[Center for chemical_process_safety_(ccps)]_guidel(bookos.org)_2

Guidelines for Evaluatingthe Characteristics of

Vapor Cloud Explosions,Flash Fires, and BLEVEs

CENTER FOR CHEMICAL PROCESS SAFETYof the

American Institute of Chemical Engineers345 East 47 Street, New York, NY 10017

Copyright © 1994American Institute of Chemical Engineers345 East 47th StreetNew 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 otherwisewithout the prior permission of the copyright owner.

Library of Congress Cataloging-in-Publication DataGuidelines for evaluating the characteristics of vapor cloud

explosions, flash fires, and BLEVEs.p. cm.

Includes bibliographical references and index.ISBN 0-8169-0474-X1. Explosions. 2. Fires. I. American Institute of Chemical

Engineers. Center for Chemical Process Safety.QD516.G78 1994660'.2804—dc20 92-38795

CIP

This book is available at a special discount when orderedin bulk quantities. For information, contact theCenter for Chemical Process Safety of theAmerican Institute of Chemical Engineers at theaddress shown above.

It is sincerely hoped that the information presented in this book will lead to an even more impressivesafety record for the entire industry; however, the American Institute of Chemical Engineers, its consult-ants, CCPS subcommittee members, their employers, their employers' officers and directors, and TNOPrins Maurits disclaim making or giving any warranties or representations, express or implied, includingwith respect to fitness, intended purpose, use or merchantability and/or correctness or accuracy of thecontent of the information presented in this document. As between (1) the American Institute of ChemicalEngineers, its consultants, CCPS subcommittee members, their employers, their employers' officersand directors, and TNO Prins Maurits and (2) the user of this document, the user accepts any legalliability or responsibility whatsoever for the consequence of its use or misuse.

ACKNOWLEDGMENTS

The Center for Chemical Process Safety of the American Institute of ChemicalEngineers owes a great deal of thanks to the dedicated and professional engineersand scientists who served with distinction on the Vapor Cloud Explosion subcommit-tee during the development of this Guidelines book. They are:

John A. Davenport (Industrial Risk Insurers), chairJohn 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 wasentrusted to TNO Prins Maurits Laboratory, Rijswijk, the Netherlands. The principalauthors were all members of the Explosion Prevention Department of the Laboratory:

Kees van WingerdenBert van den BergDaan van LeeuwenPaul MercxRolf van Wees

Their technical expertise is evident in both the characterization of the phenomenathat this book explores (Chapters 2-6) and the practical examples that illustratethese phenomena (Chapters 7-9).

The authors and the subcommittee were well served during this transnationaleffort 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. KelloggT. O. Gibson, Dow ChemicalD. L. Macklin, Phillips PetroleumS. J. Schechter, Rohm and Haas

Finally, CCPS is grateful to Dr. B. H. Hjertager, Telemark Institute of Technol-ogy and Telemark Innovation Centre, Porsgrunn, Norway, for preparing "A CaseStudy of Gas Explosions in a Process Plant Using a Three-dimensional ComputerCode" (Appendix F).

A NOTE ON NOMENCLATUREAND UNITS

The equations in this volume are from a number of reference sources, not allof which use consistent nomenclature (symbols) and units. In order to facilitatecomparisons within sources, the conventions of each source were presentedunchanged.Nomenclature and units are given after each equation (or set of equations) in thetext. Readers should ensure that they use the proper values when applying theseequations to their problems.

GLOSSARY

Blast: A transient change in the gas density, pressure, and velocity of the airsurrounding an explosion point. The initial change can be either discontinuousor gradual. A discontinuous change is referred to as a shock wave, and agradual change is known as a pressure wave.

BLEVE (Boiling Liquid, Expanding Vapor Explosion): The explosively rapidvaporization and corresponding release of energy of a liquid, flammable orotherwise, upon its sudden release from containment under greater-than-atmo-spheric pressure at a temperature above its atmospheric boiling point. A BLEVEis often accompanied by a fireball if the suddenly depressurized liquid is flam-mable and its release results from vessel failure caused by an external fire. Theenergy released during flashing vaporization may contribute to a shock wave.

Burning velocity: The velocity of propagation of a flame burning through a flam-mable gas-air mixture. This velocity is measured relative to the unburnedgases immediately ahead of the flame front. Laminar burning velocity is afundamental property of a gas-air mixture.

Deflagration: A propagating chemical reaction of a substance in which the reactionfront advances into the unreacted substance rapidly but at less than sonic velocityin the unreacted material.

Detonation: A propagating chemical reaction of a substance in which the reactionfront advances into the unreacted substance at or greater than sonic velocity inthe unreacted material.

Emissivity: The ratio of radiant energy emitted by a surface to that emitted by ablack body of the same temperature.

Emissive power: The total radiative power discharged from the surface of a fireper 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 formof radiant heat. The inner core of the cloud consists almost completely of fuel,whereas the outer layer (where ignition first occurs) consists of a flammablefuel-air mixture. As the buoyancy forces of hot gases increase, the burningcloud tends to rise, expand, and assume a spherical shape.

Flame speed: The speed of a flame burning through a flammable mixture of gasand air measured relative to a fixed observer, that is, the sum of the burningand translational velocities of the unburned gases.

Flammable limits: The minimum and maximum concentrations of combustiblematerial in a homogeneous mixture with a gaseous oxidizer that will propagatea flame.

Flash vaporization: The instantaneous vaporization of some or all a liquid whosetemperature is above its atmospheric boiling point when its pressure is suddenlyreduced to atmospheric.

Flash fire: The combustion of a flammable gas or vapor and air mixture in whichthe flame propagates through that mixture in a manner such that negligible orno damaging overpressure is generated.

Impulse: A measure that can be used to define the ability of a blast wave to dodamage. 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, themomentum of which induces the surrounding atmosphere to mix with thedischarged material.

Lean mixture: A mixture of flammable gas or vapor and air in which the fuelconcentration 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 fuelconcentration 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 blastwave passes by it.

Stoichiometric ratio: The precise ratio of air (or oxygen) and flammable materialwhich would allow all oxygen present to combine with all flammable materialpresent to produce fully oxidized products.

Superheat limit temperature: The temperature of a liquid above which flash vapor-ization can proceed explosively.

Surface-emissive power: See Emissive power.

Transmissivity: The fraction of radiant energy transmitted from a radiating objectthrough the atmosphere to a target after reduction by atmospheric absorptionand scattering.

TNT equivalence: The amount of TNT (trinitrotoluene) that would produce ob-served damage effects similar to those of the explosion under consideration. Fornon-dense phase explosions, the equivalence has meaning only at a considerabledistance from the explosion source, where the nature of the blast wave arisingis 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 offlammable vapor, gas, or mist in which flame speeds accelerate to sufficientlyhigh velocities to produce significant overpressure.

View factor: The ratio of the incident radiation received by a surface to the emissivepower from the emitting surface per unit area.

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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

vi Contents

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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 ........................................................................... 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

1INTRODUCTION

The American Institute of Chemical Engineers (AIChE) has been involved withprocess safety and loss control for chemical and petrochemical plants for more thanthirty years. Through its strong ties with process designers, builders, operators,safety professionals, and academia, AIChE has enhanced communication and fos-tered improvements in the safety standards of the industry. Its publications andsymposia on causes of accidents and methods of prevention have become informationresources 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 firstCCPS project was the publication of a document entitled Guidelines for HazardEvaluation Procedures. In 1987 Guidelines for Use of Vapor Cloud DispersionModels was published and in 1989 Guidelines for Chemical Process QuantitativeRisk Analysis and Guidelines for Technical Management of Chemical Process Safetywere published. The present book has evolved from the eighth CCPS project.

This text is intended to provide an overview of methods for estimating thecharacteristics of vapor cloud explosions, flash fires, and boiling-liquid-expanding-vapor explosions (BLEVEs) for practicing engineers. The volume summarizes andevaluates 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 thephenomena covered and presents methods for calculating the possible consequencesof incidents. It also offers an overview and resource reference for experts. It shouldprovide managers with a basic understanding of the phenomena, methods of calcula-tion to estimate consequences, and the limitations of each method. The authors alsohope 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. Chapters1 through 6 offer detailed background information. They describe pertinent phenom-ena, give an overview of past experimental and theoretical research, and providemethods for estimating consequences. Chapter 2 describes the phenomena covered,identifies various accident scenarios leading to each of the events, and describesactual accidents. In Chapter 3, principles such as dispersion, deflagration, detona-tion, 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 givebackground 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 forvapor cloud explosions, BLEVEs, and flash fires, respectively, by presenting sampleproblems. These problems contain sufficient detail to allow an engineer to use themethods presented to evaluate specific hazards.

The authors have not attempted to describe all experimental and theoreticalresearch in the field. Rather, the most important activities and their results arecovered in order to offer an adequate understanding of the basic physical principles.

This volume does not address subjects such as toxic effects, explosions inbuildings and vessels, runaway reactions, condensed-phase explosions, pool fires,jet flames, or structural responses of buildings. Furthermore, no attempt is madeto cover the frequency or likelihood that a related accident scenario will occur.References to other works are provided for readers interested in these phenomena.

2PHENOMENA:

DESCRIPTIONS, EFFECTS, ANDACCIDENT SCENARIOS

Accidents involving fire have occurred ever since man began to use flammableliquids 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 andreliability engineering which meet or exceed established codes of practice. Thesecodes include well-designed pressure relief and blowdown systems, adequate main-tenance and inspection programs, management of human factors in system designand, perhaps most important, a full understanding and support by responsible man-agers of risk management efforts. Nevertheless, despite all of these precautions,accidents may still occur, sometimes resulting in death, serious injury, damage tofacilities, loss of production, and damage to reputation in the community.

Mathematical models for calculating the consequences of such events shouldbe employed in order to support efforts toward mitigation of their consequences.Mitigating measures may include reduction of storage capacity; reduction of vesselvolumes; 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, andBLEVEs has grown enormously in recent years as a result of many internationalefforts. Insights gained regarding the processes of generation of overpressure, radia-tion, and fragmentation have resulted in the development of reasonably descriptivemodels 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. Effectsdescribed are supported by several case histories. Chapter 3 will present details ofdispersion, 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 gasfrom a storage tank, process or transport vessel, or pipeline. Generally speaking,several features need to be present for a vapor cloud explosion with damagingoverpressure to occur.

First, the released material must be flammable and at suitable conditions ofpressure 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, butsignificant blast-pressure damage is unlikely. Should the cloud be allowed to formover a period of time within a process area, then subsequently ignite, blast pressuresthat develop can result in extensive, widespread damage. Ignition delays of 1 to 5minutes are considered the most probable for generating vapor cloud explosions,although major incidents with ignition delays as low as a few seconds and greaterthan 30 minutes are documented.

Third, a sufficient amount of the cloud must be within the flammable range ofthe material to cause extensive overpressure. A vapor cloud will generally havethree regions: a rich region near the point of release, a lean region at the edge ofthe cloud, and a region in between that is within the flammable range. The portionof the vapor cloud in each region depends on many factors, including type andamount of the material released; pressure at time of release; size of release opening;degree of confinement of the cloud; and wind, humidity, and other environmentaleffects (Hanna and Drivas 1987).

Fourth, the blast effects produced by vapor cloud explosions can vary greatlyand are determined by the speed of flame propagation. In most cases, the mode offlame propagation is deflagration. Under extraordinary conditions, a detonationmight occur.

A deflagration can best be described as a combustion mode in which thepropagation rate is dominated by both molecular and turbulent transport processes.In the absence of turbulence (i.e., under laminar or near-laminar conditions), flamespeeds for normal hydrocarbons are in the order of 5 to 30 meters per second. Suchspeeds are too low to produce any significant blast overpressure. Thus, under near-laminar-flow conditions, the vapor cloud will merely burn, and the event wouldsimply be described as a large flash fire. Therefore, turbulence is always present invapor cloud explosions. Research tests have shown that turbulence will significantlyenhance the combustion rate in deflagrations.

Turbulence in a vapor cloud explosion accident scenario may arise in any ofthree ways:

• by turbulence associated with the release itself (e.g., jet release or a catastrophicfailure of a vessel resulting in an explosively dispersed cloud);

• by turbulence produced in unburned gases expanding ahead of a flame propagat-ing 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, witha jet release within a congested area.

These mechanisms may cause very high flame speeds and, as a result, strongblast pressures. The generation of high combustion rates is limited to the congestedarea, or the area affected by the turbulent release. As soon as the flame enters anarea without turbulence, both the combustion rate and pressure will drop.

In the extreme, the turbulence can cause a sufficiently energetic mixture toconvert from deflagration to detonation. This mode of flame propagation is attendedby propagation speeds in excess of the speed of sound (2 to 5 times the speed ofsound) and maximum overpressures of about 18 bar (260 psi). Once detonationoccurs, turbulence is no longer necessary to maintain its speed of propagation. Thismeans that uncongested and/or quiescent flammable portions of a cloud may alsocontribute to the blast. Note, however, that for a detonation to propagate, theflammable part of the cloud must be very homogeneously mixed. Because suchhomogeneity rarely occurs, vapor cloud detonations are unlikely.

Whether a deflagration or detonation occurs is also influenced by the availableenergy of ignition. Deflagration of common hydrocarbon-air mixtures requiresan ignition energy of approximately 10~4 Joules. By contrast, direct initiation ofdetonation of normal hydrocarbon-air mixtures requires an initiation energy ofapproximately 106 joules; this level of energy is comparable to that generated by ahigh-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 vaporcloud explosion, as well as the conditions leading to a flash fire or a vapor clouddetonation (Figure 2.1).

2.2. FLASH FIRES

A flash fire results from the ignition of a released flammable cloud in which thereis essentially no increase in combustion rate. In fact, the combustion rate in a flashfire does increase slightly compared to the laminar phase. This increase is mainlydue to the secondary influences of wind and surface roughness.

Figure 2.1 identifies the conditions necessary for the occurrence of a flashfire. Only combustion rate differentiates flash fires from vapor cloud explosions.Combustion rate determines whether blast effects will be present (as in vapor cloudexplosions) or not (as in flash fires).

The principal dangers of a flash fire are radiation and direct flame contact. Thesize of the flammable cloud determines the area of possible direct flame contact

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 flashfires. 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 liquidat 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 tobe flammable to cause a BLEVE. In fact, BLEVE, which is an acronym for"boiling-liquid-expanding-vapor explosion," was first applied to a steam explo-sion. Nonflammable liquid BLEVEs produce only two effects: blast due to theexpansion of the vapor in the container and flashing of the liquid, and fragmentationof the container.

BLEVEs are more commonly associated with releases of flammable liquidsfrom vessels as a consequence of external fires. Such BLEVEs produce, in additionto blast and fragmentation effects, buoyant fireballs whose radiant energy can burnexposed skin and ignite nearby combustible materials. A vessel may rupture for a

Releaseand

dispersion

No ignition

Ignition

Detonation

Deflagration

no enhancement

Deflagration

enhancementby turbulence

Detonationtransition

no transition

Deflagration

Detonationhomogenous

cloud

Local detonationnon-homogenous

cloud

Result

NONE

Vapor douddetonation

Flashfire

Vapor douddetonation

Vapor doudexplosion

Vapor doudexplosion

different reason and not result in immediate ignition of its flammable contents. Ifthe flammable contents mix with air, then ignite, a vapor cloud explosion or flashfire will result.

A BLEVE's effects will be determined by the condition of the container'scontents and of its walls at the moment of container failure. These conditions alsorelate to the cause of container failure, which may be

an external fire,mechanical impact,corrosion,excessive internal pressure, ormetallurgical failure.

The blast and fragmentation effects of a BLEVE depend directly on the internalenergy of the vessel's contents—a function of its thermodynamic properties andmass. This energy is potentially transformed into mechanical energy in the formof blast and generation of fragments.

Fluid in a container is a combination of liquid and vapor. Before containerrupture, the contained liquid is usually in equilibrium with the saturated vapor. Ifa 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 liq-uid-container-wall interface, and, depending on temperature, throughout theliquid.

Depending on liquid temperature, instantaneous boiling may occur throughoutthe bulk of the liquid. Microscopic vapor bubbles begin to form and grow. Throughthis process, a large fraction of the liquid can vaporize within milliseconds. Instanta-neous boiling will occur whenever the temperature of the liquid is higher than thehomogeneous nucleation temperature or superheat limit temperature. The liberatedenergy in such cases is very high, causing high blast pressures and generation offragments with high initial velocities, and resulting in propulsion of fragments overlong distances. If the temperature is below the superheat limit temperature, theenergy for the blast and fragment generation is released mainly from expansion ofvapor in the space above the liquid. Energy, based on unit volume, from this sourceis about one-tenth the energy liberated from a failing container of liquid above thesuperheat limit.

The pressure and temperature of a container's contents at the time of failurewill depend on the cause of failure. In fire situations, direct flame impingementwill weaken container walls. The pressure at which the container fails will usuallybe about the pressure at which the safety valve operates. This pressure may be asmuch as 20 percent above the valve's setting. The temperature of the container'scontents will usually be considerably higher than the ambient temperature.

If a vessel ruptures as a result of excessive internal pressure, its burstingpressure may be several times greater than its design pressure. However, if therupture is due to corrosion or mechanical impact, bursting pressure may be lower

than the design pressure of the vessel. Temperatures in these situations will dependon process conditions.

Internal energy prior to rupture also affects the number, shape, and trajectoryof fragments. Ruptures resulting from BLEVEs tend to produce few fragments, butthey can vary greatly in size, shape, and initial velocities. Large fragments, forexample, those consisting of half of the vessel, and disk-shaped fragments can beprojected for long distances. Rocketing propels the half-vessel shapes, whereasaerodynamic forces account for the distances achieved by disk-shaped fragments.

A BLEVE involving a container of flammable liquid will be accompanied bya fireball if the BLEVE is fire-induced. The rapid vaporization and expansionfollowing 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 ispossible. In the buoyancy stage, combustion propagates to the center of the cloudcausing a massive fireball.

Radiation effects due to the fireball depend on

• the diameter of the fireball as a function of time and the maximum diameterof the fireball;

• the height of the center of the fireball above its ignition position as a functionof 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 willdetermine the consequences of radiation.

Investigations of the effects of BLEVEs (Chapter 6) are usually limited to theaspect of thermal radiation. Blast and fragmentation have been of less interest, andhence, not studied in detail. Furthermore, most experiments in thermal radiationhave been performed on a small scale.

2.4. HISTORICAL EXPERIENCE

Selection of incidents described was based on the availability of information, thekind and amount of material involved, and severity of damage. Accidents occurringon public property generally produce better published documentation than thoseoccurring on privately owned property.

The vapor cloud explosion incidents described below cover a range of factors:

• Material properties: Histories include incidents involving hydrogen (a highlyreactive gas), propylene, dimethyl ether, propane, cyclohexane (possibly partly

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than the design pressure of the vessel. Temperatures in these situations will dependon process conditions.

Internal energy prior to rupture also affects the number, shape, and trajectoryof fragments. Ruptures resulting from BLEVEs tend to produce few fragments, butthey can vary greatly in size, shape, and initial velocities. Large fragments, forexample, those consisting of half of the vessel, and disk-shaped fragments can beprojected for long distances. Rocketing propels the half-vessel shapes, whereasaerodynamic forces account for the distances achieved by disk-shaped fragments.

A BLEVE involving a container of flammable liquid will be accompanied bya fireball if the BLEVE is fire-induced. The rapid vaporization and expansionfollowing 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 ispossible. In the buoyancy stage, combustion propagates to the center of the cloudcausing a massive fireball.

Radiation effects due to the fireball depend on

• the diameter of the fireball as a function of time and the maximum diameterof the fireball;

• the height of the center of the fireball above its ignition position as a functionof 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 willdetermine the consequences of radiation.

Investigations of the effects of BLEVEs (Chapter 6) are usually limited to theaspect of thermal radiation. Blast and fragmentation have been of less interest, andhence, not studied in detail. Furthermore, most experiments in thermal radiationhave been performed on a small scale.

2.4. HISTORICAL EXPERIENCE

Selection of incidents described was based on the availability of information, thekind and amount of material involved, and severity of damage. Accidents occurringon public property generally produce better published documentation than thoseoccurring on privately owned property.

The vapor cloud explosion incidents described below cover a range of factors:

• Material properties: Histories include incidents involving hydrogen (a highlyreactive gas), propylene, dimethyl ether, propane, cyclohexane (possibly partly

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as a mist), methane (generally classified as a low-reactivity gas), and naturalgas liquids.

• Period of time covered: Explosions occurring over the period between the years1948 and 1989 are reported.

• Quantity released: Releases ranged in quantity from 110 kg (240 Ib) to 70,000kg (150,000 Ib);

• Site characteristics: Releases occurred in settings ranging from rural to verycongested industrial areas.

• Availability of information: Very well-documented incidents (e.g., Flixbor-ough) as well as poorly documented incidents (e.g., Ufa) are described.

• Severity: Death tolls and damage from pressure effects vary widely in casespresented.

Most incidents discussed occurred several years ago, but it should be emphasizedthat 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 vaporcloud explosions, flash fires appear to have occurred as well, including those atFlixborough, Port Hudson, East St. Louis, and Ufa. The selection and descriptionsof 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 Explosionin Chemical Plant

On June 1, 1974, a cyclohexane vapor cloud was released after the rupture of apipe bypassing a reactor. In total, approximately 30,000 kg of cyclohexane wasreleased. The cyclohexane formed a cloud which ignited after a period of approxi-mately 30 to 90 seconds. As a result, a very strong explosion occurred which causedthe death of 28 people and injured 36 people. The plant was totally destroyed and1821 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) havedescribed extensively the vapor cloud explosion that occurred in the reactor sectionof the caprolactam plant of the Flixborough Works on June 1,1974. The FlixboroughWorks is situated on the east bank of the River Trent. The nearest villages areFlixborough [800 meters (one-half mile) away], Amcotts [800 meters (one-halfmile) away], and Scunthorpe [4.9 km (approximately three miles) away].

The cyclohexane oxidation plant contained a series of six reactors. The reactorswere fed by a mixture of fresh cyclohexane and recycled material. The reactorswere connected by a pipe system, and the liquid reactant mixture flowed from onereactor into the other by gravity. Reactors were designed to operate at a pressureof 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 toremove the reactor and install a bypass. A 20-inch diameter bypass pipe was installedconnecting the two flanges of the reactors. Bellows originally present between thereactors were left in place. Because reactor flanges were at different heights, thepipe had a dog-leg shape (Figure 2.3).

On May 29, the bottom isolating valve on a sight glass on one of the vesselsbegan to leak, and a decision was made to repair it. On June 1, start-up of theprocess following repair began. As a result of poor design, the bellows in the bypassfailed and a release of an estimated 30 tons cyclohexane occurred. The leakageformed a strong, turbulent, free jet. Fifty percent of the released cyclohexane flashedoff as vapor; the remainder formed a mist. (The degree of mist evaporation dependson the amount of air aspirated by the jet.)

After a period of 30 to 90 seconds following release, the flammable cloud wasignited. The time was then about 4:53 P.M. The explosion caused extensive damageand started numerous fires. The blast shattered control room windows and causedthe collapse of its roof. It demolished the main office block, only 25 m from theexplosion center. Twenty-eight people died, and thirty-six were injured. The plantwas totally destroyed (Figures 2.4 and 2.5), and 1821 houses and 167 shops andfactories in the vicinity of the plant were damaged.

Sadee et al. (1976-1977) give a detailed description of structural damage dueto the explosion and derived blast pressures from the damage outside the cloud

Figure 2.3. Bypass on cyclohexane reactors.

(Figure 2.6). Several authors estimated the TNT mass equivalence based upon thedamage incurred. Estimates vary from 15,000 and 45,000 kg.

Estimates of pressures inside the cloud vary widely. Gugan (1978) calculatedthat the forces required to produce damage effects observed, such as the bendingof 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 releasedits entire contents. The rupture was due to the generation of excessive pressurescreated by long solar exposure following initial overfilling. The gas was ignited after10 to 25 seconds. The ensuing vapor cloud explosion caused the death of 207people and injured 3818.

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

R2526Support poles

R 2524

Support poles

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

Figure 2.4. Area of spill showing removed reactor.

Figure 2.5. Damage to congested area of Flixborough works.

Distance from ground zero (m)

Figure 2.6. Blast-distance relationship outside the cloud area of the Flixborough explosion.

catastrophic failure was, according to the original data, due to overfilling of thecar. On the day of the explosion, the ambient temperature reached approximately30° to 320C (86° to 9O0F). Heating and consequent expansion of its contents resultedin hydraulic rupture.

An alternative explanation, proposed by Marshall (1986) is that there was adefect in the construction of the tank car. The increase in vapor pressure caused

Pressure — distance curvefor 16t TNT detonated atheight of 45m

Pre

ssur

e (k

Pa)

(Vertical bars were drawn based on observed damage.)

by the higher temperature resulted in the tank car failure. The failure had takenplace principally along a welded horizontal seam. Witnesses claim to have seen abrownish-white cloud appearing from the tank car, accompanied by a whistlingsound, before the car ruptured completely.

According to Giesbrecht et al. (1981), there was a delay of 10 to 25 secondsbetween the moment of the initial large release and the moment of ignition. Theexplosion must have been very violent in view of the extensive structural damageto the plant. The high death toll was due to the high population density in thevicinity 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 oftotal destruction plus severe damage was 3,200,000 ft2 (300,000 m2) (Figures2.7-2.9). The main cause of the explosion was the turbulence generated by therelease itself. The release did, however, occur in a very congested area.

Port Hudson, Missouri, USA: Vapor Cloud Explosionafter 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 effectswere very severe. The blast was equivalent to that of 50,000 kg of detonating TNT.

Figure 2.7. Remains of exploded tank car.

Figure 2.8. Damage from the 1948 BASF explosion.

Burgess and Zabetakis (1973) describe the Port Hudson explosion, which took placeon December 9, 1970. At 10:07 P.M., an abnormality occurred at a pumping stationon a liquid propane line 24 km (15 miles) downstream from Port Hudson. At 10:20P.M., there was a sudden increase in the throughput at the nearest upstream pumpingstation, indicating a major break in the line. During the first 24 minutes, an estimated23,000 kg (50,000 Ib) of liquid propane escaped. The noise of escaping propanewas noticed at about 10:25 P.M. A plume of white spray was observed to be rising15 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 observeda white cloud settling into the valley around a complex of buildings. Weatherconditions were as follows: low wind (approximately 2.5 m/s [8 ft/s]) and near-freezing 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 pressurepulse was felt and one witness was knocked down.

After the valley was illuminated, a flash fire was observed, which consumedthe remainder of the cloud. After the explosion and flash fire, a torch fire resultedat the point of the initial release. Buildings in the vicinity of the explosion weredamaged (Figures 2.10 and 2.11).

Total destruction Severe damage Moderate damage

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 groundfloor of this building, partitioned into four rooms, contained six deep-freeze units.Gas could have entered the building via sliding garage doors, and ignition couldhave occurred at the controls of a refrigerator motor.

Damage from the blast in the vicinity was calculated to be equivalent to a blastof 50,000 to 75,000 kg of TNT. According to Burgess and Zabetakis (1973), thePort Hudson vapor cloud detonated. As far as is known, this is the only vapor cloudexplosion 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 (750kg; 1650 Ib) liquid propane. During maneuvering, the tank fell from the shovel; aportion of its contents was released as a result. After a delay of 30 seconds, theensuing vapor cloud was ignited. The explosion caused substantial blast and firedamage. There were no casualties.

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o

f re

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damage criteria accordingto Schardm o

Glasstoneo

limiting curves

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 ofconstruction 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 metaland brick. All construction buildings were on one side of a street. Three houseswere under construction on the other side of the street. Several cars were parkedin the street (Figure 2.12). The weather was calm and cool, with a 2-5 m/s (6-16ft/s) breeze and a temperature of 130C (550F).

Just after 10:00 A.M., a tank filled with approximately 1500 1 (750 kg; 1650Ib) 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 releaseof 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 propanetank indicate that approximately 110 kg (240 Ib) of propane was released. After30 seconds, the cloud was ignited by a heater in a construction building.

Several construction buildings collapsed from the explosion (Figure 2.13). Thefacade of the factory partially collapsed, the brick wall was partially caved in, anda large number of windows in this wall were shattered. The glass roof of the factory

Polaroid works hut canteen officehuts

managershuttoilef

.nut

parked cars hoge Bolhofstraat

container building materials

concrete slabsnorth

direction of the winddwellings underconstruction

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 bythe pressure wave. Roof tiles of the houses under construction at approximately 50m (160 ft) were displaced. Windows up to 15Om (500 ft) from the explosion centerwere 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 dischargedfrom a vent. The resulting cloud was ignited. The subsequent explosion resulted inminor structural blast damage. About 75 persons were injured, primarily from glassbreakage, and 1 person was killed.

Gugan (1978) describes the accident that occurred in Raunheim, Germany on Janu-ary 16, 1966. Surplus methane was being vented unintentionally to the atmosphere.Liquid methane passed to a vaporizer having a maximum capacity of 4000 kg. Thevaporizer was instrumented to control the internal liquid level. Although the actualcause of release has never been established, it appears that the liquid-level controllerfailed, allowing a slug of liquid methane to be ejected from the vent. This releasewould 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 awhite cloud expanding slowly over the ground and drifting in the direction of thecontrol room. As the cloud reached the control room, it was ignited. It is likelythat the ignition source were furnaces about 50 m (160 ft) from the vaporizer inthe opposite direction. Structural damage was not severe, and blast damage onlyslight. Glass breakage was extensive up to 400 m (1300 ft) from the center of theexplosion and slight up to 1200 m (4000 ft). One person was killed and seventy-five injured, primarily from flying glass.

Probably no more than 500 kg of liquid methane was involved. This wouldhave formed a cloud 1 m deep (3 ft) and 40 m (130 ft) in radius (assuming astoichiometric 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 propylenecollided with a standing hopper car at a shunting yard in East St. Louis, Illinois. Asa 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 230people were injured.

A National Transportation Safety Board Railroad Accident Report (1973) describesthe accident which occurred in a shunting yard in East St. Louis, Illinois. Arrivingcars are classified in the yard, then delivered to outbound carriers. On arrival, carsare inspected. They are then pushed up a mound, uncoupled, and allowed to rolldown a descending grade onto one of the classification tracks. This process is called"humping." Cars are directed and controlled by a computerized switching and speed-control system.

On the morning of January 22, 1972, a 44-car cut was being classified. Onecar, an empty hopper, was humped without incident but stopped approximately 400m (1300 ft) short of its planned coupling point. Later, three tank cars containingpropylene were humped as a unit and directed onto the same track as the emptyhopper. The cars should have been slowed by the speed control system, but werenot, probably because of greasy wheels. An overspeed alarm was given. The unitran 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. Liquefiedpropylene was spilled, and propylene vapor was observed as a white cloud spreadingat ground level. The hopper car was set into motion by the impact from the three-car unit, and the four cars rolled down the track together until they struck carsstanding at 700 m (2300 ft) from the hump end of the track. This impact resultedin an enlargement of the tear in the leading tank car.

1 heavy struckural2 ligM structural &

heavy cosmetic3 Light cosmetic &

glassU Light glass5 heavy structural

large buildings6 plate glass

Figure 2.14. Explosion damage.

Flames were first observed at or near an unoccupied caboose. A flash fireresulted, propagating toward the punctured car area. "An orange flame then spreadupward, and a large vapor cloud flared with explosive force. Estimates of the timelapse between these occurrences range from 2 to 30 seconds. Almost immediatelythereafter, a second, more severe, explosion was reported."

The explosions resulted in 223 injuries. Buildings and a number of freight carswere damaged (Figure 2.14). Car damage included both inward and outwarddeformities.

Jackass Flats, Nevada, USA: Hydrogen-Air Explosion during Experiment

On January 9,1964, a test was run at Los Alamos Scientific Laboratory to measurethe acoustic sound levels developed during the release of gaseous hydrogen athigh flow rates. The released hydrogen ignited and exploded.

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

winddirection

on acoustic fields, this particular experiment was run without the flare. Releaseswere vertical and totally unobstructed. High-speed motion pictures were takenduring the test from two locations.

During the test, hydrogen flow rate was raised to a maximum of approximately55 kg/s (120 Ib/s). About 23 seconds into the experiment, a reduction in flow ratebegan. Three seconds later, the hydrogen exploded. Electrostatic discharges andmechanical sparks were proposed as probable ignition sources. The explosion waspreceded 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 fol-lowed 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 ofits holding clips. High-speed motion pictures indicate that the vertical downwardflame speed was approximately 30 m/s (100 ft/s); the flame was undisturbed byeffluent velocity. This value is roughly ten times the burning velocity expected forlaminar-flow conditions, but is reasonable because a turbulent free jet was present,thereby enhancing flame burning rate. According to Reider et al. (1965), blastpressure at 45 m (150 ft) from the center was calculated to be 0.5 psi (0.035 bar)

reactor

area

D 400' tower

O flare

Figure 2.15. Test-cell layout.

fillstat

motordrivebWg crvo

evallab

testcell

LH2 dewars

movable

shed

H.P. gas

based on explosion damage. They state that approximately 90 kg (200 Ib) of hydro-gen 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 leakclose to the Trans-Siberian railway track between the towns of Asma and Ufa. Aflammable cloud of leakage covered the railway track. At the moment two trainspassed through the cloud shortly after midnight, it was ignited. The blast was enor-mous, and considerable portions of both trains were derailed. The death toll wasapproximately 650.

Lewis (1989) describes the accident, which occurred in Siberia on the night of June3 and early hours of June 4, 1989. Late on June 3, 1989, engineers in charge ofthe 0.7 m (28 in.) pipeline, which carried natural gas liquids from the gas fieldsin western Siberia to chemical plants in Ufa in the Urals, noticed a sudden drop inpressure at the pumping end of the pipeline. It appears that the engineers respondedby 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 apoint 800 m (0.5 mi) away from the Trans-Siberian double railway track. The areawas a wooded valley. Throughout the area, there had been a strong smell of gas afew hours before the blast. The gas cloud was reported to have drifted for a distanceof 8 km (5 mi).

Two trains coming from opposite directions approached the area where thecloud was present. Each consisted of an electrically powered locomotive and 19coaches constructed of metal and wood. The turbulence of the trains probably mixedup the vapor and mist with overlying air to form a flammable cloud portion. Eithertrain could have ignited the cloud, most likely at catenary wires which poweredthe locomotives.

Two explosions seem to have taken place in quick succession, and a flash firesubsequently ran down the railroad track in two directions. A considerable part ofeach train was derailed. Four rail cars were blown sideways from the track by theblast, 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 theirhomes. One of the burn victims later died.

A National Transportation Safety Board report (1979) describes a flash fire resultingfrom the rupture of 20-cm (8 in.) pipeline carrying liquefied propane. The sectionof the pipeline involved extends from a pumping station at Birmingham Junction,Iowa, to storage tanks at a terminal in Farmington, Illinois. Several minutes beforemidnight on August 3, 1978, the pipeline ruptured while under 1200 psig pressurein a cornfield near Donnellson, Iowa. Propane leaked from an 838-cm (33-in.) splitand then vaporized. "The heavier-than-air cloud moved through the field and acrossa highway following the contour of the land." The cloud eventually covered 30.4ha (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. Twoother houses and a car were damaged. Two persons died in the farmhouse. Threepersons who lived across the highway from the ruptured pipeline had heard thepipeline burst and were fleeing their house when the propane ignited. All threepersons received burns on over 90% of their bodies, and one later died from theburns. 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). Itwas left burning until the valves were shut off to isolate the failed pipe section.

The investigation following the accident showed that the pipeline rupture wasdue to stresses induced in, and possibly by damage to, the pipeline resulting fromits repositioning three months before. This work had occurred in conjunction withroad work on the highway adjacent to the accident site. The pipeline had beendented and gouged.

Lynchburg, Virginia, USA: Propane Fire

On March 9,1972, an overturned tractor-semitrailer carrying liquid propane resultedin a propane release. The propane cloud was later ignited. The resulting fire killedtwo persons; five others were injured.

National Transportation Safety Board report (1973), describes an accident involvingthe overturning of a tractor-semitrailer carrying liquid propane under pressure. OnMarch 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 ona sharp curve while driving on a downgrade at a point 11 km (7 mi) north ofLynchburg, Virginia. Meanwhile, an automobile approached the curve from theother 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, thetruck rolled onto its right side.

The manhole-cover assembly on the tank struck a rock; the resulting ruptureof the tank head caused propane to escape. There were woods on one side of theroad; on the other side a steeply rising embankment and trees and bushes, and thena steep dropoff to a creek.

The truck driver left the tractor, ran from the accident site in the direction thetruck had come from, and warned approaching traffic. The driver of a first arrivingcar stopped and tried to back up his car, but another car blocked his path. Theoccupants of these cars got out of their vehicles. Three occupants of nearby housesat a distance of 60 m (195 ft), near the creek and about 20 m (60 ft) below thetruck, fled after hearing the crash.

An estimated 4000 gallons (8800 kg; 19,500 Ib) of liquefied propane wasdischarged. At the moment of ignition, the visible cloud was expanding but hadnot 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, buthad not reached the occupants at a distance of approximately 125 m (410 ft). Thecloud 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 ofat least 120 m (400 ft). No concussion was felt. The truck driver (at a distance of80 m or 270 feet) was caught in the flames and probably died immediately. Themotorists and residents were outside the cloud but received serious burns.

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

FIRST SOUTHBOUND CAR HEREWHEN TRUCK FIRST SEEN

TRUCK HERE WHEN FIRSTSEEN BY SOUTHBOUND CAR

FIRST CAR STOPPED 150' NORTH

OF TRUCK THEN BACKEDTO X X

TRUCK EVASIVE MANEUVERSSTARTED HERE

(1480 Feet South

of Accident Site)

Mai imumSaU Spvtd

20

Rock OutcroppingResidenceOutbui ldings

GOUGE MARKS FROM RIGHTTRAILER TANDEM WHEELS

Woods

Continous Downgrade(Average - 7.52%)

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Virginia Highway Department

Sand and Gravel Storage Area

POINT OF IMPACT

Figure 2.17. Details of accident site.

Woods

Woods

Trees

SOUTHBOUND CARSBACKED TO HEREAND STOPPED 450'NORTH OF TRUCK

TRUCKDRIVER1SBODY

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, onSeptember 2, 1976. A rail car carrying 231,000 kg (470,000 Ib) (90% full) ofcarbon 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 passingthrough 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 carbondioxide from the safety valve, after which the tank exploded 15 m (50 ft) in frontof a group of other rail cars. Other evidence indicates that the explosion occurredafter impact with these cars.

Parts of the tank were projected to distances up to 360 m (1200 ft). Twenty-two pieces of the tank were recovered, constituting approximately 80% of theoriginal tank. Debris was found clustered in two separate areas, namely, within theradii of 5° to 20° and 65° to 95° from the car's direction of movement. Three emptytank cars located up to a distance of three railroad tracks from the exploded carwere 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 recoveredpiece 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 dioxideproduction and filling plant exploded in rapid succession. The explosion completelydestroyed the tank yard of the plant and killed nine people. Fifteen people wereinjured.

Voros and Honti (1974) described the incident. A carbon dioxide purification plantin Repcelak, Hungary, produced carbon dioxide from natural sources. It was lique-fied and supercooled after purification by ammonia refrigeration, then stored intanks 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 housewere on the opposite side of the vessels. On January 2, 1969, at 1:50 P.M., one ofthe vessels (C) was filled from the production plant. During filling, the vesselexploded (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 PLANT-BEFORE EXPLOSION

!.PURIFICATION BUILDING2. PROCESS LABORATORY 3.FILLING UNITA. WAREHOUSE 5.BOILER HOUSE

6. BOILER HOUSE CHIMNEY7. 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 vesseltore off a 30 X 30 cm (12 x 12 in.) piece of plate from its side. The release ofcarbon dioxide through this hole caused the vessel to be thrown into the processlaboratory like a rocket, resulting in five casualties. The explosion caused vesselB to be torn loose from its connecting pipes, but without further consequences.

Fragments flying in all directions caused the deaths of four persons. Within anarea of 150 m (500 ft) around the tank yard, many people were injured. Amongthem were fifteen who suffered from serious injury by freezing and the impactof 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 afragment weighing 1000 kg (2200 Ib) landed 250 m (820 ft) away. A large amountof carbon dioxide was released, causing the immediate vicinity of the yard to becovered 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 pressureand level readings in the tanks. Residual water could cause meters to fail fromice formation.

The material of construction of the vessels D and C was not suited for useunder low temperature conditions. Vessels A and B were, however, suitable. Thelocation 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 aftermaking a delivery in a hospital in Brooklyn, New York. The force of the explosionand subsequent fires caused the deaths of the driver and bystander. Thirty otherpeople were injured and substantial property damage resulted.

A report of the National Transportation Safety Board (1971) describes the ruptureof a tank truck of liquefied oxygen. On May 29, a tank truck was filled with 2550gallons (14,000 kg; 30,800 Ib) of liquefied oxygen at a producing facility in NewJersey. After filling was completed, the truck was parked loaded overnight. Thefollowing day, the truck departed for several scheduled delivery stops. The firststop 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 cabof the truck, and began to maneuver the truck in the yard of the hospital. The trucktank ruptured, and the remaining contents of the tank were spewed into the areaaround the truck. Vigorously burning fires started in the oxygen-enriched atmo-sphere.

The driver and a bystander were fatally injured by the fire and explosion. Thirtyother persons sustained minor injuries, including twenty-four who sustained injuries

from broken glass and forces of the explosion. Four firemen and two policemenwere treated for minor injuries suffered during emergency response efforts. Thetruck and its tank were damaged extensively. Site damage was limited to the areaaround the truck. Minor additional damage to window glass and light structuralcomponents occurred up to 18Om (600 ft) from the truck. The storage tank andassociated piping were still intact after the accident.

The ensuing investigation showed that the entire tank fracture sequence occurredwithin about 1 second, suggesting a very rapid pressure rise. The sequence of eventsprobably began with an initiating reaction between one or more reactants locatedin the "upper roadside baffle bracket area" and oxygen. This reaction triggered anoxidation of the aluminum surrounding the cavity which, in turn, triggered anintense, heat-producing reaction between the aluminum of the tank and the oxy-gen 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 carryingliquefied petroleum gas (LPG), derailed in the town of Crescent City, Illinois. Thederailment caused one of the tanks to be punctured, then release LPG. The ensuingfire, 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 wereinjured. There was extensive property damage.

A National Transportation Safety Board report (1972), Eisenberg et al. (1975), andLees (1980) each describe the accident. At 6:30 A.M. on June 21, 1970, 15 railcars, 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 thederailed cars in front of it (Figure 2.20). Its coupler then struck the tank of thetwenty-sixth car and punctured it. The released LPG was ignited by some unidenti-fied source, possibly by sparks produced by the derailing cars. The resulting fireballreached a height of several hundred feet and extended into the part of the townsurrounding the tracks. Several buildings were set on fire.

The safety valves of other cars operated, thereby releasing more LPG. At 7:33A.M., the twenty-seventh car ruptured with explosive force. Four fragments werehurled in different directions (Figure 2.21). The east end of the car dug a crater inthe track structure, and was then hurled about 18Om (600 ft) eastward. The westend of the car was hurled in a southwesterly direction for a total distance of about90 m (300 ft). This section struck and collapsed the roof of a gasoline servicestation. Two other sizable portions of the tank were hurled in a southwesterlydirection 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 endof this car was hurled about 60 m (200 ft) southward across the street, where itentered a brick apartment building. The north end of the car was hurled throughthe air in a northwesterly direction over the roofs of several houses, landed in anopen 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 carwhich included about one-half of the tank was propelled along the ground in anortheasterly direction for about 18Om (600 ft). It destroyed two buildings andcame to rest in a third.

At about 10:55 A.M., the thirty-second and thirty-third car ruptured almostsimultaneously. 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 puncturedits head, resulting in further propane releases. The other end of the car also struckthe thirty-fourth car, ricocheted, and then struck the protective housing of the thirty-fifth car. The housing and valves of the thirty-fifth car broke off, permitting moreLPG 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 storagesphere ignited. The fire burned around the vessel and led to boiling liquid expandingvapor explosions. The accident caused eighteen deaths and eighty-one injuries.

IChemE (1987) describes the accident. An LPG storage installation at the Feyzinrefinery in France consisted of four 1200 m3 (43,000 ft3) propane spheres, four2000 m3 (70,000 ft3) butane spheres, and two horizontal bullet pressure vessels forpropane and butane storage (Figure 2.22). The LPG storage spheres were about450 m (1500 ft) away from the nearest refinery and about 300 m (1000 ft) fromthe nearest houses in the village. The shortest distance between an LPG sphere andthe nearby highway was 42 m (140 ft). Spaces between individual spheres rangedfrom 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 separatefrom the LPG in storage. Thus, it was necessary to drain off this solution first priorto sampling. On the morning of January 4, 1966, an operator opened two valvesin series on the bottom off-take line from a propane storage sphere in order to drainoff the sodium hydroxide solution. Contrary to instructions, the operator first openedthe lower valve completely, then started to regulate takeoff rate by adjusting theupper valve. Only a small amount of caustic soda and some propane came out. Heclosed the valve, then opened it again slightly, but there was no flow. He thenopened the valve wider. The blockage, presumably hydrate or ice, cleared, andpropane gushed out.

The operator and two workers accompanying him were unable to close theupper valve. They did not attempt to close the lower valve immediately, and by

FeyzinVil lage400 m away

Destruction

Some damage

Railway

Motorway

Fuel oil tanks Petrol tanks

LPG tanks

Figure 2.22. Feyzin storage site layout.

the time they did, this valve was also frozen open. It was 6:40 A.M.. All threeworkers then left on foot to turn in an alarm and seek help. They did not use thephone 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 onthe nearby highway and to stop the flow from the sphere. A vapor cloud about 1 mdeep spread toward the highway. Unfortunately, a minor road was not sealed offin time, and a car entered the gas cloud from this road and stopped. The cloudprobably 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 wasfatally burned. The fire traveled back to the sphere igniting the gas escaping fromthe sphere.

At 7:30 A.M., an attempt was made by at least 10 refinery workers to extinguishthe fire with dry chemical. This effort was nearly successful, but supply of drychemical was exhausted before the fire was extinguished.

The relief valve on the sphere opened at 7:45 A.M., and relieved gas wasimmediately ignited.

At 8:30 A.M., water pumped from a canal became available. It was used tocool other exposed spheres, but the sphere from which the initial spill of propaneoccurred 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 itselfthrough broken pipework. Three other butane spheres ruptured without creatingany flying missiles. The village of Feyzin, 400 m (0.25 mi) from the blast sitesuffered widespread but minor blast damage.

San Juan Ixhuatepec, Mexico City, Mexico: Series of BLEVEsat LPG Storage Facility

On November 19,1984, an initial leak and flash fire of LPG resulted in the destructionof a large storage facility and a portion of the built-up area surrounding the storagefacility. Approximately 500 people were killed and approximately 7000 were injured.The storage facility and the built-up area near the facility were almost completelydestroyed.

Pietersen (1988) describes the San Juan Ixhuatepec disaster. The storage site con-sisted of four spheres of LPG with a volume of 1600 m3 (56,500 ft3) and two sphereswith a volume of 2400 m3 (85,000 ft3). An additional 48 horizontal cylindrical tanksof various dimensions were present (Figure 2.24). At the time of the disaster, thetotal site inventory may have been approximately 11,000-12,000 m3 (390,000-420,000 ft3) of LPG.

Early in the morning of November 19, 1984, large quantities of LPG leakedfrom 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 ofabout 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 penetratedhouses, which were subsequently destroyed by internal explosions. A violent explo-sion, probably involving the BLEVE of several storage tanks, occurred 1 minuteafter the flash fire. It resulted in a fireball and the propulsion of one or two cylindricaltanks. Heat and fragments resulted in additional BLEVEs.

The explosion and fireball completely destroyed the four smaller spheres. Thelarger spheres remained intact, although their legs were buckled. Only 4 of the 48cylindrical tanks were left in their original position. Twelve of the ruptured cylindri-cal tanks reached distances of more than 100 m (330 ft), and one reached a distanceof 1200 m (3900 ft). Several buildings on the site collapsed and were destroyedcompletely. Residents living as far away as approximately 300 m (1000 ft) fromthe center of the storage site (Figure 2.25) were killed or injured.

Pietersen compared damage results to effect and damage models that wereavailable at the time. His main findings follow:

• Overpressure effects due to the vessel failure appear to be determined by gasexpansion, 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 eithervideo or still cameras.

• Very rapidly expanding ground-level fireballs occurred whenever vessels failed.

Figure 2.24. Installation layout.

