the limits of the seismic and well data except that no horizontal fault intersections (branchlines) can be modelled by the software in the reservoir interval. This means that in this case, there are no compromises defining the geometric fault framework to account for corner point gridding, in either the geological or simulation models. The model has 11 zones that conform to the major stratigraphic boundaries identified through well correlations and seismic mapping. The model covers an area of approximately 40 km2 and approximately 450 m depth range. There are approximately 9 million cells with average dimensions of 50 m 50 m 1.8 m. There are significant differences locally in these dimensions within some layers and near faults. In particular the Ty Formation cells have average thickness of 1 m, and some triangular cells truncated by faults have approximately half the area of non-truncated cells. Most layers have either top or base truncations against adjacent layers, in order to simulate

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Fig. 9. Histograms of predicted fault permeability for all sand-to-sand connections in the Ringhorne geological model from each fault timing scenario. The permeabilities are linked to fault deformation history and processes and material properties consistent with that potential history.

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Fig. 10. Geological model cells with all cross-fault sand-to-sand juxtapositions coloured by predicted fault permeability (10–0.00001 mD). Each scenario is linked to the specific fault deformation history described. The mid-case permeability assumes 700 m maximum reservoir burial at the time of last fault movement.

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depositional lapping geometries. Cells within layers have constant thickness where not truncated. As previously mentioned the channel geometries are data constrained to the resolution of bar complex sets (as delimited by approximately 10 –15 m vertical seismic resolution at the reservoir depth). Below that limit, sands are stochastically placed using sequential indicator simulation of channel objects. Porosity is predicted in the geological model using indicator simulation based on well logs and lithofacies maps. This is a commonly used geostatistical technique for populating larger scale distributions of properties based on log and/or seismic data (Isaaks & Srivastava 1989). Permeability is modelled as a simple cloud transform from porosity using the poroperm relationship defined by core sample analysis. The resultant geological model forms the basis for multiphase flow simulation. The close proximity of the two Statfjord producing wells to each other, and to the intervening fault, combined with seismic quality, provide unusually precise constraints on the modelling of high resolution stratigraphy in the immediate vicinity of the fault plane, where it has the greatest effect on across-fault flow. Flow simulations were conducted using ExxonMobil’s proprietary multiphase flow simulator EMpower (Tm). A number of simulation models were run during the course of this study. Some models represented progressive stages in the level of geological sophistication as additional geological data were incorporated. Other models were run simply to test the effect of different upscaling assumptions, various fault permeability scenarios, and pressure support related to aquifer drive. In all simulation models the fluid properties, such as density, viscosity and gas saturation functions, are derived from pressure/volume/temperature analysis of Ringhorne oil samples. At the time of the study Ringhorne wells were producing oil and insignificant water, so even though the model used relative permeabilities and capillary pressures to control rates and pressure distributions over time, the flow across faults is interpreted to have been mainly single phase (liquid hydrocarbons). In other words, the capillary and relative permeability properties of the fault zone are viewed as second order effects in this study and are considered no further. There are several generations of simulation models for which specific changes were implemented to better mimic subsurface conditions and properties. Some parameters are constant for all models, as listed below: † There are 11 units in the model and 47 horizontal layers that were determined using flow optimization and minimizing swept volume errors.

† There is no lateral scale-up - areal grid spacing is approximately 50 m 50 m for both geological and simulation models, with local refinement around faults and wells using unstructured gridding. Scale-up procedures follow accepted industry practices (Stern 2005). † Simulation grids are upscaled in the vertical direction compared to the geological model; the specific upscaling methods vary between simulation models and are described in more detail in following sections. Simulation layers vary in thickness from about 2–8 m, depending upon local stratigraphy. † Three relative permeability curves are used: a low permeability curve with cutoff of 500 mD; a middle curve for permeability between 500 and 3500 mD; and a high curve, for permeability greater than 3500 mD. † Oil production rates in the simulation model were matched to actual rates from the four producing wells in the field, two completed in the Statfjord and two in the Ty Formation. The Ty wells have little or no impact on the Statfjord fluid pressures, but were included in the simulations for completeness and to address business objectives. † Average injection pressures are modelled for two injection wells. The averaging intervals, from 30 to 10 days, were adjusted downwards during the course of the simulation modelling. The intention was to capture possible impacts on pressure predictions relative to changes in geological parameters. During simulation it was found that the geological parameters overwhelm the injection averaging variations. † Two virtual wells were placed on the flanks of the structure to simulate a larger aquifer volume than was included in the model. These wells pump at a rate sufficient to match farfield aquifer pressures observed in wells some distance from the key faults in the model. Without the aquifer wells the limited aquifer volume attached to the reservoir model would experience greater than observed pressure depletion that could be erroneously attributed to other causes, such as fault properties, matrix permeability or reservoir pore volume inaccuracies.

Discussion 1st generation modelling The initial simulation model used analytical averaging methods to upscale the geological model cells to the simulation model cells (Stern 2005). The model incorporates the highest quality geological architecture, rock, and fluid data interpretations

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Fig. 11. Oblique view of the Ringhorne EMpower simulation model. The cells are colour coded by horizontal permeability with a low cutoff of 500 mD. AW wells simulate the impact of a larger aquifer on the flanks of the structure. Wells 25/08-C-6 and C-4 are the primary producers that are separated by 150 m on either side of a key fault. Injection wells are labeled WI.

available for the field at this stage. Faults are in inclined to match seismic interpretations. Areal gridding is refined around faults and throughout the main reservoir section (Fig. 11), and is relatively coarse on the flanks of the field below the oil–water contact. The production rates used in the model were based on historical data averaged over 30 to 60 day intervals. Water injection pressures were modelled using a constant average value for the entire well history. In summary, this model consists of unstructured gridding for accurate fault and stratigraphy representation, good quality fluid composition data, pressure data, rate data, and field specific relative permeability and capillary pressure curves. In comparison to this, fit-for-purpose models that some industry simulations are routinely conducted on, can carry far more uncertainty over many, sometimes all, of these inputs. When coupled with control provided by the high resolution seismic data and advantageous well placements, the Ringhorne simulation models can therefore be considered to be a ‘high quality’ representation of the reservoir. For the purposes of evaluating fault transmissibility predictions, the simulation results for the 25/08-C-4 and 25/ 08-C-6 producers are the most relevant and interpretation efforts are focused on them. The simulated and actual flowing bottomhole pressures recorded in the 25/08-C-4 and C-6 wells are shown in Figure 12. Several simulations

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were run on the same geological model in order to test the simulator response to different scenarios of fault material permeability. The simulation results include end-member cases for the impact of faults on reservoir performance. The first case treats the faults as discontinuities only; there are no fault zone materials or intrinsic fault permeability properties in this simulation. This result is the ‘open’ case, where the transmissibility multiplier is set to 1 for all faulted connections. The second case considers the faults to be permeability barriers over their entire extent. This is the ‘sealed’ case, where the transmissibility multiplier is set to 0 for all faulted connections. Also included in the simulation results are the three specific fault material permeability scenarios previously described that correspond to the ranges in allowable fault deformation timing. The cases represent high, mid and low permeability predictions. The pressure response in the 25/08-C-6 well first shows a steep decline for 112 days, followed by a gradual increase and finally gradual decline. The initial pressure drop is due to hydrocarbon depletion on aquifer pressure support alone. After 112 days the Fault Block 1 water injector went online and pressure increased in response. The rest of the history shows the gradual decline response from continued hydrocarbon production that is not balanced by water injection. The open case shows the least pressure drawdown, due to good pressure support from the flanks of the structure and good drainage from other compartments. The well history data show a greater drawdown than allowed by the most restrictive simulation model, where the faults are treated as seals. The fact that the simulation model can not mimic the degree of observed pressure drawdown suggests too great a pore volume, connectivity, or permeability in the simulation model. All three fault permeability scenarios fall fairly near the open case. The 25/08-C-4 historical data show a gradual drawdown for the first 50 days reflecting the production from C-6, followed by a steep pressure decline as the well was put on stream during which the FB1 compartment pressure drops substantially (51 bars, or 750 psi). After water injection starts at 112 days, the pressure quickly rebounds and shows an overall good balance between injection and production in that average reservoir pressures are relatively flat to increasing. The simulation model first overpredicts the degree of pressure drop, then underpredicts it once C-4 starts producing. The initial drawdown prior to any injection is far greater than even the sealed case predicts, consistent with observations from the 25/08-C-6 results. The simulation results show uniformly lower average pressures than the historical data. This is consistent with either too much pore volume or connectivity,

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Fig. 12. Initial simulation results suggest that the model has too much connectivity, too high a pore volume, or permeabilities throughout the model are too high. Comparison between history and simulation results for the 25/ 08-C-6 well suggest that the faults are fairly irrelevant since the entire range from open to sealed is less than the difference between the historical data and simulation results. 25/08-C-4 results could be interpreted to show that faults underwent ‘breakdown’, implying that initially sealed faults became permeable over production time.

or too high a permeability in the simulation model, as the effect of injection is dispersed throughout the model rather than strongly elevating pressures in the 25/08-C-4 well vicinity. After 600 days the pressures for open and sealed cases in FB1 due to production from C-4 are much different than the open and sealed cases for C-6 in FB2. The FB1 simulation results show greater drawdown for the open

case than the sealed case, which has the smallest pressure drop. In FB2 the sealed case has the greatest pressure drop. These differences are due to cross-block flow. The simulations with sealed faults prevent FB1 from being depleted by production in FB2. In the open case both producers draw from FB1 thus pressures are depleted more rapidly. The dramatic differences between the

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simulation and history data suggest that the faults are fairly irrelevant in this model and that other factors in the simulation model overwhelm the pressure responses.

2nd generation modelling Improvements were made to the simulation model via enhanced upscaling, better production/injection history matching, and a change to a shaledominated layer affecting aquifer support. Single phase flow-based scale averaging was used for upscaling, theoretically this is the optimal upscaling approach because it calculates an effective permeability based on a calculated pressure drop between cells (Stern 2005). Previous models used average production rates over 30 to 60 day intervals, this model matched daily historical rates explicitly. Simulations incorporating these two changes showed only minor differences compared to the 1st generation models, therefore results are not plotted separately. A more significant change was made to the simulation injection well pressures. They were updated to capture an added 20 bar average injection pressure around day 394. This change produced significant improvements in the simulation results relative to historical data for well C-4, but they were relatively minor for C-6. The results are not plotted separately as the impact occurs after day 394 when injection and production are well balanced, so these results have less significance for evaluation of fault permeability. When these engineering changes were shown to have a relatively minor overall effect, an additional explanation was sought for the overall higher pressures in the simulation model. It was discovered that several significant aquifer connections existed across shale layer S3. A decision was made to remove these vertical connections between the aquifer and the overlying S4 and shallower reservoir sands over the extent of Fault Block 2, in order to test the impact of this shale on connectivity of the simulation pressures. The S3 is interpreted to be an extensive floodplain deposit with high lateral continuity, and low potential for vertical connections, so the adjustment is consistent with stratigraphic understanding. There was a significant effect on the overall simulation results and this change is responsible for most of the improvement in the simulation model compared to history. The combined affect of all the changes described above are shown in Figure 13. The 25/08-C-6 simulation results for the sealed fault case are very close to the historical pressure data. However, the largest drawdown in the early part of the history is still not well matched by any of the simulations. The 25/08-C-4 data also show a large drawdown prior to day 112 that is not

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matched by any simulation, though later history brackets the simulation results. The large pressure fluctuations, which are not matched by the relatively smooth simulation pressures, are attributed to using averaged injection well pressures in the simulation. Considering the geological setting of the 25/08-C-4 well, located within an areally restricted mostly fault-bound block, the drawdown prior to first injection is the best test of the permeability of the fault separating FB1 and FB2. During the first 112 days the fault experiences the greatest pressure differential, thus the fault permeability has a correspondingly greater effect on cross fault flow during this period. Later production is balanced to some degree by injection, and the pressure drop on either side of the fault due to the closely spaced producers is not as dramatic. Variations in injection and production due to topside facilities maintenance activities is also greater in the later history. Therefore the best test of fault permeability is the early drawdown prior to day 112. Failure of even the most restrictive case (sealed faults) to match the pressure drawdown during this interval suggests that the model is still over connected. Geological causes for the elevated connectivity were explored by examining the existing interpretations in the FB1 area. The efforts focused on S3 shale integrity, reservoir permeability predictions and the fault relay ramp at the south end of FB1 (Fig. 14).

3rd generation modelling The mapped relay ramp shows significant throw gradients to either side, and a relatively thin ramp relative to the fault lengths. These observations, together with simulation results, suggest that the ramp could be breached (e.g. Imber et al. 2004). To determine whether or not the ramp exists, and the likelihood of it containing a fault, the seismic interpretations of strata around the ramp were examined in detail. Consecutive cross-sections perpendicular to the FB1 south-bounding fault show the offset S5 horizon (Fig. 14). Subtle throw reduction can be seen where the relay ramp is interpreted, but there is no clear evidence for an intact ramp. In fact, the relatively horizontal bedding above S5 on the hanging wall side strongly suggests that if a ramp exists, it is breached by a fault with throw near the limits of seismic resolution. The strong impact of interpreting the S3 shale as a continuous layer in FB2, led to an evaluation of the shale continuity in FB1. Two wells that penetrate the shale in FB1 show that it is approximately 10 m thick, and contains up to 16% sand. These sands are interpreted from the wells to be small isolated channels that should not provide good vertical connectivity. Within the geological model 16% of

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Fig. 13. Second generation simulation model uses flow-based scale average upscaling, corrected aquifer support and removed vertical connections across the S3 shale in FB2 (see text for more details). These results still do not adequately describe early drawdown observed in both wells. Even the sealed case cannot match the greatest drawdown.

S3 cells are modelled as stochastic channel sands (Fig. 15). Stair-stepping of stacked channels created three vertical connections between S2 and S4 sands during upscaling, thus allowing the aquifer in S2 to communicate with the oil bearing sands in S4. These chance aquifer connections are highly improbable given the well log interpretation

of the depositional environment and stratigraphic setting of the S3 shale. The predicted mean S7 reservoir sand corresponds to a permeability of approximately 2500 mD. Well test analysis of pressure buildups from 25/08-C-6 indicates that the S7 reservoir permeability is approximately 0.74 times the predicted

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Fig. 14. Serial seismic sections 0across the mapped relay ramp at the south end of FB1 show clear fault offsets0 in 0 0 A– A , less clear offsets in B–B (through the ramp), and clear offsets again in C–C . Most reflectors in B–B have sharp truncations of nearly horizontal beds above S5 in the hanging wall (5 vertical exaggeration). Deeper beds show a combination of truncation and drag consistent with a breached relay ramp. Purple surface is top of S5 grid sitting within the seismic volume.

permeability, or approximately 1800 mD. It is not unusual practice to make history matching changes of 200% or 300% or more to statistically predicted permeability, so a 26% drop interpreted from the well test analysis is considered a very minor adjustment. In order to align the simulations with the new geology interpretations, some modifications were made to the 3rd generation simulation model. The erroneous chance connections across the S3 shale in FB1 were keyed out; and reservoir connections along the relay ramp were assigned a transmissibility multiplier consistent with the presence of a fault

with approximately 10 m of throw (described below). Affecting the transmissibility in this way accounts for the presence of fault zone materials, but does not reflect the changes in juxtaposition that would result if a fault were explicitly included across the ramp. About 50 cell connections were affected by this change (compared to several thousand total across fault connections between FB1 and FB2), so the potential impact of not correctly modelling juxtapositions is probably small. The transmissibility multipliers used in the simulation were estimated by compiling multipliers from nearby fault connections, and choosing average

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Fig. 15. Oblique 3D views of S3 shale layering in the model, showing how some S3 cells are modelled as stochastic channel sands based on well control. Chance stacking of channels creates several vertical connections during upscaling between the aquifer in S2 sands and oil in S4 sands. These across-shale aquifer connections are highly improbable based on environment of deposition interpretations, and the degree of aquifer support implied by the connections is not supportable by any simulation result.

values from a scatter plot of throw versus transmissibility multiplier corresponding to each timing scenario (Fig. 16). This approach is fast and easy to implement, and ensures consistency between the relay multipliers and the multipliers used on nearby faults. This simplistic approach would not be appropriate for a fault with large surface area or many connections, but is justified in this case given the very small number of connections modified and the relatively large differences in multipliers between scenarios (Fig. 16). After layer S3 modification, the 25/08-C-6 and 25/08-C-4 simulation results show a marked

improvement relative to the historical downhole pressure data (Fig. 17). The 25/08-C-6 minimum case pressures are now consistent with historical pressures over most of the well history. However, the 25/08-C-4 historical data are not well matched by any of the scenarios after about 60 days. Even the sealed fault case cannot match the observed C-4 maximum drawdown, suggesting that some flow element is still not correctly represented in the model. In the absence of the 25/ 08-C-4 pressure data the C-6 results may have been interpreted erroneously to signify a very pessimistic fault permeability.

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Fig. 16. Scatter plots of transmissibility multiplier for fault connections in the immediate vicinity of FB1 relay ramp. Mean values for a 10 m throw fault in the ramp were chosen for each scenario using these plots.

The final simulation model incorporated all previous changes plus the relay ramp fault multipliers. The simulations now account for all first order geological observations and interpretations. The 25/08-C-6 and 25/08-C-4 results are in good overall agreement with the mid-permeability case due to overall decreased connectivity (Fig. 18). The early pressure drawdown in C-6 is still not perfectly matched by any scenario, but the historical

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data after injection startup correspond very well withthe mid-case fault permeability prediction. The greater than predicted drawdown suggests that some element of the geology is still missing from the simulation model, but is a second order effect compared to the re-interpretations and subsequent model modifications. There is a consistent approximately 2 bar difference between the earliest well data and that predicted by the midfault permeability case over the first 394 days of production. This corresponds to the time period prior to increased average water injection pressure. As mentioned previously, the extreme FB1 pressure drawdown prior to injection on day 112 represents the single best test of the permeability of the key fault separating FB1 and FB2 (Fig. 19). There are several points of correspondence between the simulation results for the mid-case fault permeability predictions and the historical pressure data. The simulation predicts an initial pressure drawdown for the open and mid cases. The sealed case also assumes the small relay ramp fault is sealed, thus no FB1 pressure drawdown due to production in FB2 occurs in this scenario. The open fault case, with no relay ramp fault, predicts a 10 bar pressure drop due to this production, while the mid case predicts a smaller 5 bar drop. The actual pressure drop was on the order of 2 to 3 bars. This suggests that the relay ramp is faulted, consistent with the seismic re-interpretation, and that the faults separating FB1 from FB2 are not sealing over production time scales. An alternative explanation is that ongoing production from other nearby fields has dropped the regional aquifer pressure between the startup time of wells 25/08-C-6 and 25/08-C-4. However, after 25/08-C-4 production begins around day 50 the simulation results correspond very well to the mid-case fault permeability scenario. This match continues through the point of greatest drawdown, which is the single best test for quantifying the fault effects on flow. There is excellent agreement between simulation and history data at this critical point, but a significant difference between history and the sealed case (approximately 20 bars). This result suggests that the faults are in fact leaking over production time. After injection startup, the history data shows the effects of unmatched high frequency injection changes, which makes comparisons with simulation predictions difficult to interpret. However, the well balanced production and injection volumes in C-4 after about day 200 render this later history mostly irrelevant for evaluating fault permeability as the faults experience much smaller pressure differentials. This is evidenced by the nearly identical pressure response for the end-member sealed

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Fig. 17. Third generation simulation model with S7 sand permeability decreased by 26%, and accidental vertical connections across the S2 shale removed. The minimum fault permeability case is in good agreement with historical pressures from the C-6 well, but under predicts drawdown in C-4. Even the sealed fault case cannot match the observed maximum drawdown in C-4, suggesting that some flow element is still not correctly represented in the model.

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Fig. 18. Final third generation simulation model has S7 sand permeability decreased by 26%, a transmissibility multiplier for a subseismic fault applied to the relay ramp at the south end of FB1, and accidental vertical connections across the S2 shale removed. These changes bring the model into agreement with known or inferred first order geology observations. Final pressures from mid-case fault permeability (most likely fault timing) are in good agreement with historical pressures from both producing wells.

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Fig. 19. Fault plane profile from the Ringhorne geological model for the key fault separating FB1 and FB2. Solid lines define highside reservoir units, dashed lines are corresponding lowside units. Colours represent predicted mid-case permeability values (10– 0.00001 mD). The oil– water contact is shown by a horizontal red line marked OWC.

and open cases after about 200 days of production (Fig. 18). However, in C-6, there is a gradual reservoir pressure depletion over time, and significant spread between open and sealed fault cases, so fault permeability predictions still affect the pressure responses observed in FB2 during later times.

3.

Conclusions 1.

2.

The faults in the Jurassic Ringhorne field are interpreted to be baffles to hydrocarbon flow, which is mostly single phase at this early stage of production. The field is nearly ideally suited for understanding the impact of faults on flow. This is due to a combination of factors: good quality seismic data that are optimized for detecting structural elements at the reservoir depth; advantageous low angle producing well placements on either side of a well imaged normal fault; good local stratigraphic control based on wells and seismic data; and fault interpretations of fairly high quality. Additionally the key fault separating the producers has a fairly uniform 60 –80 m throw across the reservoir sands, thus minimizing segmentation issues that arise when faults tip out in the reservoir or have large throw gradients. It is possible to constrain the depths of the reservoir interval at the time of faulting, but there exists some uncertainty in the deformation timing. Within the constraints of this uncertainty it is possible to define a moderate

4.

confidence ‘most-likely’ fault permeability prediction, this is the mid-case scenario. The input parameters leading to all cases were selected prior to any reservoir simulation modelling. Simulation results show that there is a meaningful pressure response due to relatively small scale connectivity issues that are common to most reservoirs in the subsurface. The presence of a small throw fault in a relay ramp and a few vertical sand pathways across an intra-reservoir shale interval proved to have a relatively large effect on flow. These connectivity elements, if undetected and left unaccounted for, would lead to dramatically different interpretations of the role of faulting in the Ringhorne field. In this case the seismic-scale faults would probably have been interpreted to be complete barriers to flow, rather than baffles, or possibly the faults would have been attributed with some sort of pressure barrier ‘breakdown’ over time. Of course our interpretations are based on simulation responses which are fundamentally nonunique due to irreducible uncertainty in input data, and the implicit nature of modelling a fault in the relay. However, given the degree of control over a combination of first order elements (e.g. stratigraphic architecture, fault framework, fluid properties, and rock properties), our detailed interpretations and modelling of the reservoir geology provide a degree of constraint that is exceptional. The fault permeability predictions implemented in the models are process-based.

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Our proprietary method considers the role that the deformation history and rock properties at the time of faulting, have on the potential to form shale and sand-based fault zone materials and the effective permeability of these materials. In this context our mid-case prediction of fault permeability at Ringhorne is a blind test of these concepts as applied to a specific reservoir. The well-constrained interpretations and state-of-the-art simulation modelling provide a good test of our processbased approach. Results from the best geologically constrained simulation model suggest that our fault property predictions are realistic, with some unresolvable uncertainty, as evidenced by the significant improvements matching Ringhorne production history. We wish to thank the Stavanger Ringhorne team (S. Ballestad, O. Tangen, T. Boone, and others) for information and graphics. D. Stern is acknowledged for simulation support and resources. The ExxonMobil Exploration and Production offices and ExxonMobil Upstream Research Company are thanked for permission to publish this paper. The manuscript benefited from reviews by S. Jolley, E. Meurer, T. Manzocchi and T. A. Knai.

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L INDSAY , N. G., M URPHY , F. C., W ALSH , J. J. & W ATTERSON , J. 1993. Outcrop studies of shale smears on fault surfaces, In: F LINT , S. S. & B RYANT , I. D. (eds) The Geological Modelling of Hydrocarbon Reservoirs and Outcrop Analogues. International Association of Sedimentologists, Special Publication, 15, 113–123. M ANZOCCHI , T., W ALSH , J. J., N ELL , P. & Y IELDING , G. 1999. Fault transmissibility multipliers for flow simulation models. Petroleum Geoscience, 5, 53– 63. M ANZOCCHI , T., H EATH , A. E., W ALSH , J. J. & C HILDS , C. 2002. The representation of two phase fault-rock properties in flow simulation models. Petroleum Geoscience, 8, 119– 132. N ELSON , R. A. 1985. Geologic Analysis of Naturally Fractured Reservoirs. Gulf Publishing, Houston, Texas. R OBERTSON , E. C. 1983. Relationship of fault displacement to gouge and breccia thickness. Mining Engineering, 35, 1426–1432. S MITH , D. A. 1966. Theoretical considerations of sealing and non-sealing faults. Bulletin of the American Association of Petroleum Geologists, 50, 363–374. S MITH , D. A. 1980. Sealing and nonsealing faults in Louisiana Gulf Coast Salt Basin. Bulletin of the American Association of Petroleum Geologists, 64, 145–172. S MITH , L., F ORSTER , C. & E VANS , J. 1990. Interaction of fault zones, fluid flow, and heat transfer at the basin scale. In: S HLOMO , P. & N ERETNIEKS , I. (eds) Hydrogeology of Low Permeability Environments. Hydrogeology, Selected Papers. 2, 41–67. S PRAGUE , A. R., P ATTERSON , P. E., H ILL , R. E. ET AL . 2002. The Physical Stratigraphy of Fluvial Strata; a

hierarchical approach to the analysis of genetically related stratigraphic elements for improved reservoir prediction. Annual Meeting of the American Association of Petroleum Geologists. Expanded Abstracts, 167–168. S TERN , D. 2005. Practical aspects of scaleup of simulation models. Journal of Petroleum Technology, 57, 74–82. T OWNSEND , C., F IRTH , I. R., W ESTERMAN , R., K IREVOLLEN , L., H ARDE , M. & A NDERSON , T. 1998. Small seismic-scale fault identification and mapping. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. J. (eds) Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 1– 25. VAN DER Z EE , W. & U RAI , J. L. 2005. Processes of normal fault evolution in a siliciclastic sequence: a case study from Miri, Sarawak, Malaysia. Journal of Structural Geology, 27, 2281– 2300. V ROLIJK , P., S HAFTO , K., M YERS , R. & B UNDS , M. 2005. Geometric effects on flow across faulted sedimentary strata; implications for fault gouge. Annual Meeting of the Geological Society of America, 37, 167. W EBER , K. J., M ANDL , G., P ILAAR , W. F., L EHNER , F. & P RECIOUS , R. G. 1978. The role of faults in hydrocarbon migration and trapping in Nigerian growth fault structures. Proceedings, Offshore Technology Conference, 10, 4, 2643– 2653. Y IELDING , G., F REEMAN , B. & N EEDHAM , T. 1997. Quantitative fault seal prediction. Bulletin of the American Association of Petroleum Geologists, 6, 897–917.

Incorporation of fault properties into production simulation models of Permian reservoirs from the southern North Sea E. B. ZIJLSTRA1, P. H. M. REEMST2 & Q. J. FISHER3 1

Shell EP Nederlandse Aardolie Maatschappij, Assen, The Netherlands (e-mail: [email protected])

2

Shell International Exploration and Production BV, Rijswijk, The Netherlands 3

Rock Deformation Research Ltd, School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK

Abstract: Reservoir compartmentalization is one of the key issues that affects the development and production phase of gas fields. To improve prediction of the effects of compartmentalization on production, a new method has been developed to allow petroleum engineers to incorporate geologically-reasonable fault rock flow properties into upscaled dynamic reservoir simulation models. The first stage of the workflow is to estimate the permeability and capillary characteristics of fault rocks within the field. These data are then combined with estimates of fault rock thickness, derived from outcrop studies, to calculate transmissibility multipliers to take into account the impact of faults on fluid flow within the dynamic model. Our method differs from most others in that we have attempted to account for the two-phase flow properties of fault rocks in the dynamic models from producing reservoirs. Application of the model to real field examples provides far faster history matching than has been achieved previously. In addition, taking into account the multi-phase flow properties of fault rocks explains production behaviour that previous models could not. Although, the focus of this study has been on the Southern Permian Basin in the North Sea, the same approach could be applied to other areas.

An ideal reservoir would behave like a tank of sand in which a high proportion of the gas originally in place could be drained by a single production well. Unfortunately, most reservoirs do not behave in this manner. Instead, the presence of sedimentary and structural heterogeneities often result in reservoirs being compartmentalized into several regions that need to be drained individually. Such compartmentalization can dramatically reduce the profitability of a reservoir by increasing the number of wells required to drain the petroleum and/or reducing the ultimate amount of petroleum that is produced. For example Corrigan (1993) suggested that the ultimate hydrocarbon recovery from many oil fields in the Brent Province of the North Sea would be lower than initially predicted due to compartmentalization. In low net: gross reservoirs, compartmentalization often occurs simply because faults juxtapose reservoir against non-reservoir (e.g. juxtaposition seal, Watts 1987). The Rotliegend in the Southern Permian Basin is generally a high net: gross reservoir, which is also commonly compartmentalized as a result of faulting. For example up to 280 bar pressure differences have built up between compartments in Rotliegend gas reservoirs from offshore Netherlands (van der Molen pers. comm. 2003). Here juxtaposition of reservoir against

non-reservoir is unlikely to be responsible for all compartmentalization. Instead, it is probably the presence of low permeability fault rocks that is often responsible for fault-related, compartmentalization (e.g. Edwards et al. 1993; Leveille et al. 1997). As fault compartmentalization has such a major impact on gas production, it is important that it is taken into account when planning production strategies. Frequently, this is achieved by assigning properties to grid-blocks or grid-block faces adjacent to faults within petroleum simulation models, which take into account the impact of fault rocks on fluid flow (e.g. Knai & Knipe 1998; Manzocchi et al. 1999). This is easily achieved in the situation where faults are acting as total barriers to fluid flow on production timescales by setting the transmissibility across the fault surface to zero. However, analysis of the petrophysical properties of fault rocks (e.g. Manzocchi et al. 1999; Fisher & Knipe 2001) demonstrates that in many situations faults are not likely to act as total barriers but instead are likely to allow some flow to occur. In this situation, it is necessary to model the faults as baffles and not total barriers to flow. As a consequence, new methods have recently been developed which permit the inclusion of geologically derived fault properties using estimates of fault rock thickness and absolute permeability (e.g. Manzocchi

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 295–308. DOI: 10.1144/SP292.17 0305-8719/07/$15.00 # The Geological Society of London 2007.

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et al. 1999). These methods have since been supplemented by others which are intended to include the multi-phase properties of fault rocks in flow simulations (Fisher & Knipe 2001; Manzocchi et al. 2002). The key challenge in the application of all such methods is determining exactly what values should be used within the simulation model to represent the impact of faults on compartmentalization. Here we describe examples of compartmentalized gas reservoirs from the Southern Permian Basin (SPB) in which faults are acting as partial barriers to gas production. A particular aim of the paper is to present a methodology that has been developed, which has significantly improved the speed and accuracy of simulating fluid flow in faultcompartmentalized gas reservoirs. An overview of the Rotliegend reservoirs in the SPB is gived. Then the methodology that has been used to incorporate fault rock properties into the simulation model is described as well as the ways in which the specific properties required for the modelling (e.g. fault permeability, fault thickness etc.) have been estimated. Three case studies are then presented outlining how this methodology has been applied and how it has helped to understand and predict the production behaviour. Finally, a discussion is presented to illustrate the advantages of the method and potential future work.

Geological setting The Rotliegend gas play in the southern North Sea consists of high net: gross sandstones of Early Permian age deposited on the southern fringe of the Southern Permian Basin, which is a postVariscan basin that extends from eastern England to the border of Russia and Poland (Glennie 1998). The Rotliegend reservoir sandstones directly overlie the prolific Carboniferous source rocks and are generally sealed by a thick caprock sequence of Zechstein evaporites. Four distinct facies associations have been recognized: fluvial, aeolian, sabkha and lacustrine. The Rotliegend reservoirs discussed in this paper are dominated by aeolian sandstones. The overall thickness of the Upper Rotliegend sandstone can be in excess of 200 m. Typically, gas is trapped in simple horst blocks and spill points generally occur at structural saddles or at the base of juxtaposed Zechstein evaporites across boundary faults. During the last few years, it has become clear that compartmentalization of the Rotliegend reservoir in different blocks is one of the key issues that impacts the development and production phase of such fields (e.g. Leveille et al. 1997). Dynamic data collected during the depletion

of Rotliegend reservoirs have been critical to the recognition of compartmentalization.

Compartmentalization concepts The concept of compartmentalization in production geology exists against the backdrop of another concept: that of a single trap that contains a single interconnected volume of petroleum in a single pressure system equilibrated on the geological timescale. Spatially bounded sub-volumes that need to be accessed individually to ensure their adequate depletion on the production timescale are called ‘compartments’. A single-cell field has one initial pressure profile, one initial free water level (FWL), one single initial composition, and one gas volume initially in place (GIIP). In a singlecell field, any well is in effective communication with all of the field’s GIIP. Such fields can easily be identified by comparing dynamic GIIP results from material balance calculations with the static GIIP calculated from geological models. Often this is achieved by plotting average field pressure divided by the compressibility factor against cumulative gas production; these are known as p/Z plots (Dake 2001). In a single-cell reservoir without aquifer support, p/Z data should plot on a straight line that would extrapolate to the GIIP calculated from the static model at p/Z ¼ 0 (Fig. 1a). Often there is also some GIIP volume located behind flow baffles, i.e. partially transmissible faults, which is indicated as ‘slow’ gas, as opposed to the ‘fast gas’ directly connected to the producers without a flow baffle (‘Fast and slow behaviour’, Fig. 1b). Data from wells drilled into a compartmentalized field with complete barriers between the compartments show an entirely different behaviour when plotted on a p/Z plot. In particular, p/Z data will tend to fall on a trend that extrapolates to a total gas production at p/Z ¼ 0 that is below the GIIP calculated from the static geological model (Fig. 1c). A closed compartment with internal flow baffles results in a behaviour as depicted in Fig. 1d. We assume that faults leak on a geological timescale, if pre-production pressure profiles and gas compositions have equilibrated. If the fault is acting as a membrane seal over geological time (e.g. Watts 1987), the gas column retained is dependent on the capillary entry pressure of the fault rock rather than its permeability. Faults in compartmentalized reservoirs may not be sealing on a geological timescale but may be significant barriers on a production timescale. The extent to which faults act as barriers on a production timescale are governed by the fault’s effective permeability (i.e. relative

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Fig. 1. P/z vs production plots, in which the average field pressure divided by the compressibility factor is plotted against cumulative gas production, for different scenarios. (a) & (b) are for single cell fields; (c) & (d) are for compartmentalized fields. (a) & (c) are fields with internal flow baffles (and associated fast– slow flow behaviour) whereas (b) & (d) are fields without internal baffles. GIIPS and GIIPD are the gas volume initially in place calculated from the static geological model and the gas production predicted from dynamic models, respectively. Abd is the pressure at field abandonment. Vprod is the total gas production. For a single cell field (a, b), no additional volumes are accessed by drilling more wells. In compartmentalized fields (c, d) remaining volume can be accessed by drilling additional wells into other compartments. Distinction between case b, c and d is impossible during early stages of depletion. See text for details.

permeability multiplied by absolute permeability) once the capillary entry pressure is exceeded.

Towards a new method for incorporation of geological fault rock properties Traditionally, in an upscaled geological model, the transmissibility across a fault surface is calculated from the permeability in the adjacent grid-blocks, and takes the reduced area of reservoir– reservoir juxtaposition into account. Further transmissibility reduction related to additional baffling effects in the fault zone is typically captured by applying transmissibility multipliers to the grid-blocks either side of the fault (hereinafter referred to as fault transmissibility multipliers) in the dynamic model (e.g. Knai & Knipe 1998; Manzocchi et al. 1999). Until recently, the traditional practice in industry was to adjust fault transmissibility

multipliers by trial-and-error, in ad hoc fashion, without serious scientific justification, in order to achieve a history match of production data (Manzocchi et al. 1999; Fisher & Jolley 2007). A key problem with this methodology is that history matches are non-unique and there has been a tendency to apply fault transmissibility multipliers to correct for various inaccuracies within the unconstrained simulation model. Ultimately, this methodology can often result in the generation of simulation models that produce very convincing history matches but only accurately predict future production for a few months in advance (e.g. Ottesen et al. 2005). A more recent trend has been to calculate geologically reasonable fault transmissibility multipliers based on estimates of fault rock thickness and absolute permeability (Manzocchi et al. 1999). This more recent, geologically reasonable, approach, is a significant improvement on methods that arrive at

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fault transmissibility multipliers on a trial-and-error basis. However, a potential problem with such an approach is that although it is appropriate for some reservoirs (e.g. Jolley et al. 2007), it does not take into account the capillary pressure and relative permeability characteristics of fault rocks (Fisher & Knipe 2001; Manzocchi et al. 2002) that are critical information for fault seal analysis in other situations (e.g. this paper, as discussed by Fisher & Jolley 2007). Following on from the conceptual fault model presented by Fisher et al. (2001), faults in gas reservoirs can be envisaged as being divided into three zones relative to the FWL (Fig. 2): 1.

Below the FWL (Zone 1 on Fig. 2) only formation water is present within the fault and therefore fault transmissibility multipliers can be calculated based on the absolute permeability of the fault rock without considering relative permeability effects.

2.

3.

Immediately above the FWL (Zone 2 on Fig. 2), the buoyancy force in the gas column will be insufficient to overcome the capillary entry pressure of the fault rock. Here the fault will have zero relative permeability to gas and can be treated as being totally sealing to gas. At some height above the FWL, here referred to as the capillary entry height, the buoyancy force in the petroleum column may be sufficient to overcome the capillary entry pressure of the fault rock (Zone 3 on Fig. 2). In this case, the fault will have a finite permeability to gas that is dependent upon the relative permeability and capillary pressure curves of the fault rock as well as its absolute permeability.

The concept outlined in Figure 2 has been used as a basis for the development of a simple method for incorporating two-phase flow properties into Rotliegend gas reservoirs, which is referred to here as the ‘capillary entry height method’. The

Fig. 2. Conceptual model for the two-phase flow behaviour of faults based on Fisher et al. (2001). (a) Represents gas saturations (red for high, blue for zero) in the fault and reservoir. (b) Shows the capillary pressure behaviour of the fault and (c) shows the relative permeability behaviour of the fault. In Zone 1, one brine is present within the fault and the adjacent undeformed reservoir, so that transmissibility multipliers can be calculated based on single-phase fault permeability measurements. In Zone 2, the fault has no gas saturation and hence it may be included as a transmissibility multiplier¼0 in the simulation model. In Zone 3, the fault has a finite permeability to gas and transmissibility multipliers should be calculated taking into account the gas relative permeability of the fault rock.

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method assumes that the fault can be divided into the three zones relative to the FWL that are described above. Below the FWL (Zone 1), fault transmissibility multipliers are calculated in exactly the same way as described in Manzocchi et al. (1999). In particular, fault transmissibility multipliers are calculated based on the size and permeability of the grid-blocks on either side of the fault as well as estimates of the fault thickness and the absolute permeability of the fault rock. For a certain height above the FWL (Zone 2) the faults are treated as being totally sealing to gas and given transmissibility multipliers equal to zero. At a height above the FWL above which the buoyancy force in the gas column exceeds the capillary entry pressure of the fault rock (Zone 3), fault transmissibility multipliers are calculated using a similar method to Zone 1. But, instead of just using the absolute permeability, the gas relative permeability of the fault rock is also used in the fault transmissibility multiplier calculation. In the examples presented in this paper it was assumed that the fault rock within Zone 3 is at irreducible water saturation (Swir) so a single relative permeability value is used throughout each model. Differences in the permeability of the grid-blocks adjacent to the fault will mean that transmissibility multipliers are likely to vary significantly along the length of a fault (Manzocchi et al. 1999). In these circumstances, the variation of transmissibility multipliers along a fault is realistic and contrasts markedly to the traditional trial-and-error method of deriving fault transmissibility multipliers where a single transmissibility multiplier is assigned to a single fault (see Manzocchi et al. 1999 for discussion of these shortcomings). The height above the FWL level at which the buoyancy force in the gas column overcomes the capillary entry pressure of the fault rock is unlikely to coincide with the interface between two grid-blocks. In other words, the boundary between Zone 2 and Zone 3 in Figure 2 is likely to occur within, as opposed to between, gridblocks. To take into account this effect within the simulation model we calculated the fault transmissibility multiplier above the FWL as the product of two terms; the relative transmissibility multiplier, TMr and the capillary entry height function, Hc (Fig. 3). The term TMr is similar to the fault transmissibility multiplier described in Manzocchi et al. (1999) but, instead of the absolute fault rock permeability, the effective permeability to gas is used in the calculation. The term Hc, is defined as:

Hc ¼

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where h1 is the thickness of the grid-block that is totally sealing to gas and h2 is the thickness of gridblock. So the resulting transmissibility multiplier would equal zero if the entire grid-block is within the zone that is totally sealing to gas (i.e. Zone 2 in Fig. 2). The transmissibility multiplier would be equal to TMr if the grid-block was entirely within the zone in which the capillary entry pressure of the fault rock had been overcome (Zone 3 in Fig. 2). In the case where the grid-block straddles zones 2 and 3 in Figure 2, the fault transmissibility is a product of TMr and Hc, which are both non-zero terms. After an initial prototype stage, since 2006 the capillary entry height concept has been fully integrated into the Shell in-house reservoir simulator (MoReS) and provides the reservoir engineer with a tool to treat fault seal in a consistent way across the simulation model, within geologically reasonable parameter ranges. Fault permeability, thickness and capillary entry height can all be altered to history match the model. The fault transmissibility multipliers within the aquifer will tend to be higher than that in the gas column because in the aquifer only a single phase, liquid, is present. In reality, the fault within the aquifer may undergo enhanced diagenesis (e.g. preferential quartz cementation or illitization) and therefore may sometimes have a lower permeability than in the gas leg. Therefore a correction factor for the aquifer is an input parameter of the model. This factor is assigned automatically to the fault grid block faces below the gas– water contact. The capillary entry height model is far simpler to implement than the method to incorporate multi-phase fault rock properties into production simulation models described by Manzocchi et al. (2002), but is missing some functionality. For example our method does not incorporate either saturation or flow rate dependencies and does not correctly model the cross-fault flow of gas within the aquifer. In the latter case, the method of Manzocchi et al. (2002) calculates pseudo-relative permeability curves for the grid-blocks adjacent to water and in so doing prevents the flow of gas across the fault within the aquifer. Despite these deficiencies, this model does account for some of the effects of fault-related multi-phase flow and has the important additional benefit of being easy to implement and understand. A key advantage of the capillary entry height model described here is its simplicity. Engineers that are familiar with MoReS can quickly learn to apply the capillary entry model to their reservoirs. Application of the capillary entry model has allowed simulation models to be history matched in far less time than was possible using a trialand-error approach. Also, as described below, the model was able to reproduce physical phenomena

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Fig. 3. Implementation of the impact of reduced permeability in a fault zone with a certain width including the transmissibility term (TMr) and the reduced gas flow interface (Hc) from the higher entry pressure in the fault zone. The TMr term is simply the thickness weighted harmonic average of the grid-block (k1) and fault permeability (kf) divided by the grid-block permeability. The Hc term is the proportion of the grid-block – grid-block juxtaposition that is permeable to gas and is calculated from the thickness of the grid-block (H1) and the thickness of the fault between the grid-blocks that are totally sealing to gas (H2). The two components of the transmissibility multiplier can be routinely calculated for each connection along a fault surface in the dynamic simulation model. Input parameters are the permeability of the undeformed grid-block and the fault rock, fault thickness, as well as the relative permeability and capillary entry pressure of the fault rock.

such as differential cross-fault changes in gas– water contact (GWC) that traditional ways of modelling fault transmissibility could not reproduce.

Input parameters for the production simulation model The basic input parameters required to calculate the fault transmissibility multipliers using the model presented above are: (i) grid-block geometries and flow properties adjacent to faults within the simulation model; (ii) fault rock flow properties (absolute permeability, capillary entry pressure and relative

permeability); and (iii) fault rock thickness. The grid-block geometries and flow properties adjacent to faults are already contained within the production simulation model and will not be discussed further. A discussion of how the fault flow properties and thickness that are used to calculate the flow transmissibility multipliers is discussed below.

Fault rock flow properties To provide a basic database on the fluid flow properties of faults within Rotliegend reservoirs we created a database of the microstructural and petrophysical

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properties (permeability and capillary entry pressure) of fault rocks present within core of Rotliegend reservoirs throughout Shell assets in the southern North Sea and from onshore Netherlands. The analytical methodologies are essentially identical to those described in Fisher & Knipe (1998, 2001). Cataclasites are by far the most common fault rock identified within Rotliegend cores (Fisher & Knipe 2001). Cataclasites develop generally (but not exclusively) from porous sandstones containing ,15% phyllosilicate material. The fluid flow properties of cataclastic faults developed are usually degraded compared to the undeformed Rotliegend reservoir mainly as a result of two processes. First, the reductions in grain-size and grain-sorting that accompany deformation allow the grain fragments to be packed more efficiently and produce a collapse of macroporosity. Second, cataclastic faults often experience enhanced quartz cementation since deformation exposes clean (unpolluted) fracture surfaces for cement nucleation.

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In hand specimen, the deformation zones that contain cataclasites are typically sub-planar, palecoloured and moderately to steeply dipping (Fig. 4). They have widths ranging from ,0.5 mm to around 10 mm and in those samples where it proved possible to determine fault displacement these are typically in the millimetre range. Examination of the cataclastic fault rocks, by back-scattered electron microscopy (BSEM), shows that they have experienced grain breakage and grain-size reduction and are zones of reduced porosity in comparison to their host sandstones. The extent of grain-size reduction and the grain-size distribution of the cataclasites varies from sample to sample. Most of these faults are dominated by grain fragments with the occasional uncrushed sand grain (Fig. 5a), although faults were also identified in which only grain fragments are present (Fig. 5b). Some of the faults also experienced significant enhanced post–deformation quartz cementation (Fig. 5c). It is likely that the increased quartz cementation reflects the presence of a large

Fig. 4. Photographs showing typical hand specimens of a cataclastic fault from Rotliegend reservoirs of the southern Permian Basin.

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Fig. 5. BSE micrographs showing cataclastic faults that have experienced: (a) a moderate grain-size reduction; (b) an extensive grain-size reduction; and (c) extensive post-deformation quartz cementation.

surface area of quartz within the fault formed as a result of cataclastic deformation. Cements are unlikely to be laterally continuous in cases where they are derived from fluids flowing along the faults because dilation is not likely to occur along the entire length of the fault (Fisher & Knipe 1998). In the case of the Rotliegend cataclasites described here, quartz cement is derived by local diagenetic reactions, such as grain-contact quartz dissolution (‘pressure solution’), and precipitation is enhanced wherever cataclastic deformation of quartz grains occurs. It is therefore possible that the areas of enhanced quartz cementation will be far more

laterally continuous than areas of cement precipitated from fluids flowing along faults. The general lack of clay along these faults means that they do not tend to experience enhanced grain-contact quartz dissolution (Fisher & Knipe 2001), which is an important fault seal process in phyllosilicateframework fault rocks (Fisher & Knipe 1998). The permeability of cataclastic faults within the Rotliegend reservoirs in the southern North Sea and onshore Netherlands was found to vary between 0.1 and 0.0001 mD (Fisher & Knipe 2001). The Hg–air threshold pressure of these fault rocks was found to vary between 100 psi and around 1500 psi. There appears to be a trend whereby the reservoirs that have been buried the deepest have cataclastic faults with the lowest permeabilities and highest threshold pressures (Fisher & Knipe 2001). This depth-related trend in flow properties of the fault rocks is probably a consequence of two effects. First, faults in reservoirs that have been buried the deepest experienced most post-faulting diagenesis (Fisher & Knipe 2001). Second, reservoirs that have been buried the deepest may have deformed under higher effective stresses resulting in more intense grain fracturing than experienced along faults formed under lower effective stresses (Fisher & Knipe 2001). Although the flow properties of these fault rocks vary hugely across the southern North Sea and onshore Netherlands (Fisher & Knipe 2001), we have found that fault permeabilities tend to vary far less within individual gas reservoirs. For example, within a given reservoir, the permeability of cataclastic faults tends to vary by less than two orders of magnitude. This probably reflects the fact that the faults in a given reservoir formed at similar burial depths and experience similar post-deformation diagenesis. The reservoirs in the examples described below all had core containing numerous fault rocks. The absolute permeability and Hg-threshold pressure of between 10 and 30 fault samples collected from core were determined for each field studied using the methodology described in Fisher & Knipe (2001). The geometric mean of the fault permeabilities was used to calculate the fault transmissibility multipliers for the capillary entry height model described above. The arithmetic mean of the Hg-injection threshold pressures was used to calculate the gas column height that could be sealed by the cataclastic fault rocks using the formula presented in Watts (1987). At the time this work was conducted there was no information on the relative permeability of fault rocks. Relative permeability data was extrapolated from some of Shell’s tight gas assets to permeability values typical of the fault rocks present in Rotliegend reservoirs. Relative permeability

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data from cataclastic faults recently obtained by Al-Hinai et al. (2006) are consistent with the values that have been used.

Fault thickness It is well established that fault thickness tends to increase with fault throw (e.g. Hull 1988). It has therefore been suggested that empirical correlations be used to estimate fault thickness from fault throw for calculating fault transmissibility multipliers (e.g. Manzocchi et al. 1999). For the present study, a constant fault rock thickness of 0.25 m was used, which is consistent with the fault rock thickness, i.e. the fault damage zones, observed in outcrop analogues of Rotliegend reservoirs found onshore UK. A constant fault thickness was used for two reasons. First, the reservoirs in the study area have reverse reactivation of normal faults and potentially strike-slip faulting, which means that application of empirical relationships between fault throw and thickness may lead to an underestimation of fault thickness Secondly, the thickness of cataclastic faults increases rapidly with the first 10 m of throw after which fault thickness is less sensitive to fault throw (Beach et al. 1999).

Application of the capillary entry height method The capillary height method has been successfully applied in three gas fields in the Southern Permian Basin, which are described below.

Field A Field A has a GIIP of 400 mrd m3 and a current capacity of 8 mln m3/d. The field is very mature and more than 85% depleted. The initial development consisted of clusters situated in the centre of the field. In recent years, further development has focused on drilling extended reach low angle wells into the flanks of the field. This is depicted in Figure 6a. All of these have encountered compartments with pressures that were significantly higher than the pressures within the strongly depleted central part of the field. This pressure distribution is consistent with the concept outlined in Figure 2 and in Figure 6b in which faults close to the flanks of the reservoir are more likely to be barriers to gas due to the lower buoyancy force within the gas column compared to that developed within the centre for the field. Prior to embarking on this new fault seal model, the Field A full field simulation model had been (tediously) matched by applying fault seal multipliers on a fault-by-fault, trial-and-error, basis to

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achieve a history match for all 200 wells. It was realized that capillary entry height would have a strong impact on the seal of normal faults in the south flank of the field. The capillary entry height model was applied using a capillary entry height of 50 m for the faults in this area, estimated from the Hg-injection data derived from faults within core. The initial history match was found to be good but was improved further using a capillary entry height of 65 m, which is only slightly higher than the core derived measurements. This discrepancy is thought to be minor compared to the uncertainties in choosing a threshold pressure from Hg-injection data and converting the results into the gas– water system. The geometric mean of the fault permeability values measured from core samples and the gas relative permeabilities extrapolated from tight gas sand data were incorporated directly into the simulation model and did not need altering to achieve the history match. Previously, the history matching of this area in which fault transmissibility multipliers were altered on an ad hoc, trial-and-error, basis had proved a very painstaking exercise that involved well over a hundred iterations. Application of the capillary entry height model resulted in a reasonable match within four runs. History match results from a selection of Field A wells with a capillary entry height of 65 m are given in Figure 7. The observed stronger baffling effect of the flank faults as compared to the crest faults was reproduced by application of the entry height method. Furthermore, the ability to history match by altering geological and petrophysical parameters such as capillary entry height, within their uncertainty range (rather than directly changing the grid-block transmissibilities by trial-and-error) provided far more confidence in the predictive capabilities of the MoReS production simulation model.

Field B (Fig. 8) Wire-line saturation logging and 4D seismic (2001 v. 1993) indicate a rise in GWC on one side of a fault within Field B, which is a mature, large offshore gas field just like Field A. The rise of water was observed in three wells. The preferential rise in GWC was best explained by invoking a ‘U-tube model’, in which a fault acts as a barrier to gas but allows water to communicate in aquifer. The matrix rock has a high permeability ranging from 100 – 600 mD, and the porosity is around 18%; net: gross ratio is one. Other reasons for the rise in GWC on one side of the fault, such as water coning near production wells, were considered but were thought unlikely to account for the wire-line saturation and 4D data. In an attempt to history match both production and 4D seismic,

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Fig. 6. (a) Field A map showing how extended reach horizontals provide access to compartments in the south flank of Field A. The drilling results indicated that these compartments were only partially depleted. (b) Schematic diagram illustrating the entry height model, in which the capillary rise of water will have the biggest impact on cross fault flow in low gas column areas.

two different simulation models were tested: a ‘Tank Model’ and a ‘Baffle model’. In the tank model, fault transmissibility multipliers were obtained by trial-and-error and were assumed homogeneous in the fault plane. In the baffle model, the same entry height implementation was applied as that used for Field A. Transmissibility multipliers were applied depending on the position above the FWL and were consistent with values from core analysis. Both models were able to history match the pressures. However, only the

baffle model predicted the observed rise of the GWC. The baffle model allows for the U-tubing effect around faults in which cross-fault water movement can occur in the water leg but cross-fault gas movement is restricted.

Field C (Fig. 9) The capillary entry height model was also used to determine the value of infill drilling in Field C, a small, low permeability gas field onshore NE

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Fig. 7. History match examples of Field A. A good match was achieved for 200 wells by applying the entry height method using a capillary entry height of 65 m. Black markers indicate the measured bottom hole pressure, the red line indicates the simulated bottom hole pressure.

Netherlands. To calculate the net present value (NPV) for a separate undrained block (Block C, proposed FC-3 well), two different methods were employed to model the dynamic fault behaviour

of an internal and a block bounding fault: a traditional fault property method (i.e. ad hoc trial-and-error assignment of transmissibility multipliers), and the capillary entry height method. Fault

Fig. 8. Comparison between seismic impedance from 4D seismic and modelled gas water rise in the dynamic simulation model of Field B. A 20 m rise of the GWC could be successfully modelled using the new method.

306 E. B. ZIJLSTRA ET AL. Fig. 9. Top reservoir map and seismic sections for Field C (onshore NE Netherlands). Seismic sections are approximately east– west oriented and contain wells FC-2 and FC-3 (black lines), showing the position of the gas–water contact (GWC – blue line). Faults seen on map are shown as grey and red lines on seismic section. Notice the much larger gas column at the (red) fault position for the infill well FC-3 than for FC-2. According to the new entry height method for fault sealing, this makes it likely that the fault in the target block will be less of a baffle than the fault near FC-2. Production has started around the time of writing and monitoring the future pressure decline will provide the ultimate test of the concept. The initial pressure of FC-3 was within the uncertainty range of the prediction.

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seal parameters in the new method were based on measurements of the permeability of faults contained within core, and the implementation into the dynamic model was analogous to Field A and Field B. Both methods were able to match the pressures in FC-1 and FC-2 (see Fig. 10) and were able to match an observed GWC rise in FC-1. Interestingly, the main difference appeared in the economic value of the undrained block: the prediction for FC-3 is much more favourable using the capillary entry height method. The reason is that this method takes into account the larger gas column in the compartment where FC-3 is drilled. Therefore the capillary rise has a smaller impact and the internal fault should be less sealing than the internal faults around the existing producers FC-1 and FC-2. The traditional fault property method assumed the same degree of baffling throughout the field. The new method resulted in an NPV increase of 50%, because of a higher prediction for the ultimate recovery. Based on the promising results obtained by applying the capillary entry height method for Field A and Field B, the decision was taken to go ahead with this marginal development and drill well FC-3 end of 2006. The initial pressure of this well was within the expected uncertainty range (partial depletion), but further pressure monitoring should provide more information about the internal

Fig. 10. The history matches of wells (a) FC-1 and (b) FC-2, using the capillary entry height method with a capillary entry height of 40 m. The red lines indicates the simulated bottom hole pressure and the black squares indicate the measured bottom hole pressure.

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flow baffles in the compartment where FC-3 is drilled. The capillary entry height method also explains why faults in Field C have a much stronger baffling effect than faults in an analogue neighbour field: probably the larger gas column in the neighbour field results in a smaller relative impact of the capillary water rise zone in the fault.

Conclusion A simple methodology has been presented for including fault properties into production simulation models for gas reservoirs from the Southern Permian Basin. The methodology involves calculating transmissibility multipliers based on estimates of fault rock thickness and the results from special core analysis measurements conducted on fault rocks: the method is the same as that employed by Manzocchi et al. (1999). An attempt is made to account for the two-phase flow properties of fault rocks by: (i) making the faults totally sealing to gas for a height above the FWL determined from the capillary entry pressure of the fault rock; and (ii) at greater distances above the FWL relative transmissibility multipliers are calculated based on estimates of the relative permeability of the fault rock. The method is simpler to implement than the method for the incorporation of multi-phase properties described by Manzocchi et al. (2002), but is not as comprehensive in its treatment of multi-phase flow. A module for the Shell in-house simulation model, MoReS, has been written so that the method can be easily applied to all faults within a given reservoir. The method has been applied to two fields with substantial production history and a far faster history match of production data was obtained than had previously been possible. The method was then applied to a less mature reservoir and the results lead to the decision to drill a compartment that might not have been drilled from the results of simulation models that had not applied the capillary entry height concept. For this reservoir the stronger baffling effect of intra-reservoir faults, as compared to a seemingly analogous neighbour field, could be explained well by the entry height method. In conclusion, two-phase flow behaviour and measured rock properties should be taken into account in fault modelling. This method has been implemented successfully in three test cases: in Field A it explains the high pressure areas in the flanks, in Field B it explains the observed GWC rise and in Field C it explains the stronger baffling effect as compared to an analogue neighbour field. In all test cases the entry height method helped to achieve a history match much faster than by using conventional trial-and-error tuning methods.

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Therefore this method is seen as a practice worth replicating in other basins.

References A L -H INAI , S., F ISHER , Q. J., A L -B USAFI , B., G UISE , P. & G RATTONI , C. A. 2006. Recent application of special core analysis to fault rocks. Proceedings of the 2006 International Symposium of the Society of Core Analysts. Trondheim, Norway, 12th to 16th September, SCA2006-15. Society of Core Analysts, Dublin, CA. B EACH , A., W ELBON , A. I., B ROCKBANK , P. J. & M C C ALLUM , J. E. 1999. Reservoir damage around faults: outcrop examples from Suez rift. Petroleum Geoscience, 5, 109– 116. C ORRIGAN , A. F. 1993. Estimation of recoverable reserves: the geologists job. In: P ARKER , J. R. (ed.) Petroleum Geology of Northwest Europe: Proceedings of the 4th Conference. Geological Society, London, 1473–1482. D AKE , L. P. 2001. Practice of Reservoir Engineering. Elsevier, Amsterdam. E DWARDS , H. E., B ECKER , A. D. & H OWELL , J. A. 1993. Compartmentalisation of an aeolian sandstone by structural heterogeneties: Permo-Triassic Hopeman Sandstone, Moray Firth, Scotland. In: N ORTH , C. P. & P ROSSER , D. J. (eds) Characterization of Fluvial and Aeolian Reservoirs. Geological Society, London, Special Publications, 73, 339–366. F ISHER , Q. J. & K NIPE , R. J. 1998. Fault sealing processes in siliciclastic sediments. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. J. (eds) Faulting and Fault Sealing in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 117–134. F ISHER , Q. J. & K NIPE , R. J. 2001. The permeability of faults within siliciclastic petroleum reservoirs of the North Sea and Norwegian Continental Shelf. Marine and Petroleum Geology, 18, 1063– 1081. F ISHER , Q. J. & J OLLEY , S. J. 2007. Treatment of faults in production simulation models. In: J OLLEY , S. J., B ARR , D., W ALSH , J. J. & K NIPE , R. J. (eds)

Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 219– 333. F ISHER , Q. J., H ARRIS , S. D., M C A LLISTER , E., K NIPE , R. J. & B OLTON , A. J. 2001. Hydrocarbon flow across sealing faults: theoretical constraints. Marine and Petroleum Geology, 18, 251– 257. G LENNIE , K. W. 1998. Petroleum Geology of the North Sea. Blackwell Scientific Publications, Oxford. H ULL , J. 1988. Thickness–displacement relationships for deformation zones. Journal of Structural Geology, 10, 431–435. J OLLEY , S. J., D IJK , H., L AMENS , J. H., F ISHER , Q. J., M ANZOCCHI , T., E IKMANS , H. & H UANG , Y. 2007. Faulting and fault sealing in production simulation models: Brent Province, northern North Sea. Petroleum Geoscience, 13, 321–340. L EVEILLE , G. P., K NIPE , R. J., M ORE , C. ET AL . 1997. Compartmentalization of Rotliegendes gas reservoirs by sealing faults, Jupiter Fields area, southern North Sea. In: Z IEGLER , K., T URNER , P. & D AINES , S. R. (eds) Petroleum geology of the southern North Sea: future potential. Geological Society, London, Special Publications, 123, 87–104. M ANZOCCHI , T., W ALSH , J. J., N ELL , P. & Y IELDING , G. 1999. Fault transmissibility multipliers for flow simulation models. Petroleum Geoscience, 5, 53–63. M ANZOCCHI , T., H EATH , A. E., W ALSH , J. J. & C HILDS , C. 2002. The representation of two-phase fault-rock properties in flow simulation models. Petroleum Geoscience, 8, 119–132. O TTESEN , S., T OWNSEND , C. & Ø VERLAND , K. M. 2005. Investigating the effect of varying fault geometry and transmissibility on recovery: Using a new workflow for structural uncertainty modeling in a clastic reservoir. In: B OULT , P. & K ALDI , J. (eds) Evaluating Fault and Cap Rock Seals. American Association of Petroleum Geologists Hedberg Series, 2, 125–136. W ATTS , N. L. 1987. Theoretical aspects of cap-rock and fault seals for single and two phase hydrocarbon columns. Marine and Petroleum Geology, 4, 274–307.

Static and dynamic connectivity in bed-scale models of faulted and unfaulted turbidites T. MANZOCCHI1, J. J. WALSH1, M. TOMASSO2,3, J. STRAND1,4, C. CHILDS1 & P. D. W. HAUGHTON2 1

Fault Analysis Group, School of Geological Sciences, University College Dublin, Belfield, Dublin 4, Ireland (e-mail: [email protected])

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Marine and Petroleum Geology Group, School of Geological Sciences, University College Dublin, Belfield, Dublin 4, Ireland 3 Current Address: Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, University Station, Box X, Austin, Texas 78713-8924, USA 4 Current Address: CSIRO Petroleum, P.O. Box 1130, Bentley, WA 6102, Australia Abstract: A range of unfaulted and faulted bed-scale models with sheet-like or lobate bed geometries and faults of comparable sizes to beds have been built and analysed in terms of bed connectivity and fractional permeability assuming permeable sands and impermeable shales and shale smears. A new method has been devised allowing amalgamation ratio to be included explicitly as model input and this property, rather than net:gross ratio, is found to be the dominant control on the connectivity of unfaulted sequences. At the geometrically representative scales considered (horizontal distances of .1 km for beds up to c. 1 m thick and faults up to c. 5 m throw), faulted sequences rarely have lower connectivities than their unfaulted sedimentological equivalents irrespective of whether fault rock properties are included. Models containing stochastically placed shale smears associated with each faulted shale horizon are generally better connected than if deterministic Shale Gouge Ratio cut-offs are applied. Despite the complex interactions between geological input and connectivity of the faulted sequences, the flow properties at representative scales are controlled by three geometrical variables describing connectivity, anisotropy and resolution. If two different faulted or unfaulted systems have identical values of these three variables they will have the same equivalent flow properties.

The objective of the work described in this paper is to investigate controls on the flow characteristics of faulted turbidite reservoirs. Many turbidite reservoirs contain sandstones interbedded with low permeability shales, and in such cases the flow properties of the rock volume depend to a large extent on the connectivity of the sandstone beds. It has been suggested that for situations in which the shales can be assumed impermeable, many flow characteristics can be estimated very rapidly using semi-analytical scaling laws derived from percolation theory (e.g. King 1990; King et al. 2002; see also Stauffer and Aharony 1994; Sahimi 1995 for background discussion on percolation theory and its applications to flow). The important system parameters for this approach are a connectivity measure, which establishes how close the network of sandstone beds is to the percolation threshold; one or more anisotropy terms, which establish flow path tortuosity in different directions; and one or more resolution terms, which establish

how closely the scale of interest (e.g. the inter-well spacing in a particular field development plan) approximates to the infinite systems for which results from percolation theory apply strictly. The central tenet to this approach is that the geological details of the system are not relevant per se, but only inasmuch as they contribute to the three parameters mentioned. This study examines faulted and unfaulted bed-scale models of idealized sheetlike turbidite geometries, and discusses geological controls on connectivity as well as whether, and how, these three more fundamental geometrical terms can be defined in anything other than the most simplistic idealizations of the reservoir geology. A glossary of the terminology used in this paper is given in the appendix. The first part of the paper concerns connectivity in unfaulted thin-bedded sheet-like or lobate bed geometries (e.g. Fig. 1), a correct representation of which is recognized as a significant challenge in turbidite modelling (e.g. Weimer et al. 2000; Browne &

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 309–336. DOI: 10.1144/SP292.18 0305-8719/07/$15.00 # The Geological Society of London 2007.

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Fig. 1. Uninterpreted and interpreted photographs of thin bedded turbidites from the Mount Messenger Formation at Tongaporutu beach, New Zealand. Note that the line drawings show sandstones in yellow and shales in grey, whereas in the photos the sandstones are reddish-brown and the shales pale grey. (a) Section showing small sandstone beds encased in shale. (b) Section showing abundant amalgamation of sandstone beds. (c) Close-up of the shale break (bed i) to the left of the rucksack in (b). Note also bed ii, which although continuous at the scale of this photo is eroded at a larger scale.

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Fig. 2. (a) Fan body width (LB) to thickness (LZ) measures for modern and ancient systems, compiled from published data. (b–c) Net:gross ratio (NTG) v. amalgamation ratio (AR) separated on the basis of environment (b) and turbidite system (c). The lines in (c) represent the trends observed in the end member systems represented by the Angel and Mt Messenger Formations (cf ¼ 0.7 and 0.03 respectively). The data in (a) are from Al Ja’aidi (2000); Badalini et al. (2000); Browne et al. (1996); Bruhn & Walker (1994); Carr & Gardner (2000); Chapin et al. (1994); Clark & Gardner (2000); DeVay et al. (2000); DeVille Wickens & Bouma (2000); Elliott (2000); Evans et al. (2003); Jennette et al. (2000); Kleverlaan (1994); Lyons (1994); Lu¨thi (1981); Mahaffie (1994); Nilsen & Abbate (1985); Nilsen (1984, 1990); Parea & Ricci-Lucchi (1975); Pickering et al. (1989); Ricchi-Lucchi (1978); Ricci-Lucchi & Pignone (1978); and Stow & Johansson (2000). With the exception of the new Mt Messenger Formation measurements, the data in (b) and (c) derive from measurements or logs presented by Amy et al. (2000); Booth et al. (2003); Browne et al. (1996); Evans et al. (2003); Haughton (1994); Johnson et al. (2001); Mattern (2002); Rozman (2000); Satur et al. (2000); Sinclair (1994); Talling (2001); and Tomasso (2001).

