Guidelines for Evaluating the Characteristics of Vapor Cloud Explosions, Flash Fires, and BLEVEs

Guidelines for Evaluating the Characteristics of Vapor Cloud Explosions, Flash Fires, and BLEVEs

CENTER FOR CHEMICAL PROCESS SAFETY of the American Institute of Chemical Engineers 345 East 47 Street, New York, NY 10017

Copyright © 1994 American Institute of Chemical Engineers 345 East 47th Street New York, New York 10017 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 permission of the copyright owner. Library of Congress Cataloging-in-Publication Data Guidelines for evaluating the characteristics of vapor cloud explosions, flash fires, and BLEVEs. p. cm. Includes bibliographical references and index. ISBN 0-8169-0474-X 1. Explosions. 2. Fires. I. American Institute of Chemical Engineers. Center for Chemical Process Safety. QD516.G78 1994 660'.2804—dc20 92-38795 CIP

This book is available at a special discount when ordered in bulk quantities. For information, contact the Center for Chemical Process Safety of the American Institute of Chemical Engineers at the address shown above. It is sincerely hoped that the information presented in this book will lead to an even more impressive safety record for the entire industry; however, the American Institute of Chemical Engineers, its consultants, CCPS subcommittee members, their employers, their employers' officers and directors, and TNO Prins Maurits disclaim making or giving any warranties or representations, express or implied, including with respect to fitness, intended purpose, use or merchantability and/or correctness or accuracy of the content of the information presented in this document. As between (1) the American Institute of Chemical Engineers, its consultants, CCPS subcommittee members, their employers, their employers' officers and directors, and TNO Prins Maurits and (2) the user of this document, the user accepts any legal liability or responsibility whatsoever for the consequence of its use or misuse.

ACKNOWLEDGMENTS The Center for Chemical Process Safety of the American Institute of Chemical Engineers owes a great deal of thanks to the dedicated and professional engineers and scientists who served with distinction on the Vapor Cloud Explosion subcommittee during the development of this Guidelines book. They are: John A. Davenport (Industrial Risk Insurers), chair John V. Birtwistle (Monsanto Chemical Company) Stanley S. Grossel (Hoffman-LaRoche, Inc.) R. A. Hawrelak (Dow Chemical Canada Inc.) Peter D. Hoffman (Hoechst Celanese) David C. Kirby (Union Carbide Corporation) Robert E. Linney (Air Products and Chemicals, Inc.) Robert A. Mancini (Amoco Corporation) M. Reid McPhail (Novacor Chemicals Ltd.) Larry J. Moore (Factory Mutual Research Corporation) Francisco N. Nazario (Exxon Research and Engineering Company) Gary A. Page (American Cyanamid Company) Ephraim A. Scheier (Mobil Research and Development Corporation) Richard F. Schwab (Allied Signal, Inc.) The task of preparing the text, examples, tables, and figures of the book was entrusted to TNO Prins Maurits Laboratory, Rijswijk, the Netherlands. The principal authors were all members of the Explosion Prevention Department of the Laboratory: Kees van Wingerden Bert van den Berg Daan van Leeuwen Paul Mercx Rolf van Wees Their technical expertise is evident in both the characterization of the phenomena that this book explores (Chapters 2-6) and the practical examples that illustrate these phenomena (Chapters 7-9). The authors and the subcommittee were well served during this transnational effort by Dr. Hans J. Pasman, then Director, Technological Research, and Mr. Gerald Opschoor, Head, Explosion Prevention Department, TNO PML. Likewise, Mr. Thomas W. Carmody, then Director, CCPS, supported this important work. William J. Minges provided CCPS staff help.

Peer review for this important and lengthy volume was provided by: Philip Comer, Technica, Inc. R. C. Frey, M. W. Kellogg T. O. Gibson, Dow Chemical D. L. Macklin, Phillips Petroleum S. J. Schechter, Rohm and Haas Finally, CCPS is grateful to Dr. B. H. Hjertager, Telemark Institute of Technology and Telemark Innovation Centre, Porsgrunn, Norway, for preparing "A Case Study of Gas Explosions in a Process Plant Using a Three-dimensional Computer Code" (Appendix F).

A NOTE ON NOMENCLATURE AND UNITS The equations in this volume are from a number of reference sources, not all of which use consistent nomenclature (symbols) and units. In order to facilitate comparisons within sources, the conventions of each source were presented unchanged. Nomenclature and units are given after each equation (or set of equations) in the text. Readers should ensure that they use the proper values when applying these equations to their problems.

GLOSSARY Blast: A transient change in the gas density, pressure, and velocity of the air surrounding an explosion point. The initial change can be either discontinuous or gradual. A discontinuous change is referred to as a shock wave, and a gradual change is known as a pressure wave. BLEVE (Boiling Liquid, Expanding Vapor Explosion): The explosively rapid vaporization and corresponding release of energy of a liquid, flammable or otherwise, upon its sudden release from containment under greater-than-atmospheric pressure at a temperature above its atmospheric boiling point. A BLEVE is often accompanied by a fireball if the suddenly depressurized liquid is flammable and its release results from vessel failure caused by an external fire. The energy released during flashing vaporization may contribute to a shock wave. Burning velocity: The velocity of propagation of a flame burning through a flammable gas-air mixture. This velocity is measured relative to the unburned gases immediately ahead of the flame front. Laminar burning velocity is a fundamental property of a gas-air mixture. Deflagration: A propagating chemical reaction of a substance in which the reaction front advances into the unreacted substance rapidly but at less than sonic velocity in the unreacted material. Detonation: A propagating chemical reaction of a substance in which the reaction front advances into the unreacted substance at or greater than sonic velocity in the unreacted material. Emissivity: The ratio of radiant energy emitted by a surface to that emitted by a black body of the same temperature. Emissive power: The total radiative power discharged from the surface of a fire per unit area (also referred to as surface-emissive power). Explosion: A release of energy that causes a blast. Fireball: A burning fuel-air cloud whose energy is emitted primarily in the form of radiant heat. The inner core of the cloud consists almost completely of fuel, whereas the outer layer (where ignition first occurs) consists of a flammable fuel-air mixture. As the buoyancy forces of hot gases increase, the burning cloud tends to rise, expand, and assume a spherical shape.

Flame speed: The speed of a flame burning through a flammable mixture of gas and air measured relative to a fixed observer, that is, the sum of the burning and translational velocities of the unburned gases. Flammable limits: The minimum and maximum concentrations of combustible material in a homogeneous mixture with a gaseous oxidizer that will propagate a flame. Flash vaporization: The instantaneous vaporization of some or all a liquid whose temperature is above its atmospheric boiling point when its pressure is suddenly reduced to atmospheric. Flash fire: The combustion of a flammable gas or vapor and air mixture in which the flame propagates through that mixture in a manner such that negligible or no damaging overpressure is generated. Impulse: A measure that can be used to define the ability of a blast wave to do damage. It is calculated by the integration of the pressure-time curve. Jet: A discharge of liquid, vapor, or gas into free space from an orifice, the momentum of which induces the surrounding atmosphere to mix with the discharged material. Lean mixture: A mixture of flammable gas or vapor and air in which the fuel concentration is below the fuel's lower limit of flammability (LFL). Negative phase: That portion of a blast wave whose pressure is below ambient. Overpressure: Any pressure above atmospheric caused by a blast. Positive phase: That portion of a blast wave whose pressure is above ambient. Pressure wave: See Blast. Reflected pressure: Impulse or pressure experienced by an object facing a blast. Rich mixture: A mixture of flammable gas or vapor and air in which the fuel concentration is above the fuel's upper limit of flammability (UFL). Shock wave: See Blast. Side-on pressure: The impulse or pressure experienced by an object as a blast wave passes by it. Stoichiometric ratio: The precise ratio of air (or oxygen) and flammable material which would allow all oxygen present to combine with all flammable material present to produce fully oxidized products. Superheat limit temperature: The temperature of a liquid above which flash vaporization can proceed explosively. Surface-emissive power: See Emissive power.

Transmissivity: The fraction of radiant energy transmitted from a radiating object through the atmosphere to a target after reduction by atmospheric absorption and scattering. TNT equivalence: The amount of TNT (trinitrotoluene) that would produce observed damage effects similar to those of the explosion under consideration. For non-dense phase explosions, the equivalence has meaning only at a considerable distance from the explosion source, where the nature of the blast wave arising is more or less comparable with that of TNT. Turbulence: A random-flow motion of a fluid superimposed on its mean flow. Vapor cloud explosion: The explosion resulting from the ignition of a cloud of flammable vapor, gas, or mist in which flame speeds accelerate to sufficiently high velocities to produce significant overpressure. View factor: The ratio of the incident radiation received by a surface to the emissive power from the emitting surface per unit area.

Contents

Acknowledgments .................................................................

viii

A Note on Nomenclature and Units .......................................

ix

Glossary ................................................................................

x

1. Introduction ...................................................................

1

2. Phenomena: Descriptions, Effects, and Accident Scenarios .......................................................

3

2.1 Vapor Cloud Explosions ....................................................

3

2.2 Flash Fires ........................................................................

5

2.3 BLEVEs .............................................................................

6

2.4 Historical Experience ........................................................

8

References ................................................................................

44

3. Basic Concepts .............................................................

47

3.1 Atmospheric Vapor Cloud Dispersion ...............................

47

3.2 Combustion Modes ...........................................................

50

3.3 Ignition ...............................................................................

55

3.4 Blast ..................................................................................

56

3.5 Thermal Radiation .............................................................

59

References ................................................................................

66

4. Basic Principles of Vapor Cloud Explosions ..............

69

4.1 Overview of Experimental Research .................................

70

4.2 Overview of Computational Research ...............................

92

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v

vi

Contents 4.3 Vapor Cloud Explosion Blast Modeling .............................

111

4.4 Summary and Discussion .................................................

135

References ................................................................................

136

5. Basic Principles of Flash Fires .................................... 147 5.1 Overview of Research .......................................................

147

5.2 Flash-Fire Radiation Models .............................................

152

5.3 Summary and Discussion .................................................

155

References ................................................................................

155

6. Basic Principles of BLEVEs ......................................... 157 6.1 Mechanism of a BLEVE ....................................................

158

6.2 Radiation ...........................................................................

161

6.3 Blast Effects of BLEVEs and Pressure Vessel Bursts ................................................................................

185

6.4 Fragments .........................................................................

223

6.5 Summary and Discussion .................................................

239

References ................................................................................

242

7. Vapor Cloud Explosions – Sample Problems ............. 247 7.1 Choice of Method ..............................................................

247

7.2 Methods ............................................................................

249

7.3 Sample Calculations .........................................................

256

7.4 Discussion .........................................................................

272

References ................................................................................

275

8. Flash Fires – Sample Problems ................................... 277 8.1 Method ..............................................................................

277

8.2 Sample Calculation ...........................................................

281

9. BLEVEs – Sample Problems ........................................ 285 9.1 Radiation ........................................................................... This page has been reformatted by Knovel to provide easier navigation.

285

Contents

vii

9.2 Blast Parameter Calculations for BLEVEs and Pressure Vessel Bursts .....................................................

292

9.3 Fragments .........................................................................

311

References ................................................................................

335

Appendix A. View Factors for Selected Configurations ............................................................... 337 A-1 View Factor of a Spherical Emitter (e.g., Fireball) .............

337

A-2 View Factor of a Vertical Cylinder .....................................

338

A-3 View Factor of a Vertical Plane Surface ............................

340

References ................................................................................

345

Appendix B. Effects of Explosions on Structures ........... 347 Appendix C. Effects of Explosions on Humans ............... 351 C-1 Introduction .......................................................................

351

C-2 Primary Effects ..................................................................

352

C-3 Secondary Effects .............................................................

355

C-4 Tertiary Effects ..................................................................

356

References ................................................................................

357

Appendix D. Tabulation of Some Gas Properties in Metric Units ................................................................... 359 Appendix E. Conversion Factors to SI for Selected Quantities ...................................................................... 361 Appendix F. Case Study of Gas Explosions in a Process Plant Using a Three-Dimensional Computer Code ............................................................. 363 Index ..................................................................................... 383

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1 INTRODUCTION The American Institute of Chemical Engineers (AIChE) has been involved with process safety and loss control for chemical and petrochemical plants for more than thirty years. Through its strong ties with process designers, builders, operators, safety professionals, and academia, AIChE has enhanced communication and fostered improvements in the safety standards of the industry. Its publications and symposia on causes of accidents and methods of prevention have become information resources for the chemical engineering profession. Early in 1985, AIChE established the Center for Chemical Process Safety (CCPS) to serve as a focus for a continuing program for process safety. The first CCPS project was the publication of a document entitled Guidelines for Hazard Evaluation Procedures. In 1987 Guidelines for Use of Vapor Cloud Dispersion Models was published and in 1989 Guidelines for Chemical Process Quantitative Risk Analysis and Guidelines for Technical Management of Chemical Process Safety were published. The present book has evolved from the eighth CCPS project. This text is intended to provide an overview of methods for estimating the characteristics of vapor cloud explosions, flash fires, and boiling-liquid-expandingvapor explosions (BLEVEs) for practicing engineers. The volume summarizes and evaluates all the current information, identifies areas where information is lacking, and describes current and planned research in the field. For the novice, this volume provides a starting point for understanding the phenomena covered and presents methods for calculating the possible consequences of incidents. It also offers an overview and resource reference for experts. It should provide managers with a basic understanding of the phenomena, methods of calculation to estimate consequences, and the limitations of each method. The authors also hope that this volume can be taken as a starting point for future research. This volume consists of two parts: Chapters 1—6 and Chapters 7—9. Chapters 1 through 6 offer detailed background information. They describe pertinent phenomena, give an overview of past experimental and theoretical research, and provide methods for estimating consequences. Chapter 2 describes the phenomena covered, identifies various accident scenarios leading to each of the events, and describes actual accidents. In Chapter 3, principles such as dispersion, deflagration, detonation, blast, and radiation are explained. Each event treated requires a different approach in estimating effects. Therefore, each type of event is covered in a separate chapter. Chapters 4, 5, and 6 give background information, including experimental and theoretical research and conse-

quence modeling techniques, on vapor cloud explosions, flash fires, and BLEVEs, respectively. Chapters 7, 8, and 9 demonstrate the consequence modeling techniques for vapor cloud explosions, BLEVEs, and flash fires, respectively, by presenting sample problems. These problems contain sufficient detail to allow an engineer to use the methods presented to evaluate specific hazards. The authors have not attempted to describe all experimental and theoretical research in the field. Rather, the most important activities and their results are covered in order to offer an adequate understanding of the basic physical principles. This volume does not address subjects such as toxic effects, explosions in buildings and vessels, runaway reactions, condensed-phase explosions, pool fires, jet flames, or structural responses of buildings. Furthermore, no attempt is made to cover the frequency or likelihood that a related accident scenario will occur. References to other works are provided for readers interested in these phenomena.

2 PHENOMENA: DESCRIPTIONS, EFFECTS, AND ACCIDENT SCENARIOS Accidents involving fire have occurred ever since man began to use flammable liquids or gases as fuels. Summaries of such accidents are given by Davenport (1977), Strehlow and Baker (1976), Lees (1980), and Lenoir and Davenport (1993). The presence of flammable gases or liquids can result in a BLEVE or flash fire or, if sufficient fuel is available, a vapor cloud explosion. The likelihood of such occurrences can be reduced by process design and reliability engineering which meet or exceed established codes of practice. These codes include well-designed pressure relief and blowdown systems, adequate maintenance and inspection programs, management of human factors in system design and, perhaps most important, a full understanding and support by responsible managers of risk management efforts. Nevertheless, despite all of these precautions, accidents may still occur, sometimes resulting in death, serious injury, damage to facilities, loss of production, and damage to reputation in the community. Mathematical models for calculating the consequences of such events should be employed in order to support efforts toward mitigation of their consequences. Mitigating measures may include reduction of storage capacity; reduction of vessel volumes; modification of plant siting and layout, including location of control rooms; strengthening of vessels and other plant items; and reinforcing of control rooms. Knowledge of the consequences of vapor cloud explosions, flash fires, and BLEVEs has grown enormously in recent years as a result of many international efforts. Insights gained regarding the processes of generation of overpressure, radiation, and fragmentation have resulted in the development of reasonably descriptive models for calculating the effects of these phenomena. This chapter describes the main features of vapor cloud explosions, flash fires, and BLEVEs. It identifies the similarities and differences among them. Effects described are supported by several case histories. Chapter 3 will present details of dispersion, deflagration, detonation, ignition, blast, and radiation. 2.1. VAPOR CLOUD EXPLOSIONS A vapor cloud explosion may be simply defined as an explosion occurring outdoors, producing a damaging overpressure (Factory Mutual Research Corporation, 1990).

It begins with the release of a large quantity of flammable vaporizing liquid or gas from a storage tank, process or transport vessel, or pipeline. Generally speaking, several features need to be present for a vapor cloud explosion with damaging overpressure to occur. First, the released material must be flammable and at suitable conditions of pressure or temperature. Such materials include liquefied gases under pressure (e.g., propane, butane); ordinary flammable liquids, particularly at high temperatures and/ or pressures (e.g., cyclohexane, naphtha); and nonliquefied flammable gases (e.g., methane, ethylene, acetylene). Second, a cloud of sufficient size must form prior to ignition (dispersion phase). Should ignition occur instantly, a large fire, jet flame, or fireball may occur, but significant blast-pressure damage is unlikely. Should the cloud be allowed to form over a period of time within a process area, then subsequently ignite, blast pressures that develop can result in extensive, widespread damage. Ignition delays of 1 to 5 minutes are considered the most probable for generating vapor cloud explosions, although major incidents with ignition delays as low as a few seconds and greater than 30 minutes are documented. Third, a sufficient amount of the cloud must be within the flammable range of the material to cause extensive overpressure. A vapor cloud will generally have three regions: a rich region near the point of release, a lean region at the edge of the cloud, and a region in between that is within the flammable range. The portion of the vapor cloud in each region depends on many factors, including type and amount of the material released; pressure at time of release; size of release opening; degree of confinement of the cloud; and wind, humidity, and other environmental effects (Hanna and Drivas 1987). Fourth, the blast effects produced by vapor cloud explosions can vary greatly and are determined by the speed of flame propagation. In most cases, the mode of flame propagation is deflagration. Under extraordinary conditions, a detonation might occur. A deflagration can best be described as a combustion mode in which the propagation rate is dominated by both molecular and turbulent transport processes. In the absence of turbulence (i.e., under laminar or near-laminar conditions), flame speeds for normal hydrocarbons are in the order of 5 to 30 meters per second. Such speeds are too low to produce any significant blast overpressure. Thus, under nearlaminar-flow conditions, the vapor cloud will merely burn, and the event would simply be described as a large flash fire. Therefore, turbulence is always present in vapor cloud explosions. Research tests have shown that turbulence will significantly enhance the combustion rate in deflagrations. Turbulence in a vapor cloud explosion accident scenario may arise in any of three ways: • by turbulence associated with the release itself (e.g., jet release or a catastrophic failure of a vessel resulting in an explosively dispersed cloud);

• by turbulence produced in unburned gases expanding ahead of a flame propagating through a congested space; • by externally induced turbulence from objects such as ventilation systems, finned-tube heat exchangers, and fans. Of course, all mechanisms may also occur simultaneously, as, for example, with a jet release within a congested area. These mechanisms may cause very high flame speeds and, as a result, strong blast pressures. The generation of high combustion rates is limited to the congested area, or the area affected by the turbulent release. As soon as the flame enters an area without turbulence, both the combustion rate and pressure will drop. In the extreme, the turbulence can cause a sufficiently energetic mixture to convert from deflagration to detonation. This mode of flame propagation is attended by propagation speeds in excess of the speed of sound (2 to 5 times the speed of sound) and maximum overpressures of about 18 bar (260 psi). Once detonation occurs, turbulence is no longer necessary to maintain its speed of propagation. This means that uncongested and/or quiescent flammable portions of a cloud may also contribute to the blast. Note, however, that for a detonation to propagate, the flammable part of the cloud must be very homogeneously mixed. Because such homogeneity rarely occurs, vapor cloud detonations are unlikely. Whether a deflagration or detonation occurs is also influenced by the available energy of ignition. Deflagration of common hydrocarbon-air mixtures requires an ignition energy of approximately 10~4 Joules. By contrast, direct initiation of detonation of normal hydrocarbon-air mixtures requires an initiation energy of approximately 106 joules; this level of energy is comparable to that generated by a high-explosive charge. A directly initiated detonation is, therefore, highly unlikely. An event tree can be used to trace the various stages of development of a vapor cloud explosion, as well as the conditions leading to a flash fire or a vapor cloud detonation (Figure 2.1).

2.2. FLASH FIRES A flash fire results from the ignition of a released flammable cloud in which there is essentially no increase in combustion rate. In fact, the combustion rate in a flash fire does increase slightly compared to the laminar phase. This increase is mainly due to the secondary influences of wind and surface roughness. Figure 2.1 identifies the conditions necessary for the occurrence of a flash fire. Only combustion rate differentiates flash fires from vapor cloud explosions. Combustion rate determines whether blast effects will be present (as in vapor cloud explosions) or not (as in flash fires). The principal dangers of a flash fire are radiation and direct flame contact. The size of the flammable cloud determines the area of possible direct flame contact

Result NONE No ignition

Release and dispersion

Vapor doud detonation

Detonation Ignition

Flashfire

Deflagration Detonation

no enhancement

Deflagration

Detonation enhancement by turbulence

homogenous cloud

Vapor doud detonation

transition

Local detonation non-homogenous cloud

Vapor doud explosion

no transition

Deflagration

Vapor doud explosion

Figure 2.1. Event tree for vapor cloud explosions and flash fires.

effects. Cloud size, in turn, depends partially on dispersion and release conditions. Radiation effects on a target depend on its distance from flames, flame height, flame emissive power, local atmospheric transmissivity, and cloud size. Until recently, very little attention has been paid to the investigation of flash fires. Chapter 5 summarizes results of investigations performed thus far.

2.3. BLEVEs A BLEVE is an explosion resulting from the failure of a vessel containing a liquid at a temperature significantly above its boiling point at normal atmospheric pressure. In contrast to flash fire and vapor cloud explosions, a liquid does not have to be flammable to cause a BLEVE. In fact, BLEVE, which is an acronym for "boiling-liquid-expanding-vapor explosion," was first applied to a steam explosion. Nonflammable liquid BLEVEs produce only two effects: blast due to the expansion of the vapor in the container and flashing of the liquid, and fragmentation of the container. BLEVEs are more commonly associated with releases of flammable liquids from vessels as a consequence of external fires. Such BLEVEs produce, in addition to blast and fragmentation effects, buoyant fireballs whose radiant energy can burn exposed skin and ignite nearby combustible materials. A vessel may rupture for a

different reason and not result in immediate ignition of its flammable contents. If the flammable contents mix with air, then ignite, a vapor cloud explosion or flash fire will result. A BLEVE's effects will be determined by the condition of the container's contents and of its walls at the moment of container failure. These conditions also relate to the cause of container failure, which may be an external fire, mechanical impact, corrosion, excessive internal pressure, or metallurgical failure. The blast and fragmentation effects of a BLEVE depend directly on the internal energy of the vessel's contents—a function of its thermodynamic properties and mass. This energy is potentially transformed into mechanical energy in the form of blast and generation of fragments. Fluid in a container is a combination of liquid and vapor. Before container rupture, the contained liquid is usually in equilibrium with the saturated vapor. If a container ruptures, vapor is vented and the pressure in the liquid drops sharply. Upon loss of equilibrium, liquid flashes at the liquid-vapor interface, the liquid-container-wall interface, and, depending on temperature, throughout the liquid. Depending on liquid temperature, instantaneous boiling may occur throughout the bulk of the liquid. Microscopic vapor bubbles begin to form and grow. Through this process, a large fraction of the liquid can vaporize within milliseconds. Instantaneous boiling will occur whenever the temperature of the liquid is higher than the homogeneous nucleation temperature or superheat limit temperature. The liberated energy in such cases is very high, causing high blast pressures and generation of fragments with high initial velocities, and resulting in propulsion of fragments over long distances. If the temperature is below the superheat limit temperature, the energy for the blast and fragment generation is released mainly from expansion of vapor in the space above the liquid. Energy, based on unit volume, from this source is about one-tenth the energy liberated from a failing container of liquid above the superheat limit. The pressure and temperature of a container's contents at the time of failure will depend on the cause of failure. In fire situations, direct flame impingement will weaken container walls. The pressure at which the container fails will usually be about the pressure at which the safety valve operates. This pressure may be as much as 20 percent above the valve's setting. The temperature of the container's contents will usually be considerably higher than the ambient temperature. If a vessel ruptures as a result of excessive internal pressure, its bursting pressure may be several times greater than its design pressure. However, if the rupture is due to corrosion or mechanical impact, bursting pressure may be lower

than the design pressure of the vessel. Temperatures in these situations will depend on process conditions. Internal energy prior to rupture also affects the number, shape, and trajectory of fragments. Ruptures resulting from BLEVEs tend to produce few fragments, but they can vary greatly in size, shape, and initial velocities. Large fragments, for example, those consisting of half of the vessel, and disk-shaped fragments can be projected for long distances. Rocketing propels the half-vessel shapes, whereas aerodynamic forces account for the distances achieved by disk-shaped fragments. A BLEVE involving a container of flammable liquid will be accompanied by a fireball if the BLEVE is fire-induced. The rapid vaporization and expansion following loss of containment results in a cloud of almost pure vapor and mist. After ignition, this cloud starts to burn at its surface, where mixing with air is possible. In the buoyancy stage, combustion propagates to the center of the cloud causing a massive fireball. Radiation effects due to the fireball depend on • the diameter of the fireball as a function of time and the maximum diameter of the fireball; • the height of the center of the fireball above its ignition position as a function of time (after liftoff); • the surface-emissive power of the fireball; • the duration of combustion. The distance of the fireball to targets and the atmospheric transmissivity will determine the consequences of radiation. Investigations of the effects of BLEVEs (Chapter 6) are usually limited to the aspect of thermal radiation. Blast and fragmentation have been of less interest, and hence, not studied in detail. Furthermore, most experiments in thermal radiation have been performed on a small scale.

2.4. HISTORICAL EXPERIENCE Selection of incidents described was based on the availability of information, the kind and amount of material involved, and severity of damage. Accidents occurring on public property generally produce better published documentation than those occurring on privately owned property. The vapor cloud explosion incidents described below cover a range of factors: • Material properties: Histories include incidents involving hydrogen (a highly reactive gas), propylene, dimethyl ether, propane, cyclohexane (possibly partly

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than the design pressure of the vessel. Temperatures in these situations will depend on process conditions. Internal energy prior to rupture also affects the number, shape, and trajectory of fragments. Ruptures resulting from BLEVEs tend to produce few fragments, but they can vary greatly in size, shape, and initial velocities. Large fragments, for example, those consisting of half of the vessel, and disk-shaped fragments can be projected for long distances. Rocketing propels the half-vessel shapes, whereas aerodynamic forces account for the distances achieved by disk-shaped fragments. A BLEVE involving a container of flammable liquid will be accompanied by a fireball if the BLEVE is fire-induced. The rapid vaporization and expansion following loss of containment results in a cloud of almost pure vapor and mist. After ignition, this cloud starts to burn at its surface, where mixing with air is possible. In the buoyancy stage, combustion propagates to the center of the cloud causing a massive fireball. Radiation effects due to the fireball depend on • the diameter of the fireball as a function of time and the maximum diameter of the fireball; • the height of the center of the fireball above its ignition position as a function of time (after liftoff); • the surface-emissive power of the fireball; • the duration of combustion. The distance of the fireball to targets and the atmospheric transmissivity will determine the consequences of radiation. Investigations of the effects of BLEVEs (Chapter 6) are usually limited to the aspect of thermal radiation. Blast and fragmentation have been of less interest, and hence, not studied in detail. Furthermore, most experiments in thermal radiation have been performed on a small scale.

2.4. HISTORICAL EXPERIENCE Selection of incidents described was based on the availability of information, the kind and amount of material involved, and severity of damage. Accidents occurring on public property generally produce better published documentation than those occurring on privately owned property. The vapor cloud explosion incidents described below cover a range of factors: • Material properties: Histories include incidents involving hydrogen (a highly reactive gas), propylene, dimethyl ether, propane, cyclohexane (possibly partly

• • • • •

as a mist), methane (generally classified as a low-reactivity gas), and natural gas liquids. Period of time covered: Explosions occurring over the period between the years 1948 and 1989 are reported. Quantity released: Releases ranged in quantity from 110 kg (240 Ib) to 70,000 kg (150,000 Ib); Site characteristics: Releases occurred in settings ranging from rural to very congested industrial areas. Availability of information: Very well-documented incidents (e.g., Flixborough) as well as poorly documented incidents (e.g., Ufa) are described. Severity: Death tolls and damage from pressure effects vary widely in cases presented.

Most incidents discussed occurred several years ago, but it should be emphasized that such incidents still occur. More recent incidents include Celanese (1987), Shell (1988), Phillips (1989), and Exxon (1989). Documentation of flash fires is scarce. In several accident descriptions of vapor cloud explosions, flash fires appear to have occurred as well, including those at Flixborough, Port Hudson, East St. Louis, and Ufa. The selection and descriptions of flash fires were based primarily on the availability of information.

Figure 2.2. Damage at Phillips, 1989.

2.4.1. Vapor Cloud Explosions Flixborough, UK: Vapor Cloud Explosion in Chemical Plant On June 1, 1974, a cyclohexane vapor cloud was released after the rupture of a pipe bypassing a reactor. In total, approximately 30,000 kg of cyclohexane was released. The cyclohexane formed a cloud which ignited after a period of approximately 30 to 90 seconds. As a result, a very strong explosion occurred which caused the death of 28 people and injured 36 people. The plant was totally destroyed and 1821 houses and 167 stores and factories in the vicinity of the plant were damaged.

Parker (1975), Lees (1980), Gugan (1978), and Sadee et al. (1976, 1977) have described extensively the vapor cloud explosion that occurred in the reactor section of the caprolactam plant of the Flixborough Works on June 1,1974. The Flixborough Works is situated on the east bank of the River Trent. The nearest villages are Flixborough [800 meters (one-half mile) away], Amcotts [800 meters (one-half mile) away], and Scunthorpe [4.9 km (approximately three miles) away]. The cyclohexane oxidation plant contained a series of six reactors. The reactors were fed by a mixture of fresh cyclohexane and recycled material. The reactors were connected by a pipe system, and the liquid reactant mixture flowed from one reactor into the other by gravity. Reactors were designed to operate at a pressure of approximately 9 bar (130 psi) and a temperature of 1550C (3110F). In March, one of the reactors began to leak cyclohexane, and it was, therefore, decided to remove the reactor and install a bypass. A 20-inch diameter bypass pipe was installed connecting the two flanges of the reactors. Bellows originally present between the reactors were left in place. Because reactor flanges were at different heights, the pipe had a dog-leg shape (Figure 2.3). On May 29, the bottom isolating valve on a sight glass on one of the vessels began to leak, and a decision was made to repair it. On June 1, start-up of the process following repair began. As a result of poor design, the bellows in the bypass failed and a release of an estimated 30 tons cyclohexane occurred. The leakage formed a strong, turbulent, free jet. Fifty percent of the released cyclohexane flashed off as vapor; the remainder formed a mist. (The degree of mist evaporation depends on the amount of air aspirated by the jet.) After a period of 30 to 90 seconds following release, the flammable cloud was ignited. The time was then about 4:53 P.M. The explosion caused extensive damage and started numerous fires. The blast shattered control room windows and caused the collapse of its roof. It demolished the main office block, only 25 m from the explosion center. Twenty-eight people died, and thirty-six were injured. The plant was totally destroyed (Figures 2.4 and 2.5), and 1821 houses and 167 shops and factories in the vicinity of the plant were damaged. Sadee et al. (1976-1977) give a detailed description of structural damage due to the explosion and derived blast pressures from the damage outside the cloud

R 2524

R2526 Support poles

Support poles

Arrangement of 20" pipe scaffolding (as deduced from the evidence)

Figure 2.3. Bypass on cyclohexane reactors.

(Figure 2.6). Several authors estimated the TNT mass equivalence based upon the damage incurred. Estimates vary from 15,000 and 45,000 kg. Estimates of pressures inside the cloud vary widely. Gugan (1978) calculated that the forces required to produce damage effects observed, such as the bending of steel, would have required local pressures of up to 5-10 bar. Ludwigshafen, Germany: Rupture of Tank Car Overheated in Sun On July 28,1948, a rail car containing liquefied dimethyl ether ruptured and released its entire contents. The rupture was due to the generation of excessive pressures created by long solar exposure following initial overfilling. The gas was ignited after 10 to 25 seconds. The ensuing vapor cloud explosion caused the death of 207 people and injured 3818.

Marshall (1986) describes the accident at BASF in Ludwigshafen drawing extensively on original data. On July 28, 1948, a railway tank car suffered a catastrophic failure and discharged its entire contents of 30,400 kg of dimethyl ether. The

Figure 2.4. Area of spill showing removed reactor.

Figure 2.5. Damage to congested area of Flixborough works.

Pressure (kPa)

Pressure — distance curve for 16t TNT detonated at height of 45m

Distance from ground zero (m)

Figure 2.6. Blast-distance relationship outside the cloud area of the Flixborough explosion. (Vertical bars were drawn based on observed damage.)

catastrophic failure was, according to the original data, due to overfilling of the car. On the day of the explosion, the ambient temperature reached approximately 30° to 320C (86° to 9O0F). Heating and consequent expansion of its contents resulted in hydraulic rupture. An alternative explanation, proposed by Marshall (1986) is that there was a defect in the construction of the tank car. The increase in vapor pressure caused

by the higher temperature resulted in the tank car failure. The failure had taken place principally along a welded horizontal seam. Witnesses claim to have seen a brownish-white cloud appearing from the tank car, accompanied by a whistling sound, before the car ruptured completely. According to Giesbrecht et al. (1981), there was a delay of 10 to 25 seconds between the moment of the initial large release and the moment of ignition. The explosion must have been very violent in view of the extensive structural damage to the plant. The high death toll was due to the high population density in the vicinity of the point of release. The TNT equivalence of the blast was estimated to be 20-60 tons (Davenport, 1983). The area of total destruction was 430,000 ft2 (40,000 m2) and the area of total destruction plus severe damage was 3,200,000 ft2 (300,000 m2) (Figures 2.7-2.9). The main cause of the explosion was the turbulence generated by the release itself. The release did, however, occur in a very congested area. Port Hudson, Missouri, USA: Vapor Cloud Explosion after Propane Pipeline Failure On December 9, 1970, a liquefied propane pipeline ruptured near Port Hudson. About 24 minutes later, the resulting vapor cloud was ignited. The pressure effects were very severe. The blast was equivalent to that of 50,000 kg of detonating TNT.

Figure 2.7. Remains of exploded tank car.

Total destruction

Severe damage

Moderate damage

Figure 2.8. Damage from the 1948 BASF explosion.

Burgess and Zabetakis (1973) describe the Port Hudson explosion, which took place on December 9, 1970. At 10:07 P.M., an abnormality occurred at a pumping station on a liquid propane line 24 km (15 miles) downstream from Port Hudson. At 10:20 P.M., there was a sudden increase in the throughput at the nearest upstream pumping station, indicating a major break in the line. During the first 24 minutes, an estimated 23,000 kg (50,000 Ib) of liquid propane escaped. The noise of escaping propane was noticed at about 10:25 P.M. A plume of white spray was observed to be rising 15 to 25 m (50 to 80 ft) above ground level. The pipeline was situated in a valley, and a highway ran at about one-half mile (800 m) from the pipeline. Witnesses standing near a highway intersection observed a white cloud settling into the valley around a complex of buildings. Weather conditions were as follows: low wind (approximately 2.5 m/s [8 ft/s]) and nearfreezing temperature (I0C; 340F). At about 10:44 P.M., the witnesses saw the valley "lighting up." No period of flame propagation was observed. A strong pressure pulse was felt and one witness was knocked down. After the valley was illuminated, a flash fire was observed, which consumed the remainder of the cloud. After the explosion and flash fire, a torch fire resulted at the point of the initial release. Buildings in the vicinity of the explosion were damaged (Figures 2.10 and 2.11).

boundary of reacted cloud

boundary of mixture cloud

peak overpressure Ap [bar]

damage criteria according to Schardm o Glasstoneo

limiting curves

Figure 2.9. Pressure-distance relationship for the 1948 BASF explosion, r = distance (m); Eves = combustion energy of railway tank car contents (MJ).

The cloud was probably ignited inside a concrete-block warehouse. The ground floor of this building, partitioned into four rooms, contained six deep-freeze units. Gas could have entered the building via sliding garage doors, and ignition could have occurred at the controls of a refrigerator motor. Damage from the blast in the vicinity was calculated to be equivalent to a blast of 50,000 to 75,000 kg of TNT. According to Burgess and Zabetakis (1973), the Port Hudson vapor cloud detonated. As far as is known, this is the only vapor cloud explosion that may have been a detonation. Enschede, The Netherlands: Release and Explosion from a Propane Tank On March 26, 1980, a power shovel was relocating a tank containing 1500 I (750 kg; 1650 Ib) liquid propane. During maneuvering, the tank fell from the shovel; a portion of its contents was released as a result. After a delay of 30 seconds, the ensuing vapor cloud was ignited. The explosion caused substantial blast and fire damage. There were no casualties.

Figure 2.10. Damage to a farm 600 m (2000 ft) from explosion center.

Figure 2.11. Damage to a home 450 m (1500 ft) from the blast center.

Van Laar (1981) describes the accident which occurred in Enschede on March 26, 1980. The explosion occurred on a building site which included a number of construction buildings. These buildings were located near a 10-m-high (32.5 ft) factory building. The wall of the building was constructed of corrugated sheet metal and brick. All construction buildings were on one side of a street. Three houses were under construction on the other side of the street. Several cars were parked in the street (Figure 2.12). The weather was calm and cool, with a 2-5 m/s (6-16 ft/s) breeze and a temperature of 130C (550F). Just after 10:00 A.M., a tank filled with approximately 1500 1 (750 kg; 1650 Ib) of liquid propane was moved by a power shovel. During relocation maneuvering, the tank fell from the shovel and its valve struck against a pile of concrete slabs. The valve was sheared from its flange by the crash, thus allowing the release of propane. The resulting vapor cloud spread like a white mist to the construction buildings. Most of the workers fled. Calculations based on the size of the hole in the propane tank indicate that approximately 110 kg (240 Ib) of propane was released. After 30 seconds, the cloud was ignited by a heater in a construction building. Several construction buildings collapsed from the explosion (Figure 2.13). The facade of the factory partially collapsed, the brick wall was partially caved in, and a large number of windows in this wall were shattered. The glass roof of the factory

Polaroid works toilef

hut

canteen

.nut parked cars

container

office huts

managers hut

hoge Bolhofstraat building materials north

concrete slabs

direction of the wind dwellings under construction

dwellings under construction

Figure 2.12. Overview of Enschede explosion.

Figure 2.13. Damage to construction buildings from propane explosion.

was completely shattered. Most parked cars were damaged by flying debris and by the pressure wave. Roof tiles of the houses under construction at approximately 50 m (160 ft) were displaced. Windows up to 15Om (500 ft) from the explosion center were broken, and two large windows 300 m (1000 ft) away were shattered. Raunheim, Germany: Explosion of Methane after Venting Operation On January 16,1966, an explosion occurred after liquefied methane was discharged from a vent. The resulting cloud was ignited. The subsequent explosion resulted in minor structural blast damage. About 75 persons were injured, primarily from glass breakage, and 1 person was killed.

Gugan (1978) describes the accident that occurred in Raunheim, Germany on January 16, 1966. Surplus methane was being vented unintentionally to the atmosphere. Liquid methane passed to a vaporizer having a maximum capacity of 4000 kg. The vaporizer was instrumented to control the internal liquid level. Although the actual cause of release has never been established, it appears that the liquid-level controller failed, allowing a slug of liquid methane to be ejected from the vent. This release would have occurred at 25 m (80 ft), the vertical height of the vent above the

vaporizer. There were low wind conditions, and the temperature was only — 120C (1O0F). Operators in the control room (50 m [160 ft] from the vaporizer) observed a white cloud expanding slowly over the ground and drifting in the direction of the control room. As the cloud reached the control room, it was ignited. It is likely that the ignition source were furnaces about 50 m (160 ft) from the vaporizer in the opposite direction. Structural damage was not severe, and blast damage only slight. Glass breakage was extensive up to 400 m (1300 ft) from the center of the explosion and slight up to 1200 m (4000 ft). One person was killed and seventyfive injured, primarily from flying glass. Probably no more than 500 kg of liquid methane was involved. This would have formed a cloud 1 m deep (3 ft) and 40 m (130 ft) in radius (assuming a stoichiometric mixture). TNT equivalency was estimated to be 1000-2000 kg, which implies that the yield was 18-36%. East St. Louis, Illinois: Vapor Cloud Explosion at Shunting Yard On January 22, 1972, an overspeeding tank car containing liquefied propylene collided with a standing hopper car at a shunting yard in East St. Louis, Illinois. As a result, the tank of the tank car was punctured, and propylene gas was released. A large vapor cloud was formed, which then ignited and exploded. More than 230 people were injured.

A National Transportation Safety Board Railroad Accident Report (1973) describes the accident which occurred in a shunting yard in East St. Louis, Illinois. Arriving cars are classified in the yard, then delivered to outbound carriers. On arrival, cars are inspected. They are then pushed up a mound, uncoupled, and allowed to roll down a descending grade onto one of the classification tracks. This process is called "humping." Cars are directed and controlled by a computerized switching and speedcontrol system. On the morning of January 22, 1972, a 44-car cut was being classified. One car, an empty hopper, was humped without incident but stopped approximately 400 m (1300 ft) short of its planned coupling point. Later, three tank cars containing propylene were humped as a unit and directed onto the same track as the empty hopper. The cars should have been slowed by the speed control system, but were not, probably because of greasy wheels. An overspeed alarm was given. The unit ran into the empty hopper at a speed of approximately 25 km/h (15 mph). The coupler of the hopper car punctured the head of the first tank car. Liquefied propylene was spilled, and propylene vapor was observed as a white cloud spreading at ground level. The hopper car was set into motion by the impact from the threecar unit, and the four cars rolled down the track together until they struck cars standing at 700 m (2300 ft) from the hump end of the track. This impact resulted in an enlargement of the tear in the leading tank car.

wind direction

1 heavy struckural 2 ligM structural & heavy cosmetic 3 Light cosmetic & glass U Light glass 5 heavy structural large buildings 6 plate glass

Figure 2.14. Explosion damage.

Flames were first observed at or near an unoccupied caboose. A flash fire resulted, propagating toward the punctured car area. "An orange flame then spread upward, and a large vapor cloud flared with explosive force. Estimates of the time lapse between these occurrences range from 2 to 30 seconds. Almost immediately thereafter, a second, more severe, explosion was reported." The explosions resulted in 223 injuries. Buildings and a number of freight cars were damaged (Figure 2.14). Car damage included both inward and outward deformities. Jackass Flats, Nevada, USA: Hydrogen-Air Explosion during Experiment On January 9,1964, a test was run at Los Alamos Scientific Laboratory to measure the acoustic sound levels developed during the release of gaseous hydrogen at high flow rates. The released hydrogen ignited and exploded.

Reider et al. (1965) describe the incident at Los Alamos Laboratory in Jackass Flats, Nevada. An experiment was conducted on January 9, 1964, to test a rocket nozzle, primarily to measure the acoustic sound levels in the test-cell area which occurred during the release of gaseous hydrogen at high flow rates. Hydrogen discharges were normally flared, but, in order to isolate the effect of combustion

on acoustic fields, this particular experiment was run without the flare. Releases were vertical and totally unobstructed. High-speed motion pictures were taken during the test from two locations. During the test, hydrogen flow rate was raised to a maximum of approximately 55 kg/s (120 Ib/s). About 23 seconds into the experiment, a reduction in flow rate began. Three seconds later, the hydrogen exploded. Electrostatic discharges and mechanical sparks were proposed as probable ignition sources. The explosion was preceded by a fire observed at the nozzle shortly after flow rate reduction began. The fire developed into a fireball of modest luminosity, and an explosion followed immediately. Damage was mainly caused by the negative phase of the generated blast wave. Walls of light buildings and heavy doors were bulged out. In one of the buildings, a blowout roof designed to open at 0.02 bar (40 lbf/ft2) was lifted from a few of its holding clips. High-speed motion pictures indicate that the vertical downward flame speed was approximately 30 m/s (100 ft/s); the flame was undisturbed by effluent velocity. This value is roughly ten times the burning velocity expected for laminar-flow conditions, but is reasonable because a turbulent free jet was present, thereby enhancing flame burning rate. According to Reider et al. (1965), blast pressure at 45 m (150 ft) from the center was calculated to be 0.5 psi (0.035 bar)

reactor motor drive bWg

fill stat

movable crvo eval lab

test cell shed area

LH2 dewars

H.P. gas

D 400' tower

O flare

Figure 2.15. Test-cell layout.

based on explosion damage. They state that approximately 90 kg (200 Ib) of hydrogen was involved in the explosion. Ufa, West-Siberia, USSR: Pipeline Rupture Resulting In Vapor Cloud Explosion On the night of June 3,1989, a pipeline carrying liquefied natural gas began to leak close to the Trans-Siberian railway track between the towns of Asma and Ufa. A flammable cloud of leakage covered the railway track. At the moment two trains passed through the cloud shortly after midnight, it was ignited. The blast was enormous, and considerable portions of both trains were derailed. The death toll was approximately 650.

Lewis (1989) describes the accident, which occurred in Siberia on the night of June 3 and early hours of June 4, 1989. Late on June 3, 1989, engineers in charge of the 0.7 m (28 in.) pipeline, which carried natural gas liquids from the gas fields in western Siberia to chemical plants in Ufa in the Urals, noticed a sudden drop in pressure at the pumping end of the pipeline. It appears that the engineers responded by increasing the pumping rate in order to maintain normal pipeline pressure. A leak had occurred in the pipeline between the towns of Ufa and Asma at a point 800 m (0.5 mi) away from the Trans-Siberian double railway track. The area was a wooded valley. Throughout the area, there had been a strong smell of gas a few hours before the blast. The gas cloud was reported to have drifted for a distance of 8 km (5 mi). Two trains coming from opposite directions approached the area where the cloud was present. Each consisted of an electrically powered locomotive and 19 coaches constructed of metal and wood. The turbulence of the trains probably mixed up the vapor and mist with overlying air to form a flammable cloud portion. Either train could have ignited the cloud, most likely at catenary wires which powered the locomotives. Two explosions seem to have taken place in quick succession, and a flash fire subsequently ran down the railroad track in two directions. A considerable part of each train was derailed. Four rail cars were blown sideways from the track by the blast, and some of the wooden cars were completely burned within 10 minutes. Trees within 4 km (2.5 mi) from the explosion center were completely flattened (Figure 2.16), and windows up to 13 km (8 mi) were broken. By the end of June, the total death toll had climbed to 645. 2.4.2. Flash Fires Donnellson, Iowa, USA: Propane Fire During the night of August 3, 1978, a pipeline carrying liquefied propane ruptured, resulting in the release of propane. An unknown source ignited the cloud. The

Figure 2.16. Aerial view of Ufa accident site.

resulting fire killed two persons and critically burned three others as they fled their homes. One of the burn victims later died.

A National Transportation Safety Board report (1979) describes a flash fire resulting from the rupture of 20-cm (8 in.) pipeline carrying liquefied propane. The section of the pipeline involved extends from a pumping station at Birmingham Junction, Iowa, to storage tanks at a terminal in Farmington, Illinois. Several minutes before midnight on August 3, 1978, the pipeline ruptured while under 1200 psig pressure in a cornfield near Donnellson, Iowa. Propane leaked from an 838-cm (33-in.) split and then vaporized. "The heavier-than-air cloud moved through the field and across a highway following the contour of the land." The cloud eventually covered 30.4 ha (75 acres) of fields and woods, surrounding a farmhouse and its outbuildings. There was a light wind, and the temperature was about 150C (in the upper 50's). At 12:02 A.M. on August 4, the propane cloud was ignited by an unknown source. The fire destroyed a farmhouse, six outbuildings, and an automobile. Two other houses and a car were damaged. Two persons died in the farmhouse. Three persons who lived across the highway from the ruptured pipeline had heard the pipeline burst and were fleeing their house when the propane ignited. All three persons received burns on over 90% of their bodies, and one later died from the burns. Fire departments extinguished smaller fires in the woods and adjacent homes.

The fire at the ruptured pipe produced flame heights of up to 120 m (400 ft). It was left burning until the valves were shut off to isolate the failed pipe section. The investigation following the accident showed that the pipeline rupture was due to stresses induced in, and possibly by damage to, the pipeline resulting from its repositioning three months before. This work had occurred in conjunction with road work on the highway adjacent to the accident site. The pipeline had been dented and gouged. Lynchburg, Virginia, USA: Propane Fire On March 9,1972, an overturned tractor-semitrailer carrying liquid propane resulted in a propane release. The propane cloud was later ignited. The resulting fire killed two persons; five others were injured.

National Transportation Safety Board report (1973), describes an accident involving the overturning of a tractor-semitrailer carrying liquid propane under pressure. On March 9, 1972, the truck was traveling on U.S. Route 501, a two-lane highway, at a speed of approximately 40 km/h (25 mph). The truck was changing lanes on a sharp curve while driving on a downgrade at a point 11 km (7 mi) north of Lynchburg, Virginia. Meanwhile, an automobile approached the curve from the other direction. The truck driver managed to return to his own side of the road, but, in a maneuver to avoid hitting the embankment on the inside of the curve, the truck rolled onto its right side. The manhole-cover assembly on the tank struck a rock; the resulting rupture of the tank head caused propane to escape. There were woods on one side of the road; on the other side a steeply rising embankment and trees and bushes, and then a steep dropoff to a creek. The truck driver left the tractor, ran from the accident site in the direction the truck had come from, and warned approaching traffic. The driver of a first arriving car stopped and tried to back up his car, but another car blocked his path. The occupants of these cars got out of their vehicles. Three occupants of nearby houses at a distance of 60 m (195 ft), near the creek and about 20 m (60 ft) below the truck, fled after hearing the crash. An estimated 4000 gallons (8800 kg; 19,500 Ib) of liquefied propane was discharged. At the moment of ignition, the visible cloud was expanding but had not reached the motorists who left their cars at a distance of about 135 m (450 ft) from the truck. The cloud reached houses about 60 m (195 ft) from the truck, but had not reached the occupants at a distance of approximately 125 m (410 ft). The cloud was ignited at the tractor-semitrailer, probably by the racing tractor engine. Other possible ignition sources were the truck battery or broken electric circuits. The flash fire that resulted was described as a ball of flame with a diameter of at least 120 m (400 ft). No concussion was felt. The truck driver (at a distance of 80 m or 270 feet) was caught in the flames and probably died immediately. The motorists and residents were outside the cloud but received serious burns.

PROPANE TANK TRACTOR-SEMITRAILER OVERTURN AND FIRE ON U.S. 501 NEAR LYNCHBURG, VIRGINIA ON MARCH 9, 1972 Rock Outcropping Residence Outbui ldings

POINT OF IMPACT

FIRST SOUTHBOUND CAR HERE WHEN TRUCK FIRST SEEN TRUCK HERE WHEN FIRST SEEN BY SOUTHBOUND CAR

SOUTHBOUND CARS BACKED TO HERE AND STOPPED 450' NORTH OF TRUCK

FIRST CAR STOPPED 150' NORTH GOUGE MARKS FROM RIGHT TRAILER TANDEM WHEELS

OF TRUCK THEN BACKED

TO X X TRUCK EVASIVE MANEUVERS STARTED HERE

TRUCKDRIVER 1 S BODY

(1480 Feet South of Accident Site)

Mai imum SaU Spvtd

20

Trees Woods

Woods Woods Continous Downgrade (Average - 7.52%) Virginia Highway Department Sand and Gravel Storage Area

Figure 2.17. Details of accident site.

Woods

2.4.3. BLEVEs Without Fire Haltern, Germany: Failure of Rail Car with Carbon Dioxide On September 2,1976, at about 8 P.M., a rail car carrying carbon dioxide exploded. One person was killed.

Leiber (1980) describes this accident, which occurred in Haltern, Germany, on September 2, 1976. A rail car carrying 231,000 kg (470,000 Ib) (90% full) of carbon dioxide exploded. The tank's contents were at 100 psi (7 bar) pressure and — 150C (50F) temperature. At the moment of the explosion, the car was passing through a railroad shunting yard in Haltern at a speed of about 16 km/h (10 mph). As it passed checkpoints, the car was observed to be releasing plumes of carbon dioxide from the safety valve, after which the tank exploded 15 m (50 ft) in front of a group of other rail cars. Other evidence indicates that the explosion occurred after impact with these cars. Parts of the tank were projected to distances up to 360 m (1200 ft). Twentytwo pieces of the tank were recovered, constituting approximately 80% of the original tank. Debris was found clustered in two separate areas, namely, within the radii of 5° to 20° and 65° to 95° from the car's direction of movement. Three empty tank cars located up to a distance of three railroad tracks from the exploded car were blown from the rails. The undercarriage of the car was bent into a V-shape (see Figure 2.1). One person was killed in the explosion. Analysis of a recovered piece of the tank car showed that failure was due to brittle fracture. Ftepcelak, Hungary: Liquid CO2 Storage Vessel Explosion On January 2, 1969, two vessels containing carbon dioxide in a carbon dioxide production and filling plant exploded in rapid succession. The explosion completely destroyed the tank yard of the plant and killed nine people. Fifteen people were injured.

Voros and Honti (1974) described the incident. A carbon dioxide purification plant in Repcelak, Hungary, produced carbon dioxide from natural sources. It was liquefied and supercooled after purification by ammonia refrigeration, then stored in tanks under a pressure of 15 bar (220 psi) at a temperature of -3O0C (-220F). The tank farm consisted of four storage vessels located approximately 15 m (50 ft) from a production building (Figure 2.19). A warehouse and a boiler house were on the opposite side of the vessels. On January 2, 1969, at 1:50 P.M., one of the vessels (C) was filled from the production plant. During filling, the vessel exploded (2:24 P.M.). Some minutes later, another vessel (D) also exploded.

Figure 2.18. Remnants of rail car carrying carbon dioxide after rupture.

LAYOUT OFTHE PLANTBEFORE EXPLOSION !.PURIFICATION BUILDING 2. PROCESS LABORATORY 3.FILLING UNIT A. WAREHOUSE 5.BOILER HOUSE 6. BOILER HOUSE CHIMNEY 7. PURIFICATION LINE ,,CD11 8.CARBON DIOXIDE STORAGE TANK YARD

Figure 2.19. Carbon dioxide production plant layout.

The explosions tore vessel A off its foundation bolts, and one foot of the vessel tore off a 30 X 30 cm (12 x 12 in.) piece of plate from its side. The release of carbon dioxide through this hole caused the vessel to be thrown into the process laboratory like a rocket, resulting in five casualties. The explosion caused vessel B to be torn loose from its connecting pipes, but without further consequences. Fragments flying in all directions caused the deaths of four persons. Within an area of 150 m (500 ft) around the tank yard, many people were injured. Among them were fifteen who suffered from serious injury by freezing and the impact of fragments. Large fragments were scattered in a circle of approximately 400 m (1300 ft) radius. A shell of 2800 kg (6000 Ib) landed at a distance of 150 m (500 ft), and a fragment weighing 1000 kg (2200 Ib) landed 250 m (820 ft) away. A large amount of carbon dioxide was released, causing the immediate vicinity of the yard to be covered with solid carbon dioxide (dry ice). The probable cause of the accident was overfilling due to level indicator failure. Water removal from carbon dioxide was not always sufficient to assure good pressure and level readings in the tanks. Residual water could cause meters to fail from ice formation. The material of construction of the vessels D and C was not suited for use under low temperature conditions. Vessels A and B were, however, suitable. The location of initial brittle fracture in vessel C was the weld seam near the manhole. Vessel D probably failed as a result of impact from a fragment from vessel C. Brooklyn, New York, USA: Liquefied Oxygen Tank Truck Explosion On May 30, 1970, a tank truck partially filled with liquefied oxygen exploded after making a delivery in a hospital in Brooklyn, New York. The force of the explosion and subsequent fires caused the deaths of the driver and bystander. Thirty other people were injured and substantial property damage resulted.

A report of the National Transportation Safety Board (1971) describes the rupture of a tank truck of liquefied oxygen. On May 29, a tank truck was filled with 2550 gallons (14,000 kg; 30,800 Ib) of liquefied oxygen at a producing facility in New Jersey. After filling was completed, the truck was parked loaded overnight. The following day, the truck departed for several scheduled delivery stops. The first stop was at a hospital in Brooklyn. A portion of the liquefied oxygen (1900 kg; 4180 Ib) was transferred to a storage tank there. After delivery, the driver disconnected the transfer lines, stepped into the cab of the truck, and began to maneuver the truck in the yard of the hospital. The truck tank ruptured, and the remaining contents of the tank were spewed into the area around the truck. Vigorously burning fires started in the oxygen-enriched atmosphere. The driver and a bystander were fatally injured by the fire and explosion. Thirty other persons sustained minor injuries, including twenty-four who sustained injuries

from broken glass and forces of the explosion. Four firemen and two policemen were treated for minor injuries suffered during emergency response efforts. The truck and its tank were damaged extensively. Site damage was limited to the area around the truck. Minor additional damage to window glass and light structural components occurred up to 18Om (600 ft) from the truck. The storage tank and associated piping were still intact after the accident. The ensuing investigation showed that the entire tank fracture sequence occurred within about 1 second, suggesting a very rapid pressure rise. The sequence of events probably began with an initiating reaction between one or more reactants located in the "upper roadside baffle bracket area" and oxygen. This reaction triggered an oxidation of the aluminum surrounding the cavity which, in turn, triggered an intense, heat-producing reaction between the aluminum of the tank and the oxygen cargo. With Fireball Crescent City, Illinois, USA: Several Fireballs from Rail Cars At 6:30 A.M. on June 21, 1970, fifteen railroad cars, including nine cars carrying liquefied petroleum gas (LPG), derailed in the town of Crescent City, Illinois. The derailment caused one of the tanks to be punctured, then release LPG. The ensuing fire, fed by operating safety valves on other cars, resulted in ruptures of tank cars, followed by projectiles and fireballs. No fatalities occurred, but 66 people were injured. There was extensive property damage.

A National Transportation Safety Board report (1972), Eisenberg et al. (1975), and Lees (1980) each describe the accident. At 6:30 A.M. on June 21, 1970, 15 rail cars, including 9 cars carrying LPG, derailed in the town of Crescent City, Illinois. The force of the derailment propelled the twenty-seventh car in the train over the derailed cars in front of it (Figure 2.20). Its coupler then struck the tank of the twenty-sixth car and punctured it. The released LPG was ignited by some unidentified source, possibly by sparks produced by the derailing cars. The resulting fireball reached a height of several hundred feet and extended into the part of the town surrounding the tracks. Several buildings were set on fire. The safety valves of other cars operated, thereby releasing more LPG. At 7:33 A.M., the twenty-seventh car ruptured with explosive force. Four fragments were hurled in different directions (Figure 2.21). The east end of the car dug a crater in the track structure, and was then hurled about 18Om (600 ft) eastward. The west end of the car was hurled in a southwesterly direction for a total distance of about 90 m (300 ft). This section struck and collapsed the roof of a gasoline service station. Two other sizable portions of the tank were hurled in a southwesterly direction and came to rest at points 18Om (600 ft) and 230 m (750 ft) from the tank.

Figure 2.20. Derailment configuration.

At about 9:40 A.M., the twenty-eighth car in the train ruptured. The south end of this car was hurled about 60 m (200 ft) southward across the street, where it entered a brick apartment building. The north end of the car was hurled through the air in a northwesterly direction over the roofs of several houses, landed in an open field, and rolled until it had traveled over 480 m (1600 ft). At 9:45 A.M., the thirtieth car in the train ruptured. The north end of the car which included about one-half of the tank was propelled along the ground in a northeasterly direction for about 18Om (600 ft). It destroyed two buildings and came to rest in a third. At about 10:55 A.M., the thirty-second and thirty-third car ruptured almost simultaneously. One of them split longitudinally but did not separate into projectiles.

Figure 2.21. Trajectories of tank car fragments.

The second one was hurled in the direction of the thirty-fourth car and punctured its head, resulting in further propane releases. The other end of the car also struck the thirty-fourth car, ricocheted, and then struck the protective housing of the thirtyfifth car. The housing and valves of the thirty-fifth car broke off, permitting more LPG to be released. Fires continued for a total of 56 hours. In all, sixteen business establishments were destroyed and seven were damaged. Twenty-five residences were destroyed, and a number of others were damaged. Sixty-six people were injured. Due to prompt evacuation, no deaths occurred. Feyzln, France, 1966, BLEVE In LPG Storage Installation On January 4, 1966, at Feyzin refinery in France, a leak from a propane storage sphere ignited. The fire burned around the vessel and led to boiling liquid expanding vapor explosions. The accident caused eighteen deaths and eighty-one injuries.

IChemE (1987) describes the accident. An LPG storage installation at the Feyzin refinery in France consisted of four 1200 m3 (43,000 ft3) propane spheres, four 2000 m3 (70,000 ft3) butane spheres, and two horizontal bullet pressure vessels for propane and butane storage (Figure 2.22). The LPG storage spheres were about 450 m (1500 ft) away from the nearest refinery and about 300 m (1000 ft) from the nearest houses in the village. The shortest distance between an LPG sphere and the nearby highway was 42 m (140 ft). Spaces between individual spheres ranged from 11.3 m (37.0 ft) to 17.2 m (56.4 ft). Samples for analysis were routinely taken from each of the LPG storage spheres. Refinery processes caused a certain amount of sodium hydroxide solution to separate from the LPG in storage. Thus, it was necessary to drain off this solution first prior to sampling. On the morning of January 4, 1966, an operator opened two valves in series on the bottom off-take line from a propane storage sphere in order to drain off the sodium hydroxide solution. Contrary to instructions, the operator first opened the lower valve completely, then started to regulate takeoff rate by adjusting the upper valve. Only a small amount of caustic soda and some propane came out. He closed the valve, then opened it again slightly, but there was no flow. He then opened the valve wider. The blockage, presumably hydrate or ice, cleared, and propane gushed out. The operator and two workers accompanying him were unable to close the upper valve. They did not attempt to close the lower valve immediately, and by

Feyzin Village 400 m away

Railway Motorway

LPG tanks Fuel oil tanks

Petrol tanks Figure 2.22. Feyzin storage site layout.

Destruction Some damage

the time they did, this valve was also frozen open. It was 6:40 A.M.. All three workers then left on foot to turn in an alarm and seek help. They did not use the phone or their truck for fear of igniting the gas. At 6:55 A.M., the alarm was sounded. Steps were then taken to stop traffic on the nearby highway and to stop the flow from the sphere. A vapor cloud about 1 m deep spread toward the highway. Unfortunately, a minor road was not sealed off in time, and a car entered the gas cloud from this road and stopped. The cloud probably was ignited by the car's right rear tail light, which had an electrical defect. The driver, who got out and started to walk, was caught in the flash fire and was fatally burned. The fire traveled back to the sphere igniting the gas escaping from the sphere. At 7:30 A.M., an attempt was made by at least 10 refinery workers to extinguish the fire with dry chemical. This effort was nearly successful, but supply of dry chemical was exhausted before the fire was extinguished. The relief valve on the sphere opened at 7:45 A.M., and relieved gas was immediately ignited. At 8:30 A.M., water pumped from a canal became available. It was used to cool other exposed spheres, but the sphere from which the initial spill of propane occurred was not protected. At 8:40 the sphere ruptured into five large fragments, producing a large fireball, killing or injuring nearly 100 people in the vicinity.

Figure 2.23. Fire at storage vessels of Feyzin refinery.

Fifty minutes later, a second sphere exploded, and a third sphere emptied itself through broken pipework. Three other butane spheres ruptured without creating any flying missiles. The village of Feyzin, 400 m (0.25 mi) from the blast site suffered widespread but minor blast damage. San Juan Ixhuatepec, Mexico City, Mexico: Series of BLEVEs at LPG Storage Facility On November 19,1984, an initial leak and flash fire of LPG resulted in the destruction of a large storage facility and a portion of the built-up area surrounding the storage facility. Approximately 500 people were killed and approximately 7000 were injured. The storage facility and the built-up area near the facility were almost completely destroyed.

Pietersen (1988) describes the San Juan Ixhuatepec disaster. The storage site consisted of four spheres of LPG with a volume of 1600 m3 (56,500 ft3) and two spheres with a volume of 2400 m3 (85,000 ft3). An additional 48 horizontal cylindrical tanks of various dimensions were present (Figure 2.24). At the time of the disaster, the total site inventory may have been approximately 11,000-12,000 m3 (390,000420,000 ft3) of LPG. Early in the morning of November 19, 1984, large quantities of LPG leaked from a pipeline or tank. The heavy LPG vapors dispersed over the 1-m-high dike (3 ft) wall into the surroundings. The vapor cloud had reached a visible height of about 2 m (6 ft) when it was ignited at a flare pit. At 5:45 A.M. , a flash fire resulted. The vapor cloud is assumed to have penetrated houses, which were subsequently destroyed by internal explosions. A violent explosion, probably involving the BLEVE of several storage tanks, occurred 1 minute after the flash fire. It resulted in a fireball and the propulsion of one or two cylindrical tanks. Heat and fragments resulted in additional BLEVEs. The explosion and fireball completely destroyed the four smaller spheres. The larger spheres remained intact, although their legs were buckled. Only 4 of the 48 cylindrical tanks were left in their original position. Twelve of the ruptured cylindrical tanks reached distances of more than 100 m (330 ft), and one reached a distance of 1200 m (3900 ft). Several buildings on the site collapsed and were destroyed completely. Residents living as far away as approximately 300 m (1000 ft) from the center of the storage site (Figure 2.25) were killed or injured. Pietersen compared damage results to effect and damage models that were available at the time. His main findings follow: • Overpressure effects due to the vessel failure appear to be determined by gas expansion, not by flash vaporization. • Fireball dimensions seemed to be smaller than those predicted by models. However, the moment of the initial vessel failure was not captured by either video or still cameras. • Very rapidly expanding ground-level fireballs occurred whenever vessels failed.

PEMiX LPG INSTALLATION SAN JUAN IXHUATEPEC , MEXICO CITY 1 : 4680

1 . 2 Spheres of 2400 m3 0 = 1 6.5 m 2. 4 Spheres of 160Om3 0 = 1 4.5 m 3. 4 cylinders of 270 m3 32 x 3.5m 0 4. 14 cylinders of 180 m3 21 x 3.5m 0 5. 21 cylinders of 36 m3 13 x 2.0 m 0 6. 6 cylinders of 54 m3 19 x 2.0m 0 3 cylinders of 4 5 m 3 1 6 x 2 . 0 m 0

Figure 2.24. Installation layout.

7. 8. 9. 10. 11. 12. 13. 14. 15.

Flare pit Pond Control room Pumphouse Fire pumps Road car loading Gas bottle store Pipe/valve manifold Water tower

16. LPG storage unigas 17. LPG storage gasomatico 18. Bottling terminal 19. Depot of cars with bottles 20. Entrance 21 . Rail car loading 23. Store 24. Garrison

untgos

gasoftottco trucks with bottltt

heavily damaged area bullets position of major sphert fragments

Figure 2.25. Area of damage.

o End Tub Fragments A Other Fragments Figure 2.26. Directional preference of projected cylinder fragments of cylindrical shape.

• Spherical tanks fragmented into ten to twenty pieces, whereas cylindrical vessels fragmented into two pieces. Because cylinders at the storage site had been stored parallel to each other, their fragments were launched in specific directions (Figure 2.26). Nijmegen, The Netherlands: Tank Truck Failure On December 18, 1978, a tank truck filled with LPG exploded after it caught fire during a transfer to the storage tank of a gasoline station. The accident resulted in destruction of the truck and the gasoline station.

Steunenberg et al. (1981) describe the following accident. On the morning of December 18, 1978, a tank truck filled with LPG departed to deliver LPG to a gasoline station in Nijmegen in The Netherlands. The gasoline station is located near a highway and 500 m (1600 ft) from the nearest buildings and houses in the city of Nijmegen. After the truck arrived and maneuvered into position, transfer lines were connected to the storage tank of the gasoline station. The transfer of LPG to the storage tank began at 8:20 A.M. After some minutes, the driver and the gasoline station employee noticed a fire under the truck. They went to extinguish the fire with small fire extinguishers, but decided that it would not be possible to stop the fire. They returned to the gasoline station building, and turned in an alarm at 8:24 A.M. The driver and the gasoline station employee fled by car. Traffic on the highway and on a nearby railway track was stopped. Inasmuch as no one was then near the gasoline station, the fire brigade decided to wait beside the nearby buildings of the city of Nijmegen. At 8:45 the tank of the truck failed; it had no safety valve. A fireball resulted, but no concussion was felt. The front end of the tank was propelled up for a distance

of approximately 50 m (160 ft). Baffles in the tank were propelled to distances of 125 m (400 ft). The storage tank remained intact. Investigations revealed that the initial fire was due to a small, continuous release from the transfer lines. The leakage was ignited by hot surfaces of the truck's engine. The fireball was found to have a maximum diameter of approximately 40 m (130 ft). It rose to 25 m (80 ft) above ground level. Wooden sticks affected by radiation from the fireball permitted an estimate of the radiation levels emitted. It was thus established that the emissive power of the LPG cloud was approximately 180 kW/m2 (16 BTU/s/ft2). Texas City, Texas, USA: Several BLEVEs at a Refinery On May 30, 1978, a sphere in a tank farm of a refinery at Texas City, Texas, was overfilled with isobutane. As a result, it cracked and released a portion of its contents, which were then ignited. The ensuing flash fire caused the sphere to fail completely. A fireball then developed. Several ensuing explosions, fireballs, and BLEVEs destroyed the refinery almost completely, causing the deaths of seven people and injuries of ten.

Davenport (1986) describes the following accident. On May 30,1978, at 2:00 A.M., the overfilling with isobutane of sphere 409 in the tank farm of a refinery at Texas City, Texas (Figure 2.27) caused the sphere to crack at a bad weld and resulted in

Figure 2.27. Tank farm, Texas City, Texas, refinery.

Figure 2.28. Fireball from sphere BLEVE, Texas City, Texas, refinery.

the partial release of its contents. The sphere was overfilled because its level indicator was not functioning properly during filling. The leaking gas was ignited by an unknown source; fire then flashed back toward the sphere. It burned for approximately 30 to 60 seconds before the sphere failed in three major portions. One of these portions traveled 80 m (260 ft). A fireball involving approximately 800 m3 (28,000 ft3) of isobutane resulted from the sphere's failure. Several BLEVEs of smaller vertical and horizontal tanks occurred soon thereafter. Tank failures were mainly seam-related. Parts were thrown in various directions up to a maximum distance of 135 m (440 ft). At 2:20 A.M., another explosion occurred, the BLEVE of sphere 407. Its fireball was less intense than the earlier one. The sphere's top section traveled 190 m (620 ft) and caused the destruction of a firewater tank and one of the plant's fire pumps. Other sections further damaged other units. The pressure relief valve of this sphere traveled 500 m (1600 ft). The damage from projectiles was much greater than that caused by the first sphere failure because they traveled farther and in more damaging directions. Smaller explosions occurred until about 6:00 A.M. There was no evidence of strong overpressure effects, although a television news broadcast showed broken windows at 3.5 km (2 miles) from the plant. San Carols de Ia Rapita, Spain: Tank Truck Failure Near Campsite On July 11, 1978, a tank truck carrying propyiene left the road and crashed into a campsite. A leak developed, and the ensuing cloud was ignited. Three minutes later the tank failed completely. A fireball was generated and fragments were projected. In total 211 people were killed. The number of injured is unknown.