16. LPG storage unigas17. LPG storage gasomatico18. Bottling terminal19. Depot of cars with bottles20. Entrance21 . Rail car loading23. Store24. Garrison

7. Flare pit8. Pond9. Control room

10. Pumphouse11. Fire pumps12. Road car loading13. Gas bottle store14. Pipe/valve manifold15. Water tower

1 . 2 Spheres of 2400 m3 0 = 1 6.5 m2. 4 Spheres of 160Om3 0 = 1 4.5 m3. 4 cylinders of 270 m3 32 x 3.5m 04. 14 cylinders of 180 m3 21 x 3.5m 05. 21 cylinders of 36 m3 13 x 2.0 m 06. 6 cylinders of 54 m3 19 x 2.0m 0

3 cylinders of 45m 3 16x2.0m0

PEMiX LPG INSTALLATIONSAN JUAN IXHUATEPEC , MEXICO CITY1 : 4680

heavily damagedarea

bullets

position of majorsphert fragments

gasoftottco

truckswithbottltt

untgos

Figure 2.25. Area of damage.

Figure 2.26. Directional preference of projected cylinder fragments of cylindrical shape.

• Spherical tanks fragmented into ten to twenty pieces, whereas cylindrical vesselsfragmented into two pieces. Because cylinders at the storage site had beenstored 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 fireduring a transfer to the storage tank of a gasoline station. The accident resulted indestruction of the truck and the gasoline station.

Steunenberg et al. (1981) describe the following accident. On the morning ofDecember 18, 1978, a tank truck filled with LPG departed to deliver LPG to agasoline station in Nijmegen in The Netherlands. The gasoline station is locatednear a highway and 500 m (1600 ft) from the nearest buildings and houses in thecity of Nijmegen. After the truck arrived and maneuvered into position, transferlines were connected to the storage tank of the gasoline station. The transfer ofLPG to the storage tank began at 8:20 A.M.

After some minutes, the driver and the gasoline station employee noticed a fireunder the truck. They went to extinguish the fire with small fire extinguishers, butdecided that it would not be possible to stop the fire. They returned to the gasolinestation building, and turned in an alarm at 8:24 A.M. The driver and the gasolinestation employee fled by car. Traffic on the highway and on a nearby railway trackwas stopped. Inasmuch as no one was then near the gasoline station, the fire brigadedecided 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

o End Tub FragmentsA Other Fragments

of approximately 50 m (160 ft). Baffles in the tank were propelled to distances of125 m (400 ft). The storage tank remained intact.

Investigations revealed that the initial fire was due to a small, continuous releasefrom the transfer lines. The leakage was ignited by hot surfaces of the truck'sengine. The fireball was found to have a maximum diameter of approximately 40m (130 ft). It rose to 25 m (80 ft) above ground level.

Wooden sticks affected by radiation from the fireball permitted an estimate ofthe radiation levels emitted. It was thus established that the emissive power of theLPG 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, wasoverfilled 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 de-stroyed the refinery almost completely, causing the deaths of seven people andinjuries 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 TexasCity, 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 indicatorwas not functioning properly during filling.

The leaking gas was ignited by an unknown source; fire then flashed backtoward the sphere. It burned for approximately 30 to 60 seconds before the spherefailed in three major portions. One of these portions traveled 80 m (260 ft).

A fireball involving approximately 800 m3 (28,000 ft3) of isobutane resultedfrom the sphere's failure. Several BLEVEs of smaller vertical and horizontal tanksoccurred soon thereafter. Tank failures were mainly seam-related. Parts were thrownin 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 fireballwas less intense than the earlier one. The sphere's top section traveled 190 m (620ft) 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 spheretraveled 500 m (1600 ft). The damage from projectiles was much greater thanthat caused by the first sphere failure because they traveled farther and in moredamaging directions.

Smaller explosions occurred until about 6:00 A.M. There was no evidence ofstrong overpressure effects, although a television news broadcast showed brokenwindows 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 acampsite. A leak developed, and the ensuing cloud was ignited. Three minutes laterthe 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 12:05P.M., the loading of a tank truck with propyiene was completed. According to weightrecords 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 weightfor the load of 23,470 kg (52,000 Ib)—well over the maximum allowable weight of19,099 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 insteadof the highway in order to avoid tolls. It was a hot summer day. As it passedthrough the village of San Carlos de Ia Rapita, observers noticed that the tank trucksped 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. (Figure2.29). Propyiene seems to have been released. The resulting vapor cloud wasignited, 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 andproduced fragments and a fireball. Blast effects were far heavier in the upward andwindward directions than otherwise. About 75 m (250 ft) from the explosion center,

Figure 2.29. Reconstruction of scene ofthe San Carlos de Ia Rapita campsitedisaster.

a single-story building was completely demolished. This failure resulted in the deathof four people. In the opposite direction, a motorcycle was still standing on itsfootrest 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 apropane pipeline break. The December 9, 1970, Explosion in Port Hudson, Mo." Bureauof 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 Interna-tional Symposium on Loss Prevention and Safety in the Process Industries. EuropeanFederation of Chemical Engineering, Sept. 1983, Harrogate, England.

Davenport, J. A. 1986. "Hazards and protection of pressure storage of liquefied petroleumgases." Fifth International Symposium on Loss Prevention and Safety Promotion in theProcess Industries, European Federation of Chemical Engineering, Conner, France.

Eisenberg, N. A., C. J. Lynch, andR. J. Breeding. 1975. "Vulnerability model. A simulationsystem for assessing damage resulting from marine spills." U.S. Department of Com-merce Report No. AD/AOI5/245. Washington: National Technical Information Service.

Factory Mutual Research Corporation. 1990. "Guidelines for the estimation of propertydamage from outdoor vapor cloud explosions in chemical processing facilities." Techni-cal Report, March 1990.

Giesbrecht, H., K. Hess, W. Leuckel, and B. Maurer, 1981. "Analysis of explosion hazardson spontaneous release of inflammable gases into the atmosphere. Part 1: Propagationand 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." ATOB-HAR-71-6.

National Transportation Safety Board. 1972. "Railroad Accident Report—Derailment ofToledo, Peoria and Western Railroad Company's Train No. 20 with Resultant Fire andTank Car Ruptures, Crescent City, Illinois, June 21, 1970. NTSB-RAR-72-2.

National Transportation Safety Board. 1973. "Highway Accident Report—Propane Tractor-Semitrailer 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 mate-rials 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 Pipe-line 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 naaraanleiding 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 theProcess Industries.

3BASIC CONCEPTS

Accident scenarios leading to vapor cloud explosions, flash fires, and BLEVEswere described in the previous chapter. Blast effects are a characteristic feature ofboth vapor cloud explosions and BLEVEs. Fireballs and flash fires cause damageprimarily from heat effects caused by thermal radiation. This chapter describes thebasic concepts underlying these phenomena.

Section 3.1 treats atmospheric dispersion in just enough detail to permit under-standing of its implications for vapor cloud explosions. Section 3.2 covers theevolution from slow, laminar, premixed combustion to an intense, explosive, blast-generating process. It introduces the concepts of deflagration and detonation. Section3.3 describes typical ignition sources and the ignition characteristics of severaltypical fuel-air mixtures. Section 3.4 covers the physical concepts of blast andblast 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 cloudexplosion or flash fire effects. Factors such as flammable cloud size, homogeneity,and location are largely determined by the manner of flammable material releasedand turbulent dispersion into the atmosphere following release. Several models forcalculating 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 flammablegases and vapors in air have been published elsewhere, for example, Nabert andSchon (1963), Coward and Jones (1952), Zabetakis (1965), and Kuchta (1985). Asummary of results is presented in Table 3.1, which also presents autoignitiontemperatures and laminar burning velocities referred to during the discussion of thebasic concepts of ignition and deflagration.

The flash point of a liquid is the minimum temperature at which its vaporpressure is sufficiently high to produce a flammable mixture with air above theliquid. Therefore, the generation of a flammable gas or vapor cloud for liquidswhose 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 Airat Atmospheric Conditions3

Gas or Vapor

MethaneEthanePropaneEthylenePropyleneHydrogenAcetoneDiethyl etherAcetyleneEthanolTolueneCyclohexaneHexaneXylene

FlammabilityLimits

(vol. %)

5.0-15.03.0-15.52.1-9.52.7-342.0-11.74.0-75.62.5-13.01.7-361.5-1003.5-151.2-7.01.2-8.31.2-7.41.0-7.6

FlashPointCC)

—————-19-20—12

—-18-15

30

AutoignitionTemperature

(0C)

595515470425455560540170305425535260240465

Laminar BurningVelocity

(mis)

0.4480.4760.4640.7350.5123.250.4440.4861.55

—————

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 aflammable aerosol-air mixture.

Data on dispersion and combustion of aerosol-air clouds are scarce, althoughBurgoyne (1963) showed that the lower flammability limits on a weight basis ofhydrocarbon aerosol-air mixtures are in the same range as those of gas- or va-por-air mixtures, namely, about 50 g/m3.

Generally, at any moment of time the concentration of components within avapor cloud is highly nonhomogeneous and fluctuates considerably. The degree ofhomogeneity of a fuel-air mixture largely determines whether the fuel-air mixtureis able to maintain a detonative combustion process. This factor is a primary determi-nant 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 de-scribed as a random motion superposed on the mean flow. Many aspects of turbulentdispersion are reasonably well-described by a simple model in which turbulence isviewed 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 meanflow. This energy is continuously transferred to smaller and smaller eddies. Suchenergy transfer continues until energy is dissipated into heat by viscous effects inthe smallest eddies of the spectrum.

Turbulence is generated by wind shear in the surface layer and in the wake ofobstacles and structures present on the earth's surface. Another powerful source ofturbulent motion is an unstable temperature stratification in the atmosphere. Theearth's surface, heated by sunshine, may generate buoyant motion of very largescale (thermals).

For a chemical reaction such as combustion to proceed, mixing of the reactantson a molecular scale is necessary. However, molecular diffusion is a very slowprocess. Dilution of a 10-m diameter sphere of pure hydrocarbons, for instance,down to a flammable composition in its center by molecular diffusion alone takesmore than a year. On the other hand, only a few seconds are required for a similardilution by molecular diffusion of a 1-cm sphere. Thus, dilution by moleculardiffusion is most effective on small-scale fluctuations in the composition. Thesefluctuations are continuously generated by turbulent convective motion.

Turbulent eddies larger than the cloud size, as such, tend to move the cloudas a whole and do not influence the internal concentration distribution. The meanconcentration distribution is largely determined by turbulent motion of a scalecomparable to the cloud size. These eddies tend to break up the cloud into smallerand smaller parts, so as to render turbulent motion on smaller and smaller scaleseffective in generating fluctuations of ever smaller scales, and so on. On the small-scale side of the spectrum, concentration fluctuations are homogenized by molecu-lar diffusion.

With this simplified concept in mind, general trends in vapor cloud dispersioncan be derived and understood. Generally, in a process of vapor cloud dispersion,two successive stages can be distinguished (Wilson et al. 1982a). An initial stageis characterized by the generation of large-scale fluctuations by large-scale turbulentmotion. When the cloud dimensions grow beyond the size of the large-scale turbu-lence in the flow field, a second stage can develop. This final stage is characterizedby a gradual reduction of concentration fluctuations. Some degree of homogeneityin the composition can arise only after the cloud dimensions have grown far beyondthe characteristic size of the large-scale turbulent motion.

Generally, accidental emissions take place close to the earth's surface. Thescale of the turbulence in the surface layer is limited by the distance to the earth'ssurface, so the characteristic size of the large-scale turbulence decreases towardsthe surface. Therefore, some degree of homogeneity in a vapor cloud is first to beexpected in a thin layer adjacent to the ground (Wilson et al. 1982b). The thicknessof 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, instanta-neous release, gravity spreads the vapor quickly over a large area. The slumpingbulk of vapor generates large-scale motion in the cloud by which the initial meanconcentration decay is fast. Some degree of homogeneity cannot be expected beforethe 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 besummarized 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 tothe earth's surface. A certain degree of homogeneity is obtained at a higher meanconcentration level as the cloud dimensions are larger and the size of the large-scaleturbulent motion is smaller. In general, a slower decay of the mean-concentrationdistribution goes hand-in-hand with a higher degree of homogeneity in a largerportion of the cloud and at a higher mean-concentration level.

The above discussion holds for dispersion by atmospheric turbulence. In addi-tion, 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 turbulentjet. Fuel mixes rapidly with air within the jet. Large-scale eddy structures near theedges 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 lowerflammability limit, and the flammable portion of the cloud would be limited to thejet itself. In practice, however, jets are usually somehow obstructed by objectssuch as the earth's surface, surrounding structures, or equipment. In such cases, alarge cloud of flammable mixture will probably develop. Generally, such a cloudwill be far from stagnant but rather in recirculating (turbulent) motion driven bythe momentum of the jet.

3.2. COMBUSTION MODES

3.2.1. Deflagration

The mechanism of flame propagation into a stagnant fuel-air mixture is determinedlargely by conduction and molecular diffusion of heat and species. Figure 3.1 showsthe change in temperature across a laminar flame, whose thickness is on the orderof one millimeter.

Heat is produced by chemical reaction in a reaction zone. The heat is trans-ported, mainly by conduction and molecular diffusion, ahead of the reaction zoneinto a preheating zone in which the mixture is heated, that is, preconditioned forreaction. Since molecular diffusion is a relatively slow process, laminar flamepropagation is slow. Table 3.1 gives an overview of laminar burning velocities ofsome of the most common hydrocarbons and hydrogen.

What are the mechanisms by which slow, laminar combustion can be trans-formed into an intense, blast-generating process? This transformation is moststrongly influenced by turbulence, and secondarily by combustion instabilities. Alaminar-flame front propagating into a turbulent mixture is strongly affected by theturbulence. Low-intensity turbulence will only wrinkle the flame front and enlargeits surface area. With increasing turbulence intensity, the flame front loses its more-or-less smooth, laminar character and breaks up into a combustion zone. In anintensely turbulent mixture, combustion takes place in an extended zone in which

location

Figure 3.1. Temperature distribution across a laminar flame.

combustion products and unreacted mixture are intensely mixed. High combustionrates can result because, within the combustion zone, the reacting interface betweencombustion products and reactants can become very large.

The interaction between turbulence and combustion plays a key role in thedevelopment of a gas explosion. Generally, flame propagation is laminar immedi-ately following ignition in an incipient gas explosion. Effective burning velocitiesare not much higher than the laminar burning velocity, and overpressures generatedare on the order of millibars. Laminar combustion generates expansion and producesa flow field. If the boundary conditions of the expansion flow-field are such thatturbulence 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 andtime, expansion flow becomes stronger. Higher flow velocities go hand in handwith more intense turbulence. This process feeds on itself; that is, a positive feedbackcoupling comes into action. In the turbulent stage of flame propagation, a gasexplosion may be described as a process of combustion-driven expansion flow withthe turbulent expansion-flow structure acting as an uncontrolled positive feedback(Figure 3.2).

If such a process continues to accelerate, the combustion mode may suddenlychange drastically. The reactive mixture just in front of the turbulent combustionzone is preconditioned for reaction by a combination of compression and of heatingby turbulent mixing with combustion products. If turbulent mixing becomes toointense, the combustion reaction may quench locally. A very local, nonreacting buthighly reactive mixture of reactants and hot products is the result.

reaction zone preheating zone

direction ofpropagation

tem

pera

ture

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

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

3.2.2. Detonation

The two basic modes of combustion—deflagration and detonation—differ funda-mentally in their propagation mechanisms. In deflagrative combustion, the reactionfront is propagated by molecular-diffusive transport of heat and turbulent mixingof reactants and combustion products. In detonative combustion, on the other hand,the reaction front is propagated by a strong shock wave which compresses themixture beyond its autoignition temperature. At the same time, the shock is main-tained by the heat released from the combustion reaction.

To understand the behavior of detonation, some basic features of detonationmust be understood. They are briefly summarized in the next few paragraphs.Various properties of detonation are reflected by different models (Picket and Davis1979). Surprisingly accurate values of overall properties of a detonation, including,for example, wave speed and pressure, may be computed from the Chapman-Jou-guet (CJ) model (Nettleton 1987). In this model, a detonation wave is simplifiedas a reactive shock in which instantaneous shock compression and the combustionfront coincide, a zero induction time and an instantaneous reaction are inherent inthis model (Figure 3.3). For stoichiometric hydrocarbon-air mixtures, the detona-tion wave speed is in the range of 1700-2100 m/s and corresponding detonationwave 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 compres-sion 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 detonationpressure, which is not attained until the reaction is complete. The duration of the

combustion expansion flow

turbulence

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 failsto propagate.

The one-dimensional representation described above is too simple to describethe behavior of a detonation in response to boundary conditions. Denisov et al.

shock/react ionwave complexpr

essu

repr

essu

re

react ion wave

induction time

shock

time

Figure 3.4. The ZND-model.

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 3.5shows how a plane configuration of a shock and a reaction wave breaks up into acellular structure. Detonation is not a steady process, but a highly fluctuating one.Its multidimensional cyclic character is determined by a process of continuous decayand reinitiation. The collision of transverse waves plays a key role in the structureof a detonation wave. The nature of this process has been described in detailmany times, for example, see Denisov et al. (1962); Strehlow (1970); Vasilev andNikolaev (1978). In this cyclic process, a characteristic length scale or cell sizecan be distinguished, at least on the average (Figures 3.5 and 3.6). The characteristiccell size reflects the susceptibility of a fuel-air mixture to detonation. Some guidevalues 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 reactivemixtures result in smaller cell sizes. Table 3.2 shows that a stoichiometric mixtureof methane and air has an exceptionally low susceptibility to detonation comparedto other hydrocarbon-air mixtures.

react ionwave shock

inductionlength

Figure 3.6. Cellular structure of a detonation.

TABLE 3,2. Characteristic Detonation Cell Sizefor Some Stoichiometric Fuel-AirMixtures

Fuel Cell Size (mm)

methane 300propane ]propylene | 55n-butane Jethylene 25ethylene oxide 18acetylene 10

3.3. IGNITION

Depending on source properties, ignition can lead to either or both of two combustionmodes, detonation or deflagration. As indicated in Chapter 2, deflagration is by farthe more likely mode of flame propagation to occur immediately upon ignition.Deflagration ignition energies are on the order of 10~4 J, whereas direct initiationof detonation requires an energy of approximately 106 J. Table 3.3 gives initiationenergies for deflagration and detonation for some hydrocarbon-air mixtures. Con-sidering the high energy required for direct initiation of a detonation, it is a veryunlikely occurrence.

In practice, vapor cloud ignition can be the result of a sparking electric apparatusor hot surfaces present in a chemical plant, such as extruders, hot steam lines orfriction between moving parts of machines. Another common source of ignition isopen fire and flame, for example, in furnaces and heaters. Mechanical sparks, forexample, from the friction between moving parts of machines and falling objects,are also frequent sources of ignition. Many metal-to-metal combinations result inmechanical sparks that are capable of igniting gas or vapor-air mixtures (Ritter1984). In general, ignition sources must be assumed to exist in industrial situations.

TABLE 3.3. Initiation Energies for Deflagration and Detonation for SomeHydrocarbon-Air Mixtures3

Gas Mixture

Acetylene-AirPropane-AirMethane-Air

Minimum Ignition Energyfor a Deflagration (mJ)

0.0070.250.28

Minimum Initiation Energyfor a Detonation (mJ)

1.29 x 105

2.5 x 109

2.3 x 1011

a 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 byrapid combustion in which high-temperature combustion products expand and affecttheir surroundings. In this fashion, the heat of combustion of a fuel-air mixture(chemical energy) is partially converted into expansion (mechanical energy). Me-chanical energy is transmitted by the explosion process into the surrounding atmo-sphere in the form of a blast wave. This process of energy conversion is very similarto that occurring in internal combustion engines. Such an energy conversion processcan be characterized by its thermodynamic efficiency. At atmospheric conditions,the theoretical maximum thermodynamic efficiency for conversion of chemicalenergy into mechanical energy (blast) in gas explosions is approximately 40%.Thus, less than half of the total heat of combustion produced in explosive combustioncan be transmitted as blast-wave energy.

In the surrounding atmosphere, a blast wave is experienced as a transient changein 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 atmo-spheric values (Figure 3.7). The shape of a blast wave is highly dependent on thenature of the explosion process.

If the combustion process within a gas explosion is relatively slow, then expan-sion is slow, and the blast consists of a low-amplitude pressure wave that is character-ized by a gradual increase in gas-dynamic-state variables (Figure 3.7a). If, on theother hand, combustion is rapid, the blast is characterized by a sudden increase inthe gas-dynamic-state variables: a shock (Figure 3.7b). The shape of a blast wavechanges during propagation because the propagation mechanism is nonlinear. Initialpressure waves tend to steepen to shock waves in the far field, and wave durationstend to increase.

3.4.2. Blast Loading

An object struck by a blast wave experiences a loading. This loading has twoaspects. First, the incident wave induces a transient pressure distribution over the

Figure 3.7. Blast wave shapes.

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 thisprocess 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 theincident wave encounters the front wall, the portion striking the wall is reflectedand builds up a local, reflected overpressure. For weak waves, the reflected overpres-sure is slightly greater than twice the incident (side-on) overpressure. As the incident(side-on) overpressure increases, the reflected pressure multiplier increases. SeeAppendix C, Eq. (C-1.4).

In Figure 3.8b, the reflected wave moves to the left. Above the structure, theincident wave continues on relatively undisturbed. As the reflected wave movesback from the front wall, a rarefaction front moves down the front face of thestructure (Figure 3.8b). In this way, the reflected overpressure is attenuated bylateral rarefaction, a process that is primarily determined by the lateral dimensionsof the structure. The top face of the structure experiences no more than the side-on wave overpressure. As the incident shock passes beyond the rear face of thestructure, it diffracts around this face, as shown in Figure 3.8c. At the instantshown in Figure 3.8c, the reflected overpressure at the front face has been completelyattenuated by the lateral rarefaction. Subsequently, the incident shock has passedbeyond the structure, the diffraction process is over, and the structure is immersedin the particle-velocity flow-field behind the leading shock front. At this stage, thestructure 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 atransient pressure distribution induced by the overpressure of the blast wave. Thiscomponent of blast loading is determined primarily by reflection and lateral rarefac-tion of the reflected overpressure. The height and duration of reflected overpressureare determined by the peak side-on overpressure of the blast wave and the lateraldimensions of the object, respectively. The Blast loading of objects with substantial

incidentshock front

rooffront backwall wall

vortex

rarefactionwave

reflectedshockfront

shock front

shock front

vortices diffractedshockfront

shock front

vortices

lateral dimensions is largely governed by the overpressure aspect of a blast wave.On the other hand, slender objects—lampposts, for example—are hardly affectedby the overpressure aspect of blast loading.

The second component of blast loading is a drag force induced by particlevelocity in the blast wave. Drag force magnitude is determined by the object'sfrontal area and the dynamic pressure of flow after the leading shock. The blastloading of slender objects is largely governed by the dynamic pressure (drag) aspectof a blast wave.

Making a detailed estimate of the full loading of an object by a blast wave isonly possible by use of multidimensional gas-dynamic codes such as BLAST (Vanden Berg 1990). However, if the problem is sufficiently simplified, analytic methodsmay do as well. For such methods, it is sufficient to describe the blast wavesomewhere in the field in terms of the side-on peak overpressure and the positive-phase duration. Blast models used for vapor cloud explosion blast modeling (Section4.3) 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 diameterd produces a blast wave of side-on peak overpressure P and positive-phase durationt+ at a distance R from the charge center. Experimental observations show that anexplosive charge of diameter Kd produces a blast wave of identical side-on peakoverpressure p and positive-phase duration Kt+ at a distance KR from the chargecenter. (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, isnot a customary unit for expressing the power of an explosive charge; chargeweight is more appropriate. Therefore, the cube root of the charge weight, whichis proportional to the charge size, is used as a scaling parameter. If the distance tothe charge, as well as the duration of the wave, are scaled with the cube root ofthe charge weight, the distribution of blast parameters in a field can be graphicallyrepresented, independent of charge weight. This technique, which is common prac-tice for high-explosive blast data, is called the Hopkinson scaling law (Hopkinson1915). It is more complete, however to scale a problem by full nondimensionaliza-tion. 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 scalinglaw (Sachs 1944), which states that the problem is fully described by the followingdimensionless groups of parameters:

AP

^o

f+c0/3

£1/3

RP^£1/3

where

AP = side-on peak overpressure (Pa)t* = blast wave duration (s)R = distance from blast center (m)E = amount of participating energy (J)P0 = ambient pressure (Pa)C0 = ambient speed of sound (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 surroundingsby convection and thermal radiation. For large fires, thermal radiation is the mainhazard; it can cause severe burns to people, and also cause secondary fires.

Thermal radiation is electromagnetic radiation covering wavelengths from 2 to16 fjim (infrared). It is the net result of radiation emitted by radiating substancessuch as H2O, CO2, and soot (often dominant in fireballs and pool fires), absorptionby these substances, and scatter. This section presents general methods to describe

the radiation effects at a certain distance from the source of thermal radiation. Twodifferent methods are used to describe the radiation from a fire: the point-sourcemodel 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 ofcombustion is emitted as radiation in all directions. The radiation per unit area andper 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 (kg/s)Hc = heat of combustion per unit of mass (J/kg)Ta = atmospheric attenuation of thermal radiation (transmissivity) (-)

It is assumed that the target surface faces toward the radiation source so that itreceives 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 = combustion rate (kg/s)Hv = heat of vaporization (J/kg)Cv = specific heat of fuel (J/kg/K)A — pool area (m2)Tb = boiling temperature (K)Ta = ambient temperature (K)0.0010 = a constant (kg/s/m2)

The fraction of combustion energy dissipated as thermal radiation (/) is the unknownparameter in the point-source model. This fraction depends on the fuel and ondimensions of the flame. Measurements give values for this fraction ranging from0.1 to 0.4 Mudan 1984; Duiser 1989). Raj and Atallah (1974) measured the fractionof radiation from 2- to 6-m pool fires of LNG and found values between 0.2 and0.25. The data from Burgess and Hertzberg (1974) for methane range from 0.15to 0.34, and for butane, from 0.20 to 0.27. The highest value they found, 0.4, wasfor 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 modelcan 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-sourcemodel. This model assumes that the fire can be represented by a solid body of asimple 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 ofthe 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 = incident radiation (W/m2)F = view factor ( — )E = emissive power of fire per unit surface area (W/m2)Ta = atmospheric attenuation factor (transmissivity) ( — )

The view factor is the fraction of the radiation falling directly on the receivingtarget. The view factor depends on the shapes of the fire and receiving target, andon the distance between them.

Emissive Power

Emissive power is the total radiative power leaving the surface of the fire per unitarea 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. Becausethe fire is not a perfect black body, the emissive power is a fraction (e) of the blackbody radiation:

E = ear4 (3.4)

where

E = the emissive power (W/m2)T = temperature of the fire (K)e = emissivity ( — )a = Stefan-Boltzmann constant = 5.67 X 10~8 W/m2/K4

The use of Stefan-Boltzmann's law to calculate radiation requires the knowledgeof the fire's temperature and emissivity. Turbulent mixing causes fire temperatureto 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 radiationvalues.

Duiser (1989) calculates emissive power from rate of combustion and releasedheat. As a conservative estimate, he uses a radiation fraction (/) of 0.35. Heproposed the following equation for calculating the emissive power of a pool fire:

(3.5)

where

E = emissive power (W/m2)m" = rate of combustion per unit area (kg/m2/s)Hc = heat of combustion (J/kg)hf = flame height (m)df = flame diameter (m)0.35 = radiation fraction/ (-)

The surface-emissive power of a propane-pool fire calculated in this way equals 98kW/m2 (31,000 Btu/hr/ft2). The surface-emissive power of a BLEVE is suggestedto be twice that calculated for a pool fire.

The surface-emissive powers of fireballs depend strongly on fuel quantity andpressure just prior to release. Fay and Lewis (1977) found small surface-emissivepowers 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 andPritchard (1982) suggest an average surface-emissive power of 150 kW/m2 (47,500Btu/hr/ft2), and a maximum value of 300 kW/m2 (95,000 Btu/hr/ft2), for industrial-sized fireballs of pure vapor. Experiments by British Gas with BLEVEs involvingfuel masses of 1000 to 2000 kg of butane or propane revealed surface-emissivepowers 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 byMudan (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 makeemissivity modeling complicated. By assuming that a fire radiates as a gray body,in other words, that extinction coefficients of the radiation adsorption are indepen-dent of the wavelength, a fire's emissivity can be written as

e = 1 - exp(-fccf) (3.6)

where

e = emissivityXf = beam length of radiation in flames (m)k = extinction coefficient (m"1)

For a fireball, jcf can be replaced by the fireball diameter (Moorhouse and Pritchard1982). 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 mediumpresent between emitter and receiver. For thermal radiation, atmospheric absorptionis primarily due to water vapor and, to a lesser extent, to carbon dioxide. Absorptionalso depends on radiation wavelength, and consequently, on fire temperature.

Duiser approximates transmissivity as

T3 = 1 - aw - ac (3.7)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 carbondioxide and upon the distance to the radiation source. The partial vapor pressureof carbon dioxide in the atmosphere is fairly constant (30 Pa), but the partial vaporpressure of water varies with atmospheric relative humidity. Duiser (1989) publishedgraphs plotting absorption factors (a) against the product of partial vapor pressureand distance to flame (Px) for flame temperatures ranging from 800 to 1800 K.

Moorhouse and Pritchard (1982) presented the following relationship to approx-imate transmissivity of infrared radiation from hydrocarbon flames through theatmosphere:

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 (m)RH = relative humidity (%)

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

Lihou and Maund (1982) define attenuation constants for hydrocarbon flamesthrough the atmosphere, which can vary from 4 x 10"4Hi"1 (for a clear day) to10~3 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 methodsdescribed earlier. Presumably, Lihou and Maund's transmissivity is to be used forconditions of low relative humidity, in which dust particles (haze) are the maincause 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 theemitting 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 (W/m2)q2 = incident radiation receiving surface (W/m2)

Application of the reciprocity relation (A1F12 = A2F21) allows the fraction of radia-tion received by the target (apart from atmospheric attenuation and emissivity) tobe expressed as

q2 = FnE (3.12)

where

F21 = view factor or geometric configuration factor (-)E = emissive power of emitting surface (W/m2)q2 = incident radiation-receiving surface (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 viewfactor from a differential plane (dA2) to a flame front (area A1) on a distance L isdetermined (Figure 3.10) by:

(3.13)

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

where

L = length of line connecting elements dA{ and dA2 (m)O1 = angle between L and the normal to CiA1 (deg)®2

= angle between L and the normal to dA2 (deg)A1 = surface area flame front (m2)dA2 = differential plane (m2)

A fireball is represented as a solid sphere with a center height H and a diameterD. Let the radius of the sphere be R (R = D12). (See Figure 3.11.) Distance x ismeasured from a point on the ground directly beneath the center of the fireball tothe receptor at ground level. When this distance is greater than the radius of thefireball, 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 Acontains equations and tables of view factors for a variety of configurations, in-cluding spherical, cylindrical, and planar geometries.

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15:345-357.

Urtiew, P. A., and A. K. Oppenheim. 1966. "Experimental observations of the transitionto 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-dimensionalblast effects. TNO Prins Maurits Laboratory report.

Vasilev, A. A., and Yu Nikolaev. 1978. Closed theoretical model of a detonation cell. ActaAstronautica 5:983-996.

Wilson, D. J., J. E. Fackrell, and A. C. Robins. 1982a. Concentration fluctuations in anelevated 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 distributionof concentration fluctuations from a ground level source. Atmospheric Environ.16(3):479-504.

Zabetakis, M. G. 1965. Flammability characteristics of combustible gases and vapors. Bureauof Mines Bulletin 627. Pittsburgh.

4BASIC PRINCIPLES OF

VAPOR CLOUD EXPLOSIONS

This chapter discusses vapor cloud explosions in detail. As described in Chapter2, a vapor cloud explosion is the result of a release of flammable material in theatmosphere, a subsequent dispersion phase, and, after some delay, an ignition ofthe 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) environ-ments. Figure 4.1 illustrates the relationship between flame speed and overpressurefor three different geometries. In order to reach these speeds, either the flame hasto accelerate or the cloud has to be ignited very strongly, thereby producing directinitiation of a detonation. As described in Chapters 2 and 3, flame acceleration isonly 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 explosivelydispersed cloud or jet release;

• in combinations of high-momentum releases and congestion.

Historically, this phenomenon was referred to as "unconfined vapor cloud explo-sion," but, in general, the term "unconfined" is a misnomer. It is more accurate tocall this type of explosion simply a "vapor cloud explosion."

This chapter is organized as follows. First, an overview of experimental researchis presented. Experimental research has focused on identifying deflagration-en-hancing mechanisms in vapor cloud explosions and on uncovering the conditionsfor a direct initiation of a vapor cloud detonation.

Theoretical research is then discussed. Most theoretical research has concen-trated on blast generation as a function of flame speed. Models of flame-accelerationprocesses and subsequent pressure generation (CFD-codes) are described as well,but in less detail.

Finally, several blast-prediction methods are described and discussed. Thesemethods are demonstrated in Chapter 7 with sample problems.

flame speed ( m/s )

Figure 4.1. Overpressure as a function of flame speed for three geometries. The relationshipsare 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 literatureseems rather confusing. In the past, ostensibly similar incidents produced extremelydifferent blast effects. The reasons for these disparities were not understood at thetime. Consequently, experimental research on vapor cloud explosions was directedtoward learning the conditions and mechanisms by which slow, laminar, premixedcombustion develops into a fast, explosive, and blast-generating process. Treatingexperimental research chronologically is, therefore, a far from systematic approachand would tend to confuse rather than clarify.

Because the major causes of blast generation in vapor cloud explosions arereasonably well understood today, we can approach the overview of experimentalresearch more systematically by treating and interpreting the experiments in groupsof roughly similar arrangements. Furthermore, some attention is given to experimen-tal research into the conditions necessary for direct initiation of a detonation of avapor cloud and the conditions necessary to sustain such a detonation.

This section is arranged as follows: First, premixed combustion is discussedbased on the experiments performed under controlled conditions. To establish theseconditions the experiments were conducted in explosion vessels, balloons, plasticbags, and soap bubbles. Second, some experiments under uncontrolled conditions

ge

ne

rate

d o

verp

ress

ure

(ba

r)

tube-l ikegeometry

double plane-conf igurat ion

denseobstacleenvironment

are discussed. In one simulation of a realistic accidental spill, fuel was released inthe open air and ignited. Experiments investigating the effects of both low- andhigh-momentum releases are discussed, that is, the effect of source-term turbulenceon flame propagation. Third, the question of influence of the presence of confiningstructures and obstructions on the propagation of a premixed combustion processis investigated. Flame propagation in mixtures confined by tubes and parallel planesin combination with obstacles is described. Finally, the conditions that can lead toinitiation 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 mixturesin a manner that had minimal effect on the expansion-combustion process. Investi-gators 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 mixtureswithin soap bubbles. They produced hemispherical and cylindrical soap bubblescontaining various mixtures of fuel-oxygen-nitrogen. The effects of obstacles inthe cloud and of jet ignition on combustion behavior were also studied.

Fuel-pair mixtures, in soap bubbles ranging from 4 to 40 cm diameter andwith no internal obstacles, produced flame speeds very close to laminar flamespeeds. Cylindrical bubbles of various aspect ratios produced even lower flamespeeds. For example, maximum flame speeds for ethylene of 4.2 m/s and 5.5 m/swere found in cylindrical and hemispherical bubbles, respectively (Table 4.Ia).This phenomenon is attributed to reduced driving forces due to the top relief ofcombustion products.

Obstacles introduced in unconfined cylindrical bubbles resulted only in localflame acceleration. Pressures measured at some distance from the cylindrical bubblewere, in general, two to three times the pressure measured in the absence ofobstacles.

Large-scale balloon experiments of flammable gases in air were carried out byLind (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. Thehighest 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). Theselarge-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 selectivediffusion (Markstein 1964). To investigate whether the flame would accelerate whenallowed to propagate over greater distances, tests were carried out in an open-sidedtest apparatus 45 m long (Harris and Wickens 1989). Flame acceleration was foundto be no greater than in the balloon experiments (Table 4.Ia).

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

Reference

Deshaies and Layer(1981)

Okasakietal. (1981)

Lind and Whitson(1977)

Brossard et al.(1985)

Schneider andPfortner(1981)

Harris and Wickens(1989)


Configuration

Hemisphericalsoap bubbles(D = 4-40 cm)

Cylindrical soapbubbles(D = 44 cm)

Hemisphericalballoons(D = 10-20 m)

Spherical balloons(D = 2.8 m)

Hemisphericalballoon(D = 20 m)

Spherical balloons(D = 6.1 m)

45-m-long open-sided tent

Fuel

CH4

C3H8

C2H4

C2H4

C4H6

CH4

C3H8

C2H4

C2H4OC2H2

C2H4

C2H2

H2

Natural gasLPGC6H12

C2H4

Natural gasLPGC6H12

C2H4

Max.FlameSpeed(mis)

3.04.05.54.2

5.58.9

12.617.322.535.4243884

788

158

101019

Max.Overpressure

(bar)

————

——————

0.0125—

0.06

————————

The introduction of obstacles within "unconfined" vapor clouds produced flameacceleration. On a small scale, an array of vertical obstacles mounted on a singleplate (60 X 60 cm) resulted in flame accelerations within the array (Van Wingerdenand Zeeuwen 1983). Maximum flame speeds of 52 m/s for acetylene-air werefound, 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-m-long apparatus incorporating grids and obstructions. Maximum flame speeds wereapproximately ten times those found in the absence of obstacles.

The influence of hemispherical wire mesh screens (obstacles) on the behaviorof 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 formethane, 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 UnconfinedControlled Conditions with Obstacles

Reference

Van Wingerden andZeeuwen (1983)


Dorgeetal. (1976)

Harrison and Eyre(1986, 1987)

Harrison and Eyre(1986, 1987)

Configuration

60 x 60 cm platewith 1 cmverticalobstacles on top

45-m-long open-sided tent withobstructionsspherical gridsin a 0.6 m cube

Sector withpipework

Sector withpipework and jetflame ignition

Fuel

CH4

C3H8

C2H4

C2H2

Natural gas

^H10

C6H12

C2H4

C2H2

C2H4

C3H8

Natural gasC3H8

Natural gas

Max.FlameSpeed(mis)

7132052506570

>2001503016

119

170

Max.Overpressure

(bar)

————

0.03-0.070.03-0.070.03-0.07

0.8——

0.2080.0520.710

Harrison and Eyre (1986, 1987) studied flame propagation and pressure devel-opment in a segment of a cylindrical cloud both with and without obstacles, andwith jet ignition (Figure 4.3). The sector was 30 m long and 10 m high, and itstop angle was 30°. The obstacles, when introduced, consisted of horizontal pipesof 0.315 m in diameter, arranged in grids. These experiments (Table 4.Ib) demon-strated the following points:

• Low-energy ignition of unobstructed propane-air and natural gas-air cloudsdoes not produce damaging overpressures.

• Combustion of a natural gas-air cloud in a highly congested obstacle arrayleads 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 apartially confined explosion produces a high combustion rate in the jet-flowregion.

• Interaction of a jet flame and an obstacle array can result in an increase offlame 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 anoverpressure of 60 mbar for hydrogen-air in a 10-m radius balloon (Schneider andPfortner 1981). For all other fuels, flame speeds were below 40 m/s and correspond-ing overpressures were below 35 mbar. Hence, weak ignition of an unconfined

Obstacle grids Polythene cover

Ignition

point

Fans

Gas supply

Pressure transducers

& Time-of-flight'

flame detectors

Arrow

shuttering walls

Inlets to recirculation ducts

Recirculation duct Concrete base

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

cloud in an unobstructed environment will generally not result in a damagingexplosion, even for relatively reactive fuels such as acetylene and hydrogen.

The introduction of obstacles results in some flame acceleration, especially forthe more reactive fuels. This effect is especially strong if the flame surface isdistorted by the presence of obstacles over its entire surface, such as were presentin the experiments of Dorge et al. (1976) and Harrison and Eyre (1986, 1987). Themore 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. Variousexperimental programs have been carried out simulating real accidents. Quantitiesof fuel were spilled, dispersed by natural mechanisms, and ignited. Full-scaleexperiments on flame propagation in fuel-air clouds are extremely laborious andexpensive, 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 uncon-fined environments free of obstacles, after dispersion of a vapor cloud by naturalmechanisms included

» LNG spill experiments in China Lake (Urtiew 1982); Hogan 1982; Goldwireet al. 1983);

• the Maplin Sands tests reported by Blackmore et al. (1982) and Hirst andEyre (1983).

These experiments are described in detail in Chapter 5, and will not be describedfurther here. The overall conclusion, from an explosion point of view, is that flamespeeds are relatively low, although atmospheric conditions alone may increase flamespeed 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 byA. 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 ablast-producing explosion.

Hoff (1983) studied the effect of igniting natural gas after a simulated pipelinerupture by firing a bullet into the gas mixture. The tests were on a 10-cm diameterpipeline operating at an initial pressure of 60 bar and a gas throughput of 400,000m3/day. The openings created in the pipeline simulated full-bore ruptures. Maximumflame speeds of approximately 15 m/s, and maximum overpressures of 1.5 mbarwere measured at a distance of 50 m.

Zeeuwen et al. (1983) observed the atmospheric disperion and combustion oflarge spills of propane (1000-4000 kg) on an open and level terrain on the Mus-selbanks, located on the south bank of the Westerscheldt estuary in the Netherlands(Figure 4.4). The main object of this experimental program was the investigationof blast effects from vapor cloud explosions. Flame-front velocities were highlydirectional and dependent upon wind speed. Average flame-front velocities of upto 10 m/s were registered. In one case, however, a transient maximum flame speedof 32 m/s was observed.

The presence of horizontal or vertical obstacles (Figure 4.4) in the propanecloud hardly influenced flame propagation. On the other hand, flame propagationwas influenced significantly when obstacles were covered by steel plates. Withinthe partially confined obstacle array, flame speeds up to 66 m/s were observed (Table4.2); they were clearly higher than flame speeds in unconfined areas. However, atpoints where flames left areas of partial confinement, flame speeds dropped to theiroriginal, low, unconfined levels.

Experiments to Investigate Effect of Source-Term Generated Turbulenceon Combustion

Giesbrech et al. (1981) published the results of experiments performed to determinethe intensity of pressure waves resulting from the rupture of liquefied gas vesselsand ignition of resulting vapor-air clouds. To this end, a series of small-scaleexperiments was performed in which vessels with sizes ranging from 0.226 to 10001, and containing propylene under 40 to 60 bar pressure, were ruptured. After apreselected time lag, vapor clouds were ignited by exploding wires, and ensuingflame 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-AirClouds under Uncontrolled Conditions

Reference

Linney(1990)

Goldwire et al.(1983)

Blackmore etal. (1982)

Hoff (1983)

Zeeuwen etal. (1983)

Giesbrecht etal. (1981)

Seifert andGiesbrecht(1986)

Stock (1987)

Configuration

Large-scale spills onland followed byignition


Large-scale spills onwater followed byignition

Ignition of spill aftersimulated pipelinerupture


Ignition of vaporclouds after vesselburst (0.226- 1000)

Ignition of vaporclouds after jetrelease

Ignition of vaporclouds after jetrelease

Fuel

Liquid H2

LNG

C3H8LNG

LNG

C3H8

C3H6

CH4H2

C3H8

Max. FlameSpeed(m/s)

13.3

2810

15

32 (withoutconfinement)

66 (withconfinement)

45

200

Max.Overpressure

(bar)

Low

0.02

0.05

0.22.0

0.2

Flame speed was observed to be nearly constant, but increased with the scaleof the experiment. Because mixing with air was limited, a volumetric expansionratio of approximately 3.5 was observed. The maximum pressure observed wasfound to be scale dependent (Figure 4.5).

Battelle (Seifert and Giesbrecht 1986) and BASF (Stock 1987) each conductedstudies on exploding fuel jets, the former on natural gas and hydrogen jets, and thelatter on propane jets. The methane and hydrogen jet program covered subcriticaloutflow 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 supercriticalwith orifice diameters of 10, 20, 40, 60, and 80 mm. The jets were started andignited after they had achieved steady-state conditions.

In the methane and hydrogen jet experiments, blast static overpressure wasmeasured at various distances from the cloud (Figure 4.6). The propane jet experi-

duration of positivepressure t* [ms]

damage analyses

maximumoverpressure*pmax [mbarj

ca lcu la ted pressurein cloud region Flixborough

197C

number ofexperiments

absolute f lameveloc i ty Sabs [m/s]

maximum flameveloci ty Sabs

vessel contents MVES [kg]

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

tnents on the other hand, produced measurements only of in-cloud static overpres-sures (Figure 4.7).

Summaries of results of these studies follow:

• In-cloud overpressure is dependent on outflow velocity, orifice diameter, andthe fuel's laminar burning velocity.

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

ORIFICE DIAMETER (mm)

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

• The maximum overpressure appeared to rise substantially when the jet waspartially confined between 2-m-high parallel walls and obstructed by some 0.5-m-diameter obstacles.

Conclusions from experiments on deflagrative combustion of fuel-air cloudsunder uncontrolled conditions follow:

• Flame acceleration was minimal after ignition of dispersed fuel-air cloudsunder unconfined conditions in the absence of obstacles.

• As previously demonstrated, the introduction of obstacles and partial confine-ment results in some flame acceleration (Zeeuwen et al. 1983).

• Source-term turbulence, as would be caused by vessel rupture or after a turbulentjet 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 partiallyconfined. Partial confinement affects the development of a gas explosion as follows:

MA

XIM

UM

EX

PLO

SIO

N P

RE

SS

UR

E (

mba

r)

• Pressure buildup in a gas explosion is caused by an interaction of expansionand combustion.

• Partial confinement hampers expansion and allows the introduction of a combus-tion enhancing flow structure.

• Additional shear- and turbulence-generating elements, such as bends and obsta-cles, will amplify feedback.

A first degree of confinement can be the introduction of parallel planes (cylindricalgeometry). In that configuration, combustion products can expand only in twodimensions. A second degree of confinement can be the introduction of a tube, thuspermitting expansion in only one dimension. Hybrid configurations, such as channelswhich are either open on top or covered by perforated plates, are also possible.Each of these configurations has been investigated extensively. Some of the mainresults are presented below.

Cylindrical Geometry

Cylindrical geometry is obtained by placing two plates parallel to each other andintroducing 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 flamepropagation between two plates 60 cm in diameter. Methane flame speeds of up to130 m/s were produced. Plates were later enlarged to 2.5 x 2.5 m, and methaneflame speeds up to 400 m/s, accompanied by an overpressure of 0.64 bar, wereproduced (Moen et al. 198Ob). Obstacled parameters were varied. The two mostsignificant variables were blockage ratio (ratio of area blocked by obstacles to totalarea) and pitch (the relative distance between two successive obstacles or obstaclerows). The positive feedback mechanism of flame-generated turbulence affecting

IGNITION WIRES

GAS OUTLETGAS 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 geome-try (2.5 x 2.5 m) as found by Moen et at. (198Ob). Tube spirals (diameter H = 4 cm) wereintroduced 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 determinedfor various obstacle configurations (Figure 4.9).

Van Wingerden and Zeeuwen (1983) demonstrated increases in flame speedsof methane, propane, ethylene, and acetylene by deploying an array of cylindricalobstacles between two plates (Table 4.3). They showed that laminar flame speedcan be used as a scaling parameter for reactivity. Van Wingerden (1984) furtherinvestigated the effect of pipe-rack obstacle arrays between two plates. Ignition ofan ethylene-air mixture at one edge of the apparatus resulted in a flame speed of420 m/s and a maximum pressure of 0.7 bar.

Hjertager (1984) reported overpressures of 1.8 bar and 0.8 bar for propane andmethane-air explosions, respectively, in a 0.5-m radial disk with repeated obstacles.

Van Wingerden (1989a) reports a comprehensive study into the effects of forest-like obstacle arrays (0.08-m diameter obstacles) on the propagation of flames in arectangular, double-plate apparatus of 2 X 4m. Rames propagated over distancesof up to 4 m from the point of ignition in some configurations. Ethylene-air mixturesgenerated 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 -AirClouds in Cylindrical Geometries

Reference

Moenetal. (1980a,b)

Van Wingerden andZeeuwen (1983)

Hjertager (1984)

Van Wingerden (1984)

Van Wingerden(1989a)

Configuration

Two plates diam. 2.5 mwith spiral tubeobstacles

Two plates 0.6 x 0.6 mwith forest ofcylindrical obstacles

Radial disk 0.5 m radiuswith pipes and flat-type obstacles

Two plates 0.5 m x 0.5 mpipe-rack obstacles

Two plates 4 m x 4 mpipe rack obstacles

Two plates verticalcylinders in concentriccircles (2 x 4 m)

Fuel

CH4H2S

CH4C3H8C2H4C3H8CH4

C2H4

C2H4

C2H4

Max.FlameSpeed(m/s)

40050

274040

225160

30

420

685

Max.Overpressure

(bar)

0.64

1.80.8

0.7

10.0

obstructed area. Obstacle parameters were varied over a wide range; flame speedsincreased with blockage ratio and pitch.