Slatt 2002). Despite strong vertical heterogeneity, these systems often appear laterally homogeneous at an outcrop scale owing to the high horizontal to vertical bed anisotropy. A compilation of width to thickness measurements from sheet-like systems (Fig. 2a) indicates that turbidite deposits at all hierarchical scales from individual beds to complete

systems are typically about 200 times longer than they are thick (+ a factor of 10). For systems of beds of about 1 m thickness or less, therefore, bed connectivity is a more significant control on inter-well flow (i.e. flow at length-scales of hundreds of metres to a few kilometres) than is the internal permeability distribution within the beds, provided

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the latter is small compared to the permeability contrast between sandstone beds and shales. Bed connectivity can be recognized at outcrop as amalgamation surfaces (e.g. Fig. 1b) and in this study we make extensive use of the amalgamation ratio (AR; Chapin et al. 1994) as a connectivity measure. Departing slightly from the ambiguous definition of Chapin et al. (1994) we define amalgamation ratio as the fraction of sandstone bed bases that are amalgamated with the underlying sandstone bed when measured on a line sample. As noted by Stephen et al. (2001), this is equivalent parametrically to the total length (or area) of amalgamation normalized by the total length (or area) of sandstone bed bases in 2D (or 3D), and therefore is analogous to the ‘connectedness ratio’ measured in the processbased fluvial models of Mackey & Bridge (1995) and Karseenberg et al. (2001). In the second part of the paper we examine the influence of faults on bed connectivity within geometrically representative systems. Previous studies (e.g. Bailey et al. 2002; James et al. 2004) have shown that the influences of fault system characteristics on connectivity are intimately tied to sedimentological characteristics, a recurring issue in our analyses. The focus of the analyses are on faults of comparable sizes to the principal sedimentological length-scales. Fault lengths and maximum fault throws range from a few times smaller to a few times larger than the length and thickness of the beds respectively. As we are principally considering beds thinner than c. 1 m, the faults are subseismic with maximum fault throws up to c. 5 m. The effects of fault rock properties are included using Shale Gouge Ratio cut-offs and by explicit stochastic shale smear modelling. In common with the assumption of a binary permeable/impermeable sedimentological system, we assume across-fault sand-onsand juxtapositions are either permeable in the absence of a shale smear, or impermeable where one or more is present. We therefore do not address permeability decreases caused by cataclastic fault rock. Much of this modelling has been inspired by the faulted turbidites of the Miocene Mt Messenger Formation, Taranaki, New Zealand (e.g. King et al. 1993; Browne et al. 1996; Browne & Slatt 2002; Childs et al. 2007). The characteristics of both the sediments and faults examined in the modelling are not, however, constrained to those observed in the field area since our aims are more general than a specific understanding of the connectivity within this particular system.

Modelling procedures – unfaulted systems In the most direct idealization of a sedimentological system with the kind of geometrical networks investigated by researchers in percolation theory,

the net:gross ratio (NTG) of a sandstone sequence, however, takes the role of the volume fraction of a continuum percolation system (e.g. King 1990; King et al. 2001). A continuum percolation system is conceptually equivalent to an unconditioned object-based model in which beds, sampled from a particular size distribution, are placed at random within the modelling volume. The principal difference is that conventional object based models are discrete (i.e. each bed occupies a particular number of cells in each direction). This discretization introduces systematic connectivity biases which depend on the number of cells occupied by each bed in each direction and are beyond the scope of this work. A more significant issue is what modifications must be made to the idealization of a sedimentological system as a continuum percolation model in order that known percolation results can be applied. Figure 3a shows a vertical cross-section (redrawn from Browne et al. 1996) of thin-bedded sandstones interpreted as compensationally-offset (sensu Mutti & Sonnino 1981) lobe-fringe deposits, from the shoreline cliff exposures of the Mt Messenger Formation at Tongapurutu, New Zealand (e.g. Fig. 1). The 230 m long and 4 m thick section is based on correlating sandstone beds between eight detailed vertical reference stations with close attention paid to the nature of bed contacts. Many of the beds terminate within the mapped section and, despite a relatively high NTG (0.65) for the sequence, only 20% of the sandstone beds can be followed across the section, but every shale bed is continuous. Significantly, no amalgamation of sandstone beds is present in this section. Figure 3b shows an example of an unconditioned object-based model where the NTG and sandstone bed size distribution from the natural example (Fig. 3a) are reproduced, but the connectivity characteristics are vastly different: 90% of the sandstones but only 75% of the shales can be traced across the section. Similar results are obtained with an object-based shale model, again scaled to the observed bed-size distribution (Fig. 3c). The reason for the discrepancies is that the models do not honour the amalgamation of the natural example. If a bed is placed at random within a system which already contains a particular NTG, there is a probability equal to this NTG that the base of the bed being placed will overlie an existing bed. Therefore an unconditioned object-based model will have AR approximately equal to NTG. Natural systems, however, generally have AR significantly lower than NTG (Fig. 2b, c), and hence are less connected than an unconditioned object-based model even if the model has the correct NTG and bed size distribution. Conditioning to produce less connected models has been discussed (e.g. Begg & Williams

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Fig. 3. (a) Bed correlation along a c. 230 m long section of thin-bedded lobe fringe facies from Tongaporutu beach, redrawn from Browne et al. (1996). (b) Sandstone beds with approximately the same size distribution and net:gross ratio (NTG) placed randomly in a shale background. (c) Shale beds with approximately the same size distribution and NTG placed randomly in a sandstone background. (d) Sandstone beds with approximately the same size distribution, amalgamation ratio (AR) and NTG placed in a shale background using the compression method. (e) 3D model with constant sized circular beds at NTG ¼ 0.7, AR ¼ 0.3. Shales are shown in grey, and the largest cluster of mutually connected sandstone bed is coloured purple. The volume of this cluster, normalized by the total volume of sandstone, defines the fractional mass (FM) of the model.

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1991) but the authors have been unable to find simple procedures permitting the generation of bedscale models in which both the NTG and AR of the beds can be defined as input. Therefore, a new method has been devised for doing this. In the method devised, a system is generated with an AR equal to the final NTG of the model, and then all cells containing shale are compressed vertically with respect to those containing sand. The resultant (thinner) model has a higher NTG than the initial model, but the same AR. This procedure allows the generation of models in which both ratios can be defined as input. The factor by which all shale cells are compressed relative to the sandstone cells is termed the compression factor (cf), and the relationships between this, AR and NTG of the final models is given by cf ¼ (1 2 NTG21)/(1 2 AR21). Our definition means that for a given NTG, models with a higher cf have higher AR, and, if cf ¼ 1, the models have the same connectivity characteristics as unconditioned object-based models. Whilst recognizing that cf is a modelling tool rather than a meaningful sedimentological parameter, it is instructive to compare the relationships between NTG and AR associated with particular values of cf with measurements from different turbidite systems (Fig. 2c). With the exception of the Mt Messenger Formation data which were collected as part of this study, only a few data have been found from the literature from individual turbidite systems. However, it appears that different systems may be roughly represented by different values of cf, with the Mt Messenger system being particularly poorly amalgamated (cf c. 0.03) compared to others (e.g. the Angel Fm where cf appears to be c. 0.7 based on data from Evans et al. 2003). There is also a hint that different environments may also be characterized by different degrees of amalgamation (Fig. 2b), with fan fringe environments appearing to be less amalgamated than proximal fan environments for the same NTG, a feature reflecting their less connected, and presumably less erosive, nature. However, there are insufficient data from individual systems for this trend to be substantiated. Figure 3d shows a 2D model generated using a cf representative of the Mt Messenger Formation measurements and the same bed-size distribution and NTG as the example Mt Messenger section (Fig. 3a). Since the AR of the natural example is now honoured, the model has very similar connectivity characteristics.

Static and dynamic connectivity in unfaulted models A stand alone software application has been written to perform the modelling. With this, a model is

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generated according to a predefined set of sedimentological and fault-related characteristics, a static connectivity analysis is performed and (if requested and if the realization contains a network of connected beds in the flow direction) the model is submitted to a commercial flow simulator, the results of which are then analysed and reported automatically along with the static analysis. This workflow implies that many models can be processed in batch with no user interaction, allowing many realizations of many thousands of parametrically distinct faulted and unfaulted turbidite bed-scale systems to be modelled. Static properties measured and reported in summary files include the amalgamation ratio and net:gross ratio of the final model, and statistics derived from a connectivity analysis. This analysis identifies all the clusters of connected sandstone beds in the model, whether (and how many) continuous clusters of sandstone are present across the model in each of the three directions, and records the fraction of the total sand volume contained in the largest cluster (e.g. Fig. 3e). This quantity is termed the fractional mass of the largest cluster (FM). For convenience we generally use FM as a measure of static connectivity, and find that FM ¼ 0.5 marks the point at which a model becomes macroscopically connected (i.e. the largest connected cluster spans the width of the model). The percolation threshold of a system is defined technically as the density of objects (m) at which an infinite cluster is first formed, and this density is referred to as the critical density (mc) of the system. If n beds of volume VB are placed randomly in a model of volume V0, the density is defined as m ¼ nVB/V0. At mc, the net:gross ratio and amalgamation ratio are also at their critical values (NTGC and ARC). Since it is impossible to generate networks of infinite extent, the percolation threshold of a system is estimated in practice by plotting the fraction of models containing connected clusters that span the modelled volume at different densities. Different curves are constructed from models at different resolutions, and their intersection point marks the threshold. Owing to boundary effects a 0.5 probability of forming a connected cluster does not necessarily mark the position of the threshold and nor does FM ¼ 0.5 (see e.g. Gimel et al. 1999 for a discussion). All percolation thresholds given in this paper have also been corrected for the discretization bias discussed above.

Static connectivity Figure 4 examines the fractional mass of the largest connected cluster of sandstone beds (FM) for models with varying NTG, AR and planform bed aspect ratio (LA/LB). When FM is compared to

NTG (Fig. 4e), three trends (associated with the three different cf values used in the models) are evident, with the least amalgamated models (cf ¼ 0.01) having very low connectivities even at NTG of 0.8 (Fig. 4e). When plotted against AR (Fig. 4f) neither the LA/LB nor NTG has an influence on connectivity, and the only thing that matters in these cases is AR, with the systems achieving FM ¼ 0.5 at AR of c. 0.28. This is the known 3D percolation threshold of a continuum system of cubes and aligned rectangular prisms (e.g. Baker et al. 2002). The orientation distribution of rectangular prisms is known to influence strongly the percolation threshold (e.g. Saar & Magna 2002) and Fig. 5 charts ARC for models in which elongated beds of constant volume are oriented at +b8 to the average bed orientation. High bed aspect ratio models have significantly lower thresholds. At the extreme of our analysis, randomly oriented (i.e. b ¼ 908) beds with LA/LB ratios of 20 have ARC 0.07 (Fig. 5c). The sandstone beds in individual models (Figs 4, 5) are all the same size. Quintanilla (2002) and Consiglio et al. (2003) examined binary systems of small and large circles or spheres, and showed that NTGC increases with increasing size variability, reaching a maximum at a particular distribution for systems with equal densities of small and large bodies. However the differences are very small; for example a system comprising equal densities of spheres of volumes 8 and 1 has NTGC less than 1% higher than a system of constant sized spheres. In a natural system a continuous range in bed size rather than a binary mix of small and large beds would be expected, and in this situation the variability in ARC as a function of bed size distribution will be smaller still. Therefore only models with constant sized beds have been used in the analyses presented here. The bed size distribution, however, is likely to have more of an influence on the connectivity of fault systems than it does on unfaulted ones. In summary, the principal sedimentological controls on the connectivity of the unfaulted bed-scale models are primarily AR, and secondarily, for systems of beds that are elongate in plan view, the orientation variability of the beds (b). Known continuum percolation thresholds (e.g. Baker et al. 2002; Saar & Manga 2002), expressed as a function of NTG, can be simply re-expressed as a function of AR to provide the thresholds of these more sedimentologically realistic models. This equivalence between the NTGC of a random system and ARC of a system generated using the compression method is an inevitable consequence of the method. We discuss the implications of this following a discussion on the dynamic connectivity of the models.

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Fig. 4. (a– c). Example realizations of systems generated with net:gross ratio (NTG) of 0.6 and amalgamation ratio (AR) of 0.26 for beds with different aspect ratios (LA /LB). (d) Fifteen cases of AR and NTG have been modelled for each of the three aspect ratios. (e) Fractional mass of the largest cluster of beds (FM) v. NTG. (f) FM v. AR. Error bars reflect the variability observed in 10 realizations and the insert shows the different symbols and colours used.

Dynamic connectivity The models submitted to the flow simulator are necessarily smaller than those used in the static analyses (which contain up to 17 million grid-blocks) and examples of high and low resolution models used in the simulator are shown in Figure 6. The objective in the dynamic simulation has been to assess representative flow characteristics of the models. If, following a static analysis, a model is recognized to be connected in one horizontal direction, injector wells are placed (in the connected cluster) at one edge of the model, and producer

wells are placed at the opposite edge, imposing a particular pressure gradient across the model. No-flow boundary conditions are assigned to the other four edges. Flow modelling has been carried out in two-phases, but using linear relative permeability curves and identical properties for the two fluids. This allows simultaneous assessment of the model permeability as well as giving an indication of how easily it is drained. The equivalent horizontal fractional permeability (FK) of a model reported in this work is defined as the permeability measured in the

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Fig. 5. (a –b) Example realizations with different bed aspect ratios (LA/LB) and orientation dispersions (b). In each case net:gross ratio (NTG) is 0.6 and amalgamation ratio (AR) is 0.17. (c) Critical amalgamation ratio (ARC) as a function of LA/LB and b.

heterogeneous model normalized by the permeability assuming a homogeneous model with NTG of 1.0 and the same sandstone permeability. As in the static analyses, the aim was to report results from 10 flow simulations of each system. Since these are generally poorly connected systems, it is necessary to generate considerably more than 10 static models of each system to get 10 connected ones. Therefore up to 1000 realizations of each system were attempted, but only 10 flow simulations were performed. This implies that at least one set of simulation results would be expected for systems with a greater than 0.1%

Fig. 6. Examples of high (a) and low (b) resolution unfaulted simulation models. Model resolution is defined as the ratio between the volume of a bed and of the model (VB/V0) and is 0.000125 in (a) and 0.00625 in (b).

chance of being connected, and 10 sets of results for systems with a greater than 1% chance. The average FK values reported are averages of all realizations generated, not just the connected ones. Hence if one realization has FK ¼ 0.5, but 9 realizations are not connected in the flow direction, the average FK reported is 0.05. Figure 7 shows FK results for two suites of highresolution models containing isotropic beds (in plan view; the thickness to length ratio used in these models is 13.333) which accrue amalgamation as a function of NTG according to two different cf values. As expected, independent trends between FK and NTG are observed (Fig. 7a). If FK is plotted against AR (Fig. 7b), both sets of models approach FK ¼ 0 at the same value of AR (ARC 0.28), but two trends are still evident. This is because, despite having the same connectivity characteristics at a particular AR, the models with the higher compression factor have a higher NTG, and hence a higher FK. If FK is normalized by NTG (Fig. 7c), both sets of models fall on the same trend. Percolation theory predicts a power-law relationship between permeability and the proximity of the system to its percolation threshold, with a 3D power-law exponent of 1.6 (e.g. Renard & de Marsily 1997). The proximity of the system to its percolation threshold is measured as a function of the density of the permeable objects (m); and NTG in a random continuum system is related to m through NTG ¼ 1 2 e 2m (or conversely m ¼ 2ln(1 2 NTG); Shante & Kirkpatrick 1971). The proximity of a particular system to the percolation threshold is given by P ¼ m/mc21 and therefore takes a positive value for connected systems and a negative value for disconnected ones. As we have discussed, AR, rather than NTG, is the important determinant of connectivity, and so the

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production is the injected fluid (had a more conventional oil –water system been modelled, these graphs would show oil recovery factor at different watercuts). Close to the threshold only a very small portion of the total sandstone in the connected cluster is associated with the flow path, and recovery of the resident fluid is low even at high ‘water-cuts’. In more connected systems, displacement of the resident fluid becomes gradually more piston-like and progressively more of the resident fluid is produced.

Finite size effects

Fig. 7. (a) Horizontal fractional permeability (FK) v. net:gross ratio (NTG) for high resolution models (VB/V0 ¼ 0.000125) built with different compression factors (red: cf ¼ 0.1. black: cf ¼ 1.0). (b) FK versus amalgamation ratio (AR), and (c) FK /NTG versus AR. Colours as in (a).

proximity term should reflect this rather than NTG. Hence we calculate m ¼ 2ln(1 2 AR) and observe the expected power-law between FK/ NTG and the P when the latter is calculated using this revised density expression (Fig. 8a). The fit to the expected power-law is very close for P , c. 1.0 (corresponding to AR ¼ 0.63). At P . 1.0 the systems are very well connected, and the trend becomes asymptotic to FK/NTG ¼ 1. Two fluid phases were used in the simulations, with each phase having identical properties and with the phase relative permeabilities adding to unity at all saturations. This permits examination of the efficiency with which the models are drained. Figure 8b shows the fraction of resident fluid drained when 1%, 10%, 50% and 90% of the

The effects of finite model sizes are shown in Figure 9. The plots show fractional permeability versus proximity to threshold for the highresolution models discussed above and at lower resolutions (e.g. Fig. 6b). The power-law relationship is only robust in very high resolution models (i.e. as VB/V0 ! 0), and lower resolution models diverge from this curve as the threshold is approached. This divergence is inevitable. A greater proportion of lower resolution models become connected below the percolation threshold, and if the probability of forming a connected model is greater than zero, so too must be the average fractional permeability. Lower resolution models are more permeable (on average) than higher resolution models (Fig. 9a), but are not necessarily more easily drained (Fig. 9b). It is important to understand the effects of finite size from a practical perspective. For example, if the sizes of the beds are (as will often be the case) significant fractions of the scale of interest, then the single permeability value determined from the percolation relationship is not appropriate, and instead the probability distribution of the property of interest should be reported (e.g. King et al. 2002).

Anisotropic systems As well as departing from the ideal power-law relationship owing to finite size effects, anisotropy also causes shifts in the fractional permeability of a system. The equation FK ¼ NTG (1 2 t0)22 considers fractional permeability as a function of a tortuosity term t0 and crops up frequently in geometrical treatments of permeability such as the microscopic Carmen-Kozeny equation (Scheidegger 1974) or the macroscopic statistical streamline equation (Begg & King 1985). The equation therefore relates permeability to a geometrically meaningful length-term (which can be calculated for different anisotropies in 2D or 3D) and can be used to deduce the fractional permeability of an anisotropic system from that of an isotropic one with the same connectivity characteristics (e.g. Fig. 10).

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(a)

(b)

Fig. 8. (a) Power-law relationship between fractional horizontal permeability normalized by net:gross ratio (FK /NTG) and the proximity of the system to the percolation threshold (P), where P is measured as a function of amalgamation ratio, for the models shown in Figure 7. (b) Drained volume (i.e. the fraction of the connected volume replaced by the injected fluid) v. P, when the indicated percentage of the production is the injected fluid.

Applicability of the unfaulted model results In contrast to random continuum network models, natural turbidite systems do not have AR approximately equal to NTG (Fig. 2). Despite this it is still possible to use known percolation results (which relate FK to NTG) for the more realistic systems examined. Instead of the power-law relationship between KF and P (calculated using the density term associated with NTG) appropriate for random continuum systems, KF for our models with variable and more realistic relationships between AR and NTG can be expressed as a

function of both NTG and P, with the latter calculated using a density term expressed as a function of AR. In the following discussion these results are generalized to provide type curves of horizontal permeability (FK) and of the vertical to horizontal permeability ratio (KV/KH), and the general applicability of the models generated using the compression method is discussed. All models resulting from this bed-placement method are based on an initial unconditioned object-based model in which NTG is equal to the target AR, and the modelling procedure then modifies NTG leaving the bed connectivity unchanged. It is therefore inevitable both that the results can be

Fig. 9. (a) Fractional horizontal permeability normalized by net:gross ratio (FK /NTG), against the proximity of the system to the percolation threshold (P) for models with different resolutions (VB /V0). The solid line shows the power-law relationship observed in the high resolution models (Fig. 8a). (b) As (a) but showing the drained volume when 10% of the production is the injected fluid.

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Fig. 10. 2D simulation results (symbols) for horizontal fractional permeability (FK) v. the proximity to the percolation threshold (P), for randomly distributed squares and rectangles aligned parallel (open symbols) or perpendicular (filled symbols) to the flow direction. The solid lines are the model fits derived from the isotropic case using geometrical arguments. See text for discussion.

related to known continuum percolation thresholds by simply expressing the thresholds as a function of AR rather than NTG, and that they emphasize AR as the pre-eminent control on connectivity. The idea that the AR is an important determinant on flow is not new and Clark & Pickering (1996), while discussing a cross-plot of AR (which they call vertical continuity) and the width to thickness ratio of the beds (i.e. LB/LZ; which they call lateral continuity) for a variety of deep-water systems, mentioned that these parameters alone should be sufficient to determine the KV/KH ratio of the system. For large systems (VB/V0 ! 0) of isotropic beds (i.e. systems with LA ¼ LB), type curves of FK and KV/KH are shown in Figure 11 for different cases of LB/LZ. These have been calculated from the results discussed above for 2D and 3D systems. Also shown in Figure 11b is the 2D log-linear relationship between KV/KH and AR derived by Stephen et al. (2001), and the clear difference between this and the (2D) curves derived in the present study is a consequence of different sedimentological idealizations of the system. In the systems considered by Stephen et al. (2001), sandstone beds are of infinite length, and portions of shale layers are removed to give the final model AR. Their models are therefore not percolation systems since horizontal flow is possible in their models at AR ¼ 0.0, and vertical flow is possible at all non-zero AR values. The different KV/KH ratio models arising from this study and from that of Stephen et al. (2001) can be reconciled by considering the spatial association between erosion and deposition. In

Fig. 11. Plots of amalgamation ratio (AR) v. (a) fractional horizontal permeability (FK/NTG) and (b) KV /KH ratio. The plots show 2D results in black and 3D results in red, and the three curves for each case are for beds with horizontal to vertical aspect ratios (LB /LZ) of 50, 200 and 600 (note that these are indistinguishable in the 2D horizontal permeability case). The 2D result of Stephen et al. (2001) is also indicated on (b). See text for discussion.

the structure-imitating (i.e. purely geometrical) models generated using the compression method, each erosion surface is associated with the amalgamating bed, and each bed has the potential to be erosive over its entire length. A simple 2D process-imitating model is used to explore these issues further. A volume is filled with sand beds from the bottom to the top with geometrical rules crudely mimicking sedimentological ones. Beds from a predefined size distribution are dropped into the model and are encouraged (but not forced) to fall as close to the bottom as possible (ensuring that towers of beds are not formed). Each bed is encased above and laterally in thin shales. Predefined erosion probabilities, specific to each model, allow individual beds to erode into the underlying sequence over a fraction of the bed thickness (e.g. Fig. 12a). As the erosion probability increases, AR increases and the models become more connected. Unlike in the structure-imitating model, however, NTG and AR do not accumulate

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Fig. 12. (a– c) Example realizations of the 2D process-imitating models close to their percolation thresholds. (a) Erosion is tied to individual beds with an erosion probability of 0.8. (b) Erosion is independent of deposition with an erosion/bed length ratio of 0.2 and an erosion frequency of 4. (c) As (b) but with an erosion/bed length ratio of 4 and an erosion frequency of 0.6. (d) 2D critical amalgamation ratio (ARC) as a function of the erosion/bed length ratio, for the case where erosion and deposition are independent. Note that these thresholds have been derived from much higher resolution models than shown in (a–c). The horizontal line shows the 2D percolation threshold for cases where erosion and deposition are linked (ARC ¼ 0.67). See text for discussion.

along curves of equal cf. However, despite this entirely different generation method, these models reproduce the critical amalgamation ratio of models generated using the compression method (i.e. ARC ¼ 0.67 in 2D). This result demonstrates that the ARC values observed in our models have a reality beyond the simple mapping between NTG and AR that is the inevitable consequence of the compression method devised for generating the models. However it does not prove that these values are universally applicable. In a second set of process-imitating models, erosion is modelled independently of deposition. In

these examples, after each bed is placed there is a probability (or a probable number) of events that erode off a certain thickness of model over a particular length; this length is reported as a fraction (or multiple) of the length of each bed. These events are not associated with any deposition, and the beds themselves are not erosive. Examples of models where the erosion length is smaller and larger than the bed lengths are shown in Figure 12b, c respectively. In these models ARC is significantly lower than in the case where erosion events are tied to the deposition of the overlying sandstone bed, even if the erosion events are significantly longer than the beds (Fig. 12d). Obviously, ARC will tend to zero as the erosion length: bed length ratio tends to zero, as it does implicitly in the models of Stephen et al. (2001). The relevance of the two approaches is almost certainly facies dependent. In some massive or thick-bedded facies, the lengths of amalgamation surfaces may be very small compared to the lengths of the beds (e.g. Fig. 13), and a 3D version of the models of Stephen et al. (2001) is more appropriate. By contrast, in thin-bedded facies, consideration of finite bed lengths is crucial, amalgamation is low, erosion and deposition are more likely to be coupled, and our approach is probably more appropriate. It is clear from these considerations that the characteristic property of a continuum percolation model (i.e. NTG) is not necessarily the appropriate parameter for characterizing connectivity in natural systems, and that it cannot simply be replaced by AR, since other, more subtle, sedimentological characteristics are also significant. Even for a relatively well characterized unfaulted system there will always be considerable uncertainty about defining an appropriate percolation threshold, yet this definition is the starting point for estimating permeability, since the proximity of the system to the threshold is the principal measure of connectivity in a percolation theory approach. The following section examines faulted versions of models generated using the compression method, recognizing that sedimentologically these models explore only the small subset of circumstances in which erosion is tied to deposition.

Connectivity in faulted models The sedimentological models generated using the compression method and for which connectivity has been analysed (e.g. Figs 4, 5) are characterized by differences in NTG, AR, bed aspect ratio (LA/ LB) and bed orientation dispersion (b). The static connectivity of these models has been shown to be governed principally by AR and secondarily,

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Fig. 13. Thickly bedded sandstones from the Mount Messenger Formation at Tongaporutu beach, New Zealand. The total cliff height is about 20 m high. Shale beds are present but the sands are frequently amalgamated by localized erosion.

for beds with higher values of LA/LB, by b. The bed size distribution does not influence significantly the connectivity of the unfaulted models, and NTG has no influence whatsoever. The remainder of the paper discusses connectivity in faulted versions of these models. The initial objectives of the modelling were to establish the principal factors controlling flow at an interbed scale in faulted sheet-like turbidite systems. To this end, static connectivity was measured in 10 realizations of c. 25 000 parametrically distinct models including variability in the four basic sedimentological parameters (listed above) as well as various fault-related parameters (discussed below). Factor analysis was used to establish sensitivities to connectivity and to connectivity changes as a function of model parameters or, more usefully, dimensionless ratios between sedimentological and fault-related parameters. These analyses have not been presented since their results indicated categorically that there are no principal factors controlling connectivity. All variables examined (including those that are not significant in unfaulted models, for example NTG and the bed size distribution) were found to be potentially significant, with the level of significance a function of the levels of other variables. Instead, following a description of the fault modelling procedures used, a couple of sets of results are presented to illustrate aspects of the connectivity responses. The discussion then returns to the central question

posed at the beginning of this paper: how can known scaling laws from percolation theory be applied to understanding flow in the models.

Fault system modelling All faulted models contain systems of randomly positioned faults of identical sizes. The examples shown in Figure 14 are applied to the unfaulted models shown in Figure 5 in which the total model thickness is 12LZ, where LZ is the bed thickness. Four different fault orientation models are used; randomly oriented, oriented parallel (+108) to the principal orientation of the long axes of the beds, oriented perpendicular (+108) to this direction, or oriented parallel and perpendicular to this direction with equal probability (the last of these orientation distribution models is termed ‘orthogonal’ in later discussion). The faults themselves are vertical, with triangular horizontal displacement profiles and no vertical displacement gradients. The fault system, characterized by a particular number of faults (NF) of length LF and maximum throw TF, is most usefully expressed in terms of dimensionless ratios between fault system variables and sedimentological ones. The beds have areal dimensions of c. LALB, where the bed aspect ratio (LA/LB) ranges from 1.0 to 20.0 (e.g. Fig. 5). Since the models have been built so

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Fault property modelling

Fig. 14. Example realizations of some of the fault systems applied to the suite of models shown in Figure 5. (a) Randomly oriented faults with L¯F ¼ 1.8, N¯F ¼ 0.5 and T¯F ¼ 2.5; see Appendix and text for definitions. (b) Faults oriented parallel to the dominant bed orientation with L¯F ¼ 1.8, NF ¼ 1.0 and T¯F ¼ 5.0. (c) as (b), but with L¯F ¼ 3.6. (d) As (c), but T¯F ¼ 1.4 and with the faults oriented both parallel and perpendicular to the preferred bed orientations (i.e. the ‘orthogonal’ orientation model).

the beds have constant LALB whatever the ratio LA/ LB, fault density can be expressed most conveniently as the expected number of fault centres F ). Fault sizes can be made dimensionper bed (N less by normalizing fault length against the F ¼ LF =ðLA LB Þ0:5 Þ, and average bed length (L maximum fault throw against bed thickness (T F ¼ TF =LZ Þ.

Models have been analysed using open faults (i.e. those involving only juxtaposition effects), sealing faults and two types of fault property predictor. The first property predictor uses Shale Gouge Ratio (SGR; Yielding et al. 1997) cut-offs. In the second method, shale smears are modelled explicitly, using the Probabilistic Shale Smear Factor (PSSF) method defined by Childs et al. (2007). The methods are illustrated in Figure 15. Figure 15a shows an Allan diagram of a fault F ¼ 3:6 and extracted from a model with L T F ¼ 5:0 (e.g. Fig. 14b). Shale layers in the footwall and hanging wall are shown in pale and dark grey, and sand-on-sand juxtapositions are highlighted in yellow. SGR is calculated at each corner of each faulted connection, assuming that sands have a clay fraction of 0.0, and shales of 1.0, and SGR cut-offs are applied to determine the state of individual sand-on-sand juxtapositions. It is assumed that individual sand-on-sand juxtapositions are either entirely sealed or wholly or partially open. If a connection is even partially open, the sandstone cells on either side of the fault are in connection, so recognition of the extent of openness is unnecessary for the connectivity analyses. Therefore the minimum SGR of the corners of the connection is taken as diagnostic of the connection SGR (individual connections will generally have different SGR values at each of their corners) and if the specified SGR cut-off is above this value the connection is open, otherwise it is closed (Fig. 15b). The second sort of fault property modelling applies the ideas of probabilistic shale smears developed by Childs et al. (2007) on the basis of observations of faults in the Mt Messenger Formation. In this approach a discrete shale smear is associated with each faulted shale layer. The smear is continuous if the Shale Smear Factor (SSF; Lindsay et al. 1993, given by normalizing the fault throw by the shale bed thickness TB) is less than a critical value (SSFC). If SSF exceeds SSFC the smear is assumed to be discontinuous and of length TB(SSFC 2 1). This smear is placed on the fault surface with equal probability anywhere between the base of the shale footwall cut-off, and the top of the hanging wall shale cut-off. The result of the process is a distribution of shale smears on the fault surface (e.g. Fig. 15c), which combine to define sealed and open sand-on-sand juxtapositions (Fig. 15d). Childs et al. (2007) term the probability at a particular location that a hole is present in the shale smears when they are modelled in this way as a Probabilistic Shale Smear Factor (PSSF). The implementation of the PSSF method used here follows exactly the 1D definitions of

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Fig. 15. Illustration of the fault property modelling. (a) Allan diagram drawn looking from the footwall side for a fault of the same scale as those shown in Figure 14b. Shale layers on the hanging wall are shown in dark grey and on the footwall in paler grey. Sand-on-sand juxtapositions are yellow. (b) as (a) but with the sand-on-sand juxtapositions coloured for SGR. (c) Probabilistic shale smears on the fault surface generated using SSFC ¼ 5. Smear tops are shown as the thicker lines, and smear bases as thinner lines. (d) Smear realization superimposed on the across-fault juxtapositions. Non-smeared sand-on-sand juxtapositions are shown in yellow.

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Childs et al. (2007), but further assumptions are needed to cover a 2D fault surface rather than a 1D trace. For example, shale layers are continuous horizontally over certain distances, and it is reasonable (but by no means necessarily correct) to assume that the shale smear derived from these layers will also be continuous over this distance. Therefore the centre of the smear is placed at an arbitrary fraction of the throw over all grid-cells over which the shale layer does not change in character. This will tend to result in shale smears that have a plunge equal to the average of the apparent dips of the layering on both sides of the fault. Algorithmic complications arise when the shale changes in character along or across the fault, for example by connecting with another shale at the end of a sandstone bed or by terminating through sandstone amalgamation. These situations have been handled in a manner that will encourage horizontal continuity of the smears, but since many of the issues associated with this kind of modelling are unresolved geologically (as it is usually only possible to measure shale smear distribution on 1D sections across faults), occasional arbitrary assumptions have been made. Figure 15d shows a realization using SSFC ¼ 5.0 for the example fault. A general decrease in open (non-smeared) sand-on-sand connection towards the higher SGR central region of the fault can be observed, but occasional partially open connections are still present even when SGR exceeds 0.3.

Connectivity with open faults The significance of the dimensionless terms for expressing the fault system parameters can be appreciated via the simplified conceptualizations shown in Figure 16 (similar arguments have been made by James et al. 2004). Figure 16a shows half a fault length, ranging in throw from a maximum TF at the centre to zero at the tip, and a sandstone bed of length LA and thickness LZ offset by the fault, for a case where the fault is considerably longer than the beds. The change in fault displacement over the length of a sandstone bed is given by dT ¼ 2TF LA/LF. If the stratigraphy is assumed to be entirely unamalgamated and periodic, the total thickness of each sandstone–shale couplet is L0 ¼ LZ/NTG. If the beds are assumed to be stacked vertically, the number of beds juxtaposed against any other bed depends on the precise placement of the sequence on each side of the fault (Fig. 16b, c) and, on average, is F ). This function might therefore 2NTG(1 þ T F =L be expected (in conjunction with the total number of faults expected per bed) to scale with connectivity. Although this sort of simplified approach goes some way towards understanding the

(a)

(b)

(c)

Fig. 16. (a) Idealized Allan diagram of a half-fault (pale grey) showing the locations of a sandstone bed in the hanging wall and footwall and a shale bed in the footwall. For the case illustrated the sandstone bed in the hanging wall (thicker line) will be juxtaposed against 2 (b) or 3 (c) sandstone beds in the footwall. See text for discussion.

connectivity changes observed in some of the geometrically more simple models which come closest to meeting the assumptions made above (i.e. models with extremely low AR, and very F ), it contains too many simhigh values of T F and L plifying assumptions to be able to explain most of our model results. A general analytical solution, though probably possible, would be extremely complex if non-trivial fault and sedimentological parameters are to be included. Figure 17 shows a selection of connectivity measurements for systems with open faults, illustrating some of the complexities and interdependencies that are a feature of the model behaviour. The figure charts the connectivity of 1920 different faulted models deriving from 60 different unfaulted models. The unfaulted models (labelled ‘UF’ in Fig. 17) are characterized by three different NTG values each for two different cf values, for models containing beds with two different aspect ratios

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Fig. 17. Fractional mass of the largest cluster of beds (FM) for different combinations of fault and sedimentological characteristics. No fault properties are included. Fault systems are characterized by the values of L¯F, ¯ F at the top of the diagram (see Appendix and text for definitions) and, within each T¯F column, by the T¯F and N four fault orientation models shown in the blow-up in (a). UF signifies an unfaulted model. (a) to (d ) are for the four basic combinations of bed aspect ratio (LA/LB) and compression factor (cf) indicated at the right of each graph. The three different panels of each graph are for the different net:gross (NTG) cases indicated, and the different coloured curves reflect different bed orientation dispersions (b). The spots show the mean FM value for 10 realizations of each system, and the error bars are +1 standard deviation.

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(LA/LB), each with five different levels of bed orientation variability (b). The 32 fault systems F and T F , for F, L are two combinations each for N the four orientation models. The circumstances in which open faults lower connectivity are comparatively rare. Based on an analysis of a coal-measures sequence, Bailey et al. (2002) found that in low dimensionality systems (i.e. those containing beds with high aspect ratios) with low net:gross ratios, faults will lower connectivity. The modelling results presented here (Fig. 17) suggest that this is only the case for well amalgamated systems (i.e. those with high cf values; Fig. 17c) and b . c. 158. High LA/LB models with lower cf values (Fig. 17d), or lower b (Fig. 17c) have larger connectivities when faulted than when unfaulted, as do all the models with lower LA/LB ratios (Fig. 17a, b). One intriguing feature of these models with LA/LB ratios of 20 and high b is the virtual reciprocity of each set of results between equivalent NTG at the different cf values (Fig. 17c, d). As mentioned, when these models have a high cf (and therefore a high AR for a given NTG) faults reduce connectivity, and where they have a low cf they increase it, but this trend is extremely systematic: each combination of fault characteristics causing connectivity lows in the first case cause connectivity highs in the second. Effects of fault orientation also appear generally to be a function of cf, with low cf models (Fig. 17b, d) showing greater sensitivity. This is not always the case however; for example the central panel of Fig. 17c with b ¼ 158 is highly sensitive to fault orientation despite a cf ¼ 1.0. A final illustration of the importance of different sensitivities owing to the settings of particular variables is evident in the central panel of Fig. 17c. In this case the difference between models with b ¼ 08 and b ¼ 158 is paramount on connectivity. However, despite similar total connectivity ranges, other sedimentological models (e.g. the central panels of Fig. 17a & d) show a much more gradual increase in connectivity with increasing b. Figure 17 shows only a subset of the models analysed, but illustrates the main conclusion: all variables (sedimentological and fault-related) examined are potentially significant controls on the connectivity (and hence flow characteristics) of the models. In certain instances some variables are not important, but generalizations require so many caveats as to render them incomprehensible. As we show below, this behaviour persists as fault properties are also considered.

Connectivity including fault properties Figure 18 shows results for the same fault systems as Figure 17 but in this case the three panels represent

different sedimentological models (Sedimentologies 1, 2 and 3 shown at the bottom of Fig. 18), and the different coloured curves show results using different SGR cut-offs (Fig. 18a) or critical SSF values (Fig. 18b). In most cases the faults provide fairly well connected models with open faults, and fairly poorly connected ones with sealing faults, but the transitional cases, however, behave very differently. Looking first at the SGR cases (Fig. 18a) most changes in connectivity occur at high SGR cut-off values for ‘Sedimentology 1’, fairly regularly across the range of cut-offs for ‘Sedimentology 2’ or at low SGR cut-off values for ‘Sedimentology 3’. Intuitively, perhaps, the dependence between connectivity and SGR cut-off should be associated with a dependence on NTG; however, no systematic trends have been identified accommodating all the ranges of other sedimentological and fault-related variables examined. The SSF cases (Fig. 18b) are very different. ‘Sedimentology 1’ shows only a weak dependence on SSFC with most models approximately midway between the connectivities observed with open and sealing faults. ‘Sedimentology 2’ shows very little change in connectivity from the open case whatever SSFC is used (these models do, however, show a systematic increase in the numbers of small, isolated clusters as SSFC increases). ‘Sedimentology 3’ shows very similar connectivity to the SGR models at reciprocal cut-offs. These examples again highlight the extreme complexity of connectivity response to geometrical details of the fault and sediment definitions, but also indicate that extremely different results arise depending on how the fault rock properties are modelled. We have already mentioned that only particular combinations of conditions allow models containing open faults to have lower connectivity than an unfaulted model. We also find that extremely severe fault property cut-offs are generally needed (i.e. low SGRC or high SSFC values). Figure 19a summarizes results for about 5000 models that include variability in all fault-related and sedimentological properties considered with the exception of b. These results show a net loss in connectivity relative to the unfaulted case in only about 10% of models in which all connections with SGR . 0.1 are sealed. Bed orientation dispersion is a prerequisite for open faults to lower connectivity (Fig. 17), so had this variable also been included in the models shown, connectivity would be lost at higher SGR cut-offs. The situation with the probabilistic smears is even more extreme (Fig. 19b). Even when SSFC as high as 10 is considered, most models are only slightly more poorly connected than when fault properties are ignored altogether (i.e. the behaviour of ‘Sedimentology 2’, Fig. 18b, is not unusual).

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Fig. 18. Fractional mass of the largest cluster of beds (FM) for different combinations of fault and sedimentological characteristics, using different (a) SGR cut-offs or (b) critical SSF values. The fault systems are the same as in Figure 17, and the characteristics of the three different sedimentological models are indicated below each panel.

Faults characterized by overlapping discontinuous shale smears, therefore, are less detrimental to large-scale connectivity than might be thought. As Childs et al. (2007) discuss, once the throw on a fault is larger than the critical smear length TB(SSFC 2 1), there is always a non-zero probability that any position on the fault is not covered by any smears. This is seen in Figure 15c, where small holes in the shale smear coverage exist right up to the centre of the fault. Although rare, these holes in most of our models are frequent enough to ensure bed-scale connectivities that are not substantially lower than those obtained if fault rocks are ignored altogether. The algorithmic similarity between SGR and the reciprocal of SSF is therefore

not manifest by equivalent connectivities when the fault smears are modelled deterministically using SGR cut-offs and stochastically using explicit shale smears. The fraction of the total connectivity change possible as a function of a fault property case is given by the change from the open-fault case normalized by the difference between the open-fault and sealing fault cases. No over-riding trends are observed when this change using an SGR cut-off is compared to the change using the reciprocal critical SSF value (Fig. 19c). More sealing fault rock property cut-off values (SGRC ¼ 1/SSFC ¼ 0.1) show more extreme differences, but even where some combinations of sedimentology and fault

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Fig. 19. Cumulative distributions of the change in the fractional mass of the largest cluster of beds (FM) from the unfaulted state as a function of (a) SGR cut-off values and (b) critical SSF values for models with aligned beds. The colours in (b) are for models with the reciprocal SSFC value to the SGRC values labelled in (a). (c) Fraction of the total possible change in FM using SGR cut-offs plotted against the same combination of faults and sedimentology using the reciprocal SSFC value, for SGRC ¼ 0.1 and 0.5. (d) As (c) but showing only the models with high L¯F and T¯F. See text for discussion.

system give similar results (SGRC ¼ 1/ SSFC ¼ 0.5), others can still show no changes in connectivity from the unfaulted case when SSFC is used despite a large change for the reciprocal SGRC. Figure 19d shows the subset of models using the F and T F ). In largest faults considered (i.e. high L these cases cut-off specific trends emerge marking the upper limit of the clouds of data from F implies a small change in Figure 19c. A high L fault displacement over the length of a bed, so the differences in plunge (parallel to the fault plane) between the smears and sand beds are lowest. Holes in the smear-covering are therefore more likely to be aligned parallel to the sand-on-sand juxtapositions so that a single hole is likely to open up fewer juxtapositions. A high T F implies that several shale smears are potentially present at any position on the fault which results in a more predictable smear distribution (Childs et al. 2007) in which holes are more likely to occur in regions of lower SGR. Connectivity across faults that are very large (both vertically and laterally) in relation to the beds may therefore be similar if explicit

smears are modelled probabilistically or if fault rocks are modelled deterministically using an SGR cut-off; however the appropriate cut-off is certainly not the reciprocal of SSFC. Most of our models contain relatively small faults, and in these cases there is little association between the responses using SGR cut-offs or by placing smears stochastically. Faults that are larger in relation to the beds are likely to have a more predictable, and more detrimental, influence on across-fault connectivity.

Dynamic connectivity Given the complexities observed in the static connectivity analyses, it is no surprise that the dynamic connectivity results (permeability, drainability) also show complex responses to combinations of fault-related and sedimentological model characteristics. These properties have the additional complication of being directional. Figure 20, for example, shows fractional permeability of isotropic beds faulted by various isotropic and anisotropic fault systems. Reinforcing

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¯ F values indicated Fig. 20. (a) Fractional permeability for cases with open faults, characterized by the L¯F, T¯F and N at the top of the figure and three fault orientation models (faults oriented parallel or perpendicular to the flow direction or at random). The six different sedimentological models are characterized by the net:gross and amalgamation ratios indicated. (b) Fractional permeability for the NTG ¼ 0.4, AR ¼ 0.063 cases for different SGR cut-offs. Cases for which no results are shown have a probability of ,0.001 of being connected in the direction of flow.

the static model results, we find that all systems containing open faults (Fig. 20a) are more permeable than their unfaulted counterparts, and the same is true of most models with SGRC 0.1 (Fig. 20b). Rather than consider these results in terms of geological model characteristics, they have been analysed within the context of percolation theory. As discussed at the start of this paper, one of the underlying implications of the theory is that connectivity, anisotropy and resolution are what control flow. These geometrical properties derive from the geological characteristics of the system,

but are not unique to any particular set of characteristics, and vastly different geological systems could have identical connectivity, anisotropy and resolution. Percolation theory suggests that these will all have the same flow properties. Figures 7 and 8 show that the fractional permeability of high resolution unfaulted models with different relationships between AR and NTG can be expressed as a function of the proximity of the system to the percolation threshold (P). For unfaulted isotropic systems (i.e. ones in which LA/LB ¼ 1.0 and hence in which b is irrelevant) generated using the compression method, P depends only on

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AR and occurs at ARC ¼ 0.28. A high resolution faulted isotropic system with the same value of P should therefore have the same fractional permeability. An immediate problem is that the percolation threshold of the faulted model is unknown, and potentially varies as a function of all sedimentological and fault-related variables discussed. It is impossible, therefore, to determine P as a function of a known system property (unlike the unfaulted models where it could be determined from AR). One of the more basic equations in percolation theory is B ¼ mVex, which relates the average number of connections per object (B), to the density (m) and the excluded volume (Vex) of the objects. The density term m has already been discussed. The excluded volume is defined as the volume surrounding the centre of an object within which the centre of any other object connected to it must lie. The critical average number of connections per bed for aligned cuboids (BC) is 2.59 (e.g. Baker et al. 2002) and, like m and mC, B and BC can be used to establish the proximity of a system to the threshold. An advantage of using B, however, is that it is a product of the sedimentological and fault-related characteristics of a single model, and like FM, can therefore be measured in each realization. Figure 21 compares FM with B for isotropic faulted models containing differences in cf and in the full range of fault-related variables considered. Irrespective of the geological details of the system, they all lie on the same trend, intersecting FM ¼ 0.5 close to the expected threshold at BC ¼ 2.59.

Connections per body (B)

Fig. 21. Fractional mass of the largest cluster (FM) v. the average number of connections per body (B) measured in faulted isotropic models (i.e. circular beds and randomly oriented faults) with otherwise widely different fault and sedimentological characteristics. The models define a trend with FM ¼ 0.5 at the known percolation threshold for unfaulted models (BC ¼ 2.59) as indicated by the dashed lines.

In addition to being controlled by proximity to the percolation threshold, the flow properties of isotropic models are functions of the model resolution (Fig. 9). A fault that entirely offsets the bed breaks it into two objects, each considered separately when calculating B. Since the number of objects has thus increased as a consequence of the fault, the average object volume (VB) must decrease, resulting in a net increase in the resolution of the models (i.e. a decrease in VB/V0). Figure 22 charts the fractional permeability and drainability of c. 200 isotropic faulted models (including, but not limited to, those shown in Fig. 20a, b) as a function of their proximity to percolation calculated from measured values of B. The data have been separated into two classes dependent on the resolution of the faulted beds, and these are compared in Figure 22 to results for unfaulted isotropic systems at the same resolutions (Fig. 9). The drainability data are noisy in both the faulted and unfaulted cases (Figs 9b, 22b); however both dynamic properties fall approximately within the same ranges as the unfaulted cases, supporting the initial notion that proximity to the percolation threshold and resolution are the only significant controls on the flow characteristics in these isotropic models.

Discussion and conclusions This study has been directed towards understanding controls on inter-bed flow in faulted sheet-like or lobate turbidite systems. Conceptually, there are geometrical parallels between interbedded sandstone/shale sequences and random percolation systems. King (1990) and King et al. (2002) have argued that, since the flow characteristics of percolation systems can be formalized mathematically (e.g. King et al. 1999a, b; Andrade et al. 2000; Lopez et al. 2003), exploiting these parallels provides a useful method for rapidly establishing likely behaviour. This paper has been concerned with establishing the strength of the parallels and, where they are present, with defining measures that allow the geological system to be expressed within the same mathematical framework as the percolation system. In common with a percolation approach, it has focused exclusively on representative, stationary volumes containing beds and faults from a single size distribution (usually constant sized). These conditions may seldom be met in a natural system since volumes of at least 7– 10 bed lengths are required for a system to be considered representative, yet gradual property trends or abrupt sedimentological transitions are often present over such length scales. The presence of different types of

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(a)

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(b)

Fig. 22. (a) Fractional permeability/net:gross ratio (FK/NTG) and (b) drained volume when 10% of the production is the injected fluid, plotted against proximity to the percolation threshold deduced from the measured average number of connections per body (B), for a wide range of isotropic faulted models. The faulted bodies have average sizes in the VB/V0 ranges indicated. The lines show the limits of the ranges of results obtained for unfaulted models at the comparable resolutions (see Fig. 9).

objects within a single volume can also modify significantly the system connectivity (e.g. a few strongly erosive channels can connect up an otherwise disconnected system of poorly amalgamated sheets). Such systems are beyond the scope of the present study. The simplest link between sedimentological and percolation systems is through the net:gross ratio. In a continuum percolation model the net:gross and amalgamation ratios are equal, but in natural systems the latter is often considerably lower than the former, resulting in systems with less sandstone connectivity at the same net:gross ratio. A modelling scheme referred to as the compression method allows models to be built with more natural associations between the two ratios, and the connectivities of models generated using this procedure have identical dependencies with respect to amalgamation ratio as random continuum models do with respect to net:gross ratio. In such systems, therefore, the principal control on connectivity is the amalgamation ratio with the orientation dispersion of elongate beds an important secondary control. The bed size distribution is not significant. A series of simple 2D models has been developed to address sedimentological implications of the compression method. This method implies that erosion is linked directly to deposition and, when it occurs, has the potential to cover the entire length of a bed. If erosion events are not associated with the deposition of an overlying bed, the systems become connected at lower amalgamation ratios which depend on the ratio between the length of the erosion events and the length of the beds. It is also likely that the bed and erosion size distributions may be significant in these cases. Hence although the connectivity of unfaulted models generated

using the compression method can be reconciled with known results, natural systems are more complex with essentially unknown percolation thresholds dependent on properties that are never included in traditional continuum percolation studies (e.g. Baker et al. 2002; Saar & Manga 2002; Consiglio et al. 2003). A series of models have investigated connectivity in systems characterized by different sedimentological and fault characteristics. All models have been built using the compression method, and sedimentary variables considered include the net:gross and amalgamation ratios of the systems, and the aspect ratios and orientation variability of the beds. Fault-system variables include fault frequency, length, maximum throw and orientation. Sandstone connectivity has been calculated using open faults, sealing faults and using two methods for predicting fault properties. In the first method across-fault juxtapositions that exceed a specified SGR cut-off are deemed sealing. In the second more innovative method, shale smears are modelled stochastically as a function of SSF cut-offs. All the beds and faults in any particular model are the same size, and the faults range from a few times smaller to a few times larger than the individual beds. We find all the fault system variables we have modelled to be influential on the connectivity of the sequences, with the particular variables being more or less influential depending on the values of other fault-related or sedimentological variables. The connectivity of faulted turbidite beds is therefore extremely complex and is controlled by interactions of different variables. Some general conclusions can be made. Open faults are rarely capable of reducing the connectivity of the system. Systems modelled with

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deterministic SGR cut-offs are less connected than systems modelled with stochastic smears with the reciprocal SSF cut-off. The two methods become more equivalent for systems with higher fault throw to bed thickness and fault length to bed length ratios. In general, low SGR (,0.1) cut-offs or high SSF cut-offs (10) are required before a faulted system becomes less connected than its unfaulted counterpart. However particular systems may lose connectivity at less extreme cut-offs. These conclusions apply to the geometrical configurations that have been examined here (i.e. intra-bed connectivity in representative volumes in which the faults are of comparable sizes to the beds). The modelling results (and others, e.g. James et al. 2004) indicate a general decrease in across-fault connectivity with a decrease in the fault displacement gradient normalized by bed size. Therefore faults that are much larger than the beds are likely to be more detrimental to over-all connectivity than faults in the systems examined, given the same shale smear modelling criteria. For inter-well distances of up to 1 km, the thickness of beds being considered is ,c. 1 m (Fig. 2a), and the faults have maximum throws of up to a few metres. Inter-well connectivity in sedimentological systems characterized by thicker units may be controlled by the continuity of individual beds or bed-sets rather than by a representative network of them. If one of these individual units is wholly or partially offset by a fault, the connectivity at the length-scale of interest (,c. 1 km) will be lowered, despite the fact that connectivity may increase within a representative network (i.e. .c. 5 km) with the same fault to bed size ratios. This apparent duality of connectivity behaviour is a consequence of the volume of interest being most appropriately represented by single objects as opposed to a representative network of them. Our flow simulation results support the notion that geological details of a representative system, irrespective of whether it is faulted or not, are important only inasmuch as they contribute to the eventual connectivity, anisotropy and resolution of the connected network of beds, and that these three terms dictate the flow behaviour. For models with simple associations between erosion and deposition, the required connectivity term (the proximity of the system to the percolation threshold) can be established as a function of amalgamation ratio. In the presence of faults an analogous connectivity term can be expressed as a function of the average number of connections per bed or fault-bounded body (B). This, however, cannot be valid in all cases. The ideas underlying percolation theory rely on the notion of random distributions of objects, and in such cases aggregate system

properties, such as the number of connections per bed, will show only a limited variability normally distributed about a mean value. It is possible to conceive of a system in which both the faults and the beds individually meet these conditions but which combine to produce a network that does not. For example a very poorly amalgamated system of beds might contain a sparse network of short faults. If these faults have high enough maximum throws they may produce a network in which B exceeds the critical value, but which is not macroscopically connected since the faults are spaced too far apart for the regions of high connectivity to be mutually connected. In this case the distribution of connections per bed will be distinctly bimodal, and the condition of spatial homogeneity required by the theory is violated. These conditions are likely to be fairly extreme, and our results show that in many cases the flow characteristics of a faulted system can be established using the three basic system measures. As a general conclusion we consider that, despite superficial similarities between interbedded sandstone–shale sequences and random percolation systems, at present it is impossible even in the absence of faults to establish a priori the proximity of a natural system to its percolation threshold, since the dependencies on the threshold as a function of natural associations between erosion and deposition are not known. This does not mean that a percolation approach to understanding flow characteristics is not of potential value. Provided a modelling scheme is used that allows inclusion of the geological factors most significant on connectivity, static modelling could be used to estimate the requisite connectivity term as a function of connections per bed. Alternatively, in an approach that would not rely on static modelling, the connectivity and anisotropy terms associated with flow in a particular reservoir might be estimated at a particular resolution through inversion of available flow data (e.g. well tests). Likely flow characteristics on a field-wide basis could then be explored using these terms at a revised resolution. We thank the following companies and their representatives for supporting our ITF brokered FIFT research project entitled ‘Quantitative characteristics of faults and fault zones and their impact on flow within deep water turbidites, onshore New Zealand’: Amerada Hess, BG Energy, BP Exploration, ConocoPhillips, Kerr-McGee North Sea, Shell, Statoil and Total. We also thank Roxar for provision of their MORE simulator used in this work. We are very grateful to A. Nicol and P. King from GNS Science (New Zealand), our partners in the FIFT project, who introduced us to the Taranaki Basin faults and turbidites, to A. Welbon and Q. Fisher for providing reviews and to S. Jolley for his editorial handling.

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Appendix – Glossary of terminology net:gross ratio (dimensionless). The fractional volume of a sequence occupied by sandstone. AR Amalgamation ratio (dimensionless). The fraction of sandstone bed bases eroded into an underlying sandstone bed when measured on a vertical sample-line. cf Compression factor. Dimensionless modelling parameter which relates AR and NTG through the expression cf ¼ (1 2 NTG21)/(1 2 AR21). L A, L B, L Z The length, width and maximum thickness of individual sandstone beds (metres). The ratio LA/LB is the bed aspect ratio referred to in the text (unless the vertical aspect ratio; LB/LZ, is mentioned explicitly). TB The thickness of a shale bed (metres). b Bed orientation dispersion (degrees). Individual sandstone beds are oriented in any model at +b8 to the principal direction of bed alignment. VB/V0 Bed volume/modelling volume. This ratio is a convenient measure of the resolution of unfaulted models since in individual models all sandstone beds are the same size. m Bed density parameter. In a random continuum system containing n beds of constant size, this density term is given by m ¼ nVB/V0. In such a system m is related to NTG through the expression NTG ¼ 1 2 e 2m. B Bed connectivity parameter. The average number of beds connected to any particular bed in a model. NTGC, ARC, The values of NTG, AR, m and B at the percolation threshold of the system. The mC, BC percolation threshold marks the density at which a large (technically infinite) volume first contains a cluster of objects that connects all the edges of the system (i.e. an infinitely large cluster). P The proximity of a system to its percolation threshold. It is given by P ¼ m/ mC 2 1 or by P ¼ B/BC 2 1. P takes positive values for macroscopically connected systems and negative ones for disconnected systems. FM The fractional mass of the largest cluster of connected sandstone beds in a model. This is the most common measure of static connectivity used in this paper and is defined as the volume of sandstone beds contained in the largest cluster normalized by the total volume of sandstone beds (see Figure 3e).

FK

NTG

KV/KH

NF

F N

LF, TF F , T F L

SGR

SGRC

SSF

SSFC

PSSF

333

Fractional horizontal permeability (dimensionless). Defined in this paper as the directional permeability normalized by the permeability of a homogeneous model with NTG ¼ 1 and the same sandstone permeability. The ratio between the vertical and horizontal permeability. Note that KV/KH in this paper is only discussed with reference to systems with isotropic horizontal permeability (i.e. in which LA ¼ LB). The number of faults in a model. For the models described in this paper, all faults in a particular model are the same size. Dimensionless fault frequency parameter expressed as the average number of fault centres (i.e. points of maximum throw) contained in each sandstone bed. The length and maximum throw of a fault (metres). Dimensionless measures of fault size normalized by bed size. They are given by F ¼ LF =ðLA LB Þ0:5 and T F ¼ TF =LZ . L Shale gouge ratio. The fraction of shale that has passed a particular point on a fault. In this work the Vshale of sandstone and shale beds are taken as 0.0 and 1.0 respectively. Shale gouge ratio cut-off. If every point within an individual sand-on-sand juxtaposition has SGR values exceeding SGRC then a continuous shale smear is assumed to be present within this juxtaposition. Shale smear factor. This is defined at a particular location on a fault surface, and for a particular shale bed, as the ratio between the local fault throw and the thickness of the shale bed. Critical shale smear factor. Shale beds with SSF exceeding this value are assumed to be disconnected from the source shale beds on both the footwall and hanging wall sides of the fault. Shale beds with lower SSF values are assumed to form continuous smears between the source layers in the hanging wall and footwall. The probability that a position on a fault is not covered by one or more shale smears, when the shale smears are assumed to be randomly positioned on a fault according to a specfic SSFC value.

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The link between a heterogeneous model and its flow response: examples from fault damage zones highlighting issues in domain discretization and flow simulation J. MA1, A. Z. VASZI2, G. D. COUPLES1 & S. D. HARRIS2 1

Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK (e-mail: [email protected])

2

Rock Deformation Research Ltd, School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK Abstract: Natural fault damage zones (FDZs) are characterized by complex geometries and topologies, and by strongly-contrasting material properties. Accurate simulation of fluid flow in such systems is dependent on the method of discretization and the mathematical representation of the flow. In this paper, we focus on the conceptual and methodological issues that link a model of a heterogeneous system and its flow response. We study FDZs as our example, where each thin fault strand is a barrier to flow. We examine two contrasting discretization schemes and apply them to 2D FDZ models that contain a realistic array of linear fault traces. Both schemes produce results that are generally in good agreement, and agree with the results calculated by a more accurate (but computationally less efficient) reference scheme. However, differences occur when the discretization approach fails to maintain the fault connectivity (topology) of the input model. It is important to guide the modelling by identifying any continuous flow pathways in the matrix linking fluid inlets and outlets (Through-Going Regions, TGRs). We illustrate a new scheme that identifies all TGRs and determines a grid that is just fine enough to resolve them.

Natural fault damage zones (FDZs) commonly contain many small faults that are thin compared to their lateral extents. The small faults form complex arrays that play a significant role in governing fluid flow within or across the entire FDZ. To predict the net flow effects of the complete system (i.e. at a coarse scale), the components of the FDZ must be idealized to create a model, and that model must then be used as an input for flow simulation leading to an upscaled flow property (see Harris et al. 2007 for a review). Although there are a number of issues that must be considered in the modelling of FDZs, including the choice of sampling scales and positions within the FDZ, and the choice of the scale of faults to be modelled, this paper is concerned with other issues related to the choices that must be made in terms of how to represent the architecture and properties of the FDZ components within the fine-scale models numerically. Specifically, we examine how aspects of the representation approach may impact the simulation output and thus the prediction of larger-scale flow effects. Fault zones commonly consist of an inner fault core zone, accommodating most of the displacement, surrounded by a complex zone of deformation, called the damage zone, extending from distances of perhaps metres to tens of metres on either side of the core zone (Chester & Logan 1986; Cowie & Scholz

1992; Caine & Forster 1999). The damage zone typically exhibits subseismic-scale, low-throw, thin faults, which are typically less than a few millimetres in thickness and which, although constituting only a small fraction of the volume of the whole zone, can provide significant additional retardation to fluid flow in combination with the flow retardation of the core zone (Knipe et al. 1998; Harris et al. 2007). In siliciclastic sedimentary rocks, these small faults may take the form of deformation bands that act as partial barriers to fluid flow (e.g. Knipe et al. 1998; Manzocchi et al. 1998; Shipton & Cowie 2001; Jourde et al. 2002; Odling et al. 2004; Harris et al. 2007). Several deformation mechanisms and processes, including cataclasis, and clay smearing and diagenesis, can result in potentially significant reduction in the permeability of conventional deformation bands in sandstones by several orders of magnitude relative to the host sedimentary rock (Knipe et al. 1998). These deformation bands may or may not be accompanied by open fractures which could enhance the bulk permeability (e.g. Jourde et al. 2002). In this paper, we are only concerned with fault damage zones where thin fault strands act as partial barriers/baffles to flow (we do not address any effects associated with open fractures). The geometrical and topological characteristics of the thin fault strands, along with their poro-perm

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 337–352. DOI: 10.1144/SP292.19 0305-8719/07/$15.00 # The Geological Society of London 2007.

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properties (in relation to the matrix properties), are the important factors that determine the net flow response of the whole FDZ. However, the physical dimensions of thin faults in FDZs mean that they are too small to be detectable individually on even the best seismic data, and other sampling methods (such as those used in wellbores) do not provide full spatial coverage. Thus, models of FDZs have to be developed using limited hard and soft data, with the attendant issues as to the accuracy or representivity of any model. Certain characteristics of the fault arrays can be obtained from well core, core plug and well logs, for example allowing a determination of fault orientations, and their terminations and crossings, that play an important role in determining fault connectivity (Manzocchi et al. 1998; Harris et al. 2003). Soft data is often obtained from outcrop analogues or from geomechanical methods (including numerical simulations or laboratory analogues). Outcrop information provides an opportunity to observe patterns and inter-relationships (such as clustering), and enables process models to be defined (Gillespie et al. 1993). Geomechanical simulations can provide additional insights into the evolution of fault systems and their localized strain–stress fields to enable the model-based predictions of small fault density and orientation distributions (Bourne & Willemse 2001; Maerten et al. 2006; Lewis et al. 2004, 2007; Couples 2005; Schopfer et al. 2006; Couples et al. 2007). It may be the case that at the present state of that specialty, metre- or larger-scale geomechanical models may have greater predictive power than do sub-metre-scale models (because at the larger scale, the predicted deformation features will be represented as bodies, albeit thin ones, of porous material, whereas at the sub-metre scale, the simulation outcomes represent deformation types that need to be treated as discrete features). Realistic FDZ models may be generated stochastically using information derived from such hard and soft data (Harris et al. 2003). The physical dimensions of the many thin faults in FDZs make it difficult to discretize the spatial domains of FDZ models, and the flow equations related to those domains. It is often impractical to discretize thin, but typically irregular (in geometry) faults explicitly and precisely because this approach generates grids or meshes that contain too many cells, making it difficult to solve the flow equations efficiently. Because FDZ models of necessity must be stochastic, many individual models need to be created, and each one taken to flow simulation, to produce bulk flow characteristics that vary as a function of the stochastic parameters. Thus, efficiency in model creation and in flow simulation, is an essential consideration.

Two types of discretization schemes for fault arrays have recently been developed: one by Odling et al. (2004) and Vaszi et al. (2004); and one by Ma et al. (2006). These two schemes represent different approaches to fault discretization and flow simulation, and both can be shown (see below) to produce accurate results when the discretization maintains the model fault connectivity. Maintaining the connectivity becomes more important when the matrix permeability is over two orders of magnitude greater than that of faults (Manzocchi et al. 1998; Walsh et al. 1998a, b; also see the results in this paper). In heterogeneous systems like those considered here, a significant problem with model discretization is to capture the critical fault connectivity without consequently inducing alterations to the connectivity of a matrix region. A matrix region that connects from the flow inlets to the flow outlets is referred to as a ThroughGoing Region (TGR), introduced in the work by Ma & Couples (2007). TGRs could influence fluid flow significantly if the fluid is forced to flow through them as the only available pathway. One of the possible settings, relevant to this work, is that the permeability contrast between the faults and matrix is high, and the TGR is not very tortuous (and thus plays an important role in the flow process). When a TGR is a flow-influential pathway, it is important to prevent it from being mis-discretized into a non-TGR. The potential impact of these discretization errors, relative to the reliability and robustness of the flow solution, requires answers to two questions. Where do the errors typically occur? What are their impacts? A sensitivity analysis is one of the classical approaches to solving this problem. Step-wise refined grids are constructed, and the solution is calculated for each grid. Any sudden change of the solution, from one grid resolution to the next, indicates the insufficiency of the grid corresponding to the former resolution. However, this approach has two important limitations. First, for a FDZ model, it is difficult to know that any particular grid resolves all flow-influential TGRs. Second, this approach is computationally expensive because a full flow solution must be obtained for each grid resolution. Ma & Couples (2007) describe a new and efficient alternative approach that addresses these two questions without incurring either of the difficulties noted above. Based on hierarchical domain decomposition, morphological analysis of objects and network flow modelling, that scheme is capable of identifying the existence of TGRs and, if they exist, the most flow-influential TGRs for a given FDZ model. Therefore, the scheme can determine a grid, called a guiding grid, which is sufficient to resolve the flow-influential TGRs. This guiding grid can then be used to constrain fault

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simplification in the subsequent construction of structured or unstructured grids for simulations. Consequently, simulated solutions on such grids will no longer be subject to the type of discretization errors that are the focus of this paper. This paper makes a comparison of the two discretization schemes (using 2D examples for simplicity and clarity) and considers the role of the guiding-grid scheme in reducing the discretization errors associated with the mis-representation of fault connectivity. For some FDZ model configurations, and some flow regimes, the concerns over discretization errors prove to be irrelevant, and both approaches yield good results. However, some model configurations reveal the existence of artefacts due to the discretization approach. For the single-phase flow considered in this work, the latter case is likely to be associated with a high permeability contrast between fault and matrix and where there is low flow tortuousity in the FDZ (see Walsh et al. 1998a, b for a further discussion). In order to account for these effects in the final analysis of uncertainty, it is essential to have a solid understanding of the link between a model and the calculated flow through that model.

Comparison of discretization schemes for FDZs The two discretization schemes to be compared are that of Odling et al. (2004) and Vaszi et al. (2004) in 2D, and that of Ma et al. (2006). Both schemes were developed to enable permeability upscaling in FDZs by solving flow equations across model domains comprising stochastic realizations of arrays of thin fault strands. Here we consider only single-phase flow to reduce the number of parameters and thus enable us to focus attention on

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the key issue of the role of discretization. When a single-phase fluid is incompressible and flows in a steady state condition, the flow equations (without gravity and source/sink terms) read as follows:

rv¼0 on V, v ¼ krp

(1)

where V is the domain of the problem, v is the Darcy velocity (flux rate across a unit area), p is the fluid pressure, and k ¼ kabs/m, where kabs is the absolute permeability tensor of the medium and m is the fluid viscosity.

