Guidelines for consequence analysis of chemical releases, Volume 1

GUIDELINES F O R C

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AMERICAN INSTITUTE OF CHEMICAL ENGINEERS CEfSfTER FOR CHEMICAL PROCESS SAFETY CENTER FOR CHEMICAL PROCESS SAFETY of the AMERICAN INSTITUTE OF CHEMICAL ENGINEERS 3 Park Avenue, New York, New York 10016-5991

Copyright © 1999 American Institute of Chemical Engineers 3 Park Avenue New York, New York 10016-5991 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior permission of the copyright owner. Library of Congress Cataloging-in Publication Data Guidelines for consequence analysis of chemical releases. p. cm. Includes bibliography and index. ISBN 0-8169-0786-2 1. Chemical plants—Accidents-Evaluation 2. Bisk assessment. TP155.G872 1999 99-10049 660 / .280^-dc21 CIP

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

P r e f a c e

The original CCPS book Guidelines for Quantitative Risk Analysis (1989) (CPQRA Guidelines) contained a long chapter on consequence analysis. When CCPS decided to update the CPQRA Guidelines in 1995, preparing a second edition for publication, there were major revisions and additions to the material on consequence analysis. These revisions included more detail on many of the consequence models, additional and updated models which reflect the current state of the art, a more complete presentation of the fundamentals of many of the models, and more worked examples. Spreadsheet solutions for all of the worked examples have also been provided. Because the revised Chapter 2, Consequence Analysis, of the CPQRA Guidelines, 2nd Edition represents an important topic in process safety, CCPS decided to publish the material as a separate book. This will make the material on consequence analysis more readily and economically available to a broader audience, which uses incident consequence analysis evaluation tools, but does not use quantitative risk analyses. This book includes all of the material in Chapter 2, Consequence Analysis, of the CPQRA Guidelines, 2nd Edition^ re-formatted as a stand alone book. All worked examples and spreadsheet problem solutions are included. All of this material will also be published in the CPQRA Guidelines, 2nd Edition.

Modeling and understanding the consequences of chemical process incidents (unplanned releases of material and/or energy) are important components of a process safety management program. This activity can be generally classified as incident consequence analysis, and it includes models for: • quantity and rate of material release—for example, flow through a hole in a pipe, evaporation from a pool • atmospheric dispersion of released materials

• thermal radiation models for fires of various types—for example, pool fires, jet fires, flash fires • overpressure and other models for different kinds of explosions—for exampie, physical explosions, vapor cloud explosions • impact models which estimate the effect of toxic materials, fires, and explosions on people, the environment, and property Consequence analysis is an important part of many corporate process risk management programs. It is also required for specified materials by many process safety regulations promulgated by national and local regulatory bodies. For example, the United States Environmental Protection Agency requires a consequence analysis of specified material incident release scenarios for materials covered by the Bisk Management Plan (RMP) regulations required by the Clean Air Act of 1990. Consequence analysis is also an important tool for Chemical Process Quantitative Risk Analysis (CPQRA). CPQRA requires identification of potential incidents (what can go wrong?), estimation of consequences of those incidents (what is the impact if it goes wrong?), estimation of the frequency of the incidents (how likely is it to happen?), and combination of this information into a quantitative measure of risk. If you are involved in process safety management activities which require modeling of the estimated consequences of chemical process incidents, you will find an introduction to the appropriate models in this book. You will also find references to more detailed information and models published in other books by CCPS and others. This book focuses on the immediate impact of unplanned releases of material and energy—fires, explosions, toxic material releases. It does not cover long term consequences of a single exposure from an incident, or the consequences of extended, lower level exposure to continuing discharges of material to the environment. If your process safety management program requires (or evolves to require) quantitative risk analysis of the risks associated with these types of incidents, the additional material you will need to understand quantitative risk analysis can be found in the Guidelinesfor Chemical Process Quantitative Risk Analysis, 2nd Edition.

A c k n o w l e d g m e n t s

The Guidelines for Consequence Analysis of Chemical Releases is a stand alone publi-

cation of material contained in Chapter 2, Consequence Analysis, of the CCPS Guidelines for Chemical Process Quantitative Risk Analysis, 2nd Edition. This material has been updated from the 1989 edition of the Guidelinesfor Chemical Process

Quantitative Risk Analysis (CPQRA Guidelines) under the guidance of the Center for Chemical Process Safety (CCPS) Risk Assessment Subcommittee (RASC). Most of the material from the CPQRA Guidelines^ which was written by the 1989 BASC members, Technica, Inc. (now Det Norske Veritas [DNV]), and several other contributors, remains in this edition. The contributions of the original edition authors are listed in the "1989 CPQRA Guidelines Acknowledgments." The material in this book was updated and revised from the original Chapter 2 of the 1989 edition of the CPQRA Guidelines by Dr. Daniel A. Crowl of Michigan Technological University. Dr. Crowl also provided a significant amount of new and updated material, a number of new worked example problems, and spreadsheet solutions for all of the worked examples. The RASC was chaired by Dennis C. Hendershot (Rohm and Haas Company), and the RASC members include Brian R. Dunbobbin and Walter Silowka (Air Products and Chemicals, Inc.), Arthur G. Mundt (Dow Chemical), William Tilton (DuPont), Scott Ostrowski (Exxon Chemicals), Donald L. Winter (Mobil), Raymond A. Freeman (Monsanto), Arthur Woltman (Shell), Thomas Janicik (Solvay Polymers), Richard M. Gustafson (Texaco), William K. Lutz (Union Carbide), Felix Freiheiter and Thomas Gibson(Center for Chemical Process Safety). The RASC also thanks the CCPS management and staff for their support of this project, including Mr. Bob Perry, Dr. Jack Weaver, and Mr. Les Wittenberg. The BASC also thanks the following for their peer review:

Chuck Fryman

FMC Corporation

William Geckler

PLG (EQE International)

Doan Hanson

United States Department of Energy, Brookhaven National Laboratory

Robert Linney

Air Products and Chemicals, Inc.

Ken Murphy

United States Department of Energy

Jerry Schroy

Solutia, Inc.

Walt Silowka

Air Products and Chemicals, Inc.

The RASC dedicates this book to two of our friends and colleagues, Mr. Donald L. Winter of Mobil Oil Corporation, and Mr. Felix Freiheiter of the Center for Chemical Process Staff. Both were significant contributors to this book, to the CPQRA Guidelines, 2nd Edition, and to other activities of the CCPS Risk Assessment Subcommittee for many years. Mr. Winter unfortunately passed away due to a sudden illness during the later stages of the writing of the book. Mr. Freiheiter also passed away as the book was being prepared for publication. Their influence can be found throughout the book.

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This volume was written jointly by the CCPS Bisk Assessment Subcommittee and Technica, Inc. The CCPS Subcommittee was chaired by R. W. Ormsby (Air Products and Chemicals), and included (in alphabetical order); R. E. DeHart, II (Union Carbide), H. H. Feng (ICI Americas, formerly of Stauffer Chemical), R. A. Freeman (Monsanto), S. B. Gibson (du Pont), D. C. Hendershot (Rohm and Haas), C. A. Master (Fluor Daniel), R. F. Schwab (Allied-Signal), and J. C. Sweeney (ARCO Chemical). T. W. Carmody, F. Freiheiter, R. G. Hill, and L. H. Wittenberg of CCPS provided staff support. The Technica team included B. Morgan, A. Shafaghi, L. G. Bacon, M. A. Seaman, L. J. Bellamy, S. R. Harris, P. Baybutt, D. M. Boult, and N. C. Harris. F. P Lees (University of Loughborough) reviewed and early draft of the document and his comments are gratefully acknowledged. The substantial contributions of the employer organizations (both in time and resources) of the Subcommittee and of Technica are gratefully acknowledged. An acknowledgment is also made to JBF Associates, Inc. (J. S. Arendt, D. F. Montague, H. M. Paula, L. E. Palko) for their preparation of the subsection on common cause failure analysis (Section 3.3.1) and inclusion of additional material in the section on fault tree analysis (Section 3.2.1), and the Meridian Corporation (C. O. Schultz and W. S. Perry) for the preparation of the section on toxic gas effects (Section 2.3.1). Two specific individuals should also be acknowledged for significant contributions:C. W. Thurston of Union Carbide for assistance in the preparation of the subsection on programmable electronic systems (Section 6.3) and G. K. Lee of Air Products and Chemicals who assisted in the preparation of the subsections

addressing discharge rates, flash and evaporation, and dispersion (Sections 2.1.1., 2.1.2, and 2.1.3). Finally, the CCPS Risk Assessment Subcommittee wishes to express its sincere gratitude to Dr. Elisabeth M. Drake for reviewing the final manuscript and her many helpful comments and suggestions.