Stinton (1983) and Lees (1980) describe this accident. On July 11, 1978, at 12:05 P.M., the loading of a tank truck with propyiene was completed. According to weight records obtained at the refinery exit after loading, it had been grossly overloaded; head space was later calculated to be inadequate. The truck scale recorded a weight for the load of 23,470 kg (52,000 Ib)—well over the maximum allowable weight of 19,099 kg (42,000 Ib). The tank truck was not equipped with a pressure relief valve. The tank truck was en route to Valencia, but traveled on a back road instead of the highway in order to avoid tolls. It was a hot summer day. As it passed through the village of San Carlos de Ia Rapita, observers noticed that the tank truck sped up appreciably and was traveling at an excessive speed. The tank truck left the road near the campsite and crashed at 4:29 P.M. (Figure 2.29). Propyiene seems to have been released. The resulting vapor cloud was ignited, possibly by camp cooking fires. One or two explosions then occurred. (Some witnesses heard two explosions.) About three minutes after the initial explosion or fire, the tank failed and produced fragments and a fireball. Blast effects were far heavier in the upward and windward directions than otherwise. About 75 m (250 ft) from the explosion center,

Figure 2.29. Reconstruction of scene of the San Carlos de Ia Rapita campsite disaster.

a single-story building was completely demolished. This failure resulted in the death of four people. In the opposite direction, a motorcycle was still standing on its footrest at a distance of only 20 (65 ft) from the blast origin. About 500 people were at the campsite at the time of the incident. Deaths, primarily from engulfment in the fireball, totalled 211.

REFERENCES Burgess, D. S., and M. G. Zabetakis. 1973. "Detonation of a flammable cloud following a propane pipeline break. The December 9, 1970, Explosion in Port Hudson, Mo." Bureau of Mines Report of Investigations No. 7752. Davenport, J. A. 1977. A survey of vapor cloud incidents. Chemical Engineering Progress. Sept. 1977, 54-63. Davenport, J. A. 1983. "A Study of Vapor Cloud Incidents—An Update." Fourth International Symposium on Loss Prevention and Safety in the Process Industries. European Federation of Chemical Engineering, Sept. 1983, Harrogate, England. Davenport, J. A. 1986. "Hazards and protection of pressure storage of liquefied petroleum gases." Fifth International Symposium on Loss Prevention and Safety Promotion in the Process Industries, European Federation of Chemical Engineering, Conner, France. Eisenberg, N. A., C. J. Lynch, andR. J. Breeding. 1975. "Vulnerability model. A simulation system for assessing damage resulting from marine spills." U.S. Department of Commerce Report No. AD/AOI5/245. Washington: National Technical Information Service. Factory Mutual Research Corporation. 1990. "Guidelines for the estimation of property damage from outdoor vapor cloud explosions in chemical processing facilities." Technical Report, March 1990. Giesbrecht, H., K. Hess, W. Leuckel, and B. Maurer, 1981. "Analysis of explosion hazards on spontaneous release of inflammable gases into the atmosphere. Part 1: Propagation and deflagration of vapor clouds on the basis of bursting tests on model vessels." Ger. Chem. Eng. 4:305-314. Gugan, K. 1978. Unconfined vapor cloud explosions. Rugby: IChemE. Hanna, S. R., and P. J. Drivas. 1987. Guidelines for Use of Vapor Cloud Dispersion Models. New York: AIChE. IChemE. 1987. The Feyzin disaster, Loss Prevention Bulletin No. 077: 1-10. Lees, F. P. 1980. Loss Prevention in the Process Industries. London: Butterworths. Leiber, C. O. 1980. Explosionen von Flussigkeitstanken. Empirische Ergebnisse—Typische Unfalle. J. Occ. Ace. 3:21-43. Lenoir, E. M., and J. A. Davenport. 1993. "A Survey of Vapor Cloud Explosions: Second Update." Process Safety Progress. 12:12-33. Lewis, D. J. 1989. Soviet blast—the worst yet? Hazardous Cargo Bulletin. August 1989. 59-60. Marshall, V. C., 1986. "Ludwigshafen—Two case histories." Loss Prevention Bulletin 67:21-33. National Transportation Safety Board. 1971. "Highway Accident Report: Liquefied Oxygen tank truck explosion followed by fires in Brooklyn, New York, May 30, 1970." ATOBHAR-71-6.

National Transportation Safety Board. 1972. "Railroad Accident Report—Derailment of Toledo, Peoria and Western Railroad Company's Train No. 20 with Resultant Fire and Tank Car Ruptures, Crescent City, Illinois, June 21, 1970. NTSB-RAR-72-2. National Transportation Safety Board. 1973. "Highway Accident Report—Propane TractorSemitrailer overturn and fire, U.S. Route 501, Lynchburg, Virginia, March 9, 1972." NTSB-HAR-73-3. National Transportation Safety Board. 1973. "Railroad Accident Report—Hazardous materials railroad accident in the Alton and Southern Gateway Yard in East St. Louis, Illinois, January 22, 1912." NTSB-RAR-73-1. National Transportation Safety Board. 1979. "Pipeline Accident report—Mid-America Pipeline System—Liquefied petroleum gas pipeline rupture and fire, Donnellson, Iowa, August 4, 1978." NTSB-Report NTSB-PAR-79-1. Parker, R. J. (Chairman), 1975. The Flixborough Disaster. Report of the Court of Inquiry. London: HM Stationery Office. Pietersen, C. M. 1988. Analysis of the LPG disaster in Mexico City. J. Haz. Mat. 20:85-108. Reider, R., H. J. Otway, and H. T. Knight. 1965. "An unconfined large volume hydrogen/ air explosion." Pyrodynamics. 2:249- 261. Sad6e, C., D. E. Samuels, and T. P. O'Brien. 1976/1977. "The characteristics of the explosion of cyclohexane at the Nypro (U.K.) Flixborough plant on June 1st 1974." J. Occ. Accid. 1:203-235. Steunenberg, C. F., G. W. Hoftijzer, and J. B. R. van der Schaaf. 1981. Onderzoek naar aanleiding van een ongeval met een tankauto te Nijmegen. Pt-Procestechniek. 36(4): 175-182. Stinton, H. G. 1983. Spanish camp site disaster. J. Haz. Mat. 7:393-401. Strehlow, R. A., and W. E. Baker. 1976. The characterization and evaluation of accidental explosions. Prog. Energy Combust. Sd. 2:27-60. Van Laar, G. F. M. 1981. "Accident with a propane tank at Enschede on 26th March 1980, Prins Maurits Laboratorium." TNO Report no. PML 1981-145. Voros, M., and G. Honti. 1974. Explosion of a liquid CO2 storage vessel in a carbon dioxide plant. First International Symposium on Loss Prevention and Safety Promotion in the Process Industries.

3 BASIC CONCEPTS Accident scenarios leading to vapor cloud explosions, flash fires, and BLEVEs were described in the previous chapter. Blast effects are a characteristic feature of both vapor cloud explosions and BLEVEs. Fireballs and flash fires cause damage primarily from heat effects caused by thermal radiation. This chapter describes the basic concepts underlying these phenomena. Section 3.1 treats atmospheric dispersion in just enough detail to permit understanding of its implications for vapor cloud explosions. Section 3.2 covers the evolution from slow, laminar, premixed combustion to an intense, explosive, blastgenerating process. It introduces the concepts of deflagration and detonation. Section 3.3 describes typical ignition sources and the ignition characteristics of several typical fuel-air mixtures. Section 3.4 covers the physical concepts of blast and blast loading and describes how blast parameters can be established and scaled. Section 3.5 introduces basic concepts of thermal radiation modeling.

3.1. ATMOSPHERIC VAPOR CLOUD DISPERSION Chapter 2 discussed the possible influence of atmospheric dispersion on vapor cloud explosion or flash fire effects. Factors such as flammable cloud size, homogeneity, and location are largely determined by the manner of flammable material released and turbulent dispersion into the atmosphere following release. Several models for calculating release and dispersion effects have been developed. Hanna and Drivas (1987) provide clear guidance on model selection for various accident scenarios. Before the size of the flammable portion of a vapor cloud can be calculated, the flammability limits of the fuel must be known. Flammability limits of flammable gases and vapors in air have been published elsewhere, for example, Nabert and Schon (1963), Coward and Jones (1952), Zabetakis (1965), and Kuchta (1985). A summary of results is presented in Table 3.1, which also presents autoignition temperatures and laminar burning velocities referred to during the discussion of the basic concepts of ignition and deflagration. The flash point of a liquid is the minimum temperature at which its vapor pressure is sufficiently high to produce a flammable mixture with air above the liquid. Therefore, the generation of a flammable gas or vapor cloud for liquids whose flash points are above the ambient temperature, e.g., xylene (see Table 3.1), is only possible if they are released at elevated temperatures or pressures. In such

TABLE 3.1. Explosion Properties of Flammable Gases and Vapors in Air at Atmospheric Conditions3

Gas or Vapor

Flammability Limits (vol. %)

Flash Point CC)

Autoignition Temperature (0C)

Laminar Burning Velocity (mis)

Methane Ethane Propane Ethylene Propylene Hydrogen Acetone Diethyl ether Acetylene Ethanol Toluene Cyclohexane Hexane Xylene

5.0-15.0 3.0-15.5 2.1-9.5 2.7-34 2.0-11.7 4.0-75.6 2.5-13.0 1.7-36 1.5-100 3.5-15 1.2-7.0 1.2-8.3 1.2-7.4 1.0-7.6

— — — — — -19 -20 — 12 — -18 -15 30

595 515 470 425 455 560 540 170 305 425 535 260 240 465

0.448 0.476 0.464 0.735 0.512 3.25 0.444 0.486 1.55 — — — — —

a

Nabert and Schon (1963), Coward and Jones (1952), Zabetakis (1965), and Gibbs and Calcote (1959).

cases, the fuel may be dispersed in the form of a warm, flammable cloud or a flammable aerosol-air mixture. Data on dispersion and combustion of aerosol-air clouds are scarce, although Burgoyne (1963) showed that the lower flammability limits on a weight basis of hydrocarbon aerosol-air mixtures are in the same range as those of gas- or vapor-air mixtures, namely, about 50 g/m3. Generally, at any moment of time the concentration of components within a vapor cloud is highly nonhomogeneous and fluctuates considerably. The degree of homogeneity of a fuel-air mixture largely determines whether the fuel-air mixture is able to maintain a detonative combustion process. This factor is a primary determinant of possible blast effects produced by a vapor cloud explosion upon ignition. It is, therefore, important to understand the basic mechanism of turbulent dispersion. Flow in the atmospheric boundary layer is turbulent. Turbulence may be described as a random motion superposed on the mean flow. Many aspects of turbulent dispersion are reasonably well-described by a simple model in which turbulence is viewed as a spectrum of eddies of an extended range of length and time scales (Lumley and Panofsky 1964). In shear layers, large-scale eddies extract mechanical energy from the mean flow. This energy is continuously transferred to smaller and smaller eddies. Such energy transfer continues until energy is dissipated into heat by viscous effects in the smallest eddies of the spectrum.

Turbulence is generated by wind shear in the surface layer and in the wake of obstacles and structures present on the earth's surface. Another powerful source of turbulent motion is an unstable temperature stratification in the atmosphere. The earth's surface, heated by sunshine, may generate buoyant motion of very large scale (thermals). For a chemical reaction such as combustion to proceed, mixing of the reactants on a molecular scale is necessary. However, molecular diffusion is a very slow process. Dilution of a 10-m diameter sphere of pure hydrocarbons, for instance, down to a flammable composition in its center by molecular diffusion alone takes more than a year. On the other hand, only a few seconds are required for a similar dilution by molecular diffusion of a 1-cm sphere. Thus, dilution by molecular diffusion is most effective on small-scale fluctuations in the composition. These fluctuations are continuously generated by turbulent convective motion. Turbulent eddies larger than the cloud size, as such, tend to move the cloud as a whole and do not influence the internal concentration distribution. The mean concentration distribution is largely determined by turbulent motion of a scale comparable to the cloud size. These eddies tend to break up the cloud into smaller and smaller parts, so as to render turbulent motion on smaller and smaller scales effective in generating fluctuations of ever smaller scales, and so on. On the smallscale side of the spectrum, concentration fluctuations are homogenized by molecular diffusion. With this simplified concept in mind, general trends in vapor cloud dispersion can be derived and understood. Generally, in a process of vapor cloud dispersion, two successive stages can be distinguished (Wilson et al. 1982a). An initial stage is characterized by the generation of large-scale fluctuations by large-scale turbulent motion. When the cloud dimensions grow beyond the size of the large-scale turbulence in the flow field, a second stage can develop. This final stage is characterized by a gradual reduction of concentration fluctuations. Some degree of homogeneity in the composition can arise only after the cloud dimensions have grown far beyond the characteristic size of the large-scale turbulent motion. Generally, accidental emissions take place close to the earth's surface. The scale of the turbulence in the surface layer is limited by the distance to the earth's surface, so the characteristic size of the large-scale turbulence decreases towards the surface. Therefore, some degree of homogeneity in a vapor cloud is first to be expected in a thin layer adjacent to the ground (Wilson et al. 1982b). The thickness of this layer will increase as the vertical dimension of the cloud grows. Most fuels at release conditions are denser than air. In case of a large, instantaneous release, gravity spreads the vapor quickly over a large area. The slumping bulk of vapor generates large-scale motion in the cloud by which the initial mean concentration decay is fast. Some degree of homogeneity cannot be expected before the stage of gravity spreading is over and density differences become negligible, unless gravity spreading is suppressed by, for instance, the topographical conditions. The effect of atmospheric dispersion on the structure of a vapor cloud may be summarized as follows. In general, the structure of a vapor cloud in the atmosphere

can be characterized as very nonhomogeneous except for a thin layer adjacent to the earth's surface. A certain degree of homogeneity is obtained at a higher mean concentration level as the cloud dimensions are larger and the size of the large-scale turbulent motion is smaller. In general, a slower decay of the mean-concentration distribution goes hand-in-hand with a higher degree of homogeneity in a larger portion of the cloud and at a higher mean-concentration level. The above discussion holds for dispersion by atmospheric turbulence. In addition, a momentum release of fuel sometimes generates its own turbulence, e.g., when a fuel is released at high pressure in the form of a high-intensity turbulent jet. Fuel mixes rapidly with air within the jet. Large-scale eddy structures near the edges of the jet entrain surrounding air. Compositional homogeneity, in such cases, can be expected only downstream toward the jet's centerline. Fuel from a fully unobstructed jet would be diluted to a level below its lower flammability limit, and the flammable portion of the cloud would be limited to the jet itself. In practice, however, jets are usually somehow obstructed by objects such as the earth's surface, surrounding structures, or equipment. In such cases, a large cloud of flammable mixture will probably develop. Generally, such a cloud will be far from stagnant but rather in recirculating (turbulent) motion driven by the momentum of the jet.

3.2. COMBUSTION MODES 3.2.1. Deflagration The mechanism of flame propagation into a stagnant fuel-air mixture is determined largely by conduction and molecular diffusion of heat and species. Figure 3.1 shows the change in temperature across a laminar flame, whose thickness is on the order of one millimeter. Heat is produced by chemical reaction in a reaction zone. The heat is transported, mainly by conduction and molecular diffusion, ahead of the reaction zone into a preheating zone in which the mixture is heated, that is, preconditioned for reaction. Since molecular diffusion is a relatively slow process, laminar flame propagation is slow. Table 3.1 gives an overview of laminar burning velocities of some of the most common hydrocarbons and hydrogen. What are the mechanisms by which slow, laminar combustion can be transformed into an intense, blast-generating process? This transformation is most strongly influenced by turbulence, and secondarily by combustion instabilities. A laminar-flame front propagating into a turbulent mixture is strongly affected by the turbulence. Low-intensity turbulence will only wrinkle the flame front and enlarge its surface area. With increasing turbulence intensity, the flame front loses its moreor-less smooth, laminar character and breaks up into a combustion zone. In an intensely turbulent mixture, combustion takes place in an extended zone in which

temperature

reaction zone

preheating zone

direction of propagation

location Figure 3.1. Temperature distribution across a laminar flame.

combustion products and unreacted mixture are intensely mixed. High combustion rates can result because, within the combustion zone, the reacting interface between combustion products and reactants can become very large. The interaction between turbulence and combustion plays a key role in the development of a gas explosion. Generally, flame propagation is laminar immediately following ignition in an incipient gas explosion. Effective burning velocities are not much higher than the laminar burning velocity, and overpressures generated are on the order of millibars. Laminar combustion generates expansion and produces a flow field. If the boundary conditions of the expansion flow-field are such that turbulence is generated, the flame front, which is convected by expansion flow, will interact with the turbulence. Turbulence increases combustion rate. As more fuel is converted into combustion products per unit of volume and time, expansion flow becomes stronger. Higher flow velocities go hand in hand with more intense turbulence. This process feeds on itself; that is, a positive feedback coupling comes into action. In the turbulent stage of flame propagation, a gas explosion may be described as a process of combustion-driven expansion flow with the turbulent expansion-flow structure acting as an uncontrolled positive feedback (Figure 3.2). If such a process continues to accelerate, the combustion mode may suddenly change drastically. The reactive mixture just in front of the turbulent combustion zone is preconditioned for reaction by a combination of compression and of heating by turbulent mixing with combustion products. If turbulent mixing becomes too intense, the combustion reaction may quench locally. A very local, nonreacting but highly reactive mixture of reactants and hot products is the result.

combustion

expansion flow

turbulence

Figure 3.2. Positive feedback, the basic mechanism of a gas explosion.

The intensity of heating by compression can raise temperatures of portions of the mixture to levels above the autoignition temperature. These highly reactive "hot spots" react very rapidly, resulting in localized, constant-volume sub-explosions (Urtiew and Oppenheim 1966; Lee and Moen 1980). If the surrounding mixture is sufficiently close to autoignition as a result of blast compression from one of the sub-explosions, a detonation wave results. This wave engulfs the entire process of flame propagation.

3.2.2. Detonation The two basic modes of combustion—deflagration and detonation—differ fundamentally in their propagation mechanisms. In deflagrative combustion, the reaction front is propagated by molecular-diffusive transport of heat and turbulent mixing of reactants and combustion products. In detonative combustion, on the other hand, the reaction front is propagated by a strong shock wave which compresses the mixture beyond its autoignition temperature. At the same time, the shock is maintained by the heat released from the combustion reaction. To understand the behavior of detonation, some basic features of detonation must be understood. They are briefly summarized in the next few paragraphs. Various properties of detonation are reflected by different models (Picket and Davis 1979). Surprisingly accurate values of overall properties of a detonation, including, for example, wave speed and pressure, may be computed from the Chapman-Jouguet (CJ) model (Nettleton 1987). In this model, a detonation wave is simplified as a reactive shock in which instantaneous shock compression and the combustion front coincide, a zero induction time and an instantaneous reaction are inherent in this model (Figure 3.3). For stoichiometric hydrocarbon-air mixtures, the detonation wave speed is in the range of 1700-2100 m/s and corresponding detonation wave overpressures are in the range of 18-22 bars. A slightly more realistic concept is the Zel'dovich-Von Neumann-Doming (ZND) model. In this model, the fuel-air mixture does not react on shock compression beyond autoignition conditions before a certain induction period has elapsed (Figure 3.4). The pressure behind the nonreactive shock is much higher than the CJ detonation pressure, which is not attained until the reaction is complete. The duration of the

pressure

shock/reaction wave complex

time Figure 3.3. The CJ-model.

induction period at the nonreactive, postshock state is on the order of microseconds. As a consequence, nonreactive, postshock pressure—the "Von Neumann spike"— is difficult to detect experimentally, and decays immediately if a detonation fails to propagate. The one-dimensional representation described above is too simple to describe the behavior of a detonation in response to boundary conditions. Denisov et al.

pressure

shock

reaction wave induction time

time Figure 3.4. The ZND-model.

reaction wave

shock

induction length

Q

b

C_

Figure 3.5. Instability of ZND-concept of a detonation wave.

(1962) showed that the ZND-model of a detonation wave is unstable. Figure 3.5 shows how a plane configuration of a shock and a reaction wave breaks up into a cellular structure. Detonation is not a steady process, but a highly fluctuating one. Its multidimensional cyclic character is determined by a process of continuous decay and reinitiation. The collision of transverse waves plays a key role in the structure of a detonation wave. The nature of this process has been described in detail many times, for example, see Denisov et al. (1962); Strehlow (1970); Vasilev and Nikolaev (1978). In this cyclic process, a characteristic length scale or cell size can be distinguished, at least on the average (Figures 3.5 and 3.6). The characteristic cell size reflects the susceptibility of a fuel-air mixture to detonation. Some guide values taken from Bull et al. (1982), Knystautas et al. (1982), and Moen et al. (1984) are given in Table 3.2 for stoichiometric fuel-air mixtures. Cell size depends strongly on the fuel and mixture composition; more reactive mixtures result in smaller cell sizes. Table 3.2 shows that a stoichiometric mixture of methane and air has an exceptionally low susceptibility to detonation compared to other hydrocarbon-air mixtures.

Figure 3.6. Cellular structure of a detonation.

TABLE 3,2. Characteristic Detonation Cell Size for Some Stoichiometric Fuel-Air Mixtures Fuel

Cell Size (mm)

methane propane ] propylene | n-butane J ethylene ethylene oxide acetylene

300 55 25 18 10

3.3. IGNITION Depending on source properties, ignition can lead to either or both of two combustion modes, detonation or deflagration. As indicated in Chapter 2, deflagration is by far the more likely mode of flame propagation to occur immediately upon ignition. Deflagration ignition energies are on the order of 10~4 J, whereas direct initiation of detonation requires an energy of approximately 106 J. Table 3.3 gives initiation energies for deflagration and detonation for some hydrocarbon-air mixtures. Considering the high energy required for direct initiation of a detonation, it is a very unlikely occurrence. In practice, vapor cloud ignition can be the result of a sparking electric apparatus or hot surfaces present in a chemical plant, such as extruders, hot steam lines or friction between moving parts of machines. Another common source of ignition is open fire and flame, for example, in furnaces and heaters. Mechanical sparks, for example, from the friction between moving parts of machines and falling objects, are also frequent sources of ignition. Many metal-to-metal combinations result in mechanical sparks that are capable of igniting gas or vapor-air mixtures (Ritter 1984). In general, ignition sources must be assumed to exist in industrial situations.

TABLE 3.3. Initiation Energies for Deflagration and Detonation for Some Hydrocarbon-Air Mixtures3 Gas Mixture Acetylene-Air Propane-Air Methane-Air a

Minimum Ignition Energy for a Deflagration (mJ)

Minimum Initiation Energy for a Detonation (mJ)

0.007 0.25 0.28

1.29 x 105 2.5 x 109 2.3 x 1011

Data from Matsui and Lee (1979) and Berufsgenossenschaft der Chemischen Industrie 1972).

3.4. BLAST 3.4.1. Manifestation A characteristic feature of explosions is blast. Gas explosions are characterized by rapid combustion in which high-temperature combustion products expand and affect their surroundings. In this fashion, the heat of combustion of a fuel-air mixture (chemical energy) is partially converted into expansion (mechanical energy). Mechanical energy is transmitted by the explosion process into the surrounding atmosphere in the form of a blast wave. This process of energy conversion is very similar to that occurring in internal combustion engines. Such an energy conversion process can be characterized by its thermodynamic efficiency. At atmospheric conditions, the theoretical maximum thermodynamic efficiency for conversion of chemical energy into mechanical energy (blast) in gas explosions is approximately 40%. Thus, less than half of the total heat of combustion produced in explosive combustion can be transmitted as blast-wave energy. In the surrounding atmosphere, a blast wave is experienced as a transient change in gas-dynamic-state parameters: pressure, density, and particle velocity. Generally, these parameters increase rapidly, then decrease less rapidly to sub-ambient values (i.e., develop a negative phase). Subsequently, parameters slowly return to atmospheric values (Figure 3.7). The shape of a blast wave is highly dependent on the nature of the explosion process. If the combustion process within a gas explosion is relatively slow, then expansion is slow, and the blast consists of a low-amplitude pressure wave that is characterized by a gradual increase in gas-dynamic-state variables (Figure 3.7a). If, on the other hand, combustion is rapid, the blast is characterized by a sudden increase in the gas-dynamic-state variables: a shock (Figure 3.7b). The shape of a blast wave changes during propagation because the propagation mechanism is nonlinear. Initial pressure waves tend to steepen to shock waves in the far field, and wave durations tend to increase.

3.4.2. Blast Loading An object struck by a blast wave experiences a loading. This loading has two aspects. First, the incident wave induces a transient pressure distribution over the

Figure 3.7. Blast wave shapes.

incident shock front roof front wall

back wall

vortex rarefaction wave reflected shock front

shock front vortices

shock front

shock front diffracted shock front

vortices

Figure 3.8. Interaction of a blast wave with a rigid structure (Baker 1973).

object which is highly dependent on the shape of the object. The complexity of this process can be illustrated by the phenomena represented in Figure 3.8 (Baker 1973). In Figure 3.8a, a plane shock wave is moving toward a rigid structure. As the incident wave encounters the front wall, the portion striking the wall is reflected and builds up a local, reflected overpressure. For weak waves, the reflected overpressure is slightly greater than twice the incident (side-on) overpressure. As the incident (side-on) overpressure increases, the reflected pressure multiplier increases. See Appendix C, Eq. (C-1.4). In Figure 3.8b, the reflected wave moves to the left. Above the structure, the incident wave continues on relatively undisturbed. As the reflected wave moves back from the front wall, a rarefaction front moves down the front face of the structure (Figure 3.8b). In this way, the reflected overpressure is attenuated by lateral rarefaction, a process that is primarily determined by the lateral dimensions of the structure. The top face of the structure experiences no more than the sideon wave overpressure. As the incident shock passes beyond the rear face of the structure, it diffracts around this face, as shown in Figure 3.8c. At the instant shown in Figure 3.8c, the reflected overpressure at the front face has been completely attenuated by the lateral rarefaction. Subsequently, the incident shock has passed beyond the structure, the diffraction process is over, and the structure is immersed in the particle-velocity flow-field behind the leading shock front. At this stage, the structure experiences the blast wave as a gust of wind which exerts a drag force. In summary, an object's blast loading has two components. The first is a transient pressure distribution induced by the overpressure of the blast wave. This component of blast loading is determined primarily by reflection and lateral rarefaction of the reflected overpressure. The height and duration of reflected overpressure are determined by the peak side-on overpressure of the blast wave and the lateral dimensions of the object, respectively. The Blast loading of objects with substantial

lateral dimensions is largely governed by the overpressure aspect of a blast wave. On the other hand, slender objects—lampposts, for example—are hardly affected by the overpressure aspect of blast loading. The second component of blast loading is a drag force induced by particle velocity in the blast wave. Drag force magnitude is determined by the object's frontal area and the dynamic pressure of flow after the leading shock. The blast loading of slender objects is largely governed by the dynamic pressure (drag) aspect of a blast wave. Making a detailed estimate of the full loading of an object by a blast wave is only possible by use of multidimensional gas-dynamic codes such as BLAST (Van den Berg 1990). However, if the problem is sufficiently simplified, analytic methods may do as well. For such methods, it is sufficient to describe the blast wave somewhere in the field in terms of the side-on peak overpressure and the positivephase duration. Blast models used for vapor cloud explosion blast modeling (Section 4.3) give the distribution of these blast parameters in the explosion's vicinity.

3.4.3. Blast Scaling The upper half of Figure 3.9 represents how a spherical explosive charge of diameter d produces a blast wave of side-on peak overpressure P and positive-phase duration t+ at a distance R from the charge center. Experimental observations show that an explosive charge of diameter Kd produces a blast wave of identical side-on peak overpressure p and positive-phase duration Kt+ at a distance KR from the charge center. (This situation is represented in the lower half of Figure 3.9.) Consequently,

Figure 3.9. Blast-wave scaling

charge size can be used as a scaling parameter for blast. Charge size, however, is not a customary unit for expressing the power of an explosive charge; charge weight is more appropriate. Therefore, the cube root of the charge weight, which is proportional to the charge size, is used as a scaling parameter. If the distance to the charge, as well as the duration of the wave, are scaled with the cube root of the charge weight, the distribution of blast parameters in a field can be graphically represented, independent of charge weight. This technique, which is common practice for high-explosive blast data, is called the Hopkinson scaling law (Hopkinson 1915). It is more complete, however to scale a problem by full nondimensionalization. To achieve this, all governing parameters, such as the participating energy E9 the ambient pressure P09 and the ambient speed of sound C0 (ambient temperature), should be taken into account in dimensional analysis. The result is Sachs's scaling law (Sachs 1944), which states that the problem is fully described by the following dimensionless groups of parameters: AP ^o f+c0/3 £1/3

RP^ £1/3

where AP t* R E P0 C0

= = = = = =

side-on peak overpressure blast wave duration distance from blast center amount of participating energy ambient pressure ambient speed of sound

(Pa) (s) (m) (J) (Pa) (m/s)

3.5. THERMAL RADIATION In general, when a flammable vapor cloud is ignited, it will start off as only a fire. Depending on the release conditions at time of ignition, there will be a pool fire, a flash fire, a jet fire, or a fireball. Released heat is transmitted to the surroundings by convection and thermal radiation. For large fires, thermal radiation is the main hazard; it can cause severe burns to people, and also cause secondary fires. Thermal radiation is electromagnetic radiation covering wavelengths from 2 to 16 fjim (infrared). It is the net result of radiation emitted by radiating substances such as H2O, CO2, and soot (often dominant in fireballs and pool fires), absorption by these substances, and scatter. This section presents general methods to describe

the radiation effects at a certain distance from the source of thermal radiation. Two different methods are used to describe the radiation from a fire: the point-source model and the surface-emitter model, or solid-flame model. 3.5.1. Point-Source Model In the point-source model, it is assumed that a selected fraction (/) of the heat of combustion is emitted as radiation in all directions. The radiation per unit area and per unit time received by a target (q) at a distance (x) from the point source is, therefore, given by

(3.1) where m = rate of combustion Hc = heat of combustion per unit of mass Ta = atmospheric attenuation of thermal radiation (transmissivity)

(kg/s) (J/kg) (-)

It is assumed that the target surface faces toward the radiation source so that it receives the maximum incident flux. The rate of combustion depends on the release. For a pool fire of a fuel with a boiling point (rb) above the ambient temperature (ra), the combustion rate can be estimated by the empirical relation:

(3.2) where m Hv Cv A Tb Ta 0.0010

= = = — = = =

combustion rate heat of vaporization specific heat of fuel pool area boiling temperature ambient temperature a constant

(kg/s) (J/kg) (J/kg/K) (m2) (K) (K) (kg/s/m2)

The fraction of combustion energy dissipated as thermal radiation (/) is the unknown parameter in the point-source model. This fraction depends on the fuel and on dimensions of the flame. Measurements give values for this fraction ranging from 0.1 to 0.4 Mudan 1984; Duiser 1989). Raj and Atallah (1974) measured the fraction of radiation from 2- to 6-m pool fires of LNG and found values between 0.2 and 0.25. The data from Burgess and Hertzberg (1974) for methane range from 0.15 to 0.34, and for butane, from 0.20 to 0.27. The highest value they found, 0.4, was for gasoline. Roberts (1982) analyzed the data from fireball experiments of Haseg-

awa and Sato (1977) and found values of 0.15 to 0.45. The point-source model can be inaccurate for target positions close to emitting surfaces.

3.5.2. Solid-Flame Model The solid-flame model can be used to overcome the inaccuracy of the point-source model. This model assumes that the fire can be represented by a solid body of a simple geometrical shape, and that all thermal radiation is emitted from its surface. To ensure that fire volume is not neglected, the geometries of the fire and target, as well as their relative positions, must be taken into account because a portion of the fire may be obscured as seen from the target. The incident radiation per unit area and per unit time (q) is given by

q = FE^

(3.3)

where q F E Ta

= = = =

incident radiation view factor emissive power of fire per unit surface area atmospheric attenuation factor (transmissivity)

(W/m2) (—) (W/m2) (—)

The view factor is the fraction of the radiation falling directly on the receiving target. The view factor depends on the shapes of the fire and receiving target, and on the distance between them. Emissive Power Emissive power is the total radiative power leaving the surface of the fire per unit area and per unit time. Emissive power can be calculated by use of Stefan's law, which gives the radiation of a black body in relation to its temperature. Because the fire is not a perfect black body, the emissive power is a fraction (e) of the black body radiation: E = ear4

(3.4)

where E T e a

= = = =

the emissive power temperature of the fire emissivity Stefan-Boltzmann constant = 5.67 X 10~8 W/m2/K4

(W/m2) (K) (—)

The use of Stefan-Boltzmann's law to calculate radiation requires the knowledge of the fire's temperature and emissivity. Turbulent mixing causes fire temperature to vary. Therefore, it can be more useful to calculate radiation from data on the

fraction of heat liberated as radiation, or else to rely solely on measured radiation values. Duiser (1989) calculates emissive power from rate of combustion and released heat. As a conservative estimate, he uses a radiation fraction (/) of 0.35. He proposed the following equation for calculating the emissive power of a pool fire: (3.5)

where E m" Hc hf df 0.35

= = = = = =

emissive power rate of combustion per unit area heat of combustion flame height flame diameter radiation fraction/

(W/m2) (kg/m2/s) (J/kg) (m) (m) (-)

The surface-emissive power of a propane-pool fire calculated in this way equals 98 kW/m2 (31,000 Btu/hr/ft2). The surface-emissive power of a BLEVE is suggested to be twice that calculated for a pool fire. The surface-emissive powers of fireballs depend strongly on fuel quantity and pressure just prior to release. Fay and Lewis (1977) found small surface-emissive powers for 0.1 kg (0.22 pound) of fuel (20 to 60 kW/m2; 6300 to 19,000 Btu/hr/ ft2). Hardee et al. (1978) measured 120 kW/m2 (38,000 Btu/hr/ft2). Moorhouse and Pritchard (1982) suggest an average surface-emissive power of 150 kW/m2 (47,500 Btu/hr/ft2), and a maximum value of 300 kW/m2 (95,000 Btu/hr/ft2), for industrialsized fireballs of pure vapor. Experiments by British Gas with BLEVEs involving fuel masses of 1000 to 2000 kg of butane or propane revealed surface-emissive powers between 320 and 350 kW/m2 (100,000-110,000 Btu/hr/ft2; Johnson et al. 1990). Emissive power, incident flux, and flame height data are summarized by Mudan (1984). Emissivity The fraction of black-body radiation actually emitted by flames is called emissivity. Emissivity is determined first by adsorption of radiation by combustion products (including soot) in flames and second by radiation wavelength. These factors make emissivity modeling complicated. By assuming that a fire radiates as a gray body, in other words, that extinction coefficients of the radiation adsorption are independent of the wavelength, a fire's emissivity can be written as e = 1 - exp(-fccf) where e = emissivity Xf = beam length of radiation in k = extinction coefficient

flames

(m) (m"1)

(3.6)

For a fireball, jcf can be replaced by the fireball diameter (Moorhouse and Pritchard 1982). Hardee et al. (1978) reported, for optically thin LNG fires, a value of k = 0.18 m"1. The emissivity of larger fires approaches unity. Transmissivity Atmospheric attenuation is the consequence of absorption of radiation by the medium present between emitter and receiver. For thermal radiation, atmospheric absorption is primarily due to water vapor and, to a lesser extent, to carbon dioxide. Absorption also depends on radiation wavelength, and consequently, on fire temperature. Duiser approximates transmissivity as

(3.7)

T3 = 1 - aw - ac where T3 = transmissivity aw = radiation absorption factor for water vapor otc = radiation absorption factor for carbon dioxide

( —) (—) (—)

Both factors depend on the respective partial vapor pressures of water and carbon dioxide and upon the distance to the radiation source. The partial vapor pressure of carbon dioxide in the atmosphere is fairly constant (30 Pa), but the partial vapor pressure of water varies with atmospheric relative humidity. Duiser (1989) published graphs plotting absorption factors (a) against the product of partial vapor pressure and distance to flame (Px) for flame temperatures ranging from 800 to 1800 K. Moorhouse and Pritchard (1982) presented the following relationship to approximate transmissivity of infrared radiation from hydrocarbon flames through the atmosphere: ra = 0.998*

(3.8)

where Ta = transmissivity jc = the distance to the source

( —) (m)

This equation is valid for distances up to 300 m. Raj (1982) presents graphs for transmissivity depending only on the relative humidity of air. His graphs can be approximated by Ta = log(14.1/W0108JT013)

(3.9)

where Ta = transmissivity jc = distance RH = relative humidity

( —) (m) (%)

This equation should not be used for relative humidities of less than 20%. The transmissivity calculated by Raj's method agrees, for distances up to 500 m, with the values calculated according to the procedure suggested by Duiser (1989).

Lihou and Maund (1982) define attenuation constants for hydrocarbon flames through the atmosphere, which can vary from 4 x 10"4Hi"1 (for a clear day) to 10~3 m"1 (for a hazy day). The mean value suggested by the authors is 7 X 10~4 m"1, which gives a transmissivity of: Ta = exp(-0.0007*)

(3.10)

where Ta = transmissivity jc = distance

( —) (m)

This equation gives higher transmissivity values than those calculated with methods described earlier. Presumably, Lihou and Maund's transmissivity is to be used for conditions of low relative humidity, in which dust particles (haze) are the main cause of attenuation. A conservative approach is to assume Ta = 1. View Factor Let F12 be the fraction of radiation impinging directly on a receiving surface. If the emitting surface equals A1, the incident radiation on the target's receiving area A2 follows from A1EF12 = A2^2

(3.11)

where E = emissive power of emitting surface q2 = incident radiation receiving surface

(W/m2) (W/m2)

Application of the reciprocity relation (A1F12 = A2F21) allows the fraction of radiation received by the target (apart from atmospheric attenuation and emissivity) to be expressed as q2 = FnE

(3.12)

where F21 = view factor or geometric configuration factor E = emissive power of emitting surface q2 = incident radiation-receiving surface

(-) (W/m2) (W/m2)

The view factor depends on the shape of the emitting surface (plane, cylindrical, spherical, or hemispherical), the distance between emitting and receiving surfaces, and the orientation of these surfaces with respect to each other. In general, the view factor from a differential plane (dA2) to a flame front (area A1) on a distance L is determined (Figure 3.10) by: (3.13)

Figure 3.10. Configuration for radiative exchange between two differential elements.

where L O1 ®2 A1 dA2

= length of line connecting elements dA{ and dA2 = angle between L and the normal to CiA1 = angle between L and the normal to dA2 = surface area flame front = differential plane

(m) (deg) (deg) (m2) (m2)

A fireball is represented as a solid sphere with a center height H and a diameter D. Let the radius of the sphere be R (R = D12). (See Figure 3.11.) Distance x is measured from a point on the ground directly beneath the center of the fireball to the receptor at ground level. When this distance is greater than the radius of the fireball, the view factor can be calculated. For a vertical surface (3.14) For a horizontal surface (3.15)

Figure 3.11. View factor of a fireball.

For a vertical surface beneath the fireball (x < D12), the view factor is given by

(3.16)

where X1 = reduced length xIR H1 = reduced length HIR

(-) (-)

For a flash fire, the flame can be represented as a plane surface. Appendix A contains equations and tables of view factors for a variety of configurations, including spherical, cylindrical, and planar geometries.

REFERENCES Baker, W. E. 1973. Explosions in Air. Austin: University of Texas Press. Berufsgenossenschaft der Chemischen Industrie. 1972. Richtlinien zur Vermeidug von Ziindgefahren infolge elektrostatischer Aufladungen. Richtlinie Nr. 4. Bull, D. C., J. E. Elsworth, and P. J. Shuff. 1982. Detonation cell structures in fuel-air mixtures. Combustion and Flame 45:7-22. Burgoyne, J. H. 1963. The flammability of mists and sprays. Second Symposium on Chemical Process Hazards. Burgess, D. S., and M. Hertzberg. 1974. Advances in Thermal Engineering. New York: John Wiley and Sons. Coward, H. F., and G. W. Jones. 1952. Limits of flammability of bases and vapors. Bureau of Mines Bulletin 503. Denisov, Yu. N., K. I. Shchelkin, and Ya. K. Troshin. 1962. Some questions of analogy between combustion in a thrust chamber and a detonation wave. 8th Symposium (International) on Combustion, pp. 1152-1159. Pittsburgh: PA: The Combustion Institute. Duiser, J. A. 1989. Warmteuitstraling (Radiation of heat). Method for the calculation of the physical effects of the escape of dangerous materials (liquids and gases). Report of the Committee for the Prevention of Disasters, Ministry of Social Affairs, The Netherlands, 2nd Edition. Fay, J. A., and D. H. Lewis, Jr. 1977. Unsteady burning of unconfined fuel vapor clouds. 16th Symposium (International) on Combustion, pp. 1397-1405. Pittsburgh, PA: The Combustion Institute. Picket, W., and W. C. Davis. 1979. Detonation. Berkeley: University of California Press.

Gibbs, G. J., and H. F. Calcote. 1959. Effect on molecular structure on burning velocity. Jr. Chem. Eng. Data. 4(3):226-237. Hanna, S. R., and P. J. Drivas. 1987. Guidelines for Use of Vapor Cloud Dispersion Models. New York: American Institute for Chemical Engineers, CCPS. Hardee, H. C., D. O. Lee, and W. B. Benedick. 1978. Thermal hazards from LNG fireball. Combust. Sd. Tech. 17:189-197. Hasegawa, K., and Sato, K. 1977. Study on the fireball following steam explosion of npentane. Second International Symposium on Loss Prevention and Safety Promotion in the Process Industries, pp. 297-304. Hopkinson, B. 1915. British Ordnance Board Minutes 13565. Johnson, D. M., M. J. Pritchard, and M. J. Wickens. 1990. "Large scale catastrophic releases of flammable liquids." Commission of the European Communities Report Contract No: EV4T.0014.UK(H). Knystautas, R., J. H. Lee, and C. M. Guirao. 1982. The critical tube diameter for detonation failure in hydrocarbon-air mixtures. Combustion and Flame. 48:63-83. Kuchta, J. M. 1985. Investigation of fire and explosion accidents in the chemical, mining, and fuel-related industries-A manual. Bureau of Mines Bulletin 680. Lee, J. H. S., and I. O. Moen. 1980. The mechanism of transition from deflagration to detonation in vapor cloud explosions. Prog. Energy Combust. Sd. 6:359-389. Lihou, D. A., and J. K. Maund. 1982. Thermal radiation from fireballs. IChemE Symp. Series. 71:191-225. Lumley, J. L., and H. A. Panofsky. 1964. The Structure of Atmospheric Turbulence. New York: John Wiley and Sons. Matsui, H., and J. H. S. Lee. 1979. On the measure of relative detonation hazards of gaseous fuel-oxygen and air mixtures. Seventeenth Symposium (International) on Combustion, pp. 1269-1280. Pittsburgh, PA: The Combustion Institute. Moen, I. O., J. W. Funk, S. A. Ward, G. M. Rude, and P. A. Thibault. 1984. Detonation length scales for fuel-air explosives. Prog. Astronaut. Aeronaut. 94:55-79. Moorhouse, J., and M. J. Pritchard. 1982. Thermal radiation from large pool fires and thermals—Literature review. IChemE Symp. Series No. 71. p. 123. Mudan, K. S. 1984. Thermal radiation hazards from hydrocarbon pool fires. Prog. Energy Combust. Sd. 10:59-80. Nabert, K., and G. Schon. 1963. Sicherheitstechnische Kennzahle brennbarer Gase und Ddmpfe. Berlin: Deutscher Eichverlag GmbH. Nettleton, M. A. 1987. Gaseous Detonations. New York: Chapman and Hall. Raj, P. K. 1982. MIT-GRI Safety & Res. Workshop, LNG-fires, Combustion and Radiation, Technology & Management Systems, Inc., Mass. Raj, P. P. K., and K. Attalah. 1974. "Thermal radiation from LNG fires." Adv. Cryogen. Eng. 20:143. Ritter, K. 1984. Mechanisch erzeugte Funken als Zundquellen. VDl-Berichte Nr.494. pp. 129-144. Roberts, A. F. 1982. Thermal radiation hazards from release of LPG fires from pressurized storage. Fire Safety J. 4:197-212. Sachs, R. G. 1944. The dependence of blast on ambient pressure and temperature. BRL Report no. 466, Aberdeen Proving Ground. Maryland. Strehlow, R. A. 1970. Multi-dimensional detonation wave structure. Astronautica Acta 15:345-357.

Urtiew, P. A., and A. K. Oppenheim. 1966. "Experimental observations of the transition to detonation in an explosive gas." Proc. Roy. Soc. London. A295:13-28. Van den Berg, A. C. 1990. BLAST—A code for numerical simulation of multi-dimensional blast effects. TNO Prins Maurits Laboratory report. Vasilev, A. A., and Yu Nikolaev. 1978. Closed theoretical model of a detonation cell. Acta Astronautica 5:983-996. Wilson, D. J., J. E. Fackrell, and A. C. Robins. 1982a. Concentration fluctuations in an elevated plume: A diffusion-dissipation approximation. Atmospheric Environ. 16(ll):2581-2589. Wilson, D. J., A. G. Robins, and J. E. Fackrell. 1982b. Predicting the spatial distribution of concentration fluctuations from a ground level source. Atmospheric Environ. 16(3):479-504. Zabetakis, M. G. 1965. Flammability characteristics of combustible gases and vapors. Bureau of Mines Bulletin 627. Pittsburgh.

4 BASIC PRINCIPLES OF VAPOR CLOUD EXPLOSIONS

This chapter discusses vapor cloud explosions in detail. As described in Chapter 2, a vapor cloud explosion is the result of a release of flammable material in the atmosphere, a subsequent dispersion phase, and, after some delay, an ignition of the vapor cloud. A flame must propagate at a considerable speed to generate blast, especially for 2-D (double-plane configurations) and 3-D (dense-obstacle) environments. Figure 4.1 illustrates the relationship between flame speed and overpressure for three different geometries. In order to reach these speeds, either the flame has to accelerate or the cloud has to be ignited very strongly, thereby producing direct initiation of a detonation. As described in Chapters 2 and 3, flame acceleration is only possible

• in the presence of outdoor obstacles, for example, congestion due to pipe racks, weather canopies, tanks, process columns, and multilevel process structures; • in a high-momentum release causing turbulence, for example, an explosively dispersed cloud or jet release; • in combinations of high-momentum releases and congestion.

Historically, this phenomenon was referred to as "unconfined vapor cloud explosion," but, in general, the term "unconfined" is a misnomer. It is more accurate to call this type of explosion simply a "vapor cloud explosion." This chapter is organized as follows. First, an overview of experimental research is presented. Experimental research has focused on identifying deflagration-enhancing mechanisms in vapor cloud explosions and on uncovering the conditions for a direct initiation of a vapor cloud detonation. Theoretical research is then discussed. Most theoretical research has concentrated on blast generation as a function of flame speed. Models of flame-acceleration processes and subsequent pressure generation (CFD-codes) are described as well, but in less detail. Finally, several blast-prediction methods are described and discussed. These methods are demonstrated in Chapter 7 with sample problems.

generated overpressure (bar)

tube-like geometry double planeconfiguration dense obstacle environment

flame speed ( m/s ) Figure 4.1. Overpressure as a function of flame speed for three geometries. The relationships are based on calculations by use of a self-similar solution (Kuhl et al. 1973).

4.1. OVERVIEW OF EXPERIMENTAL RESEARCH At first glance, the science of vapor cloud explosions as reported in the literature seems rather confusing. In the past, ostensibly similar incidents produced extremely different blast effects. The reasons for these disparities were not understood at the time. Consequently, experimental research on vapor cloud explosions was directed toward learning the conditions and mechanisms by which slow, laminar, premixed combustion develops into a fast, explosive, and blast-generating process. Treating experimental research chronologically is, therefore, a far from systematic approach and would tend to confuse rather than clarify. Because the major causes of blast generation in vapor cloud explosions are reasonably well understood today, we can approach the overview of experimental research more systematically by treating and interpreting the experiments in groups of roughly similar arrangements. Furthermore, some attention is given to experimental research into the conditions necessary for direct initiation of a detonation of a vapor cloud and the conditions necessary to sustain such a detonation. This section is arranged as follows: First, premixed combustion is discussed based on the experiments performed under controlled conditions. To establish these conditions the experiments were conducted in explosion vessels, balloons, plastic bags, and soap bubbles. Second, some experiments under uncontrolled conditions

are discussed. In one simulation of a realistic accidental spill, fuel was released in the open air and ignited. Experiments investigating the effects of both low- and high-momentum releases are discussed, that is, the effect of source-term turbulence on flame propagation. Third, the question of influence of the presence of confining structures and obstructions on the propagation of a premixed combustion process is investigated. Flame propagation in mixtures confined by tubes and parallel planes in combination with obstacles is described. Finally, the conditions that can lead to initiation and sustaining of a vapor cloud detonation are examined.

4.1.1. Unconfined Deflagration under Controlled Conditions Unconfined, controlled conditions were established by retaining fuel-air mixtures in a manner that had minimal effect on the expansion-combustion process. Investigators at the University of Poitiers (Desbordes and Manson 1978; Girard et al. 1979; Deshaies and Leyer 1981; Leyer 1981; Okasaki et al. 1981; Leyer 1982) demonstrated such effects on a laboratory scale by igniting flammable gas mixtures within soap bubbles. They produced hemispherical and cylindrical soap bubbles containing various mixtures of fuel-oxygen-nitrogen. The effects of obstacles in the cloud and of jet ignition on combustion behavior were also studied. Fuel-pair mixtures, in soap bubbles ranging from 4 to 40 cm diameter and with no internal obstacles, produced flame speeds very close to laminar flame speeds. Cylindrical bubbles of various aspect ratios produced even lower flame speeds. For example, maximum flame speeds for ethylene of 4.2 m/s and 5.5 m/s were found in cylindrical and hemispherical bubbles, respectively (Table 4.Ia). This phenomenon is attributed to reduced driving forces due to the top relief of combustion products. Obstacles introduced in unconfined cylindrical bubbles resulted only in local flame acceleration. Pressures measured at some distance from the cylindrical bubble were, in general, two to three times the pressure measured in the absence of obstacles. Large-scale balloon experiments of flammable gases in air were carried out by Lind (1975, 1977) (Figure 4.2), Brossard et al. (1985), Harris and Wickens (1989) and Schneider and Pfortner (1981). No obstacles were placed in the balloons. The highest flame speed from among these tests was obtained by Schneider and Pfortner (1981) in a 20-m diameter balloon with a hydrogen-air mixture (Table 4. Ia). These large-scale tests showed no significant overpressures. In all of these tests, flame acceleration was minimal or absent. Acceleration, when it occurred, was entirely due to intrinsic flame instability, for example, hydrodynamic instability (Istratov and Librovich 1969) or instability due to selective diffusion (Markstein 1964). To investigate whether the flame would accelerate when allowed to propagate over greater distances, tests were carried out in an open-sided test apparatus 45 m long (Harris and Wickens 1989). Flame acceleration was found to be no greater than in the balloon experiments (Table 4.Ia).

TABLE 4.1 a. Summary of Results of Experiments on Deflagration under Unconfined Controlled Conditions without Obstacles

Reference Deshaies and Layer (1981) Okasakietal. (1981)

Lind and Whitson (1977)

Brossard et al. (1985) Schneider and Pfortner(1981) Harris and Wickens (1989)

Harris and Wickens (1989)

Configuration Hemispherical soap bubbles (D = 4-40 cm) Cylindrical soap bubbles (D = 44 cm) Hemispherical balloons (D = 10-20 m)

Spherical balloons (D = 2.8 m) Hemispherical balloon (D = 20 m) Spherical balloons (D = 6.1 m)

45-m-long opensided tent

Fuel

CH4 C3H8 C2H4 C2H4

C4H6

CH4 C3H8 C2H4 C2H4O C2H2 C2H4 C2H2

H2

Natural gas

LPG C6H12 C2H4 Natural gas

LPG C6H12 C2H4

Max. Flame Speed (mis)

Max. Overpressure (bar)

3.0 4.0 5.5 4.2

— — — —

5.5 8.9 12.6 17.3 22.5 35.4 24 38 84

— — — — — — 0.0125

7 8 8 15 8 10 10 19

— 0.06

— — — — — — — —

The introduction of obstacles within "unconfined" vapor clouds produced flame acceleration. On a small scale, an array of vertical obstacles mounted on a single plate (60 X 60 cm) resulted in flame accelerations within the array (Van Wingerden and Zeeuwen 1983). Maximum flame speeds of 52 m/s for acetylene-air were found, versus 21 m/s in the absence of obstacles, over 30 cm of flame propagation. Harris and Wickens (1989) report large-scale tests in an open-sided 45-mlong apparatus incorporating grids and obstructions. Maximum flame speeds were approximately ten times those found in the absence of obstacles. The influence of hemispherical wire mesh screens (obstacles) on the behavior of hemispherical flames was studied by Dorge et al. (1976) on a laboratory scale. The dimensions of the wire mesh screens were varied. Maximum flame speeds for methane, propane, and acetylene are given in Table 4.1b.

Figure 4.2. Hemispherical balloon tests set-up as used by Lind and Whitson (1977).

TABLE 4.1 b. Summary of Results of Experiments on Deflagration under Unconfined Controlled Conditions with Obstacles

Reference Van Wingerden and Zeeuwen (1983)

Harris and Wickens (1989) Dorgeetal. (1976)

Harrison and Eyre (1986, 1987) Harrison and Eyre (1986, 1987)

Configuration 60 x 60 cm plate with 1 cm vertical obstacles on top 45-m-long opensided tent with obstructions spherical grids in a 0.6 m cube

Sector with pipework Sector with pipework and jet flame ignition

Fuel CH4 C3H8 C2H4 C2H2 Natural gas ^H10 C6H12 C2H4 C2H2 C2H4 C3H8 Natural gas C3H8 Natural gas

Max. Flame Speed (mis) 7

13 20 52 50 65 70 >200 150 30

16 119 170

Max. Overpressure (bar)

— — — — 0.03-0.07 0.03-0.07 0.03-0.07 0.8 — —

0.208 0.052 0.710

Harrison and Eyre (1986, 1987) studied flame propagation and pressure development in a segment of a cylindrical cloud both with and without obstacles, and with jet ignition (Figure 4.3). The sector was 30 m long and 10 m high, and its top angle was 30°. The obstacles, when introduced, consisted of horizontal pipes of 0.315 m in diameter, arranged in grids. These experiments (Table 4.Ib) demonstrated the following points: • Low-energy ignition of unobstructed propane-air and natural gas-air clouds does not produce damaging overpressures. • Combustion of a natural gas-air cloud in a highly congested obstacle array leads to flame speeds in excess of 100 m/s (pressure in excess of 200 mbar). • High-energy ignition of an unobstructed cloud by a jet flame emerging from a partially confined explosion produces a high combustion rate in the jet-flow region. • Interaction of a jet flame and an obstacle array can result in an increase of flame speed and production of pressures in excess of 700 mbar. The results in Tables 4. Ia and 4. Ib demonstrate that in the absence of obstacles, the highest flame speed observed was 84 m/s, and it was accompanied by an overpressure of 60 mbar for hydrogen-air in a 10-m radius balloon (Schneider and Pfortner 1981). For all other fuels, flame speeds were below 40 m/s and corresponding overpressures were below 35 mbar. Hence, weak ignition of an unconfined

Obstacle grids

Polythene cover

Ignition point

Arrow

Fans

shuttering walls

Pressure transducers Gas supply

Inlets to recirculation ducts

& Time-of-flight' flame detectors Recirculation duct

Concrete base

Figure 4.3. Experimental apparatus for investigation of effects of pipe racks on flame propagation (Harrison and Eyre 1986 and 1987).

cloud in an unobstructed environment will generally not result in a damaging explosion, even for relatively reactive fuels such as acetylene and hydrogen. The introduction of obstacles results in some flame acceleration, especially for the more reactive fuels. This effect is especially strong if the flame surface is distorted by the presence of obstacles over its entire surface, such as were present in the experiments of Dorge et al. (1976) and Harrison and Eyre (1986, 1987). The more reactive the fuel, the more effect obstacles seem to have on flame acceleration (Harris and Wickens 1989).

4.1.2. Unconfined Deflagration under Uncontrolled Conditions Accidental vapor cloud explosions do not occur under controlled conditions. Various experimental programs have been carried out simulating real accidents. Quantities of fuel were spilled, dispersed by natural mechanisms, and ignited. Full-scale experiments on flame propagation in fuel-air clouds are extremely laborious and expensive, so only a few such experiments have been conducted. Experiments to Study Deflagration of Fuel-Air Clouds after a Dispersion Process Experimental programs partly devoted to the study of deflagration speeds in unconfined environments free of obstacles, after dispersion of a vapor cloud by natural mechanisms included » LNG spill experiments in China Lake (Urtiew 1982); Hogan 1982; Goldwire et al. 1983); • the Maplin Sands tests reported by Blackmore et al. (1982) and Hirst and Eyre (1983). These experiments are described in detail in Chapter 5, and will not be described further here. The overall conclusion, from an explosion point of view, is that flame speeds are relatively low, although atmospheric conditions alone may increase flame speed somewhat. The maximum flame speed observed for LNG was 13.3 m/s (China Lake), and for propane (Maplin Sands), 28 m/s. Linney (1990) summarized the liquid hydrogen release tests performed by A. D. Little Inc. in 1958, by Lockheed in 1956-1957, and by NASA in 1980. Both high- and low-pressure releases were studied. None of the tests resulted in a blast-producing explosion. Hoff (1983) studied the effect of igniting natural gas after a simulated pipeline rupture by firing a bullet into the gas mixture. The tests were on a 10-cm diameter pipeline operating at an initial pressure of 60 bar and a gas throughput of 400,000 m3/day. The openings created in the pipeline simulated full-bore ruptures. Maximum flame speeds of approximately 15 m/s, and maximum overpressures of 1.5 mbar were measured at a distance of 50 m.

Zeeuwen et al. (1983) observed the atmospheric disperion and combustion of large spills of propane (1000-4000 kg) on an open and level terrain on the Musselbanks, located on the south bank of the Westerscheldt estuary in the Netherlands (Figure 4.4). The main object of this experimental program was the investigation of blast effects from vapor cloud explosions. Flame-front velocities were highly directional and dependent upon wind speed. Average flame-front velocities of up to 10 m/s were registered. In one case, however, a transient maximum flame speed of 32 m/s was observed. The presence of horizontal or vertical obstacles (Figure 4.4) in the propane cloud hardly influenced flame propagation. On the other hand, flame propagation was influenced significantly when obstacles were covered by steel plates. Within the partially confined obstacle array, flame speeds up to 66 m/s were observed (Table 4.2); they were clearly higher than flame speeds in unconfined areas. However, at points where flames left areas of partial confinement, flame speeds dropped to their original, low, unconfined levels. Experiments to Investigate Effect of Source-Term Generated Turbulence on Combustion Giesbrech et al. (1981) published the results of experiments performed to determine the intensity of pressure waves resulting from the rupture of liquefied gas vessels and ignition of resulting vapor-air clouds. To this end, a series of small-scale experiments was performed in which vessels with sizes ranging from 0.226 to 1000 1, and containing propylene under 40 to 60 bar pressure, were ruptured. After a preselected time lag, vapor clouds were ignited by exploding wires, and ensuing flame propagation and pressure effects were recorded.

Figure 4.4. Obstacle array used in large-scale propane explosion tests by Zeeuwen et al. (1983).

TABLE 4.2. Overview of Test Results on Deflagrative Combustion of Fuel-Air Clouds under Uncontrolled Conditions

Reference Linney(1990) Goldwire et al. (1983) Blackmore et al. (1982) Hoff (1983) Zeeuwen et al. (1983) Giesbrecht et al. (1981) Seifert and Giesbrecht (1986) Stock (1987)

Configuration

Fuel

Large-scale spills on land followed by ignition Large-scale spills on land followed by ignition Large-scale spills on water followed by ignition Ignition of spill after simulated pipeline rupture Large-scale spills on land followed by ignition

Liquid H2

Ignition of vapor clouds after vessel burst (0.226- 1000) Ignition of vapor clouds after jet release Ignition of vapor clouds after jet release

Max. Flame Speed (m/s)

Low

LNG

13.3

C3H8 LNG

28 10

LNG

15

C3H8

C3H6

32 (without confinement) 66 (with confinement) 45

CH4 H2

C3H8

Max. Overpressure (bar)

0.02 0.05 0.2 2.0

200

0.2

Flame speed was observed to be nearly constant, but increased with the scale of the experiment. Because mixing with air was limited, a volumetric expansion ratio of approximately 3.5 was observed. The maximum pressure observed was found to be scale dependent (Figure 4.5). Battelle (Seifert and Giesbrecht 1986) and BASF (Stock 1987) each conducted studies on exploding fuel jets, the former on natural gas and hydrogen jets, and the latter on propane jets. The methane and hydrogen jet program covered subcritical outflow velocities of 140, 190, and 250 m/s and orifice diameters of 10, 20, 50, and 100 mm. In the propane jet program, outflow conditions were supercritical with orifice diameters of 10, 20, 40, 60, and 80 mm. The jets were started and ignited after they had achieved steady-state conditions. In the methane and hydrogen jet experiments, blast static overpressure was measured at various distances from the cloud (Figure 4.6). The propane jet experi-

duration of positive pressure t* [ms] damage analyses maximum overpressure *pmax [mbarj

c a l c u l a t e d pressure in cloud region

Flixborough 197C

number of experiments

absolute flame v e l o c i t y S abs [m/s]

maximum flame velocity Sabs

vessel contents M VES [kg]

Figure 4.5. Flame velocity, peak overpressure, and overpressure duration in gas cloud explosions following vessels bursts (Giesbrecht et al. 1981).

tnents on the other hand, produced measurements only of in-cloud static overpressures (Figure 4.7). Summaries of results of these studies follow: • In-cloud overpressure is dependent on outflow velocity, orifice diameter, and the fuel's laminar burning velocity.

Figure 4.6. Decay of peak overpressure with distance for ignited subcritical 10-mm diameter hydrogen gas jets at various velocities, UQ. A = mean value.

MAXIMUM EXPLOSION PRESSURE (mbar)

ORIFICE DIAMETER (mm) Figure 4.7. Maximum overpressure in vapor cloud explosions after critical-flow propane jet release dependent on orifice diameter: (a) undisturbed jet; (b) jet into obstacles and confinement.

• The maximum overpressure appeared to rise substantially when the jet was partially confined between 2-m-high parallel walls and obstructed by some 0.5m-diameter obstacles. Conclusions from experiments on deflagrative combustion of fuel-air clouds under uncontrolled conditions follow: • Flame acceleration was minimal after ignition of dispersed fuel-air clouds under unconfined conditions in the absence of obstacles. • As previously demonstrated, the introduction of obstacles and partial confinement results in some flame acceleration (Zeeuwen et al. 1983). • Source-term turbulence, as would be caused by vessel rupture or after a turbulent jet release, enhances combustion in vapor clouds. • Any release mode producing a combination of partial confinement, obstacles, and turbulence of unburned gases results in very strong explosion effects.

4.1.3. Partially Confined Deflagration Flame propagation develops differently when the combustion process is partially confined. Partial confinement affects the development of a gas explosion as follows:

• Pressure buildup in a gas explosion is caused by an interaction of expansion and combustion. • Partial confinement hampers expansion and allows the introduction of a combustion enhancing flow structure. • Additional shear- and turbulence-generating elements, such as bends and obstacles, will amplify feedback. A first degree of confinement can be the introduction of parallel planes (cylindrical geometry). In that configuration, combustion products can expand only in two dimensions. A second degree of confinement can be the introduction of a tube, thus permitting expansion in only one dimension. Hybrid configurations, such as channels which are either open on top or covered by perforated plates, are also possible. Each of these configurations has been investigated extensively. Some of the main results are presented below. Cylindrical Geometry Cylindrical geometry is obtained by placing two plates parallel to each other and introducing a gas mixture between them. The gas is usually ignited in the center. Obstacles are introduced to enhance the combustion rate (Figure 4.8). Moen et al. (198Oa) published results of an investigation performed on flame propagation between two plates 60 cm in diameter. Methane flame speeds of up to 130 m/s were produced. Plates were later enlarged to 2.5 x 2.5 m, and methane flame speeds up to 400 m/s, accompanied by an overpressure of 0.64 bar, were produced (Moen et al. 198Ob). Obstacled parameters were varied. The two most significant variables were blockage ratio (ratio of area blocked by obstacles to total area) and pitch (the relative distance between two successive obstacles or obstacle rows). The positive feedback mechanism of flame-generated turbulence affecting IGNITION WIRES

GAS OUTLET

GAS INLET

GAS OUTLET

Figure 4.8. Experimental setup to study flame propagation in a cylindrical geometry.

Figure 4.9. Flame speed-distance relationship of methane-air flames in a double plate geometry (2.5 x 2.5 m) as found by Moen et at. (198Ob). Tube spirals (diameter H = 4 cm) were introduced between the plates (plate separation D). The pitch P (see Figure 4.8 for definition) was held constant. P = 3.8 cm. (a) HID = 0.34; (b) HID = 0.25; (c) HID = 0.13.

flame propagation is reflected by the flame speed-distance relationships determined for various obstacle configurations (Figure 4.9). Van Wingerden and Zeeuwen (1983) demonstrated increases in flame speeds of methane, propane, ethylene, and acetylene by deploying an array of cylindrical obstacles between two plates (Table 4.3). They showed that laminar flame speed can be used as a scaling parameter for reactivity. Van Wingerden (1984) further investigated the effect of pipe-rack obstacle arrays between two plates. Ignition of an ethylene-air mixture at one edge of the apparatus resulted in a flame speed of 420 m/s and a maximum pressure of 0.7 bar. Hjertager (1984) reported overpressures of 1.8 bar and 0.8 bar for propane and methane-air explosions, respectively, in a 0.5-m radial disk with repeated obstacles. Van Wingerden (1989a) reports a comprehensive study into the effects of forestlike obstacle arrays (0.08-m diameter obstacles) on the propagation of flames in a rectangular, double-plate apparatus of 2 X 4m. Rames propagated over distances of up to 4 m from the point of ignition in some configurations. Ethylene-air mixtures generated flame speeds of up to 685 m/s and pressures of up to 10 bar inside an

TABLE 4.3. Overview of Test Results on Deflagrative Combustion of Fuel -Air Clouds in Cylindrical Geometries

Reference Moenetal. (1980a,b) Van Wingerden and Zeeuwen (1983) Hjertager (1984) Van Wingerden (1984)

Van Wingerden (1989a)

Configuration

Fuel

Max. Flame Speed (m/s)

Two plates diam. 2.5 m with spiral tube obstacles Two plates 0.6 x 0.6 m with forest of cylindrical obstacles Radial disk 0.5 m radius with pipes and flattype obstacles Two plates 0.5 m x 0.5 m pipe-rack obstacles Two plates 4 m x 4 m pipe rack obstacles Two plates vertical cylinders in concentric circles (2 x 4 m)

CH4 H2S

400 50

CH4 C3H8 C2H4 C3H8 CH4

27 40 40 225 160

C2H4

30

C2H4

420

0.7

C2H4

685

10.0

Max. Overpressure (bar) 0.64

1.8 0.8

obstructed area. Obstacle parameters were varied over a wide range; flame speeds increased with blockage ratio and pitch. Some of these tests were repeated recently on a larger scale (scaling factor 6.25) with ethylene, propane, and methane as fuels (Figure 4.10). Findings from the small-scale tests were generally confirmed. However, flame speeds and overpressures were higher than those found in the equivalent small-scale tests, and ethylene tests resulted in detonations. On the basis of some of the tests described above, Van Wingerden (1989b) argued that simple scaling of vapor cloud explosion experiments is possible for flame speeds of up to approximately 50-100 m/s. Tubes Experiments in tubes are not directly applicable to vapor cloud explosions. An overview of research in tubes is, however, included for historical reasons. An understanding of flame-acceleration mechanisms evolved from these experiments because this mechanism is very effective in tubes. Chapman and Wheeler (1926, 1927) conducted early flame-propagation experiments in tubes. They observed continuous flame acceleration and substantial increases in acceleration in tubes with internal obstructions (Table 4.4). These early findings were subsequently confirmed by many others, including Dorge et al. (1979,

G a s A n a l y s i s Sample P o i n t s I g n i t i o n Point

Figure 4.10. Large-scale test setup for investigation of flame propagation in a cylindrical geometry. Dimensions: 25 m long, 12.5 m wide, and 1 m high. Obstacle diameter 0.5 m. TABLE 4.4. Overview of Test Results on Deflagrative Combustion of Fuel-Air Clouds in Tubes

Reference Chapman and Wheeler (1926, 1927) Dorgeetal. (1981) Chan etal. (1980)

Moenetal. (1982) Hjertager etal. (1984, 1988) Lee etal. (1984)

Configuration

Fuel

Max. Flame Speed (mis)

2.4 m long pipe, D = 50 mm with orifice plates

CH4

420

3.9

2.5 m long pipe, D = 40 mm with orifice plates 0.45 m, 63 mm ID pipe and 1.22 m, 152 mm ID pipe both with orifices 10 m, 2.5m ID pipe with orifices

CH4

770

12.0

CH4

550

10.9

CH4 C3H8

500 650

4.0 13.9

DDTa

DDTa

1 1 m, 50 mm ID pipe with H2 orifices or spirals

•DDT = deflagration-detonation transition.

Max. Overpressure (bar)

1981), Chan et al. (1980), Lee et al. (1984), Moen et al. (1982), and Hjertager et al. (1984). Most investigators used tubes open only at the end opposite the point of ignition. For tubes with very large aspect ratios (length/diameter), the positive feedback mechanism resulted in a transition to detonation for many fuels, even when the tubes were unobstructed. Introduction of obstacles into tubes reduced considerably the distance required for transition to detonation. A tube 10 m long and 2.5 m inside diameter was used for experiments with methane (Moen et al. 1982) and propane (Hjertager et al. 1984). These often-cited experiments showed that very intense gas explosions were possible in this tube, which had an aspect ratio of only 4 but which contained internal obstructions. Pressures of up to 4.0 bar for methane and 13.9 bar for propane were reported. Obstruction parameters, for example, blockage ratio and pitch, were varied. As with cylindrical geometry, explosions became more severe with increasing obstacle density. Hjertager et al. (1988a) and Hjertager et al. (1988b) performed experiments in the same tube. They showed that creating nonhomogeneous clouds in the tube by establishing realistic leak sites (e.g., guillotine breaks in pipes and gasket failures in flanges) resulted in pressure similar to or lower than those from homogeneous stoichiometric clouds. Nonstoichiometric clouds generate lower overpressures and flame speeds. Experiments on a small scale with stoichiometric methane-air mixtures were carried out by Chan et al. (1980). Comparisons of results of these experiments with those performed by Moen et al. (1982) revealed that simple scaling is not possible for the results of explosions with very high flame speeds, in other words, flame speeds resulting from very intense turbulence. Channels Several investigations were performed in channels (Table 4.5). In experiments in which the channel was completely confined, flame speed enhancements were similar to those observed in tubes. In experiments in which channels were open on top, thus allowing combustion products to vent, far lower flame speeds were measured. Partially opening one side of a channel permitted varying degrees of confinement. Urtiew (1981) performed experiments in an open test chamber 30 cm high x 15 cm wide x 90 cm long. Obstacles of several heights were introduced into the test chamber. Possibly because there was top venting, maximum flame speeds were only on the order of 20 m/s for propane-air mixtures. Chan et al. (1983) studied flame propagation in an obstructed channel whose degree of confinement could be varied by adjustment of exposure of the perforations in its top. Its dimensions were 1.22 m long and 127 x 203 mm in cross section. Results showed that reducing top confinement greatly reduced flame acceleration. When the channel's top confinement was reduced to 10%, the maximum flame speed produced for methane-air mixtures dropped from 120 m/s to 30 m/s.

TABLE 4.5. Overview of Test Results on Deflagrative Combustion of Fuel -Air Clouds in Channels

Reference Chan etal. (1983)

Urtiew(1981)

Elsworth et at. (1983) Sherman etal. (1985) Taylor (1987)

a

Configuration

Fuel

Max. Flame Speed (mis)

Channel 1.22 m, 127 x 203 mm2 baffles top venting Channel 0.9 m, 0.3 x 0.15 m baffles, open top Channel 52 m, 5 m, 1 -3 m baffles, open top Channel 30.5 m, 2.44 m, 1 .83 m no obstalces Channel 2 m, 0.05 x 0.05 m obstacles top venting

CH4

350

0.15

C3H8

20

—

C3H8 H2

C3H8

Max. Overpressure (bar)

12.3

0.0

DDTa

DDTa

80

—

DDT =7deflagration-detonationtransition.