DFFM The discretization scheme of Odling et al. (2004) and Vaszi et al. (2004) is based on the ControlVolume Finite-Difference method implemented on a structured grid. This scheme is referred to as the Discrete Fault Flow Model (DFFM). Instead of trying to model faults directly, DFFM requires a fine structured grid to be defined on which the flow impact of the faults is accounted for by modifying the transmissibility between control-volumes according to the occurrence of faults, and their individual properties and geometries (Fig. 1). A control volume of DFFM is defined around each grid cell node (see Fig. 1a). This scheme uses a staggered grid arrangement where fluxes, q, are associated with the midpoints of control volume edges, and pressures, p, at the grid cell nodes (see Fig. 1b). Permeability is defined on a different grid in which a cell is centred at a midpoint of a control volume facet (see Fig. 1c). The flow equations (Equation 1) are then discretized on each control volume to conserve mass (i.e. Equation 2a). Fluxes are related to nodal pressures

Fig. 1. Illustration of DFFM control volume finite difference scheme. (a) grid cells (divided by solid lines) and control volumes (divided by dotted lines); (b) discrete pressures (red) and fluxes (blue); (c) permeability grid.

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via Darcy’s law along each grid canonical direction as shown in Equations 2b to 2c. (qiþ1=2, j qi1=2, j ) þ (qi, jþ1=2 qi, j1=2 ) ¼ 0 (2a) qi+1=2, j ¼ +Ti+1=2, j (pi+1, j pi, j )

(2b)

qi, j+1=2 ¼ +Ti, j+1=2 ( pi, j+1 pi, j )

(2c)

where T is transmissibility defined as follows: Ti+1=2, j ¼ ki+1=2, j Dy=mDx and Ti, j+1=2 ¼ ki, j+1=2 Dx=mDy. k is a permeability defined at a the centre of a permeability cell as shown in Figure 1c. After replacing the fluxes in Equations 2a by the relationships in 2b and 2c, we can derive linear equations involving pressures (Equation 3), which is a 5-point scheme: (Tiþ1=2, j þ Ti1=2, j þ Ti, jþ1=2 þ Ti, j1=2 )pi, j (Tiþ1=2, j piþ1, j þ Ti1=2, j pi1, j ) (3) (Ti, jþ1=2 pi, jþ1 þ Ti, j1=2 pi, j1 ) ¼ 0 Modification to the transmissibility is accomplished through changing the permeability of relevant cells. On the permeability grid, whenever a cell is cut by one or more faults, its permeability is adjusted. For each cell intersected by one or more faults, DFFM converts each fault intersecting that cell into equivalent fault(s) aligned with each grid canonical direction. An equivalent fault would look like a staircase as shown in Figure 2. For each segment of the staircase, a permeability modification is made for the component of the matrix permeability perpendicular to that segment by calculating a harmonic average of the matrix permeability and the fault permeability along that grid direction. This modification accounts for the fault thickness, the cell scale and permeability. For further details of the DFFM formulation, and the procedure for adjusting permeability, the reader is referred to the paper of Odling et al. (2004). Harris et al. (2007) apply the 3D version

Fig. 2. Illustration of transformation of a fault into a staircase effective fault.

of DFFM to explore the impact of the parameters defining FDZs on the predicted bulk FDZ permeability, connectivity, ‘efficiency’ as a barrier or retarder to flow, and the ‘effective’ fault rock throw to thickness relationship for FDZs. Note that similar strategies to incorporate faults into matrix have been developed by other authors (see Manzocchi et al. 1998, 1999; Walsh et al. 1998a, b).

Implicit/explicit discretization of faults and mixed finite-element method Ma et al. (2006) propose a different discretization scheme for FDZ models where fault traces (in 2D) are assumed to be piecewise linear segments. This scheme was adapted from similar schemes for flow modelling in open-fracture systems (e.g. Granet et al. 2001; Karimi-Fard & Firoozabadi 2003; Karimi-Fard et al. 2003). Given an input fault model, the scheme discretizes the matrix only and represents the faults implicitly by a set of edges of the relevant matrix cells (in an unstructured grid). This approach is referred to as implicit discretization of faults (IDF). An IDF grid, which is a geometrical grid, captures the fault connectivity precisely while utilizing only a fraction of the number of cells that might be required if faults are discretized explicitly and exactly along with the matrix (see Ma et al. 2006), another approach which is referred to as the explicit discretization of faults (EDF) method. EDF is used later in this paper to generate a reference solution. Unlike the schemes for fractured systems, which must model fluid flow both along and across each fracture, the IDF scheme described here neglects the along-fault flow under the assumptions that fault strands have permeability lower than the matrix and are very thin compared to the dimensions of the model domain. To model across-fault flow, the IDF scheme expands each fault segment (cell edge) numerically into a fault parallelogram cell, which closely represents the corresponding original fault segment. The geometrical grid and the fault cells form a computational grid on which the scheme discretizes the flow equations to model both matrix-to-matrix and across-fault flows. The underlying numerical discretization scheme employed is the mixed finite-element method (MFEM) of Raviart & Thomas (1977). MFEM is one of the techniques that possesses two important features required by fluid flow simulation through heterogeneous models, i.e. local mass conservation and flux continuity (see Klausen & Russell 2004 for a review of some those techniques). MFEM has been shown, by numerical experiments, to improve the accuracy of predictions

LINKING HETEROGENEOUS MODEL AND FLOW

of the approximate flux within heterogeneous media that have anisotropic and discontinuous permeability distributions (Durlofsky 1994). For simplicity, the scheme used here is labelled as IDF þ MFEM. To construct a reference case, where fault strands are explicitly represented in the models, we use a scheme that is labelled as EDF þ MFEM. Figure 3 illustrates the IDF approach and the expansion of fault cell-edges. Note that the connecting cells between adjacent fault segments are not required. Figure 4 shows grids generated for a fault model using IDF and EDF using the grid generation package Triangle (Shewchuk 2002). EDF þ MFEM can be implemented following the standard finite-element assembly procedure. To construct a global system of equations for solving both pressure and flux unknowns simultaneously, elementary matrices and right-hand vectors are constructed by MFEM discretization for every cell, and then the contributions of all cells are assembled one by one with respect to both cell facets and cells to form that global system. As shown, IDF þ MFEF could be implemented using the same assembly procedure above but excluding the contributions associated with those fault-cell facets that are not common to a matrix cell. In effect, this neglects the along-fault flow. IDF þ MFEM is able to achieve higher computational efficiency than EDF þ MFEM for dense fault models, though the efficiency may vary according to the fault configuration, the fault-to-matrix permeability contrast, and the flow direction. Note that IDF þ MFEM and EDF þ MFEM can and have been implemented in both two and three dimensions,

Fault Edges

(a) Geometrical Grid

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although only the implementations for 2D problems are considered in this paper. The accuracy of IDF þ MFEM has been analysed analytically and numerically (Ma et al. 2006). Apart from the standard errors due to numerical discretization, there are two additional types of error that arise because of: neglecting the along-fault flow; and expanding the matrix (area or volume) as a result of treating each fault as being composed of zero-thickness linear segments. In terms of the total volumetric flow rate at a model face, the amount of error due to the former is much smaller than, and partly compensates for the overestimate due to, the latter. These two types of error will be small when fault strands are thin and the total volume of the fault-material region is small relative to the model domain. These conditions apply to most cases of interest. Note that EDF þ MFEM produces more accurate results than IDF þ MFEF does because, unlike the latter, the former represents individual faults exactly and does not introduce additional simplifications in numerical discretization.

Comparison of DFFM and IDF þ MFEM DFFM and IDF þ MFEM are based on very different approaches to the discretization of FDZ models. DFFM discretizes the flow equation using a Control-Volume Finite-Difference method on a regular structured grid, and takes into account the flow impacts of the faults by modifying, locally, the matrix permeability of those cells that intersect with one or more of the fault strands. DFFM represents the fault connectivity accurately only if

Fault Cells

Omitted Connecting Cells

(b) Computational Grid

Fig. 3. Illustration of the implicit discretization of faults: (a) a geometrical grid for the fault model where the faults form the edges of matrix triangular elements shown in thick lines. (b) a computational mesh constructed from the geometrical grid in (a) where the faults have been modelled as rectangular cells (hachured) with omitted ‘connecting’ cells (black). The rectangular cells are expanded from fault edges numerically rather than physically to approximate the fault segments. From Ma et al. (2006).

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(b)

(a)

(c) Fig. 4. A fault model and grids generated using IDF and EDF. (a) a simple fault model; (b) a geometrical grid generated by IDF for the whole model, where faults are shown as thick lines; and (c) a part of a grid generated using EDF corresponding to the indicated portion of the fault model in (a). From Ma et al. (2006).

the selected regular grid is sufficiently fine (see below). DFFM can only consider a diagonal tensor permeability. On the other hand, IDF þ MFEM decomposes a FDZ model, which is assumed to contain (in 2D) piecewise linear fault segments only, into an unstructured grid in which the fault pattern of the model can be represented accurately by the edges of the matrix cells. The method discretizes the flow equations using the MFEM on that grid plus the fault cells that are expanded from the edges of matrix cells that are adjacent to the faults. The MFEM allows full tensor permeability to be specified for the matrix. Computationally, DFFM generally should be more efficient than IDF þ MFEM because it uses a very simple data structure to manage grid and other data and it forms a system of equations for solving pressure unknowns, rather than equations for both pressure and flux unknowns as required by the latter. DFFM domain discretization is trivial even for a FDZ model that contains a large number of faults and this step does not require any special tools. In contrast, IDF relies on special tools to generate unstructured grids, and these tools typically involve intensive computation, especially for FDZ models that contain many faults. However, since IDF represents the fault

connectivity accurately for piecewise linear faults, it is possible to generate an unstructured grid that has far fewer cells than a comparable DFFM grid in terms of the accuracy of results calculated on them (see in the next section). Although these issues concerning efficiency may be important in choosing which approach to use in solving a particular problem, our purpose here is not about efficiency. Rather, it is, about examining the way that these approaches can introduce errors.

Application of DFFM and IDF 1 MFEM to FDZ examples DFFM and IDF þ MFEF are applied to two FDZ models, Model 1 and Model 2 as in Figure 5(a and b) respectively, to allow a numerical comparison of the simulation consequences associated with these two schemes. These two test models are different-sized subregions of a random 2D horizontal slice through a small part of a large-scale 3D fault damage zone model containing on the order of 106 fault strands. The full model was generated stochastically using the technique of Harris et al. (2003) based on spatial distributional properties derived from two normal faults: the Moab fault in

LINKING HETEROGENEOUS MODEL AND FLOW

(a)

(b) Fig. 5. The two fault models, (a) Model 1 and (b) Model 2, considered in this paper. An enlarged version of Model 2 is shown in Figure 7a where the intersections among the faults and between them and boundaries can be seen more clearly.

Utah, USA, and the Ninety Fathom fault in NE England (see Harris et al. 2003 for details). The selected region corresponds to a part of the fault damage zone with a relatively low density of deformation bands, involving subzones positioned close to the main fault in its footwall block. Models 1 and 2 contain 119 and 19 straight-line fault traces that are 1 mm in thickness (the constant thickness assumption reduces the parameter space for this analysis). The model domains are 10 m 10 m and 2 m 2 m, respectively. Each of the models has multiple TGRs in the vertical direction (referring to the coordinates as printed on these pages; ‘vertical’ is actually horizontal in the original model, and subparallel to the main fault), but no TGRs occur in the horizontal direction of these models, which is roughly perpendicular to the main fault (see Ma & Couples 2007). The numerical calculations are designed as follows. Using Darcy’s law, single-phase steadystate fluid flow is simulated for each model, for horizontal and vertical flow directions (meaning across-fault and along-fault flows), separately, to calculate the upscaled permeability over the model domain. The matrix permeability is assumed to be isotropic, and fixed at 1 millidarcy

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(mD), whereas the fault permeability is also isotropic but takes on a range of values, namely 102i mD fi ¼ 1, . . . ,6g. The flow boundary conditions are defined as follows. For the vertical flow case, a constant unit pressure gradient (the pressure is in Pascals) is applied from the bottom to the top, with no fluid flow across either side boundary. For the horizontal flow, a constant unit pressure gradient is applied from the left to the right sides, with no fluid flow across either of the bottom and top boundaries. Thus, upscaled permeability in the X and Y directions (strictly speaking, the X and Y components of an upscaled tensor permeability) is calculated separately for each case. The conditions imposed are in line with those used in local permeability upscaling with simple, pre-defined boundary conditions (see Durlofsky 2003; Pickup et al. 2005). If the pre-defined boundary conditions do not coincide with the actual fluid flow regime in the examined model region within its larger context, then these arbitrary conditions can lead to incorrect upscaled fluid flow properties (Christie 1996; Wu et al. 2002). Flodin et al. (2004) provide a detailed account of this problem in faulted sandstone reservoirs. Upscaling is applicable when the size of the coarse cell is much greater than the effective scale of the heterogeneities within the model. However, this condition may be violated even for faults that are thin and short with respect to the coarse cell scale. This is because the faults can connect to one another and have an effective scale much greater than that of the length of individual fault strands. Recent subgrid simulation techniques may be capable of addressing these issues (Hou & Wu 1997; Arbogast 2002; Chen & Hou 2002; Chen et al. 2003; Jenny et al. 2003; Aarnes 2004; Ma & Couples 2004). These multi-scale issues are not considered further in this paper since its aim is to compare DFFM and IDF þ MFEM numerically.

Domain discretization Models 1 and 2 are discretized using DFFM, IDF and EDF. Three grid resolutions, 200 200, 500 500 and 1000 1000, are used to generate DFFM grids, denoted with the reference names D200, D500, and D1000. Two IDF grids are generated for each model with the following constraints: the minimum angle in every cell of a grid is 10 degrees, and the maximum area of each cell is less than 1/1000 or 1/30000 of that model domain. The reference names are denoted as I1000 and I30000, respectively. An EDF grid is constructed for both models with the constraints: the minimum angle in every cell of that grid is 10 degrees, and the maximum area is less than 1/ 30000 of the area of the model. The reference

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Table 1. Statistics of the number cells of the grids used in the numerical comparison. M and F indicate the number of matrix cells and the number of fault cells, respectively. For each IDF grid, the number of fault cells is equal to the number of fault edges in that grid E30000

Model 1 Model 2

D200

M

F

595337 71771

287431 18465

40000 40000

D500

250000 250000

name for this model is denoted as E30000. E30000 grids have been verified to contain such a large number of cells that the upscaled permeability values calculated using EDF þ MFEM become stable and thus these models provide the best available predictions for the ‘true’ upscaled permeability of the two fault models. Therefore, the E30000 models are used as references for the results of DFFN and IDF þ MFEM below. Table 1 shows the statistics of the number of cells in the generated grids.

Numerical results of upscaling For both Model 1 and Model 2, and for both the vertical and horizontal flow directions, EDF þ MFEM, DFFM and IDF þ MFEM were applied, respectively, to generate models to calculate upscaled flow corresponding to the labels E30000, selected D# and I# (where # indicates the grid size as described above). For each fault permeability (i.e. kf ¼ 102i mD, i ¼ 1, . . . , 6), the corresponding model upscaled permeability values, denoted as KE, KD# and KI#, are calculated. The results show that: 1) KE, KD# and KI# are in relatively good agreement; 2) KD# and KI# match more closely to KE with high-resolution grids than they do with lowresolution grids (as expected); 3) both DFFM and IDF þ MFEM can over- and under-estimate the upscaled permeability (with errors as large as 10% in some situations with DFFM); and 4) KE, KD# and KI# decrease as the fault permeability decreases, and they ‘converge’ to a smaller value for the horizontal (across-fault) flow than for the vertical (along-fault) flow, because the fault segments form completely connected barriers/baffles to the horizontal flow but not to the vertical flow (see Fig. 5). To compare DFFM and IDF þ MFEM in detail, the relative errors, (KE 2 KD#)/KE and (KE 2 KI#)/KE, are analysed (i.e. taking the result of EDF þ MFEM as the reference). Figure 6a–d

D1000

1000000 1000000

I1000

I30000

M

F

M

F

4679 1906

3631 706

48472 46708

9338 2630

shows these relative errors and KE (red solid lines) as a function of the fault-strand permeability for each of the two models and for each of the two flow directions. Note that DFFM results corresponding to KD200 are also shown in Figure 6d to provide a direct comparison between them and those of KE30000 for that particular case. For horizontal flow (across the fault zone), IDF þ MFEM relative errors, (KE 2 KI1000)/KE and (KE 2 KI30000)/KE, behave similarly. The relative errors peak around a fault permeability of 0.0001 mD and 0.001 mD for Model 1 and Model 2, respectively, but the errors become smaller at higher and lower fault-to-matrix permeability contrasts. The distribution of the relative errors as a function of fault permeability seems to indicate that, for IDF þ MFEM, there is a transition from the faults having little effect on flow (lower permeability contrasts), to the faults forming a significant barrier to flow (higher permeability contrasts). In the transition, it may be necessary to model the fault geometry accurately, or the errors could impact the results. On the other hand, DFFM relative errors, (KE 2 KD1000)/KE for Model 1 and (KE 2 KD200)/KE for Model 2, show a different pattern. Note that D1000 and D200 are at the same grid resolution, taking into account the sizes of the models. The largest absolute errors are less than 7% and 3% for Model 1 and Model 2, respectively. Note that for all models the errors are small for fault permeability greater than 0.001 mD and of little significance in practice. This agrees well with the results of Walsh et al. (1998a, b). For vertical flow (along the fault zone), the relative errors behave differently from the case for the horizontal flow errors. For IDF þ MFEM, the relative errors, especially those of I1000, appear to increase for both models as the fault permeability decreases. Ma et al. (2006) argue that this trend may be explained as follows. First, as the faultstrand permeability reduces, the amount of fluid flowing along each fault decreases and could, therefore, compensate less for the primary error (i.e. flow over-estimation) due to the geometrical expansion of the matrix that occurs with the IDF scheme. Second, as the fault-to-matrix permeability contrast

0.03

I1000

0.4

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I30000

0 0.000001 0.00001 0.0001

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0 0.000001 0.00001 0.0001

0.001

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(d)

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D1000

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I1000

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0 I30000

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–0.02 0.001

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(b)

Model 2 (H)

1

Model 1 (V)

1

Relative Error

0.6

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Model 2 (V)

1 0.9 0.8 0.7 0.6

0.12

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0.1

E30000

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D200

0.06 I30000

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0.04

I1000

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0.5

Relative Error

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Upscaled Permeability (mD)

Upscaled Permeability (mD)

0.07

0.8

(a)

(c)

E30000

Upscaled Permeability (mD)

Model 1 (H) D1000

Relative Error

1

Relative Error

Upscaled Permeability (mD)

LINKING HETEROGENEOUS MODEL AND FLOW

0

0.4 0.000001 0.00001 0.0001

–0.02 0.001

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0.1

Fault Permeability (mD)

Fig. 6. Upscaled permeability and relative errors for different discretization schemes and resolutions: (a) Model 1 for horizontal flow; (b) Model 1 for vertical flow; (c) Model 2 for horizontal flow; (d) Model 2 for vertical flow. The relative error is defined as (KE 2 KDjI#)/KE, where KE is the upscaled permeability by EDF þ MEFE on respective models corresponding to E30000, while KDjI# is the upscaled permeability by DFFM and IDF þ MFEF on respective models corresponding to DjI# given in Table 1 where # is the number. The KD200 results are also plotted in (d) for a direct comparison with E30000 results. The upscaled permeability results for E30000, and D200 in (d), are shown as solid lines whereas the relative errors are shown as broken lines.

becomes much greater, a larger fraction of the fluid flow must occur in the TGRs between the faults, and finer meshes are required to represent complex structures of faults especially along and inside each TGR. The former is likely to be more important than the latter for sparse fault models, but vice versa for dense fault models. Therefore, for Model 1, as it is a dense model, the increase in the relative errors may reflect a relative inadequacy of discretization inside TGRs when the fault-to-matrix permeability contrast is high. For Model 2, as it is sparse, the monotonic increase in error may be better explained as an artefact of the over-sized matrix. These reasons also seem to explain why the relative errors of IDF þ MEFM are more sensitive to the grid resolution for Model 1 than for Model 2 (see the error magnitudes of I1000). On the other hand, the DFFM errors for Model 1 peak between 0.00001 and 0.0001 mD and (KE 2 KD500)/KE is less than 6%. For Model 2, there is an apparent inconsistency between (KE 2 KD200)/ KE and (KE 2 KD1000)/KE. (KE-KD200)/KE increases monotonically to about 12% as the fault permeability decreases, whereas (KE 2 KD1000)/ KE, like for Model 1, peaks around 0.001 mD at a maximum of 2%. This inconsistency is investigated (see below) to examine whether the D1000 may

resolve additional fault-pattern features that cannot be resolved by the D200. (KE 2 KD500)/ KE is calculated for Model 2, but not shown here and is about 2% smaller than (KE 2 KD200)/KE at every fault permeability value.

Importance of accurate discretization of TGRs The fault connectivity of Model 2 is analysed in detail and shows that the D200 grid misrepresents the fault connectivity at two locations. These two locations are marked by the two red boxes in Figure 7a. A zoom-in view of each of them is given at the left column of Figure 7b. At each location, the gap between faults is less than 5 mm and so cannot be resolved with a regular grid of 200 200. A regular grid of 1000 1000 is sufficient to resolve the gaps. The zoom-in views of equivalent faults corresponding to D200 and D1000 at those locations are shown at the middle column and the right column of Figure 7b, respectively. Further analysis also shows that for this model the D500 grid is not sufficient to resolve the gaps either. This suggests that the two TGRs passing through the two gaps, respectively,

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Original

(a)

D200

D1000

(b)

Fig. 7. DFFM discretization for Model 2: (a) Model 2 and the two gaps at locations marked by two red boxes; (b) zoom-in views of the fault model (left), and the equivalent faults corresponding to D200 (middle) and D1000 (right) at the two locations. There are two TGRs, which pass through the two gaps, respectively, and are mis-discretized into non-TGRs in the D200 (also in D500 not shown here). D1000 is sufficient to resolve these two TGRs. The dark thick lines in the bottom row of (b) indicate segments of the bottom boundary of the model.

influence the fluid flow and are responsible for the increase of the relative errors for Model 2 for the vertical flow.

Summary of numerical comparisons The numerical output shows that both schemes (i.e. DFFM and IDF þ MFEM) can produce reasonably accurate upscaled permeability values in comparison with the reference case (i.e. EDF þ MFEM), if there is no TGR in a model or there is no flow-influential TGR being mis-discretized into a non-TGR (as shown for the cases corresponding to Fig. 6a, b and c). However, DFFM may not resolve the gaps between faults when they are smaller than the resolution of the regular grid. In other words, given any particular regular grid, DFFM can misrepresent a TGR as a non-TGR if the model has passages narrower than the resolution of the cells, in which case, DFFM will not be able to account correctly for the fluid flow contribution of that TGR. This is why in the work of Odling et al. (2004) an additional procedure was used to determine a fine grid that ensures all gaps between all faults are resolved for a FDZ, though that procedure seems not to be able to determine coarser grids that lead to equally acceptable results with small enough errors. Unlike DFFM, IDF þ MFEM does not suffer from this problem since it represents the fault connectivity accurately. But this is only true for fault models where faults are in the form of piecewise linear segments (or planar faces in 3D). For a model with irregular-shaped faults, the faults may have to be approximated into these simpler forms in order to use standard meshing methods (e.g. Delaunay triangulation) to construct IDF grids.

This is particularly true for 3D FDZ models (see Taniguchi & Fillion 1996; Karimi-Fard 2004). The required approximation process could alter the true fault connectivity of a FDZ model, and any resulting discrepancy in the fault connectivity might have significant impacts on the reliability and robustness of simulated flow if some of the alterations occur at critical places. Thus, like DFFM, IDF þ MFEM could also suffer from the mis-discretization of TGRs in complex models. Hence, an effective solution to both types of misdiscretization is necessary in practice no matter which scheme is selected when the discretization errors are anticipated to affect the solutions significantly. Researchers performing simulations should recognize that there is a continuing need to appreciate the way that models and their outcome are linked by the choices that must be made within the simulation process. It is not possible to say that any scheme is always safe to use. Clearly a good choice of specific techniques can only be made by taking into account of other factors (e.g. data errors, stochastic model errors) that could affect the uncertainty of outcomes to different degrees.

Using the guiding-grid scheme for accurate domain discretization Ma & Couples (2007) describe a generic guiding grid scheme that can be used to prevent flow-influential TGRs from being mis-discretized into non-TGRs. This scheme may be applied to FDZ where the flow is likely to take place in TGRs rather than non-TGRs (e.g. high permeability contrast cases). For a given FDZ model, this scheme determines the existence of TGRs and, if they exist,

LINKING HETEROGENEOUS MODEL AND FLOW

it identifies a sufficiently fine guiding grid that resolves all flow-influential TGRs. This guiding grid can then be used to guide the construction of regular structured grids (e.g. for approaches like DFFM) or the TGR-preserved linearization of faults prior to the construction of IDF-based unstructured grids (as illustrated here for the case of IDF þ MFEM). This scheme is centred on a Quadtree decomposition. For a model, the Quadtree decomposition partitions each cell recursively into four equal parts (in 2D) if that cell intersects with any fault. This process starts from the whole model, i.e. set to be the initial cell, and records a subdivision level, starting from 0. For any level, TGRs can be identified from connected regions of cells, each of which does not intersect with any fault at a level not greater than the given level. Two properties, the number of TGRs (N_TGRs) and the volume (i.e. area) of TGRs (V_TGRs), can be extracted at each level to provide rough qualitative information on the additional fluid flow contribution due to any emerging TGR. In order to estimate the flow-influence of TGRs efficiently and directly, a flow-equivalent porous medium ‘pipe’ can be constructed for each TGR

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along its skeleton (Ma & Couples 2007). Assembling all of the pipes into a network, and attaching the inlets and outlets, allows the single-phase steady-state flow to be estimated by a low-cost calculation. The changes in the total volumetric flow rate, along with N_TGRs and V_TGRs, as a function of decomposition level, allow us to determine whether a sufficient resolution has been reached. The result of the Quadtree decomposition can easily be converted into a binary image that consists of the matrix pixels (1) and fault pixels (0) (i.e. those cells that contain the matrix only, or otherwise). If the subdivision is terminated at a level of 10 for example, a converted binary image will have a size of 210 210 pixels. This binary image can simply be used as a regular grid input for DFFM. Figure 8 summarizes the adaptive scheme for constructing a guiding grid. An input fault model (Fig. 8a) is decomposed by Quadtree (Fig. 8b) to identify the existence of TGRs and to estimate their geometrical properties (Fig. 8c). Flow networks are constructed to represent each TGR along its skeleton (Fig. 8d), allowing an estimation of its flow influence. The total flow influence of all TGRs (expressed in terms of upscaled permeability

Fig. 8. An adaptive procedure for constructing a guiding grid for a fault model. Cells of different sizes and colours in (b) and (c) correspond to different decomposition levels. The images shown do not represent the final decomposition, since that produces cells that are too small to distinguish at the scale required to show the whole model in this printed page.

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in this case) and TGR geometrical properties are then analysed with respect to the decomposition level (Fig. 8e). Steps (b) to (e) are repeated for the next decomposition level until the increase of each estimate is small. At that decomposition level, the Quadtree is output to construct a guiding grid (Fig. 8f). This scheme could be extended to 3D. Note that a grid determined using this scheme does not necessarily resolve all gaps between faults but only those gaps in corresponding flow-influential TGRs. The reader is referred to the work of Ma & Couples (2007) for more details on this scheme, including its computational efficiency.

Ma & Couples 2007) that the relative change of Keff is a good and robust indicator of additional flow contribution of each newly-emerged TGR when the subdivision level is high. Based on these results, a regular grid comprising 210 210 cells (i.e. 1024 1024) should be sufficient to resolve the narrow TGRs. For Model 2, this has been confirmed to be true in the analysis given above.

Remarks on the guiding-grid scheme In the guiding-grid scheme, the flow influence of each TGR is estimated by calculating the singlephase steady-state flow along the flow network of porous media that have homogeneous and isotropic permeability. This is merely to determine, in an unbiased manner, whether newly-emerged TGRs, i.e. those that are identified as the decomposition progresses, are likely to contribute a significant amount of fluid flow relative to that of existing TGRs. If so, the newly-emerged TGRs should be maintained explicitly in discretization. The actual petro-physical quantities for the systems should be specified at subsequently constructed computational grids. This scheme should be of use, in principle, for multi-phase and multi-component flow too as long as fluid flow takes place predominately in TGRs. Note that this condition can be violated in some fluid flow scenarios as a result of complex interactions between flow mechanisms (e.g. capillary, gravity, etc), differences in flow properties (e.g. fault-to-matrix permeability contrast, phasemobility, etc) and flow boundary conditions (Manzocchi et al. 1998, 1999). A DFFM regular grid determined using the guiding grid scheme can sometimes contain far more cells than necessary because the grid cells are not aligned with faults. Some of the adjacent rows or columns in that grid could be merged

Example of guiding grids for DFFM The guiding-grid scheme was applied to Model 1 and Model 2 to determine appropriate regular grids for DFFM for the vertical flow case only, since there is no TGR in the horizontal direction of these models. For both models, the matrix permeability is set to be 1 mD and the fault is assumed to be impermeable to flow. Figure 9 shows the estimated properties as a function of the subdivision level up to level 11. Data for levels 12 and 13 are not shown because N_TGRs becomes constant and the relative changes of V_TGRs and Keff, from one level to the next, converge after level 10. Note that N_TGRs, V_TGRs and Keff show a non-linear relationship between one and another. Similar non-linear relationships are found by Manzocchi et al. (1999) and Walsh et al. (1998a, b) between the proportion of gaps on a fault and its effective permeability. For Model 1 and Model 2, the relative changes of the upscaled permeability are about 10% and 7% due to the emergence of TGRs, i.e. 5th and 6th TGRs for Model 1, and 3rd and 4th TGRs for Model 2, at level 9 and 8, respectively. It has been shown (see

6

V_TGR_1

N_TGR_1

100

60 40

2

20 V_TGR_2

0 0 (a)

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6 Level

8

0.6 Keff

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V_ TGRs(%)

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80 4

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0

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0 (b)

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4

6 Level

8

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Fig. 9. N_TGRs, V_TGRs and the upscaled permeability, Keff, along the vertical direction as a function of the subdivision level, respectively. Faults are assumed to be impermeable for this suite of models. Note that # indicates the model numbers.

LINKING HETEROGENEOUS MODEL AND FLOW

without altering the representations of TGRs. Hence, in practice, the guiding grid scheme might be used in conjunction with a simple post-process to reduce the number of cells.

Discussion In this paper, we have sought to develop new insights into the factors that can impact the reliability of flow simulation results for heterogeneous systems. The characteristics of fault damage zones make them ideal cases for this purpose. FDZs exhibit extreme property contrasts: in the simplification adopted here, we have only considered a single matrix material type, and a single fault-strand material type, but these materials may have permeabilities that differ by six orders of magnitude or greater. The geometry of FDZs reveals (even in our simplification) that the objects (e.g. the fault strands in our two-component systems) have extreme aspect ratios that demand special approaches in building models and running simulations. The stochastic assembly of large numbers of fault-strand objects (as happens when we create an individual FDZ model) leads to unpredictable variations in the detailed topology of the resulting fault arrays from one realization to the next. Issues related to the connectivity of the fault strands, and how the connectivity is represented during discretization, have been shown to play an important role in governing the bulk system flow behaviour. One of the comforting outcomes of our work is that we have been able to show that there are multiple numerical approaches (control-volume-finitedifference and mixed-finite-element methods have been examined within this work) that solve the flow equations with a high degree of accuracy when flow-influential TGRs are represented accurately. However, referring to the results presented in this paper we have shown that small changes in the spatial locations of fault strands (i.e. variations in the coordinates describing the end points of the lines representing these elements) can lead to differences (on the order of 10%) in the calculated flow that passes through the whole system (in some flow conditions). Does this outcome have any significance? The reasons for making permeability predictions are directly linked with economic motivations, commonly involving an estimation of the volumes of fluids that can be extracted from or injected into, a specific subsurface situation, given a set of operating conditions. If the particular subsurface situation involves heterogeneity and complexity, such as a FDZ, then the prediction of fluid flow could vary depending on the modelling/simulation approach that is taken. The prediction is uncertain

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due to several factors, but one of those factors is the solution error (Christie et al. 2005). Our results need to be considered in terms of whether it is possible, based on an understanding of the compatibility of the approach that is selected, relative to the idealized model of the subsurface, to say that the solution error is small or large in comparison with the errors that arise because the model itself is uncertain (‘the model errors’ in the terminology of Christie et al. 2005). Model errors and solution errors can combine in ways that cancel the net error, or they can combine so as to increase the net error. We have demonstrated that these errors can become entangled in practice if one does not examine possible artefacts associated with the discretization methods used. Our results illustrate that differences in the connectivity (topology in the broad sense) of the fault array can lead to differences in the bulk flow through the system. These effects may be apparent in terms of their impact on fluid flow in one direction, but not in another. Since reality is not known, a model of a fault array may, or may not, be a good representation of that reality. We can say that the details of the model are in error to some extent. The resulting model error (or uncertainty) may be irrelevant in some flow circumstances, but if the flow system changes (this could happen, for example, in an oil reservoir after the drilling of new wells), the model error, or as we have shown here, the way that the model is represented numerically (i.e. the discretization process), may become important considerations. The analysis described in this paper is not exhaustive. We have identified an issue related to the way that seemingly-minor geometrical variations (either in a model, or in the way that the model is represented during discretization) can result in changes to the flow predictions of a heterogeneous system. We have not developed a set of robust rules that identify the actual scales at which these effects will be manifest in all fault systems. Perhaps that work is worth doing, and the approach based on the identification of TGRs may make that study feasible. When we create stochastic realizations of FDZs, we must choose a minimum length scale (if we accept that faults occur in power-law distributions; see Harris et al. (2003) for a review of these concepts) when we generate each model. Since there is a link between a model and how it is represented numerically, it is not clear how one would decide where to draw the boundary (between faults that are included in the model, and those which are ignored because they are ‘too small’). The impracticality of running simulations with smaller and smaller grids means that a multi-scale approach will be required to address this topic.

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The analysis described in this paper has reinforced the appreciation of the link between the configuration of a model and the results of simulating flow through that model. We can ask the question: do the ‘lessons’ revealed in our examination of FDZ upscaling apply equally to cases of large-scale models of faulted reservoirs and their flow simulation? It has become standard practice to represent faults as transmissibility modifiers within a regular grid in reservoir simulators. Using a corner-point style of grid, one can create models that more closely replicate the geometry of fault systems, and there are facilities (such as non-neighbour connections) that permit the user to address many of the issues associated with gridbased models. However, there are potential penalties for adopting some of these methods. For example, corner-point grids may lead to significant numerical errors if the flow is not parallel to the grid coordinates. Fault intersections, and other geometric complexities, may tempt the user to make inappropriate use of the geometric methods that are available in typical finite-difference simulators. Our work highlights the need to give some additional consideration to the interplay between model discretization and the resulting flow simulation.

Conclusions DFFM and IDF þ MFEM have been evaluated to explore their relative merits and weaknesses for 2D FDZ models comprised of arrays of low permeability fault strands. The two schemes employ very different approaches to account for the flow impact of thin faults. DFFM converts fault strands into equivalent fault networks aligned with the canonical directions of a regular grid, and modifies the permeability for those grid cells that intersect with one or more faults using simple averaging schemes. Hence DFFM can handle arbitrary-shaped faults but can only maintain the fault connectivity approximately. On the other hand, by adopting a modified finite element approach, IDF þ MFEM represents piecewise linear faults as facets of the elements of a grid to achieve the purpose of maintaining precise fault connectivity. IDF þ MFEM makes use of a more accurate scheme than that of DFFM to model intra-matrix and fault-across flow, and allows the full permeability tensor to be specified for the matrix. Computationally, DFFM is simpler than IDF þ MFEM as it requires a simple data management internally and does not require any sophisticated and computationally expensive grid-generating tools. A typical DFFM grid can contain more cells than a comparable IDF grid, but the formulation of DFFM results in

a less-expensive calculation. The simpler calculation design also means that DFFM can work effectively with models that have many faults. Both of the schemes work equally well for example 2D models that do not contain TGRs using grids with reasonably low resolutions. For models with TGRs, DFFM is prone to discretization errors due to mis-discretizing TGRs into non-TGRs when the resolution of a selected regular grid is not sufficiently high. This remains true even for linear faults, and the flow contribution resulting from misdiscretized TGRs is not accounted for accurately. The magnitude of the solution error due to such discretization errors depends on the configuration of faults, the fault-to-matrix permeability contrast, and the flow direction. As IDF þ MFEM is capable of handling piecewise linear faults only, for models with non-linear faults, a pre-processing would be required to approximate faults into the required form. If this process cannot maintain the fault connectivity of the original fault network, it will also result in similar discretization errors that could become equally significant if they occur at critical places on the flow paths. Hence, both of the schemes can suffer from the same problem of failing to maintain the true fault connectivity, though the problem occurs at different stages in different ways. The guiding-grid scheme proposed by Ma & Couples (2007) is an effective solution to this problem for DFFM. This scheme can be used to screen for the existence of TGRs for a fault model. Upon identifying the existence of TGRs, it can, at the same time, be used to identify a guiding grid, which resolves flow-influential TGRs. We have shown that such grids can be used effectively to construct suitable DFFM grids. The comparisons that we have undertaken here highlight the role of topology and how discretization methods can inadvertently mask the flow effects associated with small connections that can occur near the ends of fault strands. If this issue is appropriately acknowledged, then both DFFM and IDF þ MFEM represent robust methods for calculating the effective flow properties of FDZs. The scheme for constructing appropriate grids makes it possible to identify important connections, and in future, to quantify and model solution errors induced by geometrical misrepresentations for a more complete set of configurations. The application of commercial reservoir simulation tools to faulted reservoirs has the potential for misdiscretization and the understanding generated here may help in examining these potential effects. We would like to thank our numerous sponsors who have partially funded this work. Special mention should go to our industrial sponsors Amerada Hess, BG Group, BP,

LINKING HETEROGENEOUS MODEL AND FLOW ConocoPhillips, Kerr KcGee, Shell, Statoil, Total and the Department of Trade and Industry, UK, who supported the BMFFFS Project within the ITF-brokered thematic programme of work on Structurally Complex Reservoirs. We would like to thank the following referees, G. Yielding, T. Taniguchi and J. Walsh, for their comments and suggestions that helped to improve the paper.

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Three-dimensional upscaling of fault damage zones for reservoir simulation S. D. HARRIS, A. Z. VASZI & R. J. KNIPE Rock Deformation Research Ltd, School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK (e-mail: [email protected]) Abstract: Major faults are surrounded by damage zones of minor faults that, in siliclastic rocks, can form barriers to flow in their own right. Reservoir flow simulation, now a routine part of reservoir management, requires equivalent hydraulic parameters on the scale of the whole fault. Geological models of structurally complex reservoirs, from which flow simulator grids are generated, require information on the 3D characteristics of fault populations. Here, 3D stochastic models of fault damage zone (FDZ) architecture are generated based on fault population statistics (offset, orientation, length, thickness, spatial distribution) measured from seismic, outcrop and core data. These FDZ models provide input to a 3D discrete fault flow model (DFFM) and we consider the case when the minor faults have permeabilities (isotropic) that are several orders of magnitude lower than the host rock, and thus form partial barriers to flow. The DFFM is used to determine and characterize the impact of the parameters defining the FDZ on the predicted bulk FDZ permeability, connectivity, ‘efficiency’ as a barrier or retarder to flow, and the ‘effective’ fault rock throw to thickness relationship for the FDZ. The latter of the summary results presented provides a means for incorporating FDZs into conventional production simulation package models of structurally complex reservoirs.

Faults are a common cause of heterogeneity within petroleum reservoirs and may have a significant influence on fluid flow (e.g. Berg 1975; Schowalter 1979; Knai & Knipe 1998; Knipe et al. 1998; Fisher et al. 2001; Koestler & Hunsdale 2002; Harris et al. 2005; Sorkhabi & Tsuji 2005). In many reservoirs, faults restrict fluid movement. The presence of sealing or retarding faults can reduce the profitability of petroleum extraction because more wells may be needed to drain the reservoir. Faults and fractures are particularly problematic to incorporate into production simulation models because: (i) they are often very thin (less than 1 mm to 1 m) compared to the size of the grid block; (ii) they can have large permeability contrasts (sometimes more than six orders of magnitude) compared to the surrounding reservoir; (iii) they have a complex structure; and (iv) their fluid flow properties are not well understood. To illustrate the problem further this study focuses on fault zone structure. Over the last decade, numerous detailed studies on fault zone architecture have shown that, in general, large-scale (seismic-scale) faults consist of a principal slip zone, along which most of the displacement occurs, surrounded by a highly complex fault damage zone (FDZ) comprising a complex and clustered array of low-throw (subseismic-scale) faults (e.g. Aydin 1978; Antonellini & Aydin 1994; Childs et al. 1997; Foxford et al. 1998). This article focuses on faults in siliclastic

sedimentary rocks. The faults within the FDZ of clastic sediments are generally composed of cataclastic fault rock gouges, containing angular grain fragments formed by the crushing of sand grains (Fisher & Knipe 1998). The grain size and porosity are therefore reduced and these faults form partial barriers to fluid flow (e.g. Gabrielsen 1990; Antonellini & Aydin 1994, 1995; Fisher & Knipe 1998). The Moab fault in Utah, USA (Foxford et al. 1998; see Fig. 1) and the Ninety Fathom fault in NE England (Knott et al. 1996) provide well-exposed examples of normal faults and their damage zones in high-porosity sandstones. Flow simulation at the reservoir scale is now a routine task for reservoir management. It would be far too intensive numerically to represent all of the low-throw faults discretely within conventional reservoir simulation packages. Thus, due to the limited resolution of such simulation grids, faults and FDZs are typically included using equivalent hydraulic parameters, such as bulk permeability, and represented as modifiers to the inter-cell transmissibility (transmissibility multipliers; Knai & Knipe 1998; Manzocchi et al. 1999). The (often difficult) job of the geologist and/or reservoir engineer is to provide these parameters. Since much of the detail of minor fault architecture within FDZs is presently below seismic resolution, the parameters describing the effective hydraulic properties of faults and their FDZs must be deduced from outcrop or core observations on fault architecture

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 353–374. DOI: 10.1144/SP292.20 0305-8719/07/$15.00 # The Geological Society of London 2007.

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Fig. 1. Photographs of (a) part of the Moab fault zone in Bartlett Wash and (b) the area around Bartlett Wash, Mill Canyon and Courthouse Springs, Utah, USA. (c) A map of all of the faults present within the box shown in (d), a photograph of the outcrop at the end of Mill Canyon. (e) A hand specimen demonstrating the complexity of the small-scale features. The damage zone of the Moab fault is composed of an anastomosing network of deformation bands (planar discontinuities generated by shear failure along which porosity, and commonly also permeability, is reduced with respect to the host rock), which, in the well-exposed canyon of Bartlett Wash, has an inner zone of well-connected, high-density deformation bands (inset to (a)) and an outer damage zone of lower-density faults.

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combined with flow modelling studies (e.g. Ottesen Ellevset et al. 1998; Walsh et al. 1998; Yielding et al. 1999; Porter et al. 2005; Fisher & Jolley 2007). Generating 3D models of FDZ architecture requires information on many parameters, including the size distribution of the fault system. In practice, 3D data on fault geometry is seldom available and the frequency distributions of fault length and throw must be deduced from 2D maps and sections or 1D logs. Previous studies (Cowie & Scholz 1992; Bour & Davy, 1999) have suggested that simple conversions, valid for spatially random systems, are not necessarily valid in natural systems. Here we investigate the bulk properties of 2D and 3D FDZs using a stochastic model of FDZ architecture that recreates the complex structure of faults based on population statistics gathered during the analysis of seismic, outcrop and core data, together with a discrete fault flow model used to derive the effective hydraulic properties from a sequence of realizations and subregions of the stochastic model. Thus summary statistics detailing the effects of the geological parameters provided as input to the stochastic model on the bulk permeability, FDZ connectivity, FDZ ‘efficiency’ as a barrier to flow, and the ‘effective’ fault rock throw to thickness relationship for FDZs will be derived.

Fault damage zones in siliclastic rocks The parameters required to generate geologically realistic stochastic models of FDZs in structurally complex reservoirs are the fault length and orientation distributions, the fault aspect ratio, length– thickness relationships both for a single fault and for fault populations, and the fault spatial distribution. A number of studies on faults in siliclastic rocks and their damage zones (Antonellini & Aydin 1994, 1995; Fowles & Burley 1994; Knott et al. 1996; Foxford et al. 1998; Beach et al. 1999; Hesthammer et al. 2000; Shipton & Cowie 2001; Flodin et al. 2001; Jourde et al. 2002; Shipton et al. 2002) have outlined their main characteristics, and a full discussion of the relevant observations from the literature is provided in Harris et al. (1999, 2003) and Odling et al. (2004, 2005). FDZs consist of a dense network of minor faults and deformation bands with a range of dips (synthetic and antithetic for larger faults of greater than 30 m displacement, and synthetic for smallerthrow faults; see Hesthammer et al. 2000) and strike orientations that ensure good connectivity (Balberg & Binenbaum 1983; Robinson 1983; Antonellini & Aydin 1994; Shipton & Cowie 2001). The FDZ width and the density of the deformation band are generally correlated as a function of the fault throw (Beach et al. 1999). Frequency profiles across FDZs show a degree of clustering,

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particularly around the larger of the minor faults within the FDZ (Antonellini & Aydin 1994; Fowles & Burley 1994; Knott et al. 1996; Knipe et al. 1997; Beach et al. 1999; Hesthammer et al. 2000; Shipton et al. 2002). In both the Moab and the Ninety Fathom faults, deformation band density generally increases toward the major slip zone, ranging from 1 to over 100 faults per metre. Fault frequency profiles across the FDZs of both faults show a general increase toward the major slip plane, with significant localized variations in frequency on the scale of tens of metres. In both the Moab and the Ninety Fathom faults, the nature of the outcrop does not allow the determination of the fault length distribution and there are no studies of fault length distributions within FDZs. Power law fault throw populations within FDZs have been observed (Knott et al. 1996; Harris et al. 2003) and, since fault length and throw are generally linearly related (see Cowie et al. 1996 for a review), it is appropriate to assume a power-law relationship for the fault length– frequency distribution with a suitable range of power law exponents (Odling et al. 2005). The strike and dip distributions of the faults are also of major importance, as they are expected significantly to influence the connectivity of the fault array. Deformation bands generally have a trend similar to that of the main slip plane (Antonellini & Aydin 1995; Shipton & Cowie 2001), but also show sufficient variation in orientation to generate good connectivity in the sub-horizontal plane. Subvertical sections of these FDZs show that the dip of deformation bands can be either unimodal or bimodal, with an angle of 208–308 between the two major dips. The thickness of the fault rock and its variation on individual faults is related to the fault length and displacement, and the lithology. Isolated normal faults are typically planar, approximately elliptical in shape, with a mean length to width aspect ratio of around 2, and have a sub-horizontal long axis (Rippon 1985; Nicol et al. 1996). The simple linear decrease in the fault throw from the centre of an isolated fault to its tip (Childs et al. 1995) is complicated by interaction with other faults. Fault displacement to length ratios for highporosity sandstones lie in the range of 1:30 to 1:500, centring on a ratio of around 1:100 (Gillespie et al. 1992), and the fault rock thickness to displacement ratio for major faults is typically 1:66 (Manzocchi et al. 1999; effective ratios of 1:170 are suggested for flow modelling). The reported information on the architecture of FDZs has provided the basis for a stochastic FDZ model that incorporates geologically realistic length and orientation distributions, length– thickness correlations and clustered spatial distributions.

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A stochastic model of a fault damage zone Individual fault and fault system parameters The stochastic fault models presented here were initially developed based on the parameters summarized in the previous section and are described in Harris et al. (1999, 2003). Each fault is represented by a simple elliptical surface whose aspect ratio follows a Gaussian frequency distribution with mean 2 and standard deviation 0.05. A linear relationship between length and displacement for each modelled fault is assumed, with the displacement decreasing linearly from the fault centre to the tip. A fault thickness to length ratio for individual faults of around 1:104 at the fault centre has been assumed in this article. Fault plane major axes (fault length) are assumed to follow a power law distribution in which the cumulative number of faults of length at least l is FðlÞ / lD3 , where higher values of the 3D power-law exponent D3 indicate the increasing dominance of small faults within the population. Exponents from D3 ¼ 1.6 to 2.8 have been used to represent the range of most commonly occurring power-law length distributions (the core of the frequency distribution of such power-law exponents found in the literature; see Bonnet et al. 2001). The fault density, N, in the model must be specified, and for larger values of D3 the fault densities are expected to be higher.

Describing fault spatial distributions The spatial distribution of faults is one of the most challenging characteristics to quantify and simulate in structurally complex reservoirs, and attempts to locate faults spatially rely on geometrical rules tested against natural patterns. Non-random spatial distributions in models of fault networks include the ‘parent–daughter’ model (Hestir et al. 1987), the ‘FracMan’ software (Golder Associates) which is a ‘nearest-neighbour’ model, the ‘war zone’ model (Black 1993; Dershowitz et al. 1998), and a multiplicative cascade technique with random input from a Le´vy-stable distribution (Belfield, 1998). Here we use a hierarchical clustering scheme, which is the most geologically realistic of the spatial clustering approaches whose geometrical and hydraulic properties were investigated by Harris et al. (2003, 2005) and Odling et al. (2004). All of the faults within the model are clustered around pre-existing larger faults, thereby producing sub-clusters of faults over several

fault-length scales, and the fault density variations compare well with observed natural examples (Harris et al. 2003; see also Fig. 2 described later). The mean strike of the clustering fault can either be equal to that of the pre-existing ‘parent’ fault that it clusters around or the strike of the single major fault plane. The mean dip of each fault will be treated similarly, and based on either the dip of the parent fault (synthetic dip orientation model: the dip distribution is controlled by the largest fault in the sub-cluster) or a set of three directions independent of the clustering, namely, the dip of the major fault and at angles +308 from the dip of the major fault (antithetic dip orientation model).

Control parameters in the FDZ model From the descriptions above, fault parameters representing a FDZ for a normal fault in semilithified siliciclastic rocks, with a length of 3 km and a throw of 30 m, have been determined and are summarized in Table 1. These parameters have been used to generate a suite of FDZ models. The fault population is constrained to lie within a length range lmin l lmax . The parameter lmin specifies the smallest allowed size for a fault in the population and is assumed to be small enough to capture the relevant flow characteristics of the FDZ, such as the upscaled properties of subregions. The validity of this choice is investigated later in this article. For all of the simulations in this article we have chosen lmax ¼ 1500 m. However, the largest fault that is actually generated in the population also depends on D3, and there is a tendency for the largest fault sampled from the population to decrease as D3 increases. The ratio of the fault length to fault thickness (the combined effect of the fault length to throw and throw to thickness ratios) is set at 104 for most of the simulations. The validity of simply scaling the results obtained using this ratio is discussed later in terms of the other FDZ parameters. The major fault plane is represented by an ellipse with a horizontal long axis of 3 km and a vertical short axis of 1.5 km. The simulated FDZ volume (with the major fault plane at its centre) measures 1 km horizontally ( y direction) parallel to the major fault trend, 150 m in the vertical direction (z direction), and is 80 m thick (x direction). This study is concerned with the characteristics of flow across the FDZ on both sides of the major fault, i.e. within two 40 m wide regions. As these two sides of the major fault are statistically similar, it is sufficient to investigate results from only a single side.

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Fig. 2. 2D cross-sections across an FDZ with D3 ¼ 2, perpendicular to the major fault for different strike and dip distribution standard deviations (s): (a) synthetic dip orientation model, horizontal cross-sections; (b) synthetic dip orientation model, vertical cross-sections; (c) antithetic dip orientation model, vertical cross-sections. A region of the FDZ has been highlighted and the closer view reveals the sub-clustering that is a feature of the hierarchical spatial distribution.

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Table 1. Fault damage zone model parameters Fault attributes Maximum fault length, lmax Minimum fault length, lmin Major fault Aspect ratio Model domain (x, y, z) Power-law exponent, D3 Major axis plunge angle Fault thickness to length ratio Orientation distribution

Geometrical characterization The structure of the FDZ can be examined by 2D horizontal and vertical cross-sections, perpendicular to the major fault. From these cross-sections one can identify regions where the faults are very densely or very sparsely packed, reflecting the spatial clustering characteristics of the particular subregions. Figure 2(a, b) shows examples of horizontal and vertical cross-sections perpendicular to the major fault, for half of the FDZ, using two different standard deviations for the strike and dip distributions (the effects on the strike population can be observed in Fig. 2a; the effects on the dip population are evident in Fig. 2b). The fault population here is obtained for the fault length–frequency exponent D3 ¼ 2 when the number of faults in the population is N ¼ 3:6 million and a synthetic dip orientation model is used. Figure 2c represents the same FDZ parameters as in Fig. 2b except that the antithetic dip orientation model is employed. The use of the dip of the major fault and the dips at +308 to this direction is clearly apparent for a dip standard deviation of 58, but it is more difficult to identify the main dip directions when this standard deviation is increased to 108. It is expected that the fault arrangement in the latter case will form a more efficient barrier to the flow across the region. Over the range of FDZ model parameters used in this paper, the synthetic dip orientation models are generally likely to create a more efficient barrier to flow. A region of the FDZ has also been highlighted in Figure 2b, and the closer view demonstrates the sub-clustering feature of the hierarchical spatial distribution of subseismic faults. The influence of the power law exponent on the geometrical characteristics of the FDZ was presented by Odling et al. (2005), and it can be observed that as D3 increases, i.e. the proportion of small to large faults increases, the fault

Value 1500 m 2.5 m Length 3000 m, throw 30 m Gaussian: mean 2, standard deviation 0.05 80 m 1000 m 150 m 1.6 to 2.4 08 1:104 Strike: standard deviation 58, 108, 158 Dip: standard deviation 58, 108, 158 Synthetic and antithetic dip orientation models

connectivity decreases and individual fault clusters can be more clearly identified, so that the bulk permeability would be expected to decrease.

Flow modelling with faults as partial flow barriers Flow through either 2D or 3D subregions of the stochastic FDZ model is simulated using a control volume, discrete fault, steady-state flow model on a regular grid for single-phase flow in porous rocks with faults as partial flow barriers. The 2D version of this discrete fault flow model (DFFM) was described in detail in Odling et al. (2004) and used to characterize some 2D upscaled flow properties. In this 2D version, both the faults and the rock matrix are discretized onto a fine regular square grid, with the aim of faithfully reproducing the topology of the fault network, and automatic checks are made to ensure that the connectivity of the network is preserved. Odling et al. (2004) provide a detailed 2D study of the influence of power law exponent, sample size and spatial distribution on the statistics of bulk permeability. The model has been extended here to 3D, where there are more possible flow pathways and therefore more chances to find high-permeability routes through the fault network, so it might be expected that the 2D flow modelling will tend to underestimate the bulk permeability. A comparison of 2D and 3D bulk permeabilities is provided later in this article. It is necessary to assess the 3D upscaled flow properties of regions containing large numbers of faults acting as partial barriers to fluid flow, and to analyse the significance of obtaining these 3D properties as opposed to the analogous 2D properties. Some preliminary results from the 3D DFFM model were reported in Vaszi et al. (2004) and Harris et al. (2005). Combined with the stochastic model for generating the 3D FDZ model, the

3D UPSCALING OF FAULT DAMAGE ZONES

DFFM is an essential tool for assessing the impact of complex fault networks on flow and determining upscaled properties of grid cells that would be included within a large-scale reservoir simulation package.

The discrete fault flow model (DFFM) For the flow of an incompressible fluid, the mass balance equation in the steady-state situation, for the elementary control volume around the node ði, j, kÞ (see Fig. 3a) is written as follows:

where Dx; Dy and Dz are the cell sizes in the x, y and z directions, respectively, m is the fluid viscosity, p(x, y, z) is the fluid pressure field and kx , ky and kz are the components of the local orthotropic permeability tensor. The subscripts on the flux terms in Equation 1 describe the boundary of the control volume over which the flux applies, so that, for example, the interfaces in the x direction for the control volume around the node (i, j, k) occur at (i 1=2, j, k) and (i þ 1=2, j, kÞ (see Fig. 3). At these interfaces, the fluxes in the x direction from Equation 2 are approximated using central finite differences as follows: qxi1=2, j, k ¼ kxi1=2, j,k

(qxiþ1=2;j;k qxi1=2;j;k ) (1)

þ (qyi;jþ1=2;k qyi;j1=2;k ) þ (qzi, j,kþ1=2 qzi;j;k1=2 ) ¼ 0,

where qx , qy , and qz are the flow fluxes in the positive x, y and z directions, respectively, and, if the flow in both the host rock and the fault rock is assumed to be laminar, then these fluxes are defined according to Darcy’s law as follows: qx ¼

kx DyDz @p ky DxDz @p , qy ¼ , m @x m @y

qz ¼

kz DxDy @p , m @z

(a)

359

(2)

qxiþ1=2, j,k

DyDz pi, j, k pi1, j, k , m Dx

(3)

DyDz piþ1, j,k pi, j, k , ¼ kxiþ1=2, j,k m Dx

and the fluxes in the y and z directions are approximated using similar expressions. The permeabilities kxi1=2, j,k and kxiþ1=2, j, k are defined on a permeability grid, the 2D representation of which is shown in Figure 3b. Thus, for example, kxiþ1=2, j, k represents the permeability of the region iDx x (i þ 1)Dx, ( j 1=2) Dy y ( j þ 1=2) Dy, (k 1=2) Dz z (k þ 1=2)Dz, and the permeability of such a region is calculated by taking the harmonic mean of the permeability of the host rock and fault rock within the region (Muskat 1937; Pickup et al. 1995). The fault rock within a region is calculated

(b) +

+

+

+

−

+ −

−

+ −

−

−

Fig. 3. A 2D (layer k) illustration of (a) the control volume around the node (i, j, k), and (b) the permeability grid.

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by discretizing the faults along the grid lines parallel to the x, y and z directions. For each grid line segment, a certain fault volume is assigned according to the thickness of the fault at the crossing location, and the corresponding permeability is defined as a (thickness) weighted harmonic mean permeability of the host rock and fault rock material. A correction must be made according to the orientation of the fault with respect to the grid and the representation of the fault as a ‘staircase’ of grid elements. The application of the correction ensures that the fault volume is conserved, i.e. the fault volume considered in the discretized region accurately approximates the original fault volume within the region. As we are concerned with the flow across the FDZ, perpendicular to the trend of the major fault, we employ the classical approach and enforce a constant global pressure gradient in the x direction, with the pressure fixed at the left- and right-hand side boundaries to pl and pr (, pl ), respectively, and no-flow conditions on the other faces of the domain. This equation system for the pressure field (linear system; five-point scheme), with the corresponding boundary conditions, is solved using the conjugate gradient method (Shewchuk 1994). Once the pressure field is obtained, the flow field can be determined using the local permeabilities. Thus, based on the total steady-state flow across a domain corresponding to a subregion of the FDZ, the equiv x in the direction of the alent (bulk) permeability K applied pressure gradient can be determined. The results presented in this article have been based on single-phase flow in a material with constant and homogeneous isotropic permeabilities kf and km for the host rock and fault rock, respectively, although the flow model could be easily adapted for more general situations. Thus, the fault to matrix permeability contrast provides a further control parameter, and a value of the permeability ratio kf =km ¼ 104 is representative of the permeability ratio commonly found between deformation bands and their host rock (Antonellini & Aydin 1994; Taylor & Pollard 2000; Fisher & Knipe 2001).

Analysing the geometric characteristics and bulk properties of subregions from the FDZ model The FDZ models have been inspected by means of 1D samples, e.g. the cumulative frequency of the fault thicknesses and frequencies along simulated cores (Harris et al. 2003), and 2D cross-sections, e.g. the distribution of fault traces (Harris et al. 2003, 2005; Odling et al. 2004, 2005; Vaszi et al. 2004). The characteristics of the FDZ can also be investigated by applying the DFFM to subregions

of the model. Thus we can observe geometrical properties, such as the fault rock volume or fault density, or properties obtained from the flow modelling, such as the bulk permeability, the flow path length of a fluid particle, the FDZ ‘efficiency’ as a barrier to flow, and the ‘effective’ fault rock throw to thickness relationship for FDZs. This section we briefly discusses these geometrical and flow properties as preparation for the sensitivity and simulation studies of the parameter inputs to the stochastic FDZ and DFFM models that follow.

Upscaling permeability The limitations of computer hardware still generally restrict reservoir simulator grids cell sizes to be significant larger than the fine-scale geological details that a geologist would ideally like to represent. The methodologies for upscaling this fine-scale structure to provide representative permeabilities on the scale of reservoir simulator grid cells remain a topic of intensive research (e.g. Sanchez-Vila et al. 1995; Kumar et al. 1997; Renard & de Marsily 1997; Jourde et al. 2002). The accurate reproduction of the flow behaviour within a grid cell requires the in situ boundary conditions of the cell, but the accurate determination of these (Almeida et al. 1996) is computationally very intensive. The classical approach of applying a constant pressure gradient parallel to the flow direction and no-flow conditions on the remaining boundaries provides only the scalar bulk permeability in this direction and considers the block in isolation. This method of upscaling has been used for faults and FDZs (Caine & Forster 1999; Flodin et al. 2001; Jourde et al. 2002) and it is this classical method of upscaling that has been applied in this article. x was The calculation of the bulk permeability K described in the previous section.

Subsampling of the fault models for input to the DFFM The stochastic FDZ models must be subsampled to provide input to the DFFM, and a large subset of the whole domain will be assessed to derive representative properties and their ranges. Unless otherwise stated, the subregions are cuboids of (x, y, z) dimensions 40 m 50 m 20 m. The major fault has been omitted from each subregion so that the effects of the FDZ, and the parameters that control its internal architecture, alone can be investigated.

Fault damage zone efficiency An estimate of bulk permeability from line sample data (e.g. Antonellini & Aydin, 1994, 1995; Shipton et al. 2002) can simply be obtained by

3D UPSCALING OF FAULT DAMAGE ZONES

calculating the (weighted) harmonic mean of the fault rock and matrix permeabilities. In 2D or 3D, this concept is analogous to replacing the fault rock in an area or volume by a single fault of uniform thickness that spans the region and is oriented perpendicular to the flow. The immediate DFFM outputs are the bulk per x of the region and the volume of the meability K fault rock within the sampled domains. From this fault rock volume we can estimate the ‘efficiency’ of the FDZ, which is defined relative to the upscaled permeability kx that would be obtained for a single fault of the same volume having a uniform thickness, spanning the whole region, and perpendicular to the pre-defined flow direction. In this simple representation, kx can be approximated by the harmonic mean of the fault rock and the matrix permeabilities (Muskat 1937; Pickup et al. 1995): A a Aa kx ¼ kf þ km ,

(4)

where a is the uniform thickness of the fault and A is the length of the subregion in the pre-defined flow direction. In this configuration the fault rock is being utilized in the most efficient way (100% efficient) as a flow barrier perpendicular to the fault, but this underestimates the bulk permeability as it assumes unidirectional flow; in reality the flow is tortuous and the result of a complex interplay between the FDZ topology and the fault rock thickness. First Equation 4 is transformed into the following form:

1 a 1 kx =km 1 ¼ A kf =km

1 :

(5)

When kx is replaced by the observed bulk per x in Equation 5, we define the a% effimeability K ciency level by taking a proportion of the single uniform fault thickness a, that is, 1 a a 1 x =km 1 ¼ 100 A kf =km 1 : K

(6)

The FDZ efficiency was first derived by Odling et al. (2004), and for 2D flow perpendicular to the major fault the FDZ is approximately 50% efficient, with minimal variation due to the power-law length exponent. The proportion of fault rock can also be determined from line samples such as cores and bore-hole logs, information that it is possible to obtain from hydrocarbon reservoirs and aquifers (e.g. Hesthammer et al. 2000; Shipton et al. 2002).

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Fault damage zone flow pathways Flow pathways through the FDZ can be simulated from the high- to the low-pressure boundary of the subregion, based on the flow velocity field. Then the number of faults crossed, the fault rock thickness, and the length of each flow pathway can be recorded. The data reported here are mean values based on a set of fluid particle pathways originating from points evenly distributed over the highpressure boundary of the subregion. Generally, if kf =km is very small then cross-fault flow is inefficient and flow pathways become very tortuous, attempting to reduce the total fault rock thickness encountered. On the other hand, if kf =km is larger, say of order 1022, then the flow pathways are likely to be straighter, and may only be influenced by the thicker faults. In Figure 4 we present some 3D visualizations from the new models of flow through some 50 m cubic subregions of the FDZ for examples of both low and higher fault densities. The influence of the faults on the flow is clear in Figure 4a, with the flow pathways striking a balance between routes that are optimal for crossing the faults and routes that are not too tortuous. Although Figure 4b is still a relatively low-density model, the flow pathways have become more tortuous and it becomes harder to visualize the flow pathways.

Fault damage zone ‘effective’ throw to thickness ratio An important summary property for characterizing the FDZ is the ‘effective’ fault throw to thickness ratio. Given a large-scale (seismic-scale) fault, the surrounding FDZ will provide an additional retardation to cross-fault flow, thus increasing the fault rock thickness that must be traversed through the FDZ and increasing the apparent thickness of the original major fault. The purpose of this property is to assess this additional contribution of the FDZ. For the new results presented in this article, we have assumed that the fault throw to thickness ratio is 100:1 for every individual fault in the domain, and determined the variation in this additional contribution using the DFFM and the resulting flow pathways through subregions up to the major fault (i.e. the major fault is omitted in the DFFM) for different control parameters in the FDZ model. As we shall show later, these results can be scaled for different subseismic fault throw to thickness ratios, and could be applied in cases when the major fault has a different ratio in comparison to the subseismicscale faults.

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Fig. 4. Flow pathways (red lines starting from the indicated white source line) through 50 m cubic subregions of the FDZ for (a) low densities of faults and (b) higher densities of faults, and visualised in Iris Explorer. The colour scale of the faults is in the range from green to purple, corresponding to faults of increasing size. In (b; left) the pathways are hard to distinguish from the faults, but in (b; right) the visualisation of the pathways alone shows that they are already much more tortuous than in (a).

Sensitivity study of the DFFM and FDZ model control parameters

fault length lmin has on the upscaled flow properties is also investigated.

This section, presents a new analysis of the sensitivity of the upscaled flow properties to the chosen values of a number of input parameters. In particular, we first investigate the extrapolation of the fault rock thickness values along flow pathways for a range of fault thickness to length ratios, as a function of the fault to matrix permeability ratio kf =km and the power-law exponent D3. The typical fault density along a horizontal core through the FDZ and the influence that the minimum modelled

Scaling of the fault rock thickness The issue of whether the fault rock thickness observed along the flow pathways can simply be scaled over a range of fault thickness to length ratios can be investigated by comparing the results obtained by re-running the DFFM against those predicted by the following simple extrapolation technique. For precisely the same fault length, orientation and spatial distributions (i.e. exactly

3D UPSCALING OF FAULT DAMAGE ZONES

the same FDZ topology), the DFFM has been used to predict this fault rock thickness based on various values of the fault thickness to length ratio. For the same range of fault thickness to length ratios, and based on the results obtained for a fault length to thickness ratio of 104 from a single run of the DFFM, the extrapolation procedure is based on forcing the flow to follow the same pathways and scaling the observed fault rock thickness according to the new fault thickness to length ratio. Figure 5 shows typical results for the variation in the mean fault rock thickness on flow pathways, for the power law exponent D3 ¼ 2 and for fault to matrix permeability ratios of kf =km ¼ 103 , 104 and 105 . The continuous lines show the results when obtained directly by re-running the DFFM model, whilst the dashed lines show extrapolated results from those obtained for the fault length to thickness ratio 104. All of the modelled and extrapolated results match very well, with only a slight loss of agreement as D3 increases and the ratio kf =km decreases (the faults become much less permeable relative to the host rock), so the fault rock thickness on the flow pathways through sample 3D subregions can be reliably scaled, at least for fault length to thickness ratios in the range 4103 to 2104 .