A c r o n y m s

AAR ACGIH ACMH AEC AGA

American Association of Railroads American Conference of Governmental Industrial Hygienists Advisory Commission on Major Hazards Atomic Energy Commission American Gas Association American Institute of Chemical Engineers—Center for AICHE/CCPS Chemical Process Safety American Institute of Chemical Engineers—Design Institute AICHE-DIERS for Emergency Relief Systems American Institute of Chemical Engineers—Design AICHE—DIPPR Institute for Physical Property Data American Industrial Hygiene Association AIHA Auto-Ignition Temperature ATT American Petroleum Institute API Accelerating Rate Calorimeter ARC American Society of Mechanical Engineers ASME Acute Toxic Concentration ATC Boiling Liquid Expanding Vapor Explosion BLEVE Community Awareness and Emergency Responses CAER Center for Chemical Process Safety CCPS Chemical Engineering Progress CEP Computational Fluid Dynamics CFD Chemical Manufacturers Association CMA Chemical Process Industry CPI Computer Processing Unit CPU Chemical Process Quantitative Risk Analysis CPQRA Chemical Rubber Company CRC

CSTR DOE DOT DSC EEC EEGL EFCE EPA EPRI ERPG ERV ESD ESV FAR FDT FEMA FMEA FTA FR HAZOP HEP HFA HMSO HRA HSE IChemE ICI IDLH IEEE IHI INPO ISBN LC LCL LD LFL LNG LOC LPG MAWP

Continuous Stirred Tank Reactor Department of Energy Department of Transportation Differential Scanning Calorimeter European Economic Community Emergency Exposure Guidance Level European Federation of Chemical Engineers Environmental Protection Agency Electric Power Research Institute Emergency Response Planning Guidelines Emergency Response Value Emergency Shutdown Device Emergency Shutdown Valve Fatal Accident Rate Fractional Dead Time Federal Emergency Management Agency Failure Modes and Effects Analysis Fault Tree Analysis Failure Rate Hazard and Operability Hazard Evaluation Procedures Human Failure Analysis Her Majesty's Stationery Office Human Reliability Analysis Health and Safety Executive Institution of Chemical Engineers (Great Britain) Imperial Chemical Industries Immediately Dangerous to Life and Health Institute of Electrical and Electronic Engineers Individual Hazard Index Institute of Nuclear Power Operations International Standard Book Number Lethal Concentration Lower Confidence Limit Lethal Dose Lower Flammable Limit Liquified Natural Gas Level of Concern Liquefied Petroleum Gas Maximum Allowable Working Pressure

MIL-HDBK MORT MSDS MTBF NAS NASA NFPA NIOSH NJ-DEP NOAA NRC NSC NTIS NTSB NUREG OREDA ORC OSHA PE PEL PERD PES PFD PHA P&ID PV PLC PLG PRA PSM R&D RLG RMP ROD ROF RSST RTECS SHTM SPEGL

Department of Defense Military Handbook Management Oversight and Bisk Tree Analysis Material Safety Data Sheets Mean Time Between Failure National Academy of Science National Aeronautical and Space Administration National Fire Protection Association National Institute for Occupational Safety and Health New Jersey Department of Environmental Protection National Oceanic and Atmospheric Administration National Research Council National Safety Council National Technical Information Service National Transportation Safety Board Nuclear Regulatory Commission Offshore Reliability Data Handbook Organization Resources Counselors, Inc. (Washington, D.C.) Occupational Safety and Health Administration Process Engineer Permissible Exposure Limits Process Equipment Reliability Data Programmable Electronic System Process Flow Diagram Preliminary Hazard Analysis Piping and Instrumentation Diagram Pressure Volume Programmable Logic Controller Pressurized Liquified Gas Probabilistic Risk Assessment Process Safety Management Research and Development Refrigerated Liquified Gas Risk Management Plan (EPA) Average Rate of Death Average Rate of Failure Reactive Systems Screening Tool Registry of Toxic Effects of Chemical Substances Storage and Handling of Highly Toxic Hazard Materials Short-Term Public Emergency Guidance Levels

SRD STEL TCPA TNT TLV TNO TXDS UCL UFL UCSIP UNIDO UVCE VCDM VCE VDI VRM VSP

Safety and Reliability Directorate (U.K. Atomic Energy Authority, Warrington, England) Short-Term Exposure Limits Toxic Catastrophe Prevention Act Trinitrotoluene Threshold Limit Values Netherlands Organization for Applied Scientific Research Toxicity Dispersion Upper Confidence Limit Upper Flammable Limit Union des Chambres Syndicates de L'Industrie de Petrole United Nations Industrial Development Organization Unconfined Vapor Vloud Explosion Vapor Cloud Dispersion Modeling Vapor Cloud Explosion Verein Deutscher Inginieure Vapor Release Mitigation Vent Sizing Package

Contents

Preface ....................................................................................

ix

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

xi

1989 CPQRA Guidelines Acknowledgments ...........................

xiii

Acronyms ................................................................................

xv

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

1

1.1 CPQRA Definitions ..................................................................

6

1.2 Consequence Analysis ...........................................................

8

2. Source Models .................................................................

15

2.1 Discharge Rate Models ...........................................................

15

2.1.1

Background ...........................................................

15

2.1.2

Description ............................................................

18

2.1.3

Example Problems ................................................

40

2.1.4

Discussion .............................................................

54

2.2 Flash and Evaporation ............................................................

57

2.2.1

Background ...........................................................

57

2.2.2

Description ............................................................

59

2.2.3

Example Problems ................................................

69

2.2.4

Discussion .............................................................

75

2.3 Dispersion Models ...................................................................

76

2.3.1

Neutral and Positively Buoyant Plume and Puff Models ...........................................................

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85

v

vi

Contents 2.3.2

Dense Gas Dispersion ........................................... 111

3. Explosions and Fires ....................................................... 127 3.1 Vapor Cloud Explosions (VCE) ............................................... 131 3.1.1

Background ........................................................... 131

3.1.2

Description ............................................................ 134

3.1.3

Discussion ............................................................. 151

3.1.4

Example Problems ................................................ 152

3.2 Flash Fires ............................................................................... 158 3.3 Physical Explosion .................................................................. 158 3.3.1

Background ........................................................... 158

3.3.2

Description ............................................................ 160

3.3.3

Example Problems ................................................ 174

3.3.4

Discussion ............................................................. 184

3.4 BLEVE and Fireball ................................................................. 185 3.4.1

Background ........................................................... 185

3.4.2

Description ............................................................ 186

3.4.3

Example Problems ................................................ 194

3.4.4

Discussion ............................................................. 199

3.5 Confined Explosions ............................................................... 201 3.5.1

Background ........................................................... 201

3.5.2

Description ............................................................ 202

3.5.3

Example Problem .................................................. 207

3.5.4

Discussion ............................................................. 208

3.6 Pool Fires ................................................................................ 210 3.6.1

Background ........................................................... 210

3.6.2

Description ............................................................ 211

3.6.3

Example Problem .................................................. 220

3.6.4

Discussion ............................................................. 223

3.7 Jet Fires ................................................................................... 225 3.7.1

Background ........................................................... 225

3.7.2

Description ............................................................ 226

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Contents

vii

3.7.3

Example Problem .................................................. 229

3.7.4

Discussion ............................................................. 231

4. Effect Models .................................................................... 235 4.1 Dose-response and Probit Functions ..................................... 236 4.1.1

Dose-response Functions ...................................... 236

4.1.2

Probit Functions .................................................... 238

4.1.3

Example Problem .................................................. 240

4.2 Toxic Gas Effects .................................................................... 241 4.2.1

Background ........................................................... 241

4.2.2

Description ............................................................ 253

4.2.3

Example Problems ................................................ 257

4.2.4

Discussion ............................................................. 261

4.3 Thermal Effects ....................................................................... 262 4.3.1

Background ........................................................... 262

4.3.2

Description ............................................................ 263

4.3.3

Example Problems ................................................ 267

4.2.4

Discussion ............................................................. 269

4.4 Explosion Effects ..................................................................... 270 4.4.1

Background ........................................................... 270

4.4.2

Description ............................................................ 271

4.4.3

Example Problem .................................................. 273

4.4.4

Discussion ............................................................. 273

5. Evasive Actions ............................................................... 275 5.1 Background ............................................................................. 275 5.2 Description .............................................................................. 278 5.3 Example Problem .................................................................... 280 5.4 Discussion ............................................................................... 280

6. Modeling Systems ............................................................ 283 References ............................................................................. 285 This page has been reformatted by Knovel to provide easier navigation.

viii

Contents

Appendix: CD ROM ............................................................... 301 Glossary ................................................................................. 305 Index ....................................................................................... 319

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1

I n t r o d u c t i o n

Consequence analysis plays an important part in Chemical Process Quantitative Bisk Analysis (CPQRA). CPQRA is a methodology designed to provide management with a tool to help evaluate overall process safety in the chemical process industry (CPI). Management systems such as engineering codes, checklists and process safety management (PSM) provide layers of protection against accidents. However, the potential for serious incidents cannot be totally eliminated. CPQBA provides a quantitative method to evaluate risk and to identify areas for cost-effective risk reduction. A complete and detailed discussion of the entire CPQBA procedure is provided by AICHE/CCPS (1999). The CPQBA methodology has evolved since the early 1980s from its roots in the nuclear, aerospace and electronics industries. The most extensive use of probabilistic risk analysis (PBA) has been in the nuclear industry. Procedures for PBA have been defined in the PBA Procedures Guide (NUREG, 1983) and the Probabilistic Safety Analysis Procedures Guide (NUREG, 1985). CPQRA is a probabilistic methodology that is based on the NUBJEG procedures. The term "chemical process quantitative risk analysis" (CPQRA) is used throughout this book to emphasize the features of this methodology as practiced in the chemical, petrochemical, and oil processing industries. Some examples of these features are • Chemical reactions may be involved • Processes are generally not standardized • Many different chemicals are used • Material properties may be subject to greater uncertainty • Parameters, such as plant type, plant age, location of surrounding population, degree of automation and equipment type, vary widely