Some of these tests were repeated recently on a larger scale (scaling factor6.25) with ethylene, propane, and methane as fuels (Figure 4.10). Findings fromthe small-scale tests were generally confirmed. However, flame speeds and overpres-sures were higher than those found in the equivalent small-scale tests, and ethylenetests resulted in detonations. On the basis of some of the tests described above,Van Wingerden (1989b) argued that simple scaling of vapor cloud explosion experi-ments 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. Anoverview of research in tubes is, however, included for historical reasons. Anunderstanding of flame-acceleration mechanisms evolved from these experimentsbecause this mechanism is very effective in tubes.

Chapman and Wheeler (1926, 1927) conducted early flame-propagation experi-ments in tubes. They observed continuous flame acceleration and substantial in-creases in acceleration in tubes with internal obstructions (Table 4.4). These earlyfindings were subsequently confirmed by many others, including Dorge et al. (1979,

Figure 4.10. Large-scale test setup for investigation of flame propagation in a cylindrical geome-try. 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-AirClouds in Tubes

Reference

Chapman andWheeler (1926,1927)

Dorgeetal. (1981)

Chan etal. (1980)

Moenetal. (1982)Hjertager etal. (1984,

1988)Lee etal. (1984)

Configuration

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

2.5 m long pipe, D = 40mm with orifice plates

0.45 m, 63 mm ID pipeand 1.22 m, 152 mmID pipe both withorifices

10 m, 2.5m ID pipewith orifices

1 1 m, 50 mm ID pipe withorifices or spirals

Fuel

CH4

CH4

CH4

CH4

C3H8

H2

Max.FlameSpeed(mis)

420

770

550

500650

DDTa

Max.Overpressure

(bar)

3.9

12.0

10.9

4.013.9

DDTa

•DDT = deflagration-detonation transition.

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

1981), Chan et al. (1980), Lee et al. (1984), Moen et al. (1982), and Hjertager etal. (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 feedbackmechanism resulted in a transition to detonation for many fuels, even when thetubes were unobstructed. Introduction of obstacles into tubes reduced considerablythe distance required for transition to detonation.

A tube 10 m long and 2.5 m inside diameter was used for experiments withmethane (Moen et al. 1982) and propane (Hjertager et al. 1984). These often-citedexperiments 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. Aswith cylindrical geometry, explosions became more severe with increasing obsta-cle density.

Hjertager et al. (1988a) and Hjertager et al. (1988b) performed experiments inthe same tube. They showed that creating nonhomogeneous clouds in the tube byestablishing realistic leak sites (e.g., guillotine breaks in pipes and gasket failuresin flanges) resulted in pressure similar to or lower than those from homogeneousstoichiometric clouds. Nonstoichiometric clouds generate lower overpressures andflame speeds.

Experiments on a small scale with stoichiometric methane-air mixtures werecarried out by Chan et al. (1980). Comparisons of results of these experiments withthose performed by Moen et al. (1982) revealed that simple scaling is not possiblefor the results of explosions with very high flame speeds, in other words, flamespeeds resulting from very intense turbulence.

Channels

Several investigations were performed in channels (Table 4.5). In experiments inwhich the channel was completely confined, flame speed enhancements were similarto 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 x15 cm wide x 90 cm long. Obstacles of several heights were introduced into thetest chamber. Possibly because there was top venting, maximum flame speeds wereonly on the order of 20 m/s for propane-air mixtures.

Chan et al. (1983) studied flame propagation in an obstructed channel whosedegree of confinement could be varied by adjustment of exposure of the perforationsin 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 flamespeed 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 -AirClouds in Channels

Reference

Chan etal. (1983)

Urtiew(1981)

Elsworth et at. (1983)

Sherman etal. (1985)

Taylor (1987)

Configuration

Channel 1.22 m, 127 x203 mm2 baffles topventing

Channel 0.9 m, 0.3 x0.15 m baffles, opentop

Channel 52 m, 5 m, 1 -3m baffles, open top

Channel 30.5 m, 2.44 m,1 .83 m no obstalces

Channel 2 m, 0.05 x0.05 m obstacles topventing

Fuel

CH4

C3H8

C3H8

H2

C3H8

Max.FlameSpeed(mis)

350

20

12.3

DDTa

80

Max.Overpressure

(bar)

0.15

—

0.0

DDTa

—

a DDT =7deflagration-detonationtransition.

In an obstacle-free channel 30.5 m long x 2.44 m x 1.83 m, hydrogen-airmixtures detonated, both with a completely closed top and with a top opening of13% (Sherman et al. 1985).

Elsworth et al. (1983) report experiments performed in an open-topped channel52 m long X 5 m high whose width was variable from 1 to 3 m. Experiments wereperformed with propane, both premixed as vapor and after a realistic spill of liquidwithin the channel. In some of the premixed combustion tests, baffles 1-2 m highwere inserted into the bottom of the channel. Ignition of the propane-air mixturesrevealed typical flame speeds of 4 m/s for the spill tests, and maximum flamespeeds of 12.3 m/s in the premixed combustion tests. Pressure transducers recordedstrong oscillations, but no quasi-static overpressure.

Taylor (1987) reports some experiments performed in a horizontal duct (2 mlong, 0.05 x 0.05 m cross section). Obstacles were placed in the channel. Thetop of the duct could be covered by perforated plates with a minimum of 6% openarea. Terminal flame speeds of 80 m/s were reported for propane in a channel witha blockage ratio of 50% and a 12% open roof.

The channel experiments produced results similar to those from tubes. Introduc-tion of venting (decrease of the degree of confinement) greatly reduces effectivenessof the positive-feedback mechanism. Obstacles appear to enhance the combustionrate considerably.

4.1.4. Special Experiments

Various experiments that do not fall under any of the other categories but still worthmentioning are grouped here as "special experiments."

Several experiments with ethylene and hydrogen investigated the effects of jetignition on flame propagation in an unconfined cloud, or on flame propagation ina cloud held between two or more walls (Figure 4.11). Such investigations werereported by Schildknecht and Geiger (1982), Schildknecht et al. (1984), Stock andGeiger (1984), and Schildknecht (1984). The jet was generated in a 0.5 x 0.5 x1-m box provided with turbulence generators for enhancing internal flame speed.Maximum overpressures of 1.3 bar were observed following jet ignition of anethylene-air cloud contained on three sides by a plastic bag. In a channel confinedon three sides, maximum pressures reached 3.8 bar in ethylene-air mixtures. Atransition to detonation occurred in hydrogen-air mixtures.

One experiment (Moen et al. 1985) revealed that jet ignition of a lean acety-lene-air mixture (5.2% v/v) in a 4-m-long, 2-m-diameter bag can produce thetransition to detonation.

A detailed study performed by McKay et al. (1989) revealed some of theconditions necessary for a turbulent jet to initiate a detonation directly. Theseexperiments are covered in more detail in Section 4.1.5.

Pfortner (1985) reports experiments with hydrogen in a lane, 10 m long and 3x 3 m in cross section, in which a fan was used to produce turbulence. In theseexperiments, a transition to detonation occurred at high fan speeds.

high speed camerafree gas cloud

gas-air mixtureunder partial confinement

orificer u R f t u L b / v c eC-EA/eRf lToB

pressure transducerssampling stations forgas mixture analysis

ignition

structures in thegas cloud

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

Flame position, m

Figure 4.12. Flame speed-distance graph showing transition to detonation in a cyclohex-ane-air experiment (Harris and Wickens 1989).

Experiments without additional turbulence produced flame speeds no higherthan 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 mlong, open-sided apparatus. The first 9 m of the apparatus was modified by thefitting 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 highspeed could be further accelerated in unconfined parts of the apparatus, whereobstacles of pipework were installed. The initial flame speed in the unconfined partsof the apparatus could be modified by introduction of obstacles in the confined part.

Experiments were performed with cyclohexane, propane, and natural gas. Ina cyclohexane experiment, the flame emerged from the confined region at a speedof approximately 150 m/s, and progressively accelerated through the unconfinedregion containing obstacles until transition into a detonation occurred (Figure 4.12).Detonation continued to occur in the unconfined region. A similar result was foundfor 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 500m/s, then decelerated rapidly in the unconfined portion with obstacles. On the otherhand, flames emerging from the confined portion at speeds above 600 m/s continuedto propagate at speeds of 500-600 m/s in the obstructed, unconfined portion of the

Front elevation oftest enclosure

Confinedinitiatingregion

Region ofpipework obstacles

Unobstructedregion

Fla

me

speed,

m/s

cloud. There were no signs of transition to detonation. Once outside the obstructedregion, 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 ofmaintaining its postshock temperature above the mixture's autoignition temperatureover some span of time (Lee and Ramamurthi 1976, Sichel 1977). Ignition of avapor cloud by some high-explosive device capable of producing such a blastwave is not a credible accident scenario. Less-powerful ignition sources result indeflagration. A detonation, therefore, may develop only through interaction of theflame propagation process with its self-induced expansion flow. Laminar-flamepropagation is inherently unstable because of aerodynamic and possibly diffu-sional-thermal influences (Markstein 1964).

Aerodynamic instabilities arise from a flow field in the vicinity of a perturbed-flame front. The converging and diverging streamlines induce a pressure distributionthat tends to preserve and amplify the perturbations. Diffusional-thermal instabili-ties may occur if the reactants (fuel and oxygen) differ widely in molecular weight.The resulting difference in diffusivity may induce a nonhomogeneous distributionin the mixture composition near the reacting zone in a perturbed-flame front whichtends to preserve and amplify the perturbations. Such flame instability is dependenton 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 mosthighly reactive mixtures, such as acetylene-oxygen or hydrogen-oxygen mixtures(Sivashinsky 1979; Kogarko et al. 1966; Sokolik 1963). In relatively low-reactivefuel-air mixtures, these phenomena seem to be controlled by the property of awrinkled-flame front, which propagates normally to its orientation so as to reduceits area (Karlovitz 1951).

Deflagration to Detonation Transition (DDT)

In relatively low-reactive fuel-air mixtures, a detonation may only arise as a conse-quence of the presence of appropriate boundary conditions to the combustion pro-cess. These boundary conditions induce a turbulent structure in the flow ahead ofthe flame front. This turbulent structure is a basic element in the feedback couplingin the process by which combustion rate can grow more or less exponentiallywith time. This fundamental mechanism of a gas explosion has been described inSection 3.2.

The thermodynamic state of a reactive mixture just prior to combustion isdetermined by adiabatic compression and by turbulent mixing with combustion

products. The unburned mixture in front of the flame is thereby preconditioned forcombustion. If turbulent mixing becomes too intense, the combustion reaction mayquench locally, resulting in a hot and highly reactive mixture of reactants andcombustion products. If, at the same time, the autoignition temperature is exceededas a result of compression, the mixture ignites again.

Such "hot spots" react instantaneously as localized, constant volume sub-explo-sions (Urtiew and Oppenheim 1966; Lee and Moen 1980). If the mixture aroundsuch 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 attainedin the absence of strong compression. They detonated acetylene-oxygen, hydro-gen-oxygen, and hydrogen-chlorine mixtures by photochemical initiation. Themechanism was called "Shock-Wave Amplification by Coherent Energy Release"(SWACER). Although photochemical initiation is not considered a very likelyignition source in an accident scenario, the SWACER mechanism was also shownto trigger detonation when a highly reactive acetylene-oxygen mixture was initiatedby 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 theSWACER mechanism and trigger detonation.

A deflagration-detonation transition was first observed in 1985 in a large-scale experiment with an acetylene-air mixture (Moen et al. 1985). More recentinvestigations (McKay et al. 1988 and Moen et al. 1989) showing that initiation ofdetonation in a fuel-air mixture by a burning, turbulent, gas jet is possible, providedthe jet is large enough. Early indications are that the diameter of the jet must exceedfive 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 deflagrationprocess when the mixture in front of the flame is sufficiently preconditioned by acombination of compression effects and local quenching by turbulent mixing. How-ever, additional factors determine whether the onset of detonation can actuallyoccur and whether the onset of detonation will be followed by a self-sustainingdetonation wave.

The nature of the restrictive boundary conditions for detonation is closely relatedto the cellular structure of a detonation wave (Section 3.2.2). It was systematicallyinvestigated in a series of flame propagation experiments in obstacle-filled tubes byLee et al. (1984). The most important results are summarized below:

• In a smooth tube, the onset of detonation will take place only if the internaltube diameter is larger than about one characteristic-detonation-cell size.

• If the tube is provided with internal obstructions, the open area cross-sectionshould be greater than about three characteristic-cell sizes. Then detonation

manifests itself as "quasi-detonation," propagating at a speed which may beconsiderably lower than CJ-wave velocity. Because of the high loss of energyto the generation of turbulence in shear layers (drag), the leading shock wavedecays, and the reaction zone tends to decouple and quench. The detonationprocess is continually reinitiated in places where the leading shock is reflected.

• Only if internal passage dimensions exceed about 13 characteristic-cell sizeswill detonation manifest itself as a fully developed CJ-detonation wave.

• Transition from a planar mode propagating in a channel into a spherical modepropagating 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 thick-

ness to be able to sustain a detonation wave. Hence, a fully unconfined fuel-aircharge should be at least 10 to 13 characteristic-cell sizes thick in order to bedetonable. 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 onlya minor role in full-scale vapor cloud explosion incidents. Only pure methane-airmay 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 be-come significant. In practice, however, methane is often mixed with higher hydro-carbons which substantially augment the reactivity of the mixture and reduce itscharacteristic-cell size.

A fuel-air mixture is detonable only if its composition is between the detonabil-ity limits. The detonation limits for fuel-air mixtures are substantially narrowerthan their range of flammability (Benedick et al. 1970). However, the question ofwhether a nonhomogeneous mixture can sustain a detonation wave is more relevantto the vapor cloud detonation problem because, as described in Section 3.1, thecomposition of a vapor cloud dispersing in the atmosphere is, in general, farfrom homogeneous.

Experiments on the detonability of nonhomogeneous mixtures are scarce. Twoexperiments reported in the literature may shed some light on this matter. Bull etal. (1981) investigated the transmission of detonation across an inert region inhydrocarbon-air mixtures under unconfined conditions. The transmission of a hy-drocarbon-air detonation across an inert region in a tube was studied by Bjerketvedtand Sonju (1984) and Bjerketvedt, Sonju, and Moen (1986).

Although apparatus for these experiments differed significantly, results arestrikingly consistent. The experiments show that detonations in stoichiometric hydro-carbon-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 itselfin a nonhomogeneous mixture. In view of the mechanism of turbulent dispersiondescribed in Section 3.1, such conditions are to be expected in freely dispersingvapor clouds.

4.1.6. Summary

In the experiments described in Section 4.1, no explosive blast-generating combus-tion was observed if initially quiescent and fully unconfined fuel-air mixtureswere ignited by low-energy ignition sources. Experimental data also indicate thatturbulence is the governing factor in blast generation and that it may intensifycombustion to the level that will result in an explosion.

Turbulence may arise by two mechanisms. First, it may result either from aviolent release of fuel from under high pressure in a jet or from explosive dispersionfrom a ruptured vessel. The maximum overpressures observed experimentally injet combustion and explosively dispersed clouds have been relatively low (lowerthan 100 mbar). Second, turbulence can be generated by the gas flow caused bythe combustion process itself an interacting with the boundary conditions.

Experimental data show that appropriate boundary conditions trigger a feedbackin the process of flame propagation by which combustion may intensify to a detona-tive 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 invapor cloud explosions are often a part of industrial settings. Dense concentrationsof process equipment in chemical plants or refineries and large groups of coupledrail cars in railroad shunting yards, for instance, have been contributing causes ofheavy blast in vapor cloud explosions in the past. Furthermore, certain structuresin nonindustrial settings, for example, tunnels, bridges, culverts, and crowdedparking lots, can act as blast generators if, for instance, a fuel truck happens tocrash in their vicinity. The destructive consequences of extremely high local combus-tion rates up to a detonative level were observed in the wreckage of the Flixboroughplant (Gugan 1978).

Local partial confinement or obstruction in a vapor cloud may easily act as aninitiator for detonation, which may propagate into the cloud as well. So far, however,only one possible unconfined vapor cloud detonation has been reported in theliterature; it occurred at Port Hudson, Missouri (National Transportation SafetyBoard Report 1972; Burgess and Zabetakis 1973). In most cases the nonhomoge-neous structure of a cloud freely dispersing in the atmosphere probably prevents adetonation from propagating.

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4.2. OVERVIEW OF COMPUTATIONAL RESEARCH

If a quiescent, homogeneous fuel-air mixture is ignited, it is initially consumedby 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 inducea flow-field structure, that is, velocity gradients and turbulence by which the combus-tion is intensified. A higher combustion rate induces faster expansion, more intenseturbulence, faster combustion, and so on. This feedback coupling in the process offlame 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 describedas a process of combustion-driven expansion flow with the turbulent structure ofthe flow acting as a positive feedback mechanism. Combustion, turbulence, andgas dynamics in this complicated process are closely interrelated. Computationalresearch 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 ofcombustion-generated flow fields. This interaction is fundamentally multidimen-sional, and can only be computed by the most sophisticated numerical methods. Asimpler approach is only possible if the concept of a gas explosion is drasticallysimplified. 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 thatpropagates at some prescribed speed.

4.2.1. Analytical Methods

Scope

Analytical methods relate the gas dynamics of the expansion flow field to an energyaddition that is fully prescribed. A first step in this approach is to examine sphericalgeometry as the simplest in which a gas explosion manifests itself. The gas dynamicsof a spherical flow field is described by the conservation equations for mass, momen-tum, and energy:

(4.1)

(4.2)

(4.3)

Previous Page

where

p = densityu = velocitye = internal energyp = pressuret = timer = radial coordinate

This section describes how this set of equations can be solved analytically bythe introduction of various simplifications. First, gas dynamics is linearized, thuspermitting an acoustic approach. Next, a class of solutions based on the similarityprinciple is presented. The simplest and most tractable results are obtained fromthe most extensive simplifications.

Acoustic Methods

a. Expanding-piston solution according to Taylor (1946). An expanding pistonis a widely used concept to simulate the expansion associated with a propagatingflame. If only small disturbances in a quiescent medium are considered, the gasdynamics 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 = velocityp — PQ = overpressureP0 = ambient densityC0 = ambient speed of soundt = timer = radial coordinate

The solution of the wave equation must be an expression of the form: <|> = (Ur)f(r - c<f)The velocity potential for the flow field in front of an expanding piston surface cannow be derived from the boundary condition so that at its surface the mediumvelocity equals the piston velocity. In this way, Taylor (1946) found

(4.7)

from which the velocity and pressure fields may be readily derived:

(4.8)

(4.9)

where

Mp = piston Mach number7 = ratio specific heats

A piston Mach number may be related to a flame Mach number if, under thecondition of low overpressure, the mass enclosed by the piston flow field is equatedto 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 numbera = isobaric expansion ratio

The maximum values of velocity and pressure developed just in front of the flameare found by substituting:

(4.13)

b. Volume-source solution according to Strehlow (1981). Another conceptto simulate the expansion of reaction products in a combustion process is an acousticmonopole. 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 propagat-ing flames by

dd> dd>u = a? and P~?O= ~poif (4-15)

(4.16)

where V is a volume-source strength and can consequently be related to combustionprocess 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 small-flame Mach numbers.

The volume-source method is not only useful in a spherical approach, but canalso be used in more arbitrary geometries, where it is possible to express the volumesource strength in a product of burning velocity and flame surface area:

V= (a- I)S1A (4-19)

where

a = volumetric expansion ratioSb = burning velocityAf = flame surface area

This concept can be generalized for more arbitrarily shaped clouds, provided thata reasonable estimate can be made of combustion process development in terms ofburning velocity and flame surface area. According to Strehlow (1981), a conserva-tive 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-gener-ated flow field.

Strehlow (1981) elaborated these recommendations for a number of cases includinga centrally ignited cylinder slice. This resulted in a remarkable result:

(4.20)

where

7 = specific heats ratioa = volumetric expansion ratioH = cylinder slice heightAfb = burning velocity Mach numberRf = flame position

This equation shows that the maximum overpressure, generated by a constant veloc-ity flame front, continually decreases as it propagates. Modeling an explosion ofan extended flat vapor cloud by a single monopole located in the cloud's center isnot, 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 concentratedin the cloud's center, but instead distributed over the entire area covered by a flatcloud. This concept was elaborated by Auton and Pickles (1978, 1980) for pancake-shaped clouds. They simulated the flow field generated by combustion by a continu-ous distribution of volume sources with a strength proportional to local cloudheight. Flame propagation was modeled by sweeping a zone of finite width overthe distribution of sources. During its passage, the zone activates the sources gradu-ally. This idea resulted in the following construction. The acoustic monopole veloc-ity potential function, <|>am, for half-space is

(4.21)

Assuming that a source produces its total volume within STT seconds during flamepassage, the volume source strength, V9 may be expressed in a suitable function:

(4.22)

where

H = cloud heighta = volumetric expansion ratio

This function expresses a volume production during flame passage which startsslowly, speeds up, and gradually declines again. The flow field generated at timet upon ignition somewhere in the environment can be computed by superposition

of the acoustic signals of all contributing sources. The contributing sources arethose 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 assump-

tion in this procedure is that the speed at which the sources are activated equalsthe speed at which the activation zone is propagated. This holds only if the flamepropagates into a quiescent mixture, which does not really happen. Computationalexperiments with the proposed model show that this assumption is increasinglyjustified as a cloud's aspect ratio increases.

A similar acoustic technique was applied by Pickles and Bittleston (1983) toinvestigate blast produced by an elongated, or cigar-shaped, cloud. The cloud wasmodeled as an ellipsoid with an aspect ratio of 10. The explosion was simulatedby a continuous distribution of volume sources along the main axis with a strengthproportional to the local cross-sectional area of the ellipsoid. The blast producedby such a vapor cloud explosion was shown to be highly directional along themain axis.

These results were analytically reproduced by Taylor (1985), who employeda velocity potential function for a convected monopole. This concept makes itpossible to model an elongated vapor cloud explosion by one single volume sourcewhich is convected along the main axis at burning velocity, and whose strengthvaries proportionally to the local cross-sectional cloud area.

Similarity Methods

Self-similarity applies to one-dimensional, time-dependent problems in which de-pendence on one of two independent variables can be eliminated by nondimen-

Source ac t ivab ion zone

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

sionalization of the other. The postulate of self-similarity applies as well to constant-velocity, piston-driven, spherical-flow fields. If, for instance, the coordinate isnondimensionalized, the distribution of gas-dynamic-state parameters is independentof time. Because an expanding piston has proven to be a useful concept in simulationof flame-generated expansion, it is not surprising that a renewed interest in similaritymethods has arisen during the last two decades. The Kuhl et al. (1973) paperoccupies a central position because, in this paper, the classical solution of a piston-driven flow field by Taylor (1946) was related to that in front of a propagatingflame. Therefore, this paper is treated in some detail below.

The similarity solution for a flow field in front of a steady piston is a specialcase from a much larger class of similarity solutions in which certain well-definedvariations in piston speed are allowed (Guirguis et al. 1983). The similarity postulatefor variable piston speed solutions, however, sets stringent conditions for the gas-dynamic state of the ambient medium. These conditions are unrealistic within thescope of these guidelines, so discussion is confined to constant-velocity solutions.

Solving the gas dynamics expressions of Kuhl et al. (1973) requires numericalintegration of ordinary differential equations. Hence, the Kuhl et al. paper wassoon followed by various papers in which KuhTs numerical "exact" solution wasapproximated 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 gas-dynamic discontinuity, namely, a shock followed by a monotonic increase in gas-dynamic variables toward the piston. If both shock and piston are regarded asboundary conditions, the intermediate flow field may be treated as isentropic. There-fore, 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 momentuminto a set of two simultaneous ordinary differential equations:

(4.23)

(4.24)

where

u = particle velocityc = speed of sound

r = coordinaters = leading shock coordinateUs = leading shock speed*y = 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 leadingshock, is met. The leading shock is found by continuous testing of the solution tothe shock jump condition expressed as

(4.25)

Now the distribution of the gas-dynamic variables can be computed from the isen-tropic relations:

where T = temperature, p = pressure, and p = density. Subscript "s" refers hereto the postshock location in the flow field, whereas in previous equations it refersto the leading shock.

Once the piston-driven flow field is known, the flame-driven flow field is foundby fitting in a steady flame front, with the condition that the medium behind it isquiescent. This may be accomplished by employing the jump conditions whichrelate the gas-dynamic states on either side of a flame front. The condition that thereaction products behind the flame are at rest enables the derivation of expressionsfor the density ratio, pressure ratio, and heat addition

(4.26)

(4.27)

(4.28)

where

R = density ratioP = pressure ratioq = heat addition

h = enthalpyy = ratio of specific heats

The subscripts "r" and "p" refer to the states of the reactants just in front of, andthe combustion products just behind, the flame front, respectively.

Since reactants are compressed in the flow field prior to combustion, heataddition takes place at an elevated temperature. If combustion is modeled as asimple heat addition to a medium whose specific heat does not change, q equalsthe heat of combustion Q at ambient temperature.

However, heat properties of reactants and products usually differ. Then q canbe 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 maybe evaluated for any position throughout the flow field. The location of the flamefront is found where Q matches the heat of combustion of the fuel-air mixture inquestion. If the coordinate of the front X1 is known, the burning velocity Machnumber can be computed from

(4.30)

where

5b = burning velocityC0 = ambient speed of soundX1 = nondimensional flame coordinateF8 = nondimensionalized particle velocity just behind

the leading shock

The formulation above allows a more general equation of state for the combustionproducts (Kuhl 1983). The method described breaks down for low piston velocities,where the leading shock Mach number approaches unity. In such cases, the numeri-cal 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 forlow flame speeds, where the strength of the leading shock approaches zero. Tocomplete the entire range of flame speeds, Kuhl et al. (1973) suggested using theacoustic solutions by Taylor (1946) as presented earlier in this section. Taylor(1946) already noted that his acoustic approach is not fully compatible with theexact solution, in the sense that they do not shade into one another smoothly. Inparticular, the near-piston and the near-shock areas in the flow field, where nonlineareffects play a part, are poorly described by acoustic methods. In addition to theseimperfections, the numerical character of Kuhl et al. (1973) method inspired variousauthors to design approximate solutions. These solutions are briefly reviewed.

A simple method to estimate the overpressure generated by constant-velocityflames was suggested by Strehlow (1975); a summary follows. The change indensity 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 isdescribed by shock-jump conditions. Now the problem can be solved by relatingthe flame Mach number and the shock Mach number.

Strehlow (1975) achieved a solution by conducting a mass balance over theflow field. Such a balance can be drawn up under the assumptions of similarity anda constant density between shock and flame. The assumption of constant densityviolates the momentum-conservation equation, and is a drastic simplification. Themaximum overpressure is, therefore, substantially underestimated over the entireflame speed range. An additional drawback is that the relationship of overpressureto flame speed is not produced in the form of a tractable analytical expression, butmust be found by trial and error.

For different regions in the flow field in front of an expanding piston, separatesolutions in the form of asymptotic expansions may be developed. An overallsolution can be constructed by matching these separate solutions. This mathematicaltechnique was employed by several authors including: Guirao et al. (1976), Gorevand 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 ofthe near-piston region for low piston Mach-numbers by Guirao et al. (1976) andGorev and Bystrov (1985). The linearized equations, however, provided a singlesolution at the location of the leading shock.

In the solution for this problem, the methods of Guirao et al. (1976) and ofGorev and Bystrov (1985) differ. Guirao et al. (1976) employed the so calledPoincare-Kuo-Lighthill method to "stretch" the coordinate in the vicinity of thesingularity. In this way, two separate solutions were found: one for the near-shockregion and one for the rest of the flow field. They were matched where the accuracyof both solutions is acceptable. A "kink" in the resulting distributions of flow-fieldparameters is inevitable.

To prevent this kink, Gorev and Bystrov (1985) suggested a correction by aproperly chosen coordinate transformation. The substitution was chosen in such away that the equations after linearization describe the desired behavior in the near-shock region during the period when the influence of the correction fades graduallytowards the piston. In this way, Gorev and Bystrov (1985) obtained an approximatesolution 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 roleas well. As already pointed out by Taylor (1946), the near-piston flow regime maybe well approximated by the assumption of incompressibility. For each of theseregions, Deshaies and Clavin (1979) developed solutions in the form of asymptoticexpansions in powers of small piston Mach number. These solutions are supposedto hold for piston Mach numbers lower than 0.35.

The approxmations reviewed so far were all developed for the low-piston Machnumber regime. Cambray and Deshaies (1978), on the other hand, developed asolution of the similarity equations by asymptotic expansions in powers of high-piston Mach numbers. These solutions are supposed to hold for piston Mach numbershigher than 0.7. Finally, Cambray et al. (1979) suggested an interpolation formulato cover the intermediate-piston Mach number range.

In order to permit brief evaluation of the qualities of the approximate analyticalsolutions reviewed, some of the expressions given in the respective papers havebeen 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 Cambrayand Deshaies (1978) are depicted together with "exact" similarity solutions forvarious piston Mach numbers in Figures 4.14-4.16. The solutions are representedby taking the leading shock's coordinate equal to one, while the gas dynamicvariables are nondimensionalized with ambient medium properties, as usual. Thepictures speak for themselves with regard to the extent to which the respectiveanalytical approximations meet their objectives.

KUHL ET AL .

GUIRAO ET OL.

non-D

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ES

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non-D

imensi

onflL

iza)

VE

LOC

ITY

non-DifncnsionALizED RADIUS non-DimEnsiono-izED RADIUS

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

KUHL CT AL«

GOREW AHD BVSTPOYno

n-D

Hne

nsio

npLi

ZB

D O

VERP

RESS

URE

non-

oim

Ens

iono

LizE

D U

ELO

CIT

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non-DimEnsionALiZED RADIUS norvoiinEnsionAuzED RADIUS

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

KUHL ET AL,

CAmBRAV ADD DESHAIES

non-

Dim

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ionA

LiZE

D O

VERP

RESS

URE

non-

Dim

Ens

tonA

LizE

D U

ELO

CIT

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non-DimcnsionALizcD RADIUS noo-DimensiorwuzED RADIUS

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

4.2.2. Numerical Methods

Scope

Acoustic and similarity methods provide useful information in relation to the mecha-nism of blast generation by gas explosions. These methods of solution, however,require drastic simplifications such as, for instance, symmetry and constant flamespeed. Consequently, they describe only hypothetical problems. In point of fact,because of a complex of flame-flow interactions, freely propagating flames donot have constant flame speeds. Furthermore, these methods do not cover decaycharacteristics.

In principle, numerical methods make it possible to solve the gas dynamics ofexplosions without any restriction. The development of numerical methods, how-ever, is largely determined by developments in computational fluid dynamics andcomputing technology. Consequently, the nature of published methods range fromvery simple methods capable of simulating one-dimensional, nonreactive, zero-viscosity flow to highly sophisticated methods capable of simulating the multidimen-sional process of premixed combustion in detail. In this section, these methods willbe 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 bytwo different gas-dynamic discontinuities:

• a contact discontinuity between the expanding combustion products and thesurrounding inert atmosphere;

• a shock phenomenon which may be formed during blast generation, but mayalso develop later as a result of nonlinear effects in the propagation mechanismof a blast wave.

In general, discontinuities constitute a problem for numerical methods. Numericalsimulation of a blast flow field by conventional, finite-difference schemes resultsin a solution that becomes increasingly inaccurate. To overcome such problems andto achieve a proper description of gas dynamic discontinuities, extra computationaleffort is required. Two approaches to this problem are found in the literature onvapor cloud explosions. These approaches differ mainly in the way in which theextra computational effort is spent.

The Lagrangean Artificial-Viscosity Approach

As a consequence of implicit mass conservation, the gas-dynamic conservationequations, expressed in Lagrangean form, can describe contact discontinuities. Toprevent oscillating behavior in places where shock phenomena are resolved in the

solution, a Von Neumann-Richtmyer artificial-viscosity term is added. In order toaffect only places where gradients are large, the artificial-viscosity term may beexpressed in local-state variables in various ways (Von Neumann and Richtmyer1950; Erode 1955, 1959; and Wilkins 1969).

Finite-difference schemes used to solve Lagrangean gas dynamics have beendescribed many times (Richtmyer and Morton 1967; Brode 1955, 1959; Oppenheim1973; Luckritz 1977; MacKenzie and Martin 1982; Van Wingerden 1984; and Vanden Berg 1984).

The Eulerian FCT Approach

A drawback of the Lagrangean artificial-viscosity method is that, if sufficient artifi-cial viscosity is added to produce an oscillation-free distribution, the solution be-comes fairly inaccurate because wave amplitudes are damped, and sharp discontinu-ities are smeared over an increasing number of grid points during computation. Toovercome these deficiencies a variety of new methods have been developed since1970. Flux-corrected transport (FCT) is a popular exponent in this area of develop-ment in computational fluid dynamics. FCT is generally applicable to finite differ-ence 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 conserva-tion equations involving shock phenomena exhibits oscillatory behavior which iscontinually amplified. To stabilize the solution, it is artificially diffused. To obtaina solution of higher quality than those obtained from artificial-viscosity methods, thediffused solution should be improved. For this purpose, the solution is "antidiffused"again. However, to prevent reintroduction of the unstable oscillatory behavior, theantidiffusion is corrected in such a way that it does not generate new maximaor minima or accentuate any existing extremes. Manipulation of diffusion andantidiffusion makes it possible to optimize the numerical algorithm in the sensethat 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 reducedand its initial pressure increased, the problem more closely approaches a point-source explosion problem. Brode (1955,1959) used the Lagrangean artificial-viscos-ity approach, which was the "state of the art" of that time. He analyzed blastsproduced by both aforementioned sources. The decaying blast wave was simulated,and blast wave properties were registered as a function of distance. The codereproduced experimentally observed phenomena, such as overexpansion, subse-quent recompression, and the formation of a secondary wave. It was found that theshape of the blast wave at some distance was independent of source properties.

The code reproduced shock-jump conditions well, but many details in the solutionwere lost because of the smearing effect of artificial viscosity.

A similar technique was used by Oppenheim et al. (1977) to analyze the blastwaves 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 ofsimilarity methods (Section 4.2.1) and used to provide initial conditions for numeri-cal computations. The main conclusion was that blast waves at some distance fromthe charge were very similar, regardless of whether the combustion mode wasdetonation or strong deflagration.

A similar computational exercise was performed by Guirao et al. (1979). Theyused 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), theyinitialized numerical computations with flow fields calculated by similarity methods.The efficiency of conversion of chemical energy (heat of combustion) into mechani-cal energy (blast) was determined by calculation of the work done by the cloud'sinterface during the positive overpressure phase of the expansion. The conclusionof Oppenheim et al. (1977), that the blast produced is only weakly dependent onthe combustion mode, was confirmed. On the other hand, the exercise revealed thatfuel-air detonation is considerably more effective in converting chemical energyinto mechanical energy than fuel-oxygen detonation.

The conclusions of Guirao et al. (1979) were fully in line with an earlier paperby Fishburn (1976). Fishburn (1976) analyzed the effectiveness of blast generationfor 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, anda 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 wascoded to take place within a zone of several cell widths and is moved over the gridat a prescribed speed. In this way, the process of blast generation was simulated,eliminating the requirement to begin the numerical blast-decay simulation with aprecomputed flow field. Moreover, the heat capacity ratio of the fluid was allowedto vary over the heat-addition zone. The coding of this feature was facilitated bythe Lagrangean character of the grid. Fishburn (1976) showed that implementationof the CJ-detonation velocity results in a flow field which compares well with aself-similar Taylor detonation wave. As with Guirao et al. (1979), Fishburn triedto find the most effective way to convert the chemical energy of the explosiveinto blast.

Whereas Fishburn was mainly interested in the detonative mode of explosion,Luckritz (1977) and Strehlow et al. (1979) focused on the simulation of generationand decay of blast from deflagrative gas explosions. For this purpose, they employeda 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 numeri-cal scheme for the solution of the gas-dynamic conservation equations, is an idealiza-tion which does not reflect realistic behavior in the large temperature rangeconsidered.

To overcome this problem, they proposed a "working-fluid heat-additionmodel." This model implies that the gas dynamics are not computed on the basisof real values for heat of combustion and specific heat ratio of the combustionproducts, but on the basis of effective values. Effective values for the heat additionand product specific heat ratios were determined for six different stoichiometricfuel-air mixtures. Using this numerical model, Luckritz (1977) and Strehlow etal. (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 acceler-ating 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 equalto the highest flame speed observed results in a conservative estimate of itsblast 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 blast-simulation code on the basis of a flux-corrected transport module of Boris (1976).Although the FCT module solves Eulerian gas dynamics, the grid was manipulatedin a Lagrangean way. Because the model implicitly conserves mass, a Lagrangeangrid allows an accurate and simple energy addition. In this way, the qualities ofboth approaches—heat addition in the Lagrangean grid and shock representationby flux-corrected transport—were combined. The performance of both approaches,

Lagrangean artificial viscosity and Eulerian FCT, was tested extensively. Flowfields generated by constant-velocity flames were compared to self-similar flowfields. In addition, a large number of flame-propagation experiments were simulated(Van Wingerden, 1984, and Van den Berg, 1984). In many respects, the perform-ance of the FCT code was found to be superior, particularly with respect to shockrepresentation and conservation of details in blast waves during propagation.

The flux-corrected-transport technique was also used by Phillips (1980), whosuccessfully simulated the process of propagation of a detonation wave by a verysimple mechanism. The reactive mixture was modeled to release its complete heatof combustion instantaneously after some prescribed temperature was attained bycompression. A spherical detonation wave, simulated in this way, showed a correctpropagation velocity and Taylor wave shape.

Two-Dimensional Methods

Fishburn et al. (1981) used the HEMP-code of Giroux (1971) to simulate gasdynamics resulting from a large cylindrical detonation in a large, flat, fuel-aircloud containing 5000 kg of kerosene. Blast effects were compared with thoseproduced by a 100,000-kg TNT charge detonated on the ground.

In addition, the numercial simulations were compared with an experiment inwhich a large heptane aerosol-air cloud was detonated. This exercise may beregarded as a continuation of previous work of Fishburn (1976), reviewed earlierin this section. Fishburn's conclusions may be summarized as follows:

• Experimentally observed behavior was qualitatively reproduced by numericalsimulation.

• The fuel-air explosion produced, in a large area covered by the cloud, substan-tially higher blast pressures than would be expected from a 100,000-kg TNTsurface blast.

Raju and Strehlow (1984) used a two-dimensional, finite-difference code tostudy the effects produced by three representative modes of vapor cloud explosion:

• a bursting, pressurized spheroid as a model for a constant-volume explosion ofan 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 Shursha-lov's (1973) modification, which makes it possible to treat the leading shock waveof the flow field and the contact discontinuity between burned and unburned materialas boundaries of a moving-grid network. The flame front was treated as a "two-gamma, working-fluid, heat-addition model," mentioned earlier. The simulationsresulted in some interesting conclusions.

• Near-field blast effects were found to be highly directional for the spheroidburst and the cylindrical detonation.

• Deflagrative combustion of an extended, flat vapor cloud is very ineffective inproducing damaging blast waves because combustion products have a high rateof side relief accompanied by vortex formation.

• The very first stage of flame propagation upon ignition, during which the flamehas a spherical shape, mainly determines the blast peak overpressure producedby the entire vapor cloud explosion.

These findings qualitatively confirm the results obtained with the simple acousticmethods, discussed previously.

A much more pronounced vortex formation in expanding combustion productswas found by Rosenblatt and Hassig (1986), who employed the DICE code tosimulate deflagrative combustion of a large, cylindrical, natural gas-air cloud.DICE is a Eulerian code which solves the dynamic equations of motion using animplicit difference scheme. Its principles are analogous to the ICE code describedby Harlow and Amsden (1971).

Combustion was modeled as a heat addition within a zone which is propagatedat burning velocity relative to expansion flow. The higher rate of side relief, in-cluding vortex formation, is a direct consequence of the incorporation of gravity,which makes it possible to simulate the buoyancy of low-density combustion prod-ucts. Buoyancy generates large, upward velocities at the expense of expansion flowin front of the flame. As a consequence, the flame propagates at a speed which isonly about twice its burning velocity.

With respect to blast effects, Rosenblatt and Hassig's (1986) conclusions arefully in line with those of Raju and Strehlow (1984). Except in a limited area atthe cloud's edge, the blast peak overpressures are produced by the very first stageof 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 ofenergy at a given speed. The fundamental mechanism of a gas explosion, namely,feedback in combustion-flow interaction, was not utilized. As a consequence, thebehavior of a freely propagating, premixed, combustion process, which is primarilydetermined by its boundary conditions, was unresolved.

The availability of large and fast computers, in combination with numericaltechniques to compute transient, turbulent flow, has made it possible to simulatethe 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 energyaddition. Energy is supplied by combustion, which is modeled as a one-step conver-sion process of reactants into combustion products. The conversion (combustion)

rate, which is primarily controlled by turbulence, is modeled according to theconcept of the eddy-dissipation model (Magnussen and Hjertager 1976). The turbu-lent structure of the flow is described with a k-e turbulence model (Launder andSpalding 1972). This concept was mathematically formulated in conservation equa-tions for mass, momentum, energy, fuel-mass fraction, turbulence kinetic energy,and the dissipation rate of turbulence kinetic energy. Omitting details, it can beexpressed 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 = densityu = particle velocitye = cvT + m^flc = energyk = turbulence kinetic energy€ = dissipation rate of turbulence kinetic energyIHf11 = fuel mass fractionp = static pressure

F* = turbulence transport coefficientRto = — Ape/k,F(Wfu) = combustion ratecv = specific heat (constant volume)T = temperatureHc = heat of combustion

The major mechanism of a vapor cloud explosion, the feedback in the interactionof combustion, flow, and turbulence, can be readily found in this mathematicalmodel. The combustion rate, which is primarily determined by the turbulenceproperties, 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 isdescribed by the equation for conservation of energy. This internal energy distribu-tion is translated into a pressure field which drives the flow field through momentumequations. The flow field acts as source term in the turbulence model, which resultsin a turbulent-flow structure. Finally, the turbulence properties, together with thecomposition, determine the rate of combustion. This completes the circle, the feed-back in the process of turbulent, premixed combustion in gas explosions. The set ofequations has been solved with various numerical methods: e.g., SIMPLE (Patankar1980); SOLA-ICE (Cloutman et al. 1976).

Over the years, this concept was refined in several ways. A scale dependencywas modeled by the introduction of scale-dependent quenching of combustion. Thefirst stage of the process was simulated by quasi-laminar flame propagation. Inaddition, three-dimensional versions of the code were developed (Hjertager 1985;Bakke 1986; Bakke and Hjertager 1987). Satisfactory agreement with experimentaldata 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. Thesetechniques will probably remain research tools, rather than routine evaluation meth-ods, until such time as available computing power and algorithm efficiencygreatly increase.

The concept of numerical simulation of turbulent premixed combustion in gasexplosion has also been adopted by others:

• Kjaldman and Huhtanen (1985) arrived at a similar concept on the basis of themultipurpose 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 aquantity of fuel constitutes a potential explosion hazard. If a quantity of flammablematerial is released, it will mix with air, and a flammable vapor cloud may result. If

Next Page

F* = turbulence transport coefficientRto = — Ape/k,F(Wfu) = combustion ratecv = specific heat (constant volume)T = temperatureHc = heat of combustion

The major mechanism of a vapor cloud explosion, the feedback in the interactionof combustion, flow, and turbulence, can be readily found in this mathematicalmodel. The combustion rate, which is primarily determined by the turbulenceproperties, 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 isdescribed by the equation for conservation of energy. This internal energy distribu-tion is translated into a pressure field which drives the flow field through momentumequations. The flow field acts as source term in the turbulence model, which resultsin a turbulent-flow structure. Finally, the turbulence properties, together with thecomposition, determine the rate of combustion. This completes the circle, the feed-back in the process of turbulent, premixed combustion in gas explosions. The set ofequations has been solved with various numerical methods: e.g., SIMPLE (Patankar1980); SOLA-ICE (Cloutman et al. 1976).

Over the years, this concept was refined in several ways. A scale dependencywas modeled by the introduction of scale-dependent quenching of combustion. Thefirst stage of the process was simulated by quasi-laminar flame propagation. Inaddition, three-dimensional versions of the code were developed (Hjertager 1985;Bakke 1986; Bakke and Hjertager 1987). Satisfactory agreement with experimentaldata 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. Thesetechniques will probably remain research tools, rather than routine evaluation meth-ods, until such time as available computing power and algorithm efficiencygreatly increase.

The concept of numerical simulation of turbulent premixed combustion in gasexplosion has also been adopted by others:

• Kjaldman and Huhtanen (1985) arrived at a similar concept on the basis of themultipurpose 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 aquantity of fuel constitutes a potential explosion hazard. If a quantity of flammablematerial is released, it will mix with air, and a flammable vapor cloud may result. If

Previous Page

the flammable mixture finds an ignition source, it will be consumed by a combustionprocess which, under appropriate (boundary) conditions, may develop an explosiveintensity and blast.

It is highly desirable that vapor cloud explosion hazards be reduced by appropri-ate risk management measures. If possible, separation between large storage ormanufacturing areas and residential areas should be sufficient to eliminate the riskof blast damage. This may not be an option for those working at a chemical plantor refinery. Designers should consider the possibility of a vapor cloud explosion inthe siting and design of process plant buildings.

For these and other purposes, blast-modeling methods are needed in order toquantify 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 equivalentexplosive charge whose blast characteristics, that is, the distribution of the blast-wave 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 highexplosives (e.g., Robinson 1944, Schardin 1954, Glasstone and Dolan 1977, andJarrett 1968). Therefore, relating the explosive power of an accidental explosionto an equivalent TNT charge is an understandable approach. Thus, damage patternsobserved in many major vapor cloud explosion incidents have been related toequivalent TNT-charge weights.

Because the need to quantify the potential explosive power of fuels arose longbefore the mechanisms of blast generation in vapor cloud explosions were fullyunderstood, the TNT-equivalency concept was also utilized to make predictiveestimates, 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 equivalentcharge weight of TNT with the following formula:

(4.37)

where

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

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

If the equivalent weight of TNT is known, the blast characteristics, in termsof the peak side-on overpressure of the blast wave, can be derived for varyingdistances from the explosion. This is done using a chart containing a scaled, graphi-cal representation of experimental data. Various data sets are available that maydiffer substantially. In Figure 4.17, for instance, two blast curves (peak side-onoverpressure versus scaled distance) are presented. They are different because theyresult 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 methodsare the simplest means of modeling vapor cloud explosions. TNT equivalency canbe regarded as a conversion factor by which the available heat of combustion canbe converted into blast energy. In one sense, TNT equivalency expresses the effi-ciency of the conversion process of chemical energy (heat of combustion) intomechanical energy (blast).

In a numerical exercise described in section 4.2.2, it was shown that, for astoichiometric, hydrocarbon-air detonation, the theoretical maximum efficiency ofconversion of heat of combustion into blast is equal to approximately 40%. If theblast energy of TNT is equal to the energy brought into the air as blast by a TNTdetonation, a TNT equivalency of approximately 40% would be the theoreticalupper limit for a gas explosion process under atmospheric conditions. However,the initial stages in the process of shock propagation in the immediate vicinity of

Ove

rpre

ssur

e (

Psi

)

Pea

k ov

erpr

essu

re (

Psi

)

(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 andPanill 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. Ifthis loss of energy is taken into account, the TNT equivalency for a gas detonationat lower blast overpressure levels is expected to be substantially higher than 40%.

Furthermore, accidental vapor cloud explosions are anything but detonationsof the full amount of available fuel. Therefore, practical values for TNT equivalen-cies of vapor cloud explosions are much lower than the theoretical upper limit.Reported values for TNT equivalency, deduced from the damage observed in manyvapor cloud explosion incidents, range from a fraction of one percent up to sometens of percent (Gugan 1978 and Pritchard 1989). For most major vapor cloudexplosion incidents, however, TNT equivalencies have been deduced to range from1% 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 generallyinvolved in actual explosive combustion.

Methods for vapor cloud explosion blast prediction based on TNT equivalencyare widely used. Over the years, many authors, companies, and authorities havedeveloped their own procedures and recommendations with respect to issues sur-rounding such predictions. Some of the differences in these procedures includethe following:

• The portion of fuel that should be included in the calculation: The total amountreleased; 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 fromobservations in major incidents; or a safe and conservative value (whether ornot dependent on the presence of partial confinement/obstruction and nature ofthe fuel).

• The TNT blast data used: A substantial scatter in the experimental data on high-explosive blast can be observed which is due to differences in experimentalsetup. Although often referenced differently, most recommendations can betracked back to ground burst data developed by Kingery and Pannill (1964).

• The energy of explosion of TNT: Values currently in use range from 1800 to2000 Btu/lb, which correspond to 4.19 to 4.65 MJ/kg.