Fault damage zone characteristics in relation to the smallest faults modelled It is important to examine the fault rock thickness and the number of faults crossed when sampling simulated horizontal cores (perpendicular to the major fault) through the FDZ. Other characteristics are also of interest along these cores, such as the fault spatial distribution or the cumulative frequency of the fault thicknesses. The minimum fault length defined in the FDZ model is typically lmin ¼ 2:5 m, and thus smaller faults than this are not accounted for. Consider a fault population with D3 ¼ 2, fault strike and dip standard deviations of 108, and the synthetic dip orientation model. We now create different FDZ models for the cases of lmin ¼ 1 m, 1.5 m, 2.5 m and 10 m with the property that when fault of length 1–1.5 m are removed from the first model we have precisely the model for lmin ¼ 1:5 m, and similarly for lmin ¼ 2:5 m and 10 m. The corresponding numbers of faults in the model are 11.25 million (lmin ¼ 1 m), 5 million (lmin ¼ 1:5 m), 1.8 million (lmin ¼ 2:5 m) and 112 500 (lmin ¼ 10 m). Along horizontal cores near to the major fault centre, approximately 160 faults are encountered for lmin ¼ 2:5 m, and this increases by 8 –13% for lmin ¼ 1:5 m but with a negligible (0.15–0.25%) increase in the observed fault rock thickness. As lmin decreases from 2.5 m to 1 m, we observe

363

(a)

(b)

(c)

Fig. 5. The scaling of fault rock thickness on flow pathways with the fault length to thickness ratio. The continuous and the dashed lines show results obtained directly by the DFFM model and extrapolated results, respectively, for D3 ¼ 2 and (a) kf =km ¼ 103 , (b) kf =km ¼ 104 and (c) kf =km ¼ 105 .

15 –22% more faults but only a 0.3–0.45% increase in fault rock thickness. As lmin increases from 2.5 m to 10 m, the number of faults observed decreases by 31 –36% and the decrease of 1.3–2% in the fault rock thickness is more significant. Thus, the effect of including smaller faults in the model

S. D. HARRIS ET AL.

(a) 1000

0.1 m

Cumulative frequency

(when lmin ¼ 1:5 m and 1 m) is to increase vastly the computational effort, but to produce only negligible changes in the fault rock thickness observed along horizontal core lines. Figure 6 shows the cumulative frequency plots of the fault thicknesses observed along these horizontal traverses for lmin ¼ 1 m (solid line), 2.5 m (dashed line) and 10 m (dotted line), and for D3 ¼ 1:6 and 2. The vertical lines on the graphs correspond to the maximum fault thickness that would be observed for faults of length below the lmin values of 2.5 m, 1 m and 0.1 m. Thus, for example, the cumulative frequency distribution for lmin ¼ 2:5 m only shows meaningful values for fault thicknesses above the 2.5 m line, as below it the cumulative frequency is affected by faults that have not been modelled. The line at 0.1 m corresponds to the typical minimum fault throw of 1 mm that is often measured in the field. Although computational limitations may prohibit the modelling of faults down to this size, it is of interest to predict the fault numbers that would be obtained on horizontal traverses, and this can be estimated from the plots in Figure 6 by extrapolating the trend of the cumulative frequency. For D3 ¼ 2 the number of faults predicted by this approach is approximately 300 faults (of observed throw at least 1 mm; based on 1.8 million faults modelled). The number of faults in the model for lmin ¼ 2:5 m can be increased and if 3.6 million faults are modelled then approximately 600 faults are observed along the simulated core, and this agrees with typical observations for a 30 m offset fault. For D3 ¼ 1:6 the larger faults dominate on the horizontal traverses and the observed fault frequencies are less affected by the choice of lmin. If 2.4 million faults are modelled for D3 ¼ 1:6 then approximately 400 faults are observed along the simulated core. To further validate the choice for lmin, the contribution of the small faults to the observed fault rock thickness along a flow pathway rather than along simulated horizontal cores was assessed. From the information recorded along these flow pathways, we can calculate the percentage of the faults smaller than a given length relative to the total number of faults encountered on the flow pathway, and the percentage of the fault rock thickness derived from the faults smaller than a given length as a proportion of the total fault rock thickness on the flow pathway. For the D3 ¼ 2 model described above with lmin ¼ 2:5 m, and for a subregion near to the centre of the domain, these percentage plots are presented in Figure 7. The various lines are for results obtained using different strike and dip standard deviations (58, 108 and 158) and fault to matrix permeability ratios (1023, 1024 and 1025), although the difference between these nine lines is not significant and it is the power-law

1m 2.5m

100

10

1

100

Fault rock thickness [m]

(b) 1000 0.1 m

Cumulative frequency

364

1m 2.5m

100

10

1

100

Fault rock thickness [m]

Fig. 6. Cumulative frequency of fault rock thickness along horizontal cores for (a) D3 ¼ 1:6 (1.2 million faults for lmin ¼ 2:5 m), and (b) D3 ¼ 2 (1.8 million faults for lmin ¼ 2:5 m), and based upon using lmin ¼ 1 m (solid line), 2.5 m (dashed line) and 10 m (dotted line). The vertical lines correspond to the maximum fault thickness that would be observed for faults of length below the lmin values of 2.5 m, 1 m and 0.1 m, based on a fault length to thickness ratio of 104. The fault strike and dip standard deviations are 108, and the synthetic dip orientation model has been used.

exponent that provides the largest control on the predictions of the small fault contributions to the observed fault rock thickness along the flow pathways. For D3 ¼ 1:6, 2 and 2.4, respectively, the faults smaller than 10 m in length make up for approximately 0.5%, 2– 3% and 5–8% of the total fault rock thickness on the flow pathway, although they also make up for approximately 20%, 30 – 40% and 45 –55% of the total number of faults on the flow pathway. This observation is independent of the standard deviation of fault strike and dip and the fault to matrix permeability contrast. The contribution of small faults to the observed fault rock thickness diminishes further as smaller cut-off values are considered, indicating that the

3D UPSCALING OF FAULT DAMAGE ZONES

365

Fig. 7. (a) The percentage of faults smaller than a given length, l, to the total number of faults on a flow pathway, and (b) the percentage of fault rock thickness from faults smaller than a given length, l, to the total fault rock thickness on a flow pathway, for D3 ¼ 2 and the synthetic dip orientation model. The various lines are for results obtained using different strike and dip standard deviations (s ¼ 58, 108 and 158) and fault to matrix permeability ratios (kf =km ¼ 103 , 1024 and 1025).

choice of lmin ¼ 2:5 m provides an accurate approximation. Thus, from the observations in this section, it is appropriate to set the size of the smallest modelled fault in the population to be lmin ¼ 2:5 m.

Geometric characteristics and bulk properties of subregions from the FDZ Results on the geometric characteristics and upscaled flow properties of various subregions of the FDZ model are discussed as functions of the DFFM and FDZ control parameters. In particular, this section considers the effect of the fault to matrix permeability contrast and the subregion height (2D versus 3D) on the bulk permeability, flow pathway length, fault rock thickness and FDZ ‘efficiency’ over different ranges of the parameters that define the FDZ.

The influence of the fault to matrix permeability contrast x =kf of the bulk perThe variation in the ratio K meability to the fault permeability with the

prescribed fault to matrix permeability ratio kf =km is presented in Figure 8 for the range kf =km ¼ 103 to 1026 and for FDZ models based on the power-law exponents D3 ¼ 1:6, 2 and 2.4, a standard deviation of 108 for the strike and dip distributions and the synthetic dip orientation model. As the fault to matrix permeability contrast increases (i.e. the permeability ratio kf =km reduces from 1023 to 1026) that this normalized bulk permeability appears to approach a constant value; that is, as expected, the primary control on the bulk permeability value is the fault permeability as the faults become very low-permeability barriers to flow. The constant value that is approached foreach value of D3 is due to the geometrical characteristics of the FDZ. As D3 increases, the proportion of small faults in the FDZ increases and, as we shall see below, the flow pathways through subregions become more tortuous and less fault rock thickness is encountered along these pathways; this results in an increase in the constant value that is approached in Figure 8. A good estimate can therefore be obtained for the bulk permeability when the fault to matrix permeability ratio is lower than 1025.

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(a)

(b)

(c)

pathway that either avoids the faults or is not influenced by the faults. The corresponding fault rock thicknesses along the flow pathways are shown in Figure 10. At the locations of the subregions of the FDZ models, the major fault would contribute approximately an additional 0.3 m of fault rock (depending on the precise location of the subregion relative to the centre of the major fault). For all three power-law exponents, the flow pathway lengths increase with increasing fault to matrix permeability contrast (decreasing ratio kf =km ), and the rate of this increase is higher for larger values of D3 (Fig. 9). Thus the largest pathway lengths are found for D3 ¼ 2:4 and kf =km ¼ 106 ; this can be explained by the larger proportion of small faults in the population compared to D3 ¼ 1:6, so that, depending on factors such as the connectivity of the subseismic fault array, the flow pathways can follow more tortuous routes across the domain to avoid the very low permeability fault rock. Conversely, this dominance of the small faults for D3 ¼ 2:4 leads to slightly shorter flow pathways compared to the D3 ¼ 1:6 case when kf =km ¼ 103 , as then the small thin faults are less significant in impeding the flow in comparison to the larger faults, and the flow pathways seem to follow an almost straight-line route across the subregions. The pathway lengths not only increase with increasing fault to matrix permeability contrast, but they also vary over a larger range, and so there is a large uncertainty in the flow pathway length when the faults are very low permeability barriers to flow due to the precise

Fig. 8. The ratio of the bulk permeability to the fault permeability as a function of the fault to matrix permeability ratio for (a) D3 ¼ 1:6, (b) D3 ¼ 2, and (c) D3 ¼ 2:4. The fault strike and dip standard deviations are 108, and the synthetic dip orientation model has been used.

Flow pathway length [m]

110 100 90

D3 = 1.6 D3 = 2 D3 = 2.4

Maximum Mean Minimum

80 70 60 50 40 Fault to matrix permeability ratio

Statistical data, based on a set of subregions for each FDZ model and a set of flow pathways originating from locations distributed evenly over the high-pressure boundary of each subregion, on the flow pathway lengths is plotted in Figure 9. The domain is 40 m wide in the x direction, and thus a pathway length of 40 m constitutes a direct

Fig. 9. Observed statistical data (the range and mean) on the flow pathway length as a function of the fault to matrix permeability ratio for D3 ¼ 1:6, 2 and 2.4. A direct route across the subregion has a pathway length of 40 m. The fault strike and dip standard deviations are 108, and the synthetic dip orientation model has been used.

3D UPSCALING OF FAULT DAMAGE ZONES

Fault rock thickness [m]

(a) 1.375

Maximum

1.350

Minimum

1.300 1.275

Fault to matrix permeability ratio

(b) Fault rock thickness [m]

reflected in the fault rock thickness values obtained, and the fault rock thickness on the flow pathways decreases rapidly as D3 increases.

Mean

1.325

1.250

0.825 0.800 0.775 0.750 0.725 Fault to matrix permeability ratio

(c) Fault rock thickness [m]

367

0.400 0.375 0.350 0.325 0.300 0.275 Fault to matrix permeability ratio

Fig. 10. Observed statistical data (the range and mean) on the fault rock thickness on flow pathways as a function of the fault to matrix permeability ratio for (a) D3 ¼ 1:6, (b) D3 ¼ 2, and (c) D3 ¼ 2:4. The fault strike and dip standard deviations are 108, and the synthetic dip orientation model has been used.

subseismic fault configurations controlled by the FDZ orientation and spatial distribution variations. The fault rock thickness on the flow pathways (Fig. 10) shows less variation with the fault to matrix permeability contrast, with the mean value decreasing only slightly as the permeability ratio kf =km reduces. This is due to the fact that a large proportion of the fault rock thickness is made up from the large faults or connected fault arrays, and the more isolated small faults that cause the flow pathways to be more tortuous and longer for a large fault to matrix permeability contrast only constitute a small proportion of the fault rock thickness encountered. The proportions of smaller versus larger faults for different values of D3 is further

Upscaled properties from two- versus three-dimensional modelling A characterization study of the FDZ model by means of the upscaled properties of 2D subregions was undertaken by Odling et al. (2004). The aim of this section is to investigate the effects of extending the DFFM from 2D to 3D. A number of upscaled properties have been analysed from this perspective. When a stochastically-generated FDZ is created, for comparison purposes the various upscaled properties of the sample regions in the FDZ can be examined as 1D, 2D or 3D properties. Thus we can assess the influences of the model parameters on the predicted upscaled properties, and determine situations when it is essential to consider 3D flow or when 2D flow predictions are adequate. For this study the FDZ is based on D3 ¼ 2:4, a standard deviation of 108 for the strike and dip distributions and the synthetic dip orientation model, and a fault to matrix permeability ratio of 1024 has been used. Sample cuboidal subregions of (x, y, z) dimensions 25 m 50 m hz have been considered at various location in the FDZ domain, where hz is the height of the subregion. For a small value of hz (hz ¼ 0:1 m) an approximation of the 2D properties is found, and then this 2D domain can gradually be ‘grown’ into 3D by considering the subregion heights hz ¼ 1m, 20 m and 50 m. Comparing Figures 11a and b shows that the maximum fault rock thickness in the corresponding domains increases, whilst the fault rock thickness on the flow pathways decreases as the flow has more freedom in crossing the domain and can choose paths that encounter less fault rock. The effect of increasing spatial freedom with increasing domain size is also illustrated by the mean length of the flow pathways across the flow domain (see Fig. 11c; note that a 25 m pathway would constitute a direct pathway across the subregion), which steadily increases with the size of the domain. As an immediate consequence of the results in Figures 11a and 11c, the bulk permeability (Fig. 11d) increases as the subregion grows in height. The trend observed in the efficiency variation (Fig. 11e) is that it decreases as the domain height increases, and this is generally expected as larger domains would form less effective barriers to the flow through them due to the increased freedom to find efficient flow pathways, and spatial variations in the fault array leading to an increased chance for the appearance of areas with

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(a)

(b)

(c)

(d)

(e)

Fig. 11. An investigation of the upscaled properties from 2D and 3D modelling, using a cuboidal subregion of (x, y, z) dimensions 25 m 50 m hz that is located near to the centre of the major fault and whose height hz increases. Summary plots are provided for (a) the mean fault rock thickness on flow pathways, (b) the thickness of a single fault of uniform thickness spanning the domain perpendicular to the flow direction and of the same volume as the fault array in the domain (maximum fault rock thickness), (c) the mean flow pathway length, (d) the ratio of the bulk permeability to the matrix permeability, and (e) the efficiency of the fault array as a barrier to flow. Here D3 ¼ 2:4, kf =km ¼ 104 , the fault strike and dip standard deviations are 108, and the synthetic dip orientation model has been used.

a reduced flow impeding effect. In general, it is not possible to identify a single cause for the efficiency decrease as the efficiency is defined as a combination of a number of factors. In fact, in a minority of situations (different FDZ and DFFM control parameters) the efficiency may not decrease as in

Figure 11e, and the topology of the fault array may be a significant factor in influencing the behaviour of these bulk properties for subregions. For D3 ¼ 1:6 the fault rock thickness along the flow pathways shows very little variation with the fault to matrix permeability ratio kf =km for the

3D UPSCALING OF FAULT DAMAGE ZONES

same domain height hz . This is due to the dominating influence of large faults in the population in terms of the fault rock thickness; these faults are likely to span the domain and thus cannot be efficiently avoided by the flow. The most significant variation in the fault rock thickness observed will be due to spatial heterogeneities in the FDZ as the domain height increases. For a larger power-law exponent, say D3 ¼ 2:4, the fault rock thickness crossed along the flow pathways varies less with the fault to matrix permeability contrast in the 2D approximation (hz ¼ 0:1 m) in comparison to the fully-3D flow case (hz ¼ 50 m). This demonstrates the influence of the large proportion of relatively small faults in the population, so that for a larger value of the fault to matrix permeability contrast these small faults can be more efficiently avoided in 3D in comparison to 2D by the flow through the subregions. Based on observations over a range of FDZ and DFFM control parameters, it can be concluded that considering the bulk permeability (and hence the fault rock thickness along the flow pathways and the FDZ efficiency) as a 3D rather than a 2D property becomes more important as the power-law increases from D3 ¼ 1:6 to 2.4, and there may be as much as a 50% increase in this value.

Summary results on the upscaled properties of the FDZ by varying the control parameters The 3D upscaled flow properties of FDZs were investigated by creating a series of summary plots for the prediction of the upscaled properties, such as the bulk permeability, flow pathway lengths, the observed fault rock thickness, the efficiency of the FDZ, and the ‘effective’ throw to thickness ratio. The ‘effective’ throw to thickness ratio can be used to provide an input to a reservoir simulator in the form of a modifier to the mapped single fault thickness that additionally includes the influence of the FDZ. The results are drawn from the database of DFFM results that were based on specified realistic ranges of the FDZ and DFFM control parameters, namely, the fault length–frequency power-law exponent D3 , the strike and dip standard deviations, the dip orientation model, the FDZ spatial properties, the fault to matrix permeability contrast, the fault density and the fault length to thickness ratio (scalable). For this purpose a number of subregions (cuboids of (x, y, z) dimensions 40 m 50 m 20 m; note that only one half of the FDZ, on one side of the major fault, is examined) have been sampled along the major fault

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within the FDZ, thus corresponding to different throw values over the range 20 –30 m. In order to illustrate the general trend observed for the fault rock thickness, Figure 12 shows the mean fault rock thickness along the flow pathways for the three power-law exponents D3 ¼ 1:6, 2 and 2.4, and for fault strike and dip standard deviations of 58, 108 and 158. The results are presented for a subregion located near to the major fault centre (a throw of approximately 30 m), but the observed behaviour is similar at other locations from the domain. In Figures 12 to 14, the thin and thick lines denote results for two different fault densities (low and high, respectively, fault density models), whereas the solid and dashed lines are for the synthetic and antithetic dip orientation models, respectively. The statistical behaviour of the fault rock thickness along the flow pathways, namely, the minimum, the mean and the maximum fault rock thicknesses, is further demonstrated in Figure 13 over varying throws (i.e. different subregions from the FDZ, so a throw range of 20–30 m; again, the three power-law exponents D3 ¼ 1:6, 2 and 2.4, and fault strike and dip standard deviations of 58, 108 and 158 are examined). As expected, Figures 12 and 13 demonstrate that the fault rock thickness decreases rapidly with increasing powerlaw exponent, and on average the high fault density models result in a larger fault rock thickness (the low fault density models do generally result in a smaller fault rock thickness, but there are exceptions caused by the statistical distribution of the faults along the length of the major fault). There is also a general trend of decreasing mean fault rock thickness when the standard deviation of the strike and dip distribution is increased from 58 to 158. This is probably due to the fact that for a standard deviation of 58 the faults are nearly parallel, and thus it is more likely that the flow has to cross most of the larger faults, whereas for a standard deviation of 158 there is an increased likelihood of the flow pathways avoiding faults and following a tortuous route through the subregion. In Figure 14 the ‘effective’ fault throw to thickness relationship in the FDZ is investigated for the three power-law exponents D3 ¼ 1:6, 2 and 2.4. This ‘effective’ fault throw to thickness is calculated by using the mean fault rock thickness observed on the flow pathways through subregions (the ‘additional’ FDZ thickness) and the thickness of the major fault at the corresponding locations and allows us to express the total FDZ thickness (major fault plus ‘additional’ FDZ contribution) relative to the major fault throw. In the examples illustrated in this article, the ratio of the fault throw to thickness is 100:1 for every individual fault (and for each fault we assume a length to

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(a)

(b) 2.0 Fault rock thickness [m]

Fault rock thickness [m]

2.0 1.5 1.0 0.5 0.0 1.6 (c)

2.0 Power-law exponent, D3

2.4

1.5 1.0 0.5 0.0 1.6

2.0 Power-law exponent, D3

2.4

Fault rock thickness [m]

2.0 Dip model Synthetic Antithetic

1.5 Fault density 1.0

Low High

0.5 0.0 1.6

2.0 Power-law exponent, D3

2.4

Fig. 12. The mean fault rock thickness (along flow pathways) near to the major fault centre for fault strike and dip standard deviations of (a) 58, (b) 108, and (c) 158. The thin and thick lines denote results for two different fault densities (low and high, respectively, fault density models), whereas the solid and dashed lines are for the synthetic and antithetic dip orientation models, respectively.

throw ratio of 100:1), although these results could be readily scaled for different ratios (as already demonstrated in this article). It is observed that the effective throw to thickness ratio varies over a large range for the complete set of control parameters, namely, on a scale of about 10:1 to 80:1, and it largely depends on the power-law exponent D3 . Values of 10:1 to 20:1 are obtained for D3 ¼ 1:6, which signifies the larger amount of fault rock as opposed to the case for D3 ¼ 2:4, when the ratio varies from about 40:1 to 80:1. Some of the observations discussed previously are also evident in Figure 14, namely, the general increase in the mean effective throw to thickness ratio as either the strike and dip standard deviations increase or the fault density increases.

Summary and conclusions The key observations from the results of this study can be summarized as follows.

(i) The stochastic FDZ model representing a fault with a throw of 30 m, in which a hierarchical clustering scheme is implemented, produces fault frequencies that are consistent with core and outcrop data of faults in poorly consolidated siliclastic sandstone with displacements of around 30 –40 m. (ii) The DFFM applied to discretized stochastic FDZ subregions gives an accurate flow representation for complex FDZ models incorporating high densities of faults, and can be used to analyse the upscaled properties of these FDZs. (iii) The bulk permeability estimated from 2D flow modelling will underestimate the bulk permeability because in 3D there is greater freedom for the fluid to find the more favourable, high-permeability pathways. The 2D results tend to underestimate the 3D bulk permeability by up to 50%. (iv) The FDZ efficiency as a flow barrier is defined relative to that of a region with one

3D UPSCALING OF FAULT DAMAGE ZONES

2.0 Fault rock thickness [m]

Fault rock thickness [m]

2.0

371

1.5 1.0 0.5 0.0

1.5 1.0 0.5 0.0

1.6

2.0 Power-law exponent, D3

2.4

1.6

2.0 Power-law exponent, D3

2.4

Fault rock thickness [m]

2.0 Dip model Synthetic Antithetic

1.5 Fault density 1.0

Low High

Maximum Mean Minimum

0.5 0.0 1.6

2.0 Power-law exponent, D3

2.4

Fig. 13. The variation in the fault rock thickness (along flow pathways) over the throw range 20–30 m present within the FDZ for fault strike and dip standard deviations of (a) 58, (b) 108, and (c) 158. The thin and thick lines denote results for two different fault densities (low and high, respectively, fault density models), whereas the solid and dashed lines are for the synthetic and antithetic dip orientation models, respectively.

uniform-thickness spanning fault that contains the same proportion of fault rock, and is thus related to the FDZ connectivity and the tortuosity of potential flow pathways. Typically, the FDZ is 50% efficient for flow perpendicular to the major fault, and predictions of the bulk permeability can be made based on the proportion of fault rock (from core or well logs). (v) Predictions of the additional retardation provided by the FDZ relative to the major fault have been analysed through observations of the bulk permeability, the fault rock thickness on flow pathways across the FDZ, and the ‘effective’ fault rock throw to thickness ratio by using the DFFM to determine the flow pathways through a sequence of stochastic FDZ models over a range of model control parameters. According to the FDZ geometric and topological characteristics defined by the DFFM parameters and the hydraulic properties imposed, predictions of the proportion of fault rock that must be crossed have been presented. Most importantly, we have demonstrated that

the total fault zone thickness (together with some uncertainty around this prediction) must be predicted from the observed throw and applied in a reservoir-scale simulator to capture the effect of the FDZ rather than a single large-scale fault. (vi) A large sequence of 3D flow simulations has been run to chart the sensitivity of upscaled flow predictions to the DFFM and FDZ model control parameters, including the power-law exponent, the fault orientation parameters, the fault to matrix permeability contrast, the fault density and the fault throw to thickness ratio. This database of results allows simple summary predictions to be made that capture the FDZ complexity (e.g. the ‘effective’ throw to thickness ratio as a modifier to the mapped seismic-scale throw) and incorporate the additional retarding influence of the subseismic faults in the FDZ, when accounting for the connectivity, spatial distribution and clustering characteristics of these small-scale faults.

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(a)

(b)

-

-

(c)

Fig. 14. The variation in the ‘effective’ fault throw to thickness value over the throw range 20–30 m present within the FDZ for fault strike and dip standard deviations of (a) 58, (b) 108, and (c) 158. The thin and thick lines denote results for two different fault densities (low and high, respectively, fault density models), whereas the solid and dashed lines are for the synthetic and antithetic dip orientation models, respectively.

The research was carried out under the ITF BMFFFs project at RDR (Rock Deformation Research Ltd, School of Earth and Environment, University of Leeds, UK) and was sponsored by Amerada Hess, BG, BP, ConocoPhillips, DTI, Kerr McGee, Statoil, Shell and Total.

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Eastern Canadian Margin, Geological Association of Canada, St John’s, Newfoundland, Canada, Special Paper, 43, 129– 142. R ENARD , P. & DE M ARSILY , G., 1997. Calculating equivalent permeability: a review. Advances in Water Research, 20, 253– 278. R IPPON , J. H. 1985. Contoured patterns of the throw and hade of normal faults in the coal measures (Westphalian) of north-east Derbyshire. Proceedings of the Yorkshire Geological Society, 45, 147–161. R OBINSON , P. C. 1983. Connectivity of fracture systems – a percolation threshold approach. Journal of Physics, A, 16, 605– 614. S ANCHEZ -V ILA , X., G IRARDI , J. P. & C ARRERA , J. 1995. A synthesis of approaches to upscaling of hydraulic conductivities. Water Resources Research, 31, 867–882. S CHOWALTER , T. T. 1979. Mechanisms of secondary hydrocarbon migration and entrapment. Bulletin of the American Association of Petroleum Geologists, 63, 723–760. S HEWCHUK , J. R. 1994. An introduction to the conjugate gradient method without the agonizing pain. School of Computer Science, Carnegie Mellon University, Pittsburgh, PA. S HIPTON , Z. K. & C OWIE , P. A. 2001. Damage zone and slip-surface evolution over mm to km scales in highporosity Navajo sandstone, Utah. Journal of Structural Geology, 23, 1825–1844. S HIPTON , Z. K., E VANS , J. P., R OBESON , K. R., F ORSTER , C. B. & S NELGROVE , S. 2002. Structural heterogeneity and permeability in faulted eolian sandstone: implications for subsurface modelling of faults. Bulletin of the American Association of Petroleum Geologists, 86, 863–883. S ORKHABI , R. & T SUJI , Y. (eds) 2005. Faults, Fluid Flow and Petroleum Traps. American Association of Petroleum Geologists Memoir 85, Tulsa, OK. T AYLOR , W. L. & P OLLARD , D. D. 2000. Estimation of in situ permeability of deformation bands in porous sandstone, Valley of Fire, Nevada. Water Resources Research, 36, 2595– 2606. V ASZI , A. Z., H ARRIS , S. D. & K NIPE , R. J. 2004. 3D upscaling of fault damage zones for reservoir modelling. In: Proceedings of the 9th European Conference on the Mathematics of Oil Recovery, Paper A016. ECMOR IX, Cannes, France. W ALSH , J. J., W ATTERSON , J., H EATH , A. & C HILDS , C. 1998. Representation and scaling of faults in fluid flow models. Petroleum Geoscience, 4, 241 –251. Y IELDING , G., O VERLAND , J. A. & B YBERG , G. 1999. Characterization of fault zones for reservoir modeling: an example from the Gullfaks field, northern North Sea. Bulletin of the American Association of Petroleum Geologists, 83, 925–951.

The modelling of fractured reservoirs: constraints and potential for fracture network geometry and hydraulics analysis ¨ KEL G. H. MA A/S Norske Shell, Tankveien 1, N-4098 Tananger, Norway (e-mail: [email protected]) Abstract: The interconnectedness of a subsurface fracture system depends on five fracture and fracture set geometry characteristics: density, orientation, dimensions (height and length), connectivity and aperture. Orientation and density can be determined with some degree of accuracy but the uncertainty ranges associated with the other characteristics will be large. Calibration with dynamic indicators will bring out the hydraulic properties of the network and can help to reduce uncertainty in the geometric characteristics. The fracture network geometry in the interwell space can be described through geostatistical analysis but more commonly it is derived from seismic data, through edge detection or the analysis and calibration of seismic velocity anisotropy attributes or curvature analysis. Geomechanical analysis is necessary to evaluate the impact on network conductivity of the changing stress state in the reservoir. Using percolation theory, a qualitative assessment can be made of how the conductivity and interconnectedness of the fracture network is developed in terms of network clusters. This integrated analysis of static and dynamic fracture data leads to the formulation of conceptual models and a set of modelling rules. A Digital (Discrete) Fracture Network model, based on these concept(s), rules and interwell interpolation data, can then be analysed in terms of expected network cluster size, distribution and hydraulics. This provides a control on the expectations embedded in the concepts prior to dynamic modelling. The uncertainties are normally quite large and very seldom will they allow construction of the definitive fracture model. The systematic and integrated analysis of fracture network geometry, constrained with dynamic indicators and subsequent network cluster analysis, are necessary preparatory steps for construction and analysis of dynamic models.

Fractured reservoirs are reservoirs in which production and recovery is influenced to a greater or lesser extent by fractures. They can be subdivided into four different types (cf. Nelson 2001; Allan & Qing Sun 2003) schematically indicated in Figure 1. The variability in fracture network interconnectedness, and in the architecture and properties of the matrix, are the basic reasons that fractured reservoirs show a large variety of behaviours during hydrocarbon production. These large uncertainties make the appraisal, development and management of fractured reservoirs difficult. Failure to assess uncertainties properly leads to missed opportunities and low hydrocarbon recovery. The special nature of fractured reservoirs lies in the interaction between, the (relatively) high pore volume, low permeability matrix (the storage domain) and the low pore volume, high permeability fracture system (the flow domain; Fig. 2). This interaction is a function of matrix architecture and fracture network geometry, but also of the mechanisms and physical processes that control the transfer of hydrocarbons from the matrix to the fracture network. The initial and developing stress state and the presence or absence of an aquifer also influence performance. For more mature fractured reservoirs the possible impact of

water flood or gas injection must be incorporated in the analysis. In Type I, II & III fractured reservoirs (sensu Fig. 1) the geometry of the fracture network is often the main control on well location and orientation. In Types II & III, if the network does not interact with matrix in a sufficient manner, the time it takes to produce hydrocarbons may make a field totally uneconomic. The natural starting point for the analysis of a fractured reservoir will be the collection and processing of fracture data followed by analysis of the geometrical aspects of that data. In tandem with the geometric analysis, dynamic data must be analysed to calibrate the possible ranges in interconnectedness of the network. Additional data (e.g. seismic) must be analysed and again calibrated with static and dynamic data to constrain the interwell space. This integrated analysis, which leads to the formulation of conceptual models and rules for fracture network model construction, will be the focus of this paper. The discussion will be illustrated by the analysis of image log data. It is stressed here that what is presented does not represent a complete analysis or modelling exercise. The examples are used only to demonstrate the applicability of the methodology. In the context of this paper fractures are defined as ‘approximately

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 375–403. DOI: 10.1144/SP292.21 0305-8719/07/$15.00 # The Geological Society of London 2007.

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Fig. 1. Schematic representation of the common subdivision of fractured reservoir types based primarily on matrix character (Nelson 2001; Allan & Qing Sun 2003).

planar features along which cohesion has been lost and only small displacement has taken place.’ This includes displacement normal and parallel to fracture walls. Some would call the latter faults, or micro-faults if displacements were small. The inclusion of faults in a fracture network, whatever their displacement, is entirely appropriate where they provide pathways for flow.

potential data source is outcrop analogues, used to fill scale gaps in the subsurface dataset. Seismic data is an indirect source, the interpretation of which will deliver a fault and horizon framework that forms the structural envelope in which the development and distribution of fractures can be analysed. It is also the main source of information on strain related subseismic structures in the inter-well space.

Data sources for fracture network geometry

Core

In most cases, fracture data will be derived from core analysis and image log interpretation. A third

Cores are often taken in a few wells only and over limited parts of the reservoir section. They provide the only direct observation of fractures in

Fig. 2. The primary elements of a fractured reservoir are the matrix as the storage domain, the fault and fracture network as the flow domain and the transfer of fluids between them. Secondary elements are the stress state, the influence of an aquifer and the effects of gas injected and waterflood. For further explanation see text.

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the subsurface, but that is limited to the borehole scale. Information on the following can be obtained: Orientation. Fracture orientation can be measured directly from core if it is oriented (e.g. with a scribe line), or indirectly using bedding plane orientation or palaeomagnetic methods (Davison & Haszeldine 1985). Under-sampling of fractures making a small angle with the borehole is a common limitation (Fig. 3).

Fig. 3. Fracture planes that are orthogonal to the borehole (i.e. the normal to the fracture plane is roughly coincident with the borehole orientation) are preferentially sampled. Fractures with a normal at a large angle to the borehole are under-sampled. This no or limited data zone, where fractures will be under-sampled or cannot be imaged, is typically 10– 158 from the borehole axis.

Connectivity. Fracture systems develop in a variety of styles depending on stress state and the characteristics of the rock sequence. As a result fractures will abut (or terminate) against other fractures, cross each other or simply terminate within rock. This is captured in the number of Y-, X- or I-nodes (Bech et al. 2001; Fig. 4a). The second aspect of connectivity is the interaction of fractures with lithostratigraphy (Fig. 4b; Loosveld & Franssen 1992). Stratabound fractures occur where bedding planes, and/or intervening shale or otherwise incompetent layers, inhibit propagation (cf. Anderson 1981; Hanson et al. 1982; Odling et al. 1999). The vertical persistence (or crossing probability) is defined as the ratio of the number of fractures that cross the boundary to the total number of fractures in the stratum (Bech et al. 2001). Together stratabound and non-stratabound fractures may form the total fracture spectrum and it requires some filtering to separate them into different sets.

Fig. 4. Connectivity is expressed through (a) fracture– fracture intersection relations labelled X-, Y- and I-nodes. Nodal proportions are captured in a ternary diagram. (b) Fracture intersection relationships with sequence interfaces (e.g. bedding) are labelled stratabound or non-stratabound.

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Quantification of both types of connectivity relationships will help to (a) decide on the fracture mechanism(s), and (b) integrate core observations with the regional structural geological history. Mechanical stratigraphy. Combining (litho-) stratigraphy and fracture characteristics, e.g. connectivity relationships and density, can reveal major contrasts between different parts of the reservoir sequences. These contrasts are commonly observed in a vertical direction related to mechanical contrasts between various units (Wennberg et al. 2006). Mechanical contrasts can also be observed in a horizontal direction where they may indicate partitioning of deformation related to folding or faulting (Stephenson et al. 2007). Relative age. This can potentially be derived from abutting and cross-cutting relationships (Fig. 5).

Consistency in such relationships is a reliable criterion (Ortega et al. 2006). The geometric relationships give only relative ages but with more detailed study of fracture fills (cf. Laubach et al. 2004), ages can be bracketed against the burial history and form an important input into the overall geological history. Aperture. This can be estimated by measuring the width of cemented or partially cemented fractures in core. The cementation history may show crack–seal episodes of progressive opening and aperture estimates must take that history into account (Laubach et al. 2004). The aperture estimate may or may not be correct. Aperture of open fractures will be affected by the in situ stress state, which may be different from the stress state that controlled the formation of currently mineralized fractures. Estimates of open fracture aperture from a core are always very uncertain because the width of open fractures at the surface may not be representative of the width at depth. Unloading effects and associated stress release, as well as damage to the fracture during coring and subsequent core handling, will affect the measurements. Dimensions. The dimensions of fractures are captured by length, height and aspect ratio (¼ length/ height). Vertical core may allow heights to be sampled, whereas core from horizontal wells allow for the sampling of length. Both require the observation of fracture terminations and those are usually few and far between. Induced fractures. The process of coring and subsequent handling of cores leads to stress changes, which can cause the formation of coring-induced fractures. They may use and enhance suitably oriented natural fractures when they propagate along them. There are few definitive criteria for distinguishing coring-induced fractures, but some fracture orientations and geometries are typical and when present should alert the observer (Kulander et al. 1990).

Fig. 5. Fracture characteristics that should be recorded, in addition to depth, azimuth and dip, are schematically presented here. (a) Bedding plane; (b) disaggregation seam offset by (c) a hybrid fracture which is an amalgamation of two fractures, an early fine grained cement lining with later blocky cement related to (d) a tensile fracture fully filled with blocky cement; E (mechanical aperture) ¼ 0.6–0.7 mm; (e) shear (closed) fracture with cataclasis; (f) open tensile fracture; low joint roughness coefficient; E , 1 mm; terminates in core.

Fracture type. To distinguish between tensile and shear fractures is really only possible in core (Kulander et al. 1990; Loosveld & Franssen 1992). Fracture types and the spatial relationship between fractures, especially that between en-echelon fractures, allow an assessment to be made of the remote stress state during fracture formation (Olsen & Pollard 1989). The distinction between fracture types is important because their spatial distribution and dimension characteristics may be significantly different (Odling et al. 1999; Cacas et al. 2001). The information will help to subdivide fractures in specific sets, assist in determining age relationships, and in general,

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supply important pointers to the structural history (Hancock 1985). Morphology. Characterizing the fractures in terms of morphology and content is important in the analysis of fractured reservoirs. There is no definitive scheme that gives all the definitions and qualifiers that should be used. It is a fit for purpose argument that determines the choice for a descriptive scheme. Some important characteristics and contrasts (Kulander et al. 1990) are captured schematically in Figure 5.

Image log Borehole image logs (BHI) are usually collected over a greater length interval than core, and thus provide a more continuous image of the subsurface. There are two main types of BHI tools (Chueng 1999). Micro-resistivity tools create electrical images using pad-mounted resistivity button arrays. Ultrasonic tools create acoustic images using a rotating transducer. In addition, lower resolution BHI tools, based on density-log technology, can be run on drill pipe to provide near real-time information on large fractures and faults (Prensky 1999). BHIs can be used to gather fracture data in the same categories as core data. In general, the same restrictions and possibilities apply but there are differences. There is the obvious difference in resolution and quality between a BHI and a core. In general BHIs will under-sample the fracture system and the resolution restrictions will mean that certain details cannot be observed (Rawnsley et al. 2004). Resistive v. conductive. Image log features with a resistive response are generally interpreted as being cemented or closed. Features that are filled with a fluid (formation water or drilling mud) that is more conductive than the host rock, are labelled as conductive and interpreted as fractures that are open and thus potential conduits for fluid flow (Lofts & Bourke 1999). This need not always be true. Certain types of cement or fracture fill could produce a resistivity contrast with the matrix equivalent to that between water and matrix, and open fractures drilled with oil based mud can be more resistive than a high water saturation reservoir. Aperture. For micro-resistivity image logs, the measured signal can be considered to be a function of fracture aperture and the conductivity of the fluid in the fracture (Luthi & Souhaite´ 1990). Resolution depends very much on the resistivity contrast between rock and fluids. Similarly, in ultrasonic tools the amplitude response can be related to aperture but is sensitive to the roughness at the intersection with the borehole wall (Chueng 1999). Verga

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et al. (2002), using apertures of cemented fractures in thin sections, evaluated the electric fracture aperture using neural network techniques. This process yielded different distributions for core and image log data. In principle, aperture determination from image logs is a possibility, but resolution issues will limit accuracy (Luthi & Souhaite´ 1990). The obvious advantage is that aperture derived from image log data is observed under reservoir conditions. Drilling induced fractures and borehole breakouts. These are the result of redistribution of the stresses around the borehole while drilling, which may cause the rock to fail (Lofts & Bourke 1999). Depending on borehole orientation, stress orientation and magnitude and mud conditions in the borehole, the rock may potentially fail in tension (tensile fractures in the direction of maximum horizontal stress) or in compression (borehole breakouts in the direction of the minimum horizontal stress). Drilling induced fractures will show up on image logs as open fractures oriented parallel to the borehole axis. Borehole breakouts are usually indicated as broad bands separated by 1808, again parallel to the borehole axis (Lofts & Bourke 1999). The importance of induced fractures and borehole breakouts lies in the fact that they can provide information about the present-day stress field (Trice 1999; Zoback et al. 2003). Core v. image log calibration. Qualitative and quantitative calibration of fracture characteristics between BHI and core is essential to reduce uncertainty in concepts and models. The calibration helps to estimate the under-sampling of BHI relative to core and to filter out induced fractures. The data from both cores and image logs is presented in itemized lists which contain information, logged against depth, on fracture type, azimuth and dip, and as much as can be determined on the other characteristics discussed in this section (Fig. 5). Important characteristics are: mechanical fracture type; whether fractures are open, closed or partially closed and show wall to wall contacts or cement; solution effects; type and character of fracture fill and relative ages of fill; aperture and an estimate of the topography of the fracture walls, usually called roughness and sometimes expressed in the Joint Roughness Coefficient (cf. Kulander et al. 1990).

Outcrop analogues Outcrops provide an opportunity to sample fracture characteristics, which, due to the limited sampling by cores and image logs, are difficult to capture in the subsurface. This applies above all to fracture dimensions and connectivity relationships. It can

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be used to guide the assessment of specific network aspects in a general or qualitative sense (Mercadier & Ma¨kel 1991; cf. Van Dijk 1998). Even if all the aspects of the geological history are comparable, the fact that the analogue sequences are found at the surface will introduce a difference. The change in stress state related to the rise of the sequences from the reservoir level (assuming that the outcrop sequence came from that level) to the surface can lead to a considerable change in the fracture network characteristics, such as density. Outcrop data is a useful source of data to construct a mechanical stratigraphy (Trice 1999; Wennberg et al. 2006; Stephenson et al. 2007), even if only in relative terms. In using outcrop analogue data, a comparison of all aspects of the geological history must be made and a compensation for the potential impact of the difference in depth and history applied before the data is used to fill the subsurface data gaps (cf. Cacas et al. 2001). Given that the problems are considerable an element of doubt about the appropriateness of the analogue will remain.

Analysis of fracture network geometry The interconnectedness of a fracture network is determined by five geometrical fracture characteristics. To build a Discrete Fracture Network, knowledge of the distribution of these characteristics (geographically, vertically and in value ranges) is a prerequisite. The geometrical fracture characteristics are: (a) orientation of specific fractures or fracture sets; (b) density expressed as spacing between fractures in general or in specific sets and clustering describing specifics of spacing distributions; (c) connectivity, which describes the interaction and overprinting relations between fracture sets and reservoir sequences; (d) aperture or width and specific properties, such as roughness and cement fill, which impact on hydraulic properties; (e) length and height, which captures the horizontal and vertical extent of fracture and fractures sets. The core and/or image log analysis and interpretation will result in an overview of specific fracture sets and relationships between them, and possibly a first pass mechanical stratigraphy scheme. Grouping in fracture sets is often based on orientation (both dip and/or strike direction) and fracture type, but any meaningful attribute or attribute combinations can be used. It must be consistent with the geological history of the reservoir and over- and under-burden (Cacas et al. 2001). The fault and horizon interpretation and the geological history provide the overall framework in which the

development and distribution of fractures and fracture sets, and their relationships in time and space are analysed. The geological history should comprise an assessment of the various structural phases and stress states the reservoirs experienced over geological time and provide information on the kind of fracturing regimes (regional, fold or fault related) that were involved in fracture network formation. It also needs to detail the kinematics of the fault–horizon framework (cf. Gauthier et al. 2000) and should include the effects that diagenesis and hydrocarbon charge had on matrix and fractures. The analysis of data has to take into account its source in terms of dimensions of the object and the derived parameter, and the scale at which data is sampled (cf. Van Dijk 1998). Data derived from boreholes and scan lines is essentially onedimensional, whereas data derived from maps and outcrop surfaces is two-dimensional. Derived parameters from borehole data can have no dimensions (number of fractures), be one-dimensional (e.g. number per unit length) or three-dimensional (e.g. orientation of a fracture plane). The inherent resolution of the data source means that mixing data sets from various sources, at various scales, is a hazardous affair if the impact of the resolution and scale differences has not been analysed.

Orientation Plotting fracture data in stereographic projections and rose diagrams gives a powerful visual overview of the data (Fig. 6). Rose diagrams or circular histograms show the contrasts in fracture strike orientation. Poles plotted on stereonets present a view of the fracture distribution in space and of angular differences. They can be constructed as equal angle nets, which honour angular relationships, or equal area nets in which spatial distribution is better represented (Phillips 1971). Contour diagrams provide focus on the centres of gravity but lose the contribution of individual measurements. The distribution of poles and/or strike orientations is used to make a first differentiation in fracture sets for specific reservoir or mechanical units. If the description of the fracture network is intended to be at a high level only, it may be sufficient to read off characteristic directions for datasets straight from pole plots or contour diagrams. Various distributions can be used to characterize a fracture dataset statistically. Commonly used are parameters based on the Fisher distribution, the equivalent for three-dimensional data to the normal distribution (Davis 2002). The data set is characterized by azimuth and dip of a mean vector and a concentration parameter K. There are tests to determine if a data set is Fisher distributed,

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Density Spacing. Density analysis involves the quantification of the spacing between fractures or of its reciprocal, frequency, i.e. the number of fractures per unit length (Ortega et al. 2006). Fracture spacing is influenced by lithology, porosity and grain size, bed thickness and stress history (Narr & Suppe 1991). Apart from the probable link to bed thickness, there are no hard and fast rules to determine spacing other than by measuring it in core or image log. Strictly speaking spacing is the orthogonal distance between two fracture planes. The standard measure of spacing in the subsurface is the downhole spacing i.e. the distance between two fractures measured along a borehole (Fig. 7). That is seldom the orthogonal distance since the value depends on the relative orientation of fractures and borehole. Spacing in a fracture set with little dispersion in orientation, and a reasonable angle with the scan line, can be corrected by using the normal downhole spacing or applying the Terzaghi correction (Fig. 7). The latter can be applied in various ways depending on orientation differences

Fig. 6. Fracture orientation display can combine polar, equal angle and equal area projections with rose diagrams, pole plots and contours. (a) Symmetrical and (b) asymmetrical rose diagrams. Stereograms show poles to planes plotted in (c) equal area and (d) equal angle projection; both lower hemisphere. (e) Contoured poles plotted in polar projection, equal angle, lower hemisphere.

but as a simple rule of thumb a K value of . 5 is often good enough to use the Fisher parameters. If that is not the case, another way of characterizing the data is through eigenvector analysis. Eigenvectors and their eigenvalues are calculated from a 33 matrix of the sums of squares and products of the direction cosines of a directional data set. They represent the greatest, intermediate and least moment of inertia of a data set, and can be used to locate the principal direction and describe the dispersion in the data set (Mardia 1972; Davis 2002). It makes little sense to use these methods on a multimodal set with clearly separated clusters. There are methods to tackle even that but splitting the set may be just as simple and effective. Splitting the data may also create problems. Defining orientation groups may work well for some fields but be difficult in others when the orientation of otherwise related sets changes in a geographical sense or with position in the mechanical stratigraphy.

Fig. 7. Graphical representation of downhole and normal downhole spacing and the Terzaghi correction (Terzaghi 1965). The last two attempt to compensate for the variable intersection angle between fractures and wellbore. For further explanation see text.

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between fracture set and scan line (cf. Davy et al. 2006). In its original form the correction consists of multiplying downhole (or scan line) spacing by the cosine of the angle between the mean pole of the fractures and the scan line (Terzaghi 1965; Priest 1993). It is not an exact solution to the problem, but the errors introduced by using a scan line of relatively uniform orientation can be reduced to a tolerable level (cf. Terzaghi 1965). Whatever correction is applied, spurious results will impact the summary statistics, especially when data sets are small. To avoid applying very high correction factors to fractures subparallel to the borehole, a truncation limit is sometimes applied or values or value ranges are weighted. The impact of sampling blind spots (Fig. 3) could be compensated for by comparison with data from wells with different orientations. But regional differences may mean that the absence of fractures in the blind spot is genuine. If compensation is applied it will increase uncertainty in the spacing calculations. Commonly used summary spacing statistics are arithmetic average, standard deviation and coefficient of variation (Cv). The latter is defined as standard deviation divided by the arithmetic mean and is a measure that is used to analyse clustering (Gillespie et al. 1993). In cumulative frequency plots the data sets can also be characterized by curve fitting techniques. The average (corrected) spacing is subjective when data is subdivided in various sets and it can only be relative when derived from image logs and can therefore be best used qualitatively rather than quantitatively. Possibilities are simple position in range schemes or breaking the range of values, for related sets, into quartiles. Calculating fracture intensity measures that are related to the dimension of the measuring region can reduce the problems with spacing parameters. P32 is a very useful measure for the threedimensional intensity of fractures and is an important parameter for fracture network modelling. It is defined as the area of fractures in a volume (m2/ m3). Assuming the wellbore to be the volume, then the fracture area for any fracture is determined by the intersection plane with the wellbore (Fig. 8). This carries the implicit assumption that it will cross the whole wellbore. P32 is scale independent and not influenced by orientation effects and fracture size (Dershowitz & Herda 1992; cf. van Dijk 1998). Clustering. A first pass assessment of the clustering in a fracture data set is made through the coefficient of variation Cv. Where standard deviation is large with respect to mean, large spacing values are mixed with small ones. The Cv will be .1 and the system is clustered. When Cv is c. 1 the large spacing values are balanced by the low values and the system is randomly spaced. Sets

Fig. 8. Persistence parameters represent fracture density related to the dimension of the measuring region. They are indicated with Pxy, where X indicates the dimension of the measurement region and Y indicates the fracture measure dimension relative to the region dimension (Dershowitz & Herda 1992).

with Cv values ,1 are uniformly or regularly spaced (cf. Gillespie et al. 1993). The scaling characteristics of different parts of the fracture network (geographically as well as fracture-type related) guide interpretation and extrapolation of the data beyond the borehole. In the 1980s and 1990s many publications appeared using fractal analytical methods to address these scaling issues (e.g. Gillespie et al. 1993; Hewett 1994). At the simplest level fractal geometry can be defined as being scale independent (or self-similar) at all scales between defined limits. In other words any portion of the system is a scaled version of the whole system (cf. van Dijk 1998). The standard way of analysing fracture data for fractal geometry is by plotting the cumulative frequency of a fault or fracture attribute in a log– log plot (Walsh et al. 1994). Commonly used attributes are spacing, throw, height and length. If the data adheres to a power-law distribution, i.e. a straight line on a log–log plot, the data can be said to have fractal geometry. The distribution is described by the fitted curve and the function exponent (D) is taken as the fractal dimension (Gillespie et al. 1993). Data in such plots generally show the effect of truncation and censoring (Priest 1993; Bech et al. 2001). The former is indicative of a loss of data in the small value realm. For image

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log data, that could be a consequence of resolution (Ortega et al. 2006). Censoring at the other end of the curve occurs when the values of the plotted measure approach the limit of the area of observation. It is important to recognize and analyse these effects because they can lead to incorrect rejection of fractal geometry when that is masked by data problems (Gillespie et al. 1993; Ortega et al. 2006). A fundamental requirement for the analysis of populations in a log–log frequency plot is that the value range in the data set is large enough. Walsh et al. (1994) state that a range of at least one order of magnitude must be sampled. Another method to analyse the geometry of fracture patterns is the box-counting technique (Walsh & Watterson 1993; Hewett 1994). The method consists of superimposing square grids of given side length d on a fracture pattern and recording the number of boxes containing fractures n. After repeating with boxes of different sizes the curve log d over log n is plotted. For a fractal pattern the central segment of the curve is a straight line of which the slope D is by analogy called the fractal dimension. Walsh & Watterson (1993) tested the methodology and formulated guidelines for its use with outcrop data. The use of this method in wells, for what is effectively onedimensional fracture data from the subsurface, has been challenged (Harris et al. 1991), because it is sensitive to data resolution and the shape of the area analysed (Cowie et al. 1996). If fractal geometry can be proven for a data set, it means that fracture properties can be extrapolated beyond the domain of the wellbore. Similarly, if it can be demonstrated at the seismic scale, it can be extrapolated to the smaller scale and be used as a proxy for fracture characteristics (Van Dijk 1998). But relating millimetre-sized discontinuities, measured in core or image log, with kilometre-sized structures is not without problems (cf. Gillespie et al. 1993). The correspondence between, for example, small and large scale faults showing similar geometries over many orders of magnitude of scale may have been demonstrated in some cases (Tchalenko 1970; Hewett 1994; Pickering et al. 1997), but to assume that fault and fracture data sets have, by definition, fractal geometry for the various attributes is far too simplistic (cf. Harris et al. 1991; Loosveld & Franssen 1992; Walsh & Watterson 1993; Cowie et al. 1996; Nicol et al. 1996). Strictly speaking it must be demonstrated that fractal geometry exists at both scales and that they fit the same distribution. Loosveld & Franssen (1992), considering networks of stratabound extensional features in a particular bed, concluded that these are characterized by regular spacing, i.e. are not scale invariant. They postulated that fracture networks consisting

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mainly of such stratabound systems would not be fractal (cf. Odling et al. 1999). Walsh et al. (1994) summarized the problem when density of subsurface data is based on total observations of fractures with and without some offset. A nondifferentiated subsurface data set will overestimate density when compared with a population of seismic faults. It implies that fault data can only be used to estimate small-scale fault density and that density of fractures without shear displacement cannot be derived in this way.

Connectivity The relative number of I-nodes to X- and Y-nodes, as well as the ratio of number of X-nodes to number of Y-nodes, can be analysed by plotting the nodal proportions in a ternary connectivity diagram (Fig. 4). These ratios are considered as first pass indicators of the interconnectedness of a fracture network. Systems dominated by I-nodes will show very low interconnectedness but with a larger proportion of X- and/or Y-nodes that will improve (Fig. 4). The interconnectedness will increase more with proportionally more X-nodes because there is the chance that they will cross yet another fracture (Manzocchi 2002). Systems that are developed in orientation clusters (i.e. relatively isolated, independent clusters of uniformly oriented fractures; Fig. 9) will show a low number of X- and/or Y-nodes but will have

(a)

(b)

(c)

Fig. 9. End members of spacing distributions. (a) Regularly spaced: multidirectional, relatively isolated fractures; (b) density-clustered: clusters of multidirectional sets; (c) orientation-clustered: clusters of unidirectional fractures.

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high Cv values. Density-clustered systems, which combine fractures of various orientations in localized clusters (Fig. 9), will show large number of X- and/or Y-nodes and also have Cv values that will indicate clustering (Manzocchi 2002). As depicted, these systems are end-members and natural systems can be expected to show more heterogeneity in cluster development. Note also that when systems are not similar, the nature of clustering may differ with scale. Fracture systems that are characterized by stratabound fractures, i.e. have a low vertical persistence, are usually regularly spaced, e.g. have Cv , 1 (Loosveld & Franssen 1992; Manzocchi 2002), with spacing related to thickness of the strata (Narr & Suppe 1991). Non-stratabound systems are typically clustered and will have high vertical persistence values (Bech et al. 2001; Fig. 4). The consequence of abutting against bedding is that fracture aspect ratios, especially in thin-bedded sequences, could be very high for stratabound systems. For non-stratabound systems the aspect ratio tends to be much lower (Loosveld & Franssen 1992; Odling et al. 1999). Connectivity relationships are difficult to establish from core and virtually impossible from image log (Trice 1999). From core it may be possible to collect a small data set for both connectivity aspects, but the uncertainty that must be attached to the connectivity of the network will be large. The connectivity picture is more often than not completely derived from outcrop analogue data.

Aperture If aperture data is available from core or image log, the first-pass evaluation is straightforward. Basic statistics can be used to characterize the distribution of aperture for various sets. There are other methods to at least estimate what the fracture aperture could be; drilling mud-loss analysis (Lietard et al. 1996; Sanfillippo et al. 1997), combinations of various wireline logs (Trice 1999) or combining porosity data with fracture density (Bona et al. 2003) are some of them. In general, any method gives a rough estimate of aperture only. It is difficult to differentiate between matrix and fracture porosity from cores and logs combined, and density data, especially from image logs is not an absolute number. Measured (¼mechanical) aperture would be equivalent to the hydraulic aperture if the fracture walls formed perfect parallel plates. This is virtually never the case and deviation from that ideal situation causes a reduction in flow (Witherspoon et al. 1980). The more pronounced the roughness of the fracture walls, the more flow is reduced. In engineering geology a number of measures are used to describe roughness (Priest 1993).

commonly used in geological problems is the joint roughness coefficient (JRC) empirically defined to estimate the rugosity of fracture asperities (Barton et al. 1985; Bakhtar et al. 1985). The JRC may be subjectively determined by comparison with standard roughness profiles (Priest 1993).

Height and length Cores and image logs do not sample enough of the subsurface, relative to fracture dimensions, to give a data set large enough to determine height and length distributions with any degree of accuracy. Additional data may come from two methods to estimate fracture dimensions. The first is data from outcrop analogues and the second is subsurface faults. The problems with the use of outcrop data have been outlined above. Even if the conditions for their use are met, a considerable uncertainty must be attached to outcrop data that fills the gaps in subsurface data. The implied assumption when seismic fault data is used is that the same power-law describes the length and/or height distributions of faults and fractures (Loosveld & Franssen 1992; Pickering et al. 1997). Applied to the problem of length and height, plotting the fault data as derived from seismic and fitting a power-law through the data would then give an indication of the overall length or height distribution of the fault–fracture continuum. One problem is that the total fault set is the result of the total geological history. It may be related to the total fracture set but it is questionable whether it always forms a continuum with the subset of open fractures, and it should not be assumed that fault or fracture data, always adhere to power-law relationships (Nicol et al. 1996).

Network geometry analysis example A dataset from three wells is used to illustrate some of the points on fracture network analysis made above. These wells are widely spaced (Fig. 10) so the problem addressed is akin to one with a few appraisal wells where fracture data is available, but could equally well represent a situation where image logs are scarce. The wells penetrated three stratigraphic units, Units 1, 2 & 3, which show relatively small differences in matrix permeability development. Fractures are interpreted from microresistivity image logs. Only fractures that were interpreted as conductive are considered here. The fracture orientations in Unit 2 are detailed in Figure 11. Well A, drilled in a 3508 orientation, shows some effect of undersampling but well B, orientated at 2908, is much less affected. The part of well D that was logged, changes orientation from 0708 to 0208 and may show some undersampling in Unit 3. Fractures are in general developed

MODELLING FRACTURED RESERVOIRS

Fig. 10. Location of the three example wells. The background represents Unit 2 matrix permeability distribution, based on facies modelling.

in consistent directional sets over the units. A broadly NE– SW direction and a north –south direction are the main orientations. There seems to be variation in direction of fracture sets in a regional sense. It will therefore not be simple to define uniform ranges to capture the main orientations in the fracture network. The four ranges indicated capture some of it but in several instances (e.g. Well D, Unit 2) the range boundaries will split what are directionally consistent trends. Variability can also be seen in dip, from near vertical to as low as 308. Overall dispersion seems to be the rule because only occasionally are poles really clustered. The average P32 values for each unit shows that well D is the most intensely fractured (Table 1).

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Wells A and B have lower but more-or-less similar values. The normal downhole spacing average for well A correlates with the P32 but less so for well B, showing that, in this case, it is not an optimal estimator of fracture density. The calculated fractal dimensions are low, in seven cases lower than 1.0, which indicates a relatively low number of small spacing values. In most cases the cumulative frequency distribution shows a better logarithmic then a power-law fit (Fig. 12; Table 1), but that could be deceptive because a logarithmic fit is less sensitive to the effects of truncation and censoring. The Cv values are indicative of clustered development only in a few cases, for sets that have low D values. Taken together this casts doubt on the fractal nature of the total set of fractures per unit. The spatial distribution and spacing data can be interpreted to indicate superposition of several orientation sets. The latter point is reinforced by density measures calculated for data sorted into the four orientation ranges (Table 2). These statistics must be used with care because application of uniform orientation ranges splits what seem to be consistent orientation sets in some units. The results show a large scatter in the spacing averages that are influenced by spurious results in small data sets. In general a considerable increase in Cv values is shown. This points to a considerable degree of clustering and potentially fractal geometry, which would be concealed if multiple sets were inappropriately grouped together. The uniformity in spacing averages across units in a specific well shows that there is an apparent absence of mechanical stratigraphy.

Fig. 11. The variability in orientation and dip in the different wells is shown in these examples for Unit 2. For further analysis the data is grouped into four orientation ranges labelled NW, north–south, NE and east– west.

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Table 1. Fracture density statistics for total fracture sets Normal Downhole Spacing Well A

B D

Fractal Dimensions

Unit

#

Avg

StDev

Cv

P32

D

R2

Log. Fit

U -1#1 U -2#1 U -1#2 U- 2#2 Unit-3 U-1 U-2 U-3 U-1 U-2 U-3

75 135 146 105 145 28 31 159 171 146 75

2.45 1.50 1.34 2.04 2.93 4.81 5.76 5.08 0.76 0.74 1.32

2.56 1.71 1.39 4.52 3.96 6.71 5.49 7.37 1.06 0.84 3.49

1.05 1.14 1.04 2.22 1.35 1.40 0.95 1.45 1.39 1.14 2.64

0.74 0.98 1.18 0.73 0.52 1.66 0.85 0.78 2.93 3.53 7.24

0.80 1.04 1.00 0.81 0.77 0.55 0.77 0.73 1.09 1.06 0.76

0.85 0.91 0.89 0.95 0.86 0.90 0.84 0.89 0.91 0.91 0.88

0.98 0.96 0.97 0.86 0.98 0.97 0.98 0.97 0.87 0.91 0.80

Numerical values are superimposed on a colour indication based on a simple position in range scheme, which comprises 4 ranges each containing 25% of the specific statistic values. Red denotes the 25% highest values for density (i.e. lowest spacing), Cv, P32 and D. #, number of measurements in a set; Avg, arithmetic mean; StDev, standard deviation; Cv, coefficient of variation; D, fractal dimension; R2, correlation coefficient; Log. Fit, correlation coefficient for a logarithmic fit of the data.

Summary In their simplest form, the end products of the geometric analyses are presented as high–medium–low

ranges for the various parameters or fixed orientations for specific orientation sets. With adequate data coverage and quality, rules can be more sophisticated, e.g. a distribution function based on curve fitting of available data. Obviously there are differences in quality and size of the fracture data set from one fractured reservoir to another but some problems will be universal. This means that we can generalize the relative value derived from the analysis of the geometrical aspects for the subsequent modelling of the fracture network. The rules determined for fracture orientation and density from core data can be considered to be hard. Density derived from image logs indicates relative differences only, due to under-sampling. Connectivity and aperture are not adequately captured due to sampling limitations. Core and image logs do not provide adequate information on fracture dimensions. That gap is often filled by extrapolation from subsurface fault data or with data from an outcrop analogue. Both methods are not without problems and fracture dimensions come associated with a considerable uncertainty. The consequence of the above is that some of the parameters, notably aperture, are often used as empirical matching parameters in dynamic modelling (Gilman 2003).

Dynamic calibration Fig. 12. Example of cumulative frequency v. spacing relationships in log– log and lin –log plots. Truncation and censoring affect the data at small and large spacing respectively.

Before a fracture network model is constructed, the fracture network geometry and geometric modelling rules must be calibrated against data that indicates flow into the borehole. Some of these so-called dynamic indicators can pinpoint flow at

MODELLING FRACTURED RESERVOIRS

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Table 2. Fracture density statistics for orientation fracture sets Normal Spacing Average

A

B

D

NS NE EW NW NS NE EW NW NS NE EW NW

Normal Spacing Cv

U-1#1

U-2#1

U-1#2

U-2#2

U3

U-1#1

U-2#1

U-1#2

U-2#2

U3

6.9 6.9 20.4 3.2

1.0 1.9

2.2 2.2

7.6 2.4

39.7 2.9

1.5 2.0

2.7 2.7

1.3 2.6

2.7 1.4

11.6 19.7 9.9 17.8 8.5 7.3 0.5 0.7 6.9

2.3

15.0

21.5 10.8 16.5 19.6 0.0 8.1 0.4 1.7 17.6

1.2 1.2 0.8 1.4

1.5 1.6 1.3 1.2 1.6 1.2 2.0 2.6 1.7

1.2

1.8

1.3 2.0 1.6 2.0

2.1 2.4 6.1 0.4 0.8

1.5 1.7 1.5 1.7 2.4

2.0 2.8 2.0 1.6

The grey cells indicate sets with no or too few (,5) measurements for which statistics have not been calculated. The colour indication is based on the same position in range scheme as used in Table 1.

a specific point or short interval along the wellbore. Examples are drilling mud losses, production logging tools (PLT), temperature logs and mini drill stem tests (mini-DST). Well tests and production data give information on flow for a larger borehole section and a larger reservoir volume. With reservoir depletion significant changes in dynamic behaviour may be introduced. Such changes could be related to changes in effective stress with depletion. The effectiveness of a fracture network can be described in terms of percolation theory (Manzocchi 2002). The use of this theory, linking geometry to flow, helps to formulate constraints for those network characteristics that are difficult to capture by geometry alone. In general, dynamic indicators are used to narrow the possible ranges rather than to generate new ideas about the fracture network.

Fracture networks and percolation theory The basic premise of percolation theory is that flow is largely controlled by the continuity of the permeability contrasts. In a network with low fracture density, fractures will be isolated and few, relatively small clusters of intersecting fractures will be present. With increasing density the number and size of network clusters will grow until a point is reached where one, the so-called spanning or percolation cluster, grows rapidly at the expense of others. When the density of fractures is expressed as the probability of a fracture occurring in a grid cell, a critical probability determines when the percolation cluster is formed. This is called the percolation threshold (Stauffer & Aharony 1994; King et al. 2001). Analysis of fracture network models shows

that with increasing interconnectedness, fracture permeability (KF) increases slowly until, on the scale of the analysed block, a level of fracture saturation is reached where KF increases rapidly (Manzocchi 2002). After that point, with increasing interconnectedness, KF will still increase but far less dramatically (Fig. 13). Bour & Davy (1997, 1998) analysed both twoand three-dimensional fault network models. Variation of density and length distribution with power-law relationships allowed definition of what they labelled the topology of connectivity. The system connectivity is defined for specific ranges of fault length fractal dimension D. However, in a fracture network the percolation threshold depends on the geometry of that network (Odling et al. 1999; Fig. 13). Orientation, length, height and aperture are individual fracture characteristics and represent the first level of characterization of network geometry (Manzocchi 2002). Connectivity, density and clustering are determined by the specifics of fracture sets and define the second level of characterization (Bech et al. 2001). Connectivity and clustering are the primary influences on the flow potential of a fracture network (Odling et al. 1999; Manzocchi 2002). Percolation threshold distributions have been determined, as a function of these two parameters, by Manzocchi (2002) for simple, twodimensional systems with relative uniform length distributions. The nodal proportions in a ternary connectivity diagram provide a first-pass indicator of the interconnectedness of a fracture network (Fig. 4). Where data plots close to the X– Y axis, high interconnectedness is possible but its translation to hydraulic performance is dependent on

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(a)

(b)

Fig. 13. Fracture network interconnectedness can be viewed as a function of five network geometry characteristics. The percolation threshold of a fracture network, on the scale of the sampling region, is reached where the fractures interact in such a way that flow from one boundary to the other becomes possible.

specific aspects of clustering (i.e. density clustering v. orientation clustering) and the dimensions of fractures. Simplistically, determining the point of rapid change, i.e. the percolation threshold, against the geometric parameters on the scale of investigation, would be a big step towards optimal fracture network modelling. But without a solid mathematical formulation of the relationship between the components (cf. Manzocchi 2002) and given the uncertainties that are attached to especially the second level characterization, this can only be used at best for a qualitative assessment of the flow in the fracture system when that is calibrated with dynamic indicators.