• Multiple impacts, such as fire, explosion, toxicity, and environmental contamination, are common. Consequence analysis is also useful for many other purposes than CPQRA. For example, consequence analysis is used for the following purposes: • Determining the acceptability of a site, or an optimum location on plant property. • Determining equipment design parameters, i.e. stack height, water deluge requirements, etc. • Comparative analysis, such as in equipment design option selection. • Identification of potential impacts on adjacent facilities, communities and populations. • Assistance in emergency response, such as evacuation vs. take cover decision making. • Compliance with regulations, particularly the EPA Bisk Management Plan (RMP). Acute, rather than chronic, hazards are the principal concern of CPQRA. This places the emphasis on rare but potentially catastrophic events. Chronic effects such as cancer or other latent health problems are not normally considered in CPQRA. Many hazards may be identified and controlled or eliminated through use of qualitative hazard analysis as defined in Guidelines for Hazard Evaluation Procedures, Second Edition (AICHE/CCPS, 1992). Qualitative studies typically identify potentially hazardous events and their causes. In some cases, where the risks are clearly excessive and the existing safeguards are inadequate, corrective actions can be adequately identified with qualitative methods. CPQRA is used to help evaluate potential risks when qualitative methods cannot provide adequate understanding of the risks and more information is needed for risk management. It can also be used to evaluate alternative risk reduction strategies. The basis of CPQRA is to identify incident scenarios and evaluate the risk by defining the probability of failure, the probability of various consequences and the potential impact of those consequences. The risk is defined in CPQEA as a function of probability or frequency and consequence of a particular accident scenario:

s = hypothetical scenario c = estimated consequence(s) / = estimated frequency

This "function" can be extremely complex and there can be many numerically different risk measures (using different risk functions) calculated from a given set of sy c J. The major steps in CPQRA5 as illustrated in Figure 1.1, are Risk Analysis: 1. Define the potential event sequences and potential incidents. This may be based on qualitative hazard analysis for simple or screening level analysis. Complete or complex analysis is normally based on a full range of possible incidents for all sources. 2. Evaluate the incident outcomes (consequences). Incident outcomes might include the total quantity of material released, a downwind vapor concentration, radiant heat flux, or an explosion overpressure. Source models (Chapter 2) and fire and explosion models (Chapter 3) are the major methods used to determine these outcomes. 3. Estimate the incident impacts on people, environment and property. The effect models take the incident outcomes of step 2 and determine the direct impacts—number of individuals affected, property damage, etc. Effect models are discussed in Chapter 4. 4. Estimate the potential incident frequencies. Fault trees or generic databases may be used for the initial event sequences. Event trees may be used to account for mitigation and postrelease events. 5. Estimate the risk. This is done by combining the potential consequence for each event with the event frequency, and summing over all events. Risk Assessment: 6. Evaluate the risk. Identify the major sources of risk and determine if there are cost-effective process or plant modifications which can be implemented to reduce risk. Often this can be done without extensive analysis. Small and inexpensive system changes sometimes have a major impact on risk. The evaluation may be done against legally required risk criteria, internal corporate guidelines, comparison with other processes or more subjective criteria. 7. If the risk is considered to be excessive, identify and prioritize potential risk reduction measures. Risk Management: Chemical process quantitative risk analysis is part of a larger management scheme. Risk management methods are described in the CCPS Guidelines for Implementing Process Safety Management Systems (AIChE/CCPS, 1994a), Guidelines for Technical Management of Chemical Process Safety (AIChE/CCPS, 1989c),

Define the potential accident scenarios

Evaluate the event consequences

Consequence Analysis

Estimate the potential accident frequencies

Estimate the event impacts

Estimate the risk

Evaluate the risk

Identify and prioritize potential risk reduction measures FIGURE 1.1. Chemical process quantitative risk analysis (CPQRA) flowchart. The dashed line indicates the steps identified as consequence analysis.

and Plant Guidelines for Technical Management

of Chemical Process Safety

(AIChE/CCPS, 1995d). The seven steps in Figure 1.1 are typical of CPQRA. However, it is important to remember that other risks, such as stakeholder concerns, financial loss, chronic health risks and bad publicity, may also be significant. These potential risks can also be estimated qualitatively or quantitatively and are an important part of the management process. CPQRA provides a tool for the engineer or manager to quantify risk and analyze potential risk reduction strategies. The value of quantification was well described by Lord Kelvin.

I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thought, advanced to the stage of science, whatever the matter may be. Joschek (1983) provided a similar definition: a quantitative approach to safety . . . is not foreign to the chemical industry. For every process, the kinetics of the chemical reaction, the heat and mass transfers, the corrosion rates, the fluid dynamics, the structural strength of vessels, pipes and other equipment as well as other similar items are determined quantitatively by experiment or calculation, drawing on a vast body of experience.

CPQRA enables the engineer to evaluate risk. Individual contributions to the overall risk from a process can be identified and prioritized. A range of risk reduction measures can be applied to the major hazard contributors and assessed using cost-benefit methods. Comparison of risk reduction strategies is a relative application of CPQRA. Pikaar (1995) has related relative or comparative CPQBA to climbing a mountain. At each stage of increasing safety (decreasing risk), the associated changes may be evaluated to see if they are worthwhile and cost-effective. Some organizations also use CPQRA in an absolute sense to confirm that specific risk targets are achieved. Further risk reduction, beyond such targets, may still be appropriate where it can be accomplished in a cost-effective manner. Hendershot (1996) has discussed the role of absolute risk guidelines as a risk management tool. Application of the full array of CPQEA techniques allows a quantitative review of a facility's risks, ranging from frequent, low-consequence incidents to rare, major events, using a uniform and consistent methodology. Having identified process risks, CPQBA techniques can help focus risk control studies. The largest risk contributors can be identified, and recommendations and decisions can be made for remedial measures on a consistent and objective basis. Utilization of the CPQBA results is much more controversial than the methodology. Watson (1994) has suggested that CPQBA should be considered as an argument, rather than a declaration of truth. In his view, it is not practical or necessary to provide absolute scientific rigor in the models or the analysis. Rather, the focus should be on the overall balance of the QBA and whether it reflects a useful measure of the risk. However, Yellman and Murray (1995) contend that the analysis "should be, insofar as possible, true—or at least a search for truth." It is important for the analyst to understand clearly how the results will be used in order to choose appropriately rigorous models and techniques for the study.

1.1 C P Q R A D e f i n i t i o n s

Table 1.1 and the Glossary define the terms used in this volume. Other tabulations of terms have been compiled (e.g., IChemE, 1985) and may need to be consulted because, as discussed below, there currently is no single, authoritative source of accepted nomenclature and definitions. CPQRA is an emerging technology in the CPI and there are terminology variations in the published literature that can lead to confusion. For example, while risk is defined in Table 1.1 as: "a measure of human injury, environmental damage or economic loss in terms of both the incident likelihood and the magnitude of the loss or injury,55 readers should be aware that other definitions are often used. For instance, Kaplan and Garrick (1981) have discussed a number of alternative definitions of risk. These include: • Risk is a combination of uncertainty and damage. • Risk is a ratio of hazards to safeguards. • Risk is a triplet combination of event, probability, and consequences. Readers should also recognize the interrelationship that exists between an incident, an incident outcome, and an incident outcome case as these terms are used throughout this book. An incident is defined in Table 1.1 as "the loss of containment of material or energy," while an incident outcome is "the physical manifestation of an incident." A single incident may have several outcomes. For example, a leak of flammable and toxic gas could result in • • • •

a jet fire (immediate ignition) a vapor cloud explosion (delayed ignition) a vapor cloud fire (delayed ignition) a toxic cloud (no ignition).

A list of possible incident outcomes has been included in Table 1.2. The third and often confusing term used in describing incidents is the incident outcome case. As indicated by its definition in Table 1.1, the incident outcome case specifies values for all of the parameters needed to uniquely distinguish one incident outcome from all others. For example, since certain incident outcomes are dependent on weather conditions (wind direction, speed, and atmospheric stability class), more than one incident outcome case could be developed to describe the dispersion of a dense gas.

TABLE 1.1. Selected Definitions for CPQRA Frequency: Number of occurrences of an event per unit of time. Hazard: A chemical or physical condition that has the potential for causing damage to people, property, or the environment (e.g., a pressurized tank containing 500 tons of ammonia) Incident: The loss of containment of material or energy (e.g., a leak of 10 lb/s of ammonia from a connecting pipeline to the ammonia tank, producing a toxic vapor cloud) ; not all events propagate into incidents. Event sequence: A specific unplanned sequence of events composed of initiating events and intermediate events that may lead to an incident. Initiating event: The first event in an event sequence (e.g., stress corrosion resulting in leak/rupture of the connecting pipeline to the ammonia tank) Intermediate event: An event that propagates or mitigates the initiating event during an event sequence (e.g., improper operator action fails to stop the initial ammonia leak and causes propagation of the intermediate event to an incident; in this case the intermediate event could be a continuous release of the ammonia) Incident outcome: The physical manifestation of the incident; for toxic materials, the incident outcome is a toxic release, while for flammable materials, the incident outcome could be a Boiling Liquid Expanding Vapor Explosion (BLEVE), flash fire, unconfined vapor cloud explosion, toxic release, etc. (e.g., for a 10 lb/s leak of ammonia, the incident outcome is a toxic release) Incident outcome case: The quantitative definition of a single result of an incident outcome through specification of sufficient parameters to allow distinction of this case from all others for the same incident outcomes. For example,a release of 10 lb/s of ammonia with D atmospheric stability class and 1.4 mph wind speed gives a particular downwind concentration profile, resulting, for example, in a 3000 ppm concentration at a distance of 2000 feet. Consequence: A measure of the expected effects of an incident outcome case (e.g., an ammonia cloud from a 10 lb/s leak under Stability Class D weather conditions, and a 1.4-mph wind traveling in a northerly direction will injure 50 people) Effect zone: For an incident that produces an incident outcome of toxic release, the area over which the airborne concentration equals or exceeds some level of concern. The area of the effect zone will be different for each incident outcome case [e.g., given an IDLH for ammonia of 500 ppm (v), an effect zone of 4.6 square miles is estimated for a 10 lb/s ammonia leak]. For a flammable vapor release, the area over which a particular incident outcome case produces an effect based on a specified overpressure criterion (e.g., an effect zone from an unconfined vapor cloud explosion of 28,000 kg of hexane assuming 1% yield is 0.18 km2 if an overpressure criterion of 3 psig is established). For a loss of containment incident producing thermal radiation effects, the area over which a particular incident outcome case produces an effect based on a specified thermal damage criterion [e.g., a circular effect zone surrounding a pool fire resulting from a flammable liquid spill, whose boundary is defined by the radial distance at which the radiative heat flux from the pool fire has decreased to 5 kW/m2 (approximately 1600 Btu/hr-ft2)] Likelihood: A measure of the expected probability or frequency of occurrence of an event. This may be expressed as a frequency (e.g., events/year), a probability of occurrence during some time interval, or a conditional probability (i.e., probability of occurrence given that a precursor event has occurred, e.g., the frequency of a stress corrosion hole in a pipeline of size sufficient to cause a 10 lb/s ammonia leak might be 1 X 10"3 per year; the probability that ammonia will be flowing in the pipeline over a period of 1 year might be estimated to be 0.1; and the conditional probability that the wind blows toward a populated area following the ammonia release might be 0.1) (continued on next page)