In an obstacle-free channel 30.5 m long x 2.44 m x 1.83 m, hydrogen-air mixtures detonated, both with a completely closed top and with a top opening of 13% (Sherman et al. 1985). Elsworth et al. (1983) report experiments performed in an open-topped channel 52 m long X 5 m high whose width was variable from 1 to 3 m. Experiments were performed with propane, both premixed as vapor and after a realistic spill of liquid within the channel. In some of the premixed combustion tests, baffles 1-2 m high were inserted into the bottom of the channel. Ignition of the propane-air mixtures revealed typical flame speeds of 4 m/s for the spill tests, and maximum flame speeds of 12.3 m/s in the premixed combustion tests. Pressure transducers recorded strong oscillations, but no quasi-static overpressure. Taylor (1987) reports some experiments performed in a horizontal duct (2 m long, 0.05 x 0.05 m cross section). Obstacles were placed in the channel. The top of the duct could be covered by perforated plates with a minimum of 6% open area. Terminal flame speeds of 80 m/s were reported for propane in a channel with a blockage ratio of 50% and a 12% open roof. The channel experiments produced results similar to those from tubes. Introduction of venting (decrease of the degree of confinement) greatly reduces effectiveness of the positive-feedback mechanism. Obstacles appear to enhance the combustion rate considerably.

4.1.4. Special Experiments Various experiments that do not fall under any of the other categories but still worth mentioning are grouped here as "special experiments." Several experiments with ethylene and hydrogen investigated the effects of jet ignition on flame propagation in an unconfined cloud, or on flame propagation in a cloud held between two or more walls (Figure 4.11). Such investigations were reported by Schildknecht and Geiger (1982), Schildknecht et al. (1984), Stock and Geiger (1984), and Schildknecht (1984). The jet was generated in a 0.5 x 0.5 x 1-m box provided with turbulence generators for enhancing internal flame speed. Maximum overpressures of 1.3 bar were observed following jet ignition of an ethylene-air cloud contained on three sides by a plastic bag. In a channel confined on three sides, maximum pressures reached 3.8 bar in ethylene-air mixtures. A transition to detonation occurred in hydrogen-air mixtures. One experiment (Moen et al. 1985) revealed that jet ignition of a lean acetylene-air mixture (5.2% v/v) in a 4-m-long, 2-m-diameter bag can produce the transition to detonation. A detailed study performed by McKay et al. (1989) revealed some of the conditions necessary for a turbulent jet to initiate a detonation directly. These experiments are covered in more detail in Section 4.1.5. Pfortner (1985) reports experiments with hydrogen in a lane, 10 m long and 3 x 3 m in cross section, in which a fan was used to produce turbulence. In these experiments, a transition to detonation occurred at high fan speeds. high speed camera

free gas cloud

gas-air mixture under partial confinement

orifice ruRftuLb/vce C-EA/eRflToB

pressure transducers sampling stations for gas mixture analysis ignition structures in the gas cloud

Figure 4.11. Experimental apparatus for investigating jet ignition of ethylene-air and hydrogen-air mixtures (Schildknecht et al., 1984).

Front elevation of test enclosure Region of pipework obstacles

Flame speed, m/s

Confined initiating region

Unobstructed region

Flame position, m Figure 4.12. Flame speed-distance graph showing transition to detonation in a cyclohexane-air experiment (Harris and Wickens 1989).

Experiments without additional turbulence produced flame speeds no higher than 54 m/s. Experiments reported by Harris and Wickens (1989) deserve special attention. They modified the experimental apparatus described in Section 4.1.1—a 45 m long, open-sided apparatus. The first 9 m of the apparatus was modified by the fitting of solid walls to its top and sides in order to produce a confined region. Thus, it was possible to investigate whether a flame already propagating at high speed could be further accelerated in unconfined parts of the apparatus, where obstacles of pipework were installed. The initial flame speed in the unconfined parts of the apparatus could be modified by introduction of obstacles in the confined part. Experiments were performed with cyclohexane, propane, and natural gas. In a cyclohexane experiment, the flame emerged from the confined region at a speed of approximately 150 m/s, and progressively accelerated through the unconfined region containing obstacles until transition into a detonation occurred (Figure 4.12). Detonation continued to occur in the unconfined region. A similar result was found for propane, in which flames emerged from the confined area at speeds of 300 m/s. Experiments performed with natural gas yielded somewhat different results. Flames emerged from the confined portion of the apparatus at speeds below 500 m/s, then decelerated rapidly in the unconfined portion with obstacles. On the other hand, flames emerging from the confined portion at speeds above 600 m/s continued to propagate at speeds of 500-600 m/s in the obstructed, unconfined portion of the

cloud. There were no signs of transition to detonation. Once outside the obstructed region, the flame decelerated rapidly to speeds of less than 10 m/s.

4.1.5. Vapor Cloud Detonation Initiation For direct initiation of detonation, a blast wave is required which is capable of maintaining its postshock temperature above the mixture's autoignition temperature over some span of time (Lee and Ramamurthi 1976, Sichel 1977). Ignition of a vapor cloud by some high-explosive device capable of producing such a blast wave is not a credible accident scenario. Less-powerful ignition sources result in deflagration. A detonation, therefore, may develop only through interaction of the flame propagation process with its self-induced expansion flow. Laminar-flame propagation is inherently unstable because of aerodynamic and possibly diffusional-thermal influences (Markstein 1964). Aerodynamic instabilities arise from a flow field in the vicinity of a perturbedflame front. The converging and diverging streamlines induce a pressure distribution that tends to preserve and amplify the perturbations. Diffusional-thermal instabilities may occur if the reactants (fuel and oxygen) differ widely in molecular weight. The resulting difference in diffusivity may induce a nonhomogeneous distribution in the mixture composition near the reacting zone in a perturbed-flame front which tends to preserve and amplify the perturbations. Such flame instability is dependent on the molecular weight of the fuel and the stoichiometry of the mixture. Flame instabilities give rise to flame-generated turbulence (Sivashinsky 1979). These phenomena are the immediate cause of onset of detonation only in the most highly reactive mixtures, such as acetylene-oxygen or hydrogen-oxygen mixtures (Sivashinsky 1979; Kogarko et al. 1966; Sokolik 1963). In relatively low-reactive fuel-air mixtures, these phenomena seem to be controlled by the property of a wrinkled-flame front, which propagates normally to its orientation so as to reduce its area (Karlovitz 1951). Deflagration to Detonation Transition (DDT) In relatively low-reactive fuel-air mixtures, a detonation may only arise as a consequence of the presence of appropriate boundary conditions to the combustion process. These boundary conditions induce a turbulent structure in the flow ahead of the flame front. This turbulent structure is a basic element in the feedback coupling in the process by which combustion rate can grow more or less exponentially with time. This fundamental mechanism of a gas explosion has been described in Section 3.2. The thermodynamic state of a reactive mixture just prior to combustion is determined by adiabatic compression and by turbulent mixing with combustion

products. The unburned mixture in front of the flame is thereby preconditioned for combustion. If turbulent mixing becomes too intense, the combustion reaction may quench locally, resulting in a hot and highly reactive mixture of reactants and combustion products. If, at the same time, the autoignition temperature is exceeded as a result of compression, the mixture ignites again. Such "hot spots" react instantaneously as localized, constant volume sub-explosions (Urtiew and Oppenheim 1966; Lee and Moen 1980). If the mixture around such a sub-explosion is preconditioned sufficiently to ignite on shock compression, a detonation wave will engulf the entire process of flame propagation. Lee et al. (1978) demonstrated that the onset of detonation can also be attained in the absence of strong compression. They detonated acetylene-oxygen, hydrogen-oxygen, and hydrogen-chlorine mixtures by photochemical initiation. The mechanism was called "Shock-Wave Amplification by Coherent Energy Release" (SWACER). Although photochemical initiation is not considered a very likely ignition source in an accident scenario, the SWACER mechanism was also shown to trigger detonation when a highly reactive acetylene-oxygen mixture was initiated by a turbulent jet of combustion products (Knystautas et al. 1979). Intense mixing of burned and unburned components within large, coherent, turbulent, eddy structures of a jet may lead to local conditions that may induce the SWACER mechanism and trigger detonation. A deflagration-detonation transition was first observed in 1985 in a largescale experiment with an acetylene-air mixture (Moen et al. 1985). More recent investigations (McKay et al. 1988 and Moen et al. 1989) showing that initiation of detonation in a fuel-air mixture by a burning, turbulent, gas jet is possible, provided the jet is large enough. Early indications are that the diameter of the jet must exceed five times the critical tube diameter, that is approximately 65 times the cell size. Conditions Necessary for Self-Sustaining Detonation The preceding section described the state of transition expected in a deflagration process when the mixture in front of the flame is sufficiently preconditioned by a combination of compression effects and local quenching by turbulent mixing. However, additional factors determine whether the onset of detonation can actually occur and whether the onset of detonation will be followed by a self-sustaining detonation wave. The nature of the restrictive boundary conditions for detonation is closely related to the cellular structure of a detonation wave (Section 3.2.2). It was systematically investigated in a series of flame propagation experiments in obstacle-filled tubes by Lee et al. (1984). The most important results are summarized below: • In a smooth tube, the onset of detonation will take place only if the internal tube diameter is larger than about one characteristic-detonation-cell size. • If the tube is provided with internal obstructions, the open area cross-section should be greater than about three characteristic-cell sizes. Then detonation

manifests itself as "quasi-detonation," propagating at a speed which may be considerably lower than CJ-wave velocity. Because of the high loss of energy to the generation of turbulence in shear layers (drag), the leading shock wave decays, and the reaction zone tends to decouple and quench. The detonation process is continually reinitiated in places where the leading shock is reflected. • Only if internal passage dimensions exceed about 13 characteristic-cell sizes will detonation manifest itself as a fully developed CJ-detonation wave. • Transition from a planar mode propagating in a channel into a spherical mode propagating in free space is possible only if the orifice dimension is larger than: —about 13 characteristic-cell sizes for circular orifices —about 10 characteristic-cell sizes for square orifices —about 13 characteristic-cell sizes for rectangular orifices of large aspect ratio (Benedick et al. 1984). • As with a high explosive, a fuel-air mixture requires a minimum charge thickness to be able to sustain a detonation wave. Hence, a fully unconfined fuel-air charge should be at least 10 to 13 characteristic-cell sizes thick in order to be detonable. If the charge is bounded by a rigid plane (e.g., the earth's surface) the minimum charge thickness is equal to 5 to 6.5 characteristic-cell sizes (Lee 1983). The characteristic magnitudes of detonation cells for various fuel-air mixtures (Table 3.2) show that these restrictive boundary conditions for detonation play only a minor role in full-scale vapor cloud explosion incidents. Only pure methane-air may be an exception in this regard, because its characteristic cell size is so large (approximately 0.3 m) that the restrictive conditions, summarized above, may become significant. In practice, however, methane is often mixed with higher hydrocarbons which substantially augment the reactivity of the mixture and reduce its characteristic-cell size. A fuel-air mixture is detonable only if its composition is between the detonability limits. The detonation limits for fuel-air mixtures are substantially narrower than their range of flammability (Benedick et al. 1970). However, the question of whether a nonhomogeneous mixture can sustain a detonation wave is more relevant to the vapor cloud detonation problem because, as described in Section 3.1, the composition of a vapor cloud dispersing in the atmosphere is, in general, far from homogeneous. Experiments on the detonability of nonhomogeneous mixtures are scarce. Two experiments reported in the literature may shed some light on this matter. Bull et al. (1981) investigated the transmission of detonation across an inert region in hydrocarbon-air mixtures under unconfined conditions. The transmission of a hydrocarbon-air detonation across an inert region in a tube was studied by Bjerketvedt and Sonju (1984) and Bjerketvedt, Sonju, and Moen (1986). Although apparatus for these experiments differed significantly, results are strikingly consistent. The experiments show that detonations in stoichiometric hydrocarbon-air mixtures are unable to cross a gap of pure air of approximately 0.2 m

thickness. These results indicate that it is difficult for a detonation to maintain itself in a nonhomogeneous mixture. In view of the mechanism of turbulent dispersion described in Section 3.1, such conditions are to be expected in freely dispersing vapor clouds.

4.1.6. Summary In the experiments described in Section 4.1, no explosive blast-generating combustion was observed if initially quiescent and fully unconfined fuel-air mixtures were ignited by low-energy ignition sources. Experimental data also indicate that turbulence is the governing factor in blast generation and that it may intensify combustion to the level that will result in an explosion. Turbulence may arise by two mechanisms. First, it may result either from a violent release of fuel from under high pressure in a jet or from explosive dispersion from a ruptured vessel. The maximum overpressures observed experimentally in jet combustion and explosively dispersed clouds have been relatively low (lower than 100 mbar). Second, turbulence can be generated by the gas flow caused by the combustion process itself an interacting with the boundary conditions. Experimental data show that appropriate boundary conditions trigger a feedback in the process of flame propagation by which combustion may intensify to a detonative level. These blast-generative boundary conditions were specified as • spatial configurations of obstacles of sufficient extent; • partial confinement of sufficient extent, whether or not internal obstructions were present. Examples of boundary conditions that have contributed to blast generation in vapor cloud explosions are often a part of industrial settings. Dense concentrations of process equipment in chemical plants or refineries and large groups of coupled rail cars in railroad shunting yards, for instance, have been contributing causes of heavy blast in vapor cloud explosions in the past. Furthermore, certain structures in nonindustrial settings, for example, tunnels, bridges, culverts, and crowded parking lots, can act as blast generators if, for instance, a fuel truck happens to crash in their vicinity. The destructive consequences of extremely high local combustion rates up to a detonative level were observed in the wreckage of the Flixborough plant (Gugan 1978). Local partial confinement or obstruction in a vapor cloud may easily act as an initiator for detonation, which may propagate into the cloud as well. So far, however, only one possible unconfined vapor cloud detonation has been reported in the literature; it occurred at Port Hudson, Missouri (National Transportation Safety Board Report 1972; Burgess and Zabetakis 1973). In most cases the nonhomogeneous structure of a cloud freely dispersing in the atmosphere probably prevents a detonation from propagating. Next Page

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4.2. OVERVIEW OF COMPUTATIONAL RESEARCH If a quiescent, homogeneous fuel-air mixture is ignited, it is initially consumed by a thin flame-front. Combustion is an exothermic process; as the hot gases expand, a flow field is generated that displaces the flame front. Boundary conditions induce a flow-field structure, that is, velocity gradients and turbulence by which the combustion is intensified. A higher combustion rate induces faster expansion, more intense turbulence, faster combustion, and so on. This feedback coupling in the process of flame propagation is the reason why, under appropriate boundary conditions, slow, laminar-flame propagation may develop into very rapid, explosive combustion. Experimental research has shown that a vapor cloud explosion can be described as a process of combustion-driven expansion flow with the turbulent structure of the flow acting as a positive feedback mechanism. Combustion, turbulence, and gas dynamics in this complicated process are closely interrelated. Computational research has explored the theoretical relations among burning speed, flame speed, combustion rates, geometry, and gas dynamics in gas explosions. The combustion-flow interactions should be central in the computation of combustion-generated flow fields. This interaction is fundamentally multidimensional, and can only be computed by the most sophisticated numerical methods. A simpler approach is only possible if the concept of a gas explosion is drastically simplified. The consequence is that the fundamental mechanism of blast generation, the combustion-flow interaction, cannot be modeled with the simplified approach. In this case flame propagation must be formalized as a heat-addition zone that propagates at some prescribed speed. 4.2.1. Analytical Methods Scope Analytical methods relate the gas dynamics of the expansion flow field to an energy addition that is fully prescribed. A first step in this approach is to examine spherical geometry as the simplest in which a gas explosion manifests itself. The gas dynamics of a spherical flow field is described by the conservation equations for mass, momentum, and energy: (4.1)

(4.2)

(4.3)

where p = density u = velocity e = internal energy p = pressure t = time r = radial coordinate This section describes how this set of equations can be solved analytically by the introduction of various simplifications. First, gas dynamics is linearized, thus permitting an acoustic approach. Next, a class of solutions based on the similarity principle is presented. The simplest and most tractable results are obtained from the most extensive simplifications. Acoustic Methods a. Expanding-piston solution according to Taylor (1946). An expanding piston is a widely used concept to simulate the expansion associated with a propagating flame. If only small disturbances in a quiescent medium are considered, the gas dynamics may be linearized and a wave equation:

(4.4) can be derived where <|> is a velocity potential so that:

(4.5) (4.6) where M = p — PQ = P0 = C0 = t = r =

velocity overpressure ambient density ambient speed of sound time radial coordinate

The solution of the wave equation must be an expression of the form: <|> = (Ur) f(r - c
from which the velocity and pressure fields may be readily derived:

(4.8)

(4.9) where Mp = piston Mach number 7 = ratio specific heats A piston Mach number may be related to a flame Mach number if, under the condition of low overpressure, the mass enclosed by the piston flow field is equated to the mass enclosed by a flame flow field: (4.10) which results in simple and tractable relations for a flame-generated flow field: (4.11)

(4.12) where Mf = flame Mach number a = isobaric expansion ratio The maximum values of velocity and pressure developed just in front of the flame are found by substituting: (4.13) b. Volume-source solution according to Strehlow (1981). Another concept to simulate the expansion of reaction products in a combustion process is an acoustic monopole. This concept is closely related to the expanding-piston model. Lighthill (1978) showed that a solution of the wave equation of the form (4.14)

also satisfies the Stokes (1849) concept of a simple source to a certain extent. Strehlow (1981) elaborated this idea to compute the flow field generated by propagating flames by u=

dd>

a?

and

dd>

P~?O= ~ po if

(4 15)

-

(4.16) where V is a volume-source strength and can consequently be related to combustion process properties such as burning velocity, expansion ratio, and flame-surface area. Elaboration yields the following for the flow field in front of a steady spherical flame: (4.17)

and

(4.18) The relationship to the Taylor expanding-piston solution becomes evident for smallflame Mach numbers. The volume-source method is not only useful in a spherical approach, but can also be used in more arbitrary geometries, where it is possible to express the volume source strength in a product of burning velocity and flame surface area: V= (a- I)S1A

(4-19)

where a = volumetric expansion ratio Sb = burning velocity Af = flame surface area This concept can be generalized for more arbitrarily shaped clouds, provided that a reasonable estimate can be made of combustion process development in terms of burning velocity and flame surface area. According to Strehlow (1981), a conservative estimate of source strength is made by • the assumption of a fixed value for the burning velocity, • the computation of flame-surface area as a function of time for a flame traveling at a fixed burning velocity through a quiescent cloud, and • the multiplication of the resulting source strength by the volumetric expansion ratio as a correction for flame-area enlargement by convection in its self-generated flow field.

Strehlow (1981) elaborated these recommendations for a number of cases including a centrally ignited cylinder slice. This resulted in a remarkable result: (4.20) where 7 a H Afb Rf

= = = = =

specific heats ratio volumetric expansion ratio cylinder slice height burning velocity Mach number flame position

This equation shows that the maximum overpressure, generated by a constant velocity flame front, continually decreases as it propagates. Modeling an explosion of an extended flat vapor cloud by a single monopole located in the cloud's center is not, however, very realistic. c. Distributed-volume source model according to Auton and Pickles (1978, 1980). A more realistic concept is attained if the volume source is not concentrated in the cloud's center, but instead distributed over the entire area covered by a flat cloud. This concept was elaborated by Auton and Pickles (1978, 1980) for pancakeshaped clouds. They simulated the flow field generated by combustion by a continuous distribution of volume sources with a strength proportional to local cloud height. Flame propagation was modeled by sweeping a zone of finite width over the distribution of sources. During its passage, the zone activates the sources gradually. This idea resulted in the following construction. The acoustic monopole velocity potential function, <|>am, for half-space is (4.21) Assuming that a source produces its total volume within STT seconds during flame passage, the volume source strength, V9 may be expressed in a suitable function: (4.22) where H = cloud height a = volumetric expansion ratio This function expresses a volume production during flame passage which starts slowly, speeds up, and gradually declines again. The flow field generated at time t upon ignition somewhere in the environment can be computed by superposition

of the acoustic signals of all contributing sources. The contributing sources are those whose locations satisfy the relation O < t - T1Ic^ - Rf/Sf < 6ir

where 5f is flame speed. The sense of this procedure may be verified in Figure 4.13. An implicit assumption in this procedure is that the speed at which the sources are activated equals the speed at which the activation zone is propagated. This holds only if the flame propagates into a quiescent mixture, which does not really happen. Computational experiments with the proposed model show that this assumption is increasingly justified as a cloud's aspect ratio increases. A similar acoustic technique was applied by Pickles and Bittleston (1983) to investigate blast produced by an elongated, or cigar-shaped, cloud. The cloud was modeled as an ellipsoid with an aspect ratio of 10. The explosion was simulated by a continuous distribution of volume sources along the main axis with a strength proportional to the local cross-sectional area of the ellipsoid. The blast produced by such a vapor cloud explosion was shown to be highly directional along the main axis. These results were analytically reproduced by Taylor (1985), who employed a velocity potential function for a convected monopole. This concept makes it possible to model an elongated vapor cloud explosion by one single volume source which is convected along the main axis at burning velocity, and whose strength varies proportionally to the local cross-sectional cloud area. Similarity Methods Self-similarity applies to one-dimensional, time-dependent problems in which dependence on one of two independent variables can be eliminated by nondimen-

Source

activabion

zone

Figure 4.13. Contributing acoustic signals superimposed on distributed-volume source model for a pancake-shaped vapor cloud explosion.

sionalization of the other. The postulate of self-similarity applies as well to constantvelocity, piston-driven, spherical-flow fields. If, for instance, the coordinate is nondimensionalized, the distribution of gas-dynamic-state parameters is independent of time. Because an expanding piston has proven to be a useful concept in simulation of flame-generated expansion, it is not surprising that a renewed interest in similarity methods has arisen during the last two decades. The Kuhl et al. (1973) paper occupies a central position because, in this paper, the classical solution of a pistondriven flow field by Taylor (1946) was related to that in front of a propagating flame. Therefore, this paper is treated in some detail below. The similarity solution for a flow field in front of a steady piston is a special case from a much larger class of similarity solutions in which certain well-defined variations in piston speed are allowed (Guirguis et al. 1983). The similarity postulate for variable piston speed solutions, however, sets stringent conditions for the gasdynamic state of the ambient medium. These conditions are unrealistic within the scope of these guidelines, so discussion is confined to constant-velocity solutions. Solving the gas dynamics expressions of Kuhl et al. (1973) requires numerical integration of ordinary differential equations. Hence, the Kuhl et al. paper was soon followed by various papers in which KuhTs numerical "exact" solution was approximated by analytical expressions. The "Exact" Solution by Kuhl et al. (1973) The flow field in front of an expanding piston is characterized by a leading gasdynamic discontinuity, namely, a shock followed by a monotonic increase in gasdynamic variables toward the piston. If both shock and piston are regarded as boundary conditions, the intermediate flow field may be treated as isentropic. Therefore, the gas dynamics can be described by only two dependent variables. Moreover, the assumption of similarity reduces the number of independent variables to one, which makes it possible to recast the conservation equations for mass and momentum into a set of two simultaneous ordinary differential equations: (4.23)

(4.24) where

u = particle velocity c = speed of sound

r rs Us *y

= = = =

coordinate leading shock coordinate leading shock speed ratio specific heats

This set can be numerically integrated starting at the piston boundary condition: F=I

and

Z = Zpiston

through the flow field until the second boundary condition, namely, the leading shock, is met. The leading shock is found by continuous testing of the solution to the shock jump condition expressed as (4.25) Now the distribution of the gas-dynamic variables can be computed from the isentropic relations:

where T = temperature, p = pressure, and p = density. Subscript "s" refers here to the postshock location in the flow field, whereas in previous equations it refers to the leading shock. Once the piston-driven flow field is known, the flame-driven flow field is found by fitting in a steady flame front, with the condition that the medium behind it is quiescent. This may be accomplished by employing the jump conditions which relate the gas-dynamic states on either side of a flame front. The condition that the reaction products behind the flame are at rest enables the derivation of expressions for the density ratio, pressure ratio, and heat addition (4.26)

(4.27)

(4.28) where R = density ratio P = pressure ratio q = heat addition

h = enthalpy y = ratio of specific heats The subscripts "r" and "p" refer to the states of the reactants just in front of, and the combustion products just behind, the flame front, respectively. Since reactants are compressed in the flow field prior to combustion, heat addition takes place at an elevated temperature. If combustion is modeled as a simple heat addition to a medium whose specific heat does not change, q equals the heat of combustion Q at ambient temperature. However, heat properties of reactants and products usually differ. Then q can be related to the heat of combustion at ambient temperature T0 by Q = q + [Ap(TV) - Vro)l - [A1OV) - hffj]

(4.29)

If the values of the gas dynamic variables are known, these expressions may be evaluated for any position throughout the flow field. The location of the flame front is found where Q matches the heat of combustion of the fuel-air mixture in question. If the coordinate of the front X1 is known, the burning velocity Mach number can be computed from (4.30) where 5b C0 X1 F8

= = = =

burning velocity ambient speed of sound nondimensional flame coordinate nondimensionalized particle velocity just behind the leading shock

The formulation above allows a more general equation of state for the combustion products (Kuhl 1983). The method described breaks down for low piston velocities, where the leading shock Mach number approaches unity. In such cases, the numerical integration marches into the point (F = O, Z = 1), which is a singularity. Analytical Approximations to the Similarity Solution As mentioned above, the numerical solution of exact equations breaks down for low flame speeds, where the strength of the leading shock approaches zero. To complete the entire range of flame speeds, Kuhl et al. (1973) suggested using the acoustic solutions by Taylor (1946) as presented earlier in this section. Taylor (1946) already noted that his acoustic approach is not fully compatible with the exact solution, in the sense that they do not shade into one another smoothly. In particular, the near-piston and the near-shock areas in the flow field, where nonlinear effects play a part, are poorly described by acoustic methods. In addition to these imperfections, the numerical character of Kuhl et al. (1973) method inspired various authors to design approximate solutions. These solutions are briefly reviewed.

A simple method to estimate the overpressure generated by constant-velocity flames was suggested by Strehlow (1975); a summary follows. The change in density over a propagating flame front dependent on flame speed, Mach number, and energy addition is fully described by the jump conditions for a flame front. The change in density over the leading shock dependent on shock Mach-number is described by shock-jump conditions. Now the problem can be solved by relating the flame Mach number and the shock Mach number. Strehlow (1975) achieved a solution by conducting a mass balance over the flow field. Such a balance can be drawn up under the assumptions of similarity and a constant density between shock and flame. The assumption of constant density violates the momentum-conservation equation, and is a drastic simplification. The maximum overpressure is, therefore, substantially underestimated over the entire flame speed range. An additional drawback is that the relationship of overpressure to flame speed is not produced in the form of a tractable analytical expression, but must be found by trial and error. For different regions in the flow field in front of an expanding piston, separate solutions in the form of asymptotic expansions may be developed. An overall solution can be constructed by matching these separate solutions. This mathematical technique was employed by several authors including: Guirao et al. (1976), Gorev and Bystrov (1985), Deshaies and Clavin (1979), Cambray and Deshaies (1978), and Cambray et al. (1979). A linearized, acoustic approach was found satisfactory for the description of the near-piston region for low piston Mach-numbers by Guirao et al. (1976) and Gorev and Bystrov (1985). The linearized equations, however, provided a single solution at the location of the leading shock. In the solution for this problem, the methods of Guirao et al. (1976) and of Gorev and Bystrov (1985) differ. Guirao et al. (1976) employed the so called Poincare-Kuo-Lighthill method to "stretch" the coordinate in the vicinity of the singularity. In this way, two separate solutions were found: one for the near-shock region and one for the rest of the flow field. They were matched where the accuracy of both solutions is acceptable. A "kink" in the resulting distributions of flow-field parameters is inevitable. To prevent this kink, Gorev and Bystrov (1985) suggested a correction by a properly chosen coordinate transformation. The substitution was chosen in such a way that the equations after linearization describe the desired behavior in the nearshock region during the period when the influence of the correction fades gradually towards the piston. In this way, Gorev and Bystrov (1985) obtained an approximate solution which holds for the entire flow field. In addition to a near-shock and an acoustic region, Deshaies and Clavin (1979) distinguished a third—a near-piston region—where nonlinear effects play a role as well. As already pointed out by Taylor (1946), the near-piston flow regime may be well approximated by the assumption of incompressibility. For each of these regions, Deshaies and Clavin (1979) developed solutions in the form of asymptotic expansions in powers of small piston Mach number. These solutions are supposed to hold for piston Mach numbers lower than 0.35.

The approxmations reviewed so far were all developed for the low-piston Mach number regime. Cambray and Deshaies (1978), on the other hand, developed a solution of the similarity equations by asymptotic expansions in powers of highpiston Mach numbers. These solutions are supposed to hold for piston Mach numbers higher than 0.7. Finally, Cambray et al. (1979) suggested an interpolation formula to cover the intermediate-piston Mach number range. In order to permit brief evaluation of the qualities of the approximate analytical solutions reviewed, some of the expressions given in the respective papers have been quantified and compared to the "exact" similarity solution by Kuhl et al. (1973). The numerical integration to obtain the solution of Kuhl et al. (1973) similarity equations was performed by fourth-order Runge-Kutta. Approximate, analytical solutions by Guirao et al. (1976), Gorev and Bystrov (1985) and Cambray and Deshaies (1978) are depicted together with "exact" similarity solutions for various piston Mach numbers in Figures 4.14-4.16. The solutions are represented by taking the leading shock's coordinate equal to one, while the gas dynamic variables are nondimensionalized with ambient medium properties, as usual. The pictures speak for themselves with regard to the extent to which the respective analytical approximations meet their objectives. KUHL ET AL .

non-DimensionouzeD ove^pnESSURE

non-DimensionflLiza) VELOCITY

GUIRAO ET OL.

non-DifncnsionALizED RADIUS

non-DimEnsiono-izED RADIUS

Figure 4.14. Flow-field parameter distributions in front of an expanding piston. Solution by matched asymptotic expansions by Guirao et al. compared to "exact" similarity solutions for various piston Mach numbers.

non-oimEnsionoLizED UELOCITV

non-DHnensionpLiZBD OVERPRESSURE

KUHL CT AL« GOREW AHD BVSTPOY

non-DimEnsionALiZED RADIUS

norvoiinEnsionAuzED RADIUS

Figure 4.15. Flow-field parameter distributions in front of an expanding piston. Solution by matched asymptotic expansions by Gorev and Bystrov compared to "exact" similarity solutions for various piston Mach numbers.

non-DimEnsionALiZED OVERPRESSURE

non-DimEnstonALizED UELOCITV

KUHL ET AL, CAmBRAV ADD DESHAIES

non-DimcnsionALizcD RADIUS

noo-DimensiorwuzED RADIUS

Figure 4.16. Flow-field parameter distributions in front of an expanding piston. Solution by asymptotic expansions by Cambray and Deshaies compared to "exact" similarity solutions for various piston Mach numbers.

4.2.2. Numerical Methods Scope Acoustic and similarity methods provide useful information in relation to the mechanism of blast generation by gas explosions. These methods of solution, however, require drastic simplifications such as, for instance, symmetry and constant flame speed. Consequently, they describe only hypothetical problems. In point of fact, because of a complex of flame-flow interactions, freely propagating flames do not have constant flame speeds. Furthermore, these methods do not cover decay characteristics. In principle, numerical methods make it possible to solve the gas dynamics of explosions without any restriction. The development of numerical methods, however, is largely determined by developments in computational fluid dynamics and computing technology. Consequently, the nature of published methods range from very simple methods capable of simulating one-dimensional, nonreactive, zeroviscosity flow to highly sophisticated methods capable of simulating the multidimensional process of premixed combustion in detail. In this section, these methods will be reviewed in increasing order of complexity. Gas Dynamics Resulting from a Prescribed Energy Addition Generally speaking, the flow field induced by a gas explosion is characterized by two different gas-dynamic discontinuities: • a contact discontinuity between the expanding combustion products and the surrounding inert atmosphere; • a shock phenomenon which may be formed during blast generation, but may also develop later as a result of nonlinear effects in the propagation mechanism of a blast wave. In general, discontinuities constitute a problem for numerical methods. Numerical simulation of a blast flow field by conventional, finite-difference schemes results in a solution that becomes increasingly inaccurate. To overcome such problems and to achieve a proper description of gas dynamic discontinuities, extra computational effort is required. Two approaches to this problem are found in the literature on vapor cloud explosions. These approaches differ mainly in the way in which the extra computational effort is spent. The Lagrangean Artificial-Viscosity Approach As a consequence of implicit mass conservation, the gas-dynamic conservation equations, expressed in Lagrangean form, can describe contact discontinuities. To prevent oscillating behavior in places where shock phenomena are resolved in the

solution, a Von Neumann-Richtmyer artificial-viscosity term is added. In order to affect only places where gradients are large, the artificial-viscosity term may be expressed in local-state variables in various ways (Von Neumann and Richtmyer 1950; Erode 1955, 1959; and Wilkins 1969). Finite-difference schemes used to solve Lagrangean gas dynamics have been described many times (Richtmyer and Morton 1967; Brode 1955, 1959; Oppenheim 1973; Luckritz 1977; MacKenzie and Martin 1982; Van Wingerden 1984; and Van den Berg 1984). The Eulerian FCT Approach A drawback of the Lagrangean artificial-viscosity method is that, if sufficient artificial viscosity is added to produce an oscillation-free distribution, the solution becomes fairly inaccurate because wave amplitudes are damped, and sharp discontinuities are smeared over an increasing number of grid points during computation. To overcome these deficiencies a variety of new methods have been developed since 1970. Flux-corrected transport (FCT) is a popular exponent in this area of development in computational fluid dynamics. FCT is generally applicable to finite difference schemes to solve continuity equations, and, according to Boris and Book (1976), its principles may be represented as follows. A higher-order, finite-difference solution of the Eulerian gas-dynamic conservation equations involving shock phenomena exhibits oscillatory behavior which is continually amplified. To stabilize the solution, it is artificially diffused. To obtain a solution of higher quality than those obtained from artificial-viscosity methods, the diffused solution should be improved. For this purpose, the solution is "antidiffused" again. However, to prevent reintroduction of the unstable oscillatory behavior, the antidiffusion is corrected in such a way that it does not generate new maxima or minima or accentuate any existing extremes. Manipulation of diffusion and antidiffusion makes it possible to optimize the numerical algorithm in the sense that it is possible to minimize errors in amplitude and phase. Applications In the earliest applications of numerical methods for the computation of blast waves, the burst of a pressurized sphere was computed. As the sphere's diameter is reduced and its initial pressure increased, the problem more closely approaches a pointsource explosion problem. Brode (1955,1959) used the Lagrangean artificial-viscosity approach, which was the "state of the art" of that time. He analyzed blasts produced by both aforementioned sources. The decaying blast wave was simulated, and blast wave properties were registered as a function of distance. The code reproduced experimentally observed phenomena, such as overexpansion, subsequent recompression, and the formation of a secondary wave. It was found that the shape of the blast wave at some distance was independent of source properties.

The code reproduced shock-jump conditions well, but many details in the solution were lost because of the smearing effect of artificial viscosity. A similar technique was used by Oppenheim et al. (1977) to analyze the blast waves produced by some gas explosions of a different nature: • a CJ-detonation, • a CJ-deflagration, and • a 35 m/s burning velocity deflagration. Flow fields resulting from these combustion modes were computed by means of similarity methods (Section 4.2.1) and used to provide initial conditions for numerical computations. The main conclusion was that blast waves at some distance from the charge were very similar, regardless of whether the combustion mode was detonation or strong deflagration. A similar computational exercise was performed by Guirao et al. (1979). They used a code based on the Eulerean FCT approach. Blasts produced by four different, but energetically equivalent, sources: • • • •

a volumetric fuel-air explosion, a volumetric fuel-oxygen explosion, a CJ fuel-air detonation, and a CJ fuel-oxygen detonation,

were analyzed to find the most effective. Following Oppenheim et al. (1977), they initialized numerical computations with flow fields calculated by similarity methods. The efficiency of conversion of chemical energy (heat of combustion) into mechanical energy (blast) was determined by calculation of the work done by the cloud's interface during the positive overpressure phase of the expansion. The conclusion of Oppenheim et al. (1977), that the blast produced is only weakly dependent on the combustion mode, was confirmed. On the other hand, the exercise revealed that fuel-air detonation is considerably more effective in converting chemical energy into mechanical energy than fuel-oxygen detonation. The conclusions of Guirao et al. (1979) were fully in line with an earlier paper by Fishburn (1976). Fishburn (1976) analyzed the effectiveness of blast generation for several different designs for a fuel-air explosion: a centrally initiated CJ detonation, an edge-initiated, imploding, overdriven detonation, a partially precompressed CJ detonation, a volumetric explosion, and a deflagration. An important conclusion was that, in a fuel-air detonation, a maximum of 37.8% of the available heat of combustion is transformed into mechanical energy (blast).

Fishburn used a Lagrangean artificial viscosity code provided with a "burn routine" in which combustion is simulated by energy addition. The energy addition was coded to take place within a zone of several cell widths and is moved over the grid at a prescribed speed. In this way, the process of blast generation was simulated, eliminating the requirement to begin the numerical blast-decay simulation with a precomputed flow field. Moreover, the heat capacity ratio of the fluid was allowed to vary over the heat-addition zone. The coding of this feature was facilitated by the Lagrangean character of the grid. Fishburn (1976) showed that implementation of the CJ-detonation velocity results in a flow field which compares well with a self-similar Taylor detonation wave. As with Guirao et al. (1979), Fishburn tried to find the most effective way to convert the chemical energy of the explosive into blast. Whereas Fishburn was mainly interested in the detonative mode of explosion, Luckritz (1977) and Strehlow et al. (1979) focused on the simulation of generation and decay of blast from deflagrative gas explosions. For this purpose, they employed a similar code provided with a comparable heat-addition routine. Strehlow et al. (1979), however, realized that perfect-gas behavior, which is the basis in the numerical scheme for the solution of the gas-dynamic conservation equations, is an idealization which does not reflect realistic behavior in the large temperature range considered. To overcome this problem, they proposed a "working-fluid heat-addition model." This model implies that the gas dynamics are not computed on the basis of real values for heat of combustion and specific heat ratio of the combustion products, but on the basis of effective values. Effective values for the heat addition and product specific heat ratios were determined for six different stoichiometric fuel-air mixtures. Using this numerical model, Luckritz (1977) and Strehlow et al. (1979) systematically registered the properties of blast generated by spherical, constant-velocity deflagrations over a large range of flame speeds. In addition, Strehlow et al. (1979) performed numerical experiments on accelerating flames. Their conclusions may be summarized as follows: • Flame acceleration does not generate extremely high overpressures. That is, numerical simulation of an explosion process with a steady flame speed equal to the highest flame speed observed results in a conservative estimate of its blast effects. • Static impulse of the blast is hardly affected by the details of flame behavior. Using a comparable heat addition model, Van den Berg (1980) constructed a blastsimulation code on the basis of a flux-corrected transport module of Boris (1976). Although the FCT module solves Eulerian gas dynamics, the grid was manipulated in a Lagrangean way. Because the model implicitly conserves mass, a Lagrangean grid allows an accurate and simple energy addition. In this way, the qualities of both approaches—heat addition in the Lagrangean grid and shock representation by flux-corrected transport—were combined. The performance of both approaches,

Lagrangean artificial viscosity and Eulerian FCT, was tested extensively. Flow fields generated by constant-velocity flames were compared to self-similar flow fields. In addition, a large number of flame-propagation experiments were simulated (Van Wingerden, 1984, and Van den Berg, 1984). In many respects, the performance of the FCT code was found to be superior, particularly with respect to shock representation and conservation of details in blast waves during propagation. The flux-corrected-transport technique was also used by Phillips (1980), who successfully simulated the process of propagation of a detonation wave by a very simple mechanism. The reactive mixture was modeled to release its complete heat of combustion instantaneously after some prescribed temperature was attained by compression. A spherical detonation wave, simulated in this way, showed a correct propagation velocity and Taylor wave shape. Two-Dimensional Methods Fishburn et al. (1981) used the HEMP-code of Giroux (1971) to simulate gas dynamics resulting from a large cylindrical detonation in a large, flat, fuel-air cloud containing 5000 kg of kerosene. Blast effects were compared with those produced by a 100,000-kg TNT charge detonated on the ground. In addition, the numercial simulations were compared with an experiment in which a large heptane aerosol-air cloud was detonated. This exercise may be regarded as a continuation of previous work of Fishburn (1976), reviewed earlier in this section. Fishburn's conclusions may be summarized as follows: • Experimentally observed behavior was qualitatively reproduced by numerical simulation. • The fuel-air explosion produced, in a large area covered by the cloud, substantially higher blast pressures than would be expected from a 100,000-kg TNT surface blast. Raju and Strehlow (1984) used a two-dimensional, finite-difference code to study the effects produced by three representative modes of vapor cloud explosion: • a bursting, pressurized spheroid as a model for a constant-volume explosion of an elongated cloud, • a cylindrical detonation of a flat vapor cloud, • steady and nonsteady cylindrical deflagrations. The code was based on a Godunov (1962) difference scheme adapted with Shurshalov's (1973) modification, which makes it possible to treat the leading shock wave of the flow field and the contact discontinuity between burned and unburned material as boundaries of a moving-grid network. The flame front was treated as a "twogamma, working-fluid, heat-addition model," mentioned earlier. The simulations resulted in some interesting conclusions.

• Near-field blast effects were found to be highly directional for the spheroid burst and the cylindrical detonation. • Deflagrative combustion of an extended, flat vapor cloud is very ineffective in producing damaging blast waves because combustion products have a high rate of side relief accompanied by vortex formation. • The very first stage of flame propagation upon ignition, during which the flame has a spherical shape, mainly determines the blast peak overpressure produced by the entire vapor cloud explosion. These findings qualitatively confirm the results obtained with the simple acoustic methods, discussed previously. A much more pronounced vortex formation in expanding combustion products was found by Rosenblatt and Hassig (1986), who employed the DICE code to simulate deflagrative combustion of a large, cylindrical, natural gas-air cloud. DICE is a Eulerian code which solves the dynamic equations of motion using an implicit difference scheme. Its principles are analogous to the ICE code described by Harlow and Amsden (1971). Combustion was modeled as a heat addition within a zone which is propagated at burning velocity relative to expansion flow. The higher rate of side relief, including vortex formation, is a direct consequence of the incorporation of gravity, which makes it possible to simulate the buoyancy of low-density combustion products. Buoyancy generates large, upward velocities at the expense of expansion flow in front of the flame. As a consequence, the flame propagates at a speed which is only about twice its burning velocity. With respect to blast effects, Rosenblatt and Hassig's (1986) conclusions are fully in line with those of Raju and Strehlow (1984). Except in a limited area at the cloud's edge, the blast peak overpressures are produced by the very first stage of flame propagation, during which the flame is spherical. Detailed Simulation of Process of Premixed Combustion In the preceding sections, combustion was modeled as a prescribed addition of energy at a given speed. The fundamental mechanism of a gas explosion, namely, feedback in combustion-flow interaction, was not utilized. As a consequence, the behavior of a freely propagating, premixed, combustion process, which is primarily determined by its boundary conditions, was unresolved. The availability of large and fast computers, in combination with numerical techniques to compute transient, turbulent flow, has made it possible to simulate the process of turbulent, premixed combustion in a gas explosion in more detail. Hjertager (1982) was the first to develop a code for the computation of transient, compressible, turbulent, reactive flow. Its basic concept can be described as follows: A gas explosion is a reactive fluid which expands under the influence of energy addition. Energy is supplied by combustion, which is modeled as a one-step conversion process of reactants into combustion products. The conversion (combustion)

rate, which is primarily controlled by turbulence, is modeled according to the concept of the eddy-dissipation model (Magnussen and Hjertager 1976). The turbulent structure of the flow is described with a k-e turbulence model (Launder and Spalding 1972). This concept was mathematically formulated in conservation equations for mass, momentum, energy, fuel-mass fraction, turbulence kinetic energy, and the dissipation rate of turbulence kinetic energy. Omitting details, it can be expressed in Cartesian tensor notation as follows: mass (4.31) momentum (4.32) energy (4.33) (4.34) turbulence

(4.35) fuel mass fraction (4.36) where

p u e k € IHf11 p

= = = = = = =

density particle velocity cvT + m^flc = energy turbulence kinetic energy dissipation rate of turbulence kinetic energy fuel mass fraction static pressure

F* Rto cv T Hc

= = = = =

turbulence transport coefficient — Ape/k,F(Wfu) = combustion rate specific heat (constant volume) temperature heat of combustion

The major mechanism of a vapor cloud explosion, the feedback in the interaction of combustion, flow, and turbulence, can be readily found in this mathematical model. The combustion rate, which is primarily determined by the turbulence properties, is a source term in the conservation equation for the fuel-mass fraction. The attendant energy release results in a distribution of internal energy which is described by the equation for conservation of energy. This internal energy distribution is translated into a pressure field which drives the flow field through momentum equations. The flow field acts as source term in the turbulence model, which results in a turbulent-flow structure. Finally, the turbulence properties, together with the composition, determine the rate of combustion. This completes the circle, the feedback in the process of turbulent, premixed combustion in gas explosions. The set of equations has been solved with various numerical methods: e.g., SIMPLE (Patankar 1980); SOLA-ICE (Cloutman et al. 1976). Over the years, this concept was refined in several ways. A scale dependency was modeled by the introduction of scale-dependent quenching of combustion. The first stage of the process was simulated by quasi-laminar flame propagation. In addition, three-dimensional versions of the code were developed (Hjertager 1985; Bakke 1986; Bakke and Hjertager 1987). Satisfactory agreement with experimental data was obtained. Appendix F is a case study by Hjertager et al. illustrating the above method. Such numerical methods will become more widely used in the long term. These techniques will probably remain research tools, rather than routine evaluation methods, until such time as available computing power and algorithm efficiency greatly increase. The concept of numerical simulation of turbulent premixed combustion in gas explosion has also been adopted by others: • Kjaldman and Huhtanen (1985) arrived at a similar concept on the basis of the multipurpose PHOENICS code. • the REAGAS code (Van den Berg et al. 1987 and Van den Berg 1989).

4.3. VAPOR CLOUD EXPLOSION BLAST MODELING The long list of vapor cloud explosion incidents indicates that the presence of a quantity of fuel constitutes a potential explosion hazard. If a quantity of flammable material is released, it will mix with air, and a flammable vapor cloud may result. If Next Page

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F* Rto cv T Hc

= = = = =

turbulence transport coefficient — Ape/k,F(Wfu) = combustion rate specific heat (constant volume) temperature heat of combustion

The major mechanism of a vapor cloud explosion, the feedback in the interaction of combustion, flow, and turbulence, can be readily found in this mathematical model. The combustion rate, which is primarily determined by the turbulence properties, is a source term in the conservation equation for the fuel-mass fraction. The attendant energy release results in a distribution of internal energy which is described by the equation for conservation of energy. This internal energy distribution is translated into a pressure field which drives the flow field through momentum equations. The flow field acts as source term in the turbulence model, which results in a turbulent-flow structure. Finally, the turbulence properties, together with the composition, determine the rate of combustion. This completes the circle, the feedback in the process of turbulent, premixed combustion in gas explosions. The set of equations has been solved with various numerical methods: e.g., SIMPLE (Patankar 1980); SOLA-ICE (Cloutman et al. 1976). Over the years, this concept was refined in several ways. A scale dependency was modeled by the introduction of scale-dependent quenching of combustion. The first stage of the process was simulated by quasi-laminar flame propagation. In addition, three-dimensional versions of the code were developed (Hjertager 1985; Bakke 1986; Bakke and Hjertager 1987). Satisfactory agreement with experimental data was obtained. Appendix F is a case study by Hjertager et al. illustrating the above method. Such numerical methods will become more widely used in the long term. These techniques will probably remain research tools, rather than routine evaluation methods, until such time as available computing power and algorithm efficiency greatly increase. The concept of numerical simulation of turbulent premixed combustion in gas explosion has also been adopted by others: • Kjaldman and Huhtanen (1985) arrived at a similar concept on the basis of the multipurpose PHOENICS code. • the REAGAS code (Van den Berg et al. 1987 and Van den Berg 1989).

4.3. VAPOR CLOUD EXPLOSION BLAST MODELING The long list of vapor cloud explosion incidents indicates that the presence of a quantity of fuel constitutes a potential explosion hazard. If a quantity of flammable material is released, it will mix with air, and a flammable vapor cloud may result. If

the flammable mixture finds an ignition source, it will be consumed by a combustion process which, under appropriate (boundary) conditions, may develop an explosive intensity and blast. It is highly desirable that vapor cloud explosion hazards be reduced by appropriate risk management measures. If possible, separation between large storage or manufacturing areas and residential areas should be sufficient to eliminate the risk of blast damage. This may not be an option for those working at a chemical plant or refinery. Designers should consider the possibility of a vapor cloud explosion in the siting and design of process plant buildings. For these and other purposes, blast-modeling methods are needed in order to quantify the potential explosive power of the fuel present in a particular setting. The potential explosive power of a vapor cloud can be expressed as an equivalent explosive charge whose blast characteristics, that is, the distribution of the blastwave properties in the environment of the charge, are known.

4.3.1. Methods Based on TNT Blast For many years, the military has investigated the destructive potential of high explosives (e.g., Robinson 1944, Schardin 1954, Glasstone and Dolan 1977, and Jarrett 1968). Therefore, relating the explosive power of an accidental explosion to an equivalent TNT charge is an understandable approach. Thus, damage patterns observed in many major vapor cloud explosion incidents have been related to equivalent TNT-charge weights. Because the need to quantify the potential explosive power of fuels arose long before the mechanisms of blast generation in vapor cloud explosions were fully understood, the TNT-equivalency concept was also utilized to make predictive estimates, i.e., to assess the potential damage effects from a given amount of fuel. The use of TNT-equivalency methods for blast-prediction purposes is quite simple. The available combustion energy in a vapor cloud is converted into an equivalent charge weight of TNT with the following formula: (4.37) where Wf WTNT Hf #TNT ae am

= the weight of fuel involved (kg) equivalent weight of TNT or yield (kg) = heat of combustion of the fuel in question (J/kg) = TNT blast energy (J/kg) = TNT equivalency based on energy (-) = TNT equivalency based on mass (-)

=

The literature is inconsistent on definitions. TNT equivalency is also called equivalency factor, yield factor, efficiency, or efficiency factor.

Overpressure (Psi)

Peak overpressure (Psi)

If the equivalent weight of TNT is known, the blast characteristics, in terms of the peak side-on overpressure of the blast wave, can be derived for varying distances from the explosion. This is done using a chart containing a scaled, graphical representation of experimental data. Various data sets are available that may differ substantially. In Figure 4.17, for instance, two blast curves (peak side-on overpressure versus scaled distance) are presented. They are different because they result from substantial differences in experimental setup, a surface burst of TNT (on the left) and a free-air burst of TNT (on the right). TNT-equivalency methods are the simplest means of modeling vapor cloud explosions. TNT equivalency can be regarded as a conversion factor by which the available heat of combustion can be converted into blast energy. In one sense, TNT equivalency expresses the efficiency of the conversion process of chemical energy (heat of combustion) into mechanical energy (blast). In a numerical exercise described in section 4.2.2, it was shown that, for a stoichiometric, hydrocarbon-air detonation, the theoretical maximum efficiency of conversion of heat of combustion into blast is equal to approximately 40%. If the blast energy of TNT is equal to the energy brought into the air as blast by a TNT detonation, a TNT equivalency of approximately 40% would be the theoretical upper limit for a gas explosion process under atmospheric conditions. However, the initial stages in the process of shock propagation in the immediate vicinity of

(a)

Ground range (ft./lbs.1/3)

(b)

Distance from burst (feet)

Figure 4.17. Side-on blast peak overpressure due to (a) a TNT surface burst. (Kingery and Panill 1964) and (b) a free-air burst of TNT (Glasstone and Dolan 1977).

a detonating TNT charge are characterized by a high dissipation rate of energy. If this loss of energy is taken into account, the TNT equivalency for a gas detonation at lower blast overpressure levels is expected to be substantially higher than 40%. Furthermore, accidental vapor cloud explosions are anything but detonations of the full amount of available fuel. Therefore, practical values for TNT equivalencies of vapor cloud explosions are much lower than the theoretical upper limit. Reported values for TNT equivalency, deduced from the damage observed in many vapor cloud explosion incidents, range from a fraction of one percent up to some tens of percent (Gugan 1978 and Pritchard 1989). For most major vapor cloud explosion incidents, however, TNT equivalencies have been deduced to range from 1% to 10%, based on the heat of combustion of the full quantity of fuel released. Apparently, only a small part of the total available combustion energy is generally involved in actual explosive combustion. Methods for vapor cloud explosion blast prediction based on TNT equivalency are widely used. Over the years, many authors, companies, and authorities have developed their own procedures and recommendations with respect to issues surrounding such predictions. Some of the differences in these procedures include the following: • The portion of fuel that should be included in the calculation: The total amount released; the amount flashed; the amount flashed times an atomization factor; or the flammable portion of the cloud after accounting for dispersion over time. • The value of TNT equivalency: A value based on an average deduced from observations in major incidents; or a safe and conservative value (whether or not dependent on the presence of partial confinement/obstruction and nature of the fuel). • The TNT blast data used: A substantial scatter in the experimental data on highexplosive blast can be observed which is due to differences in experimental setup. Although often referenced differently, most recommendations can be tracked back to ground burst data developed by Kingery and Pannill (1964). • The energy of explosion of TNT: Values currently in use range from 1800 to 2000 Btu/lb, which correspond to 4.19 to 4.65 MJ/kg. Below are examples of some of the many different approaches used. Their proponents' recommendations are quoted as literally as possible. Some of them are demonstrated in detail in chapter 7. Dow Chemical Co. (Brasie and Simpson 1968) Brasie and Simpson (1968) use the Kingery and Pannill (1964) TNT blast data to represent blast parameter distributions, and the US Atomic Energy Commission's recommendations (Glasstone 1962) for the attendant structural damage. Brasie and Simpson (1968) base their recommendation for the TNT equivalency of vapor clouds on the damage observed in three chemical-plant explosion incidents. Analyzing the

damage in these incidents, they deduced a TNT yield which is highly dependent on the distance to the explosion center. Although values for TNT equivalency ranging from 0.3% to 4% have been observed, Brasie and Simpson recommend, for predictive purposes, conservative values for TNT equivalency as follows: 2% for near-field, and 5% for far-field effects (based on energy), applied to the full quantity of fuel released. In a later paper, Brasie (1976) gives more concrete recommendations for determining the quantity of fuel released. A leak potential can be based on the flashing potential of the full amount of liquid (gas) stored or in process. For a continuous release, a cloud size can be determined by estimating the leak rate. For a combined liquid-vapor flow through holes of very short nozzles, the leak rate (mass flow per leak orifice area) is approximately related to the operating overpressure according to: Wh = 2343P0-7

(4.38)

where Wh is leak mass flux in kilograms per second per square meter and P is operating overpressure in bars. This estimation formula seems to give reasonable answers up to about 2 to 70 bars operating overpressure. It is not valid beyond the thermodynamic critical pressure. The leak rate may be factored for the actual flash fraction. The flow rate of release, W9 can be found as the product of the mass flux and the cross sectional area of the leak orifice. The weight of flammable fuel in the cloud can be estimated by multiplying the rate of release by the time span needed to attain the lower flammability limit in the drifting plume. In a conservative approach, for stable atmospheric conditions (characterized by an ambient wind speed of 2.23 m/s), the time span can be approximated by (4.39) where tf W M /

= = = =

time span rate of release molecular weight lowerflammabilitylimit

(s) (kg/s) (kg/kMol) (vol%)

TNT equivalency should be applied to the quantity of fuel calculated with the above equations. For planning purposes, Brasie (1976) recommends the use of TNT equivalencies of 2%, 5%, and 10% (based on energy) in calculations to determine the sensitivity of geometry to the yield. UT Research (Eichler and Napadensky 1977) In their research to determine safe stand-off distances between transportation routes and nuclear power plants, Eichler and Napadensky (1977) recognized that the

blast effects produced by vapor cloud explosions are highly dependent on mode of combustion. They recognized the possibility that rapid deflagration or detonation of all combustibles involved might result in much higher TNT equivalencies than those recommended by Brasie and Simpson (1968) and others. In addition, they recognized that blast effects from vapor cloud explosions are often highly directional. Therefore, they determined an upper limit of TNT equivalency for vapor cloud explosions by analyzing the blast produced in experiments in which spherical fuel-air charges of varying compositions were detonated (Kogarko et al. 1966; Balcerzak et al. 1966; Woolfolk and Ablow 1973). They concluded that the blast from a detonating fuel-air charge can be reasonably well represented by TNT blast data. Because a distance-dependent TNT equivalency was anticipated, they determined TNT equivalency for stoichiometric fuel-air charges only for the level of 1 psi (0.069 bar) peak side-on overpressure. They found a value of about 20%, based on energy. In addition, Eichler and Napadensky derived TNT equivalencies from the damage observed in some major vapor cloud explosion incidents of the 1970s: • The Flixborough explosion was analyzed on the basis of damage figures presented by Munday and Cave (1975). Assuming a 60,000 kg cyclohexane release, they found a TNT equivalency of 7.8% on the basis of energy, which corresponds with a mass equivalency of 81.7%. These equivalences were calculated on the basis of the full quantity of material released. • For the Port Hudson vapor cloud explosion, they found TNT equivalencies of 8.7% and 96%, based on energy and mass basis, respectively. These equivalencies were calculated from damage data presented by Burgess and Zabetakis (1973), and are based on the full quantity of fuel (31,750 gallons, 70,000 kg) of propane released. • Although the blast effects of the East St. Louis tank-car accident (NTSB 1973) were found to be highly asymmetric, average TNT equivalencies of 10% on an energy basis and 109% on a mass basis were found. These equivalencies were calculated based on the assumption of a full tank-car inventory (55,000 kg) of a mixture of propylene and propane. • Another tank car was punctured at Decatur (NTSB report 1975). TNT equivalencies of 4.3-10.2% and 47-111% were calculated on energy and mass bases, respectively. These equivalencies were calculated based upon a full tank car inventory (152,375 Ib, 68,000 kg) of isobutane. Taking into account the possibility of highly directional blast effects, Eichler and Napadensky (1977) recommend the use of a safe and conservative value for TNT equivalency, namely, between 20% and 40%, for the determination of safe standoff distances between transportation routes and nuclear power plants. This value is based on energy; it should be applied to the total amount of hydrocarbon in the largest single, pressurized storage tank being transported.

HSE (1979 and 1986)

"side-on" overpressure, bar

Although it recognized that much higher values have been occasionally observed in vapor cloud explosion incidents, the U.K. Health & Safety Executive (HSE) states that surveys by Brasie and Simpson (1968), Davenport (1977, 1983), and Kletz (1977) show that most major vapor cloud explosions have developed between 1% and 3% of available energy. It therefore recommends that a value of 3% of TNT equivalency be used for predictive purposes, calculated from the theoretical combustion energy present in the cloud. To allow for spray- and aerosol-formation, the mass of fuel in the cloud is assumed to be twice the theoretical flash of the amount of material released, so long as this quantity does not exceed the total amount of fuel available. Blast effects are modeled by means of TNT blast data according to Marshall (1976), while 1 bar is considered to be upper limit for the in-cloud overpressure (Figure 4.18). Because experience indicates that vapor clouds which are most likely to explode

,, , -,^- * „ actual distance, m "scaled distance" = -g mkg~1M

\/WTNT Figure 4.18. Peak side-on overpressure due to a surface TNT explosion according to Marshall (1976). (TNT in kilograms.)

are those which have formed rapidly, the HSE recommends ignoring the effect of cloud drift. Given a certain release of a given fuel, the procedure of vapor cloud explosion blast modeling according to HSE can be subdivided into a number of successive steps: • Determine the flash fraction on the basis of actual thermodynamic data. • The cloud inventory is equal to the flash fraction times the amount of fuel released. To allow for spray and aerosol formation, the cloud inventory should be multiplied by 2. This number may not, of course, exceed the total amount of fuel released. • The equivalent weight of TNT can now be calculated according to: W /•/ W^1n = 0.03 ^ (4.40) "TNT

where WTNT = equivalent weight of TNT or yield W^ = the weight of fuel in the cloud //TNT = TNT blast energy Hf = heat of combustion of fuel in question

(kg) (kg) (J/kg) (J/kg)

• Once the equivalent charge weight of TNT is estimated, the blast peak overpressures in the field can be found by applying this charge weight to the scaled distance in the blast chart (Figure 4.18). • The positive-phase duration of the blast wave from a vapor cloud explosion is in the range of 100 and 300 ms. Exxon (unpublished) To estimate the total quantity of material in the vapor cloud, Exxon suggests that the following guidelines be used: • If a gas is released, the quantity of material in the cloud (to be used in the calculation) is the lesser of (a) the total inventory of material or (b) the product of the rate of release times the time required to stop the leak. • If a liquid is released, the quantity of material in the cloud (to be used in the calculation) is the product of the liquid's evaporation rate and the time required for the cloud to reach a likely ignition source, as limited by the quantity spilled. The quantity spilled is the lesser of (a) the total inventory of material or (b) the product of the rate of release and the time required to stop the leak. • If the material released is either in two phases or flashing, the quantity of material in the cloud (to be used in the calculation) is the lesser of (a) the product of twice the fraction vaporized and the total inventory of material or (b) the product of twice the fraction vaporized, the rate of release, and the time required to stop the leak.

Exxon recognizes that blast effects by vapor cloud explosions are influenced by the presence of partial confinement and/or obstruction in the cloud. Therefore, in order to determine an equivalent TNT yield for vapor clouds, Exxon recommends use of the following values for TNT equivalency on an energy basis: • 3% if the vapor cloud covers an open terrain; • 10% if the vapor cloud is partially confined or obstructed. The open-terrain factor should be used if the release occurs in flat terrain and few structures are nearby, for example, in an isolated tank farm consisting of one or two well-spaced tanks. Otherwise, the partial-confinement yield factor should be used to give reasonably conservative damage estimates. These figures were developed on the basis of the gross quantities of material released in accidents. They may underpredict blast if used in conjunction with the amount of flammable mixture in the cloud developed from dispersion calculations. If the amount of fuel based on dispersion calculations is to be used, higher TNT equivalencies would be justified. The upper limit on yield factor in such instances would be 80%. These guidelines are recommended for application in combination with the Kingery and Panill (1964) TNT surface (ground range) burst data (Figure 4.17). Industrial Risk Insurers (1990) As a tool for estimating the loss of property potential of vapor cloud explosion incidents at chemical plants or refineries, the possibility of two credible incidents is considered. • A credible spill for Probable Maximum Loss Potential. The minimum spill source is the largest process vessel. The maximum spill size is the combined contents of the largest process vessel, or train of process vessels connected together if not readily isolated. Between these extremes, a credible spill may be estimated after taking into account the presence of remotely operated shutoff valves adequate for an emergency, and automatic dump or flare systems. • A credible spill for Catastrophic Loss Potential. For a catastrophic loss potential, the spill size should be based on the contents of vessels or connected vessel train. The existence of shutoff valves between vessels should not be considered. In addition, the catastrophic failure of major storage tanks should be considered. Leaks in pipelines carrying materials of concern from large-capacity, off-site, remote storage facilities must be considered. For this purpose, it must be assumed that the pipeline is completely severed and that the spill will run for 30 minutes. Industrial Risk Insurers (1990) states that the TNT equivalency of actual chemical plant vapor cloud explosions is in the range of 1% to 5%. A value of 2% based on

OI/SMETER OF OVERPRESSURE CIRCLES - FEET

YIELD - TONS OF TNT

Figure 4.19. Diameters of side-on overpressure circles for various explosive yields (1 ton = 2000 Ib) (based on free-air bursts).

available energy is recommended for use in estimating probable maximum and catastrophic losses. This TNT equivalency should be used in combination with airburst TNT-blast data according to Glasston and Dolan (1977), represented in Figure 4.19. Figure 4.19 presents blast data so as to permit the diameters of overpressure circles to be read as a function of charge weight for various side-on overpressures. Factory Mutual Research Corporation (FMRC) (1990) According to FMRC (1990), a credible spill scenario at a chemical plant or refinery consists of • a 10-minute release from the largest vessel or train of vessels through the connection that will allow the greatest discharge; • a 10-minute release from an atmospheric or pressurized tank based on gravity and storage pressure as the driving force (the operation of internal excess flow valves, if present, may be considered in mitigating the amount discharged); • a 10-minute release from above-ground pipelines carrying material from a largecapacity, remote source; • loss of the entire contents of the tank for mobile tanks, such as rail and truck transportation vessels.

The quantity of fuel in a cloud is calculated by use of release and (flash) vaporization models that have been extensively described by Hanna and Drivas (1987). To account for aerosol formation during vaporization, the flash fraction should be doubled up to, but not exceeding, a value of unity. Pool vaporization is also considered. The equivalent charge weight of TNT is calculated on the basis of the entire cloud content. FMRC recommends that a material-dependent yield factor be applied. Three types of material are distinguished: Class I (relatively nonreactive materials such as propane, butane, and ordinary flammable liquids); Class II (moderately reactive materials such as ethylene, diethyl ether, and acrolein); and Class III (highly reactive materials such as acetylene). These classes were developed based on the work of Lewis (1980). Energy-based TNT equivalencies assigned to these classes are as follows:

Class I II III

TNT Equivalency 5% 10% 15%

TNT-blast data for hemispherical surface bursts are used to determine the blast effects due to the equivalent charge. These blast data are based on the Army, Navy, and Air Force Manual (1990). Hazard Reduction Engineering Inc. (Prugh 1987) One of the complicating factors in the use of a TNT-blast model for vapor cloud explosion blast modeling is the effect of distance on the TNT equivalency observed in actual incidents. Properly speaking, TNT blast characteristics do not correspond with gas explosion blast. That is, far-field gas explosion blast effects must be represented by much heavier TNT charges than intermediate distances. To some extent, Prugh (1987) remedied this problem by introducing the concept of virtual distance. On the basis of literature data, Prugh determined a virtual distance, dependent on the weight of fuel involved in the vapor cloud explosion, expressed in an empirical relation. If virtual distance is added to real distance in estimating blast effects, then these effects can be approximated from a single equivalent TNT charge covering the entire field. In fact, this is the approximate yield observed for far-field blast effects. To express the maximum potential explosive power of a fuel, a safe and conservative value for TNT equivalencies of vapor cloud explosions was estimated from literature data on major incidents, after correction for virtual distance. Prugh (1987) concluded that the maximum energy-based TNT equivalency is highly depen-

dent on the quantity of fuel present in the cloud, and ranges from 2% for 100 kg up to 70% for 10 million kg of fuel. These TNT equivalencies should be used in combination with high-explosive blast data by Baker (1973). Instead of graphical representation, Prugh (1987) recommends the use of simple equations which relate basic blast parameters to distance from the explosion center. These expressions can be readily implemented in a spreadsheet on a personal computer. British Gas (Harris and Wickens 1989) On the basis of an extended experimental program described in Section 4.1.3, Harris and Wickens (1989) concluded that overpressure effects produced by vapor cloud explosions are largely determined by the combustion which develops only in the congested/obstructed areas in the cloud. For natural gas, these conclusions were used to develop an improved TNT-equivalency method for the prediction of vapor cloud explosion blast. This approach is no longer based on the entire mass of flammable material released, but on the mass of material that can be contained in stoichiometric proportions in any severely congested region of the cloud. An equivalent TNT charge, expressing the explosive potential of a congested/ obstructed region, should be calculated based on a 20% TNT equivalency of available energy. This TNT equivalency should be applied in combination with TNTblast data developed by Marshall (1976) (Figure 4.18). Harris and Wickens (1989) argue that, for releases of gases considered more reactive than natural gas, this approach might be inappropriate because, under specific circumstances, transition to detonation engulfing any portion of the cloud may occur. The Harris and Wickens (1989) approach appears to be very similar to the multienergy method (Van den Berg 1985), whose background is described in more detail in Section 4.3.2. In addition, the nature of partially confined, obstructed, and congested areas is described in more detail there.

4.3.2. Methods Based on Fuel-Air Charge Blast Vapor cloud explosion blast models presented so far have not addressed a major feature of gas explosions, namely, variability in blast strength. Furthermore, TNT blast characteristics do not correspond well to those of gas-explosion blasts, as evidenced by the influence of distance on TNT equivalency observed in vapor cloud explosion blasts. The Baker-Strehlow Method An extensive numerical study was performed by Strehlow et al. (1979) to analyze the structure of blast waves generated by constant velocity and accelerating flames propagating in a spherical geometry. This study resulted in the generation of plots

of dimensionless overpressure and positive impulse as a function of energy-scaled distance from the cloud center. The study examined flamed speeds ranging from low velocity deflagrations to detonations. The time period covered by numerical calculations was extended well after the flame had extinguished and yielded blast parameters out to considerable distances from the source region. Thus, the pressure and impulse curves encompass regions both inside and outside the combustion zone. Baker and his colleagues (1983) compared the Strehlow et al. (1979) curves to experimental data, then applied them in research programs, accident investigations, and predictive studies. They developed the methods for use of Strehlow's curves. Application of the Baker-Strehlow method for evaluating blast effects from a vapor cloud explosion involves defining the energy of the explosion, calculating the scaled distance (R)9 then graphically reading the dimensionless peak pressure (P5) and dimensionless specific impulse (I5). Equations (4.41) and (4.42) provide the means to calculate incident pressure and impulse based on the dimensionless terms. (4.41) where R r P0 E ^V^o

= = = = =

scaled distance distance from target to center of vapor cloud atmospheric pressure energy dimensionless overpressure (Figure 4.20)

(-) (m) (Pa) (J) (-) (4.42)

where /5 i A0 PQ E

= = = = =

scaled impulse incident impulse speed of sound in air atmospheric pressure energy.

(-) (Pa-s) (m/s) (Pa) (J)

Graphical solution of Figures 4.20 and 4.21 requires selection of the proper curve based on the maximum flame speed attained. Strehlow et al. (1979) studies showed that a constant speed flame and an accelerating flame with the same maximum speed generated equivalent blast waves. Thus, flame speed data from experimental studies and accident investigations can be used objectively to select the proper curve. Each curve is labeled with two flame speeds: Mw and Msu. The flame speed Mw is relative to a fixed coordinate system (i.e., on the ground), whereas Msu represents the flame speed relative to the gases moving ahead of the flame front. Both Mw and Msu Mach numbers are calculated relative to the ambient speed of

Pentolite Bursting Sphere

Figure 4.20. Dimensionless blast side-on overpressure for vapor cloud explosions (Strehlow etal. 1979).

sound. While Mw is the appropriate parameter for comparison to most experimental data, the user should not assume that all experimental data are reported on this basis. Flame speed is a function of confinement, obstacle density, fuel reactivity, and ignition intensity. Confinement and obstacles have a coupled effect, so flame speed cannot be inferred from experiments that model only one of the user's parameters correctly. Fuel reactivity is a qualitative parameter that is generally used to categorize a fuel's propensity to accelerate to high flame speeds. It is generally accepted that hydrogen, acetylene, ethylene oxide, and propylene oxide have high reactivity; methane and carbon monoxide have low reactivity; and all other hydrocarbons have average reactivity. Ignition sources may be either soft or hard. Open flame, spark, or hot surfaces are examples of soft ignition sources, while jet and high explosives are categorized as hard ignition sources. Ignition intensity has almost no influence on flame speed for soft ignition sources; confinement, obstacles, and fuel reactivity are most important here. By contrast, ignition intensity is the most important variable if a hard ignition source is present.

Literature provides the basis for a user to objectively determine the maximum flame speed that will be achieved with a particular combination of confinement, obstacles, fuel reactivity, and ignition source. _ The energy term E must be defined to calculate energy-scaled standoff/?. The energy term represents the sensible heat that is released by that portion of the cloud contributing to the blast wave. Any of the accepted methods of calculating vapor cloud explosive energy are applicable to the Baker-Strehlow method. These methods include: • Estimating the volume within each congested region, calculating the fuel mass for a stoichiometric mixture, multiplying the fuel mass by the heat of combus® BURSTING SPHERE a BAKER ( PENTOLITE ) A MACH 8-0 ADDITION MACH 5-2 ADDITION ( C J ) MACH MACH MACH MACH

4.0 2.0 1.0 0.5

ADDITION ADDITION ADDITION (M 8 * 0.12 8) ADDITION (M^ O.O662)

IMPULSE ( ENERGY

SCALED ), |.