Mud losses and wireline methods Drilling mud losses, PLT inflow zones and temperature logs can potentially link fluid inflow to relative short borehole intervals. They can be used to investigate which part of the fracture network (orientation set, mechanical stratigraphy) is driving production performance. Losses in general give only a qualitative assessment of fracture porosity.

Only with careful recording and analysis can a more quantitative assessment of effective aperture of the fracture system be made (Lietard et al. 1996; Sanfillippo et al. 1997). Monitoring of inflow and outflow mud rates with high-resolution flow meters permits the detection of conductive fractures and potentially an evaluation of the hydraulic fracture width (Verga et al. 2000). Loss volumes can provide an indication of the extent of a fracture network beyond the wellbore. Linking losses to fractures still requires integration with other data, since they could also be linked to local matrix properties, e.g. high porosity (cf. Beda & Carugo 2001). PLTs can be used to analyse the proportional contribution to the total flow of specific wellbore intervals and when matrix conductivity is well constrained, to calculate an estimate of apparent fracture permeability or conductivity (Sullivan et al. 2006; Barr et al. 2007). The result is generally an interpretation of the flow characteristics of a composite fracture zone, rather than of individual fractures. With thin, high permeability beds present, the distinction between fractures or matrix may be complicated. Modelling the PLT response in terms of

MODELLING FRACTURED RESERVOIRS

matrix–fracture interaction for a variety of fracture scales and fracture and matrix properties (Barr et al. 2007) will improve the interpretation. Correlation with mud loss data may improve the interpretation of otherwise ambiguous results (Clifford et al. 2005). Temperature logs may perform a similar function to PLTs, where points of different temperature in the drilling fluid along the wellbore could represent open and flowing fractures. Typically, inflowing oil is warmer than the drilling mud (cf. Serra 1986). However, gas expands when it enters the borehole and causes a temperature drop. Wireline formation testing tools can be used for mini-DSTs. Using the tool straddled by two isolating packers, the formation can be tested in various configurations for a variety of objectives (Whittle et al. 2003; Coelho et al. 2005). With good isolation, detailed information can be obtained on the flow characteristics of a small interval of the formation (Verga et al. 2002). Interpretation methodologies are those used for well tests. The formation pressure data acquired through formation testing tools in the standard way may also provide important information in fractured reservoirs. Observed depletion or increased pressures may indicate the network interconnectedness during production or injection.

Well tests and production data Well tests, interference and tracer tests and production data, characterize the flow from a considerable sector of the borehole which can be turned into information on the extent of the fracture network beyond the borehole. Reservoir performance can be evaluated through pressure transient tests by measuring flow rates and pressures under changing flowing conditions. The interpretation and modelling of well test data in a fractured reservoir is a complex subject in itself (Aguilera 1995) and outside the scope of this paper. The objective of well test analysis is to ascertain how reservoir properties change with distance from the tested well (Doe 1991). The shape of the curve of pressure derivative data plotted against time allows an assessment of that spatial development (Wei 2000). The data is analysed for reservoir permeability thickness (Kh), the flow capacity or productivity index (PI) and drilling/completion formation damage. The interpretation of pressure transient tests is non-unique and requires a good knowledge of the underlying geological context such as matrix quality and distribution, the hydrocarbon specifics and some conceptual picture of the fracture network (Wei et al. 1998). A simple starting point is the ratio of well test permeability (Kh) over matrix permeability (Reiss 1980), termed the fracture productivity Index (FPI). This

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gives a first indication of the extent of the fracture network beyond the wellbore. Increasingly, the tendency is to construct dedicated dynamic models that incorporate detailed and realistic fracture– matrix geology to model and analyse pressure transient test data (Rawnsley & Wei 2001; Leckenby et al. 2007). The main aim is then to establish the key geometric elements and configuration and/or physical processes. An interference test is a multi-well test where pressure changes v. time are measured in one or more observation wells around a producer or injector. These measurements can be analysed for permeability and storage capacity of the fracture system connecting the wells (Araujo et al. 1998; Baker et al. 2000). Pulse testing is an extension of interference testing where short production or injection periods alternate with shut-in periods. A tracer test has a similar objective using the travel time of an injected tracer. The timing of arrival of pulses or a tracer in observation wells is indicative of the permeability between wells. The changes in production rates of oil, gas and water can provide information on the extent of the fracture network in the vicinity of a well or in between wells. The fracture network extent around a well can be analysed with techniques based on decline curve analysis and associated derivatives (Agarwal et al. 1998; Li & Horne 2005). The extent between wells can be analysed with simple rank correlation techniques but more elaborate techniques using principal component analysis are also applied (cf. Main et al. 2007).

Stress and reservoir performance The conductivity of fracture systems in the subsurface will be sensitive to the magnitude and orientation of the in-situ stress state and possible changes thereof. Jolly et al. (2000) refer to experimental work suggesting that fractures normal to the minimum principal stress are most conductive. Alternatively there is also evidence that conductivity might be related to the amount of shear stress acting on the fracture plane (Heffer et al. 1999). This is formulated in the concept of critical stress, which postulates that during slip, porosity and permeability are increased in response to dilation. The latter is the consequence of the roughness of the fracture surfaces (Barton et al. 1995). Both mechanisms are to some extent interdependent. More pronounced roughness might translate into a higher resistance to shear along the plane as a result of interlocking asperities thereby preventing or reducing fracture closure even if normal stress increases. Jolly et al. (2000) studied both mechanisms in generic fracture network models and concluded that in both cases their models were sensitive to stress orientation and changes in

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magnitude and that those changes would be apparent in pressure transient tests. In most fractured reservoirs, the (local) in-situ stress state will change with depletion and with water injection (Jolly et al. 2000). In essence the pressure drawdown leads to an increase in effective stress. This in turn may cause a reduction in effective permeability especially if it is primarily related to the fracture network (Buchsteiner et al. 1993). When anisotropy in stress state and in fracture network orientation combine in certain ways it may result in anisotropic changes in the permeability field (Heffer et al. 1999). With water injection, reservoir pressures will increase locally and that may lead to the formation or reactivation of fractures and the creation of new flow paths. Stress-related change in dynamic behaviour may be indicated by changes in well test results i.e. a reduction in Kh and PI over time and by production rate changes. These effects listed above are not exclusively related to stress changes but may be linked to flow in the reservoir such that water or gas block the flow of oil through relative permeabililty effects, or to mechanical problems in a well. With depletion, the pressure drop may increase the normal stress acting on a fracture plane and cause elastic closure of the fracture. The effects of a considerable pressure drop may be irreversibly plastic (McDermott & Kolditz 2004). Santarelli et al. (1998) presented data to show that the stress path, i.e. the change of effective stress magnitude and of horizontal to vertical stress ratios, is an important factor in explaining reservoir performance. If plastic deformation is a consequence of this stress path, it can have important consequences during re-pressurization since it is essentially irreversible. Various empirical models have been developed to assess the effect of depletion on fracture permeability (Walsh 1981; Barton et al. 1985; Buchsteiner et al. 1993). Such models have to be idealized. They require quantification of parameters (e.g. fracture width, height, asperity characteristics and rock mechanical parameters) that in most cases are not known in detail. The potential importance of stress changes reinforces the need to analyse the initial and changing stress state in a reservoir.

Dynamic calibration example Co-visualization diagrams (Fig. 14; cf. Rawnsley et al. 2004) of the three wells discussed earlier show the diversity of the fracture network and its flow response. In well A, mud losses start at 3760 m and keep occurring at regular intervals along the well bore. Loss rates start at 2–4 m3/h and remain relatively stable. Near the top of Unit 3 losses and loss rate increase at a point that coincides with a spike on the temperature log and

a peak in the NE fracture intensity log. However, earlier temperature log peaks are not associated with losses. In well B losses start at around 4370 m (3 m3/h) and show a similar pattern as in well A. Interpretation of PLT data shows only one inflow interval just before the point where losses started. The fact that this interval coincides with the only major interval of NE fracture density seems significant. The NE and the NS fractures are developed in well defined separate intervals and do not seem to be part of the same fracture spectrum. In well D losses are similar to wells A & B. Losses start near top Unit 2 (3.5 m3/h) but thereafter rates diminish gradually even while new loss points are recorded. The PLT is interpreted to show inflow in four intervals, all contributing roughly the same proportion to total flow. The first interval is not associated with losses but coincides with the most intense NE-fractures interval. The point where losses started coincides with a break in drilling and a small increase in mud weight when drilling was resumed. The bottom PLT interval, contributing slightly more than the others, is also related to a NE-fracture intensity peak. Well D has a higher degree of fracture intensity as shown for instance by P32 data (Table 1). The inflow is developed over considerable parts of the wellbore. This may be related to the matrix permeability in well D combined with relatively high fracture density. In the other two wells the flow is linked to specific parts of the fracture network, i.e. fracture corridors occurring where intensity peaks. The mud loss record supports such an interpretation. Loss rates of a few m3/h and the frequent occurrence of dynamic losses could be indicative of a fracture network where occasional densely fractured zones, i.e. fracture corridors, link up the wellbore to the larger scale fracture network. The fracture intensity curves in the co-visualization diagrams are always very spiky showing the clustered nature of the fracture sets. Major spikes on the different curves do not as a rule coincide but are located at different points along the wellbore. A system that is density clustered (Fig. 9) should show a high degree of coincidence of the fracture clusters in the orientation ranges. The fact that this is not shown here leads to the conclusion that the system is more orientation clustered.

Summary Calibration of fracture network geometry with dynamic indicators aims to define conductive properties and calibrate the spatial development of fracture interconnectedness. The latter can only be qualitatively assessed beyond the wellbore, both vertically and horizontally. The calibration should also be used to investigate if aperture assessments,

MODELLING FRACTURED RESERVOIRS

391

Fig. 14. Co-visualization diagrams combine fracture characteristics (here through density curves for different orientation ranges) with dynamic indicators to assist in identification of those parts of the fracture network that can be associated with flow.

e.g. those derived from cores, image logs and outcrop, are realistic (Gilman 2003). This should take into account the differences between mechanical and hydraulic aperture, and subsurface stress and stress release when core is taken to the surface. Methodologies to evaluate dynamic indicators are numerous and data acquisition conditions vary. During drilling the conditions (e.g. pressure) in the borehole can be significantly different from those when a PLT is taken under flowing conditions after well clean up. The realization that conditions play a role is important for proper interpretation since different indicators need not show a comparable response over the same wellbore interval. Dynamic calibration is made easy by the integration of information and interpretation in co-visualization displays. Where only orientation and density are known in detail, the analysis helps to formulate constraints for dimensions, aperture and connectivity for the network as a whole as well as specific fracture sets.

Inter-well interpolation The geometric analysis and dynamic calibration of a fracture network is a prerequisite for the construction of a model of the fractured reservoir on any scale. In addition, some idea must be formed about fracture network characteristics in the inter-

well space. Geostatistics are by now a standard approach for conventional reservoirs (Davis 2002), but it does not seem to be in common use for fracture networks. Curvature of geological surfaces derived from seismic data has been used to assess the degree of fracturing. Seismic anisotropy is used to evaluate spatial attributes of fractures and fracture systems. Geomechanical methods can be employed to derive fracture distributions from existing fault geometries and stress states.

Geostatistics Interpolation into the inter-well space can be done through the analysis of fracture network characteristics with geostatistical methods, e.g. variograms and subsequent kriging of the data (Olarewaju et al. 1997) or neural network techniques (Ouenes & Hartley 2000). Gauthier et al. (2002) use standard statistical methods to derive fracture frequency from well data. Several reservoir characteristics, which potentially can be correlated with fracture frequency, are then analysed statistically to determine a possible field-wide fracture frequency distribution. This approach seems to be the general one. Geological drivers (e.g. structure, lithology, porosity) are linked through standard statistics and/or geostatistics to fracture density derived from well data (Bourbiaux et al. 2002), whereas dynamic

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indicators are used as additional constraints (cf. Ouenes & Hartley 2000). For conventional reservoirs the geostatistical analysis is based on well data combined with a formulation of reservoir architecture based on facies analysis (Davis 2002). Often the reservoir architecture is dominated by one direction and shows relatively long correlation distances. A fracture network is normally defined by multiple directions, certainly in density but also in orientation, and will have much shorter correlation distances. In conventional reservoirs, the horizontal dimensions dominate the problem, whereas for fracture networks it is a threedimensional problem. To validate the geostatistical approach will therefore be more difficult in the fracture case.

Curvature In it simplest form curvature of geological surfaces is defined as the reciprocal of the radius of curvature. The computation involves the calculation of the second derivatives of the surface and the specification of various other geometry and scale-related measures (Roberts 1998; Bergbauer & Pollard 2003). Various calculated measures are used to quantify the degree of deformation (or strain) and subsequently to predict fracture orientation and density. Curvature has been used to assess of the degree of fracturing, e.g. through comparison with well fracture data (Lisle 1994) or production data (Belfield 2000). However, the numerical techniques are not universally accepted and without filtering for different scales of surface irregularities, questionable results may be produced (Bergbauer et al. 2003). A significant problem with the technique is that total curvature is related to the total structural history whereas open fractures may only be related to part of that history (Heffer et al. 1999; Belfield 2000).

Seismic anisotropy In principle, seismic velocity anisotropy can be used to determine spatial attributes of fractures smaller than the seismic measurement resolution (Hudson 1981; Crampin 1981; Armstrong et al. 1994; Lynn 2004). In rock with vertically aligned fractures, elastic properties vary in the direction crossing the fracture but not along the fracture plane. The effect is that waves travelling along the fracture travel faster than waves crossing the fracture and waves thus affected arrive at the recording point at different times, giving rise to azimuthal velocity anisotropy. Models built with synthetic, controlled data sets show the potential value of the methodology (Will et al. 2005; Freudenreich et al. 2006). When real data is used the results are more

variable. Gray & Head (2000) found good correspondence between Amplitude Versus Offset (AVO) and Amplitude Versus Azimuth (AVAZ) analysis results and well fracture orientation data, but predicted fracture density was more difficult to link to well performance. They explain this by postulating that in their example, well performance is governed by fracture orientation rather than density. The velocity anisotropy approach has been applied to, among others, the Clair field on the UKCS (Smith & McGarrity 2001; Barr et al. 2007). Fracture density and/or orientation estimates derived from seismic anisotropy must be considered to be relative and qualitative until calibrated properly. For instance the basic response of a dense system of short fractures may not differ much from that of a less dense system of longer fractures. The anisotropy response of a multidirectional fracture system, where several directions and associated apertures are combined, will be very difficult to analyse and verify (Maultzsch et al. 2003; Liu et al. 2003). The spatial averaging implicit in the seismic method is insensitive to factors, such as connectivity, that are critical to flow. In the use of seismic fracture predictors results must be generated with the key geometric aspects of the fracture network in mind. Since the generation of the anisotropy attribute is creating another model, it must be calibrated against the data, both static and dynamic, that was used to describe the fracture network geometry (Boerner et al. 2003; Will et al. 2005).

Geomechanical methods Geomechanical (e.g. finite element and finite difference) techniques use the estimated current or inferred historic stress state to evaluate the orientation and density of fractures with respect to a fault framework (Heffer et al. 1999; Bourne et al. 2000). With the stress state or displacement boundary conditions, a strain tensor is generated that serves as an indicator of fracture orientation and density. Multiple deformation events can be modelled sequentially by applying variable boundary conditions, e.g. displacements changing in orientation and magnitude with time. The results depend very much on the accuracy of the input data. Both stress state and rock strength parameters are generally poorly constrained. The resolution of the fault framework is also an important factor that determines output quality. Geomechanical methods can be used to couple stress state changes due to depletion with fluid flow (Heffer et al. 1999; Bagheri & Settari 2005). This allows an assessment of conductivity changes in the whole fracture network or a specific fracture orientation.

MODELLING FRACTURED RESERVOIRS

Summary The results obtained using all these techniques to evaluate the inter-well space are variable. Special care should be taken when they are based, implicitly or explicitly, on the use of scale invariant or fractal mathematical relationships. Continuity between small and large scale parameters such as fracture and fault dimensions and density, is possible but should not be assumed. Most methodologies present an indicator of fracture density and possibly orientation, often with limited vertical resolution. Whatever technique is used, results must be calibrated against representative well data. Since, as was discussed earlier, density and orientation are not necessarily the most influential parameters on fracture network conductivity, the inter-well interpolation results should come with a considerable error margin.

Conceptual models and modelling rules Given the complexity of fractured reservoirs, it is not realistic to assume that addressing the problem in the sequential order of geometric analysis – dynamic calibration – inter-well interpolation will constitute a fully integrated, optimal analysis. In practice, an iterative process is preferred in which specific aspects are studied in conjunction and used to reinforce sub-processes. The process should focus initially on evaluating those geometric

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elements (orientation and density) that can deliver hard rules. When combined with dynamic indicators, it is possible to constrain the more elusive rules for fracture dimensions, connectivity and aperture. The process involves the formulation of conceptual models and modelling rules. A conceptual model describes the various components of the fracture network in terms of geometry and dynamic behaviour (Rogers & Al Ansari 2004). The starting point for conceptualizing could be the widely used subdivision of fractured reservoirs (Nelson 2001; cf. Allan & Qing Sun 2003; Fig. 1). However, it is not so simple because most fractured reservoirs can be classified vertically and horizontally in two or even more classes. The standard scheme differentiates primarily on the basis of the matrix characteristics and much less on fracture network characteristics (Fig. 1). The discussion given above on percolation theory shows the importance of the variability in that network. Classification and conceptual model must take both matrix architecture and fracture network interconnectedness into account. The first is a function of the distributions of net reservoir rock, porosity and permeability. The simple scheme shown in Figure 15 cannot be considered to present a rigorous classification but it allows an evaluation of the fractured reservoir in terms of type and in terms of well performance. Such schemes can be used, after fracture network geometry and dynamic indicators have been integrated, to plot wells relative to each other. Note that it does not address the complexity of the

Fig. 15. A conceptual model for a fractured reservoir must take both the matrix quality and fracture network interconnectedness into account. The implication of percolation theory is that around the critical region of the percolation threshold, sharp differences in well performance could occur. The relative location of a well in such a scheme is based on the interaction between the fractures and matrix, e.g. as expressed by well performance on test and production against an assessment of fracture network geometry and interconnectedness.

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transfer process between matrix and fractures. Nevertheless plots like this show what is observed and hence can be used to make a first assessment of the effectiveness of that transfer process. Modelling rules follow from the analysis of the geometrical aspects of the fracture network. Such rules may be uniform over the whole field but in general the set of rules will show differences laterally and vertically. Together with inter-well interpolation results, the conceptual model and the formulated rules form the basis for subsequent modelling of the fractured reservoir.

Conceptual model and modelling rules example The fracture data (P32) shows that well D is the most intensely fractured whereas wells A and B are less fractured (Table 1). The data is interpreted as a superposition of several orientation sets with a considerable degree of orientation clustering (Fig.14). In wells A and B the flow is linked to the relatively high density peaks, i.e. fracture corridors, but in well D the network possibly also contributes as it is linked directly to better quality matrix. The analysis of the wells shows that interconnectedness of the fracture network is variable but it seems unlikely that an effective spanning cluster exists at the scale of the three wells. Rather network clusters will be developed at a scale not exceeding that of the inter-well spacing. Fracture orientation is dominated by NE-oriented sets. Purely from a numerical point of view, and indicated by the dynamic calibration, this orientation seems to be the one primarily associated with flow. Conceptually (Fig. 16), the reservoir can be represented by a relatively dense system of dominant NE-oriented fracture clusters with additional clusters in north–south, east– west and NW orientations. The latter are probably similar in density and dimensions. The length of the NE-oriented clusters and the abutting relationships between NE and the other orientations are uncertainties that must be addressed in fracture network modelling. Potentially well D is the most promising well in terms of performance, based on fracture density and matrix development. Assuming that fracture corridors control the performance, it can be expected that well D will be connected to a larger portion of the total network compared to the other wells. Well B would be the lowest in that respect. The relative positions of the wells on the typing chart of Figure 15, assume a percolation threshold at the well scale and a matrix that will only be capable of low flow rates in the absence of fractures. From the analysis of the example data the following fracture network modelling rules can be specified:

Fig. 16. For the example wells the fracture network consists of relatively low density (NW, north– south and east–west-oriented) fracture clusters, which show variable abutting relationships with more densely spaced NE-oriented fracture clusters. The length of the NE-oriented clusters and the abutting relationships are uncertainties that should be addressed in fracture network modelling.

(a) the fracture network consists of network clusters at a maximum size of the well scale; (b) the network is dominated by NE fractures (53%); fracture clusters in the north–south (20%), east– west (15%) and NW (12%) orientation ranges will be modelled in lesser proportions; (c) fracture density (P32) is structurally controlled, i.e. it is characterized by regional differences; (d) connectivity relationships between fractures have not been established and these are used as a modelling uncertainty parameter. Considering that the dynamic indicator calibration of the three wells favoured the NE fracture orientation for flow, the option that the NE orientation represents through going fractures and other orientations abut against it in variable proportions will be considered; (e) mechanical stratigraphy is not indicated by the fracture density, which seems to be uniform over the units and in the modelling exercise unit boundaries will not inhibit fracture propagation. Note that this is not necessarily correct since similar densities can also occur when boundaries do inhibit propagation; (f) as a consequence of rule (e) the vertical dimension of fractures is controlled by the thickness

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of the modelled units; the horizontal dimension will be controlled by the inferred network cluster size, i.e. the maximum length will not exceed well length and will probably be less; analysis of network clusters in constructed models will have to be used to establish suitable ranges. No inter-well interpolation results are available other than the large-scale permeability in Unit 2 (Fig. 10). This will be used as a proxy for density distributions for the orientation ranges in the model. This map was derived from reservoir architecture modelling work not discussed further here.

Fracture network modelling The objective of fracture network modelling is to study the interconnectedness and hydraulic potential of the network and, when it meets certain criteria, pass the essential elements on to a reservoir simulation model. The latter can be a coarse full field model that is used to manage field development and evaluate reserves. Alternatively, it can be a detailed sector model to analyse specific issues concerning one or a few wells. The choice for simulation methodology ranges from relatively simple matrix models with a permeability multiplier to cater for the fracture network, via dual medium (dual porosity or dual permeability) models to explicitly modelled fractures. What determines the choice must be the capacity of the chosen method to represent the complexity of the real fracture to matrix connection while preserving the essence of the real reservoir (Gilman 2003) as has been captured in the conceptual models and modelling rules. Irrespective of method, size and grid dimensions, a good model is one that captures the important flow mechanisms and geometrical aspects and gives reasonable estimates of past and future performance of the area modelled. Given that objectives may be different and that conceptual models, modelling rules and inter-well constraints carry large uncertainty ranges, there are no simple schemes to guide the modelling of fracture networks.

Discrete Fracture Network modelling Discrete Fracture Network (DFN) models are constructed by generating, through a combination of deterministic and stochastic methods, fracture sets with variable dimensions, orientations, density and interaction relationships (Rawnsley et al. 2004). The modelling of a fracture network usually takes place in the same geocellular framework as has been used for the matrix (Cacas et al. 2001; Bourbiaux et al. 2002). Considering that lithology contrasts commonly play a role in development of

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a natural fracture network, this is a logical choice to begin with. The first phase of constructing a DFN model deals with translating geometry rules and inter-well interpolation results into a fracture network, which is calibrated against the data derived from wells (Bech et al. 2001). The second phase involves analysis of the interconnectedness in the fracture network. The numerical proportions of network clusters (i.e. groups of fractures connected with each other) and number of fractures in a network cluster are indicators of the level of interconnectedness at the scale of the model. With that data, an assessment can be made of how the model relates to the percolation threshold as that was estimated in conceptual terms. The last phase deals with assigning hydraulic properties to the fracture network. The most direct way is to assign an (hydraulic) aperture value to the modelled fractures. In simple models that could be a fixed value for all fractures but can be made more complex by using probability density functions that are sampled differently for different fracture sets. An alternative is to work with fracture porosity maps that are interpolated per grid cell, with aperture assigned proportionally to fractures in the cell (cf. Dershowitz et al. 2000). A deterministic approach in which conductive features are identified and assigned values or value ranges (cf. Barr et al. 2007) is at the other end of the scale. Fracture porosity, which is a function of fracture spacing and aperture, is difficult to determine and modelling it properly is a challenge. When a fractured reservoir has reasonable matrix permeability and the matrix provides the storage, the value of the fracture porosity is relatively unimportant in terms of volume. The fracture volumes become important in economic terms when matrix storage is relative low. However, fracture porosity is always important as it determines fracture permeability (Witherspoon et al. 1980).

DFN modelling example The network modelling method used for the example presented here is based on fracture growth on various scales and orientation, using controlled relationships with unit boundaries and between fracture sets. The constraints are combined in a series of probability maps or grids that contain a numerical definition of specific parameters. The method is fully explained by Swaby & Rawnsley (1997) and Rawnsley et al. (2004). For the example, fracture sets have been constructed that can be combined in various ways to form a model. Four sets of NE clusters, with maximum lengths 2000 m, 1500 m, 1000 m and 500 m respectively, are constructed using the permeability

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distribution map (Fig. 10) to control density. High permeability is assumed to equate to high density. Fracture sets for the north–south, NW and east – west orientations were constructed with length distributions constrained by an impedance factor attached to the NE-2000 set. The impedance value indicates the fraction of intersecting fractures for which growth is stopped against the impeding set or unit boundary. For the model these constraints were: (1) fully constrained with impedance 1.0 and (2), (3) and (4) with impedance values of respectively 0.75, 0.5 & 0.25. Density constraints are chosen to ensure that, rather than a full fracture network, all constructed sets model fracture clusters. In this way sixteen fracture sets were generated: four NE sets and twelve (4 3) orientation fracture sets. For the latter the same permeability map was used as a constraint but to account for the observed lower densities, the probability of growing a fracture was half that of the NE sets. Models created by combining specific fracture sets were investigated for network cluster development. In Table 3 the results of such an analysis for the combinations of NE sets with the other orientation sets are shown for specific impedance values. The number of network clusters (i.e. 25 or more fractures connected) and the percentage of the total number of fractures in the largest cluster, characterize a model. For low NE impedance (0.25), one single cluster makes up almost the total network in all models. Such models will be well above a percolation threshold on the scale of the model and are not considered to reflect the well results. In contrast, for the total impedance case (1.0), the models, with the exception of that with the NE-2000 fracture set, show none or only one cluster that contains more than 25 fractures. These models are well below the percolation threshold on the scale of the model and are also considered invalid. For two of the models the network cluster data is shown in Figure 17. Model #01 (NE-2000 combined with impedance 1.0 orientation sets) shows clusters associated with the well where the NE fractures dominate totally.

Proportionally the well A cluster is much larger than that linked to well D. In model #09 (NE-1000 combined with impedance 0.5 orientation sets) the NE fractures are still dominant but the length distribution contrast with the other clusters is much smaller. Proportionally, network clusters linked to wells A and D are balanced in this model and this reflects better what was expected in conceptual terms. The size of the well A cluster in both models is a consequence of the relatively high matrix permeability in the vicinity of well A (Fig. 10). Density in the generated fracture sets is linked to the size of this area. On the basis of dynamic well analysis a larger network cluster was expected for well D. This could mean that the modelled permeability distribution is a poor proxy for fracture density. On the other hand, differences in regional overprinting relationships, between one or more of the orientation sets with respect to the NE set, may also be a potential factor. Such regional differences could be related to the orientation-clustered nature of the network. It would require more complex models with local impedance differences to investigate this further. The two models are also compared in terms of fracture porosity, which was calculated here in a 50 m 50 m grid model (Fig. 18). For the same aperture assigned to both NE fracture sets and the orientation-clustered fracture sets, the differences between the two models are considerable. Model #01 again shows the dominance of the NE direction, but in model #09 the other orientations are also important. The effects on flow of the various configurations can be analysed dynamically with these fracture network models, e.g. using well test results as matching criteria (cf. Rawnsley & Wei 2001). The fracture sets generated are very simple, i.e. they have a single orientation and only contain vertical fracture clusters. Given that the models are non-unique, the choice of simplicity was deliberate in order to generate representative sets of models that capture the identified uncertainties. Here, where the focus is on the length of the

Table 3. Fracture model clustering data Imp. 1.00 0.75 0.50 0.25

NE-2000 29 2 2 1

13.0% 95.0% 95.0% 99.0%

NE-1500 1 34 1 1

0.1% 15.0% 98.0% 97.0%

NE-1000 0 33 3 1

0.0% 5.0% 86.0% 96.0%

NE-0500 0 9 26 1

0.0% 1.0% 13.0% 92.0%

The table lists the number of clusters with more than 25 connected fractures and the number of fractures in the largest cluster as a percentage of the total number of fractures in a particular model. Imp., the impedance value (proportion of a secondary set which terminates against a primary set) attached to the NE-2000 fracture sets for the generation of north–south, east–west and NW fracture sets.

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Fig. 17. Fracture network model calibration against network clusters. The bargraphs show the range of mean þ/2 standard deviation for the fracture sets in the four orientation ranges. For further explanation see text.

dominant fracture orientation and its interaction with the other orientations that can be adequately represented with unidirectional sets of vertical fractures. Compared with multidirectional, variable dip sets, these simple sets will elucidate

greater contrasts between the different models. Once a preferred model has been chosen, multidirectional, variable dip sets can be generated to achieve greater refinement (cf. Leckenby et al. 2007).

Fig. 18. Comparison of fracture network porosity for models #01 and #09. Warm colours are high fracture porosity values. The histograms show the (normalized) fracture porosity distribution in the two models. See text for further discussion.

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The step to simulation modelling The basic equation that describes flow in fractures is the cubic law which implies that fracture conductivity for an ideal open fracture, i.e. for a fracture between parallel plates that are not in contact with each other, and assuming laminar flow, is uniquely defined by aperture (Witherspoon et al. 1980). The natural deviation from a situation of parallel plates causes a reduction in flow, which for example, can be accounted for by the Joint Roughness Coefficient, when the effective fracture permeability is calculated (Bakhtar et al. 1985). Provided that a reasonable estimate of JRC can be made, the impact of the adjusted aperture on fracture permeability KF can be evaluated. Using the cubic law without aperture correction implies that the calculated fracture conductivity will represent an absolute upper limit. The effective permeability of a fracture network depends on the geometry of that network and the conductivity of individual fractures. Using the cubic law the (intrinsic) permeability of a single fracture is related to the square of the aperture (L 2); fracture conductivity is equal to the permeability multiplied by aperture (L 3). Schemes to compute the effective fracture permeability range from relative simple vectorial decomposition schemes of the fracture permeability in X, Y and Z directions of the chosen grid, to full-scale simulation methods. Oda’s method (Dershowitz et al. 2000) determines an effective permeability tensor by integration of fracture conductivity of fracture sets of specific orientation or orientation ranges. It is a quick method but it does not incorporate the effects of fracture size and connection to other fractures. In principle, therefore, it can only be used for well-connected fracture networks (Dershowitz et al. 2000; Will et al. 2005). Fracture permeability simulation methods derive a directional permeability by applying flow and no-flow boundary conditions to the grid and solving for specific orientations (Dershowitz et al. 2000). Bourbiaux et al. (1999) describe methods based on the discrete modelling of fractures and matrix in what is called the joint element method. The simulation methods incorporate the connectivity aspects that are neglected in the grid cell solution schemes, but are sensitive to the assumptions made for boundary conditions. The simpler schemes are often chosen because explicit simulation methods are computationally intensive. The above methodologies involve upscaling from the geological scale, i.e. the geometric and hydraulic characteristics of the fracture network, to a representative formulation of fracture permeability and the fracture network geometry on the reservoir simulation grid scale (Bourbiaux et al. 1999). The characteristics of a fracture

network are potentially measured at a metre scale or lower whereas the grid dimensions are tens of metres or higher. Transferring the DFN to a grid expresses the problem in terms of averages of the small-scale quantities (Gilman 2003) and effectively the reservoir model becomes a simplified representation of the actual fractured reservoir (Gorell & Bassett 2001). To represent the detailed geology adequately requires that the consequences of upscaling are properly thought through. The dimensions and the interconnectedness of the fracture network and the flow interaction between the fracture network and the matrix must be captured at an appropriate scale, e.g. the representative elementary volume (REV) or the minimum volume for which a physical property can be measured and still be applied as an average value over a larger area (Trice 1999; Dershowitz et al. 2000; Bourbiaux et al. 2002). The REV approach assumes that a representative elemental volume exists at a scale of the chosen grid cell size. In a fracture network where the scale of interconnectedness varies widely that may not be achieved easily (Dershowitz et al. 2000). The considerations that determine the choice of grid dimensions are related to those that determine the choice of simulation model type and will be discussed below. The objective could be to model the full field, represented by relatively large-scale features such as faults and fracture corridors, or at the other end of the scale to analyse local well test data (Rawnsley & Wei 2001; Gorell & Bassett 2001; Bourbiaux et al. 2002). This is not an either–or decision. Small-scale sector models may be indispensable in reducing the uncertainty in concepts and models. Detailed analysis can bring out the key components of the system that must be represented in the larger scale reservoir simulation model (Rawnsley & Wei 2001; Araujo et al. 2004). The capacity of computers to handle models of a certain size will be one limitation. If, because of resource constraints, grid dimensions become larger than fracture dimensions, a different modelling strategy or sector modelling to derive ‘pseudo-properties’, which compensate for deficiencies introduced during upscaling, may be required (Gilman 2003). In fractured reservoirs, the fluid transfer from matrix to fracture commonly occurs at rates that are considerably lower than the flow within the fractures (Kazemi et al. 1992; Daly & Mu¨ller 2004). When that is the case the permeability of the fracture network and of the matrix must be represented separately and additional terms to govern the flow from matrix to fracture must be included. Bourbiaux et al. (2002) summarized the requirements for various simulation methodologies. A single medium (or single porosity) model can be

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used for dense, well-connected fracture networks where the exchange between the small matrix blocks and the dense fracture system is virtually instantaneous. At the scale of the grid model, the problem has become a homogeneous one (cf. Waldren & Corrigan 1985). A dual porosity– single permeability model is required where the kinematics of matrix to fracture transfer are such that the matrix is only the source of fluids. If matrix to matrix flow has to be modelled, dual porosity –dual permeability representation is required. In the dual porosity –single permeability model flow takes place in the fractures and between matrix and fractures. Matrix blocks are assumed to be completely surrounded by fractures. In dual porosity–dual permeability models, matrix to matrix and fracture to matrix flow is also possible. This representation is more geologically realistic (Gilman 2003) but computationally intensive. In the subsurface, matrix blocks will not be floating but must support stresses through matrix block contacts (Baker & Kuppe 2000). Finally, when the dimensions of the fracture network make them major conduits for fluid flow at a scale well beyond that of the matrix blocks, explicit modelling, where fractures are represented directly by specific grid cells, may be required. Computational requirements mean that the simple representations are often preferred. The separate representation of fracture flow means that the model must account for the different contribution of matrix and fractures and their interaction. The basic idealized formulation to describe this has been proposed by Warren & Root (1983). The matrix to fracture flow is described by a transfer function in which the shape factor accounts for the shape and dimensions of matrix blocks. This formulation has been extended in numerous ways to account for multi-phase flow and for different types of recovery mechanisms (cf. Waldren & Corrigan 1985; Kazemi et al. 1992; Bourbiaux et al. 1999 & 2002; If & Frykman 2005). The fluid exchange between matrix and fractures depends on the pressure differences between matrix and fractures and viscous, capillary and gravity effects. Which one of these plays the greater role depends on various factors (Waldren & Corrigan 1985) and the formulation of the shape factor is not without problems. For the various flow mechanisms, different values of the shape factor are required (Bourbiaux et al. 1999). Given that there is an obvious sensitivity in the shape factor computation with respect to the grid dimension, it is considered to be a history matching parameter (Gilman 2003). In simple terms, dynamic modelling requires that the permeability distribution of the fracture network and of the matrix will be combined in a meaningful way. The rules and concepts can be

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used to construct a digital fracture network model, which in turn can be used to evaluate and calculate the effective fracture permeability field. The results of the integrated analysis of static and dynamic data captured in rules and conceptual model are the basis for a considered choice with respect to grid dimensions, simulation model type and transfer function, to ascertain that the constructed model is appropriate for the intended analysis.

Concluding remarks Proper modelling of fractured reservoirs to analyse and predict performance is essential to implement the right development options thereby assuring optimal recovery. Available data from cores and image logs, even when available in abundance, cannot provide a description of the geometry of a fracture network that is enough to construct the definitive fracture model. Cores and image logs simply cannot provide sufficient information on fracture dimensions, aperture and connectivity. This means that considerable uncertainty has to attach to these parameters when the data is used for fracture network modelling. The construction of a fracture network model is therefore not a simple matter of combining concepts and rules but requires analysis in its own right. Even with a set of relatively restrictive rules, as used in the example described here, several equi-probable DFN models can be generated. Dynamic modelling can be carried out by capturing the total range of possibilities through scenario modelling (i.e. using the same model with changes in parameter values), or through the building of several models addressing different static and/or dynamic concepts. Analysis of the fracture network models against the background of concepts and rules, and revisiting those when appropriate, is essential to constrain parameter ranges and scenarios. Complex digital models of fractured reservoirs are computationally time consuming and thus expensive to run and difficult to interpret and adjust. There is thus an obvious incentive to construct simple models that are based on the dominant processes and geometries that control performance. There are no hard rules to govern the choice of modelling strategy and methodology, other than a requirement that it reflects the contrast between fractures and matrix as well as serving the reservoir simulation objectives. In that choice fit-for-purposes-simplicity is generally better then complex modelling for the sake of complexity. The fact that we can build such models, having powerful computers and versatile modelling software, does not mean that we must. Fractured reservoirs are difficult to analyse, model and manage and there are no universally

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applicable ‘rules of thumb’. Methodologies that work for one fractured reservoir may fail totally in others. But by using workflows in which the analysis of data is integrated correctly, the understanding of a fractured reservoir can be greatly improved and useful conceptual, static and dynamic digital models can be constructed. The analysis of the fracture network in terms of geometry and dynamics and its translation into concepts and modelling rules, which are then tried and tested in DFN mode, is a key element in this workflow. New methodologies to improve data acquisition and analysis, some of which are discussed in this volume, will continue to improve this workflow. This paper is published with the permission of Shell International Exploration & Production. The critical comments of D. Barr, P. Frykman and R. Jolly are gratefully acknowledged. The views of numerous Shell colleagues I have worked with over the years influenced my own views on fractured reservoirs and are reflected in this paper. The opinions expressed, however, are the sole responsibility of the author.

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Numerical simulation of multi-phase fluid flow in structurally complex reservoirs ¨ I1, S. GEIGER2, S. G. ROBERTS3, A. PALUSZNY1, M. BELAYNEH1, S. K. MATTHA 4 A. BURRI , A. MEZENTSEV1, H. LU1, D. COUMOU5, T. DRIESNER5 & C. A. HEINRICH5 1

Department of Earth Sciences, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, UK (e-mail: s.mattha¨[email protected]) 2

Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK and Edinburgh Collaborative on Subsurface Science and Engineering (ECOSSE) 3

Department of Mathematics, Mathematical Sciences Institute, Australian National University, Canberra, ACT 02000, Australia

4

Department of Mathematics, ETH Zu¨rich, Ra¨mistrasse 101. 5, CH-8092, Zurich, Switzerland

5

Department of Earth Sciences, ETH Zu¨rich, Clausiusstrasse 25, CH-8092, Zurich, Switzerland Abstract: Realistic simulation of structurally complex reservoirs (SCR) is challenging in at least three ways: (1) geological structures must be represented and discretized accurately on vastly different length scales; (2) extreme ranges and discontinuous variations of material properties have to be associated with the discretized structures and accounted for in the computations; and (3) episodic, highly transient and often localized events such as well shut-in have to be resolved adequately within the overall production history, necessitating a highly adaptive resolution of time. To facilitate numerical experiments that elucidate the emergent properties, typical states and state transitions of SCRs, an application programmer interface (API) called complex systems modelling platform (CSMP þþ) has been engineered in ANSI/ISO C þþ. It implements a geometry and process-based SCR decomposition in space and time, and uses an algebraic multigrid solver (SAMG) for the spatio-temporal integration of the governing partial differential equations. This paper describes a new SCR simulation workflow including a two-phase fluid flow model that is compared with ECLIPSE in a single-fracture flow simulation. Geologically realistic application examples are presented for incompressible 2-phase flow, compressible 3-phase flow, and pressure-diffusion in a sector-scale model of a structurally complex reservoir.

The recovery of hydrocarbons from the subsurface is an application area where a good understanding of the geology can have a dramatic impact. Establishing the impact of geological features on multiphase flow requires Earth scientists to work with reservoir engineers in the building of forward models of reservoir production. Examination of current best practice suggests that decisive geological information can be lost at this interface because, faced with the wealth of collected data, reservoir teams struggle to discriminate between observations that are critical for fluid flow and are usually forced to simplify the geological model in order to apply conventional simulation tools and/ or obtain the desired history match within a limited amount of time. Reservoir engineering heavily relies on meta-models (e.g. dual porosity, multiple continuum etc.), effective material properties, and other approximations made at the field scale. Thus, model-guided intuition of the impact of the original underlying geological features on

flow may be flawed, especially if their size is below the level of seismic resolution. Since the actual reservoir system is only partially revealed by measurements, cause and effect chains may be difficult to interpret so that misconceptions may survive for a long time. The inverse correlation between geological complexity and final recovery (Fisher 1991) indicates that there is room for improvement in model-guided reservoir management. The goal of any such forward modelling is to understand how physical processes known to operate in a complex reservoir will interact and what system behaviour these interactions result in. The better our understanding of these couplings becomes, the more accurately we can assess how a reservoir will respond to a certain management strategy and which field data must be acquired to constrain such sensitivities. Numerous studies have demonstrated that structurally complex reservoirs have a strongly heterogeneous permeability and may contain many

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 405–429. DOI: 10.1144/SP292.22 0305-8719/07/$15.00 # The Geological Society of London 2007.

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high-aspect ratio faults, discontinuous layers and fractures (e.g. Nelson 1985). Multi-phase fluid flow is the consequence of an intricate and spatially variable interplay of viscous, gravitational and capillary forces in this complex geometry. Bulk velocities vary spatially over 5–8 orders of magnitude and are subject to non-linear feedbacks between saturation and total mobility (Mattha¨i et al. 2005a). Most commercial reservoir simulators only operate on structured grids, and these are not capable of incorporating all of the elements of cross-cutting inclined faults combined with layer offsets. Thus, non-neighbour connections, transmissibility multipliers and shape factors are used to patch the grids and to account for the missing features. Yet, simulation results show that such simplified models can lack physical realism (Mattha¨i et al. 2005a; Belayneh et al. 2006). Various studies (e.g. Durlofsky 1993; Kim & Deo 2000; Geiger et al. 2004; Monteagudo & Firoozabadi 2004; KarimiFard et al. 2005) have demonstrated numerical methods that are, in theory, suitable to model flow in geometrically complex structures but have only applied them to proof-of-concept flow geometries as opposed to field-data based geological interpretations with a hierarchy of structures. We have developed a multi-purpose simulation workflow and reservoir simulation modules for multi-phase flow, diffusion and transport processes in structurally complex reservoirs resolved in sufficient detail to capture both seismic and subseismic features at the same time. This methodology has been applied successfully to model single-phase and multi-phase flow in fractures, reactive transport, formation of ore deposits, and convection in hydrothermal systems (Mattha¨i & Roberts 1996; Mattha¨i et al. 1998, 2004, 2005a; Geiger et al. 2002, 2005; Mattha¨i & Belayneh 2004; Coumou et al. 2006; Belayneh et al. 2006). Importantly, our workflow also relies on state-of-the-art computer aided design (CAD), meshing, and numerical tools including an algebraic multigrid solver for systems (SAMG, Stu¨ben 1999).

Methodology The sequential steps of the new simulation workflow are; (1) feature representation and geological interpretation of the model geometry in CAD; (2) hybrid finite-element discretization of the model geometry; (3) discretization of the governing equations using operator splitting in a combined finite-element and finite-volume framework; (4) a posteriori mesh adaptation for the pressure equation based on an estimate of the discretization error; (5) simulation; (6) visualization and analysis of results; and (7) upscaling. Details of Steps 3 and 4

are described in Geiger et al. (2004) and Paluszny et al. (2007). Steps 5 and 6 are shown in Belayneh et al. (2006) and Mattha¨i et al. (2005b). Step (7) constitutes a separate subject which is touched upon by Mattha¨i et al. (2005a). Here we present an overview of Steps 1 and 2, discussing Step 3 in some detail, including relevant aspects of the required software engineering, some of which are described in an associated appendix. Steps 5 and 6 are illustrated in the results section.

CAD-based model building/geological interpretation and hybrid finite element discretization Geological models of structurally complex reservoirs are characterized by a feature-rich geometry with a large number of volumetric sub-domains bounded by irregularly shaped surfaces. The traditional representation of such geological interpretation-based geometries by non-smooth polyhedral surfaces is sufficient for visualization purposes but unsatisfactory for unstructured finite-element meshing due to inherent geometric discretization errors. In these circumstances, there may be tiny gaps where polyhedral surfaces are used to delimit the extent of strata truncated by faults and the discontinuous nature of these entities may result in erratic intersection lines. Also, although it is textbook knowledge that the degree of mesh refinement should be tailored to the needs imposed by the equations that are being solved, the commonly used polyhedral surfaces predefine mesh resolution when the geological interpretation is prepared. Furthermore, typical geo-cellular models lack intersection curves where surfaces cross-cut each other and there is no information on how surfaces combine into volumetric entities (Preparata & Shamos 1985). This means that the surface-delimited volumetric subdomains of the model are defined only indirectly and cannot be addressed or analysed as separate entities. These problems are readily solved if the so-called Boundary REPresentation format (BREP) is used at the geological interpretation stage. This method has been extensively tested and is well established because BREP represents the standard in computer aided design (CAD) for engineering applications (Lienhardt 1991). BREP approximates the shape by the outer boundary of an object, in terms of highly stable smooth Non-Uniform B-spline curves and surfaces (NURBS). From an interpreting geologist’s point of view, NURBS have the advantage that geometrical changes made as the understanding evolves impact only the immediate vicinity of the modified point, curve or surface. NURBS are also ideally suited to match geometry across regions with variable

SIMULATING MULTI-PHASE FLOW IN SCR

data density. In CAD, NURBS entities are stored hierarchically in a consistent topological tree structure. This topology ascertains that geometric search, curvature analysis, surface area and volume determination operations on the constructed model are performed with maximum efficiency. Free-form CAD tools also implement absolutely critical design proofing operations such as orientation consistency checks, identification of non-matching surfaces, and tests whether ensuing sub-volumes are water-tight. Methods and algorithms for automatic meshing of free-form NURBS geometry are a lively area of research. Current meshing tools (e.g. Baker 1989; Shephard & Georges 1991; Thompson et al. 1998; Owen 2002) use the BREP format because, by definition, it is not possible to represent complex free-form (as opposed to analytical) geometry by Cartesian structured grids (Thompson et al. 1985). The only feasible alternative is automatic unstructured meshing (Baker 1989; George & Borouchaki 1998; Owen & Saigal 2001). The automatic generation of tetrahedral meshes representing layers or massive rock is not a problem, but the situation is different for large-aspect ratio geological structures such as faults and fractures. Realistic simulation of multi-phase flow including capillary and gravitational effects requires fracture and fault meshes with internal degrees of freedom, i.e. several layers of elements have to be placed inside individual fractures. The ensuing small element size leads to prohibitively large overall element numbers and existing incremental meshing algorithms (Juanes et al. 2002; Bogdanov et al. 2003) do not work well between close subparallel surfaces producing highly distorted tetrahedra that can cause numerical errors (Thompson et al. 1998). Automatic generation of all-hexahedral unstructured meshes for free-form geometry is extremely difficult. Although a number of new robust algorithms for hexahedral meshing were proposed recently (White 1995; Blacker 1996), these methods still cannot handle arbitrary multiply connected geometry without intensive operator intervention. As a further possibility, surface only representations of fractures (e.g. Juanes et al. 2000; Bogdanov et al. 2003) have been introduced but they preclude the necessary internal degrees of freedom and cannot be used to model sealing faults because the nodes on either side are shared. As a good compromise between the complexity and efficiency of all-hexahedral meshing and the simplicity of automatic tetrahedralization hexahedradominant hybrid meshes containing other types of elements including prisms and pyramids can be created by post-processing of an initial tetrahedral mesh (Mattha¨i et al. 2005a; Paluszny et al. 2007). Such a hybrid mesh will contain hexahedral

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elements in geometrically unconstrained regions, whereas more shape-adaptive element types will populate regions of geometric complexity. To achieve the transition from hexahedral elements to tetrahedra, pyramid and prism elements are introduced (Fig. 1). The hybrid meshing approach is called indirect meshing (e.g. Owen & Saigal 2001). Threedimensional hybrid meshes contain 15– 20 percent fewer nodes and up to 12 times fewer elements than tetrahedral plus triangle meshes. They require less memory for mesh storage and the sparseness of solution matrices is increased. A decisive advantage of indirect hybrid meshing is that surface-only fracture and fault representations can subsequently be extruded into volumes of high aspect ratio elements, mostly thin prisms. This technique, developed for the detailed resolution of boundary flows in aerospace applications, is our preferred way to capture thin or sheet-like features like fracture, faults, dykes and pinching out layers. Figure 1 presents cross sections (cut planes) through three-dimensional hybrid element meshes of large-aspect ratio structures. Tapering of the prism layers representing there brings extra realism to the fracture representation. The matrix domain is meshed by a hexahedra-dominated hybrid mesh. The latter is the most economic solution in terms of element numbers and node connectivity. As is described in the following section on the discretization of the governing equations, nodecentred control volumes are used for the mass conservative solution of the transport equations. Control volumes are formed around the nodes of the hybrid finite-element mesh via the introduction of subdividing surfaces, positioned such that they match between the different types of element (Fig. 2). The generalization of this method to hybrid meshes has required us to develop a new consistent isoparametric finite volume tessellation for hybrid meshes, including volume and surface integration points (Paluszny et al. 2007). The key feature of this tessellation is that the resulting mesh does not have to be stored in memory. Storage is required only for a single stencil per finite element type in parametric space because fast mapping techniques can be applied to generate the finite volume integrals in the solution process.

Engineering of simulation software A careful examination of reservoir and/or geohydrological simulation software in 1995, when we decided to write CSMP þþ, lead us to the conclusion that existing architectures, especially implementations in procedural languages imposed limitations that stood in the way of reproducing

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Fig. 1. Structure discretization with high aspect ratio prism and hexahedral elements (mesh generated with Tetra, ANSYS Corp.). (a) Cross-section of hybrid element mesh of a bifurcating fault; (b) pointed tip of single fracture represented by tapering prism layers.

and disentangling complex geological phenomena. In spite of the somewhat reduced shortcomings of packages in 2006, reservoir teams often do not get near to using even their functionality. For example, most teams model faults as transmissibility multipliers without even attempting to work out what these mean in real terms (e.g. their permeability, thickness etc.). By contrast this article proposes that one should begin modelling a poorly understood system by including as many of its known characteristic features and potentially important component processes as is possible so that simulations can discriminate between noninfluential ones from others which determine reservoir behaviour. One may start with a geometrically simple model with small material property

contrasts, but to make predictions comparable with field data, a realistic geometry and material property ranges have to be introduced. It may only take a few realistic simulations to identify how sector- or field-scale models can be simplified without loss of accuracy, but for the structurally complex reservoirs identified by Fisher (1991), a large part of this step still lies ahead of us (cf. Gilman 2003). The if-in-doubt leave-in strategy is based on, albeit limited, experience that diagnostic model behaviour will ensue only if models and /or the represented physics are system specific (Matthai et al. 2004, 2005a; Geiger et al. 2005, 2006b). The human readiness to ignore selective geological facts combined with the inability to anticipate side

SIMULATING MULTI-PHASE FLOW IN SCR

409

Fig. 2. Node-centred control volumes in a hybrid finite element mesh. (a) lines meet at the central node of a single finite volume delimited by coloured translucent surfaces and sectors in four different finite element types marked by the different colours. (b) Multiple translucent finite volumes arise from finite-element finite-volume stencils with facets, the outward-pointing normals of which are marked by red cones. Note the pyramid stencils in the upper left of the graph.

effects of deliberate changes to natural systems is illustrated by a rich literature (cf. Nelson 1985; Reisner 1987). The if-in-doubt leave-in simulation approach leads to software design objectives and an implementation approach that differ considerably from those motivating conventional reservoir simulation tools. These and the basic functionality of CSMP þ þ code are reviewed in the Appendix.

Governing equations and numerical solution methods Derivation of governing equations

Mc ¼

The governing equations that describe compressible and incompressible single- and multi-phase fluid flow in porous media can be derived from mass balance equations and Darcy’s law. For simplicity, the discussion is restricted to isothermal fluid flow and explicit transport schemes. Non-isothermal fluid flow can also be simulated with CSMP þ þ (Mattha¨i et al. 2004; Geiger et al. 2006a). The mass balance for a chemical component c (e.g. H2O, CO2, CHX, NaCl) is given by: @Mc þ r Fc ¼ qc , @t

into different phases a which are commonly oleic o, gaseous g, or aqueous a. The partition behaviour is a function of pressure and composition, and also temperature in non-isothermal systems. The phase state and PVT properties are given by equations of state (e.g. Soave 1972; Haar et al. 1984; Spycher et al. 2003; Driesner & Heinrich in press). In reservoir engineering applications, these are often simplified in the form of a Black-Oil model (cf. Aziz & Settari 1979). The mass of component c per unit volume is given by the sum of the mass Mca of component c in each phase a:

(1)

X

Mca ¼ f

a

X a

Sa rca (2)

a [ fo, g, ag: Here, f is the porosity of the rock, S the saturation, i.e. the volume fraction of the pore space that is occupied by a, and rca the density of c in a. It is also useful to define a phase density ra which is simply the sum of all component densities rca contributing to phase a:

ra ¼

nc X

rca ,

(3)

c¼1

where M is the mass of component c per unit volume, Fc the flux vector of c, and qc a source or sink specific to c. A component c can partition

where nc is the total number of components c. The saturations of all fluid phases must add up to one,

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410

oil –gas–water system:

i.e. satisfy the relation: X

Sa ¼ 1 a [ fo, g, ag:

pcoa ¼ po pa pcgo ¼ pg po pcga ¼ pg pa :

(4)

a

If one phase is absent, for example Sg ¼ 0, the system reduces to two-phase flow and if two phases are absent, for example Sg ¼ So ¼ 0, to single-phase flow. Yet, the same set of equations is still applicable. The flux vector Fc describes the transport of c in the different phases a and is given by: Fc ¼

X

a [ fo, g, ag,

va rca

(5)

a

where va the velocity of phase a. If it is assumed that the rock matrix is incompressible, the fluid densities are constant, and the phases are immiscible, the conservation equation (Eqn 1) simplifies to the classical saturation equation:

ð9Þ

The generic Equations 1 to 9 describe isothermal single- and multi-phase fluid flow in porous or fractured media. The PVT properties, relative permeabilities, and capillary pressures are derived from empirical correlations or experimental data. For the numerical solution, it is convenient to formulate an additional equation that describes the evolution of the fluid pressure at constant concentration and saturation. To derive this equation, it is helpful to define the total mass and flux in each phase, Ma and Fa, respectively; Ma ¼

nc X

Mca ¼ fra Sa

a [ fo, g, ag,

c¼1

Fa ¼

nc X

(10) Fca ¼ ra va

a [ fo, g, ag:

c¼1

f

@Sa þ r va ¼ qa @t

a [ fo, ag:

(6)

Assuming, for simplicity, that sources or sinks are absent (q ¼ 0), Law 1 can now be rewritten as a conservation equation for the mass of phase a:

The velocity va at which phase a flows is given by Darcy’s law:

va ¼

kra ðSa Þ kðrpa ra gÞ ma

(7)

a [ fo, g, ag

vt ¼

va

a [ fo, g, ag:

(11)

Expanding Ma using the chain rule and summing over all phases present yields X @Ma

and the sum of the three phase velocities yields the total velocity vt X

@Ma þ r Fa ¼ 0 a [ fo, g, ag: @t

@t

a

X

@f @r þ fSa a @t @t a @Sa þfra a [ fo, g, ag: @t

¼

Sa ra

(12)

(8)

a

The relative permeability kr and the viscosity m are generally combined as the phase mobility la ¼ kra =ma . Note that the relative permeability kra is a function of the saturation Sa (e.g. Brooks & Corey 1964; Stone 1970; van Genuchten 1980). Furthermore, k is the permeability tensor, p the fluid pressure, and g ¼ ½0, 0, gT -the gravitational acceleration vector. To complete the equations, the difference between the phase pressures must be defined. These are given by the capillary pressure pc, which is a known function of saturation. Three capillary pressures exist for an

From Equation 4 it is apparent that the sum of the saturation is always one and hence the sum of the saturation-time derivatives is constant. Since rock matrix and fluid are compressible, f and ra change as a function of pressure. By inserting Equation 12 into 11, taking the derivatives of f and ra with respect to p, and dividing the final equation by ra, we obtain: @p X @f 1 @ ra þf Sa @p ra @p @t a þ

X 1 r Fa ¼ 0 a [ fo; g; ag: ra a

(13)

SIMULATING MULTI-PHASE FLOW IN SCR

Defining the fluid compressibility as ba and rock compressibility as bF

ba ¼

1 @ ra ra @p

and

bf ¼

@f , @p

(14)

and inserting Darcy’s law (Eqn 7) into Equation 13, yields the transient diffusion equation for the fluid pressure: X

(

Sa bf þ fba

a

@p ¼ bt ¼ ) @p @t @t

X 1 r ra la k(r( p þ pcaa ) ra g) ra a

(

)

(15)

a [ fo; g; ag: In this formulation, the fluid pressure p is set equal to the pressure of the aqueous phase pa. The capillary pressure between the aqueous phase and the oleic or gaseous phase, pcaa, is given by Equation 9. If rock matrix and fluid phases are incompressible and the fluid density is constant, Equation 15 simplifies to a steady-state diffusion equation 0¼

X

(

r la k(r( p þ pcaa ) ra g)

)

a

¼ r vt a [ fo, ag:

(16)

Equations 15 and 16 are non-linear because bt, ra, la and pcaa are functions of pressure or saturation, which both change as the pressure field evolves.

Numerical solution This section discusses how we solve the governing equations on the discretized geological structure using finite element and finite volume methods. The pressure and mass balance equations for compressible (Eqns 1 and 15) and incompressible (Eqns 6 and 16) fluid flow provide us with a system of equations that can be solved efficiently using numerical methods. It has long been recognized that the nature of the pressure and mass balance equations is fundamentally different (cf. Gerritsen & Durlofsky 2005). The pressure equation is a non-linear diffusion equation and of parabolic (compressible) or elliptic (incompressible) character. The mass balance equation is a non-linear advection equation and of hyperbolic character. Hence, pressure and mass balance equations are usually solved by a sequential approach that allows

411

us to choose the numerical method that is best suited for solving diffusion and advection equations, respectively (cf. Gerritsen & Durlofsky 2005): First, the pressure field is updated while holding concentration and saturation constant (Eqns 15 or 16). Then, the fluid velocities are computed from Darcy’s law (Eqn 7) by differentiating the pressure field. They are subsequently employed to solve the mass balance equations (Eqns 1 or 6) while holding the pressure constant. This decoupled approach is also termed Implicit Pressure Explicit Saturation (IMPES; Aziz &Settari 1979) or Implicit Pressure Explicit Concentration method (IMPEC; Gerritsen & Durlofsky 2005). In recent years, the combination of finite element and finite volume methods on unstructured grids has received a lot of attention for solving multi-phase fluid flow in complex geological structures (e.g. Kim & Deo 2000; Geiger et al. 2004; Monteagudo & Firoozabadi 2004; Karimi-Fard et al. 2005; Mattha¨i et al. 2005a). As previously discussed, unstructured finite element meshes enable resolution of complex geometries with great detail. Still, the finite element method is only used to compute the fluid pressure because finite volume methods are better suited than finite element methods for the solution of mass balance equations (cf. Chung 2002). They can also resolve steep gradients in saturation and concentration when higher-order accuracy is used. These advantages commonly alleviate the solution error that is introduced by a sequential approach and is of the order of the timestep, ODt. The following section discusses how the compressible pressure equation (Eqn 15) can be solved by the finite element method and the mass balance equation (Eqn 1) by the finite volume method. We use the classical Bubnov–Galerkin finite element method for the integration of the flux term r ðra la krpÞ over a finite element with an irreducible formulation (cf. Huyakorn & Pinder 1983). Although mixed-element methods yield a pressure and velocity field that is consistent for compressible flows (e.g. Durlofsky 1993), they are unsuitable for fracture-matrix systems in which the direction of flow changes abruptly across material interfaces and it has been debated if the extra computational costs are justified (Cordes & Kinzelbach 1996). Recent studies (Geiger et al. 2004, 2006b; Mattha¨i & Belayneh 2004; Mattha¨i et al. 2005a) have further demonstrated that excellent results can be obtained when using a classical Galerkin formulation to solve the pressure equation for non-linear problems on complex geometries. In the Bubnov –Galerkin finite element formulation, we represent our geological domain by the computational domain V. It is discretized as a set

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of finite elements (triangles or quadrilaterals in 2D, tetrahedra, hexahedra, prism or pyramid elements in 3D) spanning the finite element space V of continuous linear or quadratic polynomials. V has n Lagrange points N ¼ fxi gni¼1 , representing the nodes or integration points of the finite elements. n It also has a set of basis functions FðxÞi i¼1 , V associated with each Lagrange point. x is the coordinate vector in one, two, or three dimensions. In its weak formulation, the pressure diffusion equation (Eqn 15) is: ð

bt V

ð

X @p Fi dx ¼ @t a

V

a

(17)

V

where, for convenience, the expression a [ fo, g, ag has been dropped. We then approximate the solution variable p using the interpolation pðx, tÞ ¼ n P pj ðtÞFj ðxÞ to arrive at the Galerkin formulation j¼1

for fixed time t: n X dpj j¼1

dt

ðtÞAij ðtÞ ¼

n X X

a

!

(18)

ð pðtÞ þ pcaa ðtÞÞj Kij ðtÞ þ qi ðtÞ ,

j¼1

where A and K are the mass and stiffness matrix, respectively, and q is the right-hand side vector. They have the following definitions:

Aij ðtÞ ¼

ð

bt Fj Fi dx V

Kij ðtÞ ¼ qi ðtÞ ¼

ð

ð

1 rFj ra la krFi dx r V a

ra la kgT rFi dx:

! n n X 1 tþDt X X tþDt A ptþDt ¼ þ Kij Dt ij a j¼1 j¼1 n n X 1 t t X tþDt X X Aij p þ qi KtþDt ptþDt ij caa : Dt a a j¼1 j¼1

(20) Equation 21 completes the finite element formulation of the compressible fluid pressure equation (Eqn 15). To solve the mass balance equation (Eqn 1) by the finite volume method, it is integrated over the finite volume Vi that is associated with the corner node i of a finite element (Fig. 2).

1 rra la k ra

ð p þ pcaa ÞrFi dx Xð þ ra la kgT rFi dx,

some algebraic modification

(19)

V

A is diagonalized using a row-summing technique. To compute the evolution of p from time t to time t þ Dt, the unconditionally stable implicit Euler formulation is best suited. This yields after

ð

@Mc dVi þ Vi @t

ð

r Fc dVi ¼

Vi

ð qc dVi :

(21)

Vi

Application of the Gauss divergence theorem to the flux term r Fc yields X @Mc Vi þ Aj nj F˜ cj ¼ qc Vi , @t j¼i f

(22)

where f is the number of faces j bounding the finite volume Vi. A is the area, respectively length in two dimensions, of face j. n is the outward normal of j. The tilde above the flux vector F˜ cj denotes that it is evaluated at the upwind finite volume, i.e. the finite volume that lies upstream of the direction of flow across face j. If F˜ cj is evaluated at the upstream finite volume, the finite volume method is first order accurate in space. This leads to dispersed saturation and concentration gradients because they cannot be resolved accurately by first order accurate methods. If F˜ cj is evaluated directly at the interface j between two neighbouring finite volumes using the gradient of Fc between these two finite volumes, the finite volume method becomes second order accurate in space. This resolves steep saturation and concentration gradients but leads to spurious oscillations, i.e. non-physical values, where gradients of Fc are steep. It is therefore necessary to apply a limiter, so-called Total Variation Diminishing (TVD) schemes (Harten 1983; Sweby 1984), to the value of F˜ cj at interface j. TVD schemes remove any spurious oscillations. They have been applied successfully to unstructured finite volumes in combination with the IMPES approach for two-phase flow simulations (e.g. Bergamaschi et al. 1999; Huber & Helmig 1999; Geiger et al. 2004; Mattha¨i et al. 2005b). It is convenient for the

SIMULATING MULTI-PHASE FLOW IN SCR

higher order evaluation of F˜ cj to express the phase velocity va in terms of the total velocity vt. This results in a fractional flow, gravity, and capillary multiplier for vt, which are evaluated individually at interface j. The necessary algebraic manipulation is omitted and given elsewhere (Aziz & Settari 1979). As mentioned before, the auxiliary finite volume grid is virtual (Paluszny et al. 2007). The mass balance equation is solved in its discretized form (Eqn 22) on this virtual grid. Two different temporal discretizations of Equation 22 are possible and each has distinct advantages. In the IMPES approach, Equation 22 is discretized in time by an explicit Euler formulation to evolve the mass balance equation from time t to time t þ Dt. This yields: Dt X t Al nl F˜ cj þ Dtqtci : Vi j¼i f

MctþDt ¼ Mct

(23)

This formulation allows a straight-forward calculation of the higher-order flux terms F˜ cj . It is stable as long as the Courant-Friedrich-Levy (CFL) criterion is met which gives the maximum permissible timestep Dtmax Dtmax ¼

ri vmax a

i [ V,

(24)

min

where ri is the radius of finite volume i and vmax the a maximum phase velocity in it. This ratio is evaluated for all finite volumes belonging to the finite element space V and its minimum yields the size of the permissible timestep. The CFL criterion displays the limitation of the IMPES approach: the phase velocities are generally highest where the finite volumes are smallest, for example in fractures. This allows a solution of the mass balance equation only for very small time-steps, although the ratio of finite volume radius to maximum velocity might be more favourable in other regions. To overcome the restrictions of the CFL criterion, Equation 22 can also be solved with an Implicit Pressure and Saturation approach (IMPSAT; Gerritsen & Durlofsky 2005; Mattha¨i et al. 2005b): Dt X tþDt Al nl F˜ cj þ DtqtþDt ci : (25) Vi j¼i f

MctþDt ¼ Mct

However, this approach requires iterations because the non-linear flux term F˜ cj must be known at time t þ Dt. This is often non-trivial, especially if F˜ cj and its gradients must be evaluated for second order accurate solutions.

413

Application of algebraic multigrid methods The resulting piecewise finite-element or finitevolume integrals of the governing equations (Eqns 20, 23, & 25) combine into systems of linear algebraic equations of the form A x ¼ b. Since the discretization of a complex three-dimensional structure often requires millions of finite element nodes, matrix A will contain millions of equations. An efficient matrix solver is therefore crucial for transient simulations of flow and transport in which the system A x ¼ b is solved repeatedly. Mattha¨i & Roberts (1996) have demonstrated that the finite element form of the transient pressure equation can be solved rapidly by algebraic multigrid methods (AMG) because A is sparse, symmetrical, and positive definite. Also, AMG methods do not require any geometric information on the computational domain. They initialize the solution vector x with a trial solution x˜ (‘v-cycle’). A x ¼ b is then restricted recursively to coarser grids and the trial solution is smoothed until A x ¼ b can be solved directly, for example by LU matrix decomposition. This solution is interpolated back onto successively finer grids to obtain an improved trial solution x˜ . Repeated smoothing, coarsening, and interpolation finally yield a solution x˜ with sufficient accuracy. We use the state-of-the-art algebraic multigrid solver SAMG (Stu¨ben 1999, 2001) for the efficient solution of the resulting matrix system. It can also be applied to the implicit solution of the mass balance equation (Eqn 25) where A is no longer symmetrical. The explicit solution of the transport equation (Eqn 23) is obtained sequentially by looping over the finite volumes (Geiger et al. 2004). AMG methods are not required.