TABLE \.l. Selected Definitions for CPQRA (cont.) Probability: The expression for the likelihood of occurrence of an event or an event sequence during an interval of time or the likelihood of occurrence of the success or failure of an event on test or demand. By definition, probability must be expressed as a number ranging from 0 to 1. Risk: A measure of human injury, environmental damage or economic loss in terms of both the incident likelihood and the magnitude of the loss or injury Risk analysis: The development of a quantitative estimate of risk based on engineering evaluation and mathematical techniques for combining estimates of incident consequences and frequencies (e.g., an ammonia cloud from a 10 lb/s leak might extend 2000 ft downwind and injure 50 people. For this example, using the data presented above for likelihood, the frequency of injuring 50 people is given as 1 X 1 0'3 X 0 .1 X 0.1 = 1 X 10"5 events per year) Risk assessment: The process by which the results of a risk analysis are used to make decisions, either through a relative ranking of risk reduction strategies or through comparison with risk targets (e.g., the risk of injuring 50 people at a frequency of 1 X 10~5 events per year from the ammonia incident is judged higher than acceptable, and remedial design measures are required)

The event tree in Figure 1.2 has been provided to illustrate the relationship between an incident, incident outcomes, and incident outcome cases.

1 . 2 . C o n s e q u e n c e Analysis

This book provides an overview of consequence and effect models commonly used in CPQRA (as shown in Figure 1.3). Accidents begin with an incident, which usually results in the loss of containment of material from the process. The material has hazardous properties, which might include toxic properties and energy content. Typical incidents might include the rupture or break of a pipeline, a hole in a tank or pipe, runaway reaction, fire external to the vessel, etc. Once the incident is known, source models are selected to describe how materials are discharged from the process. The source model provides a description of the rate of discharge, the total quantity discharged (or total time of discharge), and the state of the discharge—solid, liquid, vapor, or a combination. A dispersion model is subsequently used to describe how the material is transported downwind and dispersed to some concentration levels. For flammable releases, fire and explosion models convert the source model information on the release into energy hazard potentials such as thermal radiation and explosion overpressures. Effect models convert these incident-specific results into effects on people (injury or death) and structures. Environmental impacts could also be considered (Paustenbach, 1989), but are not considered here. Additional refinement is provided by mitigation factors, such as water sprays, foam systems, and sheltering or

TABLE 1.2. CPQRA Hazards, Event Sequences, Incident Outcomes, and Consequences Event Sequences Process hazards

Initiating events

Intermediate events

Incident outcomes

Significant inventories of: Flammable materials Combustible materials Unstable materials Corrosive materials Asphyxiants Shock sensitive materials Highly reactive materials Toxic materials Inerting gases Combustible dusts Pyrophoric materials Extreme physical conditions High temperatures Cryogenic temperatures High pressures Vacuum Pressure cycling Temperature cycling Vibration/liquid hammering

Process upsets Process deviations Pressure Temperature Flow rate Concentration Phase/state change Impurities Reaction rate/heat of reaction Spontaneous reaction Polymerization Runaway reaction Internal explosion Decomposition Containment failures Pipes, tanks, vessels, gaskets/seals Equipment malfunctions Pumps, valves, instruments, sensors, interlock failures Loss of utilities Electrical, nitrogen, water, refrigeration, air heat transfer, fluids, steam, ventilation Management systems failure Human error Design Construction Operations Maintenance Testing and inspection External events Extreme weather conditions Earthquakes Nearby accidents' impacts Vandalism/sabotage

Risk reduction factors Propagating factors Control/operator responses Equipment failure Alarms safety system failure Control system response Ignition sources Manual and automatic ESD Furnaces, flares, Fire/gas detection system incinerators Safety system responses Vehicles Relief valves Electrical switches Depressurization systems Static electricity Isolation systems Hot surfaces High reliability trips Cigarettes Back-up systems Management systems failure Mitigation system responses Human errors Dikes and drainage Omission Flares Commission Fire protection systems Fault diagnosis (active and passive) Decision-making Explosion vents Domino effects Toxic gas absorption Other containment failures Emergency plan responses Other material release Sirens/warnings External conditions Emergency procedures Meteorology Personnel safety equipment Visibility Sheltering Escape and evacuation External events Early detection Early warning Specially designed structures Training Other management systems

Analysis Discharge Flash and evaporation Dispersion Neutral or positively buoyant gas Dense gas Fires Pool fires Jet fires BLEVES Flash fires Explosions Confined explosions Unconfined vapor cloud explosions (UVCE) Physical explosions (PV) Dust explosions Detonations Condensed phase detonations Missiles Consequences Effect analysis Toxic effects Thermal effects Overpressure effects Damage assessments Community Workforce Environment Company assets

INCIDENTS

INCIDENTOUTCOME Toxic Vapor Atmospheric Dispersion

100Ib/min Release of HCN from a Tank Vent

Jet Fire

BLEVE of HCN Tank

INCIDENT OUTCOME CASES S mph Wind, Stability Class A 10 mph Wind, Stability Class D 15 mph Wind, Stability Class E etc.

Tank Full Tank 50% Full etc. After 15 min. Release

Unconfined Vapor Cloud Explosion

After 30 min. Release After 60 min. Release

etc. FIGURE 1.2. The relationship between incident, incident outcome, and incident outcome cases for a hydrogen cyanide (HCN) release.

evacuation, which tend to reduce the magnitude of potential effects in real incidents. Good overviews of consequence models are given in TNO (1979), Lees (1986, 1996), Rijnmond Public Authority (1982), Mecklenburgh (1985), Warren Centre (1986), Marshall (1987), Crowl and Louvar (1990), and Fthenakis (1993). The objective of this book is to review the range of models currently available for consequence analysis. Some material on these models is readily available, either in the general literature or as part of the AICHE/CCPS publication series. Where otherwise available, detailed model descriptions are not provided; instead, the reader is directed to the specific references. Otherwise, a description adequate for initial calculations is provided. This book is primarily designed for use by process engineers to estimate the consequences of specific incidents which might occur in a typical chemical plant. However, anyone with a background in engineering, or an interest in this area will find this book useful. A CD-ROM is provided containing all the worked examples in this book, implemented by spreadsheet. Please consult the section on the CD-ROM for more details.

Selection of a Release Incident * Rupture or Break in Pipeline * Hole in a Tank or Pipeline * Runaway Reaction * Fire External to Vessel * Others Selection of Source Model to Describe Release Incident Results may Include: * Total Quantity Released (or Release Duration) * Release Rate * Material Phase Selection of Dispersion Model (if applicable) * Neutrally Buoyant * Heavier than Air •Others Results may Include: * Downwind Concentration * Area Affected * Duration Flammable Selection of Fire and Explosion Model * TNT Equivalency * Multi-Energy Explosion * Fireball * Baker-Strehlow * Others Results may Include: * Blast Overpressure * Radiant Heat Flux

Flammable ^and/or Toxic?

Toxic

Selection of Effect Model * Response vs. Dose * Probit Model * Others Results may Include: * Toxic Response * No. of Individuals Affected * Property Damage Mitigation Factors: * Escape * Emergency Response * Shelter in Place * Containment Dikes •Other Risk Calculation

FIGURE 1.3. Overall logic diagram for the consequence models for releases of volatile, hazardous substances.