Below are examples of some of the many different approaches used. Their propo-nents' recommendations are quoted as literally as possible. Some of them aredemonstrated 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 torepresent blast parameter distributions, and the US Atomic Energy Commission'srecommendations (Glasstone 1962) for the attendant structural damage. Brasie andSimpson (1968) base their recommendation for the TNT equivalency of vapor cloudson the damage observed in three chemical-plant explosion incidents. Analyzing the

damage in these incidents, they deduced a TNT yield which is highly dependenton the distance to the explosion center.

Although values for TNT equivalency ranging from 0.3% to 4% have beenobserved, Brasie and Simpson recommend, for predictive purposes, conservativevalues for TNT equivalency as follows: 2% for near-field, and 5% for far-fieldeffects (based on energy), applied to the full quantity of fuel released.

In a later paper, Brasie (1976) gives more concrete recommendations for deter-mining the quantity of fuel released. A leak potential can be based on the flashingpotential of the full amount of liquid (gas) stored or in process. For a continuousrelease, a cloud size can be determined by estimating the leak rate. For a combinedliquid-vapor flow through holes of very short nozzles, the leak rate (mass flow perleak 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 isoperating overpressure in bars. This estimation formula seems to give reasonableanswers up to about 2 to 70 bars operating overpressure. It is not valid beyond thethermodynamic critical pressure. The leak rate may be factored for the actual flashfraction. The flow rate of release, W9 can be found as the product of the mass fluxand the cross sectional area of the leak orifice. The weight of flammable fuel inthe cloud can be estimated by multiplying the rate of release by the time spanneeded to attain the lower flammability limit in the drifting plume. In a conservativeapproach, for stable atmospheric conditions (characterized by an ambient windspeed of 2.23 m/s), the time span can be approximated by

(4.39)

where

tf = time span (s)W = rate of release (kg/s)M = molecular weight (kg/kMol)/ = lower flammability limit (vol%)

TNT equivalency should be applied to the quantity of fuel calculated with theabove equations. For planning purposes, Brasie (1976) recommends the use of TNTequivalencies of 2%, 5%, and 10% (based on energy) in calculations to determinethe sensitivity of geometry to the yield.

UT Research (Eichler and Napadensky 1977)

In their research to determine safe stand-off distances between transportation routesand nuclear power plants, Eichler and Napadensky (1977) recognized that the

blast effects produced by vapor cloud explosions are highly dependent on mode ofcombustion. They recognized the possibility that rapid deflagration or detonationof all combustibles involved might result in much higher TNT equivalencies thanthose recommended by Brasie and Simpson (1968) and others. In addition, theyrecognized that blast effects from vapor cloud explosions are often highly direc-tional. Therefore, they determined an upper limit of TNT equivalency for vaporcloud explosions by analyzing the blast produced in experiments in which sphericalfuel-air charges of varying compositions were detonated (Kogarko et al. 1966;Balcerzak et al. 1966; Woolfolk and Ablow 1973). They concluded that the blastfrom a detonating fuel-air charge can be reasonably well represented by TNTblast data. Because a distance-dependent TNT equivalency was anticipated, theydetermined TNT equivalency for stoichiometric fuel-air charges only for the levelof 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 dam-age observed in some major vapor cloud explosion incidents of the 1970s:

• The Flixborough explosion was analyzed on the basis of damage figures pre-sented 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 corres-ponds with a mass equivalency of 81.7%. These equivalences were calculatedon the basis of the full quantity of material released.

• For the Port Hudson vapor cloud explosion, they found TNT equivalencies of8.7% and 96%, based on energy and mass basis, respectively. These equivalen-cies 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% onan energy basis and 109% on a mass basis were found. These equivalencieswere calculated based on the assumption of a full tank-car inventory (55,000kg) of a mixture of propylene and propane.

• Another tank car was punctured at Decatur (NTSB report 1975). TNT equivalen-cies 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 carinventory (152,375 Ib, 68,000 kg) of isobutane.

Taking into account the possibility of highly directional blast effects, Eichler andNapadensky (1977) recommend the use of a safe and conservative value for TNTequivalency, namely, between 20% and 40%, for the determination of safe stand-off distances between transportation routes and nuclear power plants. This value isbased on energy; it should be applied to the total amount of hydrocarbon in thelargest single, pressurized storage tank being transported.

HSE (1979 and 1986)

Although it recognized that much higher values have been occasionally observedin vapor cloud explosion incidents, the U.K. Health & Safety Executive (HSE)states that surveys by Brasie and Simpson (1968), Davenport (1977, 1983), andKletz (1977) show that most major vapor cloud explosions have developed between1% and 3% of available energy. It therefore recommends that a value of 3% ofTNT equivalency be used for predictive purposes, calculated from the theoreticalcombustion energy present in the cloud.

To allow for spray- and aerosol-formation, the mass of fuel in the cloud isassumed to be twice the theoretical flash of the amount of material released, solong as this quantity does not exceed the total amount of fuel available. Blast effectsare modeled by means of TNT blast data according to Marshall (1976), while 1bar 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

"sid

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

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

\/WTNT

are those which have formed rapidly, the HSE recommends ignoring the effect ofcloud drift.

Given a certain release of a given fuel, the procedure of vapor cloud explosionblast modeling according to HSE can be subdivided into a number of successivesteps:

• 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 shouldbe multiplied by 2. This number may not, of course, exceed the total amountof 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 (kg)W^ = the weight of fuel in the cloud (kg)//TNT = TNT blast energy (J/kg)Hf = heat of combustion of fuel in question (J/kg)

• Once the equivalent charge weight of TNT is estimated, the blast peak overpres-sures in the field can be found by applying this charge weight to the scaleddistance in the blast chart (Figure 4.18).

• The positive-phase duration of the blast wave from a vapor cloud explosion isin the range of 100 and 300 ms.

Exxon (unpublished)

To estimate the total quantity of material in the vapor cloud, Exxon suggests thatthe following guidelines be used:

• If a gas is released, the quantity of material in the cloud (to be used in thecalculation) is the lesser of (a) the total inventory of material or (b) the productof 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 thecalculation) is the product of the liquid's evaporation rate and the time requiredfor 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 ofmaterial in the cloud (to be used in the calculation) is the lesser of (a) theproduct 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 timerequired to stop the leak.

Exxon recognizes that blast effects by vapor cloud explosions are influenced by thepresence of partial confinement and/or obstruction in the cloud. Therefore, in orderto determine an equivalent TNT yield for vapor clouds, Exxon recommends use ofthe 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 fewstructures are nearby, for example, in an isolated tank farm consisting of one ortwo well-spaced tanks. Otherwise, the partial-confinement yield factor should beused to give reasonably conservative damage estimates.

These figures were developed on the basis of the gross quantities of materialreleased in accidents. They may underpredict blast if used in conjunction with theamount of flammable mixture in the cloud developed from dispersion calculations.If the amount of fuel based on dispersion calculations is to be used, higher TNTequivalencies would be justified. The upper limit on yield factor in such instanceswould be 80%. These guidelines are recommended for application in combinationwith the Kingery and Panill (1964) TNT surface (ground range) burst data (Fig-ure 4.17).

Industrial Risk Insurers (1990)

As a tool for estimating the loss of property potential of vapor cloud explosionincidents at chemical plants or refineries, the possibility of two credible incidentsis considered.

• A credible spill for Probable Maximum Loss Potential. The minimum spillsource is the largest process vessel. The maximum spill size is the combinedcontents of the largest process vessel, or train of process vessels connectedtogether if not readily isolated. Between these extremes, a credible spill maybe estimated after taking into account the presence of remotely operated shutoffvalves 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 vesseltrain. 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 as-sumed that the pipeline is completely severed and that the spill will run for30 minutes.

Industrial Risk Insurers (1990) states that the TNT equivalency of actual chemicalplant vapor cloud explosions is in the range of 1% to 5%. A value of 2% based on

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 andcatastrophic losses. This TNT equivalency should be used in combination with air-burst TNT-blast data according to Glasston and Dolan (1977), represented in Figure4.19. Figure 4.19 presents blast data so as to permit the diameters of overpressurecircles 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 refineryconsists of

• a 10-minute release from the largest vessel or train of vessels through theconnection that will allow the greatest discharge;

• a 10-minute release from an atmospheric or pressurized tank based on gravityand storage pressure as the driving force (the operation of internal excess flowvalves, if present, may be considered in mitigating the amount discharged);

• a 10-minute release from above-ground pipelines carrying material from a large-capacity, remote source;

• loss of the entire contents of the tank for mobile tanks, such as rail and trucktransportation vessels.

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The quantity of fuel in a cloud is calculated by use of release and (flash) vaporizationmodels that have been extensively described by Hanna and Drivas (1987). Toaccount for aerosol formation during vaporization, the flash fraction should bedoubled up to, but not exceeding, a value of unity. Pool vaporization is alsoconsidered.

The equivalent charge weight of TNT is calculated on the basis of the entirecloud content. FMRC recommends that a material-dependent yield factor be applied.Three types of material are distinguished: Class I (relatively nonreactive materialssuch as propane, butane, and ordinary flammable liquids); Class II (moderatelyreactive materials such as ethylene, diethyl ether, and acrolein); and Class III (highlyreactive materials such as acetylene). These classes were developed based on thework of Lewis (1980). Energy-based TNT equivalencies assigned to these classesare as follows:

Class TNT Equivalency

I 5%II 10%III 15%

TNT-blast data for hemispherical surface bursts are used to determine the blasteffects 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 cloudexplosion blast modeling is the effect of distance on the TNT equivalency observedin actual incidents. Properly speaking, TNT blast characteristics do not correspondwith gas explosion blast. That is, far-field gas explosion blast effects must berepresented by much heavier TNT charges than intermediate distances.

To some extent, Prugh (1987) remedied this problem by introducing the conceptof virtual distance. On the basis of literature data, Prugh determined a virtualdistance, 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 inestimating blast effects, then these effects can be approximated from a singleequivalent TNT charge covering the entire field. In fact, this is the approximateyield observed for far-field blast effects.

To express the maximum potential explosive power of a fuel, a safe andconservative value for TNT equivalencies of vapor cloud explosions was estimatedfrom 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 kgup to 70% for 10 million kg of fuel.

These TNT equivalencies should be used in combination with high-explosiveblast data by Baker (1973). Instead of graphical representation, Prugh (1987) recom-mends the use of simple equations which relate basic blast parameters to distancefrom the explosion center. These expressions can be readily implemented in aspreadsheet 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 vaporcloud explosions are largely determined by the combustion which develops only inthe congested/obstructed areas in the cloud. For natural gas, these conclusions wereused to develop an improved TNT-equivalency method for the prediction of vaporcloud explosion blast. This approach is no longer based on the entire mass offlammable material released, but on the mass of material that can be contained instoichiometric 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 avail-able energy. This TNT equivalency should be applied in combination with TNT-blast data developed by Marshall (1976) (Figure 4.18). Harris and Wickens (1989)argue that, for releases of gases considered more reactive than natural gas, thisapproach might be inappropriate because, under specific circumstances, transitionto detonation engulfing any portion of the cloud may occur.

The Harris and Wickens (1989) approach appears to be very similar to themultienergy method (Van den Berg 1985), whose background is described in moredetail 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 majorfeature of gas explosions, namely, variability in blast strength. Furthermore, TNTblast characteristics do not correspond well to those of gas-explosion blasts, asevidenced by the influence of distance on TNT equivalency observed in vapor cloudexplosion blasts.

The Baker-Strehlow Method

An extensive numerical study was performed by Strehlow et al. (1979) to analyzethe structure of blast waves generated by constant velocity and accelerating flamespropagating in a spherical geometry. This study resulted in the generation of plots

of dimensionless overpressure and positive impulse as a function of energy-scaleddistance from the cloud center. The study examined flamed speeds ranging fromlow velocity deflagrations to detonations. The time period covered by numericalcalculations was extended well after the flame had extinguished and yielded blastparameters out to considerable distances from the source region. Thus, the pressureand impulse curves encompass regions both inside and outside the combustion zone.

Baker and his colleagues (1983) compared the Strehlow et al. (1979) curvesto experimental data, then applied them in research programs, accident investiga-tions, and predictive studies. They developed the methods for use of Strehlow'scurves.

Application of the Baker-Strehlow method for evaluating blast effects from avapor cloud explosion involves defining the energy of the explosion, calculatingthe scaled distance (R)9 then graphically reading the dimensionless peak pressure(P5) and dimensionless specific impulse (I5). Equations (4.41) and (4.42) provide themeans to calculate incident pressure and impulse based on the dimensionless terms.

(4.41)

where

R = scaled distance (-)r = distance from target to center of vapor cloud (m)P0 = atmospheric pressure (Pa)E = energy (J)^V^o = dimensionless overpressure (Figure 4.20) (-)

(4.42)

where

/5 = scaled impulse (-)i = incident impulse (Pa-s)A0 = speed of sound in air (m/s)PQ = atmospheric pressure (Pa)E = energy. (J)

Graphical solution of Figures 4.20 and 4.21 requires selection of the proper curvebased on the maximum flame speed attained. Strehlow et al. (1979) studies showedthat a constant speed flame and an accelerating flame with the same maximumspeed generated equivalent blast waves. Thus, flame speed data from experimentalstudies and accident investigations can be used objectively to select the propercurve. Each curve is labeled with two flame speeds: Mw and Msu. The flame speedMw 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

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

sound. While Mw is the appropriate parameter for comparison to most experimentaldata, 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, andignition intensity. Confinement and obstacles have a coupled effect, so flame speedcannot be inferred from experiments that model only one of the user's parameterscorrectly. Fuel reactivity is a qualitative parameter that is generally used to categorizea fuel's propensity to accelerate to high flame speeds. It is generally accepted thathydrogen, acetylene, ethylene oxide, and propylene oxide have high reactivity;methane and carbon monoxide have low reactivity; and all other hydrocarbons haveaverage reactivity.

Ignition sources may be either soft or hard. Open flame, spark, or hot surfacesare examples of soft ignition sources, while jet and high explosives are categorizedas hard ignition sources. Ignition intensity has almost no influence on flame speedfor soft ignition sources; confinement, obstacles, and fuel reactivity are most im-portant here. By contrast, ignition intensity is the most important variable if a hardignition source is present.

Pentolite

BurstingSphere

Literature provides the basis for a user to objectively determine the maximumflame 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/?. Theenergy term represents the sensible heat that is released by that portion of the cloudcontributing to the blast wave. Any of the accepted methods of calculating vaporcloud explosive energy are applicable to the Baker-Strehlow method. These meth-ods include:

• Estimating the volume within each congested region, calculating the fuel massfor a stoichiometric mixture, multiplying the fuel mass by the heat of combus-

® BURSTING SPHEREa BAKER ( PENTOLITE )A MACH 8-0 ADDITION

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

tion, and treating each congested volume within the flammable portion of thecloud as a separate blast source (see Multienergy Method).

• Estimating the total release of flammable material within a reasonable amountof time (generally 2 to 5 minutes) and multiplying this by the heat of combustionof the material times an efficiency factor (generally in the range of 1% to 5%for ordinary hydrocarbons).

• Estimating the amount of material within flammable limits (usually by dispersionmodeling) and multiplying this by the heat of combustion times an efficiencyfactor (usually higher than the one applied above, generally 5% to 20%).

Once the energy has been calculated, it must be multiplied by a ground reflectionfactor (i.e., hemispherical expansion factor), because Figures 4.20 and 4.21 arebased on spherical expansion parameters. The ground reflection factor is generally2 for vapor clouds that are in contact with the ground. If a vapor release is elevatedand 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 vaporcloud explosions will be relatively close to the ground, and a factor of 1.7 to 2.0is appropriate.

Yellow Book, Committee for the Prevention of Disasters (1979)

Wiekema (1980) used, as a model for vapor cloud explosion blast, the gas dynamicsinduced by a spherical expanding piston (Yellow Book 1979). A piston-blast modeloffers the possibility to introduce a variable initial strength of the blast. The pistonblast 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 ofthe blast wave dependent on the distance from the blast center for three arbitrarilychosen piston velocities. The graph is completed with experimental data fromdetonation of fuel-air mixtures developed by Kogarko (1966). Data are reproducedin a Sachs-scaled representation.

This approach makes it possible to model a vapor cloud explosion blast byconsideration of the two major characteristics of such a blast. These are, first, itsscale, 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 fuelquantity within flammability limits present in the cloud. Initial blast strength wasdetermined by factors which have been found to be major factors affecting theprocess of turbulent, premixed combustion, for example, the fuel's nature and theexistence 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 withinthese extremes, for example, ethane, ethylene, propane, propylene, butane, andisobutane, were classified as medium-reactivity fuels.

Figure 4.22. The piston-blast model.

Subsequently, it was assumed that blast strength is primarily determined bythe fuel's reactivity (Figure 4.22), and that partial confinement, congestion, andobstruction 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 fromdamage patterns observed in major accidental vapor cloud explosions (Gugan 1978).From these estimates, it can be concluded that there is little, if any, correlationbetween the quantity of combustion energy involved in a vapor cloud explosion

before combustion

after combustion

low reactivity

medium reactivity

and the equivalent-charge weight of TNT required to model its blast effects. Someof these discrepancies are due to differences in the definition of the amount ofmaterial contained in the cloud.

Evaluation of experimental data from work covered in Section 4.1 tends toconfirm this concludion. These data indicate that, for quiescent clouds, both thescale and strength of a blast are unrelated to fuel quantity present in a cloud. Theseparameters are, in fact, determined primarily by the size and nature of partiallyconfined and obstructed regions within the cloud. The factor of reactivity of thefuel-air mixture is of only secondary influence.

These principles are recognized in the multienergy method for vapor cloudexplosion blast modeling (Van den Berg 1985; Van den Berg et al. 1987). Considera-tions underlying the multienergy method for vapor cloud explosion blast model-ing follow.

There is increasing acceptance of the proposition that a fuel-air cloud originat-ing from an open air, accidental release is very unlikely to detonate. The nonhomoge-neity of the cloud's fuel-air mixture, inherent in atmospheric turbulent dispersion(Section 3.1), generally prevents the propagation of a detonation (Van den Berg1987). The severe explosion on December 7, 1970, at Port Hudson, Missouri,where nearly all of a large, unconfined vapor cloud detonated, is attributable toseveral exceptional coincidences. Those included the location, which was a shallowvalley, the calm atmospheric conditions, and the exceptionally long ignition de-lay—all of which provided the opportunity for molecular diffusion to mix the densepropane cloud sufficiently with air (NTSB report 1972 and Burgess and Zabetakis1973). The subsequent detonation is unprecedented among documented incidents.Therefore, in the vast majority of cases, the assumption of deflagrative combustionis a sufficiently safe approach to vapor cloud explosion hazard assessment.

Experimental research during the last decade (Section 4.1) has shown clearlythat deflagrative combustion generates blast only in those portions of a quiescentvapor cloud which are sufficiently obstructured and/or partially confined (Zeeuwenet al. 1983; Harrison and Eyre 1987; Harris and Wickens 1989; Van Wingerden1989a).

The conclusion that a partially confined and/or obstructed environment is condu-cive to deflagrative explosive combustion has now found wide acceptance (Tweed-dale 1989). Moreover, those cloud portions already in turbulent motion when igni-tion occurs may develop explosive, blast-generative combustion. Consequently,high-velocity, intensely turbulent jets within a flammable-vapor cloud (Section4.1.2), such as those resulting from fuel releases from high-pressure sources, shouldbe viewed as possible blast sources. The remaining portions of a cloud containinga flammable vapor-air mixture burn out slowly without contributing significantlyto blast. This model is called the Multi-Energy concept. Contrary to other modelingmethods, in which a vapor cloud explosion is regarded as an entity, the Multi-Energy concept defines a vapor cloud explosion as a number of sub-explosionscorresponding 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 rail-car switching yards (Baker et al. 1983), each blanketed in a large vapor cloud. Theblast effects from each should be considered separately.

Blast effects can be represented by a number of blast models. Generally, blasteffects from vapor cloud explosions are directional. Such effects, however, cannotbe modeled without conducting detailed numerical simulations of phenomena. Ifsimplifying assumptions are made, that is, the idealized, symmetrical representationof blast effects, the computational burden is eased. An idealized gas-explosion blastmodel was generated by computation; results are represented in Figure 4.24. Steadyflame-speed gas explosions were numerically simulated with the BLAST-code (Vanden Berg 1980), and their blast effects were calculated.

Figure 4.24 represents the blast characteristics of a hemispherical fuel-aircharge of radius R0 on the earth's surface, derived for a fuel-air mixture with aheat of combustion of 3.5 X 106 J/m3. The charts represent only the most significantblast-wave parameters: side-on peak overpressure (AP8) and the positive-phase blast-wave duration (7*) as a function of distance from the blast center (R). The dataare fully nondimensionalized, with charge combustion energy (E) and parameterscharacterizing the state of the ambient atmosphere: pressure (P0) and speed ofsound (CQ). This way of scaling (Sachs scaling) takes into account the influence ofatmospheric conditions. Moreover, Sachs scaling allows the blast parameters to beread in any consistent set of units.

Initial blast strength in Figure 4.24 is represented by a number ranging from1 (very low strength) up to 10 (detonative strength). The initial blast strength numberis 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. Pressurewaves, produced by fuel-air charges of low strength, show an acoustic overpressuredecay behavior and a constant positive-phase duration. On the other hand, shockwaves in the vicinity of a charge of high initial strength exhibit a more rapidoverpressure decay and a substantial increase in positive-phase duration. Eventually,

combustion energy-scaled distance (R)

po = atmospheric pressureC0 = atmospheric sound speedE = amount of combustion energyR0 = charge radius

Figure 4.24. Fuel-air charge blast model.


the high-strength blast develops a behavior approximating acoustic decay in the farfield. Another significant feature is that, at a distance larger than about 10 chargeradii from the center, a fuel-air charge blast is more-or-less independent of initialstrength for values of 6 (strong deflagration) and above.

In the application of the multienergy concept, a particular vapor cloud explosionhazard is not determined primarily by the fuel-air mixture itself but rather by theenvironment into which it disperses. The environment constitutes the boundaryconditions for the combustion process. If a release of fuel is anticipated somewhere,the explosion hazard assessment can be limited to an investigation of the environ-ment's potential for generating blast.

The procedure for employing the multienergy concept to model vapor cloudexplosion blast can be divided into the following steps:

• Assume that blast modeling on the basis of deflagrative combustion is a suffi-ciently safe and conservative approach. (The basis for this assumption is thatan unconfined vapor cloud detonation is extremely unlikely; only a single eventhas been observed.)

• Identify potential sources of strong blast present within the area covered by theflammable 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, multistoryparking 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 highpressure.

The remaining fuel-air mixture in the cloud is assumed to produce a blast ofminor 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 areasidentified as blast sources. This estimate can be based on the overall dimen-sions of the areas and jets. Note that the flammable mixture may not fill anentire blast-source volume and that the volume of equipment should beconsidered where it represents an appreciable proportion of the wholevolume.

—Calculate the combustion energy E [J] for each blast by multiplication ofthe 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 stoichiomet-ric 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, asource strength of 7 seems to more accurately represent actual experience.Furthermore, for side-on overpressures below about 0.5 bar, no differencesappear for source strengths ranging from 7 to 10.

—The blast resulting from the remaining unconfined and unobstructed parts ofa cloud can be modeled by assuming a low initial strength. For extendedand quiescent parts, assume minimum strength of 1. For more nonquiescentparts, which are in low-intensity turbulent motion, for instance, because ofthe momentum of a fuel release, assume a strength of 3.

—If such an approach results in unacceptably high overpressures, a moreaccurate estimate of initial blast strength may be determined from the growingbody of experimental data on gas explosions (reviewed in Section 4.1), orby performing an experiment tailored to the situation in question.

—Another very promising possibility is the application of numerical simulationby use of advanced computational fluid dynamic codes, such as FLAGS(Hjertager 1982, 1989), EXSIM (Hjertager 1991), PHOENICS (Kjaldmanand Huhtanen 1985) or REAGAS (Van den Berg 1989), outlined in Section4.2.2. Van den Berg et al. (1991) demonstrated one way to use such codesfor vapor cloud explosion blast modeling. An example of the use of theseadvanced codes is shown in Appendix F.

—Further definition of initial blast strength is, however, a major research needthat is so far unmet.

• Once the energy quantities E and the initial blast strengths of the individualequivalent fuel-air charges are estimated, the Sachs-scaled blast side-on over-pressure and positive-phase duration at some distance R from a blast sourcecan be read from the blast charts in Figure 4.24 after calculation of the Sachs-scaled distance:

(4.43)

where

R = Sachs-scale distance from charge (-)R = real distance from charge (m)E = charge combustion energy (J)P0 = ambient pressure (Pa)

The real blast side-on overpressure and positive-phase duration can be calculatedfrom the Sachs-scaled quantities:

P8 = A/>s - P0 (4.44)

and

(4.45)

where

PS^ = side-on blast overpressure (Pa)AP8 = Sachs-scaled side-on blast overpressure (-)P0 = ambient pressure (Pa)t+ = positive-phase duration (s)t+ = Sachs-scaled positive-phase duration (-)E = charge combustion energy (J)C0 = ambient speed of sound (m/s)

—If separate blast sources are located close to one another, they may beinitiated almost simultaneously. Coincidence of their blasts in the far fieldcannot be ruled out, and their respective blasts should be superposed. Thesafe and most conservative approach to this issue is to assume a maximuminitial blast strength of 10 and to sum the combustion energy from eachsource in question. Further definition of this important issue, for instancethe determination of a minimum distance between potential blast sources sothat their individual blasts may be considered separately, is a factor inpresent research.

—If environmental and atmospheric conditions are such that vapor cloud disper-sion can be expected to be very slow, the possibility of unconfined vaporcloud detonation should be considered if, in addition, a long ignition delayis likely. In that case, the full quantity of fuel mixed within detonablelimits should be assumed for a fuel-air charge whose initial strength ismaximum 10.

4.3.3. Special Methods

In the overview of experimental research, it was shown that explosive, blast-generating combustion in gas explosions is caused by intense turbulence whichenhances combustion rate. On one hand, turbulence may be generated during agas explosion by an uncontrolled feedback mechanism. A turbulence-generativeenvironment, in the form of partially confining or obstructing structures, must bepresent for this mechanism to be triggered.

On the other hand, turbulence may also be generated by external sources. Forexample, fuels are often stored in vessels under pressure. In the event of a totalvessel 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 turbulentfuel-air mixture is ignited, explosive combustion and blast can result.

Special methods tailored to these phenomena have been developed for modelingsuch effects. These methods consist of a collection of experimental data framed ingraphs or semiempirical expressions.

Explosively Dispersed Vapor Cloud Explosions (Giesbrecht et al. 1981). TheGiesbrecht et al. (1981) model is based on a series of small-scale experiments inwhich 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 representedas a function of fuel mass.

The solid lines in Figure 4.5 represent extrapolations of experimental data tofull-scale vessel bursts on the basis of dimensional arguments. Attendant overpres-sures were computed by the similarity solution for the gas dynamics generated bysteady flames according to Kuhl et al. (1973). Overpressure effects in the environ-ment were determined assuming acoustic decay. The dimensional arguments usedto 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 experimentaldata obtained in two different programs on exploding jets: a program on naturalgas and hydrogen jets by Seifert and Giesbrecht (1986), and a program on propanejets by Stock (1987). These tests have been described in Section 4.1.2; a summaryof general conclusions follows.

• Overpressure within a vapor cloud is dependent upon outflow velocity, orificediameter, and laminar flame speed expressed in the following semi-empiricalrelation:

Pmax = (constant)^ 8X^0)09 (4.46)

where

^max = in-cloud overpressure (Pa)M1 = laminar flame speed (m/s)M0 = outflow velocity (m/s)J0 = orifice diameter (m)

• The semiempirical theory underlying this equation can be extended to describeblast overpressure decay. If acoustic behavior is assumed, results can be framedin the following expression for blast overpressure as a function of distance fromthe blast center.

P = (au°Q9dl0-

9 + b)/r (4.47)

where

for natural gas: a = 840, b = 23for hydrogen: a = 3728, b = 55

P — overpressure at distance r (Pa)r = distance from blast center (m)

4.4. SUMMARY AND DISCUSSION

The great attractiveness of TNT equivalency methods is the very direct, empiricalrelation between a charge weight of TNT and resulting strucural damage. Therefore,TNT equivalency is a useful tool for calculating the property-damage potential ofvapor clouds. The various methods reviewed, however, cover a large range ofvalues for TNT equivalency which all are, in some sense, applicable.

TNT equivalencies given by the sources identified below are based upon aver-ages deduced from damage observed in a limited number of major vapor cloudexplosion incidents:

• Brasie and Simpson: 2%-5% of the heat of combustion of the quantity offuel spilled.

• The UK Health & Safety Executive: 3% of the heat of combustion of the quantityof fuel present in the cloud.

• Exxon: 3%-10% of the heat of combustion of the quantity of fuel present inthe cloud.

• Industrial Risk Insurers: 2% of the heat of combustion of the quantity offuel spilled.

• Factory Mutual Research Corporation: 5%, 10%, and 15% of the heat ofcombustion of the quantity of fuel present in the cloud.

These figures can be used for predictive purposes to extrapolate "average majorincident conditions" to situations under study, provided the actual conditions understudy correspond reasonably well with "average major incident conditions." Sucha condition may be broadly described as a spill of some tens of tons of a hydrocarbonin an environment with local concentrations of obstructions and/or partial confine-ment, for example, the site of an "average" refinery or chemical plant with denseprocess equipment or the site of a railroad marshaling yard with a large number ofclosely parked rail cars. It must be emphasized that the TNT equivalencies listedabove 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 ispossible only if the actual conditions within the cloud are considered. This is thestarting point in the multienergy concept for vapor cloud explosion blast modeling(Van den Berg 1985). Harris and Wickens (1989) make use of this concept bysuggesting that blast effects be modeled by applying a 20% TNT equivalency onlyto 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 explosionsare poorly represented by TNT blast. Nevertheless, TNT-equivalency methods aresatisfactory, 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 pointfor, say, advanced design of blast-resistant structures, TNT blast may be a lessthan satisfactory model. In such cases, the blast wave's shape and positive-phaseduration must be considered important parameters, so the use of a more realisticblast model may be required. A fuel-air charge blast model developed through themultienergy concept, as suggested by Van den Berg (1985), results in a morerealistic representation of a vapor cloud explosion blast.

Because it is usually very difficult to evaluate beforehand the conditions whichmay induce an initial blast, a conservative approach is to apply an initial blaststrength of 10 to the fuel-air charge blast model. This model, however, offerspossibilities for future development.

The multienergy approach allows experimental data and advanced computa-tional methods to be incorporated in blast modeling procedures. A database con-taining a complete overview of data on vapor cloud explosion incidents and gasexplosion experiments should be developed for this purpose. Such a database couldbe used to easily and inexpensively determine more appropriate values for initialblast strength. A database cannot, however, possibly cover all situations that mayarise in practice. These voids could be filled by computed values. Therefore, thedesign and development of computer codes, such as FLAGS (Hjertager 1982 and1989) and REAGAS (Van den Berg 1989), are of paramount importance.

Although the model of spherical fuel-air charge blast is the most realisticavailable, it is nevertheless a highly idealized concept that, at best, applies only tothe far field. Near-field blast effects are mostly directional as a consequence of apreferential direction in the combustion process induced by partial confinement. Inaddition, structural blast loading is influenced largely by neighboring objects. Sucheffects can only be studied and quantified by simulation with multidimensionalnumerical methods such as BLAST (Van den Berg 1980). Codes such as REAGASand BLAST could be utilized in vapor cloud explosion hazard analysis, as describedby Van den Berg et al. (1991).

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Richtmyer, R. D. and K. W. Morton. 1967. Difference methods for initial value problems.New York: Interscience.

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Schneider, H., and H. Pfortner. 1981. Flammen und Druckwellenausbreitung bei der Defla-gration von Wasserstoff-Luft-Gemischen, Fraunhofer-Institute fur Treib- und Explosiv-stoffe (ICT), Pfinztal-Berghaven, West Germany.

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Sherman, M. P., S. R. Tiezsen, W. B. Bendick, W. Fisk, and M. Carcassi. 1985. "Theeffect of transverse venting on flame acceleration and transition to detonation in a largechannel." Paper presented at the 10th Int. Coll. on Dynamics of Explosions and ReactiveSystems. Berkeley, California.

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5BASIC PRINCIPLES OF FLASH FIRES

A flash fire is the nonexplosive combustion of a vapor cloud resulting from a releaseof flammable material into the open air, which, after mixing with air, ignites. InSection 4.1, experiments on vapor cloud explosions were reviewed. They showedthat combustion in a vapor cloud develops an explosive intensity and attendant blasteffects only in areas where intensely turbulent combustion develops and only ifcertain conditions are met. Where these conditions are not present, no blast shouldoccur. The cloud then burns as a flash fire, and its major hazard is from the effectof heat from thermal radiation.

The literature provides little information on the effects of thermal radiationfrom flash fires, probably because thermal radiation hazards from burning vaporclouds are considered less significant than possible blast effects. Furthermore, flashcombustion 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 substantiallylower than in case of a pool fire.

In order to compute the thermal radiation effects produced by a burning vaporcloud, it is necessary to know the flame's temperature, size, and dynamics duringits propagation through the cloud. Thermal radiation intercepted by an object in thevicinity is determined by the emissive power of the flame (determined by the flametemperature), the flame's emissivity, the view factor, and an atmospheric-attenuationfactor. 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 labori-ous and expensive. Therefore, experimental data on the dynamics of flash fires andattendant thermal radiation are scarce. Urtiew (1982), Hogan (1982) and Goldwireet al. (1983) reported on LNG, liquid methane, and liquid nitrogen spill experimentsin China Lake. The facility could hold up to 40 m3 of liquefied gas, which couldbe either partially or completely released during a single spill test on a water testbasin. In total, ten experiments were performed, five primarily for the study ofvapor dispersion and burning vapor clouds, and five for investigating the occurrenceof explosions exhibiting rapid phase transitions.

All vapor burn tests were performed with LNG except for one with liquidmethane. 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 ioniza-tion gauges (to permit three-dimensional measurement of local flame speed anddirection), calorimeters (to measure local heat release of the burning cloud), ther-mometers (to measure local flame temperatures), radiometers (to collect data onthe 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 re-vealed maximum heat fluxes of 160-300 kW/m2. Figure 5.1 shows the calorimeterpositions, the final contours of the flash fire, and heat-flux data from calorimeterspositioned near or in the flames. No data are available on flame propagation duringthe vapor-burn tests.

The Maplin Sands tests were reported by Blackmore et al. (1982) and Hirstand Eyre (1983). Quantities of 20 m3 LNG and refrigerated liquid propane werespilled on the surface of the sea in the Thames estuary. The experimental programconsisted of both instantaneous and continuous releases. The resulting vapor clouddispersion and the subsequent combustion of the clouds was observed by instrumen-tation deployed on 71 floating pontoons (Figure 5.2). On the masts of 20-30 selectedpontoons, 27 wide-angle radiometers (to measure average incident radiation) and24 hydrophones (to measure flame-generated overpressures) were mounted. Anothertwo special pontoons provided platforms for meteorological instruments. The instru-ments provided vertical profiles of temperature and wind speed up to 10 m abovesea level, together with measurements of wind direction, relative humidity, solarradiation, water temperature, and wave height.

The major objective of the experimental program was to obtain data that couldbe used to assess the accuracy of existing models for vapor cloud dispersion. Thecombustion experiments were designed to complement this objective by providinganswers to the question, "What would happen if such a cloud ignited?"

Combustion behavior differed in some respects between continuous and instan-taneous spills, and also between LNG and refrigerated liquid propane. For continu-ous spills, a short period of premixed burning occurred immediately after ignition.This was characterized by a weakly luminous flame, and was followed by combus-tion of the fuel-rich portions of the plume, which burned with a rather low, brightyellow flame. Flame height increased markedly as soon as the fire burned back tothe liquid pool at the spill point, and assumed the tilted, cylindrical shape that ischaracteristic of a pool fire.

The LNG pool fire was clean and brightly emissive, but pool fires of refrigeratedliquid propane produced very smokey flames. Following instantaneous spills, cloudshad 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 notoccur. The highest measured flame speeds occurred during the premixed stage ofcombustion. In propane tests, average flame speeds of up to about 12 m/s wereobserved. 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 inflame speeds capable of producing damaging overpressures.

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

Hea

t flu

x -

kW/m

2

Hea

t flu

x -

kW/m

2

Hea

t flu

x -

kW/m

2

Hea

t fl

ux

-kW

/m2

C5G08 C5G06

C5T03 C5T04

Figure 5.2. Setup of the Maplin Sands experiments.

Similar behavior was observed for LNG clouds during both continuous andinstantaneous tests, but average flame speeds were lower; the maximum speedobserved in any of the tests was 10 m/s. Following premixed combustion, the flameburned through the fuel-rich portion of the cloud. This stage of combustion wasmore evident for continuous spills, where the rate of flame propagation, particularlyfor LNG spills, was very low. In one of the continuous LNG tests, a wind speedof only 4.5 m/s was sufficient to hold the flame stationary at a point some 65 mfrom the spill point for almost 1 minute; the spill rate was then reduced.

Radiation effects, as well as combustion behavior, were measured. LNG andrefrigerated liquid propane cloud fires exhibited similar surface emissive powervalues of about 173 kW/m2.

Zeeuwen et al. (1983) observed the atmospheric dispersion and combustion oflarge 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. Thermalradiation effects were not measured because the main objective of this experimentalprogram was to investigate blast effects from vapor cloud explosions.

Tests were performed in open terrain. Obstacles and partial confinement werealso introduced (see also Section 4.1). Under unconfined conditions, flame-front

Stondord pontoonswi th 4 m mastsPontoons with 10 m most*

Meteorological instruments

Spillpoint Dike

Pipeline

Gas hoftdttAf ptoM

velocities were, of course, highly directional and dependent on wind speed. Flamebehavior 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: theleaner the mixture, the lower the flame height. In mixtures whose compositionswere within flammability limits, flame heights were about 1-2 m. In mixtureswhose compositions exceeded the upper flammability limit, average flame heightsof 2-5 m were observed. Flame heights of up to 15 m were observed, but only asplumes near the point of release. Video shots showed that the combustion productsdo not rise vertically after generation. Rather, they flow horizontally toward existingplumes, join them, then rise.

Figure 5.3 shows a moment of flame propagation in an unconfined propanecloud. On the left side, a flame is propagating through a premixed portion of thecloud; its flame is characteristically weakly luminous. In the middle of the photo-graph, fuel-rich portions of the cloud are burning with characteristically higherflames 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-fireradiation is that of Raj and Emmons (1975), who modeled a flash fire as a two-dimensional, turbulent flame propagating at a constant speed. The model is basedon the following experimental observations:

• The cloud is consumed by a turbulent flame front which propagates at a velocitywhich is roughly proportional to ambient wind speed.

• When a vapor cloud burns, there is always a leading flame front propagatingwith uniform velocity into the unburned cloud. The leading flame front isfollowed by a burning zone.

• When gas concentrations are high, burning is characterized by the presence ofa tall, turbulent-diffusion, flame plume. At points where the cloud's vapor hadalready mixed sufficiently with air, the vertical depth of the visible burningzone 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 illustratesthe model, consisting of a two-dimensional, turbulent-flame front propagating at agiven, constant velocity S into a stagnant mixture of depth d. The flame base ofwidth W is dependent on the combustion process in the buoyant plume above theflame base. This fire plume is fed by an unburnt mixture that flows in with velocityU0. 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 theplume results in a relation between visible-flame height and the upward velocity ofgases UQ at the flame base. The theoretical solution to this simplified problem iscorrected on the basis of empirical data on flame heights of diffusion flames (Steward1964). In free-burning vapor clouds, however, the upward flame-base velocity M0

is unknown. However, experimental observations indicate a nearly proportionalrelation 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 toburning velocity S by the creation of a mass balance for the triangular area boundedby the flame front and flame base (Figure 5.4). This results in the following approxi-mate, semiempirical expression:

(5.1)

where

H = visible flame height (m)d = cloud depth (m)S = burning speed (m/s)

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

g = gravitational acceleration (m/s2)P0 = fuel-air mixture density (kg/m3)pa = density of air (kg/m3)r = stoichiometric mixture air-fuel mass ratio

wherew = frl'i f°r *>*« (5.2)a(l - <|)st)

w = O f or <{> ^ <()st

a = constant pressure expansion ratio for stoichiometric combustion (typi-cally 8 for hydrocarbons)

<|> = fuel-air mixture composition (fuel volume ratio)<|>st = stoichiometric mixture composition (fuel volume ratio)

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

unburntvapor

dependent on the cloud's composition. If the cloud consists of pure vapor, forexample, a hydrocarbon, w represents the inverse of the volumetric expansionresulting from constant-pressure stoichiometric combustion: w = 1/9. If, on theother hand, the mixture in the cloud is stoichiometric or lean, there is no combustionin the plume; the flame height is equal to the cloud depth, w = O. The behaviorof the expression for w should, of course, smoothly reflect the transition from oneextreme condition to the other.

The model gives no solution for the dynamics of a flash fire, and requires aninput value for the burning speed S. From a few experimental observations, Rajand Emmons (1975) found that burning speed was roughly proportional to ambientwind speed Uw:

S = 2.3I/W

Radiation effects from a flash fire are now fully determined if vapor cloud composi-tion, 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 shapeof 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 contributionsby all successive flame positions during flame propagation. This is an impossiblevalue to compute with the simplified approach just described. Because there aremany uncertainties (e.g., cloud composition, location of ignition site) which greatlyinfluence the final result, a conservative approach is recommended for practicalapplications:

• 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 cross-section moving at burning speed through the stationary cloud.

The radiative power per unit area intercepted by some plane in the environmentcan now be computed from:

q = EF^ (5.3)

where

q = intercepted heat radiation (kW/m2)E = emissive power (kW/m2)F = geometric view factor for a vertical-plane emitter (-)Ta = atmospheric attenuation (transmissivity) (-)

The fundamentals of thermal radiation modeling are treated in Chapter 3. Thevalue for emissive power can be computed from flame temperature and emissivity.Emissivity is primarily determined by the presence of nonluminous soot within theflame. The only value for flash-fire emissive power ever published in the openliterature 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 tobe nearly equal: 173 kW/m2. Geometric view factors for circular and plane verticalemitters can be read from tables and graphs in Appendix A.

The atmospheric attenuation factor takes into account the influence of absorptionand scattering by water vapor, carbon dioxide, dust, and aerosol particles. One canassume, as a conservative position, a clear, dry atmosphere for which Ta = 1.


Flash-fire modeling is largely underdeveloped in the literature; there are large gapsin the information base. Hardly any information is available concerning flash-fireradiation; the only data available have resulted from experiments conducted to meetother 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 calmatmospheric conditions, burning velocities become improbably small, and flash-fireduration proportionately long. The effect of view factors, which change continuouslyduring 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 composi-

tion, 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 alreadyavailable.

REFERENCES

Blackmore, D. R., J. A. Eyre, and G. G. Summers. 1982. Dispersion and combustionbehavior 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 NationalLaboratory Report UCID-19953. VoIs. 1 and 2.

Hirst, W. J. S., and J. A. Eyre. 1983. Maplin Sands experiments 1980: Combustion of largeLNG 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-airexplosions, 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 Sectionof 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 liquefiedgaseous fuels spill safety program. Fuel-air explosions, pp. 929-948. Waterloo, Can-ada: University of Waterloo Press.

Zeeuwen, J. P., C. J. M. Van Wingerden, and R. M. Dauwe. 1983. Experimental investiga-tion 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.

6BASIC PRINCIPLES OF BLEVEs

The phenomenon of BLEVE is discussed in this chapter. "BLEVE" is an acronymfor boiling liquid, expanding vapor explosion. As indicated in Chapter 2, mostBLEVEs are accompanied by fireball radiation, fragmentation, and blast effects.This chapter treats each of these effects separately. First, some general informationis given. Next, effects are treated in the following order: radiation, fragmentation,and blast. Experimental investigations, theoretical approaches, and prediction meth-ods are given for each effect.

The term "BLEVE" was first introduced by J. B. Smith, W. S. Marsh, andW. L. Walls of Factory Mutual Research Corporation in 1957. Walls (1979), thenwith the National Fire Protection Association, defined a BLEVE as the failure ofa major container into two or more pieces, occurring at a moment when the containedliquid 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 aliquid that is at a superheat temperature for atmospheric conditions. A BLEVEresults in sudden, vigorous liquid boiling and the production of a shock wave.Liquids normally stored under pressure have boiling points below ambient tempera-ture. A liquid whose boiling point is above ambient temperature, but heated beforerelease by an external heat source to a temperature above its boiling point, can alsogive rise to a BLEVE.

The main hazard posed by a BLEVE of a container filled with a flammableliquid, 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 failureof a container of flammable material under pressure during fire engulf ment. Failureis 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 ofcontainment 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 flashfire may arise if container failure is not due to fire impingement. The calculationof effects from these kinds of vapor cloud explosions is treated in Sections 4.3.3and 5.2.

A container can fail for a number of reasons. It can be damaged by impactfrom an object, thus causing a crack to develop and grow, either as a result ofinternal pressure, vessel material brittleness, or both. Thus, the container mayrupture completely after impact. Weakening the container's metal beyond the pointat 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 fromcorrosion, internal overheating, manufacturing defects, etc.

When a container is engulfed in a fire, its metal is heated and loses mechanicalstrength. At wetted surfaces, supplied heat is transmitted to its liquid contents, thusraising liquid temperature but keeping the wetted portion of the vessel relativelycool. 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'sunwetted area (vapor space) will raise the local wall temperature, thereby weakeningits metal. Jet fires may even affect the mechanical strength of the metal below theliquid level. A safety valve, even if properly designed and in working order, willnot prevent a BLEVE.

6.1. MECHANISM OF A BLEVE

In this section, the phenomenon of BLEVE is discussed according to theoriesproposed by Reid (1976), Board (1975), and Venart (1990). Reid (1979, 1980)based a theory about the BLEVE mechanism on the phenomenon of superheatedliquids. 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 activesites. These active sites occur at interfaces with solids, including vessel walls.

Boiling in the bulk of the fluid generally takes place at submicron nucleationsites as impurities, crystals, or ions. When there is a shortage of nucleation sitesin the bulk of the liquid, its boiling point can be exceeded without boiling; thenthe liquid is superheated. There is, however, a limit at a given pressure abovewhich a liquid cannot be superheated, and when this limit is reached, microscopicvapor bubbles develop spontaneously in the pure liquid (without nucleation sites).

The maximum superheat temperature for a material under a given pressure canbe found in pressure-volume diagrams. The superheated liquid state for a certainisotherm is represented in Figure 6.1 by the dashed line starting at V1, P1. Thesuperheat state can, however, only be extrapolated to a value of P and V wheredP/dV at constant temperature becomes zero. Following the isotherm with increasingvolume implies an increasing pressure, which is physically unrealistic. The super-heat temperature limit T1 occurs at a pressure P1 (Figure 6.1). The locus of valueswhere (dP/dV)T equals zero is called the spinodal curve (Reid 1976). The superheatlimit temperature can be calculated from thermodynamics when the equation ofstate is known. According to Reid (1976), however, there is no satisfactory correla-tion among P, V9 and T in the superheated liquid region.

Opschoor (1974) applied the Van der Waals equation of state to estimate themaximum superheat temperature for atmospheric pressure (rsl) from the criticaltemperature (rc) (i.e., that temperature above which a gas cannot be liquefied bypressure alone) as follows:

T81 = 0.84rc (6.1.1)

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 super-heat limit temperature of:

Tsl = 0.895!TC (6.1.2)

Reid (1976) further determined that the superheat temperature limit for "a widerange 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 temperaturelimit of 530C at atmospheric pressure. The superheat temperature limit calculatedfrom the Van der Waals equation is 380C, whereas the value calculated from theRedlich-Kwong equation is 580C. These values indicate that, though an exactequation among P9 V9 and T in the superheat liquid region is not known, theRedlich-Kwong equation of state is a reasonable alternative.

The superheat-temperature-limit locus for propane is plotted by Reid (1979) ina PJ-diagram together with the vapor pressure (Figure 6.2). When the liquid isheated, for example, from A to B, a sudden drop in pressure to 1 atmosphere (C)

liquidphase

vaporphase

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

Critical

Fuel

Propanen-Butanelsobutane1 ,3-ButadieneVinyl chlorideEthanen-Pentanen-HexaneWater

Temp.(K)

370426407425429305469507647

Press,(bar)

43.636.537.537.6—49.033.429.9

218

Superheat Limit

Temp.(K)

326377361377374269421457553

Press,(bar)

18.316.615.518.5—

21.715.413.764.1

Normal BoilingTemp.

(K)

231272261269260184309342373

a 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 superheat-temperature 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 pressureto atmospheric will cross the superheat-temperature-limit curve at E, and, at thispoint, the liquid-vapor system will explode. For any situation below point D onthe vapor pressure curve, sudden reduction to atmospheric pressure will not lead

CRITICAL POINT

PR

ESS

UR

E (a

im)

SUPERHEATUMlT 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-temperature-limit 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-liquidinterface, causes a shock wave, some of the liquid is atomized, thus enhancingrapid heat transfer to the droplets. This action produces further expansion andatomization. When the droplets are heated to a temperature equal to the superheattemperature limit, rapid evaporation (flashing liquid) may cause an explosion. Infact, 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 atmosphericpressure (McDevitt et al. 1987).

Venart (1990) suggests that intermittent pressurization by external heat in afire-induced BLEVE and subsequent depressurization by the pressure-relief devicecauses incipient vapor nuclei to form within the liquid. Rapid depressurization toatmospheric pressure then generates a vaporization wave in the now-superheatedliquid. This phenomenon causes rapid growth of vapor-bubble nuclei. The two-phase fluid is first atomized into a fine aerosol, then vaporized quickly throughefficient transfer of heat from air to the aerosol droplets. Ignition of this vapor-airmixture, if the substance is flammable, results in a rapid deflagration, sometimesgiving rise to blast generation.

The formation of droplets and their rapid, efficient vaporization is the reasonthat 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 fuelcan be found in droplets. This value depends upon initial mass and degree ofsuperheat, that is, amount by which the fuel's temperature exceeds its boiling point.

A theory that adequately explains all BLEVE phenomena has not yet beendeveloped. Reid's (1979, 1980) theory seems to be a good approach to explain thestrong blast waves that may be generated. But even when a liquid's temperature isbelow the superheat limit, the liquid may "flash" within seconds after depressuriza-tion, 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 mixtureis flammable, the BLEVE can form a fireball with intense heat radiation. Eacheffect is discussed in the following sections.

6.2. RADIATION

This section covers radiation due to BLEVEs with accompanying fireballs. First, abrief description is given of experimental investigations of BLEVEs and their fire-balls. Next, some fireball models, primarily for predicting fireball diameter andcombustion duration, are presented. Most of these models evolved from experimen-tal results. Finally, some radiation models, based on experiments and theory, aregiven.

6.2.1. Experimental Investigations

Small-Scale Experiments

Four parameters often used to determine a fireball's thermal-radiation hazard arethe mass of fuel involved and the fireball's diameter, duration, and thermal-emissivepower. Radiation hazards can then be calculated from empirical relations. Fordetailed calculations, additional information is required, including a knowledge ofthe change in the fireball's diameter with time, its vertical rise, and variations inthe fireball's emissive power over its lifetime. Experiments have been performed,mostly on a small scale, to investigate these parameters. The relationships obtainedfor each of these parameters through experimental investigation are presented inlater sections of this chapter.

Small-scale experiments with fireballs have been carried out by a number ofinvestigators, and can be roughly divided into two categories. The first includesexperiments in which a spherical gas-air mixture contained by a thin envelope atambient 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 vaporpressure has been reached, and the released vapor is then ignited. Measurement offireball diameter, liftoff time, combustion duration, and final height is captured byfilming with high-speed cameras. Radiometers are used to measure radiation; andtemperature is measured by thermocouples or by determination of fireball colortemperature (Lihou and Maund 1982).

Fay and Lewis (1977) used spherical gas samples inside soap bubbles whosevolumes ranged from 20 to 190 cm3. Typically, a sphere was ignited with resistancewire, and the combustion process was then filmed with a high-speed camera. Thefireball's maximum height and diameter, as well as the time needed to completecombustion, were evaluated. The fireball's thermal radiation was sensed by a radia-tion detector. Figure 6.3 relates fireball burning time and size to initial propane

burn

out t

ime

(sec

)

max

imum

dia

met

er (c

m)

vapor volume cm 3 vapor volume cm 3

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 suchresults.

Hasegawa and Sato (1977) used hermetically sealed, spherical glass vessels,each filled with n-pentane and containing an electric heater and a thermocouple forliquid-temperature measurement. After sufficient warmup, a vessel was broken witha remote-controlled hammer. The unconfined vapor cloud that formed after vesselrupture 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 werevaried 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 about1480C. The combustion process was filmed with a high-speed camera.

After vessel rupture, the superheated liquid vaporized in a white cloud consist-ing of vapor and fine droplets. After ignition, the flame propagated through thecloud, forming a fireball. Fireball size increased as combustion proceeded, and thefireball was lifted by gravitational buoyancy forces.

The amount of liquid that will evaporate can be calculated if it is assumed thatall heated liquid will be exposed to air (see Section 6.3.3.3). Results of calculationscan then be compared with experimental results. When the calculated percentageof 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 remainderformer a pool fire on the ground. Thus, these results imply that, when calculatedflash evaporation is less than 36% of the available fuel, fuel in the fireball can beexpected to amount to approximately three times the amount of flashed vapor.

Hasegawa and Sato analyzed motion pictures and radiation measurements at adistance 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, radiationto initial vapor pressure.

Lihou and Maund (1982) used soap bubbles filled with flammable gas whichwere blown on the bottom of a "fireball chamber" to form fireballs. A hemisphericalbubble was formed on a wire mesh 200 mm above the base of the measuringchamber in order to permit study of elevated sources. The gas bubble was ignitedby direct contact with a candle flame, and the combustion process was filmed at aspeed 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 rangingfrom 100 to 800 ml. (For methane, this corresponds to a mass range from 0.07 to0.6 g, and for butane, from 0.24 to 1.9 g.) Measured temperatures ranged from 1000K 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-airfireball 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 justprior to ignition. Integrating heat-flux calorimeters, located either inside the balloonsor at their edges, were used to measure the thermal output.

Figure 6.4. Typical test results for a 400-ml butane fireball (Lihou and Maund, 1982), whereD0 = initial diameter of gas sphere; DI = diameter of fireball at liftoff (at time J1); Dc = diameterat end of combustion (duration tc).

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

time from ignition seconds

tem

pera

ture

K

measured max temp,

measured mean temp.

max

mean

measured elevation

elev

atio

n m

wire mesh level

calculated from measurementspredicted from model

equi

pmen

t dia

met

er m

formed a pool decreased, with a corresponding increase in the droplet-formingportion.

An additional important quantitative result of these experiments is that, afterthe rupture, droplets large enough to be captured by camera (2.8 to 3.5 mm) werethrown outward with velocities up to 3.6 m/s, a rate much faster than the velocityof the vapor cloud front.

Large-Scale Experiments

In view of the results from these small-scale experiments, and the increasing numberof severe accidents involving large masses of fuel, there is a clear need for large-scale 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 fora completely different reason, namely, to study effects of vapor cloud explosions(see Section 6.4), fireballs were nevertheless generated. These experiments in-volved vessles of various sizes (0.226-1000 1) and containing propylene at 40 to60 bar gauge pressure. The vessels were ruptured, and the released propylene wasignited after a preselected time lag. One of these tests, involving 452 kg of propyl-ene, produced a fireball 45 m in diameter.

Hardee and Lee (1973) reported some experimental data on tests run on propanefireballs containing propane masses of 1 kg, 29 kg, and 454 kg, and with approxi-

50

ml, f

ille

d5

Om

I.

1/2

fille

d10

Om

I, fille

d1

0O

mI,

1/

2 fille

d

5O

mI, f

illed

5O

mI.

1

/2 fi

lle

d10

Om

I. fille

d1

00

ml,

1/2

fille

d

5O

mI, f

ille

d5

Om

I.

1/2

fille

d1

00

ml,

fille

d1

0O

mI, 1

/2 fill

ed

Fra

ctio

n

Superheat (0C)

Figure 6.5. Fraction of pool and aerosol mass generated after loss of containment of smallvessels containing CFC 114, depending on degree of superheat and degree of filling (Schmidlietal. 1990).

Aerosol

Pool

Vapour

mately 100% excess air in the fuel-air mixtures. Total incident heat within thefireballs 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 fueland oxygen. For consistency in this volume, fireball diameters are expressed as afunction 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 kgup to 5000 kg (Lihou and Maund 1982).

British Gas conducted full-scale experiments on the effects of BLEVEs fromboth standard- and extended-size containers. These experiments involved 1000 or2000 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 vesselwas ruptured by detonation of a linear-shaped explosive charge placed upon its top.Detonation resulted in a fracture which propagated along the vessel wall, resultingin its catastrophic failure. Fixed ignition sources placed at distances of 2 and 5 mfrom the vessel ignited the released fuel. Instrumentation for the experiments con-sisted of video and high speed movie cameras, radiometers, thermocouples, andpressure transducers.

Results have been presented on one experiment. It involved a 5.659-m3 vesselcontaining 1000 kg of butane with a fill ratio of 39%. The vessel's contents wereheated 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 pressurepulses occurred. They are plotted in Figure 6.6 as the overpressure-time relationshipmeasured at 25 m from the vessel.

The thermal flux recorded by a radiometer 50 m from the vessel is shown inFigure 6.7; it indicates a peak value of 66 kW/m2. The total heat dosage at thispoint 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 theBritish Gas tests, as back-calculated from radiometer readings. Peak values ofsurface-emissive powers were approximately 100 kW/m2 higher than these averagevalues, but only for a short duration. Other large-scale tests include those conductedto 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 BLEVEoccurred (after 24.5 minutes of exposure), no data on the resulting fireball werepresented.

The German Federal Institute for Material Testing (BAM) carried out full-scalefire tests on commercial liquefied-propane storage tanks. Tank volume was 4.85m3 in each test (Schoen et al. 1989; Droste and Schoen 1988; Schulz-Forberg etal. 1984). Unprotected and protected tanks filled with propane (50% filled) wereexposed to a fire. In some tests, the propane was preheated.

secondshock

combustion

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

overPressUre

mba _r

inci

dent

flux

kW

/m2

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 TestsPerformed by British Gasa

Test No.

12345

Fuel

butanebutanebutanebutanepropane

Mass(kg)

20001000200020002000

Release Pressure(bar)

15157.5

1515

Average Surface-Emissive Power

(kW/m2)

370350320350340

• From Johnson et a!. (1990).

The aim of the tests was to study tank-wall performance. Nevertheless, afew data on BLEVE effects are presented by Schulz-Forberg et al. (1984). Anoverpressure of 130 mbar was measured at 80 m from the tank position in one ofthe tests, and was attributed to combustion. Temperatures and pressures at themoment of tank failure were beyond the superheat limit: 345-357 K and 24-39bar, respectively (see propane data in Table 6.1). Fireball development from onetest is presented in a series of photographs. The maximum diameter was approxi-mately 50 m, and duration was approximately 4 seconds. Fragmentation data, tothe extent published, are given in Section 6.3.

Experiments show that emissive power depends on fireball size. Moorhouseand Pritchard (1982) present a graph of the relationship of fireball size and emissivepower from results obtained by several investigators, among them, Hasegawa andSato 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 theadiabatic flame temperature, according to the Stefan-Boltzmann's law:

£max = <r7t (6.2.1)

where the proportionality constant a = 5.67 X 10~u kW/m2/K4 (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 thecombustion zone, and absorption of radiation in the fireball itself. The emissivepower (E) is therefore lower than the maximum emissive power (En^) of the blackbody radiation:

E = CE102x (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 (m"1)D = fireball diameter (m)

For methane-air fireballs, Hardee et al. (1978) found an E^ of 469 kW/m2. If anextinction coefficient of k = 0.18 m"1 (as measured in LNG fires) is used, thecurve 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 powerto rise as its diameter grows. The results of the experiments described above revealthat the fireball properties of greatest influence on radiation effects are:

Haseg. Fay + Hardee Johnson

Em

issi

ve

Pow

er

(kW

/m2)

Maxmrxm Fireball Diameter (m)

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

TABLE 6.3. Overview of Experimental Research on Fireball Generation

Emiss. PowerkW/rn2

Fireball DiameterDc(m)

Fireball DurationUs)

Fuel Massmf (kg)FuelsContainmentReference

3220

123

110-413

320-375

0.2-0.7

1.5-2.2

2.7-15

0.4-0.80.3-0.6

-40

12-15

56-88

0.4-0.8

1.8-2.4

0.8-1.7

0.5-1.00.4-0.7

-1.5

1.0-1.4

4.5-9.2

20-190 (cm3)

0.1-1

0.3-30

1.5-6(g)

0.1-452

7.5-14.5

1000-2000

CH4

C2H6

CH4

^sH12

^H1QCH4

C3H6

LPG

^H10

C3H8

Soap bubble

Polyethylene bags

Glass sphere pressurized

Soap bubbles

Pressurized tank

Pressurized tanks

Pressurized tanks

Fay and Lewis 1977

Hardeeetal. 1978

Hasegawa and Sato1977, 1987

Lihou and Maund1982

Maureretal. 1977

Baker: in Roberts 1982

Johnson et al. 1990

• 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;• fireball surface-emissive power;• total combustion duration.

The total radiation received by an object also depends on the fireball's positionrelative to the object (i.e., the view factor) and radiation adsorption by theatmosphere.

6.2.2. Fireball Diameter and Duration

Empirical Formula for Fireball Diameter and Duration

Several authors have published empirical equations from experiments and fromtheoretical considerations combined with experimental results. The equations de-scribe fireball combustion duration and maximum diameter as functions of originalfuel mass. Table 6.4 presents a summary of published results. An average value ispresented by the publications of Roberts (1982), Jaggers et al. (1986) and Pape etal. (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) (m)mf = mass of fuel (kg)tc = combustion duration (s)

Because the preceding equations also reflect the average of the previous empiricalformulas, they are recommended for use in predicting maximum fireball diameterand fireball combustion duration.

Fireball Diameter Models

A fireball's radiation hazard can be assessed by two factors: its diameter (either asa function of time or original amount of fuel) and combustion duration. Fireballmodels presented by Lihou and Maund (1982), Roberts (1982), and others startwith a hypothetical, premixed sphere of fuel and air (in some cases, oxidant) atambient 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)]

FireballDiameter

(m)

FireballDuration

(s)Data SourceFuelsReference

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

0.30mfo° 320(1)

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 mf

173

0.825mf026

0.825mf026

High 1968

Raj 1977ExperimentsExperimentsMaurer et al. 1977Hardeeetal. 1978Literature and modelBader 1971; Hardee and Lee 1973Data of Hasegawa and Sato 1977Maurer et al. 1977

LiteratureLiterature

Rocket fuel

C3H8

^sH12C3H6

CH4

C3H8

LJhou and Maund 1982

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

Pietersen 1985Pitblado 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.

(O0C and 1 atm) is a constant, if vapor is treated as a ideal gas, the initial diameterof 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 (kg/kmol)VM = mol volume at 273 K and atmospheric pressure

(i.e., 22.4m3/kmol)Ta = initial (ambient) temperature (K)mf = mass of fuel (kg)ma = mass of air (kg)D0 = initial sphere diameter (m)

When the initial sphere consists only of vapor, the value of /na must be taken aszero, and M equals the molecular weight of the fuel. Most models are tested withlow-molecular-weight alkanes.

Isothermal Model

A fireball is assumed to burn with a constant temperature Tc in the isothermal fireballmodel of Lihou and Maund (1982). Combustion is controlled by the supply of airand ceases after a time tc, which is correlated empirically with the mass of flammablegas in the initial vapor sphere. It is assumed that a fraction (1 — fc) of the fuel isused to form soot, and the remaining fraction/c burns stoichiometrically, producingan increase of n{ moles per mole of flammable gas. The stoichiometric molar ratioof 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 = diameter (m)Tc = temperature of fireball (K)Ta = temperature of ambient air (K)dDldt = rate of increase of fireball diameter (kept constant (m/s)

by most modelers)dVJdt = rate of air entrainment (m3/s)JJL = stoichiometric molar fuel-air ratio (-)H1 = increase in total number of moles per mole of (-)

flammable gas

The rate of combustion is set equal to the rate of heat applied to warm the entrainedair plus the radiative heat losses:

(6.2.8)

where

a = Stefan-Boltzmann constant (5.67 x 1(T11 kW(m2K4)) (kW/m2K4)e = emissivity (-)VM = mol volume (i.e., 22.4 nrVkmol) (m3/kmol)M = molecular weight of fuel (kg/kmol)Ma = molecular weight of air (kg/kmol)hc = lower heat of combustion of fuel (i.e., combustion heat (kJ/kg)

minus heat of evaporation of formed water)Cp3 = specific heat of air at constant pressure [kJ/(kgK)]

When substituting dVJdt from Equation (6.2.7), the following equation for thetemperature 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 initialdiameter of the sphere (D0) [Eq. (6.2.6)], the fireball's temperature and maximumdiameter can be calculated. From this model, it follows that the temperature of thefireball, and thus its emissive power, is independent of initial fuel mass.

From measurements of rising fireballs, Lihou and Maund (1982) found thatthe velocity of rise equals the rate of increase of the diameter, and that, for methaneand butane, dDldt is close to 10 m/s. They therefore suggest a simple relationshipto calculate the height z (m) of the fireball:

z = 1Or and thus zc = 10rc (6.2.13)

where zc is the final height (m).

The initial cloud fraction used to form soot (1 — /c) can be estimated as theratio 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 anemissivity of e = 1, the following expressions for fireball diameter and durationcan be given:

Tc = 193OK, Dc = 5.70<3 and tc = QA5mlf/3

The temperature for methane and butane calculated with the isothermal model is afactor 1.4 times greater than the average temperature measured by Lihou and Maund(1982) in their small-scale tests, although higher local maximum temperatures weremeasured. In this model, combustion is stoichiometric, thus leading to very highfireball temperatures which, in turn, lead to high radiation emissions. Effectivesurface emissions measured experimentally were one-half the value calculated fromthis model, because combustion is not stoichiometric and emissivity is less thanunity.

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 inenthalpy can be related to the initial mass ratio of fuel to air. If R = ma/mf for astoichiometric mixture, the enthalpy rise (H) can be approximated by

H = (^mahc)/R for ma Rmf (6.2.14)

and

H = (T}mfhc)/R for ma > Rmf (6.2.15)

where

hc = heat of combustion (kJ/kg)TJ = thermal efficiency that recognizes fuel losses and (-)

unburned fuel (TI < 1)R = mass ratio of fuel-air mixture (ma/mf) (-)

Now, the maximum diameter of the fireball can be written:

(6.2.16)

where

P0 = density of combustion products at initial temperature T0 (kg/m3)Cp = average specific heat of mixture considered to be constant (kJ/kgK)

from T0 to maximum fireball temperature

If mJRmf = 1 and t] = 1, the diameter Dc for a stoichiometric combustion equalsthe empirical relation cited by Pape et al. (1988), namely, Dc = 5.8m1/3. Accordingto Roberts (1982), the factor TJ lies between 0.75 and 1.

This model also produces a high temperature for combustion of a stoichiometricmixture of fuel and air, because it assumes that all combustion energy contributesto the increase in enthalpy and neglects energy lost by radiation. However, for anair/fuel ratio of 1.5 to 2 and with TJ = 0.75, the fireball temperature approximatesthat 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 buoyancyand entrainment are dominant. Hardee and Lee (1978) give the following expressionfor liftoff time tlo:

tlo = \.\m\16 (6.2.17)

This is consistent with data published by High (1968). Because liftoff is buoyancy-controlled, its relation to initial mass must have a power of 1/6, as shown by afireball model of Fay and Lewis (1977).

In general, hazard calculations assume that fireballs are spherical and touchthe 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 vapor-ization equals 36% or more, all released fuel contributes to the BLEVE and eventu-ally to the fireball. For lower flash-vaporization ratios, part of the fuel forms theBLEVE, and the remainder forms a pool. It is assumed that, if flash vaporizationis below 36%, three times the calculated quantity of the flash vaporization contributesto the BLEVE.

Small-scale experiments by Schmidli et al. (1990) showed that, as degree ofsuperheat increases, the quantity of fuel forming a pool decreases and dropletformation increases. These results support the proposition that more fuel is involvedin a BLEVE than calculated from flash evaporation.

For hazard prediction purposes, the amount of gas in a BLEVE can be assumedto be three times the amount of flash evaporation, up to a maximum of 100% ofavailable fuel.

6.2.5. Fireball Radiation

The main hazard from a BLEVE fireball is its thermal radiation, which can causesecondary fires and can burn people severely. Rapid mixing, combustion, and

evaporation of fuel droplets produce a fireball whose thermal emission exceedsnormal flame emissions. Methods for calculating radiation from fires and fireballsare described in Section 3.5.

Section 3.5 mentions two approaches, the point-source model and the solid-flame model. In the point-source model, it is assumed that a certain fraction of theheat of combustion is radiated in all directions. This fraction is the unknown param-eter of the model. Values for fireballs are presented in Section 3.5.1. The point-source model should not be used for calculating radiation on receptors whose planeintercepts the fireball (see Figure 6.9B).

The solid-flame model, presented in Section 3.5.2, is more realistic than thepoint-source model. It addresses the fireball's dimensions, its surface-emissivepower, atmospheric attenuation, and view factor. The latter factor includes theobject'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 beyondthat presented in Section 3.5.2. Furthermore, view factors applicable to fireballsare discussed in more detail.

fireball fireball

receptor 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 modeldeveloped from the generalized formulation (presented in Section 3.5.1) and Rob-erts'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{ = mass of fuel in the fireball (kg)T8 = atmospheric transmissivity (-)/fc = net heat of combustion per unit mass (J/kg)R = radiative fraction of heat of combustion (-)L = distance from fireball center to receptor (m)q = radiation received by the receptor (W/m2)

Hymes suggests the following values of R:

R =0.3; fireballs for vessels bursting below relief valve pressureR = 0.4; fireballs 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 persquare meter.

Emissive Power. Pape et al. (1988) used data of Hasegawa and Sato (1977) todetermine a relationship between emissive power and vapor pressure at time ofrelease. For fireballs from fuel masses up to 6.2 kg released at vapor pressures to20 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 measuredin small-scale experiments. A reduction in emissive power as scale increased wasalso found in pool fires. A reasonable emissive power associated with large-scalereleases of hydrocarbon fuels seems to be 350 kW/m2. The values obtained byBritish 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 Lfrom 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<f> is theview angle, and © is the angle between the normal vector to the surface and theline connecting the target point and the center of the sphere (see Figure 6.9), theview factor (F) is given by

(6.2.21)

and

(6.2.22)

where

r = radius of fireball (r = D/2) (m)D = diameter of fireball (m)L = distance to center of sphere (m)& = angle between normal to surface and connection of

point to center of sphere (radians)24> = view angle (radians)

In Figure 6.9B, the extended surface intersects the sphere in such a way thata 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 beneaththe center of the fireball to the receptor at ground level (Figure 3.11). For a horizontalsurface, 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) (m)H = height of center of fireball (m)X = distance along ground between receptor and a point directly

beneath center of fireball (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 re-ceived, radiation must be integrated over combustion time: a time-dependent heightand diameter (giving a time-dependent view factor) must be used. For large-scaleBLEVEs, the assumption that the fireball is at its maximum diameter and "rests"on the ground will yield a somewhat conservative prediction of thermal radiationhazard. However, note that the initial hemispherical shape of the developing fireballcould 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 themeasured radiation flux q received by a detector at a distance L (m) from the centerof 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 levelof 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)

Time to Reach PainRadiation Intensity Threshold(Btu/hr/fi2) (kW/m2) (s)

500 1.58 60740 2.33 40920 2.90 30

1500 4.73 162200 6.94 93000 9.46 63700 11.67 46300 19.87 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 third-degree burns.

Thermal effects depend on radiation intensity and duration of radiation expo-sure. American Petroleum Institute's Recommended Practice 521 (1982) reviewsthe effects of thermal radiation on people. In Table 6.5, data on time to reach painthreshold are given. As a point of comparison, the solar radiation intensity on aclear, hot summer day is about 1 kW/m2 (317 Btu/hr/ft2). Criteria for thermaldamage 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 andQuanta (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 equipmentMinimum energy required to ignite wood at indefinitely

long exposures

12.5 Minimum energy required for piloted ignition of wood, meltingof plastic tubing

9.5 Pain threshold reached after 8 s; second degree burnsafter 20 s

4.0 Sufficient to cause pain to personnel if unable to reach coverwithin 20 s; however, blistering of the skin (second degreeburns) is likely; 0% lethality

1.6 Will cause no discomfort for long exposure

exposure time (sec)

Figure 6.10. Tolerance times to burn-injury levels for various incident heat fluxes (Hymes1983).

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 radiationduration in seconds.

Buildings and process equipment suffer severe damage for incident heat fluxesof 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 wouldbe damaged after an exposure of 1000 s to the heat fluxes quoted above.

I 1 I I I T

3° burns, to bare skin (2mm)

50% lethality (averageclothing)

-1 % lethality (averageclothing)

start of 2° burns

range for blisteringof bare skin i.e.threshold

inci

dent

hea

t flu

x (k

W/m

2)

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 50,000kg 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 radiationdamage using data and correlations from nuclear weapons testing. The probabilityof fatality was found to be generally proportional to the product f/4/3, where t is theradiation duration and / is the radiation intensity. Table 6.7 shows the data used todevelop estimates of fatalities from thermal radiation data.

6.2.7. Case Studies

Although descriptions of many BLEVE accidents are available, data on fireballdimensions and height rely on accident eyewitnesses, so data on radiation are verylimited. Nevertheless, it appears possible to compare calculated fireball dimensionswith those actually witnessed in accidents.

Fireball Dimensions. Moorhouse and Pritchard (1982) published a list of accidentsand the reported fireball diameters and heights. Table 6.8 relates these data tocalculated dimensions. The following relationship can be used to calculate thefireball diameter:

Dc = 5.8mf1/3 (6.2.28)

where:

Dc = diameter of fireball (m)mf = initial fuel mass (kg)

TABLE 6.7. Relationship of Death from Radiation Burns to Radiation Leveland Duration

Probability of Fatality Duration, t Radiation Intensity, I Dosage, t!4/3

(%) (sec) (kW/m2) [sec(kW/m2)413]

1 1.43 146.0 10991 10.1 33.1 10731 45.2 10.2 100050 1.43 263.6 241750 10.1 57.9 226450 45.2 18.5 221099 1.43 586.0 700899 10.1 128.0 654699 45.2 39.8 6149

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

CaIc.Year Place Fuel m^ (t) zc (m) Dc (m) Dc (m)

1970 Crescent City, IL Propane 75 250 150-200 2451971 Houston, TX Vinyl chloride 165 — 300 3181972 Lynchburg, VA Propane 9 — 120 1201973 Kingman, AR Propane 45 — 300 2061974 St. Paul, MN LPG 10 100 100 1251974 Aberdeen, Scotl. Butane 2 — 7 0 7 31976 Belt, MT LPG 80 — 300 2501978 Lewisville, AR Vinyl chloride 110 — 305 278

as proposed by Roberts (1982) and Jaggers et al. (1986). All available fuel wasassumed to be consumed in the calculation of diameters in Table 6.8.

As Table 6.8 shows, agreement between witnesses' estimates of fireball dimen-sions 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 aBLEVE 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 thefireball, 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 inbetter agreement with witnesses' estimates.

Pietersen (1985) gives the following damage due to BLEVEs at the San Juanicoaccident site:

Paint comes off wood 400 mGlass damage 600 mCurtains and artificial grass set on fire 600 mBrowning leaves 1200 mHeat damaged plastic flags 1200 m

Radiation effects from a fireball of the size calculated above, and assumed to bein contact with the ground, have been calculated by Pietersen (1985). A fireballduration 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 testsby 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 byLihou 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 givenby Pietersen. Leaf-browning at 1200 m agrees with the threshold value of 1050 mfor wood combustion. The fact that glass is broken and cloth is ignited at a distanceof 600 m is, in a broad sense, in reasonable agreement with the threshold valuefor equipment damage. Nevertheless, it is difficult to comment on the validity ofmodels because available damage information is limited, even though the SanJuanico 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 producesmost of the blast effects. Rapid expansion of vapor produces a blast identical tothat of other pressure vessel ruptures, and so does flashing liquid. Therefore, it isnecessary to calculate blast from pressure vessel rupture in order to calculate aBLEVE blast effect.

This section first presents literature review on pressure vessel bursts andBLEVEs. Evaluation of energy from BLEVE explosions and pressure vessel burstsis emphasized because this value is the most important parameter in determiningblast strength. Next, practical methods for estimating blast strength and durationare presented, followed by a discussion of the accuracy of each method. Examplecalculations 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

Radiation Intensity DistanceEffect (kW/m2) (m)

Level of minor discomfort 1.6 3000Threshold of pain 4.0 1850Combustion of wood threshold 12.5 1050Hazardous for equipment level 37.5 560

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for a vertical surface was used. The "hazard range to severe burns" proposed byLihou 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 givenby Pietersen. Leaf-browning at 1200 m agrees with the threshold value of 1050 mfor wood combustion. The fact that glass is broken and cloth is ignited at a distanceof 600 m is, in a broad sense, in reasonable agreement with the threshold valuefor equipment damage. Nevertheless, it is difficult to comment on the validity ofmodels because available damage information is limited, even though the SanJuanico 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 producesmost of the blast effects. Rapid expansion of vapor produces a blast identical tothat of other pressure vessel ruptures, and so does flashing liquid. Therefore, it isnecessary to calculate blast from pressure vessel rupture in order to calculate aBLEVE blast effect.

This section first presents literature review on pressure vessel bursts andBLEVEs. Evaluation of energy from BLEVE explosions and pressure vessel burstsis emphasized because this value is the most important parameter in determiningblast strength. Next, practical methods for estimating blast strength and durationare presented, followed by a discussion of the accuracy of each method. Examplecalculations 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

Radiation Intensity DistanceEffect (kW/m2) (m)

Level of minor discomfort 1.6 3000Threshold of pain 4.0 1850Combustion of wood threshold 12.5 1050Hazardous for equipment level 37.5 560

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in the surrounding air traveling from the explosion center at a velocity greater thanthe speed of sound. The fluid expands spherically and does not mix immediatelywith the surrounding air, so a sort of fluid "bubble" is formed which has an interfacewith surrounding air. The released fluid's momentum causes it to overexpand, andthe pressure within the bubble then drops below ambient pressure. After the fluidbubble reaches its maximum diameter, it collapses again, thus producing a phaseof negative pressure and reversed wind direction in the surrounding air. The bubblerebounds upon reaching its minimum diameter, thus producing a second shock.The bubble will continue to oscillate before coming to rest, producing ever-smallerpressure waves.

The most important blast-wave parameters are peak overpressure ps and positiveimpulse is, as shown in Figure 6.11. The deep negative phase and second shockare clearly visible in this figure.

The strength and shape of a blast wave produced by a sudden release of fluiddepends on many factors, including type of fluid released, energy it can producein expansion, rate of energy release, shape of the vessel, type of rupture, andcharacter of surroundings (i.e., the presence of wave-reflecting surfaces and ambientair pressure). The type of fluid is very important. It can be a gas, a superheatedliquid, a liquid, or some combination of these. Unsuperheated liquid cannot producea blast, so the volume of unsuperheated liquid in a vessel need not be considered.

In the following subsections, a selection of the theoretical and experimentalwork on pressure vessel bursts and BLEVEs will be reviewed. Attention will firstbe focused on an idealized situation: a spherical, massless vessel filled with ideal

pres

sure

(ps

i)

time (sec)

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

gas and located high above the ground. Increasingly realistic situations will bediscussed 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 locatedfar from surfaces that might reflect the shock wave. Furthermore, it is assumed thatthe vessel will fracture into many massless fragments, that the energy required torupture the vessel is negligible, and that the gas inside the vessel behaves as anideal gas. The first consequence of these assumptions is that the blast wave isperfectly spherical, thus permitting the use of one-dimensional calculations. Second,all energy stored in the compressed gas is available to drive the blast wave. Certainequations can then be derived in combination with the assumption of ideal gasbehavior.

Experimental Work. Few experiments measuring the blast from exploding, gas-filled pressure vessels have been reported in the open literature. One was performedby Boyer et al. (1958). They measured the overpressure produced by the burst ofa small, glass sphere which was pressurized with gas.

Pittman (1972) performed five experiments with titanium-alloy pressure vesselswhich were pressurized with nitrogen until they burst. Two cylindrical tanks burstat 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 werepressurized to extremely high pressures with argon until they burst. Nominal burstpressures ranged from 100 MPa to 345 MPa. Experiments were performed justabove ground surface.

Finally, Esparza and Baker (1977a) conducted twenty small-scale tests in amanner similar to that of Boyer et al. (1958). They used glass spheres of 51 mmand 102 mm diameter, pressurized with either air or argon, to overpressures rangingfrom 1.22 MPa to 5.35 MPa. They recorded overpressures at various places andfilmed the fragments. From these experiments, it was learned that, compared to theshock wave produced by a high explosive, shock waves produced by bursting gas-filled vessels have lower initial overpressures, longer positive-phase durations, muchlarger 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 gaseffects must be dealt with at high pressures.

Numerical Work. The results of experiments described above can be better under-stood when compared to the results of numerical and analytical studies. Numericalstudies, in particular, provide real insight into the shock formation process. Chushkinand Shurshalov (1982) and Adamczyk (1976) provide comprehensive reviews ofthe many studies in this field. The majority of these studies were performed formilitary 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 fromvolumes of high-pressure gas as well. Only the most important contributions willbe reviewed here.

Many numerical methods have been proposed for this problem, most of themfinite-difference methods. Using a finite-difference technique, Erode (1955) ana-lyzed the expansion of hot and cold air spheres with pressures of 2000 bar and1210 bar. The detailed results allowed Erode to describe precisely the shock forma-tion process and to explain the occurrence of a second shock.

The process starts with expansion from the initial volume. This creates a shockwave in the surrounding air, called the main shock, which travels faster than thecontact 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 thevessel. Behind this wave, an inwardly moving shock forms. It does not acquire anet 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 outwardtoward the contact surface. At the time it strikes the contact surface, the gases atthe contact surface are more dense and much cooler than surrounding air. Conse-quently, the shock is partially reflected on the contact surface. The portion that istransmitted is called the second shock; it may eventually overtake the main shock.

Baker et al. (1975) used a finite-difference method with artificial viscosity toobtain blast parameters of spherical pressure vessel explosions. They calculatedtwenty-one cases, varying pressure ratio between vessel contents (gas) and sur-rounding 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 apractical method to calculate blast parameters of bursting pressure vessels, so theysynthesized the results into graphs presenting shock overpressure and impulse as afunction 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 blastparameters 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 aspherical vessel. Baker et al. provide the following guidelines for adapting thismethod to surface bursts of nonspherical vessels: Multiply the energy of the explo-sion 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 nonsym-metrical shock wave. The latter multiplication factors were determined experimen-tally for high explosives. In Section 6.3.2., instead of a free-air burst, a surfaceburst of a spherical vessel is assumed as the standard model, and the procedure isrearranged. 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 theexperimental results of Esparza and Baker (1977) indicates that values in Figure6.21 overstate slightly the shock overpressure, even after taking into account thekinetic energy absorbed by fragments. Impulses compare well.

Adamczyk (1976) noted that this work shows that equivalence with high explo-sives is usually attained only in the far field for high bursting-pressure ratios andtemperature ratios. When low bursting-pressure ratios or temperature ratios areused, overpressure curves do not coalesce in the far field; hence, equivalence withhigh explosives may not be attained. He noted that many of the curves that do notcoalesce are those with gases whose sound speeds are relatively low speeds. Suchcurves represent situations in which the potential energy within the sphere is notconverted efficiently to kinetic energy of the medium. Such conversion depends onpropagation of the rarefaction wave into surrounding gas. However, since this wavepropagates at sonic velocity, a considerable time lapses before it releases the energystored in the high-pressure gas. This analysis suggests that the rate of conversionof potential energy to the surrounding gas can be an important parameter in blast-phenomena considerations.

Guirao and Bach (1979) used the flux-corrected transport method (a finite-difference 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 inwhich the unburned fuel-air mixture is instantaneously transformed into combustiongases. By this route, they obtained spheres whose pressure ratios (identical withtemperature ratios) were 8.3 to 17.2, and whose ratios of specific heats were 1.136to 1.26. Their calculations of shock overpressure compare well with those of Bakeret al. (1975). In addition, they calculated the work done by the expanding contactsurface between combustion products and their surroundings. They found that only27% to 37% of the combustion energy was translated into work.

Analytical Work. Analytical work performed on pressure vessel explosions can bedivided into two main categories. The first attempts to describe shock, and thesecond is concerned with the thermodynamic process.

The peak overpressure developed immediately after a burst is an importantparameter for evaluating pressure vessel explosions. At that instant, waves aregenerated at the edge of the sphere. The wave system consists of a shock, a contactsurface, and rarefaction waves. As this wave system is established, pressure at thecontact surface drops from the pressure within the sphere to a pressure within theshock wave.

Initial shock-wave overpressure can be determined from a one-dimensionaltechnique. It consists of using conservation equations for discontinuities throughthe shock and isentropic flow equations through the rarefaction waves, then matchingpressure and flow velocity at the contact surface. This procedure is outlined inLiepmann and Roshko (1967) for the case of a bursting membrane contained in ashock tube. From this analysis, the initial overpressure at the shock front can becalculated with Eq. (6.3.22). This pressure is not only coupled to the pressure inthe 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 thisapproach, the states of the gases before the beginning and after the completion of

the explosion process are compared. Explosion energy can thus be calculated. Thisenergy is a very important parameter because, of all the variables, it has the greatestinfluence on blast parameters and thus on the destructive potential of an explosion.

The thermodynamic method has limitations. Since the method ignores theintermediate stages, it cannot be used to determine shock-wave parameters. Further-more, a shock wave is an irreversible thermodynamic process; this fact complicatesmatters 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 ofexplosion energy because it is very easy and can be applied to a wide range ofexplosions. Therefore, this method has been applied by practically every workerin the field.

Unfortunately, there is no consensus on the measure for defining the energyof an explosion of a pressure vessel. Erode (1959) proposed to define the explosionenergy simply as the energy, £ex,Br» that must be employed to pressurize the initialvolume from ambient pressure to the initial pressure, that is, the increase in internalenergy between the two states. The internal energy U of a system is the sum ofthe kinetic, potential, and intramolecular energies of all the molecules in the system.For an ideal gas it is

(6.3.1)

where

U = internal energy (J)p = absolute pressure (Pa)V = volume (m3)7 = ratio of specific heats of gas in system (-)

Therefore £Cx,Br *s

(6.3.2)

where the subscript 1 refers to initial state and the subscript O refers to ambientconditions.

Other investigators use the work done by the expanding surface between thegases 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 equalto 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 andresidual internal energies.

£ex,wo ^ U 1 - U 2 (6.3.3)

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

Thus, for an ideal gas, the work is

(6.3.4)

For an ideal gas, pV1 is constant for isentropic expansion (that is, without energyaddition 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</Ecx Br can be written as

f^ = J- [(I - P1) - (1 + P1)I1^i (6.3.7)

^ex,Br PI

where P1 is the nondimensional overpressure in the initial state (P1Tp0) - 1- Thisfunction is depicted in Figure 6.13.

Investigators of vapor cloud explosions (Chapter 4) often use the combustionenergy as a measure for the energy of the explosion. This energy heats, and therebypressurizes, the initial volume. Combustion energy is equal to the change in internalenergy 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 differenceof a few percent.

Adamczyk (1976) is one of the few who tried to incorporate energy lossesfrom the irreversible shock process into the calculation. He proposes to use thework 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 givenby Eq. (6.3.22). The further development of pressure at the contact surface canonly be evaluated numerically. However, the actual p- V process can be adequatelyapproximated by the dashed curve in Figure 6.12. In this process, the constant-pressure segment represents irreversible expansion against an equilibrium counter-pressure p3 until the gas reaches a volume V3. This is followed by an isentropicexpansion to the end-state pressure pQ. For this process, the point (p3, V3) is noton the isentrope which emanates from point (pl9 V1), since the first phase of theexpansion process is irreversible. Adamczyk calculates point (p3, V3) from theconservation 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> (6<3.9)Pi ~ Po

is defined, EeX)M/EexEr for the entire process can be expressed as a function of £,P1, and Tf1.

](6.3.10)

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

combustion energy and Brode's energy is taken into account, their results are about10% lower than those resulting from Eq. (6.3.10). This small difference indicatesthat 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 vesselis somewhere inside the control volume.) Before the vessel bursts, the internalenergy 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, thepressure 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 internalenergy 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). Aslanovand 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 andwith experiments.

In Figures 6.13, 6.14, and 6.15, the proposed measures for the explosionenergy are compared. Figure 6.13 gives the ratio Eexwo/EeKEr for three values ofthe ratio of specific heats of the pressurized gas, and Figure 6.14 does the samefor £ex,AG^ex,Br Figure 6.15 gives an impression of the ratio EGxM/E^BT for Adam-czyk's definition of the explosion energy. This ratio is different for every type ofgas. In this figure, the pressurized gas was air of 300, 3000, and 30,000 K. Theambient 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 givewidely varying results. They all approach Brode's equation for high initial overpres-sures, but for initial pressures of practical interest, the results vary by a factor of4. Thus, there is no consensus on the definition of the most important variable ofan explosion, its energy. All experimental and most numerical results given in theliterature use Brode's definition. However, when the fluid is a nonideal gas or aliquid, almost everyone uses the work done in expansion as the explosion energy(see Section 6.3.2.). The available prediction methods for blast parameters arebased 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 A J1XT0 O T/TO + T/T0

y=1.4 1 10 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 andfollowing 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, theshock wave produced by the explosion will reflect on the earth's surface. Thereflected wave overtakes the first wave and increases its strength. The resultingshock wave is similar to a shock wave which would be produced in free air by theoriginal 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, hisresults are inconclusive, because the number of cases he studied was small andbecause the grid he used was coarse. Baker et al. (1975) recommend, on the basisof experimental results with high explosives, the use of a method described in detailin Section 6.3.3. That is, multiply the volume of the explosion by 2, read theoverpressure and impulse from graphs for free-air bursts, and multiply them by afactor 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 almostevery actual pressure vessel burst. Loss of symmetry means that detailed calculations

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

and experimental measurements become much more complicated, because the calcu-lations and measurements must be made in two or three dimensions instead of one.Numerical calculations of bursts of pressurized-spheroid gas clouds were made byRaju and Strehlow (1984) and by Chushkin and Shurshalov (1982). Raju andStrehlow (1984) compute the expansion of a gas cloud corresponding to a constantvolume 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 timesfollowing the explosion are shown as solid and dashed curves. The shape of theshock wave is almost elliptical, with ellipticity decaying to sphericity as the shockgradually degenerates into an acoustic wave.

Scaled peak overpressure and positive impulse as a function of scaled distanceare given in Figures 6.17 and 6.18. The scaling method is explained in Section3.4. Figures 6.17 and 6.18 show that the shock wave along the axis of the vesselis initially approximately 50% weaker than the wave normal to its axis. Since strongshock waves travel faster than weak ones, it is logical that the shape of the shockwave approaches spherical in the far field. Shurshalov (Chushkin and Shurshalov

lead wave cloud interface

1982) performed a similar calculation; results confirmed those of Raju and Strehlow(1984). Shurshalov also found that the shock wave approaches a spherical shapemore rapidly when the explosion is stronger.

Even greater differences in shock pressure can be found when the pressurevessel does not burst evenly, but ruptures into two or three pieces. In that case, ajet emanates from the rupture, and the shock wave becomes highly directional.Pittman (1976) found experimental overpressures along the line of the jet to begreater, by a factor of four or more, than pressures along a line in the oppositedirection from the jet. Baker et al. (1978b) tried to analyze, with a two-dimensionalnumerical code, the case of a spherical vessel bursting into two equal parts. Theymay have used a massless vessel in their calculations, but their vessel probably hada mass typical of normal storage vessels. This is not clear from their description.

Baker et al. analyzed only six cases, including three different overpressuresand three ratios of specific heat, each at ambient temperature. In addition, they hadto use a large cell size because of limitations in computer power. They found thatoverpressures along the line of the jet could be predicted by a method similar tothe 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

BAKER'S PENTOLITE 5--BURSTING SPHERE

MA

X

OV

ER

PR

ES

SU

RE P

e 2>

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

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 apressure 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 outsidea 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 whetherthe 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 vesselis available to drive the blast wave. In fact, energy must be spetot to rupture thevessel and propel its fragments. In some cases, the vessel expands before bursting,thus absorbing additional energy. Should a vessel also contain liquid or solids, afraction of the available energy may be spent in its propulsion.

Vessel Expansion. In most cases, vessels rupture without significant expansion. Inmost cases in which a vessel is exposed to external fire, the vessel wall temperaturedistribution is very uneven. Then, typically, only a small bulge is produced before

IMP

UL

SE

(E

NE

RG

Y

SC

AL

ED

) j c

o1 - - P H I = O 2 - - P H I = 4 5 3--PHI = 90

4--BAKER 1 S PENTOLITE 5--BURSTlNG SPHERE

the vessel bursts. If a vessel fails as a result of mechanical attack, there is noexpansion. Vessel expansion can be a significant factor if rupture results from aninternal pressure build-up, but that topic is outside the scope of this volume. Forthese reasons, expansion of the vessel may be safely neglected.

Vessel Rupture. The energy needed to rupture a vessel is very low, and can beneglected in calculation of explosion energy. For a typical steel vessel, ruptureenergy is on the order of 1 to 10 kJ, that is, less than 1% of the energy of asmall explosion.

Fragments. As will be explained in Section 6.4, between 20% and 50% of availableexplosion energy may be transformed into kinetic energy of fragments and liquidor solid contents.

6.3.2. Blast from BLEVEs

A vessel filled with a pressurized, superheated liquid can produce blasts uponbursting in three ways. First, the vapor that is usually present above the liquid cangenerate a blast, as from a gas-filled vessel. Second, the liquid will boil upondepressurization, and, if rapid boiling occurs, a blast will result. Third, if the fluidis combustible and the BLEVE is not fire induced, a vapor cloud explosion mayoccur (see Section 4.3.3.). In this subsection, only the first and second types ofblast will be investigated.

Experimental Work. Although a great many investigators studied the release ofsuperheated 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 etal. (1978a) reports on a study done by Esparza and Baker (1977b) in which liquidCFC-12 was released from frangible glass spheres in the same manner as in theirstudy of blast from gas-filled spheres. The CFC was below its superheat limittemperature. No significant blast was produced.

Investigators at BASF (Maurer et al. 1977; Giesbrecht et al. 1980) conductedmany small-scale experiments on bursting cylindrical vessels filled with propylene.The vessels were completely filled with liquid propylene at a temperature of around340 K (which is higher than the superheat limit temperature Jsl) and a pressure ofaround 60 bar. Vessel volumes ranged from 0.226 x 10~3 m3 to 1.00 m3. Thevessels were ruptured with small explosive charges, and after each release, theresulting cloud was ignited. While the experiments focused on explosively dispersedvapor clouds and their subsequent deflagration, the pressure wave developed fromthe flashing liquid was measured.

The investigators found that overpressures from the evaporating liquid com-pared 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 LPGBLEVEs similar to those conducted by BASF. The experimenters measured very lowoverpressures from the evaporating liquid, followed by a shock that was probably theso-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 probablyresulted from experimental procedures involving ignition of the release. The liquidwas below the superheat limit temperature at time of burst.

Theoretical Work. Theoretical work on the blast from superheated liquid addressestwo 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'stheory is as follows: Before the vessel ruptures, its liquid is in equilibrium with itssaturated vapor. Upon rupture, vapor blows off and liquid pressure drops rapidly.Equilibrium is lost, and liquid vaporizes vigorously at the liquid-vapor and theliquid—solid interfaces. Such vaporization, however, may be insufficient to maintainpressure. If the liquid is below its superheat limit temperature, it may not boilthroughout the bulk of the liquid, because forces between its molecules are strongerthere than at the liquid-vapor and liquid-solid interfaces. However, if the liquidis above its superheat limit temperature when the pressure drops, further microscopicbubbles begin to form and grow. Because this phenomenon occurs almost instantane-ously throughout the bulk of the liquid, a large fraction of liquid can be transformedinto vapor within milliseconds. The precise timing is governed by the time it takesfor the decompression wave to pass through the liquid.

Instantaneous boiling takes place only if the temperature of a liquid is higherthan its superheat-limit temperature Tsl (also called the homogeneous-nucleationtemperature), in which case, boiling occurs throughout the bulk of the liquid. Thistemperature is only weakly dependent on the initial pressure of the liquid and thepressure to which it depressurizes. As stated in Section 6.1., Tsl has a value ofabout 0.89rc, where Tc is the (absolute) critical temperature of the fluid.

Thus, the BLEVE theory predicts that, when the temperature of a superheatedliquid is below 7sl, liquid flashing cannot give rise to a blast wave. This theory isbased on the solid foundations of kinetic gas theory and experimental observationsof homogeneous nucleation boiling. It is also supported by the experiments of BASFand British Gas. However, because no systematic study has been conducted, thereis no proof that the process described actually governs the type of flashing thatcauses strong blast waves. Furthermore, rapid vaporization of a superheated liquidbelow its superheat limit temperature can also produce a blast wave, albeit a weak

one. Also, present work (Venert 1990) suggests that certain operations can causea fluid to become pre-nucleated, which enables the fluid to flash explosively upondepressurizing.

Analysis of an incident (Van Wees 1989) involving a carbon dioxide storagevessel suggests that carbon dioxide can evaporate explosively even when its tempera-ture is below rsl. This may occur because carbon dioxide crystallizes at ambientpressure, thus presenting enough nucleation sites for liquid to flash.

The theory explains why a succession of shocks may occur in BLEVEs. A firstshock is produced by the escape of vapor, a second by evaporating liquid, a thirdby the "second shock" of the oscillating fluid bubble, and possible additional shocksproduced by combustion of released fluid. It is also possible for these shocks tooverlap each other, especially at greater distances from the explosion.

Determination of the energy released by flashing liquid is a problem addressedby 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 airas it expands isentropically. In this case, the change in internal energy must becalculated 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 reasonableagreement with experimental results from BASF studies. The procedure is presentedin more detail by Baker et al. (1978b).

Wiedermann (1986b) presents an alternative method for calculating work doneby 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 onefluid parameter, lambda. Unfortunately, this parameter is known for very few fluids.

TNT Equivalence. Explosion strength is often expressed as "equivalent mass ofTNT' in order to permit estimates of possible explosion damage. For BLEVEs andpressure vessel bursts, using this equivalence is unnecessary because the methodsmentioned above give explosion blast parameters which relate directly to the amountof possible damage potential. However, the concept of TNT equivalence is stilluseful because it appeals to those who seldom deal with blast parameters. Forreasons explained in Section 4.3.1, BLEVEs or pressure vessel bursts cannot readilybe compared to explosions of TNT (or other high explosives). Only the main pointsare 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 thewave travels from the source, thus causing rapid decay of overpressures presentat close range.

• Blast waves close to the source of pressure vessel bursts differ greatly fromthose from TNT blasts.

• The impulse at close range from a pressure vessel burst is greater than a TNTexplosion with the same overpressure. Therefore, it is conservative to use

damage relationships which are based on nuclear explosions, such as those inTable 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 energyin TNT.

For these reasons, the concept of TNT equivalency appears to have little applicationto near-field estimates.

In the method which will be presented in Section 6.3.3., the blast parametersof pressure vessel bursts are read from curves of pentolite, a high explosive, fornondimensional distance R above two. For these ranges, using TNT equivalencemakes sense. Pentolite has a specific heat of detonation of 5.11 MJ/kg, versus 4.52MJ/kg for TNT (Baker et al. 1983). The equivalent mass of TNT can be calculatedas follows for a ground burst of a pressure vessel:

WTNT = <6'3'14)

where

WTNT = equivalent mass of TNT (kg)/ITNT = heat of detonation of TNT (4.52 MJ/kg)E6x = energy of explosion (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), ratherthan overpressure, determine the extent of damage. Table 6.10 was prepared forblast waves of nuclear explosions, and generally provides conservative predictionsfor other types of explosions. More information on the damage caused by blastwaves 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 vesselbursts and BLEVEs will be presented. All methods are related; that is, one basicmethod and two variations are presented. The choice of method depends upon phaseof the vessel's contents and distance to the blast wave's "target," as illustrated inFigure 6.19.

The application of information in Figure 6.19 requires some explanation. Thedecision as to which calculation method to choose should be based upon the phaseof the vessel's contents, its boiling point at ambient pressure Tb, its critical tempera-ture Jc, and its actual temperature T. For the purpose of selecting a calculationmethod, 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

Corrugated asbestos sidingCorrugated steel or

aluminumWood siding panels

standard houseconstruction

Concrete or cinder-blockwall panels 8 or 12 inchthick (not reinforced)

Self-framing steel panelbuilding

Oil storage tankWooden utility polesLoaded rail carsBrick wall panel 8 or 1 2 inch

thick (not reinforced)

Failure

Usually shattering, occasionalframe failure

ShatteringConnection failure followed

by bucklingFailure, usually at main

connections, allowing awhole panel to be blown in

Shattering of wall

Collapse

RuptureSnapping failureOverturnedShearing, flexure failure

Approx. Side-onOverpressure

(bar) (psi)

0.03-0.07 0.5-10.07-0.14 1-2

0.07-0.14 1-2

0.07-0.14 1-2

0.14-0.20 2-3

0.20-0.28 3-40.20-0.28 3-4

0.34 50.48 7

0.55 7-8

blast-parameter calculation should be based upon the total amount of energyreleased.

Temperature determines whether or not the liquid in a vessel will boil whendepressurized. The liquid will not boil if its temperature is below the boiling pointat ambient pressure. If the liquid's temperature is above the superheat-limit tempera-ture 7sl (rsl = 0.89rc), it will boil explosively (BLEVE) when depressurized.Between these temperatures, the liquid will boil violently, but probably not rapidlyenough to generate significant blast waves. However, this is not certain, so it isconservative 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," canonly 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 thebasic 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 effectsfrom the rupture of gas-filled pressure vessels. They include a method for calculatingthe overpressure and impulse of blast waves from the rupture of spherical or cylindri-

start

liquid ,2 ^ ideal gasphase contents)

no blasteffects

calc. energy withexplosive flashingmethod

calc. energy withbasic method

vapor,non-ideal gas

range

far field

calc. enenexplosive flashingmethod

end

near field

refined method

continue withbasic method

collect data

temperature

assumeexplosiveflashing

explosiveflashing

Figure 6.19. Selection of blast-calculation method.

cal vessels located at ground level. The relationship of overpressure to distance fora rupturing pressure vessel depends strongly upon the pressure, temperature, andratio of specific heats of the contained gas. When pressures and temperatures arehigh, blast waves in the far field are very similar to those generated by highexplosive-detonation. This similarity forms the basis for the basic method, in whichthe compressed gas's stored energy is first calculated, then overpressure and impulseare read from charts which relate detonation-blast parameters to charges of highexplosive with the same energy.

The general procedure of the basic method is shown in Figure 6.20. Thismethod is suitable for calculations of bursts of spherical and cylindrical pressurevessels which are filled with an ideal gas, placed on a flat surface, and distant fromother obstacles which might interfere with the blast wave.

calc. PS and is

check P8

Figure 6.20. Basic method.

start

collect data

calculate energy

3calculated R of 'target1

step 7 ofexplosive flashing

methodcheck R

refined method

determine P8

determine I

adjust P8 and I

end

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 = energy of compressed gas (J)P1 = absolute pressure of gas (N/m2)P0 = absolute pressure of ambient air (N/m2)V1 = volume of gas-filled space of vessel (m3)^y1 = ratio of specific heats of gas in system (-)

This energy measure is equal to Erode's definition of the energy, multiplied by afactor 2. The reason for the multiplication is that the Erode definition applies tofree-air burst, while Eq. (6.3.15) is for a surface burst. In a free-air burst, explosionenergy 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 suchcases, use the refined method, described in Section 6.3.3.2., to obtain a moreaccurate pressure estimate.

Step 5: Determine P8.To determine the nondimensional side-on overpressure P8, read P8 from Figure 6.21or 6.22 for the appropriate R. Use the curve labelled "high explosive" if Figure6.21 is used.

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

high e cplosive

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 or6.24 for the appropriate R. Use the curve labeled "vessel burst." For R in the rangeof 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 symmetri-cal blast wave, such as would result from the explosion of a hemispherical vesselplaced directly on the ground. In practice, vessels are either spherical or cylindrical,and placed at some height above the ground. This influences blast parameters. Toadjust for these geometry effects, Ps and 7 are multiplied by some adjustment factorsderived from experiments with high-explosive charges of various shapes.

Tables 6.1 Ia and 6.1 Ib gives multipliers for adjusting scaled values for cylindri-cal vessels of various R and for spheres elevated slightly above the ground, respec-tively.

The blast wave from a cylindrical vessel is weakest along its axis. (See Figures6.17 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 side-on impulse is from nondimensional side-on peak overpressure P8 and nondimensionalside-on impulse 7:

(6.3.17)

(6.3.18)

where aQ is speed of sound in ambient air in meters per second. For sea-levelaverage 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 Section6.3.3.5). Under some circumstances, the calculated ps might be higher than theinitial pressure in the vessel P1, which is physically impossible. If this shouldhappen, 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 pressurevessel bursts and high explosives. This similarity holds only at some distance fromthe 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, exceptwhen the pressure vessel is filled with a very hot high-pressure gas.

Baker et al. (1978a) developed a method which can predict blast pressures inthe near field. This method is based on results of numerical simulations (see Section6.3.1.1) and replaces Step 5 of the basic method (Figure 6.20). The refined method'sprocedure is shown in Figure 6.25.

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

al. 1975).

vessel burst

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

Multiplier for

R PS 1

<0.3 4 22*0.3^1.6 1.6 1.1>1.6^3.5 1.6 1>3.5 1.4 1

Step 1: Collect additional data.In addition to the data collected in Step 1 of the basic method, the following dataare needed:

• the ratio of the speed of sound in the compressed gas to its speed in ambientair, 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 (K)T1 = absolute temperature of compressed gas (K)M1 = molar mass of compressed gas (kg/kmol)Af0 = molar mass of ambient air (29.0 kg/kmol)yQ and ^1 are specific heat ratios (-)

Step 2: Calculate the initial distance.This refinement assumes that an explosion's blast wave will be completely symmetri-cal. Such a shape would result from the explosion of a hemispherical vessel placed

TABLE 6.11 b. Adjustment Factors for Spherical VesselsSlightly Elevated above Ground(Baker et al. 1975)

Multiplier for

R PS /

<1 2 1.6>1 1.1 1

2 calculate startingdistance

calculate P8,

4 locate starting pointon Fig. 6.21

determine P8

'continue with step 6of basic method

Figure 6.25. Refined method to determine P8.

directly on the ground. Therefore, a hemispherical vessel is used instead of theactual vessel for calculation purposes.

Calculate the hemispherical vessel's radius r0 from the volume of the actualvessel V1:

(6.3.20)

This is the starting distance on the overpressure versus distance curve. It must betransformed into the nondimensional starting distance, /?0, with:

(6.3.21)

start from step 4of basic method

collect additional data

Step 3: Calculate the initial peak overpressure P80.The peak shock pressure directly after the burst, /?so, is much lower than the initialgas pressure in the vessel P1. As the shock wave travels away from the vessel, thepeak shock pressure decreases. The nondimensional peak-shock overpressure di-rectly after the burst P80 is defined as (pso/p0) ~~ 1 - It is given by the followingexpression (see Section 6.3.1.1):

(6.3.22)

where

P1 = initial absolute pressure of compressed gas (Pa)P0 = ambient pressure (Pa)P80 = nondimensional peak shock overpressure directly after burst: (-)

PSO = (PjPo) ~ 1P80 = peak shock overpressure directly after burst (Pa)70 = ratio of specific heats of ambient air (-)7j = ratio of specific heats of compressed gas (-)aQ = speed of sound in ambient air (m/s)^1 = speed of sound in compressed gas (m/s)

This is an implicit equation which can only be solved by iteration. One might usea spreadsheet or a programmable calculator to solve for P80 from this equation. Analternative 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 nondimen-sional peak pressure at that radius were calculated. As a blast wave travels outward,its pressure decreases rapidly. The relationship between the peak pressure P8 andthe distance R depends upon initial conditions. Accordingly, Figure 6.21 containsseveral curves. Locate the correct curve by plotting (R, P80) in the figure, asillustrated in Figure 6.28.

Step 5: Determine P8.To determine the nondimensional side-on overpressure P8, read P8 from Figure 6.21for the appropriate R (calculated in Step 3 of the basic method). Use the curvewhich goes through the starting point, or else draw a curve through the startingpoint parallel to the nearest curve. Continue with Step 6 of the basic method inSection 6.3.3.2.

6.3.3.3. Method for Explosively Flashing Liquids and Pressure Vessel Burstswith Vapor or Nonideal Gas

In the preceding subsections, bursting vessels were assumed to be filled with idealgases. In fact, most pressure vessels are filled with fluids whose behavior cannotbe described, or even approximated, by the ideal-gas law. Furthermore, manyvessels are filled with superheated liquids which may vaporize rapidly, or evenexplosively, when depressurized.

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

Equation (6.3.15) is not accurate for the calculation of explosion energy ofvessels filled with real gases or superheated liquids. A better measure in these casesis the work that can be performed on surrounding air by the expanding fluid, ascalculated from thermodynamic data for the fluid. In this section, a method will bedescribed for calculating this energy, which can then be applied to the basic methodin order to determine the blast parameters.

In many cases, both liquid and vapor are present in a vessel. Experimentsindicate that the blast wave from expanding vapor is often separate from thatgenerated by flashing liquid. However, it is conservative to assume that the blastwaves 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 firewhose heat raises vessel pressure and reduces its wall strength. Safety-valvedesign allows actual pressure to rise to a value 1.21 times the safety valve-opening pressure.)

• Ambient pressure p0.• Quantity of the fluid (volume V1 or mass).

determine u,

5 calculate specificwork

calculate energy

Figure 6.29. Calculation of energy of flashing liquids and pressure vessel bursts filled withvapor or nonideal gas.

start

collect data

check the fluid

determine U1

calculate R

continue with step 5of basic method

• 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 isreached, 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 at39 bar, or 2.5 times the opening pressure of its safety valve. Note also that thismethod 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 forthe fluid at its initial and final (expanded to ambient pressure) states are needed aswell. 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 Edmisterand Lee (1984), among others. The method or determining the thermodynamic datawill 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 commonfluids, namely:

ammoniacarbon dioxideethaneisobutanenitrogenoxygenpropane.

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 energybetween the fluid's initial and final states. Most thermodynamic tables and graphsdo not present W1, but only h, p9 v, T (the absolute temperature), and s (the specificentropy). 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 Vapor

Pi eex eex/vf eex eex/vf

Fluid T1(K) (105 Pa) (kJ/kg) (MJ/m3) (kJ/kg) (MJ/m3)

Ammonia, 7S, = 361.0 K324.8 21.2 82.5 46.2 297.0 4.89360.0 48.0 152.5 74.7 365.0 14.80400.0 102.8 278.5 95.7 344.0 47.00

Carbon dioxide, 7S| = 270.8 K244.3 14.8 54.4 58.2 98.0 3.77255.4 21.1 60.9 62.1 109.0 6.00266.5 29.1 68.1 65.6 117.0 9.17

Nitrogen, T8, = 112.3 K104.0 10.0 13.2 8.78 41.9 1.75110.0 14.5 18.2 11.3 47.7 2.98120.0 24.8 28.6 15.0 53.5 6.66

Oxygen, 7sl = 137.7 K120.0 10.1 12.8 12.5 43.9 1.73130.0 17.3 18.7 16.8 53.4 3.65140.0 27.5 27.2 22.1 60.0 7.00

Exp

ansi

on

work

. kJ

/kg

Exp

ansi

on

work

, B

tu/lb

m

Temperature, K

—I— saturated —A— saturated —©— saturatedethane propane i so—butane

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

where

h = specific enthalpy (enthalpy per unit mass) (J/kg)u = specific internal energy (J/kg)p = absolute pressure (N/m2)v = specific volume (m3/kg)

To use a thermodynamic graph, locate the fluid's initial state on the graph. (For asaturated fluid, this point lies either on the saturated liquid or on the saturated vaporcurve, at a pressure P1.) Read the enthalpy A1, volume V1, and entropy S1 from thegraph. 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. Acrude estimate of a mixture's internal energy can be made by summing the internalenergy 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 determinedas follows: If a thermodynamic graph is used, assume an isentropic expansion(entropy s is constant) to atmospheric pressure pQ. Therefore, follow the constant-entropy line from the initial state to pQ. Read A2 and V2 at this point, and calculatethe specific internal energy M2.

When thermodynamic tables are used, read the enthalpy Af, volume vf, andentropy 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 atambient pressure. Then use the following equation to calculate the specific internalenergy M2:

M2 = (1 - X) hf + XAg - (1 - X)p0vf - XPovg (6.3.24)

where

X = vapor ratio (S1 — sf)/(sg — sf)s = specific entropySubscript 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 calculationsare given for seven common gases in Table 6.12 and Figures 6.30 and 6.31. Thefluid temperature at the moment of burst must be known. If only pressure is known,

Temperature, K

—I— saturated —*— saturated —e— saturatedethane propane 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 limittemperature Tsl, initial conditions, and specific work done in expansion based uponisentropic expansion of either saturated liquid or saturated vapor until atmosphericpressure 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 inFigure 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 linehas been drawn only to show the relationship between the points; a curve reflectingan actual event would be smooth. Note that a liquid has much more energy perunit of volume than a vapor, especially carbon dioxide. Note: It is likely that carbondioxide can flash explosively at a temperature below the superheat limit temperature.This may result from the fact that carbon dioxide crystallizes at ambient pressureand thus provides the required number of nucleation sites to permit explosivevaporization.

Step 6: Calculate expansion energy.To calculate expansion energy, multiply the specific expansion work by the massof fluid released or else, if energy per unit volume is used, multiply by the volume

Temperature. FE

xpansi

on

work

, M

J/m

3

Exp

ansi

on

work

, B

tu/ft3

of fluid released. Multiply the result by 2 to account for reflection of the shockwave 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 presentin 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 "tar-get" as follows:

r i1735"te]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 thenear field cannot be made for nonideal gases, because Eq. (6.3.22) applies only toideal gases. Therefore, blast pressure is conservatively estimated by determiningthe blast pressure resulting from detonation of a high-explosive charge having thesame 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 wavedoes not reflect on the ground. Thus, the available energy E6x is spread over twicethe 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 byvessel-height compensation factors.

6.3.3.5. Accuracy

The methods presented above give upper estimates of blast parameters. Since themeasured blast parameters of actual pressure-vessel bursts vary widely, even underwell-controlled conditions, and since these methods are based on a highly schema-tized model, the blast parameters of actual bursts may be much lower.

The main sources of deviation lie in estimates of energy and in release-processdetails. It is unclear whether the energy equations given in preceding sections aregood estimates of explosion energy. In addition, energy translated into kinetic

energy of fragments and ejected liquid is not subtracted from blast energy. Thismay produce an error of up to 50%, which translates into an overstatement ofoverpressure 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 vesselruptures from ductile, rather than brittle, fracture, a highly directional shock waveis produced. Overpressure in the other direction may be one-fourth as great. Theinfluences of release direction are not noticeable at great distances. Uncertaintiesfor a BLEVE are even higher because of the fact that its overpressure is limited byinitial 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 tempera-tures or for pre-nucleated fluids. Furthermore, the energies of evaporating liquidand expanding vapor are taken together, while in practice, they may produce separateblasts. Finally, in practice, there are usually structures in the vicinity of an explosionwhich will reflect blast or provide wind shelter, thereby influencing the blastparameters.

In practice, overpressures in one case might very well be only one-fifth ofthose 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, releasedenergy 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 hazardousand may result in damage to structures and injuries to people. Primary missileeffects are determined by the number, shape, velocity, and trajectory of fragments.

When a high explosive detonates, a large number of small fragments with highvelocity and chunky shape result. In contrast, a BLEVE produces only a fewfragments, varying in size (small, large), shape (chunky, disk-shaped), and initialvelocities. Fragments can travel long distances, because large, half-vessel fragmentscan "rocket" and disk-shaped fragments can "frisbee." The results of an experimentalinvestigation described by Schulz-Forberg et al. (1984) illustrate BLEVE-inducedvessel fragmentation.

All parameters of interest with respect to fragmentation will be discussed. Theextent of damage or injury caused by these fragments is, however, not covered inthis volume. (Parameters of the terminal phase include first, fragment density andvelocity at impact, and second, resistance of people and structures to fragments.)

Figure 6.32 illustrates results of three fragmentation tests of 4.85-m3 vessels50% full of liquid propane. The vessels were constructed of steel (StE 36; unalloyed

Next Page

energy of fragments and ejected liquid is not subtracted from blast energy. Thismay produce an error of up to 50%, which translates into an overstatement ofoverpressure 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 vesselruptures from ductile, rather than brittle, fracture, a highly directional shock waveis produced. Overpressure in the other direction may be one-fourth as great. Theinfluences of release direction are not noticeable at great distances. Uncertaintiesfor a BLEVE are even higher because of the fact that its overpressure is limited byinitial 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 tempera-tures or for pre-nucleated fluids. Furthermore, the energies of evaporating liquidand expanding vapor are taken together, while in practice, they may produce separateblasts. Finally, in practice, there are usually structures in the vicinity of an explosionwhich will reflect blast or provide wind shelter, thereby influencing the blastparameters.

In practice, overpressures in one case might very well be only one-fifth ofthose 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, releasedenergy 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 hazardousand may result in damage to structures and injuries to people. Primary missileeffects are determined by the number, shape, velocity, and trajectory of fragments.

When a high explosive detonates, a large number of small fragments with highvelocity and chunky shape result. In contrast, a BLEVE produces only a fewfragments, varying in size (small, large), shape (chunky, disk-shaped), and initialvelocities. Fragments can travel long distances, because large, half-vessel fragmentscan "rocket" and disk-shaped fragments can "frisbee." The results of an experimentalinvestigation described by Schulz-Forberg et al. (1984) illustrate BLEVE-inducedvessel fragmentation.

All parameters of interest with respect to fragmentation will be discussed. Theextent of damage or injury caused by these fragments is, however, not covered inthis volume. (Parameters of the terminal phase include first, fragment density andvelocity at impact, and second, resistance of people and structures to fragments.)

Figure 6.32 illustrates results of three fragmentation tests of 4.85-m3 vessels50% full of liquid propane. The vessels were constructed of steel (StE 36; unalloyed

Previous Page

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

fine-grained steel with a minimum yield strength of 360 N/mm2), and had wallthicknesses of 5.9 mm (Test 1) and 6.4 mm (Tests 2 and 3). Vessel overpressureat moment of rupture was 24.5 bar in the first test, 39 bar in the second test, and30.5 bar in the third.

Research on predictions of fragment velocity and range has heretofore beenconcentrated on the idealized situation of the gas-filled, pressurized vessel. Othercases, including those of nonideal gas-filled vessels and vessels containing combina-tions of gas and liquid, are now being investigated (Johnson et al. 1990). Fragmentvelocity and range can be assumed to depend on the total available energy of avessel'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 rupturewhen 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 isassumed that the total internal energy E of the vessel contents is translated into

Test 21) 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)

jlOOm ,

Test3

1) right half of thetank 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 ofthe tank shell (12Om)

b) place of discovery(40m away from a))

1) tank shell and lefthead (2Om)

2) right head (45m)3) pipe for liquid

discharge (140)

fragment kinetic energy. Two simple relations are obtained:

(6.4.1)

where

Vj = initial fragment velocity (m/s)Ek = kinetic energy (J)M = total mass of the empty vessel (kg)

Kinetic energy (Ek) is calculated from internal energy E. Internal energy can becalculated from [similar to Eq. (6.3.2)]:

(6.4.2)

in which

P1 = absolute pressure in vessel at failure (N/m2)PQ = ambient pressure outside vessel (N/m2)V = internal volume of vessel (m3)y = ratio of specific heats (-)

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 itspressure can be made. If failure is initiated by a rise in initial pressure in combinationwith a malfunctioning or inadequately designed pressure-relief device, the pressureat rupture will equal the vessel's failure pressure, which is usually the maximumallowable working pressure times a safety factor. For initial calculations, a usualsafety factor of four can be applied for vessels made of carbon steel, although highervalues 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 externaloverheating and can reach a maximal value of 1.21 times the opening pressure of thesafety valve. This maximal value is called the accumulated pressure. As overheatingreduces the vessel's wall strength, failure occurs at the point at which its strengthis 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 atfailure will be the operating pressure.

Application of Eqs. (6.4.1) and (6.4.2) produce a large overestimation of theinitial velocity V1. As a result, refinements were developed in the methods fordetermining 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 benegligible. Assuming adiabatic expansion, the highest fraction of energy availablefor 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) hasrefined 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 factork 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 calculatedwith the above equations is still an upper limit.

In Baum (1984), the fraction of total energy translated into kinetic energy isderived 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; Collins1960; Moskowitz 1965; and Pittman 1972.) From these experiments, the fractiontranslated to kinetic energy was found to be between 0.2 to 0.5 of the total energyderived 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 predictinitial fragment velocity. In the course of these efforts, a model introduced byGrodzovskii and Kukanov (1965) has been improved by various investigators. Inthis model, the acceleration force on fragments is determined by taking into accountgas flow through ever-increasing gaps between fragments. This approach recognizesthat not all available energy is translated to kinetic energy. Hence, calculated initialvelocities are reduced.

Velocities of fragments from spherical pressure vessels bursting into two equalportions have been analytically determined for ideal gases by the work of Taylorand Price (1971). The theory was expanded to include a large number of fragmentsby Bessey (1974) and to cylindrical geometries by Bessey and Kulesz (1976). Bakeret al. (1978b) modified the theory for unequal fragments. In calculations of initialvelocity, the energy necessary to break vessel walls is neglected.

Baker et al. (1975) compare computer-code predictions of fragment velocityfrom spheres bursting into a large number of pieces and with some experimental

Figure 6.33. Fragment velocity versus scaled pressure. ( - • - • - • ) • spheres according toV1 = 0.8Sa0F

055 [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 frombursting glass spheres and bursting titanium alloy spheres, respectively. The calcu-lated and measured velocities agree rather well after reported difficulties in velocitymeasurement are taken into account.

The results of a parameter study were used to compose a diagram (Figure6.33) which can be used to determine initial fragment velocity (Baker et al. 1978aand 1983).

Figure 6.33 can be used to calculate the initial velocity V1 for bursting pressurizedvessels filled with ideal gas. The quantities to be substituted, in addition to thosealready defined (pl9 p0» and V), are

O0 = speed of sound in gas at failure (m/s)M = mass of vessel (kg)K = factor for unequal fragments (-)p = scaled pressure (-)

with

P = (Pi^ P«W/(Ma$ (6.4.7)

cylindrical

spherical

cylindrical

Separate regions in Figure 6.33 account for scatter of velocities of cylinders andspheres separating into 2, 10, or 100 fragments. The assumptions used in derivingthe figure are from Baker et al. (1983), namely,

• The vessel under gas pressure bursts into equal fragments. If there are onlytwo fragments and the vessel is cylindrical with hemispherical end-caps, thevessel bursts perpendicular to the axis of symmetry. If there are more than twofragments and the vessel is cylindrical, strip fragments are formed and expandradially 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 temperatureat failure:

al = TyR/m (6.4.8)

where

OQ = speed of sound (m/s)R = ideal gas constant (J/Kkmol)T = absolute temperature inside vessel at failure (K)m = molecular mass (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 thecylindrical axis, K was calculated by Baker etal. (1983). Factor A'can be determinedfor a fragment with mass Aff with the aid of Figure 6.34. The dotted lines in thefigure 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 forthe determination of K was presented that gives totally different values. No explana-tion 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 developedby 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 (kg)E = energy (J)Af = mass of casing or vessel (kg)

Moore's equation was derived for fragments accelerated from high explosivespacked in a casing. The equation predicts velocities higher than actual, especiallyfor low vessel pressures and few fragments. According to Baum (1984), the Mooreequation predicts velocity values between the predictions of the equations given atthe beginning of this section and the values derived from Figure 6.33.

Other empirical relations for ideal gas are given in Baum (1987); recommendedvelocities 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 (6.4.10)moo

where m is mass per unit area of vessel wall and r the radius of the vessel. For asmall number of fragments, F can be written as:

(6.4.11)

where

r = radius of vessel (m)A = area of detached portion of vessel wall (m2)Mf = mass of fragment (kg)

From these values of F9 the following empirical relations for initial velocity havebeen derived:

• For an end-cap breaking from a cylindrical vessel:

Vj =20oF05 (6.4.12)

• For a cylindrical vessel breaking into two parts in a plane perpendicular toits axis:

V1 = 2.18CIo[F(LiR)1'2]*3 (6.4.13)

where in F

A = irr2 (m2)L = length of cylinder (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 multiplefragments:

(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 veryhigh pressures, van der Waals forces become important, that is, intermolecularforces and finite molecule size influence the gas behavior. Another nonideal situationis 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, situa-tions. Two publications by Wiederman (1986a,b) treat nonideal gases. He uses aco-volume parameter, which is apparent in the Nobel-Abel equation of state of anonideal gas, in order to quantify the influence on fragment velocity. The co-volumeparameter is defined as the difference between a gas's initial-stage specific volumeand its associated perfect gas value.

For a maximum value for the scaled pressure p = 0.1, a reduction in V1 of10% was calculated when the co-volume parameter was applied to a sphere breakingin half. In general, fragment velocity is lower than that calculated in the ideal-gascase. Baum (1987) recommends that energy E be determined from thermodynamicdata (see Section 6.3.2.3) for the gas in question.

Wiederman (1986b) treats homogeneous, two-phase fluid states and some ini-tially single-phase states which become homogeneous (single-state) during decom-pression. It was found that fragment hazards were somewhat more severe for asaturated-liquid state than for its corresponding gas-filled case. Maximum fragmentvelocities occurring during some limited experiments on liquid flashing could becalculated 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 veloc-ity can be determined by calculation of the energy contained in the gas. This valuecan be refined by taking into account the released energy of the expanding, originallycompressed liquid.

6.4.3. Discussion

In Baum (1984), a comparison is made between the models described in Section6.4.1. This comparison is depicted in Figure 6.35. The energy E was calculatedwith k according to Baum's refinement.

In Figure 6.35, lines have been added for a sphere bursting into 2 or 100 piecesfor p\lp$ = 50 and 10, in accordance with Figure 6.33. Obviously, the simplerelations 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 (Baum1984), so under normal conditions, few fragments are expected, and Figure 6.33can be applied. However, if an operation or process is not under control and pressurerises dramatically, higher scaled-energy values can be reached.

In the relationships proposed by Brode (1959) and in Figure 6.33, velocity hasno upper limit, although Figure 6.33 is approximately bounded by scaled pressuresof 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 fromBaum 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 = 23: P1Xp0 =10; number of fragments = 1004: P1Xp0 = 50; number of fragments = 100.

of massless fragments equals the maximum velocity of the expanding gas (the peakcontact-surface velocity). In Figure 6.35, this maximum velocity is depicted by thehorizontal lines for P1Tp0 = 10 and 50. If values in Figure 6.33 are extrapolatedto 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 bothlow and high energy levels.

For lower scaled pressures, velocity can be calculated with the equation pro-posed by Baum (1987) which produces disintegration of both cylindrical and spheri-cal vessels into multiple fragments (V1 = 0.8Sa0F

055). Such a result can also beobtained 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 fragmentsin the low scaled-pressure regions of these equations or curves probably resultsfrom the nature of the laboratory tests from which the equations were derived. Inthose tests, small vessels made of special alloys were used; such alloys and sizesare 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 highervelocities than the Baker et al. model (1983), but for cylinders, this equation giveslower velocities.

Note that work on ideal-gas-filled pressurized vessels, though extensive, is notcomplete. Furthermore, work on other cases, such as nonideal gases, flashingliquids, and gas plus loose paniculate matter, has either just begun or not evenbegun. Because failure mode cannot be predicted accurately, the worst case mustbe assumed. The worst case may produce high calculated velocities and, conse-quently, large fragment ranges.

6.4.4. Ranges for Free Flying Fragments

After a fragment has attained a certain initial velocity, the forces acting upon itduring flight are those of gravity and fluid dynamics. Fluid-dynamic forces aresubdivided into drag and lift components. The effects of these forces depend onthe 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 initialtrajectory angle of

(6.4.17)

(6.4.18)

where

R = horizontal range (m)H = height fragment reaches (m)g = gravitational acceleration (m/s2)Ot4 = initial angle between trajectory and a horizontal surface (deg)V1 = initial fragment velocity (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 setof differential equations. Baker et al. (1983) plotted solutions of these equations ina diagram for practical use. They assumed that the position of a fragment duringits flight remains the same with respect to its trajectory, that is, that the angle ofattack remained constant. In fact, fragments probably tumble during flight. Plotsof 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)

CLALCpAo

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 = scaled initial velocity (-)R = scaled maximal range (-)R = maximal range (m)P0 = density of ambient atmosphere (kg/m3)C0 = drag coefficient (-)A0 = exposed area in plane perpendicular to trajectory (m2)g = gravitational acceleration (m/s2)Mf = mass of fragment (kg)

In Figure 6.36, two more parameters are used, namely

CL = lift coefficientAL = exposed area in plane parallel to trajectory (m2)

These curves were generated by maximization of range through variation of theinitial 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 velocitychanges 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 onlyin specific intervals of scaled velocity. In the case of thin plates, which have largeC1A1J(C1^1)) ratios, the so-called "frisbeeing" effect occurs, and the scaled rangemore than doubles the range calculated when fluid forces are neglected.

The dotted line in the curve denotes the case for which fluid dynamic forcesare neglected R1n^ = v\lg [Eq. (6.4.19)]. In most cases, "chunky" fragments areexpected. The lift coefficient will be zero for these fragments, so only drag andgravity will act on them; the curve with CLAL/(CDA0) = O is then valid. Drag forcebecomes significant for scaled velocities greater than 1. Drag coefficients for variousshapes can be found in Table 6.13. More information about lift and drag can befound in Hoerner (1958).

For fragments having plate-like shapes, the lift forces can be large, so predictedranges can be much larger then the range calculated with R10n = v\/gy especiallywhen the angle of attack a4 is small (ot| = approximately 10°). The sensitivity ofthe angle of attack model is high, however. For example, an angle of attack ofzero 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 propul-sion of large fragments for unexpectedly long distances. Baker et al. (1978b) arguedthat 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 initialstage of flight, thereby accelerating the fragment as vapor escapes through theopening. Baker et al. (1978b) provided equations for a simplified rocketing problemand a computer program for their solution, but stated that the method was not yetready to be used for range prediction. Baker et al. (1983) applied this method totwo cases, and compared predicted and actual ranges of assumed rocketed fragments.This approach may be applicable to similar cases; otherwise, the computer programshould be employed.

Ranges for rocketing fragments can also be calculated from guidelines givenby 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 flashesare assumed to be the same.

Ranges were calculated for a simulated accident with the methods of Baker etal. (1978a,b) and Baum (1987). It appears that the difference between these ap-proaches is small. Initial trajectory angle has a great effect on results. In manycases (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 distribu-tions of mass, velocity, or range of fragments, and very little information on thenumber of fragments to be expected. Apparently, these models are not developedsufficiently to account for these parameters. More information can probably befound in the analysis of results of accidental explosions. It appears, however, thatvital information is lacking for most such events.

Baker (1978b) analyzed 25 accidental vessel explosions for mass and rangedistribution and fragment shape. This statistical analysis is considered the mostcomplete in the open literature. Because data on most of the 25 events consideredin the analysis were limited, it was necessary to group like events into six groupsin order to yield an adequate base for useful statistical analysis.

Information on each group is tabulated in Table 6.14. The values for energyrange in Table 6.14 require some discussion. In the reference, all energy valueswere calculated by use of Eq. (6.4.2). Users should do the same in order to selectthe right event group. Furthermore, some energy values given are rather low; it isdoubtful that they are correct.

Statistical analyses were performed on each of the groups to yield, as dataavailability permitted, estimates of fragment-range distributions and fragment-massdistributions. The next sections are dedicated to the statistical analysis accordingto the Baker et al. (1978b) method.

TABLE 6.14. Groups of Like Events

Numberof

FragmentsVessel Mass

(kg)Vessel ShapeSource Energy Range

(J)Explosion Material

Numberof

Events

EventGroup

Number

14

2835311411

25,542 to 83,900

25,464145,8426343 to 784048.26 to 187.33511.7

Railroad tank car

Railroad tank carCylinder pipe and spheresSemi-trailer (cylinder)SphereCylinder

1.487 x 105 to 5.95 x 105

381 4 to 3921 .35.198 x 1011

549.62438 x 109 to 1133 x 1010

24.78

Propane,Anhydrousammonia

LPGAirLPG, PropyleneArgonPropane

4

91231

1

23456

6.4.6.1. Fragment Range Distribution

It was shown in the reference that the fragment range distribution for each of thesix groups of events follows a normal, or Gaussian, distribution. It was then shownthat the chosen distributions were statistically acceptable. The range distributionsfor each group are given in Figures 6.37a and 6.37b. With this information, it ispossible to determine the percentage of all the fragments which would have a rangesmaller than, or equal to, a certain value. Table 6.15 gives an overview of statisticalresults 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 informationin Figures 6.37a and 6.37b, the percentage of fragments having a mass smallerthan or equal to a certain value can be calculated. Table 6.16 gives a statisticalsummary for event groups 2, 3, and 6.


It should now be clear that there are a number of unsolved problems with regardto BLEVEs. These problems are summarized in this section.

With regard to radiation:

• Additional experiments should be performed on a large scale to establish theemissive power of fireballs generated by BLEVEs. The effects of flammablesubstances involved, fireball diameter, and initial pressure should beinvestigated.

• 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 vesselbursts 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 beeninvestigated thoroughly. Parameters presently used are derived from investiga-tions of free-air bursts.

perc

enta

ge o

f fra

gmen

ts w

ith ra

nge

equa

l to

or le

ss th

an R

perc

enta

ge o

f fra

gmen

ts w

ith ra

nge

equa

l to

or le

ss th

an 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 Log-Normal Range Distributions (base e)for Six Event Groups

Event Group Estimated Mean Estimated Standard Deviation

1 4.57 0.912 4.10 1.063 4.28 0.654 4.63 0.795 5.66 0.456 3.67 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 homogeneousnucleation temperature 7sl will not give rise to strong blast generation has notbeen verified.

With regard to missiles:

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

perc

enta

ge o

f fra

gmen

ts w

ith m

ass

equa

l or

less

than

M

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 Deviationsfor Log-Normal Range Distributions (base e)for Event-Groups 2, 3, and 6

Event Group Estimated Mean Estimated Standard Deviation

2 7.05 2.123 6.62 1.056 1.42 2.78

to such factors as conditions within the vessel and properties of the vessel'smaterials.

• Methods do not exist to predict even the order of magnitude of the number offragments produced. One assumes failure either into two parts or into a largenumber of fragments. The effect of parameters such as material, wall thickness,and initial pressure are not known.

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American Petroleum Institute. 1982. Recommended Practice 521.

perc

enta

ge o

f fra

gmen

ts w

ithm

ass

equa

l or l

ess

than

M

mass M (kg)

Figure 6.39. Fragment-mass distribution for event group 6.

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7VAPOR CLOUD EXPLOSIONS-

SAMPLE PROBLEMS

The methods described in this chapter are meant for practical application; back-ground information is given in Chapter 4. If a quantity of fuel is accidentallyreleased, it will mix with air, and a flammable vapor cloud may result. If theflammable vapor meets an ignition source, it will be consumed by a combustionprocess which, under certain conditions, may develop explosive intensity and blast.

The explosion hazard of a vapor cloud can be quantified in terms of its explosivepower after ignition. The explosive power of a vapor cloud can be expressed as anequivalent 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 dis-cusses in detail two fundamental approaches to quantification of explosive power,together with advantages and disadvantages. In addition, there are two differentblast models, each of which has certain benefits. This chapter offers guidance ontheir use. Application of each method is described in Section 7.2. and demonstratedin Section 7.3. Section 7.1. offers some guidance on choosing an approach and ablast model.

7.1. CHOICE OF METHOD

7.1.1. Two Approaches

In the first approach, a vapor cloud's potential explosive power is proportionallyrelated to the total quantity of fuel present in the cloud, whether or not it is withinflammable limits. This approach is the basis of conventional TNT-equivalencymethods, in which the explosive power of a vapor cloud is expressed as an energeti-cally equivalent charge of TNT located in the cloud's center. The value of theproportionality factor, that is, TNT equivalency, is deduced from damage patternsobserved in a large number of vapor cloud explosion incidents. Consequently, vaporcloud explosion-blast hazard assessment on the basis of TNT equivalency mayhave limited utility.

The second approach, the multienergy method (Van den Berg 1985) reflectscurrent consensus that turbulence is the major cause of explosive, blast-generating

combustion. One source of turbulence is high-velocity flow as fuel is released froma container, for example, a pressurized vessel or leaking pipe. Explosive combustionrates may develop in such a turbulent fuel-air mixture. Another source of turbulenceis combustion within a partially confined/obstructed environment. In such cases,turbulence is generated by combustion-induced expansion flow, resulting in uncon-trolled positive feedback, which causes exponential increases in the combustionwith respect to both speed and overpressure. Several blast effects may result.

The consequence of the second approach is that, if detonation of unconfinedparts of a vapor cloud can be ruled out, the cloud's explosive potential is notprimarily determined by the fuel-air mixture in itself, but instead by the nature ofthe fuel-release environment. The multienergy model is based on the concept thatexplosive combustion can develop only in an intensely turbulent mixture or inobstructed and/or partially confined areas of the cloud. Hence, a vapor cloud explo-sion is modeled as a number of subexplosions corresponding to the number of areaswithin the cloud which burn under intensely turbulent conditions.

The two approaches lead to completely different procedures for vapor cloudexplosion 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 blastcenter and is determined by cloud drift.

If, on the other hand, the multienergy model is employed, the total quantityof fuel present in a cloud is of minor importance. Instead, the environment isinvestigated with respect to potential blast-generative capabilities. Fuel-air jets andpartially 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 offuel present in these blast-generating areas.

7.1.2. Two Blast Models

TNT-equivalency methods express explosive potential of a vapor cloud in terms ofa charge of TNT. TNT-blast characteristics are well known from empirical databoth in the form of blast parameters (side-on peak overpressure and positive-phaseduration) and of corresponding damage potential. Because the value of TNT-equiva-lency used for blast modeling is directly related to damage patterns observed inmajor vapor cloud explosion incidents, the TNT-blast model is attractive if overalldamage 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 blastdiffer substantially. Whereas a TNT charge produces a shock wave of very highamplitude and short duration, a gas explosion produces a blast wave, sometimesshockless, of lower amplitude and longer duration. In structural analysis, waveshape and positive-phase duration are important parameters; these can be moreeffectively predicted by techniques such as the multienergy method.

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

7.2. METHODS

7.2.1. Conventional TNT-Equivalency Methods

Conventional TNT-equivalency methods state a proportional relationship betweenthe total quantity of flammable material released or present in the cloud (whetheror not mixed within flammability limits) and an equivalent weight of TNT expressingthe cloud's explosive power. The value of the proportionality factor—called TNTequivalency, yield factor, or efficiency factor—is directly deduced from damagepatterns observed in a large number of major vapor cloud explosion incidents. Overthe years, many authorities and companies have developed their own practices forestimating the quantity of flammable material in a cloud, as well as for prescribingvalues for equivalency, or yield factor. Hence, a survey of the literature reveals avariety of methods.

To demonstrate the general procedure in applying TNT-equivalency methodsin this work, one of the many methods, namely, that recommended by the UKHealth & Safety Executive (HSE 1979; HSE 1986), is followed. Note that this isonly one of many variations on the basic TNT-equivalency method; see Chapter 4for 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 totalquantity of fuel in the cloud; it can be determined according to the followingstepwise 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 (K)and boiling temperature at ambient pressure

L = latent heat of vaporization (kJ/kg)exp = base of natural logarithm (2.7183) (-)

• The weight of fuel Wf in the cloud is equal to the flash fraction times thequantity of fuel released. To allow for spray and aerosol formation, the cloudinventory 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™ (7-2)^TNT

where

WTNT = equivalent weight of TNT (kg)Wf = weight of fuel in the cloud (kg)H1 = heat of combustion fuel (MJ/kg)//TNT = blast energy TNT = 4.68 MJ/kgcte = TNT-equivalency/yield factor = 0.03 (-)

7.2.7.2. Determine Blast Effects

In Figure 7.1, the side-on blast wave peak overpressure produced by a detonationof a TNT charge is graphically represented as dependent on the Hopkinson-scaleddistance 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:

* = r <7-3>WTNT

where

R = Hopkinson-scaled distance (m/kg173)WTNT = charge weight of TNT (kg)R = real distance from charge (m)

If the scaled distance R is known, the corresponding side-on blast peak overpressurecan 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 unconfinedparts of a vapor cloud can be ruled out, strong blast is generated only by thosecloud portions which burn under intensely turbulent conditions. Such cloud portionsinclude, for instance, intensely turbulent fuel-air jets resulting from a high-pressure

actual distance, . ,„"scaled distance" = ^ — mkg-''3

\/wTNT

Figure 7.1. Hopkinson-scaled TNT charge blast.

release or areas in the cloud where congestion/obstruction or partial confinementacts as turbulence-generating boundary conditions in the expansion flow. The conse-quence is that vapor cloud explosion blast should be approached as a number ofsub-blasts corresponding with the number of potential blast sources identified inthe cloud. Therefore, the explosive potential of a vapor cloud can be expressed asa corresponding number of equivalent fuel-air charges whose characteristics canbe determined by following the flow chart below in a step-by-step approach:

Assume deflagrative combustion.

IIdentify blast sources.

IDetermine charge energies.

I

"sid

e-on

" ov

erpr

essu

re, b

ar

Estimate charge strengths.

iCalculate scaled distance.

4Read scaled-blast properties from chart.

ICalculate 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 intenselyturbulent motion when reached by the flame. Such cloud areas are described in theintroduction to this section. Practical examples of potential centers of strong blastin vapor cloud explosions are

• High-velocity jets releasing fuel at high pressure as a result of a pipe or ves-sel 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 ofconsideraly 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 partiallyconfined/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 identi-fied as blast sources. This can be done on the basis of the overall dimensionsof 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 correctedif equipment represents an appreciable proportion of the volume.

• Calculate the combustion energy E (J) for each blast by multiplying the individ-ual volumes of mixture by 3.5 x 106 J/m3. Table 7.1 demonstrates that 3.5x 106 J/m3 is a reasonable average value for the heat of combustion of astoichiometric 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 overpressuresranging from a few millibars under completely unconfined or unobstructed condi-tions to greater than 10 bars under severely confined and obstructed conditions.

Therefore, for a safe and conservative estimate of the strength for the sourcesof strong blast, an initial strength of 10 should be chosen; however, a source strengthof 7 seems to more accurately represent actual experiment. The rest of the cloud,which is unconfined and unobstructed, will produce blast of considerably lowerstrength. 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 inpresent research.

7.2.2.4. Blast Effects

Once the energy quantities E and the initial blast strengths of the individual equiva-lent 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)

Fuel

MethaneEthaneEthylenePropanePropyleneButaneButyleneCyclohexaneHydrogen

Heat of Combustion(288 K, 1 atm)

(MJIm3)

3460.55686.481.5

112.4107.1167.310.2

StoichiometricVolume Ratio

(%)

9.55.66.54.04.43.13.42.3

29.5

Heat of CombustionStoichiometrically

Mixed with Air(MJIm3)

3.233.393.643.463.593.483.643.853.01

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

R = —^-r (7.4)(E/PQ)m

where

R = Sachs-scaled distance from charge center (-)R = real distance from the charge center (m)

dim

ensi

onle

ss m

axim

um 's

ide

on1 o

verp

ress

ure

(AP

g)

R —° combustion energy-scaled distance (R)

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

dim

ensi

onle

ss p

ositi

ve p

hase

dur

atio

n (t

+)


P0 « atmospheric pressureC0 = atmospheric sound speedE = amount of combustion energyR0 = charge radius

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

E = charge combustion energy (J)P0 = ambient pressure (Pa)

The real blast side-on overpressure and positive-phase duration can be calculatedfrom the Sachs-scaled quantities:

(7.5a)

and

<7.5b)

where

AP5 = side-on blast overpressure (Pa)APS = Sachs-scaled side-on blast overpressure (-)PQ = ambient pressure (Pa)t+ = positive-phase duration (s)f+ = Sachs-scaled positive-phase duration (-)

E = charge combustion energy (J)C0 = ambient speed of sound (m/s)

If separate blast sources are located close to one another, they may be initiatedalmost simultaneously. Coincidence of their blasts in the far-field cannot be ruledout, and their respective blasts should be superimposed. The safe and most conserva-tive approach to this issue is to assume a maximum initial blast strength of 10 andto sum the combustion energy from each source in question. Further definition ofthis important issue, for instance, the determination of a minimum distance betweenpotential blast sources for separate consideration of their individual blasts, is afactor in present research.

7.3. SAMPLE CALCULATIONS

The outcome of a vapor cloud explosion hazard assessment can depend greatly onthe 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 asF9110, F9120, and F9130) and a 50-m diameter butane storage tank (indicated asF9210) on an open site (Figures 7.3a and 7.3b). To diminish inflow of heat fromthe soil, the butane storage tank is placed 1 m above the earth's surface on a concretepylon array (Figure 7.3a). A parking lot with space for 100 cars is situated next tothe tank farm. An accidental release of 20,000 kg of propane is postulated in thisenvironment. The propane is released from a 0.1-m-diameter leak in the unloadingline of sphere F9120. The propane is released at about 8 bars overpressure andmixes with air in a high-velocity jet.

Quantify the explosive potential of a vapor cloud which results from the postu-lated 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 substantialarea, including the tank farm and parking lot. An overview of the tank farm siteis given by the map in Figure 7.3b.

Dataheat of combustion propane = 46.3 MJ/kgmean specific heat liquid propane = 2.41 kJ/kg/Klatent heat propane = 410 kJ/kgboiling temperature of propane at ambient pressure = 231 Kambient temperature = 293 K

F-9210

F-9110 F- 9120

unloadingcontrol room

car park

unloading control room

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

7.3.1.1. Conventional TNT-Equivalency Method

Determine charge weight. The HSE TNT-equivalency method expresses the poten-tial explosive power of a vapor cloud as one, single, equivalent TNT-charge locatedin the cloud's center. The equivalent charge weight of TNT is proportionally relatedto the quantity of fuel in the cloud and can be determined according to the followingstepwise procedure:

• Determine the flash fraction of the fuel on the basis of actual thermodynamicdata, using Eq. (7.1):

where

F = flash fraction (-)Cp = mean specific heat (kJ/kg/K)Ar = temperature difference between ambient temperature

and boiling temperature at ambient pressure (K)L = latent heat (kJ/kg)

• The weight of fuel in the cloud is equal to the flash fraction times the quantityof fuel released. To allow for spray and aerosol formation, the cloud inventoryshould 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 inventoryequals:

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 = equivalent weight of TNT (kg)Wf = weight of fuel in the cloud (kg)Hf = heat of combustion fuel (MJ/kg)J/TNT = blast energy TNT = 4.68 MJ/kg (MJ/kg)ctc = TNT-equivalency / yield factor = 0.03 (-)

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

where

R = Hopkinson-scaled distance (m/kg1/3)R = real distance !from the charge (m)WJNT = charge weight of TNT (kg)

Once the Hopkinson-scaled distance from the charge is known, the correspondingside-on peak overpressure can be read from the chart in Figure 7.1. Table 7.2 givesresults for several distances.

7.3.1.2. Multienergy Method

The multienergy method applies only if detonation of unconfined parts of a vaporcloud can be ruled out. If so, the explosive potential of a vapor cloud is determinedprimarily by the blast-generative properties of the environment in which the vaporis released and disperses. Consequently, a vapor cloud explosion can be regardedas a number of subexplosions. Therefore, the first step in applying the multienergymethod in vapor cloud explosion hazard assessment is

Identify potential sources of blast:

• The space beneath the storage tank. This configuration of extended parallelplanes, internally provided with a large number of vertical obstacles (the pylonforest), is an outstanding example of blast-generative boundary conditions.

• The parking lot. The partially confined space beneath a large number of closelyparked cars provides a condition allowing a combustion process to develophigh-strength blast.

• The jet by which the propane is released. The jet's propane-air mixture is inintensely turbulent motion and will develop an explosive combustion rate andblast effects on ignition.

• In the rest of the cloud, which is unconfined and unobstructed, no explosivecombustion rates can be maintained nor developed.

TABLE 7.2. Side-On Peak Overpressure for Several Distances from ChargeExpressing Explosive Potential of a Vapor Cloud at a Storage Sitefor Liquefied Hydrocarbons

Distance from Scaled Distance from Charge Side-on Peak OverpressureCharge (m) (m/kg1'3) (bar)

50 3.24 0.68100 6.48 0.21200 12.95 0.084500 32.38 0.025

1000 64.77 0.013

Determine the size of equivalent fuel-air charges. Consider each blast sourceseparately. Assume that the full quantity of fuel-air mixture present within thevolume identified as a source of blast contributes to blast in a hemispherical fuel-aircharge. The contributing combustion energy within each charge is found by assum-ing a stoichiometric composition, then multiplying charge volumes by the heat ofcombustion, 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 parkinglot can only be estimated, so a conservative assumption should be used. Assumethat a maximum number of 100 cars are parked closely together. An averagecar occupies an area of approximately 6 x 3 = 18 m2 (including interveningspace), 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 18m2 = 54Om3

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 estimatedif a simplifying assumption is made that the jet flow is not influenced by rigidobjects. If not, according to the Yellow Book (1979), the volume of flammablemixture 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 quantityof combustion energy within the cloud (20,000 x 4613 = 926,000 MJ) isinvolved in explosive-blast-generating combustion. The rest of the cloud con-tains the greater part of the propane which represents a quantity of combustionenergy of

926,000 - 9513 = 916,487 MJ.

In summary, the potential explosive power of the vapor cloud can be expressed asfour equivalent fuel-air charges whose initial strengths remain to be determined.

Determine the initial strengths of the charges. A quick, simple, yet conservativeapproach to estimating the initial strengths of the four charges expressing the poten-tial explosive power of the vapor cloud follows:

• Assume that the three fuel-air charges identified above as sources of strongblast each has a maximum initial strength, 7.

• Assume that the remainder of the cloud is of minor blast significance, andassign its fuel-air charge a value of 2.

Therefore, the potential explosive power of the vapor cloud can be expressed asfour equivalent fuel-air charges whose characteristics and locations are listed inTable 7.3.

Equivalent charges expressing the vapor cloud's potential explosive power arenow known, both in scale and in strength. Their corresponding blast effects remainto be determined.

Blast effects. Scales and strengths of charges have been determined above. Nextcalculate the nondimensionalized distances for the respective charges at any wanteddistance R from the blast centers using Eq. (7.4):

* = _*-_(EIP^

where

R = nondimensionalized distance from charge (-)R = distance from charge (m)E = charge combustion energy (J)P0 = ambient pressure = 101,325 Pa

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

— sonCharge I: R = ^ = 12.3

(6870 x 106/101,325)1/3

TABLE 7.3. Characteristics and Locations of Charges Expressing PotentialExplosive Power of Vapor Cloud at Liquefied Hydrocarbon StorageTank Farm

CombustionEnergy

Site MJ Strength Location

Butane tank (charge I) 6,870 7 Center of the spaceunderneath tank

Parking lot (charge II) 1,890 7 Center of parking lot

Propane-air jet (charge III) 753 7 Center of jet

Rest of the cloud (charge IV) 916,487 2 Center of cloud

Charge II:

Charge III:

Charge IV:

Once the nondimensionalized distances from each charge are determined, the corres-ponding nondimensionalized blast parameters can be read from charts in Figure7.2a and b. These nondimensionalized blast parameters are collected in Table 7.4.

The nondimensionalized side-on peak overpressures and their respective posi-tive-phase durations can be transformed into real values for side-on peak overpres-sures 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 fromThree Charges, Read from Charts in Figure 7.2a and b

R E Strength _ _Charge (m) (MJ) Number R AP8 i+

Charge I 500 6,870 7 12.3 0.019 0.47Charge Il 500 1,890 7 18.9 0.012 0.50Charge III 500 753 7 25.6 0.009 0.52Charge IV 500 916,487 2 2.40 0.006 3.0

where

AP5 = side-on peak overpressure (Pa)AP5 = nondimensionalized side-on peak overpressure (-)P0 = ambient pressure = 101,325 Paf + = positive-phase duration (s)f+ = nondimensionalized positive-phase duration (-)E = charge combustion energy (J)C0 = ambient speed of sound = 340 m/s

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

7.3.2. Vapor Cloud Explosion as a Consequence of Pipe Ruptureat a Chemical Plant

Problem. Large quantities of combustible materials are stored and processed inprocess industries, often under high pressures and at high temperatures. Such activi-

TABLE 7.5a. Side-On Peak Overpressure and Positive-Phase Durationof Blast Produced by Charge I (E = 6870 MJ, StrengthNumber 7)

~ f l ~ ~ A p s ~

(m) R AP8 (kPa) (bar) t+ (s)

50 1.23 0.34 34.5 0.34 0.32 0.38100 2.45 0.12 12.2 0.12 0.35 0.042200 4.90 0.052 5.27 0.053 0.43 0.052500 12.3 0.019 1.93 0.019 0.47 0.056

1000 24.5 0.0090 0.91 0.009 0.50 0.060

TABLE 7.5b. Side-On Peak Overpressure and Positive-Phase Durationof Blast Produced by Charge Il (E = 1890 MJ, StrengthNumber 7)

~R " ~~ AP8 ~

(m) R AP8 (kPa) (bar) i+ (s)

50 1.89 0.17 17.2 0.17 0.35 0.027100 3.77 0.070 7.09 0.071 0.40 0.031200 7.54 0.032 3.24 0.032 0.45 0.035500 18.9 0.012 1.22 0.012 0.50 0.039

1000 37.7 0.0055 0.56 0.006 0.54 0.042

TABLE 7.5c. Side-On Peak Overpressure and Positive-Phase Durationof Blast Produced by Charge III (E = 753 MJ, StrengthNumber 7)

~R ~ ~ * P * ~


50 2.56 0.11 13.2 0.13 0.37 0.021100 5.12 0.050 5.07 0.051 0.40 0.023200 10.2 0.023 2.33 0.023 0.46 0.026500 25.6 0.009 0.91 0.009 0.50 0.029

1000 51.2 0.0040 0.41 0.004 0.55 0.032

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

~R~ ~ I A p s ~


50 0.24 0.20 2.03 0.02 4.0 2.5100 0.48 0.020 2.03 0.02 3.2 2.0200 0.96 0.013 1.32 0.013 3.0 1.8500 2.40 0.006 0.59 0.006 3.0 1.8

1000 4.80 0.0028 0.28 0.003 3.0 1.8

ties pose vapor cloud explosion hazards. This was demonstrated, for example, bythe 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 andPritchard (1982) serve as starting points for this case study. Because a pipe betweentwo reactor vessels in the oxidation plant (see plan) ruptured, a large amount ofcyclohexane 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 alarge vapor cloud covering a substantial part of the plant area (Figure 7.4). Inaddition to the oxidation plant and the caprolactam plant, indicated in Figure 7.4as 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 anignition source, probably somewhere in the hydrogen plant. The fire flashed backto the gas leak where, in between the densely spaced process equipment of theoxidation plant and the caprolactam plant, it found conditions under which intenseand explosive combustion developed. The consequences were devastating. Twenty-eight 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 andblast 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 asystem consisting of five reactor vessels containing a total quantity of 250,000 kg(Gugan 1978). However, a complete discharge is unlikely. If an almost completedischarge of the two vessels adjacent to the ruptured pipe is assumed, a total quantityof 100,000 kg of cyclohexane would have been released.

Dataheat of combustion cyclohexane = 46.7 MJ/kgmean specific heat liquid cyclohexane = 1.8 kJ/kg/Klatent heat cyclohexane = 674 kJ/kgprocess temperature in reactor vessels = 423 Kboiling 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, equivalent-TNT charge located at the cloud's center. The equivalent-charge weight of TNT isproportionally related to the fuel quantity within the cloud and can be determinedaccording 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 (kJ/kg/K)A7 = temperature difference between process temperature and

boiling temperature at ambient pressure (K)L = latent heat (kJ/kg)e = base of natural logarithm = 2.718 (-)

• The weight of fuel in the cloud is equal to the flash fraction times the quantityof fuel released. To allow for spray and aerosol formation, the cloud inventoryshould 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 thecloud 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 = equivalent weight of TNT (kg)Wf = weight of fuel in the cloud (kg)Hf = heat of combustion fuel (MJ/kg)//TNT = TNT blast energy = 4.68 MJ/kgae = TNT-equivalency / yield factor = 0.03 (-)

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 chargecan be found by calculating the Hopkinson-scaled distance using Eq. (7.3):

where

R = Hopkinson-scaled distance (m/kg173)R = real distance from the charge (m)WTNT = charge weight of TNT (kg)

Once the Hopkinson-scaled distance from the charge is known, the correspondingside-on peak overpressure can be read from the chart in Figure 7.1. Table 7.6includes these values for several distances.

TABLE 7.6. Side-On Peak Overpressure for SeveralDistances from Charge ExpressingExplosive Power of the Flixborough VaporCloud Explosion

Distance fromCharge(m)

50100200500

10002000

Scaled Distancefrom Charge

(m/kg1/3)

2.34.69.2

234692

Side-On PeakOverpressure

(bar)

1.20.390.130.040.0180.010

7.3.2.2. Multienergy Method

The multienergy approach treats vapor cloud explosions as a number of subexplo-sions, and recognizes that the explosive potential of a vapor cloud is primarilydetermined by the blast-generative properties of the environment in which the vaporis released and disperses. Therefore, the following steps to determining blast strengthand 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: theoxidation and caprolactam plants (indicated in Figure 7.4 as Section 7 and 27) andalso the more-or-less open area toward the hydrogen plant.

The photographs in Figures 7.5a and 7.5b, showing the wreckage of both thecyclohexane oxidation plant and caprolactam plants, clearly illustrate elements ofpartial confinement as previously described: densely spaced process equipmentmounted in open buildings consisting of parallel concrete floors. The areas coveringthe cyclohexane oxidation and caprolactam plants should be considered sources ofstrong blast. No significant contribution to blast should be expected from the restof the cloud, because it is unconfined and unobstructed.

Determine the scale of equivalent fuel-air charges. Consider each blast sourceseparately. Assume that the entire volume of fuel-air mixture present in each cloudportion identified as a source of strong blast contributes to the blast. The blastoriginating from each source is modeled as though it were from a hemisphericalfiiel-air charge. The combustion energy contributing to each respective charge isfound by assuming a stoichiometric composition and by multiplying the volume ofeach source by the fuel's heat of combustion, 3.5 MJ/m3.

The scale of the charge representing the potential explosive power of the singlesource of strong blast identified is determined by calculation of the quantity ofcombustion energy of flammable mixture within the partially confined volume. Inthis case, it is the volume of space between parallel concrete floors and obstructedby the densely spaced equipment in both the hexane oxidation plant and the caprolac-tam plant. On the basis of the scale of the plan in Figure 7.4 and the photographsin Figures 7.5a and 7.5b, an approximate estimate of the partially confined orobstructed 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 amore-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 toestimation of initial strengths of the charges expressing the potential explosivepower 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 strongblast is assumed to be of strength number 10.

• The fuel-air charge expressing the explosive power within the rest of the vaporcloud is assumed to be of strength number 2.

Thus, the potential explosive power of the vapor cloud can be expressed as twoequivalent fuel-air charges whose characteristics and locations are listed in Ta-ble 7.7.

Once equivalent charges expressing the vapor cloud's potential explosive powerare known, both in scale and strength, corresponding blast effects can then bedetermined.

Blast effects. The side-on peak overpressures and positive-phase durations of blastwaves produced by the respective charges for any selected distance, R, can befound by calculating separately for each charge

jg = R(ElP0)

1'3

where

R = nondimensionalized distance from charge (-)R = distance from charge (m)E = charge combustion energy (J)P0 = ambient pressure = 101,325 Pa

Calculate the properties of the blast produced at a distance of 1000 m fromeach of the two charges. The nondimensionalized distance equals

— 1000Charge I: R = ^ = 8.3

(175,000 x 106/101,325)1/3

TABLE 7.7. Characteristics and Locations of Fuel-Air Charges Expressing PotentialExplosive Power of the Flixborough Vapor Cloud

Combustion Energy StrengthE (MJ) (Number) Location

Equipment 175,000 10 Center of equipment(charge I)

Rest of the cloud 1,412,800 2 Center of cloud(charge II)

TABLE 7.8. Nondimensionalized Blast Parameters at 1000 m Distancefrom Two Charges, Read from Charts in Figures 7.2aand 7.2b.

R E Strength _ _(m) (MJ) Number R AP8 i+

Charge I 1000 175,000 10 8.3 0.028 0.45Charge Il 1000 1,412,800 2 4.2 0.0032 3.0

Charge U:

Once the nondimensionalized distances from each charge are known, the correspond-ing nondimensionalized blast parameters can be read from the charts in Figures7.2a and 7.2b. The nondimensionalized blast parameters read are tabulated inTable 7.8.

The nondimensionalized side-on peak overpressures and positive-phase dura-tions read from the tables can be converted into real values for side-on peak overpres-sures and positive-phase durations as follows:

Charge I:

'+ =

Charge II:

'+

where

AP8 = side-on peak overpressure (Pa)AP8 = nondimensionalized side-on peak overpressure (-)P0 = ambient pressure = 101,325 Paf + = positive-phase duration (s)t+ = nondimensionalized positive-phase duration (-)E = charge combustion energy (J)C0 = ambient speed of sound = 340 m/s

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

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

B I I AP* ~(m) R AP8 (kPa) (bar) i+ (s)

50 0.41 3.4 345 3.45 0.15 0.053100 0.83 0.70 70.9 0.71 0.19 0.067200 1.67 0.21 21.3 0.21 0.29 0.102500 4.17 0.065 6.59 0.066 0.40 0.141

1000 8.34 0.028 2.84 0.028 0.45 0.1592000 16.67 0.013 1.32 0.013 0.49 0.1735000 41.68 0.0050 0.51 0.005 0.53 0.187

TABLE 7.9b. Side-on Peak Overpressure and Positive-Phase Durationof Blast Produced by Charge Il (E = 1,412,800 MJ, strengthnumber 2)

f l I ~ A P s ~


100 0.42 0.020 2.03 0.020 3.3 2.3200 0.83 0.016 1.62 0.016 3.0 2.1500 2.08 0.0065 0.66 0.007 3.0 2.1

1000 4.15 0.0032 0.32 0.003 3.0 2.12000 8.31 0.0016 0.16 0.002 3.0 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 tankfarm 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 HSETNT-equivalency method and the multienergy method. The results, in the form ofside-on blast peak overpressures for various distances from blast centers, are listedin Table 7.10. In addition, some peak overpressures estimated by Sadee et al. (1976/1977) from Flixborough-incident damage patterns are included. The photographs inFigures 7.6a and 7.6b illustrate the practical effects of such overpressures.

The two methods gave considerably different results when applied to the liquidhydrocarbon storage site case study. The TNT-equivalency method systematically

TABLE 7.10. Results of INT-Equivalency Method and Multienergy Method Appliedto Two Case Studies

Side-on Blast PeakOverpressure (bar)

Distance Storage Site Flixborough D/s,a/7ce

(m) TNT ME TNT ME Observed (m)

50 0.68 0.34 1.2 3.45100 0.21 0.12 0.39 0.71

0.45-0.55 1200.45-0.55 1300.50-0.70 1350.30-0.40 160

200 0.084 0.052 0.13 0.210.20-0.35 2200.20-0.28 2300.17-0.20 2300.17-0.20 2900.13-0.15 3350.13-0.15 3500.10-0.14 400

500 0.025 0.019 0.04 0.0660.10-0.12 5350.03-0.04 7000.02-0.03 8250.04-0.06 8850.01 -0.02 945

1000 0.013 0.009 0.018 0.0280.02-0.03 11900.01-0.02 1340

2000 <0.010 0.0130.007 24400.007 2745

predicts a heavier blast effect than the multienergy method. On the other hand, theoutcomes of the two methods for the Flixborough vapor cloud explosion case studyshow relatively good agreement, particularly for the intermediate field. In both thenear and far fields, side-on peak overpressure results diverge. This divergence isindicative of the difference between decay characteristics of TNT and fuel-airblasts.

Blast overpressures calculated by the TNT-equivalency method are in reason-able agreement with the overpressures deduced from observed damage (Sadee etal. 1976/1977). This is to be expected, because the Flixborough incident is one ofthe 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 peakoverpressure level: 0.45-0.55 bar (Sadee et al. 1976/1977). (b) Damage to row of houses 535m from explosion center. Estimated peak overpressure level: 0.10-0.12 bar (Sadee et al1976/1977).

3% (HSE method) was based. Therefore, a TNT equivalency of 3% is a reasonablemeasure of expression of the explosive power of a vapor cloud under conditionssimilar to those at Flixborough. Such conditions may be considered "typical majorincident" conditions.

Generally speaking, "typical major incident" conditions correspond to a releaseof some ten thousands of kilograms of some hydrocarbon at the site of a chemicalplant or refinery that is characterized by the presence of obstructed and partiallyconfined areas in the form of densely spaced equipment. The relative agreementwith results derived from the multienergy method indicates that application of thisconcept is a reasonable approach for this case study.

On the other hand, a TNT equivalency of 3% is expected to fail in situationswhere "typical major incident" conditions do not apply. This explains why theoutcomes 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 cloudexplosion blast prediction. J. Haz. Mat. 12:1-10.

Yellow Book. Committee for the Prevention of Disasters, 1979. Methods for the calculationof physical effects of the escape of dangerous materials, P.O. Box 69, 2270 MAVoorburg, The Netherlands.

8FLASH 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 wasshown that the combustion process in a vapor cloud develops an explosive intensityand attendant blast effects only if certain conditions are met. These conditionsinclude

• 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 beexpected. That is, under fully unconfined and unobstructed conditions, the cloudburns as a flash fire, and the major hazard encountered is heat effect from ther-mal radiation.

The subject of flash fires is a highly underdeveloped area in the literature. Onlyone mathematical model describing the dynamics of a flash fire has been published.This model, which relates flame height to burning velocity, dependent on clouddepth and composition, is the basis for heat-radiation calculations. Consequently,the calculation of heat radiation from flash fires consists of determination of theflash-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 acloud's depth and composition, and to flame speed. On the basis of experimentalobservations, flame speed was roughly related to wind speed. Flame height can becomputed from the following expression:

(8.1)

where

H = visible flame height (m)S = 2.3 x £/w = flame speed (m/s)C/w = wind speed (m/s)d = cloud depth (m)g = gravitational acceleration (m/s2)P0 = fuel-air mixture density (kg/m3)pa = density of air (kg/m3)r = stoichiometric air-fuel mass ratio (-)a = expansion ratio for stoichiometric combustion under (-)

constant pressure (typically 8 for hydrocarbons)

W =o^l fOT *>*«a(l - c|>st)

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 afunction of time must be specified. The position and shape of a flame depend uponcloud shape and location of the ignition point within the cloud. If the cloud is aplume, flame shape can be approximated by a flat plane of constant cross-sectionconsuming the plume in a lengthwise direction. If, on the other hand, the cloudshape is more circular (pancake-shaped), flame shape is dependent on the locationof ignition site. Central ignition results in a circular flame, while in the case ofedge ignition, the flame shape should be approximated by a flat plane whose cross-sectional area varies during propagation. Flame shape is important in calculatingflame-radiation emissions. A geometric view factor is used to describe the effectsof 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 = radiation heat flux (kW/m2)E = emissive power (kW/m2)F = geometric view factor (-)Ta = atmospheric attenuation (transmissivity) (-)

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 thereceiving and the transmitting surfaces. Geometric view factors are tabulated andgraphically represented in Appendix A for cylindrical and plane vertical transmittersand for various orientations of receiving surfaces. Equations describing the atmo-spheric transmissivity are discussed in Section 3.5.2.

The thermal radiation intensity of a flash fire can be calculated after parameterssuch as cloud shape and gas or vapor concentration distribution have been determinedthrough dispersion calculations. Subsequently, the thermal radiation intensity iscalculated 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 molecu-lar weights:

(8.4)

Calculate the stoichiometric air-fuel mass ratio, r, from the stoichiometric mixturecomposition, <|>st, and air and fuel molecular weights:

(8.5)

Calculate w from the actual mixture composition <|>, the stoichiometric mixturecomposition <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 varyduring 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 hasa 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 assumptionsabout flame shape should result in higher radiation levels than one might actuallyexpect. Some examples are shown in Figure 8.1. In Figures 8.1a and 8.1b, theflame shape is assumed to be flat, whereas in Figure 8.1c, the flame is cylindrical.In these figures, the following notation is used:

D = cloud diameter (m)L = ignition source height (m)R = cloud radius (m)S = flame speed (m/s)t = time (s)W = flame width (m)4 = ignition source (-)

8.1.2.3. Radiation Heat Flux

Radiation heat flux is strongly time dependent, because both the flame surface areaand the distance between the flame and intercepting surfaces vary during the courseof a flash fire. The path of this curve can be approximated by calculating theradiation heat flux at a sufficient number of discrete points in time.

The problem focuses on determination of the geometric view factor, which canbe 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 givenassuming 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 thedistance in meters between flame and object.

• Determine the radiation heat flux using q = EFr3 on the basis of E = 173kW/m2.

8.2. SAMPLE CALCULATION

A massive amount of propane is instantaneously released in an open field. The cloudassumes a flat, circular shape as it spreads. When the internal fuel concentration inthe cloud is about 10% by volume, the cloud's dimensions are approximately 1 mdeep 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 arenot anticipated. Therefore, thermal radiation and direct flame contact are the onlyhazardous 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 at100 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 mixturecomposition <|>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 flamedependent on time) should first be specified. For simplification, assume the cloudto be stationary during the full period of flash-fire propagation. As a conservativestarting point, assume that the transmitting (flame) and receiving surfaces are verticaland 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 becomputed if it is assumed that the flame appears as a flat plane, 33 m high, whichpropagates 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 andback, 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 anddistance from the flame to the intercepting surface vary during the course of a flashfire. The path of this curve can be approximated by calculation of the radiation heatflux at a sufficient number of points of time.

The problem focuses on the determination of the geometric view factor. Forexample, the view factor after 5 seconds of flame propagation can be calculatedas 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 areequal, so T1 equals rn. Values for Xr and hr are calculated for the portions of theflame on each side of a normal from the center of the receptor onto the flame

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 inhalf 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 AppendixA for the appropriate Xr and hr. This results in F = 0.062 for each portion ofthe 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) W(m) X(m) hr Xr F T3 q (kW/m2)

O O 150 O5 84 127 1.02 3.02 0.12 0.69 1410 100 104 0.86 2.08 0.20 0.70 2515 92 81 1.07 1.76 0.30 0.72 3720 54 58 1.59 2.94 0.30 0.74 3821 36 53 2.39 2.94 0.26 0.74 3321.7 O 50 O

flat radiator

receiver

Figure 8.3. Graphical presentation for sample problem of the radiation heat flux as a functionof time.

Radiation heat flux is graphically represented as a function of time in Figure8.3. The total amount of radiation heat from a surface can be found by integrationof the radiation heat flux over the time of flame propagation, that is, the area underthe curve. This result is probably an overstatement of realistic values, because theflame will probably not burn as a closed front. Instead, it will consist of severalplumes which might reach heights in excess of those assumed in the model but willnevertheless probably produce less flame radiation. Moreover, the flame will notburn as a plane surface but more in the shape of a horseshoe. Finally, wind willhave a considerable influence on flame shape and cloud position. None of theseeffects has been taken into account.

9BLEVEs—SAMPLE PROBLEMS

In this chapter, applications of the calculation methods used to predict the hazardsof BLEVEs, as described in Chapter 6, are demonstrated in the solution of sampleproblems. Fire-induced BLEVEs are often accompanied by fireballs; hence, prob-lems include calculation of radiation effects. A BLEVE may also produce blastwaves and propel vessel fragments for long distances. The problems include calcula-tions for estimating these effects as well. Calculation methods for addressing eachof 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 followingfireball properties are known:

• the maximum diameter of the fireball, that is, fuel mass contributing to fire-ball 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 sum-mary is presented below.

9.1.1. Fuel Contribution to Fireball

Hasegawa and Sato (1977) showed that when the calculated amount of flashingevaporation of the liquid equals 36% or more, all of the contained fuel contributesto the BLEVE and eventually to the fireball. For lower flash-off values, part of thefuel forms the BLEVE and part of it forms a pool. It is assumed that if the flashingevaporation is lower than 36%, three times the quantity of the flashing liquidcontributes to the BLEVE.

For prediction purposes, the amount of gas in a BLEVE can be taken as threetimes 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 willcontribute to the BLEVE fireball.

9.1.2. Fireball Size and Duration

Many small-scale experiments have been carried out to measure the durations andmaximum diameters of fireballs. These experiments have resulted in the develop-ment of empirical relations among the total mass of fuel in the fireball and its durationand diameter. Fireball diameter estimates, as published by several investigators andmodelers, are presented in Table 6.4.

Average values for calculation of fireball diameter and duration are availablefrom the more recent publications of Roberts (1982) and Pape et al. (1988), whoproduced 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 (m)tc = fireball duration (s)mf = mass of fuel in fireball (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 spheri-cal fireball.

9.1.3. Radiation

For a receptor not normal to the fireball, radiation received can be calculated basedon the solid flame model as follows:

q = EFTA (9.1.2)

where

q = radiation received by receptor (kW/m2)E = surface emissive power (kW/m2)F = view factor (-)Ta = atmospheric transmissivity (-)

The surface-emissive power E9 the radiation per unit time emitted per unit area offireball surface, can be assumed to be equal to the emissive powers measured infull-scale BLEVE experiments by British Gas (Johnson et al. 1990). These entailedthe release of 1000 and 2000 kg of butane and propane at 7.5 and 15 bar. Testresults revealed average surface-emissive powers of 320 to 370 kW/m2; see Table6.2. A value of 350 kW/m2 seems to be a reasonable value to assume for BLEVEsfor 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 asphere (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 beneaththe center of the fireball to the receptor at ground level. When this distance isgreater 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 diameterand "rests" on the ground will predict thermal hazard quite accurately.

Atmospheric transmissivity ra can be estimated by use of one of the equationspresented in Chapter 3, Section 3.5.2, which describes the graphs presented inAppendix 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 totalradiation hazard must include the received radiation integrated over the combus-tion time.

The point-source model can also be used to calculate the radiation received bya receptor at some distance from the fireball center. 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 theduration of the combustion phase of a fireball. According to this approach, the peakthermal input at distance L is given by

(9.1.7)

where

mf = mass of fuel in the fireball (kg)Ta = atmospheric transmissivity (-)Hc = net heat of combustion per unit mass (J/kg)R = radiative fraction of heat of combustion (-)L = distance from fireball center to receptor (m)q = radiation received by the receptor (W/m2)

Hyme suggests the following values of RT = 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 canbe 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) isinvolved in a traffic accident, and the tank truck is engulfed by fire from burninggasoline. The tank is 90% filled with propane. Assume that all of the propanewill contribute to the fireball. Radiation effects are calculated below; blast andfragmentation 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 weightof 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 thefireball 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 350kW/m2.

• Estimate the atmospheric transmissivity. Since no data are known about therelative humidity, use ra = 1.

• Estimate the geometric view factor. The center of the fireball has a height of66.5 m, and thus the view factor (for a vertical object) follows from the relationgiven 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 pointdirectly below the center of the fireball, that is, the position of the tank. Thisdistance must be greater than the radius of the fireball, because actual develop-ment of the fireball often involves, first, an initial hemispherical shape, whichwould 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.

• 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 canbe 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 theradiation received by an object relatively distant from the fireball is to use thepoint-source model. From this approach, the peak thermal input at distance Lfrom the center of the fireball is

= 2.2T8K^X'67

q ~ 4irL2 (9.1.9, same as 9.1.7)

Substituting the appropriate values for the variables, yields the following:

mf = 11,958kgTa = 1.0Hc = 4.636 x 107 J/kgR = 0.4 (It is assumed that the relief valve operated prior to vessel rupture.)q = 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 afunction of both the radiation received and the fireball duration. The impactcan be estimated from Figure 9.1. In this case, the fireball duration is estimatedto 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 isshown in Table 9.2. Note that while there is a difference of about 15% in theradiation levels estimated from the two models, the estimated impact on humansis essentially the same.

TABLE 9.1. Radiation on a (Vertical) Receptor from a 6000-gallon Propane TankTruck BLEVE Calculated with Solid Flame and Point SourceRadiation Models

Ground Distance(m)

100200500

1000

View Factor

0.2550.09450.01720.00439

Solid FlameRadiation(kW/m2)

89336.01.5

Point SourceRadiation (Hymes)

(kW/m2)

122396.81.7

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

GroundDistance

(m) Solid Flame Model Point Source Model

100 third degree bums, 50% lethality third degree bums, 50% lethality200 second degree bums 1% lethality500 some pain some pain

1000 below pain threshold below pain threshold

inci

dent

hea

t flu

x (k

W/m

2)

3* burns, to bare skin (2mm)50% lethality (averageclothing)

-1 % lethality (averageclothing)

start of 2* burns

range for blisteringof bare skin i.e.threshold

9.2. BLAST PARAMETER CALCULATIONS FOR BLEVEs ANDPRESSURE VESSEL BURSTS

In this section, three examples of blast calculations of BLEVEs and pressure vesselbursts will be given. The first example is designed to illustrate the use of all threemethods described in Section 6.3.2. The second is a continuation of sample problem9.1.5, 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 explo-sion, the distance is calculated at which a given overpressure is reached. The thirdexample 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 therepair, the vessel is pressure tested with nitrogen gas at a pressure 25% abovedesign. If the vessel bursts during the test, a large storage tank, located 15 mfrom the vessel, and a control building, located 100 m from the vessel, might beendangered. 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 appropriatecalculation method. The only information needed for selection of a method is thephase of the fluid. Nitrogen at ambient temperature can be regarded as an ideal gasat 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) anddescribed 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

liquidphase contents

ideal gas

temperature calc. energy withbasic method

explosiveflashing

assumeexplosiveflashing

vapor,non-ideal gas

rangenear field

no blasteffects



refined method

end continue withbasic method

Figure 9.2. Selection of blast calculation method.

• The shape of the vessel is cylindrical. It is placed horizontally on saddles atgrade 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

step 7 ofexplosive flashing '

method

calculated R of 'target1

/4 ITN( check R J

R<2

R<2

determine P8

determine I

Tadjust P8 and I

refined method

Figure 9.3. Procedure for basic method.

calc. P8 and is

check P8

end

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 methodmay be followed or the refined method must be used. The control building lies ata nondimensional range of 6.9, so the basic method may be followed. The rangeof the large storage tank is less than 2, so the refined method must be used to obtainan 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 readfrom 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 Figure6.23. 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 perfectlysymmetrical, P5 and 7 are adjusted, depending on R.

To account for the vessel's placement slightly above grade, P8 is multipliedby 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, fromthe nondimensional side-on peak overpressure P8 and the nondimensional side-onimpulse 7, Eqs. (6.3.17) and (6.3.18) are used:

— /O273E173

Ps ~ Po = ^sPo 's = ° cx

^o

The ambient speed of sound O0 is approximately 340 m/s. Substitution gives

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 peakoverpressure 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-testingis 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 tooshort for the basic method to be applied with good results. Therefore, the refinedmethod is used to calculate blast parameters at the large storage tank. The refinedmethod is illustrated schematically in Figure 9.4 (equal to Figure 6.25) and describedin Section 6.3.3.2.

Step 1: Collect additional data.

• The ratio of the speed of sound in the compressed nitrogen to the speed ofsound in the ambient air, Ci1Ja0, is approximately 1.

• The ratio of specific heats of the ambient air is 1.40.

start from step 4of basic method

2 calculate startingdistance

calculate P8,

4 locate starting pointon Rg. 6.21

collect additional data

determine P8


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 burstof 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 one-eighth 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 inthe figure.

Step S: Determine P8.To determine the nondimensional side-on peak overpressure P8 at the large storagetank, P8 is read from Figure 6.21. The nondimensional distance was computed inSection 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. ForR= 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 perfectlysymmetrical, P8 and 7 are adjusted, depending on R. To account for the vessel'splacement slightly above ground level, P8 is multiplied by 1.1. To account for thevessel's cylindrical shape, P8 is multiplied by 1.6 and 7 is multiplied by 1.1. Thus,

P8 and / become:

P8= 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 thenondimensional side-on peak overpressure P8 and the nondimensional side-on im-pulse 7, Eqs. (6.3.17) and (6.3.18) are used:

- Jo213E 1/3

Ps-Po = o 's = f^*o

The ambient speed of sound a0 is approximately 340 m/s. Substitution gives

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 PVBecause 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 valveis 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 withpropane, and one in which the vessel is almost empty (10% filled).

Use of Figure 9.2 requires that the temperature of the liquid be comparedto its boiling point and its superheat-limit temperature. Table 6.1 provides thesetemperatures: 7b = 231 K, and T81 = 326 K. It is obvious that the liquid's tempera-ture can easily rise above the superheat limit temperature when the vessel is exposedto a fire. Therefore, the explosively flashing-liquid method must be selected. Thismethod is described schematically in Figure 9.5 (equal to Figure 6.29), and de-scribed in Section 6.3.3.3.


• The failure overpressure is assumed to be 1.21 times the opening pressure ofthe safety valve. Thus:

Pl = 1.21 x 1.5 + 0.1 = 1.9 MPa (19 bar).

start

check the fluid

determine u 1

determine u,

5 calculate specificwork

Figure 9.5. Calculation of energy of explosively flashing liquids and bursts of pressure vesselsfilled 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.

collect data

calculate energy

calculate R


TABLE 9.3. Thermodynamic Data for Propane

TI Pl fy hg Vf VQ S, Sg

(KJ (MPa; (kJ/kg) (kJ/kg) (m*/kg) (m*/kg) (kJ/kg.K) (kJ/kg.K)

327.7 1.90 674.31 948.32 2.278 x 10~3 0.0232 4.7685 5.6051230.9 0.10 421.27 849.19 1.722 x 10~3 0.419 3.8721 5.7256

• Thermodynamic data are read from a table given in Perry and Green (1984)and interpolated. Subscript "f" denotes the saturated liquid (fluid) state, andsubscript "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 fluidsin Figure 6.30, Steps 3 to 5 are followed for this example. The solution for thefilled vessel will be given first.

Step 3: Determine U1.The specific internal energy of the fluid at the failure state is calculated withEq. (6.3.23):

h = u + pv

The vessel is assumed to be filled with saturated liquid and vapor. The specificinternal energy of the saturated liquid can be computed by substituting the appropri-ate 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 fractionchanges 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 readfrom Figure 6.21. The nondimensional distance R equals 0.66. Reading from thecurve labeled "high explosive," a P8 of 1.15 is found. The procedure is continuedwith 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. ForR = 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 perfectlysymmetrical, P& and 7 are adjusted, depending on R. To account for the vessel'splacement 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 7is 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 fromthe nondimensional side-on peak overpressure P8 and the nondimensional side-onimpulse 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 impulseat 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 Figure6.23. For R = 4.4,7 = 0.012.

Step 7: Adjust Ps and I for geometry effects.P and 7 becomes

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 PrNo corrections are necessary. Hence, the calculated blast parameters at the controlbuilding are as follows: a side-on peak overpressure of 7.7 kPa and a side-onimpulse 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. There-fore, 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 liquidmass 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 thesecomputations 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 E6x _ Ps ~ Po /» _ Ps - Po 4Status (MJ) R (kPa) (Pa.s) R (kPa) (Pa.s)

N2 filled 300.0 1.04 63 230 6.9 4.2 3180% filled 1140.8 0.67 368 516 4.4 7.7 8610% filled 372.8 0.97 170 410 6.4 4.6 42

• The explosion of a vessel full of liquid above the superheat limit temperaturehas much more energy, and therefore, causes a much more severe blast than agas- or vapor-filled vessel.

• The nitrogen-filled vessel and the 10%-filled vessel have approximately thesame energy; therefore, scaled distances at the large storage tank and the controlbuilding are similar. However, the overpressure at the large storage tank ismuch 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 theunsymmetrical blast wave at R = 1.0.

• This calculation takes into account only the blast from the expansion of vesselcontents. In fact, this blast may be followed by one from a vapor cloud explo-sion. This possibility must be considered separately with the methods presentedin earlier chapters.

9.2.3. Sample Problem: Tank Truck BLEVE

Sample problem 9.1.5 demonstrated the calculation of thermal radiation from theBLEVE of a tank truck. This 6000-gallon (22.7 m3) tank was 90% filled withpropane, 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 adistance of 300 to 360 m.

In this section, the blast from the BLEVE will be investigated but not the blastwhich may be caused by a vapor cloud explosion. A variation in the calculationmethod will be presented. Instead of determination of blast parameters at a givendistance from the explosion, the distance at which a given overpressure is reachedwill be calculated. The distance to which fragments may be thrown will be calculatedin Section 9.3.

The use of Figure 9.2 requires that liquid propane's temperature relative to itsboiling point and superheat-limit temperature be known. Table 6.1 gives thesetemperatures: Tb = 231 K, and 7sl = 326 K. It is obvious that the liquid temperaturecan easily rise above the superheat-limit temperature when the vessel is exposed toa fire. Therefore, the explosively flashing-liquid method must be selected. The

method for explosively flashing liquids is drawn schematically in Figure 9.5 (equalto Figure 6.29) and described in Section 6.3.3.3.


• 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 ofdamage chosen is window pane breakage. This can be expected at overpressuresgreater than 6 kPa (0.06 bar).

• The shape of the vessel is cylindrical. It is placed horizontally on saddles atgrade 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 or6.31 if its temperature is unknown. Saturated propane at a pressure of 1.9 MPa (19bar) has a temperature of 328 K, almost the superheat-limit temperature. Note thatit is assumed that temperature is uniform, which is not necessarily the case. FromFigure 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 Section9»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 thevapor can be calculated by multiplying the expansion work per unit volume by thevapor 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 whicha 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 usingEq. (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 isadjusted, depending on R9 which is not yet known. As a first guess, assume thatR is greather than 3.5. To account for the vessel's location slightly above theground, P8 is divided by 1.1. To account for a cylindrical vessel, P8 is divided by1.4. 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 assumedin 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 calculatingdistance of a given overpressure, one or two iterations may be necessary. Thenumber 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 theMexico City incident (Section 2.4.3, Pietersen 1985), will be investigated. ThisBLEVE occurred a few minutes after the initial vapor cloud explosion and probablyinvolved two 1600-m3 spheres. The spheres were probably 50% full at the time ofthe accident.

The BLEVE of the spheres probably shifted a number of cylindrical vesselsfrom their foundations. Furthermore, it probably produced damage in the built-uparea. However, because destruction by intense fire in that area was complete, thiscannot be confirmed. Beyond a range of 300 m, no glass damage due to blast wasobserved. This indicates that the side-on overpressure at that range was well below3 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, butthe 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 inFigure 9.2. The liquid temperature is believed to be about 339 K, which is thetemperature equivalent to the relief valve set pressure. The superheat limit tempera-tures 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 flashingliquid method must be chosen. However, because the temperature of the LPG isbelow the superheat limit temperature (Tsl) for butane and above it for propane, itis uncertain whether the liquid will flash. Therefore, the calculation will first beperformed with the inclusion of vapor energy only, then with the combined energyof vapor and liquid.

The calculation method for explosively flashing liquids is drawn schematicallyin 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. (Limitedinformation is available on the actual LPG composition at the time of theaccident.)

• 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 givenin 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 multi-plying expansion work per unit mass by fluid mass. Both propane and butane mustbe 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 Liquid Vapor Liquid + Vapor

0% O 22.1 22.150% 40.8 11 51.8

100% 81.6 O 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 storagetank, P& is read from Figure 6.22. The results for the different fill ratios are givenin Table 9.6.

The procedure is continued with Step 6 of the basic method, described inSection 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 perfectlysymmetrical, P8 is adjusted, depending on R. The adjusted P8 is given in Table9.7. In this case, the only adjustment needed for R greater than 1 is to multiply by1.1 (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 nondimensionalside-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. Thisconclusion is consistent with the findings of Pietersen, although he assumed that

TABLE 9.6. Nondimensional Pressure P3 of the Explosion(Unadjusted)

Vapor Vapor + Liquid

Fill Ratio R P3 R Ps

0% 4.5 0.045 4.5 0.04550% 5.7 0.035 3.4 0.065

100% — — 2.9 0.080

TABLE 9.7. Overpressure at 300 m from the Mexico City BLEVE (Adjusted P5 and ps)

Combined Expansion of VaporExpansion of Vapor Only and Flashing of Liquid

Fill Ratio _ Ps _ Ps(vol %) P8 (kPa) P8 (kPa)

O 0.05 3.7 0.05 3.750 0.039 2.9 0.072 5.4

100 — — 0.088 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 explosiveflashing of liquid cannot be excluded.

9.3. FRAGMENTS

The quantification of hazards associated with the fragments propelled from anexploding, pressurized vessel should involve the determination of their masses andrange distributions, as well as their velocities and shapes. Research on fragmentparameters 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 willbe repeated here. It appears, however, that these models are incomplete. They givealmost no information on the number of fragments to be expected and only providethe means to calculate one velocity value. Furthermore, a number of assumptionshave to be made in order to calculate range, without which unrealistically longranges would result.

The limitations of mathematical modeling described above increase the impor-tance of statistical analysis of accidental explosions. However, gathering all neededdata to perform a statistical analysis is often very complicated, so results are oftenincomplete. Wherever possible, both theoretical and statistical models should bothbe applied in estimating effects.

The procedure described in the following section permits step-by-step quantifi-cation of fragment-related parameters. The numbers in the flow diagram in Figure9.6 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 determiningfragment characteristics are fully adequate, and it is sometimes difficult to decide

start

vessel

contents

situation £failure

analytical thooseapproach

statistical

collect data

determineenergy

idealgas

gasonly

flashingseesection

thermodyn.data

,fragments.

eq. 9.3.5 number offragments

initial velocity

table 9.8 choice ofeventgroup

fig. 9.9 rangedistribution

group2.3,6

fig. 9.10,9.11

massdistribution

E<0,*eq 9.3.5.

method 1

method 2

method 3

idealgas

fragmentrange

eq.9.3.13,'9.3.14,9.3.15 neglecf

fluidforce,

fig. 9.8 end

Figure 9.6. Decision diagram for determining fragment characteristics.

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 statisti-cal approach (9.3.3) should be applied. Another factor favoring choice of thestatistical analysis approach is that it is faster, because the theoretical approachrequires 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 thevessel itself, its contents, and the condition at failure. These data include:

For the vessel:shape (cylindrical or spherical)diameter Dlength Lmass Mwall thickness t

For vessel contents:density (kg/m3)volume V (m3)chemical and physical propertiesthermodynamic qualitiesliquid/gas ratio

For the condition at failure:internal pressure P1 (Pa)internal temperature T (K)

Knowledge of thermodynamic data is especially important for vessels containingliquids 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 theassumed cause of the failure, an estimate of pressure can be made:

• If failure is initiated by an increase in internal pressure in combination with amalfunctioning of the pressure relief, the pressure at failure will equal the failurepressure of the vessel. This failure pressure is usually the maximum workingpressure multiplied by a safety factor. For carbon-steel vessels, this safety factorcan be taken as four. More precise calculations are possible if the vessel'sdimensions and material parameters are known.

• If failure is due to external heat applied to the vessel (e.g., from fire), thevessel'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 thestarting relief pressure.

• If failure is initiated by corrosion or impact of a missile or fragment, it can beassumed that failure pressure will be the normal operating pressure.

Once a vessel's internal pressure at failure is determined or assumed, the temperatureof 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 explosionfollowing rupture. For both the statistical and the theoretical models, a value forthis energy must be calculated. The first equation for a vessel filled with an idealgas was derived by Erode (1959):

(9.3.1)

where

P1 = internal pressure at failure (Pa)PQ = ambient pressure (Pa)V = volume of the vessel (m3)y = ratio of specific heats (-)

This equation is well known and often used to calculate initial fragment velocity,but its application can result in gross overestimation. Assuming adiabatic expansionof 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 equationwas used as a basis for calculation.

The energy of liquids and gases in pressurized vessels cannot be straightfor-wardly determined by application of the above equations. Upon vessel depressuriza-tion, the liquid portion starts to boil, thus contributing to released energy. Thermo-dynamic 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 flash-ing 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 (Section6.3.2). If so, energy has to be determined from thermodynamic data. If not, theenergy can be calculated very easily by substitution of the volume of the gas for VhiEq. (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 endcaps or half of the vessel itself, were reported to have traveled unexpectedly longdistances. It was argued that these fragments were accelerated during their flightby expelling the liquid entrapped in the fragment.

In Baker et al. (1983), a computer program to calculate the release of energyas a function of time was developed based on the rocketing problem. However, ifone assumes that available energy is released instantaneously, as occurs in the caseof flashing liquids, an upper limit of the initial velocity of the fragment is obtained.Apparently, rocketing fragments are equal to fragments of an exploding vesselwhere liquid flashing occurs. The unexpected long fragment ranges result from theextra available energy of the liquid. Therefore, no special method for calculatingranges 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 ofthe number of fragments. The number of fragments will usually be high for a high-explosive detonation in which the casing disintegrates completely. This will alsobe 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 fragmentsfrom such events tend to be low, usually from 2 to 10 pieces.

Baum (1984) states that the scaled energy, which is determined by:

F I0'5i=iSJ <9-3-5>where

E = scaled energy (-)E = energy (J)M = vessel mass (kg)O0 = speed of sound in the gas (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. Thisvalue is the initial fragment velocity V1. It is used to calculate either the range offragment travel or, if collision with an obstacle occurs before maximum range isattained, impact velocity.

A number of methods and equations are available to determine the initialvelocity. These are described elsewhere in this volume. To avoid confusion, onlythree methods are given here. Method 1 calculates the initial velocity, both forvessels filled with ideal gases and for vessels filled with liquid and vapor. In mostcases, this method will give an upper velocity limit. Method 2 is only valid forgas-filled vessels, but there, velocity depends upon the shape of the vessel andexpected number of fragments. For scaled energies larger than 0.8, method 1 resultsin 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, butmethods 1 and 2 are recommended.

Method 1The simplest method is based on the total kinetic energy Ek of the fragments:

(9.3.6)

where

V1 = initial fragment velocity (m/s)Ek = kinetic energy (J)M = vessel mass (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 whencompared with experimental results. This is logical because a portion of the energywill be diverted into the creation of a blast wave. Negligible portions of the energywill go into rupturing the vessel, producing noise, and raising atmospheric tem-perature.

It appeared from experiments that the actual total kinetic energy generated is0.2 to 0.5 times the energy calculated by Eqs. (9.3.2) and (9.3.4). Therefore, it isappropriate to adjust earlier calculations based on ideal gases as follows:

£k = 0.2-£^- (9.3.7)

where

Ek = kinetic energy (J)P1 = absolute pressure in vessel (Pa)V = volume of the gas in vessel (m3)*Y = ratio of specific heats (-)

Thus, EI is 20% of the energy calculated for nonideal gases or for flash-vaporizationsituations. 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 2A computer program was developed based upon theoretical considerations. Theresults of a parameter study were used to compose a diagram (Figure 9.7) for usein 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 isdetermined by

P = (Pi-PoW (9.3.8)MaI

where

P = scaled pressure (-)P1 = internal pressure at failure (Pa)PQ = ambient pressure (Pa)V = volume (m3)M = mass of the vessel (kg)O0 = speed of sound in gas at failure (m/s)

cylindrical

spherical

cylindrical

Figure 9.7. Fragment velocity versus scaled pressure (Baker et al. 1983). V1 = initial fragmentvelocity. ( ): spheres based on V1 = 0.88a0/=°55 [Eq. (6.4.15)]. ( ): cylinders basedpon V1 = 0.8Sa0/=

055 [Eq. (6.4.15)].

Separate regions in the figure account for the scatter of velocities for spheres andcylinders separating into 2, 10 or 100 fragments. The number of fragments mustfirst 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 cylindricalvessel bursts perpendicularly to the axis of symmetry. For more than twofragments, the cylindrical vessel bursts into strip fragments which expand radi-ally 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 theserestrictions are not valid.

The speed of sound O0 of the contained gas at failure temperature must becalculated:

og = yRT/m (9.3.9)

where

R = ideal gas constant (J/Kkmol)T = absolute temperature (K)m = molecular mass (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. Forhigh scaled-pressure values (i.e., scaled energy larger than 0.8), method 3 shouldbe used.

MethodsThis 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 (kg)M — mass of vessel (kg)

Moore's equation was derived from fragments accelerated from high explosivespacked in a casing. Baum (1984) showed, in comparing different models, thatthe Moore equation tends to follow the theoretical upper-velocity limit for highscaled energies.

9.3.2.6. Ranges for Free-Flying Fragments

The simplest relationship for calculating the range of a free-flying obstacle with agiven initial velocity is derived when fluid-dynamic frictional forces, that is, liftand drag forces, are neglected. Then the only force acting on the fragment is thatof gravity, and the vertical and horizontal range, H and R9 are dependent on theinitial velocity V1 and the initial trajectory angle OL1 as follows:

(9.3.13)

and

(9.3.14)

where

H = vertical range (m)R = horizontal range (m)cq = initial trajectory angle (rad)g = gravitational acceleration (m/s2)

The trajectory angle has a great influence on the range. The maximum range isfound for an angle of 45°:

(9.3.15)

It can be assumed that, should the vessel burst into two halves, fragments willtravel parallel to their axes. If the vessel is initially positioned horizontally, thetrajectory angle will be 5° to 10°.

The results of a computer analysis of parameters for fragment ranges, includingdrag and lift forces, are plotted in Figure 9.8. The developers assumed that fragmentpositions remain constant with respect to trajectory. Figure 9.8 plots the scaledmaximum range R and the scaled initial velocity V1 given by

(9.3.16)

and

(9.3.17)

where

V1 = initial fragment velocity (m/s)V1 = scaled initial velocity (-)R = scaled range (-)R = actual range (m)P0 = density of ambient air (kg/m3)C0 = drag coefficient (-)AD = exposed area in the plane perpendicular to the trajectory (m2)Mf = mass of the fragment (kg)

The curves in Figure 9.8 were generated by maximizing range through variationof initial trajectory angle, so the angle for maximum range does not necessarilyequal 45°. In most cases "chunky" fragments are expected. The lift coefficient isthen zero, and the curve with C1AJyC0A0 = O is valid. It can be seen from Figure9.8 that, for scaled velocities larger than 1, drag force becomes important, andranges will be shorter than those calculated with Eq. (9.3.16). Values for dragcoefficients C0 can be found in Table 9.8.

Should a fragment be a thin plate, lift force becomes important, and the rangewill 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 velocitywhere this "frisbeeing" effect occurs.

9.3.3. Statistical Analysis of Fragments

In Baker (1978b), an analysis was made of 25 accidental vessel explosions todetermine the mass and range distributions of fragments. Most of these results arepresented here. Because data were limited, it was necessary to cluster like eventsinto 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 offragment range and mass distributions. Range distributions for each group aregiven in Figures 9.9a and b. Interpretation of this information makes it possible todetermine which percentage of fragments has a range smaller than or equal to agiven value.

Event groups 2,3, and 6 appeared to yield useful information on mass distribu-tion. They are presented in Figures 9.10 and 9.11. These figures can be used in amanner similar to that recommended for Figures 9.9a and b, namely, to determinethe 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 empiricallyderived 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

Number ofFragmentsMass (kg)ShapeExplosion Source Material

Number ofEvents

Event GroupNumber

142835311411

25,542 to 83,90025,464145,842

6,343 to 7,84048.26 to 187.33

511.7

Railroad tank carRailroad tank carCylinder pipe and spheresSemitrailer (cylinder)SphereCylinder

Propane, anhydrous ammoniaLPGAirLPG propyleneArgonPropane

491231

123456

perc

enta

ge o

f fra

gmen

ts w

ith r

ange

equa

l to

or le

ss th

an R

range R (m)

perc

enta

ge o

f fra

gmen

ts w

ith r

ange

equa

l to

or le

ss th

an R

range R (m)

Figure 9.9. Fragment range distribution for each group (Baker et al. 1978b).

perc

enta

ge o

f fra

gmen

ts w

ith m

ass

equa

l or

less

than

M

mass M (kg)

Figure 9.10. Fragment mass distribution for event groups 2 and 3 (Baker et al. 1978b).

perc

enta

ge o

f fra

gmen

ts w

ithm

ass

equa

l or

less

than

M

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 usedfor the storage of propane. The wall thickness of the vessel is 3 mm, its materialis carbon steel, and its length-to-diameter ratio is 10. The vessel is pressurized afterfabrication with nitrogen to 24 bar. After testing, the safety valve will be set at 15bar for normal operation.

Two different situations will be examined for maximum fragment range: failureduring testing, and failure due to an external fire.

Case 1—Failure during TestingBecause the maximum fragment range is required, the theoretical approach will beapplied. Only the initial velocity and the maximum range of the fragments can becalculated with the theoretical approach.

First, energy must be calculated. Differences among results from the variousequations are illustrated here by the application of each to the problem. Brode [Eq.(9.3.1)] gives

where

P1 = internal pressure at failure (Pa)PQ = ambient pressure (Pa)V = vessel volume (m3)y = ratio of specific heats (-)

Equation (9.3.2) gives

Equation (9.3.3) gives

Equation (9.3.4) gives:

so

As was expected, the Erode equation (9.3.1) gives higher values for energy thanthe 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 thekinetic 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 (J)P1 = absolute pressure in the vessel (Pa)V = volume of the gas in the vessel (m3)

Substituting,

This value appears to be in good agreement with the one calculated with the moretheoretical approach.

In order to determine which method should be applied for die calculation ofinitial velocity, the scaled energy should first be determined (see Section 9.3.2.5).With Eq. (9.3.5):

where

E = scaled energy (-)E = energy (J)M = vessel mass (kg)O0 = speed of sound in the gas (m/s)

The mass M of the vessel can be calculated, assuming hemispherical end caps of5 mm thickness, to be 2723 kg. The speed of sound aQ in nitrogen can be calculatedwith Eq. (9.3.9):

where

R = ideal gas constant (J/(kkmol)T = absolute temperature (K)m = molecular mass (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 anideal gas, both methods 1 and 2 can be applied.

Method 1.The initial velocity, according to Eq. (9.3.6), is:

where


Then the mean initial fragment velocity will be:

Method 2.The initial velocity can also be calculated from Figure 9.7. Calculation of scaledpressure yields

Since the vessel is under a test in which pressure is increased slowly, it can beexpected 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. Iffluid-dynamic forces (lift and drag) are neglected, maximum range will be attainedwhen the fragment is propelled at an angle of 45°. The range is then independentof the fragment's mass and shape and is simply the ratio of the velocity squared togravitational acceleration Eq. (9.3.15). The initial trajectory angle is taken intoaccount by Eq. (9.3.14):

vf sin(2aj)A —

8

where

H = vertical range (m)R = horizontal range (m)Oi1 = initial trajectory angle (rad)g = gravitational acceleration (m/s2)

For cylinders with horizontal axes, the initial trajectory will be low, typically 5° or10°. Table 9.10 shows maximum ranges for initial velocities calculated by eachmethod with various low trajectory angles assumed.

It is obvious that very long maximum ranges are attained if lift and dragforces are neglected. Taking these forces into account can reduce maximum rangessignificantly. Fragments, in this case, are expected to be rather blunt, so the liftcoefficient is taken as zero.

The scaled velocity can be calculated with Eq. (9.3.17). By applying the curvein Figure 9.8, a value for scaled range is found, from which the actual range canbe 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. Thefirst consists of the end cap, with a mass of 123 kg, Ad = 1.86 m2 (diameter ofthe 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

Velocity vt Ran9e <m)

(m/s) OL = 5° a = 70° OL = 45°

Method 1 159 448 882 2580Method 2 105 195 385 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 = initial fragment velocity (m/s)Vj = scaled initial velocity (-)R = scaled range (-)R = actual range (m)P0 = density of ambient air (kg/m3)CD = drag coefficient (-)A0 = exposed area in the plane perpendicular to the trajectory (m2)Mf = mass of the fragment (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 onfragment mass and shape. The theory is, however, only capable of determininginitial velocity. Unless assumptions are made as to fragment shape, mass, andtrajectory angle, fluid forces must be neglected; very long ranges will result.

Case 2—Failure Due to OverheatingAfter a successful test with nitrogen, the vessel is placed in service and filled withpropane. 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 1.21times the relief pressure. Because the tensile strength of the vessel's steel walldrops 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 alsoheated. 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 heatedto a temperature above the superheat limit temperature at failure, and no liquidflashing occurs. To demonstrate the influence of fill ratio, cases of 80% and 10%fill ratio are considered.

Explosively flashing liquidThe decision diagram in Figure 9.6 shows that the energy has to be determined inthis 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 gradelevel; a factor of 2 was applied to account for surface reflection. This factor shouldnot be applied in determining available internal energy. Therefore, the availableinternal 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 theinitial velocity, the scaled energy should be determined (see Section 9.3.2.4).Applying Eq. (9.3.5):

where

E = scaled energy (-)E = energy (J)M = vessel mass (kg)O0 = speed of sound in gas (m/s)

The mass M of the vessel was calculated to be 2723 kg. The speed of sound a0 inpropane can be calculated [from Eq. (9.3.9)] as follows:

OQ = yRT/mt

where

R = ideal gas constant [J/(Kkmol)]T = absolute temperature (K)m = molecular mass (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 bothcases. 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 vesselwas 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 differentinitial trajectory angles with Eq. (9.3.14):

where

R = horizontal range (m)Ct1 = initial trajectory angle (rad)g = gravitational acceleration (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 ina direction parallel to the axis of the vessel. The trajectory angle will therefore be5 to 10°.

Nonflashing liquidIn case the liquid does not flash, the available internal energy can be calculatedwith Eq. (9.3.1) or (9.3.2) taking V equal to the volume of the gas (see Section9.3.2.2 and flow chart in Figure 9.6). For initial calculations Eq. (9.3.7) isappropriate.

with

Ek = the kinetic energy (J)P1 = the absolute pressure in the vessel (Pa)V = the volume of the gas in the vessel (m3)

The safety valve was set at 15 bar, so the failure pressure equals the maximuminternal 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 1O7J

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 (%) V1 (m/s) a = 5° a = 70° a = 45°

80 283 1419 2795 817210 217 834 1643 4805

The maximum fragment range for different initial trajectory angles can again becalculated with Eq. (9.3.6):

where


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 differentinitial trajectory angles with Eq. (9.3.14):

where

R = horizontal range (m)(Xj = initial trajectory angle (rad)g = gravitational acceleration (m/s2)

Clearly, from Table 9.12, the more dangerous case not involving flashing liquidis the 10% filled vessel.

9.3.4.2. Statistical Analysis

Sample problem 9.1.6. demonstrated the calculation of the thermal radiation froma 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 (%) vt (m/s) a = 5° a = 70° a = 45°

10 221 865 1705 498480 104 192 377 1104

TABLE 9.13. Fragment Distribution

Percentage of FragmentsRange Expected within Range

(m) W

12 133 10

110 50550 90

1100 99

with propane and burst due to fire engulfment at an overpressure of 1.8 MPa (18bar). The resulting thermal radiation was sufficient to cause third-degree burns ata distance of 300 to 360 m. The blast was sufficient to cause injuries from windowpane fragments at a distance of 100 m.

Here, the statistical approach will be used to predict the range distribution ofthe 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 choiceis clearly event group 1.

• Number of fragments. The number of fragments to be expected can then beread 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 eventgroup 1. Table 9.13 gives an impression of the distribution of the fragments.

• Mass distribution. No statistical information can be obtained on the massdistribution (see decision diagram in Figure 9.6). It can, however, be concludedthat there is considerable danger from fragments at a distance up to 1000 m.Of all the effects (heat radiation, blast, and fragments), fragments can causedamage 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 onExplosion Hazards Evaluation. Southwest Research Institute.

Baker, W. E., J. J. Kulesz, R. E. Ricker, P. S. Westine, V. B. Parr, L. M. Vargas, andP. K. Moseley. 1978b. Workbook for Estimating the Effects of Accidental Explosionsin 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. ExplosionHazards and Evaluation. New York: Elsevier.

Baum, M. R. 1984. The velocity of missiles generated by the disintegration of gas pressurizedvessels and pipes. Trans. ASME. 106:362-368.

Baum, M. R. 1987. Disruptive failure of pressure vessels: preliminary design guide linesfor fragment velocity and the extent of the hazard zone. Advances in Impact, BlastBallistics, 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. Heidel-berg, pp. 297-304.

Hymes, I. 1983. The physiological and pathological effects of thermal radiation. UnitedKingdom Atomic Energy Authority, SRD R 275.

Johnson, D. M., M. J. Pritchard, and M. J. Wickens. 1990. Large scale catastrophic releasesof 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.

AVIEW FACTORS FOR SELECTED

CONFIGURATIONS

In this appendix, the view factors for three configurations are given:

1. radiation from a sphere2. radiation from a vertical cylinder3. 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 withrespect to the emitter. The angle between the normal to the surface and the connec-tion 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 anglebetween the connection of the surface to the center of the sphere and the tangentto 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 (m)r = radius of sphere (m)0 = orientation angle (rad)

In this case, the sphere is in full sight.When, on extension, the receiving surface intersects with the sphere (@ > TT/

2 — <I>), the receiver can not "see" the total emitter. The view factor F is thengiven as

(A-2)

where

r = fireball radius (r = D/2) (m)D = fireball diameter (m)L = distance to center of sphere (m)& = angle between the normal to surface and connection of point

to center of sphere (rad)24> = view angle (rad)L1 = reduced length LIr (-)

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 verticallyplaced cylinder with a height h and a ground surface radius r. The view factor of

fireball fireball

receptor receptor

Figure A-1. View factor of a fireball. (A) Receiver "sees" the sphere completely. (B) Receiver"sees" the sphere partially.

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 theaxis 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)

degrees

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 factorsgenerated 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 receiverare parallel to each other. The view factor is calculated from the sum of viewfactors from surface I and surface II (see Figure A-5). Surfaces I and II are definedas those to the left and the right of a plane through the center of the receiver andperpendicular 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

Xr 0.1 0.2 0.5 1.0 2.0hr

3.0 5.0 6.0 70.0 20.0

1. horizontal target (1000 x Fh)1.11.21.31.41.52.03.04.05.0

10.020.0

1.11.21.31.41.52.03.04.05.0

10.020.0

13244201161

330196130947128953

2421206538245

41530822717313556191061

332243178130972751

354291242203170731973

3603072682382121265022111

3623102722462221457138213

36231217725022815891573771

2. vertical target (1000 x Fv)4493973442962531264724153

45341337634231219486472961

4544163833543292361328053133

45441638435633224515010069194

3. maximum view factor (10001.11.21.31.41.52.03.04.05.010.020.0

356201132947228953

48133123617713856191061

5594662873232711294824153

57550544839835520888472961

5805174684273922671418354133

58151947243340028516610673194

45441638435633324816111586297

X Fmax)58152047443640429418512994307

36231227825122916095624391

45441638435733324916311991329

581521474436404296189134100349

3633132782522311641037354173

454416384357333249165123974214

5815214754374052991951431114514

3633142791532321661077861268

4554173853573332501671251004821

5815214754374063001971471175522

Figure A-4. Maximum view factors of a cylindrical flame as function of dimensionless distanceto 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 forany distance C from the emitter.

The view factors Fh, F^ and Fmax can easily be found by summing the viewfactors calculated from the surfaces I and II. Values of the view factor Fmax asfunction 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 0.3 0.5 1.0 1.5 2.0 3.0 5.0

1. horizontal target (1000 x Fh)0.1 146 276 341 400 443 456 461 465 4670.2 53 146 221 310 389 413 423 430 4350.3 25 83 144 236 337 371 386 397 4030.5 9 34 68 137 249 296 318 336 3461.0 2 8 17 42 111 161 190 219 2381 . 5 1 3 6 1 7 5 3 8 8 1 1 4 1 4 6 1 7 02 . 0 1 3 8 2 8 5 1 7 1 1 0 0 1 2 63.0 1 3 10 20 31 50 755.0 1 2 5 9 16 31

(Table continues on p. 344.)

TABLE A-2. (Continued)

"rXr 0.1 0.2 0.3 0.5 1.0 1.5 2.0 3.0 5.0

2. vertical target (1000 x Fv)0.1 353 447 474 489 496 497 497 497 4980.2 223 352 414 461 484 488 489 490 4900.3 156 274 349 421 466 474 477 478 4790.5 94 178 245 335 416 435 442 445 4471.0 41 80 117 180 277 318 335 347 3521.5 22 44 65 105 179 222 245 264 2742.0 14 17 41 66 120 157 180 204 2183.0 7 13 20 32 62 86 105 129 1485.0 2 5 7 12 24 35 45 61 80

3. maximum view factor (1000 x Fmax)0.1 382 525 584 632 665 674 678 681 6820.2 229 381 469 555 621 639 647 652 6550.3 158 286 377 483 575 602 613 622 6260.5 94 181 255 362 484 526 544 558 5651.0 41 80 188 185 299 356 385 410 4251.5 22 44 66 106 187 239 270 302 3222.0 14 27 41 67 123 165 194 227 2523.0 7 13 20 33 62 88 109 138 1655.0 2 5 7 12 24 36 46 63 86

Figure A-6. Maximum view factor of a plane surface as function of dimensionless distanceto emitter.

REFERENCES

Buschman, Jr., A. J., and C. M. Pittman. 1961. Configuration factors for exchange ofradiant energy between antisymmetrical sections of cylinders, cones and hemispheresand 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.

BEFFECTS OF EXPLOSIONS

ON STRUCTURES

Acquisition of practical knowledge in the field of explosion-induced structural dam-age is still heavily dependent upon empirical data. Such data, however, usuallygive information only about those overpressure levels which relate to certain degreesof damage. Other parameters, such as duration, impulse, and shape of the blastwave are not taken into account. Tables containing such information are frequentlypublished. The best known are contained in Glasstone (1966, 1977), a frequentlycited reference.

The earliest tables were compiled from data collected from nuclear weapontests, in which very high yield devices produced sharp-peaked shock waves withlong durations for the positive phase. However, these data are used for other typesof blast waves as well. Caution should be exercised in application of these simplecriteria to buildings or structures, especially for vapor cloud explosions, which canproduce blast waves with totally different shapes. Application of criteria fromnuclear 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 itis damaged beyond economical repair. Severe damage (zone B) suggests partialcollapse and/or failure of some bearing members. A building in zone C (moderatedamage) 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 panelsand roofs. More detailed information is given in Table B-2, which is based onGlasstone (1977).

Information of the influence of duration on the level of damage can be foundin 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 inLondon from World War II bomb attacks. These data permitted the developmentof a relationship among damage, distance, and type of bomb, and thus permittedcalculation of explosion yields. Baker (1983) converted this relationship into apressure-impulse diagram containing iso-damage curves (Figure B-I). The curvesin this figure represent the threshold of side-on blast-wave parameters that producea 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 asmultiple reflections and shielding due to the presence of other structures.

TABLE B-2. Damage Produced by Blast

o/ae-onoverpressure(kPa)

0.150.20.30.712

33.5-7

587-15

101515-2018

20

20-28

3035

35-505050-55

6070

Description of Damage

Annoying noiseOccasional breaking of large window panes already under strainLoud noise; sonic boom glass failureBreakage of small windows under strainThreshold for glass breakage"Safe distance," probability of 0.95 of no serious damage beyond

this value; some damage to house ceilings; 10% window glassbroken.

Limited minor structural damageLarge and small windows usually shattered; occasional damage to

window framesMinor damage to house structuresPartial demolition of houses, made uninhabitableCorrugated asbestos shattered. Corrugated steel or aluminum

panels fastenings fail, followed by buckling; wood panel (standardhousing) fastenings fail; panels blown in

Steel frame of clad building slightly distortedPartial collapse of walls and roofs of housesConcrete or cinderblock walls, not reinforced, shatteredLower limit of serious structural damage 50% destruction of

brickwork of housesHeavy machines in industrial buildings suffered little damage; steel

frame building distorted and pulled away from foundationsFrameless, self-framing steel panel building demolished; rupture of

oil storage tanksCladding of light industrial buildings rupturedWooden utility poles snapped; tall hydraulic press in building

slightly damagedNearly complete destruction of housesLoaded tank cars overturnedUnreinforced brick panels, 25-35 cm thick, fail by shearing or

flexureLoaded train boxcars completely demolishedProbable total destruction of buildings; heavy machine tools moved

and badly damaged

TABLE B-1. Damage Levels

Zone

ABCD

Damage Level

Total destructionSevere damageModerate damageLight damage

Side-on overpressure(kPa)

>83>35>17>3.5

Figure B-1. Pressure impulse diagrams for damage to brick houses. Line 1: Threshold for lightdamage. Line 2: Threshold or moderate damage: partial collapse of roof; some bearing wallfailures. 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 Hazardsand 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 Disas-ters. Washington: The Office of Oil and Gas, Department of the Interior.

CEFFECTS 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 overpressureeffects, explosion-wind effects, impact from fragments and debris, collapse ofbuildings, and heat-radiation effects. Heat-radiation effects are not treated here; seeChapter 6, Figure 6.10 and Table 6.6.

Explosion effects are commonly separated into a number of classes. The maindivision is between direct and indirect effects. Sometimes, direct effects are referredto as primary effects, and indirect effects are then subdivided into secondary andtertiary effects.

Direct, Primary Effects

The main direct, primary effect to humans from an explosion is the sudden increasein pressure that occurs as a blast wave passes. It can cause injury to pressure-sensitive human organs, such as ears and lungs.

Indirect Effects

Primary fragments originate from the explosion source, for example, a pressurevessel. In general, those fragments have a high velocity. The impact of fragmentsand debris from sources not originating from the explosion source are secondaryeffects. Secondary fragments result when the blast tears off parts of structures, forexample, bricks, roof tiles, and glass. Such fragments, except for glass, are rela-tively blunt and have low velocities. Glass window panes and fragments, however,are small, sharp, and sometimes have high velocities. Thus, they are capable ofcausing injuries at much greater distances from explosion centers than usually resultfrom other secondary fragments.

Building collapse can be regarded as a secondary effect, although it is notcommon to group this effect within any class.

The explosion wind following a blast can carry persons away, causing injuryas a result of their falling, tumbling over, or colliding with obstacles. This effectis referred to as a tertiary effect.

Effects are described, together with criteria to calculate the probable degreeof lethality.

C-2. PRIMARY EFFECTS

Lethality Due to Lung Injury

As the external pressure on the chest wall becomes larger than its internal pressureduring the passage of a blast wave, the chest wall moves inward, thus causinginjury. Because the inward motion takes time, the duration of the blast wave isimportant. Results of animal tests indicate that overpressure is only important forlong durations, and impulse is important for relatively short durations (White etal. 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 inrelation to the blast wave, from which the chance of survivability can be calculated.Those diagrams were combined in a pressure-impulse diagram, which is depictedin Figure C-I. The scaled overpressure P equals PIp0, in which P is the actualpressure acting on the body, and pQ is the ambient pressure. The scaled impulsei equals:

7 = //(pj/2m1/3) (C-Ll)

in which i is impulse and m is mass of the body. The impulse is the integral ofoverpressure over the blast-wave duration. For initial calculations, impulse can beapproximated 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 equalsthe 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 smallin 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 overpressurePs plus the pressure Q caused by the explosion wind multiplied with the dragcoefficient 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) Diffractionof incident wave: P = P8 + O. (C) Body subjected to reflection (standing): P = PT. (D) Bodysubjected to reflection (prone): P = Pr (Bowen et al. 1968).

In general the drag coefficient depends on the shape of the structure. In the caseof 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 (FiguresC-2C and C-2D), the pressure P acting on the body equals the reflected pressure Pr:

(C-1.4)

Ear Damage

The ear is a very sensitive and complex organ that responds to very small variationsin pressure. It was argued in Hirsch (1968) that ear drum rupture is decisive as toear damage from blast waves. Figure C-3 shows the percentage of eardrum rupturesas a function of side-on overpressure P8.

Overpressure duration probably has some influence on ear damage, but noliterature 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 impulseregion.

perc

enta

ge e

ardr

um ru

ptur

e

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 Dueto Impact of a Mass of 4.5 kg

Impact Velocity (mis) Level of Injury

3.1 Mostly safe4.6 Threshold7.0 Near 100% lethal

C-3. SECONDARY EFFECTS

For purposes of determining fragment effects on humans, cutting and noncuttingfragments should be distinguished from each other. Cutting fragments penetrate theskin, whereas injuries from noncutting fragments result from contact pressure atimpact. 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 (TableC-I).

A fragment is generally considered to be dangerous if it has a kinetic energyof 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 metersper second.

The kinetic energy criterion can be applied for fragment masses between 4.5and 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 frag-

ments/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 heavystructural parts. Pictures taken after earthquakes or bomb attacks reveal that verticalmembers 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) Injury

3.0 Mostly safe6.4 Lethality threshold

16.5 Lethality near 50%42.0 Lethality near 100%

building collapse may appear total, it is not unusual for some people to survivewithin the spaces formed by the collapsed structure.

Earthquake statistics reveal that about 50% of those inside a collapsing buildingwill be killed, either immediately or as a result of injuries sustained. Other dataare lacking, but one could assume a similar percentage for people inside buildingsthat collapse as a result of blast. This assumption is supported by the fact that, inboth cases, the event is sudden and unexpected, so there is neither a place nor thetime to find other shelter.

C-4. TERTIARY EFFECTS

Air particles in a blast wave have a certain velocity which, in general, flow in thesame 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 tobe incurred as a person tumbles and slides along the surface, but upon collisionwith an obstacle, consequences may be deadly. Such consequences depend uponvelocity at impact, the hardness and shape of the obstacle, and the portion of thebody involved in the collision. Table C-2 gives injury criteria.

Based on the pressure and impulse of the incident blast wave, the maximumvelocity can be calculated of a human body during transportation by the explosionwind. Figure C-4 shows the impact velocity Vm for the lethality criterion for wholebody 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 tothe 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 objectsresulting 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.

DTABULATION OF SOME GAS

PROPERTIES IN METRIC UNITS

Critical Conditions

Gas or vapor

AcetyleneAirAmmoniaArgonBenzene

n-Butane/so-butyleneCarbon dioxideCarbon monoxideChlorine

EthaneEthyl chlorideEthyleneHeliumn-Heptane

n-HexaneHydrogenHydrogen sulfideMethaneNatural gas

NitrogenPentyleneOxygenPropaneWater vapor

ChemicalFormula

C2H2

N2 + O2

NH3

AC6H6

C4H10C4H8

CO2

COCl2

C2H6

C2H5CIC2H4

HeC7H16

C6H14

H2

H2SCH4

—

N2

C5H10

O2

C3H8

H2O

MolecularMass

26.0528.9717.0339.9478.11

58.1256.1044.0128.0170.91

30.0764.5228.054.00

100.20

86.172.02

34.0816.0418.82

28.0270.1332.0044.0918.02

SpecificHeat Ratio

1.241.401.311.661.12

1.091.101.301.401.36

1.191.191.241.661.05

1.061.411.321.311.27

1.401.081.401.131.33

Abs.Press,(bar)

62.437.7

112.848.649.2

38.040.074.035.277.2

48.852.751.22.3

27.4

30.313.090.046.446.5

33.940.450.342.5

221.2

AbS.Temp.

(K)

309.4132.8406.1151.1562.8

425.6418.3304.4134.4417.2

305.6460.6283.3

5.0540.6

508.333.3

373.9191.1210.6

126.7474.4154.4370.0647.8

ECONVERSION FACTORS TO SI FOR

SELECTED QUANTITIES

An asterisk before a number indicates that the conversion factor is exact, and allsubsequent digits are zero.

TABLE E-1A. Conversion Factors to Sl Units

To Convert From

British thermal unit (Btu,International Table)

Btu/lb-deg F (heat capacity)

Btu/hourBtu/secondBtu/ft2-hr-deg F (heat

transfer coefficient)Btu/ft2-hour (heat flux)

Btu/ft-hr-deg F (thermalconductivity)

degree Fahrenheit (0F)degree Rankine (0R)fluid ounce (U.S.)footfoot (U.S. Survey)foot of water (39.20F)foot2

foot/second2

foot2/hourfoot-pound-forcefoot2/secondfoot3

gallon (U.S. liquid)graminchinch of mercury (6O0F)

To

joule (J)

joule/kilogram-kelvin(J/kg-K)

watt (W)watt (W)joule/meter^second-

kelvin (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)

Multiply By

1.0550559 x 103

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)71.8tk = 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

inch of water (6O0F)inch2

inch3

kilocaloriekilogram-force (kgf)mile (U.S. Statute)mile/hourmillimeter of mercury (O0C)pound-force (lbf)pound-force-second/ft2

pound-mass(lbm avoirdupois)

pound-mass/foot3

pound-mass/foot-secondpsiton (long, 2240 lbm)ton (short, 2000 lbm)torr (mm Hg, O0C)watt-houryard

To

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)

kilogram/meter3 (kg/m3)pascal-second (Pa-s)pascal (Pa)kilogram (kg)kilogram (kg)pascal (Pa)joule (J)meter (m)

Multiply By

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

4.44822164.7880258 x 101

*4.5359237 x 10~1

1.66018463 x 101

1.48816396.8947573 x 103

1.0160469 x 103

*9.718474 x 102

1.3332237 x 102

*3.6000000 x 103

*9. 1440000 x 10~1

FA CASE STUDY

OF GAS EXPLOSIONSIN A PROCESS PLANT

USING A THREE-DIMENSIONALCOMPUTER CODE

B. H. Hjertager, S. Enggrav, J. E. F0rrisdahl and T. SolbergTelemark 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 crucialin obtaining an acceptable level of safety. In order to perform such assessments,good predictive tools are needed. These tools should take account of relevantparameters, such as geometrical design variables and gas cloud distribution. Atheoretical model must therefore be tested against sufficient experimental data priorto becoming a useful tool. The experimental data should include variations ingeometry as well as gas cloud composition, and the model should give reasonablepredictions 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 detailsthat can influence the process to be simulated. Examples of such geometries areheat exchangers with thousands of tubes and several baffles and regenerators withmany internal heat absorbing obstructions. In the present context the geometriesfound inside modules on offshore oil and gas producing platforms and in onshoreprocess plants constitute relevant examples of the complex geometries at hand.There are at least two routes for describing such geometries. First, we may chooseto 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 detaileddescription will always need large computer resources both with regard to memoryand calculation speed. It is not feasible with present or even future computers toimplement the detailed method of solving such problems. We are therefore forcedto use the second line of approach, which incorporates the so-called porosity/distributed resistance (PDR) formulation of the governing equations. This methodwas proposed by Patankar and Spalding (1974) and has been applied to analysis ofheat exchangers, regenerators, and nuclear reactors. Sha et al. have extended themethod to include advanced turbulence modeling. The presence of geometricaldetails modifies the governing equations in two ways. First, only part of the totalvolume is available to flow, and secondly, solid objects offer additional resistanceto 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 invented volumes or unconfmed vapor clouds by modeling the burning velocity ofthe propagating flame. This may be successful if we have a simple mode of flamepropagation such as axial, cylindrical, or spherical in volumes without obstructionsin the flow. If these are present, however, it is almost impossible to track the flamefront throughout complex geometries. It has been apparent that in these siutationsit is more useful to model the propagation by calculating the rate of fuel combustionat different positions in the flammable volume. It is also important to have a modelthat is able to simulate both subsonic and supersonic flame propagation to enablea true prediction of what can happen in an accident scenario. One such model thatin 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 hasbeen tested against experimental data from various homogeneous stoichiometricfuel-air mixtures in both large- and small-scale geometries. Similar models for gasexplosions have subsequently also been proposed by Kjaldman and Huhtanen(1986), Marx et al. (1985), Martin (1986), and Van den Berg (1989). All the abovemodels are similar in nature. They use finite-domain approximations to the governingequations. Turbulence influences are taken into account by the k-e model of Launderand Spalding, and the rate of combustion is modeled by variants of the "eddy-dissipation" model of Magnussen and Hjertager. The Bakke and Hjertager modelsare incorporated in two computer codes named FLAGS (FLame Acceleration Simu-lator) and EXSIM (EXplosion SIMulator). The solution method used is the SIMPLEtechnique of Patankar and Spalding (1972). The model of Kjaldman and Huhtanenuses the general PHOENICS code of Spalding. The model of Marx et al. usesthe CONCHAS-SPRAY computer code, which embodies the ICE-ALE solutiontechnique. The model of Van den Berg is similar to the Hjertager model and isincorporated into a code named REAGAS. Finally, the model of Martin that isembodied 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 theEXSIM code, to a case study of gas explosions in a process plant. The scenariowas specified by Mancini for use in a workshop at a recent conference arranged bythe Center for Chemical Process Safety of the American Institute of ChemicalEngineers (CCPS/AIChE 1991).

1.5. Contents of Paper

First, the scenario is defined, followed by a brief summary of the code. Next, thevarious clouds and ignition positions are defined, then the results are given, andfinally some concluding remarks are made.

2. SCENAMO DESCWPTION

GeneralFigure 1 shows part of a solvent phase polypropylene plant. The plant consists ofthree process lines, denoted A, B, and C. During a risk assessment review, ascenario was identified that involved a release of reactor contents from a locationnear the west end of the "A" line. Estimates are needed of the blast overpressuresthat would occur if the resulting cloud of vapor, mist, and power ignites.

Release characteristicsDescription: A slurry of polypropylene powder in hexane/propylene liquid

Rate: 4000 kg/min

Composition: Propylene monomer 20 wt%Hexane 50 wt%Polypropylene powder 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 afterwhich it would gradually decrease to zero in another 4-5 min.

Location: The postulated release would occur at an elevation of about 6 m aboveground level (a.g.l.) and in a horizontal direction. The flashing liquidjet is likely to impact on surrounding equipment.

Figure 1. Layout of the solvent phase polypropylene plant with the leak location.

Ignition sourcesNo obvious "hard" ignition sources, such as fired heaters, are present in the areashown. It may be assumed that ignition is possible anywhere within the flam-mable area.

Ambient conditionsWind very light (1/2 m/sec) toward north but variable (±30° of due north). Tempera-ture: 2O0C. Relative humidity: 50%. Pressure: 1.0 bar abs. Stability: class D.

Site informationFigure 1 shows only facilities in the near vicinity of the release. There are a numberof other facilities in the expanded area including propylene storage and unloading,solvent storage, laboratories, utilities, administration building, product finishingand shipping facilities, cooling towers, etc.

Process linesEach of the three process lines is supported within a structural steel framework thatis 20 m tall. Each line contains a number of vessels (reactors, flash drums, separa-

tors, hold tanks, etc.), heat transfer equipment, powder dryers, powder handlingequipment, and associated pumps, piping, etc.

Compressor buildingMost of the equipment in this steel-framed building is located at a floor level about2 m above ground. Above this level the building is covered with light weight wallsto its maximum height of 8 m above ground. Below the 2 m level the sides of thebuilding are open.

Powder blending and storage areaThis area consists of a number of powder and pellet storage silos along with hoppers,blenders, product conveying equipment, etc.

Other buildingsThe motor control center (MCC) and Substation have concrete block load bearingwalls of ordinary construction. The control house is of blast resistant constructionwith reinforced concrete walls and roof designed for 0.2 bar static. All three build-ings 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 modeledbased 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 wellas 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 theEXSIM code, we use the CAD system named AutoCAD with a specially writteninterface program. Figure 1, prepared by this method, gives the details of thegeometry we use for the modeling study. The plant is represented by approximately70 obstructions. The calculation domain as shown in Figure 1 is 140 x 105 x 30m in the Jt-, y-, and z-directions. The grid resolution used was 37 x 28 X 17 gridpoints equally spaced along the three directions.

4.2. Case Assumptions

Fuel-air cloudsAnalysis had shown that the fuel behaved like ethylene-air mixture and the cloudcould be so large that it could fill the whole calculation domain up to about 20 mhigh. The ethylene-air gas cloud was assumed to be a homogeneous stoichiometricmixture 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 positionsFigure 2 shows the three ignition positions that were chosen:

1. IGNl: outside the process line area2. IGN2: inside the process line area3. IGN3: under the compressor building

Summary of casesTable 1 gives a summary of the conditions for the cases that were run

TABLE F-1.

Case 1 Case 2 Case 3 Case 4

Cloud size Small Large Large LargeIgnition position IGN1 IGN1 IGN2 IGN3

Figure 2. Plot plan of process plant showing the three ignition positions and the eight pressuremonitoring points.

5. RESULTS AND DISCUSSION

5.1. General

The output from each case produces a wealth of information, including distributionof pressure, combustion products, rates of combustion, velocity components, etc.The results of each case will be summarized by presenting the pressure time historiesat the eight locations that were presented in Figure 2 together with the flame speedalong 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. Thelargest pressure is found at location p8 in Figure 4, and it amounts to approx. 0.2

CASE1

Pre

ssu

re

(bar

)

Figure 3. Pressure-time histories at four locations (p1-p4) in the process plant. Case 1.

CASE1

Pre

ssu

re

(bar

)


CASE1

Fla

me

spee

d, (m

/s)

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 flamespeed in Figure 5 accelerates to about 200 m/s. In this figure the flame acceleratesthrough 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 linearea. The cloud is a large one covering the whole calculation domain up to 20 mabove ground level.

The eight pressure-time histories are shown in Figures 6 and 7, whereas theflame speed along the ^-direction from the ignition point is shown in Figure 8. Thelargest pressure is now found at location p7 in Figure 7, and it amounts to approxi-mately 0.15 bar, which is about the same as for Case 1. The flame speed in Figure8 accelerates to a speed of about 200 m/s. In this figure the flame acceleratesthrough the process lines and decelerates between the lines. This flame speed contouris very similar to Case 1.

CAS E2

Pre

ssu

re

(ba

r)

Figure 6. Pressure time histories at four locations (p1 -p4) in the process plant. Case 2.

CASE2

Pre

ssu

re

(ba

r)

Figure 7. Pressure time histories at four locations (p5-p8) in the process plant. Case 2.

CASE2

Fla

me

spee

d,

(m/s

)

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 thecenter 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 inFigure 11, and along the ^-direction is shown in Figure 12. The largest pressure isnow found at location p4 in Figure 9; it amounts to approx. 4.0 bar. The pressureat the control house location (pi) is approx. 1.2 bar, which is much larger than forCase 1 and Case 2. The flame speed in Figure 11 accelerates to a speed of about300 m/s in both directions away from the ignition point. The maximum flame speedin the jc-direction shown in Figure 12 is between 600 and 650 m/s. The change ofignition position from the edge (Case 2) to the center has significantly increasedthe peak pressures and flame speeds.

Figure 13 shows contour maps at an instant in time when 75% of the fuel isleft in the calculation domain. Each contour plot shows contour values for thefollowing 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

CASE3P

ress

ure

(b

ar)

Figure 9. Pressure-time histories at four locations (p1 -p4) in the process plant. Case 3.

CASE3

Pre

ssu

re

(ba

r)


CASE3F

lam

e

spee

d,

(m/s

)

Figure 11. Flame speed versus distance along the y-direction through the ignition location.Case 3.

CASE3

Fla

me

spee

d,

(m/s

)

Figure 12. Flame speed versus distance along the x-direction through the ignition location.Case 3.

XY-PLANES

Z = 1.00 M K = 2 FUEL FRACTION LEFT - 0.75

TIME = 1521.72 MSEC TIME CYCLE NO. - 126

PORO

SITY

VEL.

VECT

ORS

X-RXIS UV-PLOT VMFIX - 540.9 M/S

FUEL

PRES

SURE

M I N - 0.000 KGFU/KG MRX - 0.063 KGFU/KG M I N - -0.056 BRR MRX - 2.403

COM

B.SR

RTE

PROD

UCTS

M I N - 0.000 KG/M3/S MRX - 17.908 KG/M3/S M I N - 0.000 KGPR/KG MRX- 0.281

Figure 13. Velocity vectors and contour maps. Case 3.

by thick curves, whereas the lowest values are denoted by dotted curves. The valuesto be displayed have been chosen to be (1) geometry in the plane; (2) velocityvectors; (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 hasleft the calculation domain in the j-direction and is about to leave the domain inthe jc-direction. The highest pressure in this situation is about 2.4 bar and is locatedclose 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 movedto 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 inFigure 16. The largest pressures are now found at location p2 in Figure 14 andlocation p5 in Figure 15; they amount to approximately 9.0 bar. The pressure atthe control house location (pi) is approximately 3.0 bar, which is much larger thanfor 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 thepeak pressures and flame speeds.

Figure 17 shows contour maps at an instant in time when 74% of the fuel isleft in the calculation domain. The peak pressure in this particular situation is about9.5 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 situationfor Case 4 is very much like the experimental data collected in several British Gasexperiments (Harris and Wickam). These experiments demonstrated the large effectof a confined explosion on the subsequent unconfined explosion.

CASE4

Pre

ssu

re

(bar

)

Time (msec)

Figure 14. Pressure-time histories at four locations (p1 -p4) in the process plant. Case 4.

CASE4P

ress

ure

(bar

)


CASE4

Flam

e sp

eed,

(m

/s)

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 K - 2 FUEL FRACTION LEFT = 0.74

TIME - 1119.26 MSEC TIME CYCLE NO. - 128

PO

RO

SIT

Y

VE

L.V

EC

TOR

S

X-RXIS UV-PLOT VMflX - 730.8 M/S

FUE

L

PR

ES

SU

RE

MIN - 0.000 KGFU/KG MRX - 0.063 MIN - -0.071 BRR MRX - 9.487

CO

MB

.SR

RTE

PRO

DU

CTS

MIN - 0.000 KG/M3/S MRX - 164.115 MIN - 0.000 KGPR/KG MRX - 0.281


XZ=PLANES

Y = 50.50 M J - 14 FUEL FRACTION LEFT - 0.74

TIME - 1119.26 MSEC TIME CYCLE NO. - 128

PO

RO

SIT

Y

VE

L.V

EC

TOR

S

CO

MB

.SR

RTE

PRES

SUR

EPR

OD

UC

TS

X-RXIS UW-PLOT VMRX - 578.8 M/S

FUE

L

M I N - 0.000 KGFU/KG MRX - 0.063 KGFU/KG M I N - -0.061 BRR MRX - 9.466


6. SUMMARY AND CONCLUDING REMARKS

The preceding case studies have shown that gas explosion calculations inside realisticprocess 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 aresummarized in the following table:

TABLE F-2.

Cloud Size

Ignition Small Large

Outside process line area 0.2 bar 0.3 barInside process line area — 4.0 barUnder compressor building — 9.0 bar

Although the status of many 3D codes makes it possible to carry out detailed scenariocalculations, further work is needed. This is particularly so for: 1) development andverification of the porosity/distributed resistance model for explosion propagationin high density obstacle fields; 2) improvement of the turbulent combustion model,and 3) development of a model for deflagration to detonation transition. More dataare needed to enable verification of the model in high density geometries. This isparticularly needed for onshore process plant geometries.

Acknowledgments

The work on gas explosions at SiT-Tel-Tek is financially supported by Shell Research Ltd. The authorsare grateful to Dr. R. A. Mancini, Amoco Corporation, for making this paper possible.

REFERENCES

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Bakke, J. R., and B. H. Hjertager. 1986b. The effect of explosion venting in obstructedchannels. In Modeling and Simulation in Engineering. New York: Elsevier, pp. 237-241.

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 transportmethod that works. J. Comp. Phys. 11:38.

CCPS/AIChE. 1991. International conference and workshop on modeling and mitigating theconsequences of accidental releases of hazardous material. New York: CCPS/AIChE.

Harris, R. J., and M. J. Wickens. 1989. Understanding vapor cloud explosions—An experi-mental 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 gasexplosions. 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 explosionpropagation in offshore modules.

Hjertager, B. H., T. Solberg, and J. E. F0rrisdahl. 199 Ib. Computer simulation of the 'PiperAlpha' gas explosion accident."

Kjaldman, L., and R. Huhtanen. 1986. Numerical simulation of vapour cloud and dustexplosions. Numerical Simulation of Fluid Flow and Heat/Mass Transfer Processes.Vol. 18, Lecture Notes in Engineering, 148-158.

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Magnussen, B. F., and B. H. Hjertager. 1976. On the mathematical modeling of turbulentcombustion with special emphasis on soot formation and combustion. 16th Symp. (Int)on Combustion. Combustion Institute, PA, pp. 719-729.

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Index

Index terms Links

A Acetone, explosion properties of 48

Acetylene detonation cell size 55 explosion properties of 48 properties of 359

Acoustic methods, vapor cloud explosion computations 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 56

384 Index terms Links


Blast (Continued) structural damage of 347

Blast case study (process plant) 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 6 157 historical experience 27 mechanism of 158

Boiling-liquid-expanding-vapor explosion (BLEVE) experimental research 161

blast effects and pressure-vessel bursts 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



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 16

Boiling-liquid-expanding-vapor explosion (BLEVE) sample problems 285 blast parameter calculations and pressure vessel bursts 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 160



N-Butane (Continued) detonation cell size 55 properties of 359

C Carbon dioxide, properties of 359

Carbon monoxide, properties of 359

Channels, vapor cloud explosion research 84

Chapman-Jouguet (CJ) model, detonation 52 53

Chlorine, properties of 359

Combustion models 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 50 described 4 ignition and 55

Deflagration to detonation transition (DDT), vapor cloud explosion research 88

Detonation combustion models 52



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 96

Drag force, blast loading 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 160 explosion properties of 48 properties of 359

Ethanol, explosion properties of 48

Ethyl chloride, properties of 359

Ethylene detonation cell size 55 explosion properties of 48 properties of 359

Ethylene oxide, detonation cell size 55

Eulerian flux-corrected transport (FCT) approach, vapor cloud explosions 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 134



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 5 147 historical experience 23

Flash fire research 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 122

Fuel-air clouds, after dispersion 75



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 10

Hopkins scaling law, blast scaling 59

Hydrogen explosion properties of 48 properties of 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



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 359

Multienergy method, vapor cloud explosions 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 290 291 thermal radiation 60

Pressure-vessel bursts, BLEVE experimental research 185

Propane chemical and physical characteristics 160



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 178 291 thermal radiation 61

Source-term generated turbulence, vapor cloud explosion experimental research 76

Structural damage, of blasts 347

Subsequent pressure generation (CFD-codes), vapor cloud explosions 69



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 201 vapor cloud explosions 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 4

Two-dimensional models, vapor cloud explosions 108

V Vapor(s), explosion properties of 48

Vapor cloud explosion(s) atmospheric vapor cloud dispersion 47 described and defined 3 69 historical experience 10 ignition 55 overview of 69

Vapor cloud explosion experimental research 69 70 blast modeling 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



Vapor cloud explosion experimental research (Continued) numerical methods 104 overview of 92

detonation 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) 337 thermal radiation, solid-flame model 64 vertical cylinder 338 341 vertical plane surface 340 342

343



Vinyl chloride, chemical and physical characteristics 160

Volume-source solution, vapor cloud explosions 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 53

54

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