Numerical simulation case studies Benchmarking of the CSMP þþ black oil model with ECLIPSE CSMP þþ based transport models have recently been benchmarked on a variety of flow problems, demonstrating their suitability for compressible and incompressible, single- and multi-phase-, isothermal and non-isothermal fluid flow problems (Geiger et al. 2006b). Here we present another benchmark of particular interest to fractured hydrocarbon reservoirs. For a three-dimensional single fracture model, solutions for incompressible twophase flow, including capillary and gravity effects with ECLIPSE are compared. The 50 20 10 m benchmark model is cut by a single vertical highpermeability fracture along its length (Fig. 3). It intersects horizontal injector and producer wells located at opposite upper and lower model edges,

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¨ I ET AL. S. K. MATTHA

Fig. 3. Model dimensions and initial fluid pressure in the fracture. The model is 50 20 10 m (length width height). The fracture (1 cm wide) cuts the rock along its length at z ¼ 10 m. The thin black lines show the outline of the finite element grid, consisting of hexahedral elements refining towards the fracture. Initially, a linear fluid pressure gradient exists in the model. It is visualized here for the fracture only using a rainbow colour scheme (red ¼ 1.0 107 Pa, blue ¼ 5.0 107 Pa).

respectively. Water is injected into initially oilsaturated rock. Relative permeability and capillary pressure saturation curves are nonlinear and linear for the rock matrix and the fracture, respectively (Table 1). The pressures at the injector and producer are held constant throughout the simulation. Initially, a linear fluid pressure gradient is present. So that we can run the model with ECLIPSE, it

has been discretized with a regular finite element grid consisting of hexahedra only. The grid is refined towards the 1 cm wide fracture which is represented by three layers of hexahedral elements with an aspect ratio of 333. Equations 6 and 16 have been solved on this grid, with Sg ¼ 0 in the finite element and finite volume framework implemented in CSMPþþ.

Table 1. Petrophysical and fluid properties used in the CSMP þþ versus ECLIPSE comparison Property

Unit Fracture

Permeability Porosity Capillary pressure Relative permeability Capillary entry pressure Residual sat. oil Residual sat. water Viscosity oil Viscosity water Density oil Density oil

212

Matrix 2

1.0 10 m 0.7 Linear model* Linear model* 500 Pa 0.1 0.05 5.0 1024 Pa s 1.0 1023 Pa s 800 kg m23 1000 kg m23

1.0 10214 m2 0.25 Brooks Corey model† Brooks Corey model† 100 Pa 0.25 0.1 5.0 1024 Pa s 1.0 1023 Pa s 800 kg m23 1000 kg m23

*Relative permeability and capillary pressure are computed as a linear function of the effective water saturation. †Relative permeability and capillary pressure are computed using the model by Brooks & Corey (1964) with an exponent of 3.

SIMULATING MULTI-PHASE FLOW IN SCR

Fig. 4. Oil saturation for the CSMP þþ two-phase simulation after 10.4 days. The oil saturation is shown in a rainbow colour scheme: (a) for the entire model; (b) along a cut plane in the fracture; and (c) perpendicular to the fracture in the centre of the model.

415

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¨ I ET AL. S. K. MATTHA

Fig. 5. Oil saturation for the ECLIPSE two-phase simulation after 10.6 days. The oil saturation is shown in a rainbow colour scheme (a) along the front of the model; (b) along a cut plane through the fracture; and (c) perpendicular to the fracture in the centre of the model.

Figures 4 and 5 are snapshots of our CSMP þþ and ECLIPSE simulations after 10.4 and 10.6 days, respectively. They demonstrate a good agreement between both codes although the discretization is different: in ECLIPSE, saturation is constant in each cell and in CSMP þþ it varies in a linear fashion which allows retention of steep gradients in saturation. The water-front in the ECLIPSE simulations appears to advance somewhat faster than in the CSMP þþ simulation. This is probably an artefact of the first order accurate solution in

ECLIPSE that tends to smear out the water–oil contact. Another small difference is that the lighter oil overrides the heavier water in the fracture. This is not observed in the CSMP þþ simulation where water appears to override the oil.

Waterflooding of fractured rock Two discrete fracture models illustrate insights which can be gained from geologically realistic simulation of multi-phase flow in fractured porous

SIMULATING MULTI-PHASE FLOW IN SCR

417

Fig. 6. Discrete fracture simulation example 1: (a) Waterflood of a 2 2 0.2 km (length width height) model of a reservoir stochastically populated with 2000 fractures with a power-law diameter range from 5– 180 m (Mattha¨i et al. 2005a); geological input data are from San Andreas formation (CA, USA, FracMan model by Paul LaPointe, Golder Associates, Inc.). Aperture is consistent with field measurements and ranges between 0.5 and 3.5 mm correlating linearly with fracture diameter. (b) Evolution of total mobility during the water flood in comparison with a Brooks-Corey curve for a strongly heterogeneous model.

media: in both, we have solved Equation 6 and Equation 15 with Sg ¼ 0. Neither could have been represented by a structured grid and both show emergent behaviour. The first (FRACS2000, Fig. 6) is a geologically fairly realistic although stochastically generated model of part of a waterwet fractured oil reservoir in the San Andreas formation, California, USA. Fracture aperture is linearly correlated with fracture diameter which has a Maxwell frequency distribution in both of two fracture sets. The fractures carry 150 times more of the cross-sectional flow than the rock matrix. Flow is fracture dominated although the model is below the fracture percolation threshold. The largest percolating cluster is about 550 m in length. Details of the parameterization of this 2-phase flow slightly compressible flow model are described in Mattha¨i et al. (2005a). Simultaneous monitoring of the evolving pattern of saturation and integral properties like total mobility reveals hidden system properties. Thus, in waterflood simulations, total mobility monotonously decreases with increasing wetting front surface area (see later) and only a small fraction of the total fracture surface area, associated with the larger fractures, becomes flooded before the irreducible saturation is reached. Since countercurrent imbibition (CCI) can only occur where water imbibes a fracture, this simulation result flaws the logic of dual porosity calculations which use a constant shape factor to estimate the effects of CCI on production. Also, total mobility is consistently lower than would be predicted from any parameterization of a Brooks-Corey relative

permeability model and the effective permeability of FRACS2000. The BC-assumption of a uniform saturation distribution is invalid for fractured systems. The second model (MARGATE, Fig. 7, cf. Belayneh et al. 2007), was constructed from a fracture map of chalk exposed in a cliff near Margate, UK. The fractures carry only about 85% of the total cross-sectional flow. The chalk at the base and top of the model is left intact. The MARGATE model was used to simulate gravitationally stabilized displacement of oil by heavier water injected at the base (Dr ¼ 200 kg m23). For the chosen injection rate, the bulk ratio between gravitational and viscous forces, G/n, is six. Thus, one would anticipate a stable horizontal oil– water contact. Figure 7b shows that this assumption is wrong. The counter-intuitive model behaviour appears logical in hindsight because the simulation shows that G/n in the fractures is less than one and that capillary forces dominate in the chalk matrix. The two discrete fracture simulation examples highlight the potential of multi-phase fluid-flow simulations with geologically realistic models. A few years ago, these simulations would not have been possible, certainly not without algebraic multigrid solvers. Beyond benchmarking and the demonstration of numerical methods on simple flow geometries, the decisive step necessary to gain new insights is the application of such new tools to relevant and realistic models. Once the controls on their behaviour have been clarified, simplifications can be made by the elimination of noninfluential features and processes.

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¨ I ET AL. S. K. MATTHA

Fig. 7. Discrete fracture simulation example 2. (a) Exposure of fractured chalk at Margate, UK; (b) 8 1 6 m (length width height) model of an adjacent outcrop. Simulation snapshot after 174 days. Water injected from the base has shot up through the fracture network. Colour shading of saturation as in previous figure (red ¼ 0.9, blue ¼ 0.0).

Well tests in structurally complex reservoirs The last application comprises the numerical simulation of a single-phase drawdown pump-test in a complex three-dimensional reservoir. Drawdown and build-up tests are routinely carried out in

hydrocarbon reservoirs. Well tests are often the only methods that allow us to estimate large-scale permeability of sedimentary units within a reservoir. The reservoir considered here extends 980 m, respectively 790 m into the horizontal directions and has a height of 310 m. It contains seven

Fig. 8. Geometry of the faulted multilayer reservoir used in the synthetic drawdown test. Its dimensions are 980 790 310 m (length width height). It contains seven folded sedimentary layers and sixteen impermeable fault zones. A horizontal well is located in the centre of LAYER 2, i.e. the second layer from the top. The top and bottom boundaries are no-flow boundaries. All other are constant pressure boundaries with pressures equal to the initial reservoir pressure pi.

SIMULATING MULTI-PHASE FLOW IN SCR

folded sedimentary layers that are cut by sixteen impermeable fault zones (Fig. 8). The petrophysical properties of the sedimentary layers and fault zones are listed in Table 2. In the synthetic drawdown test presented here, a horizontal well in the centre of LAYER2 extracts fluid from a 30-m completion well at a constant rate of 25 m3 per day for 100 days. The horizontal boundaries (top and bottom) are now-flow boundaries. All other boundaries are held fixed at the initial reservoir pressure. To simulate drawdown in this reservoir, we discretized it with 1.67 million finite elements and 278 054 nodes. On this discretization, we solve Equation 15 with Sa ¼ 1 and So ¼ Sg ¼ 0 using the finite element formulation given by Equation 20. Figure 9 shows the pressure contours after 100 days of production. The pressure departs significantly from a radial drawdown: Drawdown pressure is not transduced across the impermeable faults and at least parts of the reservoir are compartmentalized. The lowest pressures are observed directly

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Table 2. Petrophysical and fluid properties used in the drawdown simulation Unit Layer1 Layer2 Layer3 Layer4 Layer5 Layer6 Layer7 Faults Well

Property ct m q pi rw B

Permeability (m2)

Porosity (%)

1.0 10215 1.0 10212 5.0 10213 1.0 10213 5.0 10214 1.0 10214 1.0 10215 Impermeable 1.0 1027

10 25 22 20 18 15 10 2–7 100

Value

Unit

5.0 10215 1.6 1023 25 2.0 107 0.125 1

Pa21 Pa s m3 day21 Pa m –

Fig. 9. Pressure contours after 100 days of production from the faulted multilayer reservoir. The red contour is within 1% of the initial reservoir pressure of 2.0 107 Pa. The lowest pressures (yellow and green colours) are found close to the horizontal well. There is a significant departure from the classical radial drawdown due to the presence of impermeable faults. The grey surfaces show the layer boundaries and fault surfaces.

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at the well. The non-radial drawdown due to reservoir heterogeneity is also apparent from the derivative plot. Well tests are commonly interpreted by comparison with analytical ‘type’ curves. They are plotted in derivative plots that display the dimensionless wellbore pressure pD and its rate of change pD0 as a function of dimensionless time tD. pD and tD are defined as pD ¼

2pkh ð pi pw Þ qBm

and tD ¼

kt , (26) fmbt rw2

k is the reservoir permeability, h the height of the reservoir, pi the initial reservoir pressure, pw the wellbore pressure, q the pumping rate, B the formation factor, and rw the wellbore radius. The response of the normalized wellbore pressure pD and its rate of change pD0 (Fig. 10) indicate that the reservoir is highly heterogeneous because pD0 deviates significantly from a slope 0.5 that is typical for the infinite acting period in a homogeneous reservoir. The results, however, do not clearly show the presence of low-permeability faults. As discussed by Mattha¨i et al. (1998), inhomogeneous reservoir permeabilities can lead to type curves that differ significantly from theoretical predictions of the responses of low-permeability

faults. Still, such simulations complement automated type-curve analyses of observed wellbore pressures in complex reservoirs well. The approach presented here allows (i) investigation of the response of wellbore pressure to geologically realistic fault structures in a geometrically complex reservoir, (ii) analysis of how simulated well tests deviate from theoretical predictions and actual dynamic data, and (iii) examination whether other well tests, for example cross-hole interference tests, would be better suited.

Discussion The structural complexity, non-linear relative permeability–capillary pressure relationships, PVT relationships in equations of state for the fluids, and the constitutive models for deforming rock make realistic simulation of SCR difficult. Usually non-linearities are linearized iteratively to obtain an internally consistent solution. Whether multiple constraints are honoured simultaneously by a fully coupled solution procedure or sequentially as in our iterative approach, the accuracy of the model will depend on the linearization strategies and how often the non-linearly coupled interdependent variables are updated. Therefore the price of a

p´D and pD´

10.0

1.0

pD p D' 0.1 1.0e+3

1.0e+4

1.0e+5

1.0e+6

1.0e+7

tD Fig. 10. Derivative plot showing the dimensionless pressure pD and its rate of change pD0 as a function of dimensionless time tD for the simulated drawdown of the faulted multilayer reservoir.

1.0e+8

SIMULATING MULTI-PHASE FLOW IN SCR

Speed Up [-]

1.0 x 104 Finite elements 1.0 x 105 Finite elements 6 0.5 x 10 Finite elements

10

1

1

10 Number of Processors [-]

Fig. 11. Scaling behaviour of parallelized CSMP þþ finite element – finite volume discretization for three meshes with different degrees of freedom.

higher accuracy is additional run-time and a genuine speedup can only be achieved by software parallelization. Although the benefit of using additional processors diminishes with the number of processors, a hundred or even thousand fold speed increase which is theoretically possible on very large clusters would have a dramatic impact on the feasibility of geologically realistic sector-scale or even field-scale simulations. Thus far, we have parallelized CSMP þþ using the MPICH library and the parallel version of the commercial algebraic multigrid solver SAMGp. First tests gave promising results, showing an almost linear speed increase with the number of processors for meshes with over one million degrees of freedom (Fig. 11). Facing criticisms like those of Sasowsky (2006), the main challenge for complex systems modellers will be to control discretization, round-off, and truncation errors so closely that they the user has the possibility to define a target level of uncertainty for a computation. In this goal-based approach, mesh refinement, time-stepping, and variable updates will be tailored accordingly before the run starts and during the simulation. Dynamic mesh adaptivity based on error metrics (e.g. Power et al. 2006) will have a major role in facing this challenge.

Conclusions A new workflow for the realistic simulation of coupled physical processes in structurally complex reservoirs is presented. Step 1, model building, involves the geological interpretation/representation of the structures of interest using a boundary representation and non-uniform regular B-spline curves and surfaces. Step 2 is to convert the

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resulting ‘water-tight’ CAD model into an unstructured hybrid finite-element mesh. This is achieved by indirect incremental meshing, starting with an octree-based tetrahedralization and surface representations of large-aspect ratio features like faults. These are later extruded into volumes by growing layers of prism elements on them. Then, as many tetrahedra as possible are converted into hexahedra. These are interfaced with the tetrahedra using pyramid and prism elements. Finally, geological attributes and material properties are transferred to this mesh. Step 3 is the multi-phase flow simulation and analysis of emergent model behaviour, elucidating how processes operating on different length scales interact. The complex systems modelling platform (CSMP þ þ) has been designed to facilitate such numerical experiments in the form of an application programmer interface (API). It implements a geology and process-based model decomposition in space and time and exploits any hierarchical aspects of solution variable fields through the application of algebraic multigrid methods to the spatio-temporal integration of the governing partial differential equations. Here, we used it for two-phase flow simulations combining finite elements with virtual finite volumes, achieving mass conservation at the lowest possible cost. A single-fracture model of this kind compared favourably with the ECLIPSE reservoir simulator. Simulation capabilities are also demonstrated for incompressible 2-phase flow and pressure-diffusion in a fractured and faulted sector-scale hydrocarbon reservoir model. Step 4, visualization, is indirectly addressed through the illustrations in this paper. Steps 5 and 6 of our workflow, analysis and upscaling, respectively, are the subjects of other publications. The authors thank the sponsors of the ITF project ‘Improved Simulation of Fractured and Faulted Reservoirs’ for their support of the development of the transport methods and modelling workflow. S. Geiger and D. Coumou thank the Swiss National Science Foundation for financial support during their Ph.D. theses. We are also grateful to K. Stu¨ben and his team the continuous support with the SAMG solver.

Appendix: software design considerations Alexandrescu (2001) illustrates how generic programming with templates and design patterns can be used to design software that deals effectively with complexity, arbitrarily combined configuration options, and commands entered through a graphical user interface. A multi-physics complex-geometry simulation would be very difficult to verify as a whole (cf. Sasowsky 2006). The key issue here is that component failure must be detected exactly where and when it originates. This applies as much to

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the software development process as to its actual application. The most stringent requirement imposed by this logic is that implementation and debugging must occur incrementally and testing of components must be possible in isolation. Once tested, further work on the tested components must not alter the already incrementally debugged code. CSMP was written in C þþ because it is a high-level programming language suitable for large software projects involving multiple programmers (Stroustrup 1994) but still permits byte level coding for maximum efficiency. Veldhuizen (1995) has shown that optimized C þþ code can match the performance of Fortran 77 code and outperform Fortran 90. However, since a better algorithm can always lead to more dramatic performance improvements than compiler-based optimization or incrementally better hardware (Skiena 1998), we regard more advanced language features like templates as far more important (Barton & Nackman 1994; Alexandrescu 2001; Vandervoorde & Josuttis 2003). This appendix summarizes how the CSMP code for complex reservoir simulations benefits from the features of Cþþ.

6.

Requirements 1 and 2 are discussed in the main text of this paper. Requirement 3 is met by the generic design of an Algorithm class whose responsibility it is to assemble finite-element and finite-volume integrals into a global sparse matrix class and essential conditions into a righthand vector class. These are composed by classes representing individual integral terms. The solution of the matrix equations is possible with a variety of numerical methods made available as subclasses of Algorithm and a Solver class using the Strategy design pattern (Gamma et al. 1995). To support (3b) two types of operator classes are desirable: 1.

Reservoir model components Any software infrastructure for the modelling of structurally complex reservoirs must support the following germane features of spatio-temporal computations: 1.

2.

3.

4.

5.

A spatial discretization of the real-world system that is continuous to the atomic scale but, given runtime and memory limitations, can only be represented at a few selected points that link up into computational cells. The number of these points, excluding those where the property that shall be computed is known already, defines the degrees of freedom (DOF) or unknowns of the problem of interest. The DOF must be able to change at runtime if a simulation is expected to resolve emergent patterns. A set of physical variables derived from the governing equations and underlying constitutive relationships which are needed to capture the behaviour of interest. Spatial and temporal coupling mechanisms relating dependent variables with one another. These are (a) basic laws of physics expressed by partial differential equations (PDEs) that apply to the entire domain or regions thereof with particular properties; (b) constitutive relationships such as relative permeability models. Spatial and temporal integration of the PDEs acting on the model (3a) reveals the behaviour of interest. This necessitates fast and memory efficient solution algorithms for large sets of linear algebraic equations. Essential conditions and initial values of the dependent physical variables must be prescribed to the model as a prerequisite for a unique solution and

because a transient model requires an initial state. The term ‘essential condition’ is preferred over ‘boundary condition’ because corresponding assignments may also be made somewhere inside the model domain. Input and output methods which transform the results of a computation into a human-readable format such as graphics, charts etc.

2.

Interrelations among physical variables that apply locally and without a need for global coupling mechanism(s). These can be expressed on unit cells of the discretization, the finite elements and finite volumes. They do not require integration or interpolation. For example, the hydraulic conductivity discretized on a finite element can be calculated from its permeability and a temperature and pressure dependent fluid viscosity discretized on its nodes. Visitors for cell-based computations and a change in reference frame (Eulerian ¼ attached to the material; Lagrangian ¼ attached to the flowing fluid) when traversing the model or specific regions thereof. The name comes from an object-oriented design pattern used for the ‘visitation’ of a hierarchy of objects (Gamma et al. 1995).

An example of a discretized geological model (Fig. A1) clarifies the basic terminology and object relationships that are considered essential. It is represented by a SuperGroup class forming a composite of C þþ Standard Template Library (STL) container classes which interconnect, manage, and store a hierarchy of Group, Element, Node and Integration-Point classes used to represent the finite element mesh, associated material properties, and discretized physical variables (Fig. A2). All these are user-defined abstract data types (ADTs; cf. Sengupta & Korobkin 1994), serving as blueprints for objects created just like any integral type: int x(12); SuperGroup model( mesh, model_topology ); The second statement constructs a computational model from a supplied mesh and topology objects. For the success of complex systems modelling it is essential that a programming language treats user-defined ADTs like in-built types, lending support to hierarchical

SIMULATING MULTI-PHASE FLOW IN SCR

423

Fig. A1. Box-shaped, discretized model of a folded rock sequence illustrating our terminology for model entities. The computational model ( ¼ geometry þ connectivity þ data) is stored by the instance ( ¼ object) ‘folded layer model’ of the ‘blueprint’ SuperGroup class. It is discretized by a finite-element mesh to which ‘permeability’ and ‘porosity’ values are assigned as material properties. Selected sub-regions of the model are identified by Group objects with unique names. Here, the Group object ‘sandstone’ is contiguous but this is not a requirement for groups. The functionality associated with groups could, for instance, be used to monitor the fluid flux through this unit.

Folded layer model SuperGroup Shale 1 Group

Shale 2

parent - daughter Sandstone

Group

Group parent - daughter

Element 1

Node 1

Element 4 shared among groups

Node 2

neighbor Element 2

Node 3

Element 3

Node 4

Node 5

shared among elements Fig. A2. Unified modelling language (UML) representation of the class hierarchy we use for the representation of an unstructured finite-element mesh. In addition to the top down connections making this a tree structure there are also neighbour element and node to element connections making it a graph which can be traversed laterally or following streamlines.

programming and incremental debugging. Compiler recognition of ADTs is notably absent from procedural languages in which traditional reservoir simulation codes are written. Among other ensuing limitations, this implies that only primitive types can be passed among code modules ruling out encapsulation as a means to deal with complexity. SuperGroup objects are aggregates of geological entities represented by Groups knowing their boundary elements, faces, and nodes. Aggregate (cf. Booch 1994) refers to a runtime association of objects. Thus, group objects can be formed dynamically as patterns evolve, for instance, during the formation of fractures. Groups are important also as a means to restrict computation to specific arbitrarily shaped model regions. This embedding limits the spatial extent of computationally expensive calculations while realistic boundary conditions are obtained from less involved global calculations. The domain decomposition into groups can also be used for spatially variable time-stepping (certain regions are solved more often than others) and for distributed computations (parallel or vector processing). Group objects are also used for monitoring fluxes through wells, across-faults and so forth. In summary, the functionality offered by Groups is essential because it carries forward into the computational model the Boolean geometric capabilities from the CAD model.

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Fig. A3. Two-dimensional triangular element mesh of a layered rock illustrating the placement of node and element variables and their numbering. In this mechanical model, grey-shading indicates domains with an elevated Young’s modulus. By contrast to a finite difference model where materials properties are averaged between adjacent grid cells, the use of arbitrarily shaped elements with piecewise constant properties supports discrete material interfaces.

Unstructured hybrid element meshes are fundamentally different from regular grids where cell neighbour information can be obtained by trivial operations. A finite element mesh is a tree-graph (Fig. A3), and elements, nodes, and integration points assume complementary roles in the assembly of integrals of governing partial differential equations. To resolve and track emergent patterns in the solution variable, this tree must be able to grow or loose branches. Such adaptations require a dynamic and multidirectional connectivity: nodes need to know their parent elements, elements their parent groups and neighbours. While there is a storage and runtime overhead associated with such operations, this connectivity also permits certain economies. Those material properties, for example, that have a constant value in a Group have to be stored only once. Since the functionality of any computational library eventually becomes insufficient, developers will need to add new capabilities. This must be possible without intervention in existing carefully unit-tested code. It can be achieved using inheritance and polymorphism (Cardelli & Wegner 1985). Abstract base classes like the aforementioned Visitor or Algorithm capture the commonalities of present and future subclasses so that developers can implement the desired new behaviour adhering to and building on standardized interfaces. A small code example serves to clarify the important role of polymorphism: function double kro(double sw, RelativePermeabilityModel rpm ); computes and returns the relative permeability for the oil phase, kro, for an input saturation of water, sw, and the supplied relative permeability model rpm. When the function kro() is implemented it is unlikely that all desirable relative permeability models are available to the implementer.

With polymorphism this is not an issue because as long as future implementations are inherited from RelativePermeabilityModel, function kro() will be able to apply them in computations such as: VanGenuchtenModel rpm; double kr_val = kro( 0.4, rpm ); The placement of material properties and physical variables on the finite element mesh is dependent on the discretization of the governing equations. By contrast with regular grid approaches, the finite element discretization supports a free-form representation of material interfaces across which properties vary discontinuously, i.e. from element to element (Fig. A3). Interoperable variable classes for scalars, vectors, and tensors need to be defined with a hardware platform independent precision to ensure portability of the code. Variable storage must be able to grow or shrink with the evolving mesh. To facilitate finite-element computations, the spatially distributed physical variables have to be associated with flags indicating to computational algorithms whether their values represent essential conditions or unknowns to be determined in the solution process. At a single finite element node, a ‘fluid pressure’ value may act as a Dirichlet condition whereas ‘force’ is flagged as Neumann variable. A simple computation of a steady-state fluid pressure distribution in which such boundary conditions are applied is illustrated by the UML activity diagram (Fig. A4). Dynamic memory allocation and polymorphism permit that the decision of whether to construct certain memory intensive objects can be made at runtime. Thus, a HydraulicFractureVisitor enhancing permeability where fluid pressure exceeds the confining stress plus the tensile strength of the rock is created only in

SIMULATING MULTI-PHASE FLOW IN SCR

start

build SuperGroup

425

read input file create finite elements from pixels build model

assign material properties & initial conditions

assign Dirichlet boundary conditions

apply interrelation to calculate K

setup computational Algorithm

compute fluid pressure and Darcy velocity

display and output results to JPEG & VTK

end Fig. A4. UML activity diagram for a calculation of a steady-state fluid pressure distribution. simulations where fluid pressure reaches a critical level. Specific solvers for matrices with certain characteristics can also be constructed on demand. To use available memory efficiently, physical variables must be managed at runtime. For each variable we define a physically meaningful value range at the outset of a computation, performing range checks during each write operation. This ascertains that component process errors are detected where they arise instead of being propagated. If process modules receive data outside of the input range for which they have been tested they will raise C þþ exceptions (Stroustrup 1994). A certain number of these exceptions will prompt a computation to terminate while the model in its prefailure state is written to disk. This approach known as persistence, enables later debugging and data recovery. Initialization of floating point variables to NaN (not-a-number) is recommended to detect the accidental use of uninitialized variables. The NaN value is part of the Institute of Electrical and Electronics Engineering (IEEE) floating point standard, propagates itself through calculations and can be queried for.

Reservoir model A simplified representation of our first command line version of a reservoir simulation program (Fig. A5),

illustrates how the described classes interact in a twophase flow simulation. This program involves Interrelation and Visitor subclasses as well as an application specific layer of high-level software including the ZonedProductionWell class. An important feature of Algorithm-based computations revealed by the reservoir simulation program is that integral forms of partial differential equations (PDEs) arising from the finite-element method are assembled term by term using PDE operator classes (Integral_NT_op_N_dV etc.). This implementation is free of the complexities arising from the use of different element shapes and interpolation functions. These have already been dealt with on a lower layer of software. Further hierarchical module integration leads to more specific albeit simpler to use objects, for instance, for the solution of the pressure equation or multi-phase transport. As a further important implementation feature, most of the classes shown are C þ þ templates (Vandevoorde & Josuttis 2003). Templates are classes or functions which are defined using placeholders for the actual data types which they will eventually be applied to. Thus, a templatized matrix class could hold integers, ADTs etc. as specified by the user who can rely upon the compiler to identify whether this would lead to illegitimate operations. Without any runtime overhead, this technology elegantly

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Fig. A5. UML sequence diagram of a basic object-oriented reservoir simulation program written using the CSMPþ þ API. Boxes represent classes, lines indicate class associations. The slim vertical box marks the lifetime of the model (SuperGroup object) after its construction from alternative formats of input data.

SIMULATING MULTI-PHASE FLOW IN SCR removes the necessity to duplicate code for operations on different data types. Among the many benefits of templates they make it possible to use the same high-level code for 1D, 2D and 3D models: SuperGroup , double,2 . double_precision_model_in_2D; SuperGroup , float,3 . single _precision_model_in_3D;

This greatly simplifies unit testing and debugging. In summary, this Appendix outlines the original object-oriented software engineering approach and implementation of a multiphysics/complex geometry code suitable for structurally complex reservoirs. Modularity through compiler-supported abstract data types, hierarchical programming using polymorphism, and templates to implement the ability to add functionality without breaking incrementally verified code are at the core of this design.

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key to hydrothermal ore formation. Geology, 32, 357–360. M ATTHA¨ I , S. K., M EZENTSEV , A. & B ELAYNEH , M. 2005a. Control-volume finite-element two-phase flow experiments with fractured rock represented by unstructured 3D hybrid meshes. SPE Paper 93341. Proceedings of the SPE Reservoir Simulation Symposium, 31 January– 2 February 2005. M ATTHA¨ I , S. K., M EZENTSEV , A., P AIN , C. C. & E ATON , M. 2005b. A high-order TVD transport method for hybrid meshes on complex geological geometry. International Journal for Numerical Methods in Fluids, 45, 1181–1187. M ONTEAGUDO , J. E. P. & F IROOZABADI , A. 2004. Control-volume method for numerical simulation of two-phase immiscible flow in two- and threedimensional discrete-fractured media. Water Resources Research, 40, W07405; doi:1029/2003/WR002996. N ELSON , R. A. 1985. Geologic Analysis of Naturally Fractured Reservoirs. Gulf Professional Publishing, Co. O WEN , S. J. 2002. Meshing software survey webpage. Word Wide Web Address: http://www.andrew.cmu. edu/user/sowen/software. O WEN , S. J. & S AIGAL , S. 2001. Formation of pyramid elements for hexahedra to tetrahedra transitions. Computational Methods in Mechanical Engineering, 190, 4505– 4518. P ALUSZNY , A., M ATTHA¨ I , S. K. & H OHMEYER , M. 2007. Hybrid finite element finite volume discretization of complex geologic structures and a new simulation workflow demonstrated on fractured rocks. Geofluids, 7, 1 –23. P OWER , P. W., P AIN , C. C., P IGGOTT , M. D. ET AL . 2006. Adjoint a posteriori error measures for goal-based anisotropic mesh optimisation. Ocean Modelling, 15, 3– 38. P REPARATA , F. P. & S HAMOS , M. I. 1985. Computational Geometry: An Introduction. Springer Verlag, New York. R EISNER , M. 1987. Cadillac Desert: a History of Water Management in the American West. Viking Penguin Inc., New York, USA. S ASOWSKY , I. R. 2006. Model verification and documentation are needed. EOS AGU Transactions, 87, 3. SENGUPTA, S. & K OROBKIN , C. P. 1994. C þþ ObjectOriented Data Structures. Springer Verlag, New York. S HEPHARD , M. S. & G EORGES , M. K. 1991. Threedimensional mesh generation by finite octree technique. International Journal for Numerical Methods in Engineering, 32, 709– 749. S KIENA , S. S. 1998. The Algorithm Design Manual. Telos, The Electronic Library of Science, Springer-Verlag, New York. S OAVE , G. 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science, 27, 1197–1203. S TONE , H. L. 1970. Probability model for estimating three-phase relative permeability. Journal of Petroleum Technology, 22, 214– 218. S PYCHER , N., P RUESS , K. & E NNIS -K ING , J. 2003. CO2 – H2O mixtures in the geological sequestration of CO2. I. Assessment and calculation of mutual solubilities from 12 to 100 degrees C and up to 600 bar. Geochimica et Cosmochimica Acta, 67, 3015–3031.

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Conductive faults and sealing fractures in the West Sole gas fields, southern North Sea D. BARR BP Exploration, Burnside Drive, Farburn Industrial Estate, Dyce, Aberdeen AB21 7PB, UK (e-mail: [email protected]) Abstract: Understanding the distribution and geometry of sealing faults and conductive natural fractures is important at all stages of field development and infill drilling. Sealing faults or fractures reduce contacted hydrocarbon volume per well by compartmentalizing the reservoir and reduce rate by locally impairing permeability. Open fractures or conductive faults enhance well productivity and contacted volume, but cause drilling difficulties and may lead to early aquifer influx or injection water breakthrough. With their lengthy drilling and production history, the West Sole area gas fields provide a natural laboratory for the study of sealing and conductive fractures and their inter-relationships. Conductive fractures were recognized early in field life, but the poor performance of some wells indicated that fractures were not uniformly distributed. As development continued, entire field segments were found to be unfractured. Subsequent appraisal drilling identified undepleted and partially depleted compartments, demonstrating that sealing faults or fractures are also present. More recent development of the satellite fields Newsham and Hoton has confirmed the presence in a single field of both conductive and sealing fractures, although there is a general inverse spatial relationship between the two. The structural history of the reservoirs provides an explanation for this phenomenon. Faulting at high pressures and temperatures during Jurassic rifting gave rise to sealing lithified cataclasite fault rocks. Inversion to form the hydrocarbon traps took place at lower pressures and temperatures. The associated brittle deformation breached sealing faults and generated open fractures.

Sealing faults and open fractures have a significant impact on oil and gas field exploration, appraisal and development. Fault seal can define hydrocarbon traps and has the potential to increase volumes in dip-closed traps. Sealing faults can also subdivide a reservoir into compartments and increase the number of wells required during appraisal and development. Faults which do not provide static seal can nevertheless present a baffle to fluid flow during production. On the other hand, previously sealing faults can become conductive due to production-induced changes in pore pressure or fluid saturation. Failure to recognize fault seal results in inappropriate well placement and inefficient fluid sweep patterns. Conductive fractures are often considered a positive feature, particularly in tight reservoirs where they significantly enhance well productivity and communication. They can also have a negative impact, e.g. allowing early water production due to aquifer communication or unexpected flow paths between water injectors and oil producers. The well placement and drilling engineering options to deal with sealing faults and open fractures during field development are often incompatible. This places a premium on their successful prediction, particularly in fields which exhibit both phenomena. The West Sole area fields in the Southern North Sea comprise several tight gas reservoirs with a 40 year appraisal and development history. They

contain both sealing faults and open fractures, and their extensive history provides valuable lessons for new fields and for infill drilling in the existing area. An important aspect of their structural history is brittle fault and fracture reactivation during inversion and uplift. This kinematically late reactivation breaches previously sealing faults and creates open fractures. Thus the two phenomena are systematically rather than randomly distributed, and knowledge of which one dominates locally can be used to improve well design and placement. This paper describes the evolution of fault seal and fracture understanding in these fields, based on static and dynamic observations, and proposes potential avenues for future prediction.

Field development history The West Sole gas field (Fig. 1b; Winter & King 1991) was the first to be developed in the UK Sector of the North Sea. It was discovered in 1965 by BP exploration well 48/6-1, which found 125 m of Permian Lower Leman Sandstone and 15 m of poorer quality Upper Leman Sandstone reservoir, separated by the 45 m thick Silverpit Shale Formation. The field is a complex, fault-bounded inversion anticline and underlies the flank of a c. 2000 m thick Zechstein salt dome (Figs 2, 3a). The gas is

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 431–451. DOI: 10.1144/SP292.23 0305-8719/07/$15.00 # The Geological Society of London 2007.

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Fig. 1. Location (a, b) and representative reservoir log (c) of the West Sole area gas fields. West Sole, Newsham and Hoton are the focus of this paper.

dry and normally pressured, and the Upper and Lower Leman reservoirs appear to share a common gas column with a gas–water contact at c. 2950 m below sea level. Field development began in 1967, with twelve production wells drilled from the WA and WB platforms (Fig. 2). A northern extension was developed from the WC platform in 1972. Later infill and step-out drilling raised the well count to 33 (including sidetracks and abandoned wells). The field has been produced by depletion drive, initially freeflowing to the terminal but later with the aid of onshore compression. There is no indication of an active aquifer, and the current reservoir pressure is ,500 psi throughout much of the field. The low relief Hyde field to the north (Fig. 2) was developed in 1993 from a separate platform tied back to West Sole. The Newsham field 6 km to the east was discovered in 1967 and developed in 1995, with a single subsea horizontal well tied back to West Sole. The Hoton field 13 km to the NE was discovered in 1977 and developed in 2001 with a triple-lateral well, drilled from a small platform tied back to West Sole.

Stratigraphy The stratigraphy of the West Sole area is typical of the central part of the Southern North Sea Permian

Basin (Fig. 1c; Glennie 1997). The Rotliegende Group was deposited during the late Permian in a semi-arid continental environment subject to periodic flooding by alluvial systems derived from the basin margins. The semi-permanent Silverpit Lake occupied the north of the basin (George & Berry 1997; Howell & Mountney 1997). The Rotliegende is separated from the underlying Carboniferous sediments by an angular unconformity. The Rotliegende was succeeded by the latest Permian Zechstein evaporite succession, which here comprises dolomite and anhydrite followed by a thick halite-dominated sequence (only the basal Lower Magnesian Limestone unit is shown in Fig. 1c). Subsidence continued through the early Mesozoic, with deposition of non-marine clastics and interbedded evaporites in the Triassic, and marine sediments in the Jurassic. The present structural configuration is dominated by the Sole Pit Trough, a NW– SE trending rift containing thick Jurassic and Cretaceous sediments (Ziegler 1990). Late Cretaceous chalk and Tertiary marine sands or shales followed, interrupted by inversionrelated unconformities. The principal reservoir is the Lower Leman Sandstone, which is separated from the thinner Upper Leman Sandstone by the shaly Silverpit Formation (Fig. 1c). The Upper Leman Sandstone passes northwards into sabkha and shale facies,

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Fig. 2. Top reservoir maps of the West Sole area fields, with platform and well locations. Wells mentioned in the text are identified by well number, posted beside the bottom-hole location. The full well name is prefixed by the block number of the surface location, e.g. N01 is 48/7a-N01 but 12Z is 48/7b-12Z.

but the other two units are consistent across the West Sole area.

Structure The present-day structure of the area is dominated by Cretaceous and Cenozoic inversion of NNW– SSE-trending normal faults which had been active during Mesozoic rifting (Figs 2, 3). West Sole and Hyde are NE-verging, Hoton and Newsham SW-verging, with the palaeo-horst between them now a topographic low (Fig. 3a). The anticlines and subsidiary faults are slightly oblique to the major faults, suggesting a degree of oblique-slip during rifting, inversion or both.

The horst-bounding faults were active before and perhaps during Rotliegende deposition. IntraCarboniferous reflectors do not match after restoring post-unconformity throw; and Rotliegende seismic facies change subtly across the faults, suggesting a contrast in depositional environment. The offset and angular rotation of intraCarboniferous reflectors is compatible with the Mesozoic hanging-wall:footwall geometry. Thus their observed pre-Rotliegende movement was normal and probably associated with Permian rifting rather than Variscan contraction. Similar control of Rotliegende depositional facies and thickness by what later became Jurassic rift faults has been described by Leveille et al. (1997b) from the south-eastern Sole Pit Trough.

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Fig. 3. Contrasting structural style in the West Sole area (depth migrated seismic sections displayed in two-way travel time). (a) West Sole (inverted hanging wall with net reverse displacement) and Newsham (partially inverted hanging wall with net normal displacement). (b) NW West Sole (NWWS) and Hyde (partially inverted hanging wall with net normal displacement. (c) Hoton Main (partially inverted hanging wall with mix of normal and reverse net displacements). (d) SE Hoton (breached footwall with primary reverse displacement; hanging wall to east passively carried and retains original normal displacement).

West Sole and Hoton are tight anticlines which have been inverted past the point at which hangingwall and footwall elevations are restored to parity. Hyde, NW West Sole and Newsham are gentler structures where hanging wall and footwall are at similar depths and the bounding fault varies along

strike from net extensional to net contractional (Figs 2, 3). The change in inversion style along strike is in part gradual or ‘soft-linked’, but there are also abrupt changes in geometry across NNE – SSW-trending transfer faults. These are traceable for tens of kilometres on 3D seismic data enhanced

SOUTHERN NORTH SEA FAULTS AND FRACTURES

by edge detection methods (cf. Leveille et al. 1997a). Locally, pre-existing ENE –WSW faults have been hard-linked into the transfer fault system, e.g. the fault between main and SE Hoton. A shortcut fault formed during inversion has bypassed this unfavourably oriented fault and linked previously offset segments of the normal fault. Hoton Main is a hanging-wall inversion anticline but Hoton SE is a ramp or tip-out anticline developed above a newly formed reverse fault. This interpretation is consistent with a contrast in the style of small-scale faulting observed in Hoton core: reactivated normal faults in the north, primary reverse faults in the south. The thick Zechstein salt sequence shows intense halokinesis, with soft-linkage between supra-salt and sub-salt structures (cf. Stewart & Coward 1992). The salt dome overlies the palaeo-horst (Fig. 3a) and shows evidence of a combined halokinetic and tectonic origin. It is asymmetric (NE flank steeper) and the Plattendolomit layer within the upper Zechstein defines a NE-verging overturned fold, with wells on the NE flank penetrating successive upright, inverted and upright younging sequences. The timing of inversion (Cretaceous or Cenozoic) is unconstrained in the West Sole area because post-Middle Jurassic sediments are eroded. Some NNE –SSW lineaments have subtle seismic expressions above the salt, which in the flanking basins affect the Upper Cretaceous Chalk and so are, at least in part, Cenozoic.

Production and drilling observations Well performance and contacted volumes West Sole wells have only limited core and no image logs, so the presence of natural fractures was originally inferred indirectly. For example, well-test permeability-thickness (Kh) quoted by Winter & King (1991) ranged from 29 mDft to 36500 mDft, yet an extrapolation of matrix permeability from core plugs yields an expected value around 200 mDft. A large Kh and well productivity range (particularly in a ‘layer-cake’ reservoir), coupled with maximum values orders of magnitude higher than any plausible matrix interpretation, is typical of a naturally fractured reservoir (Fig. 4a; cf. Nelson 2001; Makel 2007). As production continued, comparable variation was seen in cumulative gas production per well and in contacted gas volume per well interpreted from material balance analyses (Fig. 4a). Contacted volume increases exponentially with well rate in West Sole (Fig. 4b). This is consistent with percolation threshold behaviour, with a rapid increase in contacted volume occurring as the fracture

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network becomes fully connected (e.g. Odling et al. 1999). The fracture contribution to well performance varies across the three fields (Fig. 5), with SE and NW West Sole respectively the most and least fractured segments and Newsham and Hoton having intermediate characteristics. The latter two were developed as matrix reservoirs, after vertical appraisal wells showed little or no fracture enhancement of Kh, but in both cases the horizontal production wells were fracture dominated. This contrast between appraisal and development outcomes demonstrates the low probability of finding sub-vertical fractures with vertical wells. Had SE West Sole been developed with horizontal rather than vertical wells, it is likely that all would have shown some fracture productivity.

Drilling indicators Drilling indicators of open fractures or conductive faults include spurt mud losses, erratic torque readings, sudden deviations in well trajectory, and core barrel jamming or recovery of rubble (e.g. Makel 2007). The last two indicators were seen in Newsham and Hoton respectively, but mud losses are the most common observation (Table 1). These reservoirs have less than 1mD matrix permeability and pore throats much less than 0.1 mm. Large losses of solid-laden mud (including, for example, 10 tonnes of lost circulation material in 48/6-31 and 40 tonnes in 48/7b-12Z) can only have been into open fractures or conductive faults. Losses into the Upper Leman Sandstone and overlying Lower Magnesian Limestone must also have been into natural fractures, because these units have even lower porosity and permeability. Nevertheless, they appear to have been depleted by Lower Leman Sand production and contribute to materialbalance reservoir volumes, showing that some fractures (more likely, conductive faults) breached the intervening Silverpit Shale.

Well stimulation and clean-up Most of the vertical appraisal and production wells were hydraulically fractured to stimulate productivity. Post-stimulation well-test rate correlates poorly with pre-stimulation rate, and poststimulation rate only moderately with long-term well performance (Fig. 4d). There are significant regional and well-by-well contrasts in pre- and poststimulation behaviour. The Hyde and northern West Sole wells delivered a consistent twofold increase in rate after fracturing, a reasonable outcome for a low permeability reservoir. Southern West Sole, Newsham and Hoton improvements range from less than unity to more than tenfold. This behaviour

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Fig. 4. (a) Normalized plots of cumulative well-test rate, contacted gas volume from material-balance analysis and well-test Kh (permeability-thickness) for 25 West Sole wells (ranked from lowest to highest in each case). A uniform distribution would show a straight line and a normal distribution an S-shaped curve. Highly skewed distributions are typical of fractured reservoirs. More than half the wells lie on the cumulative Kh line predicted from matrix properties alone and have little or no fracture contribution. (b) Contacted gas volume plotted per well against well rate. Strong correlations between rate and volume are typical of fractured reservoirs and result from percolation-threshold behaviour, where an increase in fracture density results in an increase in network connectivity. (c) Plot of best monthly rate v. cumulative production required to achieve it. Obvious contamination of the rate history due to summer shutdowns or increased drawdown due to compression installation has been filtered out, but some subtle contamination may remain. (d) Pre-stimulation rate as a predictor of final test rate, and final test rate as a predictor of best monthly rate.

occurred in fields now known to be naturally fractured and possible explanations include: 1. 2.

near-wellbore damage (e.g. fracture blockage by drilling solids) was cleared by the fracture treatment; the hydraulic fracture propagated into a natural fracture and either the proppant intended to keep the hydraulic fracture open was displaced too far from the well (bad), or the hydraulic fracture remained conductive and connected the well to a regional fracture system (good);

3.

the imposed overpressure caused shear reactivation of a pre-existing fault or fracture, with destruction of apertures which had been propped by natural asperities.

Well-test rate varies much less across the West Sole field than does permeability-height (Kh, Fig. 4a). The best wells (those with the largest natural fracture contribution), did not achieve maximum rate until several months into production. The range in maximum rates (Fig. 6) is thus larger than that in test rates. The likely explanation is progressive

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Fig. 5. Distribution of conductive natural fractures and sealing faults in the West Sole area, based on dynamic data.

clean-up of the near-wellbore fracture system, by slumping and dispersal of dense drilling and completion fluids away from the producing fractures. The northern wells, lacking natural fractures, consistently had early production rates comparable to their test rates. A delay in achieving peak rate has a significant economic impact, because potential gas production is effectively deferred until the end of field life. The Newsham and Hoton development wells did not show significant rate improvement attributable to delayed clean-up of the fracture system. That could be because of a fundamental difference in the nature or geometry of their fracture networks (see later), or alternatively to differences in drilling, loss-control and completion strategy (horizontal, unstimulated versus vertical, stimulated; and the use of cement to seal the biggest mud-loss zone in Hoton, permanently blocking those fractures).

Wells with high well-test Kh often have high ‘skin’, even after production clean-up. High positive skin implies that a flow restriction is present between the reservoir and the wellbore (e.g. Dake 1978, p. 115– 118). The likely cause is residual damage caused by drilling fluids lost into fractures. Clear evidence that drilling-induced damage had been an issue comes from the last two southern West Sole wells. They were drilled using coiled tubing and solids-free nitrified foam, to maintain drilling fluid pressure equal to reservoir pressure and control losses into the then highly depleted reservoir. The second one was a re-drill of a mechanically abandoned well (well 2 in Fig. 6), which in its original form had a very high well-test skin and took eight months to clean up. Despite that, it had been one of the best wells in the field. Its replacement (well 11) tested at 80% of the original

Table 1. Fault or fracture related drilling fluid losses in some West Sole area wells Field West Sole West Sole West Sole West Sole West Sole Hyde Newsham Hoton Hoton Hoton

Well

Formation

Fluid lost (barrels)

Largest single loss

48/6-2 48/6-2 48/6-4 48/6-4 48/6-31 48/6-36Z 48/7a-N01 48/7b-3 48/7b-8 48/7b-12Z

Lower Leman Sandstone Carboniferous Lower Magnesian Limestone Upper Leman Sandstone Lower Leman Sandstone Lower Leman Sandstone Lower Leman Sandstone Lower Leman Sandstone Lower Leman Sandstone Lower Leman Sandstone

303 24 817 62 27885 1292 1269 40 1269 3970

270 24 267 62 1296 277 250 na 250 na

na, detail not available.

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Compartmentalization

Fig. 6. Post-stimulation well-test rates or best production rates (whichever was the higher) obtained in West Sole using alternative drilling and completion technologies. The ‘naturally fractured’ set includes all wells drilled in the fractured WA and WB segments. Low rate wells are interpreted to be damaged by drilling fluids or lost-circulation material, or to have encountered small unfractured domains within the fractured segment. Those labelled ‘hydraulic fracture’ were drilled in the unfractured WC segment and given large fracture treatments with the intention of creating new fractures in matrix-dominated reservoir. The long horizontal wells were drilled in nominally unfractured regions to maximize intersections with high permeability aeolian sand lenses. The coiled tubing wells were drilled in the fractured WA/WB segments, nominally on-balance with 200–300 m horizontal sections targeting fracture zones identified on seismic and from previous well intersections.

well’s test rate, and 50% of its post-clean-up rate, despite a near 80% decline in reservoir pressure. It went straight into exponential decline without lengthy clean-up. The earlier coiled-tubing well (well 30) suffered fluid losses when the drilling fluid pressure temporarily exceeded reservoir pressure and cleaned up over several months of production. Its cleaned-up rate was limited by a mechanical restriction in the wellbore, but analysis indicated that had it not been damaged, it would have performed similarly to well 11.

The West Sole field has a uniform gas composition and measured pressure gradients are consistent with a single connected gas column. There is no evidence for static (pre-production) fault seal. Newsham has a single pressure gradient but shows indirect evidence of static fault seal: the field appears to close against a NE– SW transfer fault which juxtaposes sand on sand (Fig. 5). Hoton is dip closed, but a 20 psi pressure differential indicates static fault seal across the central east –west fault, despite extensive sand-on-sand juxtaposition. Production pressure data reveals a more complex picture (Fig. 7). WA and WB bottom-hole pressures tracked one another closely between 1992 and 1999, but WC pressures less so: lagging WA– WB by c. 200 psi and with c. 100 psi variation within WC. Figure 7 includes two replacements for mechanically abandoned wells. The southern one came on production at similar bottomhole pressure to its neighbours, implying continued depletion during the break in local production and so good lateral communication. In contrast the northern one came on at higher pressure, implying limited depletion while the original well was not producing, and depleted rapidly in its first year of production, consistent with a small connected gas volume. Both observations show that lateral communication is poorer in the WC reservoir than in WA– WB. The NW West Sole and NW Lobe subhorizontal wells lie north of a regional lineament (termed the ‘Charlie fault’ in West Sole, Fig. 5), and were drilled in south-to-north order. The first well lies 1 km from the nearest WC producer, which itself is about 1 km from its nearest WC neighbour: but the pressure differential is c. 2000 psi against c. 200 psi. The Charlie fault is the only plausible barrier between the two wells, despite it having a 1 km wide, 100 m high sand-on-sand juxtaposition in the gas column. Pressures measured in both NW Lobe wells showed differential depletion of tens to hundreds of psi across non-reservoir sabkha and fluvial units as well as across small-scale faults. This confirmed the presence of partially sealing (baffling) faults, and the absence of through-going conductive fractures which would have preserved vertical pressure continuity. (The subsequent decline of NW Lobe pressures to WC levels is attributed to high offtake rates rather than to breakdown of fault seal between the two segments.) The NW West Sole well 48/6-41 was drilled after 5 years of NW Lobe production yet was essentially at virgin pressure, despite .2500 psi depletion in a well less than 1 km distant. The two segments are separated by a complex relay zone comprising

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Fig. 7. Pressure history of West Sole wells during the development of the NW part of the field between 1992 and 1999. The two replacement wells were drilled after a break in local production and are discussed in the text.

several small faults, all with large sand-on-sand contact areas in the gas column. The NW West Sole well contacted only part of the mapped gas volume so that segment must be internally compartmentalized, presumably by further sealing faults. The Newsham production well is fracture dominated, but its failure to contact the full gas volume of the field implies that sealing or baffling faults are also present. The structure of the field is simple, with internal faults having extensive sand-on-sand juxtaposition. The same applies to Hoton Main. These fields show more complex behaviour than West Sole, where large segments are either fractured with no baffles or baffled with no open fractures. Hoton and Newsham have enough open fractures to boost well productivity, but not enough to connect the entire field or to breach all potentially sealing faults. Patches of well connected fractures must be separated by areas which fall below the percolation threshold, or by sealing faults against which the conductive fractures terminate.

Competition between compartmentalization and open fracturing Predicting sealing faults and conductive fractures is a key objective in field development and infill

drilling. Conductive fractures enhance well productivity, and in West Sole they also contribute to well longevity because the most fractured wells contact the largest gas volume. (The exponential relationship in Fig. 4b means that volume rises faster with fracture intensity than does offtake rate.) But later in field life, the well productivity benefit of conductive fractures may be nullified by greater drilling damage due to increased drilling fluid losses into depleted reservoir. On the other hand, fault seal has the potential to preserve highpressure targets for infill drilling, but also to limit the contacted gas volume per well. A simple empirical observation in the West Sole area is the inverse spatial relationship between open fractures and sealing faults (Fig. 5). Thus it would be optimistic to expect a highly fractured well to be isolated from the rest of the field and still at high pressure. On the other hand, the well productivity impact of a failure to find open fractures is likely to be mitigated by poor connectivity to existing production and a high reservoir pressure. In comparing Figure 3 with Figure 5, it appears that the most fractured segments are the most inverted, although not necessarily the most deformed. In fields with a single episode of progressive deformation, there is likely to be a direct link between bulk strain and fracturing. In the Sole Pit Trough, faults formed during extension

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and burial were reactivated during inversion and uplift. Brittle reactivation under conditions of falling temperature and effective stress would breach previously sealing faults and create open fractures in their envelopes. That deformation sequence is supported by core observations on the relative timing of different fracture types (see later). Intermediate cases with both open fractures and fault baffles could result from partial breaching of seals or full breaching of only some seals (e.g. only those faults which formed a connected, active network during inversion), or fracturing within a deformed compartment but not in an adjacent undeformed compartment.

Core and image log observations Petrography Both open and closed natural fractures can be recognized in West Sole area cores. Granulation seams (lithified cataclasites or deformation bands) are the most common deformation feature (Fig. 8). Grain-size reduction caused by shearing was followed by pervasive quartz cementation, promoted by the large grain surface area and availability of reactive fractured surfaces (cf. Fisher & Knipe 1998; Fisher et al. 2000.). Self-cementation typically occurs where deformation took place at temperatures greater than 90 8C and is common in the Southern North Sea Rotliegende (e.g. Leveille et al. 1997b). The granulation seams are associated with small-scale faults and invariably have some shear displacement (Fig. 9a). The majority are extensional and probably formed during Jurassic rifting of the Sole Pit Trough (the reservoir was already at c. 3 km burial depth and so at a suitable temperature for quartz cementation). Some,

Fig. 8. Relative proportions of fracture types in West Sole, Newsham and Hoton core and Newsham image log.

particularly in SE Hoton, have net reverse displacement. They probably formed during Cretaceous inversion; at least in its early stages, the reservoir would still have been deeply buried and at higher temperatures than today. Cataclasite samples taken from Newsham core had permeabilities between 0.0004 mD and 0.0012 mD, with Hg-air capillary entry pressures of 800 psi–1000 psi. Fault-rock permeability is three to four orders of magnitude lower than that of undeformed reservoir, and fault-rock porosity three to four times lower (Fig. 9e). Where continuous or well connected, these granulation seams will present significant barriers to flow. Clay-rich fault rocks are relatively unimportant in the Rotliegende because of limited clay mineral availability. Phyllosilicate-framework fault rock, where quartz grains and interstitial clays are intimately mixed, occurs only rarely, typically in sabkha facies (Figs 8, 9d). These facies are laterally extensive but of limited thickness. Clay smears are probably developed within and in close proximity to the Silverpit Shale, but no core is available to confirm that. With the shaly unit c. 45 m thick, only the largest faults will juxtapose the Upper and Lower Leman sands, and even they are likely to have been sealing or baffling because of clay smear. However, the shale is now highly indurated, so brittle reactivation of such faults could generate open fractures or breccias to connect the sands, as indicated by production pressure communication across the shale. Pure tensile fractures or joints are rare in West Sole area core. With a current reservoir depth of 3000 m, and most deformation having taken place deeper, it would have taken substantial fluid overpressure to put the reservoir into a Mode 1 failure regime. Most open fractures have shear displacements and formed in association with, or more likely by reactivation of, fault-related granulation seams (Fig. 9a, b). Fractures are kept open by mismatching wall geometries at scales ranging from millimetres to centimetres, and by partial mineralization. The dominant cementing phases are dolomite and anhydrite, but siderite and quartz also occur. Quartz overgrowths (e.g. C in Fig. 9b) suggest that some open fractures formed at high temperatures, consistent with substantial burial depth. Brittle reactivation of granulation seams is common at both the mesoscopic (Fig. 9a) and microscopic (Fig. 9b) scales. One or both walls of an open fracture typically show grain-size reduction and quartz cementation. Where the fracture occurs entirely within a granulation seam (Fig. 9b) a contemporaneous origin is possible. However, fractures often follow the granulation seam:host rock interface, jogging between one side and another to take ‘short-cuts’ through the host rock. This

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Fig. 9. Conductive and sealing fractures in West Sole core. (a) Cemented granulation seam or lithified cataclasite (CG) on normal-displacement shear fracture. Larger shear fracture to right of image was originally cataclastic but suffered brittle reactivation with development of partially open voids at releasing bends or jogs (POG, partially-open jog; C, cement-filled jog). (b) Brittle fracture which reactivated a pre-existing granulation seam. Mismatching faces due to shear displacement and partial mineralization (A, B, C) will help prop the fracture open, but communication with the matrix will be inhibited where the fracture is confined within the fine-grained granulation seam (D). (c) Completely cemented fracture or vein. A, siderite; B, D, (stained) ferroan dolomite; C, cemented granulation seam. The fracture reactivates the granulation seam but appears to step between the centre and the edge. (d) Muddy granulation seam or phyllosilicate framework fault-rock developed in sabkha. (e) Cemented granulation seam crossing image from top left to bottom right has substantially reduced porosity and permeability as a result of grain size reduction and quartz overgrowths. Porosity is stained dark blue in the photomicrographs.

suggests that the granulation seam predated the fracture and presented a mechanical heterogeneity which was exploited by later deformation. A fracture with this geometry is shown in Figure 9c. Although it is completely carbonate cemented, it is otherwise indistinguishable from a typical open fracture. This leads to the suggestion that open and cemented fractures are genetically related; on a large scale, most fractures are partially cemented and the cores randomly sample fully open and fully cemented patches along their length. On that basis the wholly:partly:uncemented proportions (21:12:3) in Figure 8 would be a measure of the cement coverage on a typical fracture, rather than of the relative proportions of three genetically distinct fracture types.

Fracture distribution Fractures in the West Sole area are organized spatially, vertically and by matrix lithofacies. Fracture density logs show distinct clusters typical of fault damage zones (Fig. 10; cf. Beach et al. 1999). Open fracture clusters have similar geometry

and distribution to closed fracture clusters, rather than being randomly or uniformly spread, or independently clustered. That supports the idea that open fractures formed during brittle reactivation of pre-existing faults. Only some clusters have open fractures, pointing to partial or incomplete rather than wholesale reactivation. Occasionally all the fractures in a cluster are open (e.g. 3178 m in 48/6-19, 3230 m in 48/7a-N01). The conclusion that these are not genetically distinct lies in the co-location of open and closed fractures elsewhere in the well, and the petrographic observations of open fractures reactivating granulation seams. The pattern repeats at all scales in all three fields, from the fine-scale fractures of 48/6-19 (effectively displaying the internal architecture of a fault zone) to the much larger features resolvable on image logs. The comparable appearance of all three well logs, at very different scales, suggests a self-similar (fractal) distribution. The wells also show spatial heterogeneity, e.g. there is a significant fault at 3195 m in 48/7b-8, and 48/7a-N01 is much less fractured beyond 4100 m. The latter implies a contrast in stress regime across the fault at the time of

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Fig. 10. Fracture density logs (corrected for borehole to fracture intersection angle, cf. Terzaghi 1965). Core fractures which could not be successfully orientated were assigned the average dip of orientated fractures in the same well. Since those wells are vertical, azimuthal sampling bias does not need to be corrected. West Sole well 48/6-19 (20 cm sliding window) and Hoton well 48/7b-8 (1 m sliding window) are from core. Newsham horizontal well 48/7a-N01 (10 m sliding window) is from an ultrasonic borehole image log.

fracturing. The well trajectory deviated spontaneously while crossing the fault, indicating that it influences the present-day stress regime. Mud losses show a variable relationship to the fracture logs (Fig. 10). The central (largest) loss in 48/7b-8 coincides with an inferred fault but the log shows few open fractures. That may be a sampling problem (some core in this zone was recovered as rubble), or that fault may have been reactivated in shear due to high mud weight rather than open under static conditions. The other loss zones coincide with only minor fracture clusters. In Newsham losses are associated with some but not all deformation clusters (the broad loss zone above 3500 m may have been into the open fracture cluster which had already been drilled). The two deepest losses correspond to very minor damage zones as detected by the image log. Open and part-open fractures are much more common in West Sole than in Newsham or Hoton

Fig. 11. Fracture frequency logged in core and image log. Fracture count in the Newsham image log was increased by a factor of seven to compensate for its lower resolution relative to core (based on analogue wells with both datasets present).

(Figs 10, 11). Hoton has a stronger production fracture signature than Newsham, yet fewer open fractures in core. The sampled Hoton wells may be unrepresentative of fractured parts of the field (neither core nor image log was acquired in the horizontal well sections). All three fields show a wide variation in total fracture density (i.e. deformation intensity) and percentage of open fractures, even between nearby wells. Fracture density correlates only weakly with the percentage of open fractures (Fig. 12a), probably because the highest deformation intensity occurs in fault envelopes where intense shearing destroys open fractures. The coefficient of variation (Cv, a measure of fracture clustering or non-randomness in fracture spacing, e.g. Odling et al. 1999) is high in most West Sole area wells (Fig. 12b). Values less than one are characteristic of regularly spaced joints, values around one of randomly spaced features and values greater than one of clustering or spatial heterogeneity. There is no obvious relationship of Cv to fracture density, although values around one occur only at high and low fracture densities. Regular spacing is typical of regional Mode 1 joint sets with spacing controlled by mechanical layer thickness, so the absence of very low Cv values is consistent with the scarcity of that fracture

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Fig. 12. Fracture statistics for West Sole area wells. (a) Proportion of open fractures plotted against total fracture density. (b), (c) Coefficient of variation and fractal dimension of fracture spacing, both plotted against total fracture density. (d) Comparison of throw statistics for fractures and seismically mapped faults, for Newsham and for various segments of West Sole. The fall-off from a power law at large and small values is due to sample size and resolution limitations respectively (e.g. Odling et al. 1999).

type in core. A reason for random spacing in the least deformed wells could be that fractures are too far apart to interact with one another. The most deformed well lies in a major fault zone and may be subject to different deformation mechanisms than the rest. Randomness could also be introduced by mesoscale mixing of fault lenses which acquired their internal characteristics elsewhere. In contrast fractal dimension, a measure of the organization of fracture spacing into self-similar hierarchies with power-law spacing distributions (Odling et al. 1999), correlates strongly with fracture density (Fig. 12c). The fractal dimension equates to the power-law slope which best describes the fracture spacing distribution. A high value (found in the most intensely fractured wells)

implies many more small fracture spacings than large. A low value implies a more even distribution. A possible mechanistic interpretation involves fault zone weakening or strain softening; large fracture spacings are preserved during progressive deformation because it is energetically more favourable to form a new fracture in an existing damage zone than to break the intact rock between damage zones. The prevalence of clustered, fractal shear fractures suggests a genetic relationship between fractures and seismic-scale faults. Power-law plots of fault and fracture throw are presented for West Sole and Newsham (Fig. 12d). Fractures and seismically mapped faults have power-law slopes around 21 and the fracture distribution lies on a downscale extrapolation of the seismic distribution,

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although with an order of magnitude intensity spread in both cases. It would be reasonable to interpolate between the two to estimate the spacing of fractures too large or sparse to be seen in core and too small to be seen on seismic data.

Fracture timing and relationship to lithofacies The fractal populations and similarity between fault and fracture statistics suggests a genetic relationship, where the primary control on fracture distribution is tectonic faulting. Primarily sealing fractures will be associated with faults active during burial and early inversion, prior to matrix compaction and cementation. Open and cementsealed fractures will be associated with brittle reactivation of selected faults during late inversion. In both cases fractured zones are expected to extend steeply through multiple stratigraphic and mechanical units, except where bounded by an upper and lower detachment (e.g. between the Zechstein salt and Silverpit shale). However, there are also significant variations in fracture type between lithofacies (Fig. 13). This can be understood if the presence of a fault or fracture zone is controlled at the reservoir scale or larger, but the individual fractures respond to their local mechanical and diagenetic environment. The aeolian sandstones are clean and well sorted, and deformation during progressive burial formed granulation seams (cf. Fisher & Knipe 1998). Diagenetic quartz and illite cementation

overlapped rift-related faulting but predated inversion (Leveille et al. 1997a), and illite from Hyde and Hoton has been dated to the Middle and Late Jurassic, also pre-inversion. Illite cementation in the matrix began before quartz cementation (Robinson et al. 1993), but granulation seams are typically quartz cemented with little or no illite (Fig. 9e), and fault damage zones logged in horizontal wells similarly lack illite (low porosity is combined with a low gamma log response). Quartz cementation in the granulation seams must have begun at lower temperatures than in the matrix, presumably promoted by the abundance of small quartz grains with clean, fractured surfaces. Subsequent faulting and fracturing was brittle, with the rigid, cemented matrix resisting granulation and pre-existing granulation seams also strengthened by quartz cementation. SE Hoton is the exception to this rule, in that half the cemented granulation seams have primary reverse displacement and are presumably inversion related. SE Hoton has suffered anomalous porosity reduction relative to its neighbours, equivalent to that expected from about 2 km of additional burial. Since it occupies a footwall location this is unlikely, and an alternative explanation is tectonic compaction due to high effective stress during inversion (cf. Casey et al. 1999). That could also explain the late formation of granulation seams; effective stress was high enough to induce grain collapse, even in an already cemented rock. Muddy sabkha contains abundant detrital clay and formed clay smears or phyllosilicate framework fault rocks during burial and inversion: it was never

Fig. 13. Fracture distribution by sedimentary facies. Closed fractures are dominantly granulation seams with shear displacement: clay-rich in muddy sabkhas, otherwise quartz cemented. Cemented fractures may once have been open but later cemented by a migrating fluid, or may have been cemented immediately by locally derived fluids or grown by a crack-seal mechanism.

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brittle enough to form open fractures. Mixed sabkhas often show refraction of faults between sandy and muddy or evaporitic layers, with cementfilled vugs or pull-apart voids in the sands. These are of limited height and were probably cemented soon after formation by redistribution of anhydrite and dolomite from the matrix. Sandy sabkha is intermediate between aeolian sand and mixed or muddy sabkha. Differences in sabkha observations between the fields may reflect real differences in fracture genesis and timing, or inconsistent description within the continuum between sandy and muddy sabkha. Fluvial sands experienced an early diagenetic event (dolomite cementation) which reduced their porosity to 6– 7% and effectively locked the quartz grains together, preventing cataclasis and forcing transgranular fracturing throughout their burial and uplift history. Most fluvial fractures are wholly or partially cemented, probably because of the ready availability of carbonate minerals in the nearby matrix. Partially open fractures are much more common in West Sole than in the other fields, particularly in the non-net fluvial sands and relative to cemented fractures. They are probably critical to large-scale connectivity, providing links between fracture subnetworks which in the other fields are confined within aeolian sands. Fracture timing may partly explain the contrasts between fields. At least some Hoton inversion took place early, at temperatures high enough to form cemented granulation seams. Most Rotliegende gas fields lack an active aquifer, even those with high permeability matrix or conductive natural fractures. This suggests that cementation is pervasive in the present-day aquifer and may have been a feature of past aquifers. West Sole could have a greater component of Cenozoic inversion, at lower temperatures and perhaps a short time before gas migration, which would inhibit cementation once gas rather than water was the mobile phase in the pore space. Lateformed fractures are more likely to have their aperture preserved than early fractures, and the thick, ductile salt topseal means that late inversion is unlikely to lead to trap breaching and loss of hydrocarbons.

Fracture orientation In West Sole both closed and open fractures predominantly dip steeply SW and SE (Fig. 14), parallel and perpendicular to the NW–SE fold axis. Subsidiary north–south and east –west striking sets lack open fractures: presumably they were either bypassed by deformation which reactivated the major faults, or were unfavourably orientated relative to the prevailing stress regime. In contrast Hoton and Newsham are dominated by

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north –south to NNE–SSW striking, subvertical fractures. These are significantly oblique to the fold axes, suggesting a strike-slip or Riedel shear origin rather than as fold accommodation features. NW –SE or NE–SW striking features, parallel to the West Sole open fractures, are rare in Hoton and absent from Newsham. Open fracture orientation could only be retrieved for the 48/7a-N01 image log, not for core data. As in West Sole, open fractures form a subset of the closed fractures, in this case with north–south strike. A secondary east –west cluster occurs, although as that orientation is very poorly developed in the all-fractures set, the proportion of east –west fractures which is open is much higher than for north–south fractures. The contrast in minor fracture orientation between superficially similar NW–SE-trending faulted anticlines provides another possible explanation for the greater density of open fractures in West Sole than in Newsham and Hoton. The formation of open fractures could have been influenced by the preexisting tectonic grain, with an absence of favourably oriented (NW–SE and NE–SW) small-scale faults resulting in an absence of open fractures.

Predicting sealing faults and open fractures Fault seal The nature of the faults and fractures seen in core makes it likely that all early-formed fractures were barriers. In fluvial sands they are cemented by carbonates and in sabkhas they are clay-rich or anhydrite cemented. Both will form perfect seals, except where there are gaps in cement coverage or between fractures. Even clean sands have quartz cemented granulation seams (lithified cataclasites) with permeability around 0.001mD and Hg-air capillary entry pressure around 1000 psi. Given these characteristics, static and dynamic fault seals are to be expected. Seal failure, whether on production or geological timescales, can be attributed to breaching by open fractures. Static seals supporting about 50 m gas column height or a 20 psi differential in gas pressure gradient are consistent with the cataclasite capillary entry pressure. Dynamic seals (or more likely baffles) have supported pressure differentials of hundreds to thousands of psi on timescales of years to decades. These are much higher than cataclasite capillary seals can support, unless multiple, continuous seals occur in series; but in that case they should also have been effective over geological time and there should be stronger static seals. Flow paths around multiple seals may be effective over geological timescales, but can be so tortuous

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Fig. 14. Orientation of (a) open and (b) all fractures logged in West Sole area wells. Rose diagrams of fracture strike are shown for individual wells, and contoured lower hemisphere Schmitt poles for each field and for the global dataset. Both are corrected for the intersection angle between fracture and wellbore (cf. Terzaghi 1965). Numbers beside each plot are actual fracture counts (before Terzaghi correction). Only those fractures which could be successfully orientated are included, which may cause some selection bias, e.g. broken or rubbled core is harder to orient than intact core. It was not possible to retrieve matched fracture type and orientation data for Hoton and Newsham cores, although as the open fracture count is low in both cases it would have been of questionable statistical significance.

that most flow on a production timescale is across fault rock (cf. Harris et al. 2007). An alternative explanation is that flow begins when the capillary seal is overcome, but the thickness and low permeability of the fault rock contribute a substantial flowing pressure drop across the fault (as described by Manzocchi et al. 1999, but with a threshold pressure which has to be exceeded before flow begins). Observations of cataclasite permeability 3–4 orders of magnitude less than the host rock, and damage zones tens of metres wide (Fig. 10), make that a viable explanation. The flow impact of a baffling fault can be represented in a reservoir simulation model by fault transmissibility multipliers (e.g. Manzocchi et al. 1999). Multipliers are most simply estimated by assuming flow perpendicular to a fault zone comprising fault-parallel bands of host rock and fault rock. In that case the effective permeability equals the thickness-weighted harmonic mean and, for a given host rock, depends only on the fault rock permeability and summed fault rock thickness. More sophisticated analyses (e.g. Harris et al. 2007) predict outcomes less than an order of magnitude

different from this simplistic assumption, and within the range of uncertainty around estimation of the other parameters. A reservoir simulation model of the NW Lobe and northern WC areas tested this approach, in an attempt to match the large producing pressure drop across the Charlie fault (.2000 psi, Figs 5 & 7) and between NW Lobe compartments (a few hundred psi). Fault-rock permeability was set at 0.001 mD based on the Newsham samples, and total fault-rock thickness at 2% of fault throw, within the range reported by Foxford et al. (1998, fig. 7) for 10 –100 m throw. Predicted pressure drops across the faults were too low and the fault-rock permeability had to be decreased (or its thickness increased) by at least an order of magnitude to achieve a satisfactory match. Although similar approaches have been successful elsewhere (e.g. Knai & Knipe 1998; Harris et al. 2002), it is not unusual for the approach to over- or underestimate fault transmissibility by an order of magnitude. Underestimates have been attributed to leakage through small patches of thin or permeable fault gouge which dominate the flow although they represent only a small volumetric proportion

SOUTHERN NORTH SEA FAULTS AND FRACTURES

(e.g. Knai & Knipe 1998). In addition, several systematic biases exist which may lead to overestimates of fault transmissibility (cf. Zijlstra et al. 2007): 1.

2.

3.

Overburden correction. Fault-rock permeability is usually measured at ,1000 psi hydrostatic confining pressure. Low permeability reservoirs (which are perhaps the closest analogues to fault gouges) typically suffer a large permeability reduction at effective reservoir stresses of several thousand psi. The permeability of anisotropic fault gouge will also depend on its relative orientation to the maximum horizontal stress in the subsurface. Relative permeability. Samples are analysed in single phase with water or air as the fluid. Fault rocks typically have high water saturations for tens or hundreds of metres above the free water level (FWL), and their relative permeability to oil or gas is likely to be in the low tens of percent at best. A ‘wall of water’. Fault rock for tens of metres above the FWL will be 100% water saturated at initial conditions, because of its high capillary entry pressure to gas. That part of the fault zone has zero relative permeability to gas and is a perfect seal (that is the basis of static fault seal). Flow across the fault need not begin when the producing compartment has been depleted by more than the capillary entry pressure. The entry pressure which has to be overcome is that from the undepleted compartment to the fault zone, not that from the fault zone to the depleted compartment. The fault zone is likely to have a high ratio of vertical to horizontal permeability (cf. Harris et al. 2007) and may have a conductive, recently slipped core even if its damage zone is not breached. In those circumstances pressure equilibration between the fault zone and the depleted compartment will be delayed and may never be achieved. Those parts of the fault zone which are initially 100% water saturated should perhaps be assigned a transmissibility multiplier of zero, reducing the flowing area between the compartments.

Another possibility arises in this part of the Southern North Sea through the combined impact of a large permeability contrast between fault rock and host rock, and fault breaching by open fractures. Flow across faults may take place through small, high-permeability breaches: the flow path through the breaches, albeit tortuous, may outcompete that through the intact fault rock. In that case a history-matched transmissibility multiplier of (say) 0.01 would bear no relationship to faultgouge permeability, but rather imply that only

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about 1% of the fault surface was breached and open to flow. Quantitative prediction would be difficult in that environment. In an oil field it should be possible to distinguish (from dynamic data) the difference between a broad zone of slow leakage and a narrow zone of rapid leakage. But the high compressibility of gas would make it difficult to be conclusive in this case.

Open fractures The concentration of open fractures in damage zones typical of tectonic faults suggests a simple fracture predictor: use seismic mapping or subseismic fault indicators such as coherency to detect the faults, and target the faults. Most West Sole drilling followed that approach, with fault detection and targeting improving in step with seismic technology. However, not all wells exceeded matrix permeability-height predictions, even in the ‘fractured’ parts of the field (Figs 4a, 5). The petrographic observations favour a model in which only faults that underwent brittle reactivation during basin inversion have associated open fractures. Since not all faults have been reactivated, not all fault damage zones contain open fractures (Fig. 10). Seismic sections show a mix of faults, some in net contraction and others in net extension (Fig. 3). If all faults were originally extensional, some must have been inverted and others carried passively (or at least underwent less reverse displacement). The most strongly inverted field segments are SE West Sole (Fig. 3a) and Hoton (Fig. 3c), and these have the strongest dynamic indicators of fracture productivity (Fig. 5). Newsham (Fig. 3a) and central West Sole are less inverted and have intermediate levels of fracture productivity. NW West Sole (Fig. 3b) remains in net extension and appears to have been carried passively, with inversion focused on the Hyde field to the east. A mechanistic model, based on the degree of inversion and given sufficiently good seismic imaging, could potentially predict the likelihood that a fault zone contains open fractures: a normal fault may be inverted, but a reverse fault must be inverted. Such a rule should be applied with caution, e.g. in SE Hoton (Fig. 3d), primary reverse faults, formed during compressional breaching of an extensional footwall, are not reactivated and not conductive. Strike-slip faults linking normal and reverse segments should also be recorded, with the aim of identifying the fault strands active during inversion and isolating potentially unfractured passive blocks. In settings with thinner salt than at West Sole, and younger preserved cover, it is possible to apply those criteria at the large scale to predict breached faults and young, potentially fractured structures.

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Fig. 15. Maximum throw v. length plots for seismically mapped faults in two West Sole segments. (a) WA–WB, strongly inverted, low R2 and poorly defined slope (least-squares fit 0.7 but a reduced major axis fit would be close to 1). (b) NW lobe, weakly inverted, high R2, slope close to 1.

A more quantitative approach to establishing the degree of inversion is shown in Figure 15. A cogenetic set of faults typically has a systematic relationship between fault length and fault throw (e.g. Walsh & Watterson 1988). Uniform inversion of such a set would preserve the systematic relationship but with a different slope. A more likely scenario is inconsistent inversion, with some faults having net normal displacement and others reverse, and varying amounts of throw reversal. Data from West Sole supports this suggestion. The WA–WB region is strongly inverted (Fig. 3a), highly fractured (Fig. 5), and shows a poor correlation between fault throw and fault length (Fig. 15a). The NW Lobe region is weakly inverted (Fig. 3b shows the structurally similar NW West Sole segment), unfractured (Fig. 5), and shows a good correlation between fault throw and fault length (Fig. 15b). In both cases the seismic data had been enhanced to maximize fault resolution and interpreted manually, guided by edge-detection methods. Faults with very small throw are often not routinely interpreted, because they do not offset reservoir simulation model layers and so are perceived to have little impact. However, in an inverted structure small throw may result from the cancellation of extensional and contractional components. Such faults have accumulated large strain under various burial conditions and can be conductive, despite their small net throw. The more fractured field segments are also associated with the tightest inversion-related folding. The absence of bed-confined, Mode 1 joints in core and the tight clustering of open

fractures in fault damage zones rules out a simple beam-bending model of outer arc extension. However, an alternative mechanism exists that is consistent with core observations and depth of burial. The Rotliegendes reservoir contained preexisting normal faults so it would behave not as a uniform beam but as one containing, aligned, nonvertical flaws. Faults which do not link directly into the active system could reactivate in response to extensional strain associated with the inversion anticline. Some faults might reactivate in extension, even during an inversion event. Indeed they may be the best candidates for open fracturing, as they would have formed under lower mean stress and would be less prone to destruction of aperturepreserving asperities during shearing. Curvature alone (cf. Stewart & Podolski 1998) is not a good fracture predictor in West Sole, but alternative approaches to modelling extensional strain have shown promise. X. Q. Ma and N. J. Kusznir (unpublished work) built a 3D elastic dislocation model of West Sole in 1994. The anticline was modelled as a tip fold ahead of a major reverse fault (i.e. only the inversion-related strain was considered). One output, finite NE–SW extensional strain (perpendicular to the fold axis), showed a moderate correlation with well-test Kh (R2 ¼ 0.2). A similar R2 value was found using a quantitative variant on the traditional West Sole approach of targeting seismically imaged faults. A fault density map was made by uniformly sampling fault centre lines to points then creating a pointdensity map with a 200 m search radius. (A radius wider than the expected damage zone was chosen

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because the faults are non-vertical but the control map was of the top of the 125 m thick Lower Leman reservoir.) This is analogous to a distance-to-faults map, but with the added feature that the predictive parameter is intensified when two or more faults lie in the same search radius. Thus fault clusters are weighted more heavily than single faults. R2 rose to 0.4 for a linear combination of the two parameters, a statistically significant value with 25 well calibration points. With better numerical modelling and fine-tuning of the mapping parameters the match could perhaps be improved, but in a fractured field where as many as 80% of wells are poor performers, even a modest predictor is better than none. This model used the same high-resolution fault set depicted in Figure 15. The same approach was applied to a routine interpretation of the same area without success. This emphasizes the need for detailed interpretation to identify all potentially conductive faults, and perhaps suggests that fractures are best preserved around small or intermediate scale faults, which are less affected by fluid flow and large shear strains. The model match worsened for total extensional strain and along-axis (NW –SE) strain had no predictive power, despite being 30% of the NE –SW strain since West Sole is a doubly plunging anticline. There is no obvious reason why along-axis strain should not have formed open fractures; indeed NE–SW and NW–SE open fractures are equally common in core (Fig. 14). Present-day maximum horizontal stress (defined from wellbore breakouts in Hyde and Hoton) is NW– SE, parallel rather than perpendicular to the fold axis. NW –SE striking fractures, opened directly by NE– SW extension or by reactivation of NW–SE-trending normal faults, are favourably orientated against subsurface closure. NE– SW striking fractures will tend to be closed by subsurface stresses, particularly when reservoir pressure is reduced by production or locally in a well test. Stress sensitivity of the fractures had previously been inferred from the observation that reservoir simulation models, history matched by applying permeability multipliers to matrix properties, typically required larger multipliers in the NW– SE flow direction. The preferred open fracture model for West Sole can be summarized thus: 1.

2.

Open fractures are associated with faults reactivated during Cretaceous or particularly Cenozoic compressional inversion, but not all faults reactivate and standard seismic indicators respond to all faults. Reactivation is either direct by reverse slip or indirect in response to bulk strain in the envelope of a larger fault or fold; reverse slip may be

3.

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observable on seismic data and bulk strain can, in principle, be modelled. Present-day stress reduces the subsurface aperture of those open factures that strike perpendicular to the NW –SE maximum compressive stress. Although most fracture walls mismatch geometrically or are propped by partial mineralization, the increase in closure stress in a depletion-drive gas field is large. With fracture conductivity (permeability times aperture) proportional to the cube of aperture, and network connectivity depending on the non-closure of pinch-points, even partial fracture closure will have a significant flow impact.

Conclusions The West Sole area gas fields display a mix of sealing faults and conductive fractures, at scales ranging from the field segment to the individual well. Most early formed faults are innately sealing, particularly those active during Jurassic Sole Pit rifting at or close to maximum burial depth and reservoir temperature. Breached or conductive faults and open fractures formed during inversion, when brittle, cemented reservoir and fault rocks deformed at lower temperatures and confining pressures. Cenozoic inversion was probably more effective than Cretaceous inversion in that regard, but it is not possible to distinguish seismically between the two. Open fracture and sealing fault distributions show an inverse spatial relationship (Fig. 5), as is expected if the open fractures formed later and breached or disrupted the sealing faults. Core data confirms this sequence of events, with cataclasites or granulation seams and other primary sealing fractures cut by later, brittle open fractures. Cemented and partially cemented brittle fractures also post-date granulation seams. It is not clear whether the degree of cementation reflects a paragenetic sequence (older or pre gas migration fractures are more cemented), or random well intersections with a single population of partially cemented fractures. Virtually none of the fractures are Mode 1 pure-opening or tensile fractures. Even the uncemented fractures show some evidence of shear displacement or wall mismatch. Fracture type depends on lithology. The preceding generalizations apply best to aeolian sand and sandy sabkha facies. Fluvial sands were subject to early diagenesis (dolomite cement) and deformed brittly throughout their burial history, but most such fractures are occluded by carbonate cement. A relative lack of cementation may explain why the fractured parts of West Sole produce better than the other fractured

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fields in the area. Fractures remain open in non-net lithofacies and provide flow connections between net facies. Muddy rocks (particularly some sabkhas) were too ductile to deform brittly during inversion and formed shale gouge type fault rocks. With anhydrite abundant in the wall-rocks, any open fractures which did form were prone to cementation. Fault seal predictors based on cataclasite petrophysical properties either drastically overestimate fault seal (because they do not account for breaching by brittle reactivation) or moderately underestimate it (probably because of systematic biases such as omission of gas– water relative permeability corrections). Open fractures have been targeted successfully in West Sole by exploiting their spatial association with seismically mapped faults, but in retrospect more use could have been made of additional drivers such as fault orientation relative to the present-day stress regime and the magnitude of inversion-related strain. This paper is published by permission of BP Exploration. Discussions with R. Knipe, Q. Fisher, N. Kusznir and members of the BP Southern North Sea subsurface team, and fracture description by G. Samways, J. Smart and T. Needham, are gratefully acknowledged. G. Ma¨kel and I. Sinclair are thanked for their constructive reviews and S. Jolley for his editorial handling.

References B EACH , A., W ELBON , A. I., B ROCKBANK , P. J. & M C C ALLUM , J. E. 1999. Reservoir damage around faults: outcrop examples from the Suez rift. Petroleum Geoscience, 5, 109– 116. D AKE , L. P. 1978. Fundamentals of Reservoir Engineering. Developments in Petroleum Science, 8, Elsevier, Amsterdam. F ISHER , Q. J. & K NIPE , R. J. 1998. Fault sealing processes in cataclastic sediments. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. J. (eds) Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 117–134. F ISHER , Q. J., K NIPE , R. J. & W ORDEN , R. H. 2000. Microstructure of deformed and non-deformed sandstones from the North Sea: implications for the origin of quartz cement in sandstones. In: Quartz Cementation in Sandstones. International Association of Sedimentologists Special Publication, 29, 129–146. C ASEY , M., C LENNELL , M. B., F ISHER , Q. J. & K NIPE , R. J. 1999. Mechanical compaction of deeply buried sandstones of the North Sea. Marine and Petroleum Geology, 16, 605–618. F OXFORD , K. A., W ALSH , J. J., W ATTERSON , J., G ARDEN , I. R., G USCOTT , S. C. & B URLEY , S. D. 1998. Structure and content of the Moab Fault Zone, Utah, USA, and its implications for fault seal prediction. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. J. (eds) Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 87–103.

G EORGE , G. T. & B ERRY , J. K. 1997. Permian (Upper Rotliegend) synsedimentary tectonics, basin development and palaeogeography of the southern North Sea. In: Z IEGLER , K., T URNER , P. & D AINES , S. R. (eds) Petroleum Geology of the Southern North Sea: Future Potential. Geological Society, London, Special Publications, 123, 31– 61. G LENNIE , K. W. 1997. Recent advances in understanding the southern North Sea Basin: a summary. In: Z IEGLER , K., T URNER , P. & D AINES , S. R. (eds) Petroleum Geology of the Southern North Sea: Future Potential. Geological Society, London, Special Publications, 123, 17– 29. H ARRIS , D., Y IELDING , G., L EVINE , P., M AXWELL , G., R OSE , P. T. & N ELL , P. 2002. Using Shale Gouge Ratio (SGR) to model faults as transmissibility barriers in reservoirs: an example from the Strathspey Field, North Sea. Petroleum Geoscience, 8, 167– 176. H ARRIS , S. D., V ASZI , A. Z. & K NIPE , R. J. 2007. Threedimensional upscaling of fault damage zones for reservoir simulation. In: J OLLEY , S. J., B ARR , D., W ALSH , J. J. & K NIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 353–374. H OWELL , J. & M OUNTNEY , N. 1997. Climatic cyclicity and accommodation space in arid to semi-arid depositional systems: an example from the Rotliegende Group of the UK Southern North Sea. In: Z IEGLER , K., T URNER , P. & D AINES , S. R. (eds) Petroleum Geology of the Southern North Sea: Future Potential. Geological Society, London, Special Publications, 123, 63–86. K NAI , T. A. & K NIPE , R. J. 1998. The impact of faults on fluid flow in the Heidrun Field. In: J ONES , G., F ISHER , Q. J. & K NIPE , R. J. (eds) Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs. Geological Society, London, Special Publications, 147, 269–282. L EVEILLE , G. P., K NIPE , R., M ORE , C., E LLIS , D., D UDLEY , G., J ONES , G., F ISHER , Q. J. & A LLINSON , G. J. 1997a. Compartmentalization of Rotliegendes gas reservoirs by sealing faults, Jupiter Fields area, southern North Sea. In: Z IEGLER , K., T URNER , P. & D AINES , S. R. (eds) Petroleum Geology of the Southern North Sea: Future Potential. Geological Society, London, Special Publications, 123, 87–104. L EVEILLE , G. P., P RIMMER , T. J., D UDLEY , G., E LLIS , D. & A LLINSON , G. J. 1997b. Diagenetic controls on reservoir quality in Permian Rotliegendes sandstones, Jupiter Fields area, southern North Sea. In: Z IEGLER , K., T URNER , P. & D AINES , S. R. (eds) Petroleum Geology of the Southern North Sea: Future Potential. Geological Society, London, Special Publications, 123, 105–122. M A¨ KEL , G. H. 2007. The modelling of fractured reservoirs: constraints and potential for fracture network geometry and hydraulics analysis. In: J OLLEY , S. J., B ARR , D., W ALSH , J. J. & K NIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 375– 403. M ANZOCCHI , T., W ALSH , J. J., N ELL , P. & Y IELDING , G. 1999. Fault transmissibility multipliers for flow simulation models. Petroleum Geoscience, 5, 53–63.

SOUTHERN NORTH SEA FAULTS AND FRACTURES N ELSON , R. A. 2001. Geologic Analysis of Naturally Fractured Reservoirs (2nd ed.). Gulf Professional Publishing, Boston. O DLING , N. E., G ILLESPIE , P., B OURGINE , B. ET AL . 1999. Variations in fracture system geometry and their implications for fluid flow in fractured hydrocarbon reservoirs. Petroleum Geoscience, 5, 373– 384. R OBINSON , A. G, C OLEMAN , M. L. & G LUYAS , J. G. 1993. The age of illite cement growth, Village Fields area, Southern North Sea: evidence from K –Ar ages and 18O and 16O ratios. American Association of Petroleum Geologists Bulletin, 77, 68–80. S TEWART , S. A. & C OWARD , M. P. 1992. Synthesis of salt tectonics in the southern North Sea, UK. Marine and Petroleum Geology, 12, 457– 475. S TEWART , S. A & P ODOLSKI , R. 1998. Curvature analysis of gridded geological surfaces. In: C OWARD , M. P., D ALTABAN , T. S. & J OHNSON , H. (eds) Structural Geology in Reservoir Characterization. Geological Society, London, Special Publications, 127, 133– 147.

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T ERZAGHI , R. D. 1965. Sources of error in joint surveys. Geotechnique, 15, 287–304. W ALSH , J. J & W ATTERSON , J. 1988. Analysis of the relationship between displacements and dimensions of faults. Journal of Structural Geology, 10, 239– 247. W INTER , D. A. & K ING , B. 1991. The West Sole Field, Block 48/6, UK North Sea. In: A BBOTS , I. L. (ed.) United Kingdom Oil and Gas Fields, 25 Years Commemorative Volume. Geological Society, London, Memoirs, 14, 517– 523. Z IEGLER , P. A. 1990. Geological Atlas of Western and Central Europe. (2nd edn). Shell International Petroleum, Maatschhappij. Z IJLSTRA , E. B., R EEMST , P. H. M & F ISHER , Q. J. 2007. Incorporation of fault properties into production simulation models of Permian reservoirs from the southern North Sea. In: J OLLEY , S. J., B ARR , D., W ALSH , J. J. & K NIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 295–308.

Coupled geomechanics – flow modelling at and below a critical stress state used to investigate common statistical properties of field production data X. ZHANG1,4, N. C. KOUTSABELOULIS1, K. J. HEFFER2, I. G. MAIN3 & L. LI3 1

Vector International Processing Systems Limited, 10 The Courtyard, Eastern Road, Bracknell, Berkshire RG12 2XB, UK 2

Heriot-Watt Institute of Petroleum Engineering, Riccarton, Edinburgh, EH14 4AS, UK 3

School of Geosciences, University of Edinburgh, Edinburgh EH9 3JW, UK

4

Present address: Schlumberger Reservoir Geomechanics Centre of Excellence, 10 The Courtyard, Eastern Road, Bracknell, Berkshire RG12 2XB, UK (e-mail: [email protected]) Abstract: An areal model of a fractured/faulted reservoir with 49 wells is developed that incorporates fully-coupled geo-mechanics and fluid flow. It is a generic example of a pattern waterflood although it is inspired by a parallel study of the Gullfaks reservoir in the North Sea, in which stress-related, fault-related and long-range correlations in rate fluctuations are observed. Based on this model, three scenarios are examined in terms of different initial stress states prior to production, each of which involves 36 months of production and injection in the presence of fracture sets and faults. The results support the concept that the long-range, stress-related and fault-related characteristics of correlations in rate fluctuations, observed not only in the Gullfaks data, but also in several other fields worldwide, are symptomatic of a system near a geomechanical critical point. These characteristics are not observed in models that are sub-critical. Short-range rate correlations are likely to exist where there are highly permeable zones between producers and injectors. Long-range rate correlations occur only within critically-stressed regions where there is active shearing or fault reactivation. The modelling results are consistent with field evidence suggesting that incipient shearing is an important mechanism coupled with reservoir flow behaviour.

A range of phenomena associated with reservoirs from original hydrocarbon migration, to productionrelated surface subsidence and induced seismicity are related to deformation, faulting/fracturing, and their interaction with fluid flow (Maillot et al. 1999; Bruno 2002; Barkved et al. 2003). To understand the geomechanical influences that affect the temporal and spatial correlations of well-rate fluctuations, fully coupled geomechanical –flow modelling approaches are used to investigate the characteristics of correlations in well-rate fluctuations based on the finite element method. The models simulate fluid flow and the geomechanical reactions of reservoirs during production, such as reactivation of faults and pre-existing discrete fracture networks, creation of new fractures and rock matrix deformation. Any of these dynamic events can result in changes with time in the conductivities of faults, fractures and rock matrix, and hence in the total permeability field of the reservoir, which will be reflected in changes in the production and injection rates at individual wells. The models are therefore able to incorporate the geomechanical influences on flow rates at wells, and so allow

examination of these influences on spatial and temporal correlations in flow rates at pairs of wells as the rates fluctuate due to an imposed noise. Fracture sets are modelled as planes of altered stiffnesses and potential failure without specific location in individual finite elements; they could be taken to represent a range of sizes, from micro-fractures to fractures at the scale of the element. Mechanical properties are assumed for the fracture sets, faults and intact rock. Initial stresses applied across the model determine whether or not the simulated reservoir is at a critically-stressed state prior to production and injection. The overall deformation of the fractured/faulted reservoir is controlled by potential Coulomb failure of the individual fractures and faults and also of the surrounding intact rock. With this complexity and the time varying nature of the conditions, in some cases approaching a critical point, it is very difficult or impossible to employ analytical techniques. Here, a coupled geomechanical –flow numerical modelling approach based on the finite element model is used to investigate the hydro-mechanical responses of a faulted and fractured reservoir.

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 453–468. DOI: 10.1144/SP292.24 0305-8719/07/$15.00 # The Geological Society of London 2007.

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Stress state within and surrounding fractured/faulted reservoirs Geological evidence suggests that the hydraulic properties of fractures and faults evolve continuously in space and time (Evans et al. 1997; Ngwenya et al. 2000; Main et al. 2001). We will show from our investigations that this is particularly true within and around a ‘fractured/faulted’ reservoir during a production period. By ‘fractured/ faulted’ we imply a reservoir containing either fractures or faults or one containing both. We are not specific in this labelling because, although our model contains only one particular configuration of faults and fractures in this study (Fig. 1), we do not yet have cause to suggest that the exact configuration of the structural features, among the many natural possibilities, is a key component in the behaviour that we will describe. Due to reservoir depletion and/or injection, local pressure variation around a well changes the effective stress state and may either promote or suppress deformation in surrounding areas, which leads to the further changes in stress and pressure within the adjacent regions. This is now widely recognized in seismic hazard studies (e.g. Scholz 1990; Harris 1998). Most shallow seismicity is associated with slip along pre-existing faults (Rummel et al. 1986; Spicak

et al. 1986). For a single fault the shear strength may be expressed by the Coulomb failure criterion

t ¼ (sn – P) tan f þ C

where t is the shear stress along the fault, sn is the normal total stress acting across the fault surface, P is the fluid pressure, f is the friction angle and C is the cohesion. Variations of local stress state within the rock mass make analysis of the stability of a system of faults according to the Coulomb criterion a complex calculation. More importantly, failure locally within the system changes the stress and may either promote or suppress deformation in surrounding areas. This principle also applies to the stress state within a faulted reservoir due to production/injection operations. The stress state surrounding a system of faulted rocks in equilibrium can be expressed with the principal effective stresses (s 10 and s 03) and orientation (u), where the Coulomb failure stress (CFS) (Harris 1998) is CFS ¼ f(s10 , s30 , u):

(2)

A change in the Coulomb failure stress, DCFS, can be due to any change in the principal stresses: DCFS ¼ f(Ds10 , Ds30 , Du)

Fig. 1. Grids of the model central region with the positions of 49 wells and 10 faults (3 major north– south faults and 7 smaller east– west faults). The model has a size of about 21 km by 21 km and the central region shown here is about 11 km by 11 km. The distance between the wells is 1 km.

(1)

(3)

If DCFS . 0, the region becomes closer to instability (fault reactivation and or new fault initialization), whereas if DCFS , 0, it moves farther from instability. During the production and/or injection of a fractured/faulted reservoir, the variation of the effective stress path is complex. In very general terms, production results in an increase in the effective principal stresses due to reservoir depletion, and fluid injection reduces the effective principal stresses. However, the change of the effective stresses at a specific location is strongly related to other conditions, such as the variation of mechanical properties, the presence of faults/fractures and the changes in fluid pressure gradients with evolution of permeability. There are at least three possible effective stress paths to bring a stable stress state to an unstable stress state: (a) s 10 increases and s 30 decreases; (b) both the s 10 and s 30 decrease, and (c) the s 10 increases and s 30 is kept constant. In fact, the effective stress changes within a faulted reservoir are much more complex than the three stress paths above. The complex stress paths may be understood by reference to a state boundary surface, as discussed by Zhang & Sanderson (2001). In principle, the state boundary surface represents a

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surface, below which a fault/fracture system is stable and the fault/fracture system is unstable if the stress state reaches it. Any stress state which would touch this surface on application of a small positive stress change is at a critical stress state. The stress state in a fractured/faulted reservoir during production/injection is variable from place to place and is changing progressively. The stress paths are further complicated by the interaction among stress, strain, pressure and permeability, which results in both changes of magnitude and direction. Studies have revealed a strong correlation between the directionality of reservoir fluid flow and the local earth stress in reservoirs (Heffer & Lean 1993; Heffer & Koutsabeloulis 1993). Changes in pore pressure in a reservoir affect not only the effective stress state, but also in many cases the total stress state (Addis 1997; Hillis 2001). The stress path is defined as change in total horizontal stress, Sh, induced by change in the pore pressure, Pp. Usually, a stress path parameter, Ap, is defined as Ap ¼ DSh/DPp for an extended region or whole reservoir: its value generally depends upon the deformational responses of the surrounding rock mass including nearby faults. For simplicity in this study, in which average pressure changes are relatively small, it is assumed that the parameter, A, is unity, and the uncertainty in effective stress has been addressed in different cases by using different stress ratios.

Fully coupled modelling of fluid flow and stress/strain behaviour There are several assumptions about the variables involved in coupling between flow and stress/ strain (Koutsabeloulis & Hope 1998; Maillot et al. 1999; Settari & Walters 1999). In this study, the coupling between flow and stress/strain involved the modification of the permeability of fractures and/or faults. In this way, the development of an extensional normal strain of fractures and/or faults increases the permeability of the fractures/ faults, and the modification of permeability has an impact on the pressure distribution, which leads to the change of the effective stresses: those effective stresses must be compatible with the fracture strains in a consistent scheme. In coupled geomechanical –flow numerical modelling, the pressure predictions due to fluid flow changes are used by a stress simulator to provide predictions of deformation and to update pore/aperture volumes, which are in turn used by a flow simulator. The effective stress calculations are performed at pre-selected times known as ‘stress steps’. The simulations are termed iterative if at a given stress

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step pore/aperture volumes are repeatedly updated in response to pressure predictions from the flow simulator. The simulations are termed explicit if only one pore/aperture volume update is permitted at a given stress step. In this current study, a fully coupled simulation is performed, in which the deformation, pressure and stress are simultaneously calculated at each stress step. The fully coupled approach offers internal consistency for solution of the hydromechanical equations, i.e. the fluid-flow equations and force-balance equation of continuum mechanics, and bypasses the need for explicit and iterative coupling strategies. Reservoir rock behaviour is often timedependent, with reservoir pressure and the hydraulic boundary conditions playing a part. To account for these effects, it is necessary to combine the equations governing the flow of fluid through the reservoir rock with the equilibrium and constitutive equations of the reservoir rock in the finite element model. To achieve that, this model makes use of the principle of effective stress. The principle of effective stress is written as: KT Dp, fDsg ¼ fDs g þ fmg 1 Ks 0

(4)

where s is the total stress, s 0 is the effective stress, p is pressure, {m} is equal to unity for the diagonal components of stress and zero for the off-diagonal components, KT is the bulk modulus of the reservoir material (solid phase plus voids), KS is the bulk modulus of the solid phase, and D indicates an increment. The Darcy velocity of fluid flow through the reservoir rock is defined by Darcy’s law. fvg ¼ ½KfDPg

(5)

where [K ] is the permeability tensor. The equation of continuity and compressibility for the fluid is given as: KT @1 r fvg Q ¼ fmg 1 KS @t " # 1n n KT @p þ þ , KS KW ðKS Þ2 @t T

T

(6)

where Q represents any fluid flow of the production and injection, 1 is strain, v is flow velocity, n is the porosity and KW is the bulk modulus of the fluid. The hydraulic behaviour of fractured/faulted rocks is considerably different from that of rocks with just matrix porosity, particularly if the fractures

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are connected. In this case, the fracture networks provide fast flow channels and the pores mainly provide fluid storage. Understanding fluid flow through fractures/faults is essential to the analysis of the hydro-mechanical properties and behaviour of fractured/faulted reservoirs. This is because the effective (bulk) permeability of fractured/faulted reservoir rock may be dominated by the permeability of fracture/fault networks, which is usually highly anisotropic. Generally, the effective permeability can be variable during reservoir depletion and injection, a function of fluid pressure and stress state that is non-linear and spatially variable. A considerable amount of experimental and theoretical research suggests that there is an approximate cubic law for flow through fractures (Witherspoon et al. 1980; Raven & Gale 1985), which can be expressed as: Q ¼ f(d 3, dp=dx),

(7)

where Q is the flow per unit length normal to the direction of the flow, d is the hydraulic aperture of fractures, and dp/dx is the pressure gradient in the direction of the flow. The permeability of a fracture system can also be highly dependent upon the stress state due to changes in the connectivity of fractures close to a percolation threshold (Zhang & Sanderson 1998). Significant permeability changes in fractures/faults can occur due to inelastic deformation despite injection pressures being much lower than the confining stress (the minimum total principal stress). In this case, the increase in permeability in the reservoir rocks can be due to dilation normal to the surface of the faults/fractures (even in a compressive stress regime), which is caused by shearing along the faults/fractures, rather than hydro-fracturing. Such shearing need not actually produce localized dynamic slip to significantly affect the permeability. Another important feature of fracture/fault flow is that flow tends to an irreducible, aperturedependent limit at the highest normal stress and smallest aperture. This means that a fracture is still to some extent permeable even under a very high normal compressive stress. In this study, an assumed relationship between permeability change and fracture normal strain change based on the above considerations is used. It is assumed that the fractures/faults possess a base-level permeability prior to production and injection, which corresponds to the residual permeability of the fractures/faults. This implies that the apertures of fractures/faults have closed to the irreducible limit under the reservoir depth, but a minimum hydraulic aperture still exists. Such deformation-related hydraulic behaviour under high normal stress was also observed by Goodman (1976), Bandis et al. (1983) and Cook (1992).

Fig. 2. Relationship between normal strain change (%) and permeability change (factor) for the fracture sets and faults. It was assumed that the initial permeability was the residual value, which implied that the apertures of fractures within the reservoir rock had the maximum closure at the assumed reservoir depth prior to production and injection operation. In addition, a maximum permeability was assumed where the fracture normal strain was larger than 2%.

In the areal model of this study, eight sets of fractures with an interval of 22.58 were simulated within the reservoir rock. A nominal permeability enhancement function was used to simulate the permeability increase of fractures due to fracture dilation. DKF =KF ¼ AF(1n =1nmax ), where 1n , 1nmax

(8)

DKF =KF ¼ A,

(9)

where 1n 1nmax

where KF is the original permeability along fractures, DKF is the enhancement of permeability along the fracture, 1n is the strain change normal to the fracture, 1nmax is a given value for the upper limit of the strain change, A is a constant for the maximum enhancement of permeability, and f( ) is an assumed function (see Fig. 2). It is assumed that the original permeability, KF, is the residual value, which implies that the apertures of fractures within the reservoir rock have the maximum closure at the reservoir depth prior to production and injection operation. In addition, a maximum permeability is assumed where the increase of fracture normal strain is larger than 2%.

Model geometry, mechanical properties and boundary conditions To understand the temporal and spatial correlations between producers and injectors, in terms of their pressure, stress, deformation, permeability and flow-rates, a 2D plane strain areal model has been developed to investigate the well rate correlations

COUPLED GEOMECHANICS–FLOW MODELLING

during oil field production. The model has a size of about 21 km by 21 km with 49 wells (25 producers and 24 injectors) in the central region of 8 km by 8 km. The distance between the wells is 1 km. There are 8 fracture sets within the intact rock with directions of 0, 22.5, 45, 67.5, 90, 112.5, 135 and 157.58, respectively. In addition, there are 3 major faults in the north–south direction and 7 smaller faults in the east –west directions, as shown in Figure 1. The simulation of the smaller east –west faults is to understand the influence of the intersections of these faults with the major north–south faults on the initialization of shear zones. The assumed hydraulically-reactive width of these faults, 100 m, is governed by the element size of the model, but such an extent of damage zone is not atypical for faults that are a few kilometres in length. The gradient with depth of the maximum horizontal total stress (SH) is 24 kPa m21 and the gradient of the minimum horizontal total stress (Sh) is 13.5 or 17.5 kPa m21 in different cases. The initial reservoir pressure gradient is 11.5 kPa m21. The more anisotropic horizontal stress state is chosen in order to place some of the fracture sets in a condition of critical stress in a strike-slip sense. This is consistent with the concept that much of the lithosphere is at or near a critically-stressed state, both locally (Barton et al. 1995; Zoback et al. 1996; Sanderson & Zhang 1999) and globally (Main & Al-Kindy 2002). For an assumed depth at 1000 m, the total maximum and minimum horizontal stresses and reservoir pressure are 24 MPa, 13.5 or 17.5 MPa and 11.5 MPa, respectively. The maximum horizontal principal stress axis, SH, is at N0/1808E or N10/1908E in different scenarios. A poro-elastoplastic (Mohr-Coulomb) constitutive model is applied to the reservoir intact rock and a Coulomb failure criterion is applied to the fracture sets and faults. The mechanical properties used for the intact rock, fracture sets and faults are shown in Table 1. The effective (bulk) permeability of the reservoir rock is assumed to be uniform prior to production with an initial value of 100 mD. However, a much lower initial permeability of 1 mD for fault-grids is assumed so that the faults serve as permeability baffles. The effective (bulk) permeabilities of the intact rock and fault-grids can increase if the fractures and faults develop an extensional normal strain due to plastic shearing, as detailed in the previous section, and enhancement of permeability can be different depending upon the properties of the fractures/faults. A boundary condition of zero displacement is assumed, which, due to the large extent of the model, has negligible influence on the results. Rate fluctuations in an oilfield have two causes: (i) operator actions (wells on-/off-stream, changes to choke settings, workovers, platform downtime, etc.) that have direct effects on individual well

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Table 1. Mechanical properties used in modelling Properties

Values

Intact rock Young’s modulus, E (GPa) Intact rock Poisson’s ratio, y Intact rock friction angle, f (o) Intact rock dilation angle, c (o) Intact rock cohesion, C (MPa) Fracture set normal stiffness, Kn (GPa m21) Fracture set shear stiffness, Ks (GPa m21) Fracture set friction angle, f (o) Fracture set dilation angle, c (o) Fracture set cohesion, C (MPa) Fault normal stiffness, Kn (GPa m21) Fault shear stiffness, Ks (GPa m21) Fault friction angle, f (o) Fault dilation angle, c (o) Fault cohesion, C (MPa)

7 0.2 35 10 2.567 4 2 30 25 2.067 1 0.5 25 5 1.567

pressures and rates; combined with (ii) inter-well responses that depend upon the physics of the reservoir behaviour. The rationale of the modelling is to simulate the operator-induced perturbations with random noise input to the well pressures that is spatially and temporally uncorrelated; and to analyse the well flow rates for correlations caused by responses through the reservoir. Therefore, the production/injection of the 49 wells subjected to monthly variation of well pressure is simulated for 36 months. During this period, the pressure at each of the 24 injectors varies randomly, with a Gaussian distribution, about an average well pressure that is 2.067 MPa (300 psi) higher than reservoir pressure. During the same time, the pressure at the 25 producers also varies randomly about an average well pressure that is 2.067 MPa lower than reservoir pressure. Due to the variation of well pressure and induced permeability change, the flow-rate at each of these wells changes monthly according to its pressure and permeability variation. Then, the correlations over time of flowrates between each pair of the 49 simulated wells are analysed with the non-parametric Spearmanrank method. In this the history of rates from each well is ranked and the correlation coefficient formed from the consequent time series of ranks from each pair of wells. To investigate the effects of stress state on well rate-correlations, three scenarios have been investigated: † In Case 1, the direction of the maximum horizontal principal stress SH is at the N10/1808E (Fig. 3) and the ratio of total stresses, Sh/SH, is 0.56, providing a critical stress state prior to production under the given mechanical conditions (note that the non-zero values of cohesion chosen for the faults and fractures contribute slightly to their stability).

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† In Case 2, the maximum horizontal principal stress SH is in the north –south direction and the ratio of total stresses, Sh/SH, is 0.56, also providing a critical stress state prior to production under the given mechanical conditions, but with active faulting and permeability enhancement different in detail from those in Case 1. † In Case 3, the maximum horizontal principal stress SH is also in the north–south direction. The total minimum horizontal stress is higher and the total stress ratio of Sh/SH is 0.73, at which the stress state prior to production is subcritical under the given mechanical conditions.

Well-rate correlations under different stress conditions Each of these three production/injection scenarios is run for a modelled period of 36 months. In all cases, the same mechanical properties, boundary conditions, production and injection pressure histories, and well configurations are applied. The

Fig. 4. Illustration of the initial stress states prior to production in three cases.

differences in the three cases are the direction of the maximum horizontal principal stress and the initial stress state, governed by the chosen Sh/SH ratio. In Cases 1 and 2, the initial stress is close to the critical state, at which a small change of the effective stress due to fluid pressure changes in the reservoir is likely to trigger global hydromechanical reaction of the reservoir, irrespective of whether the change is at a local scale or a global scale (Zhang et al. 2007). In Case 3, the initial stress state prior to production is in a subcritical state. The initial stress state in the three cases is illustrated in Figure 4. Shear failure in the model is governed, not only by the assumed initial stress state, but also by the cohesions and orientations of the individual faults and fractures and the complexity of the stress state that evolves during production and injection.

Case 1: SH at N10/1908E with Sh/SH ratio of 0.56

Fig. 3. Well configuration and direction of the applied maximum horizontal principal stress in Case 1. The evolution of pressure, stress, plastic shear strain, permeability and flow-rate around the local region of I18, P19, I19 and P20 were examined for the first 4 months of production and injection.

The pressure changes at the producers and injectors cause changes in effective stresses that, because of near-criticality, result in the development of plastic shear strains around wells. Figure 5 shows the developed plastic shear strains around two producers P19 and P20 and two injectors I18 and I19 (see Fig. 3) after the production of 1 month and 4 months. Although a relatively small change in pressure occurs, significant plastic shear strains develops around the two injectors due to the critical stress state prior to production. It is apparent that the developed plastic shear strains are larger around injector I19 than around injector I18. This is due to a major fault near injector I19 and the proximity to the intersection of the major fault and a smaller fault, exemplifying fault-related reservoir rock failure. Note that the direction of the developed plastic shear bands is in the NE direction, which

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Fig. 5. Development of plastic shear strains ranging between 0.909E-3 and 0.1E-1 around wells I18, P19, I19 and P20 after Month 1 (a) and Month 4 (b) during production/injection operations in Case 1 (see Fig. 3 for the locations of the wells).

makes an angle of about 30 degrees with the SH direction, exemplifying reservoir rock failure related to stress direction. The changes in plastic shear strains with production/injection between 1 and 4 months that are detectable by close examination of the details of Figure 5 may seem slight, but, due to the high sensitivity of fracture permeability to strain, cause significant permeability changes (see Fig. 6) and therefore significant flow rate changes at the wells. Particular permeability enhancement is observed along the plastic shear bands developed around injector I19, which therefore support high and time-dependent flow velocities, as shown in Figure 7. Generally, significant changes in well rates are governed by fault-related, stress-related and time-dependent geomechanical phenomena. Figure 8 shows the Spearman rank correlation coefficients of rates at 49 wells during 36 months of production/injection. For most of the wells, the rate correlation coefficients are less than 0.5. However, significant positive correlation coefficients exist between some well pairs. For each of 49 wells, there are 48 correlation coefficients between 48 pairs of wells. From the approximate t-statistics calculated from the correlation coefficients with 34 degrees of freedom, the correlation

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Fig. 6. Enhanced permeability around wells I18, P19, I19 and P20 after Month 1 (a) ranging between 0.106E-5 and 0.925E-5 (m2) and Month 4 (b) between 0.24E-5 and 0.216E-4 (m2) during production/injection operations in Case 1. The changes in permeability are related to the development of the plastic shear strains in Figure 5.

Fig. 7. Velocity of flow around wells I18, P19, I19 and P20 after Month 1 (a) ranging between 0.723E-6 and 0.651E-5 (m s21) and Month 4 (b) ranging between 0.128E-5 and 0.116E-4 (m s21) during production/ injection operations in Case 1. The flow velocity is controlled by the modified permeability and pressure gradient.

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coefficients corresponding to the 1% and 5% significance levels are 0.424 and 0.329 respectively. A correlation coefficient of 0.2 is significant only at the 24% level. A map of permeability after 36 months of production/injection in Case 1 is shown in Figure 9 with the well rate correlation coefficients (the highest value at a well) indicated by the colour code of the circular well symbols. Figure 10 shows the flow velocity pattern of the reservoir at the end of month 36 with the same indicators of rate correlation coefficients. The three wells showing highest positive rate correlations are related to a fast flow channel over a short range. An interesting feature of short-range rate correlations is their dependence on the type of wells involved. Note that there is a highly permeable zone between injectors I16 and I19 (see Figs 3 & 9), but the rate correlation coefficient between the two is only 0.1. This suggests that short-range rate correlations may not exist between injector pairs or between producer pairs. One possible reason is because the sensitivity of flow variation between a pair of wells is related to not only the permeability, but also the pressure gradient between them. The

Fig. 9. Correlation coefficients in Case 1, superimposed on the permeability map ranging between 0.1E-7 and 0.1E-5 (m2) after 36 months of production/injection. Due to production/injection, more than two orders of permeability enhancement are observed along the developed plastic shear zones. The well rate correlation coefficients (the highest value at a well) are indicated by the colour of the well symbol.

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Fig. 10. Rate correlations in Case 1, superimposed on the flow velocity pattern ranging between 0.1E8 and 0.1E4 (m s21). It is apparent that short-range rate correlations are strongly related to the presence of fast flow channels and such channels are subparallel to the maximum horizontal principal stress. The short-range rate correlations occur between adjacent injectors and producers, which result from direct hydraulic links.

permeability between two injectors and between two producers might be high, but the pressure gradient between two producers and between two injectors is relatively low. Alternatively, for short inter-well distances between well pairs, the hydraulic interference is negative (increasing rate at one well tends to reduce rate at the offset well), whilst the geomechanical interference is positive (strain dilatation at one well tends to produce dilatation at the offset well). It is possible that those opposing trends tend to cancel each other. For either reason, correlated flow variation is not significant between two close injectors or between two close producers: short-range rate correlations (hydraulic links) only exist between an injector– producer pair. Figure 11 shows the plastic shear strain pattern of the reservoir at the end of month 36 with selected rate correlation coefficients indicated. Here, high positive rate correlations are marked only between non-neighbouring wells. It is apparent that such long-range high positive rate correlations occur near the plastic zones (the major faults and the created plastic shear bands). This suggests that long-range rate correlations are predominantly related to geomechanical links. The long-range rate correlations occur between injectors and producers, between producers and between injectors, and appear to involve a different mechanism from that of short-range rate correlations. There may be no

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Fig. 11. Long-range rate correlations in Case 1, which are marked on the plastic shear strain pattern ranging between 0 and 0.02. Long-range rate correlations are likely to occur near the plastic zones (the major faults and the created plastic shear bands). This indicates that long-range rate correlations are related to geomechanical links. The distance between geomechanically correlated well pairs is much longer than that between hydraulically correlated well pairs. The long-range rate correlations may occur between injectors and producers, between producers and between injectors.

direct flow between a pair of wells that have a longrange correlation insofar as some of the well pairs with high correlations at long-range are separated by low permeability faults. As demonstrated by Zhang et al. (2007), a small change in effective stress may trigger global geomechanical and hydraulic reaction, no matter whether the change is at a local scale or a large scale. If a pair of wells separated by a long distance are within a system at a critical stress state, the hydraulic change around one well (for example pressure change and flow change) may cause the geo-mechanics to change locally, then the local change in geo-mechanics may trigger a geomechanical change around the other well, despite the large separation. The geomechanical change around the remote well may, in turn, lead to the change in its hydraulic responses, such as permeability, pressure and flow. Thus, the mechanisms of long-range rate correlations are local hydraulic responses plus longrange mechanical responses plus local hydraulic responses (local-hydraulic þ long-mechanical þ local-hydraulic). In this way, correlated flow rates may occur between a pair of wells over a long distance, even though no direct hydraulic links exist between them. Such long-range rate correlations require the presence of a critical stress state

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of the well pairs have a rate correlation coefficient less than 0.5. Again, significantly higher positive correlation coefficients exist between some well pairs. Figures 14 and 15 show the correlation coefficients projected on the permeability pattern and the flow velocity pattern, respectively. The plastic shear strain pattern of the reservoir at the end of month 36 with the indicated rate correlation coefficients is shown in Figure 16. The high correlations that are related to fast flow channels are marked in Figure 15, and the high positive rate correlations between non-neighbouring wells are marked in Figure 16. Again, short-range correlations are related to hydraulic links and occur between adjacent producer–injector pairs only. Long-range correlations are not related to hydraulic links and are likely to occur near plastic zones (the major faults and the newly-created plastic shear bands). The long-range rate correlations may occur between injector–producer, producer–producer, or injector –injector pairs.

Case 3: SH in the north –south direction with Sh/SH ratio of 0.73

Fig. 12. The direction of the maximum horizontal principal stress and the configuration of the producers and injectors in Case 2.

encompassing both wells, when the rocks are strongly susceptible to small perturbations (metastability) and may respond at a long distance from perturbing loads.

Case 2: SH in the north – south direction with Sh/SH ratio of 0.56 In Case 2, the direction of the maximum horizontal principal stress is north– south, parallel to the major faults (Fig. 12). The ratio of the total minimum horizontal principal stress (Sh) to the total maximum horizontal principal stress (SH) is still 0.56. Under these conditions, the stress state prior to production around the reservoir is again largely close to the critical state. The pressure changes around the wells cause plastic failure around the injectors, and the permeability in these regions changes. However, the induced plastic shear zones and highly permeable channels are locally different from those in Case 1. Figure 13 shows the Spearman rank correlation coefficients of rates at 49 wells during 36 months of production/injection. Similar to Case 1, most

In the previous scenarios, the stress prior to production around the reservoir is close to the critical state. In this case, the same horizontal stress direction in Case 2 is applied, but a higher Sh/SH of 0.73 is used. Under these conditions, the stress prior to production is well below the critical state, which we term sub-critical. The same production and injection schedule is performed. Spearman rank correlation coefficients of rates at 49 wells during 36 months of production/injection (Fig. 17) show that unlike Cases 1 and Case 2, no significantly high positive correlation coefficients exist between well pairs. Figure 18 shows the mean effective stress around the wells at the end of month 36. Essentially, due to the subcritical stress state prior to production, the effective stress changes due to pressure change around the wells during production and injection violate neither the Mohr-Coulomb failure criterion for the intact rock, nor the Coulomb failure criterion for the fractures and faults. As a result, no plastic shear failure occurs during the period of production and injection, and no plastic-failure-induced permeability enhancement develops. Thus, the permeability of the reservoir rock around the wells is still uniform, and the faults still serve as permeability barriers. Under such hydraulic conditions, the flows around the wells are determined by the pressure change only, as shown in Figure 19. Neither strong geomechanical links nor strong hydraulic links exist between the wells. For such a reservoir, at a stress state which is not critical

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Fig. 13. Spearman rank correlation coefficients of rates at 49 wells during 36 months of production/injection in Case 2. Each of the columns shows the correlation coefficients of one well with the others. Wells No-1 to No-25 denote producers P1 to P25, and wells No-26 to No-49 denote injectors I1 to I24 (Fig. 12).

Fig. 14. Correlation coefficients in Case 2, which are marked on the modified permeability ranging between 0.1E-7 and 0.1E-5 (m2) after 36 months of production/ injection. Due to production/injection, more two orders of permeability enhancement are observed along the developed plastic shear zones. The well rate correlation coefficients (the highest value at a well) are indicated by the colour of the well symbol.

Fig. 15. Short-range rate correlations in Case 2, which are marked on the flow velocity pattern ranging between 0.1E-8 and 0.1E-4 (m s21). It is apparent that short-range rate correlations are strongly related to the presence of fast flow channels and such channels are parallel to the maximum horizontal principal stress. The short-range rate correlations occur between adjacent injectors and producers only.

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Fig. 16. Long-range rate correlations in Case 2, which are marked on the plastic shear strain pattern ranging between 0 and 0.02. Long-range rate correlations are likely to occur near the plastic zones (the major faults and the created plastic shear bands). This indicates that long-range rate correlations are related to geomechanical links. The distance between geomechanically correlated well pairs is much longer than that between hydraulically correlated well pairs. The long-range rate correlations may occur between injectors and producers, between producers and between injectors.

prior to production, no strong correlations are expected, as shown in Figure 17. Almost no well pair has a rate correlation coefficient larger than 0.5, except for producers P4 and P12 which have a coefficient of 0.53. The results in this case demonstrate that reservoir stress state prior to production plays an important role in the hydraulic and geomechanical responses of a reservoir, and thus strongly influences the correlations between the wells.

Discussion In this study, the injection pressure is much lower than the confining stress (the minimum total principal stress), so no hydraulic fracturing occurs. The increase in permeability in the reservoir rocks is due to the dilatation normal to the surface of the faults/fractures, which is caused by the shearing along the faults/fractures. This suggests that strong rate correlations might occur over broad areas characterized by compressive stress regimes in which normal components of fault displacements are likely to be large due to significant dilation. The spatial decay of the correlations in rate fluctuations

is very different between the near-critical and subcritical cases. Proportional cumulative correlation coefficients are calculated for the three cases. These are defined by ranking the well pairs in order of their separation distances, accumulating the Spearman rank correlation coefficients with increasing distance, and then dividing by the cumulative number of well pairs that are spaced within each distance. Figure 20 shows these calculated values against distance for the three cases. For the near-critical cases, 1 and 2, the spatial decay of correlation approximates a power-law, albeit only over 1 order of magnitude in distances. The exponent of the power-law is 20.7 + 0.1. For the subcritical case 3, the correlations are an order of magnitude lower at short distances, and decay rapidly even further at larger separation distances. The distance at which the rapid decay begins is calculated to correspond to a dimensionless diffusion time tD ¼ Kt=ðSs mr 2 Þ of about 0.25 (K is permeability; t is time, taken as the one month time-step; Ss is the storage at constant stress; m is the fluid viscosity; r is the distance); this is the approximate dimensionless time which limits the influence of Darcy diffusion, beyond which correlations due to Darcy flow would indeed be expected to rapidly decrease. In contrast, the near-critical cases show a continued trend of correlation to greater distances. In terms of the cumulative number of correlated well pairs normalized by the cumulative total number of well pairs with distance, the field data also show apparent power-law decay (Fig. 21), although the exponent is 20.15 to 20.25. The field data show no sign of dropping away at any distance in the manner of the numerical Case 3. The interaction between deformation and permeability is likely to be the most important mechanism for rate correlation in fractured/faulted reservoir rocks. In the current study, only the permeability changes of fractures/faults are accounted for in the assessment of rate correlations. However, where the permeability of reservoir rocks is predominantly controlled by pore permeability, a more comprehensive model including updating permeabilities of intact rocks should be developed. In spite of the limitations above, this geomechanical model can be used as an improved predictive tool for planning and managing waterfloods, particularly for fractured/faulted reservoirs. In conjunction with an assessment of the correlations in rate fluctuations, the geomechanical approach can assist in reservoir waterflood design, provide predictive power for production decisions, and examine the potential for rapid responses to geomechanical events. This is more important in fields with a small number of wells, where statistical techniques can only sparsely sample the full hydro-mechanical patterns within the field; and also in immature

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Fig. 17. Spearman rank correlation coefficients of rates at 49 wells during 36 months of production/injection in Case 3. Each of the columns shows the correlation coefficients of one well with the others. Wells No-1 to No-25 denote producers P1 to P25, and wells No-26 to No-49 denote injectors I1 to I24 (Fig. 12).

developments, where the hydro-mechanical patterns are yet to be established. Long-range, fault-related and stress-related correlations in rate have been observed in several fields to date (Heffer et al. 1997). The commonality of their characteristics suggests that geomechanical influences are an intrinsic component of reservoir fluid flow. However, it may be that the stress states of the fields hitherto analysed are particularly

close to critical, and that other fields are more stable; in other fields permeability may not be so sensitive to shearing, or deformation may not occur by brittle shear. In some fields the stress state and fault properties may be such as to cause the faults to be the dominant sites of shearing, in contrast with the new shear bands created during production in this model; such a change might well alter the detail of the characteristics of the rate correlations, although not the broad pattern. Further field analyses combining statistical and geomechanical assessments are necessary in order to

Fig. 18. Mean effective stresses ranging between –9000 kPa and 211000 kPa around wells at the end of 36 months of production and injection in Case 3.

Fig. 19. Flow velocity ranging between 0.1E-5 and 0.1E-8 (m s21) around wells at the end of 36 months of production and injection in Case 3.

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1 0.1 0.01 0.001 0.0001 0.00001 1

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Fig. 20. Spatial decay of average correlations of rate fluctuations in the 3 numerical cases. The average correlation coefficient is measured as the cumulative Spearman rank correlation coefficient for well pairs to a given separation (lag) distance divided by the cumulative number of all well pairs to that separation distance. The red and blue lines show the decay for the 2 near-critical cases 1 and 2 respectively: these are consistent with power-law decay (dashed line), with an exponent of 20.7 + 0.1. The green line shows the decay for the subcritical case 3: the values of correlation are much lower, and decay at a faster rate beyond the separation distance corresponding to a dimensionless time, tD c. 0.25 (indicated by the short vertical line above the abscissa axis), as expected with Darcy flow.

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define the limits of the hydro-mechanical behaviour described in this paper. The implication that geomechanics is generally intrinsic to reservoir flow behaviour at many scales carries with it the corollary that coupled geomechanical–flow modelling should at least be 1

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Lag distance (km) Fig. 21. Spatial decay of correlations of rate fluctuations in the Gullfaks field. The proportion of correlated wells is measured as the cumulative number of correlated well pairs with separation (lag) distance divided by the cumulative number of all well pairs to that separation distance. The individual curves are for total field production times of 85 (blue), 103 (red), 115 (yellow) and 133 (green) months. The decays are consistent with power-law behaviour, with exponents in the range 20.14 to 20.24.

considered seriously for valid prediction of reservoir flows. Coupled modelling can be applied in different contexts: † As an investigation tool for conceptual studies. At this level, detailed information of a reservoir may not be required and the emphasis is put on the recovery mechanisms and the effects of individual parameters, such as stress condition, geomechanical properties, well configurations, lithology, porosity-permeability characteristics, degree of fracturing, sedimentology, trap type, reservoir geometry, etc. This type of modelling would enhance the understanding of recovery mechanisms. † As an aid in reservoir waterflood design to examine the directionality of reservoir flows. Due to the complexity of the stress field in some real reservoirs, the directionality of flow between a pair of wells is controlled not only by the far-field maximum horizontal stresses, but also by the presence of faults/fractures near the wells. It may also be significantly altered by contrasts in the areal pattern of offtakes and injections leading to strong pressure, and therefore stress, gradients; thermoelastic stress changes can also be significant. Coupled modelling can be used to predict the flow directions around wells within a local region, which is particularly important in regions where there are faults between wells. Under a given in-situ stress condition and production and injection schedule, the flow directions between each pair of wells can be predicted. † As a predictive tool for reservoir-specific production-injection simulations. At this level, detailed information for a reservoir is necessary, including the field geological setting, geomechanical properties, hydraulic parameters, the in-situ stress condition, faults and the production/ injection schedules. The results from this type of modelling may explain the different production efficiency of some producers and predict changes during the lifetime of a reservoir. In addition, these results can provide information to identify hydraulic compartments where no correlations exist. In this way, this geomechanical approach has the potential to predict the short- to medium-term oil production by examining the short- and long-range of rate correlations together with the geomechanical responses

Conclusions A fully coupled stress –flow model which allows the dynamic responses of geomechanical –flow behaviour at individual wells to be investigated, including pressure, stress, strain, permeability and fluid

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flow, applied to three scenarios near or below a critical stress state, has shown the following. † Support for the concept that the characteristics of correlations in rate fluctuations seen in a variety of field data (viz: long-range, stressrelated and fault-related) are symptomatic of a system near a geomechanical critical point. These characteristics are not observed in models that are subcritical. † Short-range rate correlations are likely to exist where there are highly permeable zones between producers and injectors. This suggests hydraulic links are the dominant mechanism for short-range rate correlations, by which the direct communication of fluid flow between producers and injectors occurs. † Long-range rate correlations occur only within critically-stressed regions where there is active faulting or fault reactivation. Long-range effects are likely to be caused by non-linear geomechanical responses, particularly shearing, rather than by direct hydraulic links. In this case, direct hydraulic links between producers and injectors are not required. Therefore, direct communication of fluid flow between the producers and injectors may not exist. † The implication that geomechanical influences are an intrinsic component of reservoir flow in at least a large proportion of fields examined to date, carries the corollary that geomechanical modelling, potentially coupled with fluid flow, should at least be seriously considered for unbiased reservoir prediction in various aspects of field management and investment decisions. The work was carried out as part of the COFFERS project with financial support, secured through the Industry Technology Facilitator (ITF), from the following nine organizations: Amerada Hess, BG Group, BP, ConocoPhillips, DTI, Kerr-McGee, Statoil, Shell and Total. The authors would like to thank J. Walsh, R. Hillis and M. Ameen for their valuable comments.

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B ANDIS , S. C., L UMSDEN , A. C. & B ARTON , N. R. 1983. Fundamentals of rock joint deformation. International Journal of Rock Mechanics & Mining Science & Geomechanical Abstracts, 20, 249–268. C OOK , N. G. W. 1992. Natural joints in rock: mechanical, hydraulic and seismic behaviour and properties under normal stress – Jaeger Memorial Dedication Lecture. International Journal of Rock Mechanics & Mining Science & Geomechanical Abstracts, 29, 198–223. E VANS , J. P., F ORSTER , S. D. & G ODDARD , J. V. 1997. Permeability of fault-related rocks, and implications for hydraulic structure of fault zones. Journal of Structural Geology, 11, 1393– 1404. G OODMAN , R. E. 1976. Methods of Geological Engineering in Discontinuous Rocks. St Paul West Pub. Co., St Paul, Minnesota, USA. H ARRIS , R. 1998. Introduction to special section: Stress triggers, stress shadows, and implications for seismic hazard. Journal of Geophysical Research, 103, 24347–24358. H EFFER , K. J. & L EAN , J. C. 1993. Earth stress orientation – a control on, and guide to, flooding directionality in a majority of reservoirs. In: L INVILLE , B. (ed.) Reservoir Characterization III. PennWell Books, Tulsa, 799– 822. H EFFER , K. J. & K OUTSABELOULIS , N. C. 1993. Stress effects on reservoir flow – numerical modelling used to reproduce field data. In: DE H AAN , H. J. (ed.) New Developments in Improved Oil Recovery. Geological Society, London, Special Publications, 84, 81–88. H EFFER , K. J., F OX , R. J., M C G ILL , C. A. & K OUTSABELOULIS , N. C. 1997. Novel techniques show links between reservoir flow directionality, Earth stress, fault structure and geomechanical changes in mature waterfloods. Society of Petroleum Engineers Journal 2, 91–98. H ILLIS , R. R. 2001. Coupled changes in pore pressure and stress in oilfields and sedimentary basins. Petroleum Geoscience, 7, 419– 425. K OUTSABELOULIS , N. C. & H OPE , S. A. 1998. Coupled stress/fluid-thermal multi-phase reservoir simulation studies incorporating rock mechanics. Society of Petroleum Engineers, SPE 47393. M AILLOT , B., N IELSEN , S. & M AIN , I. 1999. Numerical simulation of seismicity due to fluid injection in a brittle poro-elastic medium. Geophysical Journal International, 139, 263 –272. M AIN , I. G. & A L -K INDY , F. H. 2002. Entropy, energy and proximity to criticality in global earthquake populations. Geophysical Research Letters, 29, doi: 10.1029/2001GL014078. M AIN , I. G., K WON , O., N GWENYA , B. T. & E LPHICK , B. 2001. Fault sealing during deformation-bands growth in porous sandstone. Geology, 28, 1131–1134. N GWENYA , B. T., E LPHICK , S. C., M AIN , I. G. & S HIMMIELD , G. B. 2000. Experimental constrains on the diagenetic self-sealing capacity of faults in high porosity rocks. Earth and Planetary Science Letters, 183, 187–199. R AVEN , K. G. & G ALE , J. E. 1985. Water flow in natural rock fractures as a function of stress and sample size. International Journal of Rock Mechanics & Mining Science & Geomechanical Abstracts, 22, 251.

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R UMMEL , F., M O¨ HRING -E RDMANN , G. & B AUMGA¨ RTNER , J. 1986. Stress constraints and hydrofracturing stress data for the continental crust. Pure and Applied Geophysics, 124, 875–892. S ANDERSON , D. & Z HANG , X. 1999. Critical stress localization of flow associated with deformation of well-fractured rock masses, with implications for mineral deposits. In: M C C AFFERY , K. J. W., L ONERGAN , L. & W ILKINSON , J. J. (eds) Microfractures, Fluid Flow and Mineralization. Geological Society, London, Special Publications, 155, 69–81. S CHOLZ , C. H. 1990. The Mechanics of Earthquakes and Faulting. Cambridge University Press, New York. S ETTARI , A. & W ALTERS , D. A. 1999. Advances in coupled geomechanical and reservoir modeling with applications to reservoir compaction. Society of Petroleum Engineers, SPE 51927. S PICAK , A., L OKAJICEK , T. & W ANIEK , L. 1986. Seismic regime of a single fault model. Pure and Applied Geophysics, 124, 788– 810. W ITHERSPOON , P. A., W ANG , J. S. Y., I WAI , K. & G ALE , J. E. 1980. Validity of cubic law for fluid

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The Statistical Reservoir Model: calibrating faults and fractures, and predicting reservoir response to water flood I. G. MAIN1, L. LI1, K. J. HEFFER2, O. PAPASOULIOTIS3,4, T. LEONARD3, N. C. KOUTSABELOULIS5 & X. ZHANG5 1

School of GeoSciences, University of Edinburgh, Edinburgh EH9 3JW, UK (e-mail: [email protected]) 2

Reservoir Dynamics Ltd, Surrey KT24 6PB, UK

3

School of Mathematics and Statistics, University of Edinburgh, Edinburgh EH9 3JW, UK

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Now at: Serono International, 15bis, chemin des Mines, Case Postale 54, CH-1211, Geneva 20, Switzerland 5

VIPS (Vector International Processing Systems) Ltd, Berkshire RG12 2XB, UK Abstract: This paper describes the new concept of a ‘Statistical Reservoir Model’ to determine significant well-pair correlations. We solve this conceptual problem using a predictive error filter, combined with Bayesian methods that identify those well pairs that are related to each other with statistical significance, for the Gullfaks reservoir in the North Sea. Significant, long-range, correlations in the whole field are found at an optimal time lag of one month. The correlation function for significantly-correlated well pairs, after normalization for the distribution of available wells, shows a long-range power-law decay that is consistent with a critical-point response at the reservoir scale. A principal component analysis shows a strong correlation with the location and orientation of faults that intersect the main producing horizon. A predictive experiment shows that the model performs very well both in history matching and predictive mode on a time scale of about one month.

Hydrocarbon reservoirs comprise subsurface bodies of rock of suitable porosity and permeability to allow the storage and transmittal of oil and gas. Producer wells are sunk into a reservoir to allow hydrocarbons to be extracted, and injector wells to provide voidage replacement and/or to maintain a positive fluid overpressure that will facilitate an efficient sweep and extraction. Pressure changes associated with both injection and production in a poro-elastic material allow geomechanics to have a significant influence on hydrocarbon production rates through changes in the effective stress field (Segall 1989; Main et al. 1994; Maillot et al. 1999; Ngwenya et al. 2003; Zimmermann & Main 2004). Geomechanics not only predicts a reservoir response in the near field, but also at long range i.e. distances much greater than would be predicted by conventional drainage models (Heffer et al. 1995; Maillot et al. 1999). Direct evidence for the relevance of far-field stress and strain changes induced by reservoir pressure changes and poro-elasticity include surface subsidence and induced micro-seismicity (Healy et al. 1968; Segall 1989; Segall & Fitzgerald 1998; Grasso & Sornette 1998; Marsan & Bean 1999, 2003; Zoback & Zinke 2002; Rutledge et al. 1998,

2004). Changes in the far-field strain, and hence pressure, may occur through compliant faults and fractures (Segall 1989; Maillot et al. 1999; Rutledge et al. 2004; Zimmermann & Main 2004) or through matrix material with a stress-sensitive porosity or permeability (Main et al. 1994; Ngwenya et al. 2003). All these mechanisms of pressure, strain and permeability change can have a direct influence on production rates at long range. Such changes are particularly significant when the systems of faults and fractures and the stress field acting on them are in, or close to, a state of incipient failure or criticality (Main 1996). In such a state the hydraulic properties of the reservoir are at their most sensitive to changes in effective stress (Main et al. 1994; Ngwenya et al. 2003; Zimmermann & Main 2004).

Long-range correlations in reservoir behaviour One of the hallmarks of a critical point system is the presence of long-range correlations. For example natural earthquake sequences exhibit long-range triggering with a correlation length of 10 km to 20 km, and a maximum triggering distance of

From: JOLLEY , S. J., BARR , D., WALSH , J. J. & KNIPE , R. J. (eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications, 292, 469–482. DOI: 10.1144/SP292.25 0305-8719/07/$15.00 # The Geological Society of London 2007.

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150 km (Huc & Main 2003). Interestingly, oilfield well-rate data had also shown correlations at lag-time of less than a month over distances up to about 20 km, distances far too large to be due to Darcy flow between the relevant injector and producer wells in the time available (Heffer et al. 1995; Papasouliotis 2000; Huc & Main 2001). The existence of long-range correlations is one more independent piece of evidence that the Earth’s crust is in a near-critical state. Another characteristic property of critical systems is the sensitivity to what might otherwise be thought of as very small fluctuations. For example, 0.1 MPa is sufficient to trigger earthquakes (Grasso & Sornette 1998; Stein 1999). Other evidence includes the very low stress perturbations required to trigger micro-earthquakes in the far field (Healy et al. 1968; Segall 1989; Shapiro et al. 1997, 1999; Grasso & Sornette 1998; Segall & Fitzgerald 1998; Maillot et al. 1999; Zoback & Zinke 2002; Rothert & Shapiro 2003; Rothert et al. 2003), micro-seismicity along pre-existing, criticallystressed natural fractures or zones of weakness (Shapiro et al. 1997, 1999), preferential fluid flow from critically-stressed fractures in borehole data (Rothert & Shapiro 2003; Rothert et al. 2003), and micro-seismicity related to important faults (Simiyu 1999). Added to these evidences for criticality, at which all scales contribute to collective behaviour, is the scale-free population dynamics of faults, fractures and natural seismicity (Main 1996). These all testify to the ability of the Earth, through tectonic forcing and threshold dynamics, to tune itself to a global state of ‘selforganized criticality’ (Bak & Tang 1989) with long-range correlations. Correlation techniques from well rate fluctuation at pairs of wells have previously been used in oilfield analysis to demonstrate a relationship with local stress state and therefore the involvement of geomechanics in reservoir flow (Heffer et al. 1995, 1999; Heffer 2002). In contrast other workers have interpreted inter-well connectivity observed with this technique in terms of more local Darcian flow (Jansen & Kelkar 1996, 1997a, b; Refunjol & Lake 1997; Soeriawinata & Kelkar 1999; Albertoni & Lake 2002). In these studies, monthly well rates at each well are treated as time series, and then the Spearman rank correlation coefficient is calculated between rate series at well pairs. The rate correlations are considered to be indicators of inter-well communication through the reservoir, and therefore provide a potential tool for planning and managing waterfloods. The orientational trend found by Heffer et al. (1995), showing a strong alignment of the direction of the correlation in stacked data with the local maximum horizontal stress axis in all

eight field cases tested, is similar to that of injection-induced micro-seismicity in a gas field (Rutledge et al. 2004). The main advantage of the Spearman rank correlation method over traditional least-squares regression or the Pearson correlation coefficient is that it does not rely on assuming an underlying frequency distribution to the rate fluctuations and is a definitive indicator of a true correlation, assessable at a chosen significance level. Its main disadvantage is that, in dealing with ranks, the phase information is lost, and hence it cannot be used for direct prediction of future rates. This paper describes a new concept in the analysis of well rate data in the form of a truly predictive ‘Statistical Reservoir Model’. We demonstrate that the model may be used for calibrating faults and fractures, and to predict reservoir response to water flood through examining the flow rate statistics of injectors and producers. The concept behind the statistical reservoir model is simple. Given only a set of input flow rates at injectors and producers in the past, how can we predict the output flow rates at producers in the future? The model produces a matrix or array of correlation coefficients that have been identified as statistically significant at a given time lag. For a single time lag the Statistical Reservoir Model is a matrix that acts like a two-dimensional ‘transfer function’, for example converting an input set of production and injection data for a given month into a predicted output the next. For the reservoir examined here we used monthly flow rates for 106 wells over 11 years. The computational algorithm takes approximately 20 minutes for each producer well, implying that the full statistical reservoir model can be determined overnight. Larger oil fields with greater sampling rates or longer lifetimes would require more time for the computation. Previous attempts to construct such statistical models have failed due to contamination of the output by chance correlations or amplified noise, but we have solved this problem using state-of-the-art Bayesian methods (Papasouliotis 2000). Here we test our new method on a field in the North Sea where there are sufficient data to establish the model, and validate the model through examining the principal components of the correlation matrix and by predicting the ‘future’ response using data not used to perform the history match. The first suite of results comparing the output of the model and its interpretation, in comparison with earthquake–earthquake correlations in natural seismicity, is presented separately (Main et al. 2006). Here we present more detail in the analysis of the results, in particular analysing the degree of predictability at different time lags. We also compare the results on real data with the output of a generic coupled

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flow – geomechanical model (Zhang et al. 2007) based on the poro-elastic mechanism operating in a near-critically-stressed crust, confirming such a geomechanical effect as a plausible mechanism for the observations.

The Statistical Reservoir Model The concept of a Statistical Reservoir Model is illustrated in Figure 1. The input data is an array of well pressure or flow rate signals, measured in the past up to the present, at different locations in the reservoirs. The output data is the pressure/rate response at a given time in the future. The array Cij is sparse because chance correlations are deliberately screened out by our new technique. The Statistical Reservoir Model itself is illustrated in Figure 2. Each element in the array is the product of a real regression slope Wij and a binary filter Nij to retain only those correlations that are significant (Nij ¼ 1). The result is a parsimonious array representing the response of the j’th producer to the i’th injector or producer at different time lags k. To determine the optimal regression model we minimize the prediction error with respect to the model parameters, resulting in a standard regression model (Draper & Smith 1998). Bayesian methods (West & Harrison 1997; Leonard & Hsu 1999; Papasouliotis 2000) are then used to determine the significance matrix. The method of solution and the Bayesian techniques used are outlined in the Appendix and presented in more detail in UK patent application 0524134.4. To calibrate the response of faults and fractures to injection and production, the significance matrix Nij, for time lags of 0 or 1 month (Fig. 2) is decomposed to obtain its principal components, each

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being a set of values across well locations. The first few principal components encapsulate the major proportion of the variance in pressure/rate fluctuations. Heffer et al. (1999) and Heffer & King (2006) describe one method of interpolating values between wells for individual components to emphasize spatial trends which are consistent with geomechanical principles. Finally we examine the performance of the model in both history-matching and predictive mode. Although the Statistical Reservoir Model is capable of predicting pressures/rates, its validity is dependent upon constancy of the physical processes in the reservoir; any changes to process can only be handled with a physically-based simulator. A combination of the two approaches is therefore the most advantageous in any practical situation.

Results The concept of the Statistical Reservoir Model presented above has been applied to flow-rate data from the Gullfaks field in the North Sea. The main Gullfaks field lies in Block 34/10 in the northern part of the Norwegian North Sea, and has been developed from three production platforms. The Gullfaks A platform started production on 22 December 1986, Gullfaks B platform on 29 February 1988 and the C platform on 4 November 1989. The recorded production data are composed of monthly measurements of flow rate (volume in standard cubic metres, Sm3) per day, averaged over 1 month intervals) taken over a period of 133 months starting from December 1986. A total of 106 platform wells, 27 injectors and 79 producers were recorded in the dataset during the time

Fig. 1. The Statistical Reservoir Model Cij as a transfer function. Future production rates Pj at time t þ 1 for the j’th producer are predicted by regression from past and present flow rates at the i’th injector Ii or producer Pi at time t, t ¼ t1, t2, . . ..

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Fig. 2. The Statistical Reservoir Model (the transfer function of Fig. 1) is the product of a real regression array W and a significance matrix N (of dimension i, j, t, where i are the predictor wells at times t, and j is a given producer) that filters out chance correlations to leave a more parsimonious but more reliable predictive tool. (Note the multiplication here is not a matrix multiplication, rather it implies each element in W is multiplied simply by the corresponding element in N.)

period December 1986 to December 1997. This field has been under water flood since January 1988. In initial examination of the raw flow rate data (treated as time series), we observed that there were some periods of zero flow rate in individual wells (e.g. see Fig. 3) due to well downtime. Further, a number of wells were operated as producers for some time prior to conversion to injectors (injection of water and/or gas). Such wells are possible sources of error or bias in examining the correlations using the Spearman rank technique, since they could provide spurious correlations and they have been treated separately by Heffer et al. (1995) and Albertoni & Lake (2002). However, such arbitrary treatment could lead to further systematic biases in determining inter-well correlations. Our new method for the Bayesian analysis includes a phase of pre-processing to handle missing data. In the regression stage, the missing values are omitted. However, in the Bayesian analysis stage, the missing values are tackled in two ways. For predictor variables, each missing value is replaced by a weighted average from neighbours. For response variables, a missing value is imputed from a Gaussian distribution, conditional on the observed values of predictor variables (Little & Rubin 1987). The flow rate at wells produce time series that are both ‘noisy’ and ‘patchy’ compared to other applications of time series analysis (Fig. 3). Injection data include many large and sudden systematic fluctuations, but fluctuations in production data seem to be less discontinuous. This illustrates the ‘damping’ effect of the hydraulic, mechanical and structural responses of a complex reservoir. Only those wells in operation for more than 24 months were selected for this test. For these data the optimal regression model (Wij) for each

producer was first established via a history match of past data, and then the Bayesian methods were used to identify those wells that are significantly related to each other (Nij). Finally the Statistical Reservoir Models (Cij) were formed for periods of 0–67, 0– 77, 0– 85, 0 –103, 0–115 and 0–133 months via the product of a real regression array and a significance matrix. In establishing the Gullfaks models, an optimal lag time of one-month was found for the most significant correlations. For example, the effect of time lag between pairs of wells on the cross-correlation and autocorrelation methods is shown in Figure 4. The one-month lag correlations have more significance than the zero-lag correlations, implying a causal relationship, but also a synchronicity in response at zero lag. The optimal time lag (onemonth) and scale lengths (several km) involved confirm that the correlations are not solely caused by Darcy flow. Examining the correlation matrix Cij, we observe that each producer has only a few wells, between about 7 and 25, that are significantly correlated to it, confirming the parsimonious nature of Cij. As an example, Figure 5 shows the spatio-temporal distribution of significant correlated well pairs, (i.e. for wells j, where N1j ¼ 1, rather than 0, in the significance matrix of Fig. 2) that are correlated to the producer well 1 over a period of 85 months. Long-range correlations are observed up to a distance of about 4.5 km and are consistent over time, in line with the results of Heffer et al. (1995), Papasouliotis (2000) and Huc & Main (2001). Such long-range correlations are similar to the correlation length-scales in hydrocarbon production-induced seismicity (Healy et al. 1968; Segall 1989; Grasso & Sornette 1998; Segall & Fitzgerald 1998; Rutledge et al. 1998, 2004; Marsan & Bean 1999, 2003;

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Fig. 3. Plot showing changes of the well flow rate (Sm3/day, averaged over 1 month) series v. time (133 months). Top: for producers A-13 & A-28 (green line). Bottom: for injectors A-11 & A-25AT (blue line), in the Gullfaks Oilfield.

Zoback & Zinke 2002) and in the natural earthquake event correlations (Huc & Main 2003). All of these are likely to be due to geomechanical feedbacks.

The correlated pairs of wells are not uniformly distributed in the reservoir, and, in this case, take up (broadly) an approximately north–south alignment. This alignment is parallel to the orientation of the

Fig. 4. Example of discrete (a) cross-correlation and (b) autocorrelation of flow rates as a function of lag time. Note that in (a) the cross-correlation between injector well 4 and producer well 78 is maximized at the lag time of one-month.

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Fig. 5. Map of the Gullfaks oilfield showing well location, type and number. Red circles denote producer wells and blue triangles injector wells. Wells that are correlated to producer well 1 (shown in blue circle) for a period of 85 months are indicated by a large green circle. For those wells j, N1j ¼ 1; for others N1j ¼ 0 in the significant matrix of Figure 2. The orientation of significant correlated well pairs varies with geographical position within the field, implying significant mechanical complexity in reservoir response.

major faults in this field (see the fault map of the Gullfaks Field, Fossen & Hesthammer 1998), similar to the alignment of hydrocarbon productioninduced seismicity with faults (Simiyu 1999; Rutledge et al. 2004), both implying a significant mechanical response. The most likely explanation of these effects is that the Gullfaks field is in, or close to, a state of criticality, such that the poro-elastic stress disturbances caused by fluctuations in flow rates induce far-field poro-elastic stress changes via large-scale inelastic deformation involving shear, possibly along faults (Main et al. 2006; Zhang et al.

2007). We shall see that this relationship with faults is complementary to a relationship with stress state. The evolution of the correlated well pairs with time for this oilfield (Fig. 6) is also consistent with that observed in induced micro-seismicity elsewhere. Figure 6 shows the evolution of the raw number of significant correlated well pairs at different distance away for six different durations for the Gullfaks oilfield data. We note that: (1)

most of the correlated wells occur at distances between 1 km and 6 km;

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Fig. 6. Number of significant correlated well pairs at different distance away for the Gullfaks oilfield data, at six different durations.

(2) (3) (4)

a peak in the number of correlated wells is reached at around 2 km; the height of the peak decrease and the curve becomes flatter with time; and no effect is detected for distances large than 10 km at this example, i.e. where no wells are available.

These results are of course strongly conditioned by the prior distribution of well location, but when corrected for the background distribution of well positions, result in a power-law correlation function and anomalously slow diffusion of the form kxl tH , where ,x. is the mean correlation length, t is the duration of the record, and the exponent H ¼ 0.33 (Main et al. 2006). The slow diffusion observed has a direct analogue in the triggering of natural seismicity (Marsan & Bean 1999, 2003; Huc & Main 2003). This result confirms that the long-range correlation is not caused by a solitary wave, which would have H ¼ 1 or Fickian pressure diffusion (H ¼ 0.5; Main et al. 2006). It is well known that the power-law behaviour of earthquakes frequency distribution has been associated with self-organized criticality (Main 1996; Grasso & Sornette 1998; Turcotte 1999). Main et al. (2006) confirmed that the correlation function of Figure 6, corrected for the well locations, is also a power-law for the period 0–85 months in the Gullfaks data. Figure 7 shows the frequency of correlations in the histogram of Figure 6 as a function

of distance for a variety of other time periods, this time normalized for the pre-existing distribution of well locations. The fall-off of correlations at the three additional durations confirms the results of Main et al. (2006), that the best fitting distribution is the power-law, as seen in earthquakes, therefore consistent with self-organized critical behaviour (Main 1996; Grasso & Sornette 1998; Turcotte 1999; Huc & Main 2003). The long-range nature (Fig. 7) observed is also in good agreement with the slowness of the fall-off in a generic coupled geomechanics –flow model but only when the pre-existing tectonic stress state is near-critical (see cases 1 and 2 in the accompanying paper of Zhang et al. 2007). To calibrate the response of faults and fractures to injection and production, the significance matrix Nij (in Fig. 2) from the established Gullfaks Statistical Reservoir Model was decomposed into its principal components (or eigenvectors) for each of the available cumulative times of analysis: 0 –67; 0–85; 0 –103; 0– 115; 0–133 months. Each principal component had a value at each of the wells in the field. Interpolation between wells was performed using the strain interpretation technique of Heffer et al. (1999) and Heffer & King (2006). In their studies, it is assumed that the rate fluctuations are direct indicators of geomechanical deformation. In particular each value is assumed to be equivalent to a function of the strain tensor at the well concerned. The interpolated strain maps of

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Fig. 7. (a) Log–log plot showing the number of correlated well pairs at a given distance normalized by available wells at that separation as a function of distance, at the three additional durations illustrated in Figure 6. They appear to exhibit a power-law spatial decline with slope ¼20.5, implying a self-organized critical behaviour. (b) Log –log plot of the spatial fall-off of Spearman rank correlations of rates from the generic coupled geomechanics and flow models (Zhang et al. 2007). The slowness of the fall-off (also consistent with a power-law with exponent c. 0.5) in cases 1 and 2 indicates the long-range nature of the correlations when the stress state is near-critical. This long-range nature is also seen in the Gullfaks data as shown in (a). In the sub-critical case 3 the correlations are smaller and fall-off more rapidly beyond the lag distance corresponding to a dimensionless time of around 0.25 (marked by a vertical black line) as expected when Darcy’s law with fixed permeability is controlling flow.

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Fig. 8. The first principal component from the correlation matrix of the established Gullfaks statistical reservoir model for 0– 67 months compared with faults mapped at top Etive Formation, Gullfaks field. The interpolated strain maps of eigenvector 1 indicate developing linearities in this field. The faults of the Gullfaks field are shown as lines, and the principal component amplitude by colour, with red indicating a higher value.

the first principal component (presented in Main et al. 2006) indicate strong linear features associated with well rate correlations in this field. The mapped first component for the early stages of field development (0–67 months), overlain on the map of faults at top Etive Formation (Fig. 8) suggests association of two of those linearities with two major north–south faults that bound a rotated fault block: supplementary NE–SW trending linearities are seen at later times (Main et al. 2006). Linearities are less clear on the interpolated strain map of the eigenvector corresponding to the second highest eigenvalue in the earlier months of development (0–67 months, Fig. 9). However, a strong north– south linearity does develop by 103 months that persists until 115 months; this linearity follows the trace of the major north–south fault that provides the boundary between the ‘domino’ and ‘horst’ regions of the structure (Fig. 9). After 133 months the emphasis of the second eigenvector has shifted further to the east. This is presumably associated with later development of the Cook and Statfjord reservoirs to the east of the initial development of the Brent reservoir. Our interpretation of these principal components is that they reveal hydraulically reactive features that align in position and orientation with the predominant faults in the area revealed by seismic data (Main et al. 2006). The

correlation of aspects of the Statistical Reservoir Model with structural properties is important because the model was not conditioned a priori by this independent data. This therefore represents an independent validation of the method. In summary, the application of the Statistical Reservoir Model to the Gullfaks field has yielded inter-well dependencies that are (a) long-range up to the scale of the field domain and (b) fault-related, with principal components of the correlation matrix that have trends along the major north –south faults. These characteristics imply that the mechanism behind the inter-well signals is not hydraulic fracturing. Although hydraulic fractures, facilitated by thermally-induced stress reductions, are quite likely to have been created as local features at each of the injector wells, it is highly unlikely that these would have caused connections between wells at distances up to field scale for two reasons: (i) injection pressures rapidly dissipate and fall below the magnitude of the minimum principal stress, which itself increases beyond the region of convective cooling from injection; (ii) long continuous hydraulic fractures would be obvious to the field operator through pressure transient tests or extremely early water breakthroughs. Characteristic (b) adds weight to the alternative explanation of shearing on or around

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Fig. 9. The second principal component from the correlation matrix for 0– 103 and 0 –133 months compared with faults top Etive, Gullfaks field, shown in (a) and (b) respectively, plotted as in Fig. 8. The interpolated strain maps of eigenvector 2 also indicate developing linearities in this field.

pre-existing faults or fractures caused mainly by the poro-elastic stress changes accompanying rate and pressure changes. Regions of dilatation and compression result from shearing which are likely to be associated with increases and decreases in local permeability respectively. Coherent shearing on a complex of faults under the over-riding influence of the in-situ stress state, whether compressive or extensional, is also consistent with characteristic (a). Additionally the north–south ‘domino-style’ faults in the western part of the field, which are

shallowly dipping at about 308 to the east, are also quite likely to be activated in sections, possibly contemporaneously with strike-slip shearing on other faults. It must be added that the interpolation technique outlined above will preferentially tend to link high values of a principal component that are spatially close. Therefore the north–south trends along faults in Figures 8 and 9, although revealing true coherences in rate fluctuation of some degree, are not necessarily reflecting the highest correlations in rate. A better way of mapping multiple-well

Fig. 10. Flow rates at producer 41 in the Gullfaks field (in blue) compared to the flow rate (in green) and the 95% upper and lower confidence limits (in red) predicted by the Statistical Reservoir Model for the Gullfaks field, established over the period indicated as ‘History Match’.

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Fig. 11. Flow rates by summing a group of 28 producers in the Gullfaks field (in blue) compared to the flow rate (in green) predicted by the Statistical Reservoir Model for the Gullfaks field, established over the period indicated as ‘History Match’.

correlations is to be sought. The relationship (b) of principal components with faults, if taken in isolation, might be explained in terms of conventional Darcy flow, focused by the faults either as barriers or as natural conduits, with no geomechanical changes involved, but this is inconsistent with (a). The Statistical Reservoir Model has also been validated independently in predictive mode, as illustrated in Figures 10 and 11. In this experiment the data was split into two sections labelled ‘past’ and ‘present’. The past history was first used to construct a predictive statistical reservoir model. The model was then left unchanged, and used recursively to predict the future response for the later part of the time series (which importantly was not used to construct the model), one month at a time. Apart from a few outlier ‘spikes’, the prediction of flow rate (month by month) is successful within 95% confidence limits that are determined not by the future data, but from calibration on past data (Fig. 10). For the aggregated rate history of a group of 28 wells, both the history match and the predicted rates are in good agreement with the observed flow rates, as shown in the summed time series of Figure 11. Some outliers survive despite the aggregation, but the prediction of flow rate again performs very well both in history matching and predictive mode, indicating a statistical convergence through averaging. This confirms that the

statistical reservoir model can in principle be used to predict the response of the reservoir to given injection scenarios at timescales of one month or so. In future tests will be necessary to validate the model in truly predictive mode using true ‘future’ data.

Discussion The results presented here show long-range correlations in flow rate that are consistent with a critical point response to stress perturbations induced by pressure change. It is difficult to suggest an alternative explanation for a power-law correlation function up to a distance of 10 km at up to one month lag. The similarity of the characteristics of correlations from Gullfaks with those from several other fields previously analysed by Heffer et al. (1995), and from generic coupled geomechanics and flow modelling by Zhang et al. (2007) both lend weight to the geomechanical explanation. However, the results at shorter range may in principle reflect a more conventional reservoir response based on geological architecture. Similarly the principal component analysis shows a pattern that follows the pre-existing normal faults revealed by seismic data which might or might not be geomechanically active in the present-day stress field. A principal

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component analysis of itself does not reveal the nature of what the principal component means. Here it may simply be reflecting the long-term sealing or transmissibility characteristics that may be modelled by conventional reservoir description. Alternatively there may be a component of incipient reactivation, consistent with the geomechanical simulations of Zhang et al. (2007), or some combination of the two. In future work it will be important to calibrate the method against independent data from tracer tests, fluid pressure monitoring or 4D seismic observations, and compare the results with conventional reservoir simulation. The term ‘critical’ is used in two senses in the literature. In the physics literature a critical point system is one with a correlation length comparable to the system size (Bruce & Wallace 1989). This is consistent with the long-range power-law correlation function, up to at least 10 km on the normalized plot of Figure 7. In the geological literature, ‘critically-stressed’ usually means a system that is locally near failure (Barton et al. 1995). ‘Selforganized criticality’ is a global concept (Bak & Tang 1989) where a large correlation length can be maintained while deformation is concentrated on larger fault systems. Simulations in anti-plane geometry show how fault populations can evolve to the critical-point system size by repeated earthquakes, resulting in ‘stress shadows’ in between the large faults, implying the system is not uniformly near failure everywhere in a local sense (Cowie et al. 1993). The statistical analysis presented above implies that the system, if not stationary, is generally evolving only slowly in time (see Fig. 7a). In other reservoirs there may be more dramatic systematic interventions that will introduce significant non-stationarity in the raw data (time series), implying that the method would be applicable only within time intervals that could be regarded as quasi-stationary. The results presented here can be interpreted solely in terms of the subsurface response to flow rate change. This implies that surface operational changes, such as control of surface injection pressure, or the application of chokes on producers, do not ‘stack’ as coherently as the geological or geomechanical responses over time. Such effects may have been screened out by the significance tests, since they may be more likely to add a random component to the time series. Nevertheless, in future it will be important to use documented data on such interventions to see if any systematic effects may be observable, and hence to devise schemes to minimize their effect on the statistical reservoir model. Here we have shown that the statistical reservoir model can in principle improve reservoir

description by highlighting faults and fractures at different scale lengths, and improve short term recovery by directly forecasting production rates. Other applications may also be possible, including screening for geomechanical effects (by looking for long range correlations); subsurface monitoring of CO2 injection (looking for evidence of reactivated faults in time-lapse mode); or in continuous testing of incremental predictions of decline curve analysis.

Conclusions We have developed a new concept, the Statistical Reservoir Model, for calibrating hydraulically reactive faults and fractures, and predicting reservoir response to water flood solely through examining the flow rate statistics of injectors and producers. The results of Main et al. (2006) and those presented here confirm that long-range correlations between well pairs are associated with reservoir faults, as observed in some previous studies based on simpler techniques. Long range correlations are found over an optimal time lag of one month that cannot be explained by Darcy flow, but that are consistent with a geomechanical origin based on the poro-elastic mechanism operating in a near-critically stressed crust. The principal components from the correlation matrix reveal features that align in position and orientation with known faults where they intersect the main producing horizon. The existence of long-range correlations in hydrocarbon production is one more independent piece of evidence that the Earth’s crust is in a nearcritical state, and underlines the importance of geomechanics in modelling reservoir response to water flood. The method has the potential to identify the most compliant structures that may be reactivated through geomechanical effects. This picture of the reservoir can therefore answer a very simple question: namely, when is it necessary to carry out a full geomechanical simulation to explain longrange effects and when is a normal drainage model (Darcy flow) sufficient? It can also be used alongside structural models developed from seismic and borehole data, notably to identify the most significant hydraulically reactive faults and fractures. The model represents a new way of examining structurally complex reservoirs, giving independent information not contained in conventional deterministic reservoir models. More work is required to validate the model in different environments, but in principle the method could be used to validate deterministic models; to interpret active faults; to predict short-term production; to optimize offtake and

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injection rates; and to highlight where there is missing information, particularly in longer-range processes. This work began as part of NERC CONNECT grant GR3/ C0022 with matching funding from BP, and was completed as part of the COFFERS project, under the Industry Technology Facilitator Complex Reservoirs Programme. We are grateful to sponsors: Hess, BG Group, BP, ConocoPhillips, DTI, Kerr-McGee, Statoil, Shell and Total, who supported this project by providing funds, data or robust and constructive criticism. We thank Statoil for providing the dataset used, but do not imply that Statoil is necessarily in agreement with any of our interpretations for the Gullfaks field.

Appendix The statistical method used in the Statistical Reservoir Model (Fig. 2) is explained here. To determine the response of the reservoir to perturbations at well sites we minimize the mean prediction error 1¼

T X M X 2 yi;t ^yi;t

(1)

t¼2 i¼1

between the observed fluid flow rate yi, t at the i’th producer for times t ¼ 2, T and that predicted, ^yi;t , by multivariate regression on a vector X tk of elements comprising the fluid flow rates x j;tk at all N producers and M injectors at time t 2 k, where k is a lag time. The solution to (1) for all yi, t is the Statistical Reservoir Model ^ t ¼ Rk Xtk , Y

(2)

where Y^t is a vector of predicted flow rates at all M producers and Rk is a matrix of the regression parameters. For more than one time lag Rk would be a three-dimensional array with elements ri;j;k : i ¼ 1; N; j ¼ 1; N þ M; k ¼ 1; K. The inversion for the optimal Statistical Reservoir Model is done in two steps. First the well pairs that are significantly correlated at different lag times are identified using a Bayesian Information Criterion (BIC. Papasouliotis (2000), modified after Leonard & Hsu (1999), eqn 1.1.6). This removes well pairs that do not significantly contribute information. Pragmatically the search is stopped for a given producer when the multivariate regression coefficient is R 2 ¼ 0.99 or a given number of iterations is completed. Second, Bayesian Dynamic Linear Modelling (Papasouliotis (2000), based on models presented in Leonard & Hsu (1999), sections 5.5 and 5.6) is used to eliminate a lower number of pairs whose optimal regression slope is not significantly different from zero. These two steps together define a binary significance matrix, Nij, where most elements are zero, resulting in a parsimonious model. Typically only 5– 25 out of the 106 wells in the field are needed to achieve R 2 ¼ 0.99 for a given producer.

481

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Index Page numbers in italic denote figures. Page numbers in bold denote tables. algebraic multigrid methods 413 Allan planes 6–7, 324 amalgamation ratio 230, 312 –321, 324, 330, 331, 333 amplitude variation with offset and azimuth (AVOA) analysis 7 –8, 126, 129, 131, 133 –134, 135 anisotropy azimuthal 124, 151 fracture characterization 173 –174 integration with geomechanics 174, 180, 182 crystal scale 126 –127 and fractional permeability 317 fracture scale 131, 133 –134, 135 grain scale 130 –131 P-wave 124, 128, 129, 130, 131, 132, 151 seismic 7 Clair reservoir 123– 135 geomathematical model 128 –129, 133, 135 and fractures 392 SAIL project 124 velocity 7 comparison with geomechanical models 151 –154 antiforms 188, 197, 199 baffles 295, 296, 297, 337, 446 Banquereau wedge 118 basins 188, 196, 199 Bayesian methods 470, 471, 472, 481 Bedding-planes slip, Buda Limestone 211– 212 surface geometrical measures 196, 197 –199 Berea sandstone, geomechanical modelling 162 Big Brushy Canyon moncline 204, 205, 206, 207, 208 extensional fault propagation folding 208 –215 binary tree method explicit 79 –81 implicit 81 – 83 Black Ven, landslide outcrop analogues 52, 53, 53 Blue Forest 3D seismic survey 138 –155 deformation 139 – 141, 140 fracture density 144 –145 fracture development 140 –141 geomechanical model comparison with velocity anisotropy 151 –154 configuration 141 –145 results 145 –151 structure and evolution 139 –141

borehole image logs 16, 379 West Sole gas field 440 –445 Boundary REPresentation format (BREP) 406– 407 braided channel complex, Ringhorne Field 276, 278 branch lines, fault editing 98, 99 Bremstein fault complex 67 Brent Group 25, 26, 27, 30, 32, 35, 37 –38, 41, 45, 46, 58, 60, 61 production simulation model 221, 224 –225, 230 seismic data 28, 33, 35, 38, 40, 42, 43, 60, 62 well correlation 38, 40 Brent Field northern North Sea 221, 224 Broom Formation 27, 30, 36, 40, 45, 46 Bubnov –Galerkin finite element method 411– 412 Buda Limestone 204, 205, 206, 207, 208, 209, 210 Bedding-plane slip 211– 212 layer extension 211 Cabo Frio fault system, Santos Basin, passive margin extension 117, 118 calcite, extensional veins, Buda Limestone 208– 215 calibration, dynamic, fracture network geometry 9, 386 –391 cambering 50, 51, 51 Campos Basin, passive margin extension 117, 118 Canyonlands, Utah, landslides 56 capillary entry height method 226, 298– 299 Rotliegende gas reservoirs 303– 307 cataclastite, fluid flow 301 –302 chalk fluid flow 3 landslides 49 Charlie fault, West Sole gas field 438, 446 Clair reservoir, west of Shetland 2, 15 seismic anisotropy 7, 124 –135 clay crystal preferred orientation 126 – 127 and permeability 10 –11 clay smear 219 –220 Mount Messenger Formation 240, 242, 244, 245, 246 Clay Smear Potential 10, 11, 223, 247, 248 compartmentalization fault 10 –14, 230, 295, 296 Rotliegende gas reservoirs 295– 307 West Sole gas field 438 –440 complex systems modelling platform (CSMPþþ) 407, 409, 413– 416, 422, 426 complexity, structural 3 –4

computer aided design, multi – phase fluid flow 406 –407 Congo Basin, passive margin extension 117, 118 connectivity dynamic 315 –317, 328– 330 fracture network geometry 377 –378, 383– 384 influence of faults 312 static 314 turbidites 311 –312 modelling faulted systems 320– 332 unfaulted systems 313 –320 continental margins, passive rollover systems, analogue modelling 103– 119 sedimentary wedge, structural evolution 114, 115 –116, 117, 118– 119 continuum percolation system 312 core analysis fracture network data 16, 376 –379 West Sole gas field 440 –445 Cormorant Field, fault seal analysis 219 –220 Cormorant Formation 27, 30, 45 Couette force 111 Coulomb failure stress 144, 145, 148, 149, 155, 453 –454, 457, 462 Courant-Friedrich-Levy criterion 413 creep, landslides 50, 72 crest line 194, 197 Cretaceous base unconformity 28, 29, 30, 35, 38 AVOA 131, 133 Statfjord East Flank 58, 67, 70 Critically stressed faults 17 –18, 453, 457, 467, 470, 480 crystal preferred orientation 124 anisotropy, Clair reservoir 125 –135 crystals, anisotropy 124, 126 –127 CSMPþþ 407, 409, 413 –416, 422, 426 curvature 6, 9 analysis 185, 189 –200 deformation prediction 188 –195 description of folded surfaces 195– 199 differential geometry 185, 186 – 188 and fracturing 392 Gaussian 186, 188, 196 cylindricity, folded surfaces 188, 195 –196, 197 – 198 D-throw 260 –261 damage drilling induced 16, 378, 379 West Sole gas field 437 –438 evolution 176 –182

484 damage (Continued) mechanics 175 –177 damage domain, seismic and geomechanical integration 174, 180, 182 debris flow 50, 51, 51, 55 deformation 11 contractional Blue Forest 3D seismic survey 139 fracture intensity 145 –146 extensional Blue Forest 3D seismic survey 139, 140, 143, 144 fracture intensity 146 –148, 150 –151 freeform 92, 93 prediction by curvature 188 –195 simple constrained (SCODEF) 92, 93 subsurface geomechanical modelling 160 –171 fault model 162 –168 loading configuration 169 –171 open fracture prediction 168 SAVFEM 161– 162 Del Rio Clay 204, 205, 206, 207, 208, 210, 213, 214, 215 Delaunay method, tetrahedral grid creation 91 diapirs, salt landslides 49 rollover systems 110, 112 – 116, 117, 118 West Sole gas field 431, 435 Detection and prediction methods 5–10 diffraction electron back –scatter 127, 128 quantitative X–ray 126, 128 dip 196, 197 discrete fault flow model 339 –340, 341 –348, 350, 358 –360 guiding grids 348– 349 sensitivity study 362– 365 discrete fracture network modelling 2, 16, 395 –398 discrete smooth interpolation 93, 94 –96 discretization fault damage zones 338 –350 discrete fault flow model 339 –340, 341 –348, 350, 358 –360 explicit discretization of faults 340 –341 implicit discretization of faults 340 –347, 350 mixed finite element method 340 –347, 350 displacement variation 6 –7 distortion, volume 92, 93 –94 interpolation 94 –96 domes 188, 189, 195 –196, 198, 199 Draupne Formation 60, 63

INDEX drill stem tests 387, 389 Dunlin Group shale 27, 30, 32, 35, 36 –38, 45, 46, 60, 61 seismic data 42, 43, 46 well correlation 37, 38 East Penguin Fault 32, 33 East Shetland Basin 29 base Cretaceous unconformity 28, 29 inversion 29, 46 tectonism 27 –28, 27, 29 East Shetland Platform 28 ECLIPSE model 413 –416 Elasto-plasticity 9, 174– 176, 179 electron back-scatter diffraction 127, 128 Emigrant Gap anticline 189 –195 curvature analysis 192 –195, 196, 199 –200 Essaouria Basin, passive margin extension 117, 118 Etive Formation 26, 27, 30, 36, 38, 39, 40, 45, 46, 60 evaporite Permian, Zechstein 296, 431, 432, 435 Triassic, Halten Terrace 70 –71 extrusion 50, 51, 51 failure criteria 144, 155 shear 146 –147, 149, 150, 152 tensile 146 –147, 150, 150, 152, 155 fault blocks 2 fault compartmentalization 10 –14 fault damage zones 8, 222, 337, 355 discretization 338– 350 flow pathways 361, 362, 365 –367 reservoir flow simulation 353, 355 –372 3D upscaling 14, 358, 360 –372 sensitivity study 362 –365 flow properties, subregions 365 –367 fault detection 5– 6 fault geometry 4–5, 25 –27, 36 –42, 56, 75 – 87, 89 –100, 103 –119, 221, 259, 261 –263, 271, 273, 279, 295 –308, 406 –429, 431, 433 –435, 441 fault modelling 75 –87 consistency 96, 98 binary tree method 79 –83 editing, in tetrahedral grids 92 –100 fused fault blocks 81 –87 pillar method 78 –79, 83 and seismic data 96, 97 fault network geometry 6–7, 75 –87 fault property algorithms 247 –251 fault seal 2, 10 –12, 220, 431, 437, 445 –447 compartmentalization 10 –14, 11 – 14, 431, 439 – 440 impact of landslides 70 modelling 12 prediction 12

production 12, 219 –231, 271 – 293 static 12, 259 – 269 fault seal analysis 12, 220 deterministic 261 Ling Gu Trap 263, 265 –266 stochastic multi –fault 259 –261 Ling Gu Trap 263, 267, 268 uncertainties 266 –267, 229 fault strands, thin, and fluid flow 337– 352 fault surfaces, modelling 75 –77 fault zones, properties 10 –12, 219 – 231, 235– 257, 353 –372, 421 –450 faults as barriers 3–4, 10 fault damage zones 8, 337, 353, 355, 358 – 359 and bed connectivity 312 modelling 312 –332 branch line, editing 98, 99 comparison with landslides 56, 57, 72 compartmentalization 10 –14, 295, 296 Rotliegende gas reservoirs 296 –307 critically stressed 17 –18 detection 5–6 extensional 56, 57 see also rifting as flow conduits 3– 4 geomechanical modelling 162 –171 geometry 4–5 listric, rollover 103, 104, 110 –116 mapping 6– 7 multi-phase flow properties 14, 220, 225 –229, 295, 299, 307 open, and connectivity 324– 326 permeability 223 –224, 271 –272, 456 in production simulation models 219 –231 propagation, folding extensional 204 –206 stratigraphic control 203 – 215 self-truncating, modelling 85, 86 subseismic 7–8, 14 upscaling 14, 358, 360 –372 transmissibility 296 –297 Ringhorne Field 278 –279 prediction modelling 279– 293 see also transmissibility multipliers truncation 80 –81, 82, 83, 84 modelling 85 – 86 see also l-faults; Y-faults finite element method 411 –412, 419 finite volume method 412 flow see debris flow; fluid flow flow domain 15 flower structures 33, 40, 41, 42, 46, 47, 76 fluid flow 3 baffles 295, 296, 297, 337, 446 cataclastite faults 301 –302 compartmentalized gas reservoirs 296 –307

INDEX fault damage zones 337 –350, 358 –372 impact of fault rock, production simulation models 222– 225 impact of faults 271 modelling 12, 16 –17 coupled geomechanical –flow modelling 453 –467 Voronoi grids 90 multi-phase 14 in faults 225 –229, 227 numerical simulation 405 –421 case studies 413 –420 governing equations 409 –411 numerical solution 411 –413 subseismic faults 14 two-phase 298 fluidization 50 folding curvature analysis 185, 189– 195 fault –propagation, stratigraphic control 203 –215 folds shape 195 –196, 198 –199 surface cylindricity 195 –196, 197 –198 surface description 195 –200 FRACS2000 model 417 Fracture Productivity Index 15 fracture scale anisotropy 131, 133 –134 fractured reservoirs 15 –18, 375– 400, 405 –427, 431 –450 fractured reservoirs, modelling 375 –400, 405 –427, 89 –100 fractures aperture 378, 379, 384 characterization 173– 182 clustering 382 –383, 396 conductive 2, 431, 437, 439 connectivity 383 –384 density, and surface curvature 186 density analysis 381 –382, 386, 387 description 16, 375 –400, 431 –450 detection 16, 123 –135, 375 –400, 431 –450 dimensions 378, 384 induced 16, 378, 379 intensity geomechanical modelling Blue Forest 3D survey 138 –155 contractional deformation 145 –146 extensional deformation 146 –148, 150 –151 mechanical stratigraphy 378 morphology 379 open 174, 431 prediction 8–10, 160, 168, 137– 155, 159, 171, 173– 182, 185 –200, 203– 215, 375 –400 West Sole gas field 439 –440, 441– 442, 445, 447 –450

orientation 377, 380 –381, 385 permeability 456 prediction 8–9, 16 relative age 378 reservoirs 15 –18 characterization 173– 182 modelling 375 –400 conceptual models 393 –395 network geometry 395 –399 analysis 380 –386 data sources 376 – 380 dynamic calibration 386 –391 inter –well interpolation 391 –393 type 376, 378 –379 free water level 14, 225 –226, 227, 228– 229, 296 gas reservoirs 298 –299 free-form deformation 92, 93 Frontier Formation 190 –191 curvature analysis 192 –195 mechanical properties 144 fundamental forms 187 –188, 196 gas reservoirs faults 298 Rotliegende, compartmentalization 295 –307 gas volume initially in place 296 gas – water contact 226, 267 Geochron framework 90, 91, 93 –94 Three-dimensional mapping 98 geomechanics kinematically informed 160 see also modelling, geomechanical geometry, differential, and curved surfaces 185, 186 –188 geostatistics, inter-well interpolation 391– 392 gliding see slides, translational goniometry, X-ray texture 127, 128 graben, keystone 104, 110 –111, 114 graben systems initiation 113, 115 kinematic development 108 – 111 grain scale anisotropy 130 –131 granite, fluid flow 3 Green River Basin, Blue Forest 3D survey 138– 155, 138 grids 76 –79, 84 Geochron framework 90, 91, 93 – 94 guiding 338, 346 –350 tetrahedral 89 –100 creation 91 fault editing 91 –100 consistency 96, 98 Voronoi, fluid flow modelling 90 Griffith-Coulomb theory 144, 155 guiding grids, discretization 338, 346 –350 Gulf of Mexico, passive margin extension 118 Gullfaks Field, Statistical Reservoir Model 471– 479

485 Halten Terrace, landslides 68, 67 seismic data 69, 70 structural controls 70 –71 Heather Formation 27, 30, 45, 58, 60, 63 seismic data 40, 42 heave 142, 144 –145, 151 Hegre Group 27, 30, 32, 35, 36, 45 – 46 hinge line 196, 197, 199 horizon modelling 83 –84 Hoton gas field 432, 433, 434 –435, 437, 438 –439, 442, 445, 447 Humber Group 32, 33, 35, 36, 45, 46 Syn-rifting 34 –35 Hyde gas field 432, 433, 434 –435 hydrocarbon flow, modelling, Ringhorne Field 282 –293 hydrocarbon potential, and landslides 49, 72 image logs see borehole image logs implicit pressure explicit saturation (IMPES) 411, 412 –413 implicit pressure and saturation (IMPSAT) 413 inclusions, anisotropy 124 inflection line 194, 196 –197, 199 inter-well interpolation 391 –393 interpolation 16 discrete smooth 93, 94 –96 inter-well 391 –393 inversion East Shetland Basin 29, 46 tetrahedral 92, 93, 94, 96 West Sole gas field 447 –449 isotropy cyclindrical transverse 176 horizontal transverse 124, 134, 135, 176 planar transverse 176 vertical transverse 124, 128, 129, 131, 133, 134, 135, 176 joint roughness coefficient 398 joints, systematic 137 Jurassic Late, Penguins Cluster 39 –40, 41, 42 Lower, Penguins Cluster 36 – 37 Middle, Penguins Cluster 37 –39 Juxtaposition diagrams see also Allan planes Klakk fault complex 67 l-faults, modelling 84 –85 landslides 49 –73 comparison with faults 56, 57, 72 complex 50, 51, 51 and hydrocarbon potential 49, 72 outcrop analogues 52 –53, 55 –56 and rifting 56, 57 seismic imaging 52, 70 triggers 50 types 50 –52, 51

486 lattice preferred orientation 124, 132 Leman Sandstone 431, 432, 435 Ling Gu Trap 261 – 269, 262, 264 deterministic fault seal analysis 263, 265 –266 shale gouge ratio 263, 265 stochastic multi –fault analysis 263, 267, 268 loading configuration, geomechanical modelling 169 –171 Magnus Embayment 28 Magnus Sandstone 25, 27, 32, 33, 46 mapping faults 6–7 three-dimensional, Geochron model 98 MARGATE model 417 meshes hybrid 406 –407, 408 see also grids mixed finite element method 340 –347, 350 Moab fault damage zone 354, 355 modelling analogue, rollover systems 105 –111 connectivity, turbidite 312 –332 coupled geomechanical –flow, field production data 453 –467 discrete fracture network 16, 395 –398 discretization 337 –350 fault damage zones discretization 337 –350 reservoir flow simulation 353, 355 –372 fault geometry 4 fault networks binary tree method 79 –83 fused fault blocks 81 –87 pillar method 78 –79, 83 fault propagation folding 203 –215, 204 fault properties 13 –14, 322, 323, 324, 326 fault seal 259 –269 fault surface 75 –77 flow 16 – 17 see also fault damage zones, reservoir flow simulation fluid flow multi-phase, numerical simulation 405 –421 software design 421 –427 Voronoi grids 90 folding 185, 189 –200 fracture networks 395 –399 fractured reservoirs 375 –400 geomechanical 159 –160 comparison with seismic velocity anisotropy 151 –154 fracture characterization 173 –182, 392 fracture intensity, Blue Forest 3D survey 138 –155

INDEX integration with seismic anisotropy 174, 180, 182 loading configuration 169 –171 subsurface deformation 160 –171 see also deformation, subsurface, geomechanical modelling horizon 83 – 84 production simulation 13 Rotliegende gas reservoirs 300 –307 seismic 4, 5, 6 seismic anisotropy, Clair reservoir 128 –129, 133 software design 421– 427 strain 8 –10 transmissibility prediction, Ringhorne Field 279 –293 velocity 89 models conceptual, fractured reservoirs 393 –395 CSMPþþ 407, 409, 413 –416, 422, 426 discrete fault flow model 339 –340, 341 –348, 350 ECLIPSE 413 –416 explicit discretization of faults 340 –341 FRACS2000 417 implicit discretization of faults 340 –347, 350 MARGATE 417 mixed finite element method 340 –347, 350 production simulation, treatment of faults 219 –231 SAVFEM 161– 162 Statistical Reservoir Model 469 –481, 471 Mohr –Coulomb failure analysis 144, 457, 462 monocline, extensional 204 –206 Big Brushy Canyon 206 –215 Mount Messenger Formation 321 fault rock types 239, 240, 241, 242 permeability 243 –244, 246 –247, 246 predictors 252 –257, 322, 323, 324, 326 –328 shale smearing 239, 240, 242– 243, 244, 245, 246– 247, 322, 323, 324, 326 – 328 thickness 239 –240, 243, 246 turbidites 236, 310, 321 amalgamation ratio 312, 313, 314, 315, 316 –321, 324, 330, 331 connectivity 312 –332 faulted, modelling 320 –330 horizontal permeability 315 –319 net:gross ratio 311, 312 –313, 314, 315, 316– 321, 324, 325, 326 unfaulted, modelling 312 –320

mud losses 388 –389, 435, 437, 442 mudslides 50, 51, 51, 55 multi-fault analysis stochastic 259– 261 Ling Gu Trap 263, 267, 268 uncertainties 266 –267 Ness Formation 27, 30, 45, 60, 61, 63 net:gross ratio 331, 333 Mount Messenger Formation 311, 312 –313, 314, 315, 316 –321, 324, 325, 326, 331, 333 Statfjord East Flank 70, 71 Newsham gas field 432, 433, 434 –435, 437, 438 –439, 442, 445, 447 Ninety Fathom fault damage zone 355 Non-uniform B-spline curves and surfaces (NURBS) 406 –407 North Sea, northern Mesozoic rifting 28 – 29, 34, 43, 45 – 46, 47 tectonic history 28 – 29, 43, 45 –46 Northern Sklinna High 67, 70 orientation see crystal preferred orientation; lattice preferred orientation; shape preferred orientation outcrop analogues 52 –53, 55 –56, 379– 380, 384 P-waves, anisotropy 124, 128, 129, 130, 131, 132, 151 parallelization, software 421 Penguin Basin 28, 31, 46 seismic data 34, 35, 36 structure 34 –36 Penguin Horst 25, 28, 31, 47 seismic data 32, 33, 47 structure 30, 32, 33, 34 Penguin Lineament 31, 47 structure 33 –34 Penguin Ridge 25, 27, 31, 46 structure 34 Penguins Cluster 25 –47, 26, 27, 28 base Cretaceous unconformity 28, 29, 30, 35, 38 complexity 25 –26 palinspastic restoration 34, 44 sealing faults 25 stratigraphy 27, 30, 45 structural evolution 36 –47, 44 tectonic history 27 – 29 percolation, continuum 312, 316, 331 percolation theory 316, 329 –331 in fracture networks 387 –388 percolation threshold 314, 316, 318, 319, 320, 329 –330, 331, 332, 333, 387– 388, 396 permeability fault rock 223 –224, 226 –228, 456 Mount Messenger Formation 243 –244, 246, 252 –254, 256

INDEX predictors 235, 247 –257 Ringhorne Field, transmissibility prediction 279 –293 faults 223 –224, 271 –272, 456 fractional horizontal 315 –319, 333 phyllosilicates, and permeability 244, 247, 248 Pierce Field, fluid flow 229 –230 pillar method, fault network modelling 78 –79, 83 planes 188, 196, 199 Poiseuille force 111 pressure transient tests 389 production data, coupled geomechanical – flow modelling 453 –467 production logging tools 387, 388– 389 production simulation modelling, Rotliegende gas reservoirs 300 –307 models accurate fault geometry 221 rock flow properties 222 –225 treatment of faults 219 –231 Quadtree decomposition 347 –348 Rannock Formation 26, 27, 30, 36, 38, 40, 45, 46, 60, 63 reservoirs faulted 3–4 fractured 3, 15 –18 modelling 375 –400 quality, seismic anisotropy 123 –135 siliciclastic 3 fluid flow 272 seismic anisotropy, Clair field 124– 135 stress-sensitive 17 – 18, 389 –390 structural complexity 1–19, 2 see also Rotliegende gas reservoirs restoration kinematic 159 – 160 palinspastic, Penguins Cluster 34, 44 three-dimensional 90 rifting and landslides 56, 57 Mesozoic, northern North Sea 28 –29, 34, 43, 45 –46, 47 Ringhorne Field 272, 273 fault transmissibility 278 –279 prediction modelling 279 –293 stratigraphy 276, 277, 278 structure and faulting 272 – 276 rockfalls 50, 51, 51 rollover systems 103– 119 analogue modelling 105 –111 diapirs 110, 113 –116, 117, 118 explusion rollovers 103 –104, 105, 114, 115, 116, 117 fault rollovers 103, 105 graben development 108 –111, 115 –116 graben initiation 113, 115 kinematics 111 –113

listric growth –faults 111 –113, 114, 115 –116 optical strain monitoring 107 –108 sedimentation 113 –119 strain rates 113 structural evolution 114, 115 –116, 117, 118 –119 Rotliegende gas reservoirs capillary entry height method 303 –307 cataclastite faults 301 –302 thickness 303 compartmentalization 295 –307 fluid flow 300 –302 geology 296 permeability 226, 229, 230 production simulation, modelling 200 –307 see also West Sole gas field Sable sub-basin, Scotia Basin, passive margin extension 117, 118 saddles 188, 196, 198, 199 SAIL project 124, 125– 126, 125, 130, 131, 134 salt rollover systems 103– 105, 104 analogue modelling 105 –111 expulsion rollover 103 – 104, 105 Zechstein 296, 432, 435 see also diapirs; evaporite Santa Elena Limestone 204, 205, 206, 207, 208, 210, 213, 214, 215 Santos Basin, Cabo Frio fault system, passive margin extension 117, 118 SAVFEM geomechanical model 161 –162 Scotia Basin Sable sub-basin, passive margin extension 117, 118 Shelburne sub-basin, passive margin extension 117, 118 seals, analysis see fault seal analysis sedimentation, rollover systems 113 –119 seismicity 469 –470, 472– 475 shale intra-reservoir 2 and permeability 10 –11 Shale Gouge Ratio 10 –11, 11, 223, 235– 236, 244, 247, 248, 251, 253, 261, 266– 267, 333 Ling Gu Trap 263, 265 Mount Messenger Formation, turbidite connectivity 322, 323, 324, 326 –328 Shale Smear Factor 10 –11, 11, 223, 235 Mount Messenger Formation 240, 245, 326 –328 Probabilistic 11, 236, 247, 249 –254, 322, 323, 324, 328, 333 shape preferred orientation 124 anisotropy 126, 130 shape-curvature 198 –199

487 shear zone permeability predictor 247, 248 –249 shear-wave splitting 7, 124, 128, 129, 130, 131 Sheep Mountain Anticline, curvature analysis 186 Shelburne sub-basin, Scotia Basin, passive margin extension 117, 118 Silverpit Formation 431, 432, 435 simple constrained deformation 92, 93 simulation see modelling Sklinna Saddle 67, 68 slides complex 50, 51, 51 rotational 50, 51, 51, 68, 69 translational 50, 51, 51, 68, 69, 72 see also landslides slip, landslides 72 Smørbukk Fault 68, 69 software design, numerical simulation 421 –427 Sole Pit Trough 432, 433, 439 – 440 Southern Permian Basin Rotliegende gas reservoirs compartmentalization 296 –307 production simulation 295– 307 see also West Sole gas field Spearman rank correlation 457, 459, 460, 462, 463, 464, 470, 472 spread, lateral 50, 51, 51 staircasing 260, 263 Statfjord Field 57 East Flank landslide complex 58, 59, 60, 61, 63, 64, 66, 70 well data 64, 65 landslide outcrop analogues 52, 55 seismic data 57 –58, 59 Statfjord Formation 27, 30, 45, 272, 276, 282 braided channel complex 276, 278 Statistical Reservoir Model 469– 481, 471 Gullfaks Field 471 –479 Stonebarrow Hill, landslide outcrop analogues 52 –53, 53, 54, 55 storage domain 15 strain elastic 174 – 176, 179 folded strata 189 modelling 8–10 Blue Forest 3D seismic survey 141 –142 coupled fluid flow and stress/ strain 455 –467 geomechanical 163 –171 rollover systems 113 optical monitoring, rollover systems 107– 108 plastic 174 –176, 179 strain softening 163 stratigraphy and interaction with fault seal 13 –14, 219– 231, 235 –257, 271 – 293, 309 –332 and fracture characteristics 378

488 stratigraphy (Continued ) multilayer, and fault propagation folding 204 strain modelling (and fracture prediction) 8–10, 137 –155, 159– 171, 173 –182, 185– 200, 203 –215, 375 –400 stress critical 17 –18 effective 455 fault modulated 142, 144, 145 –146, 147 folded strata 189 in fractured/faulted reservoirs 453 –455 geomechanical modelling 163 –171 in situ 141, 142– 144, 143, 148, 151, 153, 154 and reservoir productivity 389 –390 modelling Blue Forest 3D seismic survey 141 –151 coupled fluid flow and stress/ strain 455 –467 shear 146, 148, 150 and well rate correlations 457 – 464 strike 196, 197 structural complexity 3–4 structural domains 199 subseismic scale faulting 7–8, 123 –135, 271 –293, 375– 400 syn-rifting, Humber Group 34 –35, 46 synforms 188, 196, 199 talus slopes 50 Tampen Spur, landslide complexes 49, 57 Taranaki Basin geology 236, 237, 238 structural characterization 238 –247 Tarbert Formation 26, 27, 30, 45, 60, 63 tectonism northern North Sea 28 –29 Penguins Cluster 27 –29 Tern-Eider Ridge 33, 45 tetrahedra

INDEX inversion 92, 93, 94, 96 see also grids, tetrahedral thin plate theory 186, 188 –189 through-going region, discretization 338, 343, 345 –350 throw 142 D-throw 260 –261 toes, compressional 50, 51, 52 topples 50, 51, 51 transmissibility 12, 222 fault 296 –297 Ringhorne Field 278– 279 prediction modelling 279 –293 transmissibility multipliers 12, 12, 13, 219 –220, 222 –225, 228, 247, 278, 297 gas reservoirs 298, 299, 300 Triassic, Penguins Cluster 45 –46 truncation, fault 80 –81, 82, 83, 84, 85 –86 turbidites bed connectivity 311 –312 modelling 312 –332 faulted systems 320 –332 unfaulted systems 312 –320 flow characteristic 309 –333 Magnus Sandstone 27, 33, 46 Mount Messenger Formation 236, 238, 310, 312 –332 Ty Formation 272, 279, 282 Upscaling flow effects of sub –seismic faults 14, 309 –332, 337 –350, 353 –371 veins, extensional, calcite, Buda Limestone 208, 209, 210, 211 –213, 214, 215 velocity anisotropy 7 velocity modelling, tetrahedral grids 89 Viking Graben 25, 28, 29 rifting 29 Ringhorne Field 272 Voigt-Reuss-Hill averaging 128, 131, 132, 133 volume distortion 92, 93 – 94 interpolation 94 –96

Voronoi grids, fluid flow modelling 90 Waipoapoa landslide 55 – 56 waterflooding prediction 470 simulation 416 –417 well pairs, rate correlation 470, 472 –474 well performance rate-correlation long range 469 –471 under stress 457 –467 West Sole gas field 435 –438 well stimulation 435 well testing analysis 389 numerical simulation 418 –420 West Penguin Fault 32, 33, 46, 47 West Sole gas field 11 –12, 15, 431– 450, 432 compartmentalization 438 –440 fault seal 437, 439 –440, 441, 445 –447 fractures 437, 441 –450 conductive 431, 437, 439, 441 distribution 441 –444 open 439– 440, 441 –442, 445, 447 –450 orientation 445 timing 444 –445 lithofacies 444 –445 mud loss 435, 437, 442 petrography 440 –441 production and drilling 435 –440 damage 437 –438 stratigraphy 432 –433 structure 433 –435, 434 well performance 435 –439 wireline formation testing 387, 389 X-ray diffraction, quantitative 126, 128 X-ray texture goniometry 127, 128 Y-faults, modelling 84, 86 Zechstein evaporite 296, 431, 432, 435

Structurally complex reservoirs form a distinct class of reservoir in which fault arrays and fracture networks, in particular, exert an overriding control on petroleum trapping and production behaviour. With modern exploration and production portfolios now commonly held in geologically complex settings, there is an increasing technical challenge to find new prospects and to extract remaining hydrocarbons from these reservoirs. This volume reviews our current understanding and ability to model the complex distribution and behaviour of fault and fracture networks, highlighting their fluid compartmentalizing effects and storage–transmissivity characteristics, and outlining approaches for predicting the dynamic fluid flow and geomechanical behaviour of these reservoirs. This collection of 25 papers provides an overview of recent progress and outstanding issues in the areas of (i) structural complexity and fault geometry, (ii) detection and prediction of faults and fractures, (iii) compartmentalizing effects of fault systems and complex siliciclastic reservoirs and (iv) critical controls affecting fractured reservoirs.

Fractured Reservoirs (Geological Society Special Publication no 270)

Geoarchaeology: Exploration, Environments, Resources (Geological Society Special Publication, No. 165) (Geological Society Special Publication, No. 165)

Structurally Complex Reservoirs - Special Publication no 292 (Geological Society Special Publication)

Fractured Reservoirs (Geological Society Special Publication no 270)

Geoarchaeology: Exploration, Environments, Resources (Geological Society Special Publication, No. 165) (Geological Society Special Publication, No. 165)

Geological Data Management (Geological Society Special Publication)

Martian Geomorphology (Geological Society Special Publication 356)

Australian Landscapes (Geological Society Special Publication 346)

Communicating Environmental Geoscience - Special Publication no 305 (Geological Society Special Publication) (No. 305)

Sustainable Groundwater Development (Geological Society Special Publication,)

Early Precambrian Processes (Geological Society Special Publication)

Phanerozoic Ironstones (Geological Society Special Publication)

Slope Tectonics (Geological Society Special Publication 351)

Palaeozoic Reefs and Bioaccumulations: Climatic and Evolutionary Controls - Special Publication no 275 (Geological Society Special Publication)

Devonian Events and Correlations : Special Publication no 278 (Geological Society Special Publication)

Fractal Analysis for Natural Hazards - Special Publication No 261 (Geological Society Special Publication)

Non-Marine Permian Biostratigraphy and Biochronology - Special Publication No. 265 (Geological Society Special Publication)

Building Stone Decay: From Diagnosis to Conservation - Special Publication no 271 (Geological Society Special Publication)

Confined Turbidite Systems (Geological Society Special Publication No. 222)

Deformation of Glacial Materials (Geological Society Special Publication No. 176)

Volcanic Degassing (Geological Society Special Publication No. 213)

Geomaterials in Cultural Heritage (Geological Society Special Publication No. 257)

Hydrothermal Vents and Processes (Geological Society Special Publication No. 87)

Climates: Past and Present (Geological Society Special Publication No. 181)

Hydrocarbons in Crystalline Rocks (Geological Society Special Publication No. 214)

The Evolving Continents: Understanding Processes of Continental Growth - Special Publication 338 (Geological Society Special Publication)

Geometry and Petrogenesis of Dolomite Hydrocarbon Reservoirs (Geological Society Special Publication No. 235)

Geometry and Petrogenesis of Dolomite Hydrocarbon Reservoirs (Geological Society Special Publication No. 235)

History of Palaeobotany: Selected Essays (Geological Society Special Publication)

Lacustrine Petroleum Source Rocks (Geological Society Special Publication)

Hydrocarbons in Contractional Belts (Geological Society Special Publication 348)

History of Palaeobotany: Selected Essays (Geological Society Special Publication)

Palaeoproterozoic Supercontinents and Global Evolution (Geological Society London, Special Publication)

Structurally Complex Reservoirs - Special Publication no 292 (Geological Society Special Publication)

Fractured Reservoirs (Geological Society Special Publication no 270)

Geoarchaeology: Exploration, Environments, Resources (Geological Society Special Publication, No. 165) (Geological Society Special Publication, No. 165)

Geological Data Management (Geological Society Special Publication)

Martian Geomorphology (Geological Society Special Publication 356)

Australian Landscapes (Geological Society Special Publication 346)

Communicating Environmental Geoscience - Special Publication no 305 (Geological Society Special Publication) (No. 305)

Sustainable Groundwater Development (Geological Society Special Publication,)

Early Precambrian Processes (Geological Society Special Publication)

Phanerozoic Ironstones (Geological Society Special Publication)

Slope Tectonics (Geological Society Special Publication 351)

Palaeozoic Reefs and Bioaccumulations: Climatic and Evolutionary Controls - Special Publication no 275 (Geological Society Special Publication)

Devonian Events and Correlations : Special Publication no 278 (Geological Society Special Publication)

Fractal Analysis for Natural Hazards - Special Publication No 261 (Geological Society Special Publication)

Non-Marine Permian Biostratigraphy and Biochronology - Special Publication No. 265 (Geological Society Special Publication)

Building Stone Decay: From Diagnosis to Conservation - Special Publication no 271 (Geological Society Special Publication)

Confined Turbidite Systems (Geological Society Special Publication No. 222)

Deformation of Glacial Materials (Geological Society Special Publication No. 176)

Volcanic Degassing (Geological Society Special Publication No. 213)

Geomaterials in Cultural Heritage (Geological Society Special Publication No. 257)

Hydrothermal Vents and Processes (Geological Society Special Publication No. 87)

Climates: Past and Present (Geological Society Special Publication No. 181)

Hydrocarbons in Crystalline Rocks (Geological Society Special Publication No. 214)

The Evolving Continents: Understanding Processes of Continental Growth - Special Publication 338 (Geological Society Special Publication)

Geometry and Petrogenesis of Dolomite Hydrocarbon Reservoirs (Geological Society Special Publication No. 235)

Geometry and Petrogenesis of Dolomite Hydrocarbon Reservoirs (Geological Society Special Publication No. 235)

History of Palaeobotany: Selected Essays (Geological Society Special Publication)

Lacustrine Petroleum Source Rocks (Geological Society Special Publication)

Hydrocarbons in Contractional Belts (Geological Society Special Publication 348)

History of Palaeobotany: Selected Essays (Geological Society Special Publication)

Palaeoproterozoic Supercontinents and Global Evolution (Geological Society London, Special Publication)

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