Consequence Analysis to Achieve a Conservative Result. All models, including consequence models, have uncertainties. These uncertainties arise due to (1) an incomplete understanding of the geometry of the release, that is, hole size, (2) unknown or poorly characterized physical properties, (3) a poor understanding of the chemical or release process, and (4) unknown or poorly understood mixture behavior, to name a few. Uncertainties that arise during the consequence modeling procedure are treated by assigning conservative values to some of these unknowns. By doing so, a conservative estimate of the consequence is obtained, defining the limits of the design envelope. This ensures that the resulting engineering design to mitigate or remove the hazard is overdesigned. Every effort, however, should be made to achieve a result consistent with the demands of the problem. For any particular modeling study, several receptors might be present which require different decisions for conservative design. For example, dispersion modeling based on a ground level release will maximize the consequence for the surrounding community, but will not maximize the consequence for plant workers at the top of a process structure. To illustrate conservative modeling, consider a problem requiring an estimate of the gas discharge rate from a hole in a storage tank. This discharge rate will be used to estimate the downwind concentrations of the gas, with the intent on estimating the toxicological impact. The discharge rate is dependent on a number of parameters, including (1) the hole area (2) the pressure within and outside the tank (3) the physical properties of the gas, and (4) the temperature of the gas, to name a few. The reality of the situation is that the maximum discharge rate of gas will occur when the leak first occurs, with the discharge rate decreasing as a function of time as the pressure within the tank decreases. The complete dynamic solution to this problem is difficult, requiring a mass discharge model cross-coupled to a material balance on the contents of the tank. An equation of state (perhaps nonideal) is required to determine the tank pressure given the total mass. Complicated temperature effects are also possible. A modelling effort of this detail is not necessarily required to estimate the consequence. A much simpler procedure is to calculate the mass discharge rate at the instant the leak occurs, assuming a fixed temperature and pressure within the tank equal to the intial temperature and pressure. The actual discharge rate at later times will always be less, and the downwind concentrations will always be less. In this fashion a conservative result is ensured. For the hole area, a possible decision is to consider the area of the largest pipe connected to the tank, since pipe disconnections are a frequent source of tank

leaks. Again, this will maximize the consequence and insure a conservative result. This procedure is continued until all of the model parameters are specified. Unfortunately, this procedure can result in a consequence that is many times larger than the actual, leading to a potential overdesign of the mitigation procedures or safety systems. This occurs, in particular, if several decisions are made during the analysis, with each decision producing a maximum result. For this reason, consequence analysis should be approached with intelligence tempered with a good dose of reality and common sense.

2

S o u r c e

M o d e l s

Source models are used to quantitatively define the release scenario by estimating discharge rates (Section 2.1), total quantity released (or total release duration), extent of flash and evaporation from a liquid pool (Section 2.2), and aerosol formation (Section 2.2). Dispersion models convert the source term outputs to concentration fields downwind from the source (Section 2.3). The relationship between source and dispersion models, and the various model types, is shown schematically in Figure 2.1. As shown in Figure 2.1, source and dispersion models are highly coupled, with the results of the source model being used to select the appropriate dispersion model.

2 . 1 . Discharge Rate Models 2.1.1. BACKGROUND

Purpose. Most acute hazardous incidents start with a discharge of flammable or toxic material from its normal containment. This may be from a crack or fracture of process vessels or pipework, from an open valve, or from an emergency vent. Such leaks may be gas, liquid, or two-phase flashing liquid-gas releases. Different models are appropriate for each of these—unfortunately there is no single model for all applications. Estimates of discharge rate and total quantity release (or duration of the release) are essential as input to other models (as shown in Figure 2.1). The total quantity released may be greater or less than the vessel volume (depending on connecting pipework, isolation valves, etc.). Philosophy. The underlying technology for gas and liquid discharges is well developed in chemical engineering theory and full descriptions are available in standard references such as Perry and Green (1984) and Crane Co. (1986).

Release of Volatile Hazardous Substance. Gas

Release Phase?

Two-Phase

Flashing?

Liquid

T> Boiling Point?

Yes Two-phase Flashing Flow Model

No

No

No Flashing

Yes Flash

Aerosol Formation?

Yes Gas and Aerosol Model

TJquid Rain out?

No

No Aerosol Transport/ Evaporation Model

Pool Formation Model

Pool Evaporation Model

Gas Density? Neutral

Dense

Dense Gas Dispersion Model

Neutral Buoyancy Dispersion Model FIGURE 2. 1. Logic diagram for discharge and dispersion models.

Yes

Reviews of discharge rate models can be found in the Guidelines for Vapor Cloud Dispersion Models (AIChE/CCPS 1987a, 1996a), its companion workbook (AIChE/CCPS, 1989a), Crowl and Louvar (1990), Fthenakis (1993), API (1995), and AIChE/CCPS (1996a). A qualitative description of the method is also presented by AIChE/CCPS (1995a). The treatment of a two-phase flashing discharge is more empirical. Initial investigations for the nuclear industry have been supplemented by the AIChE Design Institute for Emergency Relief Systems (DIERS) as described by Fisher (1985), Fisher et al. (1992), and Boicourt (1995). The design philosophy with the DIERS models is to select the minimal discharge rate at the design pressure of the process unit, and to maximize the relief area via selection of a minimal mass flux model. Many of these models also assume no-slip which tends to result in the lowest mass discharge predictions. Use of these mass flux models to represent source models will result in an under-prediction of the discharge rate and hence, for dispersion problems, a nonconservative result. Table 2.1 shows how the objective of the study determines the conservative design approach and hence the source model selected. If the objective of the study is to protect the vessel via emergency relief system design, then a source model is chosen to minimize the relief system mass flow and thus maximize the relief area. A two-phase flow model would typically be selected as the source model. If, on the other hand, the objective of the study is to design a downstream containment/treatment system, then a source model is selected to maximize the mass flow discharge. A single-phase liquid discharge model might be appropriate here. Finally, if the study objective is to determine the community consequences of the release, then a source model is selected to maximize the mass discharge and maximize the downwind concentrations. TABLE 2.1. Conservative Design Approaches Based on the Objective of the Risk Study Objective of Study

Conservative Design Approach

1. Protect vessel from overpressure

Estimate minimum flow through emergency relief system.

2. Design downstream treatment system.

Estimate maximum flow through emergency relief system to give maximum load on downstream equipment.

3. Estimate external consequences of emergency relief system release.

(a) Estimate maximum discharge from emergency relief system to give maximum source term and downwind concentrations. (b) Consider most likely release.

Applications. Discharge models are the first stage in developing the majority of consequence estimates used in CPQRA, as shown in Figure 1.3. The applications of interest are those relating to two categories of process release: emergency engineered releases (e.g., relief valves) and emergency unplanned releases (e.g., containment failures). Continuous releases (e.g., process vents) and fugitive emissions (e.g., routine storage tank breathing losses) are not typically the focus of CPQRA. 2.1.2. DESCRIPTION

Description of Technique The first step in the procedure is to determine an appropriate scenario. Table 2.2 contains a partial list of typical scenarios grouped according to the material discharge phase, i.e., liquid, gas, or two-phase. Figure 2.2 shows some conceivable discharge scenarios with the resulting effect on the material's release phase. Additional information is available elsewhere (AIChE/CCPS, 1987a, 1995a, 1996a; Lees, 1986,1996; World Bank, 1985). Several important issues must be considered at this point in the analysis. These include: release phase, thermodynamic path and endpoint, hole size, leak duration, and other issues. Release Phase. Discharge rate models require a careful consideration of the phase of the released material. The phase of the discharge is dependent on the release process and can be determined by using thermodynamic diagrams or data,

TABLE 2.2 Typical Release Outcomes (Emergency Engineered or Emergency Unplanned Releases), and the Relationship to Material Phase Liquid Discharges • Hole in atmospheric storage tank or other atmospheric pressure vessel or pipe under liquid head • Hole in vessel or pipe containing pressurized liquid below its normal boiling point Gas Discharges • Hole in equipment (pipe, vessel) containing gas underpressure • Relief valve discharge (ofvapor only) • Boiling-off evaporation from liquid pool • Relief valve discharge from top of pressurized storage tank • Generation of toxic combustion products as a result of fire Two-Phase Discharges • Hole in pressurized storage tank or pipe containing a liquid above its normal boiling point • Relief valve discharge (e.g.,due to a runaway reaction or foaming liquid)

A Wind — Direction

Pure Vapor Jet

V

B

Immediately Resulting Vapor Cloud

V PLi

PL

Small Hole in Vapor Space of a Pressurized Tank

Catastrophic Failure of Pressurized Tank

C

Jet 3

D Liquid Jet1

Jet 2

V

PL

d Jet 4 Escape of Liquified Gas from a Pressurized Tank

Intermediate Hole in Vapor Space of a Pressurized Tank E

F

V m.

Evaporating Cloud

Liquid Jet ,SS Spill

Liquid in Bund

Spillage of Refrigerated Liquid into Bund G V RL Fragmenting Jet

Spillage of Refrigerated Liquid onto Water

Boiling Pool

V: Vapor PL: Liquified Gas Under Pressure RL: Refrigerated Liquid d: Droplets

High-Velocity Fragmenting Jet from Refrigerated Containment Vessel FIGURE 2.2. illustrations of some conceivable release mechanisms. In most cases the jet could be two-phase (vapor plus entrained liquid aerosol). From Fryer and Kaiser (1979).

or a vapor-liquid equilibrium model, and the thermodynamic path during the release. Standard texts on vapor-liquid equilibrium (Henley and Seader, 1981; Holland, 1975; King, 1980; Smith and Missen, 1982; Smith and Van Ness, 1987; Walas, 1985) or any of the commercial process simulators provide useful guidance on phase behavior. The starting point of this examination is defined by the initial condition of the process material before release. This may be normal process conditions or an abnormal state reached by the process material prior to the release. The end point of the pathway will normally be at afinalpressure of one atmosphere.