MACH 0.25 ADDITION (M $ « 0.034) r KERNEL ADDITION TAU - 0.2 w KERNEL ADDITION T A U - 2 0

RADIUS

( ENERGY

SCALED ) , R

Figure 4.21. Dimensionless blast side-on specific impulse for vapor cloud explosions (Strehlow etal. 1979).

tion, and treating each congested volume within the flammable portion of the cloud as a separate blast source (see Multienergy Method). • Estimating the total release of flammable material within a reasonable amount of time (generally 2 to 5 minutes) and multiplying this by the heat of combustion of the material times an efficiency factor (generally in the range of 1% to 5% for ordinary hydrocarbons). • Estimating the amount of material withinflammablelimits (usually by dispersion modeling) and multiplying this by the heat of combustion times an efficiency factor (usually higher than the one applied above, generally 5% to 20%). Once the energy has been calculated, it must be multiplied by a ground reflection factor (i.e., hemispherical expansion factor), because Figures 4.20 and 4.21 are based on spherical expansion parameters. The ground reflection factor is generally 2 for vapor clouds that are in contact with the ground. If a vapor release is elevated and does not disperse to ground level, a factor between 1 and 2 must be selected. Because blast waves are generated in confined regions of vapor clouds, most vapor cloud explosions will be relatively close to the ground, and a factor of 1.7 to 2.0 is appropriate. Yellow Book, Committee for the Prevention of Disasters (1979) Wiekema (1980) used, as a model for vapor cloud explosion blast, the gas dynamics induced by a spherical expanding piston (Yellow Book 1979). A piston-blast model offers the possibility to introduce a variable initial strength of the blast. The piston blast was generated by computation, and is graphically represented in Figure 4.22. The figure shows the peak side-on overpressure and the positive-phase duration of the blast wave dependent on the distance from the blast center for three arbitrarily chosen piston velocities. The graph is completed with experimental data from detonation of fuel-air mixtures developed by Kogarko (1966). Data are reproduced in a Sachs-scaled representation. This approach makes it possible to model a vapor cloud explosion blast by consideration of the two major characteristics of such a blast. These are, first, its scale, as determined by the amount of combustion energy involved and, second, its initial strength, as determined by combustion rate in the explosion process. Blast scale was determined by use of dispersion calculations to estimate fuel quantity within flammability limits present in the cloud. Initial blast strength was determined by factors which have been found to be major factors affecting the process of turbulent, premixed combustion, for example, the fuel's nature and the existence within the cloud of partial confinement or obstacles. The most common fuels were divided into three groups according to reactivity. The low-reactivity group included ammonia, methane, and natural gas; hydrogen, acetylene, and ethylene oxide were classified as highly reactive. Those within these extremes, for example, ethane, ethylene, propane, propylene, butane, and isobutane, were classified as medium-reactivity fuels.

before combustion

after combustion

low reactivity

medium reactivity

Figure 4.22. The piston-blast model.

Subsequently, it was assumed that blast strength is primarily determined by the fuel's reactivity (Figure 4.22), and that partial confinement, congestion, and obstruction in the cloud were only secondary influences. These assumptions are, however, highly questionable. The Multienergy Method (Van den Berg 1985) A comprehensive collection of estimates of TNT equivalencies was deduced from damage patterns observed in major accidental vapor cloud explosions (Gugan 1978). From these estimates, it can be concluded that there is little, if any, correlation between the quantity of combustion energy involved in a vapor cloud explosion

and the equivalent-charge weight of TNT required to model its blast effects. Some of these discrepancies are due to differences in the definition of the amount of material contained in the cloud. Evaluation of experimental data from work covered in Section 4.1 tends to confirm this concludion. These data indicate that, for quiescent clouds, both the scale and strength of a blast are unrelated to fuel quantity present in a cloud. These parameters are, in fact, determined primarily by the size and nature of partially confined and obstructed regions within the cloud. The factor of reactivity of the fuel-air mixture is of only secondary influence. These principles are recognized in the multienergy method for vapor cloud explosion blast modeling (Van den Berg 1985; Van den Berg et al. 1987). Considerations underlying the multienergy method for vapor cloud explosion blast modeling follow. There is increasing acceptance of the proposition that a fuel-air cloud originating from an open air, accidental release is very unlikely to detonate. The nonhomogeneity of the cloud's fuel-air mixture, inherent in atmospheric turbulent dispersion (Section 3.1), generally prevents the propagation of a detonation (Van den Berg 1987). The severe explosion on December 7, 1970, at Port Hudson, Missouri, where nearly all of a large, unconfined vapor cloud detonated, is attributable to several exceptional coincidences. Those included the location, which was a shallow valley, the calm atmospheric conditions, and the exceptionally long ignition delay—all of which provided the opportunity for molecular diffusion to mix the dense propane cloud sufficiently with air (NTSB report 1972 and Burgess and Zabetakis 1973). The subsequent detonation is unprecedented among documented incidents. Therefore, in the vast majority of cases, the assumption of deflagrative combustion is a sufficiently safe approach to vapor cloud explosion hazard assessment. Experimental research during the last decade (Section 4.1) has shown clearly that deflagrative combustion generates blast only in those portions of a quiescent vapor cloud which are sufficiently obstructured and/or partially confined (Zeeuwen et al. 1983; Harrison and Eyre 1987; Harris and Wickens 1989; Van Wingerden 1989a). The conclusion that a partially confined and/or obstructed environment is conducive to deflagrative explosive combustion has now found wide acceptance (Tweeddale 1989). Moreover, those cloud portions already in turbulent motion when ignition occurs may develop explosive, blast-generative combustion. Consequently, high-velocity, intensely turbulent jets within a flammable-vapor cloud (Section 4.1.2), such as those resulting from fuel releases from high-pressure sources, should be viewed as possible blast sources. The remaining portions of a cloud containing a flammable vapor-air mixture burn out slowly without contributing significantly to blast. This model is called the Multi-Energy concept. Contrary to other modeling methods, in which a vapor cloud explosion is regarded as an entity, the MultiEnergy concept defines a vapor cloud explosion as a number of sub-explosions corresponding to the various sources of blast in the cloud.

Figure 4.23. Vapor cloud containing two blast-generative objects.

Figure 4.23 illustrates two common blast-generators: chemical plants and railcar switching yards (Baker et al. 1983), each blanketed in a large vapor cloud. The blast effects from each should be considered separately. Blast effects can be represented by a number of blast models. Generally, blast effects from vapor cloud explosions are directional. Such effects, however, cannot be modeled without conducting detailed numerical simulations of phenomena. If simplifying assumptions are made, that is, the idealized, symmetrical representation of blast effects, the computational burden is eased. An idealized gas-explosion blast model was generated by computation; results are represented in Figure 4.24. Steady flame-speed gas explosions were numerically simulated with the BLAST-code (Van den Berg 1980), and their blast effects were calculated. Figure 4.24 represents the blast characteristics of a hemispherical fuel-air charge of radius R0 on the earth's surface, derived for a fuel-air mixture with a heat of combustion of 3.5 X 106 J/m3. The charts represent only the most significant blast-wave parameters: side-on peak overpressure (AP8) and the positive-phase blastwave duration (7*) as a function of distance from the blast center (R). The data are fully nondimensionalized, with charge combustion energy (E) and parameters characterizing the state of the ambient atmosphere: pressure (P0) and speed of sound (CQ). This way of scaling (Sachs scaling) takes into account the influence of atmospheric conditions. Moreover, Sachs scaling allows the blast parameters to be read in any consistent set of units. Initial blast strength in Figure 4.24 is represented by a number ranging from 1 (very low strength) up to 10 (detonative strength). The initial blast strength number is indicated in the charts at the location of the charge radius. In addition, Figure 4.24 gives a rough indication of the blast-wave shape, which corresponds to the characteristic behavior of a gas-explosion blast. Pressure waves, produced by fuel-air charges of low strength, show an acoustic overpressure decay behavior and a constant positive-phase duration. On the other hand, shock waves in the vicinity of a charge of high initial strength exhibit a more rapid overpressure decay and a substantial increase in positive-phase duration. Eventually,

combustion energy-scaled distance (R)

combustion energy-scaled distance (R) p o C0 E R0

Figure 4.24. Fuel-air charge blast model.

= atmospheric pressure = atmospheric sound speed = amount of combustion energy = charge radius

the high-strength blast develops a behavior approximating acoustic decay in the far field. Another significant feature is that, at a distance larger than about 10 charge radii from the center, a fuel-air charge blast is more-or-less independent of initial strength for values of 6 (strong deflagration) and above. In the application of the multienergy concept, a particular vapor cloud explosion hazard is not determined primarily by the fuel-air mixture itself but rather by the environment into which it disperses. The environment constitutes the boundary conditions for the combustion process. If a release of fuel is anticipated somewhere, the explosion hazard assessment can be limited to an investigation of the environment's potential for generating blast. The procedure for employing the multienergy concept to model vapor cloud explosion blast can be divided into the following steps: • Assume that blast modeling on the basis of deflagrative combustion is a sufficiently safe and conservative approach. (The basis for this assumption is that an unconfined vapor cloud detonation is extremely unlikely; only a single event has been observed.) • Identify potential sources of strong blast present within the area covered by the flammable cloud. Potential sources of strong blast include —extended spatial configuration of objects such as process equipment in chemical plants or refineries and stacks of crates or pallets; —spaces between extended parallel planes, for example, those beneath closely parked cars in parking lots, and open buildings, for example, multistory parking garages; —spaces within tubelike structures, for example, tunnels, bridges, corridors, sewage systems, culverts; —an intensely turbulent fuel-air mixture in a jet resulting from release at high pressure. The remaining fuel-air mixture in the cloud is assumed to produce a blast of minor strength. • Estimate the energy of equivalent fuel-air charges. —Consider each blast source separately. —Assume that the full quantities of fuel-air mixture present within the partially confined/obstructed areas and jets, identified as blast sources in the cloud, contribute to the blasts. —Estimate the volumes of fuel-air mixture present in the individual areas identified as blast sources. This estimate can be based on the overall dimensions of the areas and jets. Note that the flammable mixture may not fill an entire blast-source volume and that the volume of equipment should be considered where it represents an appreciable proportion of the whole volume. —Calculate the combustion energy E [J] for each blast by multiplication of the individual volumes of mixture by 3.5 X 106 J/m3. This value (3.5 x

106 J/m3) is a typical one for the heat of combustion of an average stoichiometric hydrocarbon-air mixture (Harris 1983). • Estimate strengths of individual blasts. —A safe and most conservative estimate of the strength of the sources of strong blast can be made if a maximum strength of 10 is assumed. However, a source strength of 7 seems to more accurately represent actual experience. Furthermore, for side-on overpressures below about 0.5 bar, no differences appear for source strengths ranging from 7 to 10. —The blast resulting from the remaining unconfined and unobstructed parts of a cloud can be modeled by assuming a low initial strength. For extended and quiescent parts, assume minimum strength of 1. For more nonquiescent parts, which are in low-intensity turbulent motion, for instance, because of the momentum of a fuel release, assume a strength of 3. —If such an approach results in unacceptably high overpressures, a more accurate estimate of initial blast strength may be determined from the growing body of experimental data on gas explosions (reviewed in Section 4.1), or by performing an experiment tailored to the situation in question. —Another very promising possibility is the application of numerical simulation by use of advanced computational fluid dynamic codes, such as FLAGS (Hjertager 1982, 1989), EXSIM (Hjertager 1991), PHOENICS (Kjaldman and Huhtanen 1985) or REAGAS (Van den Berg 1989), outlined in Section 4.2.2. Van den Berg et al. (1991) demonstrated one way to use such codes for vapor cloud explosion blast modeling. An example of the use of these advanced codes is shown in Appendix F. —Further definition of initial blast strength is, however, a major research need that is so far unmet. • Once the energy quantities E and the initial blast strengths of the individual equivalent fuel-air charges are estimated, the Sachs-scaled blast side-on overpressure and positive-phase duration at some distance R from a blast source can be read from the blast charts in Figure 4.24 after calculation of the Sachsscaled distance: (4.43)

where R R E P0

= = = =

Sachs-scale distance from charge real distance from charge charge combustion energy ambient pressure

(-) (m) (J) (Pa)

The real blast side-on overpressure and positive-phase duration can be calculated from the Sachs-scaled quantities: P8 = A/>s - P0

(4.44)

and

(4.45) where PS^ AP8 P0 t+ t+ E C0

= = = = = = =

side-on blast overpressure Sachs-scaled side-on blast overpressure ambient pressure positive-phase duration Sachs-scaled positive-phase duration charge combustion energy ambient speed of sound

(Pa) (-) (Pa) (s) (-) (J) (m/s)

—If separate blast sources are located close to one another, they may be initiated almost simultaneously. Coincidence of their blasts in the far field cannot be ruled out, and their respective blasts should be superposed. The safe and most conservative approach to this issue is to assume a maximum initial blast strength of 10 and to sum the combustion energy from each source in question. Further definition of this important issue, for instance the determination of a minimum distance between potential blast sources so that their individual blasts may be considered separately, is a factor in present research. —If environmental and atmospheric conditions are such that vapor cloud dispersion can be expected to be very slow, the possibility of unconfined vapor cloud detonation should be considered if, in addition, a long ignition delay is likely. In that case, the full quantity of fuel mixed within detonable limits should be assumed for a fuel-air charge whose initial strength is maximum 10. 4.3.3. Special Methods In the overview of experimental research, it was shown that explosive, blastgenerating combustion in gas explosions is caused by intense turbulence which enhances combustion rate. On one hand, turbulence may be generated during a gas explosion by an uncontrolled feedback mechanism. A turbulence-generative environment, in the form of partially confining or obstructing structures, must be present for this mechanism to be triggered. On the other hand, turbulence may also be generated by external sources. For example, fuels are often stored in vessels under pressure. In the event of a total vessel failure, the liquid will flash to vapor, expanding rapidly and producing fast, turbulent mixing. Should a small leak occur, fuel will be released as a high-velocity, turbulent jet in which the fuel is rapidly mixed with air. If such an intensely turbulent fuel-air mixture is ignited, explosive combustion and blast can result.

Special methods tailored to these phenomena have been developed for modeling such effects. These methods consist of a collection of experimental data framed in graphs or semiempirical expressions. Explosively Dispersed Vapor Cloud Explosions (Giesbrecht et al. 1981). The Giesbrecht et al. (1981) model is based on a series of small-scale experiments in which vessels of various sizes (0.226-1000 1) containing propylene were ruptured. (See Section 4.1.2, especially Figure 4.5.) Flame speed, maximum overpressure, and positive-phase duration observed in explosively dispersed clouds are represented as a function of fuel mass. The solid lines in Figure 4.5 represent extrapolations of experimental data to full-scale vessel bursts on the basis of dimensional arguments. Attendant overpressures were computed by the similarity solution for the gas dynamics generated by steady flames according to Kuhl et al. (1973). Overpressure effects in the environment were determined assuming acoustic decay. The dimensional arguments used to scale up the turbulent flame speed, based on an expression by Damkohler (1940), are, however, questionable. Exploding Jets (Stock et al. 1989). Stock et al. (1989) collected experimental data obtained in two different programs on exploding jets: a program on natural gas and hydrogen jets by Seifert and Giesbrecht (1986), and a program on propane jets by Stock (1987). These tests have been described in Section 4.1.2; a summary of general conclusions follows. • Overpressure within a vapor cloud is dependent upon outflow velocity, orifice diameter, and laminar flame speed expressed in the following semi-empirical relation: Pmax = (constant)^ 8X^0)09

(4.46)

where ^max = in-cloud overpressure M1 = laminar flame speed M0 = outflow velocity J0 = orifice diameter

(Pa) (m/s) (m/s) (m)

• The semiempirical theory underlying this equation can be extended to describe blast overpressure decay. If acoustic behavior is assumed, results can be framed in the following expression for blast overpressure as a function of distance from the blast center. P = (au°Q9dl0-9 + b)/r where for natural gas: for hydrogen:

a = 840, a = 3728,

b = 23 b = 55

(4.47)

P — overpressure at distance r r = distance from blast center

(Pa) (m)

4.4. SUMMARY AND DISCUSSION The great attractiveness of TNT equivalency methods is the very direct, empirical relation between a charge weight of TNT and resulting strucural damage. Therefore, TNT equivalency is a useful tool for calculating the property-damage potential of vapor clouds. The various methods reviewed, however, cover a large range of values for TNT equivalency which all are, in some sense, applicable. TNT equivalencies given by the sources identified below are based upon averages deduced from damage observed in a limited number of major vapor cloud explosion incidents: • Brasie and Simpson: 2%-5% of the heat of combustion of the quantity of fuel spilled. • The UK Health & Safety Executive: 3% of the heat of combustion of the quantity of fuel present in the cloud. • Exxon: 3%-10% of the heat of combustion of the quantity of fuel present in the cloud. • Industrial Risk Insurers: 2% of the heat of combustion of the quantity of fuel spilled. • Factory Mutual Research Corporation: 5%, 10%, and 15% of the heat of combustion of the quantity of fuel present in the cloud. These figures can be used for predictive purposes to extrapolate "average major incident conditions" to situations under study, provided the actual conditions under study correspond reasonably well with "average major incident conditions." Such a condition may be broadly described as a spill of some tens of tons of a hydrocarbon in an environment with local concentrations of obstructions and/or partial confinement, for example, the site of an "average" refinery or chemical plant with dense process equipment or the site of a railroad marshaling yard with a large number of closely parked rail cars. It must be emphasized that the TNT equivalencies listed above should not be used in situations in which "average major incident conditions" do not apply. A more deterministic estimate of a vapor cloud's blast-damage potential is possible only if the actual conditions within the cloud are considered. This is the starting point in the multienergy concept for vapor cloud explosion blast modeling (Van den Berg 1985). Harris and Wickens (1989) make use of this concept by suggesting that blast effects be modeled by applying a 20% TNT equivalency only to that portion of the vapor cloud which is partially confined and/or obstructed.

TNT blast is, however, a poor model for a gas explosion blast. In particular, the shape and positive-phase duration of blast waves induced by gas explosions are poorly represented by TNT blast. Nevertheless, TNT-equivalency methods are satisfactory, so long as far-field damage potential is the major concern. If, on the other hand, a vapor cloud's explosive potential is the starting point for, say, advanced design of blast-resistant structures, TNT blast may be a less than satisfactory model. In such cases, the blast wave's shape and positive-phase duration must be considered important parameters, so the use of a more realistic blast model may be required. A fuel-air charge blast model developed through the multienergy concept, as suggested by Van den Berg (1985), results in a more realistic representation of a vapor cloud explosion blast. Because it is usually very difficult to evaluate beforehand the conditions which may induce an initial blast, a conservative approach is to apply an initial blast strength of 10 to the fuel-air charge blast model. This model, however, offers possibilities for future development. The multienergy approach allows experimental data and advanced computational methods to be incorporated in blast modeling procedures. A database containing a complete overview of data on vapor cloud explosion incidents and gas explosion experiments should be developed for this purpose. Such a database could be used to easily and inexpensively determine more appropriate values for initial blast strength. A database cannot, however, possibly cover all situations that may arise in practice. These voids could be filled by computed values. Therefore, the design and development of computer codes, such as FLAGS (Hjertager 1982 and 1989) and REAGAS (Van den Berg 1989), are of paramount importance. Although the model of spherical fuel-air charge blast is the most realistic available, it is nevertheless a highly idealized concept that, at best, applies only to the far field. Near-field blast effects are mostly directional as a consequence of a preferential direction in the combustion process induced by partial confinement. In addition, structural blast loading is influenced largely by neighboring objects. Such effects can only be studied and quantified by simulation with multidimensional numerical methods such as BLAST (Van den Berg 1980). Codes such as REAGAS and BLAST could be utilized in vapor cloud explosion hazard analysis, as described by Van den Berg et al. (1991).

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Strehlow, R. A. 1981. "Blast wave from deflagrative explosions: an acoustic approach." AIChE Loss Prevention. 14:145-152. Taylor, G. I. 1946. "The air wave surrounding an expanding sphere." Proc. Roy. Soc. London. Series A, 186:273-292. Taylor, P. H. 1985. "Vapor cloud explosions—The directional blast wave from an elongated cloud with edge ignition." Comb. Sd. Tech. 44:207-219. Taylor, P. H. 1987. "Fast flames in a vented duct." 21st Symp. (Int.) on Combustion. The Combustion Institute, Pittsburgh, PA. Tweeddale, M. 1989. Conference report on the 6th Int. Symp. on Loss Prevention and Safety Promotion in the Process Industries, J. of Loss Prevention in the Process Industries. 1989. 2(4):241. Urtiew, P. A., and A. K. Oppenheim. 1966. "Experimental observations of the transition to detonation in an explosive gas." Proc. Roy. Soc. A295:13-28. Urtiew, P. A. 1981. "Flame propagation in gaseous fuel mixtures in semiconfined geometries." report no. UCID-19000. Lawrence Livermore Laboratory. Urtiew, P. A. 1982. "Recent flame propagation experiments at LLNL within the liquefied gaseous fuels spill safety program." Fuel-air explosions, pp. 929-948, University of Waterloo Press, Waterloo. Van den Berg, A. C. 1980. "BLAST—a 1-D variable flame speed blast simulation code using a 'Flux-Corrected Transport' algorithm." Prins Maurits Laboratory TNO report no. PML 1980-162. Van den Berg, A. C. 1984. "Blast effects from vapor cloud explosions." 9th Int. Symp. on the Prevention of Occupational Accidents and Diseases in the Chemical Industry. Lucera, Switzerland. Van den Berg, A. C. 1985. "The Multi-Energy method—A framework for vapor cloud explosion blast prediction." J. ofHaz. Mat. 12:1-10. Van den Berg, A. C. 1987. "On the possibility of vapor cloud detonation." TNO Prins Maurits Laboratory report no. 1987-IN-50. Van den Berg, A. C., C. J. M. van Wingerden, J. P. Zeeuwen, and H. J. Pasman. 1987. "Current research at TNO on vapor cloud explosion modeling." Int. Conf. on Vapor Cloud Modeling. Cambridge, MA. proceedings, pp. 687-711, AIChE, New York. Van den Berg, A. C. 1989. "REAGAS—a code for numerical simulation of 2-D reactive gas dynamics in gas explosions." TNO Prins Maurits Laboratory report no. PML1989-IN48. Van den Berg, A. C., C. J. M. van Wingerden, and H. G. The. 1991. "Vapor cloud explosion blast modeling." International Conference and Workshop on Modeling and Mitigation the Consequences of Accidental Releases of Hazardous Materials, May 21-24, 1991. New Orleans, USA. proceedings, pp. 543-562. Van Wingerden, C. J. M., and J. P. Zeeuwen. 1983. Flame propagation in the presence of repeated obstacles: influence of gas reactivity and degree of confinement." J. of Haz. Mat. 8:139-156. Van Wingerden, C. J. M., and A. C. Van den Berg. 1984. "On the adequacy of numerical codes for the simulation of vapor cloud explosions." Commission of the European Communities for Nuclear Science and Technology, report no. EUR 9541 EN/I. Van Wingerden, C. J. M. 1984. "Experimental study of the influence of obstacles and partial confinement on flame propagation." Commission of the European Communities for Nuclear Science and Technology, report no. EUR 9541 EN/n. Van Wingerden, C. J. M. 1988a. "Experimental investigation into the strength of blast waves generated by vapor cloud explosions in congested areas." 6th Int. Symp. Loss Prevention and Safety Promotion in the Process Industries. Oslo, Norway, proceedings. 26:1-16.

Van Wingerden, C. J. M. 1989b. "On the scaling of vapor cloud explosion experiments." Chem. Eng. Res. Des. 67:334-347. Van Wingerden, C. J. M., A. C. Van den Berg, and G. Opschoor. 1989. "Vapor cloud explosion blast prediction." Plant!Operations Progress. 8(4):234-238. Von Neumann, J., and R. D. Richtmyer. 1950. "A method for numerical calculations of hydrodynamical shocks." J. ofAppl. Phys. 21:232-237. Wiekema, B. J. 1980. "Vapor cloud explosion model." J. ofHaz. Mat. 3:221-232. Wilkins, M. L. 1969. "Calculation of elastic-plastic flow." Lawrence Radiation Laboratory report no. UCRL-7322 Rev. I. Woolfolk, R. W., and C. M. Ablow. 1973. "Blast waves for non-ideal explosions." Conference on the Mechanism of Explosions and Blast Waves, Naval Weapons Station. Yorktown, VA. Yellow Book. 1979. Committee for the Prevention of Disasters, 1979: Methods for the calculation of physical effects of the escape of dangerous materials, P.O. Box 69, 2270 MA Voorburg, The Netherlands. Zeeuwen, J. P., C. J. M. Van Wingerden, and R. M. Dauwe. 1983. "Experimental investigation into the blast effect produced by unconfined vapor cloud explosions." 4th Int. Symp. Loss Prevention and Safety Promotion in the Process Industries. Harrogate, UK, IChemE Symp. Series 80:D20-D29.

5 BASIC PRINCIPLES OF FLASH FIRES A flash fire is the nonexplosive combustion of a vapor cloud resulting from a release of flammable material into the open air, which, after mixing with air, ignites. In Section 4.1, experiments on vapor cloud explosions were reviewed. They showed that combustion in a vapor cloud develops an explosive intensity and attendant blast effects only in areas where intensely turbulent combustion develops and only if certain conditions are met. Where these conditions are not present, no blast should occur. The cloud then burns as a flash fire, and its major hazard is from the effect of heat from thermal radiation. The literature provides little information on the effects of thermal radiation from flash fires, probably because thermal radiation hazards from burning vapor clouds are considered less significant than possible blast effects. Furthermore, flash combustion of a vapor cloud normally lasts no more than a few tens of seconds. Therefore, the total intercepted radiation by an object near a flash fire is substantially lower than in case of a pool fire. In order to compute the thermal radiation effects produced by a burning vapor cloud, it is necessary to know the flame's temperature, size, and dynamics during its propagation through the cloud. Thermal radiation intercepted by an object in the vicinity is determined by the emissive power of the flame (determined by the flame temperature), the flame's emissivity, the view factor, and an atmospheric-attenuation factor. The fundamentals of heat-radiation modeling are described in Section 3.5.

5.1. OVERVIEW OF RESEARCH Full-scale experiments on flame propagation in fuel-air clouds are extremely laborious and expensive. Therefore, experimental data on the dynamics of flash fires and attendant thermal radiation are scarce. Urtiew (1982), Hogan (1982) and Goldwire et al. (1983) reported on LNG, liquid methane, and liquid nitrogen spill experiments in China Lake. The facility could hold up to 40 m3 of liquefied gas, which could be either partially or completely released during a single spill test on a water test basin. In total, ten experiments were performed, five primarily for the study of vapor dispersion and burning vapor clouds, and five for investigating the occurrence of explosions exhibiting rapid phase transitions. All vapor burn tests were performed with LNG except for one with liquid methane. The tests were carried out to study the nature and behavior of the burning

process in an unconfined environment. The burning process was measured by ionization gauges (to permit three-dimensional measurement of local flame speed and direction), calorimeters (to measure local heat release of the burning cloud), thermometers (to measure local flame temperatures), radiometers (to collect data on the intensity of radiation), and infrared (IR) imaging from a helicopter overhead. These instruments were all located downwind of the spill pond. Heat-flux data obtained from calorimeters present in the fire-affected area revealed maximum heat fluxes of 160-300 kW/m2. Figure 5.1 shows the calorimeter positions, the final contours of the flash fire, and heat-flux data from calorimeters positioned near or in the flames. No data are available on flame propagation during the vapor-burn tests. The Maplin Sands tests were reported by Blackmore et al. (1982) and Hirst and Eyre (1983). Quantities of 20 m3 LNG and refrigerated liquid propane were spilled on the surface of the sea in the Thames estuary. The experimental program consisted of both instantaneous and continuous releases. The resulting vapor cloud dispersion and the subsequent combustion of the clouds was observed by instrumentation deployed on 71 floating pontoons (Figure 5.2). On the masts of 20-30 selected pontoons, 27 wide-angle radiometers (to measure average incident radiation) and 24 hydrophones (to measure flame-generated overpressures) were mounted. Another two special pontoons provided platforms for meteorological instruments. The instruments provided vertical profiles of temperature and wind speed up to 10 m above sea level, together with measurements of wind direction, relative humidity, solar radiation, water temperature, and wave height. The major objective of the experimental program was to obtain data that could be used to assess the accuracy of existing models for vapor cloud dispersion. The combustion experiments were designed to complement this objective by providing answers to the question, "What would happen if such a cloud ignited?" Combustion behavior differed in some respects between continuous and instantaneous spills, and also between LNG and refrigerated liquid propane. For continuous spills, a short period of premixed burning occurred immediately after ignition. This was characterized by a weakly luminous flame, and was followed by combustion of the fuel-rich portions of the plume, which burned with a rather low, bright yellow flame. Flame height increased markedly as soon as the fire burned back to the liquid pool at the spill point, and assumed the tilted, cylindrical shape that is characteristic of a pool fire. The LNG pool fire was clean and brightly emissive, but pool fires of refrigerated liquid propane produced very smokey flames. Following instantaneous spills, clouds had time to spread and move with the wind away from the spill point before ignition. In these tests, combustion was mostly of the premixed type; pool fires did not occur. The highest measured flame speeds occurred during the premixed stage of combustion. In propane tests, average flame speeds of up to about 12 m/s were observed. Higher transient flame speeds, up to 28 m/s in one instance, were detected, but there was no sustained acceleration. Such acceleration could have resulted in flame speeds capable of producing damaging overpressures.

C5G06 Heat flux - kW/m2

Heat flux - kW/m2

C5G08

C5T04 Heat flux-kW/m 2

Heat flux - kW/m2

C5T03

Figure 5.1. Final contours in Coyote test no. 5, calorimeter positions and calorimeter heat-flux data (Qoldwire et al., 1983).

Spill point Stondord pontoons w i t h 4 m masts Pontoons with 10 m most* Meteorological instruments

Dike

Pipeline

Gas hoftdttAf ptoM

Figure 5.2. Setup of the Maplin Sands experiments.

Similar behavior was observed for LNG clouds during both continuous and instantaneous tests, but average flame speeds were lower; the maximum speed observed in any of the tests was 10 m/s. Following premixed combustion, the flame burned through the fuel-rich portion of the cloud. This stage of combustion was more evident for continuous spills, where the rate of flame propagation, particularly for LNG spills, was very low. In one of the continuous LNG tests, a wind speed of only 4.5 m/s was sufficient to hold the flame stationary at a point some 65 m from the spill point for almost 1 minute; the spill rate was then reduced. Radiation effects, as well as combustion behavior, were measured. LNG and refrigerated liquid propane cloud fires exhibited similar surface emissive power values of about 173 kW/m2. Zeeuwen et al. (1983) observed the atmospheric dispersion and combustion of large spills of propane (1000-4000 kg) in open and level terrain on the Musselbanks, located on the south bank of the Westerscheldt estuary in The Netherlands. Thermal radiation effects were not measured because the main objective of this experimental program was to investigate blast effects from vapor cloud explosions. Tests were performed in open terrain. Obstacles and partial confinement were also introduced (see also Section 4.1). Under unconfined conditions, flame-front

velocities were, of course, highly directional and dependent on wind speed. Flame behavior was very similar to that observed in the Maplin Sands tests for propane. Average flame-front velocities of up to 10/ms were measured. In one case, however, a transient maximum flame speed of 32 m/s was observed. Flame height appeared to be highly dependent on mixture composition: the leaner the mixture, the lower the flame height. In mixtures whose compositions were within flammability limits, flame heights were about 1-2 m. In mixtures whose compositions exceeded the upper flammability limit, average flame heights of 2-5 m were observed. Flame heights of up to 15 m were observed, but only as plumes near the point of release. Video shots showed that the combustion products do not rise vertically after generation. Rather, they flow horizontally toward existing plumes, join them, then rise. Figure 5.3 shows a moment of flame propagation in an unconfined propane cloud. On the left side, a flame is propagating through a premixed portion of the cloud; its flame is characteristically weakly luminous. In the middle of the photograph, fuel-rich portions of the cloud are burning with characteristically higher flames in a more-or-less cylindrical, somewhat tilted, flame shape.

Figure 5.3. Moment of flame propagation in a propane-air cloud (Zeeuwen et al., 1983).

5.2. FLASH-FIRE RADIATION MODELS The only computational approach found in the literature to modeling flash-fire radiation is that of Raj and Emmons (1975), who modeled a flash fire as a twodimensional, turbulent flame propagating at a constant speed. The model is based on the following experimental observations: • The cloud is consumed by a turbulent flame front which propagates at a velocity which is roughly proportional to ambient wind speed. • When a vapor cloud burns, there is always a leading flame front propagating with uniform velocity into the unburned cloud. The leading flame front is followed by a burning zone. • When gas concentrations are high, burning is characterized by the presence of a tall, turbulent-diffusion, flame plume. At points where the cloud's vapor had already mixed sufficiently with air, the vertical depth of the visible burning zone is about equal to the initial, visible depth of the cloud. The model is a straightforward extension of a pool-fire model developed by Steward (1964), and is, of course, a drastic simplification of reality. Figure 5.4 illustrates the model, consisting of a two-dimensional, turbulent-flame front propagating at a given, constant velocity S into a stagnant mixture of depth d. The flame base of width W is dependent on the combustion process in the buoyant plume above the flame base. This fire plume is fed by an unburnt mixture that flows in with velocity U0. The model assumes that the combustion process is fully convection-controlled, and therefore, fully determined by entrainment of air into the buoyant fire plume. The application of conservation of mass, momentum, and energy over the plume results in a relation between visible-flame height and the upward velocity of gases UQ at the flame base. The theoretical solution to this simplified problem is corrected on the basis of empirical data on flame heights of diffusion flames (Steward 1964). In free-burning vapor clouds, however, the upward flame-base velocity M0 is unknown. However, experimental observations indicate a nearly proportional relation between the visible flame height H and flame base width W\ namely, HIW = 2. With this empirical fact, it is possible to relate visible flame height to burning velocity S by the creation of a mass balance for the triangular area bounded by the flame front and flame base (Figure 5.4). This results in the following approximate, semiempirical expression:

(5.1) where H = visible flame height d = cloud depth S = burning speed

(m) (m) (m/s)

unburnt vapor

Figure 5.4. Schematic representation of a flammable-vapor cloud burning unconfined.

g P0 pa r where

= = = =

w =

gravitational acceleration fuel-air mixture density density of air stoichiometric mixture air-fuel mass ratio

fr

frl'i ° *>*«

a(l - <|)st)

(m/s2) (kg/m3) (kg/m3)

(5.2)

= O f or <{> ^ <()st = constant pressure expansion ratio for stoichiometric combustion (typically 8 for hydrocarbons) <|> = fuel-air mixture composition (fuel volume ratio) <|>st = stoichiometric mixture composition (fuel volume ratio)

w a

Because the Raj and Emmons (1975) expression for w cannot be applied in a straightforward manner, the expression given here differs from that recommended by Raj and Emmons (1975). It should be emphasized that w, which represents the inverse of the volumetric expansion due to combustion in the plume, is highly

dependent on the cloud's composition. If the cloud consists of pure vapor, for example, a hydrocarbon, w represents the inverse of the volumetric expansion resulting from constant-pressure stoichiometric combustion: w = 1/9. If, on the other hand, the mixture in the cloud is stoichiometric or lean, there is no combustion in the plume; the flame height is equal to the cloud depth, w = O. The behavior of the expression for w should, of course, smoothly reflect the transition from one extreme condition to the other. The model gives no solution for the dynamics of a flash fire, and requires an input value for the burning speed S. From a few experimental observations, Raj and Emmons (1975) found that burning speed was roughly proportional to ambient wind speed Uw: S = 2.3I/W Radiation effects from a flash fire are now fully determined if vapor cloud composition, as well as the geometry of the flame front (dependent on time), is known. Vapor cloud composition is, of course, place- and time-dependent, and the shape of flame front will greatly depend on cloud shape and ignition site within the cloud. The total radiation intercepted by an object equals the summation of contributions by all successive flame positions during flame propagation. This is an impossible value to compute with the simplified approach just described. Because there are many uncertainties (e.g., cloud composition, location of ignition site) which greatly influence the final result, a conservative approach is recommended for practical applications: • During flash-fire propagation, the cloud's location is assumed to be stationary, and its composition fixed and homogeneous. • The flame-surface area dependent on time is approximated by a plane crosssection moving at burning speed through the stationary cloud. The radiative power per unit area intercepted by some plane in the environment can now be computed from:

q = EF^

(5.3)

where q E F Ta

= = = =

intercepted heat radiation emissive power geometric view factor for a vertical-plane emitter atmospheric attenuation (transmissivity)

(kW/m2) (kW/m2) (-) (-)

The fundamentals of thermal radiation modeling are treated in Chapter 3. The value for emissive power can be computed from flame temperature and emissivity. Emissivity is primarily determined by the presence of nonluminous soot within the flame. The only value for flash-fire emissive power ever published in the open literature is that observed in the Maplin Sands experiments reported by Blackmore

et al. (1982). They found emissive power for both LNG and propane flash fires to be nearly equal: 173 kW/m2. Geometric view factors for circular and plane vertical emitters can be read from tables and graphs in Appendix A. The atmospheric attenuation factor takes into account the influence of absorption and scattering by water vapor, carbon dioxide, dust, and aerosol particles. One can assume, as a conservative position, a clear, dry atmosphere for which Ta = 1.

5.3. SUMMARY AND DISCUSSION Flash-fire modeling is largely underdeveloped in the literature; there are large gaps in the information base. Hardly any information is available concerning flash-fire radiation; the only data available have resulted from experiments conducted to meet other objectives. Many items have not yet received sufficient attention. The only model ever published in the literature is poor. The fact, for instance, that burning speed is taken as proportional to wind speed implies that, under calm atmospheric conditions, burning velocities become improbably small, and flash-fire duration proportionately long. The effect of view factors, which change continuously during flame propagation, requires a numerical approach. Below is a partial list of topics which need further investigation: • influence of cloud composition on emissive power of flash-fire flames; • dynamics of flash fires: dependency of flame speed and height on cloud composition, wind speed, and ground surface roughness; • a dynamic model which includes effects of nonhomogeneous cloud composition and of wind speed on cloud position; • numerical simulation. It should be possible to glean at least some pertinent data from test data already available.

REFERENCES Blackmore, D. R., J. A. Eyre, and G. G. Summers. 1982. Dispersion and combustion behavior of gas clouds resulting from large spillages of LNG and LPG onto the sea. Trans. L Mar. E. (TM). 94: (29). Goldwire, H. C. Jr., H. C. Rodean, R. T. Cederwall, E. J. Kansa, R. P. Koopman, J. W. McClure, T. G. McRae, L. K. Morris, L. Kamppiner, R. D. Kiefer, P. A. Urtiew, and C. D. Lind. 1983. "Coyote series data report LLNL/NWC 1981 LNG spill tests, dispersion, vapor burn, and rapid phase transition." Lawrence Liver more National Laboratory Report UCID-19953. VoIs. 1 and 2.

Hirst, W. J. S., and J. A. Eyre. 1983. Maplin Sands experiments 1980: Combustion of large LNG and refrigerated liquid propane spills on the sea. Heavy Gas and Risk Assessment //, pp. 211-224. Boston: D. Reidel. Hogan, W. J. 1982. The liquefied gaseous fuels spill effects program: a status report. Fuel-air explosions, pp. 949-968. Waterloo, Canada: University of Waterloo Press, 1982. Raj, P. P. K., and H. W. Emmons. 1975. On the burning of a large flammable vapor cloud. Paper presented at the Joint Technical Meeting of the Western and Central States Section of the Combustion Institute. San Antonio, TX. Stewart, F. R. 1964. Linear flame heights for various fuels. Combustion and Flame 8: 171-178. Urtiew, P. A. 1982. Recent flame propagation experiments at LLNL within the liquefied gaseous fuels spill safety program. Fuel-air explosions, pp. 929-948. Waterloo, Canada: University of Waterloo Press. Zeeuwen, J. P., C. J. M. Van Wingerden, and R. M. Dauwe. 1983. Experimental investigation into the blast effect produced by unconfined vapor cloud explosions. 4th Int. Symp. on Loss Prevention and Safety Promotion in the Process Industries. Series 80, Harrogate, UK, pp. D20-D29.

6 BASIC PRINCIPLES OF BLEVEs The phenomenon of BLEVE is discussed in this chapter. "BLEVE" is an acronym for boiling liquid, expanding vapor explosion. As indicated in Chapter 2, most BLEVEs are accompanied by fireball radiation, fragmentation, and blast effects. This chapter treats each of these effects separately. First, some general information is given. Next, effects are treated in the following order: radiation, fragmentation, and blast. Experimental investigations, theoretical approaches, and prediction methods are given for each effect. The term "BLEVE" was first introduced by J. B. Smith, W. S. Marsh, and W. L. Walls of Factory Mutual Research Corporation in 1957. Walls (1979), then with the National Fire Protection Association, defined a BLEVE as the failure of a major container into two or more pieces, occurring at a moment when the contained liquid is at a temperature above its boiling point at normal atmospheric pressure. According to Reid (1976, 1980), a BLEVE is the sudden loss of containment of a liquid that is at a superheat temperature for atmospheric conditions. A BLEVE results in sudden, vigorous liquid boiling and the production of a shock wave. Liquids normally stored under pressure have boiling points below ambient temperature. A liquid whose boiling point is above ambient temperature, but heated before release by an external heat source to a temperature above its boiling point, can also give rise to a BLEVE. The main hazard posed by a BLEVE of a container filled with a flammable liquid, and which fails from engulfment in a fire, is its fireball and resulting radiation. Consequently, Lewis (1985) suggested that a BLEVE be defined as a rapid failure of a container of flammable material under pressure during fire engulf ment. Failure is followed by a fireball or major fire which produces a powerful radiant-heat flux. In the present context, the term "BLEVE" is used for any sudden loss of containment of a liquid above its normal boiling point at the moment of its failure. It can be accompanied by vessel fragmentation and, if a flammable liquid is involved, fireball, flash fire, or vapor cloud explosion. The vapor cloud explosion and flash fire may arise if container failure is not due to fire impingement. The calculation of effects from these kinds of vapor cloud explosions is treated in Sections 4.3.3 and 5.2. A container can fail for a number of reasons. It can be damaged by impact from an object, thus causing a crack to develop and grow, either as a result of internal pressure, vessel material brittleness, or both. Thus, the container may rupture completely after impact. Weakening the container's metal beyond the point at which it can withstand internal pressure can also cause large cracks, or even

cause the container to separate into two or more pieces. Weakening can result from corrosion, internal overheating, manufacturing defects, etc. When a container is engulfed in a fire, its metal is heated and loses mechanical strength. At wetted surfaces, supplied heat is transmitted to its liquid contents, thus raising liquid temperature but keeping the wetted portion of the vessel relatively cool. The specific heat capacity of vapor, however, is far lower. Furthermore, vapor is a relatively poor heat-transfer medium. Hence, heat supplied to the tank's unwetted area (vapor space) will raise the local wall temperature, thereby weakening its metal. Jet fires may even affect the mechanical strength of the metal below the liquid level. A safety valve, even if properly designed and in working order, will not prevent a BLEVE.

6.1. MECHANISM OF A BLEVE In this section, the phenomenon of BLEVE is discussed according to theories proposed by Reid (1976), Board (1975), and Venart (1990). Reid (1979, 1980) based a theory about the BLEVE mechanism on the phenomenon of superheated liquids. When heat is transferred to a liquid, the temperature of the liquid rises. When the boiling point is reached, the liquid starts to form vapor bubbles at active sites. These active sites occur at interfaces with solids, including vessel walls. Boiling in the bulk of the fluid generally takes place at submicron nucleation sites as impurities, crystals, or ions. When there is a shortage of nucleation sites in the bulk of the liquid, its boiling point can be exceeded without boiling; then the liquid is superheated. There is, however, a limit at a given pressure above which a liquid cannot be superheated, and when this limit is reached, microscopic vapor bubbles develop spontaneously in the pure liquid (without nucleation sites). The maximum superheat temperature for a material under a given pressure can be found in pressure-volume diagrams. The superheated liquid state for a certain isotherm is represented in Figure 6.1 by the dashed line starting at V1, P1. The superheat state can, however, only be extrapolated to a value of P and V where dP/dV at constant temperature becomes zero. Following the isotherm with increasing volume implies an increasing pressure, which is physically unrealistic. The superheat temperature limit T1 occurs at a pressure P1 (Figure 6.1). The locus of values where (dP/dV)T equals zero is called the spinodal curve (Reid 1976). The superheat limit temperature can be calculated from thermodynamics when the equation of state is known. According to Reid (1976), however, there is no satisfactory correlation among P, V9 and T in the superheated liquid region. Opschoor (1974) applied the Van der Waals equation of state to estimate the maximum superheat temperature for atmospheric pressure (rsl) from the critical temperature (rc) (i.e., that temperature above which a gas cannot be liquefied by pressure alone) as follows: T81 = 0.84rc

(6.1.1)

vapor phase liquid phase

Figure 6.1. Pressure-vapor diagram of a typical material (Reid 1976).

Reid (1976) used the equation-of-state of Redlich-Kwong, which predicts a superheat limit temperature of: Tsl = 0.895!TC

(6.1.2)

Reid (1976) further determined that the superheat temperature limit for "a wide range of industrial compounds" falls within the narrow interval of 0.89rc to 0.907C. Reid (1976) and many other authors give pure propane a superheat temperature limit of 530C at atmospheric pressure. The superheat temperature limit calculated from the Van der Waals equation is 380C, whereas the value calculated from the Redlich-Kwong equation is 580C. These values indicate that, though an exact equation among P9 V9 and T in the superheat liquid region is not known, the Redlich-Kwong equation of state is a reasonable alternative. The superheat-temperature-limit locus for propane is plotted by Reid (1979) in a PJ-diagram together with the vapor pressure (Figure 6.2). When the liquid is heated, for example, from A to B, a sudden drop in pressure to 1 atmosphere (C)

TABLE 6.1. Boiling Point, Critical Temperature and Pressure, and Measured Superheat-Temperature Limits and Pressures for Some Industrial Fuels8 Superheat Limit

Critical Fuel Propane n-Butane lsobutane 1 ,3-Butadiene Vinyl chloride Ethane n-Pentane n-Hexane Water a

Temp. (K)

Press, (bar)

Temp. (K)

Press, (bar)

370 426 407 425 429 305 469 507 647

43.6 36.5 37.5 37.6

326 377 361 377 374 269 421 457 553

18.3 16.6 15.5 18.5

—

49.0 33.4 29.9 218

—

21.7 15.4 13.7 64.1

Normal Boiling Temp. (K) 231 272 261 269 260 184 309 342 373

From Handbook of Chemistry & Physics, 69th ed; NB: 1 bar = 14.5 psi.

will cause the liquid to be superheated to a temperature below the superheattemperature limit. In this case, no shock wave will be generated by the vaporization. When, on the other hand, the liquid is heated to temperature D, a drop in pressure to atmospheric will cross the superheat-temperature-limit curve at E, and, at this point, the liquid-vapor system will explode. For any situation below point D on the vapor pressure curve, sudden reduction to atmospheric pressure will not lead

PRESSURE (aim)

CRITICAL POINT

SUPERHEAT UMlT LOCUS

TEMPERATURE(0C) Figure 6.2. Pressure-vapor curve and superheat limit locus for propane (Reid 1979).

to a BLEVE with a strong shock wave because, since the superheat-temperaturelimit curve is not reached, the liquid does not flash explosively. Another theory of liquid-liquid explosion comes from Board et al. (1975). They noticed that when an initial disturbance, for example, at the vapor-liquid interface, causes a shock wave, some of the liquid is atomized, thus enhancing rapid heat transfer to the droplets. This action produces further expansion and atomization. When the droplets are heated to a temperature equal to the superheat temperature limit, rapid evaporation (flashing liquid) may cause an explosion. In fact, this theory resembles the theory of Reid (1979), except that only droplets, and not bulk liquid, have to be at the superheat temperature limit of atmospheric pressure (McDevitt et al. 1987). Venart (1990) suggests that intermittent pressurization by external heat in a fire-induced BLEVE and subsequent depressurization by the pressure-relief device causes incipient vapor nuclei to form within the liquid. Rapid depressurization to atmospheric pressure then generates a vaporization wave in the now-superheated liquid. This phenomenon causes rapid growth of vapor-bubble nuclei. The twophase fluid is first atomized into a fine aerosol, then vaporized quickly through efficient transfer of heat from air to the aerosol droplets. Ignition of this vapor-air mixture, if the substance is flammable, results in a rapid deflagration, sometimes giving rise to blast generation. The formation of droplets and their rapid, efficient vaporization is the reason that there is more vapor in the cloud than the amount which flashed off originally. Schmidli et al. (1990) determined that 5 to 50% of the mass of the original fuel can be found in droplets. This value depends upon initial mass and degree of superheat, that is, amount by which the fuel's temperature exceeds its boiling point. A theory that adequately explains all BLEVE phenomena has not yet been developed. Reid's (1979, 1980) theory seems to be a good approach to explain the strong blast waves that may be generated. But even when a liquid's temperature is below the superheat limit, the liquid may "flash" within seconds after depressurization, resulting in a blast wave, a fireball, and fragmentation. A BLEVE can cause damage from its blast wave and from container fragments; such fragments can be propelled for hundreds of meters. If the vapor-air mixture is flammable, the BLEVE can form a fireball with intense heat radiation. Each effect is discussed in the following sections.

6.2. RADIATION This section covers radiation due to BLEVEs with accompanying fireballs. First, a brief description is given of experimental investigations of BLEVEs and their fireballs. Next, some fireball models, primarily for predicting fireball diameter and combustion duration, are presented. Most of these models evolved from experimental results. Finally, some radiation models, based on experiments and theory, are given.

6.2.1. Experimental Investigations Small-Scale Experiments

maximum diameter (cm)

burnout time (sec)

Four parameters often used to determine a fireball's thermal-radiation hazard are the mass of fuel involved and the fireball's diameter, duration, and thermal-emissive power. Radiation hazards can then be calculated from empirical relations. For detailed calculations, additional information is required, including a knowledge of the change in the fireball's diameter with time, its vertical rise, and variations in the fireball's emissive power over its lifetime. Experiments have been performed, mostly on a small scale, to investigate these parameters. The relationships obtained for each of these parameters through experimental investigation are presented in later sections of this chapter. Small-scale experiments with fireballs have been carried out by a number of investigators, and can be roughly divided into two categories. The first includes experiments in which a spherical gas-air mixture contained by a thin envelope at ambient pressure was released, then ignited (soap bubble experiments). The second category includes BLEVE simulation, in which a pressurized, heated flask containing liquid or liquefied fuel is broken after the desired vapor pressure has been reached, and the released vapor is then ignited. Measurement of fireball diameter, liftoff time, combustion duration, and final height is captured by filming with high-speed cameras. Radiometers are used to measure radiation; and temperature is measured by thermocouples or by determination of fireball color temperature (Lihou and Maund 1982). Fay and Lewis (1977) used spherical gas samples inside soap bubbles whose volumes ranged from 20 to 190 cm3. Typically, a sphere was ignited with resistance wire, and the combustion process was then filmed with a high-speed camera. The fireball's maximum height and diameter, as well as the time needed to complete combustion, were evaluated. The fireball's thermal radiation was sensed by a radiation detector. Figure 6.3 relates fireball burning time and size to initial propane

vapor volume cm 3

vapor volume cm3

Figure 6.3. Burning time (fp) and maximum fireball diameter (D) as function of initial fuel volume (Vv) of propane (Fay and Lewis 1977).

volume. Correlations, which will be covered later, have been developed for such results. Hasegawa and Sato (1977) used hermetically sealed, spherical glass vessels, each filled with n-pentane and containing an electric heater and a thermocouple for liquid-temperature measurement. After sufficient warmup, a vessel was broken with a remote-controlled hammer. The unconfined vapor cloud that formed after vessel rupture was ignited by a flame placed at a distance of 1 m from the vessel's center. The amounts of pentane charged ranged from 0.3 to 6.2 kg. Temperatures were varied from 4O0C to 1120C, corresponding to vapor pressures of 0.1 to 0.77 MPa. All temperatures were below the superheat limit, which, for w-pentane, is about 1480C. The combustion process was filmed with a high-speed camera. After vessel rupture, the superheated liquid vaporized in a white cloud consisting of vapor and fine droplets. After ignition, the flame propagated through the cloud, forming a fireball. Fireball size increased as combustion proceeded, and the fireball was lifted by gravitational buoyancy forces. The amount of liquid that will evaporate can be calculated if it is assumed that all heated liquid will be exposed to air (see Section 6.3.3.3). Results of calculations can then be compared with experimental results. When the calculated percentage of flash evaporation exceeded 36%, all fuel became an aerosol for fireball formation. At lower percentages, a portion of the fuel formed the fireball, and the remainder former a pool fire on the ground. Thus, these results imply that, when calculated flash evaporation is less than 36% of the available fuel, fuel in the fireball can be expected to amount to approximately three times the amount of flashed vapor. Hasegawa and Sato analyzed motion pictures and radiation measurements at a distance of 15 m from the center of the glass vessel. They then correlated, first, fireball duration and maximum diameter to initial fuel mass and, second, radiation to initial vapor pressure. Lihou and Maund (1982) used soap bubbles filled with flammable gas which were blown on the bottom of a "fireball chamber" to form fireballs. A hemispherical bubble was formed on a wire mesh 200 mm above the base of the measuring chamber in order to permit study of elevated sources. The gas bubble was ignited by direct contact with a candle flame, and the combustion process was filmed at a speed of 64 frames per second. The fireball's color temperature was measured. Lihou and Maund (1982) carried out two series of experiments (Figure 6.4). One series involved butane-filled bubbles whose masses ranged from 1.5 to 6 g. The second series was performed with methane and butane in volumes ranging from 100 to 800 ml. (For methane, this corresponds to a mass range from 0.07 to 0.6 g, and for butane, from 0.24 to 1.9 g.) Measured temperatures ranged from 1000 K to 1400 K for butane fireballs, and from 1100 K to 1700 K for methane fireballs. Hardee et al. (1978) investigated pure methane and premixed methane-air fireball reactions. They used balloons filled either with 0.1 to 10 kg pure methane, or else with stoichiometric air-methane mixtures. The balloons were cut open just prior to ignition. Integrating heat-flux calorimeters, located either inside the balloons or at their edges, were used to measure the thermal output.

temperature K

time from ignition seconds

max measured max temp, measured mean temp.

elevation m

mean

measured elevation

equipment diameter m

wire mesh level

calculated from measurements predicted from model

Figure 6.4. Typical test results for a 400-ml butane fireball (Lihou and Maund, 1982), where D0 = initial diameter of gas sphere; DI = diameter of fireball at liftoff (at time J1); Dc = diameter at end of combustion (duration tc).

Experiments by Schmidli et al. (1990) were focused on the distribution of mass on rupture of a vessel containing a superheated liquid below its superheattemperature limit. Flasks (50-ml and 100-ml capacity) were partially filled with butane or propane. Typically, when predetermined conditions were reached, the flask was broken with a hammer. Expansion of the unignited cloud was measured by introduction of a smoke curtain and use of a high speed video camera. Large droplets were visible, but a portion of the fuel formed a liquid pool beneath the flask. Figure 6.5 shows that, as superheat was increased, the portion of fuel that

formed a pool decreased, with a corresponding increase in the droplet-forming portion. An additional important quantitative result of these experiments is that, after the rupture, droplets large enough to be captured by camera (2.8 to 3.5 mm) were thrown outward with velocities up to 3.6 m/s, a rate much faster than the velocity of the vapor cloud front. Large-Scale Experiments

5OmI, filled 5OmI. 1/2 filled 100ml, filled 10OmI, 1/2 filled

5OmI, filled 5OmI. 1/2 filled 10OmI. filled 100ml, 1/2 filled

Aerosol

Fraction

50ml, filled 5OmI. 1/2 filled 10OmI, filled 10OmI, 1/2 filled

In view of the results from these small-scale experiments, and the increasing number of severe accidents involving large masses of fuel, there is a clear need for largescale or full-scale experiments. Few large-scale test results are available, however. Table 6.3 gives an overview of some fireball experiments performed to date. Although the experiments reported by Maurer et al. (1977) were performed for a completely different reason, namely, to study effects of vapor cloud explosions (see Section 6.4), fireballs were nevertheless generated. These experiments involved vessles of various sizes (0.226-1000 1) and containing propylene at 40 to 60 bar gauge pressure. The vessels were ruptured, and the released propylene was ignited after a preselected time lag. One of these tests, involving 452 kg of propylene, produced a fireball 45 m in diameter. Hardee and Lee (1973) reported some experimental data on tests run on propane fireballs containing propane masses of 1 kg, 29 kg, and 454 kg, and with approxi-

Pool Vapour

Superheat ( 0 C) Figure 6.5. Fraction of pool and aerosol mass generated after loss of containment of small vessels containing CFC 114, depending on degree of superheat and degree of filling (Schmidli etal. 1990).

mately 100% excess air in the fuel-air mixtures. Total incident heat within the fireballs was measured. Data points have been given only in graphs. High (1968) reported data on fireball size for several rocket propellant systems. Data were available for a kerosene type of fuel, liquid hydrogen, and liquid oxygen. Maximum fireball diameter was expressed as a function of the total weights of fuel and oxygen. For consistency in this volume, fireball diameters are expressed as a function of fuel mass only. If a stoichiometric mixture of fuel and oxygen is assumed, it is possible to convert High's data. High used amounts of fuel ranging from 1 kg up to 5000 kg (Lihou and Maund 1982). British Gas conducted full-scale experiments on the effects of BLEVEs from both standard- and extended-size containers. These experiments involved 1000 or 2000 kg of butane or propane released under a pressure of 6 to 15 bar gauge (Johnson et al. 1990). Contents of a vessel were adjusted so that release mass, release pressure, and fill ratio were all known at the moment of release. The vessel was ruptured by detonation of a linear-shaped explosive charge placed upon its top. Detonation resulted in a fracture which propagated along the vessel wall, resulting in its catastrophic failure. Fixed ignition sources placed at distances of 2 and 5 m from the vessel ignited the released fuel. Instrumentation for the experiments consisted of video and high speed movie cameras, radiometers, thermocouples, and pressure transducers. Results have been presented on one experiment. It involved a 5.659-m3 vessel containing 1000 kg of butane with a fill ratio of 39%. The vessel's contents were heated to 990C, which is near but still below the superheat-limit temperature, producing an internal pressure of 14.6 bar gauge. Vessel failure was then initiated. Measured pressure-time histories indicated that a number of separate pressure pulses occurred. They are plotted in Figure 6.6 as the overpressure-time relationship measured at 25 m from the vessel. The thermal flux recorded by a radiometer 50 m from the vessel is shown in Figure 6.7; it indicates a peak value of 66 kW/m2. The total heat dosage at this point was 115 kJ/m2, and the duration of the fireball was about 4 seconds. Table 6.2 presents an overview of surface-emissive powers measured in the British Gas tests, as back-calculated from radiometer readings. Peak values of surface-emissive powers were approximately 100 kW/m2 higher than these average values, but only for a short duration. Other large-scale tests include those conducted to investigate the performance of fire-protection systems for LPG tanks. Anderson et al. (1975) presents results of an experiment with an unprotected, fully loaded 125-m3 railroad tank car fully engulfed by fire. Although a BLEVE occurred (after 24.5 minutes of exposure), no data on the resulting fireball were presented. The German Federal Institute for Material Testing (BAM) carried out full-scale fire tests on commercial liquefied-propane storage tanks. Tank volume was 4.85 m3 in each test (Schoen et al. 1989; Droste and Schoen 1988; Schulz-Forberg et al. 1984). Unprotected and protected tanks filled with propane (50% filled) were exposed to a fire. In some tests, the propane was preheated.

o v e r P r e s s

combustion

second shock

U

r

e m b a_ r

incident flux kW/m2

Figure 6.6. Overpressures measured at 25 m from a butane-tank BLEVE (Johnson et al. 1990).

times Figure 6.7. Variation of incident radiation with time at 50 m from a BLEVE of a butane tank (Johnson et a). 1990).

TABLE 6.2. Average Surface-Emissive Powers Measured in the Tests Performed by British Gasa

Test No. 1 2 3 4 5

Fuel

Mass (kg)

Release Pressure (bar)

Average SurfaceEmissive Power (kW/m2)

butane butane butane butane propane

2000 1000 2000 2000 2000

15 15 7.5 15 15

370 350 320 350 340

• From Johnson et a!. (1990).

The aim of the tests was to study tank-wall performance. Nevertheless, a few data on BLEVE effects are presented by Schulz-Forberg et al. (1984). An overpressure of 130 mbar was measured at 80 m from the tank position in one of the tests, and was attributed to combustion. Temperatures and pressures at the moment of tank failure were beyond the superheat limit: 345-357 K and 24-39 bar, respectively (see propane data in Table 6.1). Fireball development from one test is presented in a series of photographs. The maximum diameter was approximately 50 m, and duration was approximately 4 seconds. Fragmentation data, to the extent published, are given in Section 6.3. Experiments show that emissive power depends on fireball size. Moorhouse and Pritchard (1982) present a graph of the relationship of fireball size and emissive power from results obtained by several investigators, among them, Hasegawa and Sato data from both 1977 and 1987. Figure 6.8 presents the Moorhouse and Pritchard (1982) graph to which the data from Johnson et al. (1990) have been added. The radiation from a black body is proportional to the fourth power of the adiabatic flame temperature, according to the Stefan-Boltzmann's law: £max =
(6.2.1) u

where the proportionality constant a = 5.67 X 10~ kW/m /K (1.71 X 10~9 Btu/h/ft2/R4. The emissive power of a fireball, however, will depend on the actual distribution of flame temperatures, partial pressure of combustion products, geometry of the combustion zone, and absorption of radiation in the fireball itself. The emissive power (E) is therefore lower than the maximum emissive power (En^) of the black body radiation: E = CE102x

2

4

(6.2.2)

where € is called the emissivity. The larger a fireball is, the stronger the absorption. An increase in absorption implies an increase in emissivity. Based on Beers's law, the following expression

for emissivity can be derived: € = 1 - exp(-*£>)

(6.2.3)

where € = emissivity k = extinction coefficient D = fireball diameter

(-) (m"1) (m)

For methane-air fireballs, Hardee et al. (1978) found an E^ of 469 kW/m2. If an extinction coefficient of k = 0.18 m"1 (as measured in LNG fires) is used, the curve shown in Figure 6.8 can be obtained from the equations given by Hardee et al. (1978). Equation (6.2.3) overstates emissivity as determined through experiments. Possible explanations are • the curve is only valid for methane; • emissive power is reduced by soot; • experimental results vary because fireball shapes are not spherical. The curve, however, seems to indicate the tendency of a fireball's emissive power to rise as its diameter grows. The results of the experiments described above reveal that the fireball properties of greatest influence on radiation effects are: Fay

+

Hardee

Johnson

Emissive Power (kW/m2)

Haseg.

Maxmrxm Fireball Diameter (m)

Figure 6.8. Influence of fireball diameter on emissive power. (—-): predictive curve for methane (Hardee et al. 1978).

TABLE 6.3. Overview of Experimental Research on Fireball Generation Fuel Mass Reference

Containment

mf (kg)

Fireball Duration Us)

Fireball Diameter

Fuels

20-190 (cm3)

0.4-0.8

0.2-0.7

32 20

Dc(m)

Emiss. Power kW/rn2

Fay and Lewis 1977

Soap bubble

CH4 C2H6

Hardeeetal. 1978

Polyethylene bags

CH4

0.1-1

1.8-2.4

1.5-2.2

123

Hasegawa and Sato 1977, 1987

Glass sphere pressurized

^sH12

0.3-30

0.8-1.7

2.7-15

110-413

Lihou and Maund 1982

Soap bubbles

^H1Q CH4

1.5-6(g)

0.5-1.0 0.4-0.7

0.4-0.8 0.3-0.6

Maureretal. 1977

Pressurized tank

C3H6

0.1-452

-1.5

-40

Baker: in Roberts 1982

Pressurized tanks

LPG

7.5-14.5

1.0-1.4

12-15

Johnson et al. 1990

Pressurized tanks

^H10 C3H8

1000-2000

4.5-9.2

56-88

320-375

• fireball diameter as a function of time and maximum diameter; • height of fireball center above its ignition position as a function of time elapsed after liftoff; •fireballsurface-emissive power; • total combustion duration. The total radiation received by an object also depends on the fireball's position relative to the object (i.e., the view factor) and radiation adsorption by the atmosphere.

6.2.2. Fireball Diameter and Duration Empirical Formula for Fireball Diameter and Duration Several authors have published empirical equations from experiments and from theoretical considerations combined with experimental results. The equations describe fireball combustion duration and maximum diameter as functions of original fuel mass. Table 6.4 presents a summary of published results. An average value is presented by the publications of Roberts (1982), Jaggers et al. (1986) and Pape et al. (1988), who gave the following equations: Dc = 5.8mJ/3

(6.2.4)

and tc = 0.45mJ/3

for mf < 30,000 kg

(6.2.5a)

tc = 2.6m}16

for m f > 30,000 kg

(6.2.5b)

where Dc = maximum diameter of fireball (at end of combustion phase) mf = mass of fuel tc = combustion duration

(m) (kg) (s)

Because the preceding equations also reflect the average of the previous empirical formulas, they are recommended for use in predicting maximum fireball diameter and fireball combustion duration. Fireball Diameter Models A fireball's radiation hazard can be assessed by two factors: its diameter (either as a function of time or original amount of fuel) and combustion duration. Fireball models presented by Lihou and Maund (1982), Roberts (1982), and others start with a hypothetical, premixed sphere of fuel and air (in some cases, oxidant) at ambient temperature. Because the molar volume of any gas at standard conditions

TABLE 6.4. Empirical Relationship of Duration to Final Diameter of Fireball [Constant Initial Fuel Mass mf(kg)]

Reference LJhou and Maund 1982 Duiser 1985 Fay and Lewis 1977 Hasegawa and Sato 1977 LJhou and Maund 1982 LJhou and Maund 1982 Roberts 1982 Williamson and Mann 1981 Moorhouse and Pritchard 1982 LJhou and Maund 1982

Fuels Rocket fuel C3H8 ^sH12 C3H6 CH4

C3H8

Pietersen 1985 Pitblado 1985 (1) mfo = mass of fuel and oxidant. (2) mf = mass of kerosene in stoichiometric mixture with oxygen. (3) m'f = m/Mf, where M1 is the molecular weight of the fuel.

Data Source High 1968 Raj 1977 Experiments Experiments Maurer et al. 1977 Hardeeetal. 1978 Literature and model Bader 1971; Hardee and Lee 1973 Data of Hasegawa and Sato 1977 Maurer et al. 1977

Literature Literature

Fireball Duration (s)

Fireball Diameter (m)

0.30mfo°320(1)

3.86mfo°-320(1) 6.20mf°-320 (2) 5.45mf1-3 6.28mf1/3 5.28mf0277 3.51mf1/3 6.36mf0325 5.8mf1/3 5.88mf1/3 5.33mf0327 12.2m'f1/3 (3) 3.46mf1/3 6.48mf0325 6.48mf0325

0.49mf° 32° (2) 1.34mf1/6 2.53mf1/6 1.1OAHf0'097

0.32mf1/3 2.57mf0167 0.45A77f1/3

1.09mf1/6 1.09mf0327 1.1 Om V3 (3) 0.31 mf173 0.825mf026 0.825mf026

(O0C and 1 atm) is a constant, if vapor is treated as a ideal gas, the initial diameter of the vapor sphere (D0) can be calculated from the released mass of fuel and air (mf + ma) and the ambient temperature (T3) by: (6.2.6) where M = average molecular weight of fuel-air mixture VM = mol volume at 273 K and atmospheric pressure (i.e., 22.4m3/kmol) Ta = initial (ambient) temperature mf = mass of fuel ma = mass of air D0 = initial sphere diameter

(kg/kmol) (K) (kg) (kg) (m)

When the initial sphere consists only of vapor, the value of /na must be taken as zero, and M equals the molecular weight of the fuel. Most models are tested with low-molecular-weight alkanes. Isothermal Model A fireball is assumed to burn with a constant temperature Tc in the isothermal fireball model of Lihou and Maund (1982). Combustion is controlled by the supply of air and ceases after a time tc, which is correlated empirically with the mass of flammable gas in the initial vapor sphere. It is assumed that a fraction (1 — fc) of the fuel is used to form soot, and the remaining fraction/c burns stoichiometrically, producing an increase of n{ moles per mole of flammable gas. The stoichiometric molar ratio of air to flammable gas is |x and dVldt is the volumetric rate of air entrainment. The rate of increase of volume can now be written as: (6.2.7) where D Tc Ta dDldt dVJdt JJL H1

= = = =

diameter temperature of fireball temperature of ambient air rate of increase of fireball diameter (kept constant by most modelers) = rate of air entrainment = stoichiometric molar fuel-air ratio = increase in total number of moles per mole of flammable gas

(m) (K) (K) (m/s) (m3/s) (-) (-)

The rate of combustion is set equal to the rate of heat applied to warm the entrained air plus the radiative heat losses: (6.2.8) where Stefan-Boltzmann constant (5.67 x 1(T11 kW(m2K4)) emissivity mol volume (i.e., 22.4 nrVkmol) molecular weight of fuel molecular weight of air lower heat of combustion of fuel (i.e., combustion heat minus heat of evaporation of formed water) Cp3 = specific heat of air at constant pressure

a e VM M Ma hc

= = = = = =

(kW/m2K4) (-) (m3/kmol) (kg/kmol) (kg/kmol) (kJ/kg) [kJ/(kgK)]

When substituting dVJdt from Equation (6.2.7), the following equation for the temperature of the fireball is derived: (6.2.9) The final diameter of the fireball Dc (m) is given by: (6.2.10) where mf is the mass of the initial fuel in kilograms. By using the duration time of combustion as recommended by Roberts (1982): tc = 0.45/n^3

(6.2.11)

the rate of increase of diameter (dDldt) is given by (6.2.12) When the four previous equations are combined with the relation for the initial diameter of the sphere (D0) [Eq. (6.2.6)], the fireball's temperature and maximum diameter can be calculated. From this model, it follows that the temperature of the fireball, and thus its emissive power, is independent of initial fuel mass. From measurements of rising fireballs, Lihou and Maund (1982) found that the velocity of rise equals the rate of increase of the diameter, and that, for methane and butane, dDldt is close to 10 m/s. They therefore suggest a simple relationship to calculate the height z (m) of the fireball: z = 1Or where zc is the final height (m).

and thus

zc = 10rc

(6.2.13)

The initial cloud fraction used to form soot (1 — /c) can be estimated as the ratio of heat of formation to heat of combustion (Lihou and Maund 1982). For propane, heat of combustion hc = 46300 kJ/kg and/c = 0.95. With an emissivity of e = 1, the following expressions for fireball diameter and duration can be given: Tc = 193OK,

Dc = 5.70<3

and

tc = QA5mlf/3

The temperature for methane and butane calculated with the isothermal model is a factor 1.4 times greater than the average temperature measured by Lihou and Maund (1982) in their small-scale tests, although higher local maximum temperatures were measured. In this model, combustion is stoichiometric, thus leading to very high fireball temperatures which, in turn, lead to high radiation emissions. Effective surface emissions measured experimentally were one-half the value calculated from this model, because combustion is not stoichiometric and emissivity is less than unity. Roberts' Model Roberts (1982) uses a fireball's heat production to calculate its final diameter. Roberts assumes that, at the moment of maximal fireball size, the total increase in enthalpy can be related to the initial mass ratio of fuel to air. If R = ma/mf for a stoichiometric mixture, the enthalpy rise (H) can be approximated by H = (^mahc)/R

for ma ^ Rmf

(6.2.14)

H = (T}mfhc)/R

for ma > Rmf

(6.2.15)

and

where hc = heat of combustion TJ = thermal efficiency that recognizes fuel losses and unburned fuel (TI < 1) R = mass ratio of fuel-air mixture (ma/mf)

(kJ/kg) (-) (-)

Now, the maximum diameter of the fireball can be written: (6.2.16) where P0 = density of combustion products at initial temperature T0 Cp = average specific heat of mixture considered to be constant from T0 to maximum fireball temperature

(kg/m3) (kJ/kgK)

If mJRmf = 1 and t] = 1, the diameter Dc for a stoichiometric combustion equals the empirical relation cited by Pape et al. (1988), namely, Dc = 5.8m1/3. According to Roberts (1982), the factor TJ lies between 0.75 and 1. This model also produces a high temperature for combustion of a stoichiometric mixture of fuel and air, because it assumes that all combustion energy contributes to the increase in enthalpy and neglects energy lost by radiation. However, for an air/fuel ratio of 1.5 to 2 and with TJ = 0.75, the fireball temperature approximates that measured by Lihou and Maund (1982). 6.2.3. Fireball Liftoff Time Few investigators have considered fireball liftoff time. According to Roberts (1982), a fireball starts liftoff in the third phase of its development, that is, when buoyancy and entrainment are dominant. Hardee and Lee (1978) give the following expression for liftoff time tlo: tlo = \.\m\16

(6.2.17)

This is consistent with data published by High (1968). Because liftoff is buoyancycontrolled, its relation to initial mass must have a power of 1/6, as shown by a fireball model of Fay and Lewis (1977). In general, hazard calculations assume that fireballs are spherical and touch the ground. Liftoff is not considered further in this volume. 6.2.4. Fireball Fuel Content Hasegawa and Sato (1977) showed that, when the calculated amount of flash vaporization equals 36% or more, all released fuel contributes to the BLEVE and eventually to the fireball. For lower flash-vaporization ratios, part of the fuel forms the BLEVE, and the remainder forms a pool. It is assumed that, if flash vaporization is below 36%, three times the calculated quantity of the flash vaporization contributes to the BLEVE. Small-scale experiments by Schmidli et al. (1990) showed that, as degree of superheat increases, the quantity of fuel forming a pool decreases and droplet formation increases. These results support the proposition that more fuel is involved in a BLEVE than calculated from flash evaporation. For hazard prediction purposes, the amount of gas in a BLEVE can be assumed to be three times the amount of flash evaporation, up to a maximum of 100% of available fuel. 6.2.5. Fireball Radiation The main hazard from a BLEVE fireball is its thermal radiation, which can cause secondary fires and can burn people severely. Rapid mixing, combustion, and

evaporation of fuel droplets produce a fireball whose thermal emission exceeds normal flame emissions. Methods for calculating radiation from fires and fireballs are described in Section 3.5. Section 3.5 mentions two approaches, the point-source model and the solidflame model. In the point-source model, it is assumed that a certain fraction of the heat of combustion is radiated in all directions. This fraction is the unknown parameter of the model. Values for fireballs are presented in Section 3.5.1. The pointsource model should not be used for calculating radiation on receptors whose plane intercepts the fireball (see Figure 6.9B). The solid-flame model, presented in Section 3.5.2, is more realistic than the point-source model. It addresses the fireball's dimensions, its surface-emissive power, atmospheric attenuation, and view factor. The latter factor includes the object's orientation relative to the fireball and its distance from the fireball's center. This section provides information on emissive power for use in calculations beyond that presented in Section 3.5.2. Furthermore, view factors applicable to fireballs are discussed in more detail.

fireball

receptor

fireball

receptor

Figure 6.9. Geometry of a radiative sphere (fireball). (A) receptor "sees" the whole fireball. (B) receptor "sees" part of the fireball.

6.2.5.1. Hymes Point-Source Model Hymes (1983) presents a fireball-specific formulation of the point-source model developed from the generalized formulation (presented in Section 3.5.1) and Roberts's (1982) correlation of the duration of the combustion phase of a fireball. According to this approach the peak thermal input at distance L is given by (6.2.18) where m{ T8 /fc R L q

= = = = = =

mass of fuel in the fireball atmospheric transmissivity net heat of combustion per unit mass radiative fraction of heat of combustion distance from fireball center to receptor radiation received by the receptor

(kg) (-) (J/kg) (-) (m) (W/m2)

Hymes suggests the following values of R: R =0.3; fireballs R = 0.4; fireballs

for vessels bursting below relief valve pressure for vessels bursting at or above relief valve pressure

6.2.5.2. Solid Flame Model The incident radiation per unit time is given by: q = FEr3

(6.2.19)

where F is the view factor and E is emissive power per unit area in watts per square meter. Emissive Power. Pape et al. (1988) used data of Hasegawa and Sato (1977) to determine a relationship between emissive power and vapor pressure at time of release. For fireballs from fuel masses up to 6.2 kg released at vapor pressures to 20 atm, the average surface-emissive power E can be approximated by E = 235/*39 (kW/m2)

(6.2.20)

where Pv is the vapor pressure in MPa. This equation is limited to vapor pressures at release time at or below 2 MPa, and thus to surface-emissive powers at or below 310 kW/m2. As previously described, full-scale BLEVE experiments by British Gas (1000 and 2000 kg of butane and propane released at 0.75 and 1.5 MPa) give average

surface-emissive powers of 320 to 370 kW/m2, respectively (Johnson et al. 1990). These values are somewhat lower than the maximum emissive powers measured in small-scale experiments. A reduction in emissive power as scale increased was also found in pool fires. A reasonable emissive power associated with large-scale releases of hydrocarbon fuels seems to be 350 kW/m2. The values obtained by British Gas were back-calculated from radiometer readings (see Section 6.2.1). View Factor. The view factor of a point on a plane surface located at a distance L from the center of a sphere (fireball) with radius r depends not only on L and r, but also on the orientation of the surface with respect to the fireball. If 2 is the view angle, and © is the angle between the normal vector to the surface and the line connecting the target point and the center of the sphere (see Figure 6.9), the view factor (F) is given by (6.2.21) and

(6.2.22) where r D L &

= = = =

radius of fireball (r = D/2) diameter of fireball distance to center of sphere angle between normal to surface and connection of point to center of sphere 24> = view angle

(m) (m) (m) (radians) (radians)

In Figure 6.9B, the extended surface intersects the sphere in such a way that a point on that surface will "see" only a portion of the sphere. In the general situation, a fireball center has a height (H) above the ground (H ^ D/2). The distance (X) is measured from a point at the ground directly beneath the center of the fireball to the receptor at ground level (Figure 3.11). For a horizontal surface, the view factor is given by (6.2.23) When the distance (X) is greater than the radius of the fireball, the view factor for

a vertical surface can be calculated from

and for a vertical surface underneath the fireball (X < D/2) the view factor is given by

(6.2.24)

where r = radius of fireball (r = D/2) H = height of center of fireball X = distance along ground between receptor and a point directly beneath center of fireball

(m) (m) (m)

In most cases, the BLEVE fireball is assumed to touch the ground (zc = D/2). The center height of a rising fireball depends on time. To calculate radiation received, radiation must be integrated over combustion time: a time-dependent height and diameter (giving a time-dependent view factor) must be used. For large-scale BLEVEs, the assumption that the fireball is at its maximum diameter and "rests" on the ground will yield a somewhat conservative prediction of thermal radiation hazard. However, note that the initial hemispherical shape of the developing fireball could engulf a large area of the ground causing direct flame contact hazard. 6.2.5.3. Alternative Empirical Equation for Radiation Received by an Object Roberts (1982) also used the data of Hasegawa and Sato (1977) to correlate the measured radiation flux q received by a detector at a distance L (m) from the center of the fireball with the hydrocarbon fuel mass mf (kg): q = 828 /nj?-771 L~2

(kW/m2)

(6.2.25)

6.2.6. Hazard Distances Hazard distances from a fireball or a BLEVE-fireball depend on the damage level of radiation that the receptor(s) can be permitted to receive. For structures, this

TABLE 6.5. Exposure Time to Reach the Pain Threshold (API 521, 1982) Radiation Intensity (Btu/hr/fi2) 500 740 920 1500 2200 3000 3700 6300

(kW/m2)

Time to Reach Pain Threshold (s)

1.58 2.33 2.90 4.73 6.94 9.46 11.67 19.87

60 40 30 16 9 6 4 2

level is the energy that will ignite wood or other combustible materials. For people, three levels can be distinguished: threshold of pain, second-degree burns, and thirddegree burns. Thermal effects depend on radiation intensity and duration of radiation exposure. American Petroleum Institute's Recommended Practice 521 (1982) reviews the effects of thermal radiation on people. In Table 6.5, data on time to reach pain threshold are given. As a point of comparison, the solar radiation intensity on a clear, hot summer day is about 1 kW/m2 (317 Btu/hr/ft2). Criteria for thermal damage are shown in Table 6.6 (CCPS, 1989) and Figure 6.10 (Hymes 1983). Lihou and Maund (1982) based their radiation limit on the work of Stoll and Quanta (1971). The average heat-flux density q2 which will cause severe blistering TABLE 6.6. Effects of Thermal Radiation Radiation Intensity (kW/m2)

Observed Effect

37.5

Sufficient to cause damage to process equipment Minimum energy required to ignite wood at indefinitely long exposures

12.5

Minimum energy required for piloted ignition of wood, melting of plastic tubing

9.5

Pain threshold reached after 8 s; second degree burns after 20 s

4.0

Sufficient to cause pain to personnel if unable to reach cover within 20 s; however, blistering of the skin (second degree burns) is likely; 0% lethality

1.6

Will cause no discomfort for long exposure

I

1

I

I

I

T

3° burns, to bare skin (2mm) 50% lethality (average clothing) -1 % lethality (average clothing) start of 2° burns incident heat flux (kW/m2)

range for blistering of bare skin i.e. threshold

exposure time (sec) Figure 6.10. Tolerance times to burn-injury levels for various incident heat fluxes (Hymes 1983).

is empirically related to the duration of the radiation tc by: q2 = 50/f°71

(6.2.26)

where q2 is the heat-flux density in kilowatts per square meter and tc is the radiation duration in seconds. Buildings and process equipment suffer severe damage for incident heat fluxes of 12.6 kW/m2 and 37.8 kW/m2, respectively. Lihou and Maund (1982) stated that, as a rule of thumb, flammable materials in buildings and process installations would be damaged after an exposure of 1000 s to the heat fluxes quoted above.

By using the Stoll and Chianta (1971) relation and their own BLEVE model, Lihou and Maund (1982) calculated a "hazard range for severe burns to people" (X) of 55 m for a BLEVE fireball of 1000 kg of propane, and of 255 m for 50,000 kg of propane. These distances can be approximated by X~3.6< 4

(6.2.27)

Eisenberg et al. (1975) developed estimates of fatalities due to thermal radiation damage using data and correlations from nuclear weapons testing. The probability of fatality was found to be generally proportional to the product f/4/3, where t is the radiation duration and / is the radiation intensity. Table 6.7 shows the data used to develop estimates of fatalities from thermal radiation data. 6.2.7. Case Studies Although descriptions of many BLEVE accidents are available, data on fireball dimensions and height rely on accident eyewitnesses, so data on radiation are very limited. Nevertheless, it appears possible to compare calculated fireball dimensions with those actually witnessed in accidents. Fireball Dimensions. Moorhouse and Pritchard (1982) published a list of accidents and the reported fireball diameters and heights. Table 6.8 relates these data to calculated dimensions. The following relationship can be used to calculate the fireball diameter: Dc = 5.8mf1/3

(6.2.28)

where: Dc = diameter of fireball mf = initial fuel mass

(m) (kg)

TABLE 6.7. Relationship of Death from Radiation Burns to Radiation Level and Duration Probability of Fatality (%)

Duration, t (sec)

Radiation Intensity, I (kW/m2)

Dosage, t!4/3 [sec(kW/m2)413]

1 1 1 50 50 50 99 99 99

1.43 10.1 45.2 1.43 10.1 45.2 1.43 10.1 45.2

146.0 33.1 10.2 263.6 57.9 18.5 586.0 128.0 39.8

1099 1073 1000 2417 2264 2210 7008 6546 6149

TABLE 6.8. Overview of BLEVE Accidents from Moorhouse and Pritchard (1932) Year

Place

Fuel

m^ (t)

zc (m)

Dc (m)

CaIc. Dc (m)

1970 1971 1972 1973 1974 1974 1976 1978

Crescent City, IL Houston, TX Lynchburg, VA Kingman, AR St. Paul, MN Aberdeen, Scotl. Belt, MT Lewisville, AR

Propane Vinyl chloride Propane Propane LPG Butane LPG Vinyl chloride

75 165 9 45 10 2 80 110

250 — — — 100 — — —

150-200 300 120 300 100 7 0 300 305

245 318 120 206 125 73 250 278

as proposed by Roberts (1982) and Jaggers et al. (1986). All available fuel was assumed to be consumed in the calculation of diameters in Table 6.8. As Table 6.8 shows, agreement between witnesses' estimates of fireball dimensions and those resulting from the calculations is actually quite good. San Juan Ixhuatepec In 1984 in San Juanico (Mexico City), a 1600-m3 tank 50% full of LPG led to a BLEVE resulting in a fireball of 365 m in diameter (Johansson, 1986; Pietersen, 1985; Section 2.4.3). If it is assumed that all the fuel (468,000 kg) formed the fireball, the diameter calculated from the relationship proposed by Roberts (1982) and Jaggers et al. (1986) is 450 m. Assume, as proposed by Lihou and Maund (1982), that only 42% of the fuel originally in the tank contributes to the BLEVE. Then the calculated diameter using Roberts equation (6.2.16) is 337 m, a value in better agreement with witnesses' estimates. Pietersen (1985) gives the following damage due to BLEVEs at the San Juanico accident site: Paint comes off wood Glass damage Curtains and artificial grass set on fire Browning leaves Heat damaged plastic flags

400 600 600 1200 1200

m m m m m

Radiation effects from a fireball of the size calculated above, and assumed to be in contact with the ground, have been calculated by Pietersen (1985). A fireball duration of 22 s was calculated from the formula suggested by Jaggers et al. (1986). An emissive power of 350 kW/m2 was used for propane, based on large-scale tests by British Gas (Johnson et al. 1990). The view factor proposed in Section 6.2.5.

for a vertical surface was used. The "hazard range to severe burns" proposed by Lihou and Maund (1982) would be 600 m for this fireball. Table 6.9 tabulates distances at which the thermal effects described by CCPS (1989) occur. There is reasonable agreement between these values and those given by Pietersen. Leaf-browning at 1200 m agrees with the threshold value of 1050 m for wood combustion. The fact that glass is broken and cloth is ignited at a distance of 600 m is, in a broad sense, in reasonable agreement with the threshold value for equipment damage. Nevertheless, it is difficult to comment on the validity of models because available damage information is limited, even though the San Juanico accident is presently one of the best-described BLEVE accidents.

6.3. BLAST EFFECTS OF BLEVEs AND PRESSURE-VESSEL BURSTS This section addresses the effects of BLEVE blasts and pressure vessel bursts. Actually, the blast effect of a BLEVE results not only from rapid evaporation (flashing) of liquid, but also from the expansion of vapor in the vessel's vapor (head) space. In many accidents, head-space vapor expansion probably produces most of the blast effects. Rapid expansion of vapor produces a blast identical to that of other pressure vessel ruptures, and so does flashing liquid. Therefore, it is necessary to calculate blast from pressure vessel rupture in order to calculate a BLEVE blast effect. This section first presents literature review on pressure vessel bursts and BLEVEs. Evaluation of energy from BLEVE explosions and pressure vessel bursts is emphasized because this value is the most important parameter in determining blast strength. Next, practical methods for estimating blast strength and duration are presented, followed by a discussion of the accuracy of each method. Example calculations are given in Chapter 9. 6.3.1. Theory and Experiment The rapid expansion of a vessel's contents after it bursts may produce a blast wave. This expansion causes the first shock wave, which is a strong compression wave TABLE 6.9. Calculated Distances from Radiation Flux Given by CCPS (1989) for a BLEVE at San Juanico Effect Level of minor discomfort Threshold of pain Combustion of wood threshold Hazardous for equipment level

Radiation Intensity (kW/m2)

Distance (m)

1.6 4.0 12.5 37.5

3000 1850 1050 560

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for a vertical surface was used. The "hazard range to severe burns" proposed by Lihou and Maund (1982) would be 600 m for this fireball. Table 6.9 tabulates distances at which the thermal effects described by CCPS (1989) occur. There is reasonable agreement between these values and those given by Pietersen. Leaf-browning at 1200 m agrees with the threshold value of 1050 m for wood combustion. The fact that glass is broken and cloth is ignited at a distance of 600 m is, in a broad sense, in reasonable agreement with the threshold value for equipment damage. Nevertheless, it is difficult to comment on the validity of models because available damage information is limited, even though the San Juanico accident is presently one of the best-described BLEVE accidents.

6.3. BLAST EFFECTS OF BLEVEs AND PRESSURE-VESSEL BURSTS This section addresses the effects of BLEVE blasts and pressure vessel bursts. Actually, the blast effect of a BLEVE results not only from rapid evaporation (flashing) of liquid, but also from the expansion of vapor in the vessel's vapor (head) space. In many accidents, head-space vapor expansion probably produces most of the blast effects. Rapid expansion of vapor produces a blast identical to that of other pressure vessel ruptures, and so does flashing liquid. Therefore, it is necessary to calculate blast from pressure vessel rupture in order to calculate a BLEVE blast effect. This section first presents literature review on pressure vessel bursts and BLEVEs. Evaluation of energy from BLEVE explosions and pressure vessel bursts is emphasized because this value is the most important parameter in determining blast strength. Next, practical methods for estimating blast strength and duration are presented, followed by a discussion of the accuracy of each method. Example calculations are given in Chapter 9. 6.3.1. Theory and Experiment The rapid expansion of a vessel's contents after it bursts may produce a blast wave. This expansion causes the first shock wave, which is a strong compression wave TABLE 6.9. Calculated Distances from Radiation Flux Given by CCPS (1989) for a BLEVE at San Juanico Effect Level of minor discomfort Threshold of pain Combustion of wood threshold Hazardous for equipment level

Radiation Intensity (kW/m2)

Distance (m)

1.6 4.0 12.5 37.5

3000 1850 1050 560

pressure (psi)

in the surrounding air traveling from the explosion center at a velocity greater than the speed of sound. The fluid expands spherically and does not mix immediately with the surrounding air, so a sort of fluid "bubble" is formed which has an interface with surrounding air. The released fluid's momentum causes it to overexpand, and the pressure within the bubble then drops below ambient pressure. After the fluid bubble reaches its maximum diameter, it collapses again, thus producing a phase of negative pressure and reversed wind direction in the surrounding air. The bubble rebounds upon reaching its minimum diameter, thus producing a second shock. The bubble will continue to oscillate before coming to rest, producing ever-smaller pressure waves. The most important blast-wave parameters are peak overpressure ps and positive impulse is, as shown in Figure 6.11. The deep negative phase and second shock are clearly visible in this figure. The strength and shape of a blast wave produced by a sudden release of fluid depends on many factors, including type of fluid released, energy it can produce in expansion, rate of energy release, shape of the vessel, type of rupture, and character of surroundings (i.e., the presence of wave-reflecting surfaces and ambient air pressure). The type of fluid is very important. It can be a gas, a superheated liquid, a liquid, or some combination of these. Unsuperheated liquid cannot produce a blast, so the volume of unsuperheated liquid in a vessel need not be considered. In the following subsections, a selection of the theoretical and experimental work on pressure vessel bursts and BLEVEs will be reviewed. Attention will first be focused on an idealized situation: a spherical, massless vessel filled with ideal

time (sec)

Figure 6.11. Pressure-time history of a blast wave from a pressure vessel burst (Esparza and Baker 1977a).

gas and located high above the ground. Increasingly realistic situations will be discussed in subsequent subsections. 6.3.1.1. Free-Air Bursts of Gas-Filled, Massless, Spherical Pressure Vessels The pressure vessel under consideration in this subsection is spherical and is located far from surfaces that might reflect the shock wave. Furthermore, it is assumed that the vessel will fracture into many massless fragments, that the energy required to rupture the vessel is negligible, and that the gas inside the vessel behaves as an ideal gas. The first consequence of these assumptions is that the blast wave is perfectly spherical, thus permitting the use of one-dimensional calculations. Second, all energy stored in the compressed gas is available to drive the blast wave. Certain equations can then be derived in combination with the assumption of ideal gas behavior. Experimental Work. Few experiments measuring the blast from exploding, gasfilled pressure vessels have been reported in the open literature. One was performed by Boyer et al. (1958). They measured the overpressure produced by the burst of a small, glass sphere which was pressurized with gas. Pittman (1972) performed five experiments with titanium-alloy pressure vessels which were pressurized with nitrogen until they burst. Two cylindrical tanks burst at approximately 4 MPa, and three spherical tanks burst at approximately 55 MPa. The volume of the tanks ranged from 0.0067 m3 to 0.170 m3. A few years later, Pittman (1976) reported on seven experiments with 0.028-m3 steel spheres that were pressurized to extremely high pressures with argon until they burst. Nominal burst pressures ranged from 100 MPa to 345 MPa. Experiments were performed just above ground surface. Finally, Esparza and Baker (1977a) conducted twenty small-scale tests in a manner similar to that of Boyer et al. (1958). They used glass spheres of 51 mm and 102 mm diameter, pressurized with either air or argon, to overpressures ranging from 1.22 MPa to 5.35 MPa. They recorded overpressures at various places and filmed the fragments. From these experiments, it was learned that, compared to the shock wave produced by a high explosive, shock waves produced by bursting gasfilled vessels have lower initial overpressures, longer positive-phase durations, much larger negative phases, and strong second shocks. Figure 6.11 depicts such a shock. Pittman (1976) also found that the blast can be highly directional, and that real gas effects must be dealt with at high pressures. Numerical Work. The results of experiments described above can be better understood when compared to the results of numerical and analytical studies. Numerical studies, in particular, provide real insight into the shock formation process. Chushkin and Shurshalov (1982) and Adamczyk (1976) provide comprehensive reviews of the many studies in this field. The majority of these studies were performed for military purposes and dealt with blast from nuclear explosions, high explosives, or

fuel-air explosions (FAEs: detonations of unconfined vapor clouds). However, many investigators studied (as a limiting case of these detonations) blast from volumes of high-pressure gas as well. Only the most important contributions will be reviewed here. Many numerical methods have been proposed for this problem, most of them finite-difference methods. Using a finite-difference technique, Erode (1955) analyzed the expansion of hot and cold air spheres with pressures of 2000 bar and 1210 bar. The detailed results allowed Erode to describe precisely the shock formation process and to explain the occurrence of a second shock. The process starts with expansion from the initial volume. This creates a shock wave in the surrounding air, called the main shock, which travels faster than the contact surface of gases originally present in the bursting vessel and ambient air. At the same time, a rarefaction wave is created which depressurizes the gas in the vessel. Behind this wave, an inwardly moving shock forms. It does not acquire a net inward velocity until the rarefaction wave has reached the center, but after that, it moves inward and reflects at the origin. This reflected shock moves outward toward the contact surface. At the time it strikes the contact surface, the gases at the contact surface are more dense and much cooler than surrounding air. Consequently, the shock is partially reflected on the contact surface. The portion that is transmitted is called the second shock; it may eventually overtake the main shock. Baker et al. (1975) used a finite-difference method with artificial viscosity to obtain blast parameters of spherical pressure vessel explosions. They calculated twenty-one cases, varying pressure ratio between vessel contents (gas) and surrounding atmosphere, temperature ratio, and ratio of the specific heats of the gases. They used ideal-gas equations of state. Their research was aimed at deriving a practical method to calculate blast parameters of bursting pressure vessels, so they synthesized the results into graphs presenting shock overpressure and impulse as a function of energy-scaled distance (Figures 6.21 and 6.23, pages 207 and 210). The method of Baker et al. is the best practical method for calculating the blast parameters of pressure vessel bursts. It will be described in detail in Section 6.3.3. Baker et al. assume, as the standard model for this method, a free-air burst of a spherical vessel. Baker et al. provide the following guidelines for adapting this method to surface bursts of nonspherical vessels: Multiply the energy of the explosion by 2 to conservatively account for the earth's reflection of the shock wave, and multiply by distance-dependent multiplication factors to account for the nonsymmetrical shock wave. The latter multiplication factors were determined experimentally for high explosives. In Section 6.3.2., instead of a free-air burst, a surface burst of a spherical vessel is assumed as the standard model, and the procedure is rearranged. Otherwise, no modifications were made to the Baker et al. method. A comparison of numerical results contained in Figures 6.21 and 6.23 with the experimental results of Esparza and Baker (1977) indicates that values in Figure 6.21 overstate slightly the shock overpressure, even after taking into account the kinetic energy absorbed by fragments. Impulses compare well.

Adamczyk (1976) noted that this work shows that equivalence with high explosives is usually attained only in the far field for high bursting-pressure ratios and temperature ratios. When low bursting-pressure ratios or temperature ratios are used, overpressure curves do not coalesce in the far field; hence, equivalence with high explosives may not be attained. He noted that many of the curves that do not coalesce are those with gases whose sound speeds are relatively low speeds. Such curves represent situations in which the potential energy within the sphere is not converted efficiently to kinetic energy of the medium. Such conversion depends on propagation of the rarefaction wave into surrounding gas. However, since this wave propagates at sonic velocity, a considerable time lapses before it releases the energy stored in the high-pressure gas. This analysis suggests that the rate of conversion of potential energy to the surrounding gas can be an important parameter in blastphenomena considerations. Guirao and Bach (1979) used the flux-corrected transport method (a finitedifference method) to calculate blast from fuel-air explosions (see also Chapter 4). Three of their calculations were of a volumetric explosion, that is, an explosion in which the unburned fuel-air mixture is instantaneously transformed into combustion gases. By this route, they obtained spheres whose pressure ratios (identical with temperature ratios) were 8.3 to 17.2, and whose ratios of specific heats were 1.136 to 1.26. Their calculations of shock overpressure compare well with those of Baker et al. (1975). In addition, they calculated the work done by the expanding contact surface between combustion products and their surroundings. They found that only 27% to 37% of the combustion energy was translated into work. Analytical Work. Analytical work performed on pressure vessel explosions can be divided into two main categories. The first attempts to describe shock, and the second is concerned with the thermodynamic process. The peak overpressure developed immediately after a burst is an important parameter for evaluating pressure vessel explosions. At that instant, waves are generated at the edge of the sphere. The wave system consists of a shock, a contact surface, and rarefaction waves. As this wave system is established, pressure at the contact surface drops from the pressure within the sphere to a pressure within the shock wave. Initial shock-wave overpressure can be determined from a one-dimensional technique. It consists of using conservation equations for discontinuities through the shock and isentropic flow equations through the rarefaction waves, then matching pressure and flow velocity at the contact surface. This procedure is outlined in Liepmann and Roshko (1967) for the case of a bursting membrane contained in a shock tube. From this analysis, the initial overpressure at the shock front can be calculated with Eq. (6.3.22). This pressure is not only coupled to the pressure in the sphere, but is also related to the speed of sound and the ratio of specific heats. The explosion process can also be described in thermodynamic terms. In this approach, the states of the gases before the beginning and after the completion of

the explosion process are compared. Explosion energy can thus be calculated. This energy is a very important parameter because, of all the variables, it has the greatest influence on blast parameters and thus on the destructive potential of an explosion. The thermodynamic method has limitations. Since the method ignores the intermediate stages, it cannot be used to determine shock-wave parameters. Furthermore, a shock wave is an irreversible thermodynamic process; this fact complicates matters if these energy losses are to be fully included in the analysis. Nevertheless, the thermodynamic approach is a very attractive way to obtain an estimate of explosion energy because it is very easy and can be applied to a wide range of explosions. Therefore, this method has been applied by practically every worker in the field. Unfortunately, there is no consensus on the measure for defining the energy of an explosion of a pressure vessel. Erode (1959) proposed to define the explosion energy simply as the energy, £ex,Br» that must be employed to pressurize the initial volume from ambient pressure to the initial pressure, that is, the increase in internal energy between the two states. The internal energy U of a system is the sum of the kinetic, potential, and intramolecular energies of all the molecules in the system. For an ideal gas it is (6.3.1) where U p V 7

= internal energy = absolute pressure = volume = ratio of specific heats of gas in system

(J) (Pa) (m3) (-)

Therefore £Cx,Br *s (6.3.2) where the subscript 1 refers to initial state and the subscript O refers to ambient conditions. Other investigators use the work done by the expanding surface between the gases originally in the vessel and the surroundings as the energy of the explosion, /sex wo. The system expands from state 1 (the initial state) to state 2, with p2 equal to the ambient pressure pQ. After expansion, it has a residual internal energy U2. The work which the system can perform is the difference between its initial and residual internal energies. £ex,wo ^ U

1

-U

2

where £Cx,wo *s ^16 work performed in expansion from state 1 to state 2.

(6.3.3)

Thus, for an ideal gas, the work is (6.3.4) For an ideal gas, pV1 is constant for isentropic expansion (that is, without energy addition or energy loss). Therefore, V2 *s: (6.3.5) This gives, for the work: (6.3.6) It is illustrative to compare work £ex>wo with added energy EtxBr. The ratio £ex,w
(6.3.7)

PI

where P1 is the nondimensional overpressure in the initial state (P1Tp0) - 1- This function is depicted in Figure 6.13. Investigators of vapor cloud explosions (Chapter 4) often use the combustion energy as a measure for the energy of the explosion. This energy heats, and thereby pressurizes, the initial volume. Combustion energy is equal to the change in internal energy from the unburned state to the burned state (without expansion). Thus, combustion energy is similar to Brode's definition of explosion energy. However, during combustion, the ratio of specific heats changes, thus creating a difference of a few percent. Adamczyk (1976) is one of the few who tried to incorporate energy losses from the irreversible shock process into the calculation. He proposes to use the work done by gas volume in a process illustrated in Figure 6.12 and described below. At the instant a pressure vessel ruptures, pressure at the contact surface is given by Eq. (6.3.22). The further development of pressure at the contact surface can only be evaluated numerically. However, the actual p- V process can be adequately approximated by the dashed curve in Figure 6.12. In this process, the constantpressure segment represents irreversible expansion against an equilibrium counterpressure p3 until the gas reaches a volume V3. This is followed by an isentropic expansion to the end-state pressure pQ. For this process, the point (p3, V3) is not on the isentrope which emanates from point (pl9 V1), since the first phase of the expansion process is irreversible. Adamczyk calculates point (p3, V3) from the conservation of energy law and finds (6.3.8)

Figure 6.12. p-V diagram showing actual and assumed path process for a bursting sphere (Adamczyk 1976).

If a new variable, £ = PsJLA> Pi ~ Po

(6<3.9)

is defined, EeX)M/EexEr for the entire process can be expressed as a function of £, P1, and Tf 1 .

]

(6.3.10)

The first term is due to the irreversible expansion from V1 to V3, and the second term to the isentropic expansion from V3 to V2. Adamczyk does not actually say how p3 should be chosen. A reasonable choice for p3 seems to be the initial-peak shock overpressure, as calculated from Eq. (6.3.22). The equation presented above can be compared to the results of Guirao et al. (1979). They numerically evaluated the work done by the expanding contact surface. When the difference between

combustion energy and Brode's energy is taken into account, their results are about 10% lower than those resulting from Eq. (6.3.10). This small difference indicates that Eq. (6.3.10) is reasonably accurate. Aslanov and Golinskii (1989) give yet another definition of explosion energy. They say that use of the work done by gas expansion underestimates the energy. The alternative they propose is derived from a rigorous thermodynamic analysis. Imagine an arbitrary control surface enclosing a volume Vc. (The pressure vessel is somewhere inside the control volume.) Before the vessel bursts, the internal energy inside the control volume is (for an ideal gas) (6.3.11) where ^0 is the ratio of specific heats of ambient air. After the explosion, the pressure eventually equals the ambient pressure, and the internal energy becomes (6.3.12) Therefore, the energy EcxAG that has crossed the control surface is (6.3.13) The difference between this equation and the equation for £ex,Wo is that the internal energy of the air that is displaced by the expanded gases is taken into account. Note that, when ^1 is equal to ^0, Eq. (6.3.13) is equivalent to Eq. (6.3.2). Aslanov and Golinskii advocate the use of the energy EexAG as the energy of the explosion. They claim that this gives a better correlation with numerical calculations and with experiments. In Figures 6.13, 6.14, and 6.15, the proposed measures for the explosion energy are compared. Figure 6.13 gives the ratio Eexwo/EeKEr for three values of the ratio of specific heats of the pressurized gas, and Figure 6.14 does the same for £ex,AG^ex,Br Figure 6.15 gives an impression of the ratio EGxM/E^BT for Adamczyk's definition of the explosion energy. This ratio is different for every type of gas. In this figure, the pressurized gas was air of 300, 3000, and 30,000 K. The ambient air was at a pressure of 1 bar and a temperture of 300 K. Analysis of Figures 6.13-6.15 makes it clear that the four definitions give widely varying results. They all approach Brode's equation for high initial overpressures, but for initial pressures of practical interest, the results vary by a factor of 4. Thus, there is no consensus on the definition of the most important variable of an explosion, its energy. All experimental and most numerical results given in the literature use Brode's definition. However, when the fluid is a nonideal gas or a liquid, almost everyone uses the work done in expansion as the explosion energy (see Section 6.3.2.). The available prediction methods for blast parameters are based on these two, conflicting, definitions.

Pressure (P1Xp0-D r=1.66

y=1.4

r=1.2

Figure 6.13. Comparison between energy definitions: EeXiWO/^ex,Bf

Pressure (P1Xp0-D Figure 6.14. Comparison between energy definitions: EwAG/EeKtBr.

Pressure (P1Xp0-D Ew y=1.4

A

J1XT0 1

O

T/TO

10

+

T /T 0

1OO

Figure 6.15. Comparison between energy definitions: £eXiAd/£eXiBr.

6.3.1.2. Surface Bursts of Gas-Filled, Massless, Spherical Pressure Vessels In the previous subsection, an idealized configuration was studied. In this and following subsections, the influences of the neglected factors will be discussed. When an explosion takes place at the surface of the earth or slightly above it, the shock wave produced by the explosion will reflect on the earth's surface. The reflected wave overtakes the first wave and increases its strength. The resulting shock wave is similar to a shock wave which would be produced in free air by the original explosion together with its mirror image. This subject has received little attention in the context of pressure vessel bursts. Pittman (1976) studied it using a two-dimensional numerical code. However, his results are inconclusive, because the number of cases he studied was small and because the grid he used was coarse. Baker et al. (1975) recommend, on the basis of experimental results with high explosives, the use of a method described in detail in Section 6.3.3. That is, multiply the volume of the explosion by 2, read the overpressure and impulse from graphs for free-air bursts, and multiply them by a factor depending on the range. 6.3.1.3. Nonspherical Bursts of Gas-Filled, Massless Pressure Vessels When a pressure vessel is not a sphere, or if the vessel does not fracture evenly, the resulting blast wave will be nonspherical. This, of course, is the case in almost every actual pressure vessel burst. Loss of symmetry means that detailed calculations

lead wave

cloud

interface

Figure 6.16. Positions of interface and lead shock versus time for a spheroid burst (Raju and Strehlow 1984).

and experimental measurements become much more complicated, because the calculations and measurements must be made in two or three dimensions instead of one. Numerical calculations of bursts of pressurized-spheroid gas clouds were made by Raju and Strehlow (1984) and by Chushkin and Shurshalov (1982). Raju and Strehlow (1984) compute the expansion of a gas cloud corresponding to a constant volume combustion of a methane-air mixture (P1Tp0 = 8.9, ^1 = 1.2). In Figure 6.16, the region originally occupied by the gas cloud is shaded, and the position and shape of the shock wave and the contact surface at different times following the explosion are shown as solid and dashed curves. The shape of the shock wave is almost elliptical, with ellipticity decaying to sphericity as the shock gradually degenerates into an acoustic wave. Scaled peak overpressure and positive impulse as a function of scaled distance are given in Figures 6.17 and 6.18. The scaling method is explained in Section 3.4. Figures 6.17 and 6.18 show that the shock wave along the axis of the vessel is initially approximately 50% weaker than the wave normal to its axis. Since strong shock waves travel faster than weak ones, it is logical that the shape of the shock wave approaches spherical in the far field. Shurshalov (Chushkin and Shurshalov

1982) performed a similar calculation; results confirmed those of Raju and Strehlow (1984). Shurshalov also found that the shock wave approaches a spherical shape more rapidly when the explosion is stronger. Even greater differences in shock pressure can be found when the pressure vessel does not burst evenly, but ruptures into two or three pieces. In that case, a jet emanates from the rupture, and the shock wave becomes highly directional. Pittman (1976) found experimental overpressures along the line of the jet to be greater, by a factor of four or more, than pressures along a line in the opposite direction from the jet. Baker et al. (1978b) tried to analyze, with a two-dimensional numerical code, the case of a spherical vessel bursting into two equal parts. They may have used a massless vessel in their calculations, but their vessel probably had a mass typical of normal storage vessels. This is not clear from their description. Baker et al. analyzed only six cases, including three different overpressures and three ratios of specific heat, each at ambient temperature. In addition, they had to use a large cell size because of limitations in computer power. They found that overpressures along the line of the jet could be predicted by a method similar to the one they presented for spherical bursts, which is described in Section 6.3.3. The main difference is that the starting point must be chosen at a lower overpressure,

P H l = O 2-- = 45 3-- = 90 5--BURSTING SPHERE

MAX OVERPRESSURE Pe

2>

BAKER'S PENTOLITE

DISTANCE (ENERGY SCALED) R Figure 6.17. P8 versus R generated by a spheroid burst (Raju and Strehlow 1984). fl = '(Po/W3. /3S = Ps/Po ~ L

1--PHI=O

2--PHI=45

3 - - P H I = 90 5--BURSTlNG SPHERE

IMPULSE ( E N E R G Y SCALED) j

c

o

4 - - B A K E R 1 S PENTOLITE

DISTANCE(ENERGYSCALED) R Figure 6.18. / versus R generated by a spheroid burst (Raju and Strehlow 1984). R = '(PO/W3; / = (/Sa0K(Po2^ W3)-

0.21 Ps0 instead of Ps0. Therefore, this method gives overpressures for the jet of a pressure vessel rupture that are lower than the overpressures of a spherical burst. It is logical that a jet's overpressures are lower because, since overpressures outside a jet are lower than inside, the jet will spread out, thus lowering its overpressure. However, the limitations of their analysis, coupled with uncertainty as to whether the vessel was massless or not, cast doubts on the accuracy of their method. 6.3.1.4. Bursts of Heavy, Gas-Filled Pressure Vessels In previous sections, it has been assumed that all energy within a pressure vessel is available to drive the blast wave. In fact, energy must be spetot to rupture the vessel and propel its fragments. In some cases, the vessel expands before bursting, thus absorbing additional energy. Should a vessel also contain liquid or solids, a fraction of the available energy may be spent in its propulsion. Vessel Expansion. In most cases, vessels rupture without significant expansion. In most cases in which a vessel is exposed to external fire, the vessel wall temperature distribution is very uneven. Then, typically, only a small bulge is produced before

the vessel bursts. If a vessel fails as a result of mechanical attack, there is no expansion. Vessel expansion can be a significant factor if rupture results from an internal pressure build-up, but that topic is outside the scope of this volume. For these reasons, expansion of the vessel may be safely neglected. Vessel Rupture. The energy needed to rupture a vessel is very low, and can be neglected in calculation of explosion energy. For a typical steel vessel, rupture energy is on the order of 1 to 10 kJ, that is, less than 1% of the energy of a small explosion. Fragments. As will be explained in Section 6.4, between 20% and 50% of available explosion energy may be transformed into kinetic energy of fragments and liquid or solid contents.

6.3.2. Blast from BLEVEs A vessel filled with a pressurized, superheated liquid can produce blasts upon bursting in three ways. First, the vapor that is usually present above the liquid can generate a blast, as from a gas-filled vessel. Second, the liquid will boil upon depressurization, and, if rapid boiling occurs, a blast will result. Third, if the fluid is combustible and the BLEVE is not fire induced, a vapor cloud explosion may occur (see Section 4.3.3.). In this subsection, only the first and second types of blast will be investigated. Experimental Work. Although a great many investigators studied the release of superheated liquids (that is, liquids that would boil if they were at ambient pressure), only a few have measured the blast effects that may result from release. Baker et al. (1978a) reports on a study done by Esparza and Baker (1977b) in which liquid CFC-12 was released from frangible glass spheres in the same manner as in their study of blast from gas-filled spheres. The CFC was below its superheat limit temperature. No significant blast was produced. Investigators at BASF (Maurer et al. 1977; Giesbrecht et al. 1980) conducted many small-scale experiments on bursting cylindrical vessels filled with propylene. The vessels were completely filled with liquid propylene at a temperature of around 340 K (which is higher than the superheat limit temperature Jsl) and a pressure of around 60 bar. Vessel volumes ranged from 0.226 x 10~3 m3 to 1.00 m3. The vessels were ruptured with small explosive charges, and after each release, the resulting cloud was ignited. While the experiments focused on explosively dispersed vapor clouds and their subsequent deflagration, the pressure wave developed from the flashing liquid was measured. The investigators found that overpressures from the evaporating liquid compared well with those resulting from gaseous detonations of the same energy.

(Energy here means the work which can be done by the fluid in expansion, £ex>wo.) This means that energy release during flashing must have been very rapid. As described in Section 6.2.1., British Gas performed full-scale tests with LPG BLEVEs similar to those conducted by BASF. The experimenters measured very low overpressures from the evaporating liquid, followed by a shock that was probably the so-called "second shock," and by the pressure wave from the vapor cloud explosion (see Figure 6.6). The pressure wave from the vapor cloud explosion probably resulted from experimental procedures involving ignition of the release. The liquid was below the superheat limit temperature at time of burst. Theoretical Work. Theoretical work on the blast from superheated liquid addresses two questions: 1. How, and under what circumstances, does the liquid flash explosively? 2. How much energy is liberated in the process? Reid (1976 and 1980) proposed the most likely explanation to the first question. His theory is described in detail in Section 6.1. (BLEVE theory). In short, Reid's theory is as follows: Before the vessel ruptures, its liquid is in equilibrium with its saturated vapor. Upon rupture, vapor blows off and liquid pressure drops rapidly. Equilibrium is lost, and liquid vaporizes vigorously at the liquid-vapor and the liquid—solid interfaces. Such vaporization, however, may be insufficient to maintain pressure. If the liquid is below its superheat limit temperature, it may not boil throughout the bulk of the liquid, because forces between its molecules are stronger there than at the liquid-vapor and liquid-solid interfaces. However, if the liquid is above its superheat limit temperature when the pressure drops, further microscopic bubbles begin to form and grow. Because this phenomenon occurs almost instantaneously throughout the bulk of the liquid, a large fraction of liquid can be transformed into vapor within milliseconds. The precise timing is governed by the time it takes for the decompression wave to pass through the liquid. Instantaneous boiling takes place only if the temperature of a liquid is higher than its superheat-limit temperature Tsl (also called the homogeneous-nucleation temperature), in which case, boiling occurs throughout the bulk of the liquid. This temperature is only weakly dependent on the initial pressure of the liquid and the pressure to which it depressurizes. As stated in Section 6.1., Tsl has a value of about 0.89rc, where Tc is the (absolute) critical temperature of the fluid. Thus, the BLEVE theory predicts that, when the temperature of a superheated liquid is below 7sl, liquid flashing cannot give rise to a blast wave. This theory is based on the solid foundations of kinetic gas theory and experimental observations of homogeneous nucleation boiling. It is also supported by the experiments of BASF and British Gas. However, because no systematic study has been conducted, there is no proof that the process described actually governs the type of flashing that causes strong blast waves. Furthermore, rapid vaporization of a superheated liquid below its superheat limit temperature can also produce a blast wave, albeit a weak

one. Also, present work (Venert 1990) suggests that certain operations can cause a fluid to become pre-nucleated, which enables the fluid to flash explosively upon depressurizing. Analysis of an incident (Van Wees 1989) involving a carbon dioxide storage vessel suggests that carbon dioxide can evaporate explosively even when its temperature is below rsl. This may occur because carbon dioxide crystallizes at ambient pressure, thus presenting enough nucleation sites for liquid to flash. The theory explains why a succession of shocks may occur in BLEVEs. A first shock is produced by the escape of vapor, a second by evaporating liquid, a third by the "second shock" of the oscillating fluid bubble, and possible additional shocks produced by combustion of released fluid. It is also possible for these shocks to overlap each other, especially at greater distances from the explosion. Determination of the energy released by flashing liquid is a problem addressed by many investigators, including Baker et al. (1978b) and Giesbrecht et al. (1980). They all define explosion energy as the work done by the fluid on surrounding air as it expands isentropically. In this case, the change in internal energy must be calculated from experimentally obtained thermodynamic data for the fluid. In Section 6.3.3., a method is given for calculating overpressure and impulse, given energy and distance. This method produces results which are in reasonable agreement with experimental results from BASF studies. The procedure is presented in more detail by Baker et al. (1978b). Wiedermann (1986b) presents an alternative method for calculating work done by a fluid. The method uses the "lambda model" to describe isentropic expansion, and permits work to be expressed as a function of initial conditions and only one fluid parameter, lambda. Unfortunately, this parameter is known for very few fluids. TNT Equivalence. Explosion strength is often expressed as "equivalent mass of TNT' in order to permit estimates of possible explosion damage. For BLEVEs and pressure vessel bursts, using this equivalence is unnecessary because the methods mentioned above give explosion blast parameters which relate directly to the amount of possible damage potential. However, the concept of TNT equivalence is still useful because it appeals to those who seldom deal with blast parameters. For reasons explained in Section 4.3.1, BLEVEs or pressure vessel bursts cannot readily be compared to explosions of TNT (or other high explosives). Only the main points are repeated here. • TNT explosions have a very high shock pressure close to the blast source. Because a shock wave is a non-isentropic process, energy is dissipated as the wave travels from the source, thus causing rapid decay of overpressures present at close range. • Blast waves close to the source of pressure vessel bursts differ greatly from those from TNT blasts. • The impulse at close range from a pressure vessel burst is greater than a TNT explosion with the same overpressure. Therefore, it is conservative to use

damage relationships which are based on nuclear explosions, such as those in Table 6.9, since the positive-phase duration of a nuclear explosion is very long. • A complicating factor is that there is disagreement over the amount of energy in TNT. For these reasons, the concept of TNT equivalency appears to have little application to near-field estimates. In the method which will be presented in Section 6.3.3., the blast parameters of pressure vessel bursts are read from curves of pentolite, a high explosive, for nondimensional distance R above two. For these ranges, using TNT equivalence makes sense. Pentolite has a specific heat of detonation of 5.11 MJ/kg, versus 4.52 MJ/kg for TNT (Baker et al. 1983). The equivalent mass of TNT can be calculated as follows for a ground burst of a pressure vessel: WTNT = ^

<6'3'14)

where WTNT = equivalent mass of TNT /ITNT = heat of detonation of TNT E6x = energy of explosion

(kg) (4.52 MJ/kg) (J)

(Calculated from procedures described in Section 6.3.3.) Table 6.10 presents some damage effects. It may give the impression that damage is related only to a blast wave's peak overpressure, but this is not the case. For certain types of structures, impulse and dynamic pressure (wind force), rather than overpressure, determine the extent of damage. Table 6.10 was prepared for blast waves of nuclear explosions, and generally provides conservative predictions for other types of explosions. More information on the damage caused by blast waves can be found in Appendix B.

6.3.3. Practical Methods for Calculating Blast Effects In this section, three methods for calculating the blast parameters of pressure vessel bursts and BLEVEs will be presented. All methods are related; that is, one basic method and two variations are presented. The choice of method depends upon phase of the vessel's contents and distance to the blast wave's "target," as illustrated in Figure 6.19. The application of information in Figure 6.19 requires some explanation. The decision as to which calculation method to choose should be based upon the phase of the vessel's contents, its boiling point at ambient pressure Tb, its critical temperature Jc, and its actual temperature T. For the purpose of selecting a calculation method, three different phases can be distinguished: liquid, vapor or nonideal gas, and ideal gas. Should more than be performed separately for each phase, and the

TABLE 6.10. Conditions of Failure of Side-on Overpressure-Sensitive Elements (Glasstone, 1957)

Structural Element Glass windows

Failure Usually shattering, occasional frame failure Shattering Connection failure followed by buckling Failure, usually at main connections, allowing a whole panel to be blown in Shattering of wall

Corrugated asbestos siding Corrugated steel or aluminum Wood siding panels standard house construction Concrete or cinder-block wall panels 8 or 12 inch thick (not reinforced) Self-framing steel panel Collapse building Oil storage tank Rupture Snapping failure Wooden utility poles Overturned Loaded rail cars Brick wall panel 8 or 1 2 inch Shearing, flexure failure thick (not reinforced)

Approx. Side-on Overpressure (bar) (psi) 0.03-0.07 0.07-0.14

0.5-1 1-2

0.07-0.14

1-2

0.07-0.14

1-2

0.14-0.20

2-3

0.20-0.28 0.20-0.28 0.34 0.48

3-4 3-4 5 7

0.55

7-8

blast-parameter calculation should be based upon the total amount of energy released. Temperature determines whether or not the liquid in a vessel will boil when depressurized. The liquid will not boil if its temperature is below the boiling point at ambient pressure. If the liquid's temperature is above the superheat-limit temperature 7sl (rsl = 0.89rc), it will boil explosively (BLEVE) when depressurized. Between these temperatures, the liquid will boil violently, but probably not rapidly enough to generate significant blast waves. However, this is not certain, so it is conservative to assume that explosive boiling will occur (see Section 6.3.2). A good estimate of the range, or distance from the vessel to the "target," can only be made after initial steps of the basic method have been completed. Therefore, this point will be explained in Section 6.3.3.1 along with a description of the basic method. 6.3.3.1. Calculation of Blast Parameters of Gas Vessel Bursts Baker et al. (1975) developed a method, presented below, for predicting blast effects from the rupture of gas-filled pressure vessels. They include a method for calculating the overpressure and impulse of blast waves from the rupture of spherical or cylindri-

start

collect data

liquid

,2 ^ ideal gas phase contents)

calc. energy with basic method

temperature

assume explosive flashing

vapor, non-ideal gas range

near field

explosive flashing far field

no blast effects

end

calc. energy with explosive flashing method

refined method

calc. enen explosive flashing method

continue with basic method Figure 6.19. Selection of blast-calculation method.

cal vessels located at ground level. The relationship of overpressure to distance for a rupturing pressure vessel depends strongly upon the pressure, temperature, and ratio of specific heats of the contained gas. When pressures and temperatures are high, blast waves in the far field are very similar to those generated by high explosive-detonation. This similarity forms the basis for the basic method, in which the compressed gas's stored energy is first calculated, then overpressure and impulse are read from charts which relate detonation-blast parameters to charges of high explosive with the same energy. The general procedure of the basic method is shown in Figure 6.20. This method is suitable for calculations of bursts of spherical and cylindrical pressure vessels which are filled with an ideal gas, placed on a flat surface, and distant from other obstacles which might interfere with the blast wave.

start

collect data

calculate energy

3 calculated R of 'target1

step 7 of explosive flashing method

check R

refined method

determine P8

determine I

adjust P8 and I

calc. PS and is

check P8

end Figure 6.20. Basic method.

Step 1: Collect data. Collect the following data: • • • • • •

the vessel's internal pressure (absolute), p the ambient pressure, pQ the vessel's volume of gas-filled space, V1 the ratio of specific heats of the gas, ^1 the distance from the center of the vessel to the "target," r, the shape of the vessel: spherical or cylindrical.

Step 2: Calculation compressed-gas energy. The energy £ex of a compressed gas is calculated as follows: (6.3.15) where Eex = P1 = P0 = V1 = ^y1 =

energy of compressed gas absolute pressure of gas absolute pressure of ambient air volume of gas-filled space of vessel ratio of specific heats of gas in system

(J) (N/m2) (N/m2) (m3) (-)

This energy measure is equal to Erode's definition of the energy, multiplied by a factor 2. The reason for the multiplication is that the Erode definition applies to free-air burst, while Eq. (6.3.15) is for a surface burst. In a free-air burst, explosion energy is spread over twice the volume of air. Step 3: Calculate R of the 'target.99 Calculate the nondimensional distance of the "target," /?, with: (6.3.16) where r is the distance in meters at which blast parameters are to be determined. This scaling method is explained in Section 3.4. Step 4: Check R. For R < 2, the basic method gives too high a value for blast overpressure. In such cases, use the refined method, described in Section 6.3.3.2., to obtain a more accurate pressure estimate. Step 5: Determine P8. To determine the nondimensional side-on overpressure P8, read P8 from Figure 6.21 or 6.22 for the appropriate R. Use the curve labelled "high explosive" if Figure 6.21 is used.

high e cplosive

Figure 6.21._NondimensionaU>verpressure versus nondimensional distance for overpressure calculations R = r(po/£ex)1/3, P5 = Ps/Po - 1 (Baker et al. 1975).

Figure 6.22. P8 versus R for pentolite. R = /WE6x)1* ^s = Ps/Po - 1 (Baker et al. 1975).

Step 6: Determine /. To determine the nondimensional side-on impulse /, read / from Figure 6.23 or 6.24 for the appropriate R. Use the curve labeled "vessel burst." For R in the range of 0.1 to 1.0, the 7 versus R curve of Figure 6.24 is more convenient. Step 7: Adjust Ps and 7 for geometry effects. The above procedure produces blast parameters applicable to a completely symmetrical blast wave, such as would result from the explosion of a hemispherical vessel placed directly on the ground. In practice, vessels are either spherical or cylindrical, and placed at some height above the ground. This influences blast parameters. To adjust for these geometry effects, Ps and 7 are multiplied by some adjustment factors derived from experiments with high-explosive charges of various shapes. Tables 6.1 Ia and 6.1 Ib gives multipliers for adjusting scaled values for cylindrical vessels of various R and for spheres elevated slightly above the ground, respectively. The blast wave from a cylindrical vessel is weakest along its axis. (See Figures 6.17 and 6.18.) Thus, the blast field is asymmetrical for a vessel placed horizontally. The method will only provide maximum values for a horizontal tank's parameters. Step 8: Calculate ps9 is. Use the following equation to calculate side-on peak overpressure ps — pQ and sideon impulse is from nondimensional side-on peak overpressure P8 and nondimensional side-on impulse 7: (6.3.17)

(6.3.18) where aQ is speed of sound in ambient air in meters per second. For sea-level average conditions, p0 is approximately 101.3 kPa and a0 is 340 m/s. Step 9: Check ps. This method has only a limited accuracy, especially in the near field (see Section 6.3.3.5). Under some circumstances, the calculated ps might be higher than the initial pressure in the vessel P1, which is physically impossible. If this should happen, take P1 as the peak pressure instead of the calculated ps. 6.3.3.2. Refinement for the Near Field The method presented above is based on the similarity of the blast waves of pressure vessel bursts and high explosives. This similarity holds only at some distance from the explosion. In the near field, the peak overpressure and impulse from a pressure

Figure 6.23. / versus R for pentollte and gas vessel bursts. R = r (Po/Eex)1/3. / = QiPoV(Po213 EW1/3) (Baker et al. 1975).

vessel burst differ greatly from those of a detonation of a high explosive, except when the pressure vessel is filled with a very hot high-pressure gas. Baker et al. (1978a) developed a method which can predict blast pressures in the near field. This method is based on results of numerical simulations (see Section 6.3.1.1) and replaces Step 5 of the basic method (Figure 6.20). The refined method's procedure is shown in Figure 6.25.

vessel burst

Figure 6.24. / versus R for gas vessel bursts. R = r(po/Eex)1/3, / = ('sao)/(Po2/3£ex1/3) (Bak®r * al. 1975).

TABLE 6.11 a. Adjustment Factors for P8 and / for Cylindrical Vessels of Various R (Baker et al. 1975) Multiplier for R

PS

1

<0.3 2*0.3^1.6 >1.6^3.5 >3.5

4 1.6 1.6 1.4

2 1.1 1 1

Step 1: Collect additional data. In addition to the data collected in Step 1 of the basic method, the following data are needed: • the ratio of the speed of sound in the compressed gas to its speed in ambient air, Ct1Ja0 • the ratio of specific heats of the ambient air, ^0 = 1.40 For an ideal gas (aja^2 is (6.3.19) where T0 = absolute temperature of ambient air T1 = absolute temperature of compressed gas M1 = molar mass of compressed gas Af0 = molar mass of ambient air yQ and ^1 are specific heat ratios

(K) (K) (kg/kmol) (29.0 kg/kmol) (-)

Step 2: Calculate the initial distance. This refinement assumes that an explosion's blast wave will be completely symmetrical. Such a shape would result from the explosion of a hemispherical vessel placed TABLE 6.11 b. Adjustment Factors for Spherical Vessels Slightly Elevated above Ground (Baker et al. 1975) Multiplier for R

PS

/

<1 >1

2 1.1

1.6 1

start from step 4 of basic method

collect additional data

2

calculate starting distance

calculate P8,

4

locate starting point on Fig. 6.21

determine P8

'continue with step 6 of basic method

Figure 6.25. Refined method to determine P8.

directly on the ground. Therefore, a hemispherical vessel is used instead of the actual vessel for calculation purposes. Calculate the hemispherical vessel's radius r0 from the volume of the actual vessel V1: (6.3.20) This is the starting distance on the overpressure versus distance curve. It must be transformed into the nondimensional starting distance, /?0, with: (6.3.21)

Step 3: Calculate the initial peak overpressure P80. The peak shock pressure directly after the burst, /?so, is much lower than the initial gas pressure in the vessel P1. As the shock wave travels away from the vessel, the peak shock pressure decreases. The nondimensional peak-shock overpressure directly after the burst P80 is defined as (pso/p0) ~~ 1 - It is given by the following expression (see Section 6.3.1.1): (6.3.22) where P1 = initial absolute pressure of compressed gas P0 = ambient pressure P80 = nondimensional peak shock overpressure directly after burst: PSO = (PjPo) ~ 1 P80 = peak shock overpressure directly after burst 70 = ratio of specific heats of ambient air 7j = ratio of specific heats of compressed gas aQ = speed of sound in ambient air ^1 = speed of sound in compressed gas

(Pa) (Pa) (-) (Pa) (-) (-) (m/s) (m/s)

This is an implicit equation which can only be solved by iteration. One might use a spreadsheet or a programmable calculator to solve for P80 from this equation. An alternative is to read P80 from Figure 6.26 or 6.27.

P1/PO Figure 6.26. Gas temperature versus pressure for constant P30 for ^y1 = 1.4 (Baker et al. 1975).

P1/PO Figure 6.27. Gas temperature versus pressure for constant P80 for ^1 = 1.66 (Baker et al. 1975).

Step 4: Locate the starting point on Figure 6.21. In Steps 2 and 3, the vessel's nondimensional radius and the blast wave's nondimensional peak pressure at that radius were calculated. As a blast wave travels outward, its pressure decreases rapidly. The relationship between the peak pressure P8 and the distance R depends upon initial conditions. Accordingly, Figure 6.21 contains several curves. Locate the correct curve by plotting (R, P80) in the figure, as illustrated in Figure 6.28. Step 5: Determine P8. To determine the nondimensional side-on overpressure P8, read P8 from Figure 6.21 for the appropriate R (calculated in Step 3 of the basic method). Use the curve which goes through the starting point, or else draw a curve through the starting point parallel to the nearest curve. Continue with Step 6 of the basic method in Section 6.3.3.2. 6.3.3.3. Method for Explosively Flashing Liquids and Pressure Vessel Bursts with Vapor or Nonideal Gas In the preceding subsections, bursting vessels were assumed to be filled with ideal gases. In fact, most pressure vessels are filled with fluids whose behavior cannot be described, or even approximated, by the ideal-gas law. Furthermore, many vessels are filled with superheated liquids which may vaporize rapidly, or even explosively, when depressurized.

Figure 6.28. Location of starting point on graph of P3 versus R (Baker et al. 1975). (Compare Figure 6.21.)

Equation (6.3.15) is not accurate for the calculation of explosion energy of vessels filled with real gases or superheated liquids. A better measure in these cases is the work that can be performed on surrounding air by the expanding fluid, as calculated from thermodynamic data for the fluid. In this section, a method will be described for calculating this energy, which can then be applied to the basic method in order to determine the blast parameters. In many cases, both liquid and vapor are present in a vessel. Experiments indicate that the blast wave from expanding vapor is often separate from that generated by flashing liquid. However, it is conservative to assume that the blast waves from each phase present are combined. This method is given in Figure 6.29. Step 1: Collect the following data: • Internal pressure/?! (absolute) at failure. (A typical BLEVE is caused by a fire whose heat raises vessel pressure and reduces its wall strength. Safety-valve design allows actual pressure to rise to a value 1.21 times the safety valveopening pressure.) • Ambient pressure p0. • Quantity of the fluid (volume V1 or mass).

start

collect data

check the fluid

determine U 1

determine u,

5

calculate specific work

calculate energy

calculate R

continue with step 5 of basic method Figure 6.29. Calculation of energy of flashing liquids and pressure vessel bursts filled with vapor or nonideal gas.

• Distance from center of vessel to "target" r. • Shape of vessel: spherical or cylindrical. Note that the recommended value for P1 is not always conservative. In some cases, heat input may be so high that the safety valve cannot vent all the generated vapor. In such cases, the internal pressure will rise until the bursting overpressure is reached, which may be much higher than the vessel's design pressure. For example, Droste and Schoen (1988) describe an experiment in which an LPG tank failed at 39 bar, or 2.5 times the opening pressure of its safety valve. Note also that this method assumes that the fluid is in thermodynamic equilibrium; yet, in practice, stratification of liquid and vapor will occur (Moodie et al. 1988). If the fluid is not listed in Table 6.12 or Figure 6.30, thermodynamic data for the fluid at its initial and final (expanded to ambient pressure) states are needed as well. These data include the properties of the fluid: • specific enthalpy h • specific entropy s • specific volume v. Thermodynamic data on fluids can be found in Perry and Green (1984) or Edmister and Lee (1984), among others. The method or determining the thermodynamic data will be explained in detail in Step 3. Step 2: Determine if the fluid is given in Table 6.12 or Figure 6.30. The work performed by a fluid as it expands has been calculated for seven common fluids, namely: ammonia carbon dioxide ethane isobutane nitrogen oxygen propane. If the fluid of interest is listed, skip to Step 5. Step 3: Determine internal energy in initial state, H1. The work done by an expanding fluid is defined as the difference in internal energy between the fluid's initial and final states. Most thermodynamic tables and graphs do not present W 1 , but only h, p9 v, T (the absolute temperature), and s (the specific entropy). Therefore, u must be calculated with the following equation: h = u + pv

(6.3.23)

TABLE 6.12. Expansion Work of NH3, CO2, N2, O2 Liquid

e

eex (kJ/kg)

eex/vf (MJ/m3)

eex (kJ/kg)

ex/vf (MJ/m3)

Ammonia, 7S, = 361.0 K 324.8 21.2 360.0 48.0 400.0 102.8

82.5 152.5 278.5

46.2 74.7 95.7

297.0 365.0 344.0

4.89 14.80 47.00

Carbon dioxide, 7S| = 270.8 K 244.3 14.8 255.4 21.1 266.5 29.1

54.4 60.9 68.1

58.2 62.1 65.6

98.0 109.0 117.0

3.77 6.00 9.17

10.0 14.5 24.8

13.2 18.2 28.6

8.78 11.3 15.0

41.9 47.7 53.5

1.75 2.98 6.66

10.1 17.3 27.5

12.8 18.7 27.2

12.5 16.8 22.1

43.9 53.4 60.0

1.73 3.65 7.00

Fluid

T1(K)

Pi (105 Pa)

Vapor

Nitrogen, T8, = 112.3 K

104.0 110.0 120.0

Oxygen, 7sl = 137.7 K

Expansion work. kJ/kg

Expansion work, Btu/lbm

120.0 130.0 140.0

Temperature, K —I— saturated ethane

—A— saturated propane

—©— saturated i so—butane

Figure 6.30. Expansion work per unit mass of ethane, propane, and isobutane.

where h u p v

= = = =

specific enthalpy (enthalpy per unit mass) specific internal energy absolute pressure specific volume

(J/kg) (J/kg) (N/m2) (m3/kg)

To use a thermodynamic graph, locate the fluid's initial state on the graph. (For a saturated fluid, this point lies either on the saturated liquid or on the saturated vapor curve, at a pressure P1.) Read the enthalpy A 1 , volume V1, and entropy S1 from the graph. If thermodynamic tables are used, interpolate these values from the tables. Calculate the specific internal energy in the initial state M1 with Eq. (6.3.23). The thermodynamic properties of mixtures of fluids are usually not known. A crude estimate of a mixture's internal energy can be made by summing the internal energy of each component. Step 4: Determine internal energy in expanded state, U1. The specific internal energy of the fluid in the expanded state M2 can be determined as follows: If a thermodynamic graph is used, assume an isentropic expansion (entropy s is constant) to atmospheric pressure pQ. Therefore, follow the constantentropy line from the initial state to pQ. Read A2 and V2 at this point, and calculate the specific internal energy M2. When thermodynamic tables are used, read the enthalpy Af, volume vf, and entropy sf of the saturated liquid at ambient pressure, /?0, interpolating if necessary. In the same way, read these values (Ag, vg, ,yg) for the saturated vapor state at ambient pressure. Then use the following equation to calculate the specific internal energy M2: M2 = (1 - X) hf + XAg - (1 - X)p0vf - XPovg

(6.3.24)

where X = vapor ratio (S1 — sf)/(sg — sf) s = specific entropy Subscript 1 refers to initial state. Subscript f refers to state of saturated liquid at ambient pressure. Subscript g refers to state of saturated vapor at ambient pressure. Equation (6.3.24) is only valid when X is between O and 1. Step 5: Calculate the specific work. The specific work done by an expanding fluid is defined as. *ex = U1- U2

(6.3.25)

where eex is specific work. (See Section 6.3.1.1.) The results of these calculations are given for seven common gases in Table 6.12 and Figures 6.30 and 6.31. The fluid temperature at the moment of burst must be known. If only pressure is known,

Expansion work, MJ/m3

Expansion work, Btu/ft3

Temperature. F

Temperature, K —I— saturated ethane

—*— saturated propane

—e— saturated iso-butane

Figure 6.31. Expansion work per unit volume of ethane, propane, and isobutane.

use thermodynamic tables to find this temperature. The table gives superheat limit temperature Tsl, initial conditions, and specific work done in expansion based upon isentropic expansion of either saturated liquid or saturated vapor until atmospheric pressure is reached. Figures 6.30 and 6.31 present the same information for saturated hydrocarbons. In Figure 6.30, the saturated liquid state is on the lower part of the curve and in Figure 6.31 it is on the upper part of the curve. Below Tsl, the line width changes, indicating that the liquid probably does not flash below that level. Note that a line has been drawn only to show the relationship between the points; a curve reflecting an actual event would be smooth. Note that a liquid has much more energy per unit of volume than a vapor, especially carbon dioxide. Note: It is likely that carbon dioxide can flash explosively at a temperature below the superheat limit temperature. This may result from the fact that carbon dioxide crystallizes at ambient pressure and thus provides the required number of nucleation sites to permit explosive vaporization. Step 6: Calculate expansion energy. To calculate expansion energy, multiply the specific expansion work by the mass of fluid released or else, if energy per unit volume is used, multiply by the volume

of fluid released. Multiply the result by 2 to account for reflection of the shock wave on the ground, as follows: En = 2^m1

(6.3.26)

where Tn1 is the mass of released fluid. Repeat Steps 3 to 6 for each component present in the vessel, and add the energies to find the total energy Eex of the explosion. Step 7: Calculate, using Eq. (6.3.16), the nondimensional range R of the "target" as follows:

5

i173

"te] r

where r is the distance in meters at which blast parameters are to be determined. Continue with Step 5 of the basic method. Note that the refinement for the near field cannot be made for nonideal gases, because Eq. (6.3.22) applies only to ideal gases. Therefore, blast pressure is conservatively estimated by determining the blast pressure resulting from detonation of a high-explosive charge having the same energy. 6.3.3.4. Blast Parameters of Free-Air BLEVEs or Pressure-Vessel Bursts For BLEVEs or pressure vessel bursts that take place far from reflecting surfaces, the above method may be used if a few modifications are made. The blast wave does not reflect on the ground. Thus, the available energy E6x is spread over twice the volume of air. Therefore, instead of using Eq. (6.3.15), calculate the energy with ^l^TT

(6-3.27)

Qr else, instead of using Eq. (6.3.26), use £ex = ejnv

(6.3.28)

Further in Step 7 of the basic method, do not multiply overpressure or impulse by vessel-height compensation factors. 6.3.3.5. Accuracy The methods presented above give upper estimates of blast parameters. Since the measured blast parameters of actual pressure-vessel bursts vary widely, even under well-controlled conditions, and since these methods are based on a highly schematized model, the blast parameters of actual bursts may be much lower. The main sources of deviation lie in estimates of energy and in release-process details. It is unclear whether the energy equations given in preceding sections are good estimates of explosion energy. In addition, energy translated into kinetic

energy of fragments and ejected liquid is not subtracted from blast energy. This may produce an error of up to 50%, which translates into an overstatement of overpressure by 25%. (See Section 6.3.1.4.) In practice, vapor release will not be spherical, as is assumed in the method. A release from a cylinder burst may produce overpressures along the vessel's axis, which are 50% lower than pressures along a line normal to its axis. If a vessel ruptures from ductile, rather than brittle, fracture, a highly directional shock wave is produced. Overpressure in the other direction may be one-fourth as great. The influences of release direction are not noticeable at great distances. Uncertainties for a BLEVE are even higher because of the fact that its overpressure is limited by initial peak-shock overpressure is not taken into account. The above methods assume that all superheated liquids can flash explosively, yet this may perhaps be the case only for liquids above their superheat-limit temperatures or for pre-nucleated fluids. Furthermore, the energies of evaporating liquid and expanding vapor are taken together, while in practice, they may produce separate blasts. Finally, in practice, there are usually structures in the vicinity of an explosion which will reflect blast or provide wind shelter, thereby influencing the blast parameters. In practice, overpressures in one case might very well be only one-fifth of those predicted by the method and close to the predicted value in another case. This inherent inaccuracy limits the value of this method in postaccident analysis. Even when overpressures can be accurately estimated from blast damage, released energy can only be estimated within an order of magnitude.

6.4. FRAGMENTS A BLEVE can produce fragments that fly away rapidly from the explosion source. These primary fragments, which are part of the original vessel wall, are hazardous and may result in damage to structures and injuries to people. Primary missile effects are determined by the number, shape, velocity, and trajectory of fragments. When a high explosive detonates, a large number of small fragments with high velocity and chunky shape result. In contrast, a BLEVE produces only a few fragments, varying in size (small, large), shape (chunky, disk-shaped), and initial velocities. Fragments can travel long distances, because large, half-vessel fragments can "rocket" and disk-shaped fragments can "frisbee." The results of an experimental investigation described by Schulz-Forberg et al. (1984) illustrate BLEVE-induced vessel fragmentation. All parameters of interest with respect to fragmentation will be discussed. The extent of damage or injury caused by these fragments is, however, not covered in this volume. (Parameters of the terminal phase include first, fragment density and velocity at impact, and second, resistance of people and structures to fragments.) Figure 6.32 illustrates results of three fragmentation tests of 4.85-m3 vessels 50% full of liquid propane. The vessels were constructed of steel (StE 36; unalloyed Next Page

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energy of fragments and ejected liquid is not subtracted from blast energy. This may produce an error of up to 50%, which translates into an overstatement of overpressure by 25%. (See Section 6.3.1.4.) In practice, vapor release will not be spherical, as is assumed in the method. A release from a cylinder burst may produce overpressures along the vessel's axis, which are 50% lower than pressures along a line normal to its axis. If a vessel ruptures from ductile, rather than brittle, fracture, a highly directional shock wave is produced. Overpressure in the other direction may be one-fourth as great. The influences of release direction are not noticeable at great distances. Uncertainties for a BLEVE are even higher because of the fact that its overpressure is limited by initial peak-shock overpressure is not taken into account. The above methods assume that all superheated liquids can flash explosively, yet this may perhaps be the case only for liquids above their superheat-limit temperatures or for pre-nucleated fluids. Furthermore, the energies of evaporating liquid and expanding vapor are taken together, while in practice, they may produce separate blasts. Finally, in practice, there are usually structures in the vicinity of an explosion which will reflect blast or provide wind shelter, thereby influencing the blast parameters. In practice, overpressures in one case might very well be only one-fifth of those predicted by the method and close to the predicted value in another case. This inherent inaccuracy limits the value of this method in postaccident analysis. Even when overpressures can be accurately estimated from blast damage, released energy can only be estimated within an order of magnitude.

6.4. FRAGMENTS A BLEVE can produce fragments that fly away rapidly from the explosion source. These primary fragments, which are part of the original vessel wall, are hazardous and may result in damage to structures and injuries to people. Primary missile effects are determined by the number, shape, velocity, and trajectory of fragments. When a high explosive detonates, a large number of small fragments with high velocity and chunky shape result. In contrast, a BLEVE produces only a few fragments, varying in size (small, large), shape (chunky, disk-shaped), and initial velocities. Fragments can travel long distances, because large, half-vessel fragments can "rocket" and disk-shaped fragments can "frisbee." The results of an experimental investigation described by Schulz-Forberg et al. (1984) illustrate BLEVE-induced vessel fragmentation. All parameters of interest with respect to fragmentation will be discussed. The extent of damage or injury caused by these fragments is, however, not covered in this volume. (Parameters of the terminal phase include first, fragment density and velocity at impact, and second, resistance of people and structures to fragments.) Figure 6.32 illustrates results of three fragmentation tests of 4.85-m3 vessels 50% full of liquid propane. The vessels were constructed of steel (StE 36; unalloyed

Test 2 1) tank shell (4m) 2) right head (4Om) 3) pipe for liquid discharge (37Om) 4) left head (6m) 5) part of the safety valve (2Om) 6) part of the tank shell 500cm3 (15Om) 7) unidentified object (appr.400m) 8) part of the tank shell (15kg (40Om) 9) part of the tank shell 40kg (3Om) tank axis (valves right)

1) tank shell and left head (2Om) 2) right head (45m) 3) pipe for liquid discharge (140)

jlOOm ,

Test3 1) right half of the tank shell (6Om) 2) right head (2Om) 3) pipe for liquid discharge (37Om) 4) left head and a quarter of the tank shell (15Om) 5) a) first touch down of another quarter of the tank shell (12Om) b) place of discovery (40m away from a))

Figure 6.32. Schematic view of vessel fragments' flight after vessel bursts in three BLEVE tests (Schulz-Forberg et al. 1984).

fine-grained steel with a minimum yield strength of 360 N/mm2), and had wall thicknesses of 5.9 mm (Test 1) and 6.4 mm (Tests 2 and 3). Vessel overpressure at moment of rupture was 24.5 bar in the first test, 39 bar in the second test, and 30.5 bar in the third. Research on predictions of fragment velocity and range has heretofore been concentrated on the idealized situation of the gas-filled, pressurized vessel. Other cases, including those of nonideal gas-filled vessels and vessels containing combinations of gas and liquid, are now being investigated (Johnson et al. 1990). Fragment velocity and range can be assumed to depend on the total available energy of a vessel's contents. If this energy is known, the vessel's contents are not significant. It is, therefore, permissible to begin by describing the effects of a vessel rupture when filled with an ideal gas.

6.4.1. Initial Fragment Velocity for Ideal-Gas-Filled Vessels 6.4.1.1. Estimate Based on Total Kinetic Energy A theoretical upper limit of initial fragment velocity can be calculated if it is assumed that the total internal energy E of the vessel contents is translated into

fragment kinetic energy. Two simple relations are obtained: (6.4.1) where Vj = initial fragment velocity Ek = kinetic energy M = total mass of the empty vessel

(m/s) (J) (kg)

Kinetic energy (Ek) is calculated from internal energy E. Internal energy can be calculated from [similar to Eq. (6.3.2)]: (6.4.2) in which P1 PQ V y

= absolute pressure in vessel at failure = ambient pressure outside vessel = internal volume of vessel = ratio of specific heats

(N/m2) (N/m2) (m3) (-)

This equation was first proposed by Erode (1959). In accidental releases, pressure within a vessel at time of failure is not always known. However, depending on the cause of vessel failure, an estimate of its pressure can be made. If failure is initiated by a rise in initial pressure in combination with a malfunctioning or inadequately designed pressure-relief device, the pressure at rupture will equal the vessel's failure pressure, which is usually the maximum allowable working pressure times a safety factor. For initial calculations, a usual safety factor of four can be applied for vessels made of carbon steel, although higher values are possible. (The higher the failure pressure, the more severe the effects.) If failure is due to fire exposure, the vessel's overpressure results from external overheating and can reach a maximal value of 1.21 times the opening pressure of the safety valve. This maximal value is called the accumulated pressure. As overheating reduces the vessel's wall strength, failure occurs at the point at which its strength is reduced to a level at which the accumulated pressure can no longer be resisted. If vessel failure is due to corrosion or impact, it can be assumed that pressure at failure will be the operating pressure. Application of Eqs. (6.4.1) and (6.4.2) produce a large overestimation of the initial velocity V1. As a result, refinements were developed in the methods for determining energy E. For a sudden rupture of a vessel filled with an ideal gas, decompression will occur so rapidly that heat exchange with surroundings will be negligible. Assuming adiabatic expansion, the highest fraction of energy available for translation to kinetic energy of fragments can be calculated with: E = Jp1WOy - 1)

(6.4.3)

where (6.4.4) (See Baker 1973.) Equation (6.4.4) is explained in Section 6.3.1.1. Baum (1984) has refined this equation by incorporating the work of air pushed away by expanding gas: (6.4.5) For pressure ratios P1Jp0 from 10 to 100 and 7 ranges from 1.4 to 1.6, the factor k varies between 0.3 and 0.6, according to the refined equation proposed by Baum (1984). These refinements can reduce the calculated value of V1 by about 45%. According to Baum (1984) and Baker et al. (1978b), the kinetic energy calculated with the above equations is still an upper limit. In Baum (1984), the fraction of total energy translated into kinetic energy is derived from data on fragment velocity measured in a large variety of experiments. (The experiments applied for this purpose include those described by Boyer et al. 1958; Boyer 1959; Glass 1960; Esparza and Baker 1977a; Moore 1967; Collins 1960; Moskowitz 1965; and Pittman 1972.) From these experiments, the fraction translated to kinetic energy was found to be between 0.2 to 0.5 of the total energy derived through Baum's refinement. Based on these figures, it is appropriate to use k = 0.2 in the equation: £k = *P\VI(i - 1)

(6.4.6)

for rough initial calculations. 6.4.1.2. Initial Velocity Based on Theoretical Considerations A great deal of theoretical work has been performed to improve ability to predict initial fragment velocity. In the course of these efforts, a model introduced by Grodzovskii and Kukanov (1965) has been improved by various investigators. In this model, the acceleration force on fragments is determined by taking into account gas flow through ever-increasing gaps between fragments. This approach recognizes that not all available energy is translated to kinetic energy. Hence, calculated initial velocities are reduced. Velocities of fragments from spherical pressure vessels bursting into two equal portions have been analytically determined for ideal gases by the work of Taylor and Price (1971). The theory was expanded to include a large number of fragments by Bessey (1974) and to cylindrical geometries by Bessey and Kulesz (1976). Baker et al. (1978b) modified the theory for unequal fragments. In calculations of initial velocity, the energy necessary to break vessel walls is neglected. Baker et al. (1975) compare computer-code predictions of fragment velocity from spheres bursting into a large number of pieces and with some experimental

cylindrical spherical

cylindrical

Figure 6.33. Fragment velocity versus scaled pressure. ( - • - • - • ) • spheres according to V1 = 0.8Sa0F055 [Eq. (6.4.15)]. ( ): cylinders according to V1 = 0.8Sa0F055 [Eq. (6.4.15)]. (From Baker et al. 1983.)

data. Boyer et al. (1958) and Pittman (1972) measured fragment velocities from bursting glass spheres and bursting titanium alloy spheres, respectively. The calculated and measured velocities agree rather well after reported difficulties in velocity measurement are taken into account. The results of a parameter study were used to compose a diagram (Figure 6.33) which can be used to determine initial fragment velocity (Baker et al. 1978a and 1983). Figure 6.33 can be used to calculate the initial velocity V1 for bursting pressurized vessels filled with ideal gas. The quantities to be substituted, in addition to those already defined (pl9 p0» and V), are O0 M K p

= = = =

speed of sound in gas at failure mass of vessel factor for unequal fragments scaled pressure

(m/s) (kg) (-) (-)

with P = (Pi^ P«W/(Ma$

(6.4.7)

Separate regions in Figure 6.33 account for scatter of velocities of cylinders and spheres separating into 2, 10, or 100 fragments. The assumptions used in deriving the figure are from Baker et al. (1983), namely, • The vessel under gas pressure bursts into equal fragments. If there are only two fragments and the vessel is cylindrical with hemispherical end-caps, the vessel bursts perpendicular to the axis of symmetry. If there are more than two fragments and the vessel is cylindrical, strip fragments are formed and expand radially about the axis of symmetry. (The end caps are ignored in this case.) • Vessel thickness is uniform. • Cylindrical vessels have a length-to-diameter ratio of 10. • Contained gases used were hydrogen (H2), air, argon (Ar), helium (He), or carbon dioxide (CO2). The sound speed a0 of the contained gas has to be calculated for the temperature at failure: al = TyR/m

(6.4.8)

where OQ R T m

= = = =

speed of sound ideal gas constant absolute temperature inside vessel at failure molecular mass

(m/s) (J/Kkmol) (K) (kg/kmol)

Appendix D gives some specific characteristics for common gases. When using Figure 6.33, for equal fragments, K has to be taken as 1 (unity). For the case of a cylinder breaking into two unequal parts perpendicular to the cylindrical axis, K was calculated by Baker etal. (1983). Factor A'can be determined for a fragment with mass Aff with the aid of Figure 6.34. The dotted lines in the figure bound the scatter region. Figure 6.34 indicates that heavier fragments will have higher initial velocities. Whether factor K is correct is doubtful. In Baker et al. (1978b), another figure for the determination of K was presented that gives totally different values. No explanation for the discrepancy has been found. It is, therefore, advisable to use K=I only. 6.4.1.3. Initial Velocity Based on Empirical Relations In addition to the theoretically derived Figure 6.33, an empirical formula developed by Moore (1967) can also be used for the calculation of the initial velocity: (6.4.9)

fragment fraction of total mass Figure 6.34. Adjustment factor for unequal mass fragments (Baker et al. 1983).

where for spherical vessels

and for cylindrical vessels

where C = total gas mass E = energy Af = mass of casing or vessel

(kg) (J) (kg)

Moore's equation was derived for fragments accelerated from high explosives packed in a casing. The equation predicts velocities higher than actual, especially for low vessel pressures and few fragments. According to Baum (1984), the Moore equation predicts velocity values between the predictions of the equations given at the beginning of this section and the values derived from Figure 6.33. Other empirical relations for ideal gas are given in Baum (1987); recommended velocities are upper limits. In each of these relations, a parameter F has been applied. For a large number of fragments, F is given by: F = ^-P°)r moo

(6.4.10)

where m is mass per unit area of vessel wall and r the radius of the vessel. For a small number of fragments, F can be written as: (6.4.11) where r = radius of vessel A = area of detached portion of vessel wall Mf = mass of fragment

(m) (m2) (kg)

From these values of F9 the following empirical relations for initial velocity have been derived: • For an end-cap breaking from a cylindrical vessel: Vj =20oF 05

(6.4.12)

• For a cylindrical vessel breaking into two parts in a plane perpendicular to its axis: V1 = 2.18CIo[F(LiR)1'2]*3

(6.4.13)

where in F A = irr2 L = length of cylinder

(m2) (m)

• For a single small fragment ejected from a cylindrical vessel: (6.4.14) Equation (6.4.14) is only valid under the following conditions: 20 < PV/P0 < 300;

7 = 1.4;

s < 0.3r

• For the disintegration of both cylindrical and spherical vessels into multiple fragments: (6.4.15) 6.4.2. Initial Fragment Velocity for Vessel Filled with Nonideal Gases In many cases, pressurized gases in vessels do not behave as ideal gases. At very high pressures, van der Waals forces become important, that is, intermolecular forces and finite molecule size influence the gas behavior. Another nonideal situation is that in which, following the rupture of a vessel containing both gas and liquid, the liquid flashes.

Very little has been published covering such nonideal, but very realistic, situations. Two publications by Wiederman (1986a,b) treat nonideal gases. He uses a co-volume parameter, which is apparent in the Nobel-Abel equation of state of a nonideal gas, in order to quantify the influence on fragment velocity. The co-volume parameter is defined as the difference between a gas's initial-stage specific volume and its associated perfect gas value. For a maximum value for the scaled pressure p = 0.1, a reduction in V1 of 10% was calculated when the co-volume parameter was applied to a sphere breaking in half. In general, fragment velocity is lower than that calculated in the ideal-gas case. Baum (1987) recommends that energy E be determined from thermodynamic data (see Section 6.3.2.3) for the gas in question. Wiederman (1986b) treats homogeneous, two-phase fluid states and some initially single-phase states which become homogeneous (single-state) during decompression. It was found that fragment hazards were somewhat more severe for a saturated-liquid state than for its corresponding gas-filled case. Maximum fragment velocities occurring during some limited experiments on liquid flashing could be calculated if 20% of the available energy, determined from thermodynamic data, was assumed to be kinetic energy (Baum 1987). For vessels containing nonflashing liquids, the energy available for initial velocity can be determined by calculation of the energy contained in the gas. This value can be refined by taking into account the released energy of the expanding, originally compressed liquid.

6.4.3. Discussion In Baum (1984), a comparison is made between the models described in Section 6.4.1. This comparison is depicted in Figure 6.35. The energy E was calculated with k according to Baum's refinement. In Figure 6.35, lines have been added for a sphere bursting into 2 or 100 pieces for p\lp$ = 50 and 10, in accordance with Figure 6.33. Obviously, the simple relations proposed by Brode (1959) and Baum (1984) predict the highest velocity. Differences between models become significant for small values of scaled energy £, in the following equation: E = [2E/(Mc$)]m

(6.4.16)

In most industrial applications, scaled energy will be between 0.1 and 0.4 (Baum 1984), so under normal conditions, few fragments are expected, and Figure 6.33 can be applied. However, if an operation or process is not under control and pressure rises dramatically, higher scaled-energy values can be reached. In the relationships proposed by Brode (1959) and in Figure 6.33, velocity has no upper limit, although Figure 6.33 is approximately bounded by scaled pressures of 0.05 and 0.2 (scaled energies of approximately 0.1 and 0.7). Baum (1984) states, however, that there is an upper limit to velocity, as follows: The maximum velocity

Figure 6.35. Calculated fragment velocities for a gas-filled sphere with -y = 1.4 (taken from Baum 1984; results of Baker et al. 1978a were added). ( ): Baum for P^p0 = 10 and 50. (- • • -): Moore for P1Tp0 = 10 and 50. Baker: 1: P1Tp0 = 10; number of fragments = 2 2: Pi/Po = 50; number of fragments = 2 3: P1Xp0 =10; number of fragments = 100 4: P1Xp0 = 50; number of fragments = 100.

of massless fragments equals the maximum velocity of the expanding gas (the peak contact-surface velocity). In Figure 6.35, this maximum velocity is depicted by the horizontal lines for P1Tp0 = 10 and 50. If values in Figure 6.33 are extrapolated to higher scaled pressures, velocity will be overestimated. The equation proposed by Moore (1967) tends to follow the upper-limit velocity. This is not surprising, because the equation was based upon high levels of energy. Despite its simplicity, its results compare fairly well with other models for both low and high energy levels. For lower scaled pressures, velocity can be calculated with the equation proposed by Baum (1987) which produces disintegration of both cylindrical and spherical vessels into multiple fragments (V1 = 0.8Sa0F055). Such a result can also be obtained by use of Figure 6.33. However, actual experience is that ruptures rarely

produce a large number of fragments. The appearance of a large number of fragments in the low scaled-pressure regions of these equations or curves probably results from the nature of the laboratory tests from which the equations were derived. In those tests, small vessels made of special alloys were used; such alloys and sizes are not used in practice. Baum's equation (V1 = 0.8Sa0F055) can be compared with curves in Figure 6.33 as F equals n times the scaled pressure, in which n = 3 for spheres and n = 2 for cylinders (end caps neglected). For spheres, Baum's equation gives higher velocities than the Baker et al. model (1983), but for cylinders, this equation gives lower velocities. Note that work on ideal-gas-filled pressurized vessels, though extensive, is not complete. Furthermore, work on other cases, such as nonideal gases, flashing liquids, and gas plus loose paniculate matter, has either just begun or not even begun. Because failure mode cannot be predicted accurately, the worst case must be assumed. The worst case may produce high calculated velocities and, consequently, large fragment ranges. 6.4.4. Ranges for Free Flying Fragments After a fragment has attained a certain initial velocity, the forces acting upon it during flight are those of gravity and fluid dynamics. Fluid-dynamic forces are subdivided into drag and lift components. The effects of these forces depend on the fragment's shape and direction of motion relative to the wind. 6.4.4. L Neglecting Dynamic Fluid Forces The simplest relationship for calculating fragment range neglects drag and lift forces. Vertical and horizontal range, zv and zh, then depend upon initial velocity and initial trajectory angle of (6.4.17)

(6.4.18) where R H g Ot4 V1

= = = = =

horizontal range height fragment reaches gravitational acceleration initial angle between trajectory and a horizontal surface initial fragment velocity

(m) (m) (m/s2) (deg) (m/s)

A fragment will travel the greates horizontal distance when Ct1 = 45°. (6.4.19)

6.4.4.2. Incorporating Dynamic Fluid Forces Incorporating the effects of fluid-dynamic forces requires the composition of a set of differential equations. Baker et al. (1983) plotted solutions of these equations in a diagram for practical use. They assumed that the position of a fragment during its flight remains the same with respect to its trajectory, that is, that the angle of attack remained constant. In fact, fragments probably tumble during flight. Plots of these calculations are given in Figure 6.36. The figure plots scaled maximal range R and scaled initial velocity V1 given by (6.4.20)

(6.4.21) CLAL CpAo

Figure 6.36. Scaled curves for fragment range predictions (taken from Baker et al. 1983) ( ): neglect of the fluid forces [Eq. (6.4.19)].

where Vj R R P0 C0 A0 g Mf

= = = = = = = =

scaled initial velocity scaled maximal range maximal range density of ambient atmosphere drag coefficient exposed area in plane perpendicular to trajectory gravitational acceleration mass of fragment

(-) (-) (m) (kg/m3) (-) (m2) (m/s2) (kg)

In Figure 6.36, two more parameters are used, namely CL = lift coefficient AL = exposed area in plane parallel to trajectory

(m2)

These curves were generated by maximization of range through variation of the initial trajectory angle. The curves are for similar lift-to-drag ratios CLALI(C^^), so by varying the angle of attack (the angle between the fragment and the trajectory) for a certain fragment, the curve to be used changes. Furthermore, scaled velocity changes because drag area A0 changes, thus making Figure 6.36 difficult to interpret. A method of calculating drag-to-lift ratio is presented in Baker et al. (1983). From Figure 6.36, it is clear that lifting force increases maximum range only in specific intervals of scaled velocity. In the case of thin plates, which have large C1A1J(C1^1)) ratios, the so-called "frisbeeing" effect occurs, and the scaled range more than doubles the range calculated when fluid forces are neglected. The dotted line in the curve denotes the case for which fluid dynamic forces are neglected R1n^ = v\lg [Eq. (6.4.19)]. In most cases, "chunky" fragments are expected. The lift coefficient will be zero for these fragments, so only drag and gravity will act on them; the curve with CLAL/(CDA0) = O is then valid. Drag force becomes significant for scaled velocities greater than 1. Drag coefficients for various shapes can be found in Table 6.13. More information about lift and drag can be found in Hoerner (1958). For fragments having plate-like shapes, the lift forces can be large, so predicted ranges can be much larger then the range calculated with R10n = v\/gy especially when the angle of attack a4 is small (ot| = approximately 10°). The sensitivity of the angle of attack model is high, however. For example, an angle of attack of zero results in no lift force at all.

6.4.5. Ranges for Rocketing Fragments Some accidents involving materials like propane and butane resulted in the propulsion of large fragments for unexpectedly long distances. Baker et al. (1978b) argued that these fragments developed a "rocketing" effect. In their model, a fragment

TABLE 6.13. Drag Coefficients (Baker et ai. 1983) SHAPE Right Circular Cylinder (long rod), side-on

Sphere

Rod, end-on

Disc, face-on

Cube, face-on

Cube, edge-on

Long Rectangular Member, face-on

Long Rectangular Member, edge-on

Narrow Strip, face-on

SKETCH

retains a portion of the vessel's liquid contents. Liquid vaporizes during the initial stage of flight, thereby accelerating the fragment as vapor escapes through the opening. Baker et al. (1978b) provided equations for a simplified rocketing problem and a computer program for their solution, but stated that the method was not yet ready to be used for range prediction. Baker et al. (1983) applied this method to two cases, and compared predicted and actual ranges of assumed rocketed fragments. This approach may be applicable to similar cases; otherwise, the computer program should be employed. Ranges for rocketing fragments can also be calculated from guidelines given by Baum (1987). As stated in Section 6.4.2, for cases in which liquid flashes off, the initial-velocity calculation must take into account total energy. If this is done, rocketing fragments and fragments from a bursting vessel in which liquid flashes are assumed to be the same. Ranges were calculated for a simulated accident with the methods of Baker et al. (1978a,b) and Baum (1987). It appears that the difference between these approaches is small. Initial trajectory angle has a great effect on results. In many cases (e.g., for horizontal cylinders) a small initial trajectory angle may be expected. If, however, the optimal angle is used, very long ranges are predicted.

6.4.6. Statistical Analysis of Fragments from Accidental Explosions Theoretical models presented in previous sections give no information on distributions of mass, velocity, or range of fragments, and very little information on the number of fragments to be expected. Apparently, these models are not developed sufficiently to account for these parameters. More information can probably be found in the analysis of results of accidental explosions. It appears, however, that vital information is lacking for most such events. Baker (1978b) analyzed 25 accidental vessel explosions for mass and range distribution and fragment shape. This statistical analysis is considered the most complete in the open literature. Because data on most of the 25 events considered in the analysis were limited, it was necessary to group like events into six groups in order to yield an adequate base for useful statistical analysis. Information on each group is tabulated in Table 6.14. The values for energy range in Table 6.14 require some discussion. In the reference, all energy values were calculated by use of Eq. (6.4.2). Users should do the same in order to select the right event group. Furthermore, some energy values given are rather low; it is doubtful that they are correct. Statistical analyses were performed on each of the groups to yield, as data availability permitted, estimates of fragment-range distributions and fragment-mass distributions. The next sections are dedicated to the statistical analysis according to the Baker et al. (1978b) method.

TABLE 6.14. Groups of Like Events Event Group Number

Number of Events

1

4

2 3 4 5 6

9 1 2 3 1

Explosion Material Propane, Anhydrous ammonia LPG Air LPG, Propylene Argon Propane

Source Energy Range (J)

Vessel Shape

Vessel Mass (kg)

Number of Fragments

1.487 x 105 to 5.95 x 105

Railroad tank car

25,542 to 83,900

14

381 4 to 3921 .3 5.198 x 1011

Railroad tank car Cylinder pipe and spheres Semi-trailer (cylinder) Sphere Cylinder

25,464 145,842 6343 to 7840 48.26 to 187.33 511.7

28 35 31 14 11

549.6 2438 x 109 to 1133 x 1010 24.78

6.4.6.1. Fragment Range Distribution It was shown in the reference that the fragment range distribution for each of the six groups of events follows a normal, or Gaussian, distribution. It was then shown that the chosen distributions were statistically acceptable. The range distributions for each group are given in Figures 6.37a and 6.37b. With this information, it is possible to determine the percentage of all the fragments which would have a range smaller than, or equal to, a certain value. Table 6.15 gives an overview of statistical results for each event group. 6.4.6.2. Fragment-Mass Distribution Pertinent fragment-mass distributions were available on three event groups (2, 3, and 6). According to the reference, they follow a normal, or Gaussian, distribution. These distributions are presented in Figures 6.38 and 6.39. As with the information in Figures 6.37a and 6.37b, the percentage of fragments having a mass smaller than or equal to a certain value can be calculated. Table 6.16 gives a statistical summary for event groups 2, 3, and 6.

6.5. SUMMARY AND DISCUSSION It should now be clear that there are a number of unsolved problems with regard to BLEVEs. These problems are summarized in this section. With regard to radiation: • Additional experiments should be performed on a large scale to establish the emissive power of fireballs generated by BLEVEs. The effects of flammable substances involved, fireball diameter, and initial pressure should be investigated. • Such experiments should also determine the influences of fill ratio, pressure, substance, and degree of superheat on mass contributing to fireball generation. With regard to overpressure generation: • It is not clear which measure of explosion energy is most suitable. Note that, in the method presented in Section 6.3, the energy of gas-filled pressure vessel bursts is calculated by use of Brode's formula, and for vessels filled with vapor, by use of the formula for work done in expansion. • Blast parameters for surface bursts of gas-filled pressure vessels have not been investigated thoroughly. Parameters presently used are derived from investigations of free-air bursts.

percentage of fragments with range equal to or less than R percentage of fragments with range equal to or less than R

Figure 6.37a. Fragment range distribution for event groups 1 and 2 (Baker et al. 1978b).

range R (m) Figure 6.37b. Fragment range distribution for event groups 3, 4, 5, and 6 (Baker et al. 1978b).

TABLE 6.15. Estimated Means and Standard Deviations for LogNormal Range Distributions (base e) for Six Event Groups Event Group

Estimated Mean

Estimated Standard Deviation

1 2 3 4 5 6

4.57 4.10 4.28 4.63 5.66 3.67

0.91 1.06 0.65 0.79 0.45 0.76

• The influence of nonspherical releases (e.g., burst of a cylindrical vessel, jetting) on blast parameters has not been thoroughly investigated. • Reid's theory that a superheated liquid which flashes below its homogeneous nucleation temperature 7sl will not give rise to strong blast generation has not been verified. With regard to missiles:

percentage of fragments with mass equal or less than M

• The fraction of explosion energy which contributes to fragment generation is unclear. Its effect on initial fragment velocity deserves more attention in relation

mass M (kg) Figure 6.38. Fragment-mass distribution for event groups 2 and 3 (Baker et al. 1978b).

TABLE 6.16. Estimated Means and Standard Deviations for Log-Normal Range Distributions (base e) for Event-Groups 2, 3, and 6 Event Group

Estimated Mean

Estimated Standard Deviation

2 3 6

7.05 6.62 1.42

2.12 1.05 2.78

to such factors as conditions within the vessel and properties of the vessel's materials. • Methods do not exist to predict even the order of magnitude of the number of fragments produced. One assumes failure either into two parts or into a large number of fragments. The effect of parameters such as material, wall thickness, and initial pressure are not known.

REFERENCES

percentage of fragments with mass equal or less than M

Adamczyk, A. A. 1976. An investigation of blast waves generated from non-ideal energy sources. UILU-ENG 76-0506. Urbana: University of Illinois. American Petroleum Institute. 1982. Recommended Practice 521.

mass M (kg) Figure 6.39. Fragment-mass distribution for event group 6.

Anderson, C., W. Townsend, R. Markland, and J. Zook. 1975. Comparison of various thermal systems for the protection of railroad tank cars tested at the FRA/BRL torching facility. Interim Memorandum Report No. 459, Ballistic Research Laboratories. Aslanov, S. K., and O. S. Golinskii. 1989. Energy of an asymptotically equivalent point detonation for the detonation of a charge of finite volume in an ideal gas. Combustion, Explosion, and Shock Waves, pp. 801-808. Bader, B. E., A. B. Donaldson, and H. C. Hardee. 1971. Liquid-propellent rocket abort fire model. J. Spacecraft and Rockets 8:1216-1219. Baker, W. E. 1973. Explosions in Air. Austin: University of Texas Press. Baker, W. E., J. J. Kulesz, R. E. Richer, R. L. Bessey, P. S. Westine, V. B. Parr, and G. A. Oldham. 1975 and 1977. Workbook for Predicting Pressure Wave and Fragment Effects of Exploding Propellant Tanks and Gas Storage Vessels. NASA CR-134906. Washington: NASA Scientific and Technical Information Office. Baker, W. E., J. J. Kulesz, P. A. Cox, P. S. Westine, and R. A. Strehlow. 1978a. A Short Course on Explosion Hazards Evaluation. Southwest Research Institute. Baker, W. E., J. J. Kulesz, R. E. Richer, P. S. Westine, V. B. Parr, L. M. Vargas, and P. K. Moseley. 1978b. Workbook for Estimating the Effects of Accidental Explosions in Propellant Handling Systems. NASA CR-3023. Washington: NASA Scientific and Technical Information Office. Baker, W. E., P. A. Cox, P. S. Westine, J. J. Kulesz, and R. A. Strehlow. 1983. Explosion Hazards and Evaluation. In Fundamental Studies in Engineering, Vol. 5. New York: Elsevier. Baum, M. R. 1984. The velocity of missiles generated by the disintegration of gas pressurized vessels and pipes. Trans. ASME. 106:362-368. Baum, M. R. 1987. Disruptive failure of pressure vessels: preliminary design guide lines for fragment velocity and the extent of the hazard zone. In Advances in Impact, Blast Ballistics, and Dynamic Analysis of Structures. ASME PVP. 124. New York: ASME. Bessey, R. L. 1974. Fragment velocities from exploding liquid propellant tanks. Shock Vibrat. Bull. 44. Bessey, R. L., and J. J. Kulesz. 1976. Fragment velocities from bursting cylindrical and spherical pressure vessels. Shock Vibrat. Bull. 46. Board, S. J., R. W. Hall, and R. S. Hall. 1975. Detonation of fuel coolant explosions. Nature 254:319-320. Boyer, D. W., H. L. Brode, I. I. Glass, and J. G. Hall. 1958. "Blast from a pressurized sphere." UTIA Report No. 48. Toronto: Institute of Aerophysics, University of Toronto. Brode, H. L. 1955. Numerical solutions of spherical blast waves. J. Appl. Phys. 26:766-775. Brode, H. L. 1959. Blast wave from a spherical charge. Phys. Fluids. 2:217. Center for Chemical Process Safety. 1989. Guidelines for Chemical Process Quantitative Risk Analysis. New York: AIChE/CCPS. Chushkin, P. L, and L. V. Shurshalov. 1982. Numerical computations of explosions in gases. (Lecture Notes in Physics 170). Proc. 8th Int. Conf. on Num. Meth. in Fluid Dynam., 21-42. Berlin: Springer Verlag. Droste, B., and W. Schoen. 1988. Full-scale fire tests with unprotected and thermal insulated LPG storage tanks. J. Haz. Mat. 20:41-53. Edmister, W. C., and B. I. Lee. 1984. Applied Hydrocarbon Thermodynamics, 2nd ed. Houston: Gulf Publishing Company. Esparza, E. D., and W. E. Baker. 1977a. Measurement of Blast Waves from Bursting Pressurized Frangible Spheres. NASA CR-2843. Washington: NASA Scientific and Technical Information Office.

Esparza, E. D., and W. E. Baker. 1977b. Measurement of Blast Waves from Bursting Frangible Spheres Pressurized with Flash-evaporating Vapor or Liquid. NASA CR2811. Washington: NASA Scientific and Technical Information Office. Fay, J. A., and D. H. Lewis, Jr. 1977. Unsteady burning of unconfined fuel vapor clouds. Sixteenth Symposium (International) on Combustion, 1397—1404. Pittsburgh: The Combustion Institute. Giesbrecht, H., K. Hess, W. Leuckel, and B. Maurer. 1980. Analyse der potentiellen Explosionswirkung von kurzzeitig in de Atmosphaere freigesetzen Brenngasmengen. Chem. Ing. Tech. 52(2): 114-122. Glass, I. I. 1960. UTIA Report No. 58. Toronto: Institute of Aerophysics, University of Toronto. Glasstone, S. 1957. The effects of nuclear weapons. USAEC. Grodzovskii, G. L., and F. A. Kpkanov. 1965. Motions of fragments of a vessel bursting in a vacuum. Inzhenemyi Zhumal 5(2):352-355. Guirao, C. M., and G. G. Bach. 1979. On the scaling of blast waves from fuel-air explosives. Pr-oc. 6th Symp. Blast Simulation. Cahors, France. Hardee, H. C., and D. O. Lee. 1973. Thermal hazard from propane fireballs. Trans. Plan. Tech. 2:121-128. Hardee, H. C., and D. O. Lee. 1978. A simple conduction model for skin burns resulting from exposure to chemical fireballs. Fire Res. 1:199-205. Hardee, H. C., D. O. Lee, and W. B. Benedick. 1978. Thermal hazards from LNG fireballs. Combust. ScL Tech. 17:189-197. Hasegawa, K., and K. Sato. 1977. Study on the fireball following steam explosion of npentane. Second Int. Symp. on Loss Prevention and Safety Promotion in the Process Ind., pp. 297-304. Heidelberg. Hasegawa, K., and K. Sato 1987. Experimental investigation of unconfined vapor cloud explosions and hydrocarbons, Technical Memorandum No. 16, Fire Research Institute, Tokyo. High, R. 1968. The Saturn fireball. Ann. N.Y. Acad. Sd. 152:441-451. Hoerner, S. F. 1958. Fluid Dynamic Drag. Midland Park, NJ: Author. Hymes, J. 1983. The physiological and pathological effects of thermal radiation. SRD R 275. U.K. Atomic Energy Authority. Jaggers, H. C., O. P. Franklin, D. R. Wad, and F. G. Roper. 1986. Factors controlling burning time for non-mixed clouds of fuel gas. /. Chem. E. Symp. Ser. No. 97. Johansson, O. 1986. BLEVES a San Juanico. Face au Risque. 222(4):35-37, 55-58. Johnson, D. M., M. J. Pritchard, and M. J. Wickens, 1990. Large scale catastrophic releases of flammable liquids. Commission of the European Communities Report, Contract No.: EV4T.0014.UK(H). Lewis, D. 1985. New definition for BLEVEs. Haz. Cargo Bull. April, 1985: 28-31. Liepmann, H. W., and A. Roshko. 1967. Elements of Gas Dynamics. New York: John Wiley and Sons. Lihou, D. A., and J. K. Maund. 1982. Thermal radiation hazard from fireballs. /. Chem. E. Symp. Ser. No. 71, pp. 191-225. Maurer, B., K. Hess, H. Giesbrecht, and W. Leuckel. 1977. Modeling vapor cloud dispersion and deflagration after bursting of tanks filled with liquefied gas. Second Int. Symp. on Loss Prevention and Safety Promotion in the Process Ind., pp. 305-321. Heidelberg. McDevitt, C. A., F. R. Steward, and J. E. S. Venart. 1987. What is a BLEVE? Proc. 4th Tech. Seminar Chem. Spills, pp. 137-147. Toronto.

Moodie, K., L. T. Cowley, R. B. Denny, L. M. Small, and I. Williams. 1988. Fire engulfment tests on a 5-ton tank. J. Haz. Mat. 20:55-71. Moore, C. V. 1967. Nucl. Eng. Des. 5:81-97. Moorhouse, J., and M. J. Pritchard. 1982. Thermal radiation from large pool fires and thermals—literature review. /. Chem. E. Symp. Series No. 71. Moskowitz, H. 1965. AIAA paper no. 65-195. Mudan, K. S. 1984. Thermal radiation hazards from hydrocarbon pool fires. Progr. Energy Combust. Sd. 10(1):59-80. Opschoor, G. 1974. Onderzoek naar de explosieve verdamping van op water uitspreidend LNG. Report Centraal Technisch Instituut TNO, Ref. 74-03386. Pape, R. P., et al. (Working Group, Thermal Radiation), 1988. Calculation of the intensity of thermal radiation from large fires. Loss Prev. Bull. 82:1-11. Perry, R. H., and D. Green. 1984. Perry's Chemical Engineers' Handbook, 6th ed. New York: McGraw-Hill. Pietersen, C. M. 1985. Analysis of the LPG incident in San Juan Ixhuatepec, Mexico City, 19 November 1984. Report TNO Division of Technology for Society, 1985. Pitblado, R. M. 1986. Consequence models for BLEVE incidents. Major Industrial Hazards Project, NSW 2006. University of Sydney. Pittman, J. F. 1972. Blast and Fragment Hazards from Bursting High Pressure Tanks. NOLTR 72-102. Silver Spring, Maryland: U.S. Naval Ordnance Laboratory. Pittman, J. F. 1976. Blast and Fragments from Superpressure Vessel Rupture. NSWC/WOL/ TR 75-87. White Oak, Silver Spring, Maryland: Naval Surface Weapons Center. Raj, P. K. 1977. Calculation of thermal radiation hazards from LNG fires. A Review of the State of the Art, AGA Transmission Conference T135—148. Raju, M. S., and R. A. Strehlow. 1984. Numerical Investigations of Nonideal Explosions. J. Haz. Mat. 9:265-290. Reid, R. C. 1976. Superheated liquids. Amer. Scientist. 64:146-156. Reid, R. C. 1979. Possible mechanism for pressurized-liquid tank explosions or BLEVE's. Science. 203(3). Reid, R. C. 1980. Some theories on boiling liquid expanding vapor explosions. Fire. March 1980: 525-526. Roberts, A. F. 1982. Thermal radiation hazards from release of LPG fires from pressurized storage. Fire Safety J. 4:197-212. Schmidli, J., S. Banerjee, and G. Yadigaroglu. 1990. Effects of vapor/aerosol and pool formation on rupture of vessel containing superheated liquid. J. Loss Prev. Proc. Ind. 3(1):104-111. Schoen, W., U. Probst, and B. Droste. 1989. Experimental investigations of fire protection measures for LPG storage tanks. Proc. 6th Int. Symp. on Loss Prevention and Safety Promotion in the Process Ind. 51:1 — 17. Schulz-Forberg, B., B. Droste, and H. Charlett. 1984. Failure mechanics of propane tanks under thermal stresses including fire engulfment. Proc. Int. Symp. on Transport and Storage of LPG and LNG. 1:295-305. Stoll, A. M., and M. A. Quanta. 1971. Trans. N.Y. Acad. ScL9 649-670. Taylor, D. B., and C. F. Price. 1971. Velocity of Fragments from Bursting Gas Reservoirs. ASME Trans. J. Eng. Ind. 938:981-985. Van Wees, R. M. M. 1989. Explosion Hazards of Storage Vessels: Estimation of Explosion Effects. TNO-Prins Maurits Laboratory Report No. PML 1989-C61. Rijswijk, The Netherlands.

Venart, J. E. S. 1990. The Anatomy of a Boiling Liquid Expanding Vapor Explosion (BLEVE). 24th Annual Loss Prevention Symposium. New Orleans, May 1990. Walls, W. L. 1979. The BLEVE—Part 1. Fire Command. May 1979: 22-24. The BLEVE—Part 2. Fire Command. June 1979: 35-37. Wiederman, A. H. 1986a. Air-blast and fragment environments produced by the bursting of vessels filled with very high pressure gases. In Advances in Impact, Blast Ballistics, and Dynamic Analysis of Structures. ASME PVP. 106. New York: ASME. Wiederman, A. H. 1986b. Air-blast and fragment environments produced by the bursting of pressurized vessels filled with two phase fluids. In Advances in Impact, Blast Ballistics, and Dynamic Analysis of Structures. ASME PVP. 106. New York: ASME. Williamson, B. R., and L. R. B. Mann. 1981. Thermal hazards from propane (LPG) fireballs. Combust. Sd. Tech. 25:141-145.

7 VAPOR CLOUD EXPLOSIONSSAMPLE PROBLEMS The methods described in this chapter are meant for practical application; background information is given in Chapter 4. If a quantity of fuel is accidentally released, it will mix with air, and a flammable vapor cloud may result. If the flammable vapor meets an ignition source, it will be consumed by a combustion process which, under certain conditions, may develop explosive intensity and blast. The explosion hazard of a vapor cloud can be quantified in terms of its explosive power after ignition. The explosive power of a vapor cloud can be expressed as an equivalent explosive charge (TNT or fuel-air) whose blast characteristics, that is, the distribution of blast-wave properties in the charge's vicinity, are known. Several methods of quantification are described in Chapter 4. Chapter 4 discusses in detail two fundamental approaches to quantification of explosive power, together with advantages and disadvantages. In addition, there are two different blast models, each of which has certain benefits. This chapter offers guidance on their use. Application of each method is described in Section 7.2. and demonstrated in Section 7.3. Section 7.1. offers some guidance on choosing an approach and a blast model.

7.1. CHOICE OF METHOD 7.1.1. Two Approaches In the first approach, a vapor cloud's potential explosive power is proportionally related to the total quantity of fuel present in the cloud, whether or not it is within flammable limits. This approach is the basis of conventional TNT-equivalency methods, in which the explosive power of a vapor cloud is expressed as an energetically equivalent charge of TNT located in the cloud's center. The value of the proportionality factor, that is, TNT equivalency, is deduced from damage patterns observed in a large number of vapor cloud explosion incidents. Consequently, vapor cloud explosion-blast hazard assessment on the basis of TNT equivalency may have limited utility. The second approach, the multienergy method (Van den Berg 1985) reflects current consensus that turbulence is the major cause of explosive, blast-generating

combustion. One source of turbulence is high-velocity flow as fuel is released from a container, for example, a pressurized vessel or leaking pipe. Explosive combustion rates may develop in such a turbulent fuel-air mixture. Another source of turbulence is combustion within a partially confined/obstructed environment. In such cases, turbulence is generated by combustion-induced expansion flow, resulting in uncontrolled positive feedback, which causes exponential increases in the combustion with respect to both speed and overpressure. Several blast effects may result. The consequence of the second approach is that, if detonation of unconfined parts of a vapor cloud can be ruled out, the cloud's explosive potential is not primarily determined by the fuel-air mixture in itself, but instead by the nature of the fuel-release environment. The multienergy model is based on the concept that explosive combustion can develop only in an intensely turbulent mixture or in obstructed and/or partially confined areas of the cloud. Hence, a vapor cloud explosion is modeled as a number of subexplosions corresponding to the number of areas within the cloud which burn under intensely turbulent conditions. The two approaches lead to completely different procedures for vapor cloud explosion hazard assessment. If conventional TNT-equivalency methods are applied, explosive potential is primarily determined by the amount of fuel present in a cloud, whether or not within flammability limits. The cloud center is the potential blast center and is determined by cloud drift. If, on the other hand, the multienergy model is employed, the total quantity of fuel present in a cloud is of minor importance. Instead, the environment is investigated with respect to potential blast-generative capabilities. Fuel-air jets and partially confined and/or obstructed areas are identified as sources of strong blast. The explosive power of a vapor cloud is determined primarily by the energy of fuel present in these blast-generating areas. 7.1.2. Two Blast Models TNT-equivalency methods express explosive potential of a vapor cloud in terms of a charge of TNT. TNT-blast characteristics are well known from empirical data both in the form of blast parameters (side-on peak overpressure and positive-phase duration) and of corresponding damage potential. Because the value of TNT-equivalency used for blast modeling is directly related to damage patterns observed in major vapor cloud explosion incidents, the TNT-blast model is attractive if overall damage potential of a vapor cloud is the only concern. If, on the other hand, blast modeling is a starting point for structural analysis, the TNT-blast model is less satisfactory because TNT blast and gas explosion blast differ substantially. Whereas a TNT charge produces a shock wave of very high amplitude and short duration, a gas explosion produces a blast wave, sometimes shockless, of lower amplitude and longer duration. In structural analysis, wave shape and positive-phase duration are important parameters; these can be more effectively predicted by techniques such as the multienergy method.

The blast originating from a hemispherical fuel-air charge is more like a gas explosion blast in wave amplitude, shape, and duration. Unlike TNT blast, blast effects from gas explosions are not determined by a charge weight or size only. In addition, an initial blast strength of the blast must be specified. The initial strength of a gas-explosion blast is variable and depends on intensity of the combustion process in the gas explosion in question.

7.2. METHODS 7.2.1. Conventional TNT-Equivalency Methods Conventional TNT-equivalency methods state a proportional relationship between the total quantity of flammable material released or present in the cloud (whether or not mixed within flammability limits) and an equivalent weight of TNT expressing the cloud's explosive power. The value of the proportionality factor—called TNT equivalency, yield factor, or efficiency factor—is directly deduced from damage patterns observed in a large number of major vapor cloud explosion incidents. Over the years, many authorities and companies have developed their own practices for estimating the quantity of flammable material in a cloud, as well as for prescribing values for equivalency, or yield factor. Hence, a survey of the literature reveals a variety of methods. To demonstrate the general procedure in applying TNT-equivalency methods in this work, one of the many methods, namely, that recommended by the UK Health & Safety Executive (HSE 1979; HSE 1986), is followed. Note that this is only one of many variations on the basic TNT-equivalency method; see Chapter 4 for a review of others. 7.2.7.7. Determine Charge Weight In the HSE method, the equivalent-charge weight of TNT is related to the total quantity of fuel in the cloud; it can be determined according to the following stepwise procedure: • Determine the flash fraction of fuel on the basis of actual thermodynamic data. Equation (7.1) provides a method of estimating the flash fraction.

(7.1) where F = flash fraction Cp = mean specific heat

(-) (U/kg/K)

Ar = temperature difference between vessel temperature and boiling temperature at ambient pressure L = latent heat of vaporization exp = base of natural logarithm (2.7183)

(K) (kJ/kg) (-)

• The weight of fuel Wf in the cloud is equal to the flash fraction times the quantity of fuel released. To allow for spray and aerosol formation, the cloud inventory should be multiplied by 2. (The weight of fuel in the cloud cannot, of course, exceed the total quantity of fuel released.) • The equivalent-charge weight of TNT can now be calculated as follows: WTNT = «e™ ^TNT

(7-2)

where WTNT Wf H1 //TNT cte

= = = = =

equivalent weight of TNT weight of fuel in the cloud heat of combustion fuel blast energy TNT = 4.68 MJ/kg TNT-equivalency/yield factor = 0.03

(kg) (kg) (MJ/kg) (-)

7.2.7.2. Determine Blast Effects In Figure 7.1, the side-on blast wave peak overpressure produced by a detonation of a TNT charge is graphically represented as dependent on the Hopkinson-scaled distance from the charge. The side-on blast peak overpressure at some real distance (R) of a charge of a given weight (W7Nr) is found by calculating:

<7-3>

* = WTNT ^r where R = Hopkinson-scaled distance WTNT = charge weight of TNT R = real distance from charge

(m/kg173) (kg) (m)

If the scaled distance R is known, the corresponding side-on blast peak overpressure can be read from the chart in Figure 7.1. 7.2.2. Multienergy Method The multienergy method is based on the concept that, if detonation of unconfined parts of a vapor cloud can be ruled out, strong blast is generated only by those cloud portions which burn under intensely turbulent conditions. Such cloud portions include, for instance, intensely turbulent fuel-air jets resulting from a high-pressure

"side-on" overpressure, bar

"scaled distance" =

actual distance, . ,„ ^ — mkg-''3 \/wTNT

Figure 7.1. Hopkinson-scaled TNT charge blast.

release or areas in the cloud where congestion/obstruction or partial confinement acts as turbulence-generating boundary conditions in the expansion flow. The consequence is that vapor cloud explosion blast should be approached as a number of sub-blasts corresponding with the number of potential blast sources identified in the cloud. Therefore, the explosive potential of a vapor cloud can be expressed as a corresponding number of equivalent fuel-air charges whose characteristics can be determined by following the flow chart below in a step-by-step approach: Assume deflagrative combustion. I Identify blast sources.

I Determine charge energies. I

Estimate charge strengths.

i Calculate scaled distance. 4 Read scaled-blast properties from chart. I Calculate real-blast properties.

7.2.2.7. Identify Potential Centers of Strong Blast Potential centers of strong blast are found in areas in a cloud which are in intensely turbulent motion when reached by the flame. Such cloud areas are described in the introduction to this section. Practical examples of potential centers of strong blast in vapor cloud explosions are • High-velocity jets releasing fuel at high pressure as a result of a pipe or vessel leak; • Densely configured objects, for example, —densely spaced process equipment in chemical plants or refineries (e.g., multilevel rack structures), —pipe racks, —piles of car wrecks, —piles of crates or drums • The spaces between long parallel planes, for example, —concrete platforms carrying process equipment in chemical plants, —beneath clusters of cars in parking lots or railroad switching yards, —open multistory buildings, for example, multistory parking garages • The space within tubelike structures, for example, —tunnels, bridges, corridors, sewage systems, culverts, etc. Portions of a cloud not meeting these criteria are assumed to produce blast of consideraly lower strength. 7.2.2.2. Determine the Energy of Equivalent Fuel-Air Charges Consider each blast center separately. • Assume that the full quantities of fuel-air mixture present within the partially confined/obstructed areas and jets, identified as blast sources in the cloud, contribute to the blasts. • Estimate the volumes of fuel-air mixture present in the individual areas identified as blast sources. This can be done on the basis of the overall dimensions of the areas and jets. Note that the flammable mixture may not fill an entire

blast source volume. Also note that the blast source volume should be corrected if equipment represents an appreciable proportion of the volume. • Calculate the combustion energy E (J) for each blast by multiplying the individual volumes of mixture by 3.5 x 106 J/m3. Table 7.1 demonstrates that 3.5 x 106 J/m3 is a reasonable average value for the heat of combustion of a stoichiometric hydrocarbon-air mixture. 7.2.2.3. Determine Initial Blast Strengths Experimental data (Section 4.1) may be used to estimate a blast's initial strength. These data indicate that deflagrative gas explosions may develop overpressures ranging from a few millibars under completely unconfined or unobstructed conditions to greater than 10 bars under severely confined and obstructed conditions. Therefore, for a safe and conservative estimate of the strength for the sources of strong blast, an initial strength of 10 should be chosen; however, a source strength of 7 seems to more accurately represent actual experiment. The rest of the cloud, which is unconfined and unobstructed, will produce blast of considerably lower strength. An initial strength of 2 seems to be a conservative estimate for this portion. Finding a better means of specifying initial strengths is, however, a major issue in present research. 7.2.2.4. Blast Effects Once the energy quantities E and the initial blast strengths of the individual equivalent fuel-air charges are estimated, the Sachs-scaled blast side-on overpressure and

TABLE 7.1. Heat of Combustion of Common Hydrocarbons and Hydrogen (Harris 1983) Heat of Combustion (288 K, 1 atm)

Fuel Methane Ethane Ethylene Propane Propylene Butane Butylene Cyclohexane Hydrogen

(MJIm3) 34 60.5 56 86.4 81.5 112.4 107.1 167.3 10.2

(%)

Heat of Combustion Stoichiometrically Mixed with Air (MJIm3)

9.5 5.6 6.5 4.0 4.4 3.1 3.4 2.3 29.5

3.23 3.39 3.64 3.46 3.59 3.48 3.64 3.85 3.01

Stoichiometric Volume Ratio

positive-phase duration at some distance R from a blast source can be read from the blast charts in Figures 7.2a and b after the Sachs-scaled distance is calculated:

R = —^-r m

(7.4)

(E/PQ)

where (-) (m)

dimensionless maximum 'side on1 overpressure (APg)

R = Sachs-scaled distance from charge center R = real distance from the charge center

R

°

—

combustion energy-scaled distance (R)

Figure 7.2a. Sachs-scaled side-on peak overpressure of blast from a hemispherical fuel-air charge.

dimensionless positive phase duration (t+)

combustion energy-scaled distance (R)

P0 « atmospheric pressure C 0 = atmospheric sound speed E = amount of combustion energy R0 = charge radius

Figure 7.2b. Sachs-scaled positive-phase duration of blast from a hemispherical fuel-air charge.

E = charge combustion energy P0 = ambient pressure

(J) (Pa)

The real blast side-on overpressure and positive-phase duration can be calculated from the Sachs-scaled quantities: (7.5a) and

<7.5b) where AP5 APS PQ t+ f+

= = = = =

side-on blast overpressure Sachs-scaled side-on blast overpressure ambient pressure positive-phase duration Sachs-scaled positive-phase duration

(Pa) (-) (Pa) (s) (-)

E C0

= charge combustion energy = ambient speed of sound

(J) (m/s)

If separate blast sources are located close to one another, they may be initiated almost simultaneously. Coincidence of their blasts in the far-field cannot be ruled out, and their respective blasts should be superimposed. The safe and most conservative approach to this issue is to assume a maximum initial blast strength of 10 and to sum the combustion energy from each source in question. Further definition of this important issue, for instance, the determination of a minimum distance between potential blast sources for separate consideration of their individual blasts, is a factor in present research.

7.3. SAMPLE CALCULATIONS The outcome of a vapor cloud explosion hazard assessment can depend greatly on the method chosen, as demonstrated in this subsection with sample calculations.

7.3.1. Vapor Cloud Explosion Hazard Assessment of a Storage Site Problem. A storage site consists of three propane storage spheres (indicated as F9110, F9120, and F9130) and a 50-m diameter butane storage tank (indicated as F9210) on an open site (Figures 7.3a and 7.3b). To diminish inflow of heat from the soil, the butane storage tank is placed 1 m above the earth's surface on a concrete pylon array (Figure 7.3a). A parking lot with space for 100 cars is situated next to the tank farm. An accidental release of 20,000 kg of propane is postulated in this environment. The propane is released from a 0.1-m-diameter leak in the unloading line of sphere F9120. The propane is released at about 8 bars overpressure and mixes with air in a high-velocity jet. Quantify the explosive potential of a vapor cloud which results from the postulated propane release, and calculate the potential blast effects. Because it is dense, the flammable propane-air cloud spreads in a thin layer and covers a substantial area, including the tank farm and parking lot. An overview of the tank farm site is given by the map in Figure 7.3b. Data heat of combustion propane = 46.3 MJ/kg mean specific heat liquid propane = 2.41 kJ/kg/K latent heat propane = 410 kJ/kg boiling temperature of propane at ambient pressure = 231 K ambient temperature = 293 K

F-9210

F-9110

F- 9120

unloading control room

car park unloading control room

Figure 7.3. (a) View of a storage tank farm for liquefied hydrocarbons, (b) Plot plan of the tank farm.

7.3.1.1. Conventional TNT-Equivalency Method Determine charge weight. The HSE TNT-equivalency method expresses the potential explosive power of a vapor cloud as one, single, equivalent TNT-charge located in the cloud's center. The equivalent charge weight of TNT is proportionally related to the quantity of fuel in the cloud and can be determined according to the following stepwise procedure: • Determine the flash fraction of the fuel on the basis of actual thermodynamic data, using Eq. (7.1):

where F = flash fraction Cp = mean specific heat Ar = temperature difference between ambient temperature and boiling temperature at ambient pressure L = latent heat

(-) (kJ/kg/K) (K) (kJ/kg)

• The weight of fuel in the cloud is equal to the flash fraction times the quantity of fuel released. To allow for spray and aerosol formation, the cloud inventory should be multiplied by 2. (The weight of fuel in the cloud may not, of course, exceed the total quantity of fuel released.) Consequently, the cloud inventory equals: Wt = 2 x 0.31 x 20,000 = 12,400 kg of propane. • The equivalent charge weight of TNT can now be calculated using Eq. (7.2) as follows:

where WTNT Wf Hf J/TNT ctc

= = = = =

equivalent weight of TNT weight of fuel in the cloud heat of combustion fuel blast energy TNT = 4.68 MJ/kg TNT-equivalency / yield factor = 0.03

(kg) (kg) (MJ/kg) (MJ/kg) (-)

Blast effects. Once the equivalent charge weight of TNT in kilograms has been determined, the side-on peak overpressure of the blast wave at some distance R from the charge can be found with Eq. (7.3):

where R = Hopkinson-scaled distance R = real distance !from the charge WJNT = charge weight of TNT

(m/kg1/3) (m) (kg)

Once the Hopkinson-scaled distance from the charge is known, the corresponding side-on peak overpressure can be read from the chart in Figure 7.1. Table 7.2 gives results for several distances. 7.3.1.2. Multienergy Method The multienergy method applies only if detonation of unconfined parts of a vapor cloud can be ruled out. If so, the explosive potential of a vapor cloud is determined primarily by the blast-generative properties of the environment in which the vapor is released and disperses. Consequently, a vapor cloud explosion can be regarded as a number of subexplosions. Therefore, the first step in applying the multienergy method in vapor cloud explosion hazard assessment is Identify potential sources of blast: • The space beneath the storage tank. This configuration of extended parallel planes, internally provided with a large number of vertical obstacles (the pylon forest), is an outstanding example of blast-generative boundary conditions. • The parking lot. The partially confined space beneath a large number of closely parked cars provides a condition allowing a combustion process to develop high-strength blast. • The jet by which the propane is released. The jet's propane-air mixture is in intensely turbulent motion and will develop an explosive combustion rate and blast effects on ignition. • In the rest of the cloud, which is unconfined and unobstructed, no explosive combustion rates can be maintained nor developed.

TABLE 7.2. Side-On Peak Overpressure for Several Distances from Charge Expressing Explosive Potential of a Vapor Cloud at a Storage Site for Liquefied Hydrocarbons Distance from Charge (m)

50 100 200 500 1000

Scaled Distance from Charge (m/kg1'3)

Side-on Peak Overpressure (bar)

3.24 6.48 12.95 32.38 64.77

0.68 0.21 0.084 0.025 0.013

Determine the size of equivalent fuel-air charges. Consider each blast source separately. Assume that the full quantity of fuel-air mixture present within the volume identified as a source of blast contributes to blast in a hemispherical fuel-air charge. The contributing combustion energy within each charge is found by assuming a stoichiometric composition, then multiplying charge volumes by the heat of combustion, 3.5 MJ/m3. • The mixture present within the space beneath the storage tank (50 m diameter, 1 m high) is transformed into a hemispherical fuel-air charge of equal volume (ignoring pylon volume): TT x 252 x 1 = 1963 m3

The energy content E of the hemispherical charge can then be calculated as E1 = 1963 x 3.5 = 6870 MJ • The quantity of mixture present beneath the cars possibly parked in the parking lot can only be estimated, so a conservative assumption should be used. Assume that a maximum number of 100 cars are parked closely together. An average car occupies an area of approximately 6 x 3 = 18 m2 (including intervening space), and the free space beneath an average car is approximately 0.3 m high. Then, 100 cars create a partially confined space of 100 x 0.3m x 18m 2 = 54Om 3 which corresponds with a quantity of energy of E1 = 540 x 3.5 = 1890 MJ

• The quantity of mixture present in the propane-air jet can only be estimated if a simplifying assumption is made that the jet flow is not influenced by rigid objects. If not, according to the Yellow Book (1979), the volume of flammable mixture in the jet equals 215m3, which corresponds to a quantity of energy of E3 = 215 x 3.5 = 753 MJ

• Only E1 + E2 + E3 = 6870 + 1890 + 753 = 9513 MJ of the total quantity of combustion energy within the cloud (20,000 x 4613 = 926,000 MJ) is involved in explosive-blast-generating combustion. The rest of the cloud contains the greater part of the propane which represents a quantity of combustion energy of 926,000 - 9513 = 916,487 MJ. In summary, the potential explosive power of the vapor cloud can be expressed as four equivalent fuel-air charges whose initial strengths remain to be determined. Determine the initial strengths of the charges. A quick, simple, yet conservative approach to estimating the initial strengths of the four charges expressing the potential explosive power of the vapor cloud follows:

• Assume that the three fuel-air charges identified above as sources of strong blast each has a maximum initial strength, 7. • Assume that the remainder of the cloud is of minor blast significance, and assign its fuel-air charge a value of 2. Therefore, the potential explosive power of the vapor cloud can be expressed as four equivalent fuel-air charges whose characteristics and locations are listed in Table 7.3. Equivalent charges expressing the vapor cloud's potential explosive power are now known, both in scale and in strength. Their corresponding blast effects remain to be determined. Blast effects. Scales and strengths of charges have been determined above. Next calculate the nondimensionalized distances for the respective charges at any wanted distance R from the blast centers using Eq. (7.4): * = _*-_ (EIP^

where R R E P0

= = = =

nondimensionalized distance from charge distance from charge charge combustion energy ambient pressure = 101,325 Pa

(-) (m) (J)

For instance, calculate the blast produced at a distance of 500 m from each of the four charges. The nondimensionalized distance equals Charge I:

—

R=

son

^ = 12.3 (6870 x 106/101,325)1/3

TABLE 7.3. Characteristics and Locations of Charges Expressing Potential Explosive Power of Vapor Cloud at Liquefied Hydrocarbon Storage Tank Farm

Site

Combustion Energy MJ

Strength

Location

Butane tank (charge I)

6,870

7

Center of the space underneath tank

Parking lot (charge II)

1,890

7

Center of parking lot

753

7

Center of jet

916,487

2

Center of cloud

Propane-air jet (charge III) Rest of the cloud (charge IV)

Charge II:

Charge III:

Charge IV: Once the nondimensionalized distances from each charge are determined, the corresponding nondimensionalized blast parameters can be read from charts in Figure 7.2a and b. These nondimensionalized blast parameters are collected in Table 7.4. The nondimensionalized side-on peak overpressures and their respective positive-phase durations can be transformed into real values for side-on peak overpressures and positive-phase durations by calculating: Charge I:

t+ Charge H:

'+ Charge HI:

t+ Charge IV: t+

TABLE 7.4. Nondimensionalized Blast Parameters at 500 m Distance from Three Charges, Read from Charts in Figure 7.2a and b Charge Charge Charge Charge Charge

I Il III IV

R (m)

E (MJ)

Strength Number

_ R

_ AP8

i+

500 500 500 500

6,870 1,890 753 916,487

7 7 7 2

12.3 18.9 25.6 2.40

0.019 0.012 0.009 0.006

0.47 0.50 0.52 3.0

where AP5 AP5 P0 f+ f+ E C0

= = = = = = =

side-on peak overpressure nondimensionalized side-on peak overpressure ambient pressure = 101,325 Pa positive-phase duration nondimensionalized positive-phase duration charge combustion energy ambient speed of sound = 340 m/s

(Pa) (-) (s) (-) (J)

This operation can be repeated for any desired distance. Results for some distances are tabulated in Tables 7.5a, 7.5b, 7.5c, and 7.5d.

7.3.2. Vapor Cloud Explosion as a Consequence of Pipe Rupture at a Chemical Plant Problem. Large quantities of combustible materials are stored and processed in process industries, often under high pressures and at high temperatures. Such activi-

TABLE 7.5a. Side-On Peak Overpressure and Positive-Phase Duration of Blast Produced by Charge I (E = 6870 MJ, Strength Number 7) A p ~ f l ~ ~ s ~

(m)

R

AP8

(kPa)

(bar)

t+

(s)

50 100 200 500 1000

1.23 2.45 4.90 12.3 24.5

0.34 0.12 0.052 0.019 0.0090

34.5 12.2 5.27 1.93 0.91

0.34 0.12 0.053 0.019 0.009

0.32 0.35 0.43 0.47 0.50

0.38 0.042 0.052 0.056 0.060

TABLE 7.5b. Side-On Peak Overpressure and Positive-Phase Duration of Blast Produced by Charge Il (E = 1890 MJ, Strength Number 7) ~R " ~~ AP8 ~

(m)

R

AP8

(kPa)

(bar)

i+

(s)

50 100 200 500 1000

1.89 3.77 7.54 18.9 37.7

0.17 0.070 0.032 0.012 0.0055

17.2 7.09 3.24 1.22 0.56

0.17 0.071 0.032 0.012 0.006

0.35 0.40 0.45 0.50 0.54

0.027 0.031 0.035 0.039 0.042

TABLE 7.5c. Side-On Peak Overpressure and Positive-Phase Duration of Blast Produced by Charge III (E = 753 MJ, Strength Number 7) ~R

~

~

P

*

*

~

(m)

R

AP8

(kPa)

(bar)

i+

(s)

50 100 200 500 1000

2.56 5.12 10.2 25.6 51.2

0.11 0.050 0.023 0.009 0.0040

13.2 5.07 2.33 0.91 0.41

0.13 0.051 0.023 0.009 0.004

0.37 0.40 0.46 0.50 0.55

0.021 0.023 0.026 0.029 0.032

TABLE 7.5d. Side-On Peak Overpressure and Positive-Phase Duration of Blast Produced by Charge IV (E = 916,487 MJ, Strength Number 2)

~R~

(m)

~

R

A

I

AP8

p

s

~

(kPa)

(bar)

i+

(s)

50

0.24

0.20

2.03

0.02

4.0

2.5

100

0.48

0.020

2.03

0.02

3.2

2.0

200

0.96

0.013

1.32

0.013

3.0

1.8

500 1000

2.40 4.80

0.006 0.0028

0.59 0.28

0.006 0.003

3.0 3.0

1.8 1.8

ties pose vapor cloud explosion hazards. This was demonstrated, for example, by the events that occurred on June 1, 1974, at the Nypro Ltd. plant at Flixborough, UK, whose layout is shown by the plot plan in Figure 7.4. Data published by Sadee et al. (1976/1977), Gugan (1978), and Roberts and Pritchard (1982) serve as starting points for this case study. Because a pipe between two reactor vessels in the oxidation plant (see plan) ruptured, a large amount of cyclohexane was released within some tens of seconds at high pressure (10 bars) and temperature (423 K). The material quickly mixed with air, thus resulting in a large vapor cloud covering a substantial part of the plant area (Figure 7.4). In addition to the oxidation plant and the caprolactam plant, indicated in Figure 7.4 as Section 7 and 27 to the right of the explosion center, the cloud covered a large, more-or-less open area toward the hydrogen plant. The flammable cloud found an ignition source, probably somewhere in the hydrogen plant. The fire flashed back to the gas leak where, in between the densely spaced process equipment of the oxidation plant and the caprolactam plant, it found conditions under which intense and explosive combustion developed. The consequences were devastating. Twentyeight people were killed, and dozens were injured. The plant was totally destroyed.

Figure 7.4. Plot plan of Nypro Ltd. plant at Flixborough, UK.

Windows were damaged for several miles. Reconstruct the explosive power and blast effects of the vapor cloud explosion on the basis of the available data. The exact amount of cyclohexane released is unclear, but it escaped from a system consisting of five reactor vessels containing a total quantity of 250,000 kg (Gugan 1978). However, a complete discharge is unlikely. If an almost complete discharge of the two vessels adjacent to the ruptured pipe is assumed, a total quantity of 100,000 kg of cyclohexane would have been released. Data heat of combustion cyclohexane = 46.7 MJ/kg mean specific heat liquid cyclohexane = 1.8 kJ/kg/K latent heat cyclohexane = 674 kJ/kg process temperature in reactor vessels = 423 K boiling temperature at ambient pressure = 353 K 7.3.2.1. Conventional TNT-Equivalency Methods Determine charge weight. If conventional TNT-equivalency methods are applied, the potential explosive power of a vapor cloud is expressed as one single, equivalentTNT charge located at the cloud's center. The equivalent-charge weight of TNT is proportionally related to the fuel quantity within the cloud and can be determined according to the following stepwise procedure: • Determine the flash fraction of fuel on the basis of actual thermodynamic data. The flash fraction for cyclohexane at 423 K can be calculated from Eq. (7.1):

where F = flash fraction Cp = mean specific heat A7 = temperature difference between process temperature and boiling temperature at ambient pressure L = latent heat e = base of natural logarithm = 2.718

(-) (kJ/kg/K) (K) (kJ/kg) (-)

• The weight of fuel in the cloud is equal to the flash fraction times the quantity of fuel released. To allow for spray and aerosol formation, the cloud inventory should be multiplied by 2. (The weight of fuel in the cloud may not, of course, exceed the total quantity of fuel released.) If a release of 100,000 kg of cyclohexane is assumed, the weight of fuel in the cloud equals:

Wf = 2 X 0.17 x 100,000 = 34,000 kg This rather speculative figure is in reasonable agreement with Sadee et al.'s (1976/1977) estimate. • The equivalent charge weight of TNT can now be calculated from Eq. (7.2) as follows:

where WTNT Wf Hf //TNT ae

= = = = =

equivalent weight of TNT weight of fuel in the cloud heat of combustion fuel TNT blast energy = 4.68 MJ/kg TNT-equivalency / yield factor = 0.03

(kg) (kg) (MJ/kg) (-)

Blast effects. Once the equivalent charge weight of TNT in kilograms is known, the side-on peak overpressure of the blast wave at some distance R from the charge can be found by calculating the Hopkinson-scaled distance using Eq. (7.3):

where R = Hopkinson-scaled distance R = real distance from the charge WTNT = charge weight of TNT

(m/kg173) (m) (kg)

Once the Hopkinson-scaled distance from the charge is known, the corresponding side-on peak overpressure can be read from the chart in Figure 7.1. Table 7.6 includes these values for several distances. TABLE 7.6. Side-On Peak Overpressure for Several Distances from Charge Expressing Explosive Power of the Flixborough Vapor Cloud Explosion Distance from Charge (m) 50 100 200 500 1000 2000

Scaled Distance from Charge (m/kg1/3)

Side-On Peak Overpressure (bar)

2.3 4.6 9.2 23 46 92

1.2 0.39 0.13 0.04 0.018 0.010

7.3.2.2. Multienergy Method The multienergy approach treats vapor cloud explosions as a number of subexplosions, and recognizes that the explosive potential of a vapor cloud is primarily determined by the blast-generative properties of the environment in which the vapor is released and disperses. Therefore, the following steps to determining blast strength and effects apply: Identify potential blast sources. Data provided by the literature (Sadee et al. 1976/ 1977; Gugan 1978; Robert and Pritchard 1982) identified potential blast sources. The plot plan in Figure 7.4 shows that the cloud covered a substantial area: the oxidation and caprolactam plants (indicated in Figure 7.4 as Section 7 and 27) and also the more-or-less open area toward the hydrogen plant. The photographs in Figures 7.5a and 7.5b, showing the wreckage of both the cyclohexane oxidation plant and caprolactam plants, clearly illustrate elements of partial confinement as previously described: densely spaced process equipment mounted in open buildings consisting of parallel concrete floors. The areas covering the cyclohexane oxidation and caprolactam plants should be considered sources of strong blast. No significant contribution to blast should be expected from the rest of the cloud, because it is unconfined and unobstructed. Determine the scale of equivalent fuel-air charges. Consider each blast source separately. Assume that the entire volume of fuel-air mixture present in each cloud portion identified as a source of strong blast contributes to the blast. The blast originating from each source is modeled as though it were from a hemispherical fiiel-air charge. The combustion energy contributing to each respective charge is found by assuming a stoichiometric composition and by multiplying the volume of each source by the fuel's heat of combustion, 3.5 MJ/m3. The scale of the charge representing the potential explosive power of the single source of strong blast identified is determined by calculation of the quantity of combustion energy of flammable mixture within the partially confined volume. In this case, it is the volume of space between parallel concrete floors and obstructed by the densely spaced equipment in both the hexane oxidation plant and the caprolactam plant. On the basis of the scale of the plan in Figure 7.4 and the photographs in Figures 7.5a and 7.5b, an approximate estimate of the partially confined or obstructed volume V of vapor can be made: V = 100 x 50 x 10 = 5 x 104 m3.

This volume corresponds with a quantity of combustion energy of E = 50,000 x 3.5 = 175,000 MJ. Consequently, the potential explosive power of the rest of the cloud, covering a more-or-less open area, can be expressed as a fuel-air charge of 34,000 x 46.7 - 175,000 = 1,412,80OMJ.

Figure 7.5. (a) Remnants of the caprolactam plant (explosion center) (Roberts and Pritchard, 1982). (b) Remnants of the cyclohexane oxidation plant (explosion center) (Gugan 1979).

Determine the initial strengths of the charges. A quick and simple approach to estimation of initial strengths of the charges expressing the potential explosive power within the vapor cloud is to use the following safe and conservative approach: • The fuel-air charge expressing the explosive power of the source of strong blast is assumed to be of strength number 10. • The fuel-air charge expressing the explosive power within the rest of the vapor cloud is assumed to be of strength number 2. Thus, the potential explosive power of the vapor cloud can be expressed as two equivalent fuel-air charges whose characteristics and locations are listed in Table 7.7. Once equivalent charges expressing the vapor cloud's potential explosive power are known, both in scale and strength, corresponding blast effects can then be determined. Blast effects. The side-on peak overpressures and positive-phase durations of blast waves produced by the respective charges for any selected distance, R, can be found by calculating separately for each charge

jg =

R (ElP0)1'3

where R R E P0

= = = =

nondimensionalized distance from charge distance from charge charge combustion energy ambient pressure = 101,325 Pa

(-) (m) (J)

Calculate the properties of the blast produced at a distance of 1000 m from each of the two charges. The nondimensionalized distance equals Charge I:

— R=

1000 ^ = 8.3 (175,000 x 106/101,325)1/3

TABLE 7.7. Characteristics and Locations of Fuel-Air Charges Expressing Potential Explosive Power of the Flixborough Vapor Cloud Combustion Energy E (MJ) Equipment (charge I) Rest of the cloud (charge II)

Strength (Number)

Location

175,000

10

Center of equipment

1,412,800

2

Center of cloud

TABLE 7.8. Nondimensionalized Blast Parameters at 1000 m Distance from Two Charges, Read from Charts in Figures 7.2a and 7.2b.

Charge I Charge Il

R (m)

E (MJ)

Strength Number

_ R

_ AP8

i+

1000 1000

175,000 1,412,800

10 2

8.3 4.2

0.028 0.0032

0.45 3.0

Charge U: Once the nondimensionalized distances from each charge are known, the corresponding nondimensionalized blast parameters can be read from the charts in Figures 7.2a and 7.2b. The nondimensionalized blast parameters read are tabulated in Table 7.8. The nondimensionalized side-on peak overpressures and positive-phase durations read from the tables can be converted into real values for side-on peak overpressures and positive-phase durations as follows: Charge I: '+ =

Charge II: '+

where AP8 AP8 P0 f+ t+ E C0

= = = = = = =

side-on peak overpressure nondimensionalized side-on peak overpressure ambient pressure = 101,325 Pa positive-phase duration nondimensionalized positive-phase duration charge combustion energy ambient speed of sound = 340 m/s

(Pa) (-) (s) (-) (J)

This operation can be repeated for any desired distance. Results for selected distances are given in Tables 7.9a and 7.9b.

TABLE 7.9a. Side-on Peak Overpressure and Positive-Phase Duration of Blast Produced by Charge I (E = 175,000 MJ, strength number 10)

B

I

(m)

50 100 200 500 1000 2000 5000

I

AP

R

AP8

(kPa)

0.41 0.83 1.67 4.17 8.34 16.67 41.68

3.4 0.70 0.21 0.065 0.028 0.013 0.0050

345 70.9 21.3 6.59 2.84 1.32 0.51

*

(bar) 3.45 0.71 0.21 0.066 0.028 0.013 0.005

i+ 0.15 0.19 0.29 0.40 0.45 0.49 0.53

~

(s)

0.053 0.067 0.102 0.141 0.159 0.173 0.187

TABLE 7.9b. Side-on Peak Overpressure and Positive-Phase Duration of Blast Produced by Charge Il (E = 1,412,800 MJ, strength number 2) f

(m) 100 200 500 1000 2000

l

I

~

R

AP8

0.42 0.83 2.08 4.15 8.31

0.020 0.016 0.0065 0.0032 0.0016

A

P

s

~

(kPa)

(bar)

i+

(s)

2.03 1.62 0.66 0.32 0.16

0.020 0.016 0.007 0.003 0.002

3.3 3.0 3.0 3.0 3.0

2.3 2.1 2.1 2.1 2.1

7.4. DISCUSSION In the preceding section, two case studies were performed: • a vapor cloud explosion hazard analysis of an imaginary leak scenario in a tank farm for liquefied hydrocarbons; • a reconstruction of the blast effects due to a real vapor cloud explosion incident, the Flixborough explosion. In each case, two different methods were used in arriving at estimates: the HSE TNT-equivalency method and the multienergy method. The results, in the form of side-on blast peak overpressures for various distances from blast centers, are listed in Table 7.10. In addition, some peak overpressures estimated by Sadee et al. (1976/ 1977) from Flixborough-incident damage patterns are included. The photographs in Figures 7.6a and 7.6b illustrate the practical effects of such overpressures. The two methods gave considerably different results when applied to the liquid hydrocarbon storage site case study. The TNT-equivalency method systematically

TABLE 7.10. Results of INT-Equivalency Method and Multienergy Method Applied to Two Case Studies Side-on Blast Peak Overpressure (bar) Distance (m)

50 100

200

500

1000

2000

Storage Site TNT

ME

0.68 0.21

0.34 0.12

0.084

0.025

0.013

0.052

0.019

0.009

Flixborough TNT

ME

D/s,a/7ce

Observed

(m)

0.45-0.55 0.45-0.55 0.50-0.70 0.30-0.40

120 130 135 160

0.20-0.35 0.20-0.28 0.17-0.20 0.17-0.20 0.13-0.15 0.13-0.15 0.10-0.14

220 230 230 290 335 350 400

0.10-0.12 0.03-0.04 0.02-0.03 0.04-0.06 0.01 -0.02

535 700 825 885 945

0.02-0.03 0.01-0.02

1190 1340

0.007 0.007

2440 2745

1.2 3.45 0.39 0.71

0.13 0.21

0.04

0.066

0.018 0.028

<0.010 0.013

predicts a heavier blast effect than the multienergy method. On the other hand, the outcomes of the two methods for the Flixborough vapor cloud explosion case study show relatively good agreement, particularly for the intermediate field. In both the near and far fields, side-on peak overpressure results diverge. This divergence is indicative of the difference between decay characteristics of TNT and fuel-air blasts. Blast overpressures calculated by the TNT-equivalency method are in reasonable agreement with the overpressures deduced from observed damage (Sadee et al. 1976/1977). This is to be expected, because the Flixborough incident is one of the major vapor cloud explosion incidents on which the TNT-equivalency value of

Figure 7.6. (a) Damage to canteen building 130 m from explosion center. Estimated peak overpressure level: 0.45-0.55 bar (Sadee et al. 1976/1977). (b) Damage to row of houses 535 m from explosion center. Estimated peak overpressure level: 0.10-0.12 bar (Sadee et al 1976/1977).

3% (HSE method) was based. Therefore, a TNT equivalency of 3% is a reasonable measure of expression of the explosive power of a vapor cloud under conditions similar to those at Flixborough. Such conditions may be considered "typical major incident" conditions. Generally speaking, "typical major incident" conditions correspond to a release of some ten thousands of kilograms of some hydrocarbon at the site of a chemical plant or refinery that is characterized by the presence of obstructed and partially confined areas in the form of densely spaced equipment. The relative agreement with results derived from the multienergy method indicates that application of this concept is a reasonable approach for this case study. On the other hand, a TNT equivalency of 3% is expected to fail in situations where "typical major incident" conditions do not apply. This explains why the outcomes of the two methods applied to the storage site case study differed.

REFERENCES Gugan, K. 1978. Unconfined vapor cloud explosions. Rugby: IChemE. Harris, R. J. 1983. The investigation and control of gas explosions in buildings and heating plant. New York: E & FN Spoor. Health & Safety Executive. 1979. Second Report Advisory Committee Major Hazards. U.K. Health and Safety Commission. Health & Safety Executive. 1986. The effect of explosions in the process industries. Loss Prevention Bulletin. 68:37-47. Roberts, A. F., and D. K. Pritchard. 1982. Blast effects from unconfined vapor cloud explosions. J. Occ. Ace. 3:231-247. Sadee, C., D. E. Samuels, and T. P. O'Brien. 1976/1977. The characteristics of the explosion of cyclohexane at the Nypro (UK) Flixborough plant on 1st June 1974. J. Occ. Ace. 1:203-235. Van den Berg, A. C. 1985. The Multi-Energy method—A framework for vapor cloud explosion blast prediction. J. Haz. Mat. 12:1-10. Yellow Book. Committee for the Prevention of Disasters, 1979. Methods for the calculation of physical effects of the escape of dangerous materials, P.O. Box 69, 2270 MA Voorburg, The Netherlands.

8 FLASH FIRES—SAMPLE PROBLEMS In this chapter, the methods described in Chapter 5 are demonstrated in cases. Section 4.1. reviewed experimentation on vapor cloud explosions. There, it was shown that the combustion process in a vapor cloud develops an explosive intensity and attendant blast effects only if certain conditions are met. These conditions include • • • •

partial confinement and/or obstruction, jet release, explosively dispersed cloud, high-energy ignition.

Consequently, if none of these conditions is present, no blast effects are to be expected. That is, under fully unconfined and unobstructed conditions, the cloud burns as a flash fire, and the major hazard encountered is heat effect from thermal radiation. The subject of flash fires is a highly underdeveloped area in the literature. Only one mathematical model describing the dynamics of a flash fire has been published. This model, which relates flame height to burning velocity, dependent on cloud depth and composition, is the basis for heat-radiation calculations. Consequently, the calculation of heat radiation from flash fires consists of determination of the flash-fire dynamics, then calculation of heat radiation.

8.1. METHOD 8.1.1. Flash-Fire Dynamics Flash-fire dynamics are determined by a model which relates flame height to a cloud's depth and composition, and to flame speed. On the basis of experimental observations, flame speed was roughly related to wind speed. Flame height can be computed from the following expression:

(8.1)

where H S C/w d g P0 pa r a

= = = = = = = = =

visible flame height 2.3 x £/w = flame speed wind speed cloud depth gravitational acceleration fuel-air mixture density density of air stoichiometric air-fuel mass ratio expansion ratio for stoichiometric combustion under constant pressure (typically 8 for hydrocarbons)

W

=o^l a(l - c|>st)

fOT

(m) (m/s) (m/s) (m) (m/s2) (kg/m3) (kg/m3) (-) (-)

*>*«

w = 0 for <|> ^ <|>st <|> = fuel-air mixture composition (fuel volume ratio) <}>st = stoichiometric mixture composition (fuel volume ratio)

(-) (-)

Flame height and speed can now be computed, but flame position and shape as a function of time must be specified. The position and shape of a flame depend upon cloud shape and location of the ignition point within the cloud. If the cloud is a plume, flame shape can be approximated by a flat plane of constant cross-section consuming the plume in a lengthwise direction. If, on the other hand, the cloud shape is more circular (pancake-shaped), flame shape is dependent on the location of ignition site. Central ignition results in a circular flame, while in the case of edge ignition, the flame shape should be approximated by a flat plane whose crosssectional area varies during propagation. Flame shape is important in calculating flame-radiation emissions. A geometric view factor is used to describe the effects of flame shape. 8.1.2. Heat Radiation The heat radiation received by an object depends on the flame's emissive power, the flame's orientation with respect to the object, and atmospheric attenuation, that is q = £FTa

(8.2)

where q E F Ta

= = = =

radiation heat flux emissive power geometric view factor atmospheric attenuation (transmissivity)

(kW/m2) (kW/m2) (-) (-)

Experimental data on the emissive power of flash fires are extremely scarce. The only value available is 173 kW/m2 for LNG and propane flash fires. Geometric

view factor can be determined from the relative positions and orientations of the receiving and the transmitting surfaces. Geometric view factors are tabulated and graphically represented in Appendix A for cylindrical and plane vertical transmitters and for various orientations of receiving surfaces. Equations describing the atmospheric transmissivity are discussed in Section 3.5.2. The thermal radiation intensity of a flash fire can be calculated after parameters such as cloud shape and gas or vapor concentration distribution have been determined through dispersion calculations. Subsequently, the thermal radiation intensity is calculated through the following steps: 8.1.2.1. Calculation of Flame Height Calculate the flame speed on the basis of the wind speed £/w:

S = 2.3 x £/w

(8.3)

Calculate the square of the ratio of fuel density and the density of air from molecular weights:

(8.4) Calculate the stoichiometric air-fuel mass ratio, r, from the stoichiometric mixture composition, <|>st, and air and fuel molecular weights:

(8.5) Calculate w from the actual mixture composition <|>, the stoichiometric mixture composition <j>st and the expansion ratio for stoichiometric combustion a:

(8.6) Calculate the flame height from the cloud depth d, gravitational acceleration g, S (Pc/Pa)2» w> ^d r as follows:

(8.7)

8.1.2.2. Assumption of Flame Shape and Dimensions during Flame Propagation In addition to flame height, other flame dimensions must also be known. In general, flame shape must be assumed. A flame's surface area and position both vary during the course of the flash fire, so, if based on manual calculations, flame shape

assumptions must be very simple. One such assumption could be that the flame has a flat front whose width is equal to the cloud's width from the moment of ignition. In general, assumptions must be conservative. That is, simplifying assumptions about flame shape should result in higher radiation levels than one might actually expect. Some examples are shown in Figure 8.1. In Figures 8.1a and 8.1b, the flame shape is assumed to be flat, whereas in Figure 8.1c, the flame is cylindrical. In these figures, the following notation is used: D L R S t W 4

= = = = = = =

cloud diameter ignition source height cloud radius flame speed time flame width ignition source

(m) (m) (m) (m/s) (s) (m) (-)

8.1.2.3. Radiation Heat Flux Radiation heat flux is strongly time dependent, because both the flame surface area and the distance between the flame and intercepting surfaces vary during the course of a flash fire. The path of this curve can be approximated by calculating the radiation heat flux at a sufficient number of discrete points in time. The problem focuses on determination of the geometric view factor, which can be read from tables and graphs in Appendix A. View factors for cylindrical flames

Figure 8.1. Flame shape assumptions.

are given for vertical cylinders only. View factors for planar flames are given assuming a vertical-plane emitter. Thus, the final steps for calculating the radiation heat flux are as follows: • • • •

Assume a flame shape. Determine the distance between the flame and the object (X). Determine the view factor (F). Determine the atmospheric transmissivity using one of the equations presented in Chapter 3, Section 3.5.2., which describes the graphs presented in Appendix A: Ta = log(14.1 RH-0108X'013)

(8.8)

where Ta is transmissivity, RH is the relative humidity in percent, and X is the distance in meters between flame and object. • Determine the radiation heat flux using q = EFr3 on the basis of E = 173 kW/m2.

8.2. SAMPLE CALCULATION A massive amount of propane is instantaneously released in an open field. The cloud assumes a flat, circular shape as it spreads. When the internal fuel concentration in the cloud is about 10% by volume, the cloud's dimensions are approximately 1 m deep and 100 m in diameter. Then the cloud reaches an ignition source at its edge. Because turbulence-inducing effects are absent in this situation, blast effects are not anticipated. Therefore, thermal radiation and direct flame contact are the only hazardous effects encountered. Wind speed is 2 m/s. Relative humidity is 50%. Compute the incident heat flux as a function of time through a vertical surface at 100 m distance from the center of the cloud. Data—Molecular Weights: Propane: 44 kg/kg-mol; Air: 29 kg/kg-mol. To calculate the flame height: • Calculate the flame speed S on the basis of the wind speed C/w:

S = 2.3 x t/w = 2.3 x 2 = 4.6 m/s • Calculate the square of mixture-air density ratio:

• Calculate the air-fuel mass ratio r from the stoichiometric mixture composition <|>st and the densities of air and fuel:

• Calculate w from the actual mixture composition <|>, the stoichiometric mixture composition <|>st and the expansion ratio for stoichiometric combustion a:

• Calculate the flame height, using the cloud depth d, gravity constant g, S (Po/pa)2, w, and r as follows:

To calculate the heat flux, the flash-fire dynamics (shape and position of the flame dependent on time) should first be specified. For simplification, assume the cloud to be stationary during the full period of flash-fire propagation. As a conservative starting point, assume that the transmitting (flame) and receiving surfaces are vertical and parallel during the full period of flame propagation, as indicated in Figure 8. Ib. The thermal radiation received by an object in the environment may now be computed if it is assumed that the flame appears as a flat plane, 33 m high, which propagates at a constant speed of 4.6 m/s during the full period of flame propagation (100/4.6 = 21.7 s). During this period, flame width varies from O to 100 m and back, according to Figure 8.1b: W = 2[R2 -(R- St)2]0-5 = 2[502 - (50 - 4.602]05 Radiation heat flux is strongly time dependent because both flame surface area and distance from the flame to the intercepting surface vary during the course of a flash fire. The path of this curve can be approximated by calculation of the radiation heat flux at a sufficient number of points of time. The problem focuses on the determination of the geometric view factor. For example, the view factor after 5 seconds of flame propagation can be calculated as follows: • Flame width is 2[502 - (50 - 4.602]0'5 = 84 m • Distance between the object and the flame is

X = 150 - (5 x 4.6) = 127 m It is assumed that the receptor's location is such that parts I and II of the flame are equal, so T1 equals rn. Values for Xr and hr are calculated for the portions of the flame on each side of a normal from the center of the receptor onto the flame

flat radiator

receiver

Figure 8.2. Definition of view factors for a vertical, flat radiator.

surface. That is, to calculate Xr and hr in this case, divide the total flame width in half to determine portions on either side of the normal on the flame surface: • Xr = XIr = X/Q.5W = 1277(0.5 X 84) = 3.02 (Figure 8.2) • hr = hlr = /I/0.5W = 43/(0.5 x 84) = 1.02 (Figure 8.2) • Calculate the view factor using the equation given in Appendix A for a vertical plane surface emitter, or else read the view factor from Table A-2 of Appendix A for the appropriate Xr and hr. This results in F = 0.062 for each portion of the flame surface, and implies a total view factor of F = 2 X 0.062 = 0.12. • Atmospheric transmissivity T3 = log(14.1 RH-0108X'013) = 0.69. • Radiation heat flux q = if E = 0.69 x 0.12 x 173 = 14 kW/m2. The results for selected points in time and distances are summarized in Table 8.1.

TABLE 8.1. Results of Calculations t(s)

O 5 10 15 20 21 21.7

W(m)

X(m)

O

150

84 100 92 54 36 O

127 104 81 58 53 50

hr

Xr

F

T3

q (kW/m2)

1.02 0.86 1.07 1.59 2.39

3.02 2.08 1.76 2.94 2.94

0.12 0.20 0.30 0.30 0.26

0.69 0.70 0.72 0.74 0.74 O

14 25 37 38 33

O

Figure 8.3. Graphical presentation for sample problem of the radiation heat flux as a function of time.

Radiation heat flux is graphically represented as a function of time in Figure 8.3. The total amount of radiation heat from a surface can be found by integration of the radiation heat flux over the time of flame propagation, that is, the area under the curve. This result is probably an overstatement of realistic values, because the flame will probably not burn as a closed front. Instead, it will consist of several plumes which might reach heights in excess of those assumed in the model but will nevertheless probably produce less flame radiation. Moreover, the flame will not burn as a plane surface but more in the shape of a horseshoe. Finally, wind will have a considerable influence on flame shape and cloud position. None of these effects has been taken into account.

9 BLEVEs—SAMPLE PROBLEMS In this chapter, applications of the calculation methods used to predict the hazards of BLEVEs, as described in Chapter 6, are demonstrated in the solution of sample problems. Fire-induced BLEVEs are often accompanied by fireballs; hence, problems include calculation of radiation effects. A BLEVE may also produce blast waves and propel vessel fragments for long distances. The problems include calculations for estimating these effects as well. Calculation methods for addressing each of these hazards will be demonstrated separately in the following order: radiation, blast effects, and fragmentation effects.

9.1. RADIATION The radiation hazard from a BLEVE fireball can be estimated once the following fireball properties are known: • the maximum diameter of the fireball, that is, fuel mass contributing to fireball generation; • the surface-emissive power of the fireball; • the total duration of the combustion. For each of these properties, data and calculation techniques are available. A summary is presented below.

9.1.1. Fuel Contribution to Fireball Hasegawa and Sato (1977) showed that when the calculated amount of flashing evaporation of the liquid equals 36% or more, all of the contained fuel contributes to the BLEVE and eventually to the fireball. For lower flash-off values, part of the fuel forms the BLEVE and part of it forms a pool. It is assumed that if the flashing evaporation is lower than 36%, three times the quantity of the flashing liquid contributes to the BLEVE. For prediction purposes, the amount of gas in a BLEVE can be taken as three times the amount of flashing liquid up to a maximum of 100% of available fuel.

A conservative approach often used is to assume that all available liquid fuel will contribute to the BLEVE fireball.

9.1.2. Fireball Size and Duration Many small-scale experiments have been carried out to measure the durations and maximum diameters of fireballs. These experiments have resulted in the development of empirical relations among the total mass of fuel in the fireball and its duration and diameter. Fireball diameter estimates, as published by several investigators and modelers, are presented in Table 6.4. Average values for calculation of fireball diameter and duration are available from the more recent publications of Roberts (1982) and Pape et al. (1988), who produced the following equations: Dc = 5.8roJ'3 and

tc = 0.45mJ/3

for mf < 30,000 kg

tc = 2.6/wf1/6

for /wf > 30,000 kg

(9.1.1)

where Dc = final fireball diameter tc = fireball duration mf = mass of fuel in fireball

(m) (s) (kg)

Because this relationship also reflects the average of all relations from Table 6.4, its use is recommended for calculating the final diameter and duration of a spherical fireball. 9.1.3. Radiation For a receptor not normal to the fireball, radiation received can be calculated based on the solid flame model as follows: q = EFTA

(9.1.2)

where q E F Ta

= = = =

radiation received by receptor surface emissive power view factor atmospheric transmissivity

(kW/m2) (kW/m2) (-) (-)

The surface-emissive power E9 the radiation per unit time emitted per unit area of fireball surface, can be assumed to be equal to the emissive powers measured in full-scale BLEVE experiments by British Gas (Johnson et al. 1990). These entailed the release of 1000 and 2000 kg of butane and propane at 7.5 and 15 bar. Test results revealed average surface-emissive powers of 320 to 370 kW/m2; see Table 6.2. A value of 350 kW/m2 seems to be a reasonable value to assume for BLEVEs for most hydrocarbons involving a vapor mass of 1000 kg or more. For a point on a plane surface located at a distance L from the center of a sphere (fireball) that can "see" all of the fireball (see Appendix A), the view factor (F) is given by (see Figure A-I): (9.1.3) where r = the radius of the fireball (r = DJ2) & = the angle between the normal to the surface and the connection of the point to the center of the sphere. In the general situation, the fireball center has a height (zc) above the ground (zc ^ DJI), and the distance (X) is measured from a point at the ground directly beneath the center of the fireball to the receptor at ground level. When this distance is greater than the radius of the fireball, the view factor can be calculated as follows: For a vertical surface: (9.1.4) For a horizontal surface: (9.1.5) In most cases, the BLEVE fireball is assumed to touch the ground (zc = DJ2). For large scale BLEVEs, the assumption that the fireball is at its maximum diameter and "rests" on the ground will predict thermal hazard quite accurately. Atmospheric transmissivity ra can be estimated by use of one of the equations presented in Chapter 3, Section 3.5.2, which describes the graphs presented in Appendix A: Ta = log[14.1 RH-0108 (L - ZV2)-°13]

(9.1.6)

where Ta is transmissivity and RH is relative humidity. The calculation of total radiation hazard must include the received radiation integrated over the combustion time. The point-source model can also be used to calculate the radiation received by a receptor at some distance from the fireball center. Hymes (1983) presents a fireballspecific formulation of the point-source model developed from the generalized

formulation (presented in Section 3.5.1) and Roberts's (1982) correlation of the duration of the combustion phase of a fireball. According to this approach, the peak thermal input at distance L is given by (9.1.7) where mf Ta Hc R L q

= = = = = =

mass of fuel in the fireball atmospheric transmissivity net heat of combustion per unit mass radiative fraction of heat of combustion distance from fireball center to receptor radiation received by the receptor

(kg) (-) (J/kg) (-) (m) (W/m2)

Hyme suggests the following values of R T = 0.3, fireballs for vessels bursting below relief valve pressure; r = 0.4, fireballs for vessels bursting at or above relief valve pressure.

9.1.4. Hazard Distances Criteria for thermal damage are given in Table 6.6 and Figure 6.10.

9.1.5. Calculation Procedure The following procedure can be followed for estimating radiation hazards: • Estimate the fireball size and duration using: Dc = 5.8mf1/3 and

(9.1.8) tc = 0.45/n^73

for mf < 30,000 kg

tc = 2.6m}16

for mf > 30,000 kg

• Assume a surface-emissive power of 350 kW/m2. • Estimate the geometric view factor on the basis of the fireball diameter and the position of the receptor using the relationships presented in Section 9.1.4, Section 3.5.2, or Appendix A. Also, tables presented in Appendix A can be applied.

• Estimate the atmospheric transmissivity Ta. • Estimate the received thermal flux q. • Determine the thermal impact.

9.1.6. Sample Problems A liquefied propane tank truck whose volume is 6000 U.S. gallons (22.7 m3) is involved in a traffic accident, and the tank truck is engulfed by fire from burning gasoline. The tank is 90% filled with propane. Assume that all of the propane will contribute to the fireball. Radiation effects are calculated below; blast and fragmentation effects for this problem will be calculated in Sections 9.2 and 9.3, respectively. • Estimate fireball diameter and duration. Liquid propane has a specific weight of 585.3 kg/m3, so the total mass of propane in the tank is: 0.9 x 22.7 x 585.3 = 11,958kg With the relations given above, the diameter (D0) and the duration (tc) of the fireball can be calculated: Dc = 5.8 x mlf/3 = 5.8 X 11958173 = 133m tc = 0.45 x mf1/3 = 0.45 x 119581'3 = 10.3s • Assume a surface emissive power. Assume a surface-emissive power of 350 kW/m2. • Estimate the atmospheric transmissivity. Since no data are known about the relative humidity, use ra = 1. • Estimate the geometric view factor. The center of the fireball has a height of 66.5 m, and thus the view factor (for a vertical object) follows from the relation given in Section 9.1.3: Fv = (X X 66.52)/(X2 + 66.52)372 where X = the distance measured along the ground from the object to a point directly below the center of the fireball, that is, the position of the tank. This distance must be greater than the radius of the fireball, because actual development of the fireball often involves, first, an initial hemispherical shape, which would engulf near-field receptors, and second, ascent of the fireball over time, which would significantly affect radiation distances to near-field receptors. Therefore, near-field radiation estimates are of questionable accuracy.

TABLE 9.1. Radiation on a (Vertical) Receptor from a 6000-gallon Propane Tank Truck BLEVE Calculated with Solid Flame and Point Source Radiation Models Ground Distance (m) 100 200 500 1000

View Factor

Solid Flame Radiation (kW/m2)

Point Source Radiation (Hymes) (kW/m2)

0.255 0.0945 0.0172 0.00439

89 33 6.0 1.5

122 39 6.8 1.7

• Estimate the radiation received at a receptor. With an attenuation factor of 1, the radiation received by a vertical receptor at a distance X from the tank can be calculated from: q = EF, = 350 X (X X 66.52)/(X2 + 66.52)3/2 The results of this calculation for various distances X are tabulated in Table 9.1. • Alternative approach: point-source model. Another method of calculating the radiation received by an object relatively distant from the fireball is to use the point-source model. From this approach, the peak thermal input at distance L from the center of the fireball is 2.2T8K^X'67 ~ 4irL2

= q

(9.1.9, same as 9.1.7)

Substituting the appropriate values for the variables, yields the following: mf Ta Hc R q

= = = = =

11,958kg 1.0 4.636 x 107 J/kg 0.4 (It is assumed that the relief valve operated prior to vessel rupture.) 1.7 x 109/L2W/m2 = 1.7 x 106/L2 kW/m2

The radiation received by an object normal to the fireball at distances of X = 100, 200, 500, and 1000 m from the tank is presented in Table 9.1. • Estimate the thermal impact. The thermal impact of a fireball on humans is a function of both the radiation received and the fireball duration. The impact can be estimated from Figure 9.1. In this case, the fireball duration is estimated to be about 10 seconds, while the estimated radiation is presented in Table 9.1. Based on these data the impact to unprotected humans can be estimated and is shown in Table 9.2. Note that while there is a difference of about 15% in the radiation levels estimated from the two models, the estimated impact on humans is essentially the same.

3* burns, to bare skin (2mm) 50% lethality (average clothing) -1 % lethality (average clothing) start of 2* burns incident heat flux (kW/m 2)

range for blistering of bare skin i.e. threshold

exposure time (sec) Figure 9.1. Injury and fatality levels for thermal radiation (Hymes 1983).

TABLE 9.2. Effect on Humans from Two Radiation Source Models Ground Distance (m) 100 200 500 1000

Solid Flame Model third degree bums, 50% lethality second degree bums some pain below pain threshold

Point Source Model third degree bums, 50% lethality 1% lethality some pain below pain threshold

9.2. BLAST PARAMETER CALCULATIONS FOR BLEVEs AND PRESSURE VESSEL BURSTS In this section, three examples of blast calculations of BLEVEs and pressure vessel bursts will be given. The first example is designed to illustrate the use of all three methods described in Section 6.3.2. The second is a continuation of sample problem 9.1.5, the BLEVE of a tank truck. A variation in the calculation method is presented; instead of determination of the blast parameters at a given distance from the explosion, the distance is calculated at which a given overpressure is reached. The third example is a case study of a BLEVE in San Juan Ixhuatepec (Mexico City).

9.2.1. Sample Problem: Cylindrical Vessel A cylindrical vessel, used for the storage of propane, has been repaired. After the repair, the vessel is pressure tested with nitrogen gas at a pressure 25% above design. If the vessel bursts during the test, a large storage tank, located 15 m from the vessel, and a control building, located 100 m from the vessel, might be endangered. What would be the side-on overpressure and impulse at these points?

9.2.1.1. Select the Calculation Method Use Figure 9.2 (equal to Figure 6.19 from Section 6.3.3) to select the appropriate calculation method. The only information needed for selection of a method is the phase of the fluid. Nitrogen at ambient temperature can be regarded as an ideal gas at these pressures. Therefore, the basic method (Section 6.3.3) is used.

9.2.7.2. Solution with Basic Method The basic method is drawn schematically in Figure 9.3 (equal to Figure 6.20) and described in Section 6.3.3. Step 1: Collect data. • The ambient pressure pQ is 0.10 MPa. • The design overpressure of the vessel is 1.92 MPa, and the test pressure is 25% higher. Therefore, the absolute internal pressure P1 is Pl

= 1.25 x 1.92 x 106 + 0.1 x 106 = 2.5 MPa (25 bar)

• The volume of the vessel, V1, is 25 m3. • The ratio of specific heats of nitrogen, ^1, is 1.40. • The distance from the center of the vessel to the receptor, r, is 100 m for the control building and 15 m for the large storage tank.

start

collect data

liquid

phase contents

ideal gas

calc. energy with basic method

temperature

assume explosive flashing

vapor, non-ideal gas range

near field

explosive flashing refined method

no blast effects

calc. energy with explosive flashing method

end

calc. energy with explosive flashing method

continue with basic method Figure 9.2. Selection of blast calculation method.

• The shape of the vessel is cylindrical. It is placed horizontally on saddles at grade level. Step 2: Calculate energy. The energy of the compressed gas is calculated with Eq. (6.3.15):

Substitution gives £ex = (2.5 x 106 - 0.1 x 106) x 2 x 25 / (1.4 - 1) = 300 MJ

Step 3: Calculate the nondimensional range R of the receptor. The nondimensional range R is calculated with Eq. (6.3.16):

start

collect data

calculate energy

calculated R of 'target1

step 7 of explosive flashing ' method

/4

(

ITN

check R

J

R<2

R<2

refined method

determine P8

determine I

T adjust P8 and I

calc. P8 and is

check P8

end Figure 9.3. Procedure for basic method.

Substitution gives, for the control building: R = 100 x (0.1 x 106/ 300 x 106)1/3 = 6.9 And, for the large storage tank: R = 15 x (0.1 x 106/300 x 106)1/3 = 1.04

Step 4: Check R. The nondimensional range R is checked to determine whether the basic method may be followed or the refined method must be used. The control building lies at a nondimensional range of 6.9, so the basic method may be followed. The range of the large storage tank is less than 2, so the refined method must be used to obtain an accurate result. This will be done in Section 9.2.1.3. Step 5: Determine P8. The nondimensional side-on peak overpressure P8 at the control building is read from Figure 6.22. For R = 6.9, P8 = 0.030. Step 6: Determine I. The nondimensional side-on impulse 7 at the control building is read from Figure 6.23. For R = 6.9,7 = 0.0073. Step 7: Adjust P8 and I for geometry effects. To account for the fact that the blast wave from the vessel will not be perfectly symmetrical, P5 and 7 are adjusted, depending on R. To account for the vessel's placement slightly above grade, P8 is multiplied by 1.1. To account for a vessel's cylindrical shape, P is multiplied by 1.4. Thus, P8 becomes: P8 = 1.1 x 1.4 x 0.03 = 0.042. No adjustment of 7 is necessary at this range. Step 8: Calculate ps and /s. To calculate the side-on peak overpressure ps -j?0 and the side-on impulse i, from the nondimensional side-on peak overpressure P8 and the nondimensional side-on impulse 7, Eqs. (6.3.17) and (6.3.18) are used: 173 /O273Ecx 's = ° ^o The ambient speed of sound O0 is approximately 340 m/s. Substitution gives

— Ps ~ Po = ^sPo

Ps - Po = 0.042 x 0.1 x 106 = 4.2 kPa (0.042 bar) /s = [0.0073 x (0.1 x 106)273 x (300 x 106)1/3]/340 = 31 Pa.s. Step 9: Check ps. Because the accuracy of this method is limited, /?s needs to be checked against P1. In this case, ps is much smaller than P1, so no corrections have to be made. Thus, the calculated blast parameters at the control building are: a side-on peak overpressure of 4.2 kPa and a side-on impulse of 31 Pa.s. Note that this pressure

is sufficient to break windows. This is the reason why, in practice, pressure-testing is performed with water or some other liquid, almost never with gas. 9.2.1.3. Solution with Refined Method As shown above, the distance from the blast site to the large storage tank is too short for the basic method to be applied with good results. Therefore, the refined method is used to calculate blast parameters at the large storage tank. The refined method is illustrated schematically in Figure 9.4 (equal to Figure 6.25) and described in Section 6.3.3.2. Step 1: Collect additional data. • The ratio of the speed of sound in the compressed nitrogen to the speed of sound in the ambient air, Ci1Ja0, is approximately 1. • The ratio of specific heats of the ambient air is 1.40.

start from step 4 of basic method

collect additional data

2 calculate starting distance

calculate P8,

4 locate starting point on Rg. 6.21

determine P8

continue with step 6 of basic method Figure 9.4. Refined method to determine P3 (Baker et al. 1978a).

Step 2: Calculate the starting distance. The starting distance is computed with Eq. (6.3.20):

Substitution gives

r0 must be transformed into the nondimensional starting distance R with Eq. (6.3.21):

Substitution gives: K0 = 2.29 x (0.1 x 106/ 300 x 106)1/3 = 0.16 Step 3: Calculate the starting peak overpressure P80. The nondimensional peak overpressure of the shock wave directly after the burst of the vessel P80 can be calculated from Eq. (6.3.22) or read from Figure 6.26. Equation (6.3.22) was solved by iteration. The result was: P80 = 3.05, or oneeighth the initial pressure in the vessel. Step 4: Locate the starting point on Figure 6.21. To select the proper curve in Figure 6.21, the starting point /?0, P80 is drawn in the figure. Step S: Determine P8. To determine the nondimensional side-on peak overpressure P8 at the large storage tank, P8 is read from Figure 6.21. The nondimensional distance was computed in Section 9.2.1: R = 1.04. When the curve is followed from the starting point, a P8 of 0.36 is found. The procedure is continued with Step 6 of the basic method, described in Section 6.3.3.1. Step 6: Determine 7. The nondimensional side-on impulse 7 at the tank is read from Figure 6.23. For R= 1.04,7 = 0.05. Step 7: Adjust P8 and I for geometry effects. To account for the fact that the blast wave from the vessel will not be perfectly symmetrical, P8 and 7 are adjusted, depending on R. To account for the vessel's placement slightly above ground level, P8 is multiplied by 1.1. To account for the vessel's cylindrical shape, P8 is multiplied by 1.6 and 7 is multiplied by 1.1. Thus,

P8 and / become:

P 8 = 1.1 x 1.6 x 0.36 = 0.63 7 = 1.1 x 0.05 = 0.055 Step 8: Calculate p, and is. To calculate side-on peak overpressure ps _-- p0 and side-on impulse i§ from the nondimensional side-on peak overpressure P8 and the nondimensional side-on impulse 7, Eqs. (6.3.17) and (6.3.18) are used: Jo213E 1/3 's = ^f^ *o The ambient speed of sound a0 is approximately 340 m/s. Substitution gives Ps-Po = ^o

Ps - Po = 0.63 x 0.1 x 106 = 63 kPa (0.63 bar) I1 = 0.055 x (0.1 x 106)2* x (300 x 106)13/340 = 233Pa.s Step 9: Check PV Because the accuracy of this method is limited, ps needs to be checked against P1. In this case, ps is much smaller than pl9 so no corrections have to be made. Thus, the calculated blast parameters at the large storage vessel are as follows: a side-on peak overpressure of 63 kPa and a horizontal impulse of 233 Pa.s. 9.2.2. Solution for Explosively Flashing Liquid After a successful pressure test, the vessel is put back into service. The safety valve is set at 1.5 MPa (15 bar). What might happen if the vessel were exposed to a fire? Consider two cases, one in which the vessel is almost completely (80%) filled with propane, and one in which the vessel is almost empty (10% filled). Use of Figure 9.2 requires that the temperature of the liquid be compared to its boiling point and its superheat-limit temperature. Table 6.1 provides these temperatures: 7b = 231 K, and T81 = 326 K. It is obvious that the liquid's temperature can easily rise above the superheat limit temperature when the vessel is exposed to a fire. Therefore, the explosively flashing-liquid method must be selected. This method is described schematically in Figure 9.5 (equal to Figure 6.29), and described in Section 6.3.3.3. Step 1: Collect data. • The failure overpressure is assumed to be 1.21 times the opening pressure of the safety valve. Thus: Pl

= 1.21 x 1.5 + 0.1 = 1.9 MPa (19 bar).

start

collect data

check the fluid

determine u 1

determine u,

5

calculate specific work

calculate energy

calculate R

continue with step 5 of basic method Figure 9.5. Calculation of energy of explosively flashing liquids and bursts of pressure vessels filled with vapor or nonideal gas.

• The ambient pressure p0 is assumed to be 0.10 MPa (1 bar). • The volume of the vessel is 25 m3. • The distance from the center of the vessel to the receptor is 100 m for the control building and 15 m for the large storage tank. • The shape of the vessel is cylindrical. It is placed horizontally on saddles.

TABLE 9.3. Thermodynamic Data for Propane TI

(KJ 327.7 230.9

hg

Vf

VQ

S,

(MPa; (kJ/kg)

Pl

fy

(kJ/kg)

(m*/kg)

(m*/kg)

(kJ/kg.K)

(kJ/kg.K)

1.90 0.10

948.32 849.19

2.278 x 10~3 1.722 x 10~3

0.0232 0.419

4.7685 3.8721

5.6051 5.7256

674.31 421.27

Sg

• Thermodynamic data are read from a table given in Perry and Green (1984) and interpolated. Subscript "f" denotes the saturated liquid (fluid) state, and subscript "g" the saturated vapor (gaseous) state. Step 2: Determine if the fluid is in Table 6.12 or Figure 6.30. Although the specific expansion energy of propane is included in the list of fluids in Figure 6.30, Steps 3 to 5 are followed for this example. The solution for the filled vessel will be given first. Step 3: Determine U1. The specific internal energy of the fluid at the failure state is calculated with Eq. (6.3.23):

h = u + pv The vessel is assumed to be filled with saturated liquid and vapor. The specific internal energy of the saturated liquid can be computed by substituting the appropriate thermodynamic data of Table 9.3 in Eq. (6.3.23): 674.31 x 103 = M1 + 1.90 x 106 x 2.278 x KT3 It follows that U1 = 669.98 kJ/kg. The specific internal energy of the saturated vapor can be computed in the same way: M1 = 948.32 x 103 - 1.90 x 106 x 0.0232 = 904.24 kJ/kg Step 4: Determine If2. The specific internal energy of the fluid after expansion to ambient pressure M2 *s calculated from Eq. (6.3.24): M2 = (1 - X)hf + Xfcg - (I - X)/>oVf - Xp0Vg As the liquid is depressurized, it partially vaporizes; as the vapor is depressurized, it partially condenses. The vapor ratio X can in both cases be calculated from: X-(S1- .sf)/(sg - Sf) For the saturated liquid: X = (4.7685 - 3.8721)7(5.7256 - 3.8721) = 0.484

U2 = (I - 0.484) X 421.27 x 103 + 0.484 X 849.19 x 103 - (1 - 0.484) x 0.1 x 106 x 1.722 x KT3 - 0.484 x 0.1 x 106 x 0.419 = 608.01 kJ/kg For the saturated vapor: X = (5.6051 - 3.8721)/(5.7256 - 3.8721) = 0.935 U2 = (I- 0.935) X 421.27 x 103 + 0.935 x 849.19 x 103 - (1 - 0.935) x 0.1 x 106 x 1.722 x 10~3 - 0.935 x 0.1 x 106 x 0.419 = 782.19kJ/kg Step 5: Calculate the specific work. The specific work done by a fluid in expansion is calculated with Eq. (6.3.25) as follows: *ex = MI -

M2

Substitution of values for the saturated liquid gives eex = 669.98 x 103 - 608.01 x 103 = 61.97 kJ/kg and for the saturated vapor *ex = 904.24 x 103 - 782.19 x 103 = 122.05 kJ/kg Note that these values could also have been read from Figure 6.30. Step 6: Calculate the explosion energy. The explosion energy is calculated with Eq. (6.3.26): £ex = 2^m1

The mass of the released fluid is W1 = V^v1

When the vessel is full, 80% of the volume is occupied by liquid. (This fraction changes only marginally when the vessel is heated by fire.) The mass of the liquid is Tn1 = 0.80 x 25 / 2.278 x KT3 = 8780 kg and the mass of the vapor is /W1 = 0.20 x 25/0.0232 = 215.5 kg This gives, for explosion energy of the saturated liquid, £ex = 2 x 61.97 x 103 x 8780 = 1088.2 MJ and, of the saturated vapor Eex = 2 x 122.05 x 103 x 215.5 = 52.6 MJ. Assuming that the blasts from vapor expansion and liquid flashing are simultaneous, the total energy of the surface explosion is: £ex = 1088.2 + 52.6 = 1140.8 MJ. Step 7: Calculate the range of the receptor. The nondimensional range of the receptor is calculated with Eq. (6.3.16):

This gives, for the BLEVE of the full vessel at the large storage vessel

and at the control building:

Computations are continued with Step 5 of the basic method. Step 5: Determine Pa. _ The nondimensional side-on peak overpressure P8 at the large storage tank is read from Figure 6.21. The nondimensional distance R equals 0.66. Reading from the curve labeled "high explosive," a P8 of 1.15 is found. The procedure is continued with Step 6 of the basic method, described in Section 6.3.3.1. Step 6: Determine 7. The nondimensional side-on impulse 7 at the tank is read from Figure 6.24. For R = Q.66,7 = 0.071.

Step 7: Adjust P8 and I for geometry effects. To account for the fact that the blast wave from the vessel will not be perfectly symmetrical, P& and 7 are adjusted, depending on R. To account for the vessel's placement slightly above grade, P8 is multiplied by 2, and 7 is multiplied by 1.6. To account for the shape of the vessel (cylindrical), P8 is multiplied by 1.6, and 7 is multiplied by 1.1. (Refer to Section 6.3.3.1.) Thus, P8 and 7 become:

P8 = 2 x 1.6 x 1.15 = 3.68 7 = 1.1 x 0.071 = 0.078 Step 8: Calculate ps and is. To calculate the side-on peak overpressure ps -_p0 and the side-on impulse ig from the nondimensional side-on peak overpressure P8 and the nondimensional side-on impulse 7, Eqs. (6.3.17) and (6.3.18) are used:

PS-PQ = ^sPo . J/«? 's The ambient speed of sound a0 is approximately 340 m/s. Substitution gives Ps ~ PQ = 3.68 x 0.1 x 106 = 368 kPa (3.68 bar) *8 = 0.078 x (0.1 x 106)273 x (1140.8 x 106)1/3/340 = 516 Pa.s Step 9: Check p,. Because the accuracy of this method is limited, ps needs to be checked against P1. In this case, ps is smaller than pl9 so no corrections are necessary. Thus, the calculated blast parameters at the large storage vessel are as follows: a side-on peak overpressure of 368 kPa and a side-in impulse of 516 Pa.s. The same procedure should be followed to calculate the pressure and impulse at the control building. This calculation will be briefly described. Step 5: Determine P8. _ _ Figure 6.22 gives a nondimensional overpressure P8 of 0.050 for R = 4.4. Step 6: Determine J. The nondimensional side-on impulse / at the control building is read from Figure 6.23. For R = 4.4,7 = 0.012. Step 7: Adjust Ps and I for geometry P and 7 becomes

effects.

P8 = 1.1 x 1.4 x 0.050 = 0.077

7 = 1.1 x 0.012 = 0.013

Step 8: Calculate ps and is. ps - Po = 0.077 X 0.1 X 106 = 7.7 kPa (0.077 bar) i, = 0.013 x (0.1 x 106)273 x (1140.8 x 106)1/3/340 = 79 Pa.s. Step 9: Check Pr No corrections are necessary. Hence, the calculated blast parameters at the control building are as follows: a side-on peak overpressure of 7.7 kPa and a side-on impulse of 86 Pa.s. 9.2.2.1. Solution for the Empty Vessel When the vessel is only 10% filled, the energy of the explosion is different. Therefore, calculations must be repeated starting from Step 6 of the flashing liquid method. Step 6: Calculate the explosion energy. Explosion energy is calculated with Eq. (6.3.26): £ex =

2

^eX7Hl

The mass of released fluid is ml = V1Xv1

When the vessel is empty, 10% of the volume is occupied by liquid. The liquid mass is

JXIO^L = 2.278 x 10~3 While the vapor mass is 0.90 X 25 . „ _ , ""=-0023^ = 969-8kg-

This gives, for explosion energy of the saturated liquid: £ex = 2 x 61.97 x 103 x 1098 = 136.1 MJ

and for the saturated vapor: E6x = 2 x 122.05 x 103 x 969.8 = 236.7 MJ. Assuming that the blasts from vapor expansion and flashing liquid are simultaneous, the total energy of the surface explosion is: E6x = 136.1 + 236.7 = 372.8 MJ The other calculations are performed as described above. The results of these computations are summarized in Table 9.4. Note the following points:

TABLE 9.4. Results of Sample Problem At large storage tank

At control building

Vessel Status

E6x (MJ)

_ R

Ps ~ Po (kPa)

/» (Pa.s)

_ R

Ps - Po (kPa)

4 (Pa.s)

N2 filled 80% filled 10% filled

300.0 1140.8 372.8

1.04 0.67 0.97

63 368 170

230 516 410

6.9 4.4 6.4

4.2 7.7 4.6

31 86 42

• The explosion of a vessel full of liquid above the superheat limit temperature has much more energy, and therefore, causes a much more severe blast than a gas- or vapor-filled vessel. • The nitrogen-filled vessel and the 10%-filled vessel have approximately the same energy; therefore, scaled distances at the large storage tank and the control building are similar. However, the overpressure at the large storage tank is much lower for the gas-filled vessel. This is, in part, due to the refined method, and in part to an abrupt change in multiplication factor used to account for the unsymmetrical blast wave at R = 1.0. • This calculation takes into account only the blast from the expansion of vessel contents. In fact, this blast may be followed by one from a vapor cloud explosion. This possibility must be considered separately with the methods presented in earlier chapters.

9.2.3. Sample Problem: Tank Truck BLEVE Sample problem 9.1.5 demonstrated the calculation of thermal radiation from the BLEVE of a tank truck. This 6000-gallon (22.7 m3) tank was 90% filled with propane, and burst due to fire engulfment at an overpressure of 1.8 MPa (18 bar). The resulting thermal radiation was sufficient to cause third degree burns to a distance of 300 to 360 m. In this section, the blast from the BLEVE will be investigated but not the blast which may be caused by a vapor cloud explosion. A variation in the calculation method will be presented. Instead of determination of blast parameters at a given distance from the explosion, the distance at which a given overpressure is reached will be calculated. The distance to which fragments may be thrown will be calculated in Section 9.3. The use of Figure 9.2 requires that liquid propane's temperature relative to its boiling point and superheat-limit temperature be known. Table 6.1 gives these temperatures: Tb = 231 K, and 7sl = 326 K. It is obvious that the liquid temperature can easily rise above the superheat-limit temperature when the vessel is exposed to a fire. Therefore, the explosively flashing-liquid method must be selected. The

method for explosively flashing liquids is drawn schematically in Figure 9.5 (equal to Figure 6.29) and described in Section 6.3.3.3. Step 1: Collect data. • The failure overpressure is 1.21 times the opening pressure of the safety valve. Thus, P1 is P1 = 1.21 x 1.5 + 0.1 = 1.9 MPa (19 bar)

• The ambient pressure p0 is assumed to be 0.10 MPa (1 bar). • The volume of the vessel is 22.7 m3. • Instead of calculation of overpressure and impulse at a fixed distance, the distance at which damage can occur will be calculated. The specific type of damage chosen is window pane breakage. This can be expected at overpressures greater than 6 kPa (0.06 bar). • The shape of the vessel is cylindrical. It is placed horizontally on saddles at grade level. Step 2: Check if the fluid is listed in Table 6.12 or Figure 6.30. Propane is a fluid for which specific expansion energy is given in Figure 6.30. Therefore, the calculation is continued with Step 5. Step 5: Calculate the specific work. The specific work done by the fluid in expansion can be read from Figures 6.30 or 6.31 if its temperature is unknown. Saturated propane at a pressure of 1.9 MPa (19 bar) has a temperature of 328 K, almost the superheat-limit temperature. Note that it is assumed that temperature is uniform, which is not necessarily the case. From Figure 6.30, the expansion work per unit mass for saturated liquid propane is *ex = 58.68 kJ/kg, and the expansion work per unit volume is: *ex = 5.14MJ/m3 Step 6: Calculate explosion energy. Explosion energy is calculated with Eq. (6.3.26): £ex

= 2

^6xW1

The mass of released liquid propane is 11,958 kg, as was calculated in Section 9»1.6. This gives, for the energy of the explosion for the saturated liquid: Eex = 2 x 58.68 x 103 X 11,958 = 1403.4 MJ

The volume of the vapor is 0.10 x 22.7 = 2.27 m3. The explosion energy of the vapor can be calculated by multiplying the expansion work per unit volume by the vapor volume:

En = 2 X 5.14 x 106 x 2.27 = 23.3 MJ Assuming that the blasts from vapor expansion and liquid flashing are simultaneous, the total energy of the surface explosion is Eex = 1403.4 + 23.3 = 1426.7 MJ Because the objective of the calculation is now to calculate the distance at which a specific pressure occurs, rather than to calculate pressure at a given distance, calculations must follow a different order. Step 8: Calculate P8. Calculate the nondimensional side-on peak overpressure P8 from /?s and pQ using Eq. (6.3.17): Ps ~ Po = ^sPo For the desired pressure:

6.0 x 103 = P8 x 1.0 x 105 It follows that P8 is equal to 0.060. Step 7: Adjust P8 for geometry effects. The blast wave from the vessel will not be perfectly symmetrical. Therefore, P8 is adjusted, depending on R9 which is not yet known. As a first guess, assume that R is greather than 3.5. To account for the vessel's location slightly above the ground, P8 is divided by 1.1. To account for a cylindrical vessel, P8 is divided by 1.4. Thus, P8 becomes: P8 = 0.0607(1.1 x 1.4) = 0.039 Step S: Determine R. _ _ To determine the nondimensional range R from the side-on peak overpressure P8, Figure 6.22 is used. For P8 equal to 0.039, R is equal to 4.0. This is, as assumed in Step 7, indeed greater than 3.5. Step 7: Calculate the range of the receptor. The range of the receptor is calculated with Eq. (6.3.16):

Substitution gives 4.0 = r[(1.0 x 105)/(1426.7 X 106)]1/3 Therefore, r is 97 m. Thus, the BLEVE of a tank truck filled with propane can cause window pane breakage up to a distance of about 100 m. Note that, with this method of calculating distance of a given overpressure, one or two iterations may be necessary. The number of iterations will be higher when the distance for a given impulse is sought, or when the refined method is used.

9.2.4. Case Study: San Juan Ixhuatepec, Mexico City, 1984 In this case study, one of the strongest blast-generating BLEVEs to occur in the Mexico City incident (Section 2.4.3, Pietersen 1985), will be investigated. This BLEVE occurred a few minutes after the initial vapor cloud explosion and probably involved two 1600-m3 spheres. The spheres were probably 50% full at the time of the accident. The BLEVE of the spheres probably shifted a number of cylindrical vessels from their foundations. Furthermore, it probably produced damage in the built-up area. However, because destruction by intense fire in that area was complete, this cannot be confirmed. Beyond a range of 300 m, no glass damage due to blast was observed. This indicates that the side-on overpressure at that range was well below 3 kPa (0.03 bar), which is a nondimensional pressure P& of 0.04. Indications are that the spheres were half-full at the time of the incident, but the overpressure at a distance of 300 m will be calculated for fill ratios of O, 50, and 100%, in order to illustrate differences. The calculation method can be selected by application of the decision tree in Figure 9.2. The liquid temperature is believed to be about 339 K, which is the temperature equivalent to the relief valve set pressure. The superheat limit temperatures of propane and butane, the constituents of LPG, can be found in Table 6.1. For propane, T&1 = 326 K, and for butane, Tsl = 377 K. The figure specifies that, if the liquid is above its critical superheat limit temperature, the explosively flashing liquid method must be chosen. However, because the temperature of the LPG is below the superheat limit temperature (Tsl) for butane and above it for propane, it is uncertain whether the liquid will flash. Therefore, the calculation will first be performed with the inclusion of vapor energy only, then with the combined energy of vapor and liquid. The calculation method for explosively flashing liquids is drawn schematically in Figure 9.5 (equal to Figure 6.29 and described in Section 6.3.3.3). Step 1: Collect data. It is assumed that

• The overpressure is produced by the burst of one sphere. • The vessel is filled with LPG at 339 K. • LPG in Mexico City consists of 50% by volume propane and 50% butane in the liquid phase, and of 80% and 20%, respectively, in the vapor phase. (Limited information is available on the actual LPG composition at the time of the accident.) • The vessel is O, 50, or 100% filled. • The ambient pressure is 75 kPa (0.75 bar). It is known that • Vessel volume is 1600 m3. • The distance from the center of the vessel to the receptor is 300 m. • The vessel is a sphere, and it is placed at grade level. Step 2: Check if the fluid is listed in Table 6.12 or Figure 6.31. Both propane and butane are fluids for which specific expansion energies are given in Figure 6.31. Therefore, calculations begin with Step 5. Step 5: Calculate the specific work. The specific work done by a fluid in expansion is read from Figure 6.31: saturated liquid butane 21 MJ/m3 saturated butane vapor 2.5 MJ/m3 saturated liquid propane 30 MJ/m3 saturated propane vapor 8 MJ/m3 Step 6: Calculate the energy of the explosion. Explosion energy can be calculated by employing a slight variation on Eq. (6.3.26), by multiplying expansion work per unit volume by fluid volume, instead of multiplying expansion work per unit mass by fluid mass. Both propane and butane must be considered. This gives, for example, for vapor energy for the 50% fill-ratio case: £ex = 2 x (8 x 106) x 0.50 x 0.80 x 1600 + 2 x 2.5 x 106 x 0.50 x 0.20 x 1600 = 11 x 1O9J = UGJ

The energies of the other fill ratios are given in Table 9.5. Step 7: Calculate the range of the receptor. The nondimensional range of the receptor is calculated with Eq. (6.3.16):

TABLE 9.5. Explosion Energy E6x (GJ) Fill Ratio

0% 50% 100%

Liquid

Vapor

Liquid + Vapor

O 40.8 81.6

22.1 11 O

22.1 51.8 81.6

This equation gives, for example, at a distance of 300 m in the 100% fill-ratio case: R = 300[(0.75 x 105)/(81.6 x 109)]173 = 2.9 Computations continue with Step 5 of the basic method. Step 5: Determine Ps. To determine the nondimensional side-on peak overpressure P8 at the large storage tank, P& is read from Figure 6.22. The results for the different fill ratios are given in Table 9.6. The procedure is continued with Step 6 of the basic method, described in Section 6.3.3.1. Step 7: Adjust P^ for geometry effects. To account for the fact that the blast wave from the vessel will not be perfectly symmetrical, P8 is adjusted, depending on R. The adjusted P8 is given in Table 9.7. In this case, the only adjustment needed for R greater than 1 is to multiply by 1.1 (see Table 6.11) to account for the vessel's placement above the ground. Step 8: Calculate ps. The side-on peak overpressure ps — pQ can be calculated from the nondimensional side-on peak overpressure P8 by use of Eq. (6.3.17): A ~ Po = JP8Po The calculated values are given in Table 9.7. It does not seem likely that the liquid flashed explosively, because the actual overpressure at 300 m in Mexico City was estimated to be below 3 kPa. This conclusion is consistent with the findings of Pietersen, although he assumed that TABLE 9.6. Nondimensional Pressure P3 of the Explosion (Unadjusted) Vapor Fill Ratio 0% 50%

100%

Vapor + Liquid

R

P3

R

Ps

4.5 5.7

0.045 0.035

4.5 3.4

0.045 0.065

—

—

2.9

0.080

TABLE 9.7. Overpressure at 300 m from the Mexico City BLEVE (Adjusted P5 and ps) Expansion of Vapor Only

Combined Expansion of Vapor and Flashing of Liquid

Fill Ratio (vol %)

_ P8

Ps (kPa)

_ P8

Ps (kPa)

O 50 100

0.05 0.039 —

3.7 2.9 —

0.05 0.072 0.088

3.7 5.4 6.6

the LPG consisted entirely of propane and that the temperature was 313 K. However, because the accuracy of this calculation method is not high (see Section 6.3.3.5) and the actual composition of the LPG is not known, the possibility of explosive flashing of liquid cannot be excluded.

9.3. FRAGMENTS The quantification of hazards associated with the fragments propelled from an exploding, pressurized vessel should involve the determination of their masses and range distributions, as well as their velocities and shapes. Research on fragment parameters has been limited to cases of pressurized vessels filled with ideal gases. Models have been developed for calculating fragments' initial velocities and ranges. These models were discussed earlier in this volume, and applicable equations will be repeated here. It appears, however, that these models are incomplete. They give almost no information on the number of fragments to be expected and only provide the means to calculate one velocity value. Furthermore, a number of assumptions have to be made in order to calculate range, without which unrealistically long ranges would result. The limitations of mathematical modeling described above increase the importance of statistical analysis of accidental explosions. However, gathering all needed data to perform a statistical analysis is often very complicated, so results are often incomplete. Wherever possible, both theoretical and statistical models should both be applied in estimating effects. The procedure described in the following section permits step-by-step quantification of fragment-related parameters. The numbers in the flow diagram in Figure 9.6 refer to the numbers of the paragraphs of this section.

9.3.1. Applying Statistical or Theoretical Approaches As emphasized above, neither statistical or theoretical methods for determining fragment characteristics are fully adequate, and it is sometimes difficult to decide

start

analytical

vessel

contents

collect data

situation £ failure

determine energy

gas only

ideal gas thermodyn. data

thoose statistical approach

see section

flashing

,fragments.

number of fragments

eq. 9.3.5

table 9.8

choice of eventgroup

fig. 9.9

range distribution

initial velocity group 2.3,6

E<0,* eq 9.3.5.

method 1

fig. 9.10, 9.11

ideal gas

method 2

method 3

eq.9.3.13, '9.3.14,9.3.15

fig. 9.8

fragment range neglecf fluid force,

end

Figure 9.6. Decision diagram for determining fragment characteristics.

mass distribution

which one to use. For calculating maximum fragment range, the theoretical approach (9.3.2) is more appropriate. For estimating mass and range distributions, the statistical approach (9.3.3) should be applied. Another factor favoring choice of the statistical analysis approach is that it is faster, because the theoretical approach requires application of a number of equations and figures.

9.3.2. Analytical Analysis 9.3.2.1. Data Collection Before calculations can begin, a great deal of data must be collected describing the vessel itself, its contents, and the condition at failure. These data include: For the vessel: shape (cylindrical or spherical) diameter D length L mass M wall thickness t For vessel contents: density (kg/m3) volume V (m3) chemical and physical properties thermodynamic qualities liquid/gas ratio For the condition at failure: internal pressure P1 (Pa) internal temperature T (K) Knowledge of thermodynamic data is especially important for vessels containing liquids that may flash. Such data may be found, for instance, in Perry and Chilton (1973). The pressure at failure is not always known. However, depending on the assumed cause of the failure, an estimate of pressure can be made: • If failure is initiated by an increase in internal pressure in combination with a malfunctioning of the pressure relief, the pressure at failure will equal the failure pressure of the vessel. This failure pressure is usually the maximum working pressure multiplied by a safety factor. For carbon-steel vessels, this safety factor can be taken as four. More precise calculations are possible if the vessel's dimensions and material parameters are known. • If failure is due to external heat applied to the vessel (e.g., from fire), the vessel's internal pressure rises, and at the same time its material strength drops.

For initial calculations, the pressure at failure will be typically 1.21 times the starting relief pressure. • If failure is initiated by corrosion or impact of a missile or fragment, it can be assumed that failure pressure will be the normal operating pressure. Once a vessel's internal pressure at failure is determined or assumed, the temperature of its contents can be calculated. 9.3.2.2. Calculation of Total Energy The total energy of a vessel's contents is a measure of the strength of the explosion following rupture. For both the statistical and the theoretical models, a value for this energy must be calculated. The first equation for a vessel filled with an ideal gas was derived by Erode (1959): (9.3.1) where P1 PQ V y

= = = =

internal pressure at failure ambient pressure volume of the vessel ratio of specific heats

(Pa) (Pa) (m3) (-)

This equation is well known and often used to calculate initial fragment velocity, but its application can result in gross overestimation. Assuming adiabatic expansion of the ideal gas, it can be derived that: (9.3.2) where *= 1 - (Po/A)(^1)/7

(9.3.3)

Baum (1984) uses a refined equation for k: k = 1 - (po/Pi)^-1^ + (y - I)OVPi)U - WPi)"17"]

(9-3.4)

If an energy value is found in literature, it is important to know which equation was used as a basis for calculation. The energy of liquids and gases in pressurized vessels cannot be straightforwardly determined by application of the above equations. Upon vessel depressurization, the liquid portion starts to boil, thus contributing to released energy. Thermodynamic data can be used to calculate this energy. (See, for instance, Section 6.3.2.) However, not all of this energy will be released instantaneously, and consequently, not all will contribute to fragment acceleration. Only in cases in which the tempera-

ture of a released liquid exceeds its superheat-limit temperature can explosive flashing occur, thus releasing all energy instantaneously. In order for the energy of liquid and gas in a pressurized vessel to be calculated, it must first be determined whether or not flashing of the liquid occurs (Section 6.3.2). If so, energy has to be determined from thermodynamic data. If not, the energy can be calculated very easily by substitution of the volume of the gas for V hiEq. (9.3.1) and (9.3.2). 9.3.2.3. Ranges for Rocketing Fragments In some accidents, large fragments, usually consisting of either the vessel's end caps or half of the vessel itself, were reported to have traveled unexpectedly long distances. It was argued that these fragments were accelerated during their flight by expelling the liquid entrapped in the fragment. In Baker et al. (1983), a computer program to calculate the release of energy as a function of time was developed based on the rocketing problem. However, if one assumes that available energy is released instantaneously, as occurs in the case of flashing liquids, an upper limit of the initial velocity of the fragment is obtained. Apparently, rocketing fragments are equal to fragments of an exploding vessel where liquid flashing occurs. The unexpected long fragment ranges result from the extra available energy of the liquid. Therefore, no special method for calculating ranges of rocketing fragments is required. 9.3.2.4. Determination of Number of Fragments There appears to be hardly any theoretical information available for calculation of the number of fragments. The number of fragments will usually be high for a highexplosive detonation in which the casing disintegrates completely. This will also be the case for a vessel that ruptures at a near-ambient temperature. By contrast, because BLEVEs usually do not develop high pressures, the number of fragments from such events tend to be low, usually from 2 to 10 pieces. Baum (1984) states that the scaled energy, which is determined by:

i=

iSJ F

I0'5

935

<-->

where E E M O0

= = = =

scaled energy energy vessel mass speed of sound in the gas

(-) (J) (kg) (m/s)

lies between 0.1 and 0.4 under normal operation for most industrial applications. In that region, few fragments are to be expected.

9.3.2.5. Calculation of Initial Velocity As a vessel ruptures, its fragments accelerate rapidly to a maximum velocity. This value is the initial fragment velocity V1. It is used to calculate either the range of fragment travel or, if collision with an obstacle occurs before maximum range is attained, impact velocity. A number of methods and equations are available to determine the initial velocity. These are described elsewhere in this volume. To avoid confusion, only three methods are given here. Method 1 calculates the initial velocity, both for vessels filled with ideal gases and for vessels filled with liquid and vapor. In most cases, this method will give an upper velocity limit. Method 2 is only valid for gas-filled vessels, but there, velocity depends upon the shape of the vessel and expected number of fragments. For scaled energies larger than 0.8, method 1 results in overestimates of velocity, and method 2 is not valid in this region. Therefore, method 3 is provided. Method 3 can also be applied for lower scaled energies, but methods 1 and 2 are recommended. Method 1 The simplest method is based on the total kinetic energy Ek of the fragments: (9.3.6) where V1 = initial fragment velocity Ek = kinetic energy M = vessel mass

(m/s) (J) (kg)

Converting the energy calculated with Eq. (9.3.2), and k according to Eq. (9.3.4), into fragment kinetic energy still results in an overestimate of the velocity when compared with experimental results. This is logical because a portion of the energy will be diverted into the creation of a blast wave. Negligible portions of the energy will go into rupturing the vessel, producing noise, and raising atmospheric temperature. It appeared from experiments that the actual total kinetic energy generated is 0.2 to 0.5 times the energy calculated by Eqs. (9.3.2) and (9.3.4). Therefore, it is appropriate to adjust earlier calculations based on ideal gases as follows: £k = 0.2-£^where Ek P1 V *Y

= = = =

kinetic energy absolute pressure in vessel volume of the gas in vessel ratio of specific heats

(J) (Pa) (m3) (-)

(9.3.7)

Thus, EI is 20% of the energy calculated for nonideal gases or for flash-vaporization situations. For scaled energies (E) larger than about 0.8 as calculated by Eq. (9.3.5), the calculated velocity is too high, so method 3 should be applied. Method 2 A computer program was developed based upon theoretical considerations. The results of a parameter study were used to compose a diagram (Figure 9.7) for use in determining initial velocity for vessels filled with an ideal gas (Baker et al. 1978a and 1983). The scaled pressure P on the horizontal axis of Figure 9.7 is determined by P = (Pi-PoW MaI

(9.3.8)

where P P1 PQ V M O0

= = = = = =

scaled pressure internal pressure at failure ambient pressure volume mass of the vessel speed of sound in gas at failure

(-) (Pa) (Pa) (m3) (kg) (m/s) cylindrical spherical

cylindrical

Figure 9.7. Fragment velocity versus scaled pressure (Baker et al. 1983). V1 = initial fragment velocity. ( ): spheres based on V1 = 0.88a0/=°55 [Eq. (6.4.15)]. ( ): cylinders based pon V1 = 0.8Sa0/=055 [Eq. (6.4.15)].

Separate regions in the figure account for the scatter of velocities for spheres and cylinders separating into 2, 10 or 100 fragments. The number of fragments must first be chosen, usually on the basis of scaled energy. The restrictions under which Figure 9.7 was derived are as follows: • Fragments are equal in size and shape. For two fragments only, the cylindrical vessel bursts perpendicularly to the axis of symmetry. For more than two fragments, the cylindrical vessel bursts into strip fragments which expand radially about the axis of symmetry, and end caps are neglected. • Wall thickness is uniform. • Cylindrical vessels have a length-to-diameter ratio of 10. • Contained gases used were either hydrogen (H2), air, argon (Ar), helium (He), or carbon dioxide (CO2). Figure 9.7 should be applied only with great caution to any situation where these restrictions are not valid. The speed of sound O0 of the contained gas at failure temperature must be calculated: og = yRT/m

(9.3.9)

where R = ideal gas constant T = absolute temperature m = molecular mass

(J/Kkmol) (K) (kg/kmol)

The vertical axis in Figure 9.7 is labeled the scaled velocity V1: v, = Vj(Ka0)

(9.3.10)

where K = factor for unequal fragments from which V1 can be calculated. The factor K takes unequal fragments into account. This factor is, however, open to discussion. One should usually assume equal fragments, that is, K = 1. It is inadvisable to extrapolate outside the regions given in Figure 9.7. For high scaled-pressure values (i.e., scaled energy larger than 0.8), method 3 should be used.

Methods This method employs an empirical equation derived by Moore (1967): (9.3.11)

where for spherical vessels

(9.3.12a)

for cylindrical vessels

(9.3.12b)

and

C = total mass of gas M — mass of vessel

(kg) (kg)

Moore's equation was derived from fragments accelerated from high explosives packed in a casing. Baum (1984) showed, in comparing different models, that the Moore equation tends to follow the theoretical upper-velocity limit for high scaled energies. 9.3.2.6. Ranges for Free-Flying Fragments The simplest relationship for calculating the range of a free-flying obstacle with a given initial velocity is derived when fluid-dynamic frictional forces, that is, lift and drag forces, are neglected. Then the only force acting on the fragment is that of gravity, and the vertical and horizontal range, H and R9 are dependent on the initial velocity V1 and the initial trajectory angle OL1 as follows: (9.3.13) and

(9.3.14) where H R cq g

= = = =

vertical range horizontal range initial trajectory angle gravitational acceleration

(m) (m) (rad) (m/s2)

The trajectory angle has a great influence on the range. The maximum range is found for an angle of 45°: (9.3.15)

It can be assumed that, should the vessel burst into two halves, fragments will travel parallel to their axes. If the vessel is initially positioned horizontally, the trajectory angle will be 5° to 10°. The results of a computer analysis of parameters for fragment ranges, including drag and lift forces, are plotted in Figure 9.8. The developers assumed that fragment positions remain constant with respect to trajectory. Figure 9.8 plots the scaled maximum range R and the scaled initial velocity V1 given by (9.3.16)

and (9.3.17) where V1 V1 R R P0 C0 AD Mf

= = = = = = = =

initial fragment velocity scaled initial velocity scaled range actual range density of ambient air drag coefficient exposed area in the plane perpendicular to the trajectory mass of the fragment

(m/s) (-) (-) (m) (kg/m3) (-) (m2) (kg)

The curves in Figure 9.8 were generated by maximizing range through variation of initial trajectory angle, so the angle for maximum range does not necessarily equal 45°. In most cases "chunky" fragments are expected. The lift coefficient is then zero, and the curve with C1AJyC0A0 = O is valid. It can be seen from Figure 9.8 that, for scaled velocities larger than 1, drag force becomes important, and ranges will be shorter than those calculated with Eq. (9.3.16). Values for drag coefficients C0 can be found in Table 9.8. Should a fragment be a thin plate, lift force becomes important, and the range will be greater than that calculated with Eq. (9.3.16). It is clear from Figure 9.8, however, that the range will only be greater for those regions of scaled velocity where this "frisbeeing" effect occurs. 9.3.3. Statistical Analysis of Fragments In Baker (1978b), an analysis was made of 25 accidental vessel explosions to determine the mass and range distributions of fragments. Most of these results are presented here. Because data were limited, it was necessary to cluster like events into six groups in order to yield an adequate base for useful statistical analysis. Information on each group is presented in Table 9.9. The original table incorporated

Figure 9.8. Scaled curves for fragment range predictions (Baker et al. 1983) [See Eqs. (9.3.15), (9.3.16), and (9.3.17)]. : Equation (9.3.15).

energy levels, but, because there are doubts about the correctness of those values, they are omitted here. Statistical analyses were performed on each group to provide estimates of fragment range and mass distributions. Range distributions for each group are given in Figures 9.9a and b. Interpretation of this information makes it possible to determine which percentage of fragments has a range smaller than or equal to a given value. Event groups 2,3, and 6 appeared to yield useful information on mass distribution. They are presented in Figures 9.10 and 9.11. These figures can be used in a manner similar to that recommended for Figures 9.9a and b, namely, to determine the percentage of fragments having a mass smaller than or equal to a given value.

9.3.4. Case Studies 9.3.4.1. Analytical Analysis As an initial example for demonstration of the use of theoretical and empirically derived equations, a problem similar to the one in Chapter 8 on blast is posed. A

TABLE 9.8. Drag Coefficients, C0 (Baker et al. 1983) SHAPE

Right Circular Cylinder (long rod), side-on

Sphere

Rod, end-on

Disc, face-on

Cube, face-on

Cube, edge-on

Long Rectangular Member, face-on

Long Rectangular Member, edge-on

Narrow Strip, face-on

SKETCH

TABLE 9.9. Groups of Similar Events Vessel Event Group Number

Number of Events

Explosion Source Material

Shape

Mass (kg)

Number of Fragments

1 2 3 4 5 6

4 9 1 2 3 1

Propane, anhydrous ammonia LPG Air LPG propylene Argon Propane

Railroad tank car Railroad tank car Cylinder pipe and spheres Semitrailer (cylinder) Sphere Cylinder

25,542 to 83,900 25,464 145,842 6,343 to 7,840 48.26 to 187.33 511.7

14 28 35 31 14 11

percentage of fragments with range equal to or less than R

range R (m)

range R (m)

Figure 9.9. Fragment range distribution for each group (Baker et al. 1978b).

percentage of fragments with range equal to or less than R

percentage of fragments with mass equal or less than M

mass M (kg)

percentage of fragments with mass equal or less than M

Figure 9.10. Fragment mass distribution for event groups 2 and 3 (Baker et al. 1978b).

mass M (kg) Figure 9.11. Fragment mass distribution for event group 6 (Baker et al. 1978b).

cylindrical vessel with a volume of 25 m3 and design pressure of 19.2 bar is used for the storage of propane. The wall thickness of the vessel is 3 mm, its material is carbon steel, and its length-to-diameter ratio is 10. The vessel is pressurized after fabrication with nitrogen to 24 bar. After testing, the safety valve will be set at 15 bar for normal operation. Two different situations will be examined for maximum fragment range: failure during testing, and failure due to an external fire. Case 1—Failure during Testing Because the maximum fragment range is required, the theoretical approach will be applied. Only the initial velocity and the maximum range of the fragments can be calculated with the theoretical approach. First, energy must be calculated. Differences among results from the various equations are illustrated here by the application of each to the problem. Brode [Eq. (9.3.1)] gives

where P1 PQ V y

= = = =

internal pressure at failure ambient pressure vessel volume ratio of specific heats

Equation (9.3.2) gives

Equation (9.3.3) gives

(Pa) (Pa) (m3) (-)

Equation (9.3.4) gives:

so

As was expected, the Erode equation (9.3.1) gives higher values for energy than the others [(9.3.2) with (9.3.3) and (9.3.4)]. The use of Eq. (9.3.2) with (9.3.4) is recommended. Twenty to fifty percent of this energy will be translated into the kinetic energy of the fragments, so the maximum kinetic energy will be: A quick estimate can be made with Eq. (9.3.7):

where Ek = kinetic energy P1 = absolute pressure in the vessel V = volume of the gas in the vessel

(J) (Pa) (m3)

Substituting,

This value appears to be in good agreement with the one calculated with the more theoretical approach. In order to determine which method should be applied for die calculation of initial velocity, the scaled energy should first be determined (see Section 9.3.2.5). With Eq. (9.3.5):

where E E M O0

= = = =

scaled energy energy vessel mass speed of sound in the gas

(-) (J) (kg) (m/s)

The mass M of the vessel can be calculated, assuming hemispherical end caps of 5 mm thickness, to be 2723 kg. The speed of sound aQ in nitrogen can be calculated with Eq. (9.3.9):

where R = ideal gas constant T = absolute temperature m = molecular mass

(J/(kkmol) (K) (kg/kmol)

a0 = (1.4 x 8314.41 X 293/28)172 = 349 m/S Then

Since the scaled energy is lower than 0.8 and nitrogen can be considered to be an ideal gas, both methods 1 and 2 can be applied. Method 1. The initial velocity, according to Eq. (9.3.6), is:

where V1 = initial fragment velocity Ek = kinetic energy M = vessel mass

(m/s) (J) (kg)

Then the mean initial fragment velocity will be:

Method 2. The initial velocity can also be calculated from Figure 9.7. Calculation of scaled pressure yields

Since the vessel is under a test in which pressure is increased slowly, it can be expected that the number of fragments generated will be low.

Assume that the vessel breaks into two equal parts at right angles to its axis. Use the graph in Figure 9.7 to determine V1. For a vessel breaking into two parts, V1 = 0.3, so: V1 = V1 x 349 = 0.3 x 349 = 105 m/s

With the initial velocity determined, the horizontal range R can be calculated. If fluid-dynamic forces (lift and drag) are neglected, maximum range will be attained when the fragment is propelled at an angle of 45°. The range is then independent of the fragment's mass and shape and is simply the ratio of the velocity squared to gravitational acceleration Eq. (9.3.15). The initial trajectory angle is taken into account by Eq. (9.3.14): A

—

vf sin(2aj) 8

where H R Oi1 g

= = = =

vertical range horizontal range initial trajectory angle gravitational acceleration

(m) (m) (rad) (m/s2)

For cylinders with horizontal axes, the initial trajectory will be low, typically 5° or 10°. Table 9.10 shows maximum ranges for initial velocities calculated by each method with various low trajectory angles assumed. It is obvious that very long maximum ranges are attained if lift and drag forces are neglected. Taking these forces into account can reduce maximum ranges significantly. Fragments, in this case, are expected to be rather blunt, so the lift coefficient is taken as zero. The scaled velocity can be calculated with Eq. (9.3.17). By applying the curve in Figure 9.8, a value for scaled range is found, from which the actual range can be calculated. This is performed for the initial velocity determined by method 1. The density of the ambient atmosphere is assumed to be 1.3 kg/m3. In this case, fragment shape and mass are parameters, so two fragments are considered. The first consists of the end cap, with a mass of 123 kg, Ad = 1.86 m2 (diameter of the vessel = 1.53 m), and Cd = 0.47 (Table 9.8). The other fragment consists of

TABLE 9.10. Ranges for Various Initial Trajectory Angles Ran

9e <m)

Velocity vt (m/s)

Method 1 Method 2

159 105

OL = 5°

448 195

a = 70°

882 385

OL = 45°

2580 1125

half of the vessel traveling parallel to its original axis. Therefore, Aff = 1362 kg, Cd = 0.47, and Ad = 1.86m2. Apply Eq. (9.3.16):

and Eq. (9.3.17):

where: V1 Vj R R P0 CD A0 Mf

= = = = = = = =

initial fragment velocity scaled initial velocity scaled range actual range density of ambient air drag coefficient exposed area in the plane perpendicular to the trajectory mass of the fragment

(m/s) (-) (-) (m) (kg/m3) (-) (m2) (kg)

For the end cap

Figure 9.8 gives R = 3.0 (C1A^C0A0 = O), so

For the fragment of half the vessel

Figure 9.8 gives R= 1.2 (C1A1JC^ = O), so

It appears that the maximum range depends not only on initial velocity but also on fragment mass and shape. The theory is, however, only capable of determining initial velocity. Unless assumptions are made as to fragment shape, mass, and trajectory angle, fluid forces must be neglected; very long ranges will result. Case 2—Failure Due to Overheating After a successful test with nitrogen, the vessel is placed in service and filled with propane. An accident occurs in which fire engulfs the vessel. The safety valve of

the vessel is sized in such a way that the maximum internal pressure will be 1.21 times the relief pressure. Because the tensile strength of the vessel's steel wall drops as it is heated, the vessel will fail at the maximum internal overpressure. Two cases will be considered. In the first case, internal temperature rises slowly, so the liquid propane is also heated. At failure, the liquid temperature will be above superheat limit temperature, and it will flash on release. In the second case, temperature rises very rapidly, so the liquid is not heated to a temperature above the superheat limit temperature at failure, and no liquid flashing occurs. To demonstrate the influence of fill ratio, cases of 80% and 10% fill ratio are considered. Explosively flashing liquid

The decision diagram in Figure 9.6 shows that the energy has to be determined in this case from thermodynamic data. This exercise was performed in Section 9.2.2, so it will not be repeated here. For the almost filled vessel, it was found that E = 1140.8 MJ, and, for the almost empty vessel, E = 372.8 MJ was found. However, these values were calculated in order to determine blast for a vessel placed at grade level; a factor of 2 was applied to account for surface reflection. This factor should not be applied in determining available internal energy. Therefore, the available internal energy for the 80% filled vessel is E = 1140.8/2 = 570.4 MJ For the almost empty vessel, the internal energy is E = 372.8/2 = 136.4 MJ In order to determine which method should be applied in the calculation of the initial velocity, the scaled energy should be determined (see Section 9.3.2.4). Applying Eq. (9.3.5):

where E E M O0

= = = =

scaled energy energy vessel mass speed of sound in gas

(-) (J) (kg) (m/s)

The mass M of the vessel was calculated to be 2723 kg. The speed of sound a0 in propane can be calculated [from Eq. (9.3.9)] as follows: OQ = yRT/mt

where R = ideal gas constant T = absolute temperature m = molecular mass

[J/(Kkmol)] (K) (kg/kmol)

Because the temperature is not known, it is assumed to be 500 K. Then og = 1.13 x 8314.41 x 500/44 = 1.07 x 107(m/s)2. And for the 10% filled case,

Because the scaled energy is higher than 0.8, method 3 has to be applied for both cases. Method 3 [Eq. (9.3.11)] gives

where, from Eq. (9.3.12b) for cylindrical vessels and C is total mass of gas and M is the mass of the vessel. The mass C is assumed to be the entire liquid inventory converted to gas. Liquid propane has a specific weight of 585.3 kg/m3, and the volume of the vessel was 25 m3. Therefore, for the 80% filled case: C = 0.8 x 585.3 x 25 = 11,706kg G = 1/[1 + 11,7067(2 x 2723)] = 0.32 and

V1 = 1.092(570.4 x 106 x 0.32/2723)°5 = 283 m/s For the 10% filled case: C = 0.1 x 585.3 x 25 = 1463kg G = 1/[1 + 1463/(2 x 2723)] = 0.79 and

V1 = 1.092(136.4 x 106 X 0.79/2723)°5 = 217 m/s

Fragment ranges will be calculated by neglecting lift and drag forces for different initial trajectory angles with Eq. (9.3.14):

where R = horizontal range Ct1 = initial trajectory angle g = gravitational acceleration

(m) (rad) (m/s2)

To assume an initial trajectory angle of 45° is probably too conservative. Directional effects can be expected. Large fragments like an end cap will travel in a direction parallel to the axis of the vessel. The trajectory angle will therefore be 5 to 10°. Nonflashing liquid In case the liquid does not flash, the available internal energy can be calculated with Eq. (9.3.1) or (9.3.2) taking V equal to the volume of the gas (see Section 9.3.2.2 and flow chart in Figure 9.6). For initial calculations Eq. (9.3.7) is appropriate.

with Ek = the kinetic energy P1 = the absolute pressure in the vessel V = the volume of the gas in the vessel

(J) (Pa) (m3)

The safety valve was set at 15 bar, so the failure pressure equals the maximum internal pressure of 1.21 x 15 = 18.15 bar. Thus, P1 = 18.15 + 1 = 19.15 bar = 1.915 x 106 Pa. This yields, for the 80% filled vessel, Ek = 0.2 x 1.915 x 106 x (1 - 0.8) x 25/(1.13 - 1) = 1.47 x 1O 7 J and for the 10% filled vessel, Ek = 0.2 x 1.915 x 106 x (1 - 0.1) x 25/(1.13 - 1) = 6.63 x 1O7J

TABLE 9.11. Ranges for Various Initial Trajectory Angles R(m) Fill Level (%)

80 10

V1 (m/s)

a = 5°

a = 70°

a = 45°

283 217

1419 834

2795 1643

8172 4805

The maximum fragment range for different initial trajectory angles can again be calculated with Eq. (9.3.6):

where V1 = initial fragment velocity Ek = kinetic energy M = vessel mass

(m/s) (J) (kg)

Then the initial fragment velocity will be, for the 80% filled vessel,

and for the 10% filled vessel:

Fragment ranges will be calculated by neglecting lift and drag forces for different initial trajectory angles with Eq. (9.3.14):

where R = horizontal range (Xj = initial trajectory angle g = gravitational acceleration

(m) (rad) (m/s2)

Clearly, from Table 9.12, the more dangerous case not involving flashing liquid is the 10% filled vessel. 9.3.4.2. Statistical Analysis Sample problem 9.1.6. demonstrated the calculation of the thermal radiation from a BLEVE of a tank trailer. This 6000-U.S.-gallon (22.7 m3) trailer was 90% filled TABLE 9.12. Ranges for Different Initial Trajectory Angles R(m)

Fill Level (%) 10 80

vt (m/s)

a = 5°

a = 70°

a = 45°

221 104

865 192

1705 377

4984 1104

TABLE 9.13. Fragment Distribution Range (m)

Percentage of Fragments Expected within Range W

12 33 110 550 1100

1 10 50 90 99

with propane and burst due to fire engulfment at an overpressure of 1.8 MPa (18 bar). The resulting thermal radiation was sufficient to cause third-degree burns at a distance of 300 to 360 m. The blast was sufficient to cause injuries from window pane fragments at a distance of 100 m. Here, the statistical approach will be used to predict the range distribution of the fragments. • Event group. First, one of the event groups in Table 9.9 has to be selected. Because the case concerns a tank truck filled with propane, the proper choice is clearly event group 1. • Number of fragments. The number of fragments to be expected can then be read from Table 9.9. The number of fragments to be expected will be about 14. • Fragment distribution. Figure 9.9a shows the fragment distribution for event group 1. Table 9.13 gives an impression of the distribution of the fragments. • Mass distribution. No statistical information can be obtained on the mass distribution (see decision diagram in Figure 9.6). It can, however, be concluded that there is considerable danger from fragments at a distance up to 1000 m. Of all the effects (heat radiation, blast, and fragments), fragments can cause damage and injury at the greatest distance from the explosion source.

REFERENCES Baker, W. E., J. J. Kulesz, P. S. Westine, and R. A. Strehlow. 1978a. A Short Course on Explosion Hazards Evaluation. Southwest Research Institute. Baker, W. E., J. J. Kulesz, R. E. Ricker, P. S. Westine, V. B. Parr, L. M. Vargas, and P. K. Moseley. 1978b. Workbook for Estimating the Effects of Accidental Explosions in Propellant Handling Systems. NASA Contractor report no. 3023. Baker, W. E., P. A. Cox, P. S. Westine, J. J. Kulesz, and R. A. Strehlow. 1983. Explosion Hazards and Evaluation. New York: Elsevier. Baum, M. R. 1984. The velocity of missiles generated by the disintegration of gas pressurized vessels and pipes. Trans. ASME. 106:362-368.

Baum, M. R. 1987. Disruptive failure of pressure vessels: preliminary design guide lines for fragment velocity and the extent of the hazard zone. Advances in Impact, Blast Ballistics, and Dynamic Analysis of Structures. ASME PVP, Vol. 124. Erode, H. L. 1959. Blast Wave from a Spherical Charge. Phys. Fluids 2:217. Hasegawa, K., and K. Sato. 1977. Study fireball following steam explosion w-pentane. Second Int. Symp. on Loss Prevention and Safety Promotion in the Process lnd. Heidelberg, pp. 297-304. Hymes, I. 1983. The physiological and pathological effects of thermal radiation. United Kingdom Atomic Energy Authority, SRD R 275. Johnson, D. M., M. J. Pritchard, and M. J. Wickens. 1990. Large scale catastrophic releases of flammable liquids. Commission of the European Communities report, Contract No.: EV4T. 0014. UK(H). Moore, C. V. 1967. Nuclear Eng. Des. 5:81-97. Mudan, K. S. 1984. Thermal radiation hazards from hydrocarbon pool fires. Progr. Energy Combust. Sd. 10(1):59-80. Pape, R. P. (Working Group Thermal Radiation). 1988. Calculation of the intensity of thermal radiation from large fires. Loss Prevention Bulletin. 82:1-11. Perry, R. H., and D. Green. 1984. Perry's Chemical Engineers' Handbook, 6th. New York: McGraw-Hill. Pietersen, C. M. 1985. Analysis of the LPG incident in San Juan Ixhuatepec, Mexico City, 19 November 1984. Report—TNO Division of Technology for Society. Roberts, A. F. 1982. Thermal radiation hazards from release of LPG fires from pressurized storage. Fire Safety J. 4:197-212.

A VIEW FACTORS FOR SELECTED CONFIGURATIONS In this appendix, the view factors for three configurations are given: 1. radiation from a sphere 2. radiation from a vertical cylinder 3. radiation from a vertical plane surface For other configurations, refer to Love (1968) and Buschman and Pittmann (1961). A view factor depends on the shapes of the emitter and receiver. Consider the receiver to be a small, plane surface at ground level with a given orientation with respect to the emitter. The angle between the normal to the surface and the connection between the surface and the center of the emitter (©) must be known.

A-I. VIEW FACTOR OF A SPHERICAL EMITTER (e.g., FIREBALL) If the distance from the receiver to the center of the sphere is L, and 4> is the angle between the connection of the surface to the center of the sphere and the tangent to the sphere, then, for ® ^ ir/2 — 4>, the view factor F is given by F = ^cos(@)

(A-I)

Li

where L = distance between receiving surface and sphere's center r = radius of sphere 0 = orientation angle

(m) (m) (rad)

In this case, the sphere is in full sight. When, on extension, the receiving surface intersects with the sphere (@ > TT/ 2 — ), the receiver can not "see" the total emitter. The view factor F is then given as

(A-2)

where r D L &

= fireball radius (r = D/2) = fireball diameter = distance to center of sphere = angle between the normal to surface and connection of point to center of sphere 24> = view angle L1 = reduced length LIr

(m) (m) (m) (rad) (rad) (-)

The view factor for incomplete visibility is given in Figure A-2.

A-2. VIEW FACTOR OF A VERTICAL CYLINDER A pool fire's flame can be represented (under no wind conditions) by a vertically placed cylinder with a height h and a ground surface radius r. The view factor of

fireball

receptor

fireball

receptor

Figure A-1. View factor of a fireball. (A) Receiver "sees" the sphere completely. (B) Receiver "sees" the sphere partially.

degrees

L/r

Figure A-2. View factors of a sphere as function of the dimensionless distance (distance/radius) (incomplete view).

a plane surface at ground level whose normal lies in one vertical plane with the axis of the cylinder is given by the following equations: hr = h/r

(A-3)

X1 = XIr

(A-4)

A = (X1 + I)2 + h2T

(A-5)

B = (X1- I)2 + A2

(A-6)

For a horizontal surface (0 = ir/2):

(A-7)

cylindrical flame

receiver

Figure A-3. View factor of a cylindrical flame.

And for a vertical surface (0 = 0):

(A-8)

The maximum view factor is given by (A-9)

For the view factor of a tilted cylinder, refer to Raj (1977). the view factors generated by Eqs. (A-7) and (A-8) are given in Table A-I and Figure A-4.

A-3. VIEW FACTOR OF A VERTICAL PLANE SURFACE In the case of a vertical plane surface, it is assumed that the emitter and receiver are parallel to each other. The view factor is calculated from the sum of view factors from surface I and surface II (see Figure A-5). Surfaces I and II are defined as those to the left and the right of a plane through the center of the receiver and perpendicular to the intersections of the receiver with the ground.

TABLE A-1. View Factors of a Vertical Cylindrical Emitter hr = 2Lf/df; Xr = 2X/c(f

hr

0.1

0.2

0.5

132 44 20 11 6 1

242 120 65 38 24 5

332 243 178 130 97 27 5 1

1.1 1.2 1.3 1.4 1.5 2.0 3.0 4.0 5.0 10.0 20.0

330 196 130 94 71 28 9 5 3

415 308 227 173 135 56 19 10 6 1

449 397 344 296 253 126 47 24 15 3

1.1

356 201 132 94 72 28 9 5 3

481 331 236 177 138 56 19 10 6 1

Xr

1.0

2.0

3.0

5.0

6.0

70.0

20.0

362 312 278 251 229 160 95 62 43 9 1

363 313 278 252 231 164 103 73 54 17 3

363 314 279 153 232 166 107 78 61 26 8

454 416 384 357 333 249 163 119 91 32 9

454 416 384 357 333 249 165 123 97 42 14

455 417 385 357 333 250 167 125 100 48 21

581 521 474 436 404 296 189 134 100 34 9

581 521 475 437 405 299 195 143 111 45 14

581 521 475 437 406 300 197 147 117 55 22

1. horizontal target (1000 x Fh) 1.1 1.2 1.3 1.4 1.5 2.0 3.0 4.0 5.0 10.0 20.0

354 291 242 203 170 73 19 7 3

360 307 268 238 212 126 50 22 11 1

362 310 272 246 222 145 71 38 21 3

362 312 177 250 228 158 91 57 37 7 1

2. vertical target (1000 x Fv) 453 413 376 342 312 194 86 47 29 6 1

454 416 383 354 329 236 132 80 53 13 3

454 416 384 356 332 245 150 100 69 19 4

3. maximum view factor (1000 1.2 1.3 1.4 1.5 2.0 3.0 4.0 5.0 10.0 20.0

559 466 287 323 271 129 48 24 15 3

575 505 448 398 355 208 88 47 29 6 1

580 517 468 427 392 267 141 83 54 13 3

581 519 472 433 400 285 166 106 73 19 4

454 416 384 356 333 248 161 115 86 29 7 X Fmax)

581 520 474 436 404 294 185 129 94 30 7

Figure A-4. Maximum view factors of a cylindrical flame as function of dimensionless distance to flame axes.

flat radiator

receiver

Figure A-5. View factor of a vertical plane surface.

For each of the two surfaces: hr = hlb

(A-IO)

X1 = XIb

(A-Il)

A = \l(h2r + X?)0-5

(A-12)

B = hj(\ + X?)0-5

(A-13)

For a horizontal target on ground level (® = ir/2), the view factor is given by (A-14) and, for a vertical surface (© = O): (A-15) The maximum view factor is given by ^max = (ft + ^)0'5

(A-16)

It must be noted that, unless ^1 = bu, Fmax is not the maximum view factor for any distance C from the emitter. The view factors Fh, F^ and Fmax can easily be found by summing the view factors calculated from the surfaces I and II. Values of the view factor Fmax as function of X1 are given in Table A-2 and Figure A-6. TABLE A-2. View Factors of a Vertical Plane Surface Emitter hr = h/b\ Xr = XIb (See Figure A-5.) "r

Xr

0.1

0.2

0.1 0.2 0.3 0.5 1.0 1.5 2.0 3.0 5.0

146 53 25 9 2 1

276 146 83 34 8 3 1

0.3

0.5

1.0

1.5

2.0

3.0

5.0

461 423 386 318 190 114 71 31 9

465 467 430 435 397 403 336 346 219 238 146 170 100 126 50 75 16 31

1. horizontal target (1000 x Fh) 341 221 144 68 17 6 3 1

400 310 236 137 42 17 8 3 1

443 389 337 249 111 53 28 10 2

456 413 371 296 161 88 51 20 5

(Table continues on p. 344.)

TABLE A-2. (Continued) "r

Xr

0.1

0.2

0.1 0.2 0.3 0.5 1.0 1.5 2.0 3.0 5.0

353 223 156 94 41 22 14 7 2

447 352 274 178 80 44 17 13 5

0.1 0.2 0.3 0.5 1.0 1.5 2.0 3.0 5.0

382 229 158 94 41 22 14 7 2

525 381 286 181 80 44 27 13 5

0.3

0.5

1.0

1.5

2.0

3.0

5.0

497 489 477 442 335 245 180 105 45

497 490 478 445 347 264 204 129 61

498 490 479 447 352 274 218 148 80

681 652 622 558 410 302 227 138 63

682 655 626 565 425 322 252 165 86

2. vertical target (1000 x Fv) 474 414 349 245 117 65 41 20 7

489 461 421 335 180 105 66 32 12

496 484 466 416 277 179 120 62 24

497 488 474 435 318 222 157 86 35

3. maximum view factor (1000 x Fmax) 584 469 377 255 188 66 41 20 7

632 555 483 362 185 106 67 33 12

665 621 575 484 299 187 123 62 24

674 639 602 526 356 239 165 88 36

678 647 613 544 385 270 194 109 46

Figure A-6. Maximum view factor of a plane surface as function of dimensionless distance to emitter.

REFERENCES Buschman, Jr., A. J., and C. M. Pittman. 1961. Configuration factors for exchange of radiant energy between antisymmetrical sections of cylinders, cones and hemispheres and their bases. NASA, Technical Note D-944. Love, T. J. 1968. Radiative heat transfer. Cincinnati, OH: C. E. Merrill. Raj, P. K. 1977. Calculation of thermal radiation hazards from LNG fires, a review of the state of the art. A.G.A. Transmission Conference, T135-148.

B EFFECTS OF EXPLOSIONS ON STRUCTURES Acquisition of practical knowledge in the field of explosion-induced structural damage is still heavily dependent upon empirical data. Such data, however, usually give information only about those overpressure levels which relate to certain degrees of damage. Other parameters, such as duration, impulse, and shape of the blast wave are not taken into account. Tables containing such information are frequently published. The best known are contained in Glasstone (1966, 1977), a frequently cited reference. The earliest tables were compiled from data collected from nuclear weapon tests, in which very high yield devices produced sharp-peaked shock waves with long durations for the positive phase. However, these data are used for other types of blast waves as well. Caution should be exercised in application of these simple criteria to buildings or structures, especially for vapor cloud explosions, which can produce blast waves with totally different shapes. Application of criteria from nuclear tests can, in many cases, result in overestimation of structural damage. Table B-I (Stephens 1970) is useful in obtaining a quick overview of damage. It describes four damage level zones. A building is totally destroyed (zone A) if it is damaged beyond economical repair. Severe damage (zone B) suggests partial collapse and/or failure of some bearing members. A building in zone C (moderate damage) is still usable, but structural repairs are required. Light damage (zone D) consists of shattered window panes, light cracks in walls, and damage to wall panels and roofs. More detailed information is given in Table B-2, which is based on Glasstone (1977). Information of the influence of duration on the level of damage can be found in Figure B-I, which was composed by Baker (1983) based on data from Jarret (1968). Jarret's data originated from descriptions of damage to brick houses in London from World War II bomb attacks. These data permitted the development of a relationship among damage, distance, and type of bomb, and thus permitted calculation of explosion yields. Baker (1983) converted this relationship into a pressure-impulse diagram containing iso-damage curves (Figure B-I). The curves in this figure represent the threshold of side-on blast-wave parameters that produce a certain level of damage to brick dwellings. The curves in Figure B-I represent primarily the transient nature of blast waves. They do not represent the interaction effects of blast waves and structures, such as multiple reflections and shielding due to the presence of other structures.

TABLE B-2. Damage Produced by Blast o/ae-on overpressure (kPa)

Description of Damage Annoying noise Occasional breaking of large window panes already under strain Loud noise; sonic boom glass failure Breakage of small windows under strain Threshold for glass breakage "Safe distance," probability of 0.95 of no serious damage beyond this value; some damage to house ceilings; 10% window glass broken. Limited minor structural damage Large and small windows usually shattered; occasional damage to window frames Minor damage to house structures Partial demolition of houses, made uninhabitable Corrugated asbestos shattered. Corrugated steel or aluminum panels fastenings fail, followed by buckling; wood panel (standard housing) fastenings fail; panels blown in Steel frame of clad building slightly distorted Partial collapse of walls and roofs of houses Concrete or cinderblock walls, not reinforced, shattered Lower limit of serious structural damage 50% destruction of brickwork of houses Heavy machines in industrial buildings suffered little damage; steel frame building distorted and pulled away from foundations Frameless, self-framing steel panel building demolished; rupture of oil storage tanks Cladding of light industrial buildings ruptured Wooden utility poles snapped; tall hydraulic press in building slightly damaged Nearly complete destruction of houses Loaded tank cars overturned Unreinforced brick panels, 25-35 cm thick, fail by shearing or flexure Loaded train boxcars completely demolished Probable total destruction of buildings; heavy machine tools moved and badly damaged

0.15 0.2 0.3 0.7 1 2

3 3.5-7 5 8 7-15 10 15 15-20 18 20 20-28

30 35 35-50 50 50-55

60 70

TABLE B-1. Damage Levels Zone A B C D

Damage Level

Side-on overpressure (kPa)

Total destruction Severe damage Moderate damage Light damage

>83 >35 >17 >3.5

Figure B-1. Pressure impulse diagrams for damage to brick houses. Line 1: Threshold for light damage. Line 2: Threshold or moderate damage: partial collapse of roof; some bearing wall failures. Line 3: Threshold for severe damage: 50 to 75 percent of bearing wall destruction. P8: side-on overpressure. is: side-on impulse (Baker et al. 1983).

REFERENCES Baker, W. E., P. S. Westine, J. J. Kulesz, and R. A. Strehlow. 1983. Explosion Hazards and Evaluation. New York: Elsevier. Glasstone, S. 1966. The Effects of Nuclear Weapons. US Atomic Energy Commission, Revised edition 1966. Glasstone, S., and P. J. Dolan. 1977. The Effects of Nuclear Weapons. US Dept. of Defense, Third edition. Jarret, D. E. 1968. Derivation of the British Explosives Safety Distances. Ann. NY Acad. Sd. 152. Stephens, M. M. 1970. Minimizing Damage from Nuclear Attack, Natural and Other Disasters. Washington: The Office of Oil and Gas, Department of the Interior.

C EFFECTS OF EXPLOSIONS ON HUMANS C-I. INTRODUCTION This appendix is a summary of the work published in the so-called Green Book (1989). Possible effects of explosions on humans include blast-wave overpressure effects, explosion-wind effects, impact from fragments and debris, collapse of buildings, and heat-radiation effects. Heat-radiation effects are not treated here; see Chapter 6, Figure 6.10 and Table 6.6. Explosion effects are commonly separated into a number of classes. The main division is between direct and indirect effects. Sometimes, direct effects are referred to as primary effects, and indirect effects are then subdivided into secondary and tertiary effects.

Direct, Primary Effects The main direct, primary effect to humans from an explosion is the sudden increase in pressure that occurs as a blast wave passes. It can cause injury to pressuresensitive human organs, such as ears and lungs.

Indirect Effects Primary fragments originate from the explosion source, for example, a pressure vessel. In general, those fragments have a high velocity. The impact of fragments and debris from sources not originating from the explosion source are secondary effects. Secondary fragments result when the blast tears off parts of structures, for example, bricks, roof tiles, and glass. Such fragments, except for glass, are relatively blunt and have low velocities. Glass window panes and fragments, however, are small, sharp, and sometimes have high velocities. Thus, they are capable of causing injuries at much greater distances from explosion centers than usually result from other secondary fragments. Building collapse can be regarded as a secondary effect, although it is not common to group this effect within any class.

The explosion wind following a blast can carry persons away, causing injury as a result of their falling, tumbling over, or colliding with obstacles. This effect is referred to as a tertiary effect. Effects are described, together with criteria to calculate the probable degree of lethality.

C-2. PRIMARY EFFECTS Lethality Due to Lung Injury As the external pressure on the chest wall becomes larger than its internal pressure during the passage of a blast wave, the chest wall moves inward, thus causing injury. Because the inward motion takes time, the duration of the blast wave is important. Results of animal tests indicate that overpressure is only important for long durations, and impulse is important for relatively short durations (White et al. 1971). Most of the criteria found in literature are extracted from Bowen et al. (1968). Diagrams of pressure versus duration are presented for various body positions in relation to the blast wave, from which the chance of survivability can be calculated. Those diagrams were combined in a pressure-impulse diagram, which is depicted in Figure C-I. The scaled overpressure P equals PIp0, in which P is the actual pressure acting on the body, and pQ is the ambient pressure. The scaled impulse i equals: 7 = //(pj/2m1/3)

(C-Ll)

in which i is impulse and m is mass of the body. The impulse is the integral of overpressure over the blast-wave duration. For initial calculations, impulse can be approximated by i = l/2Ptp

(C-1.2)

in which tp is the duration of the overpressure in the blast wave. The overpressure P depends on the position of the human body (Figure C-2). If body position is such that no obstruction of the incident wave occurs, P equals the side-on overpressure P8 of the blast wave (Figure C-2 A). If the body is upright (Figure C-2B), the incident wave is disturbed. Because the human body is small in relation to the length of the blast wave, the reflection phase can be neglected. Then the resulting overpressure on the chest wall equals the side-on overpressure Ps plus the pressure Q caused by the explosion wind multiplied with the drag coefficient Cd of the body: (C-1.3)

survivability

threshold

Figure C-1. Pressure-impulse diagram for lung injury. P: scaled overpressure. /: scaled impulse. (Bowenetal. 1968).

Figure C-2. Position of human body. (A) No obstruction of incident wave: P = P6. (B) Diffraction of incident wave: P = P8 + O. (C) Body subjected to reflection (standing): P = PT. (D) Body subjected to reflection (prone): P = Pr (Bowen et al. 1968).

In general the drag coefficient depends on the shape of the structure. In the case of a human body a value of 1 is considered to be accurate enough. If the body is near a surface against which the blast wave can reflect (Figures C-2C and C-2D), the pressure P acting on the body equals the reflected pressure Pr: (C-1.4)

Ear Damage

percentage eardrum rupture

The ear is a very sensitive and complex organ that responds to very small variations in pressure. It was argued in Hirsch (1968) that ear drum rupture is decisive as to ear damage from blast waves. Figure C-3 shows the percentage of eardrum ruptures as a function of side-on overpressure P8. Overpressure duration probably has some influence on ear damage, but no literature on this subject was found. Because the ear can respond to high frequencies, blast wave loading normally lies in the pressure region rather than in the impulse region.

REIDER 1968

HENRY 1945

VADALA 1930

Figure C-3. Eardrum rupture as a function of overpressure (Hirsch 1968).

TABLE C-1. Criteria for Skull Fracture Due to Impact of a Mass of 4.5 kg Impact Velocity (mis) 3.1 4.6 7.0

Level of Injury Mostly safe Threshold Near 100% lethal

C-3. SECONDARY EFFECTS For purposes of determining fragment effects on humans, cutting and noncutting fragments should be distinguished from each other. Cutting fragments penetrate the skin, whereas injuries from noncutting fragments result from contact pressure at impact. The open literature contains only scarce and incomplete data. However, criteria were found to describe the impact of a mass of 4.5 kg to the head (Table C-I). A fragment is generally considered to be dangerous if it has a kinetic energy of at least 79 J. But values of 40 to 60 J were found to cause serious wounds. Kinetic energy Ek equals: Ek = l/2mfv? where mf is the fragment mass in kilograms and vf is the impact velocity in meters per second. The kinetic energy criterion can be applied for fragment masses between 4.5 and 0.1 kg. For smaller masses, the following equation can be used: V50 = 1247PX273 + 22.03 in which V50 = penetration velocity at which 50% of fragments penetrate the skin * = a shape factor which equals 4740 kg/m372 for the most damaging fragments /nf = fragment mass The equation was derived empirically from experiments on animals, isolated skin, and materials resembling skin.

Collapse of Buildings Humans inside collapsing buildings are subjected to the impact of very heavy structural parts. Pictures taken after earthquakes or bomb attacks reveal that vertical members usually fail, leaving a stack of floors on top of another. Although a

TABLE C-2. Injury Criteria for Whole Body Impact Impact Velocity (mis) 3.0 6.4 16.5 42.0

Injury Mostly safe Lethality threshold Lethality near 50% Lethality near 100%

building collapse may appear total, it is not unusual for some people to survive within the spaces formed by the collapsed structure. Earthquake statistics reveal that about 50% of those inside a collapsing building will be killed, either immediately or as a result of injuries sustained. Other data are lacking, but one could assume a similar percentage for people inside buildings that collapse as a result of blast. This assumption is supported by the fact that, in both cases, the event is sudden and unexpected, so there is neither a place nor the time to find other shelter.

C-4. TERTIARY EFFECTS Air particles in a blast wave have a certain velocity which, in general, flow in the same direction as the propagation of the blast wave. This explosion wind can sweep

Figure C-4. Impact velocity and injury criteria as a function of side-on overpressure and impulse (Bowenetal. 1968).

people away, carry them for some distance, and throw them against obstacles. Upright people are most vulnerable (Figure C-2B). No lethal injuries are likely to be incurred as a person tumbles and slides along the surface, but upon collision with an obstacle, consequences may be deadly. Such consequences depend upon velocity at impact, the hardness and shape of the obstacle, and the portion of the body involved in the collision. Table C-2 gives injury criteria. Based on the pressure and impulse of the incident blast wave, the maximum velocity can be calculated of a human body during transportation by the explosion wind. Figure C-4 shows the impact velocity Vm for the lethality criterion for whole body impact as a function of side-on overpressure Ps and impulse /s.

REFERENCES Bowen, J. G., E. R. Fletcher, and D. R. Richmond. 1968. Estimate of man's tolerance to the direct effects of air blast. Lovelace Foundation for Medical Education and Research. Albuquerque, NM. Green Book 1989. Methods for the determination of possible damage to people and objects resulting from releases of hazardous materials. Published by the Dutch Ministry of Housing, Physical Planning and Environment. Voorburg, The Netherlands. Code: CPR.6E Hirsch, F. G. 1968. Effects of overpressure on the ear, a review. Ann. NY Acad. Sd. White, C. S., R. K. Jones, and G. E. Damon. 1971. The biodynamics of air blast. Lovelace Foundation for Medical Education and Research. Albuquerque, NM.

D TABULATION OF SOME GAS PROPERTIES IN METRIC UNITS

Critical Conditions Molecular Mass

Specific Heat Ratio

Abs. Press, (bar)

AbS. Temp. (K)

Gas or vapor

Chemical Formula

Acetylene Air Ammonia Argon Benzene

C2H2 N2 + O2 NH3 A C6H6

26.05 28.97 17.03 39.94 78.11

1.24 1.40 1.31 1.66 1.12

62.4 37.7 112.8 48.6 49.2

309.4 132.8 406.1 151.1 562.8

n-Butane /so-butylene Carbon dioxide Carbon monoxide Chlorine

C4H10 C4H8 CO2 CO Cl2

58.12 56.10 44.01 28.01 70.91

1.09 1.10 1.30 1.40 1.36

38.0 40.0 74.0 35.2 77.2

425.6 418.3 304.4 134.4 417.2

Ethane Ethyl chloride Ethylene Helium n-Heptane

C2H6 C2H5CI C2H4 He C7H16

30.07 64.52 28.05 4.00 100.20

1.19 1.19 1.24 1.66 1.05

48.8 52.7 51.2

305.6 460.6 283.3

2.3

5.0

27.4

540.6

n-Hexane Hydrogen Hydrogen sulfide Methane Natural gas

C6H14 H2 H2S CH4 —

86.17 2.02 34.08 16.04 18.82

1.06 1.41 1.32 1.31 1.27

30.3 13.0 90.0 46.4 46.5

508.3 33.3 373.9 191.1 210.6

Nitrogen Pentylene Oxygen Propane Water vapor

N2 C5H10 O2 C3H8 H2O

28.02 70.13 32.00 44.09 18.02

1.40 1.08 1.40 1.13 1.33

33.9 40.4 50.3 42.5 221.2

126.7 474.4 154.4 370.0 647.8

E CONVERSION FACTORS TO SI FOR SELECTED QUANTITIES An asterisk before a number indicates that the conversion factor is exact, and all subsequent digits are zero. TABLE E-1A. Conversion Factors to Sl Units

To

To Convert From British thermal unit (Btu, International Table) Btu/lb-deg F (heat capacity) Btu/hour Btu/second Btu/ft2-hr-deg F (heat transfer coefficient) Btu/ft2-hour (heat flux) Btu/ft-hr-deg F (thermal conductivity) degree Fahrenheit (0F) degree Rankine (0R) fluid ounce (U.S.) foot foot (U.S. Survey) foot of water (39.20F) foot2 foot/second2 foot2/hour foot-pound-force foot2/second foot3 gallon (U.S. liquid) gram inch inch of mercury (6O0F)

Multiply By

joule (J)

1.0550559 x 103

joule/kilogram-kelvin (J/kg-K) watt (W) watt (W) joule/meter^secondkelvin (J/m2-s-K) joule/metei^-second (J/m2-s) joule/meter-second-kelvin (J/m-s-K) kelvin (K) kelvin (K) meter3 (m3) meter (m) meter (m) pascal (Pa) meter2 (m2) meter/second2 (m/s2) mete^/second (m2/s) joule (J) meters/second (m2/s) meter3 (m3) meter3 (m3) kilogram (kg) meter (m) pascal (Pa)

4.1868000 x 103 2.93077107 x 10~1 1.0550559 x 103 5.6782633 3.1545907 x 10~3 1 .7307347 tk = (tf + 459.67)71.8 tk = V1.8

*2.9573530 x 10~1 *3.0480000 x 10~1 3.0480061 x 10~1 2.98898 x 103 *9.2903040 x 10~2 *3.0480000 x 10~1 *2.5806400 x 10~5 1.3558179 *9.2903040 x 10~2 2.8316847 x 10~2 3.7854118 x 10~3 *1. 0000000 x 10~3 *2.5400000 x 10~2 3.37685 x 103

(Table continues on p. 362.)

TABLE E-1A. (Continued) To Convert From

To 0

inch of water (6O F) inch2 inch3 kilocalorie kilogram-force (kgf) mile (U.S. Statute) mile/hour millimeter of mercury (O0C) pound-force (lbf) pound-force-second/ft2 pound-mass (lbm avoirdupois) pound-mass/foot3 pound-mass/foot-second psi ton (long, 2240 lbm) ton (short, 2000 lbm) torr (mm Hg, O0C) watt-hour yard

Multiply By

pascal (Pa) meter2 (m2) meter3 (m3) joule (J) newton (N) meter (m) meter/second (m/s) pascal (Pa) newton (N) pascal-second (Pa-s) kilogram (kg)

2.48843 x 102 *6.4516000 x 1Q-4 *1. 6387064 x 1Q-5 *4. 1868000 x 103 *9.8066500 *1. 6093440 x 103 M.4704000 x 1Q-1 1.3332237 x 102 4.4482216 4.7880258 x 101 *4.5359237 x 10~1

kilogram/meter3 (kg/m3) pascal-second (Pa-s) pascal (Pa) kilogram (kg) kilogram (kg) pascal (Pa) joule (J) meter (m)

1.66018463 x 101 1.4881639 6.8947573 x 103 1.0160469 x 103 *9.718474 x 102 1.3332237 x 102 *3.6000000 x 103 *9. 1440000 x 10~1

F A CASE STUDY OF GAS EXPLOSIONS IN A PROCESS PLANT USING A THREE-DIMENSIONAL COMPUTER CODE B. H. Hjertager, S. Enggrav, J. E. F0rrisdahl and T. Solberg Telemark Institute of Technology (SiT) and Telemark Innovation Centre (Tel-Tek) Kj0lnes, N-3900 Porsgrunn, Norway

I. INTRODUCTION 1.1. The Problem Gas explosion hazard assessment in flammable gas handling operations is crucial in obtaining an acceptable level of safety. In order to perform such assessments, good predictive tools are needed. These tools should take account of relevant parameters, such as geometrical design variables and gas cloud distribution. A theoretical model must therefore be tested against sufficient experimental data prior to becoming a useful tool. The experimental data should include variations in geometry as well as gas cloud composition, and the model should give reasonable predictions without use of geometry or case-dependent constants. 1.2. Complex Geometry Modeling All geometries found in industrial practice may contain a lot of geometrical details that can influence the process to be simulated. Examples of such geometries are heat exchangers with thousands of tubes and several baffles and regenerators with many internal heat absorbing obstructions. In the present context the geometries found inside modules on offshore oil and gas producing platforms and in onshore process plants constitute relevant examples of the complex geometries at hand. There are at least two routes for describing such geometries. First, we may choose to model every detail by use of very fine geometrical resolution, or second, we

may describe the geometry by use of some suitable bulk parameters. A detailed description will always need large computer resources both with regard to memory and calculation speed. It is not feasible with present or even future computers to implement the detailed method of solving such problems. We are therefore forced to use the second line of approach, which incorporates the so-called porosity/ distributed resistance (PDR) formulation of the governing equations. This method was proposed by Patankar and Spalding (1974) and has been applied to analysis of heat exchangers, regenerators, and nuclear reactors. Sha et al. have extended the method to include advanced turbulence modeling. The presence of geometrical details modifies the governing equations in two ways. First, only part of the total volume is available to flow, and secondly, solid objects offer additional resistance to the flow and additional mixing in the flow.

1.3. Relevant Works It has in the past been usual to predict the flame and pressure development in vented volumes or unconfmed vapor clouds by modeling the burning velocity of the propagating flame. This may be successful if we have a simple mode of flame propagation such as axial, cylindrical, or spherical in volumes without obstructions in the flow. If these are present, however, it is almost impossible to track the flame front throughout complex geometries. It has been apparent that in these siutations it is more useful to model the propagation by calculating the rate of fuel combustion at different positions in the flammable volume. It is also important to have a model that is able to simulate both subsonic and supersonic flame propagation to enable a true prediction of what can happen in an accident scenario. One such model that in principle meets all these needs has been proposed by Hjertager (Hjertager et al., 1982a,b, 1989, 1991) and Bakke and Hjertager (1986a,b, 1987). The model has been tested against experimental data from various homogeneous stoichiometric fuel-air mixtures in both large- and small-scale geometries. Similar models for gas explosions have subsequently also been proposed by Kjaldman and Huhtanen (1986), Marx et al. (1985), Martin (1986), and Van den Berg (1989). All the above models are similar in nature. They use finite-domain approximations to the governing equations. Turbulence influences are taken into account by the k-e model of Launder and Spalding, and the rate of combustion is modeled by variants of the "eddydissipation" model of Magnussen and Hjertager. The Bakke and Hjertager models are incorporated in two computer codes named FLAGS (FLame Acceleration Simulator) and EXSIM (EXplosion SIMulator). The solution method used is the SIMPLE technique of Patankar and Spalding (1972). The model of Kjaldman and Huhtanen uses the general PHOENICS code of Spalding. The model of Marx et al. uses the CONCHAS-SPRAY computer code, which embodies the ICE-ALE solution technique. The model of Van den Berg is similar to the Hjertager model and is incorporated into a code named REAGAS. Finally, the model of Martin that is embodied in a computer code named FLARE uses the flux-corrected transport (FCT) of Boris and Book.

1.4. Objectives The present work will apply one of the above mentioned 3D codes, namely the EXSIM code, to a case study of gas explosions in a process plant. The scenario was specified by Mancini for use in a workshop at a recent conference arranged by the Center for Chemical Process Safety of the American Institute of Chemical Engineers (CCPS/AIChE 1991).

1.5. Contents of Paper First, the scenario is defined, followed by a brief summary of the code. Next, the various clouds and ignition positions are defined, then the results are given, and finally some concluding remarks are made.

2. SCENAMO DESCWPTION General Figure 1 shows part of a solvent phase polypropylene plant. The plant consists of three process lines, denoted A, B, and C. During a risk assessment review, a scenario was identified that involved a release of reactor contents from a location near the west end of the "A" line. Estimates are needed of the blast overpressures that would occur if the resulting cloud of vapor, mist, and power ignites. Release characteristics Description: A slurry of polypropylene powder in hexane/propylene liquid Rate: 4000 kg/min Composition: Propylene monomer Hexane Polypropylene powder

20 wt% 50 wt% 30 wt%

Temperature/Pressure: 7O0C/12 bar abs. Adiabatic flash of liquid phase: 40 wt% vaporized; 90% of propylene vaporized; 20% of hexane vaporized; 320C temperature. Duration: It is estimated that the above rate can be maintained for 5-6 min after which it would gradually decrease to zero in another 4-5 min. Location: The postulated release would occur at an elevation of about 6 m above ground level (a.g.l.) and in a horizontal direction. The flashing liquid jet is likely to impact on surrounding equipment.

Figure 1. Layout of the solvent phase polypropylene plant with the leak location.

Ignition sources No obvious "hard" ignition sources, such as fired heaters, are present in the area shown. It may be assumed that ignition is possible anywhere within the flammable area. Ambient conditions Wind very light (1/2 m/sec) toward north but variable (±30° of due north). Temperature: 2O0C. Relative humidity: 50%. Pressure: 1.0 bar abs. Stability: class D. Site information Figure 1 shows only facilities in the near vicinity of the release. There are a number of other facilities in the expanded area including propylene storage and unloading, solvent storage, laboratories, utilities, administration building, product finishing and shipping facilities, cooling towers, etc. Process lines Each of the three process lines is supported within a structural steel framework that is 20 m tall. Each line contains a number of vessels (reactors, flash drums, separa-

tors, hold tanks, etc.), heat transfer equipment, powder dryers, powder handling equipment, and associated pumps, piping, etc. Compressor building Most of the equipment in this steel-framed building is located at a floor level about 2 m above ground. Above this level the building is covered with light weight walls to its maximum height of 8 m above ground. Below the 2 m level the sides of the building are open. Powder blending and storage area This area consists of a number of powder and pellet storage silos along with hoppers, blenders, product conveying equipment, etc. Other buildings The motor control center (MCC) and Substation have concrete block load bearing walls of ordinary construction. The control house is of blast resistant construction with reinforced concrete walls and roof designed for 0.2 bar static. All three buildings are 4 m tall.

3. COMPUTATION METHOD The EXSIM code incorporates the method proposed by Hjertager (1982b, 1989) whereby the coupling between gas flow, turbulence, and combustion are modeled based on state-of-the-art methods. The characteristics of the EXSIM code are: • 3D Cartesian coordinates • The PDR (Porosity/Distributed Resistance) method for describing the geometry (Patankar and Spalding) • The k-e turbulence model (Launder and Spalding) • The "eddy-dissipation" model for turbulent combustion (Hjertager 1982b); Bakke and Hjertager 1986a; Magnussen and Hjertager 1976), including: —one-step reaction —laminar phase combustion for low local Reynolds numbers —ignition/extinction criteria • The SIMPLE solution method, including compressibility (Hjertager 1982a) • Upwind-type discretization in space, implicit in time The papers that have been done over the past few years by Hjertager (1989, 1991) and Hjertager et al. (1991a,b) give a review of the validation of the method as well as recent applications to offshore modules.

4. BASIS FOR SCENARIOS 4.1. Geometry Modeling In order to specify the process plant geometry and to prepare an input file for the EXSIM code, we use the CAD system named AutoCAD with a specially written interface program. Figure 1, prepared by this method, gives the details of the geometry we use for the modeling study. The plant is represented by approximately 70 obstructions. The calculation domain as shown in Figure 1 is 140 x 105 x 30 m in the Jt-, y-, and z-directions. The grid resolution used was 37 x 28 X 17 grid points equally spaced along the three directions.

4.2. Case Assumptions Fuel-air clouds Analysis had shown that the fuel behaved like ethylene-air mixture and the cloud could be so large that it could fill the whole calculation domain up to about 20 m high. The ethylene-air gas cloud was assumed to be a homogeneous stoichiometric mixture with the shape of a box. The following two cloud assumptions were chosen: 1. Small: 55 x 105 x 20 m: placed on the ground along the process line area. 2. Large: 140 x 105 x 20 m: covering the whole of the process plant up to 20m. Ignition positions Figure 2 shows the three ignition positions that were chosen: 1. IGNl: outside the process line area 2. IGN2: inside the process line area 3. IGN3: under the compressor building Summary of cases Table 1 gives a summary of the conditions for the cases that were run

TABLE F-1.

Cloud size Ignition position

Case 1

Case 2

Case 3

Case 4

Small IGN1

Large IGN1

Large IGN2

Large IGN3

Figure 2. Plot plan of process plant showing the three ignition positions and the eight pressure monitoring points.

5. RESULTS AND DISCUSSION 5.1. General The output from each case produces a wealth of information, including distribution of pressure, combustion products, rates of combustion, velocity components, etc. The results of each case will be summarized by presenting the pressure time histories at the eight locations that were presented in Figure 2 together with the flame speed along some selected directions. Some contour plots will also be presented. 5.2. Case 1 This case has the small cloud, and ignition is outside the process line area. The eight pressure-time histories are shown in Figures 3 and 4, whereas the flame speed along the y-direction from the ignition point is shown in Figure 5. The largest pressure is found at location p8 in Figure 4, and it amounts to approx. 0.2

Pressure

(bar)

CASE1

Figure 3. Pressure-time histories at four locations (p1-p4) in the process plant. Case 1.

Pressure

(bar)

CASE1

Figure 4. Pressure-time histories at four locations (p5-p8) in the process plant. Case 1.

Flame speed, (m/s)

CASE1

Flame position, (m), y—direction

Figure 5. Flame speed versus distance along the y-direction through the ignition location. Casel.

bar. The pressure at the control house location (pi) is approx. 0.15 bar. The flame speed in Figure 5 accelerates to about 200 m/s. In this figure the flame accelerates through the process lines and decelerates between the lines.

5.3. Case 2 This case has the same ignition position as Case 1, that is, outside the process line area. The cloud is a large one covering the whole calculation domain up to 20 m above ground level. The eight pressure-time histories are shown in Figures 6 and 7, whereas the flame speed along the ^-direction from the ignition point is shown in Figure 8. The largest pressure is now found at location p7 in Figure 7, and it amounts to approximately 0.15 bar, which is about the same as for Case 1. The flame speed in Figure 8 accelerates to a speed of about 200 m/s. In this figure the flame accelerates through the process lines and decelerates between the lines. This flame speed contour is very similar to Case 1.

Pressure

(bar)

CAS E2

Figure 6. Pressure time histories at four locations (p1 -p4) in the process plant. Case 2.

Pressure

(bar)

CASE2

Figure 7. Pressure time histories at four locations (p5-p8) in the process plant. Case 2.

Flame speed, (m/s)

CASE2

Flame position, (m), y-direction

Figure 8. Flame speed versus distance along the y-direction through the ignition location. Case 2.

5.4. Case 3 This case uses the large cloud, as in Case 2, but the ignition point is moved to the center of the process line area (IGN2). The pressure-time histories for this case are shown in Figures 9 and 10, whereas the flame speed along the y-direction from the ignition point is shown in Figure 11, and along the ^-direction is shown in Figure 12. The largest pressure is now found at location p4 in Figure 9; it amounts to approx. 4.0 bar. The pressure at the control house location (pi) is approx. 1.2 bar, which is much larger than for Case 1 and Case 2. The flame speed in Figure 11 accelerates to a speed of about 300 m/s in both directions away from the ignition point. The maximum flame speed in the jc-direction shown in Figure 12 is between 600 and 650 m/s. The change of ignition position from the edge (Case 2) to the center has significantly increased the peak pressures and flame speeds. Figure 13 shows contour maps at an instant in time when 75% of the fuel is left in the calculation domain. Each contour plot shows contour values for the following percentages of the maximum in the plane in question: 0.95, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05. In the plots the highest value is denoted

Pressure

(bar)

CASE3

Figure 9. Pressure-time histories at four locations (p1 -p4) in the process plant. Case 3.

Pressure

(bar)

CASE3

Figure 10. Pressure-time histories at four locations (p5-p8) in the process plant. Case 3.

Flame speed, (m/s)

CASE3

Figure 11. Flame speed versus distance along the y-direction through the ignition location. Case 3.

Flame speed, (m/s)

CASE3

Figure 12. Flame speed versus distance along the x-direction through the ignition location. Case 3.

XY-PLANES

Z = 1.00 M

K= 2

POROSITY

UV-PLOT

FUEL 0.000 KGFU/KG

MRX -

0.063 KGFU/KG

MIN-

0.000 KG/M3/S

MRX -

17.908 KG/M3/S

MIN-

VMFIX - 540.9 M/S

-0.056 BRR

MRX -

2.403

MRX-

0.281

PRODUCTS

COMB.SRRTE MIN-

126

PRESSURE

X-RXIS

MIN-

TIME CYCLE NO. -

0.75

VEL.VECTORS

TIME = 1521.72 MSEC

FUEL FRACTION LEFT -

0.000 KGPR/KG

Figure 13. Velocity vectors and contour maps. Case 3.

by thick curves, whereas the lowest values are denoted by dotted curves. The values to be displayed have been chosen to be (1) geometry in the plane; (2) velocity vectors; (3) mass fraction of fuel; (4) overpressure; (5) rate of combustion of fuel; and (6) mass fraction of combustion products. The figure shows that the flame has left the calculation domain in the j-direction and is about to leave the domain in the jc-direction. The highest pressure in this situation is about 2.4 bar and is located close to the compressor building.

5.5. Case 4 This case uses the large cloud, as in Cases 2 and 3, but the ignition point is moved to the center of the space under the compressor building (IGN3). The pressure-time histories for this case are shown in Figures 14 and 15, whereas the flame speed along the ^-direction from the ignition point is shown in Figure 16. The largest pressures are now found at location p2 in Figure 14 and location p5 in Figure 15; they amount to approximately 9.0 bar. The pressure at the control house location (pi) is approximately 3.0 bar, which is much larger than for the previous cases. The flame speed in Figure 16 accelerates to about 1200 m/s. The change of ignition position to a confined space has significantly increased the peak pressures and flame speeds. Figure 17 shows contour maps at an instant in time when 74% of the fuel is left in the calculation domain. The peak pressure in this particular situation is about 9.5 bar. Figure 18 shows contour maps in the jcz-planes through the ignition point. The figure shows that the leading flamefront is close to the ground. The situation for Case 4 is very much like the experimental data collected in several British Gas experiments (Harris and Wickam). These experiments demonstrated the large effect of a confined explosion on the subsequent unconfined explosion.

Pressure

(bar)

CASE4

Time (msec)

Figure 14. Pressure-time histories at four locations (p1 -p4) in the process plant. Case 4.

Pressure (bar)

CASE4

Figure 15. Pressure-time histories at four locations (p5-p8) in the process plant. Case 4.

Flame speed, (m/s)

CASE4

Flame position, (m). x-direction

Figure 16. Flame speed versus distance along the x-direction through the ignition location. Case 4.

XY=PLANES

Z =

1.00 M

TIME CYCLE NO. -

POROSITY

UV-PLOT

128

VMflX - 730.8 M/S

PRESSURE

FUEL

0.000 KGFU/KG

MRX -

0.063

MIN -

0.000 KG/M3/S

MRX -

164.115

MIN -

-0.071 BRR

MRX -

9.487

MRX -

0.281

PRODUCTS

COMB.SRRTE

MIN -

FUEL FRACTION LEFT = 0.74

1119.26 MSEC

X-RXIS

MIN -

2

VEL.VECTORS

TIME -

K-

0.000 KGPR/KG

Figure 17. Velocity vectors and contour maps. Case 4.

XZ=PLANES

Y = 50.50 M

POROSITY FUEL

UW-PLOT

128

VMRX - 578.8 M/S

MRX -

0.063 KGFU/KG

MIN-

-0.061 BRR

MRX -

9.466

PRODUCTS

0.000 KGFU/KG

COMB.SRRTE

TIME CYCLE NO. -

0.74

PRESSURE

X-RXIS

MIN-

1119.26 MSEC

VEL.VECTORS

TIME -

J - 14 FUEL FRACTION LEFT -

Figure 18. Velocity vectors and contour maps. Case 4.

6. SUMMARY AND CONCLUDING REMARKS The preceding case studies have shown that gas explosion calculations inside realistic process plant layouts are possible, using the state-of-the-art 3D computer model, named EXSIM. The peak pressures found in the four chosen calculation cases are summarized in the following table:

TABLE F-2. Cloud Size Ignition Outside process line area Inside process line area Under compressor building

Small

Large

0.2 bar — —

0.3 bar 4.0 bar 9.0 bar

Although the status of many 3D codes makes it possible to carry out detailed scenario calculations, further work is needed. This is particularly so for: 1) development and verification of the porosity/distributed resistance model for explosion propagation in high density obstacle fields; 2) improvement of the turbulent combustion model, and 3) development of a model for deflagration to detonation transition. More data are needed to enable verification of the model in high density geometries. This is particularly needed for onshore process plant geometries.

Acknowledgments The work on gas explosions at SiT-Tel-Tek is financially supported by Shell Research Ltd. The authors are grateful to Dr. R. A. Mancini, Amoco Corporation, for making this paper possible.

REFERENCES Bakke, J. R., and B. H. Hjertager. 1986a. Quasi-laminar/turbulent combustion modeling, real cloud generation and boundary conditions in the FLACS-ICE code. CMI No. 865402-2. Chr. Michelsen Institute, 1986. Also in Bakke's Ph.D. thesis "Numerical simulation of gas explosions in two-dimensional geometries." University of Bergen, Bergen, 1986. Bakke, J. R., and B. H. Hjertager. 1986b. The effect of explosion venting in obstructed channels. In Modeling and Simulation in Engineering. New York: Elsevier, pp. 237241. Bakke, J. R., and B. H. Hjertager. 1987. The effect of explosion venting in empty volumes. Int. J. Num. Meth. Eng. 24:129-140. Boris, J. P., and D. L. Book. 1973. Flux-corrected transport I: SHASTA-A fluid transport method that works. J. Comp. Phys. 11:38. CCPS/AIChE. 1991. International conference and workshop on modeling and mitigating the consequences of accidental releases of hazardous material. New York: CCPS/AIChE. Harris, R. J., and M. J. Wickens. 1989. Understanding vapor cloud explosions—An experimental study. Inst. Gas Engineers 55th Autumn Meeting, Communication 1408. Hjertager, B. H. 1982a. Simulation of transient compressible turbulent reactive flows. Comb. Sd. Tech. 41:159-170.

Hjertager, B. H. 1982b. Numerical simulation of flame and pressure development in gas explosions. SM study No. 16. Ontario, Canada: University of Waterloo Press. 407-426. Hjertager, B. H. 1989. Simulation of gas explosions. Modeling Ident Contr. 10:227-247. Hjertager, B. H. 1991. Explosions in offshore modules. IChemE Symposium Series No. 124, pp. 19-35. Also in Process Safety and Environmental Protection, Vol. 69, Part B, May 1991. Hjertager, B. H., T. Solberg, and K. O. Nymoen. 199 Ia. Computer modeling of gas explosion propagation in offshore modules. Hjertager, B. H., T. Solberg, and J. E. F0rrisdahl. 199 Ib. Computer simulation of the 'Piper Alpha' gas explosion accident." Kjaldman, L., and R. Huhtanen. 1986. Numerical simulation of vapour cloud and dust explosions. Numerical Simulation of Fluid Flow and Heat/Mass Transfer Processes. Vol. 18, Lecture Notes in Engineering, 148-158. Launder, B. D., and D. B. Spalding. 1974. The numerical computation of turbulent flows. Comput. Meth. Appl. Mech. Eng. 3:269-289. Magnussen, B. F., and B. H. Hjertager. 1976. On the mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. 16th Symp. (Int) on Combustion. Combustion Institute, PA, pp. 719-729. Mancini, R. A. 1991. Private communication. Martin, D. 1986. Some calculations using the two-dimensional turbulent combustion code Flare. SRD Report R373. UK Atomic Energy Authority. Marx, K. D., J. H. S. Lee, and J. C. Cummings. 1985. Modeling of flame acceleration in tubes with obstacles. Proc. of llth IMACS World Congress on Simulation and Scientific Computation. 5:13-16. Patankar, S. V, and D. B. Spalding. 1972. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat and Mass Transfer. 15:1787-1806. Patankar, S. V., and D. B. Spalding. 1974. A calculation procedure for the transient and steady-state behavior of shell-and-tube heat exchangers. In N. H. Afgan and E. V. Schliinder (eds.), Heat Exchangers: Design and Theory Sourcebook. New York: McGraw-Hill, pp. 155-176. Sha, W. T., C. I. Yang, T. T. Kao, and S. M. Cho. 1982. Multi-dimensional numerical modeling of heat exchangers. J. Heat Trans. 104:417-425. Spalding, D. B. 1981. A general purpose computer program for multi-dimensional one- and two-phase flow. Mathematics and Computers in Simulation, IMACS, XXII. 267-276. Van Den Berg, A. C. 1989. REAGAS—a code for numerical simulation of 2-D reactive gas dynamics in gas explosions. PML-TNO Report PML 1989-IN48.

Index Index terms

Links

A Acetone, explosion properties of

48

Acetylene detonation cell size

55

explosion properties of

48

properties of Acoustic methods, vapor cloud explosion computations

359 93

Air, properties of

359

Ammonia, properties of

359

Argon, properties of

359

Atmospheric vapor cloud dispersion, described

47

B Baker-Strehlow method, vapor cloud explosion research

122

Benzene, properties of

359

Blast

56

blast loading

56

blast scaling

58

human damage of

351

blast wave and

356

in building collapse

355

ear damage

354

lung injury

352

overview

351

skull fracture

355

manifestation

This page has been reformatted by Knovel to provide easier navigation.

56

383

384

Index terms

Links

Blast (Continued) structural damage of Blast case study (process plant)

347 363

computation method

367

overview of

363

results

369

scenario basis

368

scenario described

365

Blast modeling, vapor cloud explosion experimental research

111

See also Vapor cloud explosion experimental research: blast modeling Blast wave, blast loading

56

Boiling-liquid-expanding-vapor explosion (BLEVE) described and defined historical experience mechanism of

6 157 27 158

Boiling-liquid-expanding-vapor explosion (BLEVE) experimental research blast effects and pressure-vessel bursts

161 185

blast characteristics

199

blast effects, calculation methods

202

theory and experiment

185

fragments

223

initial velocity (ideal gases)

224

initial velocity (nonideal gases)

230

models compared

231

overview of

223

ranges for fragments (free-flying)

233

ranges for fragments (rocketing)

235

statistical analysis

237

radiation

161

case studies

183

fireball diameter and duration

171

This page has been reformatted by Knovel to provide easier navigation.

385

Index terms

Links

Boiling-liquid-expanding-vapor explosion (BLEVE) experimental research (Continued) fireball fuel content

176

fireball liftoff time

176

fireball radiation

177

hazard distances

180

large-scale experiments

165

overview of

161

small-scale experiments Boiling-liquid-expanding-vapor explosion (BLEVE) sample problems blast parameter calculations and pressure vessel bursts

16 285 292

case study

308

cylindrical vessel

292

explosively flashing liquid

298

tank truck

305

fragments

311

analytical analysis

313

case studies

321

overview of

311

statistical analysis

320

statistical and theoretical applications

311

radiation

285

fireball, fuel contribution to

285

fireball size and duration

286

hazard calculation procedure

288

hazard distances

288

problems

289

radiation calculation

286

Building collapse, human damage of

355

1,3-Butadiene, chemical and physical characteristics

160

N-Butane chemical and physical characteristics This page has been reformatted by Knovel to provide easier navigation.

160

386

Index terms

Links

N-Butane (Continued) detonation cell size properties of

55 359

C Carbon dioxide, properties of

359

Carbon monoxide, properties of

359

Channels, vapor cloud explosion research

84

Chapman-Jouguet (CJ) model, detonation

52

Chlorine, properties of Combustion models

359 50

deflagration

50

detonation

52

Computational research (vapor cloud explosions)

92

analytical methods

92

numerical methods

104

overview of

92

See also Vapor cloud explosion experimental research Conversion factor table

361

Cyclohexane, explosion properties of

48

Cylindrical geometry, vapor cloud explosion experimental research

80

D Deflagration combustion models described ignition and

50 4 55

Deflagration to detonation transition (DDT), vapor cloud explosion research

88

Detonation combustion models

This page has been reformatted by Knovel to provide easier navigation.

52

53

387

Index terms

Links

Detonation (Continued) ignition and

55

vapor cloud explosion experimental research

88

Diethyl ether, explosion properties of

48

Distributed-volume source model, vapor cloud explosions, computational research Drag force, blast loading

96 58

E Ear damage

354

Emissive power, thermal radiation, solid-flame model

61

Emissivity, thermal radiation, solid-flame model

62

Ethane chemical and physical characteristics explosion properties of properties of Ethanol, explosion properties of Ethyl chloride, properties of

160 48 359 48 359

Ethylene detonation cell size

55

explosion properties of

48

properties of Ethylene oxide, detonation cell size Eulerian flux-corrected transport (FCT) approach, vapor cloud explosions

359 55 105

"Exact" solution, vapor cloud explosions

98

Expanding-piston solution, vapor cloud explosions

93

Exploding jets, experimental research

134

Explosion. See Blast Explosively dispersed vapor cloud explosions, experimental research

This page has been reformatted by Knovel to provide easier navigation.

134

388

Index terms

Links

F Fireball diameter and duration of, BLEVE experimental research

171

fuel content of, BLEVE experimental research

176

liftoff time of, BLEVE experimental research

176

radiation of, BLEVE experimental research

177

view factors for

337

Flame acceleration, vapor cloud explosions

69

See also Vapor cloud explosion experimental research Flammable gases, explosion properties of

48

Flash fire(s) described and defined historical experience Flash fire research

5 147 23 147

overview of

147

radiation models

152

Flash fire sample problems

277

calculation

281

method

277

dynamics

277

heat radiation

278

Fragments, boiling-liquid-expanding-vapor explosion (BLEVE) experimental research

223

See also Boiling-liquid-expanding-vapor explosion (BLEVE) experimental research: fragments; Boiling-liquid-expanding-vapor explosion (BLEVE) sample problems: fragments Free-flying fragments BLEVE experimental research

233

BLEVE sample problems

319

Fuel-air charge blast-based models Fuel-air clouds, after dispersion

This page has been reformatted by Knovel to provide easier navigation.

122 75

389

Index terms

Links

G Gas dynamics, vapor cloud explosions

104

Gas properties, tabulation of

359

Geometry modeling, blast case study using

363

H Hazard distances, BLEVE experimental research

180

Heat radiation, flash fire sample problems

278

Helium, properties of

359

N-Hexane chemical and physical characteristics

160

properties of

359

Hexane, explosion properties of

48

Historical experience

8

BLEVE

27

flash fires

23

generally

8

vapor cloud explosions Hopkins scaling law, blast scaling

10 59

Hydrogen explosion properties of properties of

48 359

Hydrogen sulfide, properties of

359

Hymes point-source model, fireball radiation

178

I Ignition, described

55

Isobutane, chemical and physical characteristics

160

Iso-butylene, properties of

359

Isothermal models, fireball diameter and duration

173

This page has been reformatted by Knovel to provide easier navigation.

390

Index terms

Links

L Lagrangean artificial-viscosity approach, vapor cloud explosions

104

Lung injury, blast damage

351

M Methane detonation cell size

55

explosion properties of

48

properties of Multienergy method, vapor cloud explosions

359 127 250 259 268

N National Transportation Safety Board (NTSB)

24

25

29

30

Natural gas, properties of

359

Nitrogen, properties of

359

O Oxygen, properties of

359

P N-pentane, chemical and physical characteristics

160

Pentylene, properties of

359

Piston-blast model, vapor cloud explosions

126

Point-source model BLEVE sample problems thermal radiation Pressure-vessel bursts, BLEVE experimental research

290 291 60 185

Propane chemical and physical characteristics

This page has been reformatted by Knovel to provide easier navigation.

160

391

Index terms

Links

Propane (Continued) detonation cell size

55

explosion properties of

48

properties of

359

Propylene detonation cell size

55

explosion properties of

48

R Radiation, boiling-liquid-expanding-vapor explosion (BLEVE) experimental research

161

See also Boiling-liquid-expanding-vapor explosion (BLEVE) experimental research: radiation Radiation models, flash fire research

152

Roberts' model, fireball diameter and duration, BLEVE experimental research

175

Rocketing fragments BLEVE experimental research

235

BLEVE sample problems

315

S Self-sustaining detonation, vapor cloud explosion experimental research

89

Similarity methods, vapor cloud explosions

97

Skull fracture, blast damage

355

Solid-flame model fireball radiation, BLEVE thermal radiation

178 291 61

Source-term generated turbulence, vapor cloud explosion experimental research Structural damage, of blasts Subsequent pressure generation (CFD-codes), vapor cloud explosions

This page has been reformatted by Knovel to provide easier navigation.

76 347 69

392

Index terms

Links

T Thermal radiation

59

generally

59

point-source model

60

solid-flame model

61

Three-dimensional computer code, blast case study using

363

TNT blast-based models BLEVE blasts vapor cloud explosions

201 112 247 258 266

Toluene, explosion properties of

48

Transmissivity, thermal radiation, solid-flame model

63

Tubes, vapor cloud explosion experimental research

82

Turbulence, vapor cloud explosions Two-dimensional models, vapor cloud explosions

4 108

V Vapor(s), explosion properties of

48

Vapor cloud explosion(s) atmospheric vapor cloud dispersion

47

described and defined

3

historical experience

10

ignition

55

overview of

69

Vapor cloud explosion experimental research blast modeling

69 111

fuel-air charge blast-based models

122

overview of

111

special methods

133

TNT blast-based models

112

computational research

92

analytical methods

92

This page has been reformatted by Knovel to provide easier navigation.

69

70

393

Index terms

Links

Vapor cloud explosion experimental research (Continued) numerical methods overview of detonation

104 92 88

deflagration to detonation transition (DDT)

88

initiation

88

self-sustaining detonation, condition required for

89

generally

70

partially confined deflagration

79

channels

84

cylindrical geometry

80

tubes

82

special experiments

86

unconfined deflagration under controlled conditions

71

unconfined deflagration under uncontrolled conditions

75

fuel-air clouds after dispersion

75

source-term generated turbulence

76

Vapor cloud explosion sample problems

247

calculations

256

chemical plant pipe rupture

263

storage site hazard assessment

256

methods multienergy method

250

selection of

247

TNT-equivalency methods

249

overview of

247

View factors

337

fireball (spherical emitter) thermal radiation, solid-flame model vertical cylinder vertical plane surface

337 64 338 341 340 342 343

This page has been reformatted by Knovel to provide easier navigation.

394

Index terms Vinyl chloride, chemical and physical characteristics Volume-source solution, vapor cloud explosions

Links 160 94

W Water, chemical and physical characteristics

160

Water vapor, properties of

359

X Xylene, explosion properties of

48

Z Zel'dovich-Von Neumann-Döhring (ZND) model

52 54

This page has been reformatted by Knovel to provide easier navigation.

53