Developments in Petroleum Science, 44
carbonate reservoir characterization: a geologic - engineering analysis, part II
DEVELOPMENTS
IN PETROLEUM
SCIENCE
Volumes 1-5, 7, 10, 11, 13-17A, 18A-B, 21, 24-26 are out of print ,
8. 9. 12. 17B.
D.W. PEACEMAN-
Fundamentals of Numerical Reservoir Simulation
L.P. D A K E - Fundamentals of Reservoir Engineering
K. M A G A R A Compaction and Fluid Migration T.D. VAN G O L F - R A C H T - Fundamentals of Fractured Reservoir Engineering E.C. DONALDSON, G.V. CHILINGARIAN and T.F. YEN (Editors) - Enhanced Oil Recovery, II. Processes and operations 19A. G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S. K U M A R - Surface Operations in Petroleum Production, I 19B. G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S. K U M A R - Surface Operations in Petroleum Production, II A.J. DIKKERS - G e o l o g y in Petroleum Production 20. E.C. DONALDSON, G.V. CHILINGARIAN and T.F. Y E N - Microbial Enhanced Oil Recovery 22. J. H A G O O R T - Fundamentals of Gas Reservoir Engineering 23. G. DA P R A T - Well Test Analysis for Naturally Fractured Reservoirs 27. E.B. NELSON (Editor) - Well Cementing 28. R . W . Z I M M E R M A N - Compressibility of Sandstones 29. G.V. CHILINGARIAN, S.J. MAZZULLO and H.H. R I E K E - Carbonate Reservoir 30. Characterization: A Geologic-Engineering Analysis, Part I E.C. DONALDSON (Editor) - Microbial Enhancement of Oil R e c o v e r y - Recent Advances 31. E. B O B O K - Fluid Mechanics for Petroleum Engineers 32. E. FJ./ER, R.M. HOLT, P. HORSRUD, A.M. RAAEN and R. RISNES - Petroleum Related 33. Rock Mechanics M.J. E C O N O M I D E S - A Practical Companion to Reservoir Stimulation 34. J.M. V E R W E I J - Hydrocarbon Migration Systems Analysis 35. L. D A K E - The Practice of Reservoir Engineering 36. W.H. SOMERTON - Thermal Properties and Temperature related Behavior of Rock/fluid Sys37. tems W.H. FERTL, R.E. CHAPMAN and R.F. HOTZ (Editors) - Studies in Abnormal Pressures 38. E. PREMUZIC and A. WOODHEAD (Editors) - Microbial Enhancement of Oil R e c o v e r y 39. Recent Advances - Proceedings of the 1992 International Conference on Microbial Enhanced Oil Recovery 40A. T. F. YEN and G.V. CHILINGARIAN (Editors) - Asphaltenes and Asphalts, 1 E.C. DONALDSON, G. CHILINGARIAN and T.F. YEN (Editors) - Subsidence due to Fluid 41. Withdrawal S.S. RAHMAN and G.V. CHILINGARIAN - Casing Design - Theory and Practice 42. B. Z E M E L - Tracers in the Oil Field 43. G.V. CHILINGARIAN, S.J. MAZULLO and H.H. R I E K E - Carbonate Reservoir Charateriza44. tion: A Geologic - Engineering Analysis, Part II
Developments in Petroleum Science, 44
carbonate reservoir characterization: a geologic, engineering analysis, part II G.V. CHILINGARIAN
School of Engineering, University of Southern California, Los Angeles, CA, U.S.A. S.J. MAZZULLO
Geology Department, Wichita State University, Wichita, KA, U.S.A. H.H. RIEKE
DGMR, P.O. Box 345, Jeddah, Saudi Arabia* Associate editors: G.C. DOMINGUEZ and E SAMANIEGO V. With contributions from: H. Cinco Ley G.M. Friedman W.E. Full S. Jalal Torabzadeh C.G.St.C. Kendall G.L. Langnes
D.E Murphy J.O. Robertson Jr. E Samaniego T.D. Van Golf-Racht N.C. Wardlaw G.L. Whittle
*presently: Petroleum Engineering Department, University of Southwestern Louisiana, Lafayette, LA, U.S.A.
ELSEVIER A m s t e r d a m - Lausanne - N e w Y o r k - Oxford - Shannon - Tokyo
1996
ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands
ISBN: 0-444-82103-1
9 1996 Elsevier Science B.V. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science B.V., Copyright & Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands. Special regulations for readers in the USA - This publication has been registered with the Copyright Clearance Center Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the copyright owner, Elsevier Science B.V. unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper. Printed in The Netherlands
Dedication
This book is dedicated to
HIS MAJESTY THE S U L T A N A N D YANG D I - P E R T U A N OF BRUNEI D A R U S S A L A M ON THE O C C A S I O N OF HIS 50TH BIRTHDAY. HIS M A J E S T Y IS A S T A U N C H A D V O C A T E A N D S U P P O R T E R OF R E S E A R C H A N D E D U C A T I O N IN THE FIELD OF G E O S C I E N C E S
To the following outstanding geologists and petroleum engineers Geologists."
Petroleum engineers."
R. G. C. Bathurst J.D. Bredehoeft R. W. Fairbridge J. W. Harbaugh PM. Harris K. Magara J.F. Read A.M. Reid G. Rittenhouse P. O. Roehl J.F. Sarg P.A. Scholle R.F. Walters
S.M. Farouq Ali K. Aziz W.E. Brigham J. C. Calhoun Jr. J.M. Campbell Sr. J.M. Coleman R. C. Earlougher L. W. Lake Ph.E. Lamoreaux K.K. Millheim N.R. Morrow M.Muskat F. Poetmann
and to our inspirer
DR. PROE N.M. STRAKHOV
This Page Intentionally Left Blank
vii
PREFACE
This second volume on carbonate reservoirs completes the two-volume treatise on this important topic to petroleum engineers and geologists. The two volumes form a complete, modem, reference to the properties and production behavior of carbonate petroleum reservoirs. This volume contains valuable glossaries to geologic and petroleum engineering terms providing exact definitions for writers and speakers. Professors will find a useful appendix devoted to questions and problems that can be used for teaching assignments as well as a guide for lecture development; in addition, there is a chapter devoted to core analysis of carbonate rocks which is ideal for laboratory instruction. Managers and Production Engineers will find a review of the latest laboratory technology for carbonate formation evaluation in the chapter on core analysis. The modem classification of carbonate rocks is presented with petroleum production performance and overall characterization using seismic and well test analyses. Separate chapters are devoted to the important naturally fractured and chalk reservoirs. Throughout the book, the emphasis is on formation evaluation and performance. The importance of carbonate reservoirs lies in the fact that they contain as much as 50% of the total petroleum reserves of the world. This is sometimes masked by the uniquely different properties and production performance characteristics of carbonate reservoirs because of their heterogeneity and the immense diversity that exists among them. This two-volume treatise brings together the wide variety of approaches to the study of carbonate reservoirs and, therefore, will fit the needs of Managers, Engineers, Geologists and Teachers. ERLE C. DONALDSON Professor Emeritus The University of Oklahoma Norman, Oklahoma
This Page Intentionally Left Blank
ix
LIST OF CONTRIBUTORS
G.V. CHILINGARIAN
School of Engineering, University of Southern California, Los Angeles, CA 90089-1211, USA
H. CINCO LEY
Division de Estudios de Posgrado, Facultad de Ingenieria, UNAM, 0451 O, Mexico D.F., Mexico
G. M. F R I E D M A N
Brooklyn College & Graduate School of the City University of New York, c/o Northeastern Science Foundation, PO Box 746, Troy, NY 12171-0746, USA
W.E. FULL
Wichita State University, Dept. of Geology, 1845 Fairmount, Wichita, KS 67260, USA
S. JALAL TORABZADEH
Mechanical Engineering Department, California State University, Long Beach, CA 90840, USA
C.G.ST.C. KENDALL
Department of Geology, University of South Carolina, Columbia, South Carolina 29208, USA
G.L. LANGNES
Kemang Indah H-5, Jakarta, Selatan, Indonesia
D. R MURPHY
Petrophysical Engineering Instructor, Head Office E&P Technical Training, Shell Oil Company, P.O. Box 576, Houston, TX 770010576, U.S.A.; Formation Evaluation Lecturer, Petroleum Engineering Graduate Program, University of Houston, Houston, TX 77204-4792, USA
S.J. M A Z Z U L L O
Wichita State University, Dept. of Geology, 1845 Fairmount, Wichita, KS 67260, USA
H.H. RIEKE, III
University of Southwestern Louisiana, Petroleum Engineering Dept., USL Box 44690, Lafayette, LA 70504-4690, USA
J.O. R O B E R T S O N JR.
Earth Engineering Inc., 4244 Live Oak Street, Cudahy, CA 90201, USA
F. S A M A N I E G O V.
UNAM, Division de Estudios de Posgrado, Facultad de Ingenieria, Apdo. Postale 70-256, Mexico 20, 04510 D.F., Mexico
T.D. VAN G O L F - R A C H T
42 Rue de Ranelagh, Paris 75016, France
N.C. WARDLAW
University of Calgary, Dept. of Geology and Geophysics, 2500 University Drive, Calgary, Alta T2N 1N4, Canada
G.L. WHITTLE
Department of Geology, University of South Carolina, Columbia, South Carolina 29208, USA
This Page Intentionally Left Blank
xi
CONTENTS
Preface List o f Contributors C H A P T E R 1. I N T R O D U C T I O N ..................................................................................................... G.V. Chilingarian, H.H. Rieke and S.J. Mazzullo ........................................................................ O v e r v i e w .......................................................................................................................................... Fluid flow relationships .................................................................................................................... I m p o r t a n c e o f fractures .............................................................................................................. S a m p l e p r o b l e m s ......................................................................................................................... H y d r o c a r b o n recovery ................................................................................................................ Reservoirs in karsted carbonates ...................................................................................................... Reservoirs in chalks .......................................................................................................................... Seismic identification o f carbonates ................................................................................................. References ........................................................................................................................................ C H A P T E R 2. S E I S M I C E X P R E S S I O N OF C A R B O N A T E R E S E R V O I R S Y S T E M S .................... C.G.St.C. Kendall, W.E. Full and G.L. Whittle Introduction ...................................................................................................................................... Seismic and synthetic s e i s m o g r a m s ................................................................................................. Seismic data ................................................................................................................................ Seismic events ............................................................................................................................ L i m i t a t i o n s o f seismic m e t h o d .................................................................................................... Synthetic seismic traces ............................................................................................................. Use o f synthetic seismic for m o d e l i n g ....................................................................................... L i m i t a t i o n s o f synthetics ............................................................................................................. Carbonate play types ......................................................................................................................... C a r b o n a t e sheet reservoirs .......................................................................................................... Carbonate organic buildups ......................................................................................................... Carbonate c l i n o f o r m plays .......................................................................................................... A n o m a l o u s carbonate reservoirs ................................................................................................. R e c o g n i t i o n o f carbonate reservoirs ................................................................................................. Seismic character o f carbonate systems .......................................................................................... B a s i n and slope ............................................................................................................................ P l a t f o r m m a r g i n .......................................................................................................................... Sand shoals ................................................................................................................................. P l a t f o r m interior .......................................................................................................................... Terrestrial .................................................................................................................................... Lakes and f a n g l o m e r a t e s ............................................................................................................. S u m m a r y and c o n c l u s i o n s ............................................................................................................... R e f e r e n c e s . ....................................................................................................................................... C H A P T E R 3. C O R E A N A L Y S I S A N D I T S A P P L I C A T I O N IN R E S E R V O I R C H A R A C T E R I Z A T I O N .................................................................................................................... D . E Murphy, G.V. C h i l i n g a r i a n and S.J. Torabzadeh Introduction ...................................................................................................................................... R e s e r v o i r characterization ................................................................................................................ R e p r e s e n t a t i v e n e s s o f core data .................................................................................................
1
1 1 2 3 7 17 47 49 50 51 59 59 59 60 62 67 68 71 72 72 72 74 79 80 81 86 86 91 95 95 97 97 98 98
105 105 106 106
xii Depth alignment o f data .............................................................................................................. Coring ............................................................................................................................................... Introduction ................................................................................................................................. Conventional whole coring ......................................................................................................... Oriented whole coring ................................................................................................................ Wireline retrievable whole coring ................................................................................................ Containerized whole coring ......................................................................................................... Pressure whole coring ................................................................................................................ Sponge whole coring .................................................................................................................. Wireline sidewall coring .............................................................................................................. Core handling .................................................................................................................................... W h o l e cores ................................................................................................................................ Sidewall cores ............................................................................................................................. Core analysis ..................................................................................................................................... Introduction ................................................................................................................................. Sampling ...................................................................................................................................... Conventional (routine) core analysis ........................................................................................... Petrographic core analysis .......................................................................................................... Special considerations for core analysis o f carbonate reservoirs .................................................... Heterogeneities ............................................................................................................................ Multimineral composition ............................................................................................................ L o w porosity and low permeability ............................................................................................ Wettability .................................................................................................................................... A c c u r a c y and reproducibility ...................................................................................................... R o c k catalogs ................................................................................................................................... Introduction ................................................................................................................................. General rock properties catalogs ................................................................................................ Specific formation rock properties catalogs ............................................................................... S u m m a r y .......................................................................................................................................... A c k n o w l e d g m e n t s ............................................................................................................................ References ........................................................................................................................................ C H A P T E R 4. F O R M A T I O N EVALUATION ................................................................................... D.P. M u r p h y Introduction ...................................................................................................................................... Formation evaluation philosophy ...................................................................................................... First and foremost: understand petrophysics ............................................................................. F o r m a t i o n properties o f interest ....................................................................................................... P r i m a r y formation properties o f interest .................................................................................... Other formation properties o f interest ........................................................................................ Formation evaluation tools ................................................................................................................ Formation evaluation situations ........................................................................................................ Formation evaluation o f drilling wells ......................................................................................... F o r m a t i o n evaluation for flood process pilots ............................................................................ Production surveillance formation evaluation ............................................................................. Petrophysical models ........................................................................................................................ Determination o f formation properties o f interest ............................................................................ O v e r v i e w ..................................................................................................................................... Simultaneous determination o f porosity, pore fluid saturations, lithology c o m p o n e n t fractions, and pore fluid properties ............................................................................................. Lithology determination .................................................................................................................... L i t h o l o g y from examination and/or analyses o f rock ................................................................. L i t h o l o g y from well logs ............................................................................................................. Porosity determination ...................................................................................................................... Porosity from examination and/or analyses o f rock ................................................................... Porosity from well logs ..............................................................................................................
107 107
107 108 110 111 111 112 113 114 115 115 116 116
116 117
118 139 144 144 145 145 145 146 146 146 147 147 148 149 149 155
155 155 155 156 156 157 157 159 159 159
160 162 164 164 165 167 167 168 178 178 179
xiii Pore fluid saturation determination ................................................................................................... Saturations from examination and/or analyses of rock .............................................................. Saturations from well logs .......................................................................................................... Pore fluid property determination ..................................................................................................... Introduction ................................................................................................................................. Formation water properties ......................................................................................................... Hydrocarbon properties .............................................................................................................. Permeability determination ................................................................................................................. Permeability from examination and/or analyses of rock ............................................................ Permeability from testing ............................................................................................................ Permeability from well logs ........................................................................................................ Fracture and vug detection ......................................................................................................... Net formation thickness determination ............................................................................................ Structural and stratigraphic determination ....................................................................................... Propagation of error considerations ................................................................................................. Summary .......................................................................................................................................... Acknowledgments ............................................................................................................................ References ........................................................................................................................................
182 182 184 196 196 196 198 201 201 203 203 205 210 212 216 220 220 221
CHAPTER 5. P E R F O R M A N C E A N D CLASSIFICATION OF CARBONATE RESERVOIRS ...... H.H. Rieke III, G.V. Chilingarian and S.J. Mazzullo Introduction ...................................................................................................................................... Technical overview ........................................................................................................................... Reservoir classification schemes ...................................................................................................... Classification of reservoirs based on fluid composition ............................................................. Classification of oil reservoirs based on drive mechanism ......................................................... Classification of carbonate reservoirs based on type of pore system ........................................ Classification based on the geological nature of the carbonate reservoirs ................................. Incremental recovery technology ..................................................................................................... Implementation and control ........................................................................................................ Infill development ........................................................................................................................ Infill drilling activity .................................................................................................................... Background and field examples .................................................................................................. Slant-horizontal-drainhole wells .................................................................................................. Advanced fracturing treatments ................................................................................................. Carbonate reservoir characterization ................................................................................................ Reservoir heterogeneity models .................................................................................................. Microscopic heterogeneity: p e r m e a b i l i t y - c o n d u c t i v i t y - p o r o s i t y relationships ..................... Laboratory and field characterization of carbonate reservoirs ........................................................ Laboratory/outcrop characterization of heterogeneity ................................................................ Determination of heterogeneity in carbonate pore systems from laboratory gas-drive tests .... Some theoretical and practical aspects of carbonate reservoir performance ............................ Summary of reservoir characteristics and primary performance data, and references for selected carbonate reservoirs categorized on pore type and drive mechanism (Table) ........................... References ........................................................................................................................................
231
C H A P T E R 6. W E L L TEST ANALYSIS IN CARBONATE RESERVOIRS ..................................... F. Samaniego V. and H. Cinco Ley Introduction ...................................................................................................................................... Pressure transient behavior of reservoirs ......................................................................................... Linear flow behavior ......................................................................................................................... Radial cylindrical flow ...................................................................................................................... Spherical flow behavior .................................................................................................................... Bilinear flow behavior ....................................................................................................................... Flow diagnosis ................................................................................................................................... Pressure drawdown analysis ............................................................................................................
231 232 234 234 243 254 274 295 297 298 300 302 310 333 358 358 389 435 435 471 480 518 534 549 549 552 554 557 557 559 563 584
xiv Skin factor ........................................................................................................................................ Pressure transient analysis for gas wells .......................................................................................... Example 6-1. Pressure buildup test in naturally-fractured gas well A-1 .................................... Example 6-2. Pressure analysis for exploratory well A-1 .......................................................... Agarwal's (1980) method to account for producing-time effects in the analysis o f buildup test .. Pressure transient analysis for high-permeability reservoirs ...................................................... Example 6-3. Pressure and flow test in oil well A- 1 .................................................................. Example 6-4. Pressure drawdown and buildup test in oil well B-1 ............................................ Example 6-5. Pressure drawdown and buildup tests in oil well B-2 .......................................... Analysis o f well interference tests .................................................................................................... Example 6-6. Transmissivity and diffusivity mapping from interference test data ................................................................................................................... Determination o f the pressure-dependent characteristics o f a reservoir ......................................... Analysis of variable flow rate using superposition, convolution and deconvolution (desuperposition) .. The superposition time graph ...................................................................................................... Drawdown type curve matching ................................................................................................ A general approach to well test analysis .......................................................................................... Additional well test examples ........................................................................................................... Example 6-7. Pulse test in well pair A4-A8 ................................................................................ Example 6-8. Pressure buildup test in well South Dome IS-2 ................................................... Example 6-9. Pressure buildup test in a partially penetrating oil well ........................................ Concluding remarks .......................................................................................................................... Nomenclature .................................................................................................................................... References ........................................................................................................................................
586 591 596 598 611 615 615 621 623 631
CHAPTER 7. NATURALLY-FRACTURED CARBONATE RESERVOIRS ...................................... T.D. Van Golf-Racht Introduction ...................................................................................................................................... Specific features o f the fractured carbonate reservoir .............................................................. Fracturing vs. geological history ...................................................................................................... Geological condition of fracturing .............................................................................................. Folding vs. fracturing ................................................................................................................. Role o f stylolites and joints ......................................................................................................... Fracture evaluation ...................................................................................................................... Basic characterization of "single fracture" and o f a "group of fractures". ............................... Simplified correlation and procedures ........................................................................................ Qualitative fracture evaluation through FINT ............................................................................. Data processing of fractures ...................................................................................................... Physical properties of fractures and matrix ..................................................................................... Porosity and permeability in fractured carbonate reservoirs ...................................................... Rock compressibility in fractured limestone reservoirs ............................................................. Relative permeability and capillary pressure curves in fractured carbonate reservoirs ............. Fractured carbonate reservoir evaluation through well production data ......................................... Single porosity case (impervious matrix) ................................................................................... Basic equations describing flow in fractures .............................................................................. Coning in fractured reservoirs .................................................................................................... Fractured limestone reservoir evaluation through transient flow well data ..................................... Basic discussion o f Warren-Root method .................................................................................. Warren-Root procedure for the evaluation o f a fractured limestone reservoir .......................... Evluation o f matrix-fractures imbibition fluid exchange .................................................................. Single-block imbibition process .................................................................................................. Simplified behavior evaluation ofimbibition process .................................................................. Evaluation o f gravity drainage matrix-fracture fluid exchange .................................................. Single-block gravity-drainage process ........................................................................................ Concluding remarks .......................................................................................................................... References ........................................................................................................................................
683
634 638 641 648 649 653 659 659 660 664 673 673 676
683 684 687 689 692 696 698 698 704 708 709 710 711 719 720 727 728 732 738 740 741 747 750 752 753 762 763 769 769
XV C H A P T E R 8. C H A L K R E S E R V O I R S ............................................................................................... G.M. F r i e d m a n G e n e r a l statement ............................................................................................................................. R e s e r v o i r s in chalks .......................................................................................................................... N o r t h Sea reservoirs ................................................................................................................... N o r t h A m e r i c a n reservoirs ......................................................................................................... Epilogue ............................................................................................................................................ R e f e r e n c e s ........................................................................................................................................ C H A P T E R 9. H Y D R O C A R B O N R E S E R V O I R S IN K A R S T E D C A R B O N A T E R O C K S ................. S.J. M a z z u l l o and G.V. Chilingarian Introduction ...................................................................................................................................... Karsts and their relationship to u n c o n f o r m i t i e s ................................................................................ Karst origins ................................................................................................................................ Karsts and causative m e c h a n i s m s o f subaerial exposure .......................... ................................. Relationships to u n c o n f o r m i t i e s .... .............................................................................................. C l a s s i f i c a t i o n o f karst reservoirs ...................................................................................................... Previous classifications ............................................................................................................... P r o p o s e d classification and e x a m p l e s ......................................................................................... H y d r o c a r b o n s p r o d u c e d from karsted carbonate reservoirs ........................................................... G e o l o g i c and p e t r o p h y s i c a l characteristics o f karsted reservoirs ................................................... R e s e r v o i r systems ....................................................................................................................... R e s e r v o i r continuity .................................................................................................................... P o r o s i t y - p e r m e a b i l i t y and r e c o v e r y efficiency in karst reservoirs ............................................. Subsurface r e c o g n i t i o n o f karsted carbonates ................................................................................. Seismic and subsurface g e o l o g i c m a p p i n g prior to drilling ........................................................ Karst r e c o g n i t i o n from drilling characteristics and well data ..................................................... Conclusions ...................................................................................................................................... R e f e r e n c e s ........................................................................................................................................ Chapter 10. F A C T O R S A F F E C T I N G OIL R E C O V E R Y F R O M C A R B O N A T E R E S E R V O I R S A N D P R E D I C T I O N OF R E C O V E R Y .............................................................................................. N.C. W a r d l a w Introduction ...................................................................................................................................... P r i m a r y r e c o v e r y .............................................................................................................................. Waterflooding and residual oil .......................................................................................................... D i s p l a c e m e n t efficiency ................................................................................................................... Effects o f fluid properties and wettability on trapping ............................................................... Effects o f r o c k - p o r e properties on trapping ..................................... .......................................... Effects o f w e t t a b i l i t y on r e c o v e r y from fractured carbonates .................................................. Volumetric sweep efficiency ............................................................................................................. C o n t i n u i t y o f beds, wells spacing and position .......................................................................... Vertical sweep ............................................................................................................................. Areal sweep ................................................................................................................................. Shales and other p e r m e a b i l i t y barriers ........................................................................................ R e s e r v o i r m o d e l s for s i m u l a t i o n o f p r o d u c t i o n ................................................................................ Biases o f core m e a s u r e m e n t s ...................................................................................................... A v e r a g i n g core data to represent flow at the g r i d - b l o c k scale .................................................... The variogram, kriging and conditional simulation ..................................................................... C o m p a r i s o n o f p e r m e a b i l i t y - d e r i v e d from core and from pressure well tests .......................... Tertiary oil r e c o v e r y in C a n a d a ........................................................................................................ Miscible solvent flooding ............................................................................................................ I m m i s c i b l e gas flooding ........................................... '................................................................... Conclusions ...................................................................................................................................... R e f e r e n c e s ........................................................................................................................................
773 773 775 775 784 792 793 797 797 798 798 800 801 806 806 807 828 833 833 841 845 847 847 851 856 856
867 867 868 870 872 874 876 880 882 882 884 884 884 886 887 888 890 894 895 895 896 898 899
xvi A P P E N D I X A . G L O S S A R Y OF S E L E C T E D G E O L O G I C T E R M S ............................................... S.J. Mazzullo and G.V. Chilingarian
905
A P P E N D I X B. P E T R O L E U M E N G I N E E R I N G G L O S S A R Y .......................................................... J.O. Robertson Jr., G.V. Chilingarian and S.J. Mazzullo R e c o m m e n d e d references ................................................................................................................
921
A P P E N D I X C. F U N D A M E N T A L S OF S U R F A C E A N D C A P I L L A R Y F O R C E S ........................... G.V. Chilingarian, J.O. Robertson Jr., G.L. Langnes and S.J. M a zz ullo Introduction ...................................................................................................................................... Interfacial tension and contact angle ................................................................................................ Effect o f contact angle and interfacial tension on m o v e m e n t o f oil ................................................ Water block ....................................................................................................................................... References ........................................................................................................................................
939
A P P E N D I X D. S A M P L E Q U E S T I O N S A N D P R O B L E M S ............................................................ G.V. Chilingarian, J.O. Robertson Jr. and S.J. Mazzullo General geology ................................................................................................................................ Source rocks ..................................................................................................................................... Capillary pressure ............................................................................................................................. Permeability and porosity ................................................................................................................. Production ........................................................................................................................................ E n h a n c e d recovery ........................................................................................................................... Logging ............................................................................................................................................. Acidizing ........................................................................................................................................... Fracturing .........................................................................................................................................
951 951 951 952 952 954 955 955 956 957
A U T H O R I N D E X .............................................................................................................................
959
S U B J E C T I N D E X ............................................................................................................................
979
937
939 939 944 949 949
Chapter 1
INTRODUCTION G.V. CHILINGARIAN, H.H. RIEKE, and S.J. MAZZULLO
OVERVIEW
The approach in Part 2 of this book builds on the various geoscience and engineering methodologies and technologies presented in the first volume. Part 1 presented fundamentals of geologic and engineering concepts for characterizing and evaluating carbonate reservoirs using a wide range of scales. Carbonate rocks are not homogeneous or isotropic in their properties. Hence, porosity, fluid saturation, bed thickness, and carbonate rock types show very little uniformity throughout reservoirs. Permeability, in most cases, also is strongly anisotropic in carbonate reservoirs. Detailed reviews of the classification, depositional models, and diagenesis of carbonate rocks in Part 1 exposed the reader to a wide range of viewpoints on these subjects. Correlations among permeability, porosity, irreducible fluid saturation, specific surface area, and capillary pressure were established, and used to characterize the static nature of fluid in carbonate reservoirs. Fluid flow dynamics in oil and gas reservoirs were reviewed. Presentation of the volumetric, material balance, and performance decline methods for oil and gas reserve estimation focused on the business side of analyzing production from carbonate reservoirs. The application of computer modeling was shown to be effective in characterizing carbonate reservoirs. Practical application of acid stimulation techniques used to increase the productivity of wells in carbonate reservoirs was discussed in the final chapter of Part 1. Part 2 concentrates on state-of-the-art technologies and practices used to obtain basic information on carbonate reservoirs. There are many challenges in properly characterizing a carbonate reservoir, such as reservoir classification schemes, incremental recovery strategies, and carbonate reservoir heterogeneity. These issues are discussed in Chapter 5. Figure 1-1 is an interactive flow diagram that presents a scheme of contemporary reservoir evaluation. Worthington (1991) pointed out that the integration of the data obtained by using downhole measurements and core analysis into a physically equivalent, unified reservoir model is a process of reservoir characterization. Such technical efforts in reservoir analysis can have only beneficial results in defining the influence of heterogeneities on fluid flow in carbonate reservoirs. Closely-spaced drilling, extensive and specialized coring, advanced well logging tools, tracer tests, digital production, and pressure monitoring provide detailed information needed to perform such analyses. Weber (1986) suggested that another reason for the improved capacity to decipher the influence ofheterogeneities on reservoirs is our ability to simulate fluid flow using advanced reservoir models with the aid of supercomputers. Both static and dynamic reservoir models are linked through reservoir characterization. In order for the link to be effective, a proper understanding of fluid flow constraints in the carbonate reservoir rocks is necessary for predicting and evaluating primary, secondary, and tertiary recovery operations. Enhancement of reservoir productivity is the goal, but it has its price.
.] [
GEOPHYSICS
i l REGIONAL/FIELD I APPRAISAL !
DRILLING/ COMPLETIONS
I
I PRE'EXIS_TING ~ i ~oG~ I
LOGS
/
/il
[ ~PaCERS. / WELLTESTS,
ICASED-HOLELOGS
=
FMS
I
,J
=
SEDIMENTOLOGY
[
I
I INTERWELL I I CORRELATION I i
FORMATION EVALUATION
li\ .....
COREANALYSIS
....
[ !
LOGS
J
MEASUREMENTS I;-"--1 Jl i
i/
I
/
[ 1
OF LOGS
i
! GEOCHEMICAL SIGNATURE
I I
FROM LOGS
Fig. 1-1. Reservoir-evaluation scheme emphasizing the role of downhole measurements; conforms to the progressive calibration of data at scales larger than mesoscopic of heterogeneity by higher-resolution measurements at smaller scales: VSP = vertical seismic profiles; MWD = measurement while drilling; FMS = formation microscanner. (After Worthington, 1991, Fig. 3; reprinted with permission of Academic Press, Inc.)
Information costs money and there are many independent operators and small companies that do not have large budgets with which to acquire sophisticated data using advanced technologies. The writers realize this problem and try to show, where it is appropriate, how minimum data can sometimes be "milked" for additional value. Operating on a small budget is not a reason not to use the latest reservoir management procedures and controls, because such an approach can give a company's operation a chance for maximizing recoverable reserves.
FLUID FLOW RELATIONSHIPS
Elkins (1969) pointed out the importance of a thorough geologic description of cores in establishing reservoir performance and analysis of the low-permeable, fractured (jointed) Hunton Limestone in the West Edmond Field, Oklahoma, U.S.A. Littlefield et al. (1948) successfully forecasted the oil-in-place volume in the West Edmond Field largely on the basis of oil-stained fracture porosity in cores. Oil was confined mainly to the fractures and dissolution channels, which made up about 10% (?) of the total reservoir void space. Littlefield et al. (1948) predicted that this system of fractures would result in severe channeling of naturally encroaching water or injected fluids with little or no benefit to the ultimate recovery of oil. This analysis was proved to be correct. Other engineers disagreed with Littlefield et al.'s (1948) inter-
pretations regarding fluid distribution, fracture continuity, and effect of fractures on reservoir performance. It was erroneously assumed by these engineers that the extensive production of oil at solution GOR meant that the entire reservoir was necessarily oil saturated. Subsequent deepening and coring a down-structure well indicated that a substantial part of the tight matrix did in fact contain free gas. It was discovered later that initial pressure buildup tests (see Chapter 6 in this book) were of insufficient duration, thus resulting in erroneous conclusions based on data first obtained. Overemphasis of any one method failed to account for the many complexities introduced by the internal anatomy of the Hunton reservoir rock (Felsenthal and Ferrell, 1972).
Importance offractures The writers have placed strong emphasis on the importance of fractures in carbonate reservoirs in these two volumes on reservoir characterization. It has been shown in the geological and engineering literature that fractures can constitute the most important heterogeneity affecting production. Craze (1950) cited carbonate reservoirs in Texas, U.S.A., which have low matrix permeabilities, that produce moveable oil from fractures and vugs. Also, Daniel (1954) discussed the influence of fractures on oil production from carbonate reservoirs of low matrix permeability in the Middle East. Reservoirs are not mechanically continuous owing to the presence of fractures. In this sense, the reservoir rock is a discontinuum rather than a continuum. The nature and spatial relationship of discontinuities, such as fractures, dissolution channels, and conductive stylolites that affect fluid flow in carbonate rocks are best evaluated using large-core analysis (see Chapter 3 in this book). Chapter 7 (in this book) discusses fractured carbonate reservoirs in detail. Geological conditions which create fractures and control fracture spacing in rocks include: (1) variations in lithology; (2) physical and mechanical properties of the rocks and fluids in the pores; (3) thickness of beds; (4) depth of burial; (5) orientation of the earth's stress field; (6) amount of differential stress (tectonic forces); (7) temperature at depth; (8) existing mechanical discontinuities; (9) rate of overburden loading or unloading; (10) gravitational compaction (rock or sediment volume reduction as a result of water loss during compaction); (11) anisotropy; and (12) continuum state at depth (competent versus incompetent character of the rocks).
Permeability of a fracture-matrix system One is interested in the total permeability of the fracture-matrix system rather than the permeability contributions of its various parts. The studies of Huitt (1956) and Parsons (1966) provided the following two equations for determining permeability values in a horizontal direction (kH) through an idealized fracture-matrix system (using English units): kH= k + 5.446 • 101~
(1-1)
where k is the matrix permeability (mD); w is the fracture width (in.); L is the distance between fractures; and ct is the angle of deviation of the fracture from the horizontal plane in degrees. If w and L are expressed in mm, then Eq. 1-1 becomes"
k. = km+ 8.44 x
107w3cos2(a/L).
(1-2)
Various mathematical models have been proposed to describe the velocity of a fluid in a fracture, to estimate tank oil-in-place in fractured reservoirs, to determine the fracture porosity, and to calculate average "height" of fractures (Chilingarian et al., 1992).
Fluid flow in deformable rockfractures Witherspoon et al. (1980) proposed a model analyzing fluid flow in deformable rock fractures. This study has ramifications with respect to the migration and production of subsurface fluids. The withdrawal of fluids from carbonate rocks can cause a fracture to close due to induced compaction of the reservoir. The above proposed model consists of a single-phase fluid flowing between smooth parallel plates. The pressure drop is proportional to the cube of the distance between plates (w = width or aperture of a fracture). For laminar flow (Witherspoon et al., 1980): q = 5.11 • 106 [w3Apa/lp],
(1-3)
where q is the volumetric rate of flow (bbl/D); w is the width (or aperture) of a fracture (in.); Ap is the pressure drop (psi); a is the width of the fracture face (ft); l is the length of the fracture (ft); and p is the viscosity of the fluid (cP). But natural fractures are rarely smooth and, therefore, head loss owing to friction, hLf, and is equal to:
hLf=
fI
d lV: 2g
]
(1-4)
where f is the friction factor, which is a function of the Reynolds Number, NRe, and relative roughness that is equal to the absolute roughness, e, divided by the width (height or aperture) of the fracture, w (or b) (Fig. 1-2). The Reynolds Number is equal to VdeP/p, where V is the velocity of flowing fluid (ft/sec); d is the equivalent diameter (ft); p is the mass per unit volume, i.e., specific weight, y, in lb/ft 3divided by the gravitational acceleration, g, in ft/sec/sec (= 32.2). Effective diameter, d , is equal to hydraulic radius, R h, times four (R h= area of flow/wetted perimeter). Lomiz6 (1951) and Louis (1969) studied the effect of absolute and relative roughness on flow through induced fractures, sawed surfaces and fabricated surfaces (e.g., by gluing quartz sand onto smooth plates). They found that results deviate from the classical cubic law at small fracture widths. Jones et al. (1988) studied single-phase flow through open-rough natural fractures. They found that NR~c (critical Reynolds Number where laminar flow ends) decreases with decreasing fracture width (b or w) for such fractures. Jones et al. (1988) suggested the following equations for open, rough fractures with single-phase flow: q = 5.06 x 104a[Apw3/flp] ~
(1-5)
|
--A
tL..
~ bmin
~
~
T bmax
i' e
Fig. 1-2. Simple fracture-fluid-flow model showing the length of the fracture, L; width, a; thickness, b; and the absolute roughness, e.
and k = 5.3 9 x 1051.t[wl/fA pp]O.5,
(1-6)
where k is the permeability in darcys; p is the density of the fluid (lb/ft3); and f is the friction factor, which is dimensionless. Based on experimental data, Lomiz6 (1951) developed many equations relating friction factor (f) and Reynolds Number (NRe) for both laminar and turbulent flows. He also prepared elaborate graphs relating friction factor, Reynolds Number, and relative roughness of fractures (e/b or e/w) (Fig. 1-3). Lomiz6 (1951) found that at the relative roughness (e/b) of less than 0.065, fractures behave as smooth ones (e/b = 0) and friction factor (f) is equal to: f = 6/NRe.
(1-7)
In the turbulent zone, with e/b varying from 0.04 to 0.24 and NRe < 4000-5000, friction factor is equal to" f = B/(NRe )n.
(1-8)
Coefficient B is equal to 0.056 and n can be found from Fig. 1-4 or by using the following equation: n = 0 . 1 6 3 - [0.684(e/b)] + [2.71/e765(e/b)].
(1-9)
The following example illustrates how to use the discussed equations and graphs, and the significance of the results.
4.0
t.uO 3.0
. . . .f.- 6. . . . .
~
~~GranularRocks
2.0
~
9
(3 C)
.,J
......
Turbulent e
x
1.0
9
~ t ~,
-.
\
lO
. . . . +--11
t
(~)
.~_.
"---t"
~.v.~,
. . . . . .
l
.....
~ .....
12 --
..
I[- ~056
14
0.00
. . . .
: _ ,
~ SmoothFractures~" % .
-1.0
0.1
1.0
2.0
3.0
4.0
6.0
5.0
LOG NA. Fig. 1-3. Chart showing the relation between friction factor, f, and Reynolds number, NRe, for laminar, transitional and turbulent fluid flow in granular rocks and smooth fractures. (Modified after Lomiz6, 1951.) No.
e,cm
e/b
3 4 9
0.055 0.055 0.175
0.327 0.205 0.854
10 11 12 13 14 15 16
0.175 0.175 0.175 0.055 0.055 0.055 0.055
0.687 0.574 0.432 0.150 0.120 0.069 0.054
~T,
0.20 r
I:1:
I
0.15 0.10 0.05
0.00
0.05
O.10
O.15
0.20
0.25
RELA TIVE ROUGHNESS, e/d Fig. 1-4. Graph showing the relation between the coefficient, n, and the relative roughness, e/b (b = d), where the coefficient B = 0.056. (Modified after Lomiz6, 1951.)
Sample problems Problem" Effect o f fractures on total permeability If w - 0.005 in., L - 1 in., a = 0 ~ and k = 1 roD, then using Eq. 1-1 kH= 6,800 mD. This example shows the overwhelming contribution which relatively small fracture can exert on total permeability.
Problem: Pressure drop in a vertical fracture Determine the pressure drop in psi in a vertical fracture (flow is in upward direction) given the following information: absolute roughness, e = 0.065 mm; fracture width (w) or height (b) = 0.68 mm; width of fracture face, a = 5 m m (a > b); length of fracture, l= 5 cm; volumetric rate of flow, q = 1 cm3/sec; specific gravity of flowing oil (sp. gr.) = 0.8; and Reynolds Number (NR= 4000) (see Fig. 1-2). Using B e m o u l i ' s Equation for flow from point 1 to point 2: p l / ) ," + V]/2g + z 1= p2/?' + V2/2g + z 2 + hlf
and
pl/)/--p2/); = Ap/y = (z 2 - Z1) "~"hlf= l + hlf, where Pl and P2 a r e pressures at points 1 and 2, respectively, in l b / f t 2 absolute; V = velocity of flowing fluid in ft/sec; z~ and z 2 = potential heads at points 1 and 2 in ft; g = gravitational acceleration, ft/sec/sec (=32.2); h~f= head loss due to friction in ft. All terms in the above equation are in ft-lb per lb of fluid flowing or in ft. q = 1 cm3/sec = 1 ( c m 3 / s e c ) x 3.531 x 10-5 (ft3/cm 3) = 3.531 x 10.5 ft3/sec A (cross-sectional area of flow) = a x b = 5 x 0.68 m m x (1.07639 • 10 -5 ft2/I/ln] 2 • 3.6597 x 10 -5 ft 2
V= q/A = 3.531 x 10-5/3.6597 x l0 -5- 0.965 ft/sec Hydraulic radius R = (flow area)/(wetted perimeter) = (a x b)/(2a + 2b) = 9.814 x 10-4 ft Equivalent diameter = d = 4R = 2ab/(a + b) - 3.9277 x 10-3 ft Inasmuch as NReiS 4000 and relative roughness, e/b = 0.065/0.68 = 0.095, one can use Eq. 1-8 (and Fig. 1-4 to determine n):
f = B/(NRe )n-- 0.056/(4000) 0.'2= 0.0207 Thus: hlf-f(l/d)(VZ/2g)
= 0.0207(0.164/3.93 x 10 -3) [(0.965)2/(2 x 32.2)] = 0.0197 ft
and
Ap = 9/(l + h~f) = [(0.8 •
62.4)(0.164 + 0.0197)]'144 = 0.062 psi
(Note the relative contribution of potential head and
hlfto Ap.)
Fracture orientation Permeabilities in carbonate rock reservoirs can be highly directional; permeabilities are often drastically different in one direction from those in another direction. This anisotropy commonly is a result of the geologic stresses imposed upon the reservoir rocks (Blanchet, 1957; Harris et al., 1960; Martin 1967; Alpay 1969; Overbey and Rough, 1971; Aguilera, 1980; Weber and Bakker, 1981; Magara, 1986; Corbett et al., 1987: Heifer and Bevan, 1990). Knowledge of this anisotropy is important in the optimum location of wells for recovery (see Chapters 5 and 10, this volume). Lineament analysis of Landsat data, airborne radar imagery, and aerial photographs have shown that lineaments observed on the surface commonly bear a striking resemblance to the orientation of major fracture directions in reservoirs in that area (Pasini and Overbey, 1969; Sabins, 1969; Partain, 1989). Fertl and Rieke (1979) used gamma ray spectral evaluation techniques to identify fractured reservoirs.
Pressureinterferencetests. Information about a specific reservoir's anisotropy can be gained during initial development of the field, if the reservoir oil is undersaturated (Felsenthal and Ferrell, 1972). Elkins and Skov (1960) investigated a reservoir's fracture orientation in the Spraberry-Driver producing area in west Texas. Although this is a sandstone reservoir production, it is a good example of the application of pressure interference test technique. They measured initial reservoir pressures in 71 wells using pressure interference tests (See Chapter 6, this volume) immediately after completion. Initial assumptions were that the reservoir is isotropic and that production resuited in circular drawdown isopotentials in the area surrounding each well. The isopotentials, however, had elliptical shapes, with the ratio of the major axis to the minor axis (a/b)proportional to the maximum/minimum permeability ratio (kax/kin). The relation between the axis and permeability ratios is: a/b = 4kax/kin.
( l-l 0)
Elkins and Skov (1960) assumed values of kax/kin and the azimuth of kax. These values were evaluated by a trial and error procedure using a computer. Seventy sets of iterations were performed to establish the "best fit" of assumed values and observed pressures using:
= Pi--P
-qluB~
E.-
4.16 fk k h
~
xy
I [(X-x~176
(1-11)
25.28(t/~oC~)
where p~ is the initial pressure in psi; p is the pressure at x,y at time t in psi; q is production rate in B/D;/.t ois oil viscosity in cP; B ~is the oil formation volume factor
Y
_•
yI \
t
I
\
t
f
f
\
t
f
It
I"--"
"- ""
j 7 / f
/
.." -X,
/
. /
/
~
-" ..',-;" /
/ /
/ / ~
/
/
')" /
/
/ /
,'
/
// 1 f
I.\/
.1"'.
~
f
~ _,"1~
/ z ~
9
,vI / / ;
/ /
/
~ " " ""
.-..---....4
9
/
\~
I ~
f
f /
/
/ /
i
~1 ' ~,
/t
f
~
I
9 ~ / / /_i/
~
11
I
- ~
il
/
/
//
,'
1
,
.' ," / A"
t
--
I
~
~ ~
/
//
,"
,' .J/
/
/ / /
/ / Ili~"2. /
/
/
/
/ /
X
//
/ / /
/
/
"~'
t
I
I."
\i
/
/ / / / t
_ y l ~ \
... ~ I
S X
I~
I
-u Fig. 1-5. Isopotential lines for k a x / k m i n - " 8. (AfterArnold et al., 1962, Fig. 2; reprintedwith permission of the Society of Petroleum Engineers.) in reservoir, bbl/STB; h is the thickness of the producing zone in ft; t is the time in days; c is total compressibility of oil, water, and rock in psi-l; ~bis fractional porosity; k is the effective permeability in the x 9 direction in darcys; ky is the effective perme. ability in the y direction in darcys; x - x ~ ~s the d~stance from producing well to pressure point in x direction in ft; andy-yo is the distance from producing well to pressure point in y direction in ft. Coordinates were rotated in each test run so that k = k and k k
. .
max
x
mln
Amold et al. (1962) presented a method for estimating reservoir anisotropy from production data using pressure buildup tests. Figure 1-5 presents a typical plot of isopotential lines for a k / k i n = 8/1 from Arnold et al.'s (1960) theoretical analysis. The center well was the producing well, and reservoir pressures in the outlying shutin wells were measured until approximate steady-state flow was established. The assumption made was that the producing wells in the reservoir were far enough from each other so that there was essentially no interference between them. Interference will distort the elliptical isopotential lines. Multiple interference can be solved by making effects additive (principle of superposit!on" Felsenthal and Ferrell, 1972). F r a c t u r e s p a c i n g 9 The distance between fractures is required input into many reservoir simulation studies and, therefore, needs to be characterized. Aguilera (1980) stated that, in some instances, the spacing is impossible to obtain from well-test analysis. Also there is a problem of measuring surface joint patterns and projecting the pattern without risk into the subsurface. Models, such as Narr and Lerche's (1984) probabilistic
10 model and Aguilera's (1988) binomial theorem approach, have been developed to calculate vertical parallel fracture spacing from cores. However, these studies do not address the lateral continuity of the pattern(s) within the reservoir. Cores from several wells would have to be analyzed in order to establish a pattern or lack of pattern with some degree of certainty. LaPoint and Hudson (1985) pointed out that joint (fracture) patterns can be divided roughly into those that are homogeneous or those that are inhomogeneous. A homogeneous pattern has characteristics, such as spacing, that are constant and independent of location. The characteristics in an inhomogeneous pattern vary, and may depend on location. Aguilera's approach is valid only for determining the spacing between vertical parallel fractures, and is lithologically sensitive due to the differences in mechanical properties. Vertical parallel fractures can play an important role in the displacement of injected gases in a carbonate reservoir during enhanced recovery operations. A good example of the influence of vertical fractures in a carbonate reservoir was revealed by the injection of CO2/N 2(a field test) in the Coulommes-Vaucourtois Field
T _ '~1 L
T
T2
_t_ -.
.
.
-fT3
$3
T BOREHOLE
Fig. 1-6. Block diagram showing a wellbore through fractured beds of two different thicknesses. Cores cut in the upper and lower beds (T~and/'4) intersect fractures. S is the spacing between fractures and T is the bed thickness. (After Narr and Lerche, 1984, Fig. 3; reprinted with permission of the American Association of Petroleum Geologists.)
11 located in the Paris Basin, France. Denoyelle et al. (1988) attempted to match the test results with the geologic description of the field. Fractures are vertical and parallel to a north-northeast to south-southeast direction, widely spaced, and exhibit no apparent slippage. This orientation corresponds to the direction of the most important tectonic feature in the basin, the Pays de Bray Fault. The production history of the field showed that the reservoir exhibits a single-porosity behavior. A secondary and weaker set of fractures may exist perpendicular to this main direction as shown by the displacement of the CO 2 toward the center of the structure. Gas analyses showed that the areal extent of the gas bubble was 15-20 times larger than the injection pattern area (Denoyelle et al., 1988). This field test shows that extreme caution has to be used when planning injection operations. If different lithologies are present, then the following analysis has to be repeated for each lithology (Aguilera, 1988). It is, however, a relatively simple technique. It is assumed that a core intercepts only some of the vertical fractures present in the reservoir (Fig. 1-6). This situation implies that some fractures are limited to a particular bed, and the probability of a core intercepting a vertical fracture in a bed using the binomial theorem is: (Q + p ) N : QN + N Q N - , p + N ( N - 1 ) lx2 N ( N - 1) ( N - 2 ) . . .
( N - r + 2)
(QN-Z)p2 + . . . . .
(QN--r+l)p,-~ + pN,
(1-12)
1 x 2 x...x(r-1) where Q is the probability of the core not intercepting a vertical fracture (Q = 1 - P ) ; P is the probability of the core intercepting a vertical fracture; r is the successive number of beds; and N is the total number of intercepted beds and is a positive integer (Aguilera, 1988). It was assumed that all beds contain vertical fractures and these may or may not be intercepted by the core as shown in Fig. 1-6. Aguilera (1988) defined the probability (P) of intercepting a vertical fracture in a bed as: P = D/S=
DI
,
(1-13)
Ta v e where D is the core diameter; S is the distance between fractures; Tav e is the average thickness of the bed (summation of individual thickness of each bed divided by the total number of intercepted beds); and I is a fracture index defined as" I-
T
',
(1-14)
S.1 where the subscript i refers to properties of the i th bed. Aguilera's (1988) approach differs from that of Narr and Lerche (1984) by using an average bed thickness rather
12 than an elaborate probabilistic model. Equation 1-14 leads to calculated fracture indices, which are close to the average measured indices (Aguilera, 1988). An application of Aguilera's (1988) procedure consists of the following steps described below. This approach also appears to be readily adaptable to obtaining fracture spacing from well logs: 1. Use Eq. 1-12 to perform a probability evaluation. The probability of intercepting a fracture in a bed is calculated using Eq. 1-13 (remember that P + Q = 1). 2. Determine the median number of fractured beds from a plot of the number of fractured beds versus the probability of intercepting at least the number of fractured beds indicated in the study (probability of success). If the probability of occurrence of a given combination of fractured and unfractured beds in the core's intercepted sequence is PC, and PS is the probability of intercepting at least the number of fractured beds indicated in a given combination, then the probability of a core intercepting unfractured beds is calculated from PC = (DI/Tave)TM,and PS is 1.0 - P C (except in the case where N is zero). 3. Plot the fracture index of 1.0 versus the expected number of fractured beds on coordinate paper. Construct a straight line through the plotted median data point and the origin. Determine the fracture index by entering the measured average number of fractured beds intercepted by an actual core or measured at the outcrop, and reading the corresponding I from the abscissa. Aguilera (1988) states that this line is an approximation that appears to give reasonable results for most practical situations. 4. The vertical fracture spacing is calculated using Eq. 1-14. 5. Using well logs [Aguilera (1988) suggested that the fractured beds be identified on the logs], calculate/, and on the basis of bed thickness obtained from the logs compute the fracture spacing. The following is a sample problem. The original data are from Narr and Lerche (1984), and were reworked by Aguilera (1988).
Problem: Calculate the vertical fracture spacing for horizontal fine-grained limestone beds of the Ordovician Axemann Formation along State Truck Route 45 near Water Street, Pennsylvania, U.S.A. Core diameter, D, is 10 cm. Average thickness of five beds being considered [(46.5 + 14 + 7.5 + 18.5 + 30.5)/5] is 23.4 cm. The probability of intercepting a fractured bed using Eq. 1-13 is [10(I/23.4)] = 0.4274(/). For an I = 1, the P is 0.4274 and Q is 0.5726. Table 1-I gives the probability evaluation for the case o f / = 1, and was compiled using Eq. 1-12 in the following manner. Five unfractured beds: PC = (0.5726) 5 - 0.0616 Four unfractured beds plus one fractured bed combination:
PC = 5(0.4274)(0.5726) 5-1= 0.2297 PS = 1.0 - 0.0616 = 0.9384
13 Three unfractured
beds plus two fractured beds combination"
5 ( 5 - 1 ) ( 0 . 5 7 2 6 ) 5-2 • ( 0 . 4 2 7 4 ) 2
PC =
= 0.3429 lx2
PS - 1.0 - 0 . 2 2 9 7 - 0 . 0 6 1 6 = 0 . 7 0 8 7 Two unfractured beds plus three fractured beds combination: 5(5-
1) • ( 5 -
PC=
2)(0.5726) 5-3x (0.4274) 3 = lx2x3
0.2560
PS = 1.0 - 0 . 3 4 2 9 - 0 . 2 2 9 7 - 0 . 0 6 1 6 = 0 . 3 6 5 8 One unfractured bed plus four fractured beds combination: 5(5-
1) x ( 5 -
2) x ( 5 -
3)(0.5726)5-4 x (0.4274) 4
PC =
= 0.O955 lx2•215
PS = 1.0 - 0 . 2 5 6 0 - 0 . 3 4 2 9 - 0 . 2 2 9 7 - 0 . 0 6 1 6 = 0 . 1 0 9 8 Five fractured beds:
PC = ( 0 . 4 2 7 4 ) 5 = 0 . 0 1 4 3 PS = 1.0 - 0 . 0 9 5 5 - 0 . 2 5 6 0 - 0 . 3 4 2 9 - 0 . 2 2 9 7 - 0 . 0 6 1 6 PS = 0 . 0 1 4 3 TABLE 1-I Probability of intercepting a fracture in a bed at fracture index I = 1, outcrop 1, case 1" (After Aguilera, 1988, Table 3" reprinted with permission of the American Association of Petroleum Geologists.) Combination of events
Probability of combination
Probability of success**
Unfractured
Fractured
(%)
(%)
5 4 3 2 1 0
0 1 2 3 4 5
6.16 22.97 34.29 25.60 9.55 1.43
93.84 70.87 36.58 10.98 1.43
* Probability of not intercepting a fracture in a bed = 0.5726, probability of intercepting a fracture in a bed = 0.4274, total number of intercepted beds = 5. Location from Narr and Lerche (1984). *" Probability of success means probability of intercepting at least the number of fractured beds indicated under combination of events column.
14 ....
I
'
l
'
l 80
I00
4
e / U
~
<
Q:
2.6
t,i.
u. 2 0 0r w r
z
I
-
I A
0 0
1 20
1 40
PROBABILITY
[ 50%1 60 OF
SUCCESS
(%}
Fig. 1-7. Probability distribution showing the number of fractured beds and the probability in the success of intercepting a certain number of fractured beds at a fracture index of 1. The number of fractured beds intercepted at 50% is 2.6. (After Aguilera, 1988, Fig. 4; reprinted with permission of the American Association of Petroleum Geologists.) Figure 1-7 is a plot of the data from Table 1-I. The number of fractured beds at 50% probability is 2.6. Figure 1-8 is constructed by plotting the expected number of fractured beds versus a fracture index of 1.0. A straight line is drawn between this point (1,2.6) and the origin. The value of Narr and Lerche's (1984) fractured beds intercepted by the core is 2.45. This value is entered on Fig. 1-8, and a fracture index of 0.94 is read from the graph. Aguilera's (1988) determined value of 0.94 compares with 0.98 measured at the outcrop and 0.83 as calculated by the probabilistic method of Narr and Lerche (1984). Narr and Lerche (1984) and Aguilera (1988) considered the effect of a bed with an angle between the core axis and bedding, 0, and an angle between the core axis and fractures,/3, on calculating a vertical fracture spacing under such conditions (Fig 19). A true fracture index (/) can be calculated using the angles 0 and ,/3: /sin0cos/3 I=
,
(1-15)
sinO +/sin/3cos/3 where I e is the apparent fracture index. Table 1-II presents Aguilera's (1988) results using Narr and Lerche's (1984) data from the above example problem: 0 = 60 ~ and fl = 30 ~ and / = 1. The calculation
15 I ,.,
(E)
I
1
!
1
5 //
~J
/
/
/
/
// .,'"
~ 11 jt
I--
/
/
I.i. mid
/
D = ao cm
O = 9o~
/ L ,"l
,=00o
-'~ /
...... iI "..... 1 :"/.. I
1 /i:/
TA
= 46 5 cm
TB
=
TC
=
TO
=
J// 9i ) / ///i!i // /'i:
TE
/i I
Norr
//
ii
14.0cm
7Scm I
"
cm
= 30.5cm and
L erche(1984)
i!
I
2 FRACTURE
3
4
5
INDEX
Fig. 1-8. Expected number of fractured beds versus fracture index (and its uncertainty) for the five beds. Mean number of fractured beds intersected by a hypothetical core plotted at 2.45. Observed fracture index measured at the outcrop is shown by an arrow at I = 0.98. The stippled bar at the lower left comer indicates one standard deviation. (After Aguilera, 1988, Fig. 5; reprinted with permission of the American Association of Petroleum Geologists.)
procedure is like in the above example with the following modification to be taken into consideration: the dip of the beds. The core penetrates an apparent thickness, T (Fig. 1-9). The average apparent thickness Taveofthe 5 beds [(53.7 + 16.2 + 8.7 + 21.4 + 35.2)/5] is 27.04 cm. The probability of intercepting a fractured bed is [ 10(//27.04)] = 0.3698(/). Equation 1-15 is used to calculate the true fracture index (I = 0.577) w h e n / = 1. The number of fractured beds at 50% probability is 2.31 and was obtained from a cartesian plot of the number of fractured beds versus probability of success (Aquilera, 1988, Fig. 7). The expected number of fractured beds intercepted by the core is 3.70 (Narr and Lerche, 1984). A fracture index of 0.79 was obtained from a cartesian plot of the expected number of fractured beds intercepted versus the fracture index (Aguilera, 1988, Fig. 8). This compares with Narr and Lerche's (1984) measured value of 0.98 and their calculated value of 0.81. As far as the drill bit is concerned, it cuts a core having an effective fracture spacing, S, for inclined beds (Fig. 1-9). Equation 1-14 was modified to reflect the true perpendicular fracture spacing, S: e
S = S(cosfl)- T(sinflcosfl), or
s S= cos/ + T(sinfl).
(1-16)
16 TABLE 1-II Probability of intercepting a fracture in a bed at an apparent fracture index I = 1, outcrop 1, case 2" (After Aquilera, 1988, Table 5; reprinted with permission o f the AmericanAssociation of Petroleum Geologists.) Combination of events
Probability of combination
Probability of success**
Unfractured
Fractured
(%)
(%)
5 4 3 2 1 0
0 1 2 3 4 5
9.94 29.16 34.23 20.08 5.89 0.69
90.06 60.90 26.67 6.58 0.69
* Probability of not intercepting a fracture in a bed = 0.6302, probability of intercepting a fracture in a bed = 0.3698, total number of intercepted beds = 5. Location from Narr and Lerche (1984). ** Probability of success means probability of intercepting at least the number of fractured beds indicated under combination of events column.
CORE
/ / / FRACTURE PITCH ANGLE
\
/
\
....
\
BEDDING
/
I
\
\
\
\
I Ii / / /
~..J
/ tl
\ \ \
/
FRACTURE PLANES
Fig. 1-9. A schematic of a fractured bed and core sample. The bedding plane is perpendicular to the core axis; Tsin0 = T, so that T = T when 0 = 90 ~ is the angle between core axis and fracture, 0 is the angle between core axis and bedding, S is the spacing of the fractures, S e is the effective fracture spacing relative to the borehole incidence, T is the bed thickness, T is the effective bed thickness parallel to the core axis. (After Narr and Lerche, 1984, Fig. 5; reprinted with permission of the American Association of Petroleum Geologists.)
17 The term S(cosfl) corrects for the apparent spacing of fractures that strike parallel to the bedding strike (fracture pitch = 0~ and T(sinflcosfl) accounts for a non-zero pitch angle. A value for S can be obtained from Eq. 1-14 (T= Tsin0). Hydrocarbon recovery
The amount of hydrocarbons recovered from carbonate reservoirs is largely controlled by variations in reservoir rock permeability arising from heterogeneities. Establishment of recovery estimates requires in some instances the use of complex computer models involving successive scaling-up of permeability. This complexity is due to the many scales of permeability variation present in a carbonate reservoir. It is imperative that petroleum engineers and geologists have a "feel" for permeability input values which go into such models. In Part 1 of this book (Chapter 8), Honarpour et al. (1992) discussed generalized permeability and relative permeability relationships for carbonate rocks. The following information focuses on the relation of k / k field-derived data and liquid saturation values for carbonate reservoirs. Some comparisons of laboratory k / k data for sandstones also are presented as reference points for the reader. The intent here is to provide data that supplement data given in Chapter 5 of this volume, which discusses the performance and classification of carbonate reservoirs. Calculation of field-derived k / k curves for solution gas-drive reservoirs can be a strong diagnostic tool for comparing solution gas-drive reservoir performance in a play. 9
g
o
.
Primary recovery
Primary recovery of oil, gas, or oil and gas can be defined as any method (natural flow or artificial lift) that may be used to produce them through a single wellbore. The fluid enters the wellbore by action of the reservoir's native energy (Langnes et al., 1972). In order to predict the primary recovery from a solution gas-drive carbonate reservoir, the relation between the ratio of gas to oil permeability ( k / k ) and the liquid saturation (SL) must be known. The k/ko values are derived from measured field data of solution gas-drive reservoirs and t~rom laboratory measurements on core samples believed to be representative of the reservoir. Starting with the gas/oil ratio in the reservoir, which is simply the ratio of gas flow to oil flow, using Darcy's law for radial flow, and correcting reservoir flow data to surface conditions results in the following equation: (1-17)
R = ( k / k ) (~oBo/~gBg) + R s,
where R is the surface gas/oil ratio (SCF/STB), Rsis the solution gas/oil ratio (SCF/ STB), k is the effective gas permeability (mD), k is the effective oil permeability (mD), ~ is the oil viscosity at reservoir conditions (cP), /.t is the gas viscosity at reservoir conditions (cP), Bo is the oil formation volume factor (reservoir barrels/STB), and B is the gas formation volume factor (reservoir barrels/SCF), If B gis reported in CF/S~F, then this value must be divided by 5.614, which is the number of cubic feet in a U.S. barrel, to convert to reservoir barrels/SCF. g
o
.
.
g
18 The reservoir oil saturations corresponding to the field-derived k/k ratio are evalu.g ated by the following equations from standard reservoir engineering ~ (e.g., 9
Dake, 1978, p. 45; Craft and Hawkins, 1959, p. 116)" S = (1 - S ) (1 - N/N)
(ao/aoi),
(1-18)
and
SL= S+ S,
(1-19)
where S is the fractional oil saturation, S is the fractional water saturation, N is the oil produced (STB), N is the oil-in-place at bubble point pressure (STB), Boi is ~he oil volume factor at bubble point pressure (reservoir barrels/STB), and S Lis the fractional I0
I
I
1
I
I
'1
I'
'1 ....
I
1
1
I,U I-"
3= I I,g ..J m ,==, U r Ill Q=: n," m
"
o
0.1 =.=,,,.,.
hi 0 Z ILl Or)
Ill
IE Q. Z
-
O.Ol
,/ 7"
0.001
I00
90 LIOUID
80 70 SATURATION,
%
60 PORE
50 SPACE
40
Fig. 1-10. Field-derived k / k data for dolomites. 1 - Fullerton-Clear Fork, Texas; 2 - Skaggs-Grayburg, New Mexico; 3 - South ~owden-Foster (Grayburg), Texas; 4 - North Cowden (Grayburg), Texas; 5 Goldsmith, North Dome (Grayburg-San Andres), Texas; 6 - Goldsmith, South Dome (Grayburg-San Andres), Texas; 7 - Wasson (San Andres), Texas; 8 - Harper (San Andres), Texas; 9 - Penwell (San Andres), Texas; 1 0 - Slaughter (San Andres), Texas. Producing formation(s) in parentheses. (Data from Arps and Roberts, 1955; after Felsenthal and Ferrell, 1972, Fig. 18; courtesy of Elsevier Publ. Co.)
19 IO
I
'!
I
I
I'
1
I
1
I
i
I......
__
RANGE FOR
OF DATA
TEN F I E L D S
u
-J m
CONSOL IDA TED S A N D (BOTSET)
0 ::) W G: (Z:
0
o.I
IJJ 0 Z
UNCONSOLIDATED
I~J (/) I~J n. a.
(LEVERETT
8
SAND
LEWIS)
z
o.ol
0.001 I00
I 90 LIQUID
80 70 60 50 SATURATION, % PORE SPACE
40
Fig. 1-11. Field-derivedk/k data for dolomites from Fig. 1-10are compared with selected laboratory k / k data for sandstones. Sandstoneg o curvesare from Botset (1940) and Leverett and Lewis (1941). (After Felsenthal and Ferrell, 1972, Fig. 19; courtesy of Elsevier Publ. Co.) liquid saturation. These equations were used to construct the field-derived k / k curves shown in Figs. 1-10 to 1-15 (Felsenthal and Ferrell, 1972). g o Figure 1-10 gives field-derivedk/k curves for Permian dolomite reservoirs in Texas and New Mexico, U.S.A. The k / k gda~a shown in Fig. 1-11 are laboratory derived for a consolidated sandstone ( k i r - ~ 0 ~ ) mD, ~b= 22%) (Botset, 1940) and unconsolidated sand (kir- 10,000 mD, ~b = 42%) (Leverett and Lewis, 1941). These data are compared to the range of 10 dolomite reservoirs presented in Fig. 1-10. Felsenthal and Ferrell (1972) stated that the k / k curves for dolomite show a remarkable and unexpectedly good agreement withgtl~e range of the literature data for consolidated and unconsolidated sand above a k g/ k o = 0.01 and corresponding to liquid saturations lower than 91.5%. The discrepancy 5etween the k g/ k o data in Fig. 1-11 could be attributed to the difficulty in measuring extremely low gas rates with sufficient accuracy in the laboratory. Felsenthal and Conley (1955) performed laboratory tests, which indicated that the k g/ k o curves in the low k g/ k o region probably match the field-derived data much . more closely than shown m Fig. 1-11.
20 I0
1
!
I
i
/ "
!
I
I
I
I
!
W I"
RANGE OF DATA FOR NINE FIELDS
W
I U
-
/
v
-_
--
W n,"
/
I i/
t
-
/
_
/
/
/I
/
t /
-----"-
/
-
I
--
--
CONSOLIDATED SAND (BOTSET)
-
0 1.1 L; Z I11 U~ ill Q: a.
0.1
/
/I
-I ~ v
--
,
Z
~
_
i I
0.01
I
-
..
I
'o
UNCONSOLIDA TED SAND (LEVERETT 8 LEWIS)
-]
I I I ! I i I ! I I
0.001 I00
90 LIQUID
80 70 SATURATION,%
60 PORE
50 SPACE
44:)
Fig. 1-12. Field-derived k / k data for sandstones compared with selected laboratory data. Data from Arps and Roberts (1955), Botsegt(~ Leverett and Lewis (1941), and Kaveler (1944). (After Felsenthal and Ferrell, 1972, Fig. 20; courtesy of Elsevier Publ. Co.)
Generally speaking, a steep k / k curve from a k/k-liquid saturation plot indicates a low solution gas-drive efficier]c37 (Felsenthal anal Ferrell, 1972). A fiat curve indicates a favorable drive efficiency. Figures 1-11 and 1-12 show a comparison between field-derived data for dolomite and sandstone reservoirs. The fields shown are all solution gas-drive reservoirs and cover a wide range of geologic ages (Ordovician to Miocene) and various geographic locations in the U.S.A. (Arkansas, California, Louisiana, Oklahoma, Texas, and Wyoming). These plots indicate that primary solution gas-drive efficiency may actually be as good as or better on a percentage pore volume basis in dolomite reservoirs than in sandstone reservoirs. Felsenthal and Ferrell (1972) suggested that the heterogeneous features of dolomites may help rather than hinder oil recovery of internal solution gas drive. Field-derived k/k data for limestones appear to span a wider range of values than was evident for dolomites (Figs. 1-13 to 1-15). Some of the limestone reservoirs contain appreciable amounts of chert. The laboratory data shown in Fig. 1-14 were obtained on full-diameter core samples, which probably possessed pore geometries representative of the reservoir. The steepest (least favorable) k / k curve is for a fractured chert and
21 I0'
I'
I
I
I
I
i
1
I
I
I
t
I
-
m
ix) Q
0.1
z
m
z
0.01 w
~~
~
v
0.001 I00
90
LIQUID
80
70
SATURATION, %
6O
50
40
PORE SPACE
Fig. 1-13. Field-derived k / k data for limestones. 1 -Haynesville (Pettit), Louisiana; 2 - West Edmond (Bois d'Arc-Hunton), Oklahoma; 3 - Wheeler (Devonian chert and limestone), Texas. (Modified after Arps and Roberts, 1955, Fig. 2; reprinted with permission of AIME.)
limestone (Stewart et al., 1953). Microscopic examination indicated that the reservoir rock in Field F is made up of a large number of small, irregularly shaped pieces of fractured chert cemented by calcite with intergranular porosity. The permeability of the test sample was 2.4 mD, associated with an unusually high (for limestone) porosity of 30.3%. High porosity may have been one reason for the steepness of the curve (Felsenthal and Ferrell, 1972). A trend of increasing steepness ofk/k curves with increasing poros. g o lty values had been observed previously for sandstones (Felsenthal, 1959). Felsenthal and Ferrell (1972) emphasized that the calculations based on Eqs. 1-17 to 1-19 are applicable only to reservoirs with gravity drainage, strong gas-cap, or water influx drives. 9
Hydrostatic and hydrodynamic pressures Many carbonate reservoirs are surrounded by very large aquifers that will offset a production-produced pressure drop by providing an influx of water into the reservoir. Water influx into the reservoir is governed by hydrostatic and hydrodynamic pressures in the aquifer. Hydrostatic pressure is defined as the static weight of a column of
22 I0
i
I
I
I
n.. t.l FIELD ..... --
I
-
o w
-
n,,
-
DATA
/
-
...,..
DATA
LABORATORY
I t
/
/
I
z
I
-
I
/
1
/
I
I i
t
///I
l
/ 0.1 - - -
I
s
I
a/I
/ /i I I
/
/,,, ,'///
- ' /I1; //,y i
'
II II.i
_z
oJ:
0.01 ~,/
v
!
0.001
9 I00
f
I 90 LIQUID
I
I
i
I
80 70 SATURATION,
I
i
f
60 PORE
SPACE
I 50 %
I 40
Fig. 1-14. Laboratory and field-derivedk/k data for limestones and chert. 1-Fractured chert and limestone, Field F; 2 - limestone with intergranula~ porosity, FieldA; 3 - with intergranular porosity, Field B. (Data from Stewart et al., 1953; After Felsenthal and Ferrell, 1972, Fig. 22; courtesy of Elsevier Publ. Co.)
water, increasing vertically downward from the ground surface to the point of production in the reservoir. Hydrodynamic pressure is the difference between a higher and a lower elevation of the piezometric surface in the aquifer. Figure 1-16 illustrates various hydrostatic pressure gradients observed in carbonate reservoirs in the U.S.A. The hydrostatic gradient for the Viola Limestone, for example, is less than that of normal sea water gradient of 0.65 psi/ft. Both the Smackover Limestone (Gulf Coast, U.S.A.) and the Ellenburger Dolomite (Texas, U.S.A.) have gradients greater than 0.465 psi/ ft. Deviation from the seawater trend line is common, and depends on the variation in the fluid density, the amount of solution gas, and the imposed hydrodynamic pressure gradient. An imposed hydrodynamic pressure gradient occurs when aquifers rise to the surface (e.g., to the edge of the structural basins, which lies considerably above the reservoir) so as to provide artesian flow. In highly permeable and extensive aquifers, which are in full communication with the reservoir, pressure gradients developed during production can extend a considerable distance outward from the reservoir. Moore and Truby (1952) made an analog study
23 I0~
I
[
!
!
I
!
!
I
I
1
I.r
..I El
J
2
......
z) o Iz; n? Iz. O I~1 r Z I~1 r ILl n? n
0.1--
m
m
Z 0.01
O.OOI I00
m
~
1
1
90 LIQUID
1 80
1
1
1
70
SATURATION~
1
1
60 96
PORE
1 50
40
SPACE
Fig. 1-15. Laboratory kolk data for reefs. 1 - Pennsylvanian reef A; 2 - Pennsylvanian reef B; 3 - Strawn Reef; 4 - Palo Pinto Re~ef.~ (Modified after Arps and Roberts, 1955, Fig. 2; reprinted with permission o f AIME.)
of five fields completed in the Ellenburger Dolomite of west Texas, U.S.A. Eighty percent of the pressure drop was due to production from the surrounding fields. Pressure interference has also been noticed in the fractured reservoirs of the Asmari Limestone of Iran and in the oolitic Smackover Limestone in southem Arkansas, U.S.A. Pressures in sealed carbonate reservoirs, such as bioherms and biostromes, could be caused by the weight of the overburden. For highly permeable and continuous oolite reservoirs, it may be necessary to consider the effects of pressure interference from surrounding reservoirs in order to make reliable material balance calculations.
Secondary recovery Definitions of several hydrocarbon recovery terms are in order. Enhanced hydrocarbon recovery is similar to that of primary except that more than one wellbore may be involved, and the reservoir's intemal energy is augmented by the injection of fluids with or without heat (Lagnes et al., 1972). There is a generally accepted, but somewhat restricted definition of secondary recovery (i.e., waterflooding). This term is used
24 0~\
I
I
I
I
1
I
I
I
I
I\\
~.Lz \ ~
9 \%
v,o,.. * V \ ~
\
L,-ESrO.E \ ~ .
\".%
~..
\
\
I-IX. t~f
\,
\
\
e II
8
SMACKOVER LIMESTONE FIELOS
m
~
I~)[LLENBURGER ~
\
\*i3 DOLOHITE $*~.' FIELOS ~ 27~94
\
',ko \
9 -
m
\,,
\
I0--
\ II
0
1
I
200o
1
I
4000
~
, 1
1
6o0o
I
8ooo
, iO
boo
INITIAL RESERVOIR PRESSURE, psi Fig. 1-16. Relation between initial reservoir pressure and depth for various carbonate reservoirs in the U.S.A. Data from the following fields were used: Viola Limestone (Kansas): (1) Wilmington, (2) Wichita, (3) Strahm, (4) Newbury, (5) Mild Creek, (6) John Creek, (7) Comiskey, and (8) Ashbum. Smackover Limestone (Arkansas): (1) Midway, (2) Buckner, (3) Village, (4) Texarkana, (5) Magnolia, (6) Schuler, (7) Big Creek, (8) Atlanta, (9) Macedonia Dorcheat, and (10) McKamie. Ellenburger Dolomite (Texas): (1) Martin, (2) Yarbrough and Allen, (3) Sweetie Peck, (4) Shafter Lake, (5) South Fullerton, (6) Block 31, (7) Bedford, (8) Embar, (9) University-Waddell, (10) Jordan, ( 11) Keystone, (12) TXL, (13) Wheeler, (14) Wilshire, (15) Monahans, (16) Todd, and (17) Elkhorn. (After Chilingar et al., 1972, Fig. 14; courtesy of Elsevier Publ. Co.)
only when water injection is started late in the production life of the reservoir, i.e., when the primary energy is nearly exhausted. The term pressure maintenance is used when the injection is initiated early in the life of the field and includes injection fluids other than water.
25 Weber (1986) pointed out that reservoir heterogeneity is one of the major reasons why enhanced oil recovery is so difficult. Waterflooding and enhanced recovery, as well as primary recovery projects that are undertaken without proper planning and/or a detailed reservoir evaluation often end in failure. These failures can be related to flow barriers (often expressed as microscopic boundaries, such as shale baffles or macroscopic compartmentalization, such as compartments formed by sealing faults in a reservoir), permeability heterogeneities, or wrong estimates on the distribution of reservoir fluids. It is difficult to generalize the impact of a given heterogeneity owing to the large variety of heterogeneity classes. Table 1-III is a generalized guide to the influence ofheterogeneities which affect major oil recovery parameters (Weber, 1986). Fault morphology and boundaries of genetic carbonate units have strong influence on the continuity of the carbonate reservoir and on the volumetric sweep efficiency during waterflooding or enhanced recovery. Permeability zonation and baffles within and between genetic units have a major impact on vertical sweep efficiencies (Weber, 1986). A non-uniform residual oil saturation distribution (ROS) arising from water flooding creates problems for EOR. Small-scale heterogeneities, such as sedimentary structures, interlamination of different rock types, pore types, and non-carbonate minerals are thought to be of great importance. Chapter 10 in this book discusses enhanced oil recovery (EOR), whereas Chapter 5 presents carbonate reservoir heterogeneity effects on primary recovery.
Geochemical logging. The elemental composition of carbonate rocks (major, minor, and trace elements) can be used for correlation purposes in carbonate rocks (Chilingar and Bissell, 1957; Wolfet al., 1967; Mattavelli et al., 1969). Elemental ratios, such as Ca/Mg and Sr/Ca, and isotope ratios, such as ~80/~60, hold much promise. The Ca/Mg ratio has been used successfully for correlation by Chilingar and Bissell (1957) and by Mattavelli et al. (1969) (Fig. 1-17). TABLE 1-III Significance of reservoir heterogeneity types for oil recovery. (After Weber, 1986, Table 1" reprinted with permission of Academic Press, Inc.) Sweep efficiency Reservior heterogeneity type
Reservoir continuity
1. Sealing fault Semi-sealing fault Non-sealing fault 2. Boundaries genetic units 3. Permeability zonation within units 4. Baffles within genetic units 5. Lamination, cross-bedding 6. Microscopic heterogeneity, Textural types, Mineralogy 7. Fracturing- Tight - Open
X
(x) (x) X
Horizontal Vertical X X X X
X X X
(x) (x) (x)
x (x) (x)
X = strong effect; (X) = moderate effect; ROS = remaining oil saturation.
ROS in swept Rock/Fluid zones interaction
(x) X X
(x) X X
26 WELL GELA
~)'~, x
"
32
Ca/2Mg
Ix
FINEAND VERYFINE DOLOMITE
,.. ].L,. .~r
i
i
J-
MEDIUMGRAINEDDOLOMITE
n-i~
x
i x
~
CALCITEIN GENERAL
x!
BRECCIAFRAGMENTS ~
X)LITE RELICS
-?:..-.or
INTRACLASTS x
~ar
x/
H
z/
,,
J"
STROMATOLITES ~']
ONCOLITES MACROFOSSILAND MACROFOSSIL RELICS
I
ANHYDRITE x
,,
IRREGULARPORESPACES INSIDE DOLOMITECRYSTALS
x
x ROMBIC PORESPACE INSIDE DOLOMITECRYSTALS
x
x: x: x
,.
=
7
/
o /
/
o
.L
/
/
,."~
~]
SCATTEREDCRYSTALSAND PATCHES OF CALCITEREPLACINGDOLOMITE VUGSANO FRACTURES FILLED BY CALCITE
A
x "
QUARTZ
t x GEOPETALFABRICS _t. =/
I/
. /
-l_,~!
.
x
x VUGSANOCAVITIESOFTEN WITHVADOSETEXTURE
x x
~x x. x x x z/-
//
,/-
/
-
.r
I x
o
_
o
o
1
x
x
~xx x
i
N
x
CORERECOVERY
x
.
i x
x x
x
x
x
x
-.~*.'.*."~*.~ /
o /
.
/
:~ /
* .I/el
:x
,
L
x
I '-'
~
FIELD
~" RAGUSA:
x,
! l.,c
x;
.!
I
I
'x PAL[ RMO
.i i :i x -!
,I ".2..._
"~
Fig. 1-17. Petrographic-petrologic log and Ca/Mg ratio line of the Taormina Formation, Gela Oil Field, Sicily, Italy; well Gela 32. (After Mattavelli et al., 1969, Fig. 1" courtesy of Elsevier Publ. Co.)
27 A geophysical-based geochemical logging tool (Hertzog et al., 1989) has been developed by Schlumberger to eventually be a cost-effective alternative to expensive and time-consuming, extensive chemical analysis of well cores. The tool known as the Geochemical Logging Tool (GLT TM) measures elemental concentrations of aluminum, silicon, calcium, iron, sulfur, gadolinium, titanium, thorium, uranium, potassium, and magnesium. The tool is used in conjunction with resistivity and nuclear logs. Application of this technology was made to a single well in a Middle East reservoir that exhibited a high degree of heterogeneity in terms of dolomitization, shale/ clay content, secondary porosity, and porosity distribution (Herron et al., 1992). Zone correlation from well-to-well was a problem. In conjunction with computer analysis programs and element concentration validation using core chemical and mineralogical data, it was possible to describe the formation with an accuracy that was not previously obtainable without full core analyses throughout the test well. Herron et al. (1992) stated that the logs clearly delineate zones of dolomitization, and quantitatively interpret the concentrations of non-carbonate minerals. This test was not able to demonstrate the usefulness of geochemical logs for well-to-well zone correlation.
Waterflooding. Fractures help to drain solution gas-drive reservoirs during primary production owing to the gas coming out of solution and expelling the oil from the pore space into the wellbore. During conventional waterflooding operations, however, these fractures become potential avenues for the injected water to bypass large volumes of oil contained in the matrix of the reservoir. Two dynamic situations arise when water is displacing oil in a water-wet reservoir. One is imbibition, in which the wetting phase (water) saturation is increasing, and the other is drainage, in which the wetting phase saturation is decreasing (Dake, 1978). Felsenthal and Ferrell (1972) described two situations where the imbibition process was not effective owing to fractures (Fig. 1-18). An operator should be cautious about early water injection (before primary production is at an end) in fractured carbonate reservoirs on the theory that one is more certain about primary production recovery. Early waterflooding under these conditions may be speculative (Tarr and Heuer, 1962). Felsenthal and Ferrell (1972) suggested that a pilot waterflood in fractured reservoirs must be used to evaluate the effect of fractures so that directional permeability trends and fracture orientation can be used to plan infill well locations and assign optimum spacing between the wells. A poorly designed well pattem can result in early water breakthrough and a poor sweep efficiency. A moderate degree of induced fracturing in order to stimulate wells is usually needed in low-permeability carbonate reservoirs so as to complete a waterflood in a reasonable time period. The degree of fracture stimulation should be kept under control. Planning and implementation of quality control procedures should be and are a responsibility of the producer, rather than the service company, in order to ensure a proper stimulation job. The degree of fracturing can be analyzed with the aid of pressure falloff analyses (Clark, 1968; Chapter 6 in this volume). Felsenthal and Ferrell (1972) noted that if fluid injection pressures exceed the parting pressure of the formation and injection is allowed to proceed without restraint and control, then excessively long fractures may form. Such fractures can lead to an early water breakthrough, leaving by-passed oil in the pore space. Fracturing of the reservoir cap rock
28
JL
l
SECONDARY
Fig. 1-18.Effect of fractures on primaryand secondaryrecoverywhere imbibition is not effective. (After Felsenthal and Ferrell, 1972, Fig. 27; courtesyof Elsevier Publ. Co.) could also result in a loss of oil and injection fluid. Chapter 13 in Part I (Hendrickson et al., 1992) of this book discusses fracturing and acidizing technology presently used by industry to stimulate carbonate reservoirs. Induced fractures in tectonically relaxed areas, characterized by normal faulting, generally have a preferred orientation. It is extremely important to recognize this directionality and to make the flood pattern take advantage of it. Cames (1966) and Lane (1969) described specially designed pilot waterflood tests to ascertain fracture and permeability directionality. Other evaluation procedures include: (1) gas injection tests discussed by Armstrong et al. (1961), Crawford (1962), and Alpay (1969); (2) interference tests performed by Elkins and Skov (1960) and Kunkel and Bagley (1965); (3) tracer flow tests by Baldwin (1966); (4) impression packer tests by Fraser and Pettitt (1962) and Anderson and Stahl (1967); (5) borehole televiewer logging to improve well completions by identifying fractures and injection thief zones by Clerke and Van Akkeron (1988); (6) seismic imaging to identify fractures and mini-caverns (Hurley, 1990; Zimmerman and Chen, 1992); and (7) downhole acoustical measurements discussed by Zemanek et al. (1969). McKinley et al. (1968) used pulse testing to successfully determine interwell properties in a highly permeable (kir-- 1,200 mD) dolomitic limestone reservoir. Campa and Romero (1969) used statistical methods for analyzing porosity trends in a carbonate reservoir. Some carbonate reservoirs that contain large gas caps underlain by comparatively thin oil zones, or which have good gravity drainage or strong natural water drives, may
29 1.0 .5 z 0 p. o (t w.
>. v-
m
OIL
.t
.o5
~E
w uJ >,
I--.
.01
WATER .005
.001 20
30 WATER
40
50
SATURATION,
60
70
%
Fig. 1-19. Average oil and water relative permeabilities for the Permian Brown and White Dolomite, Panhandle Field, Texas, U.S.A. (After Abemathy, 1964, Fig. 4; reprinted with permission of AIME.) be not conducive to waterflooding. Felsenthal and Ferrell (1972) pointed out that there may be exceptions, but one should proceed cautiously under such circumstances. A basic evaluation of residual oil saturation behind the water front is needed so that the flood could be modified to lower this saturation. Buckley and Leverett's (1942) classical paper and Pirson's (1958) pioneering book presented the basic equations for such analyses:
fw
1 1 +(kro/aw/~/ao ) '
(1-20)
1 1 + (/Co )---~w---/~o/Cw
(1-21)
or fw
30 where fw is the fractional flow of water at the producing end of the system. Equations 1-20 and 1-21 are identical as long as the relative permeabilities koand kware referred to the same base permeability. An example would be that kir and k in the presence of the irreducible water saturation. Abernathy (1964) provided some typical laboratorybased koand krwversus saturation curves for dolomites in Figs. 1-19 to 1-21. There are a wide range of"end point" krwvalues, ranging from 0.04 (Fig. 1-19) to 0.52 (Fig. 121). It is these "end point" values that govern injectivities into the matrix of the rock (Felsenthal and Ferrell, 1972). Abernathy (1964) noted that the curve for absolute permeabilities greater than 1.8 mD has higher k values than the curve for absolute permeabilities less than 1.8 mD, at the same water saturation (Fig. 1-20). There was no corresponding change in the k curve. Figure 1-22 is a typical k / k ratio curve based on laboratory measurements. Hendrickson (1961) suggested that, if complete relative permeability curves are not available, then one should let the k / k ratio equal 1,000 at the connate water saturation and 0.01 at the residual oil saturation. By connecting the two points with a straight o
w
1.0
OIL
.5
'•
K <'1.8 md
WATER
z 0 m
K > 1.8 md
uI..e~
\
.05
\
>., I-..I (13
\\ .01
w 3E
I=: I,&J a,.
~
I
.005
I,=.1 I-_1
.001
o=:
090 0 5
.0001 I0
20
30 40 50 60 70 W A T E R SATURATION, %
80
Fig. 1-20. Average oil and water relative permeabilities, Permian Grayburg-Brown Dolomite, Foster Field, Texas, U.S.A. (AfterAbemathy, 1964, Fig. 8; reprinted with permission of AIME.)
31 1.0 .5 O/L WATER
.I z
o I-. m
o
.05
Q:
I-.J m
.~
.01
n,,
tu
.005
I.,I i.d n,,
.OOl .0005
''
.OOOIt 20
I
1
1
I
30
40
50
60
WATER
70
SATURATION,%
Fig. 1-21. Average oil and water relative permeabilities, Permian San Andres Dolomite, Welch Field, Texas, U.S.A. (After Abernathy, 1964, Fig. 12; reprinted with permission of AIME.)
line (Fig. 1-22; dashed line), the resulting data can be used in Eq. 1-20. Very useful information can be gained from laboratory measurements of the "end points" of oilwater relative permeability curves, such as values for (1) the critical oil saturation at which oil will first begin to flow, (2) initial (residual or irreducible) water saturation in a water-wet rock, (3) oil permeability at residual water saturation, and (4) a means by which relative permeability values can be estimated between the end points. It is a common experience that the performance of individual wells varies widely in a carbonate reservoir. Complex situations require a synergistic approach between engineers and geologists. Excellent examples of such cooperation have been reported
32 I000
I00
I0
ko/kw
.01 I0
20
:50 40 50 60 WATER SATURATION, %
70
80
Fig. 1-22. Typical k / k ratios. Solid curve: based on laboratory measurements (Tarr and Heuer, 1962). Dashed line: based on approximation (Hendrickson, 1961). (After Felsenthal and Ferrell, 1972, Fig. 31" courtesy of Elsevier Publ. CO.)
in the petroleum engineering literature. Willingham and McCaleb (1967), for example, reviewed engineering and geologic data from the Permian Phosphoria reservoir of the Cottonwood Creek Field, Wyoming. Their analysis defined geologic heterogeneities consisting of extensive lithofacies changes and variations in fracture frequency. As a result, there was a revision of operating practices that led to beneficial changes in secondary recovery operations, causing an increase in production from 2,100 to 3,600 B/D of oil during the first year. A recent detailed study was conducted by integrating geologic, engineering, and economic evaluations of three Texas reservoirs (Dune, Robertson Clear Fork and West Ranch fields) along with data from other reservoirs in order to delineate the resource and production potential of unrecovered mobile oil (ICF and BEG, 1990a,b,c,d,e).
33
~srsc ~s~rm
IE Fig. 1-23. A three-dimensional diagram showing the depositional facies relationship of the San Andres Dolomite in the Means Field, Texas, U.S.A. (After George and Stiles, 1977, Fig. 2; reprinted with permission of the Society of Petroleum Engineers.) Many of these fields are old (some have been producing before World War II), and have been subjected to secondary or enhanced recovery. A majority of these reservoirs are found in the dolomitized strata of the Lower Clear Fork, Upper Clear Fork, and Glorieta formations and some in the Grayburg and San Andres formations. The West Ranch Field produces from the non-carbonate clastic Oligocene Frio Formation and will not be discussed (ICF and BEG, 1990c). The Dune Field and Robertson Clear Fork Unit produce from carbonates that were formed on the semi-restricted Central Basin Platform (west Texas and southeastern New Mexico, U.S.A.) in shallow, moderate-to high-energy depositional environments. Most of the producing fields on the Central Basin Platform exhibit a complex interfingering of various carbonate facies types. Numerous transgressions and regressions of the sea during deposition caused rapid vertical and lateral lithologic changes, which created very stratified reservoirs (Ward et al., 1986). The Means Field, Texas, U.S.A., is an example of this complex facies relationship (Fig. 1-23). The schematic block diagram shows an intertidal-lagoon-bank depositional sequence (George and Stiles, 1977). The best porosity generally occurs in the oolitic facies, whereas the skeletal facies deposited in front of the oolite bank has good secondary porosity formed by leaching. Although Fig. 1-23 is generalized, it does help explain some of the problems in waterflooding from this type of reservoir. Table 1-IV compares the average reservoir properties of the Means Field with those of the Fullerton and Robertson fields. The low primary recoveries were the basis for initiating waterfloods in these three fields. In highly heterogeneous carbonate sequences, as shown in Fig. 1-23, there may be more than 50 individual pay stringers. George and Stiles (1977) pointed out that only rarely will all of these pay zones be completed in a specific well. This practice presents problems in establishing reliable reserves by not accounting for mobile oil behind pipe. Volumetric reserve calculations will be incorrect owing to inexact data on the individual pay stringers. Material balance reserve calculations require that only the oil-in-place, which is contacted by the producing wells, should be considered, and those zones that have not been completed will not
34 TABLE 1-IV Average reservoir properties of three Permian carbonate reservoirs, in west Texas, U.S.A., undergoing waterflooding. (Data from George and Stiles, 1977; courtesy of the Society of Petroleum Engineers) Reservoir parameters
Fullerton
Means
Robertson
Area, ac Depth, ft Formation Gross thickness, ft. Depositional environment Heterogeneity Porosity, % Permeability, mD Connate water, % Primary drive mechanism
17,300 7,000 Clear Fork 600 Shallow shelfward Numerous 9.9 3 22 Solution gas
15,723 4,400 San Andres 300 Carbonate margin Porosity 9.0 20 29 Combination solution gas and water
4,800 6,500 Clear Fork 1,400 Shelf-margin stringers Stringers 6.3 0.65 30 Solution gas
Primary recovery factor (OOIP), %
18
15
8
Fluid parameters Stock tank gravity, ~ Oil viscosity, cP Formation volume factor Saturation pressure, psi
42 0.75 1.62 2,370
29 6 1.04 310
32 1.2 1.25 1,700
influence such calculations. A discussion on various heterogeneous and homogeneous carbonate reservoir models was presented by Mazzullo and Chilingarian (1992) in Chapter 3, Part 1. A full exploitation of the unrecovered mobile oil resource in these carbonate rocks hinges upon the ability to characterize carbonate reservoir heterogeneity, such as pay continuity of stratified horizons and permeability discontinuities. In addition, ineffective well completions complicate the calculations. Results of the individual reservoir assessments can then be extrapolated to groups of reservoirs with common carbonate depositional histories, collectively known as "plays" (ICF and BEG, 1990a). Methodologies developed in the ICF and BEG study and additional case histories are presented in Chapter 5 of this book. Waterflood recovery predictions. Felsenthal and Ferrell (1972) discussed instances where waterflood performance in carbonate reservoirs matched prediction. The prediction methods used were modifications of the methods of Stiles (1949) and Dykstra and Parsons (1950). Hendrickson (1961) described a close agreement between prediction and performance in a five-spot pilot waterflood in the Permian San Andres Dolomite, Welch Field, Texas, U.S.A. Figure 1-24 illustrates the results. The band concept was employed by Hendrickson to predict the flood performance. The band concept combines the layer cake principle of Stiles with the fractional flow Eq. 1-19. Permeability values were arranged in descending order. The resulting array was then subdivided into 10 bands of equal pore volume. Each band's performance was calculated separately, and then the individual values were added to obtain the total predicted reservoir performance.
35 500
i
I
I
1
I
i
I
CA LCUI..A rED
r.u m
_
400
ooooo A C T U , 4 L o
_7
300
o r ILl I--
ZOO
~s~
u r
o,=,= I--
3
t
--I m
o I
2
0 I 0 sS _~OsS
....
.
i'"--
~o
s
0
.
=: uJ
SS S
oo.O
,--.
I00
0
4
sS
oOO
-"
..d
=E r
ssS
o~" d O
=
I00
,.,"o'o" " 200
300
WATER
400
500
600
700
INJECTED~ M BBL
Fig. 1-24. Calculated versus actual performance, Permian San Andres Dolomite, Welch Field pilot waterflood, Texas, U.S.A. (After Hendrickson, 1961, Fig. 1" reprinted with permission of AIME.)
Abernathy (1964) performed an additional evaluation of the Welch Field and two other pilot floods in carbonate reservoirs (Table l-V). He used three prediction methods: (1) Stiles (1949), (2) Craig et al. (1955), and (3) a combination of the two methods known as the Craig-Stiles method. The results shown in Figs. 1-25 to 1-27 indicate that the Craig-Stiles method gave the best predictions for the three fields (Felsenthal and Ferrell, 1972).
I00
I
~'
~
'u
I
~
i
2 z"
o_a_
80
I.:~ u. a o..J
60
a . I - -o
40
~
zo
INJECTION STARTED
~I-.U.l
/ / I
I
0 0
5
I0
1
I
1
I
I
15
ZO
2.5
:50
:5,5
40
PERCENT OF ORIGINAL O I L - I N - P L A C E RECOVERED
Fig. 1-25. Comparison of actual performance with two prediction calculations, Permian San Andres Dolomite, Welch Field pilot waterflood, Texas, U.S.A. Legend: 1 -actual; 2-calculated by Craig-Stiles method; and 3 -calculated by the band method. (AfterAbernathy, 1064, Fig. 13; reprinted with permission of the Society of Petroleum Engineers.)
36 TABLE 1-V Comparison o fwaterflood predictions and performances in selected Permian carbonate reservoirs, Texas, U.S.A. (After Abemathy, 1964; reprinted with permission of AIME) Field Welch
Panhandle
Foster
Formation
San Andres Dolomite
Brown and White Dolomite
Grayburg-Brown Dolomite
Average depth, ft Net pay, ft Average prosity, % Average permeability (cores), mD Connate water saturation, % B 0, res. bbl/STB /.t0, cP Pw, cP ~ gravity BHP at start of flood, psi N p/ N at start of flood Current actual recovery, % oil-in-place Calculated ultimate recovery under flood, % oil-in-place
4,950 75 10 6.3 23 1.008 at 325 psi 2.32 at 325 psi 0.82 34.4 325 0.03
3,000 65 11.7 7.2 39 1.044 2.33 0.83 40
4,200 129 8.6 2.6 23 1.061 at 244 psi 2.91 at 244 psi 0.80 35 244 0.12
0.256 ~
21.7
34.2
21
38
35
38
* Includes gas injection.
The Craig-Stiles method provides for growth of the swept zone after initial water breakthrough, reduction of the residual oil in the swept zone after water breakthrough, and liquid resaturation of initial gas space before flooding in each layer. Oil recovery in stock tank barrels, N from a given layer is equal to: N--
W E(Swr-Swi)gs-S
i
]1
Bo '
(1-22)
where V is the pore volume (reservoir barrels), S i s the final average fractional water saturatio~n in the swept area, Swiis the initial fractional water saturation at the start of the flood, S i is the initial fractional gas saturation at the start of the flood, Eas is the fractional areal sweep efficiency, and B ~is the oil formation volume factor (reservoir barrels/STB). After resaturation of the reservoir was complete (fillup had occurred), water injection was set equal to total liquid production. Felsenthal and Ferrell (1972) pointed out that when using the Craig-Stiles method, special care should be taken to subdivide the reservoirs into only a few layers so that the combined performance of the layers was representative of the performance of the entire reservoir. The layering technique of Miller and Lents (1946), which requires sufficient core analysis data, was used. The Welch Field was subdivided into 12 layers, whereas the Foster and Panhandle fields were subdivided into 3 layers. Core analysis data provided the permeability values and associated reservoir properties for
37 o .J
po ~,
INJECTION STARTED
IOO
r
8o
7 . ~
/
/
~= ~o o
/
-
40-
a. e:
20
I-. '~
0
~ t 3r
\
I
i
,.
26
l
i
28 %
i
l
i
30 ORIGINAL
l
I
J
32
34
OIL-IN-PLACE
I
/ t J
36
38
RECOVERED
Fig. 1-26. Calculated versus actual performance, Permian Brown and White Dolomite, Panhandle Field pilot waterflood, Texas, U.S.A. Legend: 1 -actual; 2-calculated by Craig-Stiles method; and 3-calculated by Craig et al. method (1955). (After Abernathy, 1964, Fig. 5" reprinted with permission of AIME.)
I
i. . . .
~
I
i
I
I
IOO
t o
80
_~
60
i
/
0 t.J :~
"I,4
START OF" INJECTION
'
//
/
, ....." -'
40
0n," a. a:
20-
M,I 3r
0
5
I0 %
ORIGINAL
15
20 OIL-IN-PLACE
25
30
35
40
RECOVERED
Fig. 1-27. Calculated versus actual performance. Permian Grayburg-Brown Dolomite, Foster Field pilot waterflood, Texas, U.S.A. Legend: 1 -actual; 2 - calculated by Craig-Stiles method; 3 - calculated by Craig et al. method (1955); and 4 - calculated by Stiles method. (After Abernathy, 1964, Fig. 9; reprinted with permission of AIME.)
each layer from the wells at the same relative position in the reservoir. No cross flow was assumed to occur between layers. As pointed out earlier, natural water drives are generally less effective in carbonate reservoirs than in sandstone reservoirs. The difference stems from the greater heterogeneity of the carbonates. Results of a 1967 API study of natural water drives in 72 sand and sandstone reservoirs and 39 limestone, dolomite, and other rock types are
38 TABLE 1-VI Range of parameters of reservoirs with water drive as the predominant recovery mechanism. (After Arps et al., 1967; reprinted with permission of the American Petroleum Institute) Sand and Sandstone
Ultimate recovery Residual oil, % pore space bbl/acre- ft Rock perameter k,mD ~, % bulk volume S i, % pore space
Limestone, dolomite, and other
Worst
Median
Best
Worst
Median
Best
63.5 155
32.7 571
11.4 1,641
90.8 6
42.1 172
24.7 1,422
11 11.1 47
568 25.6 25
4,000 35.0 5.2
10 2.2 50
127 15.4 18
1,600 30.0 3.3
*Values shown for each separate parameter; values do not necessarily belong to same case history.
summarized in Table 1-VI. Carbonate reservoirs contain higher percentages of residual oil than do sand and sandstone reservoirs. Improvements in overcoming reservoir heterogeneities, thereby increasing the additional production of the unrecovered mobile oil, are discussed in Chapter 5, Part 2 (Rieke et al.).
Injection rate predictions. Injection calculations require knowledge of either k h or k h permeability capacity terms. This information can, in many cases, be derived from koh data obtained from pressure buildup tests, when the reservoir was undersaturated, and from appropriate relative permeability test data (Felsenthal and Ferrell, 1972). For water injection predictions the k h can be evaluated using: kh
= kh
• (k'rw/k'ro),
(1-23)
where k'rwiS the relative permeability to water at residual oil saturation, and k'ro is the relative permeability to oil at irreducible water saturation. Typical k'rwand k'rodata are represented by the end points of the oil-water relative permeability curves shown in Figs. 1-19 to 1-22. Gas well tests yield k h data, but these tests are often affected by turbulence in the wellbore region. A factogr of turbulence can be evaluated either from well tests (Energy Resources Conservation Board, 1975) or from laboratory tests. Gewers and Nichols (1969) measured turbulence factors on cores from microvugular carbonate gas reservoirs in the Turner Valley Member of the Rundle Formation (Mississippian) of western Canada. Values were obtained that were as much as one order of magnitude higher than previously reported for non-vuggy rocks. Felsenthal and Ferrell (1972) stated that the best approach for obtaining k h data is to use the results of injectivity tests and/or subsequent pressure falloff tests. Care must be taken during the injectivity tests that the formation is not being fracture parted, which results in an erroneously high permeability capacity value. Creation of new fractures can be evaluated with the aid of step-rate injectivity tests (Yuster and Calhoun, 1945). In these tests, injection rates are increased stepwise and plotted against (Pw-Po), where
39 Pw is the bottomhole injection pressure and p~ is the shut-in formation pressure. It is assumed that no new fractures are being opened as long as the curve is a straight line and goes through the origin of a Cartesian plot. One of the limitations of this method for determining kh values is that it does not take into consideration the spatial distribution of flow capacity values within the reservoir. P6rez-Rosales (1979) presented a statistical method for obtaining the continuous areal distribution of the flow capacity in heterogeneous reservoirs. The mathematical technique used is normal distribution analysis, which allows the representation of random distributions as a linear combination of normal density functions. It was postulated by P6rez-Rosales (1979) that natural random spatial distributions can be considered as the supposition of elementary distributions, known as basic accumulations. The mathematical model of basic accumulations is the normal distribution. A limestone reservoir (Cretaceous), Sitio Grande Field located in southeast Mexico, was chosen by P6rez-Rosales to illustrate the method. Flow capacity values corresponding to each of the 18 wells were determined by using pressure buildup tests described by P6rez-Rosales (1978). Two three-dimensional spatial distributions of the kh variability in the Sitio Grande Field are presented in Fig. 1-28. Fracturing or pressure parting pressures can also be predicted and evaluated by means of the fracture gradient presented by Hubbert and Willis (1957) and Eaton (1969): PDf =
Po_ -D
_
1-v
+ -D- '
(1-24)
where pfis the bottomhole pressure that causes fracture propagation, p is the reservoir pressure, Po is the overburden pressure, D is the depth, and v is the Poisson's ratio. A plot indicating observed fracture gradients and Poisson's ratios for a Mississippian limestone reef and a Permian dolomite reservoir is shown in Fig. 1-29. Analysis of pressure falloff tests is described in detail by Matthews and Russell (1967, pp. 72-83). A method developed by Hazebroek et al. (1958) appears to apply well to carbonate reservoirs (Felsenthal and Ferrell, 1972). His method yields a k h value and also a dimensionless skin factor, s, which is defined as: s + In
rJrw=O.O0708(Pw-p)(kh/il~w),
(1-25)
where r is the external boundary radius, ft; rwiS the wellbore radius, ft; i is the stabilized injection rate, bbl/D, before pressure falloff testing; and/~wiS the viscosity of the water, cP. If the skin factor is negative, one may assume that r is in effect larger than the originally assumed value based on hole size. The effective wellbore radius, rw~, which later must be substituted into all injectivity prediction equations, can then be evaluated by setting s = 0. This results in:
rwe= re -a, where a = O.O0708(Pw-Pr
(1-26)
40 A
B.
Fig. 1-28. Flow capacity (kh) distributions in the Sitio Grande Field (Cretaceous), Mexico. A - South to north view; B - north to south view. Numbers refer to well numbers. (After Perez-Rosales, 1979, Figs. 7 and 8; reprinted with permission of the Society of Petroleum Engineers.)
41 1.0 POISSON RATIO
-I w
I--
Z~
P
-II-. o. I,i j Q
~. z m
I--z t,d ,,,.. c~ <~
0.5
(..)
o/t
1
1
1
1
o s. I . "
l 0.5
FORM. DEPTH
l
~
i
l
I.O
PRESS., ~
psi f- T
"
Fig. 1-29. Observed fracture pressure gradients and Poisson' s ratios as a function of the shut-in formation pressure/depth ratios, o - Mississippian limestone reef at 6,500-ft depth; A Permain dolomite reservoir at 3,900-ft depth. (After Felsenthal and Ferrell, 1972, Fig. 36; courtesy of Continental Oil Co. and Elsevier Publ. Co.)
Clark (1968) devised a practical method for evaluating the true matrix permeability of a formation. This method has been found to be useful for evaluating the properties of carbonate rocks surrounding water injection wells. Millheim and Chichowicz (1968) described a similar method for low-permeability fractured gas wells. Both methods first evaluate the effect of possible induced fractures and then separate this effect from the contribution of the rock matrix. Adams et al. (1968) described transient pressure tests in a complex gas reservoir, indicating a tight dolomite matrix near the wellbore and a higher matrix permeability at some distance from the well.
Infill drilling strategy. Infill drilling as a recovery strategy was briefly mentioned in the Introduction Chapter of Volume 1 of this book. Here in Volume 2, the application of this incremental recovery strategy to carbonate reservoirs in west Texas is discussed in Chapter 5. Van Everdingen and Kriss (1980) noted that in the past the relationship between primary ultimate recovery and well spacing was not well established because of the lack of consideration of reservoir heterogeneity. Infill drilling, which decreases the spacing between wells, can increase the ultimate recovery of mobile oil during waterflooding. The optimum location of infill wells is in certain
42 situations an important cost-reducing production strategy for heterogeneous carbonate reservoirs. Waterflood programs utilizing knowledge about in-situ stress in a number of carbonate reservoirs located in the Permian Basin have shown improvement in reservoir pressures and production rates (Nolen-Hoeksema et al., 1992). The improvement is due to the strategic placement of injector and infill wells with respect to the major insitu stress. Measured in-situ stress magnitude and orientation values by using microfracturing techniques and borehole televiewer revealed that directional waterflood effects in the oil reservoirs coincided with hydraulic-fracture propagation directions. The new well patterns and spacing minimized floodwater channeling (Nolen-Hoeksema et al., 1992). Wu et al. (1989) presented results of a decline curve analysis coupled with an economic evaluation of waterflood infill drilling projects in 14 Clear Fork and 11 San Andres Permian carbonate reservoirs in west Texas (Table 1-VII). Results indicated that there was a statistical medium value increase of 7.78% in recovery of the original-oil-in-place using infill drilling waterflooding over conventional waterflood for the Clear Fork units. There was a statistical medium value increase in oil recovery of 11.38% of the original-oil-in-place using infill drilling waterflooding over conventional waterflooding for the San Andres units. From an economic viewpoint, Wu et al. (1989) showed that in general the San Andres units had a higher rate of return for infill drilling waterflood projects owing to a shallower reservoir depth and a higher infill drilling recovery efficiency.
Enhanced recovery Enhanced oil recovery processes are usually divided into three main categories: miscible flooding, chemical flooding, and thermal recovery. These methods have not been widely used by independent operators owing to constraints such as scarce financial resources, lack of technical knowledge and expertise, absence of detailed reservoir data, inherent high economic risk, and unstable sale price. Designing an EOR project in a carbonate reservoir requires a "best effort" reservoir characterization, which can be used in a model to predict the performance of the project. The more realistic the reservoir description is, the more reliable the EOR performance predictions will be (Dowling, 1970). Application of carbonate depositional environmental concepts will lead to better definition of field limits, quality and continuity of each zone, including delineation of potential productive zones that were either cased off or not penetrated as a result of early evaluation techniques. In order to meet the requirement of optimal design, process screening and initial computer model studies are performed before the EOR process is pilot tested in the field. Miscible flooding. Miscible flooding is a technique where a solvent bank rich in LPG (ethane through butane) is generally injected at the existing gas-oil contact and then driven downward by dry gas. A miscible fluid displacement of the oil results from a reduced capillary force. There is no phase boundary or interface existing between the oil and displacing fluids. Recoveries as high as 96% of the initial oil-inplace are claimed for these processes, which include processes such as high-pressure dry gas (Lee and Reitzel, 1981; DesBrisay et al., 1981), enriched gas (Davis et al.,
TABLE 1-VII Reservoir properties, recovery efficiencies, and well spacing data for waterflood infill drilling in the Permian Clear Fork and San Andres carbonate reservoirs, west Texas, U.S.A. (After Wu et al., 1989, Tables 1 and 2; reprinted with permission of the Society of Petroleum Engineers) Field/Unit
N
Primary
Initial waterflood Infill drilling
(Acres)
Depth Thick- Poro- Permea- B 0 Gravity S i ness sity bility (RBL/ (ft) (ft) (%) (mD) STB) (~ (%)
320 720 4,850 29,542 4,693 2,133 3,120 6,828 2,000 8,510 4,400 3,760 4,320 4,720
3,170 3,170 6,380 6,700 5,800 6,525 6,700 6,700 6,450 7,350 5,675 6,600 6,400 6,400
34 32 30 72 218 78 102 105 100 101 85 150 82 180
7.0 7.0 12.7 10.0 6.3 5.0 7.0 5.6 6.2 5.2 6.4 6.4 5.1 6.4
8.0 3.0 6.0 3.0 0.7 1.2 7.7 3.0 3.0 1.0 1.0 1.0 0.1 1.0
1.18 1.18 1.23 1.62 1.27 1.15 1.15 1.15 1.15 1.28 1.25 1.25 1.30 1.25
30.5 30.5 32.2 42.0 34.6 27.0 29.0 28.0 28.0 34.7 35.0 30.0 30.0 35.0
40.0 38.0 27.0 23.6 30.0 30.0 35.0 42.3 38.6 24.0 27.0 32.0 35.0 27.0
3.0 6.5 84.9 738.0 275.0 39.5 80.5 162.0 51.3 206.0 110.0 152.0 68.9 247.0
8.65 7.88 12.66 13.56 15.37 9.33 20.80 20.57 14.20 22.31 17.31 9.12 14.53 16.76
105 116 55 40 70 50 45 45 40 53 50 45 53 36
16.00 9.54 16.85 21.33 17.75 17.08 30.79 29.56 32.19 23.60 21.55 10.90 15.71 22.61
45 54 49 36 40 50 35 40 30 38 50 40 53 30
25.10 13.09 28.51 37.04 21.40 25.53 39.12 52.56 50.49 29.75 27.70 14.25 20.29 24.54
25 25 44 29 18 40 22 27 20 30 40 35 40 25
San Andres Units Adair 5,338 Fuhrman-Mascho/Blk 9 3,948 Johnson/J.L. "AB" 840 Johnson/Grayburg 3,720 Means 14,328 Ownby 2,960 Shafter Lake 11,080 Triple-N/Grayburg 2,192 Wasson/Denver 25,505 Wasson/Willard 13,360 W Seminole 3,720
4,900 4,450 4,100 4,150 4,300 5,200 4,300 4,325 4,800 5,100 5,112
50 80 60 50 200 32 49 20 200 111 118
14.1 7.0 8.0 6.7 9.0 14.1 6.5 12.1 10.0 8.5 9.9
3.7 4.0 1.8 5.3 29.0 4.5 5.0 6.6 5.0 1.5 20.7
1.12 1.12 1.20 1.20 1.04 1.35 1.24 1.23 1.31 1.31 1.38
33.5 29.0 38.8 32.5 29.3 32.0 32.0 31.9 33.0 32.0 32.4
35.0 30.0 30.0 21.8 28.8 38.0 25.0 40.0 15.0 20.0 18.0
168.0 79.0 19.6 45.7 382.0 52.0 165.0 20.0 2108.0 624.0 174.0
15.02 8.41 7.36 21.41 23.88 11.17 12.30 14.30 7.27 11.86 8.13
49 51 56 45 52 60 45 80 66 60 62
25.31 10.68 12.12 31.23 39.03 20.59 19.09 25.60 23.50 19.35 16.52
41 29 36 34 35 50 35 60 43 44 41
41.64 13.25 34.29 36.06 45.44 29.11 21.03 37.10 46.15 29.32 24.49
23 23 10 27 33 41 31 40 18 35 31
Clear Fork Units: Diamond M/Jack Diamond M/McLaughlin Flanagan/U. Clear Fork Fullerton/U. Clear Fork N. Roberston Ownby Prentice/Central Prentice/NE Prentice/SW Russel Wasson/Gaines Wasson/Gibson Wasson/North Wasson/South
Area
Recovery Spacing RecoverySpacing Recovery Spacing (MMSTB) (%N) (Acres/W) ( % N ) (Acres/W) ( % N ) (Acres/W)
4~
44 1976; Young and Martin, 1980), and carbon dioxide or nitrogen injection (Watts et al., 1980; Holm, 1987; Stein et al., 1989). The general rule of thumb is that naturally-fractured carbonate reservoirs are poor candidates for miscible CO 2flooding. Beliveau et al. (1993) reported on a pilot miscible CO 2 flood in the Midale Field (Mississippian) located in southeastern Saskatchewan, Canada. The results of the pilot test showed that a substantial tertiary recovery is obtainable using CO 2in a fractured reservoir owing to favorable gravity effects and open vertical fracture system. The pilot injection wells were aligned in pairs along the fracture system, providing two linedrive injection rows (Beliveau et al., 1993), and the flood was non-cyclical. The test was designed to displace oil in the off-trend direction (perpendicular to the strike of the predominant vertical fracture system). A scale-up of the CO 2pilot results, using a dual-porosity simulator, showed that a tertiary recovery of 20% OOIP can be expected from a field-scale CO 2flood (Beliveau et al., 1993). Also, there are unique opportunities for very efficient vertical miscible displacement drives in the Devonian pinnacle reef reservoirs in western Canada (Willmon, 1966; Young and Martin, 1980; Mazzocchi et al., 1988).
Cyclicflooding. The principle behind cyclic flooding is to move oil out of the rock matrix by forcing an injection fluid, either water or gas and water, into the rock, thereby raising reservoir pressure. A depressuring phase follows forcing oil from the matrix. Cycles can be repeated several times. During the depressuring phase of the cycle, water is retained by capillary attraction, and oil is released into the natural fractures or high-permeability zones (Felsenthal and Ferrell, 1972). This process is used in reservoirs that are difficult to waterflood by conventional methods. This process is closely related to the imbibition process described by Graham and Richardson (1959) and Mattax and Kyte (1962). Bokserman and Shalimov (1967), Tatashev (1968), and Felsenthal and Ferrell (1969) presented laboratory data and theoretical analysis supporting the concept of cyclic flooding. One of the best examples of an application of cyclic flooding is from the Permian Spraberry trend in the Midland Basin, west Texas, U.S.A. Although the Spraberry reservoir is composed mainly of a massive siltstone, there are shale and shaly limestone interbeds present (Marshall, 1952). The major void space in the reservoir is in nearly vertical fractures. What was learned early on from cyclic flooding in the Spraberry was conveniently applied to fractured carbonate reservoirs. Field data on the use of cyclic flooding in the Spraberry Field, Texas, U.S.A. were presented by Elkins and Skov (1963). Here, injection wells had been lined up carefully with the fracture trend. The spacing of the fractures ranged from a few inches to a few feet. Matrix permeability was less than 1 mD, and porosity was in the 8-15% range. High injection rates were used to repressure the reservoir to above the bubble point pressure. The injection was stopped upon reaching this pressure. Within a few days, oil production rose substantially and then gradually declined. The pressuring phase lasted 1 month, whereas the depressuring phase lasted about 7 months. This process was repeated three times, causing substantial oil rate increases, but each cycle produced less oil than the preceding one. Only one pressure cycle was successful in the extremely low-permeable Cretaceous Austin Chalk and the Buda Limestone, Salt Flat Field, Texas, U.S.A. These
45 formations are characterized by a tight matrix (k~ = 0.1 mD; ~b = 12%). The low permeability shown by cores was confirmed by well performance. Hester et al. (1965) described a fairly successful test in one well that yielded 10,000 bbl of oil after water was injected into it at pressures just below the fracturing pressure. Only one third of the injection water was produced back. A second cycle essentially failed to produce any oil, probably because of low permeability and the lack of intemal energy to push the oil into the wellbore during the depressuring phase of the cycle. Today, the standard recovery strategy for the Austin Chalk is to drill horizontal wells to intersect the major vertical fracture systems. Horizontal wells also have been used to improve miscible flood performance in carbonate reservoirs (Patel and Broomhall, 1992; Trocan et al., 1992). Willingham and McCalef (1967) and Elkins (1969) reported somewhat more successful applications of the injection-production scheme described above. The first project occurred in a highly-fractured portion of the Permian Phosphoria Formation at Cottonwood Creek, Wyoming, U.S.A. Twelve former water injection wells (cumulative injection of 25.4 million bbl of water) were put on production. After 2-3 weeks they started to produce oil. At the end of 1 year the wells were producing 1,850 B/D of oil with a 67% water cut. In the second case, a former injection well after receiving 1 million bbl of water produced 131,500 bbl of "cyclic" oil from the heterogeneous Devonian Bois d'Arc Limestone, West Edmond Field, Oklahoma, U.S.A. In both instances, conventional waterfloods were unsuccessful in the areas surrounding these wells. Successful cyclic flooding in a highly-permeable fractured carbonate reservoir was described by Vasilechko et al. (1969). The injection-production scheme in this project was similar to the one reported for the Spraberry Field in Texas, U.S.A. During the water injection phase, which lasted 1.5-2 months, formation pressure was increased. Injection was stopped for 1-1.5 months to allow depressuring of the reservoir. Contrary to the Spraberry, the reservoir of the A 4 Formation in the Pokrovsk Field, Russia, had a high permeability and porosity (k = 1,065 mD; ~b= 23%). Cyclic flooding was started after conventional waterflooding produced oil at a 75% water cut. During 8 cycles, about 1.5 million extra bbl of oil were recovered. As expected, production declined with each successive cycle. Vasilechko et al. (1969) concluded that cyclic waterflooding should be effective in other carbonate reservoirs as well. Thermal recovery. Thermal recovery methods consist of cyclic steam stimulation, steamflooding, in-situ combustion and their variations. The latter method does not hold much promise in carbonate reservoirs, inasmuch as field tests have not be encouraging. Results of unsuccessful tests are important in pointing out the failures that often are not discussed in the literature. Marchant and Menzie (1966) reported on the California Company's experimental field test in the Irvine-Fumace Field located in eastem Kentucky, U.S.A. This reservoir is the coarsely crystalline Silurian Lockport Dolomite (Comiferous p a y - a driller's term) and the test was not successful. Marchant and Menzie (1966) studied the changes in limestone under in-situ combustion temperatures in the laboratory. Limestone supplies its own fuel at high temperatures in the form of free carbon, carbon monoxide and oxygen. A temperature of 1300~ is required for the following reaction to occur at atmospheric pressure for
46 limestone: 3 C a C O 3 + heat -~ 3CaO + C O 2 -1- 0 2 ) , whereas dolomite will break down at about 1000~ and lower if sulfur is an impurity (Marchant and Menzie, 1966). It should be noted that in the manufacturing of lime, temperatures are much higher, usually between 2000 and 2500~ (Boynton and Gutschick, 1960), giving the following reactions: (1) for limestone: C a C O 3 + heat ~ 3CaO + CO2, and (2) for dolomite: CaCOa/MgCO 3 + heat ~ CaO/MgO + 2 C O 2. With high calcium limestone, 44% of the weight of the limestone is lost and with dolomite the loss is 48%. Limestone does not begin to evolve C O 2 freely until a temperature of approximately 1800~ is reached under normal kiln conditions, as reported by Boynton and Gutschick (1960). They also noted that both reactions are chemically reversible by the absorption of CO 2. A more stable form is a hydrated lime that is formed under the conditions of adding water to the lime: CaO + HzO ~ C a ( O H ) z + heat. The tests by Marchant and Menzie (1966) showed that the samples underwent complete bleaching, sustained appreciable loss in weight, had a large increase in effective porosity, exhibited increase in air permeability, and became a weak incompetent "chalk-like" material. It is apparent that carbonates mechanically breakdown under high in-situ combustion temperatures, thereby reducing the pore space and providing flow channels. Sahuquet and Ferrier (1980), however, noted that the decomposition of limestones during steamflooding occurs without unfavorable effects. Briggs et al. (1988) estimated that the amount of heavy oil contained in carbonate reservoirs is 1.6 x 1012 bbl of oil-in-place worldwide. Very little attention has been paid to this resource owing to the conceptually difficult task of recovering viscous oil from naturally-fractured carbonate rocks. Nolan et al. (1980) discussed thermal expansion as a mechanism (which would move oil into fractures) operative during steamflooding of carbonate reservoirs. Previously, Elf Aquitaine initiated a steam-drive pilot test in 1977 in the Lacq Superieur Field (reservoir is a lower Senonian limestone of Upper Cretaceous age) (Sahuquet and Ferrier, 1980). This is an anticlinal field that is located in the southwestern part of France. Primary production began in 1950 and by 1975 only 17% of the original oilin-place was recovered from this heterogeneous and fractured reservoir. The reservoir is surrounded by a large aquifer, which maintains a constant, but low, reservoir pressure. The producing limestone beds in the anticline exhibit two facies: (1) central portion of the anticline contains very fractured, occasionally karstic dolomites (porosity values range from 10-15%) and a matrix having permeability of about 1 mD. The fractured nature of this zone gives rise to a high productivity: (2) the north-west and south-east parts of the field contain limestones with an average porosity of 20% and permeability ranging from 1-10 mD. This facies contains only few microfractures and its productivity is low (Sahuquet and Ferrier, 1980). The 21.5 ~ API crude has a viscosity of 17.5 x 10-3 Pa.s. Sahuquet and Ferrier (1980) stated that steam-drive was chosen because the matrix blocks could be efficiently heated by heat conduction. The oil trapped in the blocks would be also heated and the oil's viscosity reduced. Thermal expansion would move the oil towards the fractures. The test was successful in increasing production. Sahuquet and Ferrier (1980) believe that the oil expelled from the matrix blocks moves quickly through the fracture network towards the producers. They also noted that these carbonates are dissociated by the steam under the pressure and temperature conditions
47 without unfavorable effects. Carbon dioxide, which is a result of this dissociation, perhaps improved the efficiency of the operations. It was suggested by Briggs et al. (1989) that a pressure cycling steam recovery process could possibly be used to recover heavy oil from the carbonate reservoirs. The concept tested in the British Petroleum laboratory involved a two-stage process of combining pressure cycling steam with imbibition and internal-gas drive and/or steam flashing. It was assumed that the fracture system would allow efficient heating of the reservoir rock matrix by thermal conduction. This could result in displacement of oil into the fractures by thermal expansion, accelerated imbibition, gravity drainage, and expansion by solution-gas drive of oil from the matrix during the blowdown phase. The mobilized oil can then be produced via the inter-connected fracture network (Briggs et al., 1989). In the Komi Republic of the former Soviet Union, a 4,330- to 4,900-ft deep, highly complicated, heterogeneous 1,150-ft- thick carbonate formation containing 18 ~ API, 700 cP heavy oil and having a reservoir temperature of 68~ was successfully steamflooded in the Usa Field. Primary and secondary recovery from this carbonate formation did not exceed 7-10% of the original oil-in-place (Bokserman et al., 1991). Average porosity of the formation was 20% with a permeability of 3 D. Beginning in 1982, superheated-water, with temperatures of 485-560~ was injected into the carbonate formation. Bokserman et al. (1991) stated that the recoverable oil reserves increased by 800 to 1,000 million bbl. They estimated that the ultimate oil recovery will reach 27% of OOIP.
RESERVOIRS IN KARSTED CARBONATES
Reservoirs in karsted carbonate rocks are discussed in Chapter 9 of this book (Mazzullo and Chilingarian). Such reservoirs are, with few exceptions, notoriously heterogeneous in terms of effective porosity and permeability in both the lateral and vertical directions. Such heterogeneity results from the irregular distribution of porous zones and the complex nature of pore systems in karsted strata, and poses special problems in reservoir development, petrophysical modeling, management, and hydrocarbon producibility. The most common type of gross porosity-permeability system represented in karsted reservoirs is sediment-filled and unfilled paleocaves and caverns. On the megascale, extreme vertical reservoir compartmentalization in fields occurs because of the presence of successive levels of cave or cavern systems separated by impermeable host strata, and by impermeable strata within individual cave or cavern level, in the productive section (e.g., Kerans, 1988; Bliefnick, 1992). Compounding this inherent heterogeneity is the fact that productive zones commonly are multiporosity systems which clearly have extreme variations in the effective porosity and permeability and, hence, in fluid flow, internal pressure gradients, and reservoir performance. The polygenetic origin of many such pore systems (i.e., where karst-related dissolution has overprinted a pre-existing porosity system) further complicates reservoir petrophysical characterizations. Pore types commonly found in karsted reservoirs include interparticle pores in cave-filling breccias, matrix porosity in host carbonates (e.g., micropores, interparticle and moldic pores, vugs, and intercrystalline
48 pores, the latter common in dolomites), dissolution-enlarged fractures and joints, and large, tortuous cavernous pores. Impermeable strata that serve as barriers to lateral fluid flow also occur irregularly throughout such sections. Many hydrocarbon reservoirs in karsted carbonate rocks have values of porosity and permeability that far exceed those for typical, average-porosity (i.e., 15% or less) carbonate reservoirs. Furthermore, they characteristically have some of the highest flow rates and recovery efficiencies of all reservoirs. Recovery efficiencies of many karsted reservoirs range from 21% (Amthor and Friedman, 1989) to as high as 80% (Brady et al., 1980). Horizontal drilling recently has proven to be an excellent method of enhancing production from compartmentalized, karsted carbonate reservoirs (Dussert et al., 1988). The few examples, wherein karstification has resulted in the formation of nearly homogeneous reservoirs with well-connected rather than compartmentalized porosity-permeability and fluid transmission systems, include Yates Field (Permian) in the Permian Basin of Texas, U.S.A. (Craig, 1988), Amposta Marino Field (Cretaceous) in Spain (Wigley et al., 1988), and Renqiu Field (Precambrian to Ordovician) in China (Guangming and Quanheng, 1982; Qi and Xie-Pei, 1984). Despite their typically heterogeneous characters, karsted carbonate reservoirs constitute one of the most economically significant category of reservoir types because of typically huge reserves. Volumes of oil and gas already produced from karsted limestones and dolomites of Precambrian to Tertiary age around the world amount to minima of 8.45 billion barrels and 911 trillion cubic feet, respectively. Total ultimate producible oil reserves (at current technology) from such reservoirs are at least 111 billion barrels, a figure that amounts to no less than 11% of total global oil reserves from Phanerozoic carbonate and siliciclastic reservoirs. Hydrocarbon production from karsted carbonate reservoirs accounts for a minimum of 18% of the hydrocarbon reserves stored in all types of traps in carbonate rocks. Traps associated with karsted carbonate reservoirs are classified into seven types based on reservoir occurrence and geometry of enclosing strata (described in Chapter 9 of this volume), all of which fall under the general category of subunconformity traps (Martin, 1966; Halbouty, 1972; Rittenhouse, 1972). The most common occurrence of karsted carbonate reservoirs is as buried hill traps, that is, residual hills on a karsted geomorphic terrane wherein intense subaerial meteoric dissolution (either monogenetic or polygenetic, and either monocyclic or polycyclic) typically has created porosity or has significantly enhanced pre-existing porosity. Buried hill traps may: (1) occur on horizontal to gently-dipping strata (Type I); (2) represent erosionally modified reefs (Type II); (3) be residual hills that, by virtue of their paleotopographic expression, isolate strata with pre-existing porosity (Type III); (4) occur in strata that have been tectonically structured (Type IV); and (5) be hybrids of these types. Many of the world's giant hydrocarbon reservoirs occur in these types of traps, including: (1) the Golden Lane and Campeche-Reforma trends (Cretaceous) in Mexico; (2) the Horseshoe Atoll Trend (Pennsylvanian) in the Permian Basin of west Texas; (3) Bu Hasa, Fahud, Fateh, and Natih fields (Cretaceous) in the Middle East; and
49 (4) Renqiu Field (Precambrian to Ordovician) in China. Other types of traps include: (1) karsted zones in structured strata (Type V: e.g., Oklahoma City Field, Ordovician, in the Anadarko Basin of Oklahoma); (2) reservoirs associated with linear fracture or fault trends (Type VI: e.g., the Albion-Scipio-Pulaski Trend in the Michigan Basin); and (3) the extremely subtle traps in karsted, gently-dipping strata (Type VII: e.g., various fields in the Ordovician dolomites of Permian Basin of Texas and New Mexico, U.S.A.). Exploration for karsted reservoirs traditionally has employed seismic surveys (conventional and 3-D; and offset-dependent seismic reflector amplitude analysis of conventional seismic), and in mature basins with ample well control, subsurface geologic mapping as well. The existence of karsted, potential reservoir zones commonly is indicated during drilling by dipmeter data, sudden drill bit drops, rapid increases in drilling rates, lost circulation, and very high initial flowing potentials.
RESERVOIRS IN C H A L K S
Chalks are fine-grained (micritic) limestones composed dominantly of the skeletons ofnannofossil coccoliths (brown algae). Although these pelagic organisms have wide environmental and latitudinal distributions (McIntyre and Be, 1967), their rates of production are slow. Hence, coccolith chalks accumulate into thick beds only in settings that have low rates of sediment input from other sources. In modem seas, chalks are accumulating mainly in the deep sea (100--4000 m depths). In contrast, the thick chalk deposits of the Cretaceous and Paleocene around the world, such as those in northwestern Europe and in the Gulf Coast and western interior seaway of the United States, likely were deposited in shallow epicontinental seas (depths of 100500 m), when high eustatic sea level stands during these times limited the amount of siliciclastic sediment input (Scholle, 1974, 1977). Newly-deposited chalks have initial interparticle porosity as high as 80%, which is rapidly reduced during early compaction and dewatering and later diagenesis to values approaching 10% (Schlanger and Douglas, 1974; Scholle, 1974, 1977). Permeability values of most chalks, exclusive of fractures, are very low, generally being less than 10 mD (Scholle, 1977). Accordingly, hydrocarbon production from chalks was, prior to the 1960s, considered to be unlikely. In fact, many major oil companies at that time simply were not interested in exploring for chalk reservoirs (see Chapter 6, this volume). As stated by Scholle (1977), significant production from chalks was once considered to be "miraculous". The discovery shortly thereafter of commercially significant hydrocarbon accumulations in chalks in the Ekofisk Complex in the North Sea, in the Gulf Coast and western interior seaway, and elsewhere in the world clearly changed that perception. Reservoirs in the North Sea, for example, have producible reserves on the order of several billion barrels of oil and trillions of cubic feet of associated gas. Although many chalk reservoirs, particularly those in the North Sea, average about 30% porosity, according to Scholle (1977) all primary interparticle porosity in chalks theoretically should be eliminated when the rocks are buried to depths of about 3000 m. The real
50 miracle is why such high porosities, which account for huge hydrocarbon storage volumes in inherently low-permeability chalks, are preserved in ancient chalk reservoirs. Several workers (Harper and Shaw, 1974; Rickards, 1974; Scholle, 1974, 1977; Byrd, 1975; Mapstone, 1975) have shown that most of this porosity is primary interparticle porosity that has been preserved because porosity reduction by mechanical and chemical compaction and cementation were retarded largely by reservoir overpressuring. In the Ekofisk area, for example, abnormally high pore pressures of 7100 psi at depths of 3050 m were reported by Harper and Shaw (1974), depths at which normal pore pressures and lithostatic loads should be only about 4300 psi and 9000 psi, respectively. As discussed in Chapter 8 of this volume (Friedman), other factors that may have contributed to porosity preservation in chalks include early entry of hydrocarbons into the reservoir, limited thickness of overburden, and the presence of pore fluids enriched in magnesium, which retards dissolution and subsequent cement reprecipitation. Fractures are ubiquitous in highly-productive chalks, and exploration for potential reservoirs always is concerned with fracture prediction and occurrence. Fractures create permeabilities of up to 200 mD in some typically low-permeability chalk reservoirs. The newest approach to enhancing production from low-permeability chalks began in the 1980's with the advent of horizontal drilling. According to Friedman (Chapter 8, this volume), a horizontally-drilled well may recover as much as five times the amount of oil as a comparable vertical well if the borehole encounters multiple sets of fractures.
SEISMIC IDENTIFICATION OF CARBONATES
Exploration for carbonate reservoirs has, as is the case for other reservoirs, been heavily dependent in the past on seismic reflection profiles. Of course, reservoirs in structured strata are relatively easy to identify on seismic sections, as are reefs. Accordingly, many hydrocarbon reservoirs have been discovered "on structures" and, particularly, in reef facies. More subtle traps in carbonate strata, for example, those developed along depositional facies pinchouts in shallow and deep-water strata, are inherently more difficult to discern using seismic exploration because of constraints due to stratal thickness and, commonly, limited impedance contrasts between potential reservoirs and enclosing strata. The various responses of carbonate strata on conventional seismic sections are discussed and illustrated in Chapter 2 of this volume (Kendall et al.). The use of seismic sequence stratigraphy in the 1970's (Mitchum et al., 1977; Vail and Mitchum, 1977) led to dramatic new advances in the exploration for potential reservoir facies in carbonate strata. Models of carbonate deposition based on seismic response, described by Bubb and Hatlelid (1977), and especially, Sarg (1988), now allow for enhanced predictive capabilities in terms of the recognition of potential reservoir facies. These models relate carbonate deposition, subsidence, and sea level changes to predicted spatial mosaics of depositional facies and potential reservoirs through time. Computer forward-modeling of carbonate rock stratigraphies has been a fundamental goal of many explorationists over the last decade as a tie-in to understanding the development
51
of sequence stratigraphies as identified on seismic sections. Chapter 2 also discusses this aspect of seismic analysis as it applies to the generation of detailed reservoir petrophysical models that allow geologists and reservoir engineers to fully exploit hydrocarbon reservoirs.
REFERENCES
Abernathy, B.F., 1964. Waterflood prediction methods compared to pilot performance in carbonate reservoirs. J. Petrol. Techn., 16(3): 2 7 6 - 382. Adams, A.R., Ramey, H.J., Jr. and Burgess, R.J., 1968. Gas well testing in a fractured carbonate reservoir. J. Petrol. Techn., 20(10): 1187 - 1194. Aguilera, R., 1980. Naturally Fractured Reservoirs. Petroleum Publ. Co., Tulsa, OK, 703 pp. Aguilera, R., 1988. Determination of subsurface distance between vertical parallel natural fractures based on core data. Bull. Am. Assoc. Petroleum Geologists, 72(7): 8 4 5 - 851. Alpay, O.A., 1969. Application of Aerial Photographic Interpretation to the Study of Reservoir Natural Fracture Systems. SPE 2567, Soc. Petrol. Engrs. 44th Ann. Fall Meeting, Denver, CO., 12 pp. Amthor, J.E. and Friedman, G.M., 1989. Petrophysical character of Ellenburger karst facies: Stateline (Ellenburger) field, Lea County, southeastern New Mexico. In: B.K. Cunningham and D.W. Cromwell (Editors), The Lower Paleozoic of West Texas and Southern New Mexico- Modern Exploration Concepts. Permian Basin Sect. Soc. Econ. Paleont. Min., Publ. 89-31, pp. 1 3 3 - 144. Anderson, T.O. and Stahl, E.J., 1967. A study of induced fracturing using an instrumental approach. J. Petrol. Techn., 19(2): 261 - 267. Arnold, M.D., Gonzales, H.T. and Crawford, P.B., 1962. Estimation of reservoir anisotropy from production data. Trans. AIME, 225(I): 301 - 304. Arps, J.J., Brons, F., van Everdingen, A.F., Buchwald, R.W. and Smith, A.E., 1967. A Statistical Study of Recovery Efficiency. Am Petrol. Instit. Bull. D14, New York, NY, 33 pp. Arps, J.J. and Roberts, T.G., 1955. The effect of the relative permeability ratio, the oil gravity, and the solution gas-oil ratio on the primary recovery from a depletion type reservoir. Trans. AIME, 204:120 127. Armstrong, F.E., Howell, W.D. and Watkins, J.W., 1961. Radioactive Inert Gases as Tracers for Petroleum Reservoir Studies. USBM Rept. Invest. 5733, 15 pp. Arnold, M.D., Gonzales, H.T. and Crawford, P.B., 1962. Estimation of reservoir anisotropy from production data. Trans. AIME, 225: 9 0 9 - 912. Baldwin, D.E., Jr., 1966. Prediction of tracer performance in a five-spot pattern. Trans. AIME, 237(1): 513-517. Beliveau, D., Payne, D.A. and Mundry, M., 1993. Waterflood and CO 2 flood of the fractured Midale Field. J. Petrol. Techn., 45(9): 881 - 887. Blanchet, P.H., 1957. Development of fracture analysis as exploration method. Bull. Am. Assoc. Petrol. Geologists, 41(8): 1748- 1750. Bliefnick, D.M., 1992. Karst-related diagenesis and reservoir development in the Arbuckle Group, Paschall #2 core, Wilburton Field, Oklahoma. In: M.P. Candelaria and C.L. Reed (Editors), Paleokarst, Karst Related Diagenesis and Reservoir Development: Examples from Ordovician-Devonian Age Strata of West Texas and the Mid-Continent. Permian Basin Sect. Soc. Econ. Paleont. Min., Publ. 92-33, pp. 137 152. Bokserman, A.A., Mamedov, Y.G. and Antonlady, D.G., 1991. Diverse methods spread thermal EOR in U.S.S.R. Oil & Gas J., 89(40): 8 2 - 84. Bokserman, A.A. and Shalimov, B.V., 1967. Cyclic input to strata with dual porosity during water displacement of oil. lzv. Akad. Nauk SSSR, Mekh. Zhidkostey i Gazov, 2 : 1 6 7 - 174. (In Russian.) Botset, H.G., 1940. Flow of gas-liquid mixtures through consolidated sand. Trans. AIME, 1 3 6 : 9 1 - 105. Boynton, R.S. and Gutschick, K.A., 1960. Lime. In: J.L. Gillson (Editor), Industrial Minerals and Rocks. AIME, New York, NY, pp. 4 9 7 - 519. Brady, T.J., Campbell, N.D.J. and Maher, C.E., 1980. Intisar "D" oil field, Libya. In: M.T. Halbouty -
-
52 (Editor), Giant Oil and Gas Fields of the Decade: 1968-1978. Am. Assoc. Petrol. Geologists, Mem.No. 30:596 pp., pp. 543 - 564. Briggs, P.J., Baron, R.P., Fulleylove, R.J. and Wright, M.S., 1988. Development of heavy oil reservoirs. J. Petrol. Techn., 40(2): 206-214. Briggs, P.J., Beck, D.L., Black, C.J.J. and Bissell, R.C., 1989. Heavy oil from fractured carbonate reservoirs. SPE 19671, Soc. Petrol. Engrs. Ann. Techn. Conf. and Exhib., San Antonio, TX, EOR/Gen. Petrol. Eng. Vol., pp. 4 1 9 - 428. Bubb, J.N. and Hatlelid, W.G., 1977. Seismic stratigraphy and global changes of sea level, part 10: seismic recognition of carbonate buildups. In: C.E. Payton (Editor), Seismic Stratigraphy- Applications to Hydrocarbon Exploration. Am. Assoc. Petrol. Geologists, Mem No. 26:516 pp., pp. 185-204. Buckley, S.E. and Leverett, M.C., 1942. Mechanism of fluid displacement in sands. Trans. AIME, 146: 1 0 7 - 111. Byrd, W.D., 1975. Geology of the Ekofisk field, offshore Norway. In: A.W. Woodland (Editor), Petroleum and the Continental Shelf of North-West Europe, 1. John Wiley & Sons, New York, 501 pp., pp. 439-445. Campa, M.F. and Romero, R.M., 1969. Statistical zonation technique and its application to the San Andres Reservoir in the Poza Rica Area, Vera Cruz, Mexico. Rev. Inst. Mex. Petrol., 1(1): 56 - 60. (In Spanish.) Carnes, P.S., 1966. Effects of Natural Fractures or Directional Permeability in Water Flooding. SPE 1423, Soc. Petrol. Engrs. 7th Biennial Secondary Rec. Symp., Wichita Falls, TX, 8 pp. Chilingar, G.V. and Bissell, H.J., 1957. Mississippian Joana Limestone of Cordilleran Miogeosyncline and use of Ca/Mg ratio in correlation. Bull. Amer. Assoc. Petrol. Geologists, 41 (10): 2257 - 2274. Chilingar, G.V., Mannon, R.W. and Rieke, H.H.,III, 1972. Introduction to Carbonate Reservoir Rocks, In: G.V. Chilingar, R.W. Mannon and H.H. Rieke,III (Editors), Oil and Gas Production from Carbonate Rocks. Am. Elsevier Publ. Co., Inc., New York, 408 pp., pp. 1 - 22. Chilingarian, G.V., Mazzullo, S.J. and Rieke, H.H., 1992. Carbonate Reservoir Characterization: A Geologic- Engineering Analysis, Part 1. Elsevier Sci.Publs. B.V., Amsterdam, The Netherlands, 639 pp. Clark, K.K., 1968. Transient pressure testing of fractured water injection wells. J. Petrol. Tech., 20(6): 639-643. Clerke, E.A. and Van Akkeron, 1988. Borehole televiewer improves completion results in a Permian Basin San Andres reservoir. SPE Prod. Engr., 3(1): 8 9 - 95. Corbett, K., Friedman, M. and Spang, J., 1987. Fracture development and mechanical stratigraphy of Austin Chalk, Texas. Bull Am. Assoc. Petrol. Geologists, 71 (1): 17 - 28 Craft, B.C. and Hawkins, M.E, 1959. Applied Petroleum Reservoir Engineering. Prentice Hall, Inc., Englewood Cliffs, NJ, 437 pp. Craig, D.H., 1988. Caves and other features of Permian karst in SanAndres Dolomite, Yates Field reservoir, west Texas. In: N.P. James and P.W. Choquette (Editors),Paleokarst. Springer-Verlag, New York, 416 pp., pp. 3 4 2 - 363. Craig, EF., Jr., Geffen, T.M. and Morse, R.A., 1955. Oil recovery performance of pattern gas or water injection operations from model tests. Trans. AIME, 204: 7 - 15. Crawford, P.B., 1962. Method proposed for determining reservoir heterogeneity prior to waterflooding. Producers Monthly, 26(10): 6 - 7 and 26(11): 20 - 21. Craze, R.C., 1950. Performance of limestone reservoirs. Trans. AIME, 189: 2 8 7 - 294. Dake, L.P., 1978. Fundamentals of Reservoir Engineering. Elsevier Sci. Publ. Co., Amsterdam, 443 pp. Daniel, E.J., 1954. Fractured reservoirs of Middle East. Bull. Am. Assoc. Petrol. Geologists, 38: 7 7 4 815. Davis, J.A., Blair, R.K. and Wagner, O.R., 1976. Monitoring and Control Program for a Large Scale Miscible Flood. SPE 6097, Soc. Petrol. Engrs. 51st Ann. Fall Techn. Conf. and Exhib., New Orleans, LA, 12 pp. Denoyelle, L., Bardon, C. and Cove de Murville, E., 1988. Interpretation of a CO2/N2injection field test in a moderately fractured carbonate reservoir. SPE Reserv. Eng., 3(1): 2 2 0 - 226. Desbrisay, C.L., EI-Ghussein, B.F., Hoist, P.H. and Misellati, A., 1981. Review of Miscible Flood Performance, Intisar 'D'Field, Socialist People's Libyan Arab Jamahiriya. SPE 10245, Soc. Petrol. Engrs. 56th Ann. Fall Techn. Conf. and Exhib., San Antonio, TX, 14 pp. Dowling, P.L., 1970.Applications of Carbonate Environmental Concepts to Secondary Recovery Projects. SPE 2987, Soc. Petrol. Engrs. 45th Ann. Techn. and Exhib. Meet., Houston, TX, 16 pp.
53 Dussert, E, Santoro, G. and Soudet, H., 1988. A decade of drilling developments pays off in offshore Italian oil field. Oil & Gas J., 86(9): 33 - 39. Dykstra, H. and Parsons, R.L., 1950. The Prediction of Oil Recovery by Waterflood, Secondary Recovery of Oil in the United States. Am. Petrol. Instit., 160 pp. Eaton, B.A., 1969. Fracture gradient prediction and its application in oilfield operations. Trans. AIME, 246: 1 3 5 3 - 1360. Elkins, L.E., 1946. The importance of injected gas as a driving medium in limestone reservoirs as indicated by recent gas-injection experiments and reservoir-performance history. APIDril. and Prod. Prac., pp. 1 6 0 - 174. Elkins, L.F., 1969. Internal anatomy of a tight, fractured Hunton lime reservoir revealed by performance West Edmond Field. J. Petrol Techn., 21 (2): 221 - 232. Elkins, L.F. and Skov, A.M., 1960. Determination of fracture orientation from pressure interference. Trans. AIME, 219:301 - 304. Elkins, L.F. and Skov, A.M., 1963. Cyclic waterflooding the Spraberry utilizes 'end effects' to increase oil production rates. Trans. AIME, 228(I): 877 - 884. Energy Resources Conservation Board, 1975. Theory and Practice of the Testing of Gas Wells. Alberta Energy Resources Conservation Board, Calgary, Alberta, Can. Felsenthal, M., 1959. Correlation of k / k data with sandstone core characteristics. Trans. AIME, 216: 2 3 8 - 261. g o Felsenthal, M. and Conley, F.R., 1955. Discussion on analysis of reservoir performance kg/ko curves and a laboratory k g/ k o curve measured on a core sample. Trans. AIME, 204: 240. Felsenthal, M. and Ferrell, H.H., 1969. Oil recovery from fracture blocks by cyclic injection. J. Petrol. Techn., 21(2): 141 - 142. Felsenthal, M. and Ferrell, H.H., 1972. Fluid flow in carbonate reservoirs. In: G.V. Chilingar, R.W. Mannon and H.H. Rieke, III (Editors), Oil and Gas Production from Carbonate Rocks. Amer. Elsevier Publ. Co., New York, 408 pp., pp. 83 - 142. Fertl, W.H. and Rieke, H.H., III, 1979. Gamma ray spectral evaluation techniques identify fractured shale reservoirs and source rock characteristics. J. Petrol. Techn., 32(11): 2053 - 2062. Fraser, C.D. and Pettitt, B.E., 1962. Results of a field test to determine the type and orientation of hydraulically induced formation fracture. J. Petrol. Techn., 14(5): 463 - 4 6 6 . George, C.J. and Stiles, L.H., 1977. Improved Techniques for Evaluating Carbonate Waterfloods in West Texas. SPE 6739, Soc. Petrol. Engrs. 52ndAnn. Fall Techn. Conf. and Exhibition, Denver, CO., 10 pp. Gewers, C.W. and Nichols, L.R., 1969. Gas turbulence factor in a microvugular carbonate. J. Can. Petrol. Techn., 8(2): 5 1 - 56. Graham, J.W. and Richardson, J.G., 1959. Theory and application of imbibition phenomena in recovery of oil. Trans. AIME, 216:377 - 381. Guangming, Z. and Quanheng, Z., 1982. Buried-hill oil and gas pools in the North China Basin. In: M.T. Halbouty (Editor), The Deliberate Search for the Subtle Trap. Am. Assoc. Petrol. Geologists, Mem. No. 32, 351 pp., pp. 3 1 7 - 3 3 5 . Halbouty, M.T., 1972. Rationale for deliberate pursuit ofstratigraphic, unconformity, and paleogeomorphic traps. Bull. Am. Assoc. Petrol. Geologists, 56(3): 5 3 7 - 541. Haldorsen, H.H. and Damsleth, E., 1993. Challenges in reservoir characterization. Bull. Am. Assoc. Petrol. Geologists, 77(4): 5 4 1 - 551. Harper, M.L. and Shaw, B.B., 1974. Cretaceous-Tertiary Carbonate Reservoirs in the North Sea. Offshore North Sea Tech. Conf., Stavanger, Norway, Paper G-IV, 4, 20 pp. Harris, J.F., Taylor, G.L. and Walper, J.L., 1960. Relation of deformational fractures in sedimentary rocks to regional and local structure. Bull. Am. Assoc. Petrol. Geologists, 44(12): 1853 - 1873. Hazebroek, P., Rainbow, H. and Matthews, C.S., 1958. Pressure fall-off in water injection wells. Trans. AIME, 213:250 - 260. Heffer, K.J. and Bevan, T.G., 1990. Scaling Relationships in Natural Fractures; Data, Theory, and Applications. SPE 20981, Europec 90, The Hague, Netherlands. Hendrickson, G.E., 1961. History of the Welch Field San Andres pilot water flood. J. Petrol. Techn., 13(8): 745 - 748. Herron, S.L., Petricola, M.J.C. and Dove, R.E., 1992. Geochemcial logging of a Middle East carbonate reservoir. J. Petrol. Engr., 44(11): 1176 - 1183. Hertzog, R., Colson, L., Seeman, B., O'Brien, M., Scott, H., McKeon, D., Wraight, P., Grau, J., Ellis, D.,
54 Schweitzer, J. and Herron, M., 1989. Geochemical logging with spectrometry tools. SPE Formation Eval., 4(2): 1 5 3 - 162. Hester, C.T., Walker, J.W. and Sawyer, G.H., 1965. Oil recovery by imbibition water flooding in the Austin and Buda formations. J. Petrol. Techn., 17(8): 919 - 925. Holm, L.W., 1987. Evolution of the CO 2flooding process. J. Petrol. Techn., 39(11): 1337- 1342. Honarpour, M.M., Chilingarial., G.V. and Mazzullo, S.J., 1992. Permeability and relative permeability of carbonate reservoirs. In: G.V. Chilingarian, S.J. Mazzullo and H.H. Rieke (Editors), Carbonate Reservoir Characterization: A Geologic- Engineering Analysis, Part 1. Elsevier Sci. Pubis. B.V., Amsterdam, 639 pp., pp. 399 - 416. Hubbert, M.K. and Willis, D.G., 1957. Mechanics of hydraulic fracturing. Trans. AIME, 210:153 - 166. Huitt, J.L., 1956. Fluid flow in simulated fractures. AIChE J., 2(2): 2 5 9 - 264. Hurley, T.J., 1990. The Pegasus Ellenburger Field, a multidisciplinary study of a fractured carbonate field in west Texas. Bull. Can. Soc. Petrol. Geol., 38(1): 167. ICF and BEG, 1990a. Production Potential of Unrecovered Mobile Oil Through Infield Development: Integrated Geologic and Engineering Studies- Overview. Vol. 1, U.S. Dept of Energy Contract No. AC22-86BC 14000, Bartlesville Project Office, Bartlesville, OK., 115 pp. ICF and BEG, 1990b. An Assessment of the Reserve Growth Potential of the San Andres/Grayburg Carbonate (South Central Basin Platform) Play in Texas. Vol. 2, U.S. Dept of Energy Contract No. AC2286BC 14000, Bartlesville Project Office, Bartlesville, OK., 78 pp. ICF and BEG, 1990c. An Assessment of the Reserve Growth Potential of the Frio Barrier-Strandplain Play in Texas. Vol. 3, U.S. Dept of Energy Contract No. AC22-86BC14000, Bartlesville Project Ofrice, Bartlesville, OK, 73 pp. ICF and BEG, 1990d. An Assessment of the Reserve Growth Potential of the Clear Fork Platform Carbonate Play in Texas. U.S. Dept of Energy Contract No. AC22-86BC 14000, Bartlesville Project Ofrice, Bartlesville, OK, 147 pp. ICF and BEG, 1990e. Producing Unrecovered Mobile Oil: Evaluation of the Potential Economically Recoverable Reserves in Texas, Oklahoma, and New Mexico. U.S. Dept of Energy Contract No. AC2286BC14000, Bartlesville Project Office, Bartlesville, OK, 77 pp. Jones, T.A., Wooten, S.O. and Kaluza, T.J., 1988. Single-Phase Flow Through Natural Fractures. Soc. Petrol. Engrs. 63d Ann. Tech. Conf. and Exhibit., Houston, TX, 7 pp. Kaveler, H.H., 1944. Engineering features of the Schuler Field and unit operation. Trans. AIME, 155: 58-87. Kerans, C., 1988. Karst-controlled reservoir heterogeneity in Ellenburger Group carbonates of west Texas. Bull. Am. Assoc. Petrol. Geologists, 72(10): 1160 - 1183. Kunkel, G.C. and Bagley, J.W., Jr., 1965. Controlled waterflooding, Means Queen Reservoir. J. Petrol. Techn., 17(12): 1385- 1390. Lane, B.B., 1969. A Skeleton Pilot Water Flood, an Aid to Proper Flood Pattern Selection. SPE 2525, Soc. Petrol. Engrs. 44th Ann. Fall Meet., Denver, CO, 7 pp. Langnes, G.L., Robertson, J.O., Jr. and Chilingar, G.V., 1972. Secondary Recovery and Carbonate Reservoirs. American Elsevier Publ. Co., New York, NY, 304 pp. LaPoint, P.R. and Hudson, J.A., 1985. Characterization and Interpretation of Rock Mass Joint Patterns. Geol. Soc. Am., Special Paper 199, 37 pp. Lee, J.I. and Reitzel, G.A., 1981. High Pressure Dry Gas Miscible Flood Brazeau River Nisku Oil Pools. SPE 10243, Soc. Petrol. Engrs. 56th Ann. Fall Techn. Conf. and Exhib., San Antonio, TX, 14 pp. Leverett, M.C. and Lewis, W.B., 1941. Steady flow of gas-oil-water mixtures through unconsolidated sands. Trans. AIME, 142:107 - 116. Littlefield, M., Gray, L.L. and Godbold, A.C., 1948. A reservoir study of the West Edmond Hunton Pool, Oklahoma. Trans. AIME, 174: 131 - 164. Lomizd, G.M., 1951. Flow in Fractured Rocks. Gos. Energ. Izd., Moscow-Leningrad, 127 pp. (In Russian.) Louis, C., 1969. A study of groundwater in jointed rocks and its influence on the stability of rock masses. Rock Mech.Res., Imp. Coll., London, Rept. No. 10, 90 pp. Magara, K., 1986. Geological Models of Petroleum Entrapment. Elsevier Applied Sci. Publ., London and New York, 327 pp. Mapstone, N.B., 1975. Diagenetic history of a North Sea chalk. Sedimentology, 22(4): 601 - 6 1 3 . Marchant, L.C. and Menzie, D.E., 1966. Limestone rock changes by in-situ combustion temperatures. Prod. Monthly, 30(11): 22 - 24.
55 Martin, F.G., 1967. Mechanics and control in hydraulic fracturing. Pet. Engr., 39(13): 63 - 72. Martin, R., 1966. Paleogeomorphology and its application to exploration for oil and gas (with examples from western Canada). Bull. Am. Assoc. Petrol. Geologists, 50(10): 2277 - 2311. Marshall, J.W., 1952. Spraberry reservoir of west Texas. Bull. Am. Assoc. Petrol. Geologists, 36(11): 2189-2191. Mattavelli, L., Chilingarian, G.V. and Storer, D., 1969. Petrography and diagenesis of the Taormina Formation, Gela Oil Field, Sicily (Italy). Sed. Geol., 3(1): 59 - 86. Mattax, C.C. and Kyte, J.R., 1962. Imbibition oil recovery from fractured water-drive reservoirs. Trans. AIME, 225(I1): 177 - 184. Matthews, C.S. and Russell, D.G., 1967. Pressure Buildup and Flow Tests in Wells. Soc. Petrol. Engrs. AIME Monograph 1, Dallas, TX, 167 pp. Mazzocchi, E., Nagel, R.G., Hunter, B.E., Peggs, J.K. and Fong, D.K., 1988. Tertiary application of a hydrocarbon miscible flood: Rainbow Keg river "B" pool. SPE 17355, Proc. Soc. Petrol. Engrs./U.S. Dept. of Energy Enhanced Oil Rec. Symp., Tulsa, OK, pp. 355 - 378. Mclntyre, A. and Be, A.W.H., 1967. Modem coccolithophoridae of the Atlantic Ocean, 1, placoliths and cyrtoliths. Deep-Sea Res., 14:561 - 597. McKinley, R.M., Vela, S. and Carlton, L.A., 1968. A field application of pulse testing for detailed reservoir description. J. Petrol. Techn., 20(3): 3 1 3 - 321. Miller, M.G. and Lents, M.R., 1946. Performance of Bodcaw reservoir, Cotton Valley Field cycling project. Am. Petrol. Inst. Drill. and Prod. Prac., pp. 1 2 8 - 149. Millheim, K.K. and Chichowicz, L., 1968. Testing and analyzing low-permeability fractured gas wells. Trans. AIME, 243:193 - 198. Mitchum, R.M., Vail, P.R. and Thompson, S., 1977. Seismic stratigraphy and global changes of sea level, part 2: the depositional sequence as a basic unit for stratigraphic analysis. In: C.E. Payton (Editor), Seismic Stratigraphy-Applications to Hydrocarbon Exploration. Am. Assoc. Petrol. Geologists, Mem. No. 26, 516 pp., pp. 5 3 - 62. Moore, W.D. and Truby, L.G., Jr., 1952. Pressure performance of five fields completed in a common aquifer. Trans. AIME, 195:297 - 302. Narr, W. and Lerche, I., 1984. A method for estimating subsurface fracture density in core. Bull. Am. Assoc. Petrol. Geologists, 68(5): 6 3 7 - 648. Nolan, J.B., Ehrlich, R. and Crookson, R.B., 1980. Applicability of Steamfloodingfor Carbonate Reservoirs. SPE 8821, First Joint Soc. Petrol. Engrs./U.S. Dept. Ener. Symp. on EOR, Tulsa, OK. Nolen-Hoeksema, R.C., Avasthi, J.M., Pape, W.C. and E1-Rabaa, A.W.M., 1992. Waterflood improvement in the Permian Basin: Impact of in-situ stress evaluations. SPE 24873, Soc. Petrol. Engrs. Ann. Techn. Conf. and Exhib., Reserv. Eng. Vol., pp. 81 - 92. Overbey, W.K., Jr. and Rough, R.L., 1971. Prediction of Oil- and Gas-Bearing Rock Fractures from Surface Structural Features. U.S. Dept. Interior, Bur. of Mines Rept. Invest. 7500, 14 pp. Parsons, R.W., 1966. Permeability of idealized fractured rocks. Trans. AIME, 237: 1 2 6 - 136. Partain, B., 1989. Retiree gets 'bright' idea. Am. Assoc. Petrol. Geologists Explorer, 10(10): 22 - 23. Pasini, J., III, and Overby, W.K., Jr., 1969. Natural and Induced Fracture Systems and Their Application to Petroleum Production. SPE 2565, Soc. Petrol. Engrs. 44th Ann. Techn. Conf. and Exhib. Meet., Denver, CO, 7 pp. Patel, R.S. and Broomhall, R.W., 1992. Use of horizontal wells in vertical miscible f l o o d s - Pembina Nisku, Alberta, Canada. SPE 24124, Proc. Soc. Petrol. Engrs./U.S. Dept. of Energy 8th EOR Symp., Tulsa, OK, pp. 215 - 227. P6rez-Rosales, C., 1978. Use of Pressure Buildup Testsfor Describing Heterogeneous Reservoirs. SPE 7451, Soc. Petrol. Engrs. 53d Ann. Techn. Conf. and Exhibition, Houston, TX, 8 pp. P6rez-Rosales, C., 1979. Use of Normal Analysis in the Description of Heterogeneous Reservoirs. SPE 8431, Soc. Petrol. Engrs. 54th Ann. Techn. Conf. and Exhibition, Las Vegas, NV, 8 pp. Pirson, S.J., 1958. Oil Reservoir Engineering. McGraw-Hill Book Co., New York, 735 pp. Qi, F. and Xie-Pei, W., 1984. Significant role of structural fractures in Renqiu buried-hill oil field in eastern China. Bull. Am. Assoc. Petrol. Geologists, 68(8): 971 - 982. Rickards, L.M., 1974. The Ekofisk Area, Discovery to Development. Offshore North Sea Tech. Conf., Stavanger, Norway, Paper G-IV, 3, 16 pp. Rittenhouse, G., 1972. Stratigraphic-trap classification. In: R.E. King (Editor), Stratigraphic Oil and Gas Fields. Am. Assoc. Petrol. Geologists, Mem. No. 16, 687 pp., pp. 1 4 - 28.
56 Sabins, KS., 1969. Thermal infrared imagery and its application to structural mapping in southern Califomia. Bull. Geol. Soc. Am., 80(3): 397-404. Sahuquet, B.C. and Ferrier, J.J., 1980. Steam Drive Pilot in a Fractured Carbonate Reservoir Lacq Superieur Field. SPE 9453, Soc. Petrol. Engrs. 55th Ann. Fall Techn. Conf. and Exhib., Dallas, TX, 12 pp. Sarg, J.E, 1988. Carbonate sequence stratigraphy. In: C.K. Wilgus, B.S. Hastings, C.G.St.C. Kendall, H.W. Posamentier, C.A. Ross and J.C. Van Wagoner (Editors), Sea-Level Changes: An Integrated Approach. Soc. Econ. Paleont. Min., Spec. Publ. No. 42, pp. 1 5 5 - 181. Schlanger, S.O. and Douglas, R.G., 1974. Pelagic ooze-chalk-limestone transition and its implications for marine stratigraphy. In: K.J. Hsu and H.C. Jenkyns (Editors), Pelagic Sediments on Land and Under the Sea. Intl. Assoc. Sedimentologists, Spec. Publ. No. 1, pp. 117 - 148. Scholle, P.A., 1974. Diagenesis of Upper Cretaceous chalks from England, Northern Ireland and the North Sea. In: K.J. Hsu and H.C. Jenkyns (Editors), Pelagic Sediments on Land and Under the Sea. Intl. Assoc. Sedimentologists, Spec. Publ. No. 1, pp. 177- 210. Scholle, P.A., 1977. Chalk diagenesis and its relation to petroleum exploration: oil from chalks, a modem miracle?. Bull. Am. Assoc. Petrol. Geologists, 61 (7): 9 8 2 - 1009. Stein, M.H., Frey, D.D., Walker, R.D. and Pariana, G.J., 1989. The Slaughter Estate Unit C02Flood: A Comparison Between Pilot and Field-Scale Performance. SPE 19375, Soc. Petrol. Engrs. Production Techn. Symp., Lubbock, TX, pp. 1 - 12. Stewart, C.R., Craig, F.F., Jr. and Morse, R.A., 1953. Determination of limestone performance characteristics by model flow tests. Trans. AIME, 198:93 - 102. Stiles, W.E., 1949. Use of permeability distribution in waterflood calculations. Trans. AIME, 186:9- 13. Tarr, C.M. and Heuer, G.J., 1962. Factors Influencing the Optimum Time to Start Water Injection. SPE 340, Soc. Petrol. Engrs. 5th Biennial Secondary Recovery Symp., Wichita Falls, TX, 10 pp. Tatashev, K.K., 1968. Effect of the change in layer pressure on the oil displacement from blocks of fissured-porous oil reservoirs by water imbibition. Geol. Nefti i Gaza, 1: 5 5 - 59. (In Russian.) Trocan, V.N., Frydl, P.M. and Robertshaw, E.S., 1992. Horizontal wells improve mature miscible flood performance- Rainbow Lake Field, Alberta, Canada. SPE 24125, Soc. Petrol. Engrs./U.S. Dept. of Energy 8th EOR Syrup., Tulsa, OK. Vail, P.R. and Mitchum, R.M., 1977. Seismic stratigraphy and global changes of sea level, part I: overview. In: C.E. Payton (Editor), Seismic Stratigraphy- Applications to Hydrocarbon Exploration. Am. Assoc. Petrol. Geologists, Mem No. 26, 516 pp., pp. 51 - 52. Van Everdingen, A.F. and Kriss, H.S., 1980. New approach to improved recovery efficiency. J. Petrol. Techn., 32(6): 1164 - 1168. Vasilechko, V.P., Gnatyuk, R.A. and Petrash, I.N., 1969. Effectiveness of cyclic water flooding in oil formations of Pre-Carpathian fields. Nauch.-Tekh. Sb. Ser. Nefiepromyslovoe Delo, 1" 1 0 - 12. Ward, R.E, Kendall, C.G.St.C. and Harris, P.M., 1986. Upper Permian (Guadalupian) facies and their association with hydrocarbons - Permain Basin, west Texas and New Mexico. Bull. Am. Assoc. Petrol. Geologists, 70(3): 239-262. Watts, R.J., Gehr, J.A., Wasson, J.A., Evans, D.M. and Locke, C.D., 1980. A Single CO 2Injection Well Minitest in a L o w - Permeability Eastern Carbonate Reservoir- A Preliminary Report. SPE 9430, Soc. Petrol. Engrs. 55th Ann. Fall Techn. Conf. and Exhib., Dallas, TX, 10 pp. Weber, K.J., 1986. How heterogeneity affects oil recovery. In: L.W. Lake and H.B. Carroll, Jr. (Editors), Reservoir Characterization. Academic Press, Inc., New York, 659 pp., pp. 487-544. Weber, K.J. and Bakker, M., 1981. Fracture and Vuggy Porosity. SPE 10332, Soc. Petrol. Engrs. 56th Ann. Fall Tech. Conf., San Antonio, TX, 11 pp. Wigley, EL., Bouvier, J.D. and Dawans, J.M., 1988. Karst and mixing-zone porosity in the Amposta Marino Field, offshore Spain. Bull. Am. Assoc. Petrol. Geologists, 72(8): 1031. Willingham, R.W. and McCaleb, J.A., 1967. The Influence of Geologic Heterogeneities on Secondary Recovery from the Permian Phosphoria Reservoir, Cottonwood Creek, Wyoming. SPE 1770, Soc. Petrol. Engrs. Rocky Mountain Reg. Meet., Casper, WY, 12 pp. Willmon, G.J., 1966. Vertical miscible flood to hike recovery by 70 million barrels. Worm Oil, 162(1): 75 -78. Witherspoon, P.A., Wang, J.S.Y., Iwai, K. and Gale, J.E., 1980. Validity of the cubic law for fluid flow in a deformable rock fracture. Water Resources Res., 16(6): 1016 - 1024. Wolf, K.H., Chilingar, G.V. and Beales, EW., 1967. Elemental composition of carbonate skeletons, min-
57 erals, and sediments. In: G.V. Chilingar, H.J. Bissell and R.W. Fairbridge (Editors), Carbonate Rocks, 9B. Elsevier Publ. Co., Amsterdam, 413 pp., pp. 2 3 - 149. Worthington, P.F., 1991. Reservoir characterization at the mesoscopic scale. In: L.W. Lake, H.B. Carroll, Jr. and T.C. Wesson (Editors), Reservoir Characterization II. Academic Press, Inc., New York, 726 pp., pp. 1 2 3 - 165. Wu, C.H., Flores, D.P., Briens, F.J., Brimhall, R.M. and Poston, S.W., 1989.An evaluation of water flood infill drilling in west Texas Clearfork and San Andres carbonate reservoirs. SPE 19783, Soc. Petrol. Engrs. Ann. Techn. Conf. and Exhib., Reser. Eng. vol., pp. 121 - 136. Young, M.N. and Martin, W.E., 1980. The Wizard Lake D-3A pool miscible flood. J. Can. Petrol. Techn., 19(2): 65 - 75. Yuster, S.T. and Calhoun, J.C., Jr., 1945. Pressure Parting. Producers Monthly, 9(4): 16 - 26. Zemanek, J., Caldwell, R.L., Glenn, E.E., Holcomb, S.V., Norton, L.J. and Straus, A.J.D., 1969. The borehole televiewer- A new logging concept for fracture location and other types ofborehole inspection. J. Petrol. Techn., 21 (6): 7 6 2 - 774. Zimmerman, L.J. and Chen, S.T., 1992. Geophysical Methods for Reservoir Characterization. SPE 23953, Proc. Soc. Petrol Engrs. Permian Basin Oil and Gas Rec. Conf., Midland, TX, pp 241 - 250.
This Page Intentionally Left Blank
59
Chapter 2 SEISMIC EXPRESSION OF CARBONATE RESERVOIR SYSTEMS CHRISTOPHER G.ST.C. KENDALL, WILLIAM E. FULL, and GREGORY L. WHITTLE
INTRODUCTION
This chapter addresses the use of seismic data, particularly where they are correlated with well information, to identify and interpret the carbonate depositional systems associated with three major types of carbonate play. Commonly, these plays can be ranked in order of decreasing size as: (1) carbonate sheets, (2) carbonate buildups, and (3) clinoform carbonate shelf margins. Sheet plays are found in carbonate shelf sediments associated with the shallow water behind the basin margin; buildup plays occur down-slope from the margin and on the shallow shelf immediately adjacent to the margin; clinoform plays are associated with the margin crest (Fig. 2-1). The depositional porosity and geometry of these plays may be modified by subsequent fracturing and diagenesis (see volume 1, Chapter 4). With the exception of chalks, most of these carbonate plays are related to highstand system tracts: the aggradational sheet play geometry is formed as shoaling-upward cycles during sea-level highstands when carbonate accumulation matches sea-level rise (keep-up); the buildup lens-like carbonate geometry is formed on drowned shelves during and following rapid sea-level rises (keep-up and give-up); and the progradational clinoform geometry of the platform margin is formed during stillstands by carbonate accumulation that not only keeps-up with the sea-level rise, but advances in a seaward direction (Kendall et al., 1991). Seismic interpretations of these plays can be tested with computer simulations which model the fill of sedimentary basins. The input parameters to such simulations are assumptions about the processes of sedimentation, sea level history and tectonic evolution of the study area and are based on currently accepted sedimentological, tectonic and eustatic models (Scaturo et al., 1989; Kendall et al., 1990; Lawrence et al., 1990). Before discussing these carbonate plays and their seismic response, it is important to provide the reader with some background on seismic and synthetic seismograms.
SEISMIC AND SYNTHETIC SEISMOGRAMS
The purpose of this discussion is to try to bring an understanding of the inherem limitations and strengths of seismic and synthetic seismogram data as they relate to the subsurface recognition of carbonate systems. Without some understanding of the principles underlying seismic analysis, the carbonate modeler is more prone to potential misinterpretation. If the reader is interested in a more complete discussion of these subjects, many points raised here are discussed in a number of works which describe: ( 1) the theory and application of seismic data and their tie to well data: Widess (1973), Dobrin (1976), Sheriff (1976, 1977, 1978), Telford et al. (1976), Coffeen (1978),
60 CARBONATE
PLAYS
IIa. Reef on Shelf ~ / x _ r - x
IIb. Reef Downslope
~ / x J ' x . _ / x
KEY
~
Limestone -~
iShale ~
Evaporite]
Fig. 2-1. Common carbonate plays include: I. Plays with sheet-like geometry formed during sea-level stillstands and rises whose aggradation matches the rise in sea level (keep-up). II. Shelf and downslope reef plays with lens-like geometry formed during and following sea-level rises (catch-up, IIa) and stillstands on shelves drowned by the rapid rise (give-up, lib). III. Clinoform plays with progradational platform margin geometry formed during sea-level stillstands, both at sea-level highs and sometimes at lows; the latter when associated with shallow basins.
McQuillin, Bacon, and Barclay (1979), Robinson, and Coruh (1980), Sengbush (1983), Kearey and Brooks (1984), Sharma (1986), and Waters (1987); and (2) synthetic seismic seismograms: Neidell (1980), Bally (1983, 1984, 1987, 1989), Schlee (1984), Berg and Woolverton (1985), and Gries and Dyer (1985). Sek~mic data
From a simplistic viewpoint, reflection seismic data are recordings of acoustic waves that have traveled through the earth starting at a known position and were reflected
61 from surfaces, be they carbonate or some other lithology, marking changes in acoustic impedence (acoustic impedance is the product of the density and seismic velocity in media). These recordings are processed to produce an image of the layered character of the earth. These layers are represented by events delineated as deflections on a seismic trace (a "wiggle" trace). Each deflection is the summed result of spatial changes in the elastic moduli (bulk modulus, rigidity, Poisson's ratio, or Young's modulus) and/or density of the rocks which result when the energy of the acoustic wave is reflected at successive layer boundaries (acoustic impedance boundaries) in the earth. The collection of variables describing the magnitude of all the seismic reflections versus time or depth is called "earth information" (eT). In an ideal earth, a source of energy, such as an explosion, produces an impulse whose overall shape is not altered except in amplitude, as it interacts with changes in earth properties along the wavefront. Mathematically, the impulse at any location in the earth could then be represented by the following function: Impulse = k (del) T
(2.1)
where: k is a constant describing the amount of energy recorded in an individual event (the amplitude squared), and (del)x represents the impulse function at time T. In this ideal situation, the seismic trace can be considered the end result of the interaction of the acoustic impulse with the earth properties. This interaction is called "convolution" and represents a filtering operation. The seismic trace (ST) can then be described by the following: S v = k (deI)T (convolve)e T
(2.2)
where: the symbol (convolve) represents the convolution (filtering) function. The convolution function represents the formula or process detailing the "how to" of the interaction of the impulse with the earth properties. Just as the earth is not physically ideal, neither is the seismic response. Deflections on seismic traces need not be a function solely of earth layering. In reality, they are the product of the convolution of non-ideal seismic impulses with less than perfect earth properties. The net outcome is that additional energy from other sources, such as multiple reflections, background noise (microquakes), occasional noise (trains, buses, cars), and coherent noises are included within the seismic traces. Additionally, the near-surface weathering zone interferes with and slows the velocity of the acoustic signal, a factor that can result in what is known as a "statics problem" where "events" appear to be displaced vertically and/or less coherent. Other influences include potential inefficiencies in the instruments, non-optimal geophone array patterns, and incomplete field recording of the seismic signals themselves. Relative to a seismic wave propagation, rock anisotropy relative to seismic wave propagation can also affect a clear definition of the earth properties. In only a few situations does the initial seismic record clearly depict the earth properties one desires to define. The seismic records are usually computer-processed so as to remove some of the undesired effects discussed above. The processing may entail trace editing, static corrections, amplitude adjustments (muting, gaining, and
62 amplitude recovery), normal move out (NMO) corrections, stacking and averaging traces, filtering (velocity and frequency varieties), deconvolutions (undoing a convolution or filtering process), and migration (the process of locating the proper position in two- and three-dimensions of a particular event). Usually, the processing is performed by specialists guided by the interpreter's specific needs. The result is that most seismic sections (collection of related individual seismic traces) are processed with specific models in mind. No standard method of seismic processing exists which enhances all the key information that can be extracted in all the portions of the seismic section. That is, the seismic processing performed for enhancing thin lithologic units in shallow subsurface sections differs appreciably from the processing required for thick units at greater depth. The more the seismic interpreter understands what processing the seismic signal has undergone, the more effective the interpretation. Without such a background, earth properties can be either missed or misinterpreted. Seismic events
A seismic event, as defined here, is simply a coherent or recognizable deflection on seismic traces that appears to be similar on two or more seismic traces. An event can be considered as two or more seismic deflections that can be correlated in some fashion, or as complicated as one wants them to be. The correlation of deflections can be based on: (1) matching relatively large amplitude trace deflections across two or more signals, or (2) matching various other waveform characteristics, such as gradually changing deflection shapes, common phases, frequencies and polarities, or any other property one wishes to define. Interval seismic velocity (average velocity within an interval of time) can also be used to correlate events. It should be noted that not every seismic event necessarily implies earth layering insofar as noise can sometimes be correlatable. Additionally, not all earth layers produce distinctive seismic shapes. The "cleanest" events on a seismic section are those defined by relatively large amplitude deflections. Events that span an increasing number of seismic traces, however, are less likely to be noiserelated. The actual amplitude of an observed event is a function of: (1) source-receiver distance; (2) properties of the media through which the wavelet (collection of acoustic frequencies comprising the initial seismic disturbance) has traveled; (3) geometric character of the traversed media; (4) noise processing of the earth; and (5) the character and spectra of energy associated with the source of the elastic disturbance. The total energy of the acoustic disturbance travels away from a source in spherical waves, and decreases as a function of the square of the distance from the source. Insofar as the square root of the energy associated with an individual disturbance is proportional to the amplitude of the disturbance, it follows that the amplitude should vary as a simple function of distance from the source. That is, if A ~ is the original
63 amplitude, then in a homogeneous media, geometric spreading (GS) can be expressed as:
(2.3)
GS = Ao/D
where: D is the distance from the source (Dobrin, 1976). The properties of the media normally affect the amplitude of the impulse wavelet in two ways: (1) as frictional dissipation; and (2) as an interaction with a surface marking a change in acoustic impedance. Frictional dissipation of the elastic energy into heat (or deformation of the grains within media, such as by compaction) causes a loss of wavelet amplitude. This loss is called "absorption" and is governed by the following equation: A - Ao e-alphaD
(2.4)
where: A is the original amplitude, A is the amplitude at distance D from the source, and alpha is the absorption coefficient which depends on the media being traversed. The absorption coefficient can vary greatly for different media, and generally reflects a high loss of energy for pulses traveling through media like anhydrite, halite, and some shales. For media such as dense carbonates, quartzite, and igneous rocks, the percent loss of energy is comparatively low. What makes the calculation and subsequent application of absorption coefficients difficult is the fact that this coefficient is dependent on (1) the frequencies present in the seismic pulse; and (2) the confining pressure (depth) of the rock, both of which must be precisely known. Figure 2-2 displays the effect of increasing depth relative to an arbitrary input wavelet. The second property of the media which affects the amplitude of the impulse wavelet is the change in acoustic impedance (which occurs where there are heterogeneities in the lithology, diagenetic fabric, or other rock properties) that form boundaries to the seismic wavefront. Acoustic impedance (p V) is the product of the bulk density of the media (p) and the velocity of the compressional wave as it passes through the media (V). An acoustic boundary occurs where there is a difference between the acoustic impedances along the path of the wavefront. It is along these boundaries that reflections, refractions, diffractions, and the creation of additional seismic disturbances are created. The amount of energy that an incoming (incident) wave disperses as reflections, refractions, and additional seismic energy, is a function of the angle of incidence and the contrast in acoustic impedance at the boundary. For normal (90 ~) incident waves, only reflected and refracted waves are generated. The proportion of incoming energy in the reflected wave can be calculated by: o
Energy = R 2 = [(p2 V2- Pl
VI)/(Pl V1 "[- P2V2 )]2
(2.5)
where: R is the reflection coefficient, Pi is the bulk density of medium i (the wave is traveling from medium i to medium i+ 1), and Vi is the P wave velocity in medium i. In this normal incidence case, the energy not reflected will be transmitted into the second medium. Angles other than 90 ~ mean less energy is reflected and new forms of seismic disturbance are created at the boundary (they can consist of reflected
64 Surface ,,
Lithology
-IO00m (350Oft)
I
I-
Seismic Response
Large positive reflection coefficient 50 hertz
1
wavelet.
ACoustic impedance of shale increases with depth. Limestone's i n c r e a s e s only sltqhtly.
Acoustic imped<;nce of shale increcs,ng with cam pact <.'~
Acoustic impedance
contro.",t dec.reo,',,::.
Decrease in wavelet frequency and strenqth with depth.
with depth.
- 3000 m ( 9900 f t )
5000m (16,500ft)
--1
S,
Smaller positive reflection coeff~cient 25 hertz wavelet.
-
Weak positive reflection coefficient and weak 12hertz wavelet.
De :~th
Fig. 2-2. Sketch showing the effect of increasing depth, through changes in acoustic impedance and seismic-wavelet frequency, on the seismic response from an acoustic-impedance contrast between clay and limestone. The Earth attenuates the seismic signal, preferentially removing the higher frequency components. The combined effect of decreasing frequency and acoustic-impedance contrasts produces a change from shallow, strong and sharp reflections to weak and long reflections at depth. (From Badley, 1985, Fig. 2.22.)
and refracted shear waves in addition to reflected and refracted P-waves). For the most part, one observes the clearest reflections when the angle of incidence is 90 ~. If there is no change in acoustic impedance, there will be no reflection observed. The greater the change in acoustic impedance, the greater is the amount of reflected energy.
65 Reflection tmcn top limestone Maximum interfenmce Decreasing amplitude No i n ~ e
\
Soparole refleclions from top ond base lim~s'l~
Ref lectic~ from bose lime.slone
Below I/,.o ,,,,ovelength ~,~ no reflectbon
Shale 3000 m/s wavelonqth (5Ore) Tuninq thickness
_
= No interference
Limestone 5CXX) m/s
Shole 3000 m/s ( ~ ~ i
50
hertz wavelet
Amplitude
Wavelength
Frequency - Number wavelengths per second 1 wavelength per second ,, 1hertz
Time
Waveform attributes
Fig. 2-3. Interference effects associated with a high acoustic-impedance wedge encased in lower acousticimpedance shale. The limestone must be thicker than half the seismic wavelength for no interference between reflections from its top and base. Maximum interference and amplitude of the resulting reflection occur at a limestone thickness equivalent to one-quarter of the seismic wavelength. For limestone thickness below one-quarter wavelength, the reflection remains the same but decreases in amplitude. Once the limestone is about one-thirtieth wavelength or less, reflections from the top and base effectively cancel, and there is no detectable seismic response. (From Badley, 1985, Fig. 2.14.)
The geometry of the reflecting boundaries can also affect amplitude. If the boundaries are convex, seismic waves can be focused. If concave, energy can be spread out resulting in loss of amplitude. There are cases where all or portions of boundaries are not observed because the waves were deflected by the geometry of the overlying boundaries. This latter point is important in areas of less-than-flat interfaces, where one might not presume to observe all the features that were expected on the seismic section. Furthermore, seismic reflections are additive and can produce constructive and destructive interference effects, especially when two or more events are closely spaced (Fig. 2-3) or when there are phase changes at closely spaced boundaries (Fig.
2-4). Extra events may be observed in a seismic section that are not directly below the geophones. These events may represent impedence boundaries outside the planes of the defined seismic section, which is a three-dimensional effect that must be considered whenever two-dimensional (or even one-dimensional) seismic data are analyzed. Moreover, boundaries that reflect acoustic disturbances in an ideal manner must be of
66 Reflection coefficients
Individual responses
Composite response
Constructive
interference I L
Destructive interference
Fig. 2-4. Constructive and destructive interferences affecting a minimum-phase normal-polarity wavelet. (From Badley, 1985, Fig. 2.10.)
a minimum area (the "Fresnel Zone"). Interaction of the acoustic wavefront with boundaries of less than minimum Fresnel sizes will result in the creation of reflection of smaller, sometimes distorted, shapes. The same holds true if there are "holes" in the reflecting boundary. To complicate matters further, the size of the Fresnel Zone is a function of the frequencies present at the wavefront. For example, the Fresnel Zone is larger at greater depths and smaller at shallower depths simply due to the fact that higher frequency acoustic signals display greater attenuation in the earth than do longer wavelength signals. The implication of this observation is that the prediction of the effect of reduced regions of acoustic boundary interaction is difficult to ascertain without computer modeling. Noise in all forms can also affect the amplitude of the signal reflected by an individual event. This noise can be random, coherent, or even induced by the recording instruments. Similarly, data processing can alter both the amplitude and character of the seismic pulse. This alteration can be caused by gain and mute procedures, or more complicatedly by Wiener filtering and other computerized signal enhancements. The net result is that distinct events can be created, enhanced, remain the same, or may even be lost by the data processing. As stated previously, the more we know about this critical step, the better we can predict where on the seismic section individual events have been affected and, more importantly, how they have or have not been altered. Finally, the amplitude of an individual event is a function of the amount of acoustic energy and, as briefly mentioned above, how this energy is distributed among the seismic spectrum of the initial acoustic impulse created by the source. For example, an initial wavelet dominated by high frequency energy would probably not help
67 PAR AIR GUN 300 c u - l n w a v e s h a p e d ( W S K - 1805- IH)
......i
AIR PAR
24
A/"x
I0 ,n
o
0 I
o
depth
H-cut
o:~
o 15 see
0
v IV'-
125Hz
0:2
6-80
o 3 sec
1 KJ
13 m d e p t h
o:1
0:2
sec
~, 0-~ sec
I
~,
0~2
U
_25o. lore
O: 2 sec
0
0-1
depth
"
0-2 sec
SPARKER
AA./L -
300 Hz
depth
SODERA MICA WATER GUN
Hz
0:1
FLEXOTIR 1 GUN
5-
O~l
FLEXlCHOC F 123- 20
15m d e p t h o:1
_ _
,
o:os
RCHOC
~]
r~/~ ~
I0 m
0.3 sec
2
GGUNS u n s in array
,,
V''"" 6m
o:os
depth
o:o~
o-o~s sec
Fig. 2-5. Signatures of a range of seismic sources used in marine seismic. (From McQuillin et al., 1979, Fig. 2/19.)
define a relatively deep structure or depositional feature. Conversely, low frequency energy commonly cannot define shallow information. The characteristics of the input signal are critical in understanding which information can be gleaned from a seismic signal. Figure 2-5 displays several initial sources used commonly in marine seismic gathering. In conclusion, the interpretation of seismic data requires a multi-disciplined approach which may not provide one with the unique solution one would expect. Limitations of seismic method In addition to the general limitations of seismic as discussed above, the application of seismic to carbonate systems seems to have shortcomings that are unattractive to many carbonate modelers. As pointed out by Rafavich et al. (1984), primary lithology and secondary mineralogy have only a relatively small influence on acoustic impedance and seismic velocities. Porosity was found to be the major factor influencing these variables, whereas other variables, including pore-fluid type and petrographic
68 fabric, seem to have little, if any, significant influence on seismic velocities. Rafavich et al. (1984) found that, in addition to porosity, an increase in bulk density also increases seismic velocity. Furthermore, increases in quartz content decrease velocity but have less influence on velocity than does porosity. Changes in calcite, dolomite, anhydrite, and clay content of the rocks can also produce complex relationships with seismic velocity, and depend greatly on burial history. In many regions, such as Little Knife field in the Williston Basin, the pressure effect on seismic velocity was found to be essentially independent of lithology, a fact that further complicated lithologic interpretations. Whereas some statistical approaches, such as examining p-wave to swave velocity ratios, can be used to discriminate between some limestones and dolomites, it appears that seismic alone cannot produce solutions. Additional information, such as well log interpretation and laboratory descriptions of rock samples, are critical to impedance models and, ultimately, to the correct formulation of the carbonate model. Despite all the limitations discussed above, often one can still recognize gross geometries, and thereby, predict presumed changes in lithofacies via the study of carbonate stratigraphy and creation of synthetic models. Synthetic models represent an essential tool for the carbonate modeler, especially where there are complex lithologic, petrophysical and tectonic relationships present. Synthetic seismic traces
Synthetic seismic cross-sections involve the use of well logs, geologic models and acoustic wave theory. Synthetic seismic records are used to predict major geologic features on a seismic section. The greater the understanding the modeler has of the Inteqrated Sonic log
V Io~
Lith. log
1_-1
p log
pV Io~
rI
rl
Itva-rq II
I
II
so,t VELOCITY
RClog RCloq
Composite seismic trace
-t .
[
Fig. 2-6. Diagram showing the hypothetical seismic response to lithologic changes along with pertinent geophysical logs. (From Badley, 1985, Fig. 2.9, after Anstey, 1980.) The symbol V is velocity, t9 is density, and RC are reflection coefficients.
69
I~
Pulse from above (wave length is 200 tt at 10,000 ft/$)
20 ms ~
Velocity, ft]$
10,000
coefficient
--0.0110 0 11,500 IS~
~
",,
13.500
11.500
-,
I
,
,-
,,,q,,,
/
I
\,
S
9.000
12,500
Reflection signal
/ above
~
/
~~#j/
Fig. 2-7. Composition of reflection from series of five interfaces with separations small in comparison to wavelength. Note change in waveform caused by reflection process. Waveforms indicated by dashed lines represent reflections with phase reversal. (From Dobrin and Savit, 1988, Fig. 8-4.)
rocks, theoretically the closer the match between the synthetic seismic sections and the seismic lines. Synthetic seismograms are constructed by determining the acoustic impedances in a rock section, and using these to determine the reflection coefficients at layer boundaries. Normally, density and velocity from which the impedance is derived are measured from sonic logs (Fig. 2-6). Insofar as the resolution of well logs is much greater than that of seismic, these logs are smoothed to minimize noise and reduce the complexity of subsequent steps in the procedure. Smoothing of the sonic log is more pronounced with greater depth. Where density is not directly measured
70 from core samples, it must be determined indirectly from velocity, lithology and depth (Dobrin, 1976). If sonic log velocity is not measured from a well, then empirical relationships can be used to derive it from resistivity and other wireline log variables. Where wells are not available, velocity and density information are estimated directly from the seismic. Velocity can be calculated from observed or modeled normal moveout (NMO) relationships, or by the analysis of the coherence of seismic amplitudes for which a range of velocities have been assumed (Dobrin 1976; Dobrin and Savit, 1988). Estimates of density are usually accomplished either by the modeling of the presumed lithology, or by using empirical relationships which tie density to derived velocity. One such formula used to estimate the density of non-evaporitic sedimentary rock density is: p = 0.23 V ~
,,',~
_
~._ '~,,,,,.',~ ~Di,",
____~, ~
9 0.1
9
l,,,if,,IP,If,'If, '.p ,.btD.D - - ~ t
*-.--
l
~r..
-
'lIIt
1.0
t~ ij~
' ~"
-
0.5
"-
--~I~I!
I ~
~,~;~,~, _:'ff'~,.
1.o
' "~ -'i~,_)1.?!: FtELD SEtSMIC DATA
SYNTHETIC SEISMIC DATA
RE.FLECTIVITY TIME SERtES
VELOCITY LOG
FtELD SEtSMIC DATA
Fig. 2-8. Visual relationship between field seismic data, synthetic seismic data, the reflectivity time series calculated from the velocity log (RC log), and the velocity log itself. (From Dobrin and Savit, 1988, Fig. 8.5, modified from Wood, 1982.)
71 where: p is bulk density, and V is the velocity of P waves through the media. These estimates are generally not as accurate as one would like, but when no other data are available they do represent a usable approximation. Given estimates for velocity and density, acoustic impedance can be calculated for each rock interval. The reflection coefficient is then calculated for each major change in acoustic impedance from this collection of data. This information is usually plotted against two-way travel time (Fig. 2-6) and results in a RC log, informally called a "reflection coefficient tree." These "trees" are as detailed as the modeler cares to make them and represent the raw input needed for synthetic seismic work. The second step in the creation of synthetic seismograms is determination of the characteristics of the seismic wavelet for the energy source that will be used to model the seismic section. For example, if the seismic section was processed with a zero-phase wavelet, then the synthetic must also be processed with a wavelet with similar properties. The reason that similar wavelets are used for both the seismic section and the synthetic is that more accurate correlations can be made between them. Given the proper wavelet reflection coefficient tree, a synthetic trace consisting of the sum of the individual reflections plotted against two-way travel time can be produced. The phase and amplitude of each reflection are determined by the sign of the reflection coefficient and its magnitude. Although there is an amplitude loss in the transmission of a seismic wave through an interface, it is usually assumed that there is none in this procedure (Sheriff, 1977). Consequently, amplitudes of individual events can be related to relative differences between the acoustic impedances of adjacent layers rather than to their absolute magnitude for that depth. The sum of all of these reflections against two-way travel time represents the synthesized seismogram for that well or station (Figs. 2-7 and 2-8). Corrections to the synthetic can then be made by comparing it to the migrated seismic section at that location, and adjusting the assumed model parameters, and then repeating the process. Several adjacent seismic traces can be plotted to form simple synthetic seismic sections in two or more dimensions.
Use of synthetic seismic for modeling The synthetic seismogram is based on an assumed geologic model which is tested by comparison with the recorded seismic. Iterative changes are made to the geologic model untii the best match is made with the seismic. The more well data, the greater confidence one has in identifying a particular depositional facies. Similarly, the greater the amount of seismic, especially on a regional scale, the more confident one is of the geologic model. Geologic models derived from one or only a relatively few seismic traces tend to be suspect. Increased seismic resolution, and advances in seismic signal processing and wavetheory, tied to the use of higher capacity computers, have opened the door to more realistic two-dimensional and three-dimensional synthetic modeling. In these models, factors such as refraction, multiples, and diffractions can be incorporated into the synthetic traces. These more complicated synthetic seismograms are referred to commonly as "wave-theory models." Whereas wave-theory models are usually more
72 computational-intensive, they often provide insight into the geologic information contained within the seismic section. Finally, because of the large number of variables that can affect an individual seismic event, unique interpretations of any one seismic section, whether based on synthetic correlations or well data, are unobtainable. Reasonable interpretations are usually the best one can hope for.
Limitations of synthetics Synthetics have not only the same limitations as seismic, but additional shortcomings as well. For instance, well logs have high vertical resolution and weaker lateral continuity, whereas seismic has generally poorer vertical resolution, but good lateral continuity. To maintain the vertical resolution of a synthetic seismic trace, the best match is achieved by using a heavily filtered sonic or density log (Sheriff, 1977, 1980). Another shortcoming is that correlations are difficult where seismic amplitudes decrease with depth and are distorted by layers of rock thinner than the wavelength of the signal. Additional deficiencies are produced by: (1) filter delays in recording and/or processing of the seismic; (2) the use of different reference data in the CDP stack; (3) phase shifts due to arbitrary choices of initial wavelet waveforms; (4) small systematic errors that accumulate in the creation of the synthetic; and (5) failure to take migration effects into account. A second series of limitations involve the modeling of lithology with synthetics. A seismic reflection is recorded only when there is a change in acoustic impedance from one interval to the next. However, even though there may be no difference in acoustic impedance at a particular lithologic surface, it is sometimes assumed that a reflection is from such a boundary. Despite these limitations, visual interpretation of reflection configurations, when used in conjunction with seismic parameters such as amplitude, frequency, continuity, and interval velocity, can lead to reasonable seismic correlation with well data, and to more accurate recognition of vertical and horizontal sequences on the seismic sections.
CARBONATE PLAY TYPES
Carbonate sheet reservoirs Carbonate sheets are the most common and can be the most widespread and largest of carbonate plays. They are commonly composed of shallow-water shelf grainstones and wackestones, often dolomitized, and are usually associated with shale and evaporite seals. Most of the giant oil fields of the Middle East (Jurassic and Cretaceous), the Williston Basin (Paleozoic and Mesozoic), and the Permian Basin of west Texas and New Mexico (Paleozoic) are developed in sheet carbonate plays and are sealed by evaporites (Fig. 2-9). There are two kinds of sheet shelf carbonate reservoir plays: (1) one which retains depositional porosity, and (2) one which has secondary porosity. These are extreme end-members, and commonly both depositional and diagenetic porosity occur together
73
SHELF SHEET C A R B O N A T E PLAY (hnlP
~haat
Marls &/or IV ~hales
~abkha Evaporites Ir Tidal Flat V Carbonates
High 9
m
oJ
Low
~
_
,
"Grainstones V
HIGHSTAND
Wackestones IV .
.
.
.
.
.
_
-o
-I-I-I.- - _~-_w~§
w~o~
l/larls &/or IV
I.
Im
SIN FAN
.........
Shales IV
I KEY ~~
Limestone ~
----
Shale
~
Evaporit
4
Fig. 2-9. Shelf sheet carbonates include: (1) Grainstone keep-up sheets that aggraded during highstands in sea-level just landward from breaks in slope, marginal to basins that lie below wave-base. (2) Dolomitized leached wackestone keep-up sheets which accumulated in epeiric seas of the continental interior when sea-level was particularly high and formed widespread interior seas.
within the same reservoir. Usually sheet carbonates are associated with shallow-water shelves of the platform interior. The best reservoirs in sheet carbonates are represented by sands that have accumulated behind the shelf-slope break. Sediment types include oolitic grainstones, or more commonly grapestones, and pellet sands with varying quantities of lime mud representing shoaling-upward cycles of tidal flat and
74 lagoonal sedimems. The shoaling-upward cycles often have a shaley, marley, or micritic transgressive unit at the base of the cycle which grades up into grain carbonates, reflecting the higher energy, low subtidal to tidal fiat settings normally associated with the central and upper part of the cycle. The cycles present within a field may be numerous or may be a single event, representing a complete geological stage. The transgressive micritic layers of the next cycle may act as seals, particularly where these are stylolitized (e.g., as in the Bu Hasa Formation of the Bu Hasa Field: Alsharan and Kendall, 1986), and overlie carbonate grainstones. Shales, which occur in an overlying cycle, may be seals to underlying cycles. Alternatively, the cycles may be terminated by prograding upper intertidal to supratidal carbonate muds with or without evaporites. This latter association with evaporites is found in many of the sheet carbonates fields and is important because it may be a seal, particularly as an updip pinchout. Commonly, the depositional porosity may be only slightly modified by some early isopachous cements which surround the carbonate grainstones and local echinoderm overgrowths. Locally, dolomitization of carbonates may occur, and porosity can result from either the leaching of the remaining carbonates or the retention of porosity present before dolomitization. Some carbonates may be completely dolomitized and porosity is developed between individual clear dolomite rhombs. In contrast, dolomite may float in the matrix of sediment and cement of carbonate sediments. These may include some porosity, but probably are not important to reservoir character. The seismic character of sheet carbonate plays is highlighted by the striking continuity of reflectors (Fig. 2-10). Local evaporite pinchouts and porosity changes will show up as changes in the amplitude of the reflectors, some of which thicken and others which disappear. Normally, a higher resolution seismic source and specialized processing must be used to see many of the individual features present in these systems.
Carbonate organic buildups Carbonate organic buildups, i.e., reefs, are the next most common carbonate play and occur on either drowned carbonate shelves (Fig. 2-11) and/or on ramps downslope from platform margins (Fig. 2-12; see also volume 1, Chapter 3). They are commonly sealed by basinal shales, micrites and/or evaporites. Examples of organic buildup reservoirs include reefs in the Upper Devonian of western Canada (sealed by shales and or evaporites); Silurian pinnacle reefs of the Michigan Basin (sealed by evaporites); Pennsylvanian algal-plate buildups of Kansas and Oklahoma (overlain by shale and non-porous carbonates); Paleocene reefs of the Sirte Basin in Libya (enveloped in shale, and in some cases, extremely low-permeability micritic rocks); and Miocene reefs in the South China Sea. Although the petroleum fields associated with carbonate organic buildups are not normally as large as those associated with sheet carbonates, once their seismic character has been established these plays are easy to identify and to drill. Even though encompassing less areal extent than sheet carbonate plays (a few square miles vs. tens of square miles), the organic buildup reservoirs can typically contain enormous quantities of oil.
s.,;
LINE
W-2
~IE
A
I i
.
.
.
.
.
.
.
.
.
.
.
.
L
a
.,
|
, . . ~
1,
,T L . .
~" . .
.
"1~ .
.
"~ . .
.
IK .
"("
""
i
"3.
.
L:3q, E P, EO~EN-
"CF CEET~.'ECU$
.3
;P"l,~r.I k'.,:,Ei(FE
"OP .JF;a.5.~E ~$~'R.E:
kil"-"Ri.J,SS~"
~C Fig. 2-10. Example of sheet shelf carbonate reservoir system in southwest-northeast seismic of Oxfordian carbonates of eastern Saudi Arabia. Synthetic tie-in for wells W-1 and W-2 shown in Fig. 2-15. Note striking continuity of reflectors throughout the section. (From Langdon and Malecek, 1987, Fig. 4.)
76 Shelf Reef
ao
High
Low
III
~V 9
HIGHSTAND WEDGE
BO
III. . II.
"~W STAND t_
WEDGE
SL-}P F_A_N.... FAN
C0
II
[ KEY ]:':':':I Limestone
i Shale I
Fig. 2-11. Give-up and catch-up slope buildups on shallow water back from the platform margin. (a) Shallow water carbonate stillstand wedge, possibly formed during low sea-level stand; (b) Buildups form on irregularities on the shelf at the stillstand following a rapid sea-level rise; (c) Bioherms initially keep pace with the rise in sea-level, and are terminated when the depth of water inhibits the growth of the reefs. Bioherms are later covered by shale deposited as the sea-level rise continues.
Overall, carbonate organic buildups are ideally suited for exploration techniques that use stratigraphic interpretation combined with seismic data geologic modeling. The reason for this is that their bed geometry shows pronounced pinches and swells, and lithofacies usually have strong acoustic contrasts with enveloping strata (Bubb and Hatlelid, 1977). Other potential carbonate reservoirs can be predicted on seismic as well, but often with less success. Carbonate organic buildups form in shallow normal-salinity marine waters, commonly at a break in slope on the sea floor, although some are also found seaward downslope, and others are found landward of this break-in-slope within slightly deeper water of platform interiors and epeiric settings. Buildups have two major forms: (1) either as continuous, elongate bodies parallel to depositional strike of the shelf edge (e.g., barrier reefs); or (2) as a series of isolated buildups which may occur on either side of the shelf break (e.g., mud-skeletal banks, mounds, pinnacles, atolls, and patch reefs) (see volume 1, Chapter 3).
77
Downslope Reef High
Low
ao ......... .
HSTAND .
.
.
.
-~T-_R'ANS-GRESS _H_I,_..
bo II
I VE
......
IN FAN
CQ
Open Lowstand C. Shale Basin
Confined Lowstand Evaporitic Basin
III
] KEY ~
Limestone ~
s
Evaporite]
Fig. 2-12. Give-upand catch-upbuildups downslope from platform margins. (a) Shallow water carbonate stillstand wedge, possibly formed during low sea-level stand. (b) Buildups form on irregularities at the base of the basin margin on small bathymetric highs (possibly downslope fans) during stillstands following rapid sea-level rise. (c) Bioherms initially keep pace with the rise in sea-level, and are terminated when the depth of water inhibits the growth of the reefs. Bioherms are later covered by either: (1) evaporites when small drops in sea-level isolate the basin; or (2) shales as the sea-level rise continues.
Although carbonate organic buildups have several general origins, (e.g., initiated over irregularities on the sea floor either on a shelf or on a ramp downslope from a shelf break), they usually begin local growth following a rapid sea level rise that, prior to the rise, had limited carbonate production. The cause of the sea level rise may be either rapid tectonic subsidence (relative rise) or eustatic. As a further complication, the organisms composing the buildup may also have been stressed by rapid sea level rise or by an increase in nutrients (Hallock and Schlager, 1986; Hallock et al., 1988) so that carbonate production was reduced. However, once a stillstand in sea level was reached, carbonate production was usually able to increase (i.e., catch-up)
78
W.
2 - 31 - I 0 9 - 8 w . 6
7- 32- I09'- 8w6
+
W. I0-27-109-9
+
*
7-32-109-8 2-31-109-6 12-33-,09-8 9
+
9
E. 2-28-109-0
9-24-109-8
+
+
SILTY LIMESTONEUNIT
~
--
--
-
0
- " ~" PRE.CAMBRIAN ..........
--~,~o~~:Ec,:--s
9 KEG
RIVER
2
I
r.--.
3
M,LES
o
i
2
3
4
0
"
,'
5.,
6
KILOMETERS
Fig. 2-13. A. Rainbow field CDP seismic section (east-west) across Devonian Rainbow field, western lauada (from Hriskevich, 1970). B. Geological cross-section across Rainbow field (after Hriskevich, 1970). (McQuillin et al., 1979, Fig. 10/7.) as the growth rates of the organisms responded to the shallower water, and a local shoaling-upward sequence commonly resulted. Organic buildups may have two end-members: (1) composed of foraminiferal-algal assemblages tied to deposition in temperate environments, vs. (2) tropical reefs wherein corals or other colonial organisms like stromatoporids or rudists grew (Simone
79 and Carannante, 1988). Some buildups are resistant to waves, while others are not, forming at or possibly below wave base. In cases where the bases of buildups occur on a downslope ramp, their number decreases seaward of the ramp margin. Buildups in isolated basins like the Michigan Basin (Silurian) sometimes seem to have grown through several phases of carbonate production, interrupted by the deposition of evaporites. The origin of these evaporites is related to lowstands of sea level which caused the isolation of the basin and resulted in hypersalinity. However, basins apparently may freshen as a consequence of periodic influx of normal marine waters several times in their history, and consequently, buildups are subsequently able to re-establish themselves as sites of carbonate accumulation after periods of evaporite deposition. Many times, the evaporites act as seals for potential and discovered reservoirs in such situations. In other cases, carbonate production ceases and instead, shales accumulate which act as sources for, and seals to, encased buildups. The seismic character of organic buildups varies according to their size and enclosing lithologies. In some cases, they are easy to locate and show up as "pimples" that disrupt the railway-like continuity of the seismic response of the adjacent shelf and basinal sediments. In other cases, they are difficult to see and are represented by subtle discontinuities in the adjacent seismic (Fig. 2-13). Buildups can be detected on seismic through the use of CDP (common depth point) flattened to specific geologic horizons. Irregularities in surface sediments and geology interfere with the seismic, but when reflectors are flattened and correlated as widespread horizons, buildups often become more obvious. The Devonian Rainbow field of Alberta, Canada, is an example of using this procedure to highlight the seismic expression of buildups (Fig. 2-13). Thus, through CDP stacking and event flattening in acoustic geophysical data, it is possible to enhance the recognition of buildups.
Carbonate clinoform plays Plays in clinoform carbonate shelf margins (both in the crest and extending to turbidite fans in the clinoform toe) are somewhat rarer than the play types described above and are usually the least productive. Limited production is due to the fact that traps are uncommon along carbonate platform margins, and any hydrocarbons that migrate into them pass through into the updip shelf, thus leaving marginal deposits water-prone (Ward et al., 1986). Fields in this play type may occur along the shelf margin (Fig. 2-14) where: (1) the carbonate margin builds up above the adjacent shelf and basin, forming a topographic high; (2) shelf evaporites extend to the shelf edge and act as seals to trap hydrocarbons in the underlying strata (this situation is not common insofar as evaporites tend to occur farther back from shelf margins); or (3) tectonism elevates the margin above the shelf and basin prior to oil migration. In contrast, hydrocarbon production from the turbidite fans in the clinoform toe is even less common because the porosity of the sediment is usually occluded by a fine matrix of carbonate mud.
80
Clinoformed Margin
KEY iT'~'I'~ Limestone ]
V
HIGHSTAND WEDGE
IV~ANSGRESSIVE
ili-- LO_'STND 'WEDGE .
.
.
.
.
Fig. 2-14. Keep-up progradational clinoform margin plays form during sea-level stillstands (usually highstands but sometimes lowstands). The marginal sediments prograde basinward, and are uncommon during rapid sea-level rises.
Examples of hydrocarbon production in reservoirs deposited in shelf margin slope settings (see volume 1, Chapter 3) are commonly sealed by evaporites, shales or dense micrites. Examples include the Lower Cretaceous clinoform buildups in the Shuaiba Formation of Saudi Arabia and the United Arab Emirates (Bu Hasa Field). The Middle Cretaceous Mishrif Formation of the United Arab Emirates also contains marginal clinoforms with the Fateh Field of Dubai being a premier example. Each of these fields has a shale seal. Other clinoform production occurs in the Midland Basin of West Texas, where Permian San Andres Formation dolomites are productive where they pass updip into evaporites. Margins also produce in the Gulf of Mexico in, for example, the Cretaceous Poza Rica trend in Mexico. Anomalous carbonate reservoirs
Other carbonate reservoirs exist which may be considered by some geologists not to fall within the above classification (see volume 1, Chapter 3). The sheet plays formed by Cretaceous chalks in the North Sea for example, are pelagic limestones wherein primary interparticle porosity and permeability were preserved by
81 overpressuring and a lack of cementation, and were further enhanced by later salt movement which fractured the reservoir rocks (see Chapter 8, this volume). The coincidence of overpressuring of chalk and the movement of salt appears unique to the North Sea. The Cretaceous chalks o f the Atlantic margin o f North A m e r i c a have not
proved productive despite early exploration attempts, and the Austin Chalk in the U.S. Gulf Coast has proved to be almost equally disappointing. Apparently, the preservation of primary porosity and creation of additional permeability have not occurred insofar as the combination of salt movement and overpressuring is missing (Scholle,
1977). RECOGNITION OF CARBONATE RESERVOIRS
The first step in the interpretation of seismic data is to establish the geologic framework of the basin under exploration, and to find any description of existing hydrocarbon fields, lithostratigraphy, and structure from a literature search. This knowledge is combined with available well information and logs, details of relative and eustatic sea level, and any gravity, magnetic or resistivity data available to the modeler. Wells =E ,<: r r
<
0 0 u3 i.u
o9
o0
uJ o0 t.~
_ _
0 -ti-
W-1
ACq
~. PZ
IMPI
ACOUSTIC IMPEDANCE ,, ......
~ - , c m 3 ~,
(ft/sec
TOP JURASSIC TOP JURASSIC
TOP R2 BASER1
TOPRSVR.R2 TOPRSVR.R1 BASER1
,o
= Km
0,
,= Km
Fig. 2-15. Correlation of the 1-D synthetic seismograms to the seismic sections at well sites W- 1 and W2. This figure correlates with Fig. 2-3. (From Langdon and Malecek, 1987, Fig. 7.)
82 are then tied to the seismic lines, and sequence boundaries are identified and related to relative sea level position (Haq et al., 1987; Vail et al., 1977; Vail 1988). A structural interpretation is then made at this time. Individual reflectors and the character of these reflectors within the defined sequences are determined (Fig. 2-15). Depositional models are established from which to infer facies characteristics and to predict carbonate sheet, organic buildup, and/or clinoform margin plays and their hydrocarbon potential. These inferences are based on analogy with producing fields in the basin and at other locations. If more than one seismic line is available, isopachs are made of the various seismic facies in order to interpret depositional setting and expand on models from which to predict potential reservoirs. For the most part, the three major carbonate reservoir systems described earlier occur at different positions within the basin: (1) sheet carbonates occur usually landward of the shelf margin or less commonly on the basin floor; (2) carbonate organic buildups generally occur along the shelf margin itself, although they may occur behind the shelf edge, on the platform, and less commonly, downslope of the margin (Fig. 2-1; see also volume 1, Chapter 3); and (3) basin margin clinoforms occur between the shelf edge and the basin margin. Sea level fluctuations, climate, age, and basin architecture affect the location of the individual carbonate settings, and ultimately, the presence or absence of potential hydrocarbon reservoirs (Kendall et al., 1991). Not only can one use seismic and well data to determine the carbonate stratigraphy of a basin and the occurrence of oil but it is also possible to relate this stratigraphy to the Haq et al. (1987) sea-level charts (Kendall et al., 1991, and Sarg, 1988), aiding the ability to predict the distribution of potential reservoirs and identify prospective areas to be drilled. This is because eustasy, the composition and rates of sedimentation, and local crustal movements control the character of stratigraphic sequences and the facies and diagenetic patterns formed by marine carbonates. Carbonate reservoirs can thus be further classified in terms of sea-level behavior at the time of their deposition. Kendall et al. (1991) classify major carbonate reservoirs as highstand keep-up sheet reservoirs, rapid rise and highstand catch-up and give-up build-up reservoirs, and highstand prograded clinoform margin reservoirs. They associate source rocks with transgressive sediments of rapid rise systems tracts. Data from seismic surveys will usually be the major sources of information on carbonate plays at a drill site. For this reason, the initial interpretation is often speculative and based more on models than on hard data. The test of the interpretation is sometimes a costly program of drilling. Computer simulation of the drill site's sedimentary history is potentially a much cheaper initial test of the interpreted basin evolution. A successful simulation computer program can account for all the relevant parameters that are responsible for the observed stratal geometry. The input parameters to the computer program are the assumptions about sedimentation processes and tectonic evolution of the study area. These assumptions should be based on currently accepted sedimentological, tectonic and eustatic models (Scaturo et al., 1989; Kendall et al., 1990; Lawrence et al., 1990) and not blind creations of the users. The user weighs these parameters according to their interpretation. If the simulated geometries match with the geometries on the seismic lines, then the interpretation is a possible solution. The simulation does not confirm the absolute truth of the interpretation, but constrains its boundary conditions.
83 There are many forward models which simulate sedimentary processes and lend themselves to testing the effects of variations in sea level and tectonic behavior. Some are two-dimensional mixed clastic and carbonate basin fill models (Aigner et al., 1987; Lawrence et al., 1987; Strobel et al., 1987; Lawrence, 1988; Helland-Hansen et al., 1989; Kendall et al., 1989a, b, c; Nakayama and Kendall, 1989; Scaturo et al., 1989; Strobel et al., 1989a, b; Tang et al., 1989; Lawrence, 1990; and French and Watney, 1990). Others are two-dimensional carbonate shelf models which respond to sea-level changes and erosion, allowing redeposition of sediment with user-defined production functions (Dromgoole et al., 1986; Lerche et al., 1987; Bice, 1988; Demicco and Spencer, 1988; Graus et al., 1988; Koerschner and Read, 1989; Spencer and Demicco, 1989; and Bosence and Waltham, 1990a, b). Both of the latter kinds of models respond to sea-level changes and erosion, allowing redeposition of sediment with user-defined production functions. Other two-dimensional simulations handle clastics alone and are used to: (1) create synthetic seismograms for sediment packages by modeling subsidence, sea level, sediment supply and erosion (Turcotte and Willemann, 1983; Turcotte and Bernthal, 1984); (2) use sediment compaction and tectonic movement to provide sedimentation rates for clastic fluvial systems (Bridge, 1975, 1979; Bridge and Leeder, 1979);
Sedpak
.3.0
Frle, a a p c j b a h . c l b
T[mesCep: 2 0 0
MYBP- O . 0 0 0 Mcxirnum An:a per 1DD0 years
1
0.0
Lithology Surface Ratio Plot
100
Left
0-000
Right
i
L
3000.0 I . . . . . . . . . 0.0
I .........
I .........
I .........
!.............. 1 . . . . . . . . . . .
Distance (kin) I~pth-W~dth-I. 20
80.0
~igh $oqievel Low
ss.o
(mtr)-.SDe.(
Fig. 2-16. Computer simulation output matching the geometries seen in the seismic line from the west margin of Bimini Bank in the Bahamas in Fig. 2-17.
84 (3) simulate transport, deposition, erosion and compaction of clastic sediments emphasizing fluid velocity (Paola, 1989; Pinter, 1990; Bitzer and Harbaugh, 1987). Other simulations are one-dimensional and: (1) use defined third-order sea-level curves to infer the origin of peritidal cyclic carbonates (Read et al., 1986; Grotzinger, 1986; Read and Goldhammer, 1988); (2) model the interdependence of sea level, depth-dependent carbonate accumulation and the flexural response of the earth's crust (Cisne et al., 1984; Cisne 1985); (3) handle diagenesis of carbonate as coupled to the eustatic record (Matthews and Frohlich, 1987; Humphrey and Quinn, 1989; Quinn, 1989). Other simulations which might be considered are those of Angevine (1981), Jordan and Flemmings (1989), Flemmings and Jordan (1990) and Slingerland and Furlong (1990), which model foreland basin settings in terms of sediment erosion and fill responding to depositional slope and relief, the rheology of the crust, plate tectonics and thermal subsidence. Finally, there are three-dimensional process models (Tetzlaff, 1986; Tetzlaff and Harbaugh, 1989; Takao et al., 1990). All these various simulations can be used to test responses to sea level variation, tectonic mechanisms that cause regional sea level variations, and whether changes in the regional .stress field are sufficient to produce "apparent" eustatic sea level variations akin to those described by Cloetingh et al. (1985), Cloetingh and Wortel (1986), and Cloetingh (1986). In particular, the mixed two-dimensional clastic/ carbonate simulations can be used to test the occurrence of eustatic sea level events and their effects, for instance, confirming or denying that there may be errors in Exxon's Om -
~....~ ;: ....
-~. -...,.~
.....
-:.,:..-~ .- -- .::
~.~...-- ---_--.~.::,_- ~ . ~ ; "E,~-~.---.'~,~." --'~"'.'. __..~--.
O.S---~.
.... . ~ ' "
1 0 _ ~~. . ~ . . . . . .-. . .~. . .
~
| E
-
.,;~
~
g' ]= ]=
~
~
----__ ~ ~ -
-
-
~
~
~
"
o.s_-
.
prograding s
e
q
.
u
.
e
n
c
.
e
~.
~
.
~
~
;~
9
~
27km
'
~1
~--
~
,
~
- ~
~
/~/Alr ~ ~ - - _ ~ ~ . ~
~ _ ~
.
1~
~
~
~
"
~
-
~
-
-
~ ~
"'~_/7
JAggradation I t.;~ -
I ~m'o-U
.~1 v
~--"~~_ 50
(s)- ~
~.
~~<-~
~---"- ' - - ~ - ~ A g g r a d a t ion ~:~mid-Miocene
~
~
~ .~.___--,,e~.. :r~:=~--,, , 9 "., ~ . , . ~ , , , ~ -~. ENE BIMINI BANK
. . ~....'~ - . . . .
.~. "
( p r o g r a d a l i o n p h u e ~ ~ ~ ~ ~ ~ . j ~ _ _ ~ . j " _..~--_..~ _ ~ ~ . . ~ t i ~
1.o" - - -
=~.,
-~.-
i o ~-"'~" 9 9~ ~ .... .~e~. __-~; ...... (s)_ ~ - ~;---~r'_, ~ ;-- - ~. ~: ~ ) ~ , " ~ " WSW STRAITS of FLORIDA }~l--,-~---Progradation O _ 9 lOkm' "-'-'~_
....
-"
~
~
/fault
- ' _ Z2,.- - -
C).3km=A -----~--~
1.5 km ,
----
- K, cont)
-
Cr.ta.oo, -'--"--
-=~
----_.I. ,v.e.- 7x._
:~shelf edge position
Fig. 2-17. Top: A West-Southwest-East-Northeast seismic section from the west margin of Bimini Bank in the Bahamas (after Eberli and Ginsburg, 1989). Sedimentary sequences are interpreted as a function of sea level (see computer simulation output in Fig. 2-16). Bottom: Cross section showing changing slope angles and tracing progradation of margin.
85 coastal onlap charts, particularly the chronology of fluctuating sea levels since the Triassic as described by Gradstein et al. (1987). Figure 2-16 illustrates an example of simulation of a seismic line from the Westem Bahamas (Eberli et al., 1990). The authors proposed that variations in eustatic sea level exerted an important control on the sedimentary sequences, and they related pulses of progradation to these sea level events. They used a sequence stratigraphic approach to seismic interpretation and used a defined sea level chart (Haq et al., 1987) to date the seismic reflectors (Fig. 2-17) (Eberli and Ginsburg, 1989). In the simulation of the seismic lines they took the sea-level curve of Haq et al. (1987) as given, and varied such parameters as rates of carbonate accumulation and tectonic movement. These parameters are known to influence carbonate platform evolution; however, not all of them are quantitatively determined. The interactions of these parameters and the assumptions can be evaluated in the simulation. Because Eberli et al. (1990) chose to use the Haq et al. (1987) curve as an input parameter for the sea level curve, the simulation of the GBB seismic lines not only tested their interpretation but also tested the sequence stratigraphy concept. They were able to test their model which proposed that third-order sea-level fluctuations were responsible for the pulses of carbonate progradation. Carbonate deposition was simulated over 60 ma. to reproduce sequence geometries seen on the seismic section. TABLE 2-1 Controls on carbonate productivity, deposition, and reservoir development System
Basin and slope
Major processes
Major facies
Plays
(Gravity and current dominated)
A. Pelagic and benthonic sediments B. Carbonate turbidites C. Carbonate debris flows
Chalks Clinoform toe Clinoform toe
D. Downslope buildups Buildups (Wave dominated) Platform margin
(Current dominated) Platform interior
Terrestrial
A. Framework reef bodies and other organic buildups B. Carbonate sand: a. Bioclastic b. Nonskeletal C. Carbonate mud and silt A. Patch reefs and mounds B. Subtidal epeiric sea, lagoon and/or bay sediments C Tidal fiat sediments A. Soils B. Dunes C. L a k e s - fresh and saline sediments D. Fanglomerates E. Cave deposits
Clinoform crests Clinoform crests
Buildups
Sheets
86 SEISMIC CHARACTER OF CARBONATE SYSTEMS
Carbonate facies and their geometries are predominantly the product of processes acting in the depositional setting (Table 2-1), and it is therefore possible to group these facies on the basis of depositional settings (Table 2-1 and Fig. 2-1). These settings occur in the basin, on the shelf margin, and the shallow shelf, commonly in association with terrigenous systems. It is because the basic basin configuration can be identified from seismic, and that within that basin configuration the geometry of carbonate bodies can be identified, that we can predict the potential occurrence of carbonate plays.
Basin and slope With the exception of chalk, carbonate plays are not common in basin settings, whereas on the slope they are found as downslope mounds and in the toe of clinoforms. The facies of the basin and slope are primarily a product of: (1) pelagic sediments in the water column which settle out to produce laterally extensive units with great continuity of bedding; and (2) turbidites and debris flow deposits from the basin margin which have less continuity. Carbonate plays which are the commonest in this setting are toes of clinoforms and downslope organic buildups. The geometry of the different sedimentary facies, and the associated plays, can be recognized in the seismic.
Pelagic sediments Pelagic calcareous sediments commonly accumulate below depths affected by NNW SP 0 ,
lP?
SE 500 ,
--.....
I000 ,
1500 i
0
25
2000 ,
f.
2500 i -0
V E ---"lOX
fK? V.E.~5x
M~E VE.--'3X
Fig. 2-18. Sequence of reflectors in a north-northwest--southeast seismic section showing Cretaceous and Paleogene basinal deposits which thicken in a southeast direction toward the anticline. TP = top of Paleogene; TK = top of Cretaceous; TLK = top of lower Cretaceous; MKE = inferred mid-Cretaceous event. Note changes in vertical exaggeration with depth. (From Ball et al., 1985, Fig. 5.)
87 wave action. They often collect along margins of shelves and platforms, and extend basinward into areas below the photic zone. Bedding is uniform and usually thin (510 mm, rarely much thicker than 1 m). Bed character is the product of gravitational settling, the dominant mechanism of deposition for this group of sediments. Bedding surfaces are planar to nodular, and sets of beds commonly are continuous over wide areas. As one moves toward a basin margin, the autochthonous sediment derives some of its character from the nature of the sediments upslope on the margin, and sometimes from the shelf itself (e.g., allochthonous components). Beds generally thicken toward this margin. The seismic response of basinal sediments reflects the character of the bedding and is commonly a series of quite continuous reflectors which thin toward the basin and thicken toward the basin slope (Fig. 2-18). Due to the higher density of these sediments, the reflections are generally well-defined when first encountered in the subsurface. Because pelagic deposits are often quite extensive, they can act as carbonate sheet reservoirs. The planar to nodular bedding can preserve porosity and constrain lateral migration of any hydrocarbons. Near the basin margin, the allochthonous material supplied from up-slope is deposited in graded beds, which may also preserve porosity and create a good reservoir character. However, this is unusual and is a high risk play in the toe of the clinoforms.
Turbidites and debris flow Basinal sediments shed from shelf margins include turbidites and debris flows. Close to platform margins, carbonate turbidites form irregular ribbons of channel-fill that are commonly deposited normal to depositional strike. Farther from margins, the turbidites form fan-shaped wedges (e.g., submarine fans) composed of evenlybedded sheets. Bedding in turbidites varies from thin to almost massive, and is irregular and discontinuous. This character reflects channel-fill and levee deposition on submarine fans. Bases of beds are contour-fills over the scoured upper surfaces of previously deposited beds. Sediment composition and grain size are extremely variable, and may include a wide range of shallow to deep water (e.g., allochthonous and autochthonous) material. Distal turbidites are characterized by regular and planar bedding, and these carbonates are commonly interbedded with marls and shales. The seismic character of these sediments is expressed by discontinuous and quite heterogeneous reflectors which are mounded and channeled, particularly close to basin margins and slopes (Fig. 2-19). Carbonate debris flow deposits are characterized by wide varieties of carbonate lithologic types and sizes of angular fragments with anomalously oriented stratification. Debris flows include megabreccias composed of blocks, which may be larger than 25 x 30 m in cross-section, floating in an enclosing matrix of lime or terrigenous muds and sands. Debris flows vary from lens-like or ribbon channel-fills, to irregular beds that are adjacent locally to carbonate basin margins. Some megabreccias are associated with high relief, active tectonism, or steep slopes, whereas others are the result of pervasive bioerosion, submarine dissolution of fore-reef carbonates by fleshwater springs, or oversteepening of platform margins. Debris flows have often been misinterpreted as shallow water conglomerates, in-situ bioherms, organic mounds,
88 LINE
H79-10
I km
MEDA 2
I
I
/~ I
9
~v,.m.,.m-,
""
.
9~ m w - , . ~ P I l ~
"
" b
' ""
"
,,,
"
'
m~,
. ~9. . . .
j
"~"........ ' ~ : ; 9, , . b ,
" ',.." ....--
.'
..
-
9 m.~"l"
:.
9~
.
.
.
.
~"
.-,-~.
.ak~ Ik~. ~ ; . . . o ~ . ~
.
9
~
-
9
~~'~
"P
p9
,,
.
,
m
~._..~.,,
"--. ~ , ~ .
,,.-"7.
--.~
~
':,l
~.l,~
""
rl~jJL.
I~
':"~""
~
. . . . .
-
,
9 . j
,, I ~'~*
" ~ -
w p , , , m ~ m m . l , , a . ~ m . n m ~ am
j,i)~
~'
,.
J~
-b
,-
' - ~ ' ~ m ~ P ' - ~ ~ ' .
~
,,' , ' '. -, ,-, ," i,l~,,.
-
9
::.
,.:r...
'
,
I.9
"_~_~:_L.
- -
.~r~,
o~,n,~,,~, ,~'"
_ , , , , c. ,". . P' , , - l ~ l ) ~ , , : b ~ o"
i l l ,.
1o
.~~',7-
_.--
;ink i
'
..,.:---:_rr'.~..~.~_~
~ ' , ~ b - , ~ ."-,"
. . . . ."..--",.2.'_--"L1."/.:.'--_,_~mab,~""
-
~,-,,.~';.:d;.''"
-
n,,,.-,a ;r
P
~ "
I -
.- : |
- _,~, ~ '
NE
,
~lla,~,
:~
~
I
~ t~
....,..~, .....
. ~ , ' ~_ . m , ., -~ l . , ,..- , :~~: ' '- "." , ~
....
1.1
~
." r ~ _ - r ~ " - ,
*~
.
-
- "
....
1.2 -
1.~
--1.4
"'..Jk 9 ,~11~,1.11
"'
Fig. 2-19. Top: Interpreted southwest-northeast seismic section (Line H79-10) showing reflectors from distal turbidite-submarine fan deposits from the northeast. Note mounding and channeling in the vicinity of the well. (Vertical scale in seconds). Bottom: Uninterpreted seismic section from above. (Vertical scale in seconds). (From Middleton, 1987, Fig. 10; Upper Devonian of Canning Basin, Western Australia.)
and reef talus, and are probably much more widespread than previously thought. See volume 1, Chapter 3, for details of reservoirs in pelagic deposits, turbidites, and debris flows. The seismic character of debris flows is such that the continuity of the reflectors varies tremendously, and, in some cases, the pinching and swelling of reflectors is so great that some of the geometries resemble downslope bioherms and organic buildups
89
LINE
2488
Northeast
-.-,.
16o, ._.. ----.----.
,, O ' r
--'----. --. .-_.--....._
_
..--.
,,.
_.~ ...
p I,,OIPll
1609
--2.5 0
a.u~otu41e OhOIO
Ct)
--......
"-3.0 $NALI[
PLATImOIM 9D l o r
SEDIMENTS
oMllmwouo I o I IIIlll~o I * kmCrOIOO0
LINE
2488
Northeast 1603
~ ~~_ 1609
O O~
Fig. 2-20. Top: Illustration of the seismic character of a detrital facies. Bottom: Series of debris flows expressed as high-amplitude, concave-upward reflectors on the slope of a southwest-northeast bypass margin in the Tertiary Terumbu Carbonate, South China Sea, Indonesia. Pinching and swelling of geometries resembles downslope buildups. (From May and Eyles, 1985, Fig. 21.)
(Fig. 2-20). Often, no internal reflections are discernible in such deposits. The graded bedding associated with both turbidite and debris flow deposits can have the kind of primary porosity necessary for a reservoir in carbonate sheet plays, but this is not common because lime mud is usually the matrix of these sediments. Various diagenetic effects can enhance this porosity (e.g., dissolution) or destroy it (e.g., cementation). The pinch and swell geometries can confine the lateral migration of any hydrocarbons.
Downslope buiMups These sometimes occur at the base of basin margin slopes (Fig. 2-12), as in the
90
Fig. 2-21. A northwest-southeast seismic section through porous Jurassic Smackover reef on the U. S. Gulf Coast. The reef, indicated by amplitude anomaly (loss of seismic character) is located on the upthrown block of a down-to-basin fault. (From Baria et al., 1982, Fig. 29.)
Shuaiba Formation of the United Arab Emirates. The buildups (i.e., reefs) form on small bathymetric highs during highstands. Buildups usually begin with a pioneer community associated with a mud mound seaward of the platform margin (Hassan et al., 1975; Alsharhan, 1985a and b). As this community becomes established, the rate of sedimentation accelerates as organisms trap and precipitate more carbonate. Eventually, the buildups reach sea-level and often a diverse wave-resistant fauna and flora develops with resistance to erosion (Hassan et al., 1975; Alsharhan, 1985). The seismic character of downslope buildups show reflectors tend to lose continuity and, in many cases, the carbonate margin is reflectionless, probably a product of the lack of acoustic contrast in these features (Fig. 2-21). Geometrically, the reflec-
91
A
A'
0-1- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .___ . . . . . . . . . . _. .
.... - :
,~.-
~
..:..... ~ , e .
_
_
T
0
,..,~,..~.~'r~l-. 2
7
5
V.F..x3
Fig. 2-22. An east-west seismic line from offshore west Africa. Note the Jurassic margin shown by sequence J3.1. The margin (on the west) loses reflection character but has relief above the lagoon and back reef.
tors that enclose the carbonate margin may bow up, tracing a tendency in the margin carbonate to thicken and have higher relief than the adjacent back reef or lagoon (Fig. 2-22). Unfortunately, velocity anomalies associated with the dense, bank-edge carbonates often cause the same effect. Anomalous thickening is also sometimes a response to early marine cementation of the basin margin which inhibits local compaction; whereas the back reef, lacking cement, is reduced in thickness by the loading of the overlying sediment (Playford, 1966). The vertical relief of downslope reefs commonly matches the depth of water on the slope and, because these reefs are common to restricted basins where small falls of sea-level can isolate a basin and initiate evaporite sedimentation, reef growth is frequently interrupted by the basin drying-up. For this reason, evaporites often act as seals to these plays. The best quality plays usually occur in the uppermost fringe of the reefs, where waves have winnowed lime mud from the carbonates that accumulated there. However, diagenesis can be quite severe because the crest is subject to subaerial exposure. Dolomitization, leaching and evaporative replacement are common. Thus both reservoir enhancement and destruction can be found in these buildups as a result of diagenesis.
Platform margin The reefs, mud-skeletal banks, and atolls of the platform margin comprise the organic buildup or clinoform plays described above. Some carbonate sheet plays occur
92 close to the margin and are represented by the sand shoal facies.
Barrier reefs and mud-skeletal banks Reefs that form a barrier on the shelf margin tend to be massively bedded but may contain associated discontinuous thin beds of coarser-grained sediment. Reef geometry is expressed as thick sheets or ribbons which parallel depositional strike. Reefs through geologic time have been built by a variety of calcareous organisms including corals, stromatoporoids, calcareous sponges, algae, and rudists (James and Ginsburg, 1979), but there have been times when lime mud banks and mud-skeletal banks have been the dominant break-in-slope buildups (e.g., during the Pennsylvanian). These mud-skeletal banks are elongate massive bodies that formed both parallel and normal to the seaward edge of the platform margin. They range from knoll-like mounds of a few square meters to massive linear belts trending for hundreds of kilometers along depositional strike. The thickness of the banks varies from 1-100 m or more. Beds may be thick to massive and range from horizontal to clinoform (see volume 1, Chapter 3). Reef and mud-skeletal banks are best developed where open marine waters shoal against the platform margin. The slope of the sea floor on which the buildups grew may have been controlled by antecedent topography, by faulting, or by the juxtaposition of active shallow-water accumulation and deeper water basin starvation. The major sub-environments for barrier reefs and mud-skeletal banks are the reef frame (the reef crest and reef wall), reef apron (fore-reef), back reef, and leeward barrier islands (sand cays). Reefs act as a sediment source to areas both landward and seaward of them. Reefs and barrier margins usually occur at a break-in-slope along platform margins, where waves once broke. They usually are discontinuous but, in some cases, are locally continuous bodies that parallel depositional strike and are sometimes part of a thick sheet of carbonate that may be overprinted by clinoforms that prograded upsection. Sediments that form at a break-in-slope may be reefal and formed by colonial organisms, or they may be dominated by lime mud or silt (e.g., mud-skeletal banks). The geometries and seismic character of both reefs and mud-skeletal banks are similar. Both beds and reflectors thicken toward the break-in-slope and, in many cases, lose character and disappear. Beyond the break-in-slope, bedding and reflectors pick up again, thin gradually, and then have a uniform thickness across the shelf. Many reefs and mud-skeletal banks accumulate at breaks-in-slope (both in outcrop and on seismic sections) and thicken locally to take on lens-like geometries seaward. In contrast, others show a clinoform geometry. Internal reflection geometry is usually absent to chaotic. However, whereas these features are extremely easy to identify on seismic it is difficult to identify dip seals seismically. It is also extremely difficult to locate prospects along shelf margins, particularly because most margins are waterprone. See volume 1, Chapter 3 for details of reservoirs in these facies types. Reef aprons are composed of debris derived from platform-margin facies (generally reef frame and in-situ fore-reef). In general, most pre-Holocene reef aprons slope between 10-30 ~ into the basin. Beds upslope become irregular and massive, whereas downslope they thin to between 5-10 cm and eventually become more constant in thickness. A general rule of thumb is that the steeper the reef apron slope, the greater
_INE 25
West
0.0
-
10
.
,
3 A N YI / A - ~ rK k
L
Palembak monoci~
!~_xu,e . ~
.
(Orolllr : I
SHELF
D/'~I~I
o r l r L r
East
(12) I .
.
.
.
.
.
.
'
Carl)ol'~ |~ 13dnk -'-~ I I , ,/I
I
I
,
~inClkel ( 1 3 )
J
. . . . "., ~
:t _
30--~
;
"
~:~,
iaepc
~~ .~:-:'~
~..~:~.-"a
4.0-
s.o-"-
.~ o
2
4
s
o
km
Fig. 2-23. East-west seismic section showing seismic mounded facies from carbonate buildups on the Banyak shelf of the South China Sea. Note discontinuity of reflectors as they approach the buildup labeled 2a. Numbers denote base of sequences. (From Beaudry and Moore, 1985, Fig. 11.)
94 ~.-2 .iooooo,,.Noooo:ou,o. o...o ,v.l.,,.:,~...~:.,,.o,.o~.~,.'.~..~~ ......'.,...~mv;,,.::gv~..;.~ .; ............. .... ,,l:;";' .............. ::: ..... :': ":r'"".'l~'~.oo....OlOO._O,jt..~,di.jj~q,a~o~~U~~le~.t.j~~l.;~~o._o ............... b: j ""' ........ oj ,,,,.-.i j. 9.ol.......ap " o.~. "~2|:,l~ ;l~.,.. ~lJ~176176 io~,..oo.:l,,,,o../,,op N .
.
.
km--~ ~ooo
0 t oop
.
Fig. 2-24. Two patch reefs in the Etosha Basin of Southwest Africa. "C" denotes the carbonate portion of the section. "B" is the base of the reefs. Note the mounded character of the continuous reflectors. The arrows below the section indicate the lateral extent of the reefs. (From Sheriff, 1980, Fig. 5.15.)
the chance that it was syndepositionally marine-cemented, and is composed partly of slumped cemented and brecciated debris derived from the upper slope and reef crest. The most precipitous Quaternary and Holocene fore-reef slopes owe most of their major topography to pre-Holocene antecedent topography. Similar fore-reef cliffs occur in the Upper Devonian of the Canning Basin in Australia (Playford, 1966), portions of the Mesozoic margin of the U.S. East Coast (Morgan and Dowdale, 1983), and Paleozoic margins in Greenland (Hurst, 1980). The seismic character of the fore-reef apron is of a series of quite continuous reflectors that converge away from the reef crest into the basin and diverge into the reef, where they lose their continuity (Fig. 2-23). The amplitudes of the reflections can be quite variable. Back reef patch reefs tend to be massive and lens-like, while the adjacent back reef sediments are widespread and sheet-like. Beds have heterogeneous lithologies and vary in thickness but are quite continuous. This shows up in the seismic, so that the result is seismic lines which exhibit more continuous reflectors with varying amplitudes (Fig. 2-24). Pinnacles and atolls Pinnacles and atolls are formed in response to relatively rapid sea level rises, and/ or relatively rapid subsidence, at times when only local carbonate production manages to keep pace with the sea level rise. These features differ from shelf-edge reefs in that they have more symmetrical geometries and have relatively less orientation with
95 respect to wave and wind directions (see volume 1, Chapter 3). Pinnacle reefs and atolls are usually localized on the floors of shallow, more isolated epeiric basins, seaward of the crest of the basin margin on downslope ramps, or landward of the margin on back reef shelves. The pinnacles and atolls, wherever they occur, are usually localized on highs, formed either by: (1) previous karst topography or some other local irregularity that caused waves to shoal and break, or (2) focused swift tidal currents and encouraged biological opportunism. Core facies of these bodies are generally massive to thick bedded, whereas flank beds are thin and irregular. Changes in texture tend to radiate outward from the core of such buildups. The seismic character of these buildups show: (1) a local thickening of reflectors; or (2) interruptions in the continuity of the seismic (Fig. 2-23) where the buildups are thin and are at the edges of seismic resolution. The internal character of these features can vary greatly.
Sand shoals Carbonate sand accumulations (see volume 1, Chapter 3) can commonly extend from near the seaward edge of banks, platforms, and shelves to back onto the shelf as carbonate sheet plays which have potential reservoir sizes of enormous proportions. Individual beds have continuity that may extend over several miles along strike and normal to it. The beds vary in thickness and lithofacies content. The consequent seismic character for these sediments is shown by continuous reflectors which have quite good continuity, especially those interbedded with evaporites or dense shales (Fig. 2-25). In some cases, the reflectors stretch across the seismic sections like railway lines. Where relatively thin beds occur with increasing depth, only a few internal random reflections are observed. It is because these sheet plays fall between the shelf interior and the platform margin that we consider them here under "Platform Margin." They could equally be called "Platform Interior" facies.
Platform interior The platform interior facies are a primary site for carbonate sheetplays, though organic buildup plays can occur here too.
Epeiric sea, lagoon or bay These depositional settings, protected by wide shallow seas, reefs, or mobile carbonate sand barriers, are characterized by continuous wide sheets of carbonate sediment. These sediments either formed in situ or were locally transported from a seaward barrier by the action of waves and currents. They are well-bedded, have a wide lateral distribution, and contain variable lithofacies, though they are more homogeneous than the immediate backreef sediments. The seismic character of these rocks is very similar to that of the backreef sands discussed above. Where these sediments are dolomitized they can form extensive carbonate sheet plays as do the tidal fiat settings discussed below. An example of this kind of play is the Lower Cretaceous Lekhwair Formation which is an important exploration objective in eastern Abu Dhabi, and contains oil and gas in one or several of its porous members. The porous grain
96 0..~0
0.1 b
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 Fig. 2-25. East-west section from the Mississippian "Chat", Mid-Continent U.S.A., showing local disappearance of generally continuous reflectors where tidal flat deposits include large lenses of evaporite minerals, chert or porous dolomite. K.C. = Kansas City; B/K.C. = base of Kansas City; Miss. = upper Mississippian boundary. (From Thomasson et al., 1989, Fig. 9.)
carbonates of the Lekhwair Formation appear as low velocity events on sonic logs and increase in thickness upwards.
7 da/flats Tidal flat sediments include those forming in the intertidal and the supratidal zones (Fig. 2-25). Sediments range from carbonate sands to muds, often dolomitized, and commonly contain algal stromatolites as well as other carbonate producers. Tidal fiat sediments occur as local wedge-shaped sheets, often widespread, that are usually dissected by channels (see volume 1, Chapter 3). Bedding is thin and even, and contacts are even and sharp. Locally, evaporitic minerals and beds are present and are represented by irregular bedding which may be nodular. Collapse breccias formed after evaporite dissolution tend to parallel depositional strike and are local in extent. The occurrence of much of the oil in the Jurassic rocks of western Abu Dhabi, Qatar and Saudi Arabia is related to this kind of tidal fiat carbonate sheet deposit and the presence of the Hith Anhydrite, which traps the hydrocarbons in these rocks (Alsharhan and Kendall 1986). Similar plays occur in the backreef shelf of the Permian Reef in New Mexico and West Texas (Ward et al., 1986).
97 The seismic character of these rocks can show quite continuous reflectors (Fig. 225), but locally these may lose intensity and disappear in response to the occurrence of the evaporite beds.
Terrestrial Terrestrial sediments include dunes, soils, lake sediments, and fanglomerates. Normally (except in a few rare instances), these types of deposits generally are not targets of hydrocarbon exploration. Dunes and soils are not commonly seen on seismic sections (for an exception, see Steeples and Miller, 1988), but lakes and fanglomerates can be recognized, and can contain carbonate sheet plays from terrestrial settings. These latter types are not common.
Lakes and fanglomerates Lakes may be present in fault-block intermontane basins or on delta plains. Carbonates may accumulate in the lakes if terrigenous influx is low and climatic conditions are favorable. The deposits vary from localized thin sheets of individual lake origin to widespread and complex sequences of beds related to stacked lakes, especially common in some rift valleys. The seismic character of lake sediments is variable, but in larger ancient lakes, seismic reflectors have considerable continuity. Local thickening and thinning of reflectors is common, particularly towards lake margins (Fig. 2-26). Fanglomerates are usually found on the down-thrown sides of faults in arid regions. The deposits are fan-shaped wedges formed of braided stream and sheet-flow deposits. The seismic character of fanglomerates is such that seismic continuity of reflectors is variable, thickening away from lake and valley centers. The continuity of internal reflectors is poor but, depending on circumstances, boundary reflections can be quite sharp. LINE
E
Jr-O-
- - ~,B-VS-
210
...........
BFS/ / / 1
i
~ ..
;:2
.r
~--~.~
N ~ _ ~ :
..,~
-
.
.__
-..
~ ,_
,:.!~.~.,..~. ~
...-~.,
~. . . . . . . . . .
~_-y,,
__
9"
~
- -~"-~
.......................
.
~
:.
.
-- ~
~
~
~
~
':
. . . . . . . . . . .
_
J
r E - 3 1
I
Fig. 2-26. East-west seismic section (Line 78) from Lake Tanganyika showing its relationship to rill geometry. Note continuity of reflectors in lake and splayed sediments influxing from the margin to the west. INAZ (interference accommodation zone) refers to the linkage of half-grabens, appearing as a topographic high (see Scott and Rosendahl, 1989, for discussion). (After Scott and Rosendahl, 1989, Fig. 8.)
98 SUMMARY AND CONCLUSIONS
Seismic interpretation of carbonates involves the use of well data tied to the seismic sections being interpreted. Three major carbonate play types can be recognized on seismic sections. These are sheets, buildups, and clinoform margins. These can be identified as part of a continuum of sedimentary facies and geometries that can be traced from basin to shelf. The basin margin is marked by continuous reflectors that thicken toward the slope. The slope is marked by reflectors that dip basinward and thicken updip to a reflectorless area at the basin margin crest. The shelf is marked by continuous railway-like reflectors which locally thin and thicken at facies changes. The seismic character of sheet plays matches that of the character of the seismic of shelf sediments; the buildup plays' seismic character are the pinch-and-swell features; the seismic of the clinoform play shows en echelon seismic wedges that reflect the progradation of basin margins. In addition to seismic and well data, the carbonate stratigraphy of a basin can be related to the Haq et al. (1987) sea-level curve. This is because eustasy, the composition and rates of sedimentation, and local crustal movements all control the character of marine carbonate sequences and their facies and diagenetic patterns. Major carbonate reservoirs can be classified in terms of sea-level behavior at the time of their deposition as: (1) highstand keep-up sheet reservoirs, (2) rapid rise and highstand catch-up and give-up buildup reservoirs, and (3) highstand progradational clinoform margin reservoirs. Associated source rocks match sediments of transgressive, rapidrise systems tracts. Computer simulation of carbonate accumulation can test seismic interpretations of these plays. The input parameters to such a simulation are assumptions about carbonate rates of accumulation, sea level history and tectonic evolution of the study area, and are based on currently accepted sedimentological, tectonic and eustatic models.
REFERENCES Aigner, T., Doyle, M. and Lawrence, D.T., 1987. Isostatic controls on carbonate platform development. Bull. Am. Assoc. Petrol. Geologists, 71: 524. Alsharhan, A.S. and Kendall, C.G.St.C., 1986. Precambrian to Jurassic rocks of Arabian Gulf and adjacent areas: their facies, depositional setting and hydrocarbon habitat. Bull. Am. Assoc. Petrol. Geologists, 70: 9 7 7 - 1002. Angevine, C.L. and Turcotte, D.L., 1981. Thermal subsidence and compaction in sedimentary basins: application to Baltimore Canyon Trough. Bull. Am. Assoc. Petrol. Geologists, 6 5 : 2 1 9 - 225. Anstey, N.A., 1980. Seismic Exploration for Sandstone Reservoirs. International Human Resources Development Corp., Boston, MA, 136 pp. Badley, M.E., 1985. Practical Seismic Interpretation. International Human Resources Development Corp., Boston, MA, 266 pp. Ball, M.M., Martin, R.G., Bock, W.D., Sylvester, R.E., Dodd, J.E. and Gilbert, L., 1985. Seismic structure and stratigraphy of northern edge of Bahamian-Cuban collision zone. Bull. Am. Assoc. Petrol. Geologists, 69:1275 - 1294. Bally, A.W. (Editor), 1983 and 1984. Seismic expression of structural styles - a picture and work atlas. Am. Assoc. Petrol. Geologists, Studies No. 15, 3 volumes. Bally, A.W. (Editor), 1987-1989. Atlas of Seismic Stratigraphy. Am. Assoc. Petrol. Geologists, Studies No. 27, 3 volumes.
99 Baria, L.R., Stoudt, D.L., Harris, P.M. and Crevello, ED., 1982. Upper Jurassic reefs of Smackover Formation, United States Gulf Coast. Bull. Am. Assoc. Petrol. Geologists, 66" 1 4 4 9 - 1482. Beaudry, D. and Moore, G.F., 1985. Seismic stratigraphy and Cenozoic evolution of West Sumatra forearc basin. Bull. Am. Assoc. Petrol. Geologists, 69: 7 4 2 - 759. Berg, O.R. and Woolverton, D.G. (Editors), 1985. Seismic Stratigraphy I I - An Integrated Approach. AAPG, Memoir 39, 276 pp. Bice, D., 1988. Synthetic stratigraphy of carbonate platform and basin systems: Geology, 16:703 - 706. Bitzer, K. and Harbaugh, J.W., 1987. Deposim: A Macintosh computer model for two-dimensional simulation of transport, deposition, erosion and compaction of clastic sediments. Computers and Geoscience, 13:611-637. Bosence, D. and Waltham, D., 1990a. Computer modeling the intemal architecture of carbonate platforms. Computers and Geosciences, 10:10 - 20. Bosence, D. and Waltham, D., 1990b. Computer modeling the internal architecture of carbonate platforms. Geology, 18: 2 6 - 30. Bridge, J.S., 1975. Computer simulation of sedimentation in meandering streams. Sedimentology, 22:3 43. Bridge, J.S., 1979. A Fortran IV program to simulate alluvial stratigraphy. Computers and Geosciences, 5:335 - 348. Bridge, J.S. and Leeder, M.R., 1979.A simulation model of alluvial stratigraphy. Sedimentology, 26:617 644. Bubb, J.N. and Hatlelid, W.G., 1977. Seismic stratigraphy and global changes in sea level, part 10: Seismic recognition of carbonate build-ups. In C.E. Payton (Editor), Seismic Stratigraphy - Applications to Hydrocarbon Exploration. AAPG Memoir 26:185 - 204. Cisne, J.L., 1985. Depth-dependent sedimentation and the flexural edge effect in epeiric seas: measuring water depth relative to the lithosphere's flexural wavelength. J. Geology, 93:657 - 576. Cisne, J.L., Gildner, R.F. and Rabe, B.D., 1984. Epeiric sedimentation and sea level: synthetic ecostratigraphy. Lethaia, 17:267 - 288. Cloetingh, S., 1986. Intraplate stresses: a new tectonic mechanism for fluctuations of relative sea level. Geology, 14: 6 1 7 - 6 2 0 . Cloetingh, S. and Wortel, R., 1986. Stress in the Indo-Australian Plate. Tectonophysics, 1 3 2 : 4 9 - 6 7 . Cloetingh, S., McQueen, H. and Lambeck, K., 1985. On a tectonic mechanism for regional sea level variations. Earth and Planetary Letts., 75:157 - 166. Coffeen, J.A., 1978. Seismic Exploration Fundamentals. Penn Well Publishing Co., Tulsa, OK, 277 pp. Demicco, R.V. and Spencer, R.J., 1989. MAPS - a basic program to model accumulation of platform sediments. Computers and Geosciences, 15: 9 5 - 105 Dobrin, M.B., 1976. Introduction to Geophysical Prospecting. McGraw-Hill Book Co., New York, 630 pp. Dobrin, M.B. and Savit, C.H., 1988. Introduction to Geophysical Prospecting. McGraw-Hill, New York, 867 pp. Dromgoole, E., Kendall, C.G.St.C., Lerche, I., Scaturo, D. and Walter, L.M., 1986. Simulation of carbonate depositional response to nutrient supply, sunlight, temperature, salinity, oxygen, sea level and tectonism. Bull. Am. Assoc. Petrol. Geologists, 70: 584. Eberli, G.E and Ginsburg, R.N., 1989. Cenozoic progradation of Northwestern Great Bahama Bank, a record of lateral platform growth and sea level fluctuations. In: J.L. Wilson, E Crevello, J.F. Sarg, and J.F. Read (Editors), Controls on Carbonate Platform and Basin Development. SEPM Spec. Publ. 44: 339-351. Eberli, G.E, Kendall, C.G.St.C., Perlmutter, M., Moore, E, Cannon, R., Biswas, G. and Bezdek, J.C., 1990. Simulation of the response of carbonate sequences to eustatic sea level changes (Tertiary, northwest Great Bahama Bank). Bull. Am. Assoc. Petrol. Geologists, 74: 647. Flemmings, P.B. and Jordan, T.E., 1990. Modelling sedimentary sequences in clastic sedimentary basins. Bull. Am. Assoc. Petrol. Geologists, 74: 654. French, J.A. and Watney, L.W., 1990. Computer modeling of Mid-Continent cyclothems and its application to the prediction of hydrocarbon reservoirs. Bull. Am. Assoc. Petrol. Geologists, 74: 657. Goldhammer, R.K. and Harris, M.T., 1989. Eustatic controls on the stratigraphy and geometry of the Latemar buildup (Middle Triassic), the dolomites of Northern Italy. In: P.D. Crevello, J.L. Wilson, J.F. Sarg and J.F. Read (Editors), Controls on Carbonate Platform and Basin Development. SEPM Special Publication, 44: 3 2 3 - 338. -
100 Goldhammer, R.K., Dunn, EA. and L.A. Hardie, 1987. High frequency glacio-eustatic sea level oscillations with Milankovitch characteristics recorded in Middle Triassic platform carbonates in Northern Italy. Am. J. Sci., 287: 8 5 3 - 892. Goldhammer, R.K., 1988. Superimposed platform carbonate cycles: eustatic response of an aggradational carbonate buildup, Middle Triassic of the Dolomites. Bull. Am. Assoc. Petrol. Geologists, 72: 190. Gradstein, F.M.,Agtergerg, F.P.,Aubry, M.P., Berggren, W.A., Flynn, J.J., Hewitt, R., Kent, D.V., Klitgord, K.D., Miller, K.G., Obradovich, J., Ogg, J.G., Prothero, D.R. and Westermann, G.E.G., 1988. Chronology of fluctuating sea levels since the Triassic: A critique. Science, 241: 5 9 9 - 601. Graus, R.R., Macintyre, I.G. and Herchenroder, B.E., 1988. Computer simulation of the Holocene facies history of a Caribbean fringing reef: Galeta Point, Panama. Proc. Fifth Internat. Congr. Coral Reefs, Tahiti, pp. 25 - 53. Gries, R.R. and Dyer, R.C., 1985. Seismic exploration of the Rocky Mountain region. Rocky Mountain Assoc. Geologists and Denver Geophys. Soc., 299 pp. Grotzinger, J.P., 1986. Cyclicity and paleoenvironmental dynamics, Rocknest platform, northwest Canada. Geol. Soc. Am. Bull., 97: 1208- 1231. Hallock, P. and Schlager, W., 1986. Nutrient excess and the demise of coral reefs and carbonate platforms. Palaios, 1: 3 8 9 - 398. Hallock, P., Hine, A.C., Vargo, G.A., Elrod, J.A. and Jaap, W.C., 1988. Platforms of the Nicaraguan Rise: examples of the sensitivity of carbonate sedimentation to excess trophic resources. Geology, 16:1104 - 1107. Haq, B., Hardenbol, J. and Vail, P.R., 1987. Chronology of fluctuating sea levels since the Triassic (250 million years to present). Science, 235: 1156- 1167. Hassan, T.H., Mudd, G.C. and Twombley, B.N., 1975. The stratigraphy and sedimentation of the Thamama Group (Lower Cretaceous) of Abu Dhabi. Ninth Arab Petroleum Congress, Paper No. 107 (B-3), Dubai, pp. 1 - 11. Helland-Hansen, W., Kendall, C., Lerche, I. and Nakayama, K., 1988. A simulation of continental basin margin sedimentation in response to crustal movements, eustatic sea level change and sediment accumulation rates. J. Math. Geology, 20:777 - 802. Helland-Hansen, W., Steel, R., Nakayama, K. and Kendall, C.G.St.C., 1989. Review and computer modelling of the Brent Group stratigraphy In: M.K.G. Whately and K.T. Pickering (Editors), Deltas: Sites and Traps for Fossil Fuels. Geol. Soc. London, Spec. Publ. 41:237 - 252. Hriskevich, M.E., 1970. Middle Devonian reef production, Rainbow area, Alberta, Canada. Bull. Am. Assoc. Petrol. Geologists, 54: 2260-2281. Humphrey, J.D. and Quinn, T.M., 1989. Coastal mixing zone dolomite, forward modeling, massive dolomitization of platform-margin carbonates. J. Sediment. Petrol., 59: 4 3 8 - 454. Hurst, J.M., 1980. Paleogeographic and stratigraphic differentiation of Silurian carbonate buildups and biostromes of North Greenland. Bull. Am. Assoc. Petrol. Geologists, 64: 5 2 7 - 548. James, N.P. and Ginsburg, R.N., 1979. The seaward marginal Belize Barrier and atoll reefs. Spec. Publ. 3, lnt. Assoc. Sediment., 191 pp. Jordan, T.E. and Flemmings, P.B., 1989. From geodynamic models to basin fill - A stratigraphic perspective: In: T.A. Cross (Editor), Quantative Dynamic Stratigraphy, Prentice-Hall, NJ, pp. 1 4 9 - 164. Kearey, P. and Brooks, M., 1984.An Introduction to Geophysical Exploration. Blackwell Scientific Publ., Oxford, England: 326 pp. Kendall, C.G.St.C., Bowen, B., Alsharhan, A., Cheong, D.K. and Stoudt, D., 1991. Eustatic controls on carbonate facies in reservoirs, and seals associated with Mesozoic hydrocarbon fields of the Arabian Gulf and the Gulf of Mexico. Marine Geology, 52:215 - 238. Kendall, C.G.St.C., Strobel, J., Jie, T., Moore, P., Cannon, R., Bezdek, J. and Biswas, G., 1989a. Simulation of the west Texas, New Mexican Permian Guadalupian basin margin- a response to eustatic change, an example of SEDPAK. In: P.M. Harris and G.A. Grover (Editors), Subsurface and Outcrop Examination of the Capitan Shelf Margin, Northern Delaware Basin. SEPM Core Workshop No. 13: 423 -426. Kendall, C.G.St.C., Moore, P., Strobel, J., Cannon, R., Bezdek, J. and Biswas, G. 1989c. Simulation of sedimentary fill of basins. Proc. Kansas Geol. Surv. Centennial (1889-1989), Conf. on Sedimentary Modeling: Computer Simulation of Depositional Sequences. Subsurface Geology Series 12, Kansas Geol. Surv., Lawrence, Kansas: 1 - 4 . Koerschner III, W.F. and Read, J.F., 1989. Field and modeling studies of cambrian carbonate cycles,
101 Virginia Appalachians. J. Sediment. Petrol., 59(5): 654-687. Langdon, G.S. and Malecek, S.J., 1987. Seismic stratigraphic study of two Oxfordian carbonate sequences, eastern Saudi Arabia. Bull. Am. Assoc. Petrol. Geologists, 71: 403 - 418. Lawrence, D.T., Doyle, M. and Aigner, T., 1989. Calibration of stratigraphic models in exploration settings. Bull. Am. Assoc. Petrol. Geologists, 73(3): 3 7 9 - 380. Lawrence, D.T., 1988. Simulation of depositional sequences in clastic, carbonate, and mixed clasticcarbonate regimes. Proc. Workshop of Quantative Dynamic Stratigraphy (Q'DS). Feb. 14-18, Colorado School of Mines: 1 2 - 13. Lawrence, D.T., Doyle, M. and Aigner, T., 1990. Stratigraphic simulation of sedimentary basins: concepts and calibration. Bull. Am. Assoc. Petrol. Geologists, 74:273 - 295. Lawrence, D.T., Doyle, M., Snelson, S. and Thorsfield, W., 1987. Stratigraphic modeling of sedimentary basins. Bull. Am. Assoc. Petrol. Geologists, 71: 582. Lerche, I., Dromgoole, E., Kendall, C.G.St.C., Walter, L.M. and Scaturo, D., 1987. Geometry of carbonate bodies: A quantitative investigation of factors influencing their evolution. Carbonates and Evaporites, 2:15 - 42. Matthews, R.K., and Frohlich, C., 1990. Orbitial forcing of glacioeustasy: evaluation of alluvial clastic source/sink term. Bull. Am. Assoc. Petrol. Geologists, 74: 714. Matthews, R.K., and Frohlich, C., 1987. Forward modeling of bank-margin carbonate diagenesis. Geology, 15: 673-676. May, J.A. and Eyles, D.R., 1985. Well log and seismic character of Tertiary Terumbu carbonates, South China Sea, Indonesia. Bull. Am. Assoc. Petrol. Geologists, 69: 1339- 1358. McQuillin, R., Bacon, M. and Barclay, W., 1979. An Introduction to Seismic Interpretation. Gulf Publ. Co., Houston, TX, 199 pp. Middleton, M.F., 1987. Seismic stratigraphy of Devonian reef complexes, northern Canning Basin, Western Australia. Bull. Am. Assoc. Petrol. Geologists, 71:1488 - 1498. Morgan, L. and Dowdall, W., 1983. The Atlantic continental margin. In: A.W. Bally (Editor), Seismic Expression of Structural Styles. Am. Assoc. Petrol. Geologists Studies in Geology Series No. 15: 3 0 35. Nakayama, K. and Kendall, C.G.St.C., 1989. A simulation of basin margin sedimentation to infer geometry and lithofacies- a carbonate example. In: A. Taira and F. Masuda (Editors), Sedimentary Facies In The Active Plate Margin. Terra Scientific Publ. Co. (TERRAPUB), Tokyo, pp. 17 - 31. Neidell, N.S., 1980. Stratigraphic modeling and interpretation: geophysical principles and techniques. AAPG Continuing Education Course Notes Series 13:145 pp. Paola, C., 1989.A simple basin-filling model for coarse alluvial systems: In: T.A. Cross (Editor), Quantative Dynamic Stratigraphy, Prentice-Hall, NJ, pp. 363 - 374. Pinter, N., 1990. Passive margin synthetic stratigraphy: eustatic control on deposition and preservation potential on the continental shelf. Bull. Am. Assoc. Petrol. Geologists, 74:741. Playford, P.E. and Lowry, D.C., 1966. Devonian reef complexes of the Canning Basin, western Australia. Geol. Surv. West. Australia Bull., 118:150 pp. Quinn, T.M., 1989. Forward modeling of bank margin carbonate diagenesis: results of sensitivity tests and initial applications: In: T.A. Cross, (Editor), Quantative Dynamic Stratigraphy, Prentice-Hall, NJ, pp. 4 4 5 - 4 5 5 . Rafavich, F., Kendall, C.G.St.C. and Todd, T.P., 1984. The relationship between acoustic properties and the petrographic character of carbonate rocks. Geophysics, 4 9 : 1 6 2 2 - 1636. Read, J.F. and Goldhammer, R.K., 1988. Use of Fischer plots to define third-order sea-level curves in Ordovician peritidal cyclic carbonates, Appalachians. Geology, 16: 8 9 5 - 899. Robinson, E.S. and Coruh, C., 1988. Basic Exploration Geophysics. John Wiley and Sons, New York, 562 pp. Ross, W.C., May, J.A., Watts, D.E. and French, J.A., 1990. Quantitative stratigraphic modeling: the role of stratigraphic data sets. Bull. Am. Assoc. Petrol. Geologists, 74: 654. Ross, W.C., 1989. Modeling relative base level surfaces. In: T.A. Cross (Editor), Quantative Dynamic Stratigraphy, Prentice-Hall, NJ, pp. 387 - 400. Sarg, J.F., 1988. Carbonate sequence stratigraphy. In: C.K. Wilgus and others (Editors), 1988. Sea-Level Changes: An Integrated Approach. Soc. Econ. Paleont. and Mineral., Spec. Publ. No. 42: 1 5 5 - 181. Scaturo, D.M., Strobel, J.S., Kendall, C.G.G.St.C., Wendte, J.C., Biswas, G., Bezdek, J. and Cannon, R., 1989. Judy Creek: a case study of a two-dimensional sediment deposition simulation. In: J.L. Wilson,
102 P. Crevello, J.F. Sarg and J.F. Read (Editors), Controls on Carbonate Platform and Basin Development. SEPM Spec. Publ. 44: 6 4 - 7 6 . Schlee, J.S. (Editor), 1984. Interregional unconformities and hydrocarbon accumulations. AAPG Mem. 36:184 pp. Scholle, P.A., 1977. Chalk diagenesis and its relation to petroleum exploration- oil from chalks a modem miracle? Bull. Am. Assoc. Petrol. Geologists, 61: 982 - 1009. Scott, D.L. and Rosendahl, B.R., 1989. North Viking graben: an East African perspective. Bull. Am. Assoc. Petrol. Geologists, 73: 155-165. Sengbush, R.L., 1983. Seismic Exploration Methods. Internat. Human Resources Development Corp., Boston, MA, 296 pp. Sharma, P., 1986. Geophysical Methods in Geology. Elsevier, Amsterdam, 428 pp. Sheriff, R.E., 1976. Inferring stratigraphy from seismic data. Bull. Am. Assoc. Petrol. Geologists, 60(4): 528-542. Sheriff, R.E., 1977. Limitations on resolution of seismic reflections and geologic detail derivable from them. In: C.E. Payton (Editor), Seismic Stratigraphy-Applications to Hydrocarbon Exploration. Am. Assoc. Petrol. Geologists Mem. No. 26, pp. 3 - 14. Sheriff, R.E., 1978. A First Course on Geophysical Exploration and Interpretation. IHRDC Press, Boston, MA, 313 pp. Sheriff, R.E., 1980. Seismic Stratigraphy. Intemat. Human Resources Development Corp., Boston, MA, 227 pp. Simone, L. and Carannante, G., 1988. The fate of Foramol ("temperate-type") carbonate platforms. Sedimentary Geology, 60:333 - 346 Slingerland, R.L. and Furlong, K.P., 1990. Shoreline position in clastic wedges of marine foreland basins: a modeling study. Bull. Am. Assoc. Petrol. Geologists, 74: 765. Spencer, R.J. and Demicco, R.V., 1989. Computer models of carbonate platform cycles driven by subsidence and eustasy. Geology, 17:165 - 168. Steeples, D.W. and Miller, R.D., 1990. Seismic-reflection methods applied to engineering, environmental, and ground-water problems. In: S. Ward (Editor), Volume on Environmental Geophysics, Review and Tutorial, Soc. Expl. Geophys.: 1 -30. Strobel, J., Kendall, C.G.St.C., Biswas, G., Bezdek, J.C. and Cannon, R., 1987. Preliminary description of the program SEDFIL with carbonate module added. In D.C. Peters and S.A. Krajewski (Editors), Proc. Denver Geo Tech Computer-Aided Methods and Modeling in Geology and Engineering, pp. 341 -349. Strobel, J., Cannon, R., Kendall, C.G.St.C., Biswas, G. and Bezdek, J., 1989. Interactive (SEDPAK) simulation of clastic and carbonate sediments. In: Shelf to Basin Settings. Computers and Geoscience 15: 1279- 1290. Strobel, J., Soewito, F., Kendall, C.G.St.C., Biswas, G., Bezdek, J. and Cannon, R., 1989. Interactive simulation (SED-pak) of clastic and carbonate sediments In: T.A. Cross (Editor), Shelf to Basin Settings. Quantative Dynamic Stratigraphy, Prentice-Hall, NJ, pp. 433-444. Syvitski, J.P.M., 1990. Numerical prediction of the sediment characteristics, including carbon content, of basin fill. Bull. Am. Assoc. Petrol. Geologists, 74: 7 7 4 - 775. Takao, I., Yamamura, T., Suinouchi, H. and Miyata, Y., 1990. Three-dimensional computer simulation system of deltaic sedimentary sequences. Bull. Am. Assoc. Petrol. Geologists, 74: 6 8 2 - 683. Tang, Jie, Kendall, C.G.St.C., Strobel, J., Cannon, R., Moore, P., Bezdek, J. and Biswas, G., 1989. Simulation of the sedimentary fill of the Sichuan Basin by Upper Permian coals and carbonate sequencesan example of the use of SEDPAK. Bull. Am. Assoc. Petrol. Geologists, 73(3): 418. Telford, W.M., Geldart, L.P., Sheriff, R.E. and Keys, D.A., 1976. Applied Geophysics. Cambridge University Press, New York, NY, 860 pp. Tetzlaff, D.M., 1986. Computer simulation model of clastic sedimentary processes. Bull. Am. Assoc. Petrol. Geologists, 70: 655. Tetzlaff, D.M. and Harbaugh, J.W., 1989. Simulating Clastic Sedimentation. Van Nostrand Reinhold, New York, NY, 202 pp. Thomasson, M.R., Kettle, R.W., Lloyd, R.M., McCormack, R.K. and Lindsay, J.P., 1989. Seismic detection and interpretation of porosity in Carboniferous age rocks of Kansas and Oklahoma. Geophysics, 54: 1371- 1383. Turcotte, D.L. and Bemthal, M.J., 1984. Synthetic coral-reef terraces and variations ofQuartemary sealevel.
103
Earth and Planetary Science Letts., 70:121 - 128. Turcotte, D.L. and Willemann, R.J., 1983. Synthetic cyclic stratigraphy. Earth and Planetary Science Letts., 63: 8 9 - 96. Vail, E, 1988. Seismic stratigraphy interpretation using sequence stratigraphy, Pt. 1: Seismic stratigraphy interpretation procedure. In: A.W. Bally (Editor), Atlas of Seismic Stratigraphy, AAPG Studies in Geology No. 27, 1:1 - 10. Vail, ER., Mitchum, R.M., Jr. and Thompson, S., 1977. Part three: Relative changes of sea level from coastal onlap. In: C.E. Payton (Editor), Seismic Stratigraphy- Applications to Hydrocarbon Exploration. Am. Assoc. Petrol. Geologists Mem. 26:63 - 82. Walker, K.R., Shanmugan, G.S. and Ruppel, S.C., 1983. A model for carbonate to terrigenous clastic sequences. Geol. Soc. Am. Bull., 94: 7 0 0 - 712. Ward, R.F., Kendall, C.G.St.C. and Harris, P.M., 1986. Hydrocarbon occurrence in Guadalupian sediments, the Permian Basin, West Texas and New Mexico. Bull. Am. Assoc. Petrol. Geologists, 70: 2 3 9 - 262. Waters, K.H., 1987. Reflection Seismology-A Toolfor Energy Exploration (3rd Ed.). John Wiley and Sons, New York, 538 pp. Widess, M.B., 1973. How thin is a thin bed? Geophysics, 8: 1176- 1180. Wood, L., 1982. Imaging the subsurface. In: K.C. Jain and R.J.P. de Figueiredo (Editors), Concepts and Techniques in Oil and Gas Exploration. Soc. Explor. Geophys., Tulsa, OK, pp. 4 5 - 90.
This Page Intentionally Left Blank
105
Chapter 3 C O R E ANALYSIS AND ITS A P P L I C A T I O N IN R E S E R V O I R CHARACTERIZATION DAVID PATRICK MURPHY, GEORGE V. CHILINGARIAN, AND S. JALAL TORABZADEH
INTRODUCTION
Core analysis involves recovery, preservation, examination, and testing of samples of sedimentary rocks (cores) to obtain information on the characteristic properties of the potentially hydrocarbon-beating reservoir rocks. The information obtained by core analysis in conjunction with other reservoir, field, basin, and analog data is used to construct the most accurate picture possible of the reservoir, its reserves and productive potential, to maximize the economic payback from the production of hydrocarbons from the reservoir. Understanding the rock properties of a reservoir from direct measurement on representative rock samples is paramount in reservoir characterization. Whole coring, which involves drilling into the formation with a hollow-section drill pipe (a core barrel and bit) to cut and retrieve the rock samples, provides us with long continuous rock samples that provide not only analytical information (porosity, permeability, etc.), but geological information as well. Sidewall cores are small rock samples individually selected and taken from the side of the borehole wall, usually with wireline tools. Core analysis has advanced over the years from a simple visual examination of lithological properties to complex procedures involving computerized tomography, magnetic resonance imaging, scanning electron microscopy, and automation of data acquisition and analyses. Core analysis provides insight into rock properties which can be incorporated into the interpretation of other formation evaluation measurement techniques such as wireline, measurement while drilling and mud logs, and drillstem and wireline tests, to develop a complete picture of the reservoir and its reserves and productivity. Core analysis data are needed in all phases of oil and gas field exploration, development, and production, which include: (1) Exploratory wells to study the structure, physical properties of the formation, and its production capacity. Core data are essential for calibration of well logs and seismic data in exploration. (2) Optimization of completion procedure for selection of best completion technique, selection of subsequent testing intervals, interpretation of drillstem test data, and evaluation of completion effectiveness. (3) Field development, including drilling, facility sizing and optimization, artificial lift, workovers and recompletions. (4) Production design, including reserve estimation, and evaluation of primary, secondary, and enhanced oil recovery processes. Core analysis can be done on either a qualitative or quantitative basis. It can provide
106 1
Routine core plug analysis |
Slabbed core
9Photogroph 9Sedimentotogy 9Lithotogy
__ ~r~
Thin sections
.4,
[ areg ul tOry[G~176176 1
/
I I
I .
~ / I "
!
9o,oo.n,,,,
] t-'or~,/efrlom I fi
Environmental 9 evidence
I~
Detail 9 pore structure
j
Small samples 1 Grain 9 size distribution [ Mineral 9 analysis [ = X-ray and SEM analysis Bio 9 dating and association
/
I
_.,,)
9Porosity
//
Permeability
/
Graindensity
/[
co. o~ state 9S.ecio, Preserved/restored 9Capillary pressure 9Relative permeabil " ' 9Acoustic properties 9Compressiveproperties 9Clay chemistry effects 9Specific tests . . . . !
Calibration of wireline logs /
J
Fig. 3-1. A pictorial view of typical information that can be obtained from core analysis. This is only a partial list. (From Archer and Wall, 1986.)
direct measurements of rock porosity, permeability, fluid saturations and their distribution, grain density, lithology, capillary pressure, wettability, electrical and acoustical properties, cation exchange capacity, multiphase flow properties such as relative permeability, petrographic properties, and pore fluid properties. Core analysis can contribute to improved reservoir characterization if measurements of rock properties are made at reservoir conditions, i.e., under in-situ stress. A pictorial view of typical information that can be obtained from core analysis is shown in Fig. 3-1.
R ES ER V O I R C H A R A C T E R I Z A T I O N
If core analyses are to provide information for reservoir characterization, the resulting data must represent the full range of reservoir properties and values or the reservoir characterization will not be comprehensive.
Representativeness of core data
Inasmuch as representative rock samples covering the full range of rock property values are needed to fully characterize the reservoir, the rock samples should not be biased towards the better quality reservoir rock, for example. One approach to determining the representativeness of core data to the reservoir (Thomeer, personal communication, 1987) is to compare histograms of rock properties from the core data to corresponding well log data. Well log data are generally the most complete data set
107 available in a well, and, therefore, should be most representative of the range of reservoir property values. A histogram of core porosity compared to a histogram of well log density-neutron crossplot porosity, and a histogram of core permeability compared to a histogram of nuclear magnetism log permeability would show if conventional core analysis porosity and permeability coverage is sufficient for characterizing the reservoir over the range of these properties. Well log density-neutron crossplot point cluster analysis or spectral density photoelectric data over the entire reservoir can be compared to core mineralogy descriptions to assure that all of the different mineralogy types have been analyzed. Well log density-neutron crossplot grain densities can be compared to core grain densities to also assure representative mineralogies for reservoir characterization.
Depth alignment of data Depth alignment of core data with other formation evaluation data is critical for accurate application of core data to reservoir characterization. Typically one of the primary well logs, e.g., a resistivity or porosity log, is selected as the well's depth reference. All other wellbore data are shifted to be on depth with the well's depth reference log. Depth alignment of core data can be done using core porosity versus well log porosity, core CT bulk density versus well log bulk density, core gamma scan data versus well log gamma ray data, core mineralogy description versus well log density-neutron point cluster analysis, core permeability versus nuclear magnetism log pore size distribution, etc. When one tries to correlate core to log data, best results are obtained when the data are regularly sampled (no bias). As heterogeneities approach sample size, denser sampling or whole core analysis will be needed to match logs. Figure 3-2 provides some insight into potential problems with core sampling.
CORING
Introduction Planning prior to coring is critical. Formation evaluation objectives dictate which (if any) core types are taken and which analyses are performed. Taking the wrong type/size core or using an inappropriate drilling fluid can prevent or invalidate core analyses that are needed to meet evaluation objectives. Cores are cut from the formation for testing by different tools using different methods and appropriate coring fluids depending on the types of data required. Whole coring encompasses a wide range of core barrels and cutting heads including conventional, oriented, wireline retrievable, containerized (rubber sleeve, PVC, fiberglass, and aluminum liners), pressure, and sponge insert core barrels. Wireline sidewall coring can obtain rock samples from the side of the borehole after the zone of interest has been drilled and logged. Wireline sidewall coring encompasses three types of coring tools including percussion, rotary drilled (the most-used wireline sidewall tool for carbonates), and gas press.
108 Less Dense
~~,,,,::.:
..................~....i
...............o...,ml
-
~ z kw.~..;;;;;;.'a Density Log
More Dense
I
I! i i II | |
I
| | ni
I Core
Dense Streak
"::::::::.'::.'.':::::r
B u Ik D e n s ity L o g
High-Graded Sampling ...:.,:,:.::~,,~,.,~......o,,,,: . ..........::::, . :.:::: 1' Core Samples, on 1' Points , 9t m" l
9n i -
1' Core Samples, Shifted a Little
Fig. 3-2. Representative core sampling for analysis is not trivial. In this example, the core contains thin (plug width plus a little) tight streaks. The density log, which averages over about a couple of feet, is shown responding to the tight streaks, but not resolving them. Three different sampling picks are shown. The high graded sampling excludes the tight streaks. The 14 sampling on 14 points only hits one tight streak, and the slightly shifted 14 sampling hits two tight streaks. These three sampling approaches create different visions of the core density. A core this heterogeneous should not be analyzed using plugs. Whole core analysis is more appropriate. (Graphic from E.C. Thomas, personal communication, 1987.)
Coring fluids are generally designed to have a very low fluid loss and high solids content to minimize spurt loss of mud filtrate into the core. The type of data that is needed from core analysis will dictate the type of coring fluid to be used. Various coring techniques, coring fluids, core handling, and preservation procedures have been discussed in detail by many investigators including Keelan (1972), Anderson (1975), Monicard (1980), IHRDC (1985), Whittaker (1985), W o r m Oil Coring Series (1985-1986), and Archer and Wall (1986). C o n v e n t i o n a l w h o l e coring
Conventional whole coring is designed for structurally competent rocks which need no special fluid containment. Conventional whole coring is the simplest of the whole coring methods (see Fig. 3-3). The conventional whole core barrel consists of an outer barrel and an inner barrel. The function of the outer barrel is to transmit rotation to the core bit, which does the cutting. As the core is cut, it slides into the inner core barrel for storage. A bearing system keeps the inner barrel stationary, even while the outer barrel rotates, so that the core (still attached to the formation at the core bit face) is not damaged by rotation.
109 DIAMONDBIT COREBARREL SAFETY JOINT
STABILIZER
CIRCULATING PORTS SWIVEL CHECK VALVE RABBIT
~
~
~
_
INNER BARREL
OUTER BARREL
CORE CATCHER CORE BIT
Fig. 3-3. The conventional coring assembly for bottomhole coring consists of the core head or bit and the core barrel or retainer. (After Whittaker, 1985.)
A check valve at the top of the inner barrel diverts mud flow to between the inner and outer barrels during coring. The check valve also allows mud to exit the inner barrel as the core enters. A core catcher at the bottom of the coring assembly retains the core in the inner barrel as the core is pulled out of the hole when core cutting is complete. Core barrel lengths are usually small multiples of 30 ft (9 m), with typical barrel lengths being 30, 60, or 90 ft (9, 18, or 27 m). One of the most probable times for a core to jam in the core barrel while coring is during a drill pipe connection at the surface. Minimizing connections by using only a 30 ft (9 m) barrel (which adds cost
110 due to more drill pipe trips to recover core) or using a top drive rig (where the rotating mechanism can move 60-90 ft (18-27 m) in the derrick without a drill pipe connection) reduces the chance of jamming the core in the barrel.
Oriented whole coring Whole core can provide much structural and stratigraphic insight if the in-situ orientation of the core is known. Davison and Haszeldine (1984) provided a review of four simple techniques, listed in Table 3-I, that are used to orient conventional cores back to their in-situ position. One of these methods is oriented whole coring. Oriented core barrels use a scribing shoe located below the core catcher (Worm Oil Coring Series, 1985-1986, Part 2). Three notches are made on the core as it enters the inner barrel. One is the identifying notch and the other two are rotated 135 ~ around the core from the identifying notch. Three notches are used because one notch cannot TABLE 3-I Methods for orienting conventional cores back to their in-situ position (Davison and Haszeldine, 1984) Method
Comments
Oriented core barrels Dipmeter a Highly deviated wells b
Can be used on any rock type sequence Must be recognizable structural plane Directional survey must be used in conjunction with regional dip knowledge Origin and age of remanent magnetism component must be identified
Paleomagnetic
Imaging logs could be used today, and would provide better accuracy than a dipmeter because of their increased circumferential coverage. There are three different types of imaging logs: electrical array, pulsed acoustic, and video camera, which are described in Table 4-I in Chapter 4 of this book. The Society of Professional Well Log Analysts Reprint Volume on Borehole Imaging (1990) provided a comprehensive reference set for these imaging logs. bSkopec et al. (1992) discussed procedures for the successful recovery of oriented horizontal core from highly fractured carbonate rocks. The authors' specific objectives for this coring included formation evaluation and drilling reasons: efficient recovery of core sections, high core recovery rates, quality core material, accurate orientation data, comprehensive core analysis, and maintenance of borehole angle while coring. To accomplish these objectives in a horizontal situation, they had to develop or adapt equipment or procedures. The problem of frequent core jamming in the coring assembly was largely overcome by the use of flexible fiberglass inner barrels and multiple core-catcher assemblies. They achieved a recovery rate of almost 100% by using shorter core sections and improved inner- and outer-barrel stabilization. For orientation purposes, a slip scribe was used in conjunction with an electronic multishot instrument that uses an array ofaccelerometers for determination of inclination. This orientation instrument alleviated many of the problems that had been associated with camera surveys. To operate the electronic multishot instrument in a horizontal configuration, it was necessary to develop specialized equipment. Skopec et al. state that their newly designed rotatable non-magnetic blade centralizer, enhanced running gear, and a high frequency shock absorber were needed to be used to obtain accurate core orientation data. To ensure positive alignment of the orientation instruments and the coring assembly, a laser alignment system was invented and used successfully. Specialized horizontal core handling procedures were developed to ensure accurate core orientation data. It is obvious that these authors needed to go beyond using off-the-shelf equipment to meet their coring objectives. Their efforts were successful because of their planning for and development and adaptation of procedures and equipment that would let them accomplish their objectives. a
111 be cut satisfactorily without causing undue core jamming. Two notches spaced equally apart could be used; however, a mistake might be made in determining which one is the identifying notch. Three notches, unequally spaced around the circumference of the core, leave no doubt about which is the identifying notch and still allow satisfactory coring. A multishot directional survey tool in a monel collar is attached to the inner barrel by a connecting rod (which, in turn, is connected to the scribing shoe). This system allows determination of the direction (based on the multishot compass) in which the identifying notch was scribed. The system is operated by a timer, and depending on the timing cycle, as with conventional surveying practices, the rotary is stopped prior to firing the multishot to allow the compass to stabilize. This gives an accurate indication of core orientation, and the process is repeated throughout the coring operation.
Wireline retrievable whole coring Wireline retrievable whole coring is used when it is more cost effective to retrieve the core to the surface by pulling the inner barrel out through the inside of the drill string using wireline rather than tripping the entire drilling string out of the hole. An empty inner barrel can then be inserted back down the inside of the drill string into the core barrel assembly by wireline for continued coring. Wireline core barrels are made in a variety of sizes and usually cut 15 or 30 ft (4.5 or 9 m) of core (Worm Oil Coring Series, 1985-1986, Part 2). One negative aspect of a wireline core barrel is that the removable inner barrel must be small enough to be retrieved through the drill pipe. Of course the core diameter would be even smaller.
Containerized whole coring Containerized whole coring is used when the core would fall apart when not kept inside of a container. It is also used for fractured formations that would jam inside of a conventional inner barrel. Types of containers include rubber sleeves, PVC liners, fiberglass liners, and aluminum liners. These containers provide physical stability, but not a pressure seal for the core. The core is typically kept inside of the container from the time it is removed from the core barrel until it arrives in the core analysis laboratory and stabilized by freezing. Rubber sleeve containerized core assembly is a complex mechanism which ratchets a thick rubber sleeve around the core as it enters the inner barrel. Barrel length is about 20 ft (6 m). When coring has been completed, the core (still surrounded by the rubber sleeve) is removed from the core barrel. Typically, rubber sleeve core barrels are the least desirable of the containerized coring devices. They are the most mechanically complex and, therefore, most subject to failure during coring. The rubber sleeve is the most easily torn container, so it is the most likely to fail as a container, and the rubber sleeve is the most flexible container, so it is the most likely to allow flexure (and subsequent damage) of the core during removal from the core barrel and during transport to the core analyses laboratory.
112 PVC liners are the least expensive of the remaining containers. However, coarse manufacturing internal diameter tolerances can lead to j a m m i n g of hard rocks in smaller-diameter portions of the liner. In addition, a PVC liner is the container least tolerant of high temperatures. Fiberglass and aluminum liners are typically the most desirable of the containers. They have the best manufacturing internal diameter tolerances and the best high temperature tolerance. They are also the least flexible of the containers.
Pressure whole coring The pressure coring apparatus retains pressure on the core in the inner barrel to prevent pressure blowdown from altering the fluid saturations of the core as it is brought to the surface (Hyland, 1983). Invasion still occurs as the core is cut, so the in-situ fluid saturations (coring with a water-based mud) are not representative of insitu conditions unless the rock is at residual oil saturation to waterflood (see Fig. 313). The p r i m a r y use of pressure coring is to provide residual oil saturation
Latch Spring
Gas reservoir
Upper seal ring
Regulator
Inner barrel
Ball valve
Core catcher Bit
Fig. 3-4. Pressure coring is a method of maintaining a core's formation fluid integrity (after invasion, but before pressure blowdown) by sealing the core chamber at downhole pressure. The pressure core barrel illustrated here has a lower ball valve that closes by ratchet action after the core barrel is picked up off bottom and the outer barrel drops downward. A nitrogen gas system then maintains pressure within the core chamber against leaks. (From WorldOil Coring Series, 1985-1986, Part 2.)
113 information from reservoirs after waterflood to assess a tertiary flood target. Pressure coring with oil-based mud and subsequent analyses can provide irreducible water saturation information. In general, pressure coring is the ultimate in coring and analysis expense. After being cut, the sealed core is brought to surface under downhole pressure, then frozen and preserved in dry ice. While still frozen, the inner barrel is removed and the core cut in sections and sent to the lab for testing. The pressure core must be kept frozen in dry ice at all times until it is analyzed.
Sponge whole coring Like pressure coring, the primary use of sponge coring is to provide residual oil saturation information from reservoirs after waterflood to assess a tertiary flood target. Sponge coring is much less expensive than pressure coring, but more expensive than conventional, oriented, or containerized coring. The inner-facing portion of the sponge coring liner is covered with an oil-wet polyurethane sponge material. As the core is brought to the surface, it will blow down. The sponge captures and retains the blow-down oil. The sponge offsetting a particular portion of the core is analyzed for oil content. The resulting oil volume is added back into the oil saturation determination for the core offsetting that particular portion of sponge. This accounts for pressure blowdown and provides accurate residual oil saturation information. Prior to running in the hole with the sponge core barrel, six 5-ft sections of the sponge liner are placed within the inner barrel and sealed. To eliminate the possibility of producing a filter cake between the core and sponge liner, the sponge is first evacuated and then pressurized with water up to 1,600 psi (11,000 KPa). This pressure is maintained as the core barrel goes into the well. Once the sponge core barrel has been run in the hole, coring procedures are the same as with conventional coring. Several features of the sponge core make it unique (Worm Oil Coring Series, 19851986, Part 2). Where CO 2 floods are in widespread operation, it is desirable to determine where CO 2 is penetrating the pay formation, and sponge coring can be modified to analyze a core for CO 2 and/or HzS. Whereas standard practice in sponge coring uses water to pressurize the inner barrel, substituting a 15% monoethylene amine solution will allow capture and analysis of up to 25 liters (6 gal) of CO 2 per ft. This is an ample amount to quantitatively examine formations as far as determining how and where CO 2 has penetrated. Water saturation of cores is another application of sponge coring. Oil mud is used for the process because, if filtrate invasion occurs, there will be less chance of water loss from the core. Some modifications are required to run water saturation with the sponge core. First, the sponge is wet and pressurized with mineral oil (with a viscosity close to that of a 30-weight motor oil) instead of water. Once coring is complete, the barrel is brought to the surface slowly after the bubble point of the oil within the core is reached. This allows gas to trickle out of the core with minimum transport of oil and water from the core. The sponge is then analyzed for water content.
114 Wireline sidewall coring Once an interval has been drilled, sidewall coring can be used to take rock core plugs from the side of the borehole. Sidewall cores yield information regarding formation lithology, and interstitial fluids. Coring points may be selected after downhole logs have identified zones of interest. Also, accurate positioning can be accomplished with standard logging depth correlation devices, e.g., a gamma ray log. However, small samples cannot provide continuous information regarding vertical section properties. Two types of sidewall coring tools are available today: rotary and percussion. Sidewall rotary coring tools (Fig. 3-5) are used the most for carbonates and other hard rock formations. After the coring tool is positioned at the desired depth, a decentralizing arm pushes it against the formation while a motorized core drill cuts a rock
TOOL POSITIONING SHOE
HYDRAULIC DRILL MOTOR ~ . . DRILL ACTUATOR PLATE DRILL BIT " FLEXIBLE HYDRAULIC LINE CORE STORAGE TUBE ---
CORE PUNCH
RECOVERED CORE
CORE RECOVERY INDICATOR
Fig. 3-5. Wireline rotary coring tool for taking sidewall samples in hard rocks. The left schematic portrays the tool drilling a sidewall core. Selection of coring locations can be made from wireline or measurement while drilling logs. The coring tool is positioned at the desired depth using a gamma ray log at the top of the coting tool. The tight schematic portrays the tool storing the core sample in the storage tube. Most wireline rotary sidewall coting tools place a marker (ball bearing or disk) between core samples to indicate missing samples (two or more markers found together in the storage tube). After sidewall cores have been taken, the wellbore can be logged with a wireline imaging log to more accurately ascertain the coring locations with respect to formation layers. (Courtesy of Halliburton Energy Services.)
115 sample from the side of the borehole wall. Then the core drill containing the core is rotated back into the tool and the rock sample is pressed into a receiving tube. The percussion sidewall coring tool is used in soft to medium-hard rocks. It is the least expensive sidewall coring device. It is positioned and the sample barrel is fired into the formation by an explosive charge. In carbonates, the sample barrel will typically bounce off the borehole wall or break without obtaining a rock sample. However, this device would be useful for obtaining sidewall cores in softer source rocks.
CORE H A N D L I N G
Core retrieval, preservation, and handling should be done by following careful and special procedures, because they dictate whether or not subsequent core analyses data would be representative of actual reservoir behavior. Whole cores
Core retrieval typically is done by one or more geotechnicians or geoscientists. About one hour before the core barrel is due at the surface, they should begin preparing the area of the rig floor that has been designated as the core retrieval area (IHRDC, 1985). Materials that should be available include a labeled set of core boxes for temporary holding of the core, geological hammer, soft metal hammer, broom, work gloves, supply of clean gloves, pencils, and note pad on clipboard. The temporary-holding core boxes are used to keep the core in correct order while it is being retrieved from the core barrel on the rig floor and after it has been removed to the work area. The work area is generally adjacent to the mud logging unit, preferably at bench height, with sufficient space for two or more people to work around it. On arrival in the work area, the core must be transferred to clean boxes, fitted together where possible and measured (IHRDC, 1985). As each piece of core is taken from the temporary box, it should be wiped clean of drilling mud using dry rags only. Obvious features (such as fractures, bedding planes, oil or gas bleeding) should be noted on a worksheet. The core piece should then be transferred to its place in the new, clean core box. Loose rubble should be put in a clean sample sack and labeled with well and core identification information and an estimation of the number of feet of core it represents. When a box is about full, the core is fitted together as well as possible and properly labeled with waterproof marker pens. A tally sheet should be kept with the core length and estimate rubble content of each box. When the total length of core is known, the length measurements are converted to depths. Missing core is always assumed to have been lost from the bottom of the barrel. Following the brief examination made while boxing the core, a more thorough description should be made of all features of the core (IHRDC, 1985). The geoscientist should also be taking small chips of core that will be used for microscopic examination. (1) Core description should include (IHRDC, 1985) the following: (2) Lithology and thickness of major formation units. (3) Dip and strike of geologic structures.
116 (4) Nature of lithological boundaries. (5) Nature of bedding planes, and of sedimentary and diagenetic structures. (6) Gradational features such as grain size. (7) Spacing and surface texture of fractures and joints. In special cases where a core sample needs to be carefully preserved, such as native-state cores for enhanced oil recovery tests or special wettability-sensitive analysis, the core, after being wrapped in plastic and aluminum foil, is dipped into a plastic-like sealing or coating material for long-term preservation. The core may be frozen and stored in dry ice for shipment to the core analyses laboratory. Detailed procedures for whole core handling can be found in IHRDC (1985). Sidewall cores
After sidewall cores have been removed from the coring tool, they can be damaged by improper handling. Wellsite personnel should be aware of the amount of sample that is required for a particular analysis, so that sufficient core can be preserved. Samples should be packaged in individual, sealed containers and protected from excessive jarring that may occur as they are transported. The container and its lid should be properly and completely labeled (Worm Oil Coring Series, 1985-1986, Part 6). The cores may be frozen and stored in dry ice for shipment to the core analysis laboratory.
CORE ANALYSIS
Introduction
Core analysis can be carried out in different ways with different degree of complexity depending upon the type of information required, the type and size of samples, and the type of analysis facilities available. In general, core analysis can be divided into the following categories: conventional (routine), special, petrographic, and geochemical core analyses. Conventional (routine) core analysis usually includes measurement of porosity, air permeability, fluid saturations, grain density, and determination of lithology and texture. Core photographs may also be taken. Special core analysis usually includes measurement of porosity and (brine and gas) permeability at reservoir stress conditions, capillary pressure, relative permeability, close-density permeability measurements, core gamma scans, electrical resistivity properties such as resistivity index and formation factor, nuclear magnetic resonance (NMR), X-ray computerized tomography (CT), acoustical properties, mechanical properties, residual saturations, preferential wettability, coreflood tests, slimhole continuous core analysis, and cation exchange capacity. Petrographic studies include such methodologies as thin section analysis, scanning electron microscopy, image analysis, X-ray diffraction, Fourier transform infrared spectroscopy, calcimetry, dating and fracture analyses. Geochemical analysis provides data concerning the hydrocarbons in the core
117 samples. Thermal extraction chromatography and pyrolysis chromatography are two "heat and sniff' methods that provide chromatographic fingerprints that can be used for hydrocarbon identification and typing. Source rock can be analyzed for richness.
Sampling Muscat (1949) pointed out that no matter how complete the coring, one is still limited to an examination and study of rock samples which can constitute, at the most, a fraction of the total reservoir volume only of the order of 0.0001%. One should keep this in mind as one compares core-derived rock properties to those derived from, for example, well testing which can have a large volume of investigation. Sampling strategy for core analysis should be influenced by this also. The reliability of core analysis data, particularly special core analysis, is strongly dependent on how the core sample is selected, preserved, and prepared for analysis. Core analysis can be performed on whole pieces (6 in. to 12 in. long: 15 to 30 cm) of core or on plugs taken from the core as shown in Fig. 3-6. Whole core analysis is more expensive and takes a longer time to complete than plug analysis. One should
Fig. 3-6. Full-diameter whole core compared to plug-size sample (round hole to the left) for fractured rocks. (After Bergosh et al., 1985.) Plug size is 2.5 cm (1 in.) diameter.
118 consider whole core analysis when the rock is so heterogeneous that a plug is not representative of the rock surrounding it. Plugs can be taken parallel or perpendicular to the core axis. The orientation should be selected based on the need for directional information, such as vertical versus horizontal permeability. Plugs should be taken in a non-biased fashion. If one selects only the best quality rocks for analysis, one will end up with a small cluster of rock property values that are not representative of the range of rock properties of the formation (making for a poor regression). One non-biased selection process would be to take a plug exactly every foot (30 cm), only moving slightly up or down or to the side if the core is physically damaged at the foot mark. Another non-biased selection process is to scan the core with a CT or NMR scanner to locate and classify different rock types; then sample each rock type a statistically significant number of times. Figure 32 shows that representative sampling is not trivial. Answers to the following questions (E.C. Thomas, personal communication, 1987) might help one pick sample points effectively: (1) What use will be made of the data? (2) How are the results going to be "averaged" to accurately characterize the full range of formation properties? When doing core sampling and analysis for reservoir characterization, one must consider the following: (1) Results needed. (2) Accuracy needed. (3) Tumaround time needed. (4) Cost. Note that (2) and (3) are mutually exclusive and (2) and (4) are strongly correlated (E.C. Thomas, personal communication, 1987). Core data, like any other formation evaluation or reservoir characterization data, should be acquired in a cost effective manner.
Conventional (routine) core analysis Conventional (routine) core analysis usually includes measurement of porosity, air permeability, fluid saturations, grain density, and determination of lithology and texture. Core photographs may also be taken. Figure 3-7 shows a typical conventional core analysis data graph based on data obtained on plug-sized samples taken every foot (30 cm). Saturation changes pinpoint gas/oil and oil/water contacts. Average data for various zones are also illustrated.
Porosity There are several core analysis methods for porosity determination (American Petroleum Institute, 1960). Typically core analysis porosity determination methods measure the bulk volume and the pore volume or grain volume of the rock sample. Most methods require that the core be cleaned of formation and filtrate fluids before or as part of the analysis process. The lower the permeability of the rock sample, the longer it takes to perform the cleaning and/or porosity analysis. Heterogeneous rocks,
119
Water Base Fluid N
......
INAk.l(
~
--~
W
!
]
1
9
CZ]
l i l t It111
OIL U]lOiTql ---.,,-
m~m..,
~
y
[-'-7
20
111
I0
40
M
~
N
Im
I~0
4OO
20O
l
IHiS0
L
.:....'. ...
5500
'Lj
!ii"
,~
..:.:..
_ _-L_ ,~1
5,570
....
_
9
!
_+.,
.
~.~,
' y:':"
n[ 9
;
1
PEru NOP.Z. = 2iS
_J,,,,r~., r,','.'.
~
;~niiOnz.
.
vent..
P [ I I M VIIIT.
-- I H
PEIIId
PonosITY
= 2!
" POItOS~
Stw
=34
-
Stw
,
a 325
PE-~-i-N~--Pi; 1 o 3
/:.! Ptx-i-n~~..
H
P [ I I M VENT. - 14,1
- 11.1 i:lr0nOStl'Y
- 17.6
= 27
= 43
J5
PEItH VENT. - 50
POnOSJTf
= 17 .
[
z
i
t
t
~
~
[
[
7,
Fig. 3-7. Conventional core analysis data graph. Porosity, lithology, oil saturation, water saturation, and permeability are plotted versus depth. (After Keelan, 1982.)
like vuggy carbonates, require whole core analysis rather than plug analysis to produce representative results. However, the larger the rock sample, the longer it takes to perform the cleaning and/or porosity analysis. Routine porosity determination methods include summation of fluids, Boyle's law, hydrostatic weighing, and mercury injection. Summation of fluids begins with determination of the gas volume in the core sample. Mercury is injected into the core sample at high pressure (1,000 psi or 7,000 KPa) using a porosimeter like that shown in Fig. 3-8. The gas is effectively compressed to a negligible volume by the mercury and the volume of mercury injected is representative of the gas volume. The core sample is then put into a saturation still retort (Fig. 314) to heat out and measure the oil and water volumes. The sum of theses volumes (gas plus water plus oil) is the pore volume. Pore volume divided by bulk volume, measured separately or at the beginning of this analysis using the porosimeter (Figs. 3-8 and 3-9a), yields the porosity of the core sample. Summation of fluids is the fastest of the conventional porosity determination methods because the core does not have to be cleaned first. However, solid kerogens will be cracked at high temperature and be counted in the oil volume. Hydrostatic weighing uses Archimedes principle to obtain porosity on a cleaned
120 core plug. Pore volume is determined from the weight of empty rock plug and the weight of the rock plug containing a wetting fluid, usually toluene, knowing the density of the toluene. Grain volume is determined hydrostatically weighing the core plug in a toluene bath, knowing the weight of the empty rock and the toluene density. Bulk volume is the sum of pore volume plus grain volume. Porosity is pore volume divided by bulk volume. Hydrostatic weighing is the most accurate method for porosity determination (it uses an analytical balance for weighing) if the wetting fluid stays in the pores during analysis. Therefore, it will not work well for vuggy rock where the toluene drains out of the vugs during weighing for pore volume determination. Boyle's law method (Fig. 3-9b) uses pressures and volumes on clean rock samples to determine grain volume. Pore volume is divided by the bulk volume (measured separately) to yield the porosity of the core sample. Boyle's law method is especially useful for vuggy rock. Mercury injection uses a porosimeter (Fig. 3-8 and Fig. 3-9a/c) on a clean rock sample to obtain bulk volume by surrounding the core sample with mercury, and pore volume by injecting mercury to fill the pore volume. Pore volume divided by bulk volume is porosity.
SCALESTOP
PYCNOMETERLID ~=~"- PRESSURE
Fig. 3-8. Ruska porosimeter for routine porosity measurement on a core plug. A core plug is surrounded by mercury to obtain the bulk volume of the sample. Mercury is pumped into the pores of the core plug to obtain void space volume. This apparatus can be used on core plugs which have been cleaned to obtain total interconnected porosity. Or it can be used on core plugs still containing oil and water to obtain gas volume as part of the summation of fluids methodology.(Schematic from Whittaker, 1985.)
121
(8)
Bulk volume pycnometer
(b) Grain volume ( Boyle's law)
Solid reference] J ~ J or sample I "1--" X XSample Reference chamber volume Solid volume
- Gas supply
P2 v s = v I - P--~2
9 v2
(Calibration curve vs against P2 / Pl-P2 can be established using steel blanks ) (C) Bulk and pore volume porosimete r
Reference mark Isolation valve
Dead weight tester
tu
Micrometer mercury pump
[~i\ ~'
'
"
l
Fig. 3-9. Measurement of core sample porosity: (a) bulk volume pycnometer, (b) grain volume (Boyle's law), and (c) bulk and pore volume porosimeter. (After Archer and Wall, 1986.)
Permeability The gas permeability of a sample is measured by placing the dry sample in a Hassler-type core holder subjected to a certain confining pressure and flowing a dry gas, usually nitrogen or air, through the sample. The pressure drop across the core and the flow rate are measured and Darcy's law is used to calculate the permeability. The gas permeability is usually measured at three or more mean pressures (average of the upstream and downstream pressures). The Klinkenberg-corrected permeability, which is equivalent to the specific or absolute liquid permeability, is obtained by plotting the gas permeability as a function of the inverse of the mean pressure and extrapolating to infinite mean pressure. A permeameter schematic is
122 WMETERS PRESSURE GAUGE
:..:~
, THERMOMETER ........|
.:
...:.:..
. . . .
< ..
:i
.
:: .:.. : ....., ...
SAMPLE HOLDER
FLOWMETER SELECTOR VALVE
Fig. 3-10. Ruska permeameter for measuring gas permeability on a plug sample. A detailed cut-away schematic of the core sample holder is shown in Fig. 3-11. (After Whittaker, 1985.) shown in Fig. 3-10, whereas a close-up schematic of the core sample holder is shown in Fig. 3-11. If plugs are taken, their orientation should be selected based on the need for directional information, e.g., vertical versus horizontal permeability. Directional permeability tests can be conducted on core plugs drilled around the core periphery or on full-diameter cores. These data are most helpful when generated on spatially oriented cores and include permeability at 30--45 ~ increments around the circumference of the rock. For heterogeneous carbonates, whole core measurements of permeability would probably be the most representative technique, unless fractures are present which may form during the pi'ocess of core recovery. Whole core permeability measurements done perpendicular to the borehole axis typically provide two measurements (see Fig. 3-12). The larger of the two measurements is termed kax. The other, taken 90 ~ to the maximum value, is termed kgo.
Fluid saturations Usually pore fluid saturations cannot be determined directly from examination or analysis of rock. Saturations of a rock brought to the surface differ from its in-situ saturations because of two factors: invasion and blowdown (Fig. 3-13). Invasion of the drilling mud filtrate will change the saturations and pore fluids of the permeable rocks. As the rock is brought from formation depth to the surface, the pressure on the rock decreases. Fluids will expand as the rock moves upward toward the surface. If the bubble point pressure of the oil is reached, gas will evolve. Expansion of gas with
123
!RMOMETER
OVERLAP
SLEEVE
TEST SAMPLE
O-RINGS
BASE
Fig. 3-11. Permeameter core holder. Gas flow is directed through the core parallel to the long axis of the core plug. (After Whittaker, 1985.)
reduced pressure (Boyles law) is much more dramatic than that of liquids. As the pore fluids expand they push pore fluids from the core, i.e., blowdown occurs. Other factors can have influence on core saturations. These include mud overbalance pressure, mud fluid/spurt loss, core diameter (large diameter is better), horizontal and vertical permeability, interphase tension between mud filtrate and reservoir oil, viscosity contrast between reservoir and invading fluids, rate of bit penetration, rate of mud circulation, coring fluid and additives (surfactants can substantially reduce core oil saturation), relative permeability, core handling and preservation, gas/ oil ratio, and core bit mud discharge direction (Core Laboratories, 1989). With water-based muds there are three situations in which invasion and blowdown might not change the pore fluid saturations: (1) Zones that are already at 100% water saturation. (2) Zones that are already at waterflood residual oil saturation, with the effects of blowdown on the oil saturation being accounted for or eliminated by the use of a sponge core liner pre-saturated with water or by the use of a pressure core barrel (Worm Oil Coring Series, 1985-1986, Part 2). (3) Zones containing very viscous (near-solid) tar or heavy oil. In these situations, the hydrocarbons (if present) are immobile to mud filtrate invasion with possibly little or no effect on the resulting lab-measured oil saturation. Blowdown either is not a factor or is accounted for.
124 F l o w g a s t h r o u g h c o r e in this d i r e c t i o n
I I I I I I I I I
o
~ - - -lliiiiiii!i!iii~i~i~i~'~'!,~!r--'-"
Screens
~,_
Whole core
Fig. 3-12. Schematic diagram showing the basis for a whole-core gas permeability apparatus. Screens and core are inserted in a Hassler-type sleeve. Gas is passed through the screens across the core and permeability is determined. Then the core is rotated 90~around the borehole axis and the permeability for that direction of gas flow is determined. Both measurements are recorded. The larger one is termed k the other is kgo. max ~
With oil-based muds there is one situation in which invasion and blowdown might not change the pore fluid saturations: (1) Zones that are at in-situ irreducible water saturation. Invasion of oil-based mud filtrate might have little or no effect on the water saturation of zones which are at irreducible water saturation. In this case, the effects of blowdown on the water saturation can be accounted for or eliminated by the use of a sponge core liner pre-saturated with mineral oil or by the use of a pressure core barrel (Worm Oil Coring Series, 1985-1986, Part 2). After the sample is selected, it undergoes the conventional procedure of fluid extraction and saturation measurement by one of the following methods: (1) high vacuum distillation of oil; (2) high-temperature (1200~ 650~ retorting at atmospheric pressure (Fig. 314); (3) distillation of water and solvent extraction of oil (Dean-Stark extraction) at low temperature (240~ 115~ (Fig. 3-15); and (4) combination techniques. High-temperature retorting is an extension of the previously discussed summation of fluids porosity determination methodology. Inasmuch as pore volume is determined by summing the gas, oil, and water volumes, fluid saturations can be determined by dividing each fluid volume by the pore volume. This is the fastest method for saturation determination. However, solid kerogens will be cracked at the high temperature and be counted in the oil saturation.
125
:i:!::.-'!:!:!:.~!i! :.:.:.:.;....-.1
i::i~!~'~l~.l----SURFACE
FLUID IN CORE
CONDITIONS
20% RESIDUAL OIL (OR LESS]" 40% WATER [MAINLY DRILLING FILTRATE) 40% GAS SPACE (DUE TO EXPANDING GAS FROM
ATMOSPHERIC TEMPERATURE & PRESSURE
OIL) , MUD FILLED BORE HOLE
BLOWDOWN OFTEN INCREASES AS PERMEABILITY DECREASES
MUD FILLED DRILL PIPE
22 % OIL 60% WATER 18% GAS
SHALE
PRESSURE & TEMPERATURE REDUCTION
(INSIDE CORE BARREL] GAS ~/ATEI OIL i POSS. MUDCAKE
-:::::"
ii!iiiii~glgiglgil ......
OIL-BEARING-!i!i!i!i!i!i!i!iiiiiiii. FORMATION
i!iii! !:i:i:i ::5:::
25% OIL WITH DISSOLVED GAS 75 % WATER (MAINLY DRILLING MUD. FILTRATE
AFTER CUTTING CORE CORE "FLUSHED"
(OVERBURDEN REMOVED]
::i]ilil]i!i!i]ii!..O.!..L, 20% WATER (IRREDUCIBLE) 80% OIL WITH DISSOLVED GAS
ORIGINAL CONDITION
Fig. 3-13. Analyzed pore fluid saturations are typically altered from in-situ conditions by water-based mud filtrate invasion and pressure blowdown. The example saturations shown in this schematic will not be representative of all formations, but the general trends will be valid. In certain situations, e.g., heavy oil or tar as the hydrocarbon phase, invasion and blowdown will not occur. Invasion may not change the oil saturation if the formation is already at residual oil saturation to waterflood. Blowdown can be prevented or accounted for by using pressure or sponge core barrels. The original in-situ stress condition surrounding the rock is removed after the core is cut. (From E.C. Thomas, personal communication, 1987.)
126 1GHT FITTING SCREW CAP
HEATING ELEMENT
SAMPLE STAINLESS STEEL SAMPLE CHAMBER (BOMB)
AIR COOLER FINS
INSULATION
;CREEN
VAPOR TIGHT SEAL
WATER OUTLET WATER INLET
%
CONDENSING TUBE
WATER BATH
RECEIVING
Fig. 3-14. Saturation still retort: fluid extraction and saturation measurement device. In addition to determinationof fluid saturations,this device and the datait supplies can be used for porosity determination by the summation of fluids method. (After Whittaker, 1985.) Dean-Stark extraction begins with an uncleaned core sample. The weight of the rock containing oil and water is measured. Then extract the core sample with a solvent, typically toluene or xylene, using the Dean-Stark apparatus (Fig. 3-15) to boil the solvent up through the core sample and then drip back down through the core sample after it has been cooled by the condenser. The solvent will remove oil from the rock with the oil staying in the solvent. The boiling temperature of the solvent is slightly above that of
127 UNIFORM I.D:" THROUGHOUT LENGTH
WATER OUT
REFLUX CONDENSER
Ale
WATER IN
GROUND
GROUND JOINT WATER T R A P ~ 5 ml CAPACITY WITH l l l O t h ml GRADUATIONS ( 1 3 0 turn • 5 ram)
EXTRACTOR
=OUR INDENTATIONS SPACED UNIFORMLY TO HOLD THE SAMPLE THIMBLE PYREX GLASS FLA~r VOLUME - 2 5 0 ml
Fig. 3-15. Dean-Stark distillation fluid extraction and saturation measurement device.A heater underneath the flask refluxes solvent through the core sample to remove water and oil from the rock pores. Water volume is obtained directly from reading the water trap. Oil volume is obtained from the weights of the rock sample before and after extraction, accounting for the weight of the water removed and knowing the oil density. (From Whittaker, 1985.)
water, so the water is removed from the core and collects in the water trap. The volume of the distilled water in the trap is converted to water weight by multiplying by the density of distilled water at the trap temperature. The solvent may not get all of the oil out of the rock sample, so further extraction may be needed. In any case, it is prudent to continue extraction until all solvent(s) come out clear, indicating that all oil has been removed from the rock sample. Next, salts left behind in the pores from the water (mostly drilling mud filtrate) need to be removed. The weight of the cleaned core sample is then measured. The weight of the oil taken from the core sample is derived from the original weight of the uncleaned core sample minus the weight of the water minus the weight of
128
the cleaned rock. Additionally, nuclear magnetic resonance measurements may be made on the solvent(s) to provide a second measure of oil volume. The water saturation is obtained by dividing the water volume by the pore volume (determined elsewhere). The oil saturation is obtained by dividing the oil weight by the oil density (determined elsewhere) and then dividing by the pore volume. The low temperature of this procedure (so that kerogens are not cracked) and the accuracy obtained by using an analytical balance, make it a very accurate saturation determination methodology.
Grain density Analyses of core for grain density to provide insight into mineralogy can be done a number of ways (American Petroleum Institute, 1960). Core analysis grain density results can be related to known grain densities for particular rock types. For example, the grain density of dolomite is in the 2.85-2.87 g/cm 3 range according to the references of Edmunson and Raymer (1979), Wells et al. (1979), Ellis et al. (1988), and Carmichael (1989). These four references provide a comprehensive listing of physical properties of rocks, including the grain or matrix properties and the responses of nuclear and acoustic logs. Grain density can also be used to calibrate density logs for porosity determination (also see Chapter 4, Vol. I, p. 247). In complex lithologies, such as carbonates with intermixed limestone, dolomite, and other minerals, grain density may vary considerably vertically within the reservoir and horizontally from well to well as shown in Fig. 3-16.
Determination of lithology and texture Examination of the core for lithology and texture determination can be done at the wellsite or in the laboratory. Containerized core barrels can hamper wellsite core examination inasmuch as the core is covered by the container. Swanson (1985) described methods for determination of lithology and texture and for documentation of results.
]/! "~40 E
~:
-.~ 30 -
~li
i
i i [_J' i '
'
ll "1 i J 1 J j i I
9
100 ,n 80
E
0
"N E ~
I~'mtW " ]
"- 20 ,-, 10 0 2.411
2.50 2.60 2.10 2.80 2.90 3.1111 3.10 Grain Density: Em/cc
Fig. 3-16. Grain density variation between wells A andB in a formationwith complex geology. (After Keelan, 1982.)
129
Core photographs Core photos allow one to "see" the core without actually having to go to where the rock is stored or transporting the core. Core photos come in many formats. Usually an overview format will cover 18 ft (5.5 m) of core per 8 • 10 in. (20 • 25 cm) photo. A detailed format will cover 18 in. (45 cm) of core per 8 • 10 in. (20 • 25 cm) photo. Core photography with both natural and ultraviolet lights reveals bedding planes, orientation and other structural features, which indicate observed difference in permeability, porosity, saturations, and depositional environment (Fig. 3-17). Ultraviolet photography reveals oil fluorescence and, hence, location of liquid hydrocarbons in the core. Special core analysis Special core analysis usually includes measurement of porosity and (brine and gas) permeability at reservoir stress conditions, capillary pressure, relative permeability, close-density permeability measurements, core gamma scans, electrical resistivity properties such as resistivity index and formation factor, nuclear magnetic resonance (NMR), X-ray computerized tomography (CT), acoustical properties, mechanical properties, residual saturations, preferential wettability, coreflood tests, slimhole continuous core analysis, and cation exchange capacity. Usually special core analysis is done on a small percentage of the core. Higher cost and longer analysis time are reasons for this. However, it is important to cover the range of pertinent rock types with special analysis (see Representativeness of core data earlier in this chapter). Stressed analyses The effective confining pressure, or mean effective stress, S ' is required to properly specify laboratory conditions for stressed core analysis so that the analysis is done under the equivalent of in-situ stress conditions. It is defined as" m
s '=
'
+ s.
+
~
(4-1)
-
It is the average of the three principle stresses minus some fraction n of the fluid pressure p, reflecting that the internal pore fluid pressure is able to carry a portion of the total material load acting on a given volume. Subscripts h, H, and V represent the three principal stresses: the least horizontal stress, the greatest horizontal stress and the vertical stress, respectively. The fraction n is defined as follows" n = 1 -13 < 1 for deformation prior to failure, and n = 1 at point of failure. The quantity f5 = K / K , where K is the elastic bulk modulus of the dry or drained porous rock frame (the matrix) and K is the bulk modulus of the individual solid grains. The matrix K can be calculate~d from the drained Young's modulus E m and Poisson's ratio v measured in conventional triaxial tests: m
g
m
m
E K
~.. m
m
.....................................
3(1 --2Vm)
(4-2)
130
Fig. 3-17. Core photographs from various depositional environments. (After Keelan, 1982.)
The grain modulus K g can be estimated from the K gt. of the individual mineral constituents i using Wood's formula, which provides the inverse or harmonic average:
131
K ..........i_..................
(4-3)
g /~ / KiVt 9) where Vi is the volume fraction of each mineral. For highly compressible rocks such as unconsolidated sands, high-porosity chalks, or diatomite, K < < K and the quantity 1 -13 is approximately 1. For "hard" rocks, however, 1 -13 may be ~s small as 0.6. Values of K may range anywhere from 1 x 104 to 2 x 106 psi (7 x 104 to 14 x 106 KPa), whereas values of K commonly range from 5 x 106 psi (35 x 106 KPa) for quartz to 12 x 106psi (84 x 106 ~d~a) for dolomite (K.S. Hansen, personal communication, 1992).
m
Capillary pressure Core analysis data in the form of drainage capillary pressure curve saturation distributions can be representative of the original hydrocarbon saturation distributions in a reservoir (Leverett, 1941; Rose and Bruce, 1949; Jodry, 1992), provided that the rock from which the data are acquired is representative of the formation. Mercury-air capillary pressure points (Purcell, 1949) can be related to reservoir height above the free water level (see the definition in Table 4-XVII, Chapter 4) of the formation by Eq. 4-3, Chapter 4, provided that the in-situ formation hydrocarbon and water specific gravities, interphase tensions, and contact angles are known. For the mercury-air capillary data, mercury is the non-wetting phase. For Eq. 4-3, Chapter 4, to be representative of the reservoir height relationship for the original saturation distribution in the reservoir, the hydrocarbons are assumed to be the non-wetting phase during the original oil migration and subsequent saturation distribution equilibrium. Thomeer (1960) provided a methodology that can uniquely describe a capillary pressure curve and quantify the saturation distribution using three parameters. These socalled Thomeer parameters that describe the capillary pressure curve can be used to calculate the original saturation at any height above the free water level in the reservoir. A correlation between the capillary pressure curve's height above free water level and the reservoir depth must be found. Smith (1990) showed examples of capillary pressure to reservoir depth correlation using well log data. Figure 4-6 in Chapter 4 shows an example of capillary pressure to reservoir depth correlation using wireline test data. Permeability can be estimated from capillary pressure core data (Purcell, 1949, for historical perspective on early work; Swanson, 1981, for use on cuttings or samples with large closure corrections; Thomeer, 1983, for general use). The Thomeer and Swanson methodologies provide permeability estimates within a factor of two, for a one standard deviation confidence level, based on their calibration data sets. For rocks with more than one pore type, Thomeer (1960) pointed out that the relatively larger pores of a rock contribute the most to the permeability and, therefore, any capillary curve permeability estimate should be based on the lower-pressure capillary curve portion of multiple-curve capillary pressure data. The Micromeritics* Autopore capillary pressure apparatus can attain mercury-air *Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or product.
132 capillary pressures up to 55,000 psi (380,000 KPa). This is a magnitude higher than can be attained by conventional mercury-air capillary pressure devices. High capillary pressures provide detailed information about microporosity distribution. The Autopore acquires capillary pressure data in two steps. The first step covers capillary pressures up to 25 psi (172 KPa), the second covers beyond 25 psi (172 KPa). Potential low accuracy of information in the immediate vicinity of 25 psi (172 KPa) is a weakness of this tool if a particular pore type has a mercury-air capillary entry pressure of 25 psi (172 KPa). Yuan (1991 a) described a quantitative method of determining pore scale heterogeneity from the apparatus for pore examination (APEX), a rate-controlled capillary pressure measurement apparatus, which can lead to a quantitative assessment on the efficiency of enhanced oil recovery processes. APEX data can be used to resolve individual pore bodies and throats. Yuan (1991 b) also described APEX models used for the determination of Archie's lithologic exponent, m, and permeability, and the models' agreement with experimental measurements on a set of samples for which the lithologic exponent, absolute permeability, and additional APEX data have been measured. A centrifuge may also be used to obtain capillary pressure data. Cores are saturated with water (or oil) and spun within air or oil at increasing speeds. Average liquid content at each speed is calculated from observations of liquid spun out. The liquid volume out is read with a stroboscope while the centrifuge is in motion. The average saturation data are used to establish a water saturation versus pressure curve (Core Laboratories, 1982).
Relative permeability A rock's relative permeability is generally defined as the effective permeability of one fluid in a multi-fluid situation divided by the specific permeability of a single fluid when only that fluid occupies the pores. Relative and effective permeabilities are specified for a particular fluid saturation situation. A relative permeability curve is made up of multiple measurements at different fluid saturations. Relative permeability is used in conjunction with the fluids' viscosities to determine the fraction flow (production percentage) of each fluid from the rock. Effective and relative permeability of carbonate reservoirs are discussed in detail in Chapter 8, Part I of this book. Matching the core wettability condition to the reservoir wettability condition is the key to obtaining relative permeability information that is truly representative of a particular reservoir. Native-state coring (taking a core without changing the rock wettability) can be difficult, if not impossible. Restored-state core analysis (aging the core containing reservoir fluids at reservoir temperature for at least a month) can be time consuming and expensive. Common methods for measuring relative permeability include steady state and unsteady state (Core Laboratories, 1982). Hawkins (1988) provided a comparison of relative permeabilities on restored-state core using the following methods: unsteady state at ambient conditions, steady state at ambient conditions, and unsteady state at reservoir conditions. Although the residual oil saturations varied, the shape of the relative permeability curves from the three methods were similar.
133
Mini-permeameters So-called mini-permeameters are pressure-decay devices that flow gas from the end of a tube-like probe that is sealed against a rock sample to estimate local permeability. Georgi and Jones (1992) discussed the evolution of mini-permeametry and the application of this technique to reservoir description. Inasmuch as the device can provide estimates of permeability with resolution down to about five mm (0.2 in.), geologists can quantify the impact of both depositional and diagenetic features on permeability. Lab-based mini-permeameters can be used on small-diameter core plugs or full-diameter core samples. Portable mini-permeameters, like the University of Texas mechanical field permeameter (Chandler et al., 1989), can be used to characterize the outcrop permeability distribution. Work done at the New Mexico Institute of Mining and Technology (Chen et al., 1993) expanded use of these tools to include porosity determination. Core gamma scans Scanning a continuous whole core with a gamma scanner is analogous to logging a well with a gamma ray log. A record is made of the rock's natural radiation versus the depth of the core. This information can be used to correlate the core recovery to reference log depths. Some core analysis labs have spectral gamma scanning devices which record the contributions of potassium, thorium, and uranium to the natural radiation of the rock, analogous to a spectral natural gamma ray logging tool. The additional information provided by a spectral gamma scan can help Out in tough correlation conditions, such as the alternating layers of radioactive and non-radioactive dolomites found in some West Texas fields. Resistivity properties Determination of the Archie formation factor, F (to obtain the lithologic exponent, m) and the resistivity index, I (to obtain the saturation exponent, n) can be done using core analysis (Archie, 1942). Detailed definitions of F, m,/, and n can be found in Chapter 4 of this book. Matching the core wettability condition to the reservoir wettability condition, is the key to obtaining resistivity property information that is truly representative of a particular reservoir. Native-state coring (taking a core without changing the rock wettability) can be difficult, if not impossible. Restored-state core analysis (aging the core containing reservoir fluids at reservoir temperature for at least a month) can be time consuming and expensive. Several laboratory techniques for measuring resistivity index curves and a study of their accuracies have been documented by de Waal et al. (1989). Mahmood et al. (1988) performed an experimental study to investigate the influence of variation in test conditions and laboratory procedures on the electrical properties of rocks. The results of resistivity measurements on a synthetic porous medium, Berea sandstone, Shannon sandstone outcrop, Shannon subsurface, and carbonate reservoir cores are presented. This study provides some insight into the complication involved in rock electrical resistivity laboratory measurements under simulated reservoir conditions. It also contributes to understanding the combined effects of temperature and pressure on resistivity properties.
134
Nuclear magnetic resonance (NMR) Nuclear magnetic resonance (NMR) scans and spectroscopy provide non-destructive three-dimensional analysis of particular nuclei in the pore liquids. NMR can be used to locate and quantify hydrogen (in water and oil), carbon (in oil), sodium (in water), and fluorine (in tracers) (Edelstein et al., 1988). Liquid-filled porosity, pore liquid saturations, pore size distribution, pore liquid viscosity and rock permeability information are obtainable. NMR responds to the liquids in the pore space. Gas in the pore space is not measured directly, but can be inferred by the difference between the NMR liquid (%BV) and the total porosity (%B V). If the pore space contains gas, the rock must be resaturated with liquid for accurate total porosity determination. Because the NMR apparatus responds to liquids, the pore liquids cannot be frozen. NMR scanning and spectroscopy can be done on whole cores, core plugs, and fluid samples. NMR scanning and spectroscopy cannot be done on rock through ferro-magnetic or other NMR-opaque containers. The use of proton NMR in tight, gypsum-bearing carbonates has been shown to be valuable for saturation determination where extraction core analysis methods proved inaccurate due to gypsum dewatering and extremely low permeability of the rock (Vinegar et al., 1991 b). Whole core analysis by 13C NMR for oil saturation determination has been demonstrated in cases where 1H NMR might not work well, like in shaly rock (Vinegar et al., 1991 a). NMR has also been demonstrated to be a useful tool in quantifying oil volume in extracts from other saturation determination procedures; such as extracts from polyurethane sponge core liners using freon-ll, Dean-Stark extracts using xylene, and miscible flooding extracts using chloroform/methanol (Tutunjian and Vinegar, 1990). Determination of formation water salinity by the use of nuclear magnetic resonance imaging of 23Na in cores has been demonstrated (Tutunjian et al., 1991), for those cut in oil-based muds. This method will work for formation water salinity determination as long as sodium is the predominant cation in the formation water. The core must be handled and protected so that pore water evaporation does not occur. Pore water evaporation would increase the apparent salinity of the water. Proton NMR measurements on tight, gypsum-bearing carbonates have also provided quantitative oil viscosity information where extraction methods proved costly due to extremely low permeability of the rock (Vinegar et al., 1991b). Whole core analysis by ~3C NMR for oil viscosity has also been demonstrated (Vinegar et al., 1991 a) without extracting the oil from the core. NMR oil viscosity determination has also been done on oil present in core analysis extracts from polyurethane sponge core liners using freon-11, from Dean-Stark extracts using xylene, and from miscible flooding extracts using chloroform/methanol (Tutunjian and Vinegar, 1990). Whole core analysis for hydrocarbon chemistry by 13C NMR has been used to determine aliphatic/aromatic ratio (Vinegar et al., 199 l a) without extracting the oil from the core. Proton NMR measurements have been shown to estimate permeability from sandstone core samples (Seevers, 1966, for first work; Howard et al., 1990, for recent work). Howard et al. related the time constant for NMR longitudinal relaxation, T/, to pore body size, for intergranular/intercrystalline rock. Kenyon et al. (1988) reasoned
135 that the permeability from NMR is, therefore, a function of the relation between the size of the pore throats to the size of the pore bodies, with NMR providing the pore body information. NMR permeability estimation for vuggy rocks will be less accurate than that for intercrystalline rocks because of the poorer relationship between pore throat size and pore body size for vugs (H.J. Vinegar, personal communication, 1992). NMR spin-lattice (T~) and spin-spin (T2) relaxation times are typically used for porosity and permeability determination because they are related to surface-to-volume ratio of pore systems by surface relaxivity which in turn is influenced by mineralogy, wettability, and concentration of paramagnetic and ferromagnetic impurities on grain surfaces. Paramagnetic ions in drilling mud filtrate may also have influence on measurements. Restrictive diffusion, another NMR measurement, is also proportional to surfaceto-volume ratio but is not dependent on surface relaxivity. Restrictive diffusion measurements also offer the possibility of estimating in-situ crude oil viscosity (Tutunjian et al., 1993). NMR scans can be made during reservoir flood tests on cores. Liquids can be tagged with tracer elements which can be seen by the scanner. The container encasing the core must be made of a NMR-transparent material such as glass.
X-ray computerized tomography (CT) X-ray computerized tomography (CT) scanning of rocks was introduced to the petroleum industry in the mid-1980s. CT scans provide quantitative, non-destructive, three-dimensional density and atomic composition core analyses. CT density scans yield porosity and fluid saturation information. CT atomic composition scans yield lithology information. Although most CT usage is for visual quality and descriptive assessment of core material, quantitative analysis can be done if the machine is properly calibrated (Coles et al., 1992). It consists of a rotating X-ray source and detector, which circles the core and takes images of different cross sections. The core setup is such that it can advance incrementally a desired distance in a certain direction and three-dimensional images can be obtained. The X-ray digital data are acquired by a computer and are converted to images that are displayed on a computer screen or printed to show various materials and heterogeneities in the core. CT scans provide spatial information with resolution as fine as a few millimeters. Cores can even remain frozen during the scan. Scans can be made through core containers, unless they are made of lead or thick stainless steel. CT scanning (Wellington and Vinegar, 1987) can be used for saturation determination. Invasion and blowdown most likely have altered the saturations from in-situ values. If two fluid phases are present, a single energy scan is sufficient to measure the two saturations. When three fluid phases are present, two different energy scans are needed to determine the three saturations. Wellington and Vinegar discussed the use of CT scanning saturation determination for flow studies, and showed results from several different types of coreflood experiments. CT scanning can be used for quality assessment of the core, with millimeter resolution, so that further analysis can be made on non-altered core samples. Several core quality problems can be seen without opening up the core container(s): whole mud invasion, fractures, and disturbed core. Use of the CT scan should be strongly
136 considered before any other core work is begun. It can save money and time by optimizing the use of good quality core for analysis and can provide useful analytical information, too (Wang et al., 1984a, 1984b; Vinegar, 1986; Wellington and Vinegar, 1987; Hove et al., 1987; Hunt et al., 1988; Withjack, 1988; Hicks et al., 1992).
Acoustic properties Acoustic properties, such as velocity (compressional and shear) and anisotropy can be measured on cores (Core Laboratories, 1989). These data can be useful in seismic calibration. Matching the core stress condition to the reservoir stress condition is a key to obtaining acoustic information that is truly representative of a particular reservoir. Effective confining pressure determination has been discussed earlier in this chapter. Mechanical properties Rock mechanical properties such as Young's modulus, Poisson's ratio, unconfined compressive strength, tensile strength, and compressibility can be determined from core measurements (Monicard, 1980). These data can be useful in quantifying the compressibility effects of formation pressure reduction on reservoir pore volume, selecting drilling parameters and equipment, predicting hydraulic fracture shape, and predicting surface subsidence. Skopec (1991) used vertical pilot-hole oriented coring and rock characterization along with open hole small-volume-hydraulic fracturing to provide valuable insight into the design of a horizontal wellbore in a naturally fractured reservoir. Results such as rock mechanical properties, fracture strike and principal in-situ stress magnitudes and directions were used to reduce risk in the drilling of horizontal wellbore and optimize its placement with respect to in-situ stresses and fracture orientation. Residual oil saturation determination The determination of residual oil saturation after waterflood provides the information concerning the target for a subsequent tertiary flood (CO 2, caustic, chemical, etc.). Direct determination methods include sponge and pressure core analysis. Both sponge and pressure core account for blowdown such that the resulting oil saturation determination is representative of the residual oil saturation after mud filtrate invasion. Other determination methods include corefloods and imbibition capillary pressure and relative permeability analyses. Wettability Reservoir wettability is not a simply defined property (Morrow, 1990). Morrow stated that classification of reservoirs as water-wet or oil-wet is a gross oversimplification. Wettability has significant effect on all multiphase flow situations of a reservoir, from source rock oil migration to tertiary flood. Two methods of quantifying wettability based on rock~rine/oil displacement behavior, the modified Amott test (Amott, 1959) and the USBM test (Donaldson et al., 1969), are in common use. Detailed fundamental information concerning wettability and its effect on reservoir performance can be found in Hirasaki (1991) and Morrow (1990).
137 Cleaning the fluids out of a core (as is done during routine core analysis) can make the core behave more water-wet. Aging the core containing reservoir fluids at reservoir temperature for at least a month can be time consuming and expensive, but is required to restore wettability at or near in-situ conditions. Hirasaki et al. (1990) evaluated wettability changes during stages of restored-state core analysis for a North Sea reservoir. Their goal was to determine the proper core analysis technique for estimating the remaining oil saturation after waterflooding. Amongst their conclusions were: (1) USBM and Amott indices measured by automated centrifuge were a good measure of wettability. (2) Core cleaning methods affect the restored state capillary pressures, relative permeabilities, and residual saturations. Traditional Dean-Stark extraction with toluene followed by chloroform-methanol did not adequately clean the cores and made the rock appear more oil-wet than more thoroughly cleaned cores. Wunderlich (1991) discussed the three situations (coring, storing, and preparation) in which core wettability can be altered. His comprehensive discussion of recommendations for obtaining samples with preserved wettability includes: Introduction. Coring. Wettability alteration due to interactions with drilling fluids. Pressure and temperature. Storing. Laboratory preparation. "No solvents" procedures. "Clean and restore" procedures. "No hysteresis" procedures. Recommendations for cleaning procedures. Experimental conditions. Concluding remarks and references. Wunderlich's recommendations provide detailed procedures for obtaining reservoir rock in a wettability state representative of in-situ wettability (also see Introduction Chapter, Vol. I, pp. 30-31).
Corefloods Reservoir performance information for characterization of the reservoir response to specific production mechanisms can be obtained from corefloods. These include waterflood tests and enhanced oil recovery (EOR) coreflood tests, such as hot water flood, steamflood, steam soak, fire flood, miscible flood, chemical flood, and CO 2 flood. Monitoring saturation changes during a coreflood can be done by CT scanning (Wang et al., 1984a, 1984b; Hove et al., 1987; Withjack, 1988) or by NMR scanning (H.J. Vinegar, personal communication, 1992). For CT, fluid densities or atomic compositions can be used to differentiate fluids. CT can see through any container except thick stainless steel or lead. For NMR, liquids can be tagged with tracer elements which can be seen by the scanner. The container encasing the core must be made of a NMR-transparent material such as glass.
138 There is always a question of how well in-situ conditions are duplicated in the laboratory even during the most careful laboratory analysis. Variances in any of the following conditions could cause discrepancies between laboratory-measured and insitu values (Wyman, 1976): (a) Fluid type (e.g., does Soltrol, a synthetic oil, represent in-situ crude?). (b) Fluid distribution (including the per cent saturation of oil initially in place). (c) Wettability (what exactly is it? how should it be measured in actual pores?). (d) Flow rate of flooding water. (e) Total quantity of flow (e.g., number of pore volumes, or time that water flows past a given point. (f) Oil/water interphase tension. (g) Pressure. (h) Temperature. (i) Fluid viscosities. (j) Length of time fluids being measured are exposed to the rock (which may affect the wettability). (k) Hysteresis effects of core restored to in-situ conditions. (1) Influence of third phase (gas). Slimhole continuous core analysis Slimhole continuous core analysis is wellsite usage of available core analysis technology on continuous small-diameter cores for cost-effective formation evaluation of exploratory wells. This approach has the potential for providing the ultimate in geological data and insight, and is also used to calibrate seismic and well log data. Spain et al. (1992) have used an on-site automated instrumentation system to extract much information from the core, developing high-speed slimhole coring into an integrated exploration tool. "Inverse logging" (logging the core instead of the borehole) is the primary goal of on-site geological evaluation. Up-hole measurements on cores included gamma scan, magnetic susceptibility, infrared mineralogy, ultraviolet fluorescence, nuclear magnetic resonance porosity, and pyrolysis (source rock) data; macroscopic and microscopic video images for analysis and archiving; and sedimentological/ lithological description. Jantzen et al. (1993) described a wellsite slimhole core logging facility which included natural gamma ray, density and caliper, porosity, permeability, total organic carbon and pyrolysis, together with high-resolution, white and UV light digital images. Drilling, mud-gas, geological, core and wireline log data provided a fully integrated formation evaluation data set. Cation exchange capacity Cation exchange capacity (CEC) is a measure of the ability of clay minerals to exchange ions between clay mineral surfaces and surrounding water. Its magnitude is a function of the rock's clay mineral type and amount (Keelan, 1982). CEC can be determined by wet chemistry techniques with an ammonium or barium exchange, through use of a correlation between CEC and adsorbed water content of test samples (Bush and Jenkins, 1977), or from membrane potential (Yuan and Diederix, 1989). Data on CEC are very important in calculation of water saturation in clay mineral-
139 bearing formations, especially if the formation water is fresh. It has also been related to stripping of ions from injection fluids, trace element accumulation, and formation overpressure. CEC effects typically are more pronounced in siliciclastics than in carbonates because carbonates tend to contain a lower percentage of clay minerals than do siliciclastics.
Petrographic core analysis Petrographic studies include such methodologies as optical mineralogy, thin-section analysis, scanning electron microscopy, image analysis, X-ray diffraction, Fourier transform infrared spectroscopy, calcimetry, dating and fracture analyses. Detailed optical mineralogy theory and techniques for mineral identification were described by Ehlers (1987). Carver (1971) provided several chapters dealing with petrographic mineral analysis, including preparation of thin sections, point counting, heavy mineral analysis, staining, and X-ray diffraction. Scholle (1978) provided a comprehensive color illustrated guide to carbonate rock constituents, texture, cements, porosities, and techniques for identification and classification.
Thin sections Thin sections are thin slides made of rock, commonly, after the pores have been impregnated with an epoxy that solidifies. They furnish samples for visual study of textural properties, for mineral identification and abundance, and the processes that have affected the rock, e.g., depositional and diagenetic activity. Petrographic microscopes utilizing optical techniques are used in this work (Core Laboratories, 1982). Carver (1971) provided details concerning procedures in sedimentary petrology. The relatively low vertical resolution (direction coincident with the objective lens axis) of petrographic microscopes makes it somewhat difficult to resolve grain boundaries, especially at higher magnifications needed to detect microporosity and small fractures. Impregnating the sample with epoxy and an admixed fluorescent dye allows the use of a confocal microscope, a specialized form of epifluorescence microscopy, which can image a very thin focal plane, or very thin layer, of the thin section (Owen et al., 1992). A series of focal plane images can be acquired and then reassembled or stacked to generate a full three-dimensional image of the thin section. Scanning electron microscopy In a scanning electron microscope (SEM), a rock sample that has been previously coated with a thin film of conductive material is bombarded with electrons in a high vacuum, resulting in a secondary electron emission picture for sample study (the SEM) and a characteristic set of X-rays (EDX spectrum). The SEM allows mineral identification and a high-magnification visual examination of microporosity, a single pore or a small group of pores and the surrounding grains or crystals of the rock. The most reliable way to identify minerals through the SEM is to compare their morphologies, i.e., shapes, to morphologies of known minerals with elemental compositions determined by the EDX system (Welton, 1984). Welton (1984) provided a SEM and EDX atlas of known minerals for comparison with unknown SEM samples.
140
Image analysis Core images come in several sizes: scanning electron microscope (very small), thin section (small), and core photographs (regular). Core images can be used for visual analysis of the rock, or can be used to acquire quantitative data for characterization of petrophysical and geological rock properties. Pore-size scale image analysis of thin sections and scanning electron micrographs provides rapid, quantitative porosity data. Image analysis also provides quantitative data concerning the size and geometric complexity of reservoir pore systems (Ehrlich and Davies, 1989). An understanding of the nature and distribution of pore types becomes increasingly important with decreasing porosity values. Reservoirs which have undergone diagenetic modification, such as carbonates, are frequently characterized by the co-existence of several disparate types of porosity. In such rocks, reservoir behavior is much less dependent on total porosity than on the pore type assemblage that makes up that porosity (Davies, 1990; Chapters 4 and 6 in Part I of this book). Examples of permeability determination from image analysis have been published for sandstones (Davies, 1990), but not for carbonates. However, a similar approach aimed at the different pore systems found in carbonates should be valid. Some recent image analysis efforts incorporate the confocal microscope (Owen et al., 1992) for quantifying petrophysical properties on layers within a thin section. Digital core photograph (or video) image analysis can be used to distinguish formation layering on a millimeter-by-millimeter basis by color differentiation (Georgi et al., 1992). Core images presented on the same scale as log data can be used to calibrate and supplement wireline logs. Bed boundary locations derived from core image analysis can be used with forward modeling to evaluate thin-bed well log response. In addition, high-resolution mini-permeametry data can be used to distinguish permeable from non-permeable layers to calibrate the image analysis and well logs. Georgi et al. (1992) reported image analysis and mini-permeameter applications for sand-shale cores. The methodologies will work for carbonates as long as there is color and permeability contrast between different geological layers.
X-ray diffraction Every crystalline material has a unique X-ray diffraction pattem, comparable to a fingerprint. Analysis of sediments of unknown composition with X-ray diffraction (XRD) can provide rapid mineralogy identification and abundance information (Core Laboratories, 1982). Smallsamples (less than 10 g) can be used.
Fourier transform infrared spectroscopy Mineral analysis by Fourier Transform Infrared (FTIR) Spectroscopy, like Core Laboratories' MINERALOG (Harville and Freeman, 1988), can provide rapid quantitative mineralogical information.* Typical samples such as drill cuttings, trimmed ends of core plugs, and sidewall core samples are suitable. FTIR may be used in combination with X-ray diffraction (XRD) to supply complementary mineralogical information on complex formations. These two techniques have * C o m p a n y names mentioned in this chapter are for reference only and are not meant as an endorsement o f any particular company or product.
141 comparable accuracies in analyzing bulk mineralogy (Ruessink and Harville, 1992). Ruessink and Harville concluded that one of these two techniques may be preferred over the other on the basis of its applicability to certain mineral classes: FTIR can analyze poorly crystalline material; XRD can deal with halides, and it offers the possibility of a detailed analysis of the clay-sized fraction of minerals. In other cases, the two techniques might be applied simultaneously to obtain complementary bulk mineral analysis information.
Calcimetry Calcimetry determines the percentage of limestone, dolomite, and insoluble residues in the rock. It is helpful in determining mineralogy, classifying rocks, and correlating various rock properties.
Dating Paleontology is the study of plant and animal fossils in order to determine the age of the rock in question. Micropaleontology is the study of fossils not identifiable without magnification using a petrographic or scanning electron microscope. Palynology is the study and classification of acid-insoluble plant fossils such as spores and pollen. The results of these studies, when related to sedimentary structures, texture, and lithologic characteristics, can also aid in the classification of depositional environments (Keelan, 1982).
Fracture analyses Detection of fractures and vugs from core can be done qualitatively by examination. A more quantitative analysis can provide detailed geological information. The study of a fractured reservoir (van Golf-Racht, 1982) must follow a special pattern, beginning with the examination of local basic characteristics of a single fracture and only afterwards continuing with the examination of a multifracture system. In establishing the relationship among the various groups of fractures, the local relationships are examined at reservoir scale by comparison, trends and extrapolation of parameters. Basic parameters obtained from an evaluation of fractures and the relationships between those parameters are shown in Fig. 3-18. Some core analysis techniques used for naturally-fractured reservoirs are listed in Table 3-II. Fracture orientation measured by a goniometer in conjunction with core orientation data obtained by coring with a special orientation tool, a goniometer (Rowley et al., 1967) defines dip and strike of observed fractures, which can be presented as shown in Fig. 3-20. Computerized goniometer and a fracture description program or fracture classification inventory list (Bergosh et al., 1985) improves the description of different fracture types and their quantification. To better present the complex nature of heterogeneous rocks, construction of a three-dimensional diagrams similar to the one shown on Fig. 3-19 (Bergosh et al. 1985) can be very helpful. These data, combined with core fracture logs (Snyder and Craft, 1977), can be used to estimate fracture depth, length, frequency, density per foot, lithology, rock hardness and fracture dip on a foot-by-foot basis. Additionally, core porosity and matrix oil saturation can be presented. This is particularly important in thick carbonates with wide variations in rock properties and sporadic zones of oil saturation that appear and disappear with depth (Keelan, 1982).
142 Single Fracture
Group of Fractures
1
/ ~
9Width
9Size
9Orientation
9Distribution -,,- Matrix Block Shapes
9Density
-Intensity-
9Nature Environment
i
I
l
(lithology) (morphology) Fig. 3-18. The basic parameters of fractures and their relationships are shown here. (After van GolfRacht, 1982.)
Table 3-II Core analysis methods for naturally-fractured reservoirs (After Bergosh et al., 1985; Bergosh and Lord, 1987) Method
Comments
CT scanner
Sees through core containers Sees interior of core Can be done under stress
Computerized goniometer
Can determine orientation of each fracture Can segregate different fracture types Must differentiate natural from induced fractures
Full-diameter core analysis
More representative than analysis on core plugs Porosity and saturation measurements Multidimensional permeability measurements Can be done under stress
Fluorescent epoxy impregnation
Slabs viewed under UV light Fracture porosity determined Can be done under stress
Many carbonate reservoir rocks are naturally fractured and require full-diameter core measurements to evaluate fracture effects. Plug analysis of dense-matrix rocks can indicate a non-productive formation, whereas the whole core analysis reflecting fracture permeabilities and porosities would indicate hydrocarbon production. In cases where actual well productivity greatly exceeds productivity calculated from permeabilities determined by core analysis, reservoir fractures not observed in the core are suspected. In some cases, fractures are observed in cores and question arises as to whether they were induced during coring of whether they occurred naturally. A study of the fracture faces, minerals contained therein, and truncation of the fractures may lead to understanding of their occurrence (Keelan, 1982).
143 S A M P L E ~# 7 6 DEPTH : 1 1 9 5 9 ' K v = 1 . 1 mD
/strike:
N38E
North I
~
~
/
-
~
-
-
strlk e: NI 8W
KH
M
KH MAX = 297 mD
strike: N89E dip : 37S
(~)F = 1.0% I
I~'~\\\\~'T
I
~
;I
- - - - s t r i k e : NIOW dip : 46N
CLOSED FRACTURE OPEN F R A C T U R E HEALED FRACTURE
Fig. 3-19. Three-dimensional core diagram ofpetrophysical properties of a naturally-fractured rock. (After Bergosh et a1.,1985.)
W.2~
Fig. 3-20. Fracture strike distribution from core fracture orientation. (After Keelan, 1982.)
144 Fracture analysis provides directional permeability information that can aid in well spacing and pattern design, evaluation of directional drilling and enhanced oil recovery projects. Knowledge of the fracture trend and current stress forces on the reservoir also aids fracture stimulation projections (Core Laboratories, 1989).
Geochemical core analysis Geochemical analysis provides data concerning the hydrocarbons in the core samples. Source rock evaluation, hydrocarbon-source rock correlation studies, regional or basin evaluation studies, and formation hydrocarbon versus contaminant identification are amongst the uses of geochemical data (Bond, 1988). A detailed introduction to geochemistry, analytical techniques, sample collection and preparation, and the evaluation and applications of geochemical data can be found in Bond (1986 and 1988).
SPECIAL CONSIDERATIONS FOR CORE ANALYSIS OF CARBONATE RESERVOIRS
Several factors typically unique to carbonates cause special considerations for core analysis of carbonate reservoir rocks. These include their heterogeneous nature, multimineral composition, low porosity and low permeability, wettability, and analyses accuracy and reproducibility.
Heterogeneities Pore space in carbonate rocks is highly variable and porosity can exist as microporosity, intergranular porosity, vuggy porosity, fracture porosity, or a combination of all four. These characteristics impose unique procedures when acquiring and analyzing carbonate reservoir cores. Core retrieval from carbonate reservoirs requires special considerations. Experience has shown that core barrels which use inner liners like fiberglass or aluminum containers are most effective in maximizing core recovery and minimizing damage to the recovered fractured core by providing a smooth, constant-diameter cylinder for the core to slide into, reducing the chance of jamming. During oriented coring (for fracture analysis), the communication and cooperation among the geologist or engineer requesting the core, the drilling, coring and surveying companies, personnel laying down and boxing the core, and the core services laboratory are the key to obtaining representative, analyzable core. The heterogeneous nature of carbonates often requires whole core rather than plug analysis. Whole core analysis is typically more costly and requires more time. The CT scan can help in early quantification ofheterogeneities, even while the core might still be in a container. In vuggy and fractured formations, it is still very helpful to drill and test plugs from the matrix part to define its properties, such as capillarity. These properties are important because they control initial water content and, hence, matrix hydrocarbon saturation. Carbonates containing multiple pore systems present challenges to obtaining representative capillary pressure data. Physically-larger pore systems, e.g., fractures and vugs, do not appear on capillary pressure measurement results or appear as apparent
145 closure effects at low capillary pressures. Physically-smaller pore systems, e.g., microporosity, require very high capillary pressure measurements to characterize.
Multimineral composition Carbonate reservoirs can contain complex mineral composition. It is not unusual to have evaporites, e.g., halite (salt), anhydrite, or gypsum (if shallow), layered with or in the pores of the carbonate rocks. Limestone and dolomite mixtures are possible. Dolomites can contain uranium salts, left in the rock during dolomitization, which make the traditionally low gamma ray rock radioactive. Inasmuch as carbonate rock composition can be multimineral, any petrophysical model (see Chapter 4) used to evaluate the rock in a drilling well, for example, needs to have as many measurements available (well logs, fluid analyses, rock analyses) as there are mineral types. Core can add a substantial amount of information to bring an evaluation to fruition. Gypsum presents a difficulty in obtaining accurate core analysis. Gypsum de-waters at temperatures just above 100~ (38~ The presence and de-watering of gypsum can be recognized by examination of core analysis saturation results. The sum of water saturation and oil saturation will total more than 100%, a physical impossibility. Core analysis of gypsum-bearing rock needs to be done below de-watering temperature. Halite (salt) can add complexity to core analysis. Pore-filling salt can dissolve during coring if the drilling mud is not kept at saturated salinity (at the downhole temperature). In this case, porosity that is not present in situ could be created by the salt dissolving out of the pores. Pore-filling or nodule salt can be a problem during Dean-Stark saturation analysis. The salt originally in solution in the mud filtrate, but left in the pores during extraction, needs to be removed for accurate oil saturation determination. Any method used to remove the mud filtrate salt can not differentiate it from salt which is part of the rock and will tend to remove all salt indiscriminately. If one knows the salinity and extracted volume of the mud filtrate, one can sort out which salt is which.
Low porosity and low permeability Rock that has low porosity and low permeability can take longer to clean and analyze if accuracy is a concern. If a drilling well disposition decision is to be based on core analyses results, one might consider doing a quick analysis to obtain results with enough accuracy needed to make the decision. Then additional slower analysis must be made to obtain results with the accuracy needed for reservoir characterization. The Klinkenberg correction to reduce gas permeability to an equivalent liquid value varies with permeability. Low-permeability formations require large corrections (Core Laboratories, 1989). Typical values are shown in Table 3-III.
Wettability Wunderlich (1991) discussed the three situations (coring, storing, and preparation) in which core wettability can be altered and, therefore, core analyses results may not be representative of in-situ conditions. Wettability changes can be due to interactions
146 Table 3-III Typical Klinkenberg permeability corrections (after Core Laboratories, 1989) Air Permeability k (mD)
Klinkenberg Permeability k, (mD)
Ratio of kl/k a
.18 1.00 10.0 100.0 1000.0
.12 .68 7.80 88.0 950.0
.66 .68 .78 .88 .95
with drilling fluids, pressure and temperature changes causing pore fluid phase changes, and exposure to air and other fluids during the core retrieval, storing, and analysis preparation processes. Wunderlich's recommendations provide detailed procedures for obtaining reservoir rock in a wettability state representative of in-situ wettability.
Accuracy and reproducibility The accuracy required of core analysis depends on how the data will be used. This is a general consideration and obviously not limited to carbonates. Thomas and Pugh (1989) discussed Amoco's* preparation of core sample sets that have been tested repetitively in-house and by commercial laboratories around the world. They discussed the data accumulated and showed the expected accuracy for measurements in a single laboratory by multiple operators over a long period of time. Results were compared to data on the same samples measured by other laboratories. Acceptable ranges of variation within a laboratory and between laboratories were defined and compared to those limits developed by experience.
ROCK CATALOGS
Introduction The use of a rock catalog to estimate missing formation property information can be beneficial. The suggestions for users from one rock catalog (Thomas and Sneider, 1971, plus updates) describe the information that can be obtained from a rock catalog as follows: (1) When one has some general concept of the reservoir type for which values of rock parameters are needed, one can search in the catalog for rocks matching this concept. By comparing properties of interest one may develop a feel for the spread in values and include this knowledge in whatever analysis is required for reservoir characterization. (2) When one has some specific petrophysical and/or geological information, the * Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or product.
147 process described in (1) is facilitated and the range of reservoir properties can be narrowed. (3) When one has substantial but incomplete information on the reservoir, one can estimate (by comparison of the data in hand with those of the catalog) the likely values of the missing data. (4) Finally, when looking at data available from one or more comprehensive rock catalogs, interrelations among rock properties can be derived. Items (1) through (3) can help solve specific formation evaluation or reservoir characterization problems. Item (4) has more general applications, e.g., pore combination modeling for the determination ofArchie' s m value from examination of a rock's pore types (see Chapter 4) was derived from rock property interrelations found in the Shell Development Company* Catalog of Petrophysical and Geological Properties of Typical Reservoir Rocks (Thomas and Sneider, 1971, plus updates), according to M.T. Myers (personal communication, 1982). Rock catalog data can be found in notebook form or on computer storage media such as floppy disks or CD-ROM. Figure 3-21 is an example of a core photograph taken directly from a CD-ROM rock catalog and shows the typical number of core plugs taken to provide the wide spectrum of data found in a rock catalog.
General rock properties catalogs General rock properties catalogs provide access to information from a wide variety of rock types. One can use general catalogs on rocks anywhere in the world. Reservoirs, Inc. and Robert M. Sneider Exploration, Inc.* have put together a World Wide Rock Catalog on a CD-ROM disk (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates). The disk can be accessed from a PC or a MAC. Comprehensive geological and engineering data are available for both sandstone and carbonate rocks. Core images include scanning electron microscope images, thin sections, and core photos. Analog rock data can be found by using information known about the rock of interest. PoroTechnologies* provide the Shell Development Company Catalog of Petrophysical and Geological Properties of Typical Reservoir Rocks (Thomas and Sneider, 1971, plus updates). All photographic, numeric, and text data have been digitized and placed on CD-ROM disks for rapid access using PC, MAC or UNIX systems. PetroTech added to the catalog data base new rock sample and thin section photomicrographs, petrophysical data tables, and "simulated cuttings" sample comparators.
Specific formation rock properties catalogs Specific formation rock properties catalogs provide access to information from the complete range of rock types of a single formation, usually from a single field. One can use specific catalogs for the field and formation from which it was created. * Company names mentionedin this chapter are for reference only and are not meant as an endorsement of any particular company or product.
148
TOP
:i:K,:
A
11111i~r: 1
"::C
(D
(E:'
,(F
(~;
////////N N NII'I' N [
POROSITY
(%)
PERMEABILITY (rod) GR. D E N S I T Y ( g / c c )
81566:31 5
]
X
A
B
C
D
E
F
Y
S.8
11.1
lO.a
to.4
11.2
v~)
s.2
e.4
361 2J12
1 s.8 2.84
e~8 :1.86
1 =.0 2.85
8.s4 2.84
o.ee 2.86
z.e4 2.85
1.01 2.B5
CORE LITHOLOGY AND DEPOSITIONAL ENVIRONMENT: L~X..BROWNTOGI~Y,MASSIYE, A .NHVDRITIC
DOLOM~. VERTICAL FRACTURE,q, $TYLOUTES LOCALLY OEV~,.OP'ED. D ~ O N A L
sum-~
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
ENVtRONMF~'r NOT
....
................................... "~ - GI~OLOGICALLY AItALYZED
Fig. 3-21. Rock catalog sampling technique which provides sufficient plug samples for the wide range of core analysis measurements found in a rock catalog. The range in porosity, permeability, and grain density values gives an idea of the heterogeneity of the rock. This core photo and data for the Shell Granger #3 are from the World Wide Rock Catalog, CD-ROM version. (From Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates.)
Reservoirs Inc. has compiled formation- and region-specific rock catalogs to address petrophysical and geological properties contributing to reservoir performance. These catalogs use rock classification systems developed specifically for rock types encountered in subject formations. Petrophysical testing for each rock type concentrates on particular local formation evaluation problems. Catalogs include: Wilcox Drilling and Completion Procedures, Vicksburg Formation, Prairie du Chien Formation, Texas and Louisiana Offshore Miocene, and a Yemen Rock Catalog (W.K. Hudson, personal communication, 1993). SUMMARY
Coring and analyses for accurate reservoir characterization requires cost-effective, acceptable-quality (meeting the accuracy needs of the particular characterization) core data over full range of rock properties of that reservoir. Of course the core data are not the only data available (or needed) and should be integrated with other formation evaluation and reservoir characterization data, either taken directly from that reservoir
149 or analogous reservoirs. To recognize problems that can be solved by core analyses (in a cost-effective manner), one might consider answering the following questions: (1) What kind of formation evaluation or reservoir characterization problems need solving? (2) Which ones of these problems can be solved by core analyses? (3) Are there other formation evaluation or reservoir characterization tools that can be used to solve these problems? (4) What is the accuracy needed in the problem solution? (5) Which evaluation tools provide the solution to these problems with the required accuracy, at the lowest cost? (6) If core analyses provides the solution, what kind and how much should be done? Which lab(s) should do it? (7) How should the problems be solved if sufficient core can not be obtained? (8) Is there other information or other problem solutions that need to be obtained from any of these tools? (9) Does this alter the decision on the cost-effective approach to obtain the formation evaluation or reservoir characterization solutions?
ACKNOWLEDGMENTS
Mr. Murphy wishes to thank Shell Oil Company for permission to contribute this chapter. Thanks also go to the Shell Development Company Information Services Library at the Bellaire Research Center, in particular to Kathy Harris, for providing references in a very timely manner.
REFERENCES American Petroleum Institute, 1960. Recommended Practice for Core-Analysis Procedure (API RP 40), Washington, DC., First Edition, Order No. 811-08300, August, 55 pp. This document is being revised as of press time. Amott, E., 1959. Observations relating to the wettability of porous rock. Trans. AIME, 216: 156-162. Anderson, G., 1975. Coring and Core Analysis Handbook. Petrol. Publ. Co., Tulsa, OK, 200 pp. Archer, J.S. and Wall, C.G., 1986. Petroleum Engineering Principles and Practice. Graham and Trotman, London, UK, 362 pp. Archie, G.E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. AIME, 146: 54-62. Bergosh, J.L. and Lord, G.D., 1987. New developments in the analysis of cores from naturally fractured reservoirs. SPE paper 16805, SPE 62nd Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Dallas, TX, Sept. 27-30:563 - 570. Bergosh, J.L., Marks, T.R. and Mitkus, A.F., 1985. New core analysis techniques for naturally fractured reservoirs. SPE paper 13653, SPE California Regional Meeting Proc., Bakersfield, CA, March 2 7 29: 599-610. Bond, J.G., 1986. Introduction to Exploration Geochemistry. GL701, International Human Resources Development Corporation, Boston, MA, 352 pp. plus video. Bond, J.G., 1988. Application of Exploration Geochemistry. GL702, International Human Resources Development Corporation, Boston, MA, 322 pp. plus video. Bush, D.C. and Jenkins, R.E., 1977. CEC determination by correlation with adsorbed water. Paper H, SPWLA 18th Ann. Logging Symp., Houston, TX, June 5-8:10 pp.
150 Carmichael, R.S. (Editor), 1989. CRC Practical Handbook of Physical Properties of Rocks and Minerals. CRC Press, Inc., Boca Raton, FL, 741 pp. Carver, R.E. (Editor), 1971. Procedures in Sedimentary Petrology. Wiley-Interscience, New York, 633 pp. Chandler, M.A., Goggin, D.J. and Lake, L.W., 1989. A mechanical field permeameter for making rapid, non-destructive, permeability measurements. J. Sed. Pet., 59(4): 613 -615. Chen, Z., McLemore, J. and Heller, J.P., 1993. The miniporopermeameter for simultaneous measurement of permeability and porosity. SPE paper 26508, SPE 68th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Houston, TX, Oct. 3--6: 897-905. Coles, M.E., Muegge, E.L. and Marek, B.F., 1992. Use of attenuation standards for CAT scanning applications within oil and gas production research. SCA paper 9223, The Soc. of Core Analysts Preprints, Oklahoma City, OK, 28 pp. Core Laboratories, 1982. A Course in Special Core Analysis. Dallas, TX. Core Laboratories, 1989. A Course in the Fundamentals of Core Analysis. Houston, TX, Ver. 3.1. Davies, D.K., 1990. Image analysis of reservoir pore systems: state of the art in solving problems related to reservoir quality. SPE paper 19407, SPE Formation Damage Control Symp. Proc., Lafayette, LA, Feb. 22-23: 73-82. Davison, I. and Haszeldine, R.S., 1984. Orienting conventional cores for geological purposes: a review of methods. J. Petrol. Geol., Bucks, England, 7(4): 461-466. de Waal, J.A., Smits, R.M.M., de Graaf, J.D. and Schipper, B.A., 1989. Measurement and evaluation of resistivity index curves. Paper II, SPWLA 30th Ann. Logging Symp., Denver, CO, July 11-14:10 pp. plus figs. Donaldson, E.C., Thomas, R.D. and Lorenz, P.B., 1969. Wettability determination and its effect on recovery efficiency. Soc. Pet. Eng. J., 9(1): 13-20. Edelstein, W.A., Vinegar, H.J., Tutunjian, P.N., Roemer, P.B. and Mueller, O.M., 1988. NMR imaging for core analysis. SPE paper 18272, SPE 63th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Houston, TX, Oct. 2-5:101 - 112. Edmunson, H. and Raymer, L.L., 1979. Radioactive logging parameters for common minerals. The Log Analyst, 20(5): 38-47. Erratum The Log Analyst, 21(2). Ehlers, E.G., 1987. Optical Mineralogy, 1Iol. 1-Theory and Technique, Vol. 2-Mineral Descriptions. Blackwell Scientific Publications, Palo Alto, CA. Vol. 1,158 pp.; Vol. 2, 286 pp. Ehrlich, R. and Davies, D.K., 1989. Image analysis of pore geometry: relationship to reservoir engineering and modeling. SPE paper 19054, SPE Gas Tech. Symp. Proc., Dallas, TX, June 7-9:15-30. Ellis, D., Howard, J., Flaum, C., McKeon, D., Scott, H., Serra, O. and Simmons, G., 1988. Mineral logging parameters: nuclear and acoustic. The Technical Review, 36(1): 38-52. Georgi, D.T. and Jones, S.C., 1992. Application of pressure-decay profile permeametry to reservoir description. Presented at the 16th Ann. SPE (Nigerian Council) Internat. Conf. and Exh., Lagos, Nigeria, Aug. 26-27:12 pp. Georgi, D.T., Phillips, C. and Hardman, R., 1992. Applications of digital core image analysis to thin-bed evaluation. Presented at the 16th Ann. SPE (Nigerian Council) Internat. Conf. and Exh., Lagos, Nigeria, Aug. 26-27:12 pp. Golf-Racht, T.D. van, 1982. Fundamentals of Fractured Reservoir Engineering. Elsevier Sci. Publ. Co., New York, 710 pp. Harville, D.G. and Freeman, D.L., 1988. The benefits and application of rapid mineral analysis provided by Fourier transform infrared spectroscopy. SPE Paper 18120, SPE 63th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Houston, TX, Oct. 2-5:141 - 150. Hawkins, 1988. Comparison of three methods of relative permeability measurement. SCA paper 8804, The Soc. of Core Analysts Preprints, 16 pp. Hicks Jr., P.J., Deans, H.A. and Narayanan, K.R., 1992. Distribution of residual oil in heterogeneous carbonate cores using X-ray CT. Soc. Pet.. Eng. Form. Eval., Sept. 7(3): 235-340. Hirasaki, G.J., 1991. Wettability: Fundamentals and surface forces. SPE Formation Evaluation, 6(3): 217-226. Hirasaki, G.J., Rohan, J.A., Dubey, S.T. and Niko, H., 1990. Wettability evaluation during restored-state core analysis. SPE paper 20506, SPE 65th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., New Orleans, LA, Sept. 23-26:361-375. Hove, A., Ringen, J.K. and Read, P.A., 1987. Visualization of laboratory corefloods with the aid of computerized tomography of X-rays. Trans. AIME, 283:148-154.
151 Howard, J.J., Kenyon, W.E. and Straley, C., 1990. Proton magnetic resonance and pore-size variations in reservoir sandstones. SPE paper 20600, SPE 65th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., New Orleans, LA, Sept. 23-26: pp. 733-742. Hunt, P.K., Engler, P. and Bajsarowicz, C., 1988. Computerized tomography as a core analysis tool: applications, instrument evaluation, and image improvement techniques. J. Petrol. Tech., 40(9): 1203-1210. Hyland, G.R., 1983. Pressure coring-an oilfield tool. SPE paper 12093, SPE 58th Ann. Tech. Conf. and Exh., San Francisco, CA, Oct. 5--8:8 pp. IHRDC, 1985. Sample and Core Handling and Analysis. GL303, International Human Resources Development Corporation, Boston, MA, 114 pp. plus video. Jantzen, R.E., Syrstad, S.O., Taylor, M.R., Spicer, P.J., Stockden, I., Dodson, T. and Saunders, M.R., 1993. Answering geological questions from slimhole coring exploration. Paper T, SPg"LA 34th Ann. Logging Symp. Trans., Calgary, AL, June 13-16, 18 pp. Jodry, R.L., 1992. Pore geometry of carbonate rocks. Carbonate Reservoir Characterization: A Geologic-Engineering Analysis, Elsevier Publ. Co., Amsterdam, Part I, Chapter 6 of this book, pp. 331377. Updated from: 1972, Oil and Gas Production from Carbonate Rocks, American Elsevier Publ. Co., Inc., New York, NY, pp. 35-82. Keelan, D.K., 1972. A critical review of core analysis techniques. J. Cdn. Petrol. Tech., 11 (2; Apr.June): 42-55. Keelan, D.K., 1982. Core analysis for aid in reservoir description. J. Petrol. Tech., 34(11): 2483-2490. Kenyon, W.E., Day, P.I., Straley, C. and Willemsen, J.F., 1988. A three-part study of NMR longitudinal relaxation studies of water-saturated sandstones. SPE Formation Evaluation, 3(3): 622-636. Leverett, M.C., 1941. Capillary behavior in porous solids. Trans. AIME, 142:152-168. Mahmood, S.M., Maerefat, N.L. and Chang, M-M., 1988. Laboratory measurements of electrical resistivity at reservoir conditions. SPE paper 18179, SPE 64th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Houston, TX, Oct. 2-5: 705- 719. Monicard, R.P., 1980. Properties of Reservoir Rocks: Core Analysis. GulfPubl. Co., Houston, TX: 168 pp. Morrow, N.R., 1990. Wettability and its effect on oil recovery. J. Petrol. Tech., 42(12): 1476-1483. Muscat, M., 1949. Physical Principles of Oil Production. McGraw-Hill, New York: 922 pp. (p. 142). Owen, L.B., Greaves, K.H., Lord, G., Bereskin, S.R. and King, E., 1992. Improved pore visualization by confocal microscopy. SCA paper 9226, The Soc. of Core Analysts Preprints, Oklahoma City, OK: 16 PP. Purcell, W.R., 1949. Capillary pressures-their measurement using mercury and the calculation of permeability therefrom. Trans. AIME, 186: 39-48. Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates. A Catalog of Geological and Engineering Properties for Sandstones and Carbonates. Reservoirs, Inc., Houston, TX, July. Eight volume notebook version and CD-ROM version. Rose, W.D. and Bruce, W.A., 1949. Evaluation of capillary character in petroleum reservoir rocks. Trans. AIME, 186: 127-142. Rowly, D.S., Burk, C.A. and Manual, T., 1967. Oriented Cores. Christensen Diamond Products Co., Salt Lake City, UT. Ruessink, B.H. and Harville, D.G., 1992. Quantitative analysis of bulk mineralogy: the applicability and performance of XRD and FTIR. SPE paper 23828, SPE Internat. Symp. on Formation Damage Control Proc., Lafayette, LA, Feb. 26-27: 533-546. Scholle, P.A., 1978. A Color Illustrated Guide to Carbonate Rock Constituents, Textures, Cements, and Porosities. Memoir 27, AAPG, Tulsa, OK, 241 pp. Seevers, D.O., 1966. A nuclear magnetic method for determining the permeability of sandstones. Paper L, SPWLA 7th Ann. Logging Symp. Trans., Tulsa, OK, May 8-11:14 pp. Skopec, R.A., 1991. In-situ stress evaluation in core analysis. SCA paper 9103, The Soc. of Core Analysts Preprints, San Antonio, TX, Aug. 21-22:14 pp. Skopec, R.A., Mann, M.M., Jeffers, D. and Grier, S.P., 1992. Horizontal core acquisition and orientation for formation evaluation. SPE Drilling Engineering, 7(1): 47-54. Smith, D.G., 1990. Predicting a down dip water level using capillary pressure relationships. Paper Z, SPWLA 31st Ann. Logging Symp. Trans., Lafayette, LA, June 24-27:11 pp. Snyder, R.H. and Craft, M., 1977. Evaluation of Austin and Buda formations from core and fracture analysis. Trans. Gulf Coast Assn. Geol. Socs., 27: 376-385.
152 Soc. of Professional Well Log Analysts, 1990. Borehole Imaging Reprint Volume. Houston, TX: 472 pp. Spain, D.R., Morris, S.A. and Penn, J.T., 1992. Automated geological evaluation of continuous slimhole cores. J. Petrol. Tech., 44(6): 662-668. Swanson, B.E, 1981. A simple correlation between permeabilities and mercury capillary pressures, jr. Petrol. Tech., 33(12): 2498-2504. Swanson, R.G., 1985. Sample Examination Manual. Am. Assoc. Petrol. Geologists, Third Printing, May. Thomas, D.C. and Pugh, V.J., 1989.A statistical analysis of the accuracy and reproducibility of standard core analysis. The Log Analyst., 30(2): 71-77. Thomas, E.C. and Sneider, R.M., 1971, plus updates. A Catalog of Petrophysical and Geological Properties of Typical Reservoir Rocks. Shell Development Co., TPR-EPR-31-7 l-P, July, 3 vol. Thomeer, J.H.M., 1960. Introduction of a pore geometrical factor defined by the capillary pressure curve. Trans. AIME, 219: 354-358. Thomeer, J.H., 1983. Air permeability as a function of three pore-network parameters. J. Petrol. Tech., 35(4): 809-814. Tutunjian, P.N. and Vinegar, H.J., 1990. Petrophysical applications of automated proton high resolution NMR spectroscopy. SCA paper 9020, The Soc. of Core Analysts Preprints, Dallas, TX, Aug. 14-16: 23 pp. Tutunjian, P.N., Vinegar, H.J. and Ferris, J.A., 1991. Nuclear magnetic resonance imaging of sodium23 in cores. SCA paper 9111, The Soc. of Core Analysts Preprints, San Antonio, TX, Aug. 21-22:18 PP. Tutunjian, P.N., Vinegar, H.J. and Ferris, J.A., 1993. Characterization of pore microgeometry by NMR diffusion measurements. Paper II, SPWLA 34th Ann. Logging Symp. Trans., Calgary, AL, June 13-16:13 PP. Vinegar, H.J., 1986. X-ray CT and NMR image of rocks. J. Petrol. Tech., 38(3): 257-259. Vinegar, H.J. and Wellington, S.L., 1987. Tomographic imaging of three-phase flow experiments. Rev. Sci. Instruments, 58(1): 96-107. Vinegar, H.J., Tutunjian, P.N., Edelstein, W.A. and Roemer, P.B., 1991a. Whole-core analysis by ~3C NMR. SPE Formation Evaluation, 6(2): 183-189. Vinegar, H.J., Tutunjian, P.N., Crabtree, P.T., Raffaldi, F.J., DiFoggio, R. and Edelstein, W.A., 1991b. NMR spectroscopy of tight, gypsum-bearing carbonates. The Log Analyst, 32(5): 527-535. Wang, S.Y., Ayral, S., Castellana, F.S. and Gryte, C.C., 1984a. Reconstruction of oil saturation distribution histories during immiscible liquid-liquid displacement by computer assisted tomography. Am. Inst. Chem. Eng. jr., 30(4): 642-646. Wang, S.Y., Ayral, S. and Gryte, C.C., 1984b. Computer assisted tomography for the characterization of oil displacement in porous media. Soc. Pet. Eng. J., 24(1): 53-55. Wellington, S.L. and Vinegar, H.J., 1987 X-ray computerized tomography. J. Petrol. Tech., 39(8): 885989. Wells, L.E., Sanyal, S.K. and Mathews, M.A., 1979. Matrix and response characteristics for sonic, density and neutron. Paper Z, SPWLA 20th Ann. Logging Symp. Trans., Tulsa, OK, June 3-6:25 pp. Welton, J.E., 1984. SEM Petrology Atlas. AAPG, Tulsa, OK, 237 pp. Whittaker, A. (Editor), 1985. Coring Operations-Procedures for Sampling and Analysis of Bottomhole and Sidewall Cores. EXLOG, Boston, MA, 174 pp. Withjack, E.M., 1988. Computed tomography for rock-property determination and fluid-flow visualization. SPE Form. Eval., 3(4): 696-704. World Oil Coring Series, 1985-1986. Composed of the following articles: Part 1 - W h y it's done. Dare Keelan, March 1985: 83-90. Part 2 - C o r e barrel types and uses. Art Park, April 1985: 83-90. Part 3 -Planning the job. Art Park, May 1985: 79-86. Part 4 - B i t considerations. Art Park, June 1985: 149-154. Part 5 -Avoiding potential problems. Art Park, July 1985: 92-98. Part 6-Sidewall operations. James B. Toney and J. Lee Speights, Aug. 1985: 29-36. Part 7-Analytical aspects of sidewall coring. M. Craft and D. Keelan, Sept. 1985: 77-90. Part 8 - P l u g and full diameter analysis. Dare Keelan, November 1985: 103-112. Part 9-Geological aspects. David G. Kersey, January 1986: 103-108. Wunderlich, R.W., 1991. Obtaining samples with preserved wettability. In: N. R. Morrow (Editor), Interfacial Phenomena in Oil Recovery. Marcel Dekker, Inc. NY, NY, Chapter 8, pp. 289-318.
153 Wyman, R.E., 1976. How should we measure residual oil saturation. Joint Convention on Enhanced Recovery, Petroleum Society of CIM-Canadian Society of Petroleum Geologists, Calgary, AL, June 711:37 pp. Yuan, H.H., 1991a. Pore scale heterogeneity from mercury porosimetry data. SPE Form. Eval., 6(3): 233 -242. Yuan, H.H., 1991 b. Advances inAPEX technology: determination of cementation exponent and absolute permeability. The Log Analyst, 43(5): 557-570. Yuan, H.H. and Diederix, K.M., 1989. The role of membrane potential measurements in shaly sand evaluation. The Log Analyst, 30(6): 415-423.
This Page Intentionally Left Blank
155
Chapter 4 FORMATION EVALUATION DAVID PATRICK MURPHY
INTRODUCTION
This chapter was written to provide a fairly detailed overview of carbonate formation evaluation. Emphasis was put on several carbonate evaluation subjects and concepts to increase reader awareness concerning the following: Philosophy of formation evaluation. Understanding petrophysics. Formation evaluation properties of interest. Formation evaluation tools. Different approaches for different evaluation situations. The definition and uses of petrophysical models. Determination of formation evaluation properties of interest. Magnitude of error in and reliability of determined results. References that provide even more detail on carbonate formation evaluation. The focus of this chapter is on formation evaluation of carbonate reservoirs. However, many of the tools and techniques discussed in this chapter can be applied to the evaluation of other rock types if a proper petrophysical model is used.
FORMATION EVALUATION PHILOSOPHY
First and foremost: understand petrophysics To accurately perform an evaluation of a formation of interest, the evaluator must understand the physics and chemistry of the rock in that formation. Petrophysics is a term used to express the physical and chemical properties of rocks which are related to the pore and fluid distributions, particularly as they pertain to the detection and evaluation of hydrocarbon-beating layers in contrast to non-hydrocarbon-bearing layers. This definition closely follows the one coined by G.E. Archie and J.H.M.A. Thomeer, and published by Archie in 1950 (J.H.M. Thomeer, personal communication, 1990; Archie, 1950). They intended that petrophysics refer to the physics of particular rock types, whereas geophysics is associated with the physics of the larger rock systems composing the earth. Contained within this definition of petrophysics are four words which should be defined very carefully in order that there will be no misunderstanding of the manner in which they are used in this chapter. These words are rock, hydrocarbons, detection, and evaluation. Rock is defined as mineral matter and its associated fluids (if fluids are present) occurring naturally in large quantities; also, a particular mass of it. This definition of rock is somewhat different from the one given in dictionaries, primarily because of
156 the inclusion of the contained fluids as part of the rock itself. Fluids contained within the rock are of particular importance, inasmuch as it is these fluids which are produced. Hydrocarbons are any of a number of compounds of hydrogen and carbon in the liquid or gaseous states. Within the producing arm of the petroleum industry these hydrocarbons usually are referred to as oil and gas, both of which are produced in great quantities. In addition, one might be interested in evaluating CO 2 reservoirs as a source of flood injectant fluid in tertiary recovery processes. In this chapter, a fluid will be designated as a gas if it is in the gaseous state. A fluid will be designated as a liquid if it is in the liquid state. A fluid will be designated as a fluid if its state is unknown or irrelevant to the situation. Detection is defined as the recognition of the presence of hydrocarbons in rock. The presence of hydrocarbons in rock does not necessarily mean they are present in either commercial, or even producible, quantities. Too often hydrocarbons are detected but are found to be nonproducible. Such might be the case when the structural configuration of the subsurface has been altered through tectonic movement of rock. Subsequent water flow through a subsurface stratum can then effectively water flood an existing accumulation. Not all of the hydrocarbons will be removed during this water flooding process. Hydrocarbons which are detected are those which have been left behind. Evaluation is defined as the determination of the volume of hydrocarbons in place in the area, e.g., one acre, surrounding the wellbore; and estimation, if possible, of the initial rate at which they can be produced. This word, evaluation, is quite definitive. In a nutshell it defines the job of the formation evaluation specialist. Evaluation entails the use of all data available including mud log and measurement while drilling information; production, drill stem, and wireline tests; cores and core analyses; and wireline log data. All of these data must fit into a consistent petrophysical and geological model that describes the physical situation. If the formation evaluation specialist understands petrophysics, he or she can understand the response of various evaluation tools, and can then best predict pertinent rock and fluid properties and the performance of the formation.
FORMATION PROPERTIES OF INTEREST
Primary formation properties of interest The job of the formation evaluation specialist is to evaluate hydrocarbon reservoirs to provide information needed for the economic optimization of that reservoir. The economics of a hydrocarbon reservoir are directly related to the volume of hydrocarbons in place, the production rate, and the optimization of spending to produce the hydrocarbon reservoir. For a person concerned about obtaining this kind of information from formation evaluation, six formation properties typically fall out as being of primary interest: (1) net formation thickness; (2) porosity; (3) pore fluid saturations; (4) permeability;
157 (5) lithology, structure, and stratigraphy; and (6) pore fluid properties. The volume of hydrocarbons in place is proportional to the product of net formation thickness, porosity, and hydrocarbon saturation. This volume is the ultimate target for the economic development of a field. Volume I, Chapter 11 of this book gives details on oil and gas reserve estimation methods. The recoverable reserves depend upon the production mechanism. Accuracies required in formation evaluation results depend on the cost of implementing that producing mechanism. Accuracies need to be tighter for pre-waterflood evaluation than for primary production evaluation because of the cost of implementing the waterflood. Formation evaluation results need to be even more accurate for pre-CO 2 flood evaluation than for waterflood evaluation because of the much higher cost of implementing a CO 2 flood. The production rate of a well is related to the combination of the net formation thickness, the permeability, and pore fluid properties, e.g., fluid viscosities. Production rate has significant impact on a well's economic performance because of the present value of future revenues and production-related expenditures. Determining the correct interpretation of the geological situation, i.e., the correct geologic model, for a hydrocarbon reservoir, allows optimal selection of well locations, prediction of well performance, and optimal management of the producing asset. Determination of the correct geologic model requires, as a minimum, knowledge of lithology, structure, stratigraphy, and net formation thickness throughout the reservoir.
Other formation properties of interest Other formation properties can provide additional insight into the hydrocarbon volume, production rate, and optimization of spending to produce the reservoir. A partial list of other formation properties of interest includes: (1) formation pressure; (2) wettability; (3) seal capacity; (4) source rock richness; (5) fractional fluid flow properties; (6) depositional environment; (7) diagenesis; (8) rock mechanical properties; and (9) acoustic velocity and anisotropy. The formation evaluation results provide the information that is needed for the economic optimization of the reservoir. The particular formation properties of interest that need to be determined depend on the specific evaluation situation.
FORMATION EVALUATION TOOLS
The principal categories of tools that are to used in the evaluation of formations are listed below. These tools are readily available and are routinely used in the acquisition of formation evaluation data. The reference(s) listed with each tool category can
158 provide the reader with an introductory overview of those tools and their application to formation evaluation: (1) wireline logging (Dewan, 1983"); (2) mud logging (Jorden and Campbell, 1984, Chapter 4); (3) measurement while drilling logging (Allen et al., 1989); (4) coring and core analyses (Worm Oil Coring Series, 1985-1986t); (5) drill stem testing (Donohue, 1984); (6) wireline testing (Atlas Wireline Services, 1989a; Schlumberger, 1981); and (7) production testing (Donohue and Ertekin, 1982; Donohue, 1986; LeBlanc, 1988). Wireline logging and measurement while drilling logging will be collectively termed well logging in this chapter. Other categories of tools that are available for use in the evaluation of formations are listed below. In carbonates, these tools seem to be used substantially less than the aforementioned principal categories of tools because they provide very specialized results that are not needed in most evaluations. The reference(s) listed with each tool category can provide the reader with an introductory overview of those tools and their application to formation evaluation: (1) single- and multi-well tracer tests (Deans, 1978); (2) geotomography (Worthington, 1984, for acoustic tomography; Dines and Lytle, 1979, for electromagnetic tomography; Kretzschmar and Witterholt, 1984, for historical background and EOR surveillance in pilots); and (3) seismic (Ausburn et al., 1977, for general seismic applications to formation evaluation; Ausburn, 1979, for well log editing to improve seismic calibration; Brown, 1986, for 3-D seismic applications). In general, the use of seismic in carbonates is limited to structural and stratigraphic determination. Fluid content detection from seismic, that works well in unconsolidated, high-porosity siliciclastic sediments (Domenico, 1977), does not generally work in consolidated, low-porosity rocks (Domenico, 1974), which would be common for carbonate reservoirs. In the design of formation evaluation programs, the choice of evaluation tools to use depends upon the formation evaluation questions that need to be answered. It is not economically prudent to run particular tools to gather information just to satisfy one's general sense of curiosity. The correct evaluation tool or tools that should be used are the ones that answer the questions that need to be answered, with acceptable accuracy, at the lowest cost. * Dewan provides a good introduction to wireline logging for readers who have little or no background in formation evaluation. Two additional references can provide much more technical detail on well logs. Tittman (1986) addresses the physics of logging measurements. The techniques universally used in formation evaluation (electrical, nuclear, and sonic) are described in some detail, whereas only short descriptions are given of less widely exploited methods such as electromagnetic propagation and nuclear magnetic resonance. Ellis (1987) emphasizes the importance of physics in well logging and includes discussions and problems which explain the mechanics of obtaining the usual petrophysical parameters from well log data. t The WorldOil (1985-1986) articles provide a good introduction to coring and core analysis for readers who have little or no background in formation evaluation. Spain et al. (1992) describe the automated geological evaluation of continuous slim-hole cores. "Inverse logging" (logging the core instead of the borehole) is the primarygoal of on-site geologicalevaluation.This approachhas the potential for providing the ultimate in geological data and insight, and is also used to calibrate seismic and well log data.
159 FORMATION EVALUATION SITUATIONS
Different formation evaluation situations require different questions that need to be answered in order to characterize a reservoir. Therefore, they require somewhat different approaches and use different combinations of the principal categories of evaluation tools to obtain formation evaluation answers. Three common formation evaluation situations are drilling wells, flood process pilots, and production surveillance.
Formation evaluation of drilling wells Formation evaluation of drilling wells provides for evaluating formations exposed by the drill bit during drilling or deepening of a well. The evaluation must provide answers to the questions concerning how to economically explore, drill, and produce the formation/well/field. A partial list of questions that might need to be answered by evaluation of a drilling well are listed in Table 4-1. Evaluation activity can be focused not only on the planned primary objectives, but also on uphole objectives that may or may not have been anticipated beforehand. Data are usually acquired in the open hole, although cased hole data can be preferable due to lower cost or can be required because of poor openhole conditions. The specific types of tools used to acquire formation evaluation data depend on the type of well, its objectives, and the questions that need to be answered. A well drilled to test a seismic play needs a plan to acquire data to calibrate the seismic. A well drilled to prove a geological model needs to acquire geological data. An infill well drilled close to the offset wells may only need to determine the location of the productive zone: all other formation properties can usually be correlated from surrounding wells. Some of the openhole data (e.g., data from mud logs, measurement-while-drilling logs, core examination) become available in near-realtime, usually within minutes or hours after the formation is penetrated. Other openhole data (e.g., wireline logs, formation tests, core analyses) become available a day or more after the formation has been penetrated by the bit. Cased hole data become available at a much later time, after casing has been set. Time involved in formation data acquisition and evaluation of drilling wells is usually costly due to the daily drilling rig cost for the data acquisition and evaluation. If casing has to be set to evaluate the well, additional expense is involved.
Formation evaluation for flood process pilots Formation evaluation for flood process pilots provides for evaluating the production of additional hydrocarbons from a formation using that process. Acquiring data to characterize the response of the formation to enhanced recovery processes is the main objective of a pilot. This usually involves the measurement of remaining oil saturation and its distribution before and after the flood process, and monitoring of the flood progress and results on a zone-by-zone basis. Methodologies for this type of evaluation are detailed by Thomas et al. (1987). A partial list of questions that might
160 TABLE 4-1 Partial list of questions that might need to be answered by the evaluation of a drilling well Specialist*
Questions
All
Which exploration, drilling, and completion approach will result in the optimum economic results?
Geologists
Does the actual geological situation fit my geological model? Is there source rock in the geological column? What is the richness of the source rock? What is the seal capacity of the seal?
Geophysicists
What are the acoustic velocities or impedances? What is the acoustic anisotropy? What are the acoustic impedance trends in this area?
Petrophysicists
What is the appropriate petrophysical model? What are the log-core relationships? Can overpressures be predicted? What is pay?
Drilling Engrs.
What What What What
pressures will be encountered? are the fracture gradients? is the rock integrity during drilling? are compatible drilling muds?
Reservoir Engrs.
What What What What
are the fluid properties? are the fractional flow characteristics of the rock? is the formation pressure? are the directional permeabilities?
Production Engrs.
How is the pay distributed vertically? Is stimulation needed? What are compatible fluids?
Facilities Engrs.
Is the production going to be oil, gas, and/or water? What are the production rates going to be? What are the produced fluid properties?
* A person involved in evaluating a well may or may not be a specialist focused on only one aspect of technology. In some cases, a single person would have the responsibilities of several or even all of the specialist jobs listed here. This table shows that there can be many different perspectives in an evaluation effort.
need to be answered by evaluation of a flood process pilot is given in Table 4-11. Examples of typical CO 2 flood process pilots are discussed by Charlson et al. (1978), and Tanner et al. (1992). These pilots involved a brine pre-flood, a CO 2 or alternating CO2/brine main flood, and a brine post-flood. Pilots can take several years to complete and they may cost several, maybe tens of millions of dollars. The evaluation procedures can involve many, if not all, of the formation evaluation tools.
Production surveillance formation evaluation Production surveillance formation evaluation provides for evaluating methodologies that optimize the profit and recovery of an already producing formation as part of the reservoir management plan for that formation. A partial list of questions that might
161 TABLE 4-11 Partial list of questions that might need to be answered by the evaluation of a flood process pilot Specialist
Questions
All
Which flood process approach will result in the optimum economic results?
Petrophysicists
What is the change in residual oil saturation and distribution caused by the process flood injectant? How do the saturations change over time? What are the errors in the saturation results?
Production Engrs.
Can adequate CO 2 injection and follow-up water injection rates be attained?
Geologists
Is the geology of the pilot area representative of the geology of the whole field? What is the importance of structure and stratification in the flood process?
Reservoir Engrs.
Is there any other process, e.g., gravity segregation, that will affect the flood response? What is the injection profile? What are the volumetric production results from the flood process pilot? What are the errors in the volumetric production results? Can a flood simulator history match be made with the flood process pilot response? Can the flood simulator be scaled up to the field level?
need to be answered by surveillance formation evaluation is given in Table 4-Ill. One example of surveillance evaluation is the monitoring of a CO 2 flood using wireline-derived petrophysical data (Kittridge, 1992). According to Kittridge, results TABLE 4-11I Partial list of questions that might need to be answered by surveillance evaluation Specialist
Questions
All
Which production approach will result in the optimum economic results?
Production Engrs.
Are there productive zones that are not perforated or completed properly? Are there thief zones that need to be closed off?. Do the completion intervals have zonal isolation integrity? What is the mechanical integrity of each wellbore? How long will each wellbore be usable?
Petrophysicists
What are the original and current fluid saturations in each zone in each well?
Reservoir Engrs.
Can a flood simulator history match be made with the field production history? What should be the fractional fluid production of each zone in each well?
Geophysicists
Will 3-D seismic or geotomography help in monitoring fluid contacts or flood fronts? Are there deeper potential hydrocarbon zones?
Several
Which zones are producing the oil, gas, and/or water? Are the fluid contacts moving in the reservoir? Is the pay moving because of water or gas encroachment? Into which zones is the injectant (e.g., water, natural gas, or carbon dioxide) being injected? At what rates should each zone in a well be producing? How does the production rate of each zone compare to that zone's potential? Why is a zone not producing up to its potential? Are there portions of the field that need additional wells?
162 obtained with surveillance monitoring of this type are useful for quantifying CO 2 saturation, monitoring flood progress and vertical sweep, identifying potential outof-zone injectant losses, and detection of non-responding layers. Another example of surveillance evaluation is flood monitoring with induction logs run in wells that are completed with fiberglass casing specifically for the purpose of induction log monitoring. Induction tool monitor logg!ng during a chemical flood, a polymer flood, and a CO 2 flood pilot is detailed by Richardson (1979). Production surveillance data acquisition need to be scheduled so as not to adversely impact the revenue from producing operations. Existing wells can be used during workovers, or in many cases, even while the well is producing. Wells drilled to or through the formation of interest during the time of surveillance can also be used to acquire formation evaluation data to assist in the surveillance effort. Or as detailed by Richardson (1979), wells can be drilled and completed solely for the purpose of surveillance data acquisition.
PETROPHYSICAL
MODELS
A petrophysical model is a description of the physics of a rock and the fluids it contains. This description is in the form of an equation or equations. The result of the equation is the formation property of interest. One example of a petrophysical model is the determination of porosity from the formation bulk density. The description of the physical situation is: the bulk density of the formation is related to its porosity and rock by a linear, volumetric mixing law. The formation bulk density is, therefore, equal to the rock matrix density weighted by its fractional volume plus the pore fluid density weighted by its fractional volume. The equation for this physical situation is:
Pb= d~Pi§(1-dP)Pr~
(4-1)
where: Pb = bulk density (g/cm3); Pl = pore fluid density (g/cm3); Pma- - rock matrix density (g/cm3); and d~ = porosity (fractional). Bulk density, Pb' is usually measured by a wireline or measurement while drilling log, whereas Pl and Pma are determined from other logs or core samples correlated to the Pb measurement. Porosity, ~, is the desired property of the formation needed for reserve definition. Equation 4-1 rearranged to solve for the desired property of interest, porosity, yields: ~b =
Pma-- Pb
Pmo--Pl
(4-2)
Petrophysical models have two general requirements. First is that the number of unknowns must be less than or equal to the number of equations. Unknowns are the
163
100% Sw line
50% Sw line
25% Sw line
Sw-n _ Rt Ro
10.0
Hydrocarbon bearing zones
Water-bearing zones form Ro (Rzero)line. Slope of line is-m.
1.0
True Resistivity, Rt, (ohm-m)
0.1
Intercept of Ro line at 100% ~ is the formation water resistivity, Rw, at the formation temperature.
0.01 1%
10%
100%
Porosity, ~, (%) Fig. 4-1. This Pickett plot (Pickett, 1966) example is a plot of porosity (from a porosity log or logs) vs. true resistivity (from a resistivity log suite) for several zones from a particular formation. This plot is a graphical representation of Archie's equation (Archie, 1942) for the determination of the formation's water saturation.
164 answers that are required (porosity, water saturation, percentage of a particular lithology type, etc.). The knowns are the available pieces of data and information (logs, core analyses, test results, geologic insight, estimates, etc.). The second requirement is that the parameters used in the equations must be readily available. One could have the best petrophysical model in the world, but if there is no way to obtain the parameters for that model, then it is not very practical. These two general requirements sometimes lead to the use of petrophysical models which are approximations of the actual physical situation. The petrophysical model used to evaluate a particular formation needs to adequately describe the physical characteristics and properties of that formation. The assumptions inherent in the petrophysical model need to be appropriate for that formation, also. For example,Archie's equation for water saturation determination (Archie, 1942) assumes that the water phase of the pore fluid is the only electrically conductive medium in the formation. An incorrect water saturation from Archie's equation will be obtained if it is applied to a rock containing pyrite inclusions, which causes the rock matrix to exhibit electrical conductivity (Clavier et al., 1976). As can be seen, one must understand the petrophysics of the rock that is being evaluated to be able to apply the appropriate petrophysical model. Petrophysical models can be presented graphically for clarity and ease of interpretation. An example is the Pickett plot (Pickett, 1966). A Pickett plot, shown in Fig. 41, is simply a graphical representation of Archie's equation (Archie, 1942), Eq. 4-13, for water saturation determination.
DETERMINATION OF FORMATION PROPERTIES OF INTEREST
Overview
The use of data available from formation evaluation tools to determine formation properties of interest utilizing a petrophysical model is detailed in the next several pages. All available data should be used in an evaluation. But many times, all required data are not available. The use of a rock catalog to estimate missing formation property information can be beneficial. The introduction to one rock catalog (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates) describes that catalog's general objectives and associated applications as follows. A. Provide a reference manual containing "analog" sandstone and carbonate rock types for a more accurate estimate of formation "zone of interest" parameters when evaluating a given well. The Rock Catalog will contain a large amount of standardized geological/petrophysical/engineering data over a broad spectrum of reservoir rock types. Geologists and engineers routinely make assumptions concerning reservoir properties during, for example, log analysis (e.g., grain density, logging parameters). The Rock Catalog provides a reference manual of "analog" rock types. That is, a limited amount of information on a particular formation "zone of interest" can lead to a Rock Catalog analog sample which, in turn, provides other geological/engineering properties and parameters which can be applied to the "unknown" interval of interest.
165
B. Provide a comprehensive geological/engineering data base over the spectrum of reservoir-quality sandstone and carbonate rock types for the acquisition of new knowledge and insight into correlations and relationships among geological and logging/fluidflow/engineeringparameters. Rock Catalog data can be used to quantify relationships among geological and petrophysical properties and to establish rock-type correlations. Such information could, for example, improve log S w calculations, which would be especially valuable where the calculated S value serves as the primary criteria for completion recommendations. The Rock Catalog will contain data correlating the various rock properties of those reservoir rock samples. The Catalog sample entry numerical classification scheme was chosen for ease of data storage and processing by computer. Such data correlation should aid the user in identifying the more relevant aspects of formation evaluation, and also to compare non-Catalog reservoir samples to an established base line. C. Estimate reservoir rock properties from visual observation of core, sidewall and/ or cuttings rock material. The Rock Catalog, in combination with simulated cuttings "comparators," will g i v e . . , a valuable tool for developing expertise in calibrating rock/pore type observations from core or cuttings to reservoir rock parameters related to formation productivity (e.g., porosity, permeability). The geologist or engineer at the well site, with Rock Catalog and comparators in hand, can evaluate core or cuttings samples to provide rapid estimates of porosity, permeability, and reservoir potential of a particular zone of interest. With time, considerable expertise can be developed in relating that macroscopic properties of rock samples with known, geological, petrophysical, and/or engineering properties (i.e., Rock Catalog samples) to estimates of drill stern/production tests across intervals of interest. Rock catalog data can be found in notebook form or on computer storage media such as floppy disks or CD-ROM (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates). Simultaneous determination of porosity, pore fluid saturations, lithology component fractions, and pore fluid properties The determination of porosity, pore fluid saturations, and lithology component fractions can be accomplished by using a multi-mineral, multi-fluid petrophysical model for simultaneous solution of each evaluation tool's response equation to each formation property. These models are usually in the form of computer programs. The number of unknowns in the formation cannot exceed the number of equations handled by the computer program. These models fall into two general classes: deterministic models and error minimization models. Deterministic models directly solve the tool response equations to provide the lithology component fractions, porosity, and pore fluid saturations.A deterministic model example is the DAK (Dolomite,Anhydrite, Potassium) model used for lithology evaluation of some West Texas Clearfork carbonate reservoirs (Clerke et al., in progress). The model uses the natural gamma ray spectroscopy potassium log response to determine the percentage of silt in the zone. The bulk density and the photoelectric cross section log responses are used to determine the percentages of dolomite and anhydrite. Log response equations for each lithology component are solved directly.
166 TABLE 4-IV General outline of error minimization petrophysical models Item
Details
Results from model
Porosity Fluid saturations Mineralogy component fractions Some number of tools (depends on model) - well logs, mud logs, core analyses, test data, etc.- but, the model must not be underdetermined. Some number of mineralogies (depends on model) Some number of fluids (depends on model) Physical properties of each fluid and mineral component Upper and lower result boundaries Logging tool accuracies Calculated from logging tool response equations Function of porosity Function of fluid properties and volume fractions Function of mineral properties and component fractions Material balance (usually built in) Upper and lower result boundaries supplied by user Model finds best fit between theoretical and actual logs. Iterative solution can begin with equal volume fractions. Solutions incorporate all logs, other data, and known constraints simultaneously. Flags indicate quality of fit (residuals, incoherence)
Input to model
Theoretical log reading
Constraints Volume fraction solution
Error m i n i m i z a t i o n m o d e l s inversely solve the log response equations to provide the lithology c o m p o n e n t fractions, porosity, and pore fluid saturations. These m o d e l s construct theoretical log readings from the logging response equations, and obtain results by finding the best fit b e t w e e n the actual and theoretical logs. A general outline o f these types o f m o d e l s is s h o w n in Table 4-IV. E x a m p l e s o f error m i n i m i z a t i o n m o d e l s (programs) are listed in Table 4-V. Multi-mineral, multi-fluid petrophysical models, either deterministic or error minimization, require that the user supply the log response parameters for each fluid and lithology c o m p o n e n t . Errors in these p a r a m e t e r s - for example, p a r a m e t e r selection is a " b o o k " value w h i c h does not exactly m a t c h that o f the f o r m a t i o n - will cause TABLE 4-V Examples of error minimization petrophysical models (programs) Model
Associated company*
References
ELAN FLAME GLOBAL OPTIMA ULTRA
Schlumberger SIPM Schlumberger Atlas Halliburton
Quirein et al., 1986 Peeters and Visser, 1991 Mayer and Sibbit, 1980 Mezzatesta et al., 1988; Rodriguez et al., 1988 Alberty and Hashmy, 1984; Gysen et al., 1987
* Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or product.
167 inaccuracy in the results. Accurate evaluation results require that the formation evaluation specialist understands the petrophysics of the rock and the fluids it contains. The use of knowledge-based or expert systems can potentially supplement the technical expertise of the formation evaluation specialist. However, knowledge-based system use in formation evaluation has rarely been reported. One knowledge-based system, LOGIX (Hoffman et al., 1988), has been used in the petrophysical interpretation of vuggy (oomoldic) carbonate reservoirs in the Middle East. The authors reported that the system's interpretation in these types of rocks encountered in five wells were checked with core data, geological descriptions, and well test data, and the agreement was excellent. Formation properties can also be determined with simpler petrophysical models. These models focus on one formation property at a time. The next sections of this chapter discuss the determination of each of the six primary formation properties of interest using simpler models. Simple petrophysical models that use well logs can usually be done by hand, using a calculator, crossplots, and/or nomographs. These models should not be used in isolation. So, also covered in the next sections of this chapter is the determination of each of these formation properties from the examination and/or analyses of rock (cores, sidewall samples, and cuttings), mud log information (cuttings analysis and hydrocarbon shows), and tests (wireline, drill stem, and production tests).
LITHOLOGY DETERMINATION
Lithology from examination and~or analyses of rock Rock samples can be from drill cuttings, whole cores, sidewall cores, and/or outcrops. Many methods exist for the determination and classification of lithology by petrographic rock examination. Carver (1971) provided several chapters dealing with petrographic mineral analysis, including preparation of thin sections, point counting, heavy mineral analysis, staining, and X-ray diffraction (XRD). A Fourier transform infrared (FTIR) spectroscopy method for petrographic mineral analysis is also available (Harville and Freeman, 1988). Ruessink and Harville (1992) compared FTIR and XRD for bulk mineral analysis. They concluded that one of these two techniques may be preferred over the other on the basis of its applicability to certain mineral classes: FTIR can analyze poorly crystalline material; XRD can deal with halides, and it offers the possibility of a detailed analysis of the clay-sized fraction of minerals. In other cases, the two techniques might be applied simultaneously to obtain complementary bulk mineral analysis information. The AAPG Sample Examination Manual (Swanson, 1985) provided practical methods and procedures for rock examination and lithologic logging, primarily of drill cuttings, but also of core and surface samples. Chapter 2 of Volume 1 of this book provides details concerning several lithologic classification methods used for carbonate rocks. Analyses of core and cuttings for grain density to provide insight into mineralogy can be done a number of ways (American Petroleum Institute, 1960). Grain density
168 results can be related to known grain densities for particular rock types. For example, the grain density of dolomite is in the 2.85-2.87 g/cm 3 range according to the references of Edmunson and Raymer (1979), Wells et al. (1979), Ellis et al. (1988), and Carmichael (1989). These four references provide a comprehensive listing of physical properties of rocks, including the grain or matrix properties and the responses of nuclear and acoustic logs. A C T scan on rock (Wellington and Vinegar, 1987) can be used for mineralogy determination. A calibrated (Coles et al., 1992) high energy CT scan for density in non-porous zones will provide grain density information. A calibrated dual energy CT scan will provide atomic composition information for the rock. CT scans provide spatial information with resolution as fine as a few millimeters. Cores can even remain frozen during the scan. Scans are totally non-destructive and can be made through core containers, unless they are made of lead or thick stainless steel.
Lithology from well logs Lithology, particularly the mineralogy aspect, can be determined or inferred from well log data, both wireline and measurement while drilling. The methods discussed in this chapter are from resistivity and spontaneous potential logs, from the use of conventional porosity/lithology log crossplots, from natural gamma ray and natural gamma ray spectroscopy logs, and from induced gamma ray spectroscopy logs. Also discussed are the reliability of determining lithology from logs, complications with determining lithology from logs, and some other considerations.
Resistivity and spontaneous potential Resistivity and spontaneous potential (SP) logs are not primarily lithology logs. In certain circumstances, however, they can indicate the lithology of a zone by one or two methods: (1) log values match trend or marker bed log values; and/or (2) log response indicates permeable vs. non-permeable zones. Resistivity logs, e.g., laterologs and induction logs, respond to changes in porosity, rock texture, pore fluid properties, and pore fluid saturations. For more details, see the section in this chapter concerning saturation determination fromArchie's equations. A zone with consistent rock types containing consistent fluids should have consistent resistivities within a region, i.e., the zone is a marker bed, and can be used to identify that particular zone and its lithology from well to well. Permeable zones are interpreted from multi-depth-of-investigation resistivity logging tools or from time-lapse logging with resistivity logging tools. These logs would show different resistivity values at different depths of investigation or at different times due to mud filtrate invasion, provided the mud filtrate and formation fluids have different resistivities. Spontaneous potential logs (Doll, 1949) require mud filtrate invasion to show response. Therefore, permeable vs. non-permeable zones can be differentiated, provided there is a contrast between the mud filtrate and formation water salinities. In low-porosity carbonates there can be problems with spontaneous potential log response due to the high formation resistivities, and the SP log may not be usable.
169
Conventional porosity/lithology log crossplots Conventional porosity/lithology logs are those which are commonly run in wells. These include: (1) (2) (3) (4) (5)
Density logs. Spectral density logs. Thermal neutron logs. Epithermal neutron logs. Acoustic logs.
Conventional porosity/lithology log crossplots are crossplots involving the aforementioned conventional porosity/lithology logs. These crossplots are two-dimensional visual representations of the log response equations to the various mineralogies. Rocks containing more than two mineralogies can be evaluated using multiple crossplots. Several of the conventional porosity/lithology crossplots are: (1) Density-neutron crossplots (see Fig. 4-2) use bulk density (or density log porosity) vs. neutron porosity for determination of mineralogy and porosity*; (2) Density-acoustic crossplots use bulk density (or density log porosity) vs. acoustic travel time for determination of mineralogy and porosity*; (3) Neutron-acoustic crossplots use neutron log porosity vs. acoustic travel time for determination of mineralogy and porosity*; (4) Density-photoelectric factor crossplots use bulk density (or density log porosity) vs. photoelectric factor for determination of mineralogy and porosity (Gardner and Dumanoir, 1980); (5) Hingle plots are plots of RJ/m vs. another log value that is proportional to porosity (e.g., bulk density, neutron porosity, or acoustic travel time) on special "Hingle" graph paper for determination of mineralogy and water saturation (Hingle, 1959); (6) M-N plots are plots of acoustic-density crossplot slope (M) vs. neutron-density crossplot slope (N) for mineral identification (Burke et al., 1969); (7) PmaaVS. Atmaamatrix identification plot compares apparent matrix density (fgmaa) to apparent matrix acoustic travel time (Atmaa) for determination of mineralogy (Clavier and Rust, 1976); (8) PmaaVS. Umaa matrix identification plot compares apparent matrix density (p~tmaa) to apparent matrix volumetric photoelectric factor (Uaa) for determination of mineralogy (Gardner and Dumanoir, 1980), see Fig. 4-3; and (9) Shear vs. compressional travel time plot for mineralogy determination (Pickett, 1963). Two concerns arise from using conventional porosity/lithology crossplots to determine lithology in complex (multiple component) rocks. First, there must be as many equations (logs) as there are unknowns (rock types). Mineralogy components found in carbonate reservoirs might be dolomite, limestone, anhydrite, gypsum, salt, chert, * These crossplots are found in each well logging service company chart book (e.g., Atlas Wireline Services, 1989b; Halliburton Logging Services, Inc., 1991; SchlumbergerEducational Services, 199la). Raymer and Biggs (1963), and Savre (1963) provide two of the early references on the subject of using crossplots and/or simultaneous log response equation solutions to determine mineralogy/porosity.
170
Porosity
Bulk
(Log)
-
Mineralogy
Density
Crossplot
versus
Neutron
Porosity
DSN-II* Fluid Density = 1.15 g/cc (1150 kg/m 3) 1.9 :~..,--:i- ,---!.- .- ::............ ~ - .~..--.ii.
~......!...,i.,-..-i......!...--i-....! ...........+..,..i.-..-!i.....~.....i....,,;.,.,,i.....l.,.,.,~ ..... ......~......~,....~...,..~......i~....... ....,~~.,.~...~..,i.-,-i-,,,-,-i,..,,H-,,...t .....~.....
-..i..,..i .....
2.0
50 45
.........::.......i...,..i................... i,....:.. ,...i.....i ..U
~.~--:-.~~---,~-~---~-T--~-~ ....... .:.~:.:.i.:.:.:i:~............. .......~,...., ...~:.~..~............. ~.i.~.~~.i..-...!..... ...~.'~..~,'~....... ..-.-~. ..,i:::~: "~ ~ " ~:=~'~ iii~
.......i....4.....~..-.+....~.....i ................
40 2,1 .... i......!-.-..i-..,.:i .i-,-i.-..-i
2.2 ~ .~.
: -'----~
~
:
}
~-
k~-:,,~,.............+:--,+.~+,~-k--+---k~+--.-+-.-+-.-+-----~
~ .: " .......... ~"-~
..... ~.............. :......~......~.....~......~ ...... i....4
...~.--+.....4.....i.......+ .,.,.i
.--.!........... ..... ..............
m-.k.....~-.....~, ............. ~.--,~
2.3
.... ....... ~.....+.....:...,..~... ..
o
30_
+....,.. ....
..... i~,---ii,,,+,.+,,,i,+,+.~,,.,i~-, i ~.-.i, 9 ,,,il............
o
20
i ~ ~i .~ ~
2,4
~""
" .... i! l! :i!ii
~ L~.L~;!L;I:..i~;:!i~i:i :IL:L~
............................
o o o
"
........!~.~----..!.-i -i~-
~!i~mi-i--'~
~ o
.
" -i
......?...r..,.i-...,V,-!--.-..i-...-.~..--.i..--.i ~
...... "~ ': i ~
-
=
2.5
~"~~:
~............. :
~ ~: ~
Z L i ~
.......i.,....i...,...i.-L,,+,...,;....
~
:: ~ ~
~
:
~ ~ i
15
E
2211SI21L:21~ILILLII -
....i .................i..,..,L.....L....i ..........
~
.................i...........t .~,,
o
..... : } i. ti 1
-+H.-+ ........................... i-~.--.i-.+.+-i-~-+-.-~ ~:i: :if i:~:/i;: 7: :,i:~. L
B
~-
2.7 _I;I:~!I:I21~II~I:I:I~.N:~. ...,..., i
i
~"~~'+"++~ . . . . . L,, . . i................................ . . . . t~................... ..... ~'~!"~-~-k "-~ .i.............i~......i.....:............................ i .............~.-. ,~.. ,..~.....i............. k
::
i
i
5
"
~ (21
0
~i 9 ...........i i..+-.i~---+--i~..-.U'-,---~--,---'~i.~ "~.-~ .'~-..i--.i..-~.~-.-..U"~
,
-5
2.8
-10
,:::::::U:::i.:;.::::.:UU:Ui+ii--i......i--..-.~ 3,0
~.....~....i ........... i..4....i~, .. ..i...i.......i.....k....i.....i......i......i.....I
..... i....~.....i...~...~r~ .yd~:tte
-5
0
i
5
i
.........
:!i ................................. i:: : :i::: :::i : ! ............~ !
............ i...i...~....i....~.....
I, ..-:..-.....-i--....-~...?--.i......!......,i,, i
!
.....J i i U : i i
i' + ~
-t5
........
.!..i .-i-.-i..-..:~-.... ~::...---.i ..--...~.........
10 t5 20 25 30 (~NLS, Neutron Limestone Porosity (%)
35
40
45
Fig. 4-2. Example of a density-neutron log crossplot. The appropriate mineralogy line, even for a single rock type such as dolomite, depends on the thermal neutron capture cross section of the rock. (From Halliburton Logging Services, I n c . , 1 9 9 1 . )
etc. An additional equation (log) is required if the pore fluid contains gas. Second, porosity/lithology log response to each separate mineralogy must be properly characterized, i.e., the log response must be known and predictable, and the petrophysical model and its parameters must match those of the rock being evaluated. For the density log this means that the log must be properly calibrated to yield bulk density. The matrix and fluid densities for the crossplot or petrophysical model must match those of the rock. For the acoustic log this means that the log must provide the desired travel
171
Mineral
P
Identification
Plot
versus
U
ma a
(MIP-2)
ma a
DSN-II* 2,4
,
:
~
..........i ........... i ........... ii
'
.......
,,
,
,
.i ..... i ........... i..... : ....... i~.
! il
i . . . .! . . . . .i ............. . . . . . . . . . . . . . . .
................... i ....... i .... i ..........
....
.}
i
! ........... !........ I ! ............
........................ l]~i! i........i
i .................... i ....
:
"
I
~
~
........
....
I
i..
1
ii
! ....... ~....
i .......... ~
I
i
-~....
}
!!
I
,
.i
. . . . . . . '~ ............!~su,p,,.o. ................... ................................................... ..... !...........~............i~............. ...... .........
. . . . . . . .................. ............................
i .........................
................. i ............. oi..Halite.i
...................... i ...........
2.5 ....................
..........!...........! ...........i...........T ~E
2.6
............i ...........
.........................
"i ................
oo
.arlZ~
~
~
,
i
i.
................
i
:
:
"
t
...
0
.....i............................................ ,!.............................................
:
2.81.
;
i
'~'
.:
!
:i ,
i i
.:
i
i ~ i
.
i
-
; ..................... ;.....................................................................
! ~
:ii,.
Dolomite:
~
i
......
1
i
i
I ~
~
.f ~i
!
i
-i. ::
:
I
i
]
~
l
! ! ........... I ....... ~ i
f ~,
i
~ ::
',
i
i
9
i:: i
i :: i
~ i
.i........ i..............i................................ !.......
I.....
~
~
I
:.
i
i
i
'
i
i
i.
:i
!
.. ........... i ....... ~
i~
.......................i..............
..
i
i
i
i
i
!
i
i
ii
...... i ........... ~................. I.................... l......... i I ~
I
...i
i i.
i
i
i
.'~ . i
ii
!
:: i
~!
.~- .... I .... !
::. i
...... l,.Anhy(~rite i
.',
.........
i ~
~ ::
.I -
-', ....
'
:
~:
i
i........ i ...... ~
.:
i
:;
..................................i .................i ......................................... ; ..............l ...................................,.......................................... ; ....................~...................... i .............................................. , ................................................................ ~..................i .....................................; ........................................ ~ ....... ~.................~......................................... ~...................................
3.0
......
i~,....... i................i ..............!........ f
:i ,
i
i..... i ...............
:
!
i
i ..............
3
Example
4
5
of a p,,~,
::
~ ..... i.......... i......... '~!
....
i
;
.......... i ............ i ....... i .......... !, ......... i............ I.........
4-3.
.
.~ ....
.............................................. ~.......................
i
3.t
......
catcitei
3
. ~.. . . . . . . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . . . . . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . ......................:.,.................
1991.)
i
,
..... .7..~"7I'.II'IIIIITI~?s
o
Fig.
~..... ~.................................... !
,
i i 2.7 ................. ~............... ~................ ~...............
",.--'
""~c,_~
~.....
i
i
" o'~Mu~covit~ i ........... i~
ii..... ~
.-
.!
i
i...... i..... !.........
i .......
i....
.i l
!
! i ....
i......... i.
.i......... i .......... ;....
i.
;
i.
.':
i-
i ..........i....... :
.ii
i .........
i
i
:
i
i
i........ ;......... ', ....
U
matrix
identification
plot.
(From
Halliburton
i
:............!.............. i ~i.
6 7 8 9 10 11 12 13 14 Urea, Apparent Matrix Volumetric Photoelectric Factor vs.
::
Logging
-~
i
15
Services,
9
.~ . . . .
16
Inc.,
17
172 time: compressional, shear, etc. The acoustic petrophysical model which best fits the rock should be used: e.g., Wyllie time average (Wyllie et al., 1956), Raymer-HuntGardner (Raymer et al., 1980), acoustic formation factor (Raiga-Clemenceau et al., 1986), Krief-Garat-Stellingwerff-Ventre (Krief et al., 1990), or a local empirical correlation with core data. Neutron log response varies with logging service company, type of logging tool, vintage of logging tool, and log acquisition software. The Atlas Wireline Services Compensated Neutron tool response to dolomite (Atlas Wireline Services, 1989b, Chart 5-35), for example, is different from the Halliburton Logging Services Compensated Neutron tool response to dolomite (Halliburton Logging Services, Inc., 1991, Chart POR-10). An example of logging tool response variation with vintage of logging tool and log acquisition software is found in the Foreword of Historical Charts (Schlumberger Educational Services, 1990): Neutron porosity equivalence curves and environmental correction charts for the Compensated Neutron Log (CNL*) tool were first presented in the 1972 charts book. These charts were modified in the 1978 charts book to represent function former changes for logs run after 1976. The openhole environmental corrections were changed slightly in the 1984 charts book based on additional lab measurements. New CNL charts presented in the 1988 and 1989 charts books are based on improved environmental corrections. Natural gamma ray and natural gamma ray spectroscopy Natural gamma ray logs measure the natural radioactivity of the formation near the borehole. If different lithologies in a particular formation have different known levels of natural radioactivity, then the natural gamma ray log can help differentiate and determine lithologies. However, some knowledge of the expected lithologies is usually needed. In some cases, e.g., differentiating limestone and chert (see Table 4-VI), the natural gamma ray log is not at all useful. Unlike the conventional gamma ray log, which measures only the total radioactivity, the spectral natural gamma ray log looks at the energy spectrum of the measured gamma radiation to provide information relating to the amounts of potassium, uranium, and thorium in the formation. The three separate element concentration curves do not lend themselves to ease of interpretation. A more useful presentation uses only two curves, a total gamma ray curve and a combination of the thorium and potassium. The difference between the two curves is the uranium contribution to the total radiation. The additional information provided by the spectral natural gamma ray log over the conventional gamma ray log can be used for the following carbonate formation evaluation purposes (see Fig. 4-4). Distinguishing shales and radioactive dolomites. Shales are typically high in potassium. The spectral natural gamma ray response in shales should show the potassium plus thorium curve to be nearly the value of the total gamma ray curve. Radioactive dolomites are radioactive due to water-soluble uranium salts that were deposited in the rock during dolomitization. The spectral natural gamma ray response in radioactive dolomites should show the potassium plus thorium curve to be a small fraction of the value of the total gamma ray curve. The uranium salts would be the major * Mark of Schlumberger.
173 TABLE 4-VI Typical relative natural gamma ray log values for various lithologies Lithology
Relative natural gamma ray value*
Anhydrite Chert Dolomite Dolomite (radioactive) Granite wash Gypsum Halite Limestone Sand (little clay or feldspar) Sand (some clay and feldspar) Shale Source rock or organic shale
Low Low Low High High Low Low Low Low to moderate Moderate High Very high
* Actual gamma ray log readings for a particular lithology will vary with tool position in the borehole, borehole diameter, mud type and density, and formation density.
contributor to the total natural radiation. Source rock delineation. Source rocks have high uranium content in the organic material. This is because a uranium molecule is large and the organic material provides a structure into which it can fit. The uranium stays behind when the kerogen converts to oil. In source rocks the uranium is typically the major contributor to the total natural radiation. General evaluation uses. Natural gamma ray spectroscopy provides three more pieces of information about any zone of interest. If the lithology, or its deposition or diagenesis, or the pore fluid(s) can be delineated by evaluating the potassium, uranium, and/or thorium content, then this tool can yield up to three more equations to help solve for the unknowns. Induced gamma ray spectroscopy
Induced gamma ray spectroscopy tools (see Table 4-VII for tool list) analyze the inelastic and capture spectra of gamma rays resulting from neutron interactions with the different elements in the formation. The gamma ray spectra analyses are used to estimate the relative yield of elements in the formation. TABLE 4-VII Induced gamma ray spectroscopy tools Service Co.*
Tool name (mnemonic)
Reference
Atlas Atlas Halliburton Schlumberger Schlumberger
Carbon/Oxygen Log (C/O) Multiparameter Spectroscopy Instrument Pulsed Spectral Gamma-Ray Tool (PSG) Induced Gamma Spectroscopy Tool (GST) Reservoir Saturation Tool (RST)
Dresser Atlas, 1981 Chace et al., 1985 Jacobson et al., 1991 Hertzog, 1978 Scott et al., 1991
* Service company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or tool.
174
Spectral Natural Gamma Ray Log Response Examples
0 Total GR (API Units) 0 --.-,----- K+Th (API Units) - - - - , -
100 100 4000 rn Shale resoonse. K+Th reading (88 API Units)is nearly the value of the total gamma ray curve (94 API Units).
Radioactive dolomite response. K+Th reading (17 API Units) is a small fraction of the value of the total gamma ray curve (94 API Units).
Source rock response. K+Th reading (89 API Units) is that of a shale. The total gamma ray value (284 API Units)is high because of the large amount of uranium in source rocks. The total gamma ray can be even larger, up to 1000+ API Units, in some cases. 4100 m GR backup scale 100-200 API Units GR backup scale 200-300 API Units
Fig. 4-4. A useful presentation of the spectral natural gamma ray log is shown here. The dashed curve is the contribution of the potassium plus the thorium to the total radiation. The other curve is the total gamma ray (GR) log response. The difference between the two curves is the uranium contribution to the total radiation. The gamma ray log values for these lithologies will not be the exact readings shown here. The relationship between the K+Th and the total curve will be similar to these responses for these lithologies. The actual gamma ray log readings for a particular lithology will vary with tool position in the borehole, borehole diameter, mud type and density, and formation density.
175 TABLE 4-VIII Elemental yields and other information from induced gamma ray spectroscopy tools Mode of measurement
Yield or information determined
Inelastic mode
Carbon Oxygen Silicon Calcium Sulfur Iron
Capture mode
Hydrogen Silicon Calcium Chlorine Iron Sulfur Titanium
Ratio of inelastic to elastic or capture counts
oc
Formation capture cross section
E
Induced gamma ray spectroscopy tools can be run in open or cased holes and provide elemental yields for the elements listed in Table 4-VIII. Ratios can be computed from the yields to aid in lithology, porosity, and saturation determination. Useful yield ratios are listed in Table 4-IX. TABLE 4-IX Useful induced gamma ray spectroscopy yield ratios Yield ratio
Common name
Uses in formation evaluation
Si/(Si + Ca) Ca/Si [inelastic] Si/Ca [capture] Fe/(Si + Ca) CI/H H/(Si + Ca) C/O
Lithology indicator Calcium/Silicon ratio Silicon/Calcium ratio Iron indicator Salinity indicator Porosity indicator Carbon/Oxygen ratio
Siliciclastics vs. carbonates Siliciclastics vs. carbonates Siliciclastics vs. carbonates and salinity Clays and pyrite Chloride salts Liquid-filled porosity and clays Hydrocarbon saturation
Results from induced gamma ray spectroscopy tools can be combined with other information to provide additional formation evaluation information. Indirect combinations of the induced gamma ray spectroscopy tool information can be done with any other formation evaluation tool by using a computer program that describes the appropriate petrophysical model for that particular tool combination and rock properties.
Geochemical logging tools Direct combination examples using induced gamma ray spectroscopy with other formation evaluation tools are the geochemical logging tools (Hertzog et al., 1989 and Schlumberger Educational Services, 1992). These tools are a combination of a capture mode induced gamma ray spectroscopy tool to analyze silicon, calcium, iron,
176 sulfur, gadolinium, and titanium; a natural gamma ray spectroscopy tool to analyze thorium, potassium, and uranium; neutron and possibly density logs for porosity and additional mineralogy information; and a second natural gamma ray spectroscopy tool adjacent to a neutron source to determine the aluminum yield. Herron et al. (1991 ) described the application of geochemical logging of a Middle East carbonate reservoir. The geochemical log provides elemental weight percentages for the formation. Mineral abundances are determined using an element-to-mineral transform that must match the mineral components of the reservoir rock.
Reliability of determining lithologyfrom logs The reliability of determining lithology from logs is directly related to: (1) How much insight and knowledge are available concerning the rocks. This is usually a function of how much work has been done in the area. (2) How well the lithology needs to be known. This is usually a function of the amount of money that will be spent on the project and what the risks are. Figure 4-5 shows a qualitative view of the reliability of lithology determination from logs under different situations. Determining lithology from logs only is much less reliable than incorporating other information. Having cuttings or core samples to examine and to calibrate log response increases the reliability of the lithology determination and provides insight into rock texture which is not readily available from well logs.
Complications There are several factors which can complicate lithology determination from logs: (1) Bad or failed logs may need to be edited or recalibrated to correct erroneous data. If a field-wide or regional study is involved, log data will probably need to be normalized to provide for a consistent interpretation. (2) Gas in the pores of the rock affects density, neutron, and acoustic log responses. An additional log or other knowledge is required to account for gas effects. (3) Pad tools, such as density and sidewall neutron logs, are especially affected by poor hole conditions. Washouts and/or rugose hole can render log response invalid. (4) Underdetermined situation (complex geology or not enough logs) requires acquiring additional log data, making some assumptions, and/or estimating properties from analogous rock types using a rock catalog. (5) The acoustic log does not "see" non-touching vuggy porosity until it becomes the dominant pore type. This causes the calculated apparent matrix travel time and subsequent lithology determination to be in error. (6) If the evaluation is applying the wrong petrophysical model, e.g., using a timeaverage model for the acoustic-porosity-lithology relationship when the rock fits an acoustic formation factor model, then the lithology interpretation will be in error. The presence of these factors increases the uncertainty in lithology determination from logs.
Other considerations The various methods oflithology determination from well logs usually only provide information concerning mineralogy, i.e., the rock's fractional mineral composition. The textural nature of the rock is not addressed nor determined at all. It is the texture
177 Reliability of Lithology D e t e r m i n a t i o n from Wireline and M W D Logs
Wildcat Well (Log-Core Work)
" xx
Confirmation Well (Much Log-Core Work) Routine Development Well
l;I
Field Step-Out Well 0.0
I
I
I
I
0.2
0.4
0.6
0.8
1.0
Reliability (Arbitrary Units) 1.0 = Very Reliable 0.0 = Not Reliable
Lithology from Logs Alone Logs + Sample Examination Logs + Sample Examination + Core Analyses + Tests + Geological Insight
-0,,-- - - , 0 , - - - v
9
v
Fig. 4-5.A qualitative view of the reliability oflithology determination from logs under different situations. (Adapted from E.C. Thomas, pers. comm., 1987.)
of the rocks which governs porosity and permeability (Archie, 1952; Enos and Sawatsky, 1981; Lucia, 1983; Jodry, 1992), and fluid saturation distribution (Leverett, 194 l; Rose and Bruce, 1949; Jodry, 1992) in the reservoir. One must look at the rock to gain insight into the rock texture.
178 POROSITY DETERMINATION
Porosity from examination and~or analyses of rock Rock samples for porosity determination can be from drill cuttings, whole cores, and/or sidewall cores. Outcrop porosities are not usually representative of reservoir porosities due to surface weathering, dissolution, and dedolomitization. For heterogeneous carbonates, larger samples tend to be more representative of the formation. Porosity estimation from rock examination is possible using, e.g., the Archie classification (Archie, 1952) or Lucia classification (Lucia, 1983). The AAPG Sample Examination Manual (Swanson, 1985) provides practical methods and procedures for rock examination and lithologic logging for porosity estimation, primarily of drill cuttings, but also of core and surface samples. Chapter 2 in Part I of this book provides details concerning several porosity classification methods used for carbonate rocks. Porosity can be determined from thin section point counting. Carver (1971) provided details concerning procedures in sedimentary petrology. The relatively low vertical resolution (direction coincident with the objective lens axis) of petrographic microscopes makes it somewhat difficult to resolve grain boundaries, especially at higher magnifications needed to detect microporosity and small fractures. Impregnating the sample with epoxy and an admixed fluorescent dye allows the use of a confocal microscope, a specialized form of epifluorescence microscopy, which can image a very thin focal plane, or very thin layer, of the thin section (Owen et al., 1992). A series of focal plane images can be acquired and then reassembled or stacked to generate a full three-dimensional image of the thin section. Image analysis of thin sections and scanning electron micrographs, provides rapid, quantitative porosity data. Image analysis also provides quantitative data conceming the size and geometric complexity of reservoir pore systems (Ehrlich and Davies, 1989). An understanding of the nature and distribution of pore types becomes increasingly important with decreasing porosity values. Reservoirs which have undergone diagenetic modification, such as carbonates, are frequently characterized by the co-existence of several disparate types of porosity. In such rocks, reservoir behavior is much less dependent on total porosity than on the pore type assemblage that makes up that porosity (Davies, 1990; Chapters 4 and 6 in Volume I of this book). There are several core analyses methods for porosity determination (American Petroleum Institute, 1960). Typically core analysis porosity determination methods measure the bulk.volume and the pore volume or grain volume of the rock sample. Most methods require that the core be cleaned of formation and filtrate fluids before or as part of the analysis process. The lower the permeability of the rock sample, the longer it takes to perform the cleaning and/or porosity analysis. Heterogeneous rocks, like vuggy carbonates, require whole core analysis rather than plug analysis to produce representative results. However, the larger the rock sample, the longer it takes to perform the cleaning and/or porosity analysis. CT scanning (Wellington and Vinegar, 1987) of core material is a non-destructive
179 method for obtaining porosity data. A calibrated (Coles et al., 1992) high energy CT scan can provide bulk density data in porous and non-porous zones. The petrophysical model associated with Eq. 4-2 can be used to determine porosity from such data. CT scans provide spatial information with resolution as fine as a few millimeters. Cores can even remain frozen during the scan. Scans can be made through core containers, unless they are made of lead or thick stainless steel. Nuclear magnetic resonance (NMR) spectroscopy and scanning (Edelstein et al., 1988) are other non-destructive methods for obtaining porosity data from core material. NMR responds to the liquids in the pore space. Therefore, if the pore space contains gas, the rock must be resaturated with liquid for accurate porosity determination. The pore liquids cannot be frozen either. The use of NMR for porosity determination in tight, gypsum-bearing carbonates has been shown to be valuable where extraction core analysis methods proved inaccurate due to gypsum dewatering and extremely low permeability of the rock (Vinegar et al., 1991 b).
Porosity from well logs Density, acoustic, and neutron logs Porosity can be obtained from well logs, both wireline and measurement while drilling. The so-called conventional porosity logs include density, spectral density, acoustic, thermal neutron and epithermal neutron logs. Earlier sections of this chapter covered the determination of lithology from multiple porosity logs. Many of those methods provide porosity as an auxiliary result. Porosity can also be obtained from using a single porosity log. However, tool response to the formation of interest, the appropriate petrophysical model, and the lithology of the formation must be known. The lithology must usually be translated into a matrix log response value for use by the petrophysical model. Matrix log response values for numerous lithologies can be found in the references by Edmunson and Raymer (1979), Wells et al. (1979), Ellis et al. (1988), and Carmichael (1989). To determine porosity from density and spectral density logs, use the petrophysical model associated with Eq. 4-2. The lithology needs to be known to obtain a matrix density value. If lithology is not available from an independent source, the spectral density photoelectric factor, Pc, curve can provide insight into lithology. Crossplots are available (Gardner and Dumanoir, 1980) for a graphical solution of using the Pe to obtain lithology, and, therefore, a matrix density, to use in the determination of porosity. The fluid density value also must be known. The formation fluid density can be obtained from fluid samples or from wireline test pressure gradients. However, the depth of investigation of nuclear logs is fairly close to the borehole wall, usually within 15 cm (6 in.) (Tittman, 1986, p. 15). Therefore, when invasion has occurred, the fluid density is dependent upon the densities and relative percentages of mud filtrate and formation fluids within the investigation volume of the density tool. When invasion has occurred, it is difficult to determine the exact fluid density within the volume of investigation of the density log. As a first order approximation, use the fluid density values from Table 4-X. If one of the formation fluids is gas, these fluid density values are too high and the calculated porosity will be too high. Density logs are usually run in open, not cased, boreholes.
180 TABLE 4-X Estimation of fluid density values for determination of porosity from a density log* Drilling mud type
Range of fluid densities (g/cm 3)
Commonly used fluid density (g/cm 3)
Supersaturated brine Brine Fresh-water Oil-based
1.15-1.2 1.05-1.15 1.00-1.05 0.75-1.0
1.2 1.1 1.0 1.0
* Assumes invasion of drilling mud filtrate. If invasion has not occurred, use fluid density of formation fluid(s). For water densities: Dewan (1983), p. 105, suggests using pf= 1.0 + 0.73 N, where N is NaC1 concentration in ppm x 10-6;Atlas Wireline Services (1989b), Chart 1-6, shows the variation of brine density with temperature, pressure, and salinity. To determine porosity from acoustic logs, use the acoustic petrophysical model which best fits the rock. Examples of acoustic petrophysical models include Wyllie time average (Wyllie et al., 1956); Raymer-Hunt-Gardner (Raymer et al., 1980); acoustic formation factor (Raiga-Clemenceau et al., 1986); Krief-Garat-Stellingwerff-Ventre (Krief et al., 1990); or a local empirical correlation with core data. Typically a local empirical correlation will be the most accurate of these models when it is based on representative formation rock. Most acoustic log porosity determination models, including the first three aforementioned models, use compressional acoustic information only. Using shear velocity information to augment compressional data can be beneficial when compressional wave amplitudes are small (Pickett, 1963) or when complex formations are encountered (Krief et al., 1990). Acoustic logs are usually run in open boreholes. If full waveform data are acquired, acoustic logs can be used to determine compressional and shear velocities and transit times in cased boreholes (see Table 4-XV for partial listing of tools and references for acoustic waveform logs). Determination of porosity from a thermal or epithermal neutron log requires knowledge of the logging service company, type of logging tool, vintage of logging tool, and log acquisition software used to obtain the log data. The lithology must also be known. Knowledge of the rock matrix and near-borehole fluid thermal neutron capture cross sections can lend more accuracy to the porosity results from a thermal neutron log (e.g., see Halliburton Logging Services, Inc., 1991, Chart POR-9; Schlumberger Educational Services, 1991 a, Charts Por- 16, - 17, and - 18). If one of the formation fluids is gas, the neutron log will determine a porosity that is too low. Neutron logs can be run in open and cased boreholes. Service company charts are available for porosity determination from each of their conventional porosity logs. Environmental corrections may need to be made to correct for the influence of the borehole and near-borehole region on the log response. Service company environmental correction charts are also available for each of their conventional porosity logs.
Pulsed neutron capture logs The pulsed neutron capture (PNC) log can be used to determine porosity. The near to far count rate ratio is used with lithology (Halliburton Logging Services, Inc., 1991,
181 Chart TMD-1 b) or sigma (Schlumberger Educational Services, 1991 a, Charts Tcor-3, -4, and -5). The logging service company may provide the PNC porosity directly on the log. Usually assumptions are made concerning the borehole environment and there is a practical upper limit on the validity of porosity determination at about ~ = 40% (Schlumberger Educational Services, 1989b, p. 3-25). If one of the formation fluids is gas, the PNC log will determine a porosity that is too low. Gas in borehole degrades the accuracy of the PNC porosity and may even make results invalid. Porosity determined from pulsed neutron capture logs is less accurate than porosity determined from conventional porosity logs. Pulsed neutron capture logs are almost always run in cased boreholes.
Induced gamma ray spectroscopy logs Induced gamma ray spectroscopy logs, their elemental yields, and their useful yield ratios are listed in Table 4-VII, Table 4-VIII, and Table 4-IX, respectively. Table 4-XI lists approaches used to determine porosity from these logs. Salinity and lithology variations cause inaccuracies in the resulting porosity. If one of the formation fluids is gas, the determined porosity will be too low. Induced gamma ray spectroscopy logs can be run in open or cased boreholes for porosity determination. TABLE 4-XI Determination of porosity from induced gamma ray spectroscopy log data Approach
Reference
Ratio of capture to inelastic counts Ratio of inelastic to capture counts H/(Si + Ca) porosity indicator ratio
Atlas Wireline Services, 1989b, Chart 7-13 Jacobson et al., 1991, p. 6 Hertzog, 1978, pp. 8-9
Geochemical logging tools The matrix density (sometimes called grain density) of the formation rock can be determined on a continuous basis from the geochemical log mineral abundance resuits (Herron et al., 1991). This matrix density can then be used with bulk density data measured from a density log run across the same formation to provide porosity (see Eq. 4-2).
Nuclear magnetism logs Brown and Gamson (1960) described the original type of nuclear magnetism log (NML) tool. This tool design was the basis for commercial NML logging tools until the 1990s. The log provided a measurement of the total hydrogen, i.e., liquid-filled porosity, called the free fluid index (FFI). The FFI represents the liquids, as a percentage of the bulk volume, that are not influenced by nearby rock materials (such as in extremely small pores) nor by local magnetic materials. Timur (1972) found the FFI to be an excellent predictor of porosity in carbonate rocks, regardless of variations in the ratio of limestone to dolomite in the matrix. The original type of commercial tool was useful at providing liquid-filled porosity, but was somewhat cumbersome to use because of the need to eliminate the borehole signal by doping the borehole with
182 magnetic material, because of the large tool diameter of about 15 cm (6 in.), and because of the hole diameter limitations of only between 18-28 cm (7-11 in.) (Schlumberger Educational Services, 1991b, p. 108). The results from the original type of commercial NML t o o l s - some of them are still available- are somewhat unsophisticated by today's standards. New nuclear magnetic resonance well logging tools (Coates et al., 1991, and Morris et al., 1993) are more in line with the technology used in the NMR core analysis tools. Many of the same measurements done by the NMR core analysis tools can be done by the new well logging tools. Porosity determination from the new tools is more accurate than that from the original type of NML tools. In addition, the borehole does not have to be doped to eliminate the effect of its signal with the new tools.
Considerations with determining porosity from logs Knowledge of the petrophysics of the rock leads to the most accurate determination of porosity from well logs. The proper petrophysical model must be used, and the logging tool response to the rock and its fluids needs to be understood. Approaching the determination of porosity with an understanding of the rock can minimize its uncertainty.
PORE FLUID SATURATION DETERMINATION
Saturations from examination and~or analyses of rock Usually pore fluid saturations cannot be determined directly from examination and/ or analysis of rock. Saturations of a rock brought to the surface differ from its in-situ saturations because of two factors: invasion and blowdown. Invasion of the drilling mud filtrate will change the saturations and pore fluids of the permeable rocks. As the rock is brought from formation depth to the surface, the pressure on the rock decreases. Fluids will expand as the rock moves upward toward the surface. If the bubble point pressure of the oil is reached, gas will evolve. Expansion of gas with reduced pressure (Boyles law) is much more dramatic than that of liquids. As the pore fluids expand they push pore fluids from the core, i.e., blowdown occurs. With water-based muds there are two situations where invasion and blowdown do not change the pore fluid saturations: (1) Zones that are already at 100% water saturation. (2) Zones containing very viscous (near-solid) tar and heavy oil. Invasion of water-based mud filtrate can have little or no effect on the resulting lab-measured oil saturation of zones which are already at residual oil saturation. In this case, the effects of blowdown on the oil saturation can be accounted for or eliminated by the use of a sponge core liner pre-saturated with water or by the use of a pressure core barrel (Worm Oil Coring Series, 1985-1986, Part 2). With oil-based muds there is one situation where invasion and blowdown do not change the pore fluid saturations: zones that are at irreducible water saturation and contain very viscous (near-solid) tar and heavy oil. Invasion of oil-based mud filtrate
183 can have little or no effect on the water saturation of zones which are at irreducible water saturation. In this case, the effects of blowdown on the water saturation can be accounted for or eliminated by the use of a sponge core liner pre-saturated with mineral oil or by the use of a pressure core barrel (Worm Oil Coring Series, 1985-1986, Part 2). Core analysis data in the form of drainage capillary pressure curve saturation distributions can be representative of the original hydrocarbon saturation distributions in a reservoir (Leverett, 1941; Rose and Bruce, 1949; Jodry, 1992), provided that the rock from which the data are acquired is representative of the formation. Mercury-air capillary pressure points can be related to reservoir height above the free water level (see the definition in Table 4-XVII) in the formation by the following equation, provided that the in-situ formation hydrocarbon and water specific gravities, interphase tensions, and contact angles are known: h=
PcHg-Air OH- ~VCOSVH_W 0.433(SG W- SG u) CrHg_AircOSOHg_Ai r
where: h
(4-3)
= height above free water level (ft);
P~m-Air = mercury-air capillary pressure (psia); SGw = specific gravity of formation water (dimensionless); SGH = specific gravity of formation hydrocarbons (dimensionless); cyH_W
~l-Ig-Air OH_W
Oug-Air
= interphase tension of formation hydrocarbon-water system (dynes/cm); interphase tension of laboratory mercury-air system (dynes/cm); = contact angle of formation hydrocarbon-water-rock system; and = contact angle of laboratory mercury-air-rock system. =
Mercury-air interphase tension and contact angle are usually taken to be 480 dynes/ cm and 140 ~ respectively. Formation values should be measured using representative, unaltered formation fluid samples at in-situ conditions. Interphase tension values often quoted in the literature, 72 dynes/cm for gas-water and 35 dynes/cm for oil-water, are for laboratory fluids (air, water, and soltrol) at ambient laboratory conditions (J.H.M. Thomeer, pers. comm., 1989), and would only match the in-situ reservoir values by coincidence. For the mercury-air capillary data, mercury is the non-wetting phase. For Eq. 4-3 to be representative of the reservoir height relationship for the original saturation distribution in the reservoir, the hydrocarbons are assumed to be the non-wetting phase during the original oil migration and subsequent saturation distribution equilibrium. Thomeer (1960) provides a methodology that can uniquely describe a capillary pressure curve and quantify the saturation distribution using three parameters. These so-called Thomeer parameters that describe the capillary pressure curve can be used to calculate the original saturation at any height above the free water level in the reservoir when combined with Eq. 4-3. A correlation between the capillary pressure curve's height above free water level and the reservoir depth must be found. Smith (1990) shows examples of capillary pressure to reservoir depth correlation using well log data. Figure 4-6 shows an example of capillary pressure to reservoir depth correlation using wireline test data.
184 Examination of the rock can provide insight into the original hydrocarbon saturation of the reservoir. Various classification methods (Archie, 1952; Lucia, 1983) have presented capillary pressure type-curves for rocks fitting specific classification criteria. Examination of rock can also provide descriptive parameters that can be used as input to a rock catalog (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates) to find a capillary pressure curve from an analogous rock. Image analysis of thin sections and scanning electron microscope photographs can be used to characterize the pore systems of a rock (Davies, 1990). The quantitative description of each pore system can be related to a particular capillary pressure curve, e.g., by pore throat diameter relationships (Washburn, 1921), for determining original fluid saturations. CT scanning (Wellington and Vinegar, 1987) can be used for saturation determination. Invasion and blowdown most likely have altered the saturations from in-situ values. If two fluid phases are present, a single energy scan is sufficient to measure the two saturations. When three fluid phases are present, two different energy scans are needed to determine the three saturations. Wellington and Vinegar (1987) discussed the use of CT scanning saturation determination for flow studies, and showed results from several different types of coreflood experiments. Proton nuclear magnetic resonance (~H NMR) spectroscopy and scanning (Edelstein et al., 1988) can be used to obtain liquid saturations from core material. Gas in the pore space is not measured directly, but can be inferred by the difference between the NMR liquid (%BV) and the total porosity (%BV). Because the NMR apparatus responds to liquids, the pore liquids cannot be frozen. The use of proton NMR in tight, gypsum-bearing carbonates has been shown to be valuable for saturation determination where extraction core analysis methods proved inaccurate due to gypsum dewatering and extremely low permeability of the rock (Vinegar et al., 1991 b). Whole core analysis by ~3C NMR for oil saturation determination has been demonstrated in cases where ~H NMR might not work well, like in shaly rock (Vinegar et al., 1991 a). NMR has also been demonstrated to be a useful tool in quantifying oil volume in extracts from other saturation determination procedures; such as extracts from polyurethane sponge core liners using freon-11, Dean-Stark extracts using xylene, and miscible flooding extracts using chloroform/methanol (Tutunjian and Vinegar, 1990).
Saturations from well logs The following section of this chapter will cover saturation determination using Archie's equations with porosity and resistivity logs, using dielectric logs, pulsed neutron capture logs, induced gamma ray spectroscopy logs, and nuclear magnetism logs.
Saturation determination from Archie's equations using porosity and resistivity logs Archie's equations (Archie, 1942) are the most-used equations for determining water saturation from well logs. The use of Archie's equations makes one critical assumption concerning the rock: the water phase in the pores of the rock is the only
185
Example of Capillary Pressure Curve Correlation to True Vertical Depth
Pc Hg/A] (psla)t
TVD (ft) 9780 -
:arDon Grad, = 0.346 psi/ft c Gravity = 0.80
400 t
300 t
200 t
9900
I
I
I
I
I
I
I
I
l
100%
SHg (% PV)
0%
0%
Sw (% PV)
100%
Free Water Level
10140 -
Other P~rtin~nt Parameters OH-W = 20 dynes/cm OH_w = 0 degrees
Formation Water Press. Grad. = 0.450 psi/ft SpecificGravity = 1.04 10260 4900
I
I
I
!
!
Wireline Test Pressure (psig)
I
I
I
5150
Fig. 4-6. The graph on the left is a mercury capillary pressure curve. It shows the distribution of nonwetting phase, in this case mercury (Hg), vs. capillary pressure. If the reservoir non-wetting phase is oil, the mercury saturation distribution is equivalent to the oil saturation distribution. The graph on the right is a plot of wireline test pressures vs. depth. The intersection of the water gradient line with the oil gradient line is the free water level (see Table 4-XVII for water level definitions). The free water level is equivalent to the zero capillary pressure value on the left graph. Conversion of capillary pressure to height above free water level is done with Eq. 4-3. The 100% water level is the equivalent depth of the extrapolated displacement pressure, Pd, of the capillary pressure curve. The capillary pressure curve provides the water saturation (Sw) at the reservoir depths shown on the wireline test data plot.
186 electrically conductive medium, i.e., the rocks contain no conductive clays or iron minerals. Of course the hydrocarbons (if present) are non-conductive also. This assumption usually works well with carbonates. Archie's (1942) equation f o r 100% water-saturated rock Begin by considering the manner in which rock resistivity varies as a function of porosity for rocks that are 100% saturated with water. The resistivity of a rock with zero porosity would be infinitely high, whereas the resistivity of a 100% porosity rock would be equal to the resistivity of the water. The resistivity of the rock at any other porosity is proportional to the resistivity of the water in the pores. Archie (1942) found that the equation given below fits his data.
(4-4)
Ro=FR w
where: R o (Rzero) F Rw
resistivity of rock containing 100% water, i.e., 0% hydrocarbons (ohm-m); = formation factor (dimensionless); and = resistivity of water in pores (ohm-m).
=
Therefore: R0
~--= F
(4-5)
w
Archie (1942) found that F was a constant for rock with a particular pore structure. He found the formation factor to be" F ~ ~--m
(4-6)
where: F = formation factor (dimensionless); = porosity (fractional); and m = lithologic exponent (dimensionless). Thus:
Ro = ~)-mRw
(4-7)
The value of m, the lithologic exponent, is a function of the rock type, in particular the rock's pore type or combination of pore types. For a large number of carbonate rocks, it falls between 1.9 and 2.2. Data from Traugott (1970) and Lucia (1983) show that vuggy carbonates can have values of m larger than 3.0. Detailed insight as to the effect of different pore types on the lithologic exponent is covered in the pore combination modeling section of this chapter. A graphical representation of Archie's equation for an example of a 100% water-saturated rock is shown in Fig. 4-7. One practical use of applying Archie's first equation in a 100% water-bearing zone is the determination of the formation water resistivity value. Rearranging Eq. 4-7:
187
Rw-- ~mRo
(4-8)
When this equation is applied in zones that are not known to be 100% water-bearing, the water resistivity, R w, is designated as the apparent water resistivity, Rw.
Archie's (1942) equation for hydrocarbon-bearing rock Archie (1942) analyzed others' data and found that the resistivity of a rock that is hydrocarbon-bearing is proportional to the resistivity of the rock as if it was 100% water saturated. The following relation fit his analysis: R = I R0
(4-9)
where" resistivity of rock containing hydrocarbons and water in pores (ohm-m); I = resistivity index (dimensionless); and R 0 (Rzero) resistivity of rock containing 100% water, i.e., 0% hydrocarbons (ohmm).
R t
=
=
Therefore"
R' I--=
(4-10)
Ro I is constant for rock with a particular pore structure and wettability. The resistivity index is defined as"
I = S -w"
(4-11)
100" 10" R o c k Resistivity
Ro (ohm-m)
~Slope
=-m
1.0 "
0.1 0.01 0.01
|
0.1 (fractional)
1.0
Fig. 4-7. This is a graphical representation o f A r c h i e ' s (1942) equation (R 0 = 100% water-saturated rock, on a log-log scale.
d~-"Rw)for an example of a
188 where" I = resistivity index (dimensionless); S = water saturation (fractional); and n = saturation exponent (dimensionless). So:
Rt =S--"Ro=S-" w w q~-mRw
(4-12)
Archie (1942) found that n, the saturation exponent, approximately equaled 2.0 for a large number of rocks. The value of n is a function of the rock pore structure and the rock's wettability. As the rock becomes less water-wet, the saturation exponent will increase. Values ofn in the 8.0-12.0 range have been found in carbonates that exhibit strong non-water wet behavior (Sweeney and Jennings, 1960). A graphical representation of Archie's (1942) equation for an example of a hydrocarbon-bearing rock is shown in Fig. 4-8. Notice the symmetry between the 100% water saturation case (Eqs. 4-4 through 47, and Fig. 4-7) and the hydrocarbon-bearing case (Eqs. 4-9 through 4-12, and Fig. 48). The symmetry suggests that the effect of electrical conductivity being taken away is similar in each case even though the physical situation is somewhat different; nonconductive rock takes away conductivity in the 100% water saturation case and nonconductive hydrocarbon takes away conductivity in the hydrocarbon-bearing case. The m value describes how fast conductivity (or resistivity) changes as porosity changes. The n value describes how fast conductivity (or resistivity) changes as water saturation changes. A form of Archie's (1942) equation which solves for water saturation is: !
S'-
(4-13)
~met
For the case where m = n = 2, the equation is simplified to:
1JRw L-"---~-
Rt
(4-14)
The only reason that the formation evaluation specialist should use m = n = 2 is if the rock in the zone of interest actually has those m and n values.
Resistivity of the flushed zone From Archie's (1942) equations, one realizes that the electrical resistivity of the flushed zone near the wellbore can be significantly different from that of the undisturbed zone, even in 100% water-saturated intervals. This is because the mud filtrate resistivity can be very different from the formation water resistivity. As complex as the invasion profile is, one can take advantage of the fact that in the flushed zone the water resistivity is known. The zone has been completely flushed
189
1000 100 Rock Resistivity Rt (ohm-m)
10 1.0
R.o. 0.1" l
0.()1
0.1
1.0
Sw (fractional) Fig. 4-8. A graphical representation of Archie's (1942) equation hydrocarbon-bearing rock, on a log-log scale.
(R t -
Sw-"Ro) for an example of a
with mud filtrate so the water phase resistivity is RmS.Rmsis normally measured at the surface and its value and the measurement temperature are recorded on the well log heading. Using a temperature vs. R vs. NaC1 concentration chart (Atlas Wireline Services, 1989b, Chart 1-5; Halliburton Logging Services, Inc., 1991, Chart GEN-5; Schlumberger Educational Services, 1991a, Chart Gen-9) or Arps equation (Arps, 1953), R ~can be calculated for any depth (temperature) in the wellbore. Archie's (1942) equation mJ still applies, so for water-bearing zones" w
Rxo
~=F=~
Rms
where" Rxo = Rms = = F = = m
-m
(4-15)
(in this case) resistivity of rock containing 100% mud filtrate (ohm-m); resistivity of mud filtrate in pores (ohm-m); formation factor (dimensionless); porosity (fractional); and lithology exponent (dimensionless).
The Archie (1942) equation for hydrocarbon-bearing zones in a form which solves for the flushed zone mud filtrate saturation, S O(fractional), is:
SxO=(RmZ) l (~m ex 0
(4-16)
The calculated difference between S and Sx0is a measure of movable hydrocarbons. Movable hydrocarbons are usually taken as a positive indication of producibility.
190 Archie 's parameters The Archie (1942) approach to water saturation determination requires knowledge or acquisition of the Archie's (1942) equation input data and parameters:
formation water resistivity, R w (ohm-m); porosity, ~ (fractional); true formation resistivity, R t (ohm-m); lithologic exponent, m (dimensionless); and saturation exponent, n (dimensionless). And for the determination of the mud filtrate saturation, Sx0, in the flushed zone: mud filtrate resistivity, Rml (ohm-m); and flushed zone resistivity, Rx0 (ohm-m). These data and parameters must be known at in-situ conditions. Determination of formation water resistivity is discussed later in this chapter. Determination of the mud filtrate resistivity is typically done by the well logging service company. A sample of representative drilling mud is filtered to obtain a sample of mud filtrate. The resistivity is measured and the temperature of the filtrate is recorded. Determination of porosity has been discussed earlier in this chapter. Determination of the true formation resistivity requires the use of a resistivity or conductivity logging tool, and is not a trivial task. Logs that have been used in the past include normal, lateral, and limestone devices (Guyod, 1944). Logs that are used today include focused resistivity logs, e.g., laterolog, guard, toroid, etc.; induction conductivity logs; and 1- to 2-MHz electromagnetic propagation tools (Maute, 1992, for a state-of-the-art review). Complications such as tool resolution vs. zone thickness, influence of the borehole resistivity, mud filtrate invasion, and limitations of logging tool performance due to tool design and calibration, typically dictate that the raw resistivity log readings, even for a deep investigating tool, do not represent the true formation resistivity. Environmental correction charts are available from the service company chart books to correct for resolution, borehole, and invasion effects. If R~ accuracy is critical, modeling and deconvolution programs specific to particular resistivity tools are available (e.g., Tumer et al., 1991, for the Halliburton Logging Services, Inc. dual laterolog). Flushed zone resistivity determination is from focused microresistivity logs. Mudcake thickness and mud resistivity affect microresistivity log response. Environmental corrections may be required to correct for these effects to obtain an accurate value of Rxo. Determination of m and n can be done using core analysis (Archie, 1942). Values for m and n can be obtained using a rock catalog (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates) from analogous rock types. Some authors have found relationships for m based on vuggy porosity vs. total porosity (Traugott, 1970, from log responses calibrated with local core control; Lucia, 1983, from examination of rock). A more holistic approach can be used for the determination of the lithologic exponent by considering all pore types as is done by pore combination modeling.
191 TABLE 4-XII Fitted lithologic exponents (k) for individual carbonate pore types (from Myers, 199lb) Carbonate pore type
Definition
Lithologic exponent (X)
Vugs Intergranular Microporosity
Pores larger than the grain size Intergranular or intercrystalline Not visible on 10x thin section
1.11 1.91 1.56
Pore combination modeling Determination of the lithologic exponent, m, can be accomplished using pore combination modeling (Myers, 1991 b) if the rock's pore types and their proportion of the total porosity can be defined. Petrographic analysis, including thin sections, and capillary pressure curves can provide pore type characterization. Table 4-XII shows Myers' (199 l b) lithologic exponent fits for each of the major carbonate pore types. An example of the application of pore combination modeling to determine m is as follows. Suppose there is a carbonate rock with 17% B V total porosity, composed of intergranular porosity (10% B V of the total) and vuggy porosity (7% B V of the total). The intergranular porosity is the dominant connected pore system and the vugs comprise the second pore system. A graphical representation of the application of pore combination modeling to obtain the composite Archie lithologic exponent, m, is shown in Fig. 4-9. The procedure starts with the dominant connected pore system. A line can be drawn from the origin (F = 1, ff = 100%) at a slope corresponding to the negative lithologic exponent for intergranular porosity (-Z,i) of -1.91. A second line is drawn starting from the intercept of the intergranular porosity line at the intergranular porosity value, 10%. The slope of this second line corresponds to the negative lithologic exponent of the vuggy porosity (-Lv),-1.11. The intercept of the vuggy porosity line at the total porosity, 17%, defines one point 100 -
Formation Factor, F (dimensionless)
10 -
=-
.
ugs)
T.Z'! = - ! " 9 1 , ,~', Slope = - m of rock in question. ~nterg
1 1
10
100
Porosity, (% BV)
Fig. 4-9. Graphical representation of determination of composite Archie lithologic exponent, m, from a carbonate with vuggy and intergranularporosity types, using pore combination modeling.
192 used in the determination of the composite Archie lithologic exponent, m. The other point is the origin (F = 1, ~) = 100%). The slope of the line between these two points defines the negative composite Archie lithologic exponent,-m. The use of pore combination modeling can be extended to describe the saturation dependence of a rock's resistivity behavior (Myers, 1991 b). The shape of curves plotted from resistivity index vs. water saturation measured data can give insight into a rock's pore system(s) and wettability. For a particular rock, pore combination modeling could be used to estimate n if the pore types are known and the wettability effect can be characterized. Myers (1991 b) pointed out that pore combination modeling provides a means for petrophysical properties to be calculated directly from a knowledge of a rock's pore structure. This allows the petrophysicist to incorporate geologic data in his/her petrophysical models. Not only does this make more accurate models possible, but such models may be changed to incorporate changing geology.
Saturation determination using dielectric logs Poley et al. (1978) found that a dielectric constant measurement of a formation can be used to determine water saturation without any knowledge of the formation water properties, provided that the measurement is done at a very high frequency (at or above 1 GHZ). Very high frequency dielectric logging tools (Calvert et al., 1977; Rau et al., 1991) and interpretation techniques (Wharton et al., 1980) are available. These tools have a shallow depth of investigation, 2-15 cm (1-6 in.) depending on the conductivity (Wharton et al., 1980). Because these tools normally respond to the flushed zone in the near-borehole region, most dielectric log saturation determination applications have been in formations containing heavy oil or tar. Viscous heavy oil or tar is not affected by invasion, so that the oil saturation in the near-borehole region is representative of the oil saturation in the rest of the formation. Dielectric log depth of investigation can be extended by using a lower frequency tool. However, the measurement is then dependent on the formation water salinity and the frequency of the measurement. Myers (1993) has characterized this dependence for carbonates, finding that dielectric dispersion in carbonates is dominated by two terms: a term proportional to the interparticle porosity and a term proportional to the vuggy porosity. The parameters in this model were found to be consistent with earlier published models for the dielectric constant in clastics (Myers, 199 l a). The dielectric log's ability to separate vuggy from interparticle porosity allows accurate determination of oil saturations through improved estimates of the Archie lithologic exponent, m (see the pore combination modeling portion of this chapter). Saturation determination using pulsed neutron capture logs Pulsed neutron capture (PNC) logs are designed to determine water saturation in a cased well (Youmans et al., 1964), after the drilling mud filtrate invasion has dissipated. PNC tool diameters are typically less than 5 cm (2 in.); thus they can be run through tubing. The log measures the thermal neutron capture cross section, E, of the formation which is related to the fractional volumes of oil, water, and rock matrix by a linear volumetric mixing law, as shown in Eq. 4-17:
193
~-~formation= ~hydrocar6on(l -- Sw)~ + ~waterL~ q" ~matrix(| -- ~)
(4-17)
where: E = thermal neutron capture cross section (capture units or cu); Sw - water saturation (fractional); and = porosity (fractional). However, the log does not actually measure the intrinsic ~formation. A diffusion correction is needed (Youmans et al., 1964). The diffusion correction is tool and environment dependent, and is part of the service company's characterization of the tool's response. Thus, the equation for the log response to the formation is: ~log-" ~hydrocarbon(1 --Sw)~ -~" ~-~wateraw~+ ~matrix(|- ~) -I- A
(4-18)
where" A = diffusion correction (capture units or cu). Thus, solving for water saturation yields: g - (1 -
S
w=
~)~matrix- Zhydrocarbon~-- A (Zwater_
hydrocarbon)
(4-19)
The logging service company will provide the necessary diffusion correction. One can obtain the values for Swa,e " and Y"hydro~arbo,, from, for example, measurement on samples or from tables in service company chart books, if the fluids' compositions are known (see the discussion of pore fluid property determination later in this chapter for details). One can obtain the value of ~ from, for example, a porosity log or logs (see the discussion of porosity determination earlier in this chapter for details). One can get a value for ~matrix from the references by Edmunson and Raymer (1979), Wells et al. (1979), Ellis et al. (1988), and Carmichael (1989), if the rock composition is known. ~matrix c a n also be obtained from a 100% S wzone as follows (in this case, the hydrocarbon terms drop out)"
~-~formation= ~matrix( l -- ~) "~- ~water ~
(4-20)
So, solving for Zmatrix yields" S motr~ =
~formation- ~Zwater 1 -- Ck
(4-21)
If the porosity of the formation is moderate to high and the salinity of the formation water is moderate to high, then the PNC logs can provide water saturation results with reasonable accuracy. However, there are some borehole and near-borehole conditions, e.g., logging just below a packer with liquid in the tubing and gas in the tubing-casing annulus, which can be problematic to obtaining an accurate ,~formaiont'
194 even after full data processing at the logging companies' computer centers (Bonnie, 1991). In carbonates with saturated saline formation water, the use of pulsed neutron capture logs for water saturation applications is usually limited to porosities above about 15% (see the discussion of error propagation later in this chapter for details). As formation water salinity gets fresher, the lower porosity limit for determining water saturation with this tool goes up. Another use of pulsed neutron capture logs is to determine residual oil saturation, S using the log-inject-log process (Richardson et al. 1973) This process involves twice logging a zone that is already at residual oil saturation. One needs to know the Later of the formation water. One then must be able to inject water of a different, but known, Later into the zone between the logging passes. It does not matter if the zone is cased with perforations or is openhole, as long as injection across the entire zone of interest occurs. Invasion should not be a concern because the zone's saturation is at S r. However, careful planning is needed to ensure that the residual oil saturation is not reduced by the evaluation method (Kidwell and Guillory, 1980). When the pulsed neutron capture log is run the first time, the resulting capture cross section as seen by the log, Z~, depends on the rock contribution, the formation water contribution, and the hydrocarbon contribution:
z~,1 = Z~matrix(1--~) "k",~water_lawO-I- ,~hydrocarbon(1--L ) O -I" A
(4-22)
Then water of a different, but known, capture cross section is injected into the formation at a slow rate so that the saturation is not changed by viscous stripping. When the pulsed neutron capture log is run the second time, the resulting capture cross section as seen by the log, 22, depends on the rock contribution (which has not changed), the injected water contribution (which has changed because of the change of its E), and the hydrocarbon contribution (which has not changed): z~2 = Z~matrix(l -- ~ )
+ Later_2L~ -st-~hyarocarbo.(1-S)qb + A
(4-23)
Combining the two equations yields:
Z~l- Z~2-~ (~water-1- ~water-2) L ~
(4-24)
Rearranging this equation yields:
~ l - 2;2 S~=Later_l-~water_ 2
(4-25)
and
27,- S 2 S=~(~water_l-~water_2) Therefore"
(4-26)
195 (1 - So,)q~ =
27, - 2; 2 Z ~ w a ter _ l - -
(4-27)
Z ~ w a ter _ 2
and S = 1or
271- S 2
(Swater_
)
(4-28)
It is common practice to leave the equation in the form of Eqs. 4-25 and 4-27 so that the results automatically incorporate the porosity-saturation product into the volumetric residual oil determination. This minimizes the error propagated to the volumetric result because of the reduction in the number of input parameters for the equation: the E values from the two log runs and for the two waters are needed, not the Z values for the hydrocarbons nor the matrix. One other saturation application of pulsed neutron capture logs has been to determine CO 2 saturation in carbonate reservoir surveillance evaluation of a tertiary flood (Kittridge, 1992). This process involved empirical correlation of PNC log response to CO 2 saturations at in-situ conditions for a specific PNC logging tool (not just a specific type of tool, but a specific physical tool, neutron source, detectors, etc.).
Saturation determination using induced gamma ray spectroscopy logs Interpretation models are published for saturation determination using induced gamma ray spectroscopy logs (Hertzog, 1978, and Jacobson et al., 1991, for interpretation models; Westaway et al., 1980, and Wyatt et al., 1992, for examples) making use of the carbon and oxygen yields. The models are affected by changes in mineralogy. Carbonates (i.e., rocks containing carbon) have significant effect on results. Saturation accuracies get worse as porosity decreases (Hertzog, 1978). But accuracies improve as logging speed is slowed or as stationary measurement time is increased (Wyatt et al., 1992). Saturation determination using nuclear magnetism logs Brown and Gamson (1960) described the original type of nuclear magnetism log (NML) tool which was the basis for commercial NML logging tools until the 1990s. The log provided a measurement of the total hydrogen, i.e., liquid-filled porosity, called the free fluid index (FFI). The original type of NML tools can determine formation fluid saturations in certain situations without knowledge of formation water salinity. Those situations include: (1) The hydrocarbon in the formation is heavy oil or tar. The tar acts as a solid, so the NML sees only the formation water saturation. (2) The formation is at residual oil saturation. The formation water signal can be eliminated by injecting a paramagnetic ion into the formation so the NML only responds to the residual oil saturation. With the original type of NML there is still a requirement to eliminate the borehole signal by doping the borehole with magnetic material. New nuclear magnetic resonance well logging tools (Coates et al., 1991, and Morris et al., 1993) are more in line with the technology used in the NMR core analysis
196 tools. Many of the same measurements done by the NMR core analysis tools can be done by the new well logging tools. Saturation determination from the new tools is more accurate than that from the original type of NML tools. In addition, the borehole and formation fluids do not have to be doped to eliminate the effect of its signal with the new tools.
PORE FLUID PROPERTY DETERMINATION
Introduction
Pore fluid property information is needed in formation evaluation and reservoir performance characterization, usually as a parameter for a particular model, e.g., the formation water resistivity parameter in Archie's (1942) equation for water saturation determination (Eq. 4-13). Pore fluid property information is also needed in the optimization of well completions and design of surface facilities for producing fields. Pore fluid property information, e.g., gas vs. oil, is needed for economic analysis. Pore fluid property information can be obtained from measurement or analysis of representative formation fluid samples. The representativeness of formation fluid samples is usually better from larger samples, e.g., from long-term production tests. Fluid samples from wireline formation tests and even drill stem tests can be contaminated with mud filtrate. Drill stem test fluid samples can also be contaminated by the mud initially trapped across the test interval below the packers and/or by a fluid cushion which is sometimes placed inside the drill string to limit the pressure differential across the packers. The drill stem test fluid sample that should be most representative of the formation fluids is the last sample caught in the test tool sample chamber, usually a volume of about two to two-and-a-half liters (about a half gallon). Earlougher (1977), Appendix D, provides a comprehensive set of correlations useful for estimating fluid properties needed when analyzing transient-test pressure data. Included are pressure-volume-temperature (PVT) properties; oil, water, and gas compressibilities; and gas, oil, and water viscosities. Although representative samples of formation fluids are the best source of data, many times representative samples are not available, so other methods (in addition to the aforementioned Earlougher correlations) are used to aid in the determination of formation water and hydrocarbon properties. Formation fluid properties discussed in this chapter are some of those that are most needed in formation evaluation and reservoir performance characterization. Formation water properties
Knowledge of formation water salinity or resistivity is needed for water saturation determination using resistivity and porosity logs. Formation water density information is needed for density log porosity determination of uninvaded wet zones and for interpretation of invasion profiles in highly permeable zones. Knowledge of formation water thermal neutron capture cross section is needed for water saturation determination using pulsed neutron capture and porosity logs.
197 Formation water density
Wireline tester pressure gradient results in 100% water-bearing zones provide formation water density information. Gunter and Moore (1987) provide procedures for wireline testing quality control that can reduce the errors in wireline test results and the subsequent determination of formation water density. Dewan (1983, p. 105), relates water density to salinity by: pj= 1.0 + 0.73N
(4-29)
where" /~= the water density (g/cm3); and = the NaC1 concentration (ppm x 10-6). Chart 1-6 of Atlas Wireline Services (1989b) shows the variation of water density with temperature, pressure, and salinity. Formation water salinity and~or resistivity
Formation water salinity can be obtained from formation water resistivity information, and visa versa, using a temperature vs. R w vs. NaCI concentration chart (Atlas Wireline Services, 1989b, Chart 1-5; Halliburton Logging Services, Inc., 1991, Chart GEN-5; Schlumberger Educational Services, 1991 a, Chart Gen-9). If ions other than Na and C1 are present, equivalent NaC1 concentrations can be determined using conversion charts (Atlas Wireline Services, 1989b, Chart 1-4; Halliburton Logging Services, Inc., 1991, Chart GEN-4; Schlumberger Educational Services, 1991 a, Chart Gen-8). Jorden and Campbell (in progress), Chapter 14, provide details conceming water composition evaluation of carbonate rocks. A single measurement log method, the use of the spontaneous potential (SP) log to determine water resistivity is not generally applied in carbonates due to the adverse effects of highly resistive zones on the SP log response. Multi-measurement log methods, all based on Archie's (1942) equations, include: (1) Pickett plots, see Fig. 4-1 (Pickett, 1966); (2) Hingle plots (Hingle, 1959); (3) apparent water resistivity, Rwa, curves, see Eq. 4-8 (Tixier et al., 1960); (4) crossplots of R vs. SP (Schlumberger Educational Services, 1989a, p. 4-4); (5) formation factor, F, overlays (Schlumberger Educational Services, 1989a, p. 8-5); and (6) the ratio technique (Schlumberger Educational Services, 1989a, p. 8-6). wa
Jorden and Campbell (in progress) point out that methods based on resistivity and porosity log combinations work better in carbonate evaluation compared to siliciclastic evaluation because the large variations in carbonate porosity allow more certainty in curve fitting and curve extrapolation. Determination of formation water salinity by the use of nuclear magnetic resonance imaging of 23Na in cores has been demonstrated (Tutunjian et al., 1991), for those cut in oil-based muds. This method will work for formation water salinity deter-
198 mination as long as sodium is the predominant cation in the formation water. The core must be handled and protected so that pore water evaporation does not occur. Pore water evaporation would increase the apparent salinity of the water. Water salinity and/or resistivity information can also be found in catalogs. Water catalogs have been published by service companies, govemment agencies, industry groups, and technical societies (e.g., Permian Basin Chapter of the AIME, 1954). Formation water thermal neutron capture cross section Formation water thennal neutron capture cross section can be obtained from pulsed neutron capture log readings in a 100% water-bearing formation. Rearranging Eq. 420 to solve for the water parameter, Z , ~ r, yields: _ "~'formation - ( 1
-- ~)~matrix
(4-30)
This equation can be presented graphically as a porosity vs. sigma crossplot (Clavier et al., 1971) to solve for the formation water thermal neutron capture cross section. Water sigma values can also be obtained from charts (Atlas Wireline Services, 1989b, Charts 7-1 and 7-2; Halliburton Logging Services, Inc., 1991, Chart TMD-2; Schlumberger Educational Services, 1991 a, Charts Tcor-2a and Tcor-2b). Knowledge of water salinity is required; although reservoir pressure, gas-oil ratio, boron compounds, and reservoir temperature effects are characterized by some of the charts. Hydrocarbon properties Determination of some hydrocarbon properties pertinent to formation evaluation are discussed below. In general, a representative formation hydrocarbon sample can be used to provide almost any hydrocarbon property desired. Hydrocarbon fluid type Hydrocarbon fluid type, gas vs. oil, can be determined from well log response (wireline and measurement while drilling), wireline tester pressure gradient results in the hydrocarbon-bearing zones, mud log show types and/or chromatographic gas detector ratios, core and cuttings analysis and examination, and mud filtrate nuclear magnetic resonance. Gas effects on density and neutron logs appear as an apparent lower bulk density and an apparent lower neutron porosity on a density-neutron crossplot. In gas-bearing zones, the resulting apparent matrix density will appear lower than the actual matrix density of the rock. Knowledge of the actual matrix density can be obtained from core analysis or other unaffected logs (e.g., photo-electric effect readings are not significantly affected by gas). Pulsed neutron capture (PNC) logs also provide indications of gas vs. oil. The thermal neutron capture cross section of gas (in the range 0-18 capture units) is typically less than that of oil (in the range 18-22 capture units. Condensate runs in the
199 range of 15-18 capture units (Schlumberger Educational Services, 1991a, Chart Tcor-1). Therefore, a gas zone may show a shift to a lower formation sigma value vs. an oil zone, all other properties being equal. In gas zones the near to far count ratio curve may go to a lower value compared to that in oil zones. PNC inelastic ratio response has proven to be an extremely diagnostic gas indicator in turbidite sands (Scheibal et al., 1992). The inelastic ratio response has provided gas indication in sands with porosities down to 9%. As long as there is a change in the formation's hydrogen content (e.g., gas vs. liquid) for similar porosity zones, the inelastic ratio response should provide gas indication in lower porosity sands and in carbonates also (J.M. Worrell, personal communication, 1992). As another indication of hydrocarbon type, the PNC-derived porosity will appear lower than the actual porosity in a gas zone. Wireline tester pressure gradients in the hydrocarbon-bearing zones provide hydrocarbon density information. This density information can be used with reservoir temperature and pressure data, also available from the wireline tester, to help differential gas from liquid hydrocarbons. Gunter and Moore (1987) provide procedures for wireline testing quality control that can reduce the errors in wireline test results and the subsequent determination of hydrocarbon density. Mud log show types are indicative of gas-bearing vs. oil-bearing formations. As a simple evaluation, if there are hydrocarbons indicated from the well log analysis and there is no oil staining in the rock show descriptions, most likely the hydrocarbon type is gas. A method which is used to quantify mud log fluorescence shows that occur outside the visible range is Quantitative Fluorescence Technique (QFT) (Delaune, 1992). This methodology works only for water-based muds. Condensate, which usually has no visible fluorescence, is easily identified with QFT. Threedimensional crossplots of show intensity vs. emission wavelength vs. excitation wavelength have been used to distinguish heavy oil from light oil from condensate. Delaune documents that if an oil sample is available to calibrate the QFT equipment, show intensity can predict oil saturation. However, the surface oil saturation in cuttings, cores, etc., have been altered from in-situ saturations because of mud filtrate invasion and pressure blowdown. Another mud log technique that is used to determine hydrocarbon type is chromatographic mud gas show ratios, the light to heavy component ratio. Application of these ratios typically requires local calibration. Core and sidewall sample examination and analysis will indicate oil staining or quantify oil content. Again, if there are hydrocarbons indicated from the well log analysis, and there is no oil found in the rock, most likely the hydrocarbon type is gas. Analysis of mud filtrate samples by nuclear magnetic resonance can identify the presence of gas, oil, or water in the formation (Youngblood, 1971). A mud filtrate sample can be obtained by the use of a wireline test tool. The mud filtrate sample is subjected to magnetic polarizations which are at right angles to the earth's magnetic field. These polarizations are of various time durations in order to indicate the thermal relaxation time, T~, of the mud filtrate sample. The relaxation time (see Table 4XIII) identifies the nature of the virgin formation fluid before contamination by the flushing action of the mud filtrate.
200 TABLE 4-XIII Nature of virgin formation fluid from T~ analysis of mud filtrate (fromYoungblood, 1971) Thermal relaxation time, T~, range 0 . 1 - 0.6 seconds 0.6- 1.2 seconds 1 . 2 - 2.5 seconds
Fluid Gas Oil Water
Hydrocarbon density Wireline tester pressure gradients in the hydrocarbon-bearing zones provide hydrocarbon density information. Gunter and Moore (1987) provide procedures for wireline testing quality control that can reduce the errors in wireline test results and the subsequent determination of hydrocarbon density. Oil viscosity Proton NMR measurements on tight, gypsum-bearing carbonates has provided quantitative oil viscosity information where extraction methods proved costly due to extremely low permeability of the rock (Vinegar et al., 199 l b). Whole core analysis by ~3C NMR for oil viscosity has also been demonstrated (Vinegar et al., 1991 a) without extracting the oil from the core. NMR oil viscosity determination has also been done on oil that is in core analysis extracts from polyurethane sponge core liners using freon-11, from Dean-Stark extracts using xylene, and from miscible flooding extracts using chloroform/methanol (Tutunjian and Vinegar, 1990). Oil chemistry Oil chemistry affects the wettability behavior of a crude oil/brine/solid system (Buckley and Morrow, 1990). They noted that subtle changes in pH can cause a drastic change in oil adhesion behavior. Dubey and Doe (1991) found that acid to base content of the oil can be useful indicators of the wetting properties of the oil in crude oil/brine/silica systems, but they indicated that it will be necessary to extend this work to other mineralogies before predictions can be made for carbonate reservoirs. In the process of doing this work, Dubey and Doe developed a new potentiometric titration method to properly quantify the base content of crude oils. Geochemical analyses can be done on small samples or even cuttings using thermal extraction chromatography (Price, 1985) or pyrolysis analyses (Horsfield et al., 1983). These techniques have been used to fingerprint hydrocarbons for evaluation of shows to determine hydrocarbon origin, oil gravity determination, and contaminant recognition. The two techniques are also used to evaluate source rock richness, to quantitatively and qualitatively identify kerogen type, and to classify bitumens and coals. Whole core analysis for hydrocarbon chemistry by ~3C NMR has been used to determine aliphatic/aromatic ratio (Vinegar et al., 1991a) without extracting the oil from the core. Hydrocarbon thermal neutron capture cross section Hydrocarbon thermal neutron capture cross section values can be obtained from charts (Atlas Wireline Services, 1989b, Charts 7-3, 7-4, 7-5 and 7-6; Halliburton
201 Logging Services, Inc., 1991, Charts TMD-3, -4, -5, and -6; Schlumberger Educational Services, 199 l a, Chart Tcor-1). Knowledge of gas/oil ratio for oil, and reservoir temperature and pressure for gas are required; although effects of condensate content and gravity of the gas are characterized by some of the charts.
P E R M E A B I L I T Y DETERMINATION
Permeability from examination and~or analyses of rock Muscat (1949) pointed out that no matter how complete the coring and precise the data, one is still limited to an examination and study of rock samples which can constitute at the most, a fraction of the total reservoir volume only of the order of 0.0001%. One should keep this in mind as one compares core-derived permeability to permeability derived from, for example, well testing which can have a large volume of investigation. Permeability measurement by direct core analyses is documented in the American Petroleum Institute (1960) reference. Absolute permeability can be measured using gas or brine. Klinkenberg-corrected gas permeability is an extrapolation of gas permeability to an apparent infinite gas pressure to approximate a liquid permeability. Effective and relative permeability of carbonate reservoirs are discussed in Volume I, Chapter 8 of this book. If plugs are taken, their orientation should be selected based on the need for directional information, e.g., vertical vs. horizontal permeability. For heterogeneous carbonates, whole core measurements of permeability would probably be the most representative core analysis technique. Whole core permeability measurements done perpendicular to the borehole axis typically provide two measurements (see Fig. 410). The larger of the two measurements is termed k o . The other, taken 90 ~ to the maximum value, is termed k90. So-called mini-permeameters are devices that flow gas from the end of a tube-like probe that is sealed against a rock sample to estimate local permeability. Georgi and Jones (1992) discussed the evolution of mini-permeametry and the application of this technique to reservoir description. Inasmuch as the device can provide estimates of permeability with resolution down to about 5 mm (0.2 in.), geologists can quantify the impact of both depositional and diagenetic features on permeability. Lab-based mini-permeameters can be used on small-diameter core plugs or full-diameter core samples. Portable mini-permeameters can be used on outcrops. Permeability can be estimated from capillary pressure core data (Purcell, 1949, for historical perspective on early work; Swanson, 1981, for use on cuttings or samples with large closure corrections; Thomeer, 1983, for general use). The Thomeer and Swanson methodologies provide permeability estimates within a factor of two, for a one standard deviation confidence level, based on their calibration data sets. For rocks with more than one pore type, Thomeer (1960) pointed out that the relatively larger pores of a rock contribute the most to the permeability and, therefore, any capillary curve permeability estimate should be based on the lower-pressure capillary curve portion of multiple-curve capillary pressure data.
202 Lucia (1983) provided a field classification of carbonate pore space and a methodology for estimating permeability from a visual description of carbonate rocks. Average particle size and interparticle porosity are used to provide permeability estimation within an order of magnitude for 70% of the rocks in Lucia's calibration data set. His methodology is meant to be applied to carbonates with interparticle porosity. The effect of adding separate vugs to a non-vuggy rock is to increase the porosity with little or no increase in permeability. As Lucia pointed out, this allows his methodology to still be used to estimate permeability in vuggy rock as long as the vugs are not touching. The intergranular porosity is used for the permeability estimation. If vugs are touching, it is the size of the connecting opening between the vugs that affects the permeability the most, and in a field description there is no effective method for making this observation. Petrographic examination can provide pore throat diameter information used for the construction of synthetic capillary pressure curves. Carver (1971) provided detailed procedures in sedimentary petrology. Estimating permeability from capillary pressure curves was discussed above. The petrographic rock description could also be used to select an analogous rock type from a rock catalog (Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates) for permeability estimation. Image analysis of thin sections and scanning electron microscope photographs can be used to characterize the pore systems of a rock. It is the pore type assemblage that can be related to permeability. Examples of permeability determination from image analysis has been published for sandstones (Davies, 1990), but not for carbonates. However, a similar approach aimed at the different pore systems found in carbonates should be valid. Flow gas through core in this direction
j
Screens
Whole core Fig. 4-10. This schematic shows the basis for a whole core gas permeability apparatus. Screens and core are inserted in a Hassler-type sleeve. Gas is flowed through the screens across the core and permeability is determined. Then the core is rotated 90~around the borehole axis and the permeabilityfor that direction of gas flow is determined. Both measurements are recorded. The larger one is termed k , the other is k90.
203 Proton NMR measurement has been shown to estimate permeability from sandstone core samples (Seevers, 1966, for first work; Howard et al., 1990, for recent work). Howard et al. related the time constant for NMR longitudinal relaxation,/'1, to pore body size, for intergranular/intercrystalline rock. Kenyon et al. (1988) reasoned that the permeability from NMR is, therefore, a function of the relation between the size of the pore throats to the size of the pore bodies, with NMR providing the pore body information. NMR permeability estimation for vuggy rocks will be less accurate than that for intercrystalline rocks because of the poorer relationship between pore throat size and pore body size for vugs (H.J. Vinegar, personal communication, 1992). In any NMR work, tool response is only to liquids, so the core must be 100% liquid saturated and the pore liquids must not be frozen.
Permeability from testing Permeability can be obtained from pressure transient analyses. The classic references on the subject are the following. Matthews and Russell (1967) presented the first comprehensive documentation of well testing and analysis. Earlougher (1977) provided a stand-alone, comprehensive update to the Matthews and Russell reference. Several references have provided newer insight into pressure transient analysis. Cinco-Ley and Samaniego-V. (1981) discussed the analysis of fractured formations. Bourdet et al. (1983) introduced a new set of type curves partially derived from the derivatives of the dimensionless pressure and time functions normally used in most type curves. Gringarten (1984) summarized analysis of reservoirs with double-porosity behavior, including both naturally fissured reservoirs and multilayered reservoirs with high permeability contrast between layers. The special cases of fractured and doubleporosity reservoirs would be applicable for heterogeneous carbonate reservoirs.
Permeability from well logs No well log can quantify permeability unilaterally; thus, well logs provide detection, not evaluation, of the permeability of a particular zone. Some well logs (e.g., resistivity logs, micrologs, calipers, and spontaneous potentials) can indicate which zones are permeable by showing mud filtrate invasion. Some well logs and their results (e.g., porosity logs, porosity-saturation combinations, and geochemical logs) can be used to estimate permeability by empirical correlation of log response to core permeability data. One possible exception to the lack of a direct permeability evaluation well logging tool may be found in recent versions of nuclear magnetic resonance logs (Coates et al., 1991). The tool response combined with T~ data (Seevers, 1966) or restrictive diffusion data (Vinegar and Rothwell, 1988) may provide permeability information (Coates et al., 1991).
Detection of permeability from mud filtrate invasion Several well logs detect permeable zones by indicating water-based mud filtrate invasion. Invasion is usually only an indication of permeability and not related to the quantitative permeability. Recent experiments (Allen et al., 1991) found that on all
204 but the tightest formations- rocks with more than 10-millidarcy permeability- filtrate is lost at rates that depend on interactions at the mud/mudcake interface at the borehole wall, not on formation properties such as permeability. The exception is when formation permeability and differential pressure (borehole vs. formation) are so low that the mud filtrate loss rate even without a mudcake is less than the equilibrium invasion loss rate during dynamic circulating conditions. In this case of formations with low permeabilities, no external mudcake forms under dynamic conditions and filtrate loss rate is controlled primarily by formation permeability. Higher differential pressures lower the permeability threshold at which this relationship exists. Wettability effects on the invasion rate are not considered. Otherwise, at higher formation permeabilities, the filtrate loss is likely to be the same into every permeable zone. The diameter of i n v a s i o n - a parameter extracted from resistivity l o g s - should, therefore, vary inversely with porosity. The microlog responds to mudcake build up on the borehole wall by the invasion process (Doll, 1950). The Doll reference provided detailed interpretation rules, and even exceptions to the rules, for detection of permeable intervals. His introduction mentioned that the microlog found its first field of application in limestone areas. When designing a formation evaluation program, do not forget about the m i c r o l o g it is old technology and does not have a prefix like array, spectral, or digital to make it more attractive. But it does an acceptable job of indicating permeable zones, and it can resolve very thin zones. Mudcake may also be seen on caliper logs. If the borehole remains at the bit diameter, i.e., in gauge, decreased hole diameter can be indicative of mudcake. If the borehole erodes somewhat, it can be difficult, if not impossible, to use a caliper log as a mudcake indicator to detect permeable zones. The effects of invasion can also be seen on resistivity log profiles if the resistivity of the invading fluids are different from that of the formation fluids. Invasion will appear as different resistivities on different depth-of-investigation logs. Or invasion will appear as different resistivities on similar depth-of-investigation logs run at different times. Resistivity logs used in this manner should have equal resolutions and be corrected for borehole effects. Otherwise, resolution differences might be interpreted as invasion. Spontaneous potential log response requires invasion into a permeable zone and a contrast between the mud filtrate resistivity and the formation water resistivity. Doll (1949) detailed the complexities of SP response in the case of limestone formations and more generally of permeable beds in highly resistive formations, e.g., permeable zones within evaporite zones or within low-porosity carbonates.
Estimation of permeability from empirical correlation One of the most generally-used empirical correlations to estimate permeability is porosity-permeability relationship. This correlation works best if there is only one pore type in the rock. For rock with only one pore type, the porosity-permeability crossplot will show a clear-cut relationship with little scatter. Additional pore types will enlarge the scatter and, therefore, enlarge the error bars of the resulting permeability estimate. The literature contains several references for estimation of permeability for hydrocarbon-bearing intergranular rocks at irreducible water saturation from log-derived
205 porosity and water saturation values (Wyllie and Rose, 1950; Morris and Biggs, 1967; Timur, 1968; Coates and Dumanoir, 1973). Non-intergranular rocks are not considered. Well logging service company chart books (e.g.,Atlas Wireline Services, 1989b; Halliburton Logging Services, Inc., 1991; Schlumberger Educational Services, 1991 a) contain graphical versions of these estimation methods (also see Chapter 7 in Vol. I of this book). Herron et al. (1991) described the application of geochemical logging mineralogy results to permeability estimation for a Middle East carbonate reservoir. The procedure incorporates porosity and a knowledge of whether a particular mineral will increase or decrease permeability (Herron, 1987). There is an inherent assumption here that the relationship between the rock's mineralogy and its texture is consistent and predictable. Fracture and vug detection
Fractured and extremely vuggy zones provide high-permeability pathways that can contribute to high well production rates. But, fractured and extremely vuggy zones are usually not beneficial for secondary or tertiary floods. They become thief zones taking expensive injectant fluids. Fracture porosity volume generally will be insignificant with respect to the total reservoir storage volume. A fracture system will generally contribute less than 1% bulk volume to the rock porosity (Hensel, 1989; Chapter 1, Part II of this book). A value of 1% bulk volume is typically within the accuracy of conventional porosity log measurements. Vuggy porosity can be significant with respect to the total reservoir storage volume. Fracture and vug detection from cores and sample examination Detection of fractures and vugs from core can be done qualitatively by examination. Or a more quantitative analysis can provide detailed geological information. The study of a fractured reservoir (Golf-Racht, 1982) must follow a special pattern, beginning with the examination of local basic characteristics of single fracture, only afterwards continuing with the examination of a multifracture system. In establishing the relationship among the various group of fractures, the local relationships are examined at reservoir scale by comparison, trends and extrapolation of parameters. Basic parameters obtained from an evaluation of fractures and the relationships between those parameters are shown in Fig. 4-11. Some core analysis techniques used for naturally-fractured reservoirs are listed in Table 4-XIV. Skopec et al. (1992) discussed procedures for the successful recovery of oriented horizontal core from highly-fractured carbonate rocks. The authors' specific objectives for this coring included formation evaluation and drilling reasons: efficient recovery of core sections, high core recovery rates, quality core material, accurate orientation data, comprehensive core analysis, and maintenance of borehole angle while coring. To accomplish these objectives in a horizontal situation, they had to develop or adapt equipment or procedures. The problem of frequent core jamming in the coring assembly was largely overcome by the use of flexible fiberglass inner barrels and multiple core-catcher assemblies. They achieved a recovery rate of almost 100% by using shorter core sections and improved inner- and outer-barrel stabilization. For
206
Single Fracture
Group of Fractures
--~
,, Distribution --~ Matrix Block Shapes
f
9Width ,, Size 9Nature
,, Orientation
, Density
-Intensity-
t.Nl Environment
I
I
l
(lithology) (morphology) Fig. 4-11. The basic parameters of fractures and their relationships are shown here. (After van GolfRacht, 1982).
orientation purposes, a slip scribe was used in conjunction with an electronic multishot instrument that uses an array of accelerometers for determination of inclination. This orientation instrument alleviated many of the problems that had been associated with camera surveys. To operate the electronic multishot instrument in a horizontal configuration, it was necessary to develop specialized equipment. Skopec et al. state that their newly designed rotatable non-magnetic blade centralizer, enhanced running gear, and a high frequency shock absorber were needed to be used to obtain accurate core orientation data. To ensure positive alignment of the orientation instruments and the TABLE 4-XIV Core analysis methods for naturally-fractured reservoirs (after Bergosh et al., 1985; Bergosh and Lord, 1987) Method
Comments
CT scanner
Sees through core containers Sees interior of core Can be done under stress
Computerized goniometer
Can determine orientation of each fracture Can segregate different fracture types Must differentiate natural from induced fractures
Full-diameter core analysis
More representative than analysis on core plugs Porosity and saturation measurements Multidimensional permeability measurements Can be done under stress
Fluorescent epoxy impregnation
Slabs viewed under UV light Fracture porosity determined Can be done under stress
207 coring assembly, a laser alignment system was invented and used successfully. Specialized horizontal core handling procedures were developed to ensure accurate core orientation data. It is obvious that these authors needed to go beyond using off-theshelf equipment to meet their coring objectives. Their efforts were successful because of their planning for and development and adaptation of procedures and equipment that would let them accomplish their objectives.
From well logs Well logs that most commonly provide fracture and vug detection and pertinent references are listed in Table 4-XV. These wireline logging tools fall into the general TABLE 4-XV Logs that can detect fractures and vugs Log type
Name of tool (reference)
Company*
Acoustic waveform
Array Sonic (Morris et al., 1984) Digital Array Acoustilog (Atlas Wireline Services, 1990) EVA Full Wave Tool (Fortin et al., 1991) Full Wave Sonic (Welex, 1986)
Schlumberger
Diplog/dipmeter
Electrical array
Pulsed acoustic
Video camera
Fracture Identification Log (Brown, 1978) High Resolution 4- or 6-Arm Diplog (Atlas Wireline Services, 1988) Six Arm Dipmeter (Goetz et al., 1986) Stratigraphic High Resolution Dipmeter (Chauvel et al., 1984) Formation Microlmager (Safinya et al., 1991) Formation MicroScanner (Ekstrom et al., 1986)
Atlas Elf Aq., CGG Halliburton Schlumberger Atlas Halliburton Schlumberger Schlumberger Schlumberger
Borehole Televiewer (Zemanek et al., 1969) Borehole Televiewer Tool (Schlumberger Educational Services, 1991b, p. 48) Circumferential Acoustic Scanning Tool (Torres et al., 1990) Circumferential Borehole Imaging Log (Faraguna et al., 1989)
generic
Video Camera (Briggs, 1964) Time Delay Video System (Offshore, 1992, p. 37)
generic
Schlumberger Halliburton Atlas
Hitwell
* Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or tool.
208 categories of acoustic waveform logs, diplogs/dipmeters, and imaging logs. Imaging logs are of three different types: electrical array, pulsed acoustic, and video camera. The Society of Professional Well Log Analysts Reprint Volume on Borehole Imaging (1990) provides a comprehensive reference set for these imaging logs. Acoustic waveform logs digitally acquire full acoustic wave data, the amplitude vs. time information from each acoustic receiver on the tool. The waveforms can provide velocity and attenuation information on compressional, shear, mud, and tube waves. Fracture and vug detection from attenuation of compressional wave amplitudes (Tixier et al., 1959) and from attenuation of shear wave amplitudes (Pickett, 1963) was noted early in the life of the acoustic log. Other references (Anderson and Walker, 1961; Morris et al., 1964) looked at the physics behind this log response. Many other acoustic waveform fracture detection techniques are discussed by Crary et al. (1987), including compressional amplitude spike analysis, X-Z waveform crisscross analysis, Stoneley wave attenuation, Stoneley reflected-to-incident energy ratio, and slowness differences of compressional, shear, and Stoneley velocities between two equally-spaced but offset transmitter-receiver pairs. Qualitative and quantitative interpretation of fracture permeability, derived from empirical correlation of acoustic waveform log tube wave data to measured fracture permeability, is discussed by Paillet (1991). Use of the diplog/dipmeter for fracture detection has been documented for West Texas Ellenburger dolomites, the South Texas Austin Chalk formation, and North Louisiana and Mississippi Cretaceous limestones (Brown, 1978). Fractures filled with water-based drilling mud show up as conductive response on any diplog/dipmeter pad that traverses the fracture. Conductive response on one or more of the pads can be interpreted as a fracture. A special curve presentation of the dipmeter log which permitted easier identification of fractured zones was named the Fracture Identification Log. The Formation MicroScanner was originated as a multi-electrode electrical array on one pad of a dipmeter, providing a resistivity image of approximately 10% circumferential coverage (depending on hole size) of the borehole. The tool was later upgraded to place electrical arrays on two and then four pads, ending up with about 40% circumferential coverage of the borehole. The Formation Microlmager was introduced as a replacement to the original resistivity imaging tool. Each of its four fixed array pads has a flip-out array pad extending to the side, which increases the coverage to about 80% of the borehole circumference. Serra (1989) provided a detailed interpretation reference for these resistivity imaging tools. A Formation Microlmager produces an image related to electrical resistivity measurements. A core or core photo produces an image of reflected light. Formations and borehole features may reflect light in a manner that is not representative of their electrical resistivities. One must be thinking in terms of electrical resistivity when looking at a Formation Microlmager image, or else an erroneous interpretation may result. The borehole televiewer tool is a pulsed acoustic logging device. The acoustic wave originates at the tool's acoustic transducer, progresses to the borehole wall, reflects off the borehole wall, and is received back at the transducer. The acoustic transducer is continuously rotated to provide complete circumferential, i.e., helical, borehole coverage as the tool is pulled up the borehole by the wireline. Two images are derived from the acoustic wave received back at the transducer: one from the first
209 arrival waveform amplitude and one from the waveform two-way time of flight. The amplitude image mainly represents the acoustic impedance (product of density and acoustic velocity) of the formation-however, the tool decentralization and the acoustic attenuation of the mud column can have significant effect. The time of flight image mainly represents subtle borehole irregularities such as vugs, fractures, and washouts -however, again the lack of tool centralization can have significant effect. If a geological feature is small, like the width of a fracture might be, it is possible that it might be plugged with drilling mud solids and might not have enough acoustic impedance contrast to be visible on a borehole televiewer log. The idea of volumetric scanning well logging from an pulsed acoustic tool (Broding, 1982) allows insight into not only features at the borehole wall, but features away from the borehole wall as long as that feature has an acoustic impedance contrast with the rock nearer the borehole wall. Rambow (1984) showed many geologically interesting examples of borehole televiewer logs. The use of a borehole televiewer for vug detection to optimize completions in a carbonate waterflood has been documented (Clerke and Van Akkeren, 1986). Massively vuggy zones acted as thief zones in a waterflood and degraded the waterflood performance if they were open to the borehole by perforations. A borehole televiewer produces an image related to acoustic impedance measurements. A core or core photo produces an image of reflected light. Formations and borehole features may reflect light in a manner that is not representative of their acoustic impedances. One must be thinking in terms of acoustic impedance when looking at a borehole televiewer image, or else an erroneous interpretation may result. Video camera logging technology is usually limited by the opaque borehole fluid. Openhole formation evaluation applications have got around this limitation by putting a clear fluid bubble in front of the camera lens (Mullins, 1966). Cased hole video camera logging can be done in a borehole containing clear fluid, but cased hole applications are usually for determining the mechanical configuration of the casing and other tubulars, not for formation evaluation. One cased hole formation evaluation application is the monitoring of the perforations for type of fluid production, e.g., oil vs. water. Crary et al. (1987) pointed out that all of these well logging fracture detection methods can, at times, mistake other geological features (such as thin soft beds and bed boundaries) and drilling features (such as washouts, induced fractures, and drill string damage) for natural fractures. They also discussed other much less useful and more ambiguous well logging fracture detection methods including resistivity log apparent invasion profiles, spectral density log response if the tool pad crosses a fracture, spectral natural gamma ray detection of uranium salts deposited on fracture faces, and spontaneous potential electrokinetic (sometimes called streaming) potential. Non-touching vug detection is possible using a comparison of acoustic log porosity with porosity derived from a density and/or neutron log. The acoustic log tends not to see the vuggy porosity until it becomes the dominant pore type, whereas the density and neutron logs see the total porosity. Traugott (1970) showed an example of detection of non-touching vugs using an acoustic log comparison to neutron log porosity. Traugott used increased vug porosity to determine the Archie' s (1942) lithologic exponent for his water saturation calculation.
210
From well testing Indications of vugs and fractures can be obtained from pressure transient analyses. Matthews and Russell (1967) and Cinco-Ley and Samaniego-V. (1981) discussed the analysis of fractured formations. Gringarten (1984) summarized analysis of reservoirs with double-porosity behavior, including both naturally-fissured reservoirs and multilayered reservoirs with high permeability contrast between layers, e.g., vuggy vs. intercrystalline porosity layers. From drilling procedures Flow from fractured zones can be detected during underbalanced drilling or while using gas as a drilling fluid. The Austin Chalk trend in Texas requires wellbores to intersect fractures to produce oil at commercial rates. Many times, a well will begin flowing when a fracture is encountered and the well may need to be put on choke to control the well while drilling proceeds. The Ellenburger Group, also in Texas, produces gas from brecciated layers within a very thick, predominantly low-porosity and low-permeability dolomite. Some of the Ellenburger wells in the J.M. Field have been drilled using produced gas from nearby wells as the drilling fluid. The drilling gas is flowed through the rig circulation system at rates up to six million cubic feet per day. The return drilling gas is flared at a safe location away from the rig. When a permeable (brecciated) gas-productive zone is encountered, the flare size increases. Drilling gas flow is then ceased and the formation gas production rate is measured. NET FORMATION THICKNESS DETERMINATION
The following definitions of depth and thickness are adapted from the Society of Professional Well Log Analysts (1984):
Measured depth (MD): Depth measured along the drilled hole. It is reported in drilling records, measured by wireline-logging cables, and shown on well logs. This depth has not been corrected for hole deviation. True vertical depth (TVD): The vertical distance between a specific location in a borehole and a horizontal plane passing through the depth datum. It is determined from directional surveys. True bed thickness (sometimes called true stratigraphic thickness): The thickness of the stratigraphic unit measured along a line normal to the direction of extension of the unit. True thickness can be derived from information determined by the dipmeter. Apparent bed thickness (sometimes called measured thickness)" Corresponds to the distance the borehole remains in the bed. The borehole may not have penetrated the bed normal to its upper or lower boundary surface because of hole deviation and formation dip. True vertical thickness: The thickness of the stratigraphic unit measured along a vertical line. True vertical thickness can be derived from information determined by the dipmeter. These thickness definitions relate to the gross formation thickness, i.e., the total thickness of the formation between its upper and lower boundary. Net formation
211 TABLE 4-XVI Methods for determination of net apparent formation thickness Tool
Concerns
Wireline logs MWD logs Mud log penetration rate Mud log cuttings Core
Usually most accurate method, except in thin beds Need accurate data acquisition time to drilling depth correlation Penetration rate can be related to net formation properties Cuttings location smears during circulation to surface Most accurate method in thin beds; missing core not considered
thickness is the thickness of the permeable rock layers in that formation which can contribute to production. Hydrocarbon productive net formation thickness, sometimes called pay thickness, is a subset of net formation thickness. Methods for determination of net apparent formation thickness are listed in Table 4-XVI. Bed boundary determination and zoning can be done from well logs. A simple approach would be to manually select bed boundaries at inflection points on log curves. A more sophisticated approach would be to use a forward modeling or deconvolution program. This approach has the potential to provide a more accurate bed thickness determination and has the added result of providing a log value for the zone. Serra (1986, Volume II, Chapter 5) related the facies as seen by a well log to the rock facies. He defined the term electrofacies as the set of log responses which characterizes a bed and permits it to be distinguished from the others. Electrofacies are observed to have certain well log shapes. A ramp-shaped log response is termed an electrosequence. An electrosequence is indicative of a geologic change. Serra noted that the ramp may reflect: (1) a progressive change in mineralogical composition with depth; (2) the evolution of a textural parameter; (3) a simultaneous variation in mineralogical composition and in texture; or (4) a saturation transition between water and hydrocarbons. Bed boundary determination should consider all of the geological and petrophysical changes in the rock and fluid sequence. As discussed in earlier sections of this chapter, well logs respond predictably to changes in lithology, porosity, pore fluid saturations, and pore fluid properties. Thus, zoning can be made directly dependent upon changes in these properties. However, well logs do not respond proportionally to permeability magnitude, unless there is a relationship between permeability and one of the other properties. Thus, well log bed boundary determination based on changes in permeability needs to be calibrated, preferably to core data. There are resolution considerations in the determination of net formation thickness. Whereas wireline logs usually provide the most accurate zone thickness values, they do have a finite resolution. If the net productive layers in the formation are thinner than the resolution of the logging tool, then the log cannot provide adequate thickness determination. Cores can show the layering with the finest resolution, if sufficient core recovery is obtained. Geological inspection provides detailed bed boundary information. Digital core image analysis can be used to distinguish layering on a millimeter-by-millimeter basis by color differentiation (Georgi et al., 1992). Core images presented on the same scale as log data can be used to calibrate and supplement
212 wireline logs. Bed boundary locations derived from core image analysis can be used with forward modeling to evaluate thin-bed well log response. In addition, highresolution mini-permeametry data can be used to distinguish permeable from nonpermeable layers to calibrate the image analysis and well logs. Georgi et al. (1992) reported image analysis and mini-permeameter applications for sand-shale cores. The methodologies will work for carbonates as long as there is color and permeability contrast between different geological layers. In cases where the well encounters hydrocarbons, but does not penetrate the hydrocarbon-water contact (sometimes called the water level), it is beneficial to determine the true vertical depth of the water level to be able to make representative reserve calculations and subsequent drilling well location selection. The term water level can have one of three different meanings depending on the context. Table 4XVII lists these definitions. The distance between these water levels is less than a meter for very good quality rocks, i.e., darcy magnitude permeability, but can be several tens of meters or more for moderate to low quality rocks. Determination of the reservoir free water level from one well penetration, which does not encounter the free water level, is possible (Roach, 1963, using pressure gradients; Smith, 1990, using capillary pressure properties), but rock and fluid properties of the reservoir must first be known. TABLE 4-XVII Reservoir water level definitions Water level
Definition
Producing water level
Shallowest of the three water levels; level above which a near water-free completion can be made; determined from production tests or from fractional water flow calculations.
100% water level
Level with 100% water saturation just below and positive hydrocarbon saturation just above; determined from core fluid saturation data, from log water saturation calculations, or from the equivalent depth of the capillary pressure extrapolated displacement pressure.
Free water level
Deepest of the three water levels; level at which competition between capillary and buoyancy forces begins in the reservoir; determined from intersection of water and hydrocarbon fluid pressure gradients from multiple wireline pressure tests, or from the equivalent depth of zero capillary pressure.
STRUCTURAL AND STRATIGRAPHIC DETERMINATION
Serra (1986) defined structure, a megascopic feature of a rock mass or rock unit, as the general disposition, attitude, arrangement, or relative positions of the rock masses of a region or area. Serra (1986) defined stratigraphy as the arrangement of rock strata, concerned with all characters and attributes of rocks (succession, age, form, distribution, composition, fossil content, geophysical and geochemical properties). Keep in mind that evaluation tools that limit data acquisition to the borehole or near~ borehole region (logging tools, cores, etc.) are seeing a limited volume and may not be representative perspective of the formation structure and stratigraphy. Evaluation
213 tools that acquire data well beyond the borehole (seismic, geotomography, etc.) will see a more megascopic picture, but will probably miss the more subtle structural and stratigraphic features. Structural and stratigraphic information is obviously available from examination of rock. Whole core can provide much insight if the in-situ orientation of the core is known. Davison and Haszeldine (1984) provided a review of four simple techniques, listed in Table 4-XVIII, that are used to orient conventional cores back to their in-situ position. Carver (1971) discussed details of the measurement of stratification orientation and the mathematical treatment of orientation data. Information can also be obtained from cuttings and sidewall cores. Cuttings and sidewall cores are of limited size and cannot provide as continuous information as whole core can. In addition, the use of cuttings suffers from problems with exact depth correlation. TABLE 4-XVIII Methods for orienting conventional cores back to their in-situ position (Davison and Haszeldine, 1984) Method
Comments
Oriented core barrels Dipmeter* Highly deviated wellst Paleomagnetic
Can be used on any rock type sequence Must be recognizable structural plane Use directional survey in conjunction with regional dip knowledge Origin and age of remanent magnetism component must be identified
* Imaging logs could be used today, and would provide better accuracy than a dipmeter because of their increased circumferential coverage. t Skopec et al. (1992) discussed the successful recovery and orientation of core from highly-fractured carbonates in horizontal wells, using an oriented core barrel.
Serra (1986, Volume II) provided comprehensive insight into the use of all types of well log data for structural (Chapter 4) and stratigraphic (Chapter 13) determination, and also for other geological uses. Serra detailed the use of well logs run in multiple boreholes providing geographical distribution. A list of well logs that provide structural and stratigraphic information from only a single borehole and the pertinent references is found in Table 4-XIX. Of all the tool types on this list, the diplog/dipmeter tools have the most history behind them (Schlumberger et al., 1933), although several somewhat different tool designs have been used over time. Digitally recorded magnetic tape data allowed for automatic computation of dipmeter logs (Moran et al., 1962). Early dipmeter interpretation techniques (Gilreath and Maricelli, 1964) utilized what was then high-density computations to define depositional and structural features. Machine computations of dipmeter surveys, with dips computed as frequently as three per meter (one per foot), were very crude by today's standards. Inasmuch as these tools are microresistivity logs, diplog/dipmeter tools can be easily run in water-based drilling mud. Special modifications have been made for these tools to be run in non-conductive oil-based mud or air-filled boreholes (e.g., Fons, 1966). Today, processing of diplog/dipmeter data can be done manually from paper log copies (consultants still advertize this service) or by computer processing using magnetic tape data (by a service company or by using commercially available software). Processing parameters and criteria depend on which geological features are important to the interpretation. Serra (1985),
214 TABLE 4-XIX Logs that can provide structural and stratigraphic information from a single borehole Log type
Name of tool (reference)
Service company*
Diplog/dipmeter
HighResolution 4- or 6-Arm Diplog (Atlas Wireline Services, 1988) Six-Arm Dipmeter (Goetz et al., 1986) Stratigraphic High Resolution Dipmeter (Chauvel et al, 1984) FormationMicrolmager (Safinya et al., 1991) Formation MicroScanner (Ekstrom et al., 1986) Azimuthal Resistivity Imager (Davies et al., 1992) Vertical Seismic Profile (Johnston and Markowitz, 1992) Array Sonic (Morris et al., 1984) Digital Array Acoustilog (Atlas Wireline Services, 1990) EVA Full Wave Tool (Fortin et al., 1991) Full Wave Sonic (Welex, 1986) Borehole Televiewer (Zemanek et al., 1969) Circumferential Acoustic Scanning Tool (Torres et al., 1990) Circumferential Borehole Imaging Log (Faraguna et al., 1989) Borehole Televiewer Tool (Schlumberger Educational Services, 199 l b, p. 48) Video Camera (Briggs, 1964) Time Delay Video System (Offshore, 1992, p. 37)
Atlas
Electrical array
Acoustic
Pulsed acoustic
Video
Halliburton Schlumberger Schlumberger Schlumberger Schlumberger generic Schlumberger Atlas Elf Aq., CGG Halliburton generic Halliburton Atlas Schlumberger generic Hitwell
* Service company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or tool. Schlumberger Limited (1986), and Atlas Wireline Services (1988) provide much insight into the interpretation of data from these tools. The diplog/dipmeter multiple independent pad (four or six) configuration also provides for a detailed caliper log of the borehole. Formation Microlmager and Formation MicroScanner tools have been discussed earlier in this chapter. Formation MicroScanner and Formation Microlmager image features can be segregated into geologically significant categories, e.g., fractures, bed boundaries, faults, unconformities, and cross bedding, using interactive workstations (Boyeldieu and Jeffreys, 1988) to aid in structural and stratigraphic interpretation.
215 Inasmuch as these tools are essentially sophisticated versions of the diplog/dipmeter tools, it is probable that resistivity imaging tools eventually will completely replace the diplog/dipmeter tools. Azimuthal Resistivity Imaging tools can provide structural and stratigraphic information, but at a resolution larger than that of the Formation MicroImager tools (Davies et al., 1992). An array of twelve azimuthal electrodes is incorporated into a dual laterolog array so as to provide twelve deep, oriented resistivity measurements while retaining the standard deep and shallow laterolog measurements. Though the fullcoverage azimuthal resistivity image has much lower spatial resolution than borehole microelectrical images, it complements these because of its lower sensitivity to shallow features such as borehole rugosity and washouts. Borehole televiewer tools have been discussed earlier in this chapter. The acoustic picture of the borehole wall provided by these pulsed acoustic tools can show the layering, fractures, vugs, etc., of the formation to provide structural and stratigraphic information, provided there is acoustic impedance contrast between these geological features and the background. Full-wave acoustic logs have been used to provide acoustic reflective imaging around a wellbore. Fortin et al. (1991) documented the imaging range to reach about 7 m (23 ft) away from the borehole. Hornby (1989) extended the imaging range to about 18 m (60 ft) away from the borehole. Vertical seismic profile (VSP) surveys have been used to provide high resolution imaging of features away from the borehole (Johnston and Markowitz, 1992). For acoustic reflective and VSP methods to be effective, the structural and/or stratigraphic features of interest must have acoustic impedance contrast with their adjacent features. Structural and stratigraphic information from these types of intermediate depth-of-investigation tools can provide a tie between information limited to or near to the borehole, e.g., from Formation MicroImager or diplog/dipmeter, and information from far away from the borehole, e.g., from seismic or geotomography. Seismic can provide information concerning structural and stratigraphic changes without the need of a borehole. Some pertinent references include Ausburn et al. (1977) for general seismic applications to formation evaluation, Ausburn (1979) for well log editing to improve seismic calibration, and Brown (1986) for 3-D seismic applications. In general, the use of seismic in carbonates is limited to structural and stratigraphic determination (see Chapter 2, Vol.II). Geotomography, i.e., cross-well tomography as shown in Fig. 4-12, can provide information concerning structural and stratigraphic changes between wellbores. A contrast, electromagnetic or acoustic impedance, between the layers of interest is needed. Resolution is no better than the minimum of the spacing between the transmitters within one wellbore or the spacing between the receivers within the other wellbore (Dines and Lytle, 1979, for electromagnetic tomography; Worthington, 1984, for acoustic tomography; Kretzschmar and Witterholt, 1984, for historical background and EOR surveillance in pilots). Distance between wellbores is limited to about 3060 m (100-200 fl) for electromagnetic tomography, and about 300--600 m (10002000 ft) for acoustic tomography. An integrated formation evaluation approach to the determination of stratigraphy can contribute significant insight into a reservoir model (Kern and Schepel, 1991).
216 Kern and Schepel described a multi-specialty team effort that interpreted 720 km (450 miles) of seismic, examined 1800 m (6000 ft) of core, correlated over 50 wells with modem openhole logs, and used petrographic analysis to develop a sequence stratigraphic-based reservoir model of a carbonate formation. The seismic data were interpreted to determine the sequence boundaries (relative sea level drops) and then tied to regional well log cross sections using synthetic seismograms. Core description emphasized recognition of depositional facies, shallowing upward depositional cycles, and depositional cycle stacking patterns. Epifluorescence petrographic examination techniques were used to determine facies and pore types of altered dolomites, and isotopic data and thin section descriptions were used to determine the diagenetic history of the dolomite. For the reservoir studied, porosity was primary and was clearly linked to facies types which were controlled by water depth. Sequence stratigraphic analysis allowed prediction of paleo water depth. Thus, for CO 2 flood optimization, completions based on sequence stratigraphic correlation will improve flood conformity by ensuring that wells are completed considering paleo water depth (or porosity) continuity. The authors felt that the results of the study will facilitate continued infill drilling, fieldwide projects to add pay and deepen wells, and subsurface mapping of reservoir flow units. The results will also aid in flood prediction, surveillance, and overall reservoir management.
PROPAGATION OF ERROR CONSIDERATIONS
In any calculation or determination, errors in the input parameters propagate through to the result. In formation evaluation situations potentially involving the spending of a large amount of money, it is prudent to know the magnitude of the error in the evaluation results and their effect on the economic results. Two methods are generally used to determine errors: partial differential error equations and Monte Carlo iterative method. The confidence level of the input error values, e.g., one standard deviation, becomes the confidence level of the propagated error. The partial differential equation technique uses the standard error equation. For the function X = f(A, B, C, D, E, F), the error equation is of the form:
(4-31) where: X AX A
.,. ,,,
= = = =
dependent variable being solved for as the result; most probable error in the result; independent variables, i.e., input parameters to the function; and errors in the independent variables or input parameters to the function.
One advantage of use of the error equation is that it provides information about the magnitude of individual parameter contributions to the error in the result. However, there are three main assumptions that must be met for valid use of the error equation:
217
Ground level One borehole contains transmitters, the other contains receivers.
I1 Wellbore 1
11 1
receiver spacing
Wellbore 2
Fig. 4-12. Geotomography (electromagnetic or acoustic) ray paths between transmitters in one wellbore and receivers in another wellbore. Layering that has contrast (electromagnetic or acoustic) can be differentiated. (1) input variables must be independent; (2) errors must be small; and (3) errors must be normally distributed. The Monte Carlo iterative technique requires a computer program to do hundreds or thousands of iterations. The technique uses probability distribution functions for each input variable. Randomly selected input values from each input distribution function are used to calculate results. The iterations provide an output probability distribution function for the result. Some economic risk analysis programs, e.g., @RISK (Palisade Corporation*, 1991), can easily be adapted to error analysis of technical computations. Programs of this type allow specified dependences between input variables. Examples of the propagation of error through to formation evaluation results are shown in Figs. 4-13 and 4-14, for a version of the previously discussedArchie's (1942) water saturation calculation equation: ! S w "- ( B R w / R t ~ m ) n (4-32) One graph, Fig. 4-13, shows the effect of small input errors. These small errors are about the best-case scenario. The other, Fig. 4-14, shows the effect of moderate input errors. These moderate errors are about the normal-case scenario. The graphs have plotted the most probable error in water saturation (% P V) as a function of the water *Company names mentioned in this chapter are for reference only and are not meant as an endorsement of any particular company or product.
218
Propagation of Small Error in Archie's Equation 0
.
.
.
.
.
15
Input Parameter Errors
10 . . . . . . . . . . . . . . . . . . . . . . . . . . .
a
Saturation Error (% PV) i
= 1.O_+O.O1
Rw = 0.1 _+0.002 ~'2-m 0
1
.
.
_
~
/
/
/
~
.
-15
-20 0
R!t = varies 5%% BV 20.0 4"-+ 1.0 = 2.0 -!- 0.05
j =2.0_+005
, , , , , , , , , 10 20 30 4 0 50 6 0 70 80 9 0 100 Water Saturation (% PV)
Fig. 4-13. The effect of small input errors (tabulated above) onArchie's (1942) water saturation calculations. The error increases as water saturation increases.
Propagation of Moderate Error in Archie's Equation
0
15 10 . Saturation Error (% PV)
-
-
InDut Parameter Errors
.
.
. .
20~ 0
.
.
. .
.
.
.
.
.
B Rw Rt (~ m n
= 1.0_+0.05 = 0.1 _+ 0.005 ~-2-m varies _+ 5% = 20.0 _+ 2.0 % B V = 2.0+0.1 = 2.0-+0.5
, , . , . , , , , 10 2 0 3 0 4 0 50 6 0 70 80 90 100 Water Saturation (% PV)
Fig. 4-14. The effect of moderate input errors (tabulated above) on Archie's (1942) water saturation calculations. The error increases as water saturation increases.
saturation (% P V) itself. The water saturation is changed by changing the true resistivity value. The error varies with the water saturation determined, and the error is largest for high water saturations (low hydrocarbon saturations). At 95% calculated water saturation, the results are 95% +7% for the small error case and 95% • 12% for the moderate error case. In either case, from log calculations only it is not possible to tell if a 95% calculated water saturation is really 95% water saturation (5% hydrocarbon saturation) or if it is really 100% water saturation (no hydrocarbons) and within
219 error bars. To come to an unambiguous conclusion, one would have to augment the log calculation with other data, e.g., hydrocarbon show information from a mud log. Of course, the error propagated through to the result can be reduced by decreasing the number of input parameters in the petrophysical model. Input parameter reduction can be attained by using a different (but still appropriate) petrophysical model or by determining several parameter values in a simultaneous dependent method. For example, the Pickett plot (Pickett, 1966) allows simultaneous determination o f R w and m (and B if included in the model) from the position of the R0 line through the water points (see Fig. 4-1). Changes in R w simultaneously change m. In this case, the interdependence of these parameters will substantially reduce the error propagated through to the resulting water saturation calculation because Archie's (1942) equation reduces to:
( R~ Sw=\Rt)
(4-33)
The resulting error in S using a Pickett plot for R wand m can be much smaller than if the variables were truly independent as in the case when R wis from a produced water sample and m is from core analysis (R.J. Conser, personal communication, 1992). Additional examples of the propagation of error through to formation evaluation results are shown in Fig. 4-15 and Fig. 4-16, for the previously discussed pulsed neutron capture log water saturation calculation:
S
--
"~---~lo--g (1 -
q~)Z~matrix
r
-
--
"~hydrocarbon r
Z~
(4-19)
"~hydrocarbon)
The errors are calculated for a resulting water saturation of 50%. One graph, Fig. 415, shows the effect of small input errors. These small errors are about the best-case
Propagation of Small Error in PNC Sw Equation Inout Parameter Errors ~oil = ~water = ~-~natrix = X;Iog t~ A = Sw =
Saturation 1 Error
(% PV) _ l
-40 ~ 0
!
|
|
|
10
20
30
40
22 + 0.25 cu 125 4- 1 cu 7 4- 0.25 cu varies 4- 0.25 cu varies + 1 % BV 0 4- 0.25 cu 50 % PV
50
Porosity (% BV) Fig. 4-15. The effect of small input errors (tabulated above) on pulsed neutron capture log water saturation calculations. The resulting water saturation is fifty percent of the pore volume. The error increases as porosity decreases. In this case, formation water is saturated (salinity). Fresher formation waters would add more error to the resulting water saturation calculation.
220
Propagation of Moderate Error in PNC Sw Equation 40 30 20
Inout Parameter Errors
................
~oil ~--,water ~matrix ~log t~ A Sw
Saturation Error (% PV) m
~30 -40
. 0
I0
20
.
. 30
.
. , 40
= 22 __ 0.5 cu = 125 + 2 cu = 7 -t- 0.5 cu varies + 1.0 cu varies __+2 % BV = 0 + 0.5 cu = 50 % PV
50
Porosity (% BV) Fig. 4-16. The effect of moderate input errors (tabulated above) on pulsed neutron capture log water saturation calculations. The resulting water saturation is fifty percent of the pore volume. The error increases as porosity decreases. In this case, formation water is saturated (salinity). Fresher formation waters would add more error to the resulting water saturation calculation.
scenario. The other, Fig. 4-16, shows the effect of moderate input errors. These moderate errors are about the normal-case scenario. The graphs have plotted the most probable error in water saturation (% PV) as a function of the porosity (% B ~ . The error is largest for low porosities. Also, inasmuch as in this case the formation water is saturated (salinity), fresher formation waters would add more error to the resulting water saturation calculation.
SUMMARY
This chapter was written to provide a fairly detailed overview of carbonate formation evaluation. The best approach to formation evaluation of carbonates, or any other rock type, is to first and foremost understand the petrophysics of the rock. If the formation evaluator understands the petrophysics of the rock, he or she can understand the response of the various evaluation tools to that rock, and can then best predict pertinent rock and fluid properties and the performance of the formation. Starting with the evaluation tool response without considering the rock can lead to ambiguous results.
ACKNOWLEDGMENTS
The author wishes to thank Shell Oil Company for permission to contribute this chapter. Two skilled Shell Oil Company petrophysical engineering instructors, E.C. Thomas and the late Charles L. Rabe, provided the definitions associated with the term petrophysics. Justin Freeman of Shell Development provided the error equations
221
for the pulsed neutron capture error graphs. The author appreciates the guidance and insight provided by other exploration and production instructors at Shell Oil Company's Head Office Training, concerning the application of their technical specialty areas to formation evaluation. James R. Jorden, Shell Oil Company Manager of Continuous Performance Improvement Training and also a skilled petrophysical engineer, has been and still is a valued discussion partner on many aspects ofpetrophysics and formation evaluation. Thanks go to the staff members of the library at Shell Development Company's Bellaire Research Center: Carmen Miller, Jeff Pharis, Mary Estrada, Sean Williams, Shirley Purcell, and Carla Rhone, who were able to find references in a very timely manner. The author also wishes to thank Lavelle Zander of Shell Oil Company's Head Office Production Training for her assistance in copying additional references. Finally, the author appreciates the review of this chapter by E.C. Thomas and James R. Jorden. Acknowledgment is made to the following publishers, service companies and professional societies for permission to reproduce material from their publications: Elsevier Scientific Publishing Company; Halliburton Logging Services, Inc.; Reservoirs, Inc.; Schlumberger Educational Services; and the Society of Professional Well Log Analysts.
REFERENCES Alberty, M. and Hashmy, K.H., 1984. Application of ULTRA to log analysis. Paper Z, SPWLA 25th Ann. Logging Symp. Trans., New Orleans, LA, June 10-13, pp. 1 - 17. Allen, D., Bergt, D., Best, D., Clark, B., Falconer, I., Hache, J-M., Kienitz, C., Lesage, M., Rasmus, J., Roulet, C. and Wraight, P., 1989. Logging while drilling. Oilfield Rev., 1(1): 4 - 17. Allen, D.,Auzerais, F., Dussan, E., Goode, P., Ramakrishnan, T.S., Schwartz, L., Wilkinson, D., Fordham, E., Hammond, P. and Williams, R., 1991. Invasion revisited. Oilfield Rev., 3(3): 1 0 - 23. American Petroleum Institute, 1960. Recommended Practice for Core-Analysis Procedure (API RP 40). Washington, D.C., First Edition, Order No. 811-08300,August: 55 pp. This document is being revised as of press time. Anderson, W.L. and Walker, T., 1961. Application of open hole acoustic amplitude measurements. SPE paper 122, presented at the SPE 36th Ann. Fall Meeting, Dallas, TX, October 8 - 11:6 pp. Archie, G.E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. AIME, 146:54 - 62. Archie, G.E., 1950. Introduction to petrophysics of reservoir rocks. Bull. Am. Assoc. Petrol. Geologists, 34(5): 943 - 961. Archie, G.E., 1952. Classification of carbonate reservoir rocks and petrophysical considerations. Bulletin Am. Assoc. Petrol. Geologists, 36:278 - 298. Arps, J.J., 1953. The effects of temperature on the density and electrical resistivity of sodium chloride solutions. Trans. AIME, 198: 3 2 7 - 330. Atlas Wireline Services, 1988. Fundamentals of Diplog Analysis. Houston, TX, Reference AT88-340: 216 pp. Atlas Wireline Services, 1989a. Formation Multi-Tester (FMT) Principles, Theory, and Interpretation. Reference A T 8 9 - 405:59 pp. Atlas Wireline Services, 1989b. Log Interpretation Charts. Houston, TX, Reference AT89- 194:203 pp. Atlas Wireline Services, 1990. Digital Array Acoustilog. Houston, TX, Reference A T 9 0 - 081:6 pp. Ausburn, B.E., 1979. Well log editing improves seismic calibration. Worm Oil, 188(4): 9 7 - 110. Ausburn B.E., Butler, J.R., Nath, A.K. and Wittick, T.R., 1977. Modem seismic methods - an aid to the petroleum engineer. SPE Paper 6862, presented at SPE 52nd Ann. Fall Tech. Conf. and Exh., Denver, CO, October 9 - 12:20 pp.
222 Bergosh, J.L. and Lord, G.D., 1987. New developments in the analysis of cores from naturally fractured reservoirs. SPE paper 16805, SPE 62nd Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Dallas, TX, September 2 7 - 30:563 - 570. Bergosh, J.L., Marks, T.R. and Mitkus, A.E, 1985. New core analysis techniques for naturally fractured reservoirs. SPE paper 13653, SPE California Regional Meeting Proc., Bakersfield, CA, March 2 7 29:599 - 610. Bonnie, R.J.M., 1991. Evaluation of various pulsed neutron capture logging tools under well-defined laboratory conditions. Paper OO, SPWLA 32nd Ann. Logging Symp. Trans., Midland, TX, June 1 6 1 9 : 9 pp. Bourdet, D., Whittle, T.M., Douglas, A.A. and Pirard, Y.M., 1983. A new set of type curves simplifies well test analysis. World Oil, 196(6): 9 5 - 104. Boyeldieu, C. and Jeffreys, P., 1988. Formation MicroScanner: new developments. Paper WW, SPWLA llth European Formation Evaluation Symp. Trans., Oslo, Norway, September 1 4 - 16:16 pp. Briggs, R.O., 1964. Development of a downhole television camera. Paper N, SPWLA 5th Ann. Logging Symp., Midland, TX, May 13 - 15. Broding, R.A., 1982. Volumetric scan well logging. Log Analyst, 23(1): 14 - 19. Brown, A.R., 1986. Interpretation of Three-dimensional Seismic Data. Am. Assoc. Petrol. Geologists Mem. 42, Tulsa, OK: 194 pp. Brown, R.J.S. and Gamson, B.W., 1960. Nuclear magnetism logging. Trans. AIME, 2 1 9 : 1 9 9 - 207. Brown, R.O., 1978. Application of fracture identification logs in the Cretaceous of North Louisiana and Mississippi. Trans. of the Gulf Coast Assoc. of Geological Societies, 28(1): 75 - 91. Buckley, J.S. and Morrow, N.R., 1990. Characterization of crude oil wetting behavior by adhesion tests. SPE/DOE paper 20263, SPE/DOE Symp. on Enhanced Oil Recovery Trans., Tulsa, OK, April 22 - 25: 871 - 8 7 7 . Burke, J.A., Campbell Jr., R.L. and Schmidt, A.W., 1969. The litho-porosity cross plot. Log Analyst, 10(6): 25 - 43. Calvert, T.J., Rau, R.N. and Wells, L.E., 1977. Electromagnetic propagation.., a new dimension in logging. SPE paper 6542, presented at the SPE 47th Ann. California Regional Meeting, Bakersfield, CA, April 1 3 - 15:15 pp. Carmichael, R.S. (Editor), 1989. CRC Practical Handbook of Physical Properties of Rocks and Minerals. CRC Press, Inc., Boca Raton, FL. Carver, R.E. (Editor), 1971. Procedures in Sedimentary Petrology. Wiley-Interscience, New York: 633 PP. Chace, D.M., Schmidt, M.G. and Duchek, M.P., 1985. The multiparameter spectroscopy instrument continuous Carbon/Oxygen l o g - MSI C/O. Paper X, CWLS 10th Form. Eval. Symp., October: 14 pp. Charlson, G.S., Bilhartz, H.L. and Stalkup, F.I., 1978. Use of time-lapse logging techniques in evaluating the Willard Unit CO 2 flood mini-test. SPE paper 7049, SPE 5th Symp. on Improved Methods for Oil Recovery Proc., Tulsa, OK, April 1 6 - 19: 1 2 7 - 136. Chauvel, Y., Seeburger, D.A. and Castro Orjuela, A., 1984. Applications of the SHDT stratigraphic high resolution dipmeter to the study of depositional environments. Paper G, SPWLA 25th Ann. Logging Symp. Trans., New Orleans, LA, June 1 0 - 13:23 pp. Cinco-ley, H. and Samaniego-V., F., 1981. Transient pressure analysis for fractured wells. J. Petrol. Tech., 33(9): 1749 - 1766. Clavier, C. and Rust, D.H., 1976. The MID plot: a new lithology technique. The Log Analyst, 17(6): 16 24. Clavier, C., Hoyle, W. and Meunier, D., 1971. Quantitative interpretation of thermal neutron decay time logs: Part I. Fundamentals and techniques. Part II. Interpretation example, interpretation accuracy, and time-lapse technique. J. Petrol. Tech., 23(6): 743 - 763. Clavier, C., Heim, A. and Scala, C., 1976. Effect of pyrite on resistivity and other logging measurements. Paper HH, SPWLA 17th Ann. Logging Symp. Trans., Denver, CO, June 9 - 12:34 pp. Clerke, E.A. and Van Akkeren, T.J., 1986. Borehole televiewer improves completion results in a Permian Basin San Andres reservoir. SPE paper 15033, SPE Permian Basin Oil & Gas Recovery Conf. Proc., Midland, TX, March 13 - 14:399 - 407. Clerke, E.A., Williams, K.W. and Pearce, L.A., in progress. The DAK formation evaluation model for the Permian Basin Clearfork, 48 pp. Coates, G.R. and Dumanoir, J.L., 1973. A new approach to improved log-derived permeability. Paper R,
223 SPWLA 14th Ann. Logging Symp., Lafayette, LA, May 6 - 9:28 pp. Coates, G.R., Miller, M., Gillen, M. and Henderson, G., 1991. The MRIL in Conoco 33-1 - A n investigation of a new magnetic resonance imaging log. Paper DD, SPWLA 32ndAnn. Logging Symp. Trans., Midland, TX, June 1 6 - 19:24 pp. Coles, M.E., Muegge, E.L. and Marek, B.F., 1992. Use of attenuation standards for CAT scanning applications within oil and gas production research. SCA paper 9223, Soc. Core Analysts Preprints, Oklahoma City, OK: 28 pp. Conser, R.J., 1992. Personal Communication. Crary, S., Dennis, B., Denoo, S., Liu, O., Brown, S., Cheung, P., Clavier, C., Herron, M., Homby, B., Hsu, K., Johnson, D., Plumb, R., Sibbit, A., van der Hijden, J., Winkler, K., Boyeldieu, C., Brie, A., Lloyd, E, Frisinger, R., Guindy, A., Watfa, M., Paul, A., Pellisier, J. and Theys, P., 1987. Fracture detection with logs. Tech. Rev., 35(1): 2 2 - 34. Davies, D.H., Faivre, O., Gounot, M-T., Seeman, B., Trouiller, J-C., Benimeli, D., Ferreira, A.E., Pittman, D.J., Smits, J-W., Randrianavony, M.,Anderson, B.I. and Lovell, J., 1992.Azimuthal resistivity imaging: A new generation laterolog. SPE paper 24676, SPE 67th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Washington, D.C., October 4 - 7:143 - 152. Davies, D.K., 1990. Image analysis of reservoir pore systems: state of the art in solving problems related to reservoir quality. SPE paper 19407, SPE Formation Damage Control Symp. Proc., Lafayette, LA, February 22 - 23:73 - 82. Davison, I. and Haszeldine, R.S., 1984. Orienting conventional cores for geological purposes: a review of methods. J. Petrol. Geol., 7(4): 461 - 466. Deans, H.A., 1978. Single-well tracer methods. Determination of Residual Oil Saturation, Chapter 7, Interstate Oil Compact Commission, Oklahoma City, OK, pp. 1 5 6 - 176. Delaune, EL., 1992. Surface techniques to measure oil concentration while drilling. Paper KK, SPWLA 33rd Ann. Logging Symp. Trans., Oklahoma City, OK, June 1 4 - 17:19 pp. Dewan, J.T., 1983. Essentials of Modern Open-Hole Log Interpretation. PennWell Publishing Company, Tulsa, OK, 361 pp. Dines, K. and Lytle, R.J., 1979. Computerized geophysical tomography. Proc. IEEE, 67(7): 1065- 1073. Doll, H.G., 1949. The SP log: Theoretical analysis and principles of interpretation. Trans. AIME, 179: 1 4 6 - 185. Doll, H.G., 1950. The Microlog - a new electrical logging method for detailed determination of permeable beds. Trans. AIME, 189:155 - 164. Domenico, S.N., 1974. Effect of water saturation on seismic reflectivity of sand reservoirs encased in shale. Geophysics, 39(6): 759-769. Domenico, S.N., 1977. Elastic properties of unconsolidated porous sand reservoirs. Geophysics, 42(7): 1339- 1368. Donohue, D.A.T., 1984. Drillstem Testing. PE 404, Video and Manual, IHRDC, Boston, MA: 146 pp. Donohue, D.A.T., 1986. Introduction to Well Testing and Measurement Techniques. PE 401, Video and Manual, IHRDC, Boston, MA: 83 pp. Donohue, D.A.T. and Ertekin, T., 1982. Gaswell Testing. PE 402, Video and Manual, IHRDC, Boston, MA: 214 pp. Dresser Atlas, 1981. Carbon~Oxygen Log. Houston, TX, Reference 5M 9417, September. Dubey, S.T. and Doe, P.H., 1991. Base number and wetting properties of crude oils. SPE paper 22598, SPE 66th Ann. Tech. Conf. and Exh. Proc., Dallas, TX, October 6 - 9: 1 2 7 - 135. Earlougher, Jr., R.C., 1977. Advances in Well Test Analysis. SPE Monograph Volume 5, Dallas, TX: 264 pp. Edelstein, W.A., Vinegar, H.J., Tutunjian, EN., Roemer, P.B. and Mueller, O.M., 1988. NMR imaging for core analysis. SPE paper 18272, SPE 63th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proe., Houston, TX, October 2 - 5:101 - 112. Edmunson, H. and Raymer, L.L., 1979. Radioactive logging parameters for common minerals. Log Analyst, 20(5): 3 8 - 4 7 . Erratum. Log Analyst, 21(2). Ehrlich, R. and Davies, D.K., 1989. Image analysis of pore geometry: relationship to reservoir engineering and modeling. SPE paper 19054, SPE Gas Tech. Symp. Proc., Dallas, TX, June 7 - 9:15 - 30. Ekstrom, M.P., Chen, M., Rossi, D.J., Locke, S. and Aron, J., 1986. High-resolution microelectrical borehole wall imaging. Paper K, presented at the 10th European Formation Evaluation Symp., Aberdeen, Scotland, April: 20 pp.
224 Ellis, D.V., 1987. Well Logging for Earth Scientists. Elsevier, New York: 532 pp. Ellis, D., Howard, J., Flaum, C., McKeon, D., Scott, H., Serra, O. and Simmons, G., 1988. Mineral logging parameters: nuclear and acoustic. Tech. Rev., 36(1): 3 8 - 52. Enos, P. and Sawatsky, L.H., 1981. Pore networks in Holocene carbonate sediments. J. Sed. Pet., 51: 961 -985. Faraguna, J.K., Chace, D.M. and Schmidt, M.G., 1989. An improved borehole televiewer system: image acquisition, analysis and integration. Paper UU, SPWLA 30th Ann. Logging Symp. Trans., Denver, CO, June 1 1 - 14:11 pp. Fons, L., 1966. New dipmeter tool logs in nonconductive mud. Oil and Gas J., 64(31): 124 - 126. Fortin, J.P., Rehbinder, N. and Staron, P., 1991. Reflection imaging around a well with the EVA fullwaveform tool. Log Analyst, 32(3): 271 - 278. Gardner, J.S. and Dumanoir, J.L., 1980. Litho-density log interpretation. Paper N, SPWLA 21st Ann. Logging Symp. Trans., Lafayette, LA, July 8 - 11:23 pp. Georgi, D.T. and Jones, S.C., 1992. Application of pressure-decay profile permeametry to reservoir description. Presented at the 16th Ann. SPE (Nigerian Council) International Conf. and Exh., Lagos, Nigeria, August 2 6 - 27:12 pp. Georgi, D.T., Phillips, C. and Hardman, R., 1992. Applications of digital core image analysis to thin-bed evaluation. Presented at the 16th Ann. SPE (Nigerian Council) International Conf. and Exh., Lagos, Nigeria, August 2 6 - 27:12 pp. Gilreath, J.A. and Maricelli, J.J., 1964. Detailed stratigraphic control through dip computations. Bull. Am. Assoc. Petrol. Geologists, 48(12): 1902- 1910. Goetz, J.F., Enderlin, M.B. and Dean, M.C., 1986. Field testing results of the six arm dipmeter. Paper M, SPWLA lOth European Formation Evaluation Symp., Aberdeen, Scotland, April 2 2 - 25:22 pp. Golf-Racht, T.D. van, 1982. Fundamentals of Fractured Reservoir Engineering. Elsevier Scientific Publishing Company, New York: 710 pp. Gringarten, A.C., 1984. Interpretation of tests in fissured and multilayered reservoirs with double-porosity behavior: theory and practice. J. Petrol. Tech., 36(4): 5 4 9 - 564. Gunter, J.M. and Moore, C.V., 1987. Improved use of wireline testers for reservoir evaluation. J. Petrol. Tech., 39(6): 635 - 644. Guyod, H., 1944. Electrical Well Logging. Welex (Halliburton Logging Services, Inc.), Houston, TX, Bulletin A132:103 pp. Gysen, M., Mayer, C. and Hashmy, K.H., 1987. A new approach to log analysis involving simultaneous optimization of unknowns and zoned parameters. Paper B, 11th Formation Evaluation Symp. Trans., Canadian Well Logging Soc.: 20 pp. Halliburton Logging Services, Inc., 1991. Log Interpretation Charts. First Printing: 367 pp. Harville, D.G. and Freeman, D.L., 1988. The benefits and application of rapid mineral analysis provided by Fourier transform infrared spectroscopy. SPE Paper 18120, SPE 63th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Houston, TX, October 2 - 5:141 - 150. Hensel Jr., W.M., 1989. A perspective look at fracture porosity. SPE Formation Evaluation, 4(4): 531 534. Herron, M.M., 1987. Estimaiing the intrinsic permeability of clastic sediments from geochemical data. Paper HH, SPWLA 28th Ann. Logging Symp. Trans., London, England, June 2 9 - July 2:23 pp. Herron, S.L., Petricola, M.J.C. and Dove, R.E., 1991. Geochemical logging of a Middle East carbonate reservoir. SPE paper 21435, SPE Middle East Oil Show Trans., Bahrain, November 1 6 - 19:821 830. Hertzog, R.C., 1978. Laboratory and field evaluation of an inelastic-neutron-scattering and capture gamma ray spectroscopy tool. SPE paper 7430, presented at the SPE 53rd Ann. Fall Tech. Conf. and Exh., Houston, TX, October 1 - 3:14 pp. Hertzog, R., Colson, L., Seeman, B., O'Brien, M., Scott, H., McKoen, D., Wraight, P., Grau, J., Ellis, D., Schweltzer, J. and Herron, M., 1989. Geochemical logging with spectrometry tools. SPE Formation Evaluation, 4(2): 153- 162. Hingle, A.T., 1959. The use of logs in exploration problems. SEG 29th International Ann. Meeting, Los Angeles, CA, November 9 - 13. Hoffman, L.J.B., Hoogerbrugge, P.J. and Lomas, A.T., 1988. LOGIX, a knowledge-based system for petrophysical evaluation. Paper R, SPWLA 29th Ann. Logging Symp., San Antonio, TX, June 5 - 8:13 PP.
225 Hornby, B.E., 1989. Imaging ofnear-borehole structure using full-waveform sonic data. SPE paper 19872, SPE 64thAnn. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., San Antonio, TX, October 8 - 11: 615 - 622. Horsfield, B., Dembicki, H. and Ho, T.T.Y., 1983. Some applications of pyrolysis to basin studies. J. Geol. Soc. London, 140:431 - 4 4 3 . Howard, J.J., Kenyon, W.E. and Straley, C., 1990. Proton magnetic resonance and pore-size variations in reservoir sandstones. SPE paper 20600, SPE 65th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., New Orleans, LA, September 23 - 26:733 - 742. Jacobson, L.A., Beals, R., Wyatt, Jr., D.F. and Hrametz, A., 1991. Response characterization of an induced gamma spectrometry tool using a Bismuth Germanate scintillator. Paper LL, SPWLA 32ndAnn. Logging Symp., Midland, TX, June 16 - 19:18 pp. Jodry, R.L., 1992. Pore geometry of carbonate rocks. Carbonate Reservoir Characterization: A Geologic - Engineering Analysis, Elsevier Publishing Company, Inc., New York, NY, Part I, Chapter 6, pp. 331 - 377. Updated from: 1972, Oil and Gas Production from Carbonate Rocks, American Elsevier Publishing Company, Inc., New York, NY, pp. 35 - 82. Johnston, L.K. and Markowitz, G., 1992. High-resolution VSP imaging to locate additional reserves in producing fields. SPE paper 24685, SPE 67th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Washington, D.C., October 4 - 7:265 - 272. Jorden, J.R. and Campbell, F.L., 1984. Well Logging I - R o c k Properties, Borehole Environment, Mud and Temperature Logging. SPE Monograph Volume 9, Dallas, TX, 167 pp. Jorden, J.R. and Campbell, F.L., in progress. Well Logging IV. SPE Monograph, Dallas, TX. Kenyon, W.E., Day, P.I., Straley, C. and Willemsen, J.F., 1988. A three-part study of NMR longitudinal relaxation studies of water-saturated sandstones. SPE Formation Evaluation, 3(3): 6 2 2 - 636. Kern, C.A. and Schepel, K.J., 1991. Formation evaluation aids application of sequence stratigraphy to optimize production of the Means San Andres Unit, Andrews County, Texas. Paper SS, SPWLA 32nd Ann. Logging Symp. Trans., Midland, TX, June 1 6 - 19:18 pp. Kidwell, C.M. and Guillory, A.J., 1980. A recipe for residual oil saturation determination. J. Petrol. Tech., 32(11): 1999-2008. Kittridge, M.G., 1992. Quantitative CO 2 flood monitoring- Denver U n i t - Wasson (San Andres) Field. SPE paper 24644, presented at the SPE 67th Ann. Tech. Conf. and Exh., Washington, D.C., October 4 - 7 : 2 1 pp. Kretzschmar, J.L. and Witterholt, E.J., 1984. Enhanced recovery surveillance using well-to-well tomography. SPE/DOE paper 12680, presented at the SPE/DOE 4th Symp. on Enhanced Oil Recovery, Tulsa, OK, April 15 - 18:21 - 26. Krief, M., Garat, J., Stellingwerff, J. and Ventre, J., 1990. A petrophysical interpretation using the velocities of P and S waves (Full-Waveform Sonic). Log Analyst, 31(6): 3 5 5 - 369. LeBlanc, D.P., 1988. Oilwell Testing. PE 403, Video and Manual, IHRDC, Boston, MA, 232 pp. Leverett, M.C., 1941. Capillary behavior in porous solids. Trans. AIME, 142:152 - 168. Lucia, F.J., 1983. Petrophysical parameters estimated from visual descriptions of carbonate rocks: a field classification of carbonate pore space. J. Petrol. Tech., 35(3): 629 - 637. Matthews, C.S. and Russell, D.G., 1967. Pressure Buildup and Flow Tests in Wells. SPE Monograph Volume 1, Dallas, TX: 172 pp. Maute, R.E., 1992. Electrical logging: state-of-the-art. Log Analyst, 33(3): 2 0 6 - 227. Mayer, C. and Sibbit, A., 1980. GLOBAL, a new approach to computer-processed log interpretation. SPE paper 9341, presented at the SPE 55th Ann. Tech. Conf. and Exh., Dallas, TX, Sept. 21 - 24:14 PP. Mezzatesta, A., Rodriguez, E. and Frost, E., 1988. OPTIMA: a statistical approach to well log analysis. Geobyte, August, 3(3): 56 - 69. Moran, J.H., Coufleau, M.A., Miller, G.K. and Timmons, J.P., 1962. Automatic computation of dipmeter logs digitally recorded on magnetic tapes. J. Petrol. Tech., 14(7): 771 - 782. Morris, C.E., Maclnnis, J., Freedman, R., Smaardyk, J., Straley, C., Kenyon, W.E., Vinegar, H.J. and Tutunjian, P.N., 1993. Field test of an experimental pulsed nuclear magnetism tool. Paper GGG, SPWLA 34th Ann. Logging Symp., Calgary, Alberta, June 13 - 16:23 pp. Morris, C.F., Little, T.M. and Letton, W.III, 1984. A new Sonic Array Tool for full waveform logging. SPE paper 13285, SPE Ann. Tech. Conf. and Exh. Proc., Houston, TX, September 16 - 19:7 pp. Morris, R.L., Grine, D.R. and Arkfeld, T.E., 1964. Using compressional and shear acoustic amplitudes
226 for the location of fractures. Jr. Petrol. Tech., 16(6): 623 - 632. Morris, R.L. and Biggs, W.P., 1967. Using log-derived values of water saturation and porosity. Paper X, SPWLA 8th Ann. Logging Syrup., Denver, CO, June 1 2 - 14:26 pp. Mullins, J.E., 1966. Stereoscopic deep well photography in opaque fluids. Paper N, SPWLA 7th Ann. Logging Syrup. Trans., Tulsa, OK, 9 pp. Muscat, M., 1949. Physical Principles of Oil Production. McGraw-Hill, New York: 922 pp. Myers, M.T., 1991a. A saturation interpretation model for the dielectric constant of shaly sands. SCA paper 9118, Soc. Core Analysts Preprints, San Antonio, TX, August 21 - 22:15 pp. Myers, M.T., 1991b. Pore combination modeling: a technique for modeling the permeability and resistivity properties of complex pore systems. SPE paper 22662, SPE 66th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Dallas, TX, October 6 - 9:77 - 87. Myers, M.T., 1993. Abstract: A model for the dielectric dispersion in carbonates. Log Analyst, 34(2): 53. Offshore, 1992. Time delay allows camera to use wireline cables. February, 52(2): 37. Owen, L.B., Greaves, K.H., Lord, G., Bereskin, S.R. and King, E., 1992. Improved pore visualization by confocal microscopy. SCA paper 9226, Soc. Core Analysts Preprints, Oklahoma City, OK: 16 pp. Paillet, F.L., 1991. Qualitative and quantitative interpretation of fracture permeability using acoustic full-waveform logs. Log Analyst, 32(3): 2 5 6 - 270. Palisade Corporation, 1991. @RISK, RiskAnalysis and Simulation Add-In for Microsoft Excel. Windows or Apple Macintosh Version, Release 1.02 User's Guide, Newfield, NY, March 25. Peeters, M. and Visser, R., 1991. A comparison of petrophysical evaluation packages: LOGIC, FLAME, ELAN, OPTIMA, and ULTRA. Log Analyst, July-August, 32(4): 3 5 0 - 357. Permian Basin Chapter of the AIME, 1954. A Survey of Resistivities of Waterfrom Subsurface Formations in West Texas. Published by Schlumberger Well Surveying Corporation, Midland, TX, September: 48 pp. Pickett, G.R., 1963. Acoustic character logs and their applications in formation evaluation. J. Petrol. Tech., 15(6): 659 - 667. Pickett, G.R., 1966. A comparison of current techniques for determination of water saturation from logs. SPE paper 1446, J. Petrol. Tech., 18(11): 1425- 1433. Poley, J.P., Nooteboom, J.J. and de Waal, P.J., 1978. Use of V.H.F. dielectric measurements for borehole formation analysis. Log Analyst, 19(3): 8 - 30. Price, J.G.W., 1985. Thermal extraction chromatography- a new technique for rapid wellbore evaluation. J. Canadian Petrol. Tech., 24(5): 64 - 68. Purcell, W.R., 1949. Capillary pressures - their measurement using mercury and the calculation of permeability therefrom. Trans. AIME, 186:39 - 48. Quirein, J., Kimminau, S., LaVigne, J., Singer, J. and Wendel, F., 1986. A coherent framework for developing and applying multiple formation evaluation models. Paper DD, SPWLA 27th Ann. Logging Syrup. Trans., Houston, TX, June 9 - 13:17 pp. Raiga-Clemenceau, J., Martin, J.P. and Nicoletis, S., 1986. The concept of acoustic formation factor for more accurate porosity determination from sonic transit time data. Paper G, SPWLA 27th Ann. Logging Symp., Houston, TX, June 9 - 13:14 pp. Rambow, F.H.K., 1984. The borehole televiewer: some field examples. Paper C, SPWLA 25th Ann. Logging Syrup., New Orleans, LA, June 1 0 - 13:21 pp. Rau, R., Davies, R., Finke, M. and Manning, M., 1991. Advances in high frequency dielectric logging. Paper S, SPWLA 32nd Ann. Logging Syrup. Trans., Midland, TX, June 1 6 - 19:18 pp. Raymer, L.L. and Biggs, W.P., 1963. Matrix characteristics derived by porosity computations. Paper X, SPWLA 4th Ann. Logging Syrup. Trans., Oklahoma City, OK, May 23 - 24:21 pp. Raymer, L.L., Hunt, E.R. and Gardner, J.S., 1980. An improved sonic transit time-to-porosity transform. Paper P, SPWLA 21st Ann. Logging Syrup. Trans., Lafayette, LA, July 8 - 11:13 pp. Reservoirs, Inc. and Robert M. Sneider Exploration, Inc., 1987, plus updates. A Catalog of Geological and Engineering Properties for Sandstones and Carbonates. Reservoirs, Inc., Houston, TX, July, Eight volume notebook version and CD-ROM version. Richardson, J.E., 1979. Monitoring flood profiles with induction logs. J. Petrol. Tech., 31 (1): 19 - 24. Richardson, J.E., Wyman, R.E., Jorden, J.R. and Mitchell, ER., 1973. Methods for determining residual oil with pulsed neutron capture logs. J. Petrol. Tech., 25(5): 593 - 606. Roach, J.W., 1963. How to determine oil-water contacts using one point control. World Oil, 157(7): 8 7 90.
227 Rodriguez, E., Tetzlaff, D.M., Mezzatesta, A. and Frost, E., 1988. Estimating rock properties by statistical methods. SPE paper 17603, SPE International Meeting on Petroleum Engineering Proc., Tianjin, People "s Republic of China, November 1 - 4 : 5 3 9 - 552. Rose, W.D. and Bruce, W.A., 1949. Evaluation of capillary character in petroleum reservoir rocks. Trans. AIME, 186: 1 2 7 - 142. Ruessink, B.H. and Harville, D.G., 1992. Quantitative analysis of bulk mineralogy: the applicability and performance of XRD and FTIR. SPE paper 23828, SPE International Symp. on Formation Damage Control Proc., Lafayette, LA, February 2 6 - 27:533 - 546. Safinya, K.A., Le Lan, P., Villegas, M. and Cheung, P.S., 1991. Improved formation imaging with extended microelectrical arrays. SPE paper 22726, SPE 66th Ann. Tech. Conf. and Exh., Formation Evaluation and Reservoir Geology Proc., Dallas, TX, October 6 - 9:653 -664. Savre, W.C., 1963. Determination of a more accurate porosity and mineral composition in complex lithologies with the use of the sonic, neutron and density surveys. J. Petrol. Tech., 15(9): 945 - 959. Scheibal, J.R., Weiland, J.L., Worrell, J.M. and Bayer, J.E., 1992. Differentiation of hydrocarbon type in laminated Pliocene/Pleistocene turbidite sands via inelastic pulsed neutron capture data. SPE paper 24725, presented at the SPE 67th Ann. Tech. Conf. and Exh., Washington, D.C., October 4 - 7:11 pp. Schlumberger, C., 1981. RFT- Essentials of Pressure Test Interpretation. ATL-Marketing, Order No. M081022:77 pp. Schlumberger, C., Schlumberger, M. and Doll, H.G., 1933. The electromagnetic teleclinometer and dipmeter. Proc. of the 1st World Petroleum Congress, London: 4 2 4 - 4 3 0 . Schlumberger Educational Services, 1989a. Log Interpretation Principles/Applications. Order No. SMP7017. Schlumberger Educational Services, 1989b. Cased Hole Log Interpretation Principles~Applications. Order No. SMP-7025. Schlumberger Educational Services, 1990. Historical Charts. Order No. SMP-7030:88 pp. Schlumberger Educational Services, 1991a. Log Interpretation Charts. Order No. SMP-7006:172 pp. Schlumberger Educational Services, 1991 b. Wireline Services Catalog. Order No. SMP-7005:111 pp. Schlumberger Educational Services, 1992. Geochemical Reservoir Analyzer- Client Document. December 8:32 pp. Schlumberger Limited, 1986. Dipmeter Interpretation. Order No. SMP-7002:76 pp. Scott, H.D., Stoller, C., Roscoe, B.A., Plasek, R.E. andAdolph, R.A., 1991 .A new compensated throughtubing carbon/oxygen tool for use in flowing wells. Paper MM, SPWLA 32nd Ann. Logging Symp., Midland, TX, June 1 6 - 19:25 pp. Seevers, D.O., 1966. A nuclear magnetic method for determining the permeability of sandstones. Paper L, SPWLA 7th Ann. Logging Symp. Trans., Tulsa, OK, May 8 - 11:14 pp. Serra, O., 1985. Sedimentary Environments from Wireline Logs. Schlumberger, Order No. M-081030/ SMP-7008, September: 211 pp. Serra, O., 1986. Fundamentals of Well-Log Interpretation. Volume 1: The Acquisition of Logging Data. Volume 2: The Interpretation of Well Logging Data. Elsevier, Amsterdam. Volume 1:423 pp.; Volume 2:684 pp. Serra, O., 1989. Formation MicroScanner Image Interpretation. Schlumberger Educational Services, Houston, TX, Order No. SMP-7028:117 pp. Skopec, R.A., Mann, M.M., Jeffers, D. and Grier, S.P., 1992. Horizontal core acquisition and orientation for formation evaluation. SPE Drilling Engineering, 7(1): 4 7 - 54. Smith, D.G., 1990. Predicting a down dip water level using capillary pressure relationships. Paper Z, SPWLA 31st Ann. Logging Symp. Trans., Lafayette, LA, June 2 4 - 2 7 : 1 1 pp. Soc. of Professional Well Log Analysts, 1984. Glossary of Terms and Expressions Used in Well Logging. Second Edition, Houston, TX: 116 pp. Soc. of Professional Well Log Analysts, 1990. Borehole Imaging Reprint Volume. Houston, TX: 472 pp. Spain, D.R., Morris, S.A. and Penn, J.T., 1992. Automated geological evaluation of continuous slim-hole cores. J. Petrol. Tech., 44(6): 6 6 2 - 668. Swanson, B.E, 1981. A simple correlation between permeabilities and mercury capillary pressures, jr. Petrol. Tech., 33(12): 2498 - 2504. Swanson, R.G., 1985. Sample Examination Manual. Am. Assoc. Petrol. Geologists, Third Printing, May. Sweeney, S.A. and Jennings, Jr., H.Y., 1960. The electrical resistivity of preferentially water-wet and preferentially oil-wet carbonate rock. Producers Monthly, 24(7): 2 9 - 32.
228 Tanner, C.S., Baxley, ET., Crump III, J.J. and Miller, W.C., 1992. Production performance of the Wasson Denver Unit CO 2 flood. SPE/DOE paper 24156, Presented at the SPE/DOE 8th Symp. on Enhanced Oil Recovery, Tulsa, OK, April 21 - 24:11 - 22. Thomas, E.C., Richardson, J.E., Shannon, M.T. and Williams, M.R., 1987. The scope and perspective of ROS measurement and flood monitoring. J. Petrol. Tech., 39(11): 1 3 9 8 - 1406. Thomeer, J.H.M., 1960. Introduction of a pore geometrical factor defined by the capillary pressure curve. Trans. AIME, 219: 3 5 4 - 358. Thomeer, J.H., 1983. Air permeability as a function of three pore-network parameters. J. Petrol. Tech., 35(4): 8 0 9 - 8 1 4 . Timur, A., 1968. An investigation of permeability, porosity, and residual water saturation relationships. Paper J, SPWLA 9th Ann. Logging Symp., New Orleans, LA, June 23 - 26:16 pp. Timur, A., 1972. Nuclear magnetic resonance study of carbonate rocks. Paper N, SPWLA 13th Ann. Logging Symp., Tulsa, OK, May 7 - 10:15 pp. Tittman, J., 1986. Geophysical WellLogging. Academic Press, Inc., Harcourt Bruce Jovanovich, Orlando. Excerpted from Methods of Experimental Physics, Volume 24: Geophysics: 175 pp. Tixier, M.P., Alger, R.P. and Doh, C.A., 1959. Sonic logging. Trans. AIME, 216: 1 0 6 - 114. Tixier, M.P., Alger, R.P. and Tanguy, D.R., 1960. New developments in induction and sonic logging, jr. Petrol. Tech., 12(5): 7 9 - 8 7 . Torres, D., Strickland, R. and Gianzero, M., 1990. A new approach to determining dip and strike using borehole images. Paper K, SPWLA 31st Ann. Logging Symp. Trans., Lafayette, LA, June 2 4 - 27:20 PP. Traugott, M.O., 1970. Log evaluation of a heterogeneous carbonate reservoir- Cato San Andres field. Paper E, SPWLA llth Ann. Logging Symp. Trans., Los Angeles, CA, May 3 - 6 : 8 pp. Tumer, K., Torres, D. and Chemali, R., 1991. A new algorithm for automatic shoulder bed correction of dual laterolog tools. Paper Q, SPWLA 32nd Ann. Logging Symp., Midland, TX, June 1 6 - 19:21 pp. Tutunjian, P.N. and Vinegar, H.J., 1990. Petrophysical applications of automated proton high resolution NMR spectroscopy. SCA paper 9020, Soc. of Core Analysts Preprints, Dallas, TX, August 14 - 16:23 PP. Tutunjian, P.N., Vinegar, H.J. and Ferris, J.A., 1991. Nuclear magnetic resonance imaging of sodium-23 in cores. SCA paper 9111, Soc. of Core Analysts Preprints, San Antonio, TX, August 21 - 22:18 pp. Vinegar, H.J. and Rothwell, W.P., 1988. NMR Imaging of Materials for Transport Properties. U.S. Patent 4719423. Vinegar, H.J., Tutunjian, P.N., Edelstein, W.A. and Roemer, P.B., 199 l a. Whole-core analysis by 13C NMR. SPE Formation Evaluation, 6(2): 183 - 189. Vinegar, H.J., Tutunjian, P.N., Crabtree, P.T., Raffaldi, EJ., DiFoggio, R. and Edelstein, W.A., 1991b. NMR spectroscopy of tight, gypsum-bearing carbonates. Log Analyst, 32(5): 527 - 535. Washburn, E.W., 1921. Note on a method of determining the distribution of pore sizes in a porous material. Proc. Nat. Acad. Sci., 7: 1 1 5 - 116. Welex, 1986. Full Wave Sonic. Houston, TX, Reference EL-1033:12 pp. Wellington, S.L. and Vinegar, H.J., 1987 X-ray computerized tomography. J. Petrol. Tech., 39(8): 8 8 5 989. Wells, L.E., Sanyal, S.K. and Mathews, M.A., 1979. Matrix and response characteristics for sonic, density and neutron. Paper Z, SPWLA 20th Ann. Logging Symp. Trans., Tulsa, OK, June 3 - 6 : 2 5 pp. Westaway, P., Hertzog, R. and Plasek, R.E., 1980. The gamma spectrometer tool in elastic and capture gamma-ray spectroscopy for reservoir analysis. SPE paper 9461, SPE 55th Ann. Fall Tech. Conf. and Exh., Dallas, TX, September 21 - 2 4 : 1 6 pp. Wharton, R.P., Hazen, G.A., Rau, R.N. and Best, D.L., 1980. Electromagnetic propagation logging: advances in technique and interpretation. SPE paper 9267, presented at the SPE 55th Ann. Fall Tech. Conf. and Exh., Dallas, TX, September 21 - 24:12 pp. Worm Oil Coring Series, 1985-1986. Composed of the following articles: Part 1 - Why it's done. Dare Keelan, March 1985:83 - 90. Part 2 - Core barrel types and uses. Art Park, April 1985:83 - 90. Part 3 - Planning the job. Art Park, May 1985:79 - 86. Part 4 - Bit considerations. Art Park, June 1985: 1 4 9 - 154. Part 5 -Avoiding potential problems. Art Park, July 1985:92 - 98. Part 6 - Sidewall operations. James B. Toney and J. Lee Speights, August 1985:29 - 36.
229 Part 7 - Analytical aspects of sidewall coring. M. Craft and D. Keelan, September 1985: 7 7 - 90. Part 8 - P l u g and full diameter analysis. Dare Keelan, November 1985: 1 0 3 - 112. Part 9 - Geological aspects. David G. Kersey, January 1986:103 - 108. Worthington, M.H., 1984. An introduction to geophysical tomography. First Break, 2(11): 20 - 26. Wyatt, D., Jacobson, L.A., Durbin, D. and Lasseter, E., 1992. Logging experience with a new induced gamma spectrometry tool. Paper Y, SPWLA 33rd Ann. Logging Symp. Trans., Oklahoma City, OK, June 14 - 17:18 pp. Wyllie, M.R.J. and Rose, W.D., 1950. Some theoretical consideration related to the quantitative evaluation of the physical characteristics of reservoir rock from electrical log data. Trans. AIME, 189:105 118. Wyllie, M.R.J., Gregory, A.R. and Gardner, G.H.F., 1956. Elastic wave velocities in heterogeneous and porous media. Geophysics, 21 (1): 41 - 70. Youmans, A.H., Hopkinson, E.C., Bergan, R.A. and Oshry, H.L., 1964. Neutron lifetime, a new nuclear log. J. Petrol. Tech., 17(3): 3 1 9 - 3 3 2 . Youngblood, W.E., 1971. Mud Filtrate Nuclear Magnetic Analysis. U.S. Patent 3611118. Zemanek, J., Caldwell, R.L., Glenn, E.E., Holcomb, S.V., Norton, L.J. and Straus, A.J.D., 1969. The borehole t e l e v i e w er - a new logging concept for fracture location and other types ofborehole inspection. J. Petrol. Tech., 21 (6): 762 - 774.
This Page Intentionally Left Blank
231
Chapter 5 PERFORMANCE AND CLASSIFICATION OF CARBONATE RESERVOIRS HERMAN H. RIEKE, III, GEORGE V. CHILINGARIAN, AND S.J. MAZZULLO
INTRODUCTION
A chapter on hydrocarbon recovery should bring together the technical insights presented in two volumes of this book to serve as a guide for operators. The objective of presenting a potpourri of technology provides a knowledge base for characterizing the reservoir's anisotropic and/or heterogenetic nature with respect to its producing capabilities. This knowledge is implemented by employing an effective field development strategy. Recoveries from reservoirs using conventional technology range from about 10-50% of the original mobile oil in place for most carbonate reservoirs as compared to 5-80% for clastic reservoirs. Over 100 billion barrels of light oil (>20 ~ API) exist in United States carbonate reservoirs as a potentially recoverable resource (Nuckols, 1992). The shallow-shelf class of carbonate reservoirs contains about 68 billion barrels of this original oil-in-place (Fig. 5-1). The remaining 22 billion barrels of original oil-in-place are in reefs, peritidal, slope-basin, and shelf-margin reservoir classes. Table 5-I shows the magnitude of the original light oil-in-place resource in the United States for shallow-shelf carbonate reservoirs. Far greater reserves
Proved Reserves 3.7 Billion Bbl
(s.s%)
Original Oil-In-Place = 68.0 Billion Bbl Fig. 5-1. Status of the original oil-in-place (>20 ~ API) for selected shallow-shelf carbonate reservoirs located in the United States. (After Nuckols, 1992; courtesy of the U.S. Department of Energy.)
232 TABLE 5-1 Magnitude of the resource base of the original oil-in-place in United States carbonate reservoirs 9 Over 100 billion barrels, nearly 1/3 of the U.S. light (>20 ~API) OOIE are from the 6 DOE carbonate reservoir classes (peritidal, shallow-shelf/restricted, shallow-shelf/open, shelf margin, reefs and slopebasin). 9 The combined shallow-shelf carbonate classes (total of 382 carbonate reservoirs) contained about 68 billion barrels (over two-thirds) of the carbonate OOIE - Shallow-shelf/open - 43 billion barrels - Shallow-shelf/restricted = 25 billion barrels 9 The remaining 32 billion barrels of carbonate OOIP resides in the remaining classes. Source: Information is from the Tertiary Oil Recovery Information System (TORIS) database, maintained by the U.S. Department of Energy, Bartlesville Project Office, Bartlesville, Oklahoma, U.S.A. The database contains data on 67% of the U.S. original oil-in-place resource (modified after Nuckols, 1992).
lie to be tapped in the Middle East in similar geological settings. Shallow-shelf carbonate reservoirs are the reserve targets that the writers will focus on in this chapter owing to their great production potential. The operational and development goals of a producer are to recover a maximum of reserves with a minimum number of wells. Such goals demand that there be a reservoir management plan in place. It is not a goal of Chapter 5 to show how to develop such a detailed plan, but rather to encourage thinking about the consequences of technical actions that affect reservoir management. A reservoir management plan needs to address the following practical questions: (1) Are the geology and engineering properties of the reservoir accurately defined? (2) What is the optimum number of wells to be drilled? (3) Are infill or enhanced recovery wells necessary? (4) Where should the wells be located? (5) What types of wells should be drilled: vertical, directional, or horizontal? (6) How should the wells be completed? (7) How will recoveries be optimized? (8) Will pressure maintenance be needed, and when? (9) When will enhanced recovery be needed? (10) How much will this all cost? The ensuing technical discussion and presented strategies are necessary in helping to formulate possible answers to some of the above-mentioned questions.
TECHNICAL OVERVIEW
Large and small oil and gas companies alike are conducting ongoing, interdisciplinary studies of reservoir characterization and analysis of production performance. Application of petrophysics, fluid flow behavior, formation evaluation, well-testing, and reserve estimation disciplines to carbonate reservoirs were presented in the other chapters of this two-volume book. That what remains is to apply this knowledge to carbonate reservoir classification schemes and production practices so that more
233 accurate and reliable predictions can be made of the reservoir's productive potential and performance. Production strategies can be formulated to recover additional uncontacted and bypassed mobile oil and gas from these reservoirs. An early attempt was made by Craze (1962) to relate well spacing, withdrawal rates, and general field development plans to ultimate performance and recovery in carbonate reservoirs. Rieke et al. (1972) also addressed the problems that arise in the development and production of carbonate reservoirs owing to their unique characteristics. Chilingar et al. (1967) noted that the complex carbonate depositional environments and post-depositional diagenetic alterations of the rock fabric, such as dolomitization, make it difficult for independent operators to acquire geologic information applicable to reservoir characterization. Data concerning many reservoirs that are already depleted or nearing depletion, which could be used as valuable case histories, represent lost knowledge. Many of these reservoirs were in their prime before the 1930s when pressure measurements and rock and fluid sampling techniques were not routinely used by the producers. Early on, Bulnes and Fitting (1945) discussed the problems associated with reservoir performance in limestones. Accurate gas/oil ratios and water/oil ratios were not available from producers because the operator only could estimate, at best, gas and water production. This lack of knowledge and paucity of data, concerning the heterogeneous nature of the geological and engineering properties of these reservoirs, needs rectifying. Worldwide economic conditions affecting oil and gas operations have changed drastically since 1982, and, therefore, require a focused attention to present-day production practices and economics. The rationale for characterizing reservoir heterogeneities is economics in that optimization of ultimate recovery occurs at a minimum cost for both major and independent producers. To increase the recoverable reserves on a reservoir, or on a well-by-well, basis is probably the least expensive way of building a reserve base. This development strategy is important in managing the production of oil and gas from carbonate reservoirs. The recognition of fluid flow barriers and their avoidance are the keys to optimizing both primary and enhanced production. Not all the problems associated with predicting carbonate reservoir performance are due to meager knowledge of the subject or economic conditions. For example, one problem is the use of the concept of reservoir analogy, which is used to predict reserves, reservoir characteristics, and future recoveries by comparison with other reservoirs. Although it can be a powerful tool in the hands of the experienced estimator for sandstone reservoirs, it carries a high risk when applied to carbonate reservoirs, because of unpredictable microscopic and megascopic variations in reservoir properties from one reservoir to another. The analog approach assumes that reservoirs with similar geological and fluid characteristics will have similar performances. The application to carbonates has been made by grouping reservoirs into larger families called plays (Galloway et al., 1983). Geologists contend that plays often exhibit similar production characteristics and production problems because they have a common geologic history that gives rise to similar heterogeneities (White, 1980). Petroleum engineers know that this is not always the case, because performance depends on many factors, such as how the reservoir is developed and produced. One geological constraint is that this genetic grouping of reservoirs should be confined to a small geographic area. Another constraint is the extent to which one can use the volumetric method to estimate accurately the reserves. Material balance analysis is the only sure
234 way of predicting a carbonate reservoir's production history. Ulmishek and Harrison (1984) discussed the criteria for analog comparisons. There are many such constraints with respect to carbonate reservoirs, because oil in carbonate reservoirs is more unevenly distributed than oil in clastic reservoirs. A central theme of this chapter is to discuss the impact of geologic parameters on the recovery of oil and gas from carbonate rocks. Every reservoir is unique in some respects and must be treated as such. It is necessary, therefore, to review additional technologies, such as sequence stratigraphy, laboratory characterization approaches, new drilling technology, and infill drilling strategies. The presentation of five selected fields at the end of this chapter, based on a variety of reservoir configurations and field performances, give examples of integrated geological engineering approaches for optimum reservoir development. Statistical data and summary of reservoir characteristics are supplied for additional selected carbonate reservoirs. RESERVOIR CLASSIFICATION SCHEMES Four carbonate reservoir classification schemes will be discussed based on" (1) fluid composition in the reservoir; (2) type of available reservoir energy (drive mechanism); (3) type of pore system; and (4) geological nature of the reservoir.
Classification of reservoirs based on fluid composition Craft and Hawkins (1958) classified hydrocarbon accumulations by fluid types regardless of the reservoir rock type, using the familiar pressure-temperature phase envelope for a hydrocarbon mixture. Possible reservoir types are dissolved-gas reservoirs (saturated or undersaturated), gas-condensate reservoirs at or above the dew point, and dry-gas reservoirs. It is sometimes helpful to expand this classification. Eremenko (1968) proposed such an expanded version based on the relative quantities by weight percent of oil, gas, and condensate present in the reservoir (Fig. 5-2). TYPE 100 IT
I
~r
n
II
"~
OF
DEPOSIT
IE
lZ
,,
~
GAS
W
z w Iz
0 ~j i
Fig. 5-2. Eremenko's (1968) classification of hydrocarbon accumulationson the basis of their oil, gas, and condensate contents. (Reprinted with the permission of Dr. N.A. Eremenko.)
235
Type 1: Highly undersaturated oil reservoir Saturation pressure is lower, by an order of magnitude or more, than formation pressure with a correspondingly low solution-gas/oil ratio. Formation pressure is the pressure acting upon the fluids contained in the pore space of the reservoir (for a complete discussion see Fertl et al., 1993). Pools are normally shallow with low-gravity oil. In extreme cases, saturation pressure may approach atmospheric, with well depths of only a few hundred feet and oil gravities as low as 8-10 ~ API. Type IIa: Moderately undersaturated oil reservoir with no free gas cap. Saturation pressure is somewhat lower than formation pressure. Type lib: Moderately undersaturated oil reservoir with initial free gas cap. Saturation pressure is lower than formation pressure. Paradoxically an initial gas cap exists in spite of the undersaturated oil zone. Reservoirs in the Asmari, Bangestan, and Khami limestones in Iran are good examples (Andresen et al., 1963). Possible explanations for this condition include changes in the depth of burial and thermal diffusion effects. Standing (1969) suggested that circulating formation waters possibly removed some gas from the oil after accumulation, owing to the differential solubility of the various hydrocarbons in water. The lighter hydrocarbons have a higher solubility in water than the heavier constituents. The importance of this subclass is that gas-cap energy is available from the inception of production. Type III: Saturated oil reservoir with no free gas cap. Reservoir pressure is initially at the bubble point pressure of the oil. Pressure depletion may result in early formation of the secondary gas cap. Type IV." Saturated oil reservoir with initialfree gas cap. Initial reservoir pressure equals saturation pressure. No retrograde condensation occurs in the gas cap with decrease in pressure. Minor amounts of liquid production may consist of natural gas liquids. Type V: Gas-condensate reservoir with black oil band. Depending on the structural position in the reservoir, liquid production from individual wells may consist entirely of condensate, a mixture of condensate and black oil, or entirely of black oil. Type VI: Gas-condensate reservoir with no black oil band. Initial producing gas/oil ratio is always greater than 3,000 standard cubic feet per barrel and normally exceeds 6,000 scf/bbl. The gas/oil ratio is a function of reservoir temperature, pressure, and gas composition. Condensate gravity is in the range of 40-50 ~ API. There does not appear to be any correlation between condensate gravity and initial producing gas/oil ratio. Type VII: Dry-gas reservoir. Reservoirs contain only "dry" gas, and no condensate forms as the pressure decreases. Application Reservoir pressure and temperature and the hydrocarbon composition determine the reservoir type (I to VII). Changes in the depth of burial of a reservoir, after entrapment of the oil and gas, may result in a change in reservoir type. A type III reservoir, for example, may revert to a type II when subjected to deeper burial caused by gravitational compaction, tectonic subsidence, or downwarping. Erosional processes can produce shallower burial depths that may cause a free gas cap to form (type III
236 reservoir becomes a type IV). As formation pressure decreases, the gas cap will expand, owing to the removal of the overburden, and force oil out of the trap at the bottom. In extreme cases, all the oil may be expelled from the trap to form a gas or gas-condensate reservoir (type VI or VII). The mechanism of gas expansion in traps caused by a decrease in pressure due to uplift or erosion is discussed by Gussow (1954) and Levorsen (1967). Observations made by these authors provide possible explanations for the difference in oil and gas content of adjacent or nearby traps. Gussow's (1954) study suggested that the nature of the hydrocarbons trapped in the reservoirs depends on the proximity of these reservoirs to source beds. As oil migrates and encounters a series of traps, the process of "differential entrapment" becomes operative. A trap filled with oil and gas may eventually lose the oil to another trap updip as oil and gas continue to migrate into the area. Figure 5-3 illustrates the differential entrapment concept.
TRAP A
TRAP B
o,,
I. /
TRAP C
.,._./
TRAP D
Woter wot.r
oil
f
Oia
Woter
Oil
2. /
Gos
Oil
3. /
Gas
Fig. 5.3. Theory of differential entrapment: different stages in the migration and accumulation of oil and gas in the interconnected traps. (Modified after Gussow, 1968, fig. 3; courtesy of the Society of Petroleum Engineers.)
237 Trap A is an oil reservoir with a free gas cap (type IV). Stage 1 (Fig. 5-3) shows that when trap A is filled additional oil cannot enter the trap unless oil spills updip into trap B, which contains only oil (type III). The migrating gas, however, will continue to be trapped in trap A during stage 1. Traps C and D contain only water. In stage 2, trap A is completely filled with gas (type VI or VII) and all the oil has been displaced to trap B, which is completely filled with oil (type III). Additional influx of oil to the system forces oil to spill out to trap C (type III). Trap D still contains only water. In stage 3, trap A remains a gas reservoir, and both oil and gas are bypassing it. Trap B now has a gas cap (type IV) and oil is bypassing it; oil is also expelled as the gas cap expands. Trap C now filled with oil still does not have a gas cap. Water fills Trap D. Gussow (1968) cited the oil and gas accumulations in the Leduc reefs on the Acheson--Homeglen-Rimbey trend, Alberta, Canada, as a general illustration of this process (Fig. 5-4). Homeglen-Rimbey is an oil reservoir with a very large gas cap. Westerose South, immediately updip, is all gas. Farther up the trend, Westerose, Bonnie Glen D-38, and Bonnie Glen D-3A are oil reservoirs with free gas caps. The presence of gas caps in the last three reservoirs, positioned updip from the two reservoirs not having gas caps, can be explained by the large difference in depth of burial between the two areas, which approximates 1,000 ft (305 m). The lower pressure in the shallower reservoirs allowed some gas to come out of solution and form a gas cap. Table 5-11 lists the reservoir parameters for the Acheson-Homeglen-Rimbey D-3 trend. The Swan Hills oil and gas fields in northern Alberta, Canada, shown in Fig. 5-5, DEPTH SUBSEA
ST. ALBERT BIG LAKE
-
ACHESON
-
Got.oE
SP,K(_
A
It II
_,,ooo, ..
HOME
- 5,000' 0il
_
~
G0$
w,,,,
~
Oense
Fig. 5.4. Cross-sectionalprofile of the Acheson--Homeglen-Rimbey-Leducreef trend. (After Horsefield, 1962 and Hnatiuk and Martinelli, 1967; reprinted with the permission of the Petroleum Society of the Canadian Institute of Mining, Metallurgy and Petroleum.)
to oo
TABLE 5-I1 Comparison of reservoir parameters for Acheson-Homeglen-Rimbey D-3 Reef Trend Pool Acheson Leduc-Woodbend Glen Park Wizard Lake Bonnie Glen Westerose Westerose South Homeglen-Rimbey
Depth (ft) 5,076 5,344 6,304 6,458 6,995 7,233 7,740 7,934
Porosity (%) Oil zone Gas cap
Connate water (%)
Permeability (md) Horizontal Vertical
Area (acres)
9.1 8.0 9.6 9.4 9.4 9.34 ... 7.6
10 15 7.6 7 6 7 10 10
3.100 1.000 1,604 700 350 1,934 1,200 250
3.640 21,600 433 3,250 8,800 1,757 10,720 14,053
7.5 7.4 ... ... 8.3 7.95 8.6 7.8
1.500 5-100 105 n.a. n.a. 195 60 72
Maximum total pay (ft)
Oil-in-place (million bbl)
Gas-in-place
234 232 421 646 711 589 673 110
149 308 28 380 625 158 0 110
10 420
Source: After Hnatiuk and Martinelli, 1967; reprinted with the permission of the Petroleum Society of the Canadian Institute of Mining.
(BcO
.oo
, ~
430 117 1,915 1,285
239
RI~
RI4
\ T68
\,
'
\
RII
RI2 \,
R9
RIO
\
\'x -...
'\
\
\
\
\
T67
swAN ,,
\
HILLS
\.
,,.,
T66
\
SOUTH SWAN
', ',\ HILLS ',\
T65
\
0
,\
,. ',
\\
I
\
.\
,
T64
CREEK
T 6.~ [.
\.
",,
.
CREEK S O U T H
T62
\
\
\
\
\
CREEK N O R T H
T61
AI . .
~.~.//~ .
.
Carson Creek
/ .
.
Carson Crk. North 43 ~
:":~'!?-!:""C A R S O N
CREEK
9
Judy Creek South 420
B
41 ~
Fig. 5.5. Differential entrapment along the Swan Hills reef trend, northern Alberta, Canada, showing oil and gas accumulations in the carbonate reefs and shoals of the Upper Devonian Beaverhill Lake Subgroup. Spill points and migration paths are shown. (Courtesy ofW.C. Gussow, 1972.)
240 are another example of differential entrapment in carbonate reservoirs (Gussow, 1968). An estimated 4.7 billion bbl oil-in-place occurs in the carbonate rocks in this succession of traps. The presence of nonassociated wet gas downdip at the Carson Field can be explained by the theory of differential entrapment. Oil originally trapped here has been flushed updip, as has some of the oil at Carson Creek North, which has a free gas cap. All the traps farther updip (Judy Creek South, Judy Creek, South Swan Hills, Swan Hills, and the C Pool of Swan Hills North) are filled with oil and have no free gas caps. The Virginia Hill Field contains only oil and may have been isolated from the other reservoirs at the time of fluid migration. Gussow (1968) discussed the effects of differential entrapment on the distribution of oil of varying gravities in the oil pools of the Swan Hills area. The mechanism is simple: where gravity effects predominate in the individual pools, the higher API gravity oil is at the top and the lower API gravity oil at the bottom. As the oil is displaced from a trap by migrating gas, the lower API gravity oil at the bottom is displaced initially updip, thereby accumulating in updip traps. Accordingly, there may be a decrease in API gravity along the migration path toward the updip edge of a basin. In fact, the oil in the Swan Hills trend ranges from 43 ~ API at Carson Creek North to 39 ~ API at Swan Hills North. Rieke et al. (1972) showed that the API gravity of Illinois Basin crudes can be characterized by simple individual frequency distribution plots. The gravity data were from producing Illinois oil fields (Bell et al., 1959). Histograms constructed for the crudes are from three formations: Cypress Formation (Mississippian, Chesterian), Aux Vases Sandstone (Mississippian, Chesterian), and the members of the Ste. Genevieve Formation (Mississippian, Valmeyeran), consisting of the Ohara Limestone, Rosiclare Limestone, and the McClosky Limestone, as presented in Fig. 5-6. The API gravity frequency distributions from each pay zone are generally similar in that they are all unimodal, with the mode lying between 36 ~ and 39 ~ API. With respect to texture, the McClosky Limestone is highly oolitic and very much like a homogeneous, clean sandstone. The API gravity histogram of the McClosky pay is nearly symmetrical (Fig. 5-6E), possibly indicating regional migration and mixing of the crude oils. Histograms of the other pay zones are irregular, but not lognormal (Fig. 56A, B and C). The McClosky Limestone is permeable over great distances. In contrast to the Illinois Basin crudes, the gravity histograms characterizing the Viking Sandstone (Cretaceous), and Frobisher Limestone (Mississippian) tend to be Gaussian (Fig. 5-6A and B). The Devonian D-1, D-2, and D-3 zones in western Canada show a possible bimodal distribution (Fig. 5-7C). These distributions show a much wider API gravity range than the crudes in Illinois (Fig. 5-6). The spread of gravity values in the Devonian carbonates illustrate the frequency distribution of differential entrapment (Fig. 5-7). Similar histograms can be useful in the correlation and prediction of other reservoir properties, and help in determining the source of the crude. The differential entrapment mechanism proposed by Gussow (1968) is a distinct possibility in instances such as those cited above. In the case of aquifers having good porosity and permeability properties over a wide area, so that regional migration of fluids is possible, the theory is plausible. It is difficult, however, to envision, as noted by Dickey (1968), "Differential entrapment as a valid explanation for oil accumulations in the common instance of oil fields with lenticular sands and limited aquifers."
241
)u
"7.:':+I :-:':':':':'i .;.Z.-.-.-~ .v.-::.', v.-.v.v, .....-::.-, v.--:.'............ v..'.'.-." ....... .. '-.'.
z t,J 3 o
4•
....... ~]~'.7. ......-..:.; .......
4O 30
z
B
~o
i..i+
u.
2o
.......
32
0
I
IJ
34
38
38
40
42
32
36
38
40
J 42
4O
42
oAPI
~
SO
34
SO
40
4O u
Z ta 50 O W O: 20 tL.
Z uJ =)
30
v:.....'. v ..": ...v...." .-...v.v. ,.-..v.., v.-:.'.., ..-..:...v,
0
.-. ....
uJ O: la.
2O
.......::. ............ ....... ,.v:..:.
:.._--_.-..~ .:.....v.. "':":: .......
IO 0
i
34
N!i
36 35 OAP!
I0
9 4O
0 32
42
~
'i'i"~':"~i
I
34
3tl oAPI
50 40
P, N
IO
o
---1 N
40
42
oAp[
Fig. 5.6. Histograms of API gravity of selected crudes in the Illinois basin. (A) Cypress Sandstone; (B) Aux Vases Sandstone; (C) Ohara Limestone; (D) Rosiclare Limestone; (E) McClosky Limestone. (From Rieke et al., 1972, fig. 5" courtesy of Elsevier Publ. Co.)
Coogan (1991) provided such an example. Differential entrapment is seen in the Silurian age gas and oil traps in northeastern area of Ohio, U.S.A. The reservoirs are lenticular shoestring sandstones showing the entrapment of oil updip to the west and gas downdip to the east. The general trend of the lenticular sandstones are towards the
242 25
,>,rO
2O
Z
I,iJ 15 :) Ct I,iJ (l:: I0 tl,.
o~ 5 i
6
28
30
32
34
36
38
40
42
36
38
40
42
~ 25
>. o z
2O
tlJ 3 cJ la.i E la.
15
I0
o<
5
0 26
28
30
32
OAPI
2~ >.. (..)
34
c
2O
z
::) n-~
I0 9
: .: ....
:~:::
0 26
28
30
32
34
36
38
40
42
OAPI
Fig. 5-7. Histograms of API gravity of selected crudes in western Canada. (A) Viking Sandstone; (B) Frobisher Limestone; (C) Devonian D-1 and D-3 limestone pays. (From Rieke et al., 1972, fig. 6; courtesy of Elsevier Publ. Co.)
northwest, away from the Appalachian Basin, ending as river mouth bars at the western delta edge (Coogan, 1991). The classification ofoil reservoirs based on fluid content is useful for several reasons. First, a reservoir is readily identifiable in its initial state on this basis. Also some interesting theories, based on the fluid content, can be advanced regarding the events leading up to its generation and migration into a trap. In addition, information on the original reservoir fluids-in-place helps one to formulate ideas on how the reservoir may behave initially and how it should be exploited. For example, if an oil reservoir is highly undersaturated, the initial production period about the bubble point pressure is predictable. Under conditions of oil expansion, oil production rates will exhibit a
243 sharp decline with a possible moderate increase in the producing gas/oil ratios. In addition, the wells can be produced at capacity during the initial period without danger of harming the reservoir. If the reservoir has an initial free gas cap, the individual well rates, especially in the wells near the gas-oil interface, should be controlled to prevent gas coning. Immediate steps should be taken to conserve gas energy and to provide for gas cap expansion, if possible, and guard against gas-cap shrinkage. In the case of a gas reservoir it is important to know whether or not it is a gas-condensate reservoir, because it directly influences production economics: special separators to recover the oil from the gas; the manner in which the reservoir is produced; and difficulty in establishing reserves. Classification of oil reservoirs based on drive mechanism Although the above reservoir categorization by fluid content is helpful, an energy drive classification is imperative for a careful study of the technology of oil and gas recovery. In many cases, performance of a reservoir throughout its productive life cannot be explained by a clearly defined drive mechanism. A combination of two or more of these mechanisms is usually operative. Classification of producing mechanisms, however, permits a stepwise examination of the predominant factors that influence reservoir behavior, either individually or in combination. The potential energy sources available to move oil and gas to the wellbore include: (1) gravitational energy of the oil acting over the vertical distance of the productive column; (2) energy of compression of the free gas in the gas cap or within the oil-producing section; (3) energy of compression of the solution-gas dissolved in the oil or the water; (4) energy of compression of oil and water in the producing section of the reservoir; (5) energy of compression of the waters peripheral to the production zone; (6) energy of capillary pressure effects; and (7) energy of the compression of the rock itself. These forces are active during the productive life of a reservoir. The predominant producing mechanism operating to produce the oil and gas reflects the relative influence each energy source has on reservoir behavior. The major drive mechanisms are: (1) solution-gas; (2) gas-cap expansion; (3) water encroachment; and (4) gravity drainage. Each drive mechanism, when effective in a pool, will give rise to a certain characteristic form of reservoir behavior, although in practice most reservoirs behave in a manner that represents a combination ("mix") of two or more drive mechanisms. For simplicity, each mechanism is described here in the context of a single-drive reservoir. The common characteristics of each drive mechanism are discussed for carbonate reservoirs having only intergranular porosity before being related to other types of porosity. Interest is centered on the record of performance: variation of oil, gas, and water production rates, gas/oil and water/oil ratios, and reservoir pressure with time. Movement of the water-oil contact and creation of a free gas cap are also of great importance. In addition, individual well performance is of concern.
244
Solution--gas drive In solutiorv-gas drive the source of reservoir energy comes from the evolution of dissolved gas in the oil reservoir as pressure declines during production. Solution-gas drive is known also as depletion drive, dissolved gas drive, or internal--gas drive. No initial free gas cap exists, and the free gas phase formed remains within the oilproducing section. The reservoir is sealed off to a large extent from communication with contiguous water zones by faults or permeability pinchouts. As a result, the water influx into the reservoir is minor as pressure declines. Figures 5-8 and 5-9 illustrate a typical solution-gas drive performance. Initially, there is no free gas phase and the instantaneous producing gas/oil ratio is equal to the original solutiorv-gas/oil ratio. Except in cases of undersaturated reservoirs, a finite gas saturation quickly develops and continues to increase as depletion proceeds. When the gas saturation reaches the equilibrium value of 5-10%, the gas phase has sufficient mobility and free gas is flowing to the wellbore with the oil. The gas/oil ratio continues to rise with increased gas saturation, reflecting the rapid increase in gas flow rate and the attendant decrease in oil production rate. At a gas saturation of 2030%, the flow of oil becomes negligible, and the gas/oil ratio will peak and then decline as the reservoir reaches the latter stages of depletion. In understanding reservoirs, where the initial reservoir pressure is substantially above the saturation pressure, as mentioned above, the production mechanism is oil expansion. Under these conditions, the producing gas/oil ratio will remain at a low level during the time that the reservoir pressure is above bubble point pressure. The GOR will approximate the solutiorr-gas/oil ratio, and ideally, should actually decrease slightly as the pressure falls, even though this is rarely observed in the field. The peak I
I
PROOUCEO GAS-OIL RATIO
~
~.~
iI
N
\ \
RESERVOR I ~~~ESSURE PRODUCTO IN
f
'
0
20
PER CENT
40
OF
~ ;
60
ULTIMATE
,%
\
80
I00
PRODUCTION
Fig. 5-8. Generalized performance of a solution-gas-drive reservoir. (After Torrey, 1961; reprinted with the permission of Prentice-Hall, Inc.)
245 "~
,,oo
~J ~n (1.
isoo
IToo ~
Vl u~ I~J
1300
Q"
II~
~
S
S
U
R
s
I
Injection Storted Moy
ul w
Q: .3
/
9,1~~
60 o 50
~
in
,
d
~ ~o
aooo
6
~oo
o
n ~
~
i
I0
Q. ~
0
0
a940
1945
19S0
19S5
o960
0
Fig. 5-9. Performance of the Slaughter SanAndres Dolomite reservoir, west Texas, under predominantly solution--gas-drive. (After Sessions, 1963; reprinted with the permission of the Society of Petroleum Engineers.)
gas/oil ratio before starting to decline, reflecting ultimate reservoir depletion, will normally be 5-10 times as great as the solution-gas/oil ratio. In purely solution--gas-drive carbonate reservoirs with intergranular porosity, reservoir pressure depends primarily on cumulative oil recovery. Neither reservoir pressure nor ultimate oil recovery is sensitive to oil production rate unless the production rate affects the producing gas/oil ratio. A rapidly increasing gas/oil ratio, after equilibrium gas saturation is reached, is in general a characteristic of solution--gas-drive reservoirs. Reducing the production rate, however, will not serve to increase the ultimate oil recovery appreciably. An exception to this rule is when excessive drawdowns of individual wells lead to extensive transient effects on the reservoir. Time is not normally a factor with solution-gas-drive reservoirs because neither water influx nor gravity segregation occurs (Craft and Hawkins, 1959). Any tendency for the reservoir to exhibit significant gravity drainage or water influx, or to form a secondary gas-cap, may make ultimate recovery sensitive to production rate. Solution--gas-drive performance is closely related to a number of physical parameters. The ratio of reservoir oil viscosity to reservoir gas viscosity (/~//~o), solution0 gas/oil ratio, formation volume factor, interstitial water saturation, and oil and gas permeability relationships largely control performance. A change in any one factor results in a change in one or more of the other factors showing the close interrelationship among these parameters. Some general and meaningful observations can be made regarding the effect of altering the value of a single factor. As oil viscosity increases, for example, there is a corresponding rise in the instantaneous producing gas/oil ratio because of greater gas bypassing. The increase in GOR results in lower solutiorv-gasdrive efficiency and lower oil recovery. As the amount of gas available in solution decreases, the oil recovery also will decline. Muskat (1949), however, found that
246 doubling the solution--gas/oil ratio resulted in only a 10% increase in ultimate recovery. The greater oil shrinkage, at higher solution-gas/oil ratios, serves to somewhat dampen the effect of increased oil solubility on oil recovery. The shrinkage effect, however, is of only minor importance. An increase in crude oil gravity (~ as an overall characteristic of the fluid system likewise results in an increase in ultimate recovery. Again, the effect is dampened at the higher gravity ranges owing to greater oil shrinkage, and the ultimate recovery will actually decrease with an increase in oil gravity in the 40-50 ~ API range.
Gas-cap drive Oil pools with initial free gas caps are subject to a gas drive, which is extemal to the oil zones and separate from the solution--gas-drive mechanism. The oil expulsion mechanism is typically a combination of solution--gas-drive within the oil column plus the added benefit of gas permeating and diffusing into the oil zone from the gas cap. The idealized performance of a gas-cap-drive reservoir is presented in Fig. 5-10. The decline in production rate and reservoir pressure are not as rapid as in solutiongas-drive reservoirs. The gas/oil ratio performance is more favorable. Gas-cap-drive reservoirs are more sensitive to production rate than are solution--gas-drive pools, because the recovery equation contains a throughput velocity term and is, therefore, rate sensitive (Craft and Hawkins, 1959, p. 368). Wells producing from intervals close to the gas cap must be produced at low rates to prevent gas coning, or recompleted to exclude the upper intervals. The overall gas/ oil ratio performance largely reflects such procedures. The performance of the Goldsmith San Andres Dolomite pool in west Texas (Fig. 5-11) early in its history, for example, typifies gas-drive performance with a gradual increase in gas/oil ratio. The oil production is curtailed, and no decline is evident. v
~ ~
~ .
T
.
_ ,
_
I
RESERVOIR __~SSURE PRODUCTION
/ '
/
/
/
I
i
PRODUCED GAS-OIL
,
.0 I o
20 PER CENT
40 OF
60 ULTIMATE
ir" 80
' ioo
PRODUCTION
Fig. 5-10. Idealized performance of a gas-cap-drive reservoir. (After Torrey, 1961; reprinted with the permission of Prentice-Hall, Inc.)
247 r a.
18oo
i
!
i
i"
i
d
i
i
i
i
I
i
i
i
{1~ 1400 u.) to iO00
2 ~~,,,
"
GAS- oIL
8000
4000
RATIo
.J Ix) m 114. u3
g
I0 l,u ~-
I
PRESSURE
0
0
WATER
0
)40
C~ _.1
20 , 193s
I
1 ~940
l
I
1
I
~ 194s
l
I
0
OO
-~
Fig. 5-11. Typical gas-cap-driveperformance, Goldsmith San Andres Dolomite reservoir in west Texas. (After Craze, 1950, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.) Some gravity segregation of oil and gas takes place in almost every gas-cap-drive reservoir. More pronounced fluid segregation will promote the expansion of the gas cap and downdip movement of the oil, with resultant higher oil recoveries. The size of the gas cap also will affect oil recovery. Normally, increased ultimate recoveries are associated with a thicker gas cap. Notable exceptions are the carbonate pools in the Acheson-Homeglen-Rimbey reef trend, Alberta, Canada, which have large gas caps underlain by thin oil bands. The estimated ultimate oil recoveries under primary production are often very low (5-10%) owing to excessive gas and water coning problems. A comparison of the performance of these reservoirs indicates that those with thicker oil bands and correspondingly thinner gas caps have higher oil recoveries. Water drive
A reservoir having high permeability (such as a fractured or cavernous limestone) in contact with an extensive aquifer will normally have an active water drive. The degree to which the reservoir withdrawals are replaced by water determines the efficiency of the water-drive mechanism. In complete water-drive systems, which are not common, substantially all the fluid withdrawals are replaced by intruding water. Some excellent examples of complete water-drive reservoirs in carbonate rocks are Arbuckle Dolomite fields in Arkansas and Kansas. If the reservoir is initially undersaturated, natural pressure maintenance by water influx may result in oil production above the bubble point pressure for an extended period. As a result of this production, a small portion of the reservoir pore space is replaced by expanding oil. Later in the life of the reservoir a free gas phase may form, which will provide part of the energy for the oil expulsion. The existence of the free gas will depend largely on the rate of withdrawal of fluids.
248 In all water-drive reservoirs, an initial pressure decline results in the necessary pressure differential at the reservoir boundary to induce water movement into the reservoir. Figure 5-12 illustrates this initial rapid production decline preceding water influx. The Schuler (Reynolds), Magnolia, Buckner, and Midway fields are Smackover limestone reservoirs, and the Hobbs and Yates reservoirs produce from a Permian dolomite. The remaining fields shown in Fig. 5-12 are sandstone reservoirs. All these reservoirs, except the solutiotr-gas-drive Schuler Jones Sand pool (which is included for comparison purposes) are subject to at least substantial, if not complete, water drive (Elliott, 1946). To summarize water-drive performance, the producing zone is in contact with a broad aquifer, normally of high permeability. A decrease in production capacity is minor until water begins to be produced. The produced gas/oil ratio is substantially constant. Figures 5-13 and 5-14 illustrate this type of performance. Recovery factor depends on reservoir rock characteristics such as pore size and fracture distribution,
~ 30OO L ~
i
i
i
"-SCHULER(REYNOLDS)
~
(LS)
"~ MAGNOLIA(LS)
"MIDWAY." ~
TURKEY )CREEKCS )
u~ 2oo.o l'r"
i.i.i r
RAMSEY (SS) "
I000
~ ' WATCHORN........ (SS)
'
~
~
~ HO'B83 ' LS) EAST TEXAS (SS)
YATES ( LS )
00
I
'
20
,
4O
,
60
1
80
I00
CUMULATIVE OIL PRODUCTION (PER CENT OF ULTIMATE RECOVERY) Fig. 5-12. Pressure-production performance of some water-drive reservoirs. (After Elliott, 1946, fig. 1" reprinted with the permission of the Society of Petroleum Engineers.)
249 I
I
I
t
1
RESERVOIR PRESSURE
OIL PRODUCTIONRATE
f
i
-
GAS-OIL RATIO
0
,
1
O
2O
PER CENT
~'40 OF
PROOUCTJONRaTE 60 80
ULTIMATE
, I00
PRODUCTION
Fig. 5-13. Idealized water-drive performance. (After Torrey, 1961" reprinted with the permission of PrenticeHall, Inc.)
values for mobility ratio (kPolkPw) and reservoir geometry. The rate at which the reservoir is produced also may affect recovery, particularly if the reservoir is subject to only partial water drive. Reservoir withdrawal rates greatly in excess of the rate of water influx can lead to performance similar to that of solution--gas-drive reservoirs. Free gas saturations in the reservoir can develop in the more permeable sections to the extent that incoming water will bypass tighter sections. The water will move preferentially into areas of high gas saturation, with a resulting loss in recovery.
Gravity drainage In oil reservoirs subject to gravity drainage, the gravity segregation of fluids during the primary production process is evident in the production history. Oil migrates downdip to maintain down-structure oil saturation at a high level, and free gas accumulates high in the structure. If a primary gas cap exists, then it will expand as a result of the segregation process. A reservoir without a primary gas cap will soon form a secondary gas cap. Early in the life of the reservoir, the gas/oil ratios of the structurally high wells will increase rapidly. A program of shutting-in wells with high gas/oil ratios and controlling individual well rates will maximize gravitational fluid movement. Figure 5-15 shows the two generalized performance cases of a gravity-drainage reservoir with and without such control. The oil gravity, permeability of the zone, and formation dip dictate the magnitude of the gravity drainage. The combination of low viscosity and low specific gravity values (high API gravity), high zone permeability, and steeply dipping beds accentuate the down-structure oil movement. Typically, in gravity-drainage reservoirs the water influx is minor and the down-dip wells produce at the lowest gas/oil ratios and have the highest oil recovery. In cases of strict gravity drainage, a major portion of the recovery occurs after complete pressure depletion. Gravity is the primary dynamic force moving the oil to the wellbore.
250
I (.f)
w~176
!i
n,Q. fie ..,.. 0 >
.
'OC~r
t.d 03 lid nr"
t.l_ (.3
4O0
I
o
0 C9
---7
n.-
i
!
C~ QD o
L.IJ I'-
]
I
i
8,=0.
:i
,
Q_ _.J . . . . .
.*
~,
1 , 9 , 3 6 ~"
9
, ,
~,
,
Fig. 5-14. Performance of a water-drive pool, Excelsior D-2 reef pool, Excelsior Field, Alberta, Canada. (Data from the Alberta Oil and Gas Conservation Commission.)
Hamon (1988) pointed out that in oil-wet fractured reservoirs, the ultimate recovery depends on the balance between the capillary and gravity forces. The water--oil capillary pressure is negative when water displaces oil from an oil-wet rock. Gravity forces must overcome the capillary resistance to the entrance of water into the fractures. If the fractures act as capillary discontinuities, then the capillary and gravity forces control the static and dynamic equilibrium of each individual matrix block (Hamon, 1988). This means that reliable field performance predictions for highly fractured reservoirs depend on representative and accurate measurements of the capillary pressure curve in the very low-pressure range (0 to-0.5 psi). Jodry (Volume I, Chapter 6) provides examples of capillary-pressure curves for such carbonate rocks. Combination-drive reservoirs
Some reservoirs may produce under the influence of one or more of the drives discussed above. A sequence of drive mechanisms in reservoirs, such as solution-gas drive, gravity drainage, water drive, may develop during primary production. Also
3WITSS3~Id HIOA~I3S':IH
3WF]S$3Wd WIOA~j3$3W
OIJ.VH710-$V0
~
011VW 710-SV9
31VW "O0~d 710
~
31VW 00ad 710
o
W
B A
Fig. 5-15. Generalized performance of a gravity-drainage pool. (A) produced without control; (B) produced under control by shutting in high gas/oil ratio wells. (Courtesy of E.C. Babson.)
252
two different drives may compete simultaneously (e.g., water-drive reservoir with a primary gas cap). Combination-drive reservoirs may be further classified as open or closed, as proposed by Babson (1965).
Open combination-drive reservoirs. The performance of open combination-drive reservoirs is affected by the method of operation and by individual well and reservoir rates. This type of reservoir is in open communication with the aquifer. Sources of energy include water drive, gravity drainage, and gas expansion. In uncontrolled operations, a gas-expansion stage may occur first, accompanied by a rising gas/oil ratio and declining pressure. A gravity-drainage stage may come next at a reduced reservoir pressure. The effects of a moderate water influx will frequently be evident in the latter stages of the life of the reservoir. Curtailing production rates will cause buildups in reservoir pressure as water influx exceeds fluid withdrawals. The performance of the D-3 Pool, Redwater Field in Alberta, Canada, which is a typical open combination-drive reservoir, demonstrates this effect (Fig. 5-16). To facilitate gravity drainage, the rate of water influx into the reservoir can be reduced by maintaining high water-withdrawal rates from the high-water/oil-ratio wells close to the water table, and controlling the rates of the wells situated higher on the structure. In order to take full advantage of the water influx, wells producing at high
1 n,"
W
oo0
/-
i i
!
i n~
W
jr c E~
I--
,WVv V , 9
/ V r'
0 ..J
0
o
III|
I1~1
rJ63
JS~J6
I~?
ISSt)
1961
Fig. 5-16. Performance of an open combination-drive pool, Redwater D-3 reef pool, Redwater Field, Alberta, Canada. (Data from the Alberta Oil and Gas Conservation Commission.)
253 water cuts should be shut-in, and rates on other wells carefully regulated to reduce problems of nonuniform water influx and coning. The combined effect of water drive and an expanding gas cap can serve as a very effective oil displacement mechanism. The Leduc D-3 Pool is currently under both water and gas-cap injection, and flushing efficiencies in the gas cap and water zone appear to be about 80%. Oil movement into the primary gas cap must be prevented when a reservoir with an initial free gas cap is subject to an active water drive. Oil encroaching into the gas cap, even if subsequently displaced, will leave a residual oil saturation, causing a substantial loss in ultimate recovery. Bruce (1944) cited the case of the Mount Holly Pool in Arkansas, producing from the Smackover oolite limestone. Due to oil lost in the shrinking primary gas cap, only 30-40% is recoverable from this reservoir. The recovery of the other Smackover reservoirs in the area is 60% or higher. Closed combination-drive reservoirs. There is no significant water encroachment in closed combination-drive reservoirs owing to the faulting and/or facies changes that are so common in carbonate rocks. A gas-expansion stage usually is followed by gravity drainage. Reservoir pressure is low, gas/oil ratios are falling, and updip wells produce very little fluid of any kind during the secondary stage. The influence of
TIME
Fig. 5-17. Generalized performance of a closed combination-drive reservoir produced without control. (Courtesy of E.C. Babson.)
254 gravity drainage depends on the net effect of the dip and permeability and the oil gravity, in addition to the individual well rates. The control of production rates to allow for effective gravity drainage is normally more critical than in the case of strict gravity-drainage reservoirs. This is due to a reduced tendency for downward oil migration. Figure 5-17 presents a generalized performance example of a closed combination-drive reservoir produced without control. A good example of this type of reservoir is the Golden Spike Field in Alberta, Canada.
Classification of carbonate reservoirs based on type of pore system Classifications, based on fluid type or drive mechanism, apply to both carbonate and sandstone oil reservoirs. A classification system for carbonate reservoirs based on the configuration of the void space is, by its very nature, unique to carbonate rocks. The fundamental difference, between the performance of sandstone and carbonate reservoirs, is due to the unique variations in limestone and dolomite porosity and their influence on fluid properties. Discussion here centers on the role of porosity and the interconnectiveness of the pore space to form permeable facies in carbonate reservoirs. Also presented is an introduction and overview on the applicability of fractal measurements to describe carbonate pore space.
Synopsis of carbonate porosity A number of porosity classifications have been proposed during the past thirty years. Most of these classifications are generic and they do not account for pore system features that may affect fluid movement and withdrawal. Such features are important factors in the production of hydrocarbons from these rocks (Kent, 1987). Both Reeckmann and Friedman (1982) and Mazzullo et al. (1992) presented a comprehensive review on pore classification schemes used to relate porosity and texture in carbonate rocks. The most notable of these classifications is that of Choquette and Pray (1970). Their scheme interprets porosity to be either related or not related to the fabric of the rock. These classifications delineate the pore geometry, pore interconnections, and relationships between lithology and porosity. All are operative on the microscopic to macroscopic scale (Chilingarian et al., 1992a). The value of this approach lies more in their applicability to exploration and carbonate reservoir description than with reservoir performance. At present there is no classification system, whether it is comprehensive, simple or complex, which is entirely satisfactory to exploration and development geologists, and reservoir engineers. Different porosity classification schemes exist for different situations. Discussion here shows the more practical application of relating porosity and permeability classification schemes to production problems in the field.
Diagenetic effects. Porosity can be considered as either primary or secondary. Primary porosity is pore space that forms in the depositional environment. Diagenetic alteration is the rule rather than the exception in carbonates. Pores that form during diagenesis are known as secondary porosity. As an example, when limestones are dolomitized, the porosity becomes vuggy or intercrystalline (Fig. 5-18). Diagenetic processes frequently modify or obscure (overprint) the primary depositional porosity
5EnlNG ,,,
klEAR SHORE
,
,
O
NORMAL SEDIMENTS SANDS skelelals pellets oolites MUDS TIDAL FLAT LAMINITES
~SSOCIATED SEDIMENTS
RESERVOIR GEOMETRY
rERRIGENOUS | CLASTICS
RIBBONS
~.EE,S
GRAIN SIZE LIMESTONE 96 DOL.95' HYDROCARBON SIGNFICANCE C M F vUGCEL~tG. CHKivu~ 9 SOURCE RES'VOIR ,,SEAL
-im--m-mm
'""
"--"" m
FAIR
FAIR
GOOD
POOR
GOOD
FAIR
POOR
GOOD
POOR
GOOD
GOOD
3ODD
3OOD
fAIR
GOOD
3ODD
GOOD
GOOD
~ooo
GOOD
EVAPORITES
Ir -, _--~.----;--- ; - - , .1 Z -I!-! ,--11.1--i
-I
-!
=IESTRICTED
[
0 M. I--
g
Q. .
r
_,
9
1 ; i i
OPEN
.
9
~LATFORM MARGIN
:ORESLOPE
3ASIN
MUDS MINOR SANDS pellets $kelelals SANDS skelelals pellets oolites SMALL PLATFORM REEFS
rE "ERRIGENOUS CLASTICS
TERRIGENOUS CLASTICS
SANDS TERRIGENOUS oohtes CLASTICS .,;k(,lelnls ORGANIC R E E F LIME MUDS SANDS MUDS MUD MOUNDS DEBRIS FLOWS PINNACLE REEFS
~UDS
r
S ' TACKEDLENSES
EVAPORITES
lilllllli SHEETS RIBBONS SMALL MOUNDS
RIBBONS
FINE rERRIGENOUS CLASTICS
AREALLY SMALL MOUNDS
EVAPORITES
SHEETS
FINE rERRIGENOUS CLASTICS CHALKS
SHEETS
iillinlil lilllilin ioinloi/i lilillili lUll/nUll m___mm
i
mmlm_
l
SALT LARGE &TOLLS SUBMERGED
PLATFORM
organic reel reef detritus
sands muds Ilminllel
FINE TERRIGENOUS
CLASTICS
LIME MUDS
LARGE
THICK MOUNDS
lUilliil/
iili/ii/n
Fig. 5-18. Summary of carbonate environments showing the relations among porosity categories and characteristics of depositional settings, IAfter Jardine and Wilshart, 1987, fig. 3; reprinted with the permission of the SEPM (Society for Sedimentary Geology).)
to t~
256 characteristics. Another type of overprint is structural styles, which are discussed in the carbonate reservoir characterization section. Jardine and Wilshart (1987) stated that porosity and permeability heterogeneities in carbonate rocks are due to the variety of carbonate depositional environments and any subsequent diagenetic alteration. Geophysical well log signatures and reservoir quality directly relate to facies and diagenesis. Existence or lack of permeability influences recovery efficiency. Permeability relates the depositional facies through textures of carbonate facies to reservoir performance. Figure 5-18 summarizes the important characteristics of these depositional settings, which form the basis of various carbonate reservoir classes, with porosity types. This classification is derived from the approach by Dunham (1962), who tied depositional texture of carbonates with reservoir rock properties. (Refer to Mazzullo et al., 1992, p. 80 for a discussion on Dunham's classification). Other applications, which appear in the petroleum engineering literature, are by Dowling (1970), Jardine et al. (1977), Reitzel and Callow (1977), and Jardine and Wilshart (1982). Diagenetic effects were defined by the Reservoir Task Force (ICF, 1992, p. II-28) in terms of the diagenetic processes that have directly influenced the flow characteristics of the reservoir. This classification focused on: (1) the pore types present in the reservoir; (2) the diagenetic process(es) most responsible for producing the pore types; and (3) the relationship of the pore types to reservoir flow characteristics. ICF (1992) provided statistics from the TORIS' data base on shallow-shelf carbonate reservoirs in the United States. Table 5-111 presents a ranking of 382 shallow-shelf carbonate rock reservoirs based on the predominant diagenetic process altering the pore space. TABLE 5-Ili Ranking of diagenetic processes for shallow-shelfcarbonate reservoirs in the U.S.A. Diagenetic process
Number of reservoirs
Percent of reservoirs
Dolomitization Compaction/Cementation Massive dissolution Grain enhancement* Dolomization with evaporites Silicification Intergranular dissolution Authigenic clay precipitation
233 57 47 29 12 4 0 0
61 15 12 8 3 1 0 0
Total
382
100
Source: Data from the Tertiary Oil Recovery Information System (TORIS) database maintained by the
U.S. Departmentof Energy,Bartlesville Project Office, Bartlesville, Oklahoma(modifiedafter ICF, 1992, table 1I-3, p. II-29).* See Chapter 4, Vol.I. Relevance. Among the early investigators studying reservoir performance of carbonate formations were Bulnes and Fitting (1945). They recognized three distinct classes of porosity in carbonates and termed them intergranular, intermediate, and
257 foramenular. Performance of carbonate rocks with an intergranular type of porosity approaches that of sandstones. Such carbonate rocks are composed of calcareous fragments (shells or oolites). The size, shape, and packing of the solid fragments determine the pore space geometry. Intermediate porosity displays, in addition to the intergranular openings, fissures, dissolution caverns, and other openings induced by dissolution and fracturing. In the case of dissolution processes, the pore space has sizes and shapes independent of the geometrical properties of the constituent fragments, grains, and crystals. The volume of fissures, fractures, vugs, and other diagenetic voids is frequently much greater than the initial intergranular pore space. Consequently, the intermediate type of porosity system is much more complex than the intergranular system. The foramenular porosity class consists of void spaces in an otherwise nonporous continuous solid, such as a fractured reservoir with essentially no matrix porosity. There are slight differences in performance between sandstone and carbonate reservoirs having intergranular porosity. For example, in carbonates permeability parallel and perpendicular to the bedding are commonly equal, whereas in sandstones permeability parallel to the bedding is much greater than that perpendicular to the bedding. Carbonate reservoirs with intermediate porosity, however, deviate in performance over a wide range from sandstone reservoirs with comparable fluid content and drive mechanism. To demonstrate this difference, it is helpful to make general comments on recent investigations of fluid flow in porous media. Originally, it was widely believed that porosity and effective permeability were sufficient to characterize reservoir rock performance. Barfield et al. (1959) and Mortada and Nabor (1961) have shown that directional permeability is also a pertinent characterization factor. Fatt (1959), Klute (1959) and Goodknight et al. (1960) proposed a fourth parameter: storage porosity, which is the pore space that contributes significantly to the pore volume of the reservoir but little to the flow capacity. In sandstones with intergranular porosity, on a microscopic scale, these regions consist of"dead-end" or "storage" pores. The variation of sandstone reservoir performance falls normally within a narrower range as compared to carbonate reservoirs of intermediate porosity. This is due to differences in the directional permeability and storage porosity. Carbonate reservoirs with intermediate porosity show a wider variation in reservoir performance. Vugular or reef carbonates illustrate the importance of directional permeability. They usually exhibit fair to good vertical permeabilities and their performance may be controlled more by movements in the vertical direction than in the horizontal. The Golden Spike Field in the western Canada Basin illustrates thin internal permeability barriers to vertical flow within a bioherm reef. Such barriers can interfere (break-up and disperse) enhanced recovery processes such as a gravity-controlled, gas-driven miscible flood. A pressure maintenance operation was established to offset rapidly declining reservoir pressure during primary production. The dead-end or storage pores in sandstones correspond to the large volumes of low-permeability matrix porosity in naturally-fractured carbonate reservoirs. Although the fracture system generally constitutes a very small percentage (<1%) of the total porosity, it serves as a path for oil movement to the wells. The matrix, which contains most of the oil, normally has low permeability and yields oil and gas to the fractures reluctantly. In carbonates, the directional permeability and the double-porosity effects
258 are more exaggerated than in sandstones. Accordingly, carbonate reservoirs will vary in performance to a much greater extent than sandstone reservoirs. Warren and Root (1963) developed an idealized model to study the characteristic behavior of reservoirs with intermediate porosity. Their unsteady-state reservoir flow model defined two additional parameters that are sufficient to distinguish the flow behavior in an intermediate-porosity rock from fluid flow in homogeneous media. One parameter relates to the degree of heterogeneity of the system, and the other is a measure of the fluid capacitance of the secondary porosity. These parameters can be evaluated from pressure buildup tests, which take the form of parallel segments. Stratified reservoirs, however, yield a similar type of buildup curve and, therefore, unambiguous interpretations are difficult. Foramenular porosity in carbonate rocks is somewhat rare (Bulnes and Fitting, 1945). This term applies to fracture porosity in a nonporous matrix. An example is the Dean-Wolfcamp pay in west Texas and the San Andres Formation in the Chaveroo and Cato fields in southwestern New Mexico (Groves and Abernathy, 1968). In the Mississippi-Solid Formation, which is a dense, massive, and cherty limestone in the S.W. Lacey Field, Kingfisher County, Oklahoma, production comes from fracture porosity (Morris and Tracy, 1965).
Porosity classification scheme It appears that a classification of carbonate reservoirs is needed based on type of pore systems and having at least a generalized correlation with reservoir performance. Kent (1987) pointed out that in reservoir studies it is more significant to determine the manner in which the nature of pore systems influences fluid flow. No one geologically-based pore structure classification can be completely satisfactory in describing the reservoir's pore structure with respect to the recovery of fluids. Rieke et al. (1972) presented the following classification, which is simple in that it has three porosity categories: (1) intergranular-intercrystalline porosity, (2) vugular-solution porosity, and (3) fracture-matrix porosity. This porosity classification can be easily connected with mercury injection analyses (Jodry, 1992) and is more appropriate than a scheme based on a relation to rock textures. Kent (1987) proposed a similar threecategory classification scheme consisting of intercrystal, cavity, and mixed (combined intercrystal and cavity) porosities.
Intergranular-intercrystalline porosity. As stated previously, carbonate reservoirs having intergranular porosity are comparable to unfractured sandstone reservoirs in behavior. The spatial distribution and the general configuration of the pores are more orderly than in systems assigned to the above categories (2) and (3). Commonly, the basic building blocks (allochemical constituents) of the system are predominantly oolites, skeletal fragments, well-rounded and equant intraclasts or pellets, or other similar transported calcareous constituents (Folk, 1959). Organic components of reefs normally would not form an intergranular pore system. In category (1), the size and the shape of the allochems have a direct bearing on the nature of the void space. Dolomitization also may create inter-rhombohedral porosity. Intergranularintercrystalline porosity is common in dolomites, micrites, and in cemented grainstones and packstones. There is also a microintercrystalline porosity.
259
Vugular-solution porosity. Vugular-solution porosity (e.g., karstic) systems are inherently more complex than either intergranular-intercrystalline or fracture-matrix porosity systems. The original pore structure has usually been altered by the formation of dissolution cavities and channels. Pore structures in many reefs usually belong in this category. Reefs formed by organic buildups, subjected to only slight disruption during burial, are prime candidates for the development of vuggy and moldic porosity. Such porosity consists of macro-to micro-size vugs. Directional permeability may be very pronounced. Although fractures may exist, they do not dominate the mechanics of fluid flow. The performance of carbonate reservoirs with vugular-solution porosity may closely resemble sandstone pool performance, but commonly differs considerably owing to a wide distribution of pore throat sizes. Fracture-matrix porosity. A double-porosity system may be well developed in reservoirs having fracture-matrix porosity. Strong directional permeability also may exist. The matrix is usually of low permeability and contains most of the hydrocarbons. The fractures contribute only a minor amount of the total hydrocarbon pore space, but allow the reservoir to produce at economic rates. Reservoir performance is markedly different from that of sandstone reservoirs. The size of the matrix "blocks" varies from a few inches to several feet. An overprint of diagenetic alterations has to be considered when using a porosity classification. Figure 5-19 presents a summary of the diagenetic processes and secondary porosity. It should be noticed that dolomitization, fractures, recrystallization, and cementation can have unfavorable effects on the porosity and permeability and, ,
PROCESS
,,
LEACHING
,,,,
UNFAVORABLE
FAVORABLE EFFECTS ,
EFFECTS ,
,
,
,,,,
INCREASE ~ & K ,,
|,,
DOLOMITIZATION
INCREASE K
CAN ALSO DECREASE ~ & K
FRACTURING JOINTS BRECCIA
INCREASE K
INCREASE CHANNELING
.
.
.
.
,
.
R E CR Y STALLIZATIO N
MAY INCREASE PORE SIZE & K .
'cEMENTATION BY CALCITE DOLOMITE ANHYDRITE PYROBITUMEN SILICA
.
.
.
.
,
DECREASE ~, & K
.
DECREASE ~ & K
Fig. 5-19. Favorable and unfavorable effects of diagenetic alteration in carbonate rocks. (After Jardine and Wilshart, 1987, fig. 5; reprinted with the permissionof the SEPM (Societyfor SedimentaryGeology).) Note: Based on extensive experience of the authors of this chapter, dolomitization usually increases porosity (~b)and permeability (k).
260 therefore, alter the flow capacity of the reservoir. Production practices used in the development and depletion of carbonate reservoirs must be in tune with the nonisotropic and heterogeneous nature of the rock fabric. Attention should be given to the spatial distribution of the composition of the reservoir rock, nature and type of the pore system, and capillary pressure conditions. These factors influence the behavior of the fluids during production. Oil recovery owing to water invasion in fractured reservoirs Oil displacement in a fractured reservoir exhibiting water influx into the fractures is controlled by the following mechanisms: (1) the flow of water under naturally imposed pressure gradients (viscous forces), and (2) imbibition, which is the spontaneous movement of water into the matrix under capillary forces. The environmental conditions of fractured carbonate reservoirs are conducive to the predominance of capillary forces over viscous forces. Water has the tendency to channel through the more permeable zones, but is offset by its imbibition into the tight matrix displacing the oil into fractures. Numerous investigators examined imbibition behavior using mathematical models and in the laboratory (e.g. see Aronofsky et al., 1958; Graham and Richardson, 1959; Handy, 1960; Mattax and Kyle, 1962; Blair, 1964; Parsons and Chancy, 1966). Graham and Richardson (1959) for example, investigated in the laboratory the role of water imbibition in the recovery of oil from a fracture-matrix porous system. Their results are particularly interesting as they pertain to fractured carbonate reservoirs. This mechanism entails water imbibing from the fracture system into the matrix with simultaneous counter-current movement of the oil from the matrix into the fractures. The rate of imbibition is directly proportional to the interfacial tension and the square root of the permeability. It is dependent on the wettability, the fluid viscosities, and the rock characteristics. Production at high gas~oil ratios from carbonates having fracture-matrix type porosity Low-permeability matrix blocks in carbonates having fracture-matrix porosity types often do not easily yield oil to fractures, through which most of the flow occurs. This results in very low matrix-block oil recoveries. In order to correct this problem, JonesParra and Reytor (1959) proposed that in some cases in order to remove the maximum amount of oil it is necessary to produce at high gas/oil ratios, with resulting lower pressure in the fractures. Low-permeability matrix thus will release the oil to fractures more readily. Jones-Parra and Reytor (1959) used the following derivations to prove their point: VFG : [NB~/Sit ] [ H(1 - f ) + S f ] ,
(5-1)
where VFG is the volume of free gas;f is the fraction of total pore volume of the lowpermeability zone (matrix) where gravity drainage is minimal; (1 -J) is the fraction of the total pore volume where gravity drainage takes place; H is the fraction of (1 -fl) occupied by gas; St is the saturation based on the total pore volume (o = oil; i - initial); S is the saturation of gas based on matrix pore volume; and N is the initial stock-tank oil-m-place, bbl. .
261 The volume of free gas also can be obtained from the following equation. VFG = B g [NR sl. - nR p - ( N - n)R s ], Imtial Produced Remaining in solution
(5-2)
where Bg is the volume in bbl occupied in the reservoir by a standard cu ft of gas, R s is gas in solution, cu ft/bbl, Rp is the cumulative produced gas/oil ratio, cu ft/bbl, and n is stock-tank oil produced, bbl. Combining Eqs. 5-1 and 5-2: n / N = {Bo~[H(1 - f )
+ Sf]/[SitBg
(R s- Rp)]} - (Rsi- Rs)I(R s Rp),
(5-3)
where B is the initial oil formation volume factor, bbl/bbl. The n / N ratio can be also obtained from the following equation. Ol
n / N = [(So./Bo, ) - (Sot/Bo) ] " (So,t/Bo,)
(5-4)
Inasmuch as the Jones-Parra and Reytor's (1959) model (Fig. 5-20) indicates that S t = (1 - H ) ( 1 - f ) + f S o ,
(5-5)
and the n / N ratio is equal to: n / N = 1 - [ ( f SoBoi)/(SoitBoi)] - [(1 - H) (1 - f )Boi/SoitBoi ]
(5-6)
Combining Eqs. 5-3 and 5-6, and solving for H: H = [(Rp/Rsi) A - B ] " [(Rp/Rsi ) C + D ] ,
(5-7)
where: A = RsiBg[1 - f + f S o - ( B o S o , / B o 3 ] , B = BgRs (1 - f + fSo) + fSgBo- (BoBgiRs~So~t/Boa), C = RsiBg (1 - f ) , and
D = (1 - f ) (Bo- BgRs). Using Eq. 5-6 and H from Eq. 5-7, the n / N ratio is equal to: n/N = E - (1- H) F ,
(5-8)
where: E = 1-[(JSoBo) / (S~tBo)], and F = [(1 -f)Boi ] " ( S i A o ) . If all the production occurs though the fractures and vugs, then the decline in productivity index ( D P I or D J) is equal to:
262 (5-9)
D J = [(1 - I4) / (,UoBo)] 9[1/(,UoBoi)] ,
where ~toiS the viscosity of the oil and (1 - H ) has been substituted for the permeability ko. By assuming that the pressure drawdown is a constant fraction of the static pressure, then
Qo/Qoi=
(5-10)
[(1 - H)(~toBo)iP ] 9(~toBoPi) ,
where Qo is the production at any pressure p, STB/D; Qoi is the production capacity at the initial conditions; and Pi is initial pressure, psi. On assuming f = 0.95 and S =0.20, Jones-Parra and Reytor (1959) found that the production declines less when producing at higher gas/oil ratios in spite of the fact that at any given stage of depletion the pressures are lower. In the opinion of the writers, the reasoning is very simple; by keeping the pressure in the fractures and vugs low, more oil will move out of the tight matrix and the oil recovery will be greater. Obviously, experts working with sandstones will object to producing at high gas/ oil ratios and will find many shortcomings in the above derivations of Jones-Parra and Reytor. These results also appear to contradict the inferences reached by Elkins (1946) on observations of a limited number of carbonate reservoirs. Elkins (1946) believed that the faster production rate in the Harper-SanAndres Pool in Texas, U.S.A., probably caused a lower recovery than did the slower production rate in the PenwellSan Andres Field in Texas. But then recovery is so low in many reservoirs with double-porosity systems that one should try unconventional methods. One of the writers (GVC) started to implement these ideas in a carbonate reservoir in the Middle East, with promising results.
f-
/-f
H
GAS
So /-H
-f
Sg
S.
01L
Fig. 5-20. Model of a carbonate reservoir, where f = fraction of total pore volume when gravity segregation does not take place; H = fraction of coarse porosity occupied by gas. (After Jones-Para and Reytor, 1959; reprinted with the permission of the Society of Petroleum Engineers.)
263 Fractal dimension analysis o f pore space
It has been shown above that the geological framework of a carbonate reservoir influences the flow of fluids during production. Production plans for carbonate reservoirs, especially ones scheduled for enhanced recovery, require detailed, integrated geological engineering studies. In order to explain and assess how production is influenced by microscale phenomena, one needs an appropriate geological description of the reservoir at that scale. The effective integration of geological properties into reservoir simulation models would significantly improve production performance. Unfortunately, most reservoir engineering models rely on Euclidean geometry for spatial descriptions. This approach is inadequate in quantifying naturally-occurring objects that appear to be purely random. Euclidean geometry provides a concise and exact description of homogeneous man-made objects, but it is not appropriate for natural shapes. These structures are too unpredictable and chaotic to be measured accurately using classical geometry. Mandelbrot (1975) inventedfractals to describe chaotic phenomena in nature. The word is derived from the Latin word 'fractus', which means to break up into fragments. Fractal geometry is a statistical approach to the spatial characterization of an object or group of objects. Fractals, therefore, provide an excellent description of many geological objects, such as the size distribution of oil and gas fields, faults, fractures, porosity, and pore microstructures, within a geometric mathematical flamework. Several statistical tests can verify the existence of self-similarity in an object. These distributions are identified as power-law phenomena, inasmuch as they do not have a characteristic length scale. Fractal shapes, therefore, are self-similar and independent of scale or scaling (resolution): that is, they are scale invariant. Although rocks are not exactly self-similar, they exhibit this characteristic in a statistical sense over a limited range of length scales. Carbonate rocks can be regarded as stochastic fractals and can be characterized by fractal dimensions. It will be shown later in this chapter that the concept of fractal statistics is being used as a powerful predictive tool in the characterization of carbonate reservoirs and for defining their heterogeneous nature. The self-similar scaling relationship of objects is introduced by the power-law: N = Cr -D ,
(5-11)
where N is the number of identical parts with a characteristic linear dimension r, C is a constant defined by the straight line intersection with the x-axis, and D is thefractal dimension. The direction of the slope of the straight line (D) is negative. In Euclidean geometry D = 0 represents a point, D = 1 represents a line, and D = 3 represents a three-dimensional object. A fractal dimension need not be an integer. The physical meaning of Eq. 5-11 is that a D-dimensional self-similar object can be subdivided into N smaller copies of itself. Each copy is scaled down by a factor r. A general rule is to scale down each iteration by halves or thirds. N is normally determined by using one of several different algorithms, such as the divider, box-counting, power spectral, or scanline. Klinkenberg (1994) reviewed such methods. The method's use depends on the object, function, or process being measured. It should be remembered, that natural fractals have limits beyond which the objects do not show a log-normal distribution.
264 One of the most favored methods of analysis is the simple square-grid counting (box algorithm). Its use in geology and geophysics is widespread. The fractal (similarity) dimension, D, is calculated by: log (N) D = log (1 / r)"
(5-12)
Arab et al. (1994) provided an example of the use of Eq. 5-12 by employing the boxcounting algorithm to characterize the spatial geometry of fault traces. This approach can be expanded and used to determine the fractal values of fractures occurring in oil and/or gas reservoirs. The writers refer the reader to Mandelbrot (1982) and Turcotte (1992) for a complete explanation of fractal principles and their general applications. The following provides an introduction to some fractals applications, which can be used to dissect carbonate rock pore systems. These discussions will provide new insights into the micro-scale nature of porosity and permeability, as well as what their fractal nature means to reservoir productivity. Heterogeneity aspects are discussed in the carbonate reservoir characterization section of this chapter. Pore microstructure. The complexity of sedimentary rocks has made geometrical measurements of pore space difficult. The reason for this is that unlike most geometrical measurements of grain size or shape, pore interfaces can contain dissolution structures, and pore fillings such as authigenic minerals. Fractal analysis of the spatial geometry and distribution of pore space is another way of describing primary, secondary, and fracture porosity. Diagenesis results in the creation of fine structures such as fractured surfaces and diagenetic minerals on the surfaces of the grains forming the walls of the pores. These microstructures can have a large effect on permeability, surface wetting, electrical resistivity, and capillary effects in carbonate reservoirs. Fractal measurements of fine structure are important in understanding fluid flow within these rocks. Krohn (1988a and b) studied the fractal nature of various rock types, including carbonates. Fractal dimensions of carbonate pores were obtained using two methods: (1) the fracture surface technique; and (2) the thin-section technique. Both techniques measured a one-dimensional section of the pore-rock interface. The fracture surface technique is an automatic method, which statistically measures structural features using scanning electron microscope images of rock surfaces (Ruzyla, 1984; Krohn, 1988a). These structural features represent protrusions of the pore surface into the pore space and consist of grains and clay particles along with bumps and pits on the mineral grain surfaces. Drawing lines across the rock surface images gives a one-dimensional look at the surface features. The statistical fluctuations are very high and, therefore, one needs to make many measurements to achieve statistical confidence. Such features are tallied for a hundred horizontal scanlines imposed upon a digitized image of a fracture surface. The count is repeated for a number of magnifications and locations. This technique does not depend on the delineation of the grain or pore space. The counting of features indicates the presence or absence of features of each size. Counting the features creates a histogram, which shows if the results follow the power-law distribution.
265 The thin-section technique requires delineating pore space from grain space and measuring the pore volume distributions for rocks (Krohn, 1988a). It is not as accurate as the fracture surface method, but it can be used to measure the amount of pore volume that does not fit power-law behavior. The above concept is similar to the Rosiwal intercept method as used in petrography (Chayes, 1956). The volume percentage of an object in a thin-section is the same as the length of the chords crossing the object divided by the total length of the randomly-placed scan lines. Random lines decrease the bias in the measured data. Both methods are based upon the premise that any image of rock surface features represents an infinitely-thin section of those features. Krohn (1988b) stated that the porosities associated with power-law behavior measured in thin-sections agree with those calculated from the following equation. ~=(L,/L2)3-D,
(5-13)
where ~bis porosity, and L~and L 2 a r e the lower and upper limits for power-law behavior. For the pore-rock interface, D should be greater than 2 and less than 3 (Krohn, 1988a). The rock-pore interface could extend from the order of 10 ,~, the size of crystal nuclei, to 100 ~m, the size of grains. Table 5-IV presents some measured fractal dimension values (surface fracture technique) from Krohn's (1988b) study. Five carbonate formations are compared with sandstones and shales. Fractal behavior exists for all carbonates, sandstones, and shales TABLE 5-IV Summary of fractal values, determined by the automatic fracture surface technique, for carbonates, sandstones and shales. A is a proportionality constant Formation
Fractal dimension
A
10-3
L2* lam
2.27 2.35 2.59 2.65 2.75
4.27 5.90 5.83 4.44 7.34
8 3 6 36 26
2.49 2.61 2.71 2.85 2.89
4.29 3.50 5.89 7.65 8.62
4 18 4 >32 40
2.54 2.74 2.75
7.19 7.11 7.33
15 > 10 33
Carbonates Arab D Bedford Limstone Austin Chalk Smackover Dolomite Smackover Limestone
Sandstones Navajo (red, fine-grained) St. Peter Navajo (red, coarse-grained) Berea Blackhawk (well s a m p l e - 188 m)
Shales Niobrara (well s a m p l e - 2 5 2 6 m) Maim (well sample - 2308 m) Mowry (well s a m p l e - 2780 m)
Source: Modified after Krohn, 1988b, table 2; courtesy of the American Geophysical Union. * L 2 marked with > denotes the lower limit for L 2 where the end of the fractal regime was not observed by Krohn.
266 E
-1.5
\
::L
\ 9
\
-20
:3
\
13
t,.
-2.5
-
O L._
.Q9
-3.0
E :3
z o
-3.5
BEDFORD
13> o ,,,,,,
LIMESTONE I
-4.0
-1.0
i
i
.
,
i
J
-0.5 Ioglo
9
9
.
I
1
i
0.0 Feature
.
.
l
.
0.5 Size,
9
.
9
I
I .0
.
i
J
I
I .5
I
!
I
2.0
lJm
Fig. 5-21. Fractal data for the Bedford Limestone showing the bifractal nature of the measured surface features. (Modified after Krohn, 1988b, fig. 12a; courtesy of the American Geophysical Union.)
with fractal dimensions ranging from 2.27 to 2.89. Although Krohn stated that only one fractal regime was found for each sample, many of the plots exhibited a bifractal (a dual fractal regime) nature. Figure 5-21 presents a bifractal example of the Bedford Limestone from Indiana, U.S.A. showing that the fractal nature of the features have limited ranges. The lowest measured D values, 2.27 and 2.35, are for the Arab D Formation and the Bedford Limestone, respectively. The highest values given in Table 5-IV, 2.85 and 2.89, were measured for the Berea Sandstone and the Blackhawk Sandstone, respectively. What interpretation can be placed on these values? There are two potential sources of fractal behavior in Krohn's study. One is the original deposition of mineral grains or carbonate particles of various sizes and roughness, and the other is diagenetic alteration by the precipitation and dissolution of minerals. Diagenesis will lead to inhomogeneous structures as smaller pores are preferentially altered owing to the reduced flow of fluids within the pores. Such alteration involves two competing processes of mineral growth and nucleation on the pore surface. Results in Table 5-IV show that higher fractal dimensions correspond to the rock pore interface filling three-dimensional space more than those associated with lower D values. The Blackhawk Sandstone has been extensively diagenetically altered, whereas the Arab D sample showed very little alteration. Both the carbonates and shales appear to be more homogeneous than sandstones with respect to their surface texture. Krohn (1988b) stated that if the rock contains some Euclidean porosity, which is not associated with the fractal pore rock interface, then the calculated porosity using Eq. 5-13 should be less than measured core porosities obtained using a Boyle's law porosimeter. Carbonate rocks can have Euclidean porosity exhibited by moldic porosity and vugs. Any match between the calculated and measured (core) porosities verifies that the pore surface and volume are fractals with the same fractal dimension.
267 Studying the diagenetic alteration of pores in sandstones, Katz and Thompson (1985) reached the following three conclusions: (1) the pore-grain interface is a fractal; (2) the pore volume is fractal; and (3) the pore interface and volume have the same fractal dimension D over the scale range from approximately 1 nm (L~) to 100 gm (L2). This latter point is important, because the pore space can be fractal or nonfractal depending on the extent of diagenetic alteration. Physically, it means that surface conditions of pores range from smooth, nonfractal walls in an unaltered rock to where the diagenetic materials fill the pore space. Another consequence of their study was that self-similarity in rock pore spaces leads naturally to an explanation of Archie's law, which depends on the geometry of the pore space. Katz and Thompson (1985) stressed that there is presently no detailed understanding of this relation. They could not draw conclusions about the transport properties of one rock from those of another with different pore geometries. The fractal structure of pore space suggests that dynamics within the pore space should scale with the length parameter L (see Eq. 5-13). Katz and Thompson (1985) presented the following equation to describe this relation with respect to conductivity, a, of a rock sample as: a - aw~ (L,/L2)Z(D-D0/Df =
O'w~ n ,
(5-14)
where the second equality is from Eq. 5-13; n = (Dr+ D ( 2 - D r ) ) / (3 - D ) Dr; a wis the ionic conductivity of the fluid filling the pore space; and Dfis the spectral dimension that must be determined on a rock-by-rock basis. Equation 5-14 is consistent with the form of Archie's law (Katz and Thompson, 1985). Roberts (1986) pointed out that the above discussion does not rule out the possibility that the pore interface and volume are both fractals, but have different fractal dimensions. This is explored next for carbonates.
Fractalpores. In order to characterize porosity with fractals one must first develop models that mimic the actual shape of pores for carbonate rocks. The same fractal concepts described in Eqs. 5-11 and 5-12 apply to a square and a cube. In fractal geometry, these two constructions are the Sierpinski carpet and the Menger sponge. A cross-section through the rock-pore system is modeled on the Sierpinski carpet and is equivalent to the face of the Menger sponge (Garrison et al., 1992). Figure 5-22 illustrates some Sierpinski carpet patterns. As one focuses down (increasing magnification) the pore space pattern does not change in distribution or shape, but only gets more minute. Shapes of different fractal dimensions can be fabricated by employing different construction algorithms. Three stages or orders are shown for each shape. Each stage is a repetition of the initial view scaled down. Conceptually speaking, such geometric constructions can be carried out ad infinitum. One then has a system, which is invisible, because it has zero surface area. The construction contains an infinite number of holes, bounded by an infinite number of threads of infinite length, in which none of the holes (pores) are interconnected. These stylized pore shapes in Fig. 5-22 compare favorably in an ideal sense with
268 :toI
I
,o,o
o o o
i
0
~
mi
am
de
IN
IN
am
IB
0
iO!
m
n
n
am
I nnn gi
~iOlO. o; Io
o o o o o
OiO O
O 0 0
=io o
ololo
a;n
n u n m
n
~I,~i=
~
u "~ -~
I
.
~ | ~
o [] o
-.I o o i I ~ 1 7 6 ~ ,o!o o ololo o o o
- , - ,u ~ | =
,,
H I
=
=
~
= i "~ =
.
.
n
n
i
Igl
U
9~ u
u
~i =
.
n
u ms
am .
a~
n~n
9
u
u
"12
n~n
-1=
B
ii[~fi] '''~'=~, A d[iii[P",j 9
, ~J,'
t;J
:~.".~"';i ~ ' . ' ~ " .
'
:....:"'::'"::":::"
:.-.L:..'"
D
"~'"--":;'"'" "H
:" ":~i
E
~...-:.-.
F
n::n.':.
~ i ~ ~ ~ ~ii..~...:---~i
G
Fig. 5-22. Sierpinski carpet patterns mimicking two-dimensional pore space. (A) a square-shaped pore having a fractal dimension of 1.87. (B) the pore is now H-shaped owing to the deposition of cement on its surface. Two squares represent the filling giving this shape a fractal dimension of 1.92. (C) growth of the pore filling reduces the pore space to an I-shape having a fractal dimension of 1.97. As the pore is filled, its surface fractal dimension approaches the Euclidean dimension of 2. Fractal dimensions were calculated using Eq. 5-12. Garrison et al. (1992) used the following four Sierpinski carpet models in their study of increasing order of pore complexity. (D) Sierpinski carpet generated with Euclidean square holes (D S = 1.8917). (E) Sierpinski carpet generated with Euclidean circular holes (D s = 1.9202). (F) Sierpinski carpet generated with Triadic Koch Island holes [prefractal (m = 3). Koch curve generator was used to give a complex perimeter reflecting boundary roughness] (D s = 1.9459). (G) Sierpinski carpet generated with Quadric Koch Island holes [prefractal (m = 3) Koch curve generator was used to change the perimeter roughness] (D s = 1.9665). m is the number of iterations of carpet generation. (After Garrison et al. (1992), figs. 4, 5, 6 and 7; reprinted with the permission of Marcel Dekker, Inc.)
those cross-sectional pore views of carbonate rocks by Teodorovich (1958) and Choquette and Pray (1970). Increased complexity in the pores due to cementation goes from left to right in Figs. 5-22 A-C. Increasing fractal values, using Eq. 5-12 to calculate these values, illustrate the complexity of the stylized pore system. Although highly stylized, the individual pore shapes can be topologically expressed as other "cementation" configurations as illustrated in Fig. 5-23. The fractal geometry of the example pore shape variations (Fig. 5-23) will be the same for a given configuration series. It should be noted that the surface area and permeability values will not always be the same for all possible configurations of a given pore. This is the basis why Teodorovich's method for estimating porosity and permeability values from thinsections works on a microscale level: that is for small rock samples (see Mazzullo and Chilingarian, 1992a). Under these conditions, the only assumption is that pore spaces are interconnected to provide permeability. On a microscopic scale, the fluid flow within a carbonate reservoir depends not only on the pore shape but also on the
269
16
12
16
14
12
12
12
10
10
12
10 Fig. 5-23. Examples of variations in pore space configurations "H" and 'T' within the original square pore shown in Figs. 5-22B and 5-22C. Dark areas represent the void space. All configurations for a given shape have the same fractal dimension. Relative surface area values* are the sums of the sides of the pore space in contact with the pore filling and rock surface. A change in the distribution of the void space can create an increase in surface area and in roughness, along with narrowing of the flow channels. All these parameters have an impact on the wettability, fluid saturations, and effective permeability values. *Below each example.
distribution of the cement ('roughness') within the pore space. Roughness increases the surface area and flow path lengths within a pore and flow network. It influences the surface tension between fluids and the rock (mineral) pore surface. Mandelbrot (1963) presented "Swiss cheese" examples of an ideal Sierpinski carpet containing circular holes mimicking pores (Fig. 5-24A). Garrison et al. (1992) used a sophisticated image analysis approach to analyze various Sierpinski carpet models in their study on pore roughness and the processes responsible for the formation of pore space in rocks. Numerous equations were developed for determining the effective fractal dimensions of a rock-pore system from measurements of hole properties and hole distributions, such as hole diameter, perimeter, and randomness. The digitized Sierpinski carpet models varied in complexity. Although Garrison et al.' s (1992) approach to analyze Sierpinski carpets was somewhat different from our approach, their calculated D s values (see Eq. 5-12) also increased (approaching the Euclidean topological dimension of 2) as the pore-shape area became more complex. The spatially ordered Sierpinski carpet models used by Garrison et al. (1992) in the order of complexity are" (1) a modified square pattern (N - 21 and 1/r - 5) having an apparent D s - 1.8917; (2) a circle (Mandelbrot's Swiss cheese), which is inscribed in the square so its diameter equals the side of the square, having an apparent D s - 1.9202; (3) a triadic Koch hole having an apparent D s - 1.9459; and (4) a quadratic Koch hole having an apparent D s - 1.9665 (Figs. 5-22D-G).
270 9
ll;-'-r.
:-iV:o~,..u.. ,.,~'~
,,,,.:..."
1"." ~ ".0 , ,+ 9 "..
".. 4m il~ ,
.o
>.
~ :. ,, ," " +.,,
t. . "
.,,
,~+.
,.
..,
. . . . . . . .
::,...'~" :,':? ,
..,
..
9
.~.
.O".. , ; . ' , ,
:,+.
9
,i+i
9
. .
...
P+r
...... I I I -." .+..
,
....
"."
,.
, : , " ' . , .t, -
"'":
9
,
"
.
. .
:
r .+. . , , ~ ' . 9 .-,,
, . -." 9"+,-...;:,;-. ~".:. ,"+; . ; I. ' II.41, : ,.
" :
"
:: , ;,.~.I
.." O . .
9
. :"" "" ":'.
9. . . . .
,,:.. ~ , o ~ % . 0 " .~
9
' I : . ' - . . "". " , i : , '
;."
.
9
,
+...
:": i." ".+
. + . ~, . . . . I i
"dl, +"
.... " , , , . . ,. 4 ...' ~.."
A
iiiiiiiii
I N ~,%,\\\\\\\NNXN\\"~N i l t~\"~ ~ ~,,\N~N.\~\\\\\\\N%,\\N~tx'qJ I ~ Ii ~\\',,~
.':':::~':':'::::"".v-'l
1 1 II
~ N N ~ N
I IIt
!1 ,x ;:.-:-,-.....:.:.:...:.-.:..:..~,~,,~,,,~
:::::::::::::::::::::::::
;:::.".'.".':.::-'-:!~X~
i l,~i 11 I ! ! 1 ~,'~ 1 I :.':~'".:".':'.'.'.;'.'.'-. i k~ I ! l~'q I~Xl II t,,'~l I -'~::'.'.':':.!'-'-,::.::-'1J] I I ! 1 k'~'~ 1 KN\NNNN\~ ~\\\\\\\\\\\\\\\\\'~" :.".'.""-'?'q I i i l
I I",
~ ~~ I~I ~H
t,,x.X'Xxl~k~ 1 1 Itx\\\\\\\~\\\\\\\\\~~~ ,,,, ~\\~ I ~ ['~ ~ ~ , , ~ ~ ~~t-~,,, ~il L~~\\\\~\\~
B
D
~1I
I IL~
N ! ~,11 '' ' '''
fi!i ili!il f:':':':':l ........
Z
:/iii:
:", :":":", :1
F -:"
"litif"
C
Fig. 5-24. (A) example of Mandelbrot's Swiss cheese, which is an ideal Sierpinski carpet with round holes. (After Mandelbrot, 1983; reprinted with permission from W.H. Freeman and Co.) (B) an example of Katz and Thompson' s (1986) Euclidean pore-space. Each one of the largest squares is of linear size L 2. The hatched areas are grains, the white squares are pores, and the dotted area is a Euclidean pore. (After Katz and Thompson, 1986, fig. 1; reprinted with the permission of the American Physical Society.) (C) Sierpinski carpet generators that produce six different looking carpets satisfying the relationship D s = N~ k with N = 65, k = 9, and D s = 1.8998; N is the number of measuring units of size 1/r n (r n is the size of measuring unit) and k is the similarity ratio, a fundamental integer equal to 1/r. The generator C is more lacunar (holes are larger and the spatial distribution is more sparse) than the carpet produced by generator A (visualize that the large hole is formed from the coalescence of 16 holes in generator A). (After Garrison et al., 1992, fig. 8; reprinted with the permission of Marcel Dekker, Inc.)
In addition, the measurement results from their image study showed that measured D s values were similar to the calculated D s values. Any discrepancies between the calculated dimensions and the actual measured surface fractal dimensions are artifacts of digitization of the hole area in the carpet (Garrison et al., 1992). Katz and Thompson (1986) commented on the problem of large, erratic pore sizes occurring in rocks. Large pores can be viewed as infrequently and randomly-occurring Euclidean fluctuations as shown in Fig. 5-24B. In this model, different probability
271 values were assigned to grain size, Euclidean pores, and open pores to create a statistically self-similar version of a Sierpinski carpet. Randomization permits overlapping of holes to create larger voids. The Euclidean (large) pores yield large variations in local porosity. Equation 5-13 can approximate the macroscopic porosity over a suitable range defined by the choices of L~ and L 2 (Katz and Thompson, 1986). A new measure, D ' which is the apparent surface fractal dimension of a Sierpinski carpet derived from the hole diameter distribution, was developed by Garrison et al. (1992). D ' values are calculated from image analyses of the pore diameter distributions of simulated carpets. This measure is necessary in order to evaluate the textural aspect of fractal carpets known as lacunarity (Garrison et al., 1992). Lacunarity is visualized as a gauge of the size of holes in the carpet and/or the tendency for holes to cluster together (Fig. 5-24C). Each of the six generated Sierpinski carpet examples have been spatially ordered and of constant lacunarity. These carpets are too simplistic to be used as rock-pore system models. More realistic carpet models can be generated if the lacunarity is allowed to vary randomly, thereby creating carpets having varying hole distributions and size clustering. To evaluate lacunarity in pore system development, the true surface fractal dimension of an equivalent square hole Sierpinski carpet (D") is calculated for a rock by using the maximum Feret diameter method as described by Garrison et al. (1993a, p. 46). If D ' is not equal to D " then lacunarity exits. The difference between the surface fractal dimension, D s, and the apparent surface fractal dimension, Ds', is known as the lacunarity symmetry index, q. If q has a negative value, then the hole population is dominated by a lacunar distribution of large holes, which appears as an apparent over-abundance of small holes (Garrison et al., 1992). A positive q indicates that the hole population is dominated by a lacunar distribution of small holes. This distribution appears as an apparent over-abundance of large holes. Garrison et al. (1993a) extended their equations and relationships from the Sierpinski carpet model study to actual rock-pore systems by applying data acquired from image analysis of sandstone and carbonate rock thin-sections. Two types of multiple fractal rock-pore systems were identified by Garrison et al. (1993a). The first system consists of singular fractals of rock-pore systems with two or more natural fractal processes with different surface fractal dimensions, each scaling over a discrete range of lengths. Garrison et al.'s (1993a) second system consists of rock-pore systems with two or more natural fractal processes, each with the same fractal dimension and each scaling over a discrete range of lengths with different integral abundances. Garrison et al. (1993a) devised a classification of natural multiple fractal objects based on curve shapes observed in size-frequency distributions plots (Fig. 5-21). Two fundamental fractal classes were identified" (1) singular fractals, and (2) multifractals. The singular fractals can be subdivided into two groups: (1) simple, and (2) disjunct. The simple fractals exhibit only one size-frequency distribution representing a single fractal population. The simple type is illustrated by the dashedstraight line shown in Fig. 5-21. The dashed-line assumes a single fractal nature of the measured surface features. The disjunct group of curve shape consists of separated parallel fractal trends representing multiple populations with same fractal dimensions. s ~
S
S
272 The multifractals also are subdivided into two groups, dextral and sinistral, based on two separated and distinct curve shapes. The dextral curve shape is illustrated by the two solid lines in Fig. 5-21, which shows the bifractal nature of the measured surface features. The upper solid line has a D s' value less than the D's value of the lower solid line (Dsu' < Ds~'). The sinistral curve shape dog-legs to the right in the opposite direction of the upper solid line in Fig. 5-21 and D s u ' > D sl ' " The fractal dimensions of two carbonate reservoir rocks were measured from thinsections using SEM-based pore image analysis by Garrison et al. (1993a). Two samples of the San Andres Dolomite from west Texas, U.S.A. have calculated surface fractal dimensions (Ds) of 1.992 and 1.984, and composite D s' values of 1.733 and 1.967, respectively. D s' results from the interpretations of the pore diameter-number (size-frequency) distributions showed that in the first sample there were four pore processes present: three well-defined and one poorly defined. In the second San Andres Dolomite sample only two well-defined processes were delineated by the D s' determinations. Both San Andres samples showed parallel apparent surface fractal distributions (disjunct relationship) occurring over different length ranges with some overlap. Two thin-sections from the Arun Limestone (Indonesia) were analyzed in the same manner. The calculated Dsvalues are 1.952 and 1.978, and have composite D s ' values of 2.394 and 2.977, respectively. The logarithmic pore diameter-number distribution results for the first Arun Limestone sample shows that three natural fractal processes with similar apparent surface dimensions of D s l ' = 2.198, D s 2 ' = 2.189, and D s 3 ' = 2.209 essentially occur over the same length ranges. The second sample has two well defined processes with dimensions Ds~i m- 2.800 and Ds2!.._ 2.865 . Both Arun Limestone samples showed parallel apparent surface fractal distributions (disjunct relationship) occurring over different length ranges with some overlap. The pore-rock systems in the San Andres Dolomite and Arun Limestone were shown that they could not be represented statistically as a single fractal process. The value of the lacunarity symmetry index provides valuable insight into the nature of the poreforming processes and to the progressive development of the pore system over geological time. Comparing the value of q and the petrographic character of the pore system can help in deciphering the pore system development in carbonate rocks. Garrison et al. (1993a) pointed out that some pore-forming and pore-altering processes, such as dissolution, progressive crystallization, recrystallization, and dolomitization, may change the pore system without dramatically changing the total pore cross-sectional area and hence the dimensions D and D ". Other processes such as compaction, cementation, and solution enhancement could alter the pore system pore diameter-number distribution, as well as the total pore cross-sectional area and hence the dimensions D s and Ds" (Garrison et al., 1993a). It was suggested by Garrison et al. (1993a) that the only ways in which these processes can be shown to be operative are by: (1) logarithmic pore-size distributions having a D s' value that is either abnormally high or low; or (2) a suite of carbonate rocks that exhibit a progressive change in D s' and Dswith progressive diagenetic alteration. At present, it is difficult to decipher the diagenetic history of carbonate rock pore space using fractals. Pore altering processes can be distinguished using logarithmic pore-size frequency plots, but can not be identified using single fractal values.
273
Fig. 5-25. An example of a Menger sponge having a fractal dimension of 2.727. This construction is a three-dimensional analog of the Sierpinski carpet pattern shown in Fig. 5-22A. (Modified after Mandelbrot, 1982; courtesy of W.H. Freeman and Co.) As stated previously, an ideal Menger sponge is a three-dimensional extension of an ideal two-dimensional Sierpinski carpet (Fig. 5-25). By using the same concepts of fractal geometry as discussed above for the Sierpinski carpet, pores o f a Menger sponge can be randomized to produce statistically self-similar systems. The Menger sponge has an infinite surface area and zero volume. The sponge can be used as a model for flow in rocks having a log-normal distribution of porosity. Turcotte (1992) presented the following equation, where porosity, ~, for a fractal medium can be related to its fractal dimensions: dp = 1 - ( r o / r n )
3-D ,
(5-15)
where r 0is the initial linear dimension of the sample (in this case a solid cube), r is the linear dimension of the Menger sponge of order n (r~ = 3r 0 (first order cube); r 2 = 9r0; r n = 3~r0), and D is the fractal dimension. For a first order cube D = ln20/ln3. Another realistic and general rock-pore model is one proposed by Kaye (1989) and McCauley (1992). Different thin rock slices (e.g., thin-sections) are stacked together to simulate a rock. This construction provides for a variation in both porosity and the number of pores from one thin slice to another. This will be discussed in more detail later in the section on a multifractal rock model. This foregoing discussion on the use of porosity classification systems brackets the scope of porosity's role in carbonate reservoirs. At present, the evaluation of a reservoir or well performance, based on present-day knowledge of porosity and
274 permeability, is effectively limited to a simple classification. In order to move to a higher level of understanding it will be necessary to overcome the inherent problems associated with scaling laws relating permeability to porosity and conductivity to porosity. Distributions of porosity and permeability, as used presently in computer models, need adjustments obtained by history matching. Wrong assumptions made about permeability and porosity distributions are corrected in this manner after a reasonable period of production. Heterogeneity creates "noise" in the system and the question is how to handle it in order to increase the production performance of a carbonate reservoir. These aspects will be discussed in the section on carbonate reservoir characterization. Classification based on the geological nature of the carbonate reservoirs At this point it should be clear that reservoir characterization and classification require a synergistic approach. This demands the use of geology, reservoir engineering, geophysics, petrophysics, and geostatistics to describe quantitatively the reservoir at various scales. Figure 5-26 gives an overview of scales used in the description of hetRELATIVE
S CA LE
. ~;IZE
MICROSCOPIC
_-~ ,U m
MESOSCOPIC
mm
RESIERVOIR PROPERTy
PICTORIAL D E S C R I P T I O N
PORE SPACE
PORE NETWORK Ol ST RIBUTION
GEOLOGIC E N T I T Y
FRAMEWORK
~~,~. LAMINATIONS
f SYSTEM
BEDDING
STRA TI GRAPHIC MEGASCOPIC
m to km
LI THOHYORAULIC UN I T
A NO STRUCTURAL TRAPS
GIGASCOPIC
~> km
REGIONAL FLOW / MIGRATION PAT TE RNS
OE PO S ITI ONA L AND DIEFORMATIONAL SYSTEMS
Fig. 5-26. Heterogeneity scaling description of pore space with respect to a reservoir and surrounding geology (From Chilingarian et al., 1992a, fig. I-2; reprinted with the permission of Elsevier Science Publishers B.V.)
275 erogeneity in reservoirs (Chilingarian et al., 1992a). The necessity for proper reservoir characterization is driven by: the maturity of oil reservoirs worldwide; war damage to reservoirs in Kuwait; improper exploitation of Russia's reservoirs; and the United States' eroding light oil (>20 ~ API) reserve base. More crude has to be recovered from the existing reservoirs. In this section, quantitative and qualitative geological information at the interwell scale will be used to formulate a geological carbonate reservoir classification scheme. A practical application of this scheme will be made in evaluating the incremental recovery of unrecovered mobile oil in carbonate reservoirs.
Background Fisher and Galloway (1983) pointed out that physical, chemical, and biologic processes active in specific depositional environments determine many reservoir attributes. These attributes directly or indirectly relate to hydrocarbon generation, migration, entrapment, and reservoir productivity. The application of sequence stratigraphic rules is important to the development of a classification of carbonate reservoirs based on their geological nature. What is desired is to be able to distinguish not only the internal facies, but also to define facies as part of the reservoir anatomy (geometry). The following four simple rules capture the essence of carbonate reservoir rocks and form a basis that leads to a semiqualitative characterization and prediction of their properties. The four rules are" (1) carbonate rocks are largely of organic origin; (2) the organic systems can build wave-resistant structures; (3) the sediments undergo extensive diagenetic alteration before and after lithification owing to the metastable nature of the carbonate minerals; and (4) these rocks sustain structural modifications. The implications of these rules in the establishment of a carbonate reservoir classification are pervasive. Depositional processes control the primary attributes of a reservoir. This concept came about in order to tie the intemal reservoir's architecture, which is a product of sedimentation style, to the additional recovery of mobile oil and recovery of residual oil from existing reservoirs. Mobile oil is the oil that can be expelled from the pore space into the well during primary or secondary recovery. Mobile oil remains in the pores of carbonate reservoirs after primary recovery for a variety of reasons. The main reason is that lithological complexity resulting from variations of reservoir properties can result in pockets of trapped oil. Residual or immobile oil is crude locked in the pore space by capillary and surface forces acting at the microscopic scale. Immobile oil can be recovered by using enhanced oil recovery (EOR) methods, such as steam injection, in-situ combustion, polymer flooding, alkaline flooding, miscible fluid displacement, carbon-dioxide flooding, and micellar-polymer flooding. Unrecovered mobile oil can be classified as either (1) areally uncontacted or bypassed oil, or (2) vertically bypassed oil. Both the areally unrecovered oil and vertically bypassed oil are present in all carbonate reservoirs. The efficiency of recovering oil is based on certain factors, which contribute to a wide range of primary, waterflooding, and EOR methodologies. These factors are tied to the physical character of the reservoir, variations in fluid properties, and drive (energy) mechanisms. A fundamental difference exists between carbonate reservoir classification schemes with respect to exploration criteria and reservoir characterization criteria.
276 Exploration criteria are sometimes confused with criteria needed to define a reservoir. Exploration identification criteria deal with the external geometry of length and width, burial depth, thermal history, and structural style of the exploration target. Reservoir characterization is defined by internal boundaries and barriers (heterogeneity), which can be related to the geometry of individual depositional components. These control fluid saturations, fluid distribution, and flow properties-the producibility of the reservoir. Galloway et al. (1983) showed that carbonate and sandstone reservoirs in west Texas can be grouped into geologically related families called plays. This analog approach defines plays as a group of geologically related reservoirs exhibiting source, trap, and reservoir characteristics. A delineation of a play depends upon the original depositional setting of the reservoir rocks. This concept contributed to the U.S. Department of Energy's supported research effort into maximizing the producibility of the United States' domestic oil resource. Reservoir classification Tyler et al. (1984) presented a reservoir classification scheme (Fig. 5-27) which compares the recovery efficiency cross-plotted against reservoir genesis and lists the drive mechanism for both clastic and carbonate oil reservoirs located in the State of Texas, U.S.A. Figure 5-27 shows that there is a well-defined trend of decreasing oil recovery from these reservoirs. Reservoirs composed of deep water sediments appear to be excellent candidates for additional oil recovery. This is due to the high percentage of nonproduced moveable oil remaining in these reservoirs at abandonment. Carbonate plays do not exhibit as broad a range of recovery efficiencies as do the clastic reservoirs. Reservoir classes. The U.S. Department of Energy is presently classifying light oil carbonate reservoirs based on seven major depositional categories (Table 5-V). The development of this classification system involved the use of the TORIS database located at the U.S. Department of Energy, Bartlesville Project Office, Bartlesville, Oklahoma, U.S.A. Trial groupings of distinct, internally consistent, carbonate reservoir classes were compiled for statistical analysis using Analysis of Variance (IOCC, 1990). The statistical analysis helps to establish a number of manageable reservoir classes that are: (1) collectively exhaustive; (2) mutually exclusive; (3) internally consistent; and (4) different from each other with regard to heterogeneity (IOCC, 1990). The reservoir groupings, although geologically defensible, are based on the premise that reservoirs from the same reservoir class will have similar heterogeneities. Depositional systems are the dominant geologic factor influencing the development of reservoir heterogeneity. The categories are differentiated on the position of their depositional environment as a function of relative water depth and diagenetic overprint. Several criticisms need to be considered when evaluating the universality of this classification system: (1) only 450 carbonate reservoirs from the United States were available from the TORIS database; (2) omission of well known reservoirs; (3) improper interpretation of the depositional setting assigned to a reservoir; (4) evaporite associations, such as structural effects of evaporite dissolution or salt
277 TABLE 5-V Classification of carbonate depositional systems and their subcategories based on the position of their depositional environment as a function of the relative water depth and basin morphology (see Fig. 528)
Peritidal Supratidal Intertidal Subtidal
Reef (sup) (int) (sub)
Pinnacle Bioherm Atoll
Shallow shelf
(p) (b) (a)
Slope/basin
Open shelf Restricted shelf
(os) (xs)
Debris fan Turbidite deposits Mounds
(df) (td) (m)
Shelf margin Rimmed shelf Ramp
Basin Drowned shelf Deep basin
(rs) (r)
(ds) (db)
Source: Modified after DOE, 199 l, table 1.
o
0
o
E
.~
v
2
"E~: ";
..~
"s
";
"~
m
o
a. 80
9
o
o
o
~.
g a.
o~
:~
\ \ \ o\
\
\ % \
60
ON
\ %
\
c
%
\
8
40-
\
", \
\
\
9
\ \
\
i
l" 1 9
\
40 ~ o
x x
"
9
\
Q
%
IT
\
20
I
\
"~ tight clostic
lJ modified by suboerlal leoching
reservoir O'&
0 Reservoir genesis 0nd drive mechanism
Fig. 5-27. Plot of the average recovery efficiency versus reservoir genesis for important clastic and carbonate oil reservoirs in Texas, U.S.A. Drive mechanisms appear next to the depositional environments: C - combination (some combination of GCE, SG, and W); G C E - gas-cap expansion; G D - gravity drainage; S G solution gas; M - mixed; and W - water. (Modified aiter Tyler et al., 1984; courtesy of the Bureau of Economic Geology.)
278 piercement structures, were not integrated into the groupings; and (5) structural compartmentalization, which is difficult to quantify, was lumped under "other" factors. The investigation scale of heterogeneity in this classification approach is at the macroscopic (interwell) level. The principle is that the internal architecture and heterogeneity of reservoirs are dominantly controlled by processes operating at the depositional level. Modifications after deposition are important in determining reservoir recovery efficiency on the macro- and mega-scale levels. Figure 5-28, a three-dimensional representation of geological data, considers the effects of the diagenetic overprint and structural compartmentalization on reservoir productivity. Figure 5-29 is a simplified version of Fig. 5-28. Reservoir class descriptions provide
FAULTED/FOLDED FOLDED
FAULTED
NATURAL FR POROSITY
, /
UNSTRUCTURED
DEPOSITIONAL SYSTEMS
Leve~and / LACUSTRINE
COMPACTION CEMENTATION GRAIN OISSOLUTIOi~
GHAIN ENHANCEMENT
PERITIIDAL |
! I ~ I
SHAL LOW SHELF
,
7 k REEF/ISLOPE/BASIN~
Snyder SHELF EDGE
Mo•dak Fairway
Glennbur~L-". . . . . . . . . . // ,
I
BASIN
/ ,
I~_~ I I I
~
t
'
\,,
Austin Chalk
i
I DOLOMITIZATION
(Evoporites)
DOLOMITIZATIO
N
MASSIVE DISSOLUTION
SIL ICl FICATION
Fig. 5-28. A three-dimensional classification scheme of carbonate reservoirs with examples of reservoirs from the U.S.A. Reservoirs can appear in more than one box. Abbreviations are defined in Table 5-V, except for ss (strike-slip fault), rf (reversed fault), and nf (normal fault). (Modified after DOE, 1991, fig. 2; courtesy of the U.S. Department of Energy.)
GEOLOGICAL RESERVOIR CLASSIFICATION SYSTEM
I
.
I CARBONATE
I
:
Deposltlonal _ System
I Dlagenetlc Overprint
,,
9 Lacustrine
9 CompactionCementation
9 Peritidal Sur~etJd~ 9 . bleftJdal . Sublidal
SILICICLASTIC
I Structural Comp, artmentallzatlon
!
Shelf Open 9 Shell
9 Natural Fracture Porosity
9 Aulhigenic
9 Faulted
9 Natural Fracture Porosity
9 Lacustrine Basin Margin
9 Dolomitization
9 Faulted
9 Alluvial F a n
Canter
- Humid (Sveam-Dominaled) A 9 n d / S e m i Arid 9Fan Deltas
9 Folded
"Ramp
Clay
9 Folded 9 Chertificalion 9 Faulted/ Folded
9 Fluvial
9 Faulted/ Folded
.
Braided Sueams 9
Meande,i~
Sueams
Delta
9
Reefs *
9 Unstructured
9 Grain Dissolution
9 Grain Enhancement
9 Massive Dissolution
Structural Compartmentalization
9 CompactionCementation
9 Dolomitization
9 Shelf M a r g i n mnmed 9 Sh~
- Ptnnade Reels . Biohecml
Overprint
I
9 Eolian - E,Os Coasud Dunes
(Evaporites)
. ResVicled Shell
I Dlagenetlc
System
9 Unslructured
RESERVOIRS
......
Deposltlonal
B 9 un
9 Shallow
9
I RESERVOIRS
- Wave-Domimlled
Silicification
F 9luvial.Dominamd - T~le- D o r n i n a t e d
-A ~
9 Strandp~ain 9l~norC.,cN'es . B~der Shorofaces Bad~ Baniers TKIal 9 Channels - W u h o ~ FmVTidal Deltas
9 Slope/Basin Delxis 9 Fans Tu, 9 l~lite Fans . Mounds
9
9 Basin D 9 r o w n e d Shell . Deep
9 Shelf (Accrelionary Processses)
Basin
Sand Waves - S a n d |10dges'Bars
9
Slol~/Basin - Tud~dde
Fans
Dol~Is F a n s 9
Basin 9Pelagic
Fig. 5-29 9 A simplified geological reservoir classification system based on depositional system, diagenetic overprint, and structural compartmentalization for carbonate and clastic reservoirs. (After Ray, 1991" courtesy of the U.S Department of Energy.) 9
t,a -..I
280 generalized geological images of carbonate reservoirs and their productivity, and a comparison is made with clastic reservoirs. This presently used classification considers in a general way whether or not the reservoir is structurally influenced.
Carbonate depositional systems and reservoir properties. The following is a generalized description of the carbonate depositional systems used in the classification with comments on reservoir drive mechanisms. For a detailed classical-geological description of depositional models refer to Volume I (Mazzullo and Chilingarian, 1992b). Recovery efficiency values can be obtained from Fig. 5-27. Lacustrine carbonate reservoirs are not common in the United States. Some fractured lacustrine carbonate reservoirs exist in the Green River Formation, Unita Basin, Utah, U.S.A. (DOE, 1991). Peritidal carbonate reservoirs are rocks deposited in intertidal to supratidal environments, including hydersaline sabkhas. Terrigenous elastics can frequently interfinger with these carbonate sediments. Where evaporation dominates evaporite deposits can be expected. One aspect that has not received much attention is carbonate tidal channel facies (Wright, 1984). The significance of carbonate tidal channels is that their migration creates a shallowing upward sequence like the prograding low-energy facies model. Reliable criteria for tidal channel recognition are lacking. Peritidal deposits are a mosaic of tidal flat, tidal channel and, where present, associated beach deposits. Sheet-like geometry of peritidal reservoirs is common, as is the typical cyclic arrangement of peritidal and subtidal deposits. Shallow shelf~restricted carbonate reservoirs include a wide variety of carbonate platform deposits originating in shallow water under arid and evaporitic climatic conditions. The term 'restricted' refers to the presence of restricted marine fossil assemblages in contrast to a system that has open marine fossil assemblages (DOE, 1991). Dolomitization of the original sediments produces extensive beds of dolomite. This results in highly stratified reservoirs having moderate to high residual oil saturations. Solution-gas-drive reservoirs predominate owing to the isolation of permeable zones. These reservoirs exhibit low to moderate recovery efficiencies. Tyler et al. (1984) revealed that this reservoir class accounts for 53% of all production from carbonate rocks in Texas, U.S.A. Shallow shelf~open carbonate reservoirs develop in a wide variety of facies deposited on a broad, shallow to moderately deep, gently sloping shelf. A carbonate ramp is a platform built from loose sediment without reef construction or lithification at the shelf break (Schlager, 1992). Recovery efficiencies can vary greatly owing to postdepositional modifications. Drive mechanisms are either solution-gas or combination types. Reefal reservoirs produce from stratigraphic reefs, such as open-shelf atolls, pinnaele reefs, and bioherms (patch). Most reefs are encased in low permeable shales, micrites, and mudstones; however, associated facies include grainstones that accumulate as flanking beds around the reefs. Dominant drive mechanism is solution-gas, sometimes augmented by a water drive. The vertical relief and lateral isolation, coupled with strongly developed layering of permeability are characteristic of these reservoirs. Irregular oil-water contacts occur owing to these facies changes. Shelf margin reservoirs are platform margin deposits, which include reefal and
281 nonreefal limestones, sometimes intercalated with sandstones, draped over the shelf margin. The reservoirs have diverse lithologies and diagenetic histories. Facies belts tend to be thin, narrow, elongated and internally complex reflecting bar, bank, and island facies deposited under low-to high-energy conditions. Permeability is highly stratified and lenticular. Most reservoirs have low recovery efficiencies. DOE (1991) recognizes two subcategories of shelf-edge reservoirs: rimmed shelves, which may contain barrier reef facies, and ramps. Slope basin reservoirs originate as carbonate submarine-fan, debris apron, and turbidity flow deposits on basin slopes around carbonate platforms. These types of reservoirs are not common and contain carbonate sands, muds and breccias. Schlager (1991) provided three rules, which govern the geometry and facies of such reservoirs: (1) The volume increase in sediment required to maintain a slope as the carbonate platform grows upward is proportional to the square of the height for conical slopes. It is proportional to the first power of height for linear slopes. (2) The slopes of most high-rising platforms are steeper than siliciclastic ones. (3) The internal angle of friction governs the angle of repose of loose sediment. At zero confining pressure the angle of repose approximates the angle of internal friction. Values for internal angles of friction for some lithified carbonates are: Wolfcamp Limestone -34.8~ Indiana limestone --42~ and Hasmark Dolomite -35.5 ~ Computer model studies by Bosscher and Southam (1992) showed that changes in composition of sediment dumped on a slope can produce unconformities (Fig. 5-30). At initial conditions, the platform grows with an empty lagoon. Sand and rubble from the reef margin are the only input into the lagoon. With time, the lagoon fills up and exports large volumes of mud burying the reef talus at a more gentle slope angle.
run tile: 2000 yrs; tizestep: I00 ?rs; platforz height: 164 ft (50 .); platf0rl width: 1312 tt (400 .); Gzargia: i0 .z/rr; Giateri0r: 4 u/rr. k: 0.66/ft (0.2/m); initial depth: 6.6 ft (2 z) iinear sea-level rise: 3u/yr; wavebase: 33 ft flO z); ziR ang]e/naxang]e: 5/35 degrees; width of section: 1083 ft [330 z). G is the gr0sth rate of the reef, and k is the lilht extinction coefficient.
unconformity caused by change in sediment composition
Fig. 5-30. An example of CARBPLAT output showing a grain-size unconformity on the slope of a continuously growing carbonate platform. The model considers a platform with an empty lagoon. Initially the lagoon and the slope receive only sand and rubble from the reef margin. After the lagoon fills up, carbonate mud is then exported to the slope covering the reef talus at a gentler slope angle, which creates a mud wedge unconformity over the reef rubble. (After Schlager, 1992, fig. 1-27a; reprinted with the permission of the American Association of Petroleum Geologists.)
282 Depositional models such as CARBPLAT help in deciphering and predicting facies when applied to the analysis of the geological nature of carbonate reservoirs and plays (Fig. 5-30). Basinal carbonate reservoirs occur in chalk deposits that accumulate from the raining down of pelagic organisms onto drowned platforms and basin floors. Friedman (see Chapter 8) recognized three categories of chalk reservoirs: (1) ones that were never deeply buried, lacking significant compaction, and having primary porosity; (2) those buried to a moderate depth and having an extensive fractured porosity; and (3) ones deeply buried, but having a high pore pressure to preserve high primary porosity.
Measurement of interwell heterogeneity- volumetric sweep. The classification systems presented in Figs. 5-28 and 5-29 have a statistical basis for their grouping. The IOCC's (1990) report suggested that the volumetric sweep efficiency (E) be used as an indicator of reservoir heterogeneity at the interwell scale. Sweep efficiency is a measure of the volume of the reservoir swept by water to the total volume subject to invasion. The aim of IOCC's methodology is to measure reservoir heterogeneity at the macroscopic scale. This approach helped IOCC to sort reservoirs into distinct classes whose members are geologically similar and which have similar heterogeneity (Table 5-V). Volumetric sweep efficiency directly reflects the gross reservoir heterogeneity along with other factors. These factors consist of well spacing, primary drive mechanism, and in secondary recovery operations, the injection rate, pressure, mobility ratio of the injection fluid relative to oil, and type of injection water. Evis broadly defined as the portion of a reservoir's hydrocarbon pore volume effectively swept by a waterflood. The volumetric sweep efficiency can be estimated from the ratio of ultimate recovery, by primary or secondary means, to the volume of displaceable mobile oil" Ultimate Recovery E = 9 v Displaceable Mobile Oil
(5-16)
As discussed in previous chapters in Volume I (Jodry, 1992; Samaniego et al., 1992), rock producibility can be determined from plots of oil and water relative permeability curves for a particular rock as a function of water saturation. Figure 5-31 is an example for a water-oil relative permeability curve for the San Andres Dolomite. The fractional displaceable mobile oil in Fig. 5-31 is the amount of oil that could be theoretically produced if the entire reservoir was reduced to its residual oil saturation. Displaceable mobile oil (Dmo), also known as just oil recovery (Craft and Hawkins, 1959), is expressed as: (1 -- Swi) - Soc Omo = (1 -
s.;,i)
,
(5-17)
where SW. l is the initial pore-water saturation, and S is the residual or critical oil saturation. This is the saturation at which oil will begin to flow as the oil saturation increases under the influence of a natural water influx or an artificial water drive. For the San
283 1.0
I
I
I
0.5 O/
0.1 Z 0 1
~" 0.05 U >.-, F.J
I
1
~9
0.01 -.---
l.iJ IX
tu 0 0 0 5
1
IX.
l.iJ > I-.
/--
_J 14.1 n,,
0.001 - -
0.0005 2O
80
30 40 50 60 WATER SATURATION,% PV
70
70
30
60
OIL
50
40
SATURATION~% PV
Fig. 5-31. Average oil and water relative permeabilities, San Andres Dolomite, Welch Field, Texas, U.S.A. For the values of S c = 0.32 and S i = 0.30 the displaceable mobile oil is 54% for the water--oil system. (Modified after Abernathy, 1964; courtesy of the Society of Petroleum Engineers.)
Andres Dolomite example in Fig. 5-31, the displaceable mobile oil is 54%. Estimation of the ultimate recovery is by decline curve analysis of historical production data. The volume of displaceable mobile oil on a reservoir condition basis can be estimated using a volumetric approach for a water drive having no gas. The equation is:
D =7758(A)(h)(~b)I (l-Si)-Sc I , mo
(1
-Si)
(5-18)
where A is the area of the reservoir, h is the net pay thickness, and ~ is fractional
284 porosity. Similar relative permeability curves are obtained for a gas-water system as for the oil-water system. For secondary recovery the volume of displaceable mobile oil for stock-tank conditions can be estimated from: = 7758 (14) (h) (~b) Dm~
S
oi
Bo i
S
orw
Boa
J
(5-19)
where Dmo is in stock tank barrels, A is in acres, h is in ft, ~ is fractional, S i -- (1 - S i - S 9gl.) and is fractional, SWl is the fractional initial water saturation, Sg! is the fractional . . . inmal gas saturation, Boi 1s the initial oil formation volume factor m reservoir bbl/ stock-tank bbl, S wis the fractional residual oil saturation in the swept zone at the end of water flooding, andB o a is the oil formation volume factor at the end ofwaterflooding (abandonment) in reservoir bbl/stock-tank bbl (IOCC, 1990). IOCC's (1990) report presented a volumetric sweep efficiency equation, which contained terms for reservoir heterogeneity, Eh,t; mobility ratio of injection fluid relative to oil, Enuid; well spacing, Ew.,; and other influences such as, primary drive mechanism and mechanical design of the waterflood, Eoth~r. The IOCC's viewpoint focuses on the additional recovery beyond primary recovery or pressure maintenance operations: E v = Ehet(Efluid)(Ewe, l)(Eother).
(5-20)
Several adjustments were made by IOCC (1990) to Eq. 5-20 for Enu~dand Ewe, by normalizing all the sweep data to a mobility ratio of 1.0 and a well spacing of 40 acres (16 ha). The residual influences (Eother) w e r e not segregated in the IOCC's analysis and remained as "noise" in the system. The adjustment for fluid behavior is a complex procedure. E vcan also be defined as the product of the areal sweep efficiency, E a, and the vertical sweep efficiency, Eh: E = E(Eh).
(5-21)
The areal sweep efficiency depends very strongly on the degree of vertical conformance (permeability variation) along the producing interval (IOCC, 1990). Fassihi (1986) described a method by which E can be determined from the empirical curves for three different water injection-well patterns: direct-line drive, staggered line drive, and five-spot. The curves are based on the measured sweep efficiency in a two-dimensional waterflood model. Fassihi's (1986) empirical equation, which fitted the curves, by using the mobility ratio, M, and fractional water cut, fw is:
1-Ea
- (alln [M + a2] + a3)fw + a41n (M + as) + a 6 .
(5-22)
Table 5-VI presents the empirical constants a, through a 6 values for the three pattern geometries. E hcan be determined by substituting the calculated value of ERfrom Eq. 5-22 into Eq. 5-21 and the value of E from Eq. 5-16. The value thus calculated is
285 TABLE 5-VI Coefficients in areal sweep efficiency correlations for three different well pattern geometries used in waterflood operations Waterflood well patterns Areal sweep coefficient
Five-spot
Direct-line drive
Staggered-line drive
aI
-0.2062 -0.0712 -0.511 0.3048 0.123 0.4394
-0.3014 -0.1568 -0.9402 0.3714 -0.0865 0.8805
-0.2077 -0.1059 -0.3526 0.2608 0.2444 0.3158
a2 a3 a4 a5
a6
Source: Modified after Fassihi, 1986; courtesy of the Society of Petroleum Engineers
consistent with data on M and Ev. A value for E , at a mobility ratio of 1.0, can be calculated using Fassihi's correction. It is now possible to adjust the volumetric sweep for the fluid effects: Eva=
EhE1. 0 ,
(5-23)
where Eva is the adjusted volumetric sweep for the fluid effects and Eal.0 is the areal sweep efficiency standardized to a mobility ratio of unity (IOCC, 1990). The effect of well spacing also can be removed by standardizing the sweep data for all reservoirs to specified well spacing. IOCC (1990) selected 40 acres (16 ha), a generalized function, which incorporates the effect of well spacing on reservoir (lateral pay) continuity. Reservoir continuity is the percentage of the total volume of reservoir rock that is in pressure communication between the injector-producer well pairs. Figure 5-32 presents a series of continuity functions based on actual field data from west Texas, U.S.A.(Gould and Sarem, 1984). This figure shows the fraction of gross pay that is continuous between the wells having different spacings. It is apparent in Fig. 5-32 that for a given reservoir a semi-log relationship exists between reservoir continuity and interwell distance. Barber et al. (1983), however, showed that such curves tend to exhibit less continuity as more data become available at smaller well spacings. The Fullerton Clear Fork and Wasson Clear Fork reservoir curves are based on relatively large spacing. Infill drilling at closer spacings could move them downward. The well spacing of a reservoir can be converted to an interwell distance by using the following geometric, power-law relationship: WD = 208.66(AC) ~ ,
(5-24)
where WD is the interwell distance in ft and A C is the well spacing in acres. The Interstate Oil Compact Commission's (1990) methodology cross plots the In(Eva) against interwell distance. A straight line is drawn between two points, one of which has the coordinates of zero interwell distance and nearly perfect sweep efficiency (0, ln[0.999]). The other point is the actual interwell distance and sweep efficiency for the reservoir or pay (WD, Eva ).
286 IO0
-~.
90
-
80
-
"
70
-
60
-
I
50
-
', !
40
-
~
-
*,.T. =,.,
_~
"
20
i"-.•
J
"~
,'-,
I
,
i.. i_ ,* w~ '_~ ,~
"
'
~ I
~
I
, "'..
~
FOld.
'O
'
'
I
I
J
I
t
i
I^
-1
i
!~ I 'I"
"-~r,,,,,I,, I# '~
,~ I~.
~.:
I~'
~,
~
I ~
I ~
,
,
f
~
12, "',.T'~'~ li~ ~
'~ I~
-I
i~
I~~ ~,,,.
I-~ I-~ ;~ '~ II t~
-'t I
i
"
ao ",. ~~ l~ "'~,~ ,'~"._,u.. ,t i ~ "'-:~
....
1
~t ~8
"~i i
,.
I I
-I
~I
I
,,~
,
-
iI I0
II
0
500
I
1,000
"'...
,,_l ~
".. -',,~
~
~
J
"'g3.
~
1,500 Dislonce
Between
II
I
I
2,000 Welle
2,500
~ ~
I .
I
3,000
3,500
(Feet)
Fig. 5-32. Pay-continuity diagram showing the fraction of gross pay that is continuous between wells at various spacings. (Modified after Gould and Sarem, 1989, fig. 5" courtesy of the Society of Petroleum Engineers.)
By interpolating or extrapolating the straight line, EvawaS obtained by IOCC at an interwell distance of 1,320 ft (40-acre well spacing). Eaat the 40-acre (402 m; 16 ha) well spacing is defined as Ehet. The semi-log function specific to each reservoir or pay zone is f(Ea, WD). f(Ea, WD) = d , , w o
+ b) ,
(5-25)
where m is the slope of the semi-log plot (ln[Ea] - ln[0.999])/WD, b is the intercept of the straight line with the y axis (ln[0.999]), and WD is the interwell distance in ft. By entering the standardized well distance (1,320 ft for 40-acre spacing) into Eq. 5-25, IOCC (1990, p. 17) adjusted the value of Eva for well spacing to yield the 40acre (16-ha) well spacing Eh~t: Ehet = f(Eva, 1320) 9
(5-26)
Table 5-VII presents the adjusted volumetric sweep efficiency values for some 450 categorized carbonate reservoirs. The IOCC analysis is a statistical resolution of carbonate reservoir data in the TORIS database. Figure 5-33 shows the data spread for the average volumetric sweep plotted against the heterogeneity indicator (Eh~t) for the
287 TABLE 5-VII Adjusted volumetric sweep efficiency values for nine carbonate reservoir subcategories defined by deposition and diagenesis. Carbonate shelf class includes shallow-shelf and shelf-margin reservoirs. Total number of reservoirs analyzed is 450. Adjusted volumetric sweep efficiency Reservoir class Peritidal Non-dolomitized Dolomitized Shelf Non-dolomitized Dolomitized Dolomitized + evaporites
Number of reservoirs analyzed
Mean
Variance
51 57
0.703 0.706
0.038 0.030
48 79 109
0.633 0.676 0.582
0.066 0.054 0.063
Reef Atoll: Non-dolomitized Others: Non-dolomitized Dolomitized
35
0.698
0.036
25 28
0.576 0.715
0.042 0.039
Slope-basin All
18
0.667
0.033
Source: Modified after IOCC, 1990, table 5
same carbonate reservoir data set. A comparison to clastic reservoirs is also illustrated in Fig. 5-33 (IOCC, 1990). This plot shows that carbonate reservoirs appear to be slightly less heterogeneous than clastic reservoirs based on volumetric sweep efficiency data from the TORIS database. Unrecoverable mobile oil ICF and BEG (1988) reported that over 80% of reserve additions in Texas, U.S.A., since 1979 can be attributed to intensive development of older reservoirs. Various primary recovery, waterflooding, and EOR techniques were used to increase recovery. The application of these methods, which produce significant amounts of additional remaining mobile and immobile oil, has proved to be highly cost effective. It is necessary to evaluate the unrecoverable mobile oil in carbonate reservoirs in order to assess various incremental recovery techniques. As mentioned previously, the efficient recovery of either mobile or immobile oil depends on the ability to map and predict the intemal architecture of carbonate reservoirs. The intemal architecture is profoundly influenced by the depositional conditions, which control the distribution of the various facies. Uncontacted mobile oil in reservoirs is attributed to many reasons such as fault compartments, flow heterogeneities, well spacing, facies changes, and physical properties of the crude. The writers concentrate in the discussion below on those methods that increase the recovery of the uncontacted and bypassed mobile oil. Uncontacted oil refers to oil trapped in isolated compartments within the reservoir, which is uncontacted by wells at current well spacing (ICF and BEG, 1988). The term
Plus One Slandard
................... c
C)
[
...................
Deviation
cJ
Mean Minus O n Slandard
Deviation
........................................................................................
CARBONATES
......................
CLAST1CS
Fig. 5-33. The heterogeneity parameter, Ehe1, range in values, and mean are presented for 25 different carbonate and clastic reservoir classes developed in the IOCC (1990) study. Carbonate reservoirs appear to have higher E,,, values than clastic reservoirs. A high Ehelvalue is indicative of a low level of heterogeneity. (After IOCC, 1990, fig. 6; courtesy of the US.Department of Energy.)
289 bypassed oil refers to oil unswept by injected fluids during secondary or enhanced oil recovery. Bypassed oil owes its origin to a high degree of vertical and areal heterogeneity or to an unfavorable mobility of the injected fluids. The determination of the amount of uncontacted oil requires knowledge about the macroscopic heterogeneity, facies information, and lateral pay continuity within the reservoir. ICF and BEG (1988) used a volumetric reservoir evaluation approach in solving this problem. A major drawback to their approach is that the solution is based on reservoir conditions after waterflooding. It does not apply to carbonate reservoirs undergoing primary production. The first step is to classify the unrecovered oil into two components: (1) areally unrecovered oil that includes both uncontacted and areally bypassed oil, and (2) vertically bypassed oil. Both areally unrecovered oil and vertically bypassed oil exist in all carbonate reservoirs. Their relative volumes depend upon the reservoir's architecture and the diagenetic effects in the producing zone(s). Determination of the gross unrecovered mobile oil volume requires data on the reservoir's ultimate production potential, fluid saturations, and the crude formation volume factor at initial, present, or abandonment conditions. By subtracting the estimated ultimate recovery (for decline curve analyses techniques refer to Mannon, 1972) from the original oil-in-place gives an estimate of the remaining oil-in-place. The volume of mobile oil remaining in the reservoir can be calculated as follows: UMOIP
= ROIP
OOIP(S~176
,
(5-27)
(Soi/Boi) where U M O I P is the unrecovered mobile oil (STB); R O I P is the remaining oil-inplace (STB), O O I P is the original oil-in-place (STB), Sra is the final fractional residual oil saturation, Boa is the oil formation volume factor at abandonment of the waterflood (bbl/STB), S i is the fraction of the initial oil saturation, and Boiis the initial oil formation volume factor (bbl/STB). The immobile oil-in-place ( I M O I P ) is defined as"
IMOIP = ROIP-
UMOIP =
OOIP(Sora/Boa) (Soi/Boi)
(5-28)
where Sor a is the final residual oil fraction in the waterflooded reservoir or zone. The distribution of unrecovered mobile oil can be determined from: U M O I P = A UO + V B P O ,
(5-29)
where A U O is the gross unrecovered mobile oil volume, and V B P O is the vertically bypassed mobile oil volume. Vertical s w e e p efficiency (Eh). To calculate the volume of vertically bypassed oil, the vertical sweep efficiency component (Eh) needs to be quantified. Fassihi (1986)
290 provided an empirical correlation for vertical sweep as a function of the mobility ratio and the fractional amount of produced water (water cut). This correlation defines vertical sweep efficiency as a function of the vertical permeability variation (DykstraParsons coefficient). Dykstra and Parsons (1950) introduced a method for describing the distribution of the absolute permeability of reservoir rocks determined from core data. It is difficult to describe heterogeneities deterministically, especially within carbonate reservoirs. Statistically, the permeability distribution defined by the cores is usually log normal. By assuming permeability to be a random function, with a known mean, variance and spatial correlation, the permeability can be characterized by a log-normal frequency distribution (Fig. 5-34). This widely used method is critical in predicting the effect of reservoir heterogeneity on waterflood performance. The method estimates the fractional waterflood coverage only for a vertically stratified reservoir with no lateral discontinuities. The Dykstra-Parsons coefficient, VDpiSequal to:
VDp=
ks0- k~ k5~ ,
(5-30)
where ks0 and ka are the 50th and the 84.1th percentile values from a log-cumulative permeability distribution. Core permeability values are arranged in a descending order of magnitude. The "greater than" permeability cumulative frequency is calculated and plotted. Figure 5-34 gives four examples of the spread of permeability values as quantified by Vop. The Vopvalues were calculated from core data for two "C" zone members of the Ordovician Red River Formation (a limestone and an interbedded dolomite and limestone) and the "D" zone member (burrowed dolomitized carbonate mudstones and wackestones) in the Williston Basin, U.S.A. This plot illustrates the degree of permeability contrast between different adjoining layers within the carbonate sequence. The Dykstra-Parsons permeability coefficient can provide a means of estimating the absolute permeability of individual layers when an average permeability value is available for the reservoir (ICF and BEG, 1988). Vop is estimated using cores from representative wells in the reservoir. The coefficient is then applied to the average permeability values to determine the vertical conformance profile throughout the reservoir. This information is used in determining the sweep efficiency of waterfloods. The Dystra-Parson coefficient also is a good indicator of the reservoir's potential during primary recovery. Honarpour et al. (1990) showed that a good statistical correlation (R = 0.9) exists between VDpvalues and initial production in a clastic reservoir. Low Vopvalues are associated with high initial oil production rates, whereas high Vop values are indicative of lower initial production rates. ICF and BEG (1988) developed a statistical correlation relating the permeability variation to the vertical heterogeneity component (H) (Fig. 5-35). This correlation helps in estimating the permeability variation coefficient for reservoirs where there is no detailed injection and production information. The correlation gives the average, minimum, and maximum values of VDpfor a known reservoir H v component and is based on an analysis of 156 reservoirs under waterflood in the states of Texas and New Mexico, U.S.A. The adopted scale ranges from H = 1 for very homogeneous
291 99.99 tO0
~.'
99.999.8 99 ' '""'1 '1 ' ''V''l~'"
~e , ,
915 '~"
90 i i i~0 70 60 ,,,'~, ,',,I,,l,l=,,
1501 40 23[0Z 0 | , ,,lW,, I,=l,,,,',-
!/I Z
5
2 ; 0.5 (~.2 0.1 0.05 i,=,,i.,,i = = w p.=l,i
II I I =
0.01 ,.,
9 -
E >:
.
_
-
-
_
I..err
t.l.I
lO
-
:E n, tJd
.....
i~
"
-
i
"
2
|
,,,
'~ ' ~ " ~
.
-
0.ol,,,I .... I , I , , I , , , , I , ~ , , I 0.01 0.0,5 0.1 0.2 0.,5 I
2
, , i,,,,L ......... li,,,l,,lll,l,, 5 I0 20 30 40 CUMULATIVE
i,lil,,,illllil,,, 50 (GO 70
FREQUENCY
X ~
80
i,,,lllt 90
ilst
I
hillhltill 98 99
I
I, 5.11,,a~ 99.8 99,9 99.99
K
Fig. 5-34. Examples showing the calculation of Dykstra-Parson coefficients using a log-normal plot of the cumulative distribution of core permeability values on log-probability paper. Core data from the "C" zone (subtidal depositional environment) of the Red River Formation, well Melby No. 4-1, Bush Lake Field, Sheridan County, Montana, U.S.A. No. 6: VDp = 0.74; 35.5 ft (11 m) of limestone composed of mudstone and wackestone containing some 12 different Archie classes (Oave = 3.9). No. 7: VDp = 0.50; 95 ft (30 m) of interbedded dolomite and limestone comprising a single Archie class (Oave = 1.8). (Core data and lithologic descriptions from Ikwuakor, 1992; courtesy of the U.S. Department of Energy.) The VDp results are very similar to values obtained from core data from the Red River Formation "D" zone (equal to the "C" Burrowed Member) in two wells (No. 1-25 Alexander and the No. 2-31 Hilton), South Horse Creek Field, Bowman County, North Dakota, U.S.A. The Dykstra-Parsons coefficients are 0.75 (well No. 1-25) and 0.53 (well No. 2-31). Higher values of VDp indicate less efficient water drive and/or waterflood systems when water displaces oil. (Modified after Longman et al., 1992, fig. 8; courtesy of the American Association of Petroleum Geologists.)
carbonate reservoirs to H v = 10 for very heterogeneous carbonate reservoirs. The following equations developed by Fassihi (1986) can be used to estimate the vertical sweep efficiency once the Dykstra-Parsons coefficient correlations are k n o w n either from direct measurements or using Fig. 5-35" x=-0.6891
+ 0.9735VDp+ 1.6453VZDp ,
(5-31)
292 i
A > v C
I
I
'
I
'
t
'a
I
i
0.9
.g
15
)
0.8
-
.............. ~ ~ o
.
.,2., .o o
~~-J"
.
,
~
0.7 n
no
0.6t
-------"-+i
~ " ~
". o.., o'~176176176 ~176176 "~176
~
......
~
~
_
13
== 0-5
~ -
.,..-.--
Data not avoiloblefor ~ s range ~*-- Of:ranShelf, Rofform--~
E3
0
Unhoclurod Chalk~ .,,O~).SIXIIf I
I
2
:3
Homogeneous
. . . .
4
Rotform
I,,,
I
I
I
i
5
6
7
8
9
Vertical Heterogeneity Descripta" (Hv)
,
I0 Heterogeneous
Fig. 5-35. Variation in the Dykstra-Parsons coefficient values cross-plotted against the vertical heterogeneity component for selected carbonate depositional systems. (Modified after ICF and BEG, 1988, fig. A-7; courtesy of the U.S. Department of Energy.)
y =
(WOR + 0.4) (18.948 - 2.499(VDp))
(M + 1 . 1 3 7 - 0.8094(Vop))10 x
(5-32)
and y = a,(Eha2 ) (1 -- Eh)a3 ,
(5-33)
where WOR is the water oil ratio; M is the mobility ratio, VDpis the Dykstra-Parsons permeability coefficient, E h is the vertical sweep efficiency, and Table 5-VIII gives values for the empirical constants a~, a2, and a 3. Equation 5-33 is solved for the vertical TABLE 5-VIII Coefficients used in Fassihi's vertical sweep correlation Coefficient
Value
aI a2 a3
3.33409 0.77373 -1.22586
Source: Data from Fassihi, 1986.
293 sweep efficiency (Eh) by iterative techniques. The volume of the vertically bypassed oil can be determined from standard engineering calculations for oil-in-place. The vertical sweep efficiency can be estimated based on areal and volumetric sweep efficiencies obtained from an analysis ofwaterflood performance. ICF and BEG (1988) presented a simplified one-step volumetric solution for E that is an expansion of Eq. 5-16"
E =
Nu
v
7758 (A) (~b) (Soi/Boi - Sor/Boa )
,
(5-34)
where N is the ultimate recovery in STB obtained from performance decline curves. Equation 5-34 can be used only with reservoirs where the entire primary drainage area is under a secondary recovery injection program. In ongoing waterflood projects, where there are no basic core data to determine VDpVDpcoefficient can be grossly estimated based on flood performance history (ICF and BEG, 1988). The methodology involves the following steps: (1) Use Eq. 5-34 to determine the volumetric sweep efficiency of the reservoir. (2) Use Eq. 5-22 to provide an estimation of the areal sweep efficiency of the reservoir. (3) Use Eq. 5-21 to determine E h. (4) By using Eqs. 5-31, 5-32 and 5-33, a value for VDpcan be determined. u
Areal sweep efficiency (H). Fassihi's correlation (Table 5-VI) excludes the effect of lateral reservoir heterogeneity. ICF and BEG (1988) pointed out that lateral reservoir heterogeneity is defined by the variability of geologic parameters at the intrawell scale. Key geological parameters include matrix porosity, effective permeability, and pay discontinuity. A reduction in well spacing reduces the effect of lateral heterogeneity in the carbonate reservoir by allowing more volume contact by the injection fluid. This increases the areal sweep and recovery efficiency. ICF and BEG (1988) prepared a family of curves that correlate the areal sweep efficiency to total well spacing for three different ranges of lateral heterogeneity components ( H ) (Fig. 5-36). A total of 484 reservoirs in the states of New Mexico, Oklahoma and Texas, U.S.A., were analyzed using the TORIS database. Low areal sweep efficiencies have values ranging from 1 - 4 , medium efficiencies range from 5 - 7, and high values range from 8 - 10. At large well spacings greater than 100 ac/2087 ft (40 ha; 636 m) per well, the sweep efficiency is low regardless of the H value (Fig. 536). Lateral heterogeneity at well spacings of less than 80 ac (32 ha) per well substantially influences areal sweep. Figure 5-36 illustrates that mean sweep efficiencies in reservoirs having low lateral heterogeneity components increase from about 60% to over 75% as well spacing decreases from 80 ac (32 ha) to 20 ac (8 ha) per well. Mean sweep efficiencies, however, in reservoirs having high H values increase from around 50% to only 65% in this well-spacing range. Constraints The discussion above is an illustration ofjust one approach that has been developed in order to evaluate a carbonate reservoir's potential using a geological classification
294 I
i, =I
l
I
I
I
I
I
i
I
i
i
I
I
I
I
I
0.9 : 0.8
c
0.7-
- Low H I ( I_
"'c
r. o <,,., u
0.6-
k_
LL 0.
0.5-
I1)
or)
0.4-
0.30.20.10
I 0
i
20
i
I
40
I
I
60
I
i
I
80
I
I00
I
I
120
I
I
140
I
160
Well Spacing (acres) Fig. 5-36. Effect of well spacing on the mean areal sweep values for three lateral heterogeneity classes. (Modified after ICF and BEG, 1988, fig. A-8; courtesy of the U.S. Department of Energy).
of reservoirs at the "macroscopic" scale. One drawback to any approach is the requirement for detailed knowledge of the reservoir's properties. This presents a problem: how to properly utilize measurements of reservoir properties taken at different scales? Worthington (1991) discussed the practical aspects of this problem of tying in downhole measurements to scale. Figure 5-37 presents the scale resolution in meters of downhole measurement technology used to obtain reservoir data. It is apparent from Fig. 5-37 that the downhole-measured data are at the mesoscopic scale. This is the scale of bed boundaries, stratification, and small-scale geological features usually obtained from well-log measurements. An integration of core data (microscopic/ mesoscopic scales) and well log data (mesoscopic scale) is necessary to provide a calibration of a particular well log response. Worthington (1991) pointed out that acquired high-resolution data under appropriate conditions can be used for the calibration of related data at larger scales. This problem of scale is very important in reservoir model studies. As an example, Wattenbarger et al. (1991) discussed how to obtain the optimal geologic representation scale (maximum grid size blocks) for representing permeability heterogeneity in reservoir models. Two numerical models were considered with respect to transport phenomena, such as tracer flows, in reservoirs. The first model explored the effects of changes in the scale at which permeability variations are explicitly represented (representation scale). They found that reservoir response may continue to change as the representation scale is decreased. This suggests that
295 DOWNHOLE MEASUREMENTS
I
r "" " -- "" "' -" "' " "-1
CTSCAN
I
TOOLS
. . . . .
I"" __--t
i
I
MEASUREMENTS
I
t. . . . . . .
"1
-
I I
MERCURY POROSIMETRY .........
'
|
I
I I
i
WELL LOGS
I
SEISMIC PROFILES
I
L ....
"l
L------'I I
I
[- . . . . . . . .
I I
I
IMAGE ANALYSIS
I
FORMATION TESTS
ASIN SIUDIES
I
L L . . . . . . . . . . . . . . . . . . . . .
I
l
10 -:~
10*
i
ANALYSIS CORE
_ I
I
i
J
i
SURFACE GEOPHYSICS
1
1
i
I
10 3
1
I
I 1
i
,1.
10 6
i
i
1
METRES I~
.-
-
MICROSCOPIC
--
~14~
MESOSCOPIC
r 14---- MAC ROSCOPIC -----'--~14'-------~ MEGASCOPIC
-=14-- GIGASCOPIC-.l,
Fig. 5-37. Scales of geologic property measurements expressed in terms of resolution. Downhole well measurements are emphasized. (Modified after Worthington, 1991, fig. 2; courtesy of the Academic Press, Inc.)
mixing induced by non-represented permeabilities can be represented implicitly using mixing parameters, such as dispersivity. The correlation length of the non-represented permeabilities was reduced by decreasing the representation scale. A second study demonstrated that the effects of small- and large-scale heterogeneities can be represented by a combination of explicit representation through varying gridblock permeabilities and implicit representation through effective mixing parameters. The robustness of the effective mixing parameters were best improved by reducing the representation scale while holding the averaging scale of the effective mixing parameters constant. In computer modeling, the costs associated with explicit representation demand that a geologic representation scale be as coarse as possible, while retaining model accuracy and robustness. Wattenbarger et al.' s (1991 ) work defined the optimal representation scale as the largest scale at which the effective mixing parameters are robust. Scaling problems, which influence reservoir concepts, and their impact on porosity and permeability are discussed in the section on carbonate reservoir characterization. INCREMENTAL RECOVERY TECHNOLOGY
Incremental recovery strategy addresses the problem of handling macroscopic heterogeneity in practice. The approach is to apply new drilling technology, and the application of secondary recovery techniques to primary development of reservoirs. There are three proven incremental recovery options available to assist operators in reducing well spacing, and to recover more of the potential unrecoverable mobile oil and gas in complex carbonate reservoirs during primary production. The three techniques discussed are: infill drilling, slant-horizontal-drainhole drilling, and advanced
296 fracturing. Other strategies applicable to waterflooding and EOR, such as polymer flooding, pressure maintenance programs, selective completion of new wells and existing wells, and profile modification, will not be discussed in this chapter. Infill drilling is a conventional method used to accelerate production from proven reserves and until recently was not thought of as a method by which an operator could increase amounts of recoverable reserves. There are four conditions affecting intrareservoir reserve growth: (1) new technology; (2) socio-economic factors; (3) leadership and improved decision-making by management; and (4) reservoir re-exploration. Holtz etal. (1992) pointed out that in Leonardian restricted-platform carbonate reservoirs in the Permian Basin, U.S.A., an average of only 18% of the original-oil-inplace is recovered from matured reservoirs. By using infill drilling strategy, however, the recovery efficiency in these Leonardian carbonate reservoirs tripled as reservoir development increased from 80-acre primary recovery to 10-acre secondary recovery (Holtz et al., 1992). Growth-rate potential of the remaining mobile oil is estimated to be 27%. Application of slant-horizontal-drainhole drilling in carbonates provides for development of naturally-fractured, low-permeability (tight) and heterogeneous carbonate reservoirs, and solves water-gas-coning problems. Advance fracturing, such as massive hydraulic fracturing, is used mainly to stimulate thick, low-permeability formations. Horizontal, lateral, or drainhole well technology is not a new concept. Lateral well drilling tool patents were filed in the early 1920s. Lateral holes with 20--40 ft (6-12 m) of penetration were used extensively in the 1930s, 1940s, and early 1950s to overcome wellbore damage and stimulating low-permeablility formations. This technology disappeared from general use with the development of hydraulic fracturing. A horizontal well can be thought of as being a controlled vertical fracture (Joshi, 1988a,b). Horizontal well technology for the purpose of improving oil and gas recovery had its beginning in the 1950s through independent research programs in Russia and United States. Advancements in directional drilling technology brought on by extended-reach requirements furthered horizontal drilling technology. Original applications of this technology addressed specific problems with vertical well completions, such as the coning down of gas or the pulling up of water from the base of oil zones. Horizontal wells can dramatically increase pay zone penetration, as compared to vertical wells, resulting in hundreds or even thousands of feet (meters) of exposure to the oil column. This capability was made possible by the development of reliable bit-guidance (directional) technology in the late 1970s, and the establishment of a viable service industry to support it in the field, during the 1980s. Today, the application of modified petroleum technology to horizontal wells in carbonate reservoirs is helping to overcome recovery problems related to flow heterogeneities. The induction of fractures with nitroglycerin, so as to stimulate wells, started around 1890. "Shooting a well" increased initial flows and ultimate recoveries of oil and gas by creating fractures and/or increasing the wellbore's diameter (rubble zone) in the target formation. The idea of using a fluid to create fractures in the subsurface is based on study of pressure parting in formations during squeeze cementing of wells, acid stimulation of carbonate reservoirs, and water injection during waterflood operations (Grebe and Stosser, 1935; Torrey, 1940; Yuster and Calhoun, 1945a,b). In 1947, a mixture of a gasoline-based napalm gel fracturing fluid was pumped into the Klepper
297 No. 1 well, Hugoton gas field, located in western Kansas (Howard and Fast, 1970). This well had been completed originally with an acid treatment of four Lower Permian limestone pay zones. The goals of the test were to increase the well's low deliverability, and to compare the effectiveness of the two stimulation treatments. Flow test results showed that the well's deliverability was not changed appreciably, and it was concluded that this process could not compete economically with acidizing in this particular limestone reservoir (Howard and Fast, 1970). Clark (1949) proposed the treatment which is known today as hydraulic fracturing. Advances in fracturing technology have made this process applicable in effectively stimulating heterogeneous carbonate reservoirs. The viability of each technique discussed above is considered more fully below.
Implementation and control The success of implementing incremental recovery techniques in the field relies on the following factors: (1) quality and amount of available reservoir and well data; (2) quality control procedures exercised in obtaining new information, and in executing the incremental recovery technique (Rieke and Perry, 1983); and (3) costs. Quality control is an important part of improved reservoir management decision making. The producer's commitment to obtain necessary reservoir information and testing of wells is expressed in the established test objectives (Barnum andVela, 1984). As an example, more common well test objectives include: (1) to identify, collect, and review all available reservoir and well data; (2) to establish and execute testing, data acquisition, and cost control procedures; (3) to obtain suitable fluid and rock samples for laboratory analysis; (4) to log the well(s), and analyze and interpret the logs; (5) to determine the nature of formation fluids and petrophysical properties; (6) to measure well productivity; (7) to measure reservoir pressure and temperature; (8) to analyze and model data for reservoir characterization; (9) to estimate well completion efficiency; (10) to conduct a post-mortem review of the effectiveness of the tests and to verify that test objectives were met; and (11) to prepare recommendations for planning the next test and reducing risk based on what was learned. Each of the above operational objectives must be specific, measurable, acceptable, realistic, and timely. Any objective failing one of the above criteria must be restated in order to provide an opportunity of minimizing risk and maximizing cost control (Rieke and Perry, 1983). Quality control involves not only establishment of the appropriate test and data acquisition procedures, but should also include sequencing of the required activities. This is normally documented by creating a flow chart showing a network of activities and management approvals. Rieke and Perry (1985) proposed that a microcomputer-based consultant system is a productive means by which such quality control procedures could be initiated and used in oil and gas field development and production activities.
298
Infill development ICF and BEG (1990b) stated that development drilling (infill and extension) accounted for 82% of reserve additions in the United States from 1979 through 1986. Step-out (extension) wells are used to define and hopefully to extend reservoir boundaries. The new rationale for step-out drilling strategy is to increase recoverable reserves and this has not been explored thoroughly for heterogeneous carbonate reservoirs. Application of advance exploration and reservoir engineering technology to stepout wells in mature reservoirs has lagged behind that of infill well technology. The accepted methodology used to define initial field boundaries is drilling and testing exploratory well(s), estimating the pay continuity from the data, and then validating the geologic model through performance and pressure-transient testing of selected development wells. The more information acquired, the better the estimation of the reservoir's boundaries, but costs are higher. This approach is part of the concept of reservoir re-exploration, which stimulates reserve growth through extension drilling, and the deepening and recompletion of bypassed zones in existing wells (Holtz et al., 1992). It should be noted that fluid, stratigraphic, or structural constraints existing in reservoirs create "fuzzy" boundaries and/or compartmentalization of the reservoirs. Some operators have pursued a strategy of extending the field boundaries in carbonate reservoirs, especially in reefs, by acquiring leases on surrounding properties that are thought to contain extensions of the production trend (E.B. Nuckols, 1993, personal communication).
Reserve-growth potential ICF and BEG (1990a,b,c,d,e) used the Tertiary Oil Recovery Information System (TORIS) to model and evaluate the unrecovered movable oil recovery (UMO) potential in selected carbonate and sandstone reservoirs. Regional economic assessments based on blanket and target infill drilling, polymer flooding, and profile modification treatments were conducted on a reservoir-by-reservoir basis to determine the current status of oil recovery in each zone and to describe producing zone characteristics affecting recovery. Target (strategic) infill drilling is a type of infill well development strategy. Other types are blanket infill development, and irregular placement of infill wells. Both approaches were technically and economically analyzed by ICF and BEG (1990d,e). The blanket approach assumes that internal reservoir heterogeneities trapping hydrocarbons are distributed randomly across reservoirs. Each well will intersect, on average, similar volumes of previously uncontacted mobile oil and associated gas (ICF and BEG, 1990d). Blanket pattern drilling will then progress at closer interwell distances over the extent of the reservoirs. In reality, carbonate reservoir geology is such that there are localized concentrations of unrecovered mobile oil (UMO) owing to variances in hydrocarbon accumulation and intra-reservoir traps created by heterogeneities. Target infill drilling requires a delineation of reservoir heterogeneities that control the hydrocarbon distribution so that wells can be strategically located. ICF and BEG (1990d) noted that for maximum productivity and economic success, targets with high UMO saturations must be drilled
299 at a much closer well spacing than what is acceptable in blanket drilling. Some generalized statistical results are presented based on economic comparison of two general cases: base case (blanket pattern infill drilling) and a d v a n c e case (target pattern infill drilling). Both cases are also compared by combining blanket and target infill drilling with two other recovery processes: polymer flooding and profile modification (ICF and BEG, 1990b). Both polymer injection and profile modification are used in secondary recovery operations to increase waterflood sweep efficiency in carbonate reservoirs. Profile modification reduces the volume of injected water that flows through previously-swept layers of the reservoir which possess good continuity and high permeability between wells. With respect to primary recovery operations, profile modification is used to seal water producing zones; cross-linked polymers are used to plug highly permeable zones. These two methods are effective both in previously produced reservoir compartments, and in compartments contacted by infill drilling. The presented statistical results are derived from the generated recoverable UMO reserve addition data contained in tables 3, 4, 8, and 9 of the ICF and BEG (1990b) report. A total of 484 reservoirs in Texas, Oklahoma, and New Mexico, U.S.A., were evaluated using TORIS. This analysis is presented as a prelude to studies of reserve-growth potential by infill drilling in specific carbonate reservoirs with a specific economic evaluation of the Dune Field, west Texas, U.S.A.. The term "reserve additions" used in the following two cases is interchangeable with "recovery potential". B a s e case scenario summary. This scenario gives predicted UMO recovery potentials by process and shows that for an oil price of $16 per barrel, polymer flooding contributed 11.6%, profile modification contributed 14.9%, and blanket infill drilling 73.6% to recoverable reserve additions (recovery potentials). At $20 per barrel, polymer flooding contributed 9.8%, profile modification 11.5%, and blanket infill drilling 78.7% to reserve additions. At $36 per barrel, polymer flooding contributed only 6.8%, profile modification 8.1%, and blanket infill drilling 85.1%. The economic viability of the blanket infill drilling's technological strength with respect to polymer flooding and profile modification is clearly shown by these statistics (ICF and BEG, 1990b; table 3). The next step in the analysis was to combine predicted reserve additions from blanket infill drilling, blanket infill drilling coupled with polymer flooding, and profile modification. The base case scenario showed that at an oil price of $16 per barrel, three combined processes account for 75.9%, whereas polymer flooding and profile modification contributed only 24.1% of predicted reserve additions. At a $20 per barrel oil price, three combined infill drilling processes accounted for 83.6% of the reserve additions, and at a $36 per barrel price the three combined processes contributed 87.6% (ICF and BEG, 1990b; table 4). Above $16 per barrel, blanket infill drilling projects (individual and combined) as a percentage of total projects would increase from 40--60%. These projects, however, would account for a greater percentage of the predicted reserve additions (ICF and BEG, 1990b; fig. 9). A d v a n c e case scenario summary. ICF and BEG's (1990b) advance case reserve potential study revealed that predicted UMO reserve additions by process for an oil price
300 of $16 per barrel to be: polymer flooding contributed 6.8%, profile modification contributed 4.4%, and target infill drilling contributed 89.1%. At $20 per barrel, polymer flooding contributed 3.8%, profile modification contributed 3.7%, and infill drilling contributed 92.5% to reserve additions. At $36, polymer flooding contributed 2.9%, profile modification contributed 3.1%, and target infill drilling contributed 94% (ICF and BEG, 1990b; table 8). Technological superiority of target infill drilling over blanket infill drilling (even when combined with other processes) is apparent at a $16 per barrel oil price. At $16 blanket infill drilling contributed 73.6% and blanket infill drilling combined with the two other processes contributed 83.6%, versus target infill drilling contribution of 89.1% to reserve additions. The disparity between target infill drilling and blanket infill drilling becomes even larger when the results of target infill drilling are combined with the other two processes: target infill drilling with polymer flooding, and target infill drilling and profile modification. This advance-case scenario shows that at a $16 oil price the three combined processes accounted for 90.6% of predicted reserve additions, whereas polymer flooding and profile modification contributed only 9.4% of reserve additions. At $20 per barrel, the three combined target infill drilling processes accounted for 93.4% of reserve additions, and at $36 per barrel, the three combined processes contributed 95% (ICF and BEG, 1990b; table 9). The current barrier to achieving high estimated recovery potentials in practice is knowledge of how and where to apply this technology to maximize per well recovery resulting from reduced well spacing.
Infill drilling activity Recently in the United States, most infill drilling attention focused on the unswept mobile oil resource in carbonate reservoirs of the Permian Basin in west Texas and southeastern New Mexico, U.S.A. (Fig. 5-38). ICF (1992) reported that 46% of all shallow-shelf carbonate reservoirs in the U.S.A. are located in this area of about 80,000 square miles (207,110 km2). Sizes of Leonardian restricted-platform carbonate reservoirs range from 160-35,000 acres (65-14,164 ha) on the Central Basin Platform of Texas and New Mexico, U.S.A. Holtz et al. (1992) stated that 84% of the 84 reservoirs studied in this play are less than 8,000 acres (3,237 ha) in size. The reservoirs have low recovery efficiencies, and occur in cyclic, interbedded carbonate and clastic sediments deposited in low-energy, semi-restricted platform environments. The depositional environments created diverse reservoir facies reflecting the mixed clastic and carbonate deposition. The facies consist of peritidal deposits of dolomites, lenticular bodies of high-energy oolite and pellet bars that accumulated on the shallow shelf, and thin zones (0.5-2-ft; 0.15-0.6-m thick) of high-energy packstones and grainstones encased in lower-permeability wackestones (see Fig. 1-23). Vertical facies changes result from variations in facies-stacking patterns caused by three orders of cyclicity, and horizontal facies changes are due to paleotopographical variations during deposition (Holtz et al., 1992). Complex postdepositional diagenetic changes are imprinted upon these sediments. It is no wonder that the resulting small-scale changes in vertical and horizontal facies patterns produce high reservoir heterogeneity and poor interwell continuity of the pay zones. Holtz et al. (1992) reported that 75% of the reservoirs are developed currently on a 40-acre (16-ha) well spacing. Well spacing
Northern Montana
W M e t o nBasin /
Mloh~an Mt
Basin Central Kansas
Control Oaein
Permian Basin East Texo# South Texas Cretaceous
Smackover
O o
Fig. 5-38. Location of shallow-shelf, light-oil carbonate reservoirs in the U.S.A. Map generated from data in the TORIS database. (Modified after ICF, 1992, fig.l 1-5" courtesy of the U.S. Department of Energy.)
t~
302 averages 33 acres (13 ha) and ranges from 10--80 acres (4-32 ha); 53 reservoirs are under primary production, 31 are under waterflooding, and 1 has been abandoned (Holtz et al., 1992). The following references adequately describe the geology and infill drilling effort in the Permian Basin: Barber et al., 1983; Barbe and Schnoebelen, 1987; Laughlin et al., 1987; ICF and BEG, 1988; Wu et al., 1989; ICF and BEG, 1990 a,b,c,d,e; ICF, 1992. Another area, containing about 4% of the oil-producing, shallow-shelf carbonate reservoirs in the U.S.A., is underlain by the Ordovician/Silurian Hunton Group and the Pennsylvanian Lansing and Kansas City Groups in Kansas and Oklahoma, U.S.A. The largest natural-gas field in the contiguous 48 states (U.S.A.) is the Hugoton Field, which is located in southwestern Kansas and in portions of the "panhandles" of Oklahoma and Texas. Production is from Lower Permian Council Grove and Chase Groups containing shallow-marine carbonate rocks. Infill drilling projects in these reservoirs are described by Sorenson et al. (1987); Cottrell et al. (1988), Fetkovich et al. (1990a,b), McCoy et al. (1990), and Siemens and Ahr (1990).
Background and field examples The concept of OlStimal well spacing for oil recovery has been a controversial subject. Before 1960, ultimate recovery by primary means was considered to be independent of well spacing (Schilthius, 1936; Elkins, 1953). Muskat (1949) discussed in detail this accepted view indicating that decreasing the distance between wells would not increase physical ultimate recovery or reserves in certain types of reservoirs. Physical ultimate recovery of a reservoir denotes the maximum possible recovery for a given production mechanism, regardless of the time required or production cost. This concept is in contrast to the idea of economic ultimate recovery, which refers to the oil and/or gas that can be recovered at a profit to the time of abandonment. The latter term does not consider "noncommercial" pay zones. Muskat (1949) stated that there is actually no significant evidence that physical ultimate recoveries do vary with well spacing. This is obviously true for very "homogeneous" reservoirs. The lack of an established relationship between primary ultimate recovery and well spacing was due possibly to a deficiency in knowledge about reservoir heterogeneities. The issue of the maximum well spacing that will effectively drain oil and gas reserves needs resolution. An analytical challenge to this issue was advanced by Davis and Shepler (1969), Driscoll (1974), Ghauri et al. (1974), Stiles (1976) and Ghauri (1980). Their investigations indicated that a blanket infill drilling pattern will increase reservoir continuity and improve waterflood pattern conformance in heterogeneous carbonate reservoirs in west Texas. Davis and Shelper (1969) reported that primary oil recovery from the Sacatosa Field in Texas was increased by about 14% when well spacing was reduced from 40 acres (16 ha) to 20 acres (8 ha). Barber et al.'s (1983) analysis of production data of infill drilling in 9 fields in Texas, Oklahoma, and Illinois proved additional oil reserves, and showed that additional oil recovery was realized by improving reservoir pay continuity with increased well density. The fields studied included dolomite, limestone, and sandstone reservoirs with porosities
303
A
_
W E L L
.
_
, B.
_
Fig. 5-39. Type cross-section in the Fullerton Clear Fork reservoir, west Texas, U.S.A. The section shows the number of pay zones identified on well logs, which are continuous between the original wells A and B, and those pay zones that exist only between the infill well and wells A and B. (After Barber et al., 1983, fig. 1; reprinted with the permission of the Society of Petroleum Engineers.)
varying from 4-21%, and with average permeabilities varying from 0.65 to about 184 mD (0.00064--0.182 ~tm2) (Barber et al., 1983). Figure 5-39 is a type cross-section illustrating the concept of limited pay continuity in a Fullerton Clear Fork reservoir of west Texas, U.S.A. Pay continuity is the percentage of pay that is continuous between wells. Two important conclusions, which were brought out by Barber et al.'s (1983) study, are: (1) increased oil recovery from the 870 infill wells in the 9 fields ranged from 56-100% of their wellbore production; and (2) additional reserves totaled 60.8 million bbl (9.7 x 106 m 3) of oil based on prevailing economic conditions in the early 1980s. The application of increasing pay continuity by infill drilling in secondary recovery operations was previously discussed in this chapter. In 1983, two of the nine fields (Dorward Field and Sand Hills area in west Texas) were still on primary production. The two examples are discussed below in order to illustrate the impact of
304 infill drilling programs on increasing additional oil recovery from reservoirs near their economic limits. Dorward Field. Dorward Field is located in Scurry and Garza Counties, Texas, U.S.A. and has commingled production from the Permian San Angelo (dolomite interbedded with shale and sandstone) and the San Andres (dolomite, anhydrite and shale) formations. The average porosities are 15% and 13.5%, respectively. Average permeability is about 3 mD (0.00296 ~tm2) in both reservoirs (Barber et al., 1983). The field was discovered in 1950, and infill drilling began in 1971 when production (average of 4.8 B/D (0.8 m3/D) per well) was nearing the economic limit. One hundred and fortynine wells on 40-acre (16-ha) spacing initially were drilled to blanket the lease; an additional 123 infill wells were drilled on a 20-acre (8-ha) spacing between 1971 and 1980. Seventeen additional wells were drilled on a 10-acre (4-ha) spacing pattern by the end of 1980 (Barber et al., 1983). All the production from the infill wells is considered as increased recovery inasmuch as the initial wells were reaching their economic limit. The infill wells would provide additional recovery of 4.6 x 106 bbl (0.73 x 106 m 3) ofoil (33,000 bbl; 5,244 m 3) per well (Fig. 5-40A). The original wells on the 40-acre spacing averaged 49,400 bbl (7,850 m 3) per well. Sand Hills Field. Infill drilling in the Sand Hills area of Crane County, Texas has been concentrated in the Tubb and McKnight reservoirs. The Tubb reservoir (Permian, Lower Clear Fork Formation) at a depth of 4,250 ft (1,295 m) was developed on a 40acre (16-ha) spacing during the period between 1936 and 1941. Development of the McKnight reservoir did not begin until 1955 and it was erratic, depending largely on recompletions from the depleting dolomites in the Tubb reservoir, coupled with additional drilling and workovers (Barber et al., 1983). The McKnight reservoir produces from the Permian, lower San Andres Formation at a depth of 3,200 ft (975 m). A 40acre (16-ha) well program was initiated from 1955 to 1965. Both of these reservoirs have poor continuity owing to the lenticular nature of the producing formations. In 1979, a 20-acre (8-ha) infill drilling program was begun and 56 wells (most dualcompleted) were drilled by 1981. These 56 wells contributed 45% of total production. The strategy was to intersect the dolomitic pay stringers that were partially depleted or had not been penetrated by the initial wells. Figure 5-40B shows the performance of both the 20-acre (8-ha) infill and 40-acre (16-ha) offset wells. A substantial amount of total production was flush production from the recently-drilled wells, because 40-acre (16-ha) development continued up to the time when the 20-acre (8-ha) infill program began. Barber et al. (1983) reported that the economic ultimate recovery of 28,400 bbl (4,513 m 3) additional oil per well compares favorably with the estimated remaining 9,000 bbl (1,430 m 3) per well from the older 40-acre (16-ha) spacing. Kansas Hugoton Field Not all infill drilling scenarios have produced positive results for carbonate reservoirs. A comprehensive assessment of infill drilling in the Hugoton gas field of Kansas and Oklahoma has failed to prove that additional gas reserves are added by drilling an additional well on the allowable acreage of 640 acres (259 ha) (Fetkovich et al., 1990a,b; McCoy et al., 1990; McCoy et al., 1994). This three-phased Phillips Petro-
305 1000
m ink. o mE
800r
[
aB
o_
800
~B 8.. em
400
im u :D
.
IO-ACRE WELL8 -
eo
OB
/
w
200 INTERFERENCE 40-ACRE
WELL8
01---
1970
1975
1980
1985
1990
1995
2000
2000
: e=
iI
I 1500
B
I-
s o m im u 1000
m_ e~ lO-Acre
500
20-Acre
40-Acre
o
, ;,o
Wells
Wells
Wells A
, o,~
,.:o
, o'.,
, o'.o
,.'.~
2000
Fig. 5-40. Production graphs showing oil production from (A) The Douthit Unit, Howard-Glasscock Field, Texas, U.S.A." and (B) Sand Hills Field, McKnight reservoir, Texas, U.S.A. (Modified after Barber et al., 1983, figs. 13 and 14; courtesy of the Society of Petroleum Engineers.) leum Company study investigated the performance of about 2,177 infill-replacement wells and their companion original wells drilled in the field. The study consisted of: (1) statistical analysis of pressure and well deliverability data from the Hugoton wells in Hamilton, Kearny, Finney, Stanton, Grant, Haskell, Morton, Stevens, and Seward counties, Kansas, U.S.A. (McCoy et al., 1994);
306 (2) a review of engineering and geological data of Mesa Petroleum Co.'s 1977 five replacement well program in Kansas (Fetkovich et al. 1990b; (3) engineering performance comparison between infill wells and companion original wells using well deliverability tests and production history (McCoy, 1990); and (4) results from a reservoir model exercise using well log and core information, historical deliverability test data, and well-production history data from wells located in Texas County, Oklahoma, U.S.A. (Fetkovich et al., 1990a). The Hugoton Embayment, which cuts across southwestern Kansas and the Texas and Oklahoma Panhandles, contains two carbonate gas-producing Lower Permian carbonates: the Council Grove Group, and the major gas reservoirs in the Chase Group. Siemens and Ahr (1990) stated that the Lower Permian section reflects cyclic sedimentation here. The rocks are composed of successive cycles of laterally continuous and mappable (based on well-log signatures), shallow marine carbonates and interlayered shaly units. The Chase Group is subdivided into interbedded limestones and shales, with dolomitic limestones and shales at the top. The shales act as barriers to vertical flow between the carbonate reservoirs as indicated by flowmeter data from the five replacement wells (McCoy et al., 1990). Dolomitization produced an intercrystalline pore system that created good areal continuity of reservoir porosity and permeability within each of the dolomitized carbonate intervals (Fetkovich et al., 1990a). Clausing (1985) illustrated the lateral continuity of the reservoir layers and shaly barrier units across the Kansas Hugoton Field using north--south and east-west geological cross-sections based on characteristic and recognizable well-log signatures. Additional evidence of good lateral communications between wells is demonstrated by similar well pressures in the newly-drilled infill wells and in the original wells (Siemens and Ahr, 1990). A multiwell, no gas-crossflow, three-dimensional gas reservoir model was developed by Fetkovich et al. (1990a) to evaluate the layered carbonate reservoirs through history-matching and forecasting reservoir performance. The model simulated surface shut-in and flowing pressures from actual tests to history-match 40 years of official annual shut-in and deliverability test data. The shut-in wellhead pressure reflects the pressure of the lowest pressure zone open to the wellbore. Fetkovich et al. (1988) demonstrated that commingled shut-in pressures in a twolayer, no-crossflow system followed the pressure in the more permeable layer assuming equal skins on each layer. The cumulative production from the well reflects production from all layers, although, each layer is being depleted at a different rate. Forecast results from the model showed that no additional reserves are added with an additional well on 640 acres (259 ha). McCoy et al.'s (1990) engineering and statistical analysis of the infill and replacement well performance data confirmed that there is no evidence of additional gas-in-place. Good lateral continuity in the reservoir was evidenced by 72-hr wellhead shut-in pressures. The average shut-in pressure for the Hugoton infill wells is 148.8 psia (1.02 MPa) with a most probable value of 143.1 psia (1.00 MPa). McCoy et al.'s (1994) results showed that the average difference between initial infill and original well shut-in pressures was 17.4 psi (0.12 MPa), with an expected value of 13.0 psi (0.09 MPa). Almost 25% of the infill wells had lower initial wellhead shut-in pressure than the wellhead shut-in pressure for the original well (McCoy et al., 1990).
307 These infill wells were tapping into the existing drainage area of the original well. Only 7.1% of the infill wells had pressures 50 psi or higher than those in the companion wells. Higher deliverabilities exhibited by the majority of infill wells did not reliably indicate new gas. McCoy et al. (1994) attributed the higher deliverabilities to a combination of two factors: (1) average higher initial pressures give infill wells having equal completion efficiencies a temporarily higher deliverability; and (2) a better well completion efficiency can have a higher official deliverability. In summary, the higher pressures and deliverabilities were attributed by McCoy et al. (1994) to differences in completion efficiencies between the infill and companion wells and by the pressure gradient in the most permeable layers. Based on this study, it is apparent that there were no microscopic to megascopic reservoir heterogeneities in the Hugoton Field, which resulted in uncontacted reservoir gas.
Economic evaluation of infill drilling scenarios- Dune Field The ICF and BEG (1990b) report gave a detailed analysis of infill drilling scenarios for Section 15 of the Dune Field (Upper Permian, Grayburg Formation) in Crane County, west Texas, U.S.A. Table 5-IX and Fig. 5-41 present the predicted results of an economic analyses for several types of blanket and target infill pattern development programs before and during waterflooding in this part of the field. The methodology used to make the predictions involved modeling of incremental primary production at progressively closer well spacings using decline curves, and secondary oil recovery using a simple waterflood model. Several ICF economic models were used in this study. The engineering-based cost and field development model simulated the development of a typical pattern by linking oil recovery and well drilling with costs and timing of the infill development. This TABLE 5-IX Economic comparison between blanket and targeted infill drilling scenarios for Section 15, Dune Field located in west Texas, U.S.A. Blanket
Targeted*
Crude oil price
Minimum econ. spacing
Econ. recov. oil
Minimum econ. spacing
($/bbl)
(acres/well) (MMB)
(acres/well)
(MMB)
Grainstone
Nongrainstone
Grainstone
$10 $20 $30
40 20 20
40 20 20
Ongoing waterflood 1.0 20 2.0 10 2.0 10
$10 $20 $30
80 40 20
80 40 20
0 0.8 1.6
A~er waterflood 80 20 10
Econ. recov. oil
Nongrainstone 40 40 40
1.8 2.6 2.6
80 40* 40
0 1.5 2.1
Source" After ICF and BEG, 1990b, table 30. *Blanket infill development to 40 acres/producer, where economic, was assumed in the targeted development scenario.
308 3000 -
- 20
~~ 2ooo-
o
"6 r
r 10
~,O
.g
ooo
m
g
0
0
10
20
30
Crude Oil Price ($/Bbl) Legend:
Base Case Ongoing Waterflood Reservoir-WideOngoing Waterflood ~,~
GeologicallyTargetedOngoing Waterflood Geologically TargetedDepleted Field
Fig. 5-41. Results of an economic evaluation of Section 15 in the Dune Field, west Texas, U.S.A. using four different development scenarios. (After ICF and BEG, 1990b, fig. 31; courtesy of the U.S. Department of Energy.) model examined the economics of changes in oil recovery as a function of when infill drilling is undertaken. Three approaches were analyzed: (1) undertaking infill drilling while waterflooding; (2) undertaking infill drilling at the start of a waterflood; and (3) undertaking infill drilling in a depleted field. An ICF industry-standard financial analysis model linked oil production, investment and operating costs, and oil prices. The target infill drilling approach assumed that a detailed description of the geologic facies of the Grayburg reservoir is clearly defined.
Field geology. The Permian (Guadalupian) Grayburg Dolomite is part of a progradational cycle composed of subtidal facies in the lower part, and tidal flat deposits in the upper part (Bebout et al., 1987). Dune field is divided into five laterally
309 extensive carbonate zones bounded by siltstones. Hydrocarbons are mainly produced from porous, dolomitized crinoidal grainstones originally deposited as bars on a shallow shelf (ICF and BEG, 1990b). The grainstone facies is bounded vertically and in an updip direction by nonporous, anhydrite-cemented pisolite and mudstone facies (supratidal). As the paleoshoreline moved basinward, the latter two facies were stacked over the bars, whose trend is oriented northwest to southeast and subparallel to depositional strike, creating lenticular bands having contrasting productivity and reservoir quality. The reservoir trap results from updip and downdip porosity pinchouts owing to facies changes along the flanks of an anticlinal structure (Bebout et al., 1987).
Economic analysis. For blanket infill pattern development in an ongoing waterflood (Section 15), an economic recovery of 1 million bbl (0.16 million m3), at an oil price of $10 per barrel, is achievable by reducing well spacing from 80 to 40 acres (32 to 16 ha) (Table 5-IX). It is economically feasible to produce a total of 2 million bbl (0.32 million m 3) of oil, at $20 per barrel, by having the 40-acre spacing reduced to 20 acres per well (16 to 8 ha). ICF and BEG (1990b) report that further blanket infill drilling below a well spacing of 20 acres per well is not economically feasible at $30 per barrel. Under the target infill drilling scenario, it was assumed by ICF and BEG (1990b) that blanket infill development would take place from 80 to 40 acres (32 to 16 ha) per producer. This single reduction in well spacing has to occur before sufficiently detailed geologic delineations become available and used in target infill drilling operations. Figure 5-41 and Table 5-IX show that more UMO recovery is obtained from target infill development than from blanket development. The results conform to the results of the TORIS study discussed previously. The minimum well spacing patterns in each facies, which are economically productive under target and blanket infill drilling program, are compared in Table 5-IX. ICF and BEG (1990b) results show that at $10 per barrel, economic infill development in an ongoing waterflood in the grainstonedominant facies is feasible up to a well spacing of 20 acres (8 ha) per producer. A geologically targeted infill development program focuses on the more heterogeneous grainstone-dominant facies, allowing closer development in this facies. Table 5-IX compared this scenario to a 40 acre (16 ha) per well spacing in the non-grainstone facies assuming blanket infill drilling at 40 acres (16 ha) per well producer. An infill drilling program starting at the end of the waterflood operation is also presented in Fig. 5-41. This scenario shows that delaying infill development lowers the economic potential at all oil prices and drilling strategies considered. It is important to implement the infill drilling program early in order to increase recoverable reserves and accelerate oil recovery. In the selective reservoir-wide case (limited knowledge), where blanket infill drilling occurs at the minimum economic spacing, the differences in UMO recovery between the blanket and target drilling narrowed as the oil price increased to $30 per barrel (Fig. 5-IX). ICF and BEG (1990b) attributed this to a larger fraction of the UMO becoming economic to develop by blanket infill drilling, resulting in a smaller share of the UMO available for strategic development. Also under blanket development, as prices rise the return from the grainstone-dominant production in the Dune Field is high enough to economically support wells in the less-homogeneous non-grainstone facies, resulting in economically recovering the
310 much less-productive, non-grainstone oil resource under the blanket infill program. The non-grainstone facies would not be economic at the prices considered in Table 5IX if evaluated separately (ICF and BEG, 1990b). Consequently, the economics of the infill wells in the grainstone-dominant facies improved considerably when these wells no longer support the non-grainstone wells. ICF and BEG's (1990b) study predicted that infill wells in the grainstone-dominant facies can produce at a considerably lower cost per barrel than an average well, allowing target development at a closer spacing than possible under blanket infill drilling. Other economic model studies by Laughlin et al. (1987) and Wu et al. (1988, 1989) on the use of blanket infill drilling in connection with waterflood recovery from west Texas carbonate reservoirs showed similar results. Some additional conclusions were reached. Laughlin et al. (1987) noted that about 68% of the infill drilling incremental payout was less than two years, with an incremental discounted cash flow rate of return greater than 20%. Also, as well spacing decreased the infill drilling incremental payout decreased and the incremental cash flow rate of return increased. According to Wu et al. (1988), as well spacing decreases, waterflood recovery increases. Decreasing spacing from 40 acres (16 ha) to 20 acres (8 ha) generally gave a 14% incremental recovery of the original oil-inplace. Wu et al. (1989) showed that San Andres waterflood units, located in the Central Basin Platform and northern Delaware Basin of west Texas had a high rate of return for infill drilling projects owing to a shallower reservoir depth, and a high infill drilling recovery efficiency.
Slant-horizontal-drainhole wells At present, horizontal drilling has developed into five separate technology categories. Each is generally defined by the radius of the well's curvature required to turn the well from a vertical borehole to a horizontal one. Each of the drilling technologies has a special set of tools, techniques, and constraints. The main well categories are: (1) Long-radius well (slant [high-angle] directional) of 600 to 2000 ft (183 to 610 m) radius of curvature. Well lengths range from about 1000 ft to over 3000 ft (305 to 914 m). (2) Medium-radius well (horizontal) having radius of 200 - 500 ft (61 - 152 m). Well lengths range from 500 to about 2000 ft ( 1 5 2 - 610 m). (3) Short-radius well (drainhole) of 20 - 40 ft ( 6 - 12 m). Drainhole length ranges from 50 to over 700 ft ( 1 5 - 213 m). (4) Ultra-short radius well (drainhole) having radius of 1 - 2 ft (0.3 - 0.6 m). Drainhole length can reach 200 ft (61 m). (5) Hybrid well: combinations of the above well categories. Choice of drilling technology is based on technical considerations, economics, legal aspects, geology, location, and the nature and depth of the target reservoir. Longradius wells are normally drilled at an angle from 7 0 - 80 ~ ( 1 . 2 - 1.4 radians) rather than horizontal to reach designated targets. Medium radius drilling is the most widely used method to drill horizontal wells on land. Short-radius wells (multiple drainholes) can be drilled from a preexisting vertical well. The ultra-short radius well method is best suited to soft or unconsolidated formations with relatively low formation pressure,
311 and are drilled using proprietary water jets. A hybrid well combines the drilling technologies of different radii, such as multiple drainholes branching off a horizontal well (or at different elevations within the vertical wellbore), resulting in many configurations. Joshi (1988b) estimated the cost of drilling a horizontal well to be 1 . 2 - 2 times that of a vertical well. The drainhole costs in 1988 ranged from $130,000 to $500,000 depending upon well depth and location.
Productivity comparison of different well configurations Joshi (1988b) stated that a horizontal well can be mathematically considered as a controlled infinite-conductivity vertical fracture of limited height. A horizontal well drains an ellipsoid, whereas a conventional vertical well drains a right circular cylindrical volume resulting in different drainage volumes for the same reservoir height (Joshi, 1988a). An in-depth comparison of productivity indices (ratio of stimulated to unstimulated PI) was made by Joshi between both a horizontal well and a fractured vertical well, and a horizontal well and a slant well. Each of these technologies compete with each other. The criteria for his initial study were restricted to reservoirs having thicknesses up to 164 ft (50 m) with steady-state, single-phase flow, local fracturing experience, and costs of stimulation treatments and horizontal drilling. Joshi (1988b) used production forecasting models to describe horizontal wells in naturallyfractured and bottom-water-drive reservoirs. Well productivity measures. The following equation was used by Joshi (1988b) to evaluate steady state oil production from a horizontal well: 5.35 x 10-4 (khh p/(PBo) qh = In
Ea+a2Lj221 L/2
(5-35)
InEhJ2 2 '21 (hrw/2)
L
forL > flh, where qh is the flow rate in ma/day, fl = ~[kh/kv , k his the horizontal permeability in mD, kvis the vertical permeability in mD, h is the reservoir thickness in m, p is oil viscosity in cP, p is the pressure drop in kPa, B o is the formation volume factor in R m a / S T m 3, L is the horizontal well or fracture length in m, r w is the wellbore radius in m, and l~ is the vertical distance between the reservoir mid-height and the horizontal well location. The term a is defined as"
I
a = (L/2) 0.5 + ~/0.25 +
(2re,h/L)
4
I 0.5
,
(5-36)
where re.h is the effective wellbore radius for a horizontal well in m. In reservoirs where the vertical permeability is lower than the horizontal permeability, a decrease in kvresults in an increase in the vertical-flow resistance in horizontal wells. This, in tum, decreases the oil production rates (Joshi, 1988a). The term~lkh/k v was used by Muskat (1949) to account for reservoir anisotropy by modifying the vertical axis as z' = h'~kh/k ~ and the average permeability as ~/kh kv . The modification of the z axis
312 makes the wellbore elliptic; therefore, Eq. 5-35 accounts for reservoir anisotropy (Joshi, 1988a). Joshi (1988a) showed that for steady-state conditions an equivalent vertical wellbore diameter of a horizontal well, r e, can be formulated, assuming equal drainage volume, re,h re,v, and equal productivity indices, (q/P)h (q/P)v: =
=
re.h (L/2) rw~=
.
(5-37)
a [1 + ~1 - ( L / 2 a ) 2 l th/2r]~ 2L The following equations can be used to compare the productivity indices of horizontal and vertical wells under steady-state conditions (Joshi, 1988b):
Jh/Jv = [In (re,v/rw)]/[ln (re,h/rwe)] ,
(5-38)
for L > flh and L < 1.8re,h , where Jh is the productivity index for the horizontal well and Jv is the productivity index for the vertical well. Units for J are m3/day/kPa (or bbl/day/psi). Joshi (1988b) showed that a similar productivity index ratio expression for the pseudo-steady state, derived from Dake's (1978, p. 145) radial inflow equations for stabilized flow conditions, is based upon the pressure drop between the drainage boundary and the wellbore (p = Pe; r = re):
Jh/Jv =
In (re,v/rw) - 0.5 In (re,h/rwe) -- 0.5
9
(5-39)
Another equation can be devised from Dake's (1978) equation, where the productivity index is derived from the pressure difference between the average reservoir pressure and the wellbore pressure"
Jh/Jv =
In (re,v/rw) - 0.75 In (re,h/rwe) -- 0.75
.
(5-40)
where Eqs. 5-39 and 5-40 are also valid for L > flh and L < 1.8re,h (Joshi, 1988b). Chang and Pautz (1992) pointed out that when the viscous force of reservoir fluid is not significantly greater than the gravity force, a gravity correction factor must be included in Joshi's productivity Eq. 5-35 and other productivity index equations given in Table 5-X. To account for the gravity effect, a correction factor (Cg), must be used to correct productivity index (J) from the equations given in Table 5-X. The Chang and Pautz (1992) equation is: Jg = Cg • J ,
(5-41)
313 where Cg is defined as, C = AP/(AP-APg),
(5-42)
or
C = , g (1 + 0.433(~,) (AH)(J)/q)
(5-43)
where AP is the average reservoir pressure minus the wellbore pressure in psi, APg is defined on page 314, psi, 9/is the specific gravity of the fluid, AH is defined on page 314, ft, and q is the flow rate, bbl/D. H o r i z o n t a l versus vertical wells. A comparison of the productivity indices ratios of unstimulated horizontal and vertical wells is presented in Table 5-XI, which is based on Eq. 5-38. The data show that for steady-state flow, productivity improvements result from an increase in the length of the horizontal well and in thin reservoirs (thickness ranging from 32 to 164 ft: 1 0 - 50 m). In reservoirs having high vertical permeability, horizontal wells are more effective producers than vertical wells under the same conditions (Joshi, 1988b). Lithology and heterogeneity of the reservoirs were not considered. A horizontal well has several advantages over a fractured stimulated well. It offers an almost permanent infinite-conductive flow path, whereas a fracture-stimulated well has the problem of fracture closure with time. Mathematically, a horizontal well can be envisioned as a fracture having a height equal to the wellbore diameter with a known direction. In contrast, hydraulic fracture heights and orientations are highly variable and their magnitudes from a practical viewpoint are for the most part unknown, although they can be estimated mathematically. These hydraulic fracturing factors introduce risks into the project that are difficult to ascertain, whereas in horizontal wells these factors are measurable. Joshi (1988b) estimated that the costs of stimulating a vertical well and of horizontal drilling could be comparable. His comparison of horizontal wells and fractured vertical wells was restricted to a horizontal length of 480 ft (146 m), and all fractures were assumed to be fully penetrating. It should be noted that most common fracture lengths range from around 66 to 131 ft ( 2 0 - 40 m), and that massive hydraulic fracturing could result in fracture half-lengths of about 787 ft (240 m). Comparisons of productivity ratios between a horizontal and vertical wells were made for an 80-acre (32-ha) drainage area by Joshi (1988b) assuming the following conditions: (1) reservoir permeability values were 0.1, 1.5, and 10 mD (0.000099, 0.00148 and 0.00987 ~tm2); (2) fracture and horizontal well lengths ranged from 66 to 1574 ft ( 2 0 - 480 m); (3) reservoir thickness ranged from 33 to 164 ft ( 1 0 - 50 m); (4) k / k h values ranged from 0.1 to 1; and (5) fracture types considered were infinite-conductivity and finite-conductivity with kfbfbeing equal to 36 (acid fracture), 70 (sand proppant), 300 (precured resin coated sand), and 1040 mD-m (Mullite- an intermediate strength manufactured proppant), where kfis the fracture conductivity in mD and bfis the fracture width in m.
314 TABLE 5-X Horizontal well productivity index equations, and nomenclature Borisov:
2rckh/laoBo
J In 4
+
(1)
In
Giger:
2 ~kL/(jaoBo)
(2)
!
L h [
(L/2re)2 L/2r
2~r.
Joshi: 0.007078khh/(iXoBo
J
in[a +ca 2-(L/2)2LI2
+
In
)
(3)
(h/2)2+ hr /2
tbr L >- h, 6 -<. h/2, and L < !.8 re.
Key: A
= = = Bo = b = CH D = F = AH = h = = J = J = k = L, L w =
Reservoir area, sq ft Half the major axis of a drainage ellipse, ft Formation volume factor of oil Reservoir width, ft Shape factor Non-darcy flow constant Kuchuk's function (table 1 of Kuchuk et al., 1988) (Depth of well b o r e ) - (Depth in the middle of pay), ft pay thickness, ft Productivity Index Gravity-corrected J value Horizontal permeability, mD Vertical permeability, mD Half the well bore length, ft Lx, Ly = Half the reservoir length and width, ft AP = (Average reservoir pressure) - (Well bore pressure), psi APg = (Hydraulic pressure at depth of well b o r e ) - (Hydraulic pressure in the middle of pay), psi a
v
315 T A B L E 5-X Continued. Babu and Odeh:
0 . 0 0 7 0 8 b k ~ ~ h k~ g
(4)
__
HV[-A/rw - 3
Bola o[in(C
Kuchuk et al.:
g
khh/70.6p o
._
F
(
L x) i ,hs
(5)
I
Yw L v Ly L
~,
L
+
L
k
~
Mutalik et al.: O.O0708kh/~toB o J
_.
In
(6)
- A +s c a +s+Dq
Mutalik et al. (modified)" O.O0708kh/laoB o J =
In
q re rw s Sca sR sz Xw, Yw 6 7
= = = = = = = = = =
-,4 +sc a +s +Dq + 1.386
Flow rate, b/d Reservoir radius, ft Well bore radius, ft Skin factor Pseudosteady-state skin factor Skin due to partial penetration Skin-related function Well bore coordinates in x and y directions, ft Vertical distance between the pay center and horizontal well location, ft Specific gravity of fluid
Source: After Chang and Pautz, 1992; reprinted with the permission of Penn Well Publ. Co.
(7)
316 TABLE 5-XI Comparison of ratios of productivity indices of unstimulated horizontal and vertical wells for an 80 acre (32 ha) well spacing, and assuming that L/2 < 0.9 (reh),rw = 0.328 ft (0.1 m), and L > h d k x Jh'Jv
L (m)
(k,/k,,) = 0.1
(kJkh)= 0.5
(k&)
h = 10 m (32.1 A) 20 50 100 120 200 300 400 480
1.37 1.98 2.18 2.83 3.55 4.22 4.76
1.15 1.76 2.35 2.54 3.19 3.91 4.61 5.17
1.29 1.88 2.46 2.65 3.29 4.01
50
-
100
120 200 300 400 480
1.43 1.61 2.22 2.88 3.50 4.00
1.35 1.95 2.15 2.80 3.51 4.19 4.73
1.53 2.14 2.33 2.99 3.71 4.39 4.94
h = 30 m (98.4 ft) 50 100 120 200 300 400 480
1.10 1.25 1.80 2.39 2.95 3.39
1.07 1.65 1.83 2.47 3.16 3.81 4.32
1.27 1.87 2.06 2.72 3.42 4.09 4.62
h=40m(131.2ft) 50
-
120 200 300 400 480
1.01 1S O 2.03 2.53
1.41 1.59 2.20 2.86 3.47 3.96
1.07
100
1.84 2.48 3.16 3.81 4.33
1.23 1.40 1.97 2.60 3.18 3.65
1.47 1.65 2.27 2.93 3.56 4.05
= 1.0
4.71
5.28
h = 20 m (65.6 ft)
h = 50 m (164.0 A) 100 120 200 300 400 480
-
2.93 -
1.27 1.75 2.20 2.56
I .65
Source: After Joshi, 1988b, table 11; reprinted with the permission of the Society of Petroleum Engineers.
317 i !
2 I
3 I
4 I
5
, 3 I
6709 I I I
;
2 i
81"/09 I II1
3 I
4 I
511789 l t t l
2
3
4
t
t
1
8
6789
i
iii
,,,
/
~.;
/v
i0 -I
8
: 10"2 I0-1
I0 0
I0 I
I0 2
I0 3
FCD Fig. 5-42. Variation in the effective wellbore radius and fracture half-length having a dimensionless fracture conductivity. (After Cinco-Ley and Samaniego, 1981, fig. 14; reprinted with the permission of the Society of Petroleum Engineers.)
Dimensionless fracture conductivities were calculated using the following equation: FCD = kfbf/(kfmXf) '
(5-44)
where kfm is formation conductivity in mD, andXf is fracture half length in m (Xf = L/2). Figure 5-42 was used to calculate the effective wellbore radius, rwe, of a fracture treatment for Fco values greater than 0.1. For FCD values less than 0.1, Joshi (1988b) used the following equation:
rwe= 0.2807
I kfbf 1 kfm ,
(5-45)
For a given formation with a given stimulation treatment, FCDdecreases as fracture length increases, implying that the incremental gain in fracture productivity declines as the fracture gets longer. Figure 5-43 is an example of Joshi's (1988b) results showing one comparison between the productivity ratios of both an unstimulated horizontal well to a stimulated vertical well, and a stimulated vertical well with respect to an unstimulated vertical well. Also included in the graph is an infinite-conductivity fracture line, which represents an idealized upper productivity improvement limit, for induced fractures. Some generalized conclusions were reached by Joshi (1988b) on the basis of his calculations. For a formation permeability of 0.1 mD (0.00001 ktm2) as shown in Fig. 5-43, the performance of horizontal wells for kv/k h > 0.5, is about 25% lower than that for a fracture having a kfbf> 700 mD-m. All fractures were assumed in his calculations
318 I
I
1
a
a
i
I
1
Formationn Permeability = O. l lmdl 4-1F~176 Thickness = 20 m J
/
lq
//
/~'_.~<~'~''~"_~..~.~.~'~~" ~/'~/
....
'
o,
f
o
L,/
~Horizontal
I t '
I
so
1
/..~-/~-~ "'" /
~ . :
>
2
I
= 300 md-m
I
,
>
,!
Fracture, k f b f = 1040 m d - m - - - ~
Infinite - Conductivity ~ Fracture
t
>
.... ~ I
=
70 m d - m
=
36
md-m
Well
I I '
go
I
I
200
2so
I
I
I
3so
,oo
I
450
500
H o r i z o n t a l Well o r Fracture L e n g t h , m
Fig. 5-43. A comparisonof productivities betweenhorizontal and stimulatedvertical wells in the 0.1-mD case. (Modified after Joshi, 1988b, fig. 6; courtesyof the Society of Petroleum Engineers.) to be fully penetrating; therefore, fracture productivities are independent of reservoir height. Horizontal well productivity depends strongly on reservoir height and the permeability ratio, kv/kh. Joshi (1988b) pointed out that if fracture lengths are about 164 ft (50 m), then all fracture treatments used will give the same productivity results for a stimulated vertical well with respect to an unstimulated vertical well. Improvement would be about 2.2 times the productivity of an unstimulated vertical well (Fig. 5-43). Further, his results revealed that for a horizontal well productivity improvement of about 3 times that ofunstimulated vertical well, horizontal well length of 656 ft (200 m) would be required in reservoirs with kv/k h values that ranged from 0.1 to 1. With respect to reservoir height, Joshi (1988b) found that horizontal wells are more effective in 33 ft (10 m) thick reservoirs than in 164 ft (50 m) thick reservoirs as was shown earlier by the data presented in Table 5-X. Figure 5-44 is an example plot showing the 5 mD (0.00493 ~tm2) case. His plots also showed that it is important to consider length limitations of fracturing and horizontal drilling in low-permeability reservoirs having formation permeabilities of less than 1 mD (0.000987 ~tm2), and in thick reservoirs. Using conventional fracturing techniques, it might be difficult to create long fracture lengths in a thick reservoir; however, using horizontal drilling it may be easy to drill long horizontal wells. Inasmuch as conventional fracture length range from 66 to 131 ft ( 2 0 - 40 m), if the maximum fracture length would be limited to 164 ft (50 m), any stimulation improvement would have to come from horizontal drilling.
319 6 1
1
I
I
._
I
I
I
1 ..
I
1
I
Formation Permeability = 5 md . . . . . . . . . k v / k h = 1.0 , Jlnfinite - ConductivltyJ , [ fracture l--q_ ~ [Horizontal W e l l ~
I
J "
2-
~_:-"Wl"
i'i~/_.-- ~ ' ~ i ' f
.- ~
=
1040
=
.................................
/"
I "~
~
.. ~ ~ . . ~ "
!
>
_,=
I
- "
=
m d - m
300
- - J
md-m
70 m d - m
-
-.-...-..--.--.-.i-
~'/~~'J
Fracture, k f b f =
36 r o d - m - - - - /
I i 0
--
o
so
,. . . .
loo
|'
''
i. . . . . .
,
-
i
. . . . .
l
lso 200 2so 500 ~so Horizontal Well or Fracture Length, m
i
(oo
"
.
4so
500
Fig. 5-44. A comparison of productivities between horizontal and stimulated vertical wells in the 5-mD case. A comparison between Figs. 5-43 and 5-44 shows that in order to reach a productivity ratio of 3, a 656 ft- (200 m)-long horizontal well with akv/kh= 1.0, or a thin 33 ft- (10 m)-pay zone with k = 5 mD and having a horizontal well length of 525 ft (160 m). (Modified after Joshi, 1988b, fig. 12; courtesy of the Society of Petroleum Engineers.)
This limit is marked in Figs. 5-43 and 5-44. It shows that in practice, longer horizontal wells may be the operational altemative to conventional stimulated wells. Costs, oil price, and local fracturing and drilling experience will determine this decision. Clearly, Joshi's (1988b) results showed that horizontal wells with a length above 656 ft (200 m) would give better productivity than conventional stimulation treatments having Xf values ranging from 66 to 164 ft (25 - 50 m), formation permeability values greater than 1 mD, and a kv/k h _>0.1. It is apparent from this study that horizontal wells are competitive with conventional stimulation treatments, especially for reservoirs having formation permeabilities greater than 1 mD (0.000987 lt.tm2). Joshi (1988b) also reported generalized results from evaluation of production forecasts for vertical and horizontal wells. Cumulative oil recovery from a horizontal well under single-phase flow conditions can be larger than from a vertical well. This is due to the larger drainage area of a horizontal well. A vertical well has a much smaller drainage area. With respect to a fractured reservoir, horizontal wells would accelerate initial production rates and improve the economics (Joshi, 1988b). In solutiorv-gas-drive reservoirs, higher recovery efficiencies associated with horizontal wells could be due to the fact that horizontal wells help gravity segregation of the produced gas.
320 704 /
. . . . . .
J 60 t
-
t. o
/ 40
.,ol o
|o
!
I~_L..._L..__I__LJ,...1.
~
9. . . .
L ....
L . J _ J
J
I
LL._
. . . .
9. . . . . .
L.__L_.L_L_LJ_.L
.._.....- ~ , "
152.4 m (500 ft) Horizontal well
t
121.9 m (400 ft
E 201
~ , -
./..
I0
JLI
Well spacing = 16.19E04 m 2 (40 acres) Initial all column thickness = 45.7 m (150 ft) Oil recovery without water coning /.~.
Vertical well
~
-
o
"""
-
0
--r
1
10
100
t
v
f
0
9
1000
Months Fig. 5-45. A comparison of cumulative oil recoveries for a conventional vertical well and two horizontal wells. (After Joshi, 1988b, fig. 18; courtesy of the Society of Petroleum Engineers.)
Segregation helps maintain reservoir pressure and this may result in a high recovery factor. Horizontal wells have a distinct advantage over vertical wells in bottom-waterdrive reservoirs by reducing water coning. Vertical wells have less reservoir contact area than horizontal wells; therefore, at the same production rates, there is a lower pressure drawdown for horizontal wells than for vertical wells. Horizontal wells are able to produce at high initial production rates, above the critical rates, without premature water coning. J0shi's (1988b) calculations showed that the reservoir oil column thickness for a horizontal well declines more rapidly than that of a vertical well, resulting in a rapid decrease in horizontal well rates when compared to those of vertical wells. Based on the premise that money is time and time is money, the higher initial oil production rates given by horizontal wells result in a higher initial recovery factor and better returns (Fig. 5-45). A word of caution: after water breakthrough in the case of a horizontal well, the water-cut will rise at a slightly faster rate than in a vertical well (Joshi, 1988b). Slant versus horizontal and vertical wells. Joshi's (1988a) study of productivity of slant (directional) vs. horizontal and vertical wells was based on the productivity equations [slant angle < 75 ~ (<1.3 rad)] ofCinco-Ley et al. (1975) and Van Der Vlis et al. (1979). A horizontal well is a special case of a directional well [slant angle is 90 ~
321 7.0
I
I 9R e s e r v o i r
I height
9 Drainage area
6.0
I
I
9IOOfl. ( 3 0 . 4 8 m
I
I
I
I
I
I eoo
I soo
I ~ooo
I ~oo
I
93 0 acres ( 1 2 . 1 4 E O 4 m t I
Horizontal - -
5.0
.--
Slant
---
4.0
3.0
.O.f~ 2.0
:0. I
Lo i - ~ - ~ ' r - ~oo 2o0
I 3o0
~
I
I
I
400
500
6o0
700
t 30.4e I
( 152.40 )
( 304.8
)
~zoo ( 365.76
)
Well length, ft. ( m } ~
30
,
4B
i
60
I
70
I
75 Well slant angle, deg.
Fig. 5-46. A comparison of slant- and horizontal-well performance in a reservoir 100 ft (30 m) thick. (After Joshi, 1988a, fig. 11" reprinted with the permission of the Society of Petroleum Engineers.)
(1.6 rad)]. The difference between these two methods is that the Van Der Vlis equation is based on effective wellbore radius of a directional well, whereas Cinco-Ley's equation considers the skin factor of a directional well. Both equations, however, show excellent agreement (Joshi, 1988a). Joshi (1988a) calculated well-productivity enhancements for reservoirs having the following conditions: (1) horizontal well lengths of 100 - 2000 ft (30 - 610 m ); (2) reservoir thickness ranging from 25 to 400 ft ( 8 - 122 m); (3) k / k h values at 0.1, 0.5, and 1; and (4) vertical-well drainage areas of 10, 20, 30, 40 and 80 acres (4, 8, 12, 16 and 32 ha). Other assumptions were that all three well scenarios have an equal drainage area, and that there is an equal reservoir contact area for slant and horizontal wells. Figures 5-46 and 5-47 show productivity comparisons of slant, horizontal, and vertical wells for 100 and 400 ft (30 and 122 m)-thick reservoirs. Joshi's results show that in a 100-ft (30-m)-thick reservoir, horizontal-well productivities are 2 - 5 times greater than those of unstimulated vertical-or slant-wells, depending on reservoir anisotropy. It was shown that a slant well, with a 6 0 - 70 ~ (1 - 1.2 radians) angle to a vertical through a pay zone, will produce oil at a rate of 2 - 3 times faster than a vertical well under similar pressure-drawdown conditions. It was stated by Joshi (1988a) that a minimum slant of 35 ~ (0.6 radians) was required to increase oil production by at least
322
4,0
m
1
9R e s e r v o i r height: = 4 0 0 ft (121.9 m I
3.5
area, . ., . . . , = -... 30 acres t =~:.~r.u,,m2 J
/
"Drainage
/
/ 3.0
_
---------
-.j
/
/
/ V o ca
/
f
Horizontal Slant
' ~ . .~, , ~ K - . - - = 1.0
~
2.5
...)
2,0
.,
I 300
f
~
... ~ ' ~
.,"J'.-.-I--'--~ 500
~
I
700
I
0.5
I
I
900
( 152.4 )
( 304.8
I
WOO
I 1300
)
I
I
I
1500 ( 457.2 )
I 1700
I 1900 ( 579.12 )
Well length, ft Ira)
30
45
60
70
75
Well slant angle, deg.
Fig. 5-47. A comparison of slant- and horizontal-well performance in a reservoir 400 ft (122 m)-thick. (After Joshi, 1988a, fig. 12; reprintedwith the permission of the Society of Petroleum Engineers.) 1.2 times that of a vertical well. In a 400 ft (122 m)-thick reservoir, however, slant wells perform better than horizontal wells if the vertical permeability is less than horizontal permeability. Chang et al. (1989) developed a well model, which was incorporated into a black oil simulator (BOAST) to make production rate predictions for vertical, horizontal, and slanted wells on a 40-acre (16-ha) well spacing. BOAST is a three-dimensional, three-phase model based on continuity equations and Darcy's expression as a momentum balance for each phase (oil, gas and water) (Fanchi et al., 1987). BOAST assumes that fluid and rock properties are single-valued functions of pressure only, and that there is no mass transfer between different phases. The model was checked against the analytical formulas of transient wellbore pressure in an infinite slab reservoir. There was good agreement between the simulation results and published pressure transient tests for both horizontal and slanted wells (Chang et al., 1989; Chang and Pautz, 1992). This is the first reported mathematical model that was validated for a slanted well simulation. Chang et al.'s (1989) results support the findings of Joshi (1988a,b) in that slanted and horizontal wells showed an advantage over vertical wells at lower formation permeability (1 mD) than at higher permeabilities greater or equal to 100 mD (0.0987 ~tm2) (Fig. 5-48). A decrease of vertical permeability reduced the production from slanted or horizontal wells simulated under the conditions given in Table 5-XII.
323
H V
-.Q .Q ql"
9Horizontal :Vertical
Well
K
Well
/
9 IOOmD H IOOrnD V
I00
!00
75
75
50
50
0
K
0
IOmD H IOmD V
25
lind
ImdV
0
500
I000 PRODUCTION
1500
25
H .=.=.....
2000
T I M E (Days)
Fig. 5-48. Cumulative oil production from vertical and horizontal wells at formation permeabilities of 1, 10 and 100 mD. (After Chang et al., 1989, fig. 16; reprinted with the permission of the Society of Petroleum Engineers.)
TABLE 5-XII Reservoir and well properties used in Chang et al.'s (1989) model for production simulation of directional wells (slanted/ horizontal/vertical) Porosity, % Permeability, mD
kx, ky k~ Formation thickness, ft Formation width/length, ft Oil formation volume factor, RB/STB Oil viscosity, cP Rock compressibility, psi -~ Formation pressure, psig Wellbore pressure, psig Well radius, ft Production time, days Well length vertical wells, ft horizontal wells, ft slanted wells, ft Slant angles, slanted wells, degrees
22 1-100
0 . 1 - ]00 50 1350 1.01 1.0 6 x 10-5 5000 4000 0.25 1830 50 5 0 - 1350 54 - 1351 2 2 - 88
Source: After Chang et al., 1989, table 6; reprinted with the permission of the Society of Petroleum Engineers)
324 Vertical permeability has a more pronounced effect on horizontal wells than on slanted wells. A slanted well having a higher slant angle (more deviation from the vertical) has a longer wellbore, and showed a higher cumulative production and earlier reduction in well production rate than a well with a smaller slant angle. Chang et al. (1989) studied the effect of eccentricity (well's position in the formation) in the model by varying the location of the horizontal well at different distances from the top and side of the reservoir. The effect of eccentricity on five years of cumulative oil production from horizontal wells having a 350 ft (93 m)-long wellbore showed that a horizontal well positioned in the middle of the reservoir produced at the highest recovery rate. A well located immediately below the middle of the formation was the next fastest producer owing to the effect of gravity. The next most productive well was situated immediately above formation's center, whereas the horizontal wellbore near the reservoir boundary produced the least (Chang et al., 1989). Horizontal versus infill wells. Giger (1983a,b) devised a replacement ratio, F R, which accounts for the different drainage areas of horizontal and vertical wells. The value o f f Rindicates the number of vertical wells required to produce at the same rate as that of a single horizontal well. The ratio assumes an equal drawdown for the horizontal and vertical wells. Giger's methods provide means by which horizontal wells can be compared to infill wells. Joshi (1988a) evaluated the influence of well spacing, reservoir thickness, and reservoir anisotropy on FR. His calculations assumed that r h = L.
I
i
i
[
I
I
I
I
I
I 9V e r t i c a l well spacing 9Reservoir
30 acres
height = I 0 0 f t
9reH =L
0
a
~
I
I
200
400
600
800
(01
( 12.t4EO4m z )
( 30.48m
)
I
I000
~q
I
I
I
1200
1400
1600
(304.81
Horizontal
. ~.o
I
1800
2000 1609.61
well lenQth, ft. (ml
Fig. 5-49. Influence of well spacing on the vertical well replacement ratio, F R. (Modified after Joshi, 1988a, fig. 7" courtesy of the Society of Petroleum Engineers.)
325 Figure 5-49 is a plot depicting F Rvalues for a 100 ft (30 m)-thick reservoir having vertical permeability equal to the horizontal permeability. A 1000 ft (305 m)-long horizontal well would replace 4.2 and 3.1 conventional vertical wells drilled on a 10 and 80 acres (4 and 32 ha) well spacing, respectively (Joshi, 1988a). The thicker the reservoir, the fewer conventional vertical wells are replaced by a horizontal well. Joshi's (1988a; fig. 8) results show that a 1000 ft (305 m)-long horizontal well would only be equivalent to 1.8 vertical wells in a 400 ft (122 m)-thick reservoir compared to 4.2 vertical wells in a 25 ft (7.6 m)-thick reservoir. With respect to reservoir anisotropy, those reservoirs having lower k / k h values show that fewer conventional vertical wells are replaced by a horizontal well. As an example from Joshi (1988a; fig. 9), a 1000 ft (305 m)-long horizontal well would only replace 2.1 vertical wells for a k / k h = 0.25; 3.1 wells for a k / k h - 0.5; and 3.3 wells for a k v / k h 1.0. The information provided in this discussion, and shown in Figs. 5-43 through 549, should help one maximize oil production by selecting between conventional vertical, stimulated vertical, slant, and horizontal wells. Horizontal wells appear to be suitable for reservoirs that are thin, show high vertical permeability, or exhibit gasand water-coning problems. Many carbonate reservoirs fit this description. There are other geologic constraints, such as multilayered reservoirs where pay zones are separated by impermeable beds, which could exclude the drilling or could require fracture stimulation of a slant/horizontal well. Slant-
horizontal-
drainhole
drilling
The application of horizontal drilling is steadily increasing worldwide. Operators are slowly applying this technology to carbonate reservoirs in several countries. Each drilled horizontal well is being tested and evaluated for its effectiveness. In the United States operators are carving out niches in horizontal plays by carefully selecting prospects, methodically planning well-site procedures, and establishing characterization of the reservoirs. A rule-of-thumb is that about 2 - 3 horizontal wells are needed to be drilled in a new area to solve localized technical and recovery problems. The focal point of the horizontal well drilling activity in the United States is the Upper Cretaceous Austin Chalk play in south Texas. There are other areas, however, that have on-going activity. The second most active play area in 1992, for example, was the Cretaceous Buda Limestone in Texas (Koen, 1992). The Buda Limestone is micritic, about 100 ft (30 m) thick, and generally with reserves that are not quite as high as from the Austin Chalk. Some other drilled carbonate targets in North America include: (1) the Cretaceous Saratoga Chalk in the Fort Jessup Field, Sabine Parish, northwestern part of Louisiana, flowing 104 bbl/day (17 m3/D) of 41.4 ~ API gravity oil and 15 Mcfd (0.42 Mm3/D) gas (Petzet, 1990); (2) the Permian Brown Dolomite in Carson County, Texas; hydraulically fractured slanted well was drilled into the bottom water zone with unsuccessful results (Petzet, 1990); (3) a horizontal well was drilled in 1990 in the Jurassic Smackover Formation, Huxford Field, Escambia County, Alabama, U.S.A. Production averaged 215 bbl/day (34 m3/D) of oil for 114 days (Petzet, 1990). The Smackover depositional environment
326 closely approximates present-day carbonate sedimentary environments in the Persian Gulf (Mancini and Benson, 1981); (4) some 200 horizontal wells were drilled in the Mississippian Madison Group (mainly carbonates) just north of the border between Saskatchewan, Canada, and North Dakota, U.S.A., producing up to 700 bbl/D (111 m3/D) oil (Lyle, 1993). These wells show dramatic improvements of as much as 13 times the production of vertical wells in the area. Lyle (1993) pointed out that as in many horizontal reservoirs that involve natural fracture systems, the wells show rapid decline after several months. Canadian operators report that their analyses indicated that more oil was being recovered in addition to the higher production rates; and (5) directional drilling into Lower Ordovician carbonates has been successful by greatly increasing the recovery of oil over vertical wells in Clinton County, south central Kentucky, U.S.A. These wells intersect fracture trends. The following is a more detailed discussion on the production results of horizontal well technology. Examples of selected carbonate reservoirs from Texas, U.S.A., Argentina, and the Middle East serve as illustrations of the application of this technology. Austin Chalk Formation. Wells in the Austin Chalk Formation present a problem owing to the extreme heterogeneity of the producing system. Upon drilling horizontal wells based on seismic data, however, producers are recovering large amounts of oil from fractured reservoirs in south Texas, U.S.A. (Kuich, 1990). The Austin Chalk produces along a trend 1 0 - 25 miles ( 1 6 - 40 km) wide and 250 miles (402 km) long from northeastem Mexico's Burro-Picachos Platform to Brazos Country, east Texas, U.S.A. The Austin Chalk in northeastem Mexico is the upper part of the Boquillas Formation, and is designated as being a source rock in this area. Zwanziger (1978) reported gas production from fractured Eagle Ford beds (lower part of the Boquillas Formation) northwest of Neuvo Laredo on the Burro-Picachos Platform. In the eastem part of Texas there is some scattered production from the Austin Chalk. The lowermost portion of the Austin Chalk supplies the majority of the oil and gas production within the entire Austin Chalk section (Poston et al., 1991). The largest producing area is the Giddings Field located in Burleson, Lee, Fayette, and Washington Counties, south Texas, U.S.A. (Fig. 5-50). The field covers about 1,200 square miles (3,107 sq km). Areally, it is one of the largest fields in the Texas Gulf Coast province. The Austin Chalk is a vertically-fractured, massive and brittle limestone containing interspersed ductile marls, and ranges in thickness from 200 to 800 ft (61 - 244 m). The rhythmically bedded chalk-marl sequences generally range from 1 to 5 ft (0.3 1.5 m) and are separated by marls ranging from 1 to 6 in. (up to 0.15 m) in thickness (Stapp, 1977). Reservoir development in the Austin Chalk is almost wholly the result of fracturing. Stapp (1977) and Poston et al. (1991) commented that the permeability of the matrix is on the order of 0.01 to 0.0001 mD (0.000001 - 0 ~m2), whereas fracture permeabilities usually range from 10 to 100 times greater. The average porosity is about 6% at the productive depths of 7,500- 9,500 ft (2286 - 2896 m) and on outcrops ranges from 30% near Dallas to 9% near Langtry, Texas, U.S.A. Vertical or near-vertical fractures in the Chalk, which trend northeast-southwest, generally parallel regional structural strike (Mexia andTalco fault zones) and have a variable density
-
327 r"--'l
......
"--
~9 , - - L" i
'
i
:
q---&
"
9
~ s,- - ' I
\
~---v
r--.-J---'-
'(" ~.
r~T
",.
v
'~
\
\
:~'~
~'./"'7..I'--
L "T'"--"3" _~ _~_~IJSTINp-~.J/'~./_~~Y "" \
|
,
o
a
.,'~~fY~
/!
9
\y/ I
iI
; FIELD i
~___
..
i!
'
!
"
GULF OF 1 MEXICO
~
i
".
9
t .... ~--.
-
;
"
,/FIE L.D~.
,,
9 \
:. . . .
~'~---II
I
4--.~-r._~X I
'-.' -
..~_-].
I
L-l---i,
,'~./
,P.
-X..
~
.J~
~.
-
L._ 9
~
:~
./
'x.,.-
----P
..:~_.'~ p ] e
q_.
N
0 v
I00 m~ i
Fig. 5-50. Location of Giddings and Pearsall Austin Chalk fields in Texas, U.S.A. (After Poston et al., 1991, fig. 1" courtesy of the U.S. Department of Energy.)
of occurrence. Typically, the natural fractures occur in swarms, where fracture spacing can be less than 1 ft (0.3 m) (Lichtenberger, 1990). Locally-occurring conjugate sets of fractures may develop in the Austin Chalk and have an effect on the ultimate recovery of oil in horizontal wells. Fractures in the Austin Chalk may or may not be fully penetrating, depending on the thickness of the marls. The determination of the
328 effective net thickness of the Austin Chalk contributing to hydrocarbon production depends on establishing the vertical extent of the fractures. If unknown, then effective net thickness for a horizontal well will have to be inferred from pressure transient tests (Lichtenberger, 1990). The development and reservoir aspects of the Giddings and Pearsall fields in south Texas (Fig. 5-50) are presented below as examples of how conjugate and single fracture systems affect flow dynamics. Horizontal wells in the two fields have different ultimate primary oil recovery responses owing to the types of fracture system creating the reservoir. Solution--gas drive is the prevailing drive mechanism.
Giddings field productivity. Kuich (1990) presented a geologic model that illustrates the developmental geology concepts of the Austin Chalk in the Giddings Field (Fig. 5-51). Based on the interpretation of seismic data and fault penetrations, most of the structural movement here apparently occurred during the Eocene. Tectonic extension of the area toward the Gulf Coast resulted in normal faulting with horsts and grabens. Seismic data indicate that near-vertical fractures are concentrated on the downthrown sides of normal faults and within the grabens. Interpretation of seismic data indicates that there are abundant, minor faults contained in only the Austin Chalk, with displacements as little as 3 0 - 100 ft ( 9 . 8 - 328 m). The larger faults cut both the upper and lower parts of the Austin Chalk (Kuich, 1990). Initial development of the Giddings Field was in the later 1970s and early 1980s
Fracture trend NE-SW ,
~
,~"
,i
S"
.~ ,.s Hori tal well, .-" .,~," "~" ~on ,." Poor produ " " cfion "Gold "~t
Tectonic extension toward Gulf Coast Geosyncline ,t
\I
i!tl
'
.
.
..
.
.
.
.
Upper
.
.
.
.
.
-
Fig. 5-51. A geologic model of fracture systems in the Austin Chalk, showing vertical wells with good and poor production, and a horizontal well intersecting a major fracture system. Conjugate micro-fractures are not shown, but are orthogonal to the NE-SW trend of the major fractures. (After Kuich, 1990, fig. 3; reprinted with the permission of the Gulf Publ. Co.)
329 using vertical wells to intersect vertical fractures. Various well-logging techniques and computer-generated interpretations involving caliper, dipmeter (multi-caliper), gamma ray, televiewer, and acoustical logs were used to detect fractures intersected by vertical wells with varying degree of success. Interpretation of electric logs did not provide an accurate evaluation of the Austin Chalk's productivity in the field (Kuich, 1990). Calcite-filled and hydrocarbon-bearing fractures could not always be adequately distinguished on the logs. Careful examination of sample cuttings could help in picking up rock chips showing fracture faces lined with calcite crystals and/or oil stains, the latter being indicative of open fractures. Owing to the spacing of major fractures, initial performance of vertical wells ranged from being highly prolific to exceptionally poor (Sheikholeslami, 1991). The prolific wells possibly were linked to only one vertical fracture system, whereas the poor wells were draining the tight matrix and not tapping unpenetrated fractures (Fig. 551). The occurrence of gas downdip of oil production, and highly variable GORs in the wells show that there is an overall lack of permeability communication within the Giddings Field (Horstmann, 1977). Major lease operators in the middle 1980s preferred to drill horizontal wells, instead of infill wells, to effectively drain the reservoir. The operational goal to be achieved by drilling horizontal wells was to intersect and produce from multiple vertical fractures. Poston et al. (1991) reported that the productivity of an individual Austin Chalk well will depend not only on the number of intersected macro- and micro-fracture systems, but also on their extent and the permeability of matrix. Sheikholeslami et al. (1991) demonstrated that there is a strong correlation between the length of a horizontal well and the producing rate ratio defined as q h / q v . Under equal pressure conditions, 500 - 2,200 ft (152 - 671 m) horizontal completions produce at rates 2.5 - 7 times higher than vertical completions (Sheikholeslami et al., 1991). Kuich (1990) and Poston et al. (1991) stated that future production and ultimate recoveries can be calculated effectively by decline curve analysis of average initial production rates. Claycomb (1983) interpreted pressure transient data from Austin Chalk vertical wells in the Giddings area. His results indicated that radial flow or linear flow due to fractures was followed by pseudoradial flow suggesting the existence of dual porosity. Lichtenberger (1990) reviewed Claycomb' s results and horizontal production data from the Giddings and Pearsall areas. The performance of the horizontal wells in the Giddings area was not always what it should have been because of pressure depletion by vertical wells. Lichtenberger's analyses suggested that there is a higher incidence of conjugate fracturing in the Giddings Field, which would improve vertical well performance through a more isotropic permeability in the horizontal plane. Claycomb's (1983) pressure transient tests supported this idea. His analysis of vertical wells showed radial or pseudoradial flow in addition to fracture signatures. Apparently, the conjugate fracture system is composed ofmicrofractures oriented normal to macro-fractures. Microfractures connect the larger fractures to each other, and act as conduits for production from matrix blocks (Poston et al. 1991). Studies of both Austin Chalk cores and outcrops show the conjugate fracture pattern; however, microfractures are not always present in cores. Flow patterns near producing Giddings Chalk wells will be governed more by the fracture geometry of the fractures intersecting the wellbore than by wellbore effects
330 (Poston et al., 1991). The flow pattern out in the reservoir is controlled by the connectivity and distribution of the natural fracture system in the rock matrix blocks and the permeability ratios of the flow regimes. Pearsall Field productivity. Lichtenberger (1990) presented pressure transient field data from horizontal wells in Pearsall Field (Fig. 5-50) together with an interpretation of the data in terms of a dual porosity model. Pressure transient well responses were different from those encountered in the Giddings Field, indicating that the fracture systems are different in the two fields. Horizontal cores taken from unfractured sections in Pearsall field indicated that the Austin Chalk matrix has negligible permeability. In the Pearsall Field area the Austin Chalk appears to contain many more smaller fractures than in the Giddings Field (Shirley, 1990). Micro-fractures appear to be important components in the producing mechanism of the chalk (Lichtenberger, 1990). Analyses of multiple buildup tests on individual wells show the same signature of wellbore storage followed by a short period of radial flow, and a good linear flow signature (Lichtenberger, 1990). Radial flow data from type curve matches and using Larsen and Hovdan's (1987) method indicated fracture permeabilities of 0 . 5 - 10 mD (0.00049- 0.00987 ~tm2). The net thicknesses drained by the horizontal wells ranged from about 100 to 350 ft ( 3 0 - 107 m) based on Lichtenberger's radial flow permeability estimates. The dual porosity model is considered to consist of a rock matrix divided into fracture-defined blocks. Fractures account for only a small fraction of total porosity, but have high permeability values. Most of the pore space is present in matrix blocks, which have low permeability. The matrix recharges the fracture system. Dual porosity is characterized by two parameters: (1) the storativity ratio, 03; and (2) the interporosity flow coefficient, ~. The equation for defining co is: ~fCf CO = ~fCf q- I~mCm '
(5-46)
where ~bfis fracture porosity, Cf is fracture wellbore storage coefficient in bbl/psi (m3/ kPa), ~bm is matrix porosity, and c m is matrix wellbore storage coefficient in bbl/psi (m3/kPa). The equation for 9~is:
)~ =
4n (n + 1)kmrw2 H2 kf
(5-47)
where n is the fracture dimensionality, k is the matrix permeability in mD (m2), r w is horizontal wellbore radius in ft (m), H is the total effective net pay thickness in ft (m), and kf is the fracture permeability in mD (m 2) (Lichtenberger, 1990). The initial production behavior of a well, using the dual porosity model concept, shows that fluid production comes out first from the fracture system. Figure 5-52 is an example from a horizontal well in Pearsall Field. As the pressure gradient between the matrix and fractures increases, recharging of the fractures will occur and a transition
331
PRESSURE p 9
Z~p
LOG or LOG
I~
I DERIVATIVE p,'
1-
LOG WELL BORE STORAGE
RADIAL FLOW
EARLY LINEAR F L O W
DOUBLE POROSITY TRANSITION
~t
LATE LNEAR FLOW
Fig. 5-52. Schematic log-log plot of the Austin Chalk pressure responses vs. closed-in time observed in horizontal wells, Pearsall Field, Texas, U.S.A. The distinct valley in the derivative curve indicates that the dual porosity recharge systems appear to be present. (After Lichtenberger, 1990, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)
period is observed where the measured pressure decline rate slows down. As the well is produced, the pressure decline rate will again increase owing to the simultaneous depletion of the fractures and the matrix. This creates a flattening in the pressure vs. time curve (Fig. 5-52). The associated valley in the derivative of the pressure data is considered to be a diagnostic feature of dual porosity behavior. Radial flow is distinguished by a shallower valley on the log-log plot of the pressure derivative versus t, whereas linear flow shows no valley at all. For Pearsall Field the dual porosity storativity ratio (co) was found by Lichtenberger to range from 0.1 to 0.01, whereas the interporosity flow coefficient (k) values ranged from 5 x 10 - 6 to 1 x 10 -8.
Argentina. Pocovi et al. (1991) reported that, in the late 1980s, 26 horizontal and drainhole wells were drilled at various locations in Argentina. Thirteen drainholes were drilled by Yacimientos Petroliferos Fiscales (YPF), the Argentine state oil company. Four of these wells were drilled in the Neuqu6n Basin carbonate reservoirs of Chihuido de la Sierra Negra and Loma de la Lata fields located in the west-central part of Argentina. The Neugu6n Basin is the second most prolific basin in the country, and major oil and gas deposits occur in Jurassic and Cretaceous formations and occasionally on top of volcanic rocks (Pucci, 1987). Major structures in the basin consist of tightly folded anticlines associated with reverse faults trending north along the Andean front. Pucci (1987) reported that, in addition to structural traps, oil has been found in stratigraphic and combination structural and stratigraphic traps. Two drainholes (YPF Nq. LLL-46q Po Hor and YPF Nq. LLL-86q Po Hor) were drilled in microfissured limestones of the Loma de la Lata Field, to test the field's
332 main oil producing horizon, the Q interval of the Lower Cretaceous Quintuco Formation. Thickness of the Q interval in well LLL-46q is 108 ft (33 m), average porosity is 6% and the formation permeability is not greater than 1 mD (0.000987 ~tm2) . The thickness of the Q interval in LLL-86q is 98 ft (30 m) (Pocovi et al., 1991). The vertical wells, from which these drainholes were drilled, showed that the Q interval was barren. Both wells proved to be unsuccessful due to either the lack of hydrocarbons or the zone being impervious. It was hoped that these drainholes would intersect hydrocarbon-bearing fractures. Such failures emphasize that future horizontal drilling in the carbonates of the area has to be carefully planned. Previously, two drainholes were drilled and are producing successfully from the low-permeable, Cretaceous Avile Sandstone (Chihuido de la Sierra Negra Field) and the tight sandstones of the Upper Jurassic Sierra Blancas Formation (Loma de la Lata Field). Middle East. In Saudi Arabia, Oman, and Abu Dhabi, horizontal wells have produced oil at rates 2 - 10 times that of offset vertical wells. The application of horizontal drilling is one method by which Saudi Aramco can increase its daily production above 8 million bbl/D. At the end of 1992, a total of 13 horizontal wells had been drilled, both onshore and offshore, into carbonates in SaudiArabia.Aalund and Rappold (1993) reported that productivity improvements in the Saudi reservoirs are due to: (1) controlling water coning and edge water influx into carbonate reservoirs having thin remaining oil columns (Ghawar F i e l d - Upper Jurassic Arab D); (2) improvement of waterflood sweep efficiency in carbonate reservoirs by having horizontal injectors and producers (Berri F i e l d - Upper Jurassic Hanifa and Hadriya reservoirs; Abqaiq F i e l d - Arab D and Hanifa reservoirs; Ghawar F i e l d - Arab D reservoir); and (3) improvement of production in thin and low-permeable sandstone and carbonate reservoirs. Horizontal drilling in Oman is extensive. Aalund and Rappold (1993) reported that some 70 horizontal wells were drilled and completed in fields of the Petroleum Development Oman (PDO) concession areas. This allowed PDO to increase its overall oil production rate without any significant increase in the number of operating rigs. The Saih Rawl Field in the central Oman, which contains undersaturated light oil in a thin oil column less than 82 ft (25 m) thick, is underlain by water that cones into the vertical wells (A1-Zarafi, 1993). The producing formation is the low-permeable, Lower to Middle Cretaceous Shuaiba (Thamama) Limestone, where oil is trapped in a flat but slightly undulating structure. In 1991, a horizontal well was drilled into the limestone resulting in an initial rate of 4,237 B/D (674 m3/D), which is about three times higher than the productivity of a vertical well. It appears that the well's performance was dictated by the oil column height, reservoir quality, and well spacing of 50 acre (20 ha). It should be noted that the well was drilled within 6 ft (2 m) of the top of reservoir (see previous discussion on the effect of horizontal well eccentricity). The Safah Field in northern Oman produces from Lower Cretaceous Shuaiba carbonates. Beydoun (1988) stated that the discovery well tested 1,650 B/D (262 m3/D) of 39 ~ API oil. The field is compartmentalized by faults and contains about 650 million bbl of oil-in-place and 54 bcf(1.53 bm 3) gas in the gas cap. Chen (1993) reported that seven horizontal wells were completed in the field, which will improve ultimate
333 recovery. The first horizontal wells came on line at 1,500- 1,800 bbl/D ( 2 3 8 - 286 m3/D) oil, which is around 5 times the rate of the vertical wells (Aalund and Rappold, 1993). Drilling cost ranged from 2.5 to 3.5 times the cost of the vertical wells (Chen, 1993). An interesting observation is that there is no direct correlation between initial well productivity index and the length of the horizontal section (Aalund and Rappold, 1993). Future horizontal wells will be placed closer to the oil-water contact owing to the presence of weak aquifer and large gas cap. A1-Muhairy and Farid (1993) reported that some 48 horizontal wells (19 onshore, 29 offshore) had been drilled in Abu Dhabi, U.A.E. The 19 onshore horizontal wells were drilled in five different fields using short, medium, and long-radius technology. Well lengths ranged from 175 ft to 2,393 ft (53 - 729 m). The discovery field (1954) of Abu Dhabi is the Bab Field. Oil and gas come from several porous limestone zones of the Lower Cretaceous Thamama Group, segregated from each other by lowpermeable lime mudstones. Bab Field was brought on line in 1964, producing 40.6 ~ API oil with 0.8% sulfur content from the B zone (Beydoun, 1988). Horizontal wells are designed in the field to recover gas from the large gas cap that occurs in the Thamama A and B zones.
Advanced fracturing treatments For a well to produce additional hydrocarbons as a result of fracturing, it must first have the oil and/or gas to produce. In addition, there must be sufficient reservoir pressure to move the oil to the induced fracture and then into the wellbore. Massive hydraulic fracturing and refracturing of wells are two advanced approaches used to recover additional oil and gas in carbonate reservoirs. These fluid-based technologies result in greater benefits than those attributed to standard formation fracturing techniques. The initial use of hydraulic fracturing was to overcome permeability heterogeneities around and near the wellbore that affected production. Hydraulic fracturing can bring various benefits to the well's ability to produce, such as: (1) increasing its productivity by creating high-flow capacity conduit(s), thereby, increasing the flow rates and flowing bottomhole pressure; (2) enlarging drainage area and flow patterns by penetrating through wellbore damage and geologic barriers, e.g., zones with low permeability and porosity; (3) stimulating reservoir flow by distributing the pressure gradient along the fracture, resulting in an increase in the pressure drop along a unit length of the fracture; (4) accelerating the recovery of oil and gas by creating a number of higherpermeability channels to the wellbore; (5) increasing the ultimate recovery of oil by penetrating isolated zones and lenses; and (6) decreasing the abandonment pressure by being able to produce more oil/gas at lower pressures. Advanced techniques were developed to extend the reach of the induced fracture(s) long distances (>50 ft: >15 m) out into the formation and overcome previous stimulations that were not up to today's standards. One problem with designing hydraulic fracturing jobs is the inability to measure accurately and cheaply the fracture's
334 height, width, length, and azimuth. Mine-back studies, where the induced fracture has been exposed, have shown that hydraulic fractures can have a high degree of tortuosity, i.e., they do not always follow a "straight" line. These induced fractures can curve back to the wellbore region by comering, are often wider at the wellbore than predicted, and can have variable heights. A fracture does not always have a consistent shape. Well logs, coupled with interpretation software, have the capability to provide logderived design values for hydraulic fracture treatments. Ameri and Rieke (1981 ) compiled a source list correlating the hydraulic fracture design parameters with the type of well logs (Table 5-XIII). Formation stimulation selection process
In Part 1 of this book, Hendrickson et al. (1992) discussed stimulation of lowpermeable carbonate reservoirs using acid fracturing. The principle behind acid fracturing is that the creation of an uneven, etched-out fracture does not allow fracture closure upon release of the fracturing pressure. No proppant is used to keep the fracture open, therefore, lowering the cost of the stimulation. Not all carbonate reservoirs, however, respond to acid stimulation. Misuse of acid treatment can be nonproductive and harmful to the well's hardware and create damage to the reservoir. A three-year fracture treatment study by the Sun E & P Company showed that there was a higher percentage of non-service company problem-fracture jobs in carbonate reservoirs (83%) than in sandstone reservoirs (67%) (Dees and Coulter, 1986). This may indicate a fluid leak-off (screen-out) problem with carbonate rocks that contain natural fractures. Inasmuch as knowledge about density of the naturally-occurring fractures in carbonate reservoirs is generally limited, this can result in highrisk fracture treatments (See Introduction Chapter in this volume). Analysis by Dees and Coulter (1986) of successful and problem jobs for carbonates and sandstones in 1985 showed that problem occurrence with deep carbonates (10,000 ft: 3048 m) was 100%. A main conclusion reached by the Sun E & P Company's in-house study is that carbonate reservoirs have a 15 - 20% higher risk than sandstone reservoirs for nonservice company job problems. These problems, whether caused by fluid loss control, fracture height containment, or other downhole factors, need to be reduced to increase success in fracture treatment of carbonate reservoirs (Dees and Coulter, 1985). The risk can be reduced by increased knowledge of the reservoir, treatment planning, instituting quality control measures, and on-the-job monitoring of fracture treatments. Criteria. Two questions are frequently asked by operators producing from carbonate reservoirs: "What is the best stimulation method for carbonate formations?", and "Under what conditions is it better to acidize, acid fracture, or hydraulic fracture?". The following guide might be useful when selecting and evaluating the type of formation treatment to be used in stimulating carbonate reservoirs (Hurst, 1961; Henrickson et al., 1992): (1) Acid fracturing is advantageous in carbonate reservoirs having a high density of naturally-occurring fractures or those not are karsted (owing to proppant drop out). (2) Proppant is used in fracturing of carbonates to create deep-penetrating fractures >100 ft (>30 m).
335 (3) Malleable proppants are used in fracturing impure, dense hard carbonates having low acid solubility, such as dolomite, with confining pressures >6,000 psi (>41.4 MPa). (4) Silica sand proppant is used in fracturing impure, dense hard carbonates having low acid solubility with confining pressures <6000 psi (<41.4 MPa). (5) Acidizing is advantageous in permeable hard carbonates having heterogeneous structures and an acid solubility >30 %, such as limestone, with high confining pressures. (6) Proppant is used in fracturing sucrosic or soft carbonates with low confining pressures.
Evaluation of results of carbonate reservoir stimulations. Black and Stubbs (1975) presented results of a study that evaluated hydraulic fracturing, acidizing, and fracture-acidizing of 25 wells in 5 fields producing from the San Andres Formation in the Permian Basin, U.S.A. (Fig. 5-53). A goal of their study was to compare formation treatments in similar types of carbonate reservoirs. Each of the selected reservoirs exhibited one or more of the three basic San Andres productive carbonate facies: reef, backreef, and lagoonal. Actual and theoretical productivity index ratios were calculated for each treatment using three methods: (1) semi-steady state conditions (McGuire and Sikora, 1960); (2) steady-state conditions (Yinsley et al., 1969); and (3) transient conditions (low-permeability reservoirs; short conductive fracture lengths) (Morse and Von Gonten, 1972). Laboratory tests indicated that permeabilities ranged from 4 to 32 mD (0.003950.03158 [.tm2), porosity ranged from 10 to 18%, and hydrochloric acid solubilities averaged about 85% for the San Andres reef cores (Black and Stubbs, 1975). The backreef facies had permeabilities ranging from <0.1 to 3 mD (<0.000098- 0.00296 lam2), porosity ranged from 4 to 10%, and hydrochloric acid solubilities averaged about 75%. The lagoonal facies had permeabilities less than 0.1 mD (<0.000098 ~m2). Fluid leak-off and spurt loss values were determined for reef and backreef cores using various fluids and fluid loss control additives, such as San Andres crude, gelled 1% KC1 water, 15 and 28% HC1 acid, highly viscous water gel, and a water external emulsion. Values obtained were used in treatment design calculations. The tests showed that for the reef rock, about 25 - 50 lb of fluid loss additive per 1000 gal (3 - 6 kg/m 3) was needed to control fluid leak-off, whereas only 25 lb of fluid loss additives per 1000 gal (6.3 kg/m 3) using gelled water or crude oil was needed for the backreef facies. Fluid leak-off for acid solutions was more severe requiring up to 5 0 - 200 lb of additive per 1000 gal ( 5 . 6 7 5 - 24.75 k g / m 3) (Black and Stubbs, 1975). Fluid loss additives are not required for the tight lagoonal facies. Acid reaction tests indicated that large amounts of fines were released with all three rock types and various acid solutions, which could cause plugging of the fractures (Black and Stubbs, 1975). The fracture flow capacity required to stimulate a formation is dependent upon formation permeability. Black and Stubbs (1975) presented three plots (Figs. 5-54, 555 and 5-56), which can be used to determine the productivity index ratio. The productivity index ratio is the productivity index of the fractured rock to the productivity index of the unfractured rock (Jfs/Ji) from relative fracture flow capacity (RCF) values. Figure 5-54 gives a comparison of fracture flow capacities for San Andres backreef
336
TABLE 5-XI11
Hydraulic fracture design parameters as derived from geophysical well logs Fracture design information obtained from basic logging tool measurements Fluid and rock quantitative data
Hole conditions or applicability BoreHole
Geological and engineering qualitative data
hole
fluid
Potential Spontaneous potential Natural earth potential SP dipmeter 3 SPs 120" apart Resistivity Short normals Laterals Guard and laterolog Induction Microlog Microlaterolog Proximity Resistivity dipmeter
Shallow zone resistivities Deep zone resistivities Moderate depth resistivities Deep zone restivities Flushed zone resistivities Flushed zone resistivities Flushed zone resistivities 3-4 shallow zone resistivities
Acoustic Velocity Wave amplitude 3-D Variable density Oscilliographs Seisviewer
Acoustic velocity Amplitude of acoustic wave Full acoustic wave display Photographs of wave train Acoustic travel time
x x
x x
x x x x x x x x x
x x x x x x x
X
x x x x x
x
x x x x x
X
X
X
x x x x x x x x x x x
X
X X
x x
X
x x
x x x
x
X
X
X
X
X
X
X
X
x x
x x x x x x
x x x x X
X X
x x x x x x x x x x x x x x x x x
x x x x x x x
x x x x x x x x x x
x x x x x x
x x x x x x x
x x x x x x x
X
X
x
x x x x x x x X x x x x
x x x x x x x x x
x x
x x x x x x x x
X
X
X
X
x
x
X
X
X X
x X X
X
X
x x
X
X
x
x
x
Seiscaliper
Acoustic travel time
X
Air gun velocity
Formation velocity
X
Noise
F r e q u e n c i e s 2 0 0 , 600,
X X
1000, 2 0 0 0 H z Nuclear Gamma ray
Natural radioactivity
Neutron
Neutron capture
x
Density
Electron density
x
Pulsed neutron
Capture cross section
x
Spectral
Gamma ray energies
Nuclear magnetism
Nuclear procession
Carbon/oxygen
C, O, Si, C a s p e c t r a
Temperature
x
X
X X
X X
X
x
x
x
X X X
X X X
X X
X X X
X X
X
x
x
x
x
X X X
X X X
X X
X X X
X X
X
x
x
x
X
X X
X
x x
x
x
x
x
x
x
x
x
x
X
X
x X
x
X
X
X X X
X
X
X X
X X
x x
X
X
X
X X
X
X
X X
X
X X X
M u d or f o r m a t i o n temperature
Chemical Salinity
Mud salinity
Hydrocarbon
H y d r o c a r b o n in m u d
x x
x
x
Mechanical Drilling depth
Drilling depths
Directional
Deviation and direction
x
inclinometer Caliper
Hole diameter - geometry
x
Photographic Borehole television
Continuous oriented
x
X X
Borehole camera
Photographs
x
X X
Source: A f t e r A m e r i a n d R i e k e , 1981, t a b l e 1" r e p r i n t e d w i t h the p e r m i s s i o n o f the S o c i e t y o f P e t r o l e u m E n g i n e e r s . * F r e s h or s a l i n e f l u i d s only. N o oil m u d s .
338 ........... ! l ! l
i~;;:;;;:
!!,!lllIlllll
!
II
I
I
Ill
--
IIII [[It
,,
.
[ ..........
.
.
.
Illllll
'
!:::::::~
i
I
II
-
II
I IIlll
[
OEBAGs LEY
I !
Z ..J
.
~*
i/' U~A ~i~
f
L~ I L""'~~
:.!, 9 9
,~
FLOYD MOTLEY ~i COTTJrE J-4,..__ ~ - ' - " " ~
HiAIJ[
I
"
~AO~IL UPt.F'rt DICKENS i KtHG
CHAVs .........j LEA
SGt~RY I F~NE-R EDDY N~LAI~
L J
/ ....... ~W. ~ x ~ o ....
i .JX.
.-
t
:~evzs
qOAeLO
./,.
REAGAN
I
"
COKE
i
i~ ~ TOM GREEN'-'~
/
JEFF DAVIS
kLCROCKETT ~l
PECOS AINS
/ /
',LI~" -
,/
j, ~. Pt~E$10O
L
BtEWSTEtZ
/ 1
i
1
!
i/
Vt~tt~t~
1
:i E1PWARD$
REPU.BUCOF MEXICO
i
FIELDS OF STUDY OTHER 8AN ANDRE$ FIELDS
Fig. 5-53. Location map of SanAndres fields in the Permian Basin, New Mexico and west Texas, U.S.A.: (1) Slaughter-Levelland Field on the Northern Platform (Cochran and Hockley counties, Texas); (2) Wasson Field on the Northern Platform (Yoakum and Gaines counties, Texas); (3) Vacuum Field in the Northwestern Shelf (Lea County, New Mexico); (4) Hobbs Field in the San Simon Channel (Lea County, New Mexico); and (5) Dune Field on the Central Basin Platform (Ector and Crane counties, Texas). (After Black and Stubbs, 1975, fig. 1; reprinted with the permission of the Society of Petroleum Engineers.)
339 c)
9
I,.--
I i I i
SAN A N D R E S CORES x Io(:-- W A S S O N FIELD I--ROCK TYPE: B A C K R E E F u_ I C L O S U R E PRESSURE" 2 0 0 0 "~
513
_ 71
PSi
-
E 40----O < 2o-n < O 10~ O ..j
=
LL 5~ 41
9
Iii E 3: D I-i 2~
(D<
'
i
.
.
.
.
/
E 1
10 2
10
10 3
SAND C O N C E N T R A T I O N ,
LB PER
I0 4
1 0 0 0 FT 2
OF PROPPED AREA
Fig. 5-54. Relation between the propped fracture flow capacity and sand concentration in the fracture for different sand sizes (Wasson Field, Yoakum and Gaines counties, west Texas, U.S.A.). (After Black and Stubbs, 1975, fig. 2" reprinted with the permission of the Society of Petroleum Engineers.)
cores using different sand sizes and concentrations, whereas Fig. 5-55 gives the acid etched fracture flow capacities without sand for two different acid solutions. Highlypermeable carbonate rocks, such as those of the San Andres reef facies, require a high fracture flow capacity in order to have a large contrast between the fracture flow capacity and the formation permeability. The permeability contrast is more significant than the length of the conductive fracture (Black and Stubbs, 1975). An example calculation of JfJJ~ ratio using data from Fig. 5-54 for the San Andres backreef facies is shown in Fig. 5-56. If there is no significant increase in Jfs/J i ratio owing to small differences in the fracture flow capacity values obtained from Fig. 5-54 using different sand concentrations, then a way to increase Jfs/Ji ratio would be to use a larger treatment volume to create a longer propped length and a larger L/r e value.An example considering 2 0 - 4 0 vs. 1 0 - 2 0 mesh sand at concentrations of 1000 lb per 1000 ft 2 (5 kg/m 2) having a ki = 1 mD (RCF = 5 and 15, respectively) gives a Jfs/Ji = 2 for both cases for L/r = 0.1 (Fig. 5-56). At L/r = 0.8, Jrs/J~ = 5 ( 2 0 - 40-mesh sand) and 5.8 (10 -20-mesh sand) showing a slight increase in the productivity of the fracture (Fig. 5-56). Table 5-XIV presents Black and Stubbs' (1975) results of San Andres treatment. Damage removal treatments using acid solution in Dune Field were successful in three wells (in the high-permeability reef facies), whereas in the backreef facies it was considered to be not successful (Table 5-XV). The general conclusion derived from Tables 5-XIV and 5-XV is that hydraulic fracturing with gelled water containing either 2 0 - 40 or 1 0 - 20 mesh sand is usually successful in stimulating San Andres wells e
e
340
,,,,,,,
"~
'
0
~
.
.
.
.._
.
.
.A
.
"'~'~.,I
. . . . . . . . . . . . .
_
w I
~
3
/
< r I,
2
-
J
,~--
SAN ANDRES CORES
--
"
WASSON FIELD ROCK TYPE: BACKREEF CLOSURE PRESSURE: 2 0 0 0 PSI
O
10
20
30
40
50
60
ACID INJECTION TIME , MINUTES
Fig. 5-55. Relation between etched fracture flow capacity and acid injection time. (After Black and Stubbs, 1975, fig. 3; reprinted with the permission of the Society of Petroleum Engineers.) producing from the backreef facies. In the low-permeability lagoonal facies, fracture treatments that give a long, moderately conductive fracture is desirable. Wells in the high-permeability- high-porosity reef facies should be stimulated using a controlled damage removal acid treatment containing a surfactant and, where required, an iron sequestering agent (Black and Stubbs, 1975). Short conductive acid fractures would also fit this requirement. A recent study by Hoover and Adams (1988) evaluated advances in fracturing techniques in San Andres dolomitic reservoirs of the Howard Glasscock Field located on the Eastern Shelf of the Permian Basin (Howard, Glasscock, Sterling and Mitchell counties, Texas, U.S.A.: Fig. 5-53). Increased fracture conductivity was required to properly implement a waterflood. The reservoir's drive mechanism is a combination drive consisting of solution-gas and water drives (small quantity of water) in the wells along the western edge of the field. Hoover and Adams (1988) discussed the application of geophysical well logging, perforating techniques, new programmable blending equipment, and computer software to increase the volume of proppants used during hydraulic fracturing of the San Andres Formation. A fracture simulator was used to design an optimum treatment program. Input data to the simulator was obtained from well logs and a test fracturing treatment. This "data frac" was performed on one of the wells to gather formation information and to determine the feasibility of using different fracturing fluids. The
341 EXAMPLE CALCULATION
Jfs > PR.ODUCTIVITYINDEXRATIO(~i_i VS RELATIVE
I L - - - - - - =,O.e
hf i = 1.0 6
dfs
RockType: Bockreef ki =0.1 mD Sond concentroltion in frocture = I000 Ib/lOOOft2 Type propp_ont used: 2 0 - 4 0 sond FC =SxlO~md-ft (From Fig. 5 - 5 4 ) W e l ~ f i ~ g = 2 0 acres re= rw= O.33feet LW=233 feet hf = I 0 0 feet hi = I 0 0 feet
CAPACITY
RCF =0.00159
hf hi
.//
X
-,
5
.=0.7 re
I'
!
L -'-0.5re
4
t.I-0.3
i i
L -13.1 -1
o
I
0.1
2
4
1.0
2
4
I0
2
4
I00
2 4
IGO0 2
4
I0000
RCF(-~i) WHERE:
Ji = PRODUCTIVITY.INDEX OF UNFRACTURED SYSTEM, bbl doy"1 psi'= Jfs = PRODUCTIVITY INDEX OF FRACTURED SYSTEM bbl day "I psi "l Jfs --= PRODUCTIVITY INDEX RATIO, FOLDS OF INCREASE di FC = Wkfl FRACTURE FLOW CAPACITY, roD-f! k i = FORMATION PERMEABILITY ( UNDAMAGED), mD hf = PROPPED FRACTURE HEIGHT, ft hi = FORMATION THICKNESS, ft r e = RADIUS OF DRAINAGE, ft r w = WELLBORE RADIUS, ft S = WELL SPACING, ACRES RCF = RELA'IIVE CAPACITY FACTOR AS IDENTIFIED ABOVE
RCF= 0.00,59 (~.i) In ( - ~ ) . V r ' ~ T RCF= O. 0 0 1 5 9 ( I ) I n ( .~-~-..).~/ Io__RCF = O. 00815 u.=~ zo ,c o~oo,,sxsx,o 3 " "= o., CCF= ~-~T'I RCF = 4 0 8 t. =Z_~ = 0 . 5 re FC L If RCF ( ~ . 1 : 4 0 8 ond T~.e= O. 5 ,
then Jfs = 4.3 fol d increose. Ji In the obove example if L were only 47 feet: _k. 4_1. : 0 . 1 r e 4tS then: Jfs = 2 . 0 fold increase
RCF (-~;) = RELATIVE CAPACITY L = CONDUCTIVE FRACTURE LENGTH, fl
Fig. 5-56. Productivity index ratio (Jfs/J~) values cross-plotted against the relative capacity (FC/ki) show the importance of long conductive fracture lengths in low-permeable carbonate rocks, such as those of the San Andres Formation backreef facies. (After Black and Stubbs, 1975, fig. 4; reprinted with the permission of the Society of Petroleum Engineers.)
fracture treatments were executed by using programmable blending equipment to accurately schedule and place the proppants. The equipment made it possible to schedule higher sand concentrations of larger mesh sizes in significantly smaller fluid volumes. Coupled with measured reservoir stress values, fracture heights could be effectively predicted, resulting in creation of controlled fracture heights. A perforating procedure was developed to ensure the desired friction pressure drop. Prior to fracturing, all perforations were acidized using 100 gal (0.4 m 3) of 15% HC1 (cationic corrosion inhibitor, nonionic non-emulsifying agent, and iron stabilizer) per perforation to insure that the perforations are open and able to accept fracturing fluids. The average treating breakdown pressure was 1,300 psi (9 MPa) and the
342 TABLE 5-XIV A comparison of actual vs. theoretical productivity index ratios as calculated by the McGuire and Sikora (1960), Tinsely et al. (1969), and Morse and Von Gonton (1972) methods for wells in five San Andres fields, Permian Basin, U.S.A. The wells are designated as A through X (first letter) and the five fields are designated as: C = Vacuum, D = Dune, H = Hobbs, S = Slaughter-Levelland, and W = Wasson (second letter). Assumed radius of drainage is 466 ft (142 m) and well spacing is 20 acres (8 ha) Conductive fracture length, ft
Productivity index ratio
Well rock type
Treatment Vol., Gal.
AW (75% B, 25% R) k = 2.98 mD
22,500 (GW, sand-out)
406
8.3 - 1.0 (64 days)
BW (B) k = 2.98 mD
27,500; GWV
221
CC (B) k = 2.98 mD
20,000; GW
DC (B) k = 2.98 mD
Actual*
Tinsley
Morset
9.0
2.1
9.2 (8 days)
2.8 (1 day)
6.6
3.7
6.3 (8 days)
861
2.4 - 2.2 (1 yr)
8.1
2.1
9.7 (8 days)
20,000; GW
497
3 . 6 - 1.8 (1 yr)
8.0
2.0
9.7 (8 days)
EC (B) k = 0.33 mD
20,000; GW
625
11.4 - 3.9 (3 yrs)
12.4
3.7
9.7 (64 days)
FC (B) k - 0.4 mD
5,250 (20% HC1; 10,500 PF)
38
2 . 1 - 1.4 (1 yr)
1.5
1.8
2.3 (32 days)
GD (B) k - 0.3 mD
5,000 (20% HC1, FSA; 5,000 PF)
112
3 . 0 - 1.4 (4 mo)
4.2
3.1
4.0 (64 days)
KH (B) k=3mD
2,500 (15% HCI, FSA)
30
2.0 (1 day)
1.5
1.6
2.1 (8 days)
MD (B, L) k - 0.11 mD
10,000 (20% HC1, FSA)
8
10.4- 1.0 (1 mo)
1.7
1.1
1.3 (128 days)
NW (50% B; 50% R) k = 0.33 mD
33.000; GW
798
12.7
3.2
9.7 (64 days)
OS (R) k - 11 mD
5,250 (15% HC1, 10,500 PF) 8,000 (15% HE1, FSA)$
29
3.0 - 1.3 (1.5 yrs)
2.1
1.5
2.0 (4 days)
28
2.6 - 1.7 (2.5 yrs)
1.9
1.5
2.0 (4 days)
3.7 - 6.4 (1.5 yrs. FR)
McGuire
343
Well rock type
Treatment Vol., Gal.
Conductive fracture length, ft
PW (50% B, 50% R) k = 5 . 5 mD
22,000; GW
597
QW
7,200
14
Productivity index ratio Actual*
McGuire
Tinsley
Morse# 10.0 (4 days)
8 . 7 - 5.8 (5 mo)
6.7
1.4
1.2 - 0 . 8
1.2
1.3
(4.5 mo)
1.5
(50% B, 50% R) k = 7 mD
(15% HC1, FSA, Matrix Acid)
(4 days)
RD (B, L) k = 0 . 3 mD
43,000; Emulsion
511
1 4 - 1.2 (3.6 mo)
12.6
3.9
9.7 (64 days)
SW (B) k = 0.1 mD
20,000; GW
595
2 . 9 - 5.1 (4 yrs 11 mo, FR @ 2 yrs 3 mo)
13.4
3.7
10.1 (128 days)
TC (B) k = 0 . 3 mD
20,000; GW
968
5.4 (1 day)
12.6
4.2
9.7 (64 days)
UW (B) k = 0 . 3 mD
20,000; GW
758
6 . 0 - 3.0 (5 mo)
12.6
3.1
9.7 (64 days)
VS (50% B, 50% R) k=2mD
8,000 15% HC1, FSA)
65
10.1 - 3.9 (1.5 yrs)
3.3
2.0
3.1 (8 days)
WS (50% B, 50% R) k = 2 . 1 mD
6,000 (15% HC1)
68
4.3-2.9 (1.5 yrs)
3.3
2.1
3.1 (16 days)
XC (B) k = 0.4 mD
5,250 (20% HC1; 8,250 PF) WO; IP
180
3.1 - 1.4 (2 yrs)
2.8
5.3 (32 days)
7.1
Source: Modified after Black and Stubbs, 1975, table 4; courtesy of the Society of Petroleum Engineers.
* Time to reach the final productivity index ratio shown. t Approximate time shown to reach steady-state flow conditions and productivity index ratio shown. :l: Retreatment 1.5 years after first treatment. GW: Gelled water GWV: Gelled water, viscous B: Backreef rock type R: Reef rock type L: Lagoon rock type PF: Pre-flush for acid treatment FSA: Fines suspension additive, acid FR: Flood response WO: Workover IP: Installed pump
344 TABLE 5-XV Evaluation of acid damage removal treatments in the San Andres Formation, Dune Field, Permian Basin, Texas, U.S.A. Well and treatment type
Volume, gal
Zone thickness, ft Gross Net
Production, B/D Before After
Rock type: Reef (Dune Field) HD 15% HCI acid, Fe additive*
2000
135
8
ID 15% HCI acid Fe additive* JD 15% HCI acid, Fe additive*
2000
140
20
45 (oil)
836 (oil)
1000
125
11
30 (oil)
867 (oil)
GD 20% HC1 suspension type acid (6.5 BPM)
5000
9.1 (oil) 3.9 (water)
7.2 (oil) 10.8 (water)
0
1016 (oil)
Rock type: Backreef (Dune Field) 51
Unknown
Source: Modified after Black and Stubbs, 1975, table 1; courtesy of the Society of Petroleum Engineers. * Iron sequestering agent.
average instant shut-in pressure ranged from 600 to 800 psi ( 4 - 5.5 MPa) (Hoover and Adams, 1988). A 1 2 - 20-mesh Texas brown sand was used to obtain adequate fracture permeability and have the required closure stress resistance. Sand volumes in the treated wells ranged from 59,000 to 109,100 gal ( 2 2 3 - 4 1 3 m3). The fracturing fluid composition consisted of: 2% KCl-based fresh water, 30 lb of hydroxypropyl guar gum gelling agent per thousand gallons of fluid, borate crosslinker, fluoro-surfactant, quaternary ammonium chloride bactericide, external oxidizer breaker, and an oil-soluble resin to control fluid loss. Table 5-XVI presents treatment parameters and fracture height data obtained from a three-stage data frac used to test the performance of several fracturing fluids. Gamma ray logging results using radioisotopes showed that all the treatments stayed within the predicted perforated interval of 182 ft (55 m). The pump schedule used on the test well was designed to give a fracture extension of about 140 ft (43 m). This distance is less than half of the attributed drainage radius for the well's spacing (Hoover and Adams, 1988).
Massive hydraulic fracturing One fracture treatment that shows promise of recovering gas and oil from lowpermeable carbonates is massive hydraulic fracturing (MHF). A conventional hydraulic fracturing job is considered by industry to be one that takes up to 100,000 gal (379 m 3) of fluid and up to 75,000 lb (34,020 kg) of proppant. The primary difference between a conventional hydraulic fracture and a massive hydraulic fracture treatments is the size of treatment. A massive hydraulic fracture treatment involves the use of up to 1,000,000 gal (3,785 m 3) of fluid and up to several million
345 TABLE 5-XVI Data from a San Andres Formation three-stage fracture treatment test evaluating one non-crosslinked and two crosslinked fluids, Howard Glasscock Field, Howard County, west Texas, U.S.A. Impregnated beads (1 millicurie of Iridium 192 per thousand gallons of fluid) were used to tag the stages for the gamma-ray log determination of fracture height
Pump rate, bpm Surface pressure, psi Bottomhole pressure, psi Perforated interval, ft Gross height (predicted), ft Net height, ft Logged fractured height, ft A. Temperature, log B. Gamma ray, log Polymer loading, ppt Crosslinked (Y/N)
Stage A
Stage B
Stage C
10 1370 1870 151 182 151
40 1915 2440 151 182 151
40 2044 2489 151 182 151
176 150 10 N
193 159 50 Y
154 159 80 Y
Source: After Hoover and Adams, 1988, table 2; reprinted with the permission of the Society of Petroleum Engineers).
pounds of sand proppant. MHF treatments are designed to create fractures that extend 500 - 2,000 ft (150 - 610 m) or more from the wellbore. The term "minimassive fracture treatment" refers to the collective use of several hydraulic fracturing techniques, such as gelled water, high amounts of 100-mesh sand in the pad fluid to control leak off, high proppant concentration as is operationally feasible ( 5 - 10 lb/ gal: 5 9 9 - 3356 kg/m3), and a quick bleed-back of the well as soon as possible (Crow, 1977). Mini-massive fracture treatment. The first mini-massive fracture job was completed in June, 1976, in the Mississippian Salem Limestone, Gibson County, southwestern Indiana, U.S.A. This reservoir has an average permeability of 0.42 mD (0.00041 pm 2) and an average porosity of 7.3% (Crow, 1977). Previous treatments on a well involved large acid jobs, and large water-base, oil-base, acid-base and viscous gel fracture treatments, which did not decrease the operator's ten year payout time. The formation was fractured with 20,000 gal (76 m 3) of gelled water (30 cP viscosity), 9,000 lb (4,082 kg) of 100 mesh sand, and 77,000 lb (34,927 kg) of 2 0 - 40 mesh sand. Injection rate was 15 bpm (2.4 ma/min) and sand concentrations ranged up to 8 lb/gal (959 kg/m 3) (Crow, 1977). The well paid out in 35 days. Another Salem Limestone well in Gibson County, Indiana, U.S.A., which had initially undergone acid fracture treatment with 31,000 lb (14,062 kg) of sand, and later acidized with 1,500 gal (5.7 m 3) of 15% HC1, did not respond to these treatments. A mini-massive treatment was performed using 30,000 gal (114 m 3) of gelled water, 20,000 lb (9,072 kg) of 100-mesh sand, 58,000 lb (26,309 kg) of 2 0 - 40-mesh sand, and 5,000 lb (2,268 kg) of 1 0 - 20 mesh sand. The well, which was producing at about 3 bbl/D (0.5 m3/D), responded with a production of 768 bbl/D (122 m3/D), declining to 90 bbl/D (14 m3/D) after 120 days (Crow, 1977).
346 The success of the fracture treatment in the above two examples is thought by Crow (1977) to be due to the prevention of premature screenouts in the very lowpermeable carbonates, and the ability to create the proper fracture penetration into the formation. Crow (1977) based his conclusions on the principle of dilatancy in rock failure: as the rock approaches its breaking (fracture) point, a myriad of tiny fractures form (Brace, 1972). All subsurface formations are under triaxial load conditions, which consist of the overburden stress and two additional horizontal stresses. Under these conditions, when a pressure is applied from within a rock, the rock will fracture in a plane perpendicular to the least amount of stress on the formation. The stresses control fracture directions and determine whether fracture planes are horizontal, vertical, or inclined. Before rupturing, tiny cracks will form and dilatancy will continue to occur along the leading edge of the fracture as it progresses outward into the formation. This explains the response failure of the previous treatments in the two Salem Limestone wells. Crow (1977) suggested the following sequence of steps in applying the mini-massive fracture procedure: Step 1: Pump a pad fluid containing 100-mesh sand (diameter: 0.0059 in.; 0.015 cm), which will enter into the tiny thief cracks and bridge the openings, thereby reducing fluid loss. This prevents premature screenouts that would prohibit the hydraulic fracture to penetrate a proper distance into the formation. Step 2: Use a viscous fracturing fluid, which will control the leakoff into the carbonate matrix. Step 3: Use as high a proppant concentration as is operationally feasible to fill the entire fracture height. A properly designed and controlled injection rate will keep the fracture within the desired interval so that the desired fracture length out into the formation can be achieved. Step 4: Bleed the well back and as fast as practical so that the fracture will close and trap the proppant while it is still suspended inthe fluid.
Massive hydraulic fracture program. The objective of this analysis was to evaluate a massive fracture stimulation program recovering natural gas from deep ( 11,000 ft: 3353 m), naturally-fractured, low-permeable gas-bearing carbonate rocks (Kozik et al., 1980, 1981). Under the sponsorship of the U.S. Department of Energy and the Mitchell Energy Corporation, two massive hydraulic fracturing tests in the Jurassic Haynesville Limestone (Cotton Valley Group), Limestone County, east Texas, U.S.A., were studied in detail to determine well spacing and fracture length radius necessary for optimum development of the Fallon and North Personville fields. The Haynesville Limestone is the lower member of the Cotton Valley Group, which covers more than 250,000 square miles (6.47 million km 2) in east Texas, western Louisiana, and southeast Arkansas (Kozik et al., 1980). The Haynesville Limestone ranges in thickness from 300 to 500 ft (91 - 152 m) and is massive, oolitic to pisolitic, and finely crystalline to micritic. Porosity ranges from 2 to 14% in the oolitic zones, whereas matrix permeability ranges from around 0.003 to 0.7 mD (0.000003 -0.00069 ~tmZ). The measured trend of naturally-occurring fractures from cores in the Muse-Duke No. 1 well is NW-SE (strike between 280 ~ and 320~ Effective and relative permeabilities to nitrogen gas were measured in the
347 1.0
i
'~ "\
MEC:
i
COTTON RELATIVE
O)
4) 1 1 3 0 2
i n
0,8
--
0.6
--
0.4
--
0.2
--
lll l
MUSE-DUKE
VALLEY
WELL
§
LIMESTONE
PERMEABILITY
VS.S
w
FT.
(n (.g o I->. I-.J .....
m
W CE
a. W ~ m
I-I
\ \ \ 0
_ 0
I 20
I 40
I 60
WATER SATURATION
I, 80
100
(Sw), %
Fig. 5-57. Variation in the relative permeability to gas with increasing water saturation in two Cotton Valley Limestone core samples from the Muse-Duke well No. 1; both cores show a similar trend. The relative permeability to gas is virtually unaffected by the presence of water up to 20% S . When S w is about 85%, relative permeability to gas approaches zero. (After Kozik et al., 1980, fig. 5; courtesy of the U.S. Department of Energy.)
laboratory at a reservoir temperature of 285 ~ F (141 o C) and at various water saturations (Fig. 5-57). Initial production rates, using standard 1970s stimulation technology, were moderately good (1 - 4 MMCF/D: 0 . 0 3 - 0.11 MMm3/D) in the Haynesville Limestone. Five of the first six wells completed received light acid stimulations and began to produce at about 1 MMCF/D per well and soon declined to 0 . 2 - 0.3 MMCF/D (0.006 - 0 . 0 0 8 MMm3/D). The Burleson No. 1 well received a hydraulic fracture treatment of 48,000 gal (182 m 3) of gelled water and 178,000 lb (80,741 kg) of sand. Initial production was 4.4 MMCF/D (0.125 MMm3/D), but declined to 0.5 MMCF/D (0.014 MMm3/D) in two years. The natural fracture system was not sufficient to maintain initial flow rates. The Muse No. 1 was the first well to receive the MHF treatment. As was the case in the mini-massive fracture stimulations, 100-mesh sand (48,000 lb: 21,773 kg) was
348 pumped ahead of the 2 0 - 4-mesh sand to control fluid loss. A total of 340,000 gal (1,287 m 3) of gelled water and 450,000 lb (204,120 kg) of 2 0 - 40-mesh sand was pumped (Kozik et al., 1980), resulting in an initial production rate in excess of 4 MMCF/D (0.113 MMm3/D) that declined to 1.1 MMCF/D (0.031 MMm3/D) after 28 months. A larger, or so called "super-massive hydraulic fracture stimulation treatment" was performed on the Muse-Duke No. 1 well following an acid stimulation of the well. This treatment consisted of using 95,000 gal (360 m 3) of treated-water prepad containing 10 lb/gal salt water; no 100-mesh sand was pumped. A total of 842,850 gal (3,190 m 3) of gelled water (Versagel) containing 2,800,000 lb (1,270,080 kg) of 2 0 - 40-mesh sand was displaced into the limestone. Initial production after fracturing was 6 MMCF/D (0.17 MMm3/D), which declined to 2.1 MMCF/D (0.06 MMm3/D) after 22 months. By 1980, four other wells were fractured using sand volumes ranging from 450,000 to 1,000,000 lb (204,120-453,600 kg). Kozik et al. (1980) reported that initial production rates indicate performance similar to the Muse No. 1 well. Figure 5-58 presents a comparison of the performance curves for the Muse No. 1, Muse-Duke No. 1, Burleson No. 1, and three best acidized wells (11year production history). 10,000-.. g,O00-~ e,O00|
FALLON
7,000~
AND NORTH PERSONVILLE LIMESTONE CO.. TEXAS 2-1-80
FIELDS
9. , o o
s,ooo ! 4,ooo !
_..use-ouKt., ...s,v.
F..c,
. -= ,.0o0 r =E 1=
1,000. 900 800 700
URLESON ,F, 1 IONAL FRAC)
6O0
500 400 300
AVERAGE OF 3 WELLS (NOT FRACED)
200
100
I
.1
9
I 1
CUMULATIVE
i
I 2
PRODUCTION
ii
i
i
I 3
(BILLION
CU. FT.)
Fig. 5-58. A comparisonbetweendaily flow rates and cumulativeproduction for massive fracture stimulation, conventional fracture treatment, and non-fracturedwells in the Cotton Valley Lime (Haynesville Limestone). (After Kozik et al., 1980, fig. 7; courtesy of the U.S. Departmentof Energy.)
349 Reservoir simulation studies of the Muse No. 1 and Muse-Duke No. 1 wells consisted of varying formation permeability, fracture length, and fracture conductivity to match well performance and assess the sensitivity of costs (Kozik et al., 1980). Unfortunately, a unique history match was not obtained for the Muse No. 1 well owing to insufficient pressure buildup data. Definitive fracture half-length could be not determined for this well. A fracture half-length of 1500 ft (457 m) was determined for the Muse-Duke No. 1 well. From the reservoir simulation history matching analysis of these two wells, the formation gas permeability ranges from 0.01 to 0.04 mD (0.00001 - 0 . 0 0 0 0 3 9 ~m2). A computer model FRACOP (Holditch et al., 1978) was used to determine optimum fracture length and well spacing for a well similar to the Muse No. 1 and the MuseDuke No. 1. The model uses reservoir and well parameters, and fracture length values, to generate a production function, which is used to determine net cash flow and net present value for any specified discount rate. Results are presented in Fig. 5-59, which shows ultimate gas recovery as a function of permeability, fracture length, and drainage area (well spacing). At a 160-acre (65-ha) spacing, increase in the fracture halflength from 250 ft to 1250+ ft ( 7 6 - 381 + m) does not have a significant influence on 30-year ultimate recovery (Kozik et al., 1980). The effect of higher permeability values ...
,,
I
I
I
i
I
12
.I .I W
K -- O , 0 4 m d
~1o
640a0.
u_ U m
8
E
J
K :
O.01md
640ec.
Is 8
-
0 lU
W m
~
0
K-~ 0 . 0 1 ,
:12011r
4 8r
0
K ~ 0.01
I
,,
800 PROPPED
,
160at,
I
I
1000
1800
FRACTURE
LENQTH
,
I
2000
,,
2800
(FT.)
Fig. 5-59. The effect of permeability upon 30-year ultimate gas recovery per well as a function of fracture half-length. Ultimate recovery increases as permeability, fracture length, and well spacing increase. Higher permeability values, however, have a pronounced effect as the drainage area increases. Results are based on a FRACOP model study using Haynesville Limestone reservoir parameters and economic costs from the Muse No. 1 and Muse-Duke No. 1 wells. (After Kozik et al., 1980, fig. 19; courtesy of the U.S. Department of Energy.)
350 becomes more pronounced as the drainage area increases. This suggests that the best well spacing would be 4 wells per section (one sq. mile = 640 ac = 259 ha), inasmuch as this well density results in a maximum recovery efficiency. Kozik et al. (1980) stated that to properly optimize well spacing and fracture length from an economic viewpoint, the maximum discounted present value profit for each case must be determined. Figures 5-60 and 5-61 show the 10% profit per section for permeabilities of 0.01 and 0.04 mD (0.00001 -0.00039 ~tm2), respectively. Table 5XVII lists the economic parameters and fracturing costs used in the study. The optimum well spacing for these conditions is 320 acres (129 ha), and the propped fracture half-length is 1500 ft (457 m).
Massive hydraulicfracturing-horizontal drilling comparisons. As described above, tight gas reservoirs with matrix permeability values in the microdarcy range can contain zones of natural fractures having relatively high permeability. A major risk associated with the development of such reservoirs is the possibility of having water breakthrough as a result of fractures tapping underlying water zones. Van Kruysdijk and Niko (1988) assessed this risk using a reservoir prototype model based on Shell Oil Company's black oil simulator. The first phase of the study assumed single-phase compressible flow, and utilized Green's function theory to derive transient pressure response. Results from the model study (Fig. 5-62) indicated that a horizontal well 3.0
320 Acres. 1140 A c r e s
2.,5
~W ~
2.0 160 A c r e s
m
~- a0 1.5 0 n
Z) 1.0
0
NOTE: F i g u r e s a r e on a per s e c t i o n b a s i s
. m
0
-0.5 800
1000
1500
2000
2500
PROPPED FRACTURE LENGTH (FT,)
Fig. 5-60. Results from a FRACOP model study showing a comparison of the 10% discounted presentvalue profit per section (one square mile: 2.59 square kilometers) with propped fracture length for a formation having 0.01 mD permeability. (After Kozik et al., 1980, fig. 21; courtesy of the U.S. Department of Energy.)
351
om IU m
8 820 Acres 640
c~ m
Acres
180 Acres
41 .9,0 N O T E : Figures are on a per section basis
I
I 500
.
lOOO PROPPED
I
.
18oo
FRACTURE
LENGTH
I 2000
,
2500
(FT.)
Fig. 5-61. Results from a FRACOP model study showing a comparison of the 10% discounted presentvalue profit per section (one square mile: 2.59 square kilometers) with propped fracture length for a formation having 0.04 mD permeability. (After Kozik et al., 1980, fig. 22; courtesy of the U.S. Department of Energy.)
TABLE 5-XVII Economic values and fracturing costs (1979 rates) used in the optimization of fracture length and well spacing evaluation from Mitchell Energy Corporation's Cotton Valley Lime (Haynesville Limestone) massive hydraulic fracturing test data, Fallon and North Personville fields, Limestone County, east Texas, U.S.A. Note that any economic evaluation or technical evaluation involving economic analyses is sensitive to each operator's economic parameters, such as current product price, price escalation or deflation, operating costs, initial investment, interest rates, and net working interest (data from Kozik et al., 1980) Economic parameters
Fixed investment: Product price: Operating expenses: Net revenue interest: Production Tax rate: Federal Income Tax rate:
$1,000,000 $1.52/MCF constant $8,400/yr constant 79.7% 13.0% 0%
Fracturing costs
Designed fracture-length radius, ft
Costs, $
250 500 750 1000 1250 1500 1750 2000
75,000 100,000 150,000 200,000 250,000 300,000 400,000 700,000
352
W.I E L. L B. O R. E
'I
y
!
I
Ze
//
Z
J ~
--X
L_ .
,,
RESIERVOIH ~
_1
A .
..-._.__
WELL|ORE
i I I I I
I I I I I
MASSIVE HYOA,tUUC FRACTURE
_ Z
~_7.T s
X'
~ / -
~
I
RLSE~K)In
B Fig. 5-62. Two semi-analytical models used to assess alternatives for draining tight naturally-fractured gas reservoirs: (A) Horizontal well reservoir model containing a naturally-fractured zone of finite width extending over the full height and width of the reservoir; (B) Double-fracture reservoir model showing a massive hydraulic fracture intersecting a vertical fracture plane. (Modified after Van Kruysdijk and Niko, 1988, figs. 1 and 5; courtesy of the Society of Petroleum Engineers.)
draining a natural fracture zone compares well with massive hydraulic fracture treatment, which connects the well to the fracture zones. Figure 5-63 presents typical pressure responses of both the horizontal well and a massive hydraulic fracture (MHF) intersecting a fracture zone. Inasmuch as the models used in Van Kruysdijk and Niko's (1988) assessment involve single-phase flow, additional advantages of the horizontal well with respect to water coning control were ignored. Table 5-XVIII presents the reservoir parameters used in this study.
353
L|
1(~
!~ !~ i-
'
'~ ..... ' "' ............... , ,, 9
9U - - H- -r, C , t t=0' , " ' , , ' s
..r ~Hr uHr kIHu
cfo = CI0 s CIOCIO :
...... "
"'""
..............
.......
,o-,
w
........
,
2.~ $ tO 1S
--.
y
V......-::
I0"*
o
I 0 "s
I0"
I 0 "s
I0"
10"
I 0~
Io'
1o'
OIMENSIONLESS TIME. I0
Fig. 5-63. Typical pressure responses of a horizontal well and a massive hydraulic fracture, both tapping a large natural fracture zone in a tight gas reservoir, with respect to dimensionless time. Cro is the dimensionless fracture conductivity and is equal to w(kf)/xf(k), where w is the fracture width, kf is the fracture permeability, Xf is the fracture wing length, and k is the reservoir (average) permeability. (After Van Kruysdijk and Niko, 1988, fig. 11; reprinted with the permission of the Society of Petroleum Engineers.)
TABLE 5-XVIII Basic reservoir parameters used in the model studies assessing the production performance of massive hydraulic fracturing and horizontal well scenarios in a naturally-fractured gas reservoir fractured zone width, w e reservoir thickness, z e reservoir width, ye wellbore length wellbore radius, r w fractured zone permeability, kns reservoir permeability, k fractured zone porosity, (I)f reservoir porosity, ~
9 30 ft 9 750 ft 9 1500 ft 9 1500 ft 9 0.3 ft 9 250 mD 9 20 I~D 9 0.01 9 0.07
Source." After van Kruysdijk and Niko, 1988, table 1" reprinted with the permission of the Society of Petroleum Engineers.
Van Kruysdijk and Niko (1988) pointed out that the horizontal well's early-time pressure response is considerably lower than that of a similar stimulation by the MHF (ignoring fracture linear flow), which is attributed to the horizontal well's direct entrance to the high-conductivity fracture zone. The MHF curve crosses the horizontal well response when the MHF conductivity is sufficiently high (above the
354 I.S
II
1.0
....
I
= C o ........ : ~. = 9
x..
-ll 0 o :. --0 I
o110=10 (x!=O.STe) oi tO 9100 (X! : O.S re) a l ID 910 ( x l - 0.2S 'ire) ot ID = I 0 0 (X! : 0.2S Ye) ol 10 : I0 (XI : 0.125 Ye) ol 10 = 100 (Xl = 0.12S Ye)
O.S
0.0
X
-O.S
b.
" ' ~ ' " t ~ -
-.---.._.__..__.....~.._._____.
I
"1.0
-I.~)
. 0.0
1.0
I
I
i
2.0
3.0
4.0
....
l
s.a
9
6.0
MHY r
1
7.o
I
s.a
!
~.0
1
~0.0
1
,I.0
1
12.0
i
13.0
|
14.0
i~.0
CfD
Fig. 5-64. Production improvements in a naturally-fractured tight gas reservoir. Both the horizontal well and the massive hydraulic fracture tap into the large zone of natural fractures as a function of the massive hydraulic fracture length, t D is dimensionless time and is equal to
k(t) O~tctY-----~,where k is reservoir permeability, t is the 2 time, t3 is the porosity, ~t is the gas viscosity, ct is the total compressibility, and yf is the fractured zone half-length. MHF fractured zone interaction at 0.5 Ye; Xf is the fracture wing length and Ye is the fractured zone length. (After Van Kruysdijk and Niko, 1988, fig. 12; reprinted with the permission of the Society of Petroleum Engineers.)
break-even point as shown in Fig. 5-64), so that the extra fracture surface compensates for the finite conductivity link to the fracture zone. The break-even point for the MHF intersecting a fracture zone with respect to a horizontal well is determined by the balance between extra fracture surface and pressure drop over the fracture wing (Fig. 5-62B) intersecting the fractured zone. Figure 5-64 illustrates the effect of MHF length and conductivity. Van Kruysdijk and Niko (1988) pointed out that short fractures (with respect to the fractured zone) require very high conductivities in order to be competitive with horizontal wells. Another drawback to massive hydraulic fracturing treatments is a lack of fracture direction control. The horizontal well can be considered then as having an advantage in the development of naturally-fractured carbonate reservoirs.
Refracturing About 80% of all active wells in the U.S.A. are producing at less than their potential. Results of recent advances in computer software, operational hardware, and materials have created opportunities to successfully refracture these existing wells. Abou-Sayed (1993) pointed out that most refracturing treatments have been applied to wells where original design parameters, materials, or operational procedures were
355 below current standards. Advance techniques, such as in the pumping of proppants, high overpressure perforating, and dynamic formation breakdown and fracture initiation are successful in improving the fracture-to-well connectivity and reducing fracture cornering and tortuosity in the near-wellbore region. An excellent example of applying refracturing technology to increase reserves was the acid refracturing of the Permian Ervay Member (dolomite), (Phosphoria Formation), in the Cottonwood Creek Unit, Washakie County, Wyoming, U.S.A. The reservoir covers about 60 mi2(155 km 2) in the Big Horn Basin and is not naturally fractured (Aud et al., 1992). The Cottonwood Creek Unit is developed on an 80 - 320 acre ( 3 2 - 130 ha) spacing. Early field development concentrated on the updip part of the reservoir owing to good production response from high-permeability streaks. At that time, the operator assumed that the field was producing from natural fractures. As development continued, poorer producing wells were drilled in lower-permeability zones. These wells were treated initially with a conventional acid fracture stimulation of 5 , 0 0 0 - 30,000 gal (19 - 114 m 3) of 15 - 28% HC1 pumped at 5 - 15 bbl/min (0.8 - 2.4 m3/min). The treatment evolved into one requiring 4 0 , 0 0 0 - 60,000 gal (151 - 2 2 7 m 3) of 28% HC1 with and without nitrogen gas. Large conventional acid fracture treatments used 125,000 gal (473 m 3) of 15% HC1 pumped at injection rates as high as 25 bbl/min (4 m3/min). Gelled acid with and without CO 2 was used as an economic alternative to the large acid treatments. Sand fracture treatments were unsuccessful owing to sand production problems associated with etched regions around the wellbore resulting from remedial matrix treatments (Aud et al., 1992). Typical porosity and permeability values are 8 - 10% and 1 mD (0.000987 ~tm2), respectively. Core analysis, however, revealed porosity values of 1 5 - 20% with associated permeabilities up to 800 mD (0.789 ~tm2). Reservoir modeling indicated that vertical permeability values are low (0.001 - 0.00001 mD: 0.00000001 - 0 ~tm2). The thin, high-permeability streaks constitute a low percentage of the reservoir, and have TABLE 5-XIX Average Phosphoria (Ervay Member) reservoir-fluid and formation properties in the Cottonwood Creek Unit, Washakie County, Wyoming, U.S.A. Original reservoir pressure, psi Original Pb, psia FVF at Pb' RB/STB Solution GOR at Pb' scf/STB Oil gravity, ~ Reservoir-fluid viscosity at Pb' cP Total compressibility at Pb, Psi-I Total compressibility at 800 psi, psiq Net pay, ft Connate water saturation, % Reservoir temperature, ~ Wetting characteristic Formation embedment strength, psi Acid solubility, %
:3608 : 1126 :1.14 : 313 :27 : 4.75 : 2.25 • 10-5 : 1.78 x 10-4 : 20 - 120 :10 : 125 :Oil :70,000 : 95
Source: After Aud et al., 1992, table 1" reprinted with permission of the Society of Petroleum Engineers.
356 values above 2 mD (0.00197 ktm2). Average reservoir parameters and their values are presented in Table 5-XIX. The reservoir originally contained an undersaturated crude with an average bubblepoint pressure of 1,126 psig (7.8 MPa). Reservoir pressure measurements indicated that the pressure, Pb, is slightly below the bubblepoint in most parts of the field (Aud et al., 1992). Waterflooding operations pressurized some areas of the reservoir, but this pressure is now dropping quickly because the waterflood is no longer operational. A detailed reservoir and geologic study involving a fully implicit, 3D, multiphase reservoir simulator with an acid fracture design program, indicated that many wells in the reservoir had short infinite-conductivity fracture half-lengths of 100 - 300 ft (30 91 m) (Aud et al., 1992). Reservoir simulation results suggested that an increase in the effective fracture half-length would increase the production rate and ultimate recovery. Five wells were retreated using 60,000 gal (227 m 3) of 15% HCI plus 60,000 gal (227 m 3) of 20% HC1. No significant incremental fracture half-lengths were obtained in these wells. The reason for the poor results was attributed to poor fracturingfluid efficiency caused by high fluid leakoff. Aud et al. (1992) pointed out that the free gas phase below the bubblepoint significantly increases reservoir fluid compressibility, and is an important parameter in the refracture treatment design. The fracture fluid encountered a highly compressible gas instead of a relatively incompressible liquid in the pores, therefore, resulting in a high leakoff. Refinement of the reservoir model resulted in a new treatment design. The wells were refractured using an external oil-emulsion acid system containing 70% by volume of 28% HC1 and 30% by volume of diesel oil and gelled water used in multiple alternating stages. Crowe and Miller (1974) developed the external oil-emulsion acid system for use in high-temperature limestone reservoirs. Fracture lengths of 250 ft (76 m) or longer were necessary to achieve reasonable economic results in wells having infinite-conductivity fracture half-lengths of 1 0 0 - 300 ft ( 3 0 - 91 m). Gelled acid treatments were not used owing to model predictions showing inadequate conductivity development in low-permeability regions. Table 5-XX presents results of the 1990 refracturing program, as well as data relative to treatment size and design. The program was successful. The sixteen wells, which were acid-fractured, showed an incremental production increase of 750 BOPD. Eleven wells of the 16 wells, which were refractured, contributed about 460 BOPD (73 m3/D) to the incremental production increase. The effective fracture half-lengths obtained by refracturing ranged from 300 to 800 ft (91 - 2 4 4 m). The refracturing treatments resulted in incremental reserves of about 105,000 bbl (16,694 m 3) of oil per well for these 11 wells. Aud et al. (1992) attributed the remaining difference of 290 BOPD (46 m3/D) of the production increase to five wells that had not been previously fracture-stimulated. Four of these wells were not stimulated on initial completion owing to high water production rates from high-permeability zones. Modeling for predicting post-fracture production response and reserves on these four wells was impossible (Aud et al., 1992). The wells were modeled only for fracture design purposes to ensure that proper flow capacity was accounted for in treatment design.
TABLE 5-XX Summary of the 1990 refracturing well stimulation results, Phosphoria Formation, Cottonwood Creek Unit, Washakie County, Wyoming, U.S.A. Acid volume (gal)
Gelled Gel load water (Ibm/ volume 1000 gal) (gal)
Well
Treatment date
Job type
165
22 Feb 90
RF
185
29 Mar 90
FR
180
24Apr90
RF
184
17May90
RF
183 190
5 June 90 20 June 90
RF RF
151
27June90
RF
172 173 163
11 July 90 25 July 90 8 Aug 90
RF RF FR
182
22 Aug 90
RF
201
5 Sept 90
FR
167 161 169
20 Sept 90 3 Oct 90 20 Oct 90
RF RF FR
88,000 E 40 40 75,000E 25 75,000 E 25 67,000E 40
168
31 Oct 90
FR
67,000 E 40
Interval Permeability thickness (mD) (ft)
Fracture half-length (ft) Initial Final
Pretreatment rate (BOPD/BWPD)
Post-treatment production rates (BOPD/BWPD) 30 days 60 days 90 days
20
65,000 L
0.5
52
200
500
14/0
122/50
58/4
54/3
20
74,000 L
1.9
59
0
300
9/0
80/15
40/3
34/0
20
75,000 L
0.3
50
300
650
15/0
95/15
55/3
50/0
40 40 25 40
65,000X 42,000 L 117,000 L 95,000 L
100 1 1.2 0.3
5 35 52 60
* *
19/0
106/50
60/3
55/0
150 200
300
30/0 6/0
198/29 33/5
130/7 18/10
120/5 17/0
40
99,000 L
1
40
100
70
6/0
127/2
83/9
73/9
20 20 40 40 80,000 E 25
119,000 L 122,000 L 19,000X 90,000 L 25,000 X 85,000 L 80,000 X 30,000 L 110,000 L 120,000 L 20,000 X 76,000 L 125,000 X
1 1.5 100 1 2.5
40 40 8 22 50
300 0
# 800 *
22/0 29/8 12/15
67/28 240/48 172/119
100
450
32/0
150/19
150 1 0.5 0.8
20 30 42 60
*
28/100
120/201
# 700 *
7/0 19/0 5/30
32/18 78/12 50/85
150 1
15 45
*
67/67
80,000 E 12,300 C 81,000 E 30,000 C 70,000 E 15,000 C 62,000E 15,000 C 80,000 E 19,000 E 10,000 C 61,000 E 11,000 C 72,000 E 74,000 E 65,000E
0 300 400 0 0
37/15 110/8 180/110 80/2
35/13 90/6 91/60 62/5
125/180
Source: After Aud et al., 1992, table 6; reprinted with the permission of the Society of Petroleum Engineers. RF = refracture treatment; E = external oil-emulsion acid; L = linear gelled water; * = high-permeability streak; FR = initial fracture treatment; C =conventional acid: 15% HCI; X = crosslinked gelled water; # = not modeled yet.
-.z
358 CARBONATE RESERVOIR CHARACTERIZATION
This section will focus on the present-day use of various mathematical strategies in determining reservoir heterogeneity. The term heterogeneity, as described previously in geological terms, is a measure of the continuity of a particular reservoir property. In the previous sections, it was shown that heterogeneity in carbonate reservoirs is the critical overall productivity parameter for characterizing these reservoirs. Examples of present-day oil-field practice to overcome heterogeneity effects were presented earlier in the chapter. A discussion of the relationship between porosity and permeability, and their heterogeneity is a central premise in the development of fluid transport models for carbonate reservoirs.
Reservoir heterogeneity models Carbonate reservoir heterogeneity is a challenge, which needs to be clearly defined not only geologically, but also from a reservoir mechanics viewpoint in order to increase well and reservoir productivity. This section acquaints the reader with some of the technical aspects by briefly discussing various approaches, with a focus on micro- to macro-scale applications to reservoir performance, used in attempting to mitigate reservoir heterogeneity problems. The production of hydrocarbon fluids from heterogeneous carbonate rocks depends on variations in reservoir and fluid properties and their spatial correlations. The concept of reservoir heterogeneity was revived in the late 1970s and early 1980s owing to advances in geoscience and engineering technology, and the political necessity to produce from complex reservoirs. There have been three (as of 1993) reservoir characterization technical conferences sponsored by The National Institute for Petroleum and Energy Research (NIPER), Bartlesville, Oklahoma, held to address reservoir heterogeneity. The first one was held in Dallas, Texas, U.S.A., in 1985 (Lake and Carroll, 1986). Haldorsen and Damsleth (1993) pointed out that despite many recent advances in reservoir characterization technology, its practice and accompanying publicity by the oil industry, there appears to be no sign of a general increase in productivity. Their statement was based on the observation that (1) there has been only a slight increase in province-average recovery factors, (2) production forecasts are still notoriously in error, and (3) the mainstream, day-to-day forecast modeling of reservoir behavior by a typical oil company has not changed appreciably since 1987. The writers do not completely agree with Haldorsen and Damsleth's statement. Our outlook is that productivity increases (or decreases) should be measured on a well-by-well basis and/or on an individual reservoir basis. Rationale for this opinion is given in the previous discussions on: (1) the classification of carbonate reservoirs based on their geological nature, and (2) the incremental recovery technology. These problems were shown to be solvable, and the solutions produced favorable returns to the operator. It should be noted that other factors have a strong influence on overall productivity of the older established reservoirs, such as: (1) present economic adversity, (2) oil price stability, (3) technology affordability and its acceptance, (4) management and staff education, (5) lack of technical and field personnel owing to company
359 downsizing, (6) sloppy practice, (7) poor planning and execution, (8) competing internal company reservoir development projects with better bottom-line returns, (9) lack of quality control, (10) large, long-term projects which are underway, and (11) the focus on higher investment returns from exploration efforts in less developed countries. These factors have a strong impact on the effectiveness of reservoir characterization "applications" to cure day-to-day production problems. The bottom-line, however, is that any approach to characterization has to be cost effective. Disregarding costs, however, it is technically possible to offer methods to the operator, whereby one can obtain precise and accurate reservoir information at various scales for reservoir modeling. These information acquisition methods could involve a 3-D seismic acquisition and processing that could provide a tomographical picture of the reservoir, interwell seismic definition of geological conditions, wellbore image analysis for fracture definition and magnitude of damage, and use of algorithms to help describe the reservoir by relating the measured petrophysical properties procured by advanced well-test and well-logging techniques. Analysis of this information involves the application of statistics and geostatistics. Such mathematical tools provide the foundation to evaluate and simulate conditions in and near the wellbore (at microscopic and mesoscopic scales) and between existing wells (at mesoscopic and macroscopic scales) (see Figs. 5-26 and 5-37) for primary recovery operations. Methods for integrating seismic data with well-log data in the construction of reservoir models, and potential pitfalls, were reviewed by Araktingi et al. (1991). A non-statistical method (Eq. 5-20) for determining interwell heterogeneity involving waterflood sweep efficiency was previously presented on page 282. Values determined in this manner are used in the design of advanced recovery operations. In present-day practice, macroscopic heterogeneity is usually addressed by using the previously discussed incremental recovery technology. Unfortunately, variability in geological aspects of carbonate reservoir heterogeneity is still a descriptive process in the minds of most geologists. Reservoir examples are frequently given in the literature using the classical descriptive approach. An example of this practice is illustrated by Mancini et al.'s (1991) study of Jurassic Smackover carbonate reservoirs in the southeastern U.S.A. This approach describes reservoir geology by portraying data variability for various geological properties as a series of generalized maps. The detail expressed in these maps depends on the amount of money spent to acquire and analyze the data and the spacing of the data both vertically and horizontally within the reservoir. In practice, it is normal not to address the vertical variations within a reservoir in great detail unless they strongly influence reservoir performance. Overall, this descriptive approach is one of defining anisotropic properties rather than dissimilar properties or heterogeneity occurring within the reservoir. Elk Basin FieM case history
The following case history describes an early example of an effort to define several megascopic (field) scale heterogeneities in a large producing carbonate reservoir. Wayhan and McCaleb (1969) described reservoir heterogeneities in the lower Mississippian Madison Limestone (Elk Basin Field), Montana, U.S.A. They instituted appropriate corrections to production operations based on the obtained geological data.
360 The methodology used to handle these heterogeneities was based on classical geological and engineering analyses practiced in the 1960s. Whether or not Wayhan and McCaleb were successful in increasing the recovery of additional oil is a matter of opinion. The Elk Basin anticline is a giant oil field which contained more than a billion barrels of oil originally in place and produced at rates in excess of 70,000 bbl/D (11,129 ma/D) from seven horizons ranging in depth from 1,000 to 6,500 ft ( 3 0 5 1981 m) (Fig. 5-65). Production from the Madison Limestone began in 1946. The early conceptual model of a homogeneous reservoir (no zonation) was influenced by the operating practice of completing the wells open-hole through the entire 920 ft (280 m) Madison section. Any low-permeable streaks were thought not to be continuous. During the first 10 years of production, the reservoir exhibited a water drive with only a slight pressure decline (Wayhan and McCaleb, 1969). Wells were drilled near the crest of the anticline so that oil would be recovered as it moved updip ahead of the natural water drive. Flank wells were added as needed to accelerate production and to ensure good areal sweep of the reservoir. The operational strategy called for progressive plug-backs to minimize lift requirements as water cuts increased in the wells. In 1957, water cuts increased, affecting the overall reservoir productivity.
',/lEST
IM
16~
49
5 0 I.~GM
43
51M
44M
45M
180
,~9 46M
40M
t 11!i'!
i
":b:-'1"'::':fl
I--
-9 r -I~
'
b
,,o'."'
104
EAST
I
L coo"
,
]4
-
I
I[~1--~,
- 1" " --l,,,,,"-"-~t;,,~i
--I
r
"
_..
~A
LEVEL
I --
..'r.."~d~?2~:;
-I000
-
~ ~.------..-. I I . . - - - ~ - - . . ~ . . \
. ;o..~o
t t \ "
L
,,--"
\
.." ,x \
N
-- "
f
r
f
t ...
~
...
-- . . . . l ~ f
_
.. ,. 000
....S I
-"
~,~,f."
Fig. 5-65. West-eastcross-section of the Elk Basin anticline showing seven producing horizons. (Modified after Wayhanand McCaleb, 1969, fig. 2; courtesy of the Society of PetroleumEngineers.)
361 A review of core analyses and well logs in 1957 revealed highly complex zonation in the Madison section. Four zones (A, B, C and D) were identified, all of which were still thought to be under a natural water drive. During the period 1 9 5 8 - 1961, singlezone completions were made in the Madison reservoir. The completions showed that the A zone exhibited solution-gas-drive, whereas the other three zones continued to show water-drive performance. In 1961, water was injected into the reservoir. The A and B zones, in early 1962, began to produce water. Wayhan and McCaleb (1969) stated that only minor waterflood response was observed and the producing rate continued to decline sharply. Operational modification in 1963 rerouted the available water to the reservoir's A-zone interior injection wells. Production rate began to improve immediately; however, by early 1965 water breakthrough occurred in the interior and production started to decline. Severe curtailment of production occurred owing to wellbore scaling of the interior offset production wells. A new integrated geological and engineering program was executed in 1965 to define the problem by gathering additional reservoir data using 12 new development wells. A detailed study was made to define the degree of continuity in the reservoir on a zone-by-zone basis. Interpretation of core and well-log data showed that the Madison reservoir has a fluid flow heterogeneity (low-permeability streaks) within its four Madison producing zones. The A zone, which for the most part was deposited in a high-energy environment, exhibited a very complex vertical and areal zonation. Zone A consists of three major oolitic pay sub-intervals with limited areal continuity. These sub-intervals are interspersed with layers of lime mud creating limited fluid communication between the subzones. The B, C, and D zones are blanket limestones deposited in a low-energy environment. The B zone was divided into two pay sub-intervals, the upper one of which has two sub-members. The C zone has a productive horizon only at its base. The D zone has only one-pay horizon. Varying degrees of dolomization in the zones occurred after lithification. Subsequent erosion, karst development giving rise to collapse features and dissolution breccias, and leaching of relict limestone by meteoric water greatly altered the original Madison heterogeneity and permeability of the A zone. A major permeability discontinuity discovered by additional drilling lies on the anticlinal crest of the A zone (Fig. 5-66). Collapse and remineralization was so severe at the crest that they created a barrier subdividing the A zone into east side and west side reservoirs. Natural water drive is from west to east in the B and D zones toward a permeability restriction in the crestal area and toward a fault on the east flank of the anticline (Wayhan and McCaleb, 1969). At the anticlinal axis, remineralization by anhydrite and calcite of the lower Madison zones reduced porosity and permeability, thereby destroying potential reservoirs. The original heterogeneity and flow characteristics of Madison section were greatly altered by erosion, solution, and diagenetic overprinting. A detailed integrated study resulted in production practice changes during the 1960s. Waterflooding changes consisted of returning water into only the A zone, and stopping water injection into the B zone. Wells were drilled on the east flank of the anticline to take advantage of lower water cuts of 1 0 - 50 % in the B and D zones. This is in contrast with the original production plan of drilling wells near the crest of the structure to recover the oil moving updip ahead of the natural water drive. Flank wells
362 PRODUCING ZONES /'-~ ~ maSOLUTION BRECCIA _ ___ '~1~ ZONE
WEST
~ ~ ~ ' ~ / "
B2""
.../
.
f"
/
/
/.::;Z,,~V.~. /".~Z',,~ Ov
. .9j ~
,
/
9"'~':'~ ~"
_.i ,,,..
/./
EA ST
.,.~,~:i, i.~
...::...~ .~ ";/"":
MINIMUM THINNING DUE TO COLLAPSE
~C,~ ,/
~
"k
, GROSt~ VENTRE
Fig. 5-66. Idealized west-to-east geological cross-section showing the axial collapsed A zone in the Elk Basin Madison reservoir. (After Wayhan and McCaleb, 1969, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)
were added as needed to accelerate production and to ensure good areal sweep efficiencies. Scaling was greatly diminished by shifting water injection to the periphery of the A zone. No definitive answer could be given by Wayhan and McCaleb on the potential magnitude of the increase in recovery that could be ascribed to the change in production practices. Their only answer is that the reservoir by 1968 has produced 5.4 million bbl of extra oil and that the current rate was 8,500 BOPD above the old trend. Numerical reservoir model studies were not performed at that time, owing to the assumption that the 'reservoir' was so complex that a model would not be beneficial (Wayhan and McCaleb, 1969).
Importance of models Weber (1982) stated that the value of having a geological/petrophysical model lies in estimating well drainage areas, completion design, and as input into the appraisal of development drilling pattems. Development of accurate reservoir performance models has been difficult owing to problems in extrapolating values for petrophysical properties between wells. The simulation of reservoir performance is now limited primarily by the petroleum industry's ability to numerically model geological uncertainty. The following discussion is a brief overview ofprobabilistic modeling presently in use by the petroleum industry. Attention is focused here on how fractal and multifractal distributions can be used to describe reservoir heterogeneity in reservoir simulation models. Application to carbonate reservoirs follows the overview discussion on fractal models. In the early development stage, knowledge of reservoir anisotropy and heterogeneity
363 is scarce. Fluid flow problems are usually solved by using volume-average approaches under conditions of minimal data. Flow characteristics in reservoirs are described by Darcy's law, which prescribes a linear relation between the pressure gradient and flow. In order to predict future reservoir performance behavior for the initial development plan, one has to use reservoir simulation models with a minimum of data. The accuracy of the model's predictions depends on the available data, which reflects the amount of investment made to procure information. It should be noted that the lack of "maximum" acquired data usually precludes accurate modeling; however, data estimation algorithms and sensitivity analyses, which evaluate various reservoir parameters relating to production, can be used in a "first pass". A statistical analysis of reservoir data is necessary to estimate the range of reservoir properties. Application of fuzzy set theory may be one way to obtain a more reliable estimation of values, inasmuch as it returns values closer to sensitivity specifications than those values fitting an exact Boolean (crisp) output. An example in the use of fuzzy set theory is given by Fang and Chen (1990). Their study on the estimation of petroleum volumes in prospect appraisals presented a comparison between the classical Monte Carlo probability approach and possibility approach (Dubois and Prade, 1988). The possibility method via fuzzy arithmetic method can handle uncertainties in the estimation of values for hydrocarbons in place when some of the data are missing, subjective, or vague. Chen and Fang (1993) pointed out that the possibility method is an appropriate alternative approach, but not a substitute for conventional methods based on probability theory. One advantage of applying either approach in numerical models is that these methods provide a low-cost, rapid procedure for preparing generalized maps and measuring risk for a "first pass" scenario. Ideally, a carbonate reservoir is envisioned to be deterministic if at every point in the reservoir true properties exist which can be measured. A resulting model description of the reservoir, however, would have to be of a statistical nature. Hewett and Behrens (1990) pointed out that incompleteness of available data and their spatial disposition, coupled with the intrinsic variability in the geology of the reservoir, would preclude deterministic mapping of properties between points. It is also more than a question of the scaling of flow processes and properties, and uncertainty resulting from missing information in reservoir descriptions. Also, the simulation has to address reservoir property continuity. These problems force one to describe the reservoir in a probabilistic manner. There are three probabilistic reservoir-property modeling techniques used in a Eulerian framework: (1) Monte Carlo simulation (Warren and Price, 1961), (2) models built up from genetic flow and lithological barrier units (Haldorsen and Lake, 1984), and (3) geostatistical interpolation using kriging (Journel and Huijbregts, 1978). There are important shortcomings in the first two techniques. The Monte Carlo approach ignores the spatial correlations in reservoir properties by assigning values to locations within the reservoir without regard to the values of the neighboring points (Hewett and Behrens, 1990). The genetic flow and lithological barrier unit model honors a stratified reservoir at each location. This technique, however, does not have variability included within the units, and the dispositions and sizes of successive units are completely independent (Hewett and Behrens, 1990). A variety of techniques are available for constructing reservoir parameter contour maps, which interpolate between data points (Crichlow, 1977; Robinson, 1982; Hohn,
364 1988). Two types of interpolation are used in geostatistics: universal kriging, and stochastic interpolation (Hewett, 1986). The choice of which one to use in modeling depends on the intended application. Kriging, which gives the minimum variance of distribution at each location, is used in reserve estimations and conditional simulations of fluid flow to predict the most likely value of concentration at a given location (Journel and Huijbregts, 1978). Stochastic interpolation intercalates between measured values using a realization of a random function having a variance structure similar to the original structure. Journel and Huijbregts (1978) stated that stochastic interpolation does not provide as good an estimate of values at any given location. It is appropriate to use stochastic interpolation in modeling the dispersion characteristics of a heterogeneous formation (Hewett, 1986). Unfortunately, the computer-generated maps give only information reflecting reservoir property variations that have a scale similar to, or larger than, the sample spacing. In most cases, well spacing controls sample spacing. Reservoir property variations at scales below the field's well spacing will be smoothed out. The variations, therefore, are not useful in the interpretation of properties at the macroscopic mapping scale. All three of the above probabilistic reservoir-modeling techniques have the same weakness attributed to deterministic interpolation schemes in that property variations at scales smaller than the data sample spacing are smoothed. Most reservoir-simulation models are based on transport equations derived for the interwell scale.
Geostatistical modeling overview. Hewett and Behrens (1990) adopted the method of geostatistics for probabilistic modeling of reservoir-property distributions. Their model addressed the issue of resolution of interwell property variations on a scale where the rock-property variations are sufficiently resolved to reproduce the effect of permeability variations on fluid-displacement fronts. They employed two geostatistical strategies to achieve the desired results in their reservoir performance model. One geostatistical strategy employed a power-law variogram model (other models are spherical, exponential, and Gaussian) defining a fractal distribution of geologic properties, whereas the other geostatistical strategy used conditional simulations to determine effective flow properties at different scales. Journel and Huijbregts (1978) defined conditional simulation as a process of constructing unsmoothed realizations of the random function that honor data at the sample point, whereas unconditional simulation is one that does not necessarily honor data values at location points. Presently, experience in using conditional simulations of process performance in heterogeneous formations is limited, and is an adopted approach used by Hewett and Behrens (1986). The first strategy used by Hewett and Behrens (1990) was to generate a description of reservoir heterogeneity by creating fractal model property distributions having any desired resolution. This allowed for the scaling of reservoir properties and addressed the problem of incomplete effective flow property information. The strategy does not consider a fault, which excludes a large-scale heterogeneity. A variogram measures similarities in the values of a variable at various distances and is a type of size measure (Yuan and Strobl, 1991). Another previously-mentioned component is connectivity, which addresses property continuity within the reservoir, and it is not well captured in the variogram. The variogram of random fractals, which is based
365 on a measure of variability, is defined by Mandelbrot and Van Ness (1968), Delhomme (1978), and Hohn (1988) as: 2r(h) = E{[Z(x + h ) - Z(x)]2},
(5-48)
where r(h) measures the mean-square variation of property as a function of the spatial separation of its sample locations; Z(x) is the value of the variable at locationx; Z(x + h) is its value at a lag distance, h, away from x; and E{ } indicates the expected or mean value of a random variable, x. The greater the variogram value, 2 r(h), the less related are the two variables. When estimating values at unsampled locations, the function v(h) is regarded as the meansquare error incurred, if the value of a sample is used from one location as the estimate for the value at a distance h away. Delhomme (1978) stated that in most cases x and h are regarded as vectors; therefore, anisotropies in the distribution can be accommodated. The above variogram is based on the behavior of fractal Brownian motion, fBm, which is a good starting point for understanding anomalous diffusion and random walks on fractals (Voss, 1988). It was pointed out by Jensen et al. (1985) that it may be necessary to include other forms for a normalized cumulative probability distribution function in order to describe distributions of permeability and other reservoir properties having skewed marginal distributions. Geological properties often exhibit correlations that can be observed over a range of scales (i.e., microscopic to megascopic). Hewett and Behrens (1990) pointed out that distributions exhibiting this nested structure can be characterized by superimposing a series of transitional variograms with different ranges and sill values. A sill value is the semi-variance value where this value essentially does not change with increasing distance. On a semi-variance vs. distance plot, the resulting curve would increase until reaching a break-point value where it then becomes essentially constant. If the sill and range for each scale increase in a geometric progression, then the form of the variogram characterizing each variation scale is said to be geometrically similar to the others. The superposition of many variograms results in a power-law variogram (Delhomme, 1978). Distributions having the form of Eq. 5-48 for their increments are said to be statistically self-similar (Manelbrot and Van Ness, 1968). Fractal distributions are characterized by a power-law semivariogram ( 89of 2v(h) of Journel and Huijbregts, 1978) model having the form:
v(h) = voh2H,
(5-49)
where Vo is a characteristic variance scale at a reference-unit lag distance; and H is known as either the Lipschitz-H61der exponent or Hurst exponent and characterizes the scaling behavior. Emanuel et al. (1989) called H an intermittency exponent, which quantifies the intermittent or "spotty" nature of the geometries of fractal distributions. Here it represents the fractal co-dimension equal to the difference between the Euclidean dimension in which the distribution is described and the fractal dimension of the distribution. The reader should be aware that there is a major drawback to the use of the Hurst exponent. The Hurst exponent is only a single scaling exponent. Most geologic analyses involve bivariant statistical conditions, which are effectively
366 examined using multiscaling statistics. The equality (Eq. 5-49) must be valid only in a statistical sense; that is, the functions r(h) and roh TM, should be realizations of the same stochastic process. Equation 5-49 implies that the variance at any scale can be determined from the variance measured at any other scale (Mandelbrot and Van Ness, 1968). As the scaling parameter H increases through the range of 0 < H < 1, the functions become smoother (Korvin, 1992). Figure 5-67 shows samples of the behavior offBm traces for different values of H and D, where D is the fractal dimension (see Eq. 5-11). When H is close to 0, the traces are roughest. As H increases in value toward unity, the persistence of correlations increases and the contribution of the smallest scales of variation (highest frequencies) decreases (Hewett, 1986). A value of H = 0.5 indicates a totally random structure. H values derived from measurements of topographic features of the earth's surface (roughness) typically fall in the range of 0.7 < H < 0.9, compared with the theoretically expected value of 0 . 5 - a Gaussian distribution (Hurst, 1957; Hewett, 1986; Emanuel et al., 1987). A class of functions known as fractional
,
~
,,, ~
H=0.2,
13=-1.8
yj V
E
r~
"
AVH ~ t,
time
Fig. 5-67. Example offi'actional Brownian motion 0CBm)traces for different values of H and D. High noise at low H values. Journel and Huijbregts (1978) stated that as H values increase, the functions become more regular (H --~ 1; D --~ 1), and the traces become mean square differentiable. A statistical analyses of vertical sequences of property variations in sedimentary environments by Mandelbrot and Wallis (1969) indicated that the properties have characteristics similar tofractional Gaussian noises (fGn) (not shown in this figure- see Hewett, 1986, fig. 4) with H > 7. (Modified after Voss, 1988, fig. 1.12; courtesy of Springer-Verlag Inc.)
367 Brownian motion (fBm) is defined when H is not equal to 89and r(h) is the error function, with: H=d-D,
(5-50)
where d is the Euclidean dimension (Hewett, 1986). When r(h) is the probability distribution function of a log-normal distribution then Eq. 5-50 simply becomes: H/2 = d - D.
(5-51)
When distributions satisfy Eq. 5-48 with a non-Gaussian cumulative probability distribution, they are referred to as fractional motions (Hewett, 1986). In the case where the fractal dimension D (see Eq. 5-11) is related to H for a twodimensional Euclidean dimension, the D value is simply D = 2 - H . Voss (1988, p. 45) stated that fractals, like traditional Euclidean shapes, typically reduce their dimension by one under intersection with a plane. As an example, the intersection of a solid three-dimensional sphere with a plane is a two-dimensional circular area; an intersection of the circular area with another plane is a one-dimensional segment; and the intersection of this line with another plane is a zero-dimensional point. Unconditional simulations were used by Hewett and Behrens (1990) to simulate the continuity and regularity of distributions described by the variogram. The techniques available for constructing these realizations included the turning-bands method, lower/upper-triangular decomposition of the covariance matrix, and spectral methods. Hewett and Behrens (1990) chose the Weierstrass-Mandelbrot random function, which is based on a Fourier series that involves a geometric progression (see Voss, 1988, p. 57, for details). The Weierstrass-Mandelbrot function, which is continuous but not differentiable, is widely used to describe irregular surfaces. This method provides an analytical representation of the realization that can be used to calculate property values at arbitrary locations. The second geostatistical strategy deals with scale averaging of fluid flow properties. Transport equations were derived for the macroscopic scale in a Eulerian framework where local continuum properties can be defined. In a simulation model, where the simulation scale is larger than the interwell scale (scaled-up model), the property variations within the volume block to which flow properties must be assigned will generally require the definition of scale-effective flow properties and fluid compositions. Hewett and Behrens (1990) stated that the primary flow properties of interest are: (1) absolute permeability, (2) dispersivity, and (3) relative permeability. Hewett and Behrens (1990) stated that the primary factor influencing the definition of effective flow properties is heterogeneity in the permeability distribution. In response to a uniform pressure gradient, fluid velocities within a volume will be proportional to the local permeability. Any heterogeneity in the permeability distribution results in a nonuniform flow velocity field. Such a field can distort the shape of a displacement front during secondary and EOR operations creating by-passed oil pockets. Hewett and Behrens (1990) reviewed the effect of permeability heterogeneity on absolute permeability, dispersivity, and relative permeability.
368 The influence of heterogeneity on effective absolute permeability has been studied by petroleum engineers and groundwater hydrologists. In modeling, the terms 'effective' or 'pseudo' permeability were associated originally with finite-difference (or element) techniques used to solve the pressure equation in conventional numerical simulations. Effective has a special meaning that may not be obvious to the reader and is equivalent to the old term 'pseudo' used previously. Effective permeability is an average value of permeability of a grid block used in reservoir simulation. Those who work in reservoir modeling use the term 'pseudo' in a different context. This term is derived from pseudoization procedures used to correct for enhanced numerical dispersion (King et al., 1993, p. 245). King (1989) pointed out that it is necessary to use a suitable effective reservoir property value in numerical models, which is determined from reservoir core samples or logs. The effective value is a single value for an equivalent homogeneous grid block in a model. As an example, grid blocks are on the scale of hundreds of meters, whereas reservoir property heterogeneities occur over a wide range of scales (refer to Figs. 5-37 and 5-81). In the case of absolute permeability the size of fluctuation ranges over many orders of magnitude. King (1989) stated that this makes it difficult to assign a single effective value to absolute permeability that would give the same mean flow. Many attempts have been made to address the above stated problem of assigning an effective absolute permeability value. The analytical methods used are based on effective medium theory (EMT) or perturbation expansions. The effective permeability estimates, however, are accurate only when permeability fluctuations are small (King, 1989). In carbonate reservoirs this is rarely the case. Warren and Price's (1963) method is still taken as the petroleum industry standard. They used numerical simulations to show that the geometric mean usually gives the closest estimate to the effective permeability for a random, isotropic distribution. As King (1989) pointed out, there are many distributions for which this is not a good estimate. Dagan (1979), in numerical simulation of groundwater flow, presented an approach that placed upper and lower boundaries on effective permeability. He established the lower boundary to equal the harmonic mean, which corresponds to the effective permeability of a layered formation to flow perpendicular to the layering direction. The upper boundary equals the arithmetic mean, which corresponds to the effective permeability to flow parallel to a similarly layered formation. His approach avoided the geometric mean. Hewett and Behrens (1990) advocated the use of conditional simulations of permeability fields that honor measured data and mimic permeability variability and spatial correlations in the field of interest to derive effective permeabilities from flow simulations. The standard to which the effective permeability calculation must be compared to is the fine-scale flow simulation. From the groundwater literature, the effect of permeability heterogeneity on the dispersion of solutes in single-phase flows provides analytical procedures for deriving effective values ofdispersivity (Dagan, 1984). Araya et al. (1988) noted that when the permeability field has a finite range of correlations, the effective dispersion coefficient becomes constant when the length of the flow path is large compared with the range of correlations. Hewett (1986) and Araya et al. (1988) noted that field measurements of dispersivity derived from tracer tests show a scale dependence. These
369 results indicate that there is an influence of long-range correlations on the dispersion characteristics of heterogeneous reservoirs. The solutions of the convective-dispersion equation with an effective dispersion coefficient will be unsatisfactory for predicting dispersion effects in interwell flows. This statement is based on the observed scale effect occurring over large distances compared with typical well spacings in oil fields. Hewett and Behrens (1990) stated that more accurate predictions of dispersivity can be obtained by simulating the flow through conditional simulations of the heterogeneous permeability distribution. Several theoretical approaches have been proposed for generating pseudo (effective) relative permeabilities in layered systems, and are based on the assumption that there is a high degree of vertical communication existing in the reservoir (Coats et al., 1971). One would make the assumption that stratified flow or vertical equilibrium conditions exist. Problems arise due to the use of pseudo relative permeability values based on flow simulation through models that are more finely resolved than the scale for which effective properties are desired. The effective relative permeability values required to reproduce the observed behavior in the fine-scale simulation are backcalculated. Hewett and Behrens (1990) advocated that these values have to be validated, and described a method to do so. Reason for validation is that if a streamwise dependence for the pseudo relative permeability is indicated, then flow properties can no longer be defined locally. Flow properties depend on the simulation's boundary conditions and the position of the coarse gridblock (scaled-up model) along fluidflow paths, which violates the basic assumption of the Eulerian formulation of the transport equations. In order to be able to scale-up in the Eulerian formulation, it is necessary to use streamtube methods and front-tracking simulators. Emanuel et al. (1989) showed that streamtube scale-up of flows in conditional simulations of heterogeneous geology have been successfully used to match waterflood production history in carbonate reservoirs. The authors refer the reader to Hewett and Behrens (1991) for a complete discussion on scaling behavior of solutions to the transport equations for flow in permeable media. How is lateral and vertical property continuity exhibited in the fractal models? Connectivity of properties between wells is an important consideration in carbonate reservoir characterization. A variogram does not examine whether particular lithofacies or units with distinct permeability values are connected. As a result, stochastic simulations designed to reproduce a particular variogram usually produce cross-sectional areas having high proportion that are connected, and low proportion areas that are disconnected (Yuan and Strobl, 1991). Hewett (1986) provided an example of stochastic interpolation between neutron porosity well logs taken from three wells in an unidentified west Texas carbonate reservoir. Figure 5-68 shows the resulting synthetic pattern obtained in his study. The cross-section exhibits a variability between the wells that is quite representative of the actual lithological units. It was pointed out by Hewett (1986) that in any smooth interpolation scheme, contours beginning at one well must either connect with data at a neighboring well, or die out between wells. Other stipulations are that no new features can arise between the wells, and all of the bedding exhibited in the original three well logs are preserved in the interpolated field (Hewett, 1986). If low porosity or low permeability zones were discontinuous
370
FRACTAL INTERPOLATION OF POROSITY LOGS H =0.8]' I"-
II1- ' 1 u') IM z (3 T
,
I-.-
-6
zoo
4oo
6o0
Boo Iooo DISTANCE, FT
izoo
04"oo
16"oo
~abo
Fig. 5-68. Iso-porosity contours of an interwell cross-section exhibiting an interpolated porosity field. Dark areas indicate porosity values less than 0.10, whereas white areas indicate porosity values generally in the range of 0 . 1 0 - 0.20; some values are higher. (Modified after Hewett, 1986, fig. 17; courtesy of the Society of Petroleum Engineers.)
within the formation, however, then the model would not reflect their actual containment. This is analogous to having a proper description of whether or not shales exist within a reservoir (as an example of a flow barrier) as: (1) distinct and continuous shale beds; (2) discontinuous shale beds (non-continuous shale stringers); (3) shale casts; (4) randomly dispersed clay particles (shaly or clayey limestone); and (5) a combination of all these conditions. Haldorsen and Lake (1984) discussed this problem of managing flow barriers (shales) in field-scale models. Two flow barrier (or a reservoir property) types are distinguished based on whether the dimensions and spatial disposition of the barriers (properties) are known. Stochastic barriers or properties cannot be correlated between wells and appear to be scattered randomly within the reservoir. Deterministic barriers or properties are continuous between the observation points. Haldorsen and Chang (1986) addressed the generation of discontinuous shales beds having a lateral extent less than the well spacing for stochastic reservoir models. The reader needs to be aware of a recent effort to develop quantitative measures of variable connectivity for stochastic reservoir simulation studies. Yuan and Strobl (1991) proposed a unique but complex approach to measure reservoir continuity, which is essential for accurate reservoir characterization. Their approach defines reservoir continuity by quantifying the connectivity of reservoir variables, and is based on mathematical morphology and image analysis. The methodology consists of two proposed measures: the connectivity number and the connectivity indicator. The connectivity number (Serra, 1982) or Euler number (Russ, 1990) is equal to the number of disconnected objects minus the number of holes in those objects. Figure 5-24A provides an example of their concept. This measure can be used on both categorical variables and continuous variables such as permeability (Yuan and Strobl, 1991). The connectivity number, however, treats all objects with the same importance regardless of their size, making it highly sensitive to small objects and noises. The connectivity indicator is equal to the total amount of rough area divided by the total sand (matrix) area, and varies between 0 and 1. Zero indicates that all object areas are disconnected, whereas 1 indicates a high degree of connectivity. It is limited to cat-
371 egorical variables and is less affected by variation associated with small objects and noise. Yuan and Strobl (1991) tested these measures on synthetic images and on an outcrop. There are several limitations to implementing the two measures: (1) the measures rely on the availability and sedimentological study of appropriate outcrop analogues; (2) the outcrops need to be matched to nearby subsurface reservoirs producing from the same formation (facies); and (3) the requirement of complete two-dimensional data from the outcrop. Well and seismic data cannot be used directly. Generally, seismic data do not have the necessary resolution for detailed reservoir continuity studies (Yuan and Strobl, 1991). In order for the petroleum industry to have better reservoir performance prediction results, models need to address four issues: (1) flow-property scale-up, (2) incomplete property information, (3) uncertainty in the reservoir's description, and (4) connectivity. Development of a performance model that indirectly considers the difference between carbonate and sandstone reservoirs by accounting for porosity and permeability heterogeneities using fractal distributions is a new approach. Fractal-based reservoir performance model Emanuel et al. (1989) presented a reservoir performance prediction method incorporating many points of Hewett's (1986) fractal geostatistical methodology and using an approach developed by Lake et al. (1981). This developed approach consists of: (1) blending detailed geological, fluid-flow and fluid-property data; (2) creating fractal distributions of reservoir property data; (3) using generated interwell data in a finite-difference simulation to obtain a crosssection representing displacement efficiency and vertical sweep; and (4) incorporating this fractional-flow information into the areal coverage of a streamtube model to obtain fluid displacement values for the section, thereby completing calculation for the areal conformance. Their goal was to have the ability to make more accurate performance predictions for large-scale waterflood and EOR projects by detailed accounting of reservoir heterogeneity with a reduced history-matching effort at a lower overall simulation cost. A generalized logic schema of this procedure is presented in Figs. 5 - 6 9 A - D . The tasks and stepwise procedures, which are similar to Emanuel et al.'s (1989) methodology, were modified in order to provide the reader with an overview picture of the connectivity of geologic quantification, data integration, simulation of geological property distributions, the scaling of effective flow properties, and the possible extension of the procedure to infill drilling. Comments about the tasks that describe the major computational operations and decisions are necessary, inasmuch as different methodologies are coupled together (Figs. 5 - 6 9 A - D). Task 1 - Collect reservoir data. As in all reservoir analyses, one has to establish first the porosity-permeability character of the reservoir in order to analyze the data for statistical structure and to develop a heterogeneous reservoir cross-sectional model between two wells (Fig. 69A). The necessary points to be considered include: (1) using conventional methods to analyze well logs and core analyses for porosity and permeability and tying the data to depth;
372 (2) establishing empirical relationships between porosity and permeability so that missing data can be generated; (3) normalizing the data to zero mean, unit variance, and a unit interval; (4) establishing the probability density of the normalized values for the data sets; (5) calculating H values using the R/S rescaled adjusted range procedure (plot of R/ S vs. time) as applied to geophysical records is described in detail by Mandelbrot and Wallis (1968; 1969a). R/S plot, variogram, and Fourier series are spectral functions used to analyze correlations defined by bivariant statistics. The procedure, which consists of analyzing random processes and time series with the help of the behavior of R(t,s)/S(t,s), is known as 'R/S analysis'. R is the sample sequential range of a stationary time series X(t) for its lag s, and S is the sequence variance, which scales as R/S -- (as) H, where a is a constant. This test evaluates the long-run behavior of statistical series and detects the presence of long-run correlations (statistical dependence) in fractal distributions (Mandelbrot and Wallis, 1969b). Dependence implies that what happened at a previous time has an after-effect in the future. Mesa and Poveda (1993) and Muller et al. (1992) provide thorough discussions on the Hurst effect and its limitations.
Task 2 - Establish fluid properties and fluid flow paths. It is necessary to have representative fluid-property and fluid-flow data from the candidate wells (Fig. 5-69B). This can be accomplished by: (1) choosing the appropriate fluid-flow path(s) for analysis based on the well pattem; (2) selecting the wells defining the flow path; (3) checking if fluid-property and fluid-flow data is available. If not, then obtain such information from corefloods from selected well cores and PVT measurements on reservoir fluids samples. Coreflood data from noncandidate wells would be suitable, if the cores are reasonably representative of the zone; (4) determining if the well pair is separated by average field spacing; and (5) establishing geological markers fi'om well logs for the wells. These markers should be correlatable not only between the well pair, but to the majority of other wells in the reservoir. If not, then either another well pair having universal correlatable markers has to be selected, or this simulation approach possibly is not applicable to the reservoir. Task 3-Perform interwell stochastic interpolation. In order to generate an interwell cross-sectional porosity-permeability map from the data sets, it is necessary to consider the following data preparations (Fig. 5-69B): (1) the property value distributions values have to exhibit a normal (Gaussian) distribution with mean zero and unit variance. If the distributions are skewed, they are transformed to normally-distributed variables before interpolation (Emanuel et al., 1989). After interpolation the distributions are transformed back to their skewed form; (2) the interpolation program starts with porosity and permeability well-log values for each of the two wells. Porosity and permeability values are selected on a foot-byfoot basis by the program for each well in the cross section and the intermediate values are generated using the fractal interpolation scheme. This process is accom-
373
DATA i OH
COLLECt
J M[JlGItlg[ t L L bOGS ~ND COHL DATA
NO
ESTABLISH REL&IIOHSHIPS BEIMEEH DAIA
, ,
J !
GENERATE
DnTA
USING TRANSFORMS
1
CALC ULAI( ,~176 R/S
UALUES USING PROC[DURE
1 Fig. 5-69A. TASK 1 flow diagram presents the activities that define the steps necessary in the collection and the analysis of data for fractal statistical structure. Initial task in a fractal geostatistical-logic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance.
plished by calculating the initial variance using the mean-square variation of values on a foot-by-foot basis between the wells. Emanuel et al. (1989) pointed out that this measures the scale of variations at the interwell distance. It is assumed that the value of H, derived from the well logs, applies to the reservoir. The interpolation equations reduce the magnitude of the variance through recursion according to a power law determined by the value of H. Emanuel et al.'s (1989) study provides an example of the interpolation equations for multiple iterations; and (3) the end results of Task 3 are porosity and permeability cross-section maps between the selected wells.
Task 4 - Develop finite-difference cross-sectional model. A vertical cross-sectional hybrid model has to be developed, which will represent interwell flow in the reservoir (Fig. 5-69C). The approach consists of: (1) Choosing the appropriate finite-difference schemes (explicit or implicit forms), creating a grid (block, lattice, or irregular pattern) having 2 0 - 100 blocks between
374
T CHOOSE HI I.LS me
tYPIFYING
/
FLOH ,PATH
NO
t S ( I . I l C ! AN /NiiLI. PRODUCER PAIR
I,.
| J
YES
SLI.~C! AN iflJit;rOR PRODUCER PAIR
TIUN MITH NELLS iRON RESERVOIR EDGE - CENTER
!
i
NO
,, CORRELATE BETMLEN HELLS USING MAJOR NAHKER~ ,
UALI DATI. D
METHOD POSSIBLY NOT APPLICABLE
YES
AND FLOM DAIR AURILABLE
INTERMELL STOCHASTIC INTERPOLATION
NEASURED DATA SKEMED
PUT -COREFLOOD RUN NFCESSARY TESTS
Fig. 5-69B (continued at top of next page).
NO
TRANSFORN TO NORMAL DISTRIBUTION
375 t ,, USE i I11' IERPOL~ T i OII PROGRI~N TO GEl" I r R A C T A L DI S l r R I B U r I OHS
1 GENERArir ! Nr ENMLLL DA rA DI S l r R l B U r I oH',
1
COHD! T | O H t DI STill BUT i OM:, 1 0 HOHOR N|.ASUII~D I UALUI:S t J
~o
1
N..~
NI.,
C r 10145
1
Fig. 5-69B (continued). TASKS 2 and 3 are shown in the flow diagram. Task 2 activities define the steps necessary to establish representative fluid property and flow data. Task 3 activities scope the stochastic interpolation procedure. Second and third tasks are part of a fractal geostatistical-logic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance. the wells and testing the stability of the solution. Crichlow (1977) provides a good discussion on developing finite-difference models. (2) Creating a simulator model that is highly detailed in the vertical direction in order to represent measured log and/or core data as closely as possible (Emanuel et al., 1989). Simulation layers should be 1 - 2 ft ( 0 . 3 - 0.6 m) thick. The intent is to model heterogeneity near the same level of detail as that of the available data. (3) Setting the transverse (y) direction of the cross-section so it represents the shape of a stream channel. Emanuel et al. (1989) noted that this geometry is intended to model the transition from radial flow near the wellbore to more linear flow midway in the pattern. Additional discussion of finite-difference models was provided in Volume I by Dominguez et al. (1992). (4) The finite-difference model is run for the projected conditions. The results will correlate as fractional flow at the producer and average interwell saturation for each phase as a function of pore volumes injected. Task 5 - Develop Streamtube Map Model. The streamtube mapping approach can take the cross-sectional data and use it to estimate field-wide performance (Fig. 569D). The two-dimensional cross-sectional results and reservoir operating conditions are used as input to a streamtube program (or conformable mapping program) to account for pattern and areal confinement effects. Streamtube models can accurately calculate the positions of fluid banks (maintaining saturation discontinuities), thereby overcoming the effects of numerical dispersion. Emanuel et al. (1989) used a single-layer
376 I
FINI;E ~ Di|'FEREHCE MODELING
~" ! I
i
RETHINK NODEL REQUIREMENTS
SELECt APPROPRIATE NODEL
i
! 9l
NO
OTHER }LOH
FLOOD YES
YES
VES
1
VES
ill
1
FORECASt MEL~ AND/OR HESERUQIR FUTURE PERFORN&NCE ..
HUN
FINITE Pl F F E R E N C [ NODEL
I
RUN
l D!X-SECt OBTAIN I OnRL 1 SPLRCEnEHI
NODEL
CHECK hHD ADJUSt DRTR DISTRIBUTIONS F AEOUIRLD
RFSULTS
,1
t
InPOSE
PLanNED PRODUCTIOH ARIES
lvtRzrv - PLoPi I PHASE ] I I
1 nODEL RUN END PROJECt
1
J
- PLOT PHASE SATURATION AS FUNCTION OF TOTAL PU!
UERIFY AVG.
FRACTIONAL F L O M RI RODUCER
1
iI
1 NO
Fig. 5-69C. TASK 4 flow diagram presents the activities that define the steps necessary in the development of an appropriate finite-difference, cross-sectional model. Fourth task in the fractal geostatisticallogic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance.
streamtube model, because the fractional flow generated by the cross-sectional simulation accounted for permeability distribution, layering and gravity override, and the model can accommodate large patterns. Streamtube maps, which are based on streamline networks, can be constructed according to Doyle and Wurl (1971): (1) Generate a streamline network having both the sides and axes of channels connecting to well pair(s) based on a combination of Darcy's law and the continuity equation for a homogeneous incompressible fluid where the effects of gravity can be
377 RUli MODEL EliD PROJECT
I MP!SE PLANNED INJ~T|Oli HATE To FORECASt _
1
l
EUTUHE PF.H~ O Rli~liCE
! NO
ADJUST GROSS F L U I D UOI DAGE TO HISTORY UALUE RERUN NODEL
!
R~U. PE~FOR~
I
_
I
STREANTUBE MODEL
UALUES ALLOFTUBES ro
GET PHASE FLOH PER HELL PER TIMESTEP
I
1
I
INCORPORATE FRACTIONAL FLOM RESULTS l l i T O STHEAIITUBE MODEL
REPEAT LAST F l U E STEPS FOR EACH STHEANTUB[
1
I
NAP IRnCT i ONAL FLOSI SOLUT I Oli ONTO EACH TUBE
CA LCULAT E CUN, PUI (GROSS f L U I D ~O L. : I H C R E MENTAL P U I )
I
TIIBE PUI INJECTED UOL. D I U I D E D BY TUBE UOLUME
]
INPUT F L U I D RATE FOR EACH IIIJECTIOH HELL
[ ,UOLUNE L L o c A rE ! l i J . ANOIIG
!
TUBES PROPORT! ONAL TO TUBE NuB 1 L i Tu
l
1
*~
NOBI L! TY DETERNI NED BY L I l l E | l i t EGRII T i ON
I
I
SELECT TiliLSTEP lliCRElikNT
Fig. 5-69D. TASK 5 flow diagram presents the activities that show the steps necessary in the use of a streamtube map model to forecast future reservoir performance. Final task in a fractal geostatistical-logic schema, which can be used to calculate the effect of waterflood, miscible gas injection, and infill drilling operations on reservoir performance.
378 neglected. Martin and Wegner (1979) expanded the approach to two-phase flow using the Buckley-Leverett theory to calculate the fluid displacement along streamlines. For details, Hewett and Behrens (1993) discussed the one-dimensional transport equation for multicomponent, multiphase flow in a porous medium and the applicable scaling laws in such a displacement process. Flow-diagrams for a streamline program, a shape-factor program, and Higgins-Leighton's waterflood program were presented by Doyle and Wurl (1971). The model used in Emanuel et al.'s (1989) study was more or less based on the streamtube model procedure discussed by Lake et al. (1981). (2) Map the fractional-flow solution onto each tube. The total mobility in each tube was determined by line integration as described by Martin and Wegner (1979). Emanuel et al. (1989) chose a timestep increment so that the injected volume is allocated among the streamtubes in proportion to tube mobility. The incremental pore volume injected for each tube is the injected volume divided by the tube's volume. The cumulative value of the injected pore volumes determines the fractional phases, such as oil, gas, water or solvent, comprising the employed recovery method. The gross fluid volume is equal to the incremental pore volume injected (Emanuel et al., 1989). The assumption is that the project is run on the basis of voidage balance between production and injection. (3) Check the model against known reservoir performance by adjusting the gross fluid voidage to the history value. (4) Repeat the calculation for each tube. Summation of all the contributions from the tubes results in the flow of each phase for each well at a given timestep (Emanuel et al., 1989). (5) Impose a planned injection rate to forecast future performance. Emanuel et al.'s (1989) above-described scale-up model is generally limited to: (1) waterflood or miscible gas injection, (2) injection/production voidage balance, and (3) Negligible pressure depletion. Hewett and Behrens (1991) pointed out that streamtube methods are not suitable for modeling primary depletion, because they are based on incompressible flow. A suggested addition of infill drilling to the overall schema (Figs. 5-69A- D) was made to show how fractal-generated interwell distributions can be used in forecasting incremental recovery of by-passed oil during primary production operations. Hewett and Behrens (1993) reviewed some of the inherent limitations to Emanuel et al.'s (1989) model. They discussed the effects of length dependency of the dispersion coefficients derived from simulations of miscible displacements. Such a length dependence precludes the definition of an effective dispersion coefficient or the use of numerical dispersion to represent the effects of permeability heterogeneity on miscible displacements. Problems arise in the application of effective relative permeabilities that change along the flow path when scaled up. Hewett and Behrens (1993) pointed out that the problems are caused by the streamwise dependence of the effective relative permeabilities, some of which are initial conditions preceding the displacement, nature of the displacement (water displacing oil, etc.), gridblock size, the streamwise position of the block to which the effective relative permeability value is assigned, making their assignment to fixed grids difficult. As shown by the flow-diagrams (Figs. 5-69A- D), complications are introduced into the model by the requirement that there be some knowledge of the flow paths before the problem can be analyzed. Numerical dispersion effects have to be kept negligible by keeping the number of cells large enough so that all the areal paths must pass
379 through the same number of cells (Hewett and Behrens, 1993). Still, such models are better than older ones and show the direction of future simulations.
Applications of Fractal Models to Carbonate Reservoirs There have been several published accounts on the application of fractal models in predicting waterflooding and enhanced oil recoveries in carbonate rocks (Emanuel et al., 1989; Beier and Hardy, 1991). Emanuel et al.' s (1989) results will be discussed as case histories. The validity of the above-discussed simulation method was tested by modeling a total of twelve reservoirs having waterflood and miscible flood projects with measured performance. Four field cases, having comparable results with the other reservoirs, were selected by Emanuel et al. (1989) for presentation. Reservoir fluid properties and model configurations are given for the four cases in Table 5-XXI. Of the four presented cases, only Quarantine Bay is a sandstone reservoir and is included in Table 5-XXI for comparison. Reef reservoir: CO 2pilot flood case history. An 800-acre (323-ha) CO 2 pilot flood in a high-water-cut carbonate reservoir, which is part of a Permian limestone reef complex, was used in Emanuel et al.'s (1989) validation study. Location of the limestone reef reservoir was not given, but it is probably either in west Texas or eastern New Mexico, U.S.A. The pilot flood involved between 40 and 50 wells. Figure 5-70 shows comparisons between reported and predicted oil and CO 2 production rates. The match between the predicted and actual oil production rate is reasonable. No adjustment was made to the geological data to match history. Emanuel et al. (1989) stated that discrepancy in the early oil production rates is partly a result of TABLE 5-XXI Reservoir properties and model dimensions for four field cases studied by Emanuel et al. (1989). Three of the fields are carbonate reservoirs, whereas Quarantine Bay is a sandstone reservoir Data for reservoir models
Grid dimensions nx n Y n_. Pressure, psi Temperature, ~ API gravity, ~ Oil FVF Solution GOR, scf/bbl Oil viscosity, cP k/k H
Model thickness (z direction), ft Model lengths (x direction), ft
Quarantine Bay
Carbonate CO 2 pilot
Waterflood test
Little Knife
100 1 40 3450 183 33 1.22 435 1.15 1.0 40 800
43 1 84 2500 130 40 1.5 1000 0.5 0.65 168 1800
43 1 84 500 85 32 1.14 320 2.7 1.0 84 1011
129 1 30 3500 245 33 1.68 1093 0.27 0.01 - 1.0 30 258
S o u r c e : After Emanuel et al., 1989, table 1" reprinted with the permission of the Society of Petroleum
Engineers.
380 45004000
.
10 4
s5oo
.
El
1--
3000 2500
f,
2ooo
=o .g
J5oo
C
103
o :1= o "o o lb.
Q. 04 0 rJ
o
A"
I000
o
500 0 0
0.5
I
I
I
I
1.5
2
2.5
I
3
I
I
3.5
4
10~ 4.5
Time from Start of CO 2 Injection, Years .,,
..
...
Fig. 5-70. A comparison between the reported and model-predicted oil and carbon dioxide production rates for a pilot flood in a carbonate reservoir. (After Emanuel et al., 1989, fig. 10; reprinted with the permission of the Society of Petroleum Engineers.) treating all wells used in the model as coming on at the project's start and that they deliver fluid at a constant average rate. Inherent to all production operations, there are going to be some of the wells shut-in from time to time and fluctuations in the fluid production rates. The average gross fluid injection/production in total reservoir barrels per day for each well, the injection volume of CO 2, and the injection water comprised the historical data used in the model. The streamtube model for the project is given in Fig. 5-71. Model and reservoir fluid data are presented in Table 5-XXI.
Dolomite reservoir: waterflood case history. A mature waterflood in a large carbonate reservoir composed of a thick sequence of dolomites and siltstones of Permian age was evaluated using the fractal model. The probable location of this reservoir is west Texas. A selected section of the reservoir was chosen consisting of six inverted nine-spots covering about 250 acres (101 ha). Emanuel et al. (1989) used an 86 x 43-cell cross-sectional model to represent the interwell geology. The model consisted of an injector and producer spaced 1,000 ft (305 m) apart. Porosity and permeability values were interpolated from core data measured at one-foot intervals through the reservoir. Cell dimensions were 2 x 23.25 ft (0.6 x 7 m), with the y dimension shaped to conform to a streamtube (Emanuel et al., 1989). Figure 5-72 shows the total project response of cumulative oil with time and water cut. The cross-sectional simulation used average water injection rates over a 20-year period. Predicted and field data match closely without any adjustment of geological data (Emanuel et al., 1989).
381 Producing Well Injection Well - - T u b e C e n t e r L.in T u b e Borders --
""
#%L 9
~
--..\
800
-
_
,\, "k,,~,
s"
""
""0
-
~ Illl
%
|
,,~\ii,
'I
I
i~_--'- --~ I "__-. . . . . ~.:. .....
.~
i,
-
J
- ~ ~ _ ~ .
i
"
700
-Ui;,,7;
"--J
o X
""
,,., . -
I
I
600 t
9
"',,,
o
r,,ll
v
-.
-.
"-:'.'.
Iu
-----
I
./,,/
,,
oo
/ l
300
~'
400
I_ / X ,
"
I
~,
m
500
I
!
-
I
~
, 9
,..
I.I.
I /
.
l
//, ,
-
i
,1~".':" "!,1... I
600
I
I
~
..~
oS
~
'.
s
imtm l ,
9
9 9
9
T ' - < "9 . . .---~-.
I
700
-z:
, ',', , /
,-----"---";, . . . . :..~.,./ ,,. I "" --'--'"~" " ' / "" / ' ~ _ ' . ] . ~'/... :
sr
'
400
,
-
'\'"" \"\"
i ;,,',,,,'1.",.
\,\,
u~ 500
'~'"" ',~'"
" f;I
m~
I
800
9
'
I
9
9
/
I
,
.I
|
900
I
i_
I000
Feet (XlOi )
Fig. 5-71. The C O 2 pilot flood pattern streamtube model. (After Emanuel et al., 1989, fig. 9; reprinted with the permission of the Society of Petroleum Engineers.)
Little Knife field: CO: (WAG) minitest case history Emanuel et al. (1989) undertook this study to test the ability of the fractal distribution to predict a detailed measurement of the vertical saturation distribution. The test interval was in the Little Knife Field, located near the central part of the Williston Basin in Billings, Dunn and McKenzie counties, North Dakota, U.S.A. Production is from the Mississippian Mission Canyon Formation and is the middle member of the Madison Group (Desch et al., 1984). The formation: (1) is about 465 ft (142 m) thick, (2) the top of the formation is at an average depth of 9650 ft (2,941 m), (3) has porosity ranging from 8.5 to 27% and averaging 14% in the dolomitic zones,
382
J 80
60 (.3 L. 0
40 9
o
Field Data
9
20
Calculated "I.... i" I0
20
30
I
I
40
5O
Time. Years
8000 .a
=E 6
6000
0 ~
0 "0
o
11.
Start of
4000
J - "
f
Wat i 9 f ~
o 0
2000 ...
E t~
,...
9
FieldData Calculated
o
m
0
I
I
I0
20
Time,
,
I
I
30
40
I 5O
Years
Fig. 5-72. A comparison between the reported field data and predicted values of water cut (%) and cumulative oil production rate for a mature waterflood in a dolomite reservoir. (After Emanuel et al., 1989, fig. 12; reprinted with the permission of the Society of Petroleum Engineers.)
383 (4) has permeability ranging from 1.0 to about 167 mD (0.000987- 0.165 ~tm2), and (5) has been subdivided into six informal zones defining a shallowing upward carbonate to anhydrite sequence. The zones are from top down: A - anhydrite, B - dolomitized packstone/wackestone, C - dolomitized wackestone, D - dolomitized wackestone, E dolomitized wackestone, and F - limestone (Lindsay and Kendall, 1985). Zones B, C, and D compose the reservoir. The original reservoir was undersaturated and had no free-gas-cap drive. Its drive mechanism is solution gas-drive with a limited edgewater drive (Desch et al., 1984). The reservoir has not been extensively waterflooded. The CO 2 non-producing minitest involved four wells drilled in an inverted fourspot configuration covering 5 acres (2 ha) with a radius of 250 ft (76 m) (Fig. 5-73), plus another well (ZAB OBS #4) drilled for pressure cores (Desch et al., 1984). The cores were used to measure oil saturation values, which in turn, were compared to calculated well-log saturation values. The central well (ZAB INJ #1) served as the injection well and remaining four wells served as non-producing observation wells. ZAB. ORS. o l
ZAB. INJ. o I
ZAB. 0 8 $ . ;,11
In
o2 lit(:
ZAB. OBS. ,e 3
Fig. 5-73. A fence diagram of zones C and D of the Mission Canyon Formation (Madison Group) through the WAG (water alternating with gas) minitest wells located in the Little Knife Field, North Dakota, U.S.A. (After Desch et al., 1984, fig. 5; reprinted with the permission of the Society of Petroleum Engineers.)
384 All observation wells were in good fluid communication with the injection well. The test consisted of a water-alternating-gas (WAG) type injection sequence with five alternating slugs of formation water and CO 2 into a 31 ft (9.4 m)-thick interval composed of lower basal C beds and upper D beds. Emanuel et al. (1989) revealed that the interval is characterized by persistent high permeability values of about 1 Darcy near its center, and diminishing to near zero at interval top and bottom. Desch et al. (1984) reported that the minitest was designed to provide the following information: (1) reduction in oil saturation due to water injection, (2) reduction in waterflood residual oil saturation due to alternate WAG, (3) extent of gravity segregation, (4) effect of stratification and crossflow, and (5) influence of reservoir heterogeneity. A numerical, three-dimensional, three-phase multicomponent compositional simulation provided a satisfactory history match of the pressures, saturations, and fluid compositions observed throughout the test. Vertical sweep by CO 2 was incomplete owing to stratification and the possible occurrence of viscous fingers; however, it was about 52%. The minitest's pattern sweep efficiency for CO 2 approached 52% of the original oil-in-place at the start of the project as compared to 37% for the waterflood (Desch et al., 1984). Emanuel et al.'s (1989) model consisted of a cross-section 250 ft (76 m) in length and 30 ft (9 m) in gross thickness. The cross-section distance is the same as the distance between the injection well and the observation well ZAB OBS No. 2 (Fig. 573). An H value of 0.65 was used in the simulation; however, cross-sectional permeability maps were generated for H values between 0.65 and 0.85. Emanuel et al. (1989) stated that these are typical values for reservoirs, which they have studied to date. The fractal permeability distribution for this zone is shown in Fig. 5-74. The predicted saturation minimum is about 3 ft (1 m) higher in the cross-section than that observed from the well logs. Vertical permeability values are much lower than the horizontal ones. Measured core permeability showed a range of kh/k ratio from 1" 1 to 100:1 (Emanuel et al., 1989). The oil saturation profiles for ZAB OBS well No. 2 are matched with the fractal model's predicted profile (Fig. 5-75). The conclusion to this exercise was that the fractal model can represent the general trend of fluid movement; however, an exact match lies beyond the certainty of the available data in most instances (Emanuel et al., 1989).
Reservoir modelingprognosis As demonstrated, fractal interpolation methods using well-log and core data from carbonate reservoirs yield a new and effective means for handling reservoir heterogeneity in simulation studies. This technique has carried heterogeneity descriptions just beyond the verbal, qualitative stage of analysis. New modifications and approaches, which are appearing frequently in the literature suggest, however, that future quantitative refinement is possible. Araktingi et al. (1993) described a menu-driven workstation application program, GEOLITH, designed to analyze reservoir data and construct reservoir simulation models with a geostatistical approach. Numerical input from well logs, core analyses, and seismic data are used to construct realistic quantitative geological reservoir models that calculate the spatial distribution of reservoir flow properties. The GEOLITH program addresses Tasks 1 through 4 (Fig. 5-69A to C).
HORIZONTAL I-1"-3 Above 600 mD
l
~
Below I.OmD
PERMEABILITY
MAP
3O
I,,1_25
(n'zo (/)15 LI.I Zlo
"1- ,3 0 I--
?_C
40
60
80
INJECTOR-
I O0
12 0
PRODUCER
i 40
160
180
200
220
240
DISTANCE, FT
Fig. 5-74. Cross-sectional map of horizontal permeability between the injection well and observation well No. 2 in the Little Knife Field, North Dakota, U.S.A. (After Emanuel et al., 1989, fig. 13; reprinted with the permission of the Society of Petroleum Engineers.)
OO
386 9845
S a t u r a t e d 011 Base Case 9850
. _ _ _ . . . S a t u r a t e d 011 Observed ......
Simulation
Top of Permeable Zone 9855
"
~
0
/ o
./..I. //"...
9 e
,(.
/./.9860
e
9
9
9865
",.
o\~
9870 Bottom
of
~'~~
Permeable Zone 9875 0
I .2
J .4
I .6
I .8
I
I
Oil S a t u r a t l o n Fig. 5-75. A comparison between simulated and observed oil saturation values in observation well No. 2, Little Knife Field, North Dakota, U.S.A. (After Emanuel et al., 1989, fig. 14; reprinted with the permission of the Society of Petroleum Engineers.)
387 Beier and Hardy (1991) made a comparison between fractional Gaussian noise fractional Brownian motion (fBm) in the generation of interwell distributions of reservoir properties as determined from well logs. As was previously discussed, Hewett (1986) reasoned that the fractal structure found in porosity well logs is fGn. Hewett (1986), however, postulated that the horizontal properties have a different spectral distribution, which is described by fBm. Well spacing is normally too large to determine the statistical structure in the horizontal distance. Hardy (1991) proposed an unique solution to this problem by analyzing the horizontal structure of sedimentary layers using distributions of dark and light regions from photographs of cores and outcrops. He found that the horizontal traces could be characterized as fGn. A comparison between the fGn and fBm methods was made using a carbonate reservoir located in southwestern New Mexico, U.S.A. This unnamed reservoir was undergoing a mature waterflood in the Permian Grayburg and San Andres dolomitic pay zones. Appropriate cross-sections using the field spacing of 20 acres (8 ha) were generated for both fGn and fBm. Performance data were calculated using a hybrid finite difference-streamtube model. Results showed that both methods matched field water cut data. The initial water saturation was the only property adjusted to obtain the match, and was made owing to initial water production from transition zones. The study revealed that the fGn distributions have lower effective permeabilities (linear flow) than thefBm distributions (Beier and Hardy, 1991). The fractals infGn are also known by the term 'fat' fractals. There were, however, only slight differences between the resulting cumulative oil vs. cumulative injection curves of the two methods. They conjectured that as the well spacing increases the simple linear interpolation and fBm will become poorer representations for reservoir heterogeneity. One interesting approach involving streamlines is conformable mapping (complex variables), which can be applied to the analysis of compressible fluids and transient behavior. A region of the reservoir or a region(s) around a well or wells can be mapped onto a conformable rectangle. The appropriate numerical analyses are then performed and transformed back to the region's original configuration. The application of conformable mapping principles to streamlines defining transient flow was discussed by Hurst (1981, 1982). Hewett and Behrens (1993) suggested that any difficulties associated with the above practical application of effective flow properties in Emanuel et al.'s (1989) model were due to their definition in an Eulerian framework. In such a framework, properties are distributed in space without regard to fluid flow paths or travel distances of fluid fronts. A Lagrangian framework, however, permits flow fronts to carry the appropriate flow properties with them, and the motion of displacing fronts is modeled explicitly. The integrated total mobility and phase fractional-flow distributions are scaled and mapped directly onto areal streamlines. The solution preserves the streamwise dependence observed in the cross-section simulation, and no new errors enter into the simulation owing to the definition of a grid. It was emphasized by Hewett and Behrens (1993) that the areal flow paths are determined by solving the streamlines corresponding to a unit mobility ratio displacement with the well rates and areal permeability thickness distribution of the reservoir. As with all new approaches there is a new set of restrictions.
(fGn) and
388
It was shown in this section that permeability values for macroscopic simulation modeling are either obtained by simple arithmetic, geometric or harmonic averages over the microscopic values, or by using advanced techniques such as perturbation expansions. None of these are valid when the distribution of local permeabilities is very wide, or when the distribution contains strong correlations. As mentioned above by Hewett and Behrens (1993), the effects of spatial anisotropies on permeability have not been addressed in detail. Another way to account for permeability values assigned to grid blocks was proposed by Aharony et al. (1991). Their approach involved a simple renormalization group scheme (method), which they termed FRACTAM. The term stands for fast renormalization (scale-up) algorithm for correlated transport in anisotropic media. The algorithm is based on real space renormalization group approach first used for the percolation bond probability (King, 1989; Aharony et al., 1991). Korvin (1992, p. 21) provides an excellent discussion on percolation theory. The idea is taken from statistical physics and is used to described the build-up of clusters to form an infinite cluster. In this section we refer to the build-up (percolate the lattice) being the construction of a connected porous network. Percolation threshold is defined (in the case of a porous network) as the point where a critical porosity and pore interconnectedness exist and fluids can flow through the pores. Below the threshold the pore system is 1
A
4 Ib
~_
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
- 0
,
2
5
i
4.
v ~
.
.
.
9 9
. . . . . . . . . . . . 9
........ ,
9
o ,
9 o
o
,
.
.
.
.
B
~
: ~
9
.......
9 .................
i
................
9
. .
9
o
.
~
i
o
,
.
9
.
9
, ,
9 9
; .......
i
,
,
.......
.
,
o
........
9
.
.......
.
+
9
9
9
9
9
9
9
9 9
.
,
. o
..
1
_
4
e
9 3! 2
_ A
.
5
Fig. 5-76. FRACTAM scheme showing how the upper left lattice is renormalized into the upper right one. Bonds 1,2, 3, 4 and 5, as shown below the lattice, are equivalent to the triangular graph and are used to determine the permeability value of the renormalized bond A. The permeability value of bond B is found similarly, from the original permeabilities of bonds 2, 3, 6, 7, and 8. (After Aharony et al., 1991, fig. 2; courtesy of Elsevier Science Publishers B.V.)
389 ineffective. Practically speaking, it is the point at which a rock is either permeable or essentially impermeable. A random resistor network can be used to describe the scaling-up of permeabilities as shown in Fig. 5-76. Here the permeability of bond A is determined by those of bonds 1, 2, 3, 4, and 5 by employing the Wheatstone bridge analogy. The permeability of bond B is found similarly, from the original permeabilities of bonds 2, 3, 6, 7, and 8. Aharony et al. (1991) then iterated FRACTAM for each of the specific squares until they were left with two effective permeability "tubes", one in the x- and one in the y-directions. Comparisons were made with "true" permeability values obtained from digitized core sample images and with generated fractal forgeries of core images. The authors found that FRACTAM was accurate to within less than 5% in all cases. Thorough background discussions on macro- and micro-scaled network models are given by Moore (1952), Fatt (1956a; 1956b; 1956c), and Rose (1957). Real space renormalization application will be discussed near the end of this section. The above deliberations reinforce the premise that oil and gas recovery applications rely on the functional relationship between the volume-average parameters described by Darcy's law and the microscopic processes occurring at the pore scale. Discussion will now focus with some detail on the numerical relations between porosity, permeability, and electrical conductivity. It is these transforms that control the input of permeability values into the macroscopic scale simulation models of carbonate reservoirs.
Microscopic heterogeneity: permeability- conductivity- porosity relationships Obtaining information on fluid flow properties inside carbonate oil reservoirs is complicated by high variability of permeability values. As pointed out previously in this chapter, one can observe intermittent variations of the absolute permeability over several orders of magnitude at a given scale, such as the core length scale. The permeability variations occur over a wide range of scales from microscopic to megascopic. Saucier (1992) emphasized that forecasting difficulties arise from the fact that the three-dimensional structure of the permeability field remains poorly defined due to the lack of information that comes from rather sparsely drilled wells. Geology and seismic data provide only poor guidelines about heterogeneity size, stratification, and fine-scaled structures. Theoretical, statistical, and empirical correlations among porosity, permeability, surface area, pore size, irreducible water saturation, and conductivity (resistivity) were discussed by Chilingarian et al. (1992c: Volume I, Chapter 7). Mathematical relationships were described based on capillary tube models and include the following factors: pore shape, tortuosity, electrical resistivity of rocks and fluids, sonic speed, and scaling. It should be remembered, however, that as any thin-section of a sedimentary rock would show, the pore space is connected in a complicated and random manner by pore throats.
Scaling exponents Unfortunately, permeability and porosity values do not closely track each other when rock samples are taken from carbonate formations having different geological histories. This is demonstrated by different samples with the same porosity values
390 exhibiting a wide range in permeability and conductivity values, especially due to fracturing. Chilingar (1964) demonstrated a reasonable correlation between porosity and permeability of cores, by considering the effect of irreducible fluid saturations, using the concept of effective porosity, ~be, which has a different physical meaning in contrast to the modeling effective properties just discussed. Effective porosity was defined by Chilingar (1964) as the fluid-saturated pore volume minus irreducible fluidsaturated volume. By taking into account specific surface area, which incorporates the influence of fractures, and irreducible fluid saturation, Chilingarian et al. (1992c) developed an excellent correlation between permeability and porosity. The differentiation of fluid flow properties inside carbonate reservoirs is complicated by the high variability of the permeability field. Two empirical equations are used generally by petroleum engineers and geologists to define the relationship between permeability and conductivity using porosity values. These empirical relationships are justified by the non-intersecting tube models of the pore space. The scaling law for permeability, k, and porosity, ~b, is: k =
(s-52)
where m is the slope of the line from a log-log plot of permeability vs. porosity. Theoretically, Eq. 5-52 follows from different capillary tube models as described by Chilingarian et al. (1992c), and cellular automata involving lattice gas hydrodynamic simulation models described by Chen et al. (1991). The cellular automata approach can be described, in a physics context, as a class of mathematical systems characterized by discreteness in space, time and state values, determinism, and local interaction. The empirical equation (Archie's formula) relating electrical rock conductivity, G, and porosity is: (5-53)
G = aGwd~ m" ,
where a is an empirical parameter that varies with the lithology of the formation. It is generally assumed that a is unity. The conductivity of the pore water is Gw, and m^ is an exponent, which is defined by log-log plots of rock conductivity vs. porosity. Wong et al. (1984) mentioned that the power-law dependence in Eq. 5-53 resembles the behavior in the usual percolation problem, except that it suggests a conduction threshold at ~b= 0. According to Wong et al. (1984), the exponents m and mn are related as follows: m = mn(m n +
1),
(5-54)
for one-dimension, and m = 2m ^,
(5-55)
for higher dimensions. The relations used by well-log analysts to quantitatively obtain permeability values from porosity take two forms. Timur (1973) proposed the following equation, which is a variation of the Schlumberger empirical formula:
391
k=0.136
IO 44~1 kSwi~r2
,
(5-56)
where S i r r is the irreducible water saturation. The weakness of Eq. 5-56 is that k is dependent on 4.4th power of porosity and the second power of the irreducible water saturation. The determination of ~band S i r r values from well logs will most certainly be in error by a small amount. These errors will be magnified by being raised to the second and 4.4th powers, and can become large depending on the size of the error up to one order of magnitude. Also, Eq. 5-56 suggests that the pore space is connected at any finite porosity. Wyllie and Rose's (1950) empirical equation was derived from a plot of their "rock textural" function cb/k ~ and irreducible water saturation, S~rr"
(5-57) wirr
where c is a constant that must have the dimensions of a length, and c A is a dimensionless constant. For a clean sand c A = 0. This equation, however, has no theoretical basis. In addition, there is a wide scatter of data points in their abovementioned plot of ~ / k ~ vs. S~rr (Wyllie and Rose, 1950; see fig. 7, p. 115 and eq. 18, p. 116). An empirical equation was developed by Chilingar et al. (1963) relating surface area per unit of pore volume, S , cm2/cm3; porosity, ~b, fractional; permeability, k, mD; and formation resistivity factoPr, F (- Ro/R w, where R ~ is the electrical resistivity of formation 100% saturated with formation water andR wis the formation water resistivity): S = 2.11 • 105/(F22~"2k) ~ . P
(5-58)
This utilitarian equation deserves attention, because the formation resistivity factor embodies the effects of grain size, grain shape, grain size distribution, and grain packing. Fractal relations between internal surface area, porosity, and permeability are discussed in the section on multifractal analysis of porous media. Using all these equations poses a problem with the spatial distributions of porosity and permeability. Very little is known about the macroscopic permeability distributions in reservoirs. As shown by the previously discussed fractal simulation models, microscopic permeability distributions have to be scaled-up. In non-fractal reservoir performance models, "history matching" is used to attempt to correct the wrong assumptions. McCauley (1992) stated that geologists sometimes assume that the distribution of permeability transverse to direction of average fluid flow within the layer has a zero correlation length. The distribution of permeabilities parallel to this average flow direction has an infinite correlation length. The assumption of a log-normal distribution is in conflict with the assumption of an infinite correlation length (McCauley, 1992). The end results of simulation efforts are unrealistic predictions for the long-range performance of a carbonate reservoir.
392 Several investigators (King, 1989; Aharony et al., 1991; McCauley, 1992) pointed out that models of fluid flow through porous rocks, both on the microscale and macroscale, typically are equivalent to resistor networks. The scaling laws expressed by Eqs. 5-52 and 5-53, however, are in conflict with measured data for permeability and electrical conductivity. Comprehending this conflict will help us to delineate the geometry of the pore-space in carbonate reservoirs. At best, only a cursory review of this very complex problem can be given in this book. The reader will be exposed to various proposed mathematical approaches that accommodate pore-system heterogeneity. Starting with McCauley's (1992) approach using two simple models, one fractal-no disorder (Sierpinski carpet model) and the other nonfractal-disordered (bond-shrinkage model) are discussed here. It will be shown that these models follow
:,
i
t
X
t.
_,
I
ry Fig. 5-77. Parallel tube model constructed from Sierpinski carpets with b = 3 and L = 1. The area is subdivided into four squares; each square is divided into b 2 subsquares, and L 2 of these subsquares are removed in the center of the initial squares. The reader is referred to Eqs. 5-11 and 5- 12. The lattice shown is at the second construction stage (see Fig. 5-22). (After Adler, 1986, fig. 1; reprinted with the permission of the American Institute of Physics.)
393 from a more general model. Both models do not include the idea of pore-space connectivity and, therefore, they do not explain on their own the difference between measured conductivity and permeability data. The general fractal--disordered (composite) model developed by McCauley (1992) includes connectivity, and qualitatively explains the experimentally known non-universal scaling exponents for permeability and conductivity.
Sierpinski carpet (parallel tubes) model. Adler's (1986) three-dimensional, fractal transverse pore-space model is based upon the geometry of the regular Sierpinski carpet constructed from parallel square cylinders (Figs. 5-77 and 5-22). In his analysis, McCauley (1992) compared a tube network model (parallel resistor network) with Adler's Sierpinski carpet model to show that the conductivity exponent m^ is completely wrong as predicted by both approaches. Parallel tube models, however, can be made to fit known permeability measurements. The tube model can be represented by an octal tree (Adler's tube model and tree models are approximately the same), where the parallel resistors are equivalent to the parallel tubes (Fig. 5-78) (McCauley, 1992). The tube equation for the effective permeability, k~, is: (5-59)
kff ~ 2nL4n '
where n is the number of generations on the tree (there are 2" branches in generation n); and L is the length of the side of a square tube so that the electrical conductivity, G 12, and the local permeability k z L 4. The volume flow rate through a pore is defined
(a) (b)
Fig. 5-78. Resistor network models. ( A ) - Binary tree model exhibited for n = 3 generations. The third generation represents the smallest pore sizes. ( B ) - Octal tree model having 2" resistors in parallel equivalent to 2" tubes in parallel. The tree model of-A- reduces approximately to this case when the smallest pores (generation with the largest n) have lengths that are very large compared with those of the pores in the first n - 1 generations. (Modified after McCauley, 1992, figs. 3b and 5; courtesy of Elsevier Science Publishers B.V.)
394 as the local permeability times the local pressure gradient; therefore, k is analogous to G. Both obey the same laws of combination for the calculation of effective permeability (McCauley, 1992). The laws are: G ~ = G l + G2
(5-60)
for two tubes in series and, G ff= G I G 2 / ( G 1 +
G2)
(5-61)
for two tubes in parallel. If the model is built upon the assumption that the length of each tube segment is roughly the same for all tubes on the tree, then the electrical conductance for the tube model for large n is: Gelf ~ 2"L.2,
(5-62)
For a large n, the last generation of tubes dominate, which are the smallest pores and the same is true of the effective permeability given by Eq. 5-59. McCauley (1992) showed that the conductivity exponent, m 6 is" mA=(2-Do)/D
o,
(5-63)
where D o is the fractal dimension and the permeability exponent, m, is" m = (4 - D o ) / D ~ ,
(5-64)
where D o < 2 for both equations. For small sandstone samples, it is known that m ^ 3/2 ~ 1.5 (from the iterated dilute limit model of Sen et al., 1981) and m ~ 15/2 ~ 7.5 as an average, whereas for carbonates m A values range from 1.6 to as high as 2.8 (de Witte, 1972; Wong et al., 1984). McCauley (1992) suggested that for any model to be reasonably correct, the orders of magnitude of these numbers should at least be reproduced using Eqs. 5-63 and 5-64. As one can see, these numbers cannot be reproduced by the tree model. Adler's (1986) model gives the resulting conductivity exponent, m A = 1, inasmuch as G ~ = ~, and the permeability exponent, m, is: m = (4 - Do)/(2 - Do),
(5-65)
which can reproduce m ~ 15/2 ~ 7.5 for sandstones; however, it is impossible to reproduce the required conductivity exponent m A values in the range of 1.5 - 2.8 for sandstones and carbonates. McCauley (1992) observed that Adler did not compute the permeability for successive stages of construction of a Sierpinski carpet. Adler computed permeability for 23~ separate tubes in parallel with each other rather than 2 ~, because the Sierpinski carpet is organized onto an octal tree. The effective permeability, when an octal tree is taken, becomes:
395 kff ~ 23nL4. ,
(5-66)
and the pore-space area is equal to: ~b = Geff= 23"L 2. ,
(5-67)
which is the pore-space area of the 23n smallest pores connected in parallel, analogous to Fig. 5-78. The above suffer from the fatal defect that ~b= Geff; therefore, m ^ = 1. This conclusion is in strong disagreement with experimental results (McCauley, 1992). It should be noted that in the tree and Adler's models, only the cross-sectional area of the pore space is distributed fractally. McCauley (1992) has argued successfully that the conductivity exponent m 6 is completely wrong, as is predicted by both the tube and the Sierpinski carpet models. Models portraying tubes that are all merely mutually parallel did not remedy this problem. Bond-shrinkage model. Wong et al.'s (1984) nonfractal model focused on the variation of pore space with porosity. It describes how pore-size distribution can influence the conductivity and permeability of brine-saturated rocks. The electrical conductivity is simulated by a random resistance network with a zero percolation threshold, which occurs at ~b= 0, and where all the resistors are in series. The rock model consists of a single, long pipe that is made by combining many tubes having different diameters (Fig. 5-79) (McCauley, 1992). Each tube segment has an area L 2, in series, and k ~ L 4. Porosity is varied by a random bond-shrinkage mechanism. Wong et al. (1984) used a binomial distribution of the different elements connected in series with each other in a one-dimensional model. To calculate porosity, the probability, p, for any particular tube to shrink n times is given by the binomial distribution"
= [1 + p ( L 2 - 1)] u ,
(5-68)
where <~> is the average pore-space area over the network, and N is the different possible diameters for a section of pipe, each with the same length L i. McCauley (1992) showed that the electrical conductivity scaling exponent is: m^ = a 2 > 1 ,
(5-69)
forp ~ 1, and Eq. 5-69 yields m^--+ 1 asp ~ 1. Derivation of Eq. 5-69 is based on the fact that the inverse conductivity is additive for resistors connected in series. McCauley (1992) pointed out that this bond-shrinkage model was originally introduced from the qualitative standpoint of percolation theory to model the zero-percolation threshold. The probability that a section of tube is shrunken n times by the factor L = 1/a (L m = a -m) from unit radius to form a section with radius L m is pm, and (1 __p)N-m is the probability to find a segment of pipe of unit radius as described by the bond shrinkage model (McCauley, 1992). The bond shrinkage model was originally introduced by Wong et al. (1984) to model the zero-percolation threshold. Hence, with P(m ^) = pm^(1 --p)N-m^N! / m ^ ! ( N - m6)! resulted in Eq. 5-68.
396
L
Fig. 5-79. Disordered, nonfractal, one-dimensional model based upon tubes of different cross-sectional area in series. (After McCauley, 1992, fig. 11" courtesy of Elsevier Science Publishers B.V.) As indicated the shrinking procedure can be repeated indefinitely with the same L to reduce the network conductance and permeability, and the total volume of the tubes. The effective permeability for this binomial distribution is equal to" -1
kfr = [1 + p(L -4 - 1)]N,
(5-70)
and m--
ln[1 + p ( L -~- 1)]
(5-71)
ln[1 + p ( L ~ - 1)] Whenever, p ~ 1, m = m^(m ^ + 1) > 2m ^, whereas m ~ 2, ifp --~ 1, which corresponds to a long pipe with constant diameter in Fig. 5-79 (McCauley, 1992). An a, o r p and a, can be chosen to fit m ^ z 3/2, but it is then impossible to obtain m ~ 15/2 as is suggested for sandstone. The predicted scaling exponent for the effective permeability is too small, which means that the fluid flows too easily (a too high permeability) through the pore-space of the bond-shrinkage rock model (McCauley, 1992).
397
.-,,...%,\\,~
,'N\\\\" ~. \ \ \ \ \ \ \
~ \\\" \
Fig. 5-80. Schematic ofMcCauley's (1992) combined model that is fractal and disordered. The model is a generalization of the model shown in Fig. 5-79 to include complete binary connectivity. The generalization to models with complete trees with order t = 3,4,5 . . . . is obvious. This new model reduces to the model presented in Fig. 5-78B where t = 2, whenever p approaches unity, but also reduces to the disordered, nonfractal one-dimensional model for the special case where t = 1. (After McCauley, 1992, fig. 12; courtesy of Elsevier Science Publishers B.V.)
Composite model. McCauley (1992) proposed that a rock model can be constructed by combining Wong et al.'s (1984) and Adler's (1986) models into a composite model having equations based on a single-scale fractal. This model would then be extended by McCauley (1992) to a general model based on multiscale fractal. The composite model corresponds to a simple parallel/series network of resistors where there is variation in both porosity and the number of pores from one thin-section to another (Fig. 5-80). The "thin-section" concept (McCauley used the term toy rock) is derived by taking multiple thin slices of a theoretical rock and stacking them so that the sections correspond to the above network. McCauley (1992) generalized results, which correspond to the binary organization of Fig. 5-80, yielding in the following relationships for porosity, permeability, and conductivity: <$> = [1 + p(2L 2 - 1)] N,
(5-72)
398 -1
Gear = [1 + p ( 2 - ' L -2 - 1)] N
(5-73)
and -1
k e~ = [1 + p ( 2 - ' L -4 - 1)]u.
(5-74)
From these equations, the composite model gives the following equations for conductivity and permeability, respectively: ln[1 + p(2-'L -2 - 1)] m^ =
(5-75)
ln[1 + p(ZL 2 - 1)]
and ln[1 + p ( 2 - ' L --4 - 1)] m=-
ln[1 + p ( Z L 2 - 1)]
,
(5-76)
Wong et al.'s (1984) exponent equations are obtained when p ~ 1 for electrical conductivity and permeability, respectively: m ^ ~ 89 2,
(5-77)
and
a2( 89 4 - 1) m~
( a 2 - 2)
,
(5-78)
McCauley (1992, p. 43) showed that the limit p --~ 1 yields the parallel tube [or Adler (1986)-1ike Sierpinski carpet model] results: m ^ = 1, and m = ( 4 - D o ) / ( 2 - D o ) , where D o = ln2/lna (ln is the natural log). If a is set equal to 2, then m ^ = 2 and m~ m 6 - 7 from Eqs. 5-77 and 5-78 (McCauley, 1992). These results are very reasonable. In order to obtain an m ^ value of 2.5, p can be kept small and a increased in Eqs. 5-75 and 5-76. Also p and a can be varied. Manipulation of the values can be made to get m ^ = 1.4 by holding a constant and increasing p, because m ^ = 1 when p = 1. McCauley (1992) showed how to get larger values of the permeability exponent for a given value of conductivity exponent. He introduced connectivity (branching) of a complete binary tree. There is a limit in the composite model, as there was in Wong et al.'s (1984) model, where both the porosity and permeability are log-normally distributed (see McCauley, 1992, p. 44). By generalizing Eqs. 5-72 to 5-76 to a complete tree or order t, McCauley (1992) simply replaced the tree order of 2 by t, where t can take on values of 1, 2, 3 , . . . . resulting in m ^ and m exponents in the log-normal limit:
399 1 + [(1-p)/2](4-Do)lna m^ ~
(5-79) 1 - [(1 - p ) / 2 ] ( 2 - Do)lna
and
m/m ^ ~, (4 - Do)/(2 - Do).
(5-80)
Multifractal rock model. McCauley (1992) stated that the log-normal limit correctly reproduced the trivial limit of parallel tubes, where p = 1. Ifp is small, then the limit cannot be reproduced in the log-normal approximation. McCauley (1992, p.45) then discussed treating Eqs. 5-72 to 5-80, which are based upon a single-scale fractal, as a multiscale or nonuniform fractal. The transverse thin-sections of pore space o f the simplest multiscale fractal are a two-scale fractal. The reader is referred to the discussion on multifractal characterization later in this chapter. McCauley (1990) and Ijjasz-Vasquex et al. (1992) provided a complete background on multifractals and their applications in dynamic systems. The simplest case of a multifractal distribution of pore-space area can be envisioned where the porosity of a very thin slice of carbonate rock has a thickness that is small compared to the size of the largest pores, as being built by iterating two length scales L~ and L 2. McCauley (1992, p. 33) stated that in the first generation (n = 1) the scale L~ occurs b times, then L 2 occurs t - b times, where b is any integer between 0 and t - 1 and b = 0. Thus, for t" tubes connected in parallel, porosity and permeability are: = [tL 2, +
(5-81)
and G=
[bL 4 +
(5-82)
McCauley suggested that it is useful to introduce the canonical partition function, which is a generating function:
Z(fl) = [bl ~ + ( t - b)l~2 ]",
(5-83)
where g(fl) = - l n Z ( f l ) / n is analogous to the Gibbs potential per particle because n is analogous to the number of particles in ordinary statistical mechanics. Models like Eq. 5-83 follow from deterministic chaos (McCauley, 1992, p. 34). McCauley's (1992) Eqs. 5-72 to 5-78 are based upon a single-scale fractal. If the transverse thin-sections of pore space are represented by a multiscale fractal, then McCauley's simplest case is that of the two-scale fractal shown by the above Eqs. 581 to 5-83. Equations 5-72 to 5-76 restated for two-scale fractal are: <~b> = [1 + p(e -g(2)-- 1)IN,
(5-84)
400 -1
Gfr = [ 1 + p(e g~2)- 1)]u,
(5-85)
-1 keff = [1 + p ( e -g(4) - 1)]N,
(5-86)
resulting in In[ 1 + p(e -~z) - 1)] m^ = -
(5-87)
In[ 1 + p(e ~2) - 1)]
and In[ 1 + p(e -g~4)- 1)] m=
In[ 1 + p(e g~2)- 1)]
.
(5-88)
The general model explains two important facts: (1) connectivity (branching) is the way to obtain a large m / m ^ ratio with m^ > 1, and (2) nonuniversality of the scaling exponents m and m ^ results by varying both the first generation length scale L~ = 1/a and the probability p. McCauley's (1992) approach and interpretation were not based upon ideas from equilibrium statistical mechanics having attributes of universal critical exponents and formal percolation theory, but are based upon ideas from chaos theory. Chaos theory describes transport far from thermal equilibrium using trees, weak universality, multifractals, and nonuniversal scaling laws. McCauley concluded that in the dynamic model, the tree order describes how different thin-sections with different porosity values connect with each other. The very small diameter pore throats provide the connections between the pores, and typically require large scale magnification of a thin-section in order to be observed. McCauley speculated that a sufficiently accurate photograph of a thin-section, which reveals the smallest pore throats, would lead to a connectivity