Thermodynamic Path and Endpoint. The specification of the endpoint and the thermodynamic pathway used to reach the endpoint is important to the development of the source model. If, for instance, initially quiescent fluid is accelerated during a release, and the endpoint is defined as moving fluid, then the assumption of an isentropic pathway is normally valid. If, however, the endpoint is defined as quiescent fluid (for example, a pool of liquid after a release), independent of any transient accelerations, then the initial and final enthalpies would be assumed equal (this does not imply that the enthalpy is constant during the release process). Table 2.3 demonstrates the impact of the various thermodynamic paths on a total energy balance for an open system. For the isenthalpic case, AT = 0 for an ideal gas since the enthalpy is a function of temperature only. For the isentropic case, Q — 0 since dS = AQJT. For the isothermal case, AH = 0 since the enthalpy for an ideal gas is a function of temperature only. For the adiabatic case, A5 = 0 for a reversible process only. For both the isentropic and adiabatic cases, the shaft work determined is a maximum for reversible processes. TABLE 2.3. Implications for Various Thermodynamis Assumptions on the Total Energy Balance Total Energy Balance: AH" + AKE + APE = Q- Ws where AH is the change in enthalpy is the change in kinetic energy is the change in potential energy is the heat (+ = input; - = output) is the shaft: work (+ = output; - = input) Assumptions: External energy balance Open system with steady flow, that is, no-accumulation of mass or energy, fixed system boundaries Term Notel

Isenthalpic: Isentropic:

Note 2

Isothermal: Adiabatic:

Note 2

NOTES: * Ideal gas only + Reversible processes only. NOTE 1: From the remaining terms of the total energy balance: NOTE 2: From the remaining terms of the total energy balance: If the process is reversible, the work calculated is the maximum work.

For isentropic releases, an equilibrium flash model can be used to determine the final temperature, composition and phase splits at ambient pressure. Clearly, if the pathway stays in the gas or liquid phase, it is modeled accordingly. However, if a phase change is encountered, then two-phase flow may need consideration in modeling the release. A pure liquid will flash at its normal boiling point, while a mixture will flash continuously and with varying compositions over the range from its dew point to bubble point temperatures. For releases of gases through pipes, either adiabatic or isothermal flow models are available (Levenspiel, 1984; Crowl and Louvar, 1990). For releases of gases at the same source temperature and pressure, the adiabatic flow model predicts a larger, i.e., conservative, flowrate, while the isothermal model predicts a smaller flowrate. The actual flowrate is somewhere in between these values. For many problems, the flowrates calculated by each approach are close in value. Hole Size. A primary input to any discharge calculation is the hole size. For releases through a relief system, the actual valve or pipe dimension can be used. For releases through holes, the hole size must be estimated. This must be guided by hazard identification and incident enumeration and selection processes (whether this would be a flange leak, medium size leak from impact, full-bore rupture, etc.). No general consensus is currently available for hole size selection. However, a number of methodologies are suggested: • World Bank (1985) suggests characteristic hole sizes for a range of process equipment (e.g., for pipes 20% and 100% of pipe diameter are proposed). • Some analysts use 2 and 4-inch holes, regardless of pipe size. • Some analysts use a range of hole sizes from small to large, such as 0.2,1,4 and 6 inches and full bore ruptures for pipes less than 6 inches in diameter. • Some analysts use more detailed procedures. They suggest that 90% of all pipe failures result in a hole size less than 50% of the pipe area. The following approach is suggested: -For small bore piping up to I W use 5-mm and full-bore ruptures. -For 2-6" piping use 5-mm, 25-mm and full-bore holes. -For 8-12" piping use 5-, 25-, 100-mm and full-bore holes. -For a large hole in a pressure vessel—assume a 10-min discharge of the contents. A complete failure is discouraged. Also, assume complete failure of incoming and outgoing lines and check if discharge of the contents through these lines will be less than 10 min. If less than 10 min, assume 10 min. -For pumps, look at the suction and discharge lines. Consider a seal leak, 5-, 25-, and 100-mm holes, depending on line sizes.

Leak Duration. The Department of Transportation (1980) LNG Federal Safety Standards specified a 10-min leak duration; other studies (Rijnmond Public Authority, 1982) have used 3 min if there is a leak detection system combined with remotely actuated isolation valves. Other analysts use a shorter duration. Actual release duration may depend on the detection and reaction time for automatic isolation devices and response time of the operators for manual isolation. The rate of valve closure in longer pipes can influence the response time. Due to the water hammer effect, designers may limit the rate of closure in liquid pipelines. Other Issues. Other special issues to consider when analyzing discharges include the following. • Time dependence of transient releases: Decreasing release rates due to decreasing upstream pressure. • Reduction in flow: Valves, pumps, or other restrictions in the piping that might reduce the flow rate below that estimated from the pressure drop and discharge area. • Inventory in the pipe or process between the leak and any isolation device. Fundamental Equations. Discharge rate models are based on a mechanical energy balance. A typical form of this balance is (2.1) where P is the pressure (force/area) p is the density (mass/volume) g is the acceleration due to gravity (length/time2) gc is the gravitational constant (force/mass-acceleration) z is the vertical height from some datum (length) v is the fluid velocity (length/time) / is a frictional loss term (Iength2/time2) Ws is the shaft work (mechanical energy/time) m is the mass flow rate (mass/time) The frictional loss term, ^ef, in Eq. (2.1) represents the loss of mechanical energy due to friction and includes losses due to flow through lengths of pipe; fittings such as valves, elbows, orifices; and pipe entrances and exits. For each frictional device a loss term of the following form is used (2.2)

where K^is the excess head loss due to the pipe or pipe fitting (dimensionless) and v is the fluid velocity (length/time) For fluids flowing through pipes, the excess head loss term K^ is given by (2.3)

where / is the Fanning friction factor (unitless) L is the flow path length (length) D is the flow path diameter (length) 2-KMethod. For pipe fittings, valves, and other flow obstructions, the traditional method has been to use an equivalent pipe length, £equiv, in Eq. (2.3). The problem with this method is that the specified length is coupled to the friction factor. An improved approach is to use the 2-Kmethod (Hooper, 1981, 1988), which uses the actual flow path length in Eq. (2.3)—equivalent lengths are not used—and provides a more detailed approach for pipe fittings, inlets and outlets. The 2-K method defines the excess head loss in terms of two constants, the Reynolds number, and the pipe internal diameter: (2.4) where ^ 1 and K00 are constants (dimensionless) NKc is the Reynolds number (dimensionless) IDmches is the internal diameter of the flow path (inches). The metric equivalent to Eq. (2.4) is given by (2.5) where ID^n is the internal diameter in mm. Table 2.4 contains a list of lvalues for use in Eqs. (2.4) and (2.5) for various types of fittings and valves. For pipe entrances and exits, a modified form of Eq. (2.4) is required to model the behavior (2.6) For pipe entrances,^ = 160 andi^, = 0.50 for a "normal" entrance, and 1.0 for a Borda type entrance. For pipe exits, ^T1 = OandX^ = 1.0. Equations are also provided for orifices (Hooper, 1981) and for changes in pipe sizes (Hooper, 1988).

TABLE 2.4. "Two-K" Constants for Loss Coefficients and Valves*

K00

Fittings Elbows

90°

45°

180°

Tees

Used as elbows

Run-through

Valves

Gate, plug, or ball

Globe Diaphragm Butterfly Check

Standard (r/D = 1), threaded Standard (r/D = 1), flanged/welded Long radius (r/D — 1.5), all types Mitered (r/D = 1.5) 1 weld (90°) 2 welds (45°) 3 welds (30°) 4 welds (22.5°) 5 welds (18°) Standard (r/D = 1), all types Long radius (r/D =1.5) Mitered, 1 weld (45°) Mitered, 2 welds (22.5°)

800 800 800 1000 800 800 800 800 500 500 500 500

Standard (r/D = 1), threaded Standard (r/D = 1), flanged/welded Long radius (r/D = 1.5), all types

1000

Standard, threaded Long radius, threaded Standard, flanged/welded Stub-in branch

500

Threaded Flanged/welded Stub-in branch Full line size Reduced trim Reduced trim

1000 1000

800 800 1000 200 250 100

^ = 1.0 ^ = 0.9 P = 0.8

Standard Angle or Y-type Dam type

300 500 1000 1500 1000 1000 800

Lift Swing Tilting disk

"From William B. Hooper, Chemical Engineering, August 24, 1981, p. 97

2000 1500 1000

0.40 0.25 0.20 1.15 0.35 0.30 0.27 0.25 0.20 0.15 0.25 0.15 0.70 0.35 0.30 0.70 0.40 0.80 1.00 1.10 0.05 0.00 0.10 0.15 0.25 4.00 2.00 2.00 0.25 10.0 0 1.50 0.50

For high Reynolds number, that is, NKc > 10,000, the first term in Eq. (2.6) is negligible andK^ = K1x. For low Reynolds number, that is, NKc < 50, the first term dominates and K^ = KJNrRe. The Fanning friction factor for flow through pipes is found from commonly available charts (Perry and Green, 1984). A generalized equation is also available to calculate the friction factor directly, or for spreadsheet use (Chen, 1979): (2.7) and (2.8)

where e is the pipe roughness, given in Table 2.5. At high Reynolds numbers (fully developed turbulent flow), the friction factor is independent of the Reynolds number. From Eq. (2.7), for large Reynolds numbers, (2.9) The Fanning friction factor differs from the Moody friction factor by a constant value of 4. The above equations provide a useful framework for modelling both incompressible and compressible fluid flow through pipes and holes. For discharge TABLE 2.5. Roughness Factor e for Clean Pipes3 Pipe material

e, mm

Riveted steel

1-10

Concrete

0.3-3

Cast iron

0.26

Galvanized iron

0.15

Commercial steel

0.046

Wrought iron

0.046

Drawn tubing

0.0015

Glass

0.0

Plastic

0.0

"Selected from Levenspiel(1984, p. 22).

modelling, the usual objective is to determine the flow rate of material. However, to determine the friction factor for a pipe, or the K factors for a fitting, the Reynolds number is required. Thus, a trial-and-error solution is required since the Reynolds number is not known until the flow rate is known. A spreadsheet can be easily applied to achieve the solution. A special case occurs at high Reynolds number, where the friction factor is constant and K^ = K00. For this case the solution is direct. Liquid Discharges. For liquid discharges, the driving force for the discharge is normally pressure, with the pressure energy being converted to kinetic energy during the discharge. Since the density remains constant during the discharge, the pressure integral in the mechanical energy balance, Eq. (2.1), can be integrated directly to result in the following simplified equation: (2.10) For pipe flow, the mass flux through the pipe is constant and, for pipes of constant cross-sectional area, the liquid velocity is constant along the pipe as well. In all cases, frictional losses occur due to the fluid flow. If the flow is considered frictionless and there is no shaft work, the resulting equation is called the Bernoulli equation, (2.11) If the balance is performed across two points on the pipe of constant cross section, then V2 = V1 and Eq. (2.11) can be simplified further. Discharges of pure (i.e. nonflashing) liquids through a sharp-edged orifice are well described by the classical work of Bernoulli and Torricelli (Perry and Green, 1984). The model is developed from the mechanical energy balance, Eq. (2.1), by assuming that the frictional loss term is represented by a discharge coefficient, CD (Crowl and Louvar, 1990). The result is (2.12) where is the liquid discharge rate (mass/time) is the area of the hole (length2) is the discharge coefficient (dimensionless) is the density of the fluid (mass/volume) is the gravitational constant (force/mass-acceleration) is the pressure upstream of the hole (force/area) is the pressure downstream of the hole (force/area)

The following guidelines are suggested for the discharge coefficient, CD (Lees, 1986): 1. For sharp-edged orifices and for Reynolds numbers greater than 30,000, the discharge coefficient approaches the value 0.61. For these conditions the exit velocity is independent of the hole size. 2. For a well-rounded nozzle the discharge coefficient approaches unity. 3. For short sections of pipe attached to a vessel with a length-diameter ratio not less than 3, the discharge coefficient is approximately 0.81. 4. For cases where the discharge coefficient is unknown or uncertain, use a value of 1.0 to maximize the computed flows to achieve a conservative result. Equation (2.11) can be used to model any discharge of liquid through a hole, provided that the pressures, hole area, and discharge coefficient are known or estimated. For holes in tanks, the pressure upstream of the hole depends on the liquid head and any pressure in the tank head space. The 2-K method presented earlier is a much more general approach and can be used to represent liquid discharge through holes, in place of Eq. (2.12). By applying the orifice equations for the 2-K method (Hooper, 1981), the discharge coefficient can be calculated directly. The result is (2.13) where^Kf is the sum of all excess head loss terms, including entrances, exits, pipe lengths and fittings, provided by Eqs. (2.2), (2.4), and (2.6). For a simple hole in a tank, with no pipe connections or fittings, the friction is caused only by the entrance and exit effects of the hole. For Reynolds numbers greater than 10,000, Kf = 0.5 for the entrance and Xf =1.0 for the exit. Thus ^Kf =1.5 and, from Eq. (2.13), CD = 0.63, which nearly matches the suggested value of 0.61. The solution procedure to determine the mass flow rate of discharged material from a piping system is as follows: 1. Given: Length, diameter, and type of pipe; pressures and elevation changes across the piping system; work input or output to the fluid due to pumps, turbines, etc.; number and type of fittings in the pipe; properties of the fluid, including density and viscosity. 2. Specify the initial point (point 1) and the final point (point 2). This must be done carefully since the individual terms in Eq. (2.10) are highly dependent on this specification. 3. Determine the pressures and elevations at points 1 and 2. Determine the initial fluid velocity at point 1.

4. Guess a value for the velocity at point 2. If fully developed turbulent flow is expected, then this is not required. 5. Determine the friction factor for the pipe using either Eq. (2.7) or Eq. (2.9). 6. Determine the excess head loss terms for the pipe, using Eq. (2.3), and the fittings, using Eq. (2.4). Sum the head loss terms and compute the net frictional loss term using Eq. (2.2). Use the velocity at point 2. 7. Compute values for all of the terms in Eq. (2.10) and substitute into the equation. If the sum of all the terms in Eq. (2.10) is zero , then the computation is completed. If not, go back to step 4 and repeat the calculation. 8. Determine the mass flow rate using the equation m = pvA. If fully developed turbulent flow is expected, the solution is direct. Substitute the known terms into Eq. (2.10), leaving the velocity at point 2 as a variable. Solve for the velocity directly. For holes in tanks, the discharge of material through the hole results in a loss of liquid and a lowering in the liquid level. For this case, Eq. (2.12) is coupled with a total mass balance on the liquid in the tank to obtain a general expression for the tank drainage time (Crowl, 1992). (2.14) where t is the time to drain the tank from volume V2 to volume V1 (time) V is the liquid volume in the tank above the leak (length3) h is the height of the liquid above the leak (length) Equation (2.14) assumes a constant leak area, A, and a constant discharge coefficient, CD. This equation can be integrated once the volume versus height function is specified, V = V(h). Results are available for a number of geometries (Crowl, 1992). Eq. (2.14) can also be integrated numerically if volume versus height data are available. The mass discharge rate of liquid from a hole in a tank is determined using the following equation (Crowl and Louvar, 1990). This assumes that friction is represented by a discharge coefficient, CD, and accounts for the pressure due to the liquid head above the hole. (2.15) where m is the mass discharge rate (mass/time)

v is the fluid velocity (length/time) A is the area of the hole (length2) CD is the mass discharge coefficient (dimensionless) gc is the gravitational constant (force/mass acceleration) P g is the gauge pressure at the top of the tank (force/area) p is the liquid density (mass/volume) g is the acceleration due to gravity (length/time2) hL is the height of liquid above the hole (length) Equation (2.15) applies to any tank of any geometry. The mass discharge decreases with time as the liquid level drops. The maximum discharge rate happens when the leak first occurs. Gas Discharges. Gas discharges may arise from several sources: from a hole at or near a vessel, from a long pipeline, or from relief valves or process vents. Different calculation procedures apply for each of these sources. The majority of gas discharges from process plant leaks will initially be sonic, or choked. Rate equations for sonic and subsonic discharges through an orifice are given in AIChE/CCPS (1987a, 1995a), API (1996), Crane Co. (1986), Crowl and Louvar (1990), Fthenakis (1993), and Perry and Green (1984). For gas discharges, as the pressure drops through the discharge, the gas expands. Thus, the pressure integral in the mechanical energy balance, Eq. (2.1), requires an equation of state and a thermodynamic path specification to complete the integration. For gas discharges through holes, Eq. (2.1) is integrated along an isentropic path to determine the mass discharge rate. This equation assumes an ideal gas, no heat transfer and no external shaft work. Refer to Table 2.3 for a summary of these assumptions. (2.16) where m CD A P1 gc M k il g

is mass flow rate of gas through the hole (mass/time) is the discharge coefficient (dimensionless) is the area of the hole (length2) is the pressure upstream of the hole (force/area) is the gravitational constant (force/mass-acceleration) is the molecular weight of the gas (mass/mole) is the heat capacity ratio, Cp/Cy (unitless) is the ideal gas constant (pressure-volume/mole-deg)

T1 is the initial upstream temperature of the gas (deg) P 2 is the downstream pressure (force/area) As the upstream pressure P 1 decreases (or downstream pressure P 2 decreases), a maximum is found in Eq. (2.16). This maximum occurs when the velocity of the discharging gas reaches the sonic velocity. At this point, the flow becomes independent of the downstream pressure and is dependent only on the upstream pressure. The equation representing the sonic, or choked case is (2.17)

The pressure ratio required to achieve choking is given by (2.18) Equation (2.18) demonstrates that choking conditions are readily produced—an upstream pressure of greater than 13.1 psig for an ideal gas is adequate to produce choked flow for a gas escaping to atmospheric. For real gases, a pressure of 20 psig is typically used. Equations (2.15) through (2.17) require the specification of a discharge coefficient, CD. Values are provided in Perry and Green (1984) for square-edged, circular orifices. For these types of discharges with N^ > 30,000, a value of 0.61 is suggested. API (1996) recommends a discharge coefficient of 0.6 for default screening purposes, along with a circular hole. For a conservative estimate with maximum flow, use a value of 1.0. Equations (2.15) through (2.17) also require a value of ^, the heat capacity ratio. Table 2.6 provides selected values. For monotonic ideal gases, k = 1.67, for diatomic gases, k = 1.4 and for triatomic gases, k = 1.32. API (1996) recommends a value of 1.4 for screening purposes. For gas releases through pipes, the issue of whether the release occurs adiabatically or isothermally is important. For both cases the velocity of the gas will increase due to the expansion of the gas as the pressure decreases. For adiabatic flows the temperature of the gas may increase or decrease, depending on the relative magnitude of the frictional and kinetic energy terms. For choked flows, the adiabatic choking pressure is less than the isothermal choking pressure. For real pipe flows from a source at a fixed pressure and temperature, the actual flow rate will be less than the adiabatic prediction and greater than the isothermal prediction. Crowl and Louvar (1990) show that for pipe flow problems the difference between the adiabatic and isothermal results are generally small. Levenspiel (1984) shows that the adiabatic model will always predict a flow larger than the

TABLE 2.6. Heat Capacity Ratios k for Selected Gases3 Chemical formula or symbol

Approximate molecular weight

Hcat

capacity ratio

(M)

k = Cp/Cy

Acetylene Air Ammonia Argon

26.0 29.0 17.0 39.9

1.30 1.40 1.32 1.67

Butane Carbon dioxide Carbon monoxide Chlorine

58.1 44.0 28.0 70.9

1.11 1.30 1.40 1.33

Ethane Ethylene Helium Hydrogen chloride

30.0 28.0 4.0 36.5

1.22 1.22 1.66 1.41

Hydrogen Hydrogen sulfide Methane Methyl chloride

2.0 34.1 16.0 50.5

1.41 1.30 1.32 1.20

Natural gas Nitric oxide Nitrogen Nitrous oxide

19.5 30.0 28.0 44.0

1.27 1.40 1.41 1.31

Oxygen Propane Propene (propylene) Sulfur dioxide

32.0 44.1 42.1 64.1

1.40 1.15 1.14 1.26

Name of gas

"From Crane (1986).

actual, provided that the source pressure and temperature are the same. Crane (1986) reports that "when compressible fluids discharge from the end of a reasonably short pipe of uniform cross-sectional area into an area of larger cross section, the flow is usually considered to be adiabatic." Crane (1986) supports this statement with experimental data on pipes having lengths of 130 and 220 pipe diameters discharging air to the atmosphere. As a result, the adiabatic flow model is the model of choice for compressible gas discharges through pipes.

For ideal gas flow, the mass flow for both sonic and nonsonic conditions is represented by the Darcy formula (Crane, 1986): (2.19) where is the mass flow rate of gas (mass/time) is a gas expansion factor (unitless) is the area of the discharge (length2) is the gravitational constant (force/mass-acceleration) is the upstream gas density (mass/volume) is the upstream gas pressure (force/area) is the downstream gas pressure (force/area) are the excess head loss terms, including pipe entrances and exits, pipe lengths and fittings (unitless). The excess head loss terms, ^Kf, are found using the 2-K method presented earlier in the section on liquid discharges. For most accidental discharges of gases, the flow is fully developed turbulent flow. This means that, for pipes, the friction factor is independent of the Reynolds number and, for fittings, Kf=K00, and the solution is direct. The gas expansion factor, Y, in Eq. (2.19) is dependent only on the heat capacity ratio of the gas, k, and the frictional elements in the flow path, ^Kf. It is determined using a complete adiabatic flow model (Crowl and Louvar, 1990) using the following procedure. First, the upstream Mach number, Ma, of the flow is determined from the following equations: (2.20)

The solution is obtained by trial and error by guessing values of the upstream Mach number, Ma, and determining if the guessed value meets the equation objectives. This can be easily done using a spreadsheet. The next step in the procedure is to determine the sonic pressure ratio. This is found from (2.21) If the actual ratio is greater than this, then the flow is sonic or choked, and the pressure drop predicted by Eq. (2.21) is used to continue the calculation. If less, then the flow is not sonic, and the actual pressure drop ratio is used.

Finally, the expansion factor, Y, is calculated from (2.22)

^-W

The above calculation to determine the expansion factor can be completed once k and the factional loss term, 2/Kf ?a r e specified. This computation can be done once and for all with the results shown in Figures 2.3 and 2.4. As shown in Figure 2.3, the pressure ratio (P1 - P2)/P\ is a weak function of the heat capacity ratio, k. The expansion factor, Y, has little dependence on k, with the value of Y

All points at or above function are sonic flow conditions.

Excess Head Loss, Kf

Expansion Factor, Y

FIGURE 2.3. Sonic pressure drop for adiabatic pipe flow for various heat capacity ratios, k. All regions above the curve represent sonic flow. [See Eqs. (2.20)-(2.22)J

Excess Head Loss, K1 FIGURE 2.4. The expansion factor Y for adiabatic pipe flow for k = 1.4, as defined by Eq. (2.22).

varying by less than 1% from the value at k = 1.4 over the range from k = 1.2 to 1.67. Figure 2.4 shows the expansion factor for k = 1.4. The functional results of Figures 2.3 and 2.4 can be fit using an equation of the form In Y = ^L(lniQ3 + B(InIQ2 + C(InJQ) 4- D , where ^4, JJ, C, and!) are constants. The results are shown in Table 2.7 and are valid for the K^ range indicated, within 1%. The procedure to determine the adiabatic mass flow rate through a pipe or hole is as follows: 1. Given: k based on the type of gas; pipe length, diameter and type; pipe entrances and exits; total number and type of fittings; total pressure drop; upstream gas density. 2. Assume fully developed turbulent flow to determine the friction factor for the pipe and the excess head loss terms for the fittings, pipe entrances and exits. The Reynolds number can be calculated at the completion of the calculation to check this assumption. Sum the individual excess head loss terms to get X^f • 3. Calculate (P1 - P2)/P\ from the specified pressure drop. Check this value against Figure 2.3 to determine if the flow is sonic. All areas above the curves in Figure 2.3 represent sonic flow. Determine the sonic choking pressure, P2, by either using Figure 2.3 directly, interpolating a value from the table, or using the equations provided in Table 2.7 4. Determine the expansion factor from Figure 2.4. Either read the value off of the figure, interpolate from the table, or use the equation provided in Table 2.7. 5. Calculate the mass flow rate using Eq. (2.19). Use the sonic choking pressure determined in step 3 in this expression. TABLE 2.7. Correlations for the Expansion Factor Y and the Sonic Pressure Drop Ratio (P1 - P2)/P\ as a Function of the Excess Head Loss Kf. The correlations are within 1% of the actual value within the range specified.

A

B

C

D

Range of Xf

Expansion factor, Y

0.0006

-0.0185

0.1141

-0.5304

0.1-100

Sonic pressure drop ratio, k= 1.2

0.0009

-0.0308

0.261

-0.7248

0.1-100

Sonic pressure drop ratio, k = 1.4

0.0011

-0.0302

0.238

-0.6455

0.1-300

Sonic pressure drop ratio, k = 1.67

0.0013

-0.0287

0.213

-0.5633

0.1-300

Function value, y

The above method is applicable to gas discharges through piping systems as well as holes.

Mass Flux, 1000 kg/m**2 - s

Two-Phase Discharge. The significance of two-phase flow through restrictions and piping has been recognized for some time (Benjamin and Miller, 1941). Beginning in the mid-1970s AIChE/DIERS has studied two-phase flow during runaway reaction venting. DIERS researchers have emphasized that this two-phase flow usually requires a larger relief area compared to all-vapor venting (Fauske et al., 1986). Leung (1986) provides comparisons of these areas over a range of overpressure. Research supported by the nuclear industries has contributed much to our understanding of two-phase flow, as have a large number of studies undertaken by universities and other independent organizations. When released to atmospheric pressure, any pressurized liquid above its normal boiling point will start to flash and two-phase flow will result. Two-phase flow is also likely to occur from depressurization of the vapor space above a volatile liquid, especially if the liquid is viscous (e.g., greater than 500 cP) or has a tendency to foam. It should be noted that the two-phase models presented below predict minimum mass fluxes and maximum pressure drops, consistent with conservative relief system design (Fauske, 1985). Thus, they may not be suitable for source modeling. The orifice discharge equation, Eq. (2.12), will always predict a maximum discharge flux. This result is shown in Figure 2.5, which shows the mass

2-Phase Theory Orifice Equation

Pressure, MPa FIGURE 2.5. The mass flux from a flashing two-phase flow as a function of the upstream pressure. The data are plotted for various pipe lengths. The orifice equation predicts a maximum flow, while the two-phase model predicts a minimum flow. (Data fromFauske, 1985.)

flux as a function of upstream pressure for identical diameter pipes of varying lengths. Note that the two-phase model predicts a minimal result, while the orifice discharge equation predicts a maximum result. Two-phase flows are classified as either reactive or nonreactive. The reactive case is typical of emergency reliefs of exothermic chemical reactions. This case is considered later. The nonreactive case involves the flashing of liquids as they are discharged from containment. Two special considerations are required. If the liquid is subcooled, the discharge flow will choke at its saturation vapor pressure at ambient temperature. If the liquid is stored under its own vapor pressure, a more detailed analysis is required. Both of these situations are accounted for by the following expression (Fauske and Epstein, 1987): (2.23)

where m is the two-phase mass discharge rate (mass/time) A is the area of the discharge (length2) GSUB is the subcooled mass flux (mass/area time) GERM is the equilibrium mass flux (mass/area time) N is a nonequilbrium parameter (dimensionless). The properties are evaluated at the storage temperature and pressure. The subcooled mass flux is given by (2.24)

where CD pf gc P Pat

is the discharge coefficient (unitless) is the density of the liquid (mass/volume) is the gravitational constant (force/mass acceleration) is the storage pressure (force/area) is the saturation vapor pressure of the liquid at ambient temperature (force/area) For saturated liquids, equilibrium is reached if the discharge pipe size is greater than 0.1 m (length greater than 10 diameters) and the equilibrium mass flux is given by (Crowl and Louvar, 1990) (2.25) where

h{% is the enthalpy change on vaporization (energy/mass) vi% is the change in specific volume between liquid and vapor (volume/mass) T is the storage temperature (absolute degrees) Cp is the liquid heat capacity (energy/mass deg) with the properties evaluated at the storage temperature and pressure. Note that the temperature must be in absolute degrees and is not associated with the heat capacity. The nonequilibrium parameter, N, accounts for the effect of the discharge distance. For short discharge distances, a nonequilibrium situation occurs and the liquid does not have time to flash during the discharge process—the flashing occurs after discharge and the liquid discharge is represented by Eq. (2.12). For discharge distances greater than 0.1 m, the liquid reaches an equilibrium state and chokes at its saturation vapor pressure. A relationship for N, the nonequilibrium parameter, is given by (Fauske and Epstein, 1987)

for

(2.26)

where AP is the total available pressure drop (force/area), L is the pipe length to the opening (length), andL c is the distance to equilibrium conditions, usually 0.1m. For L = 0, Eqs. (2.23) and (2.26) reduce to Eq. (2.12), describing liquid discharge through a hole. There are many equally valid techniques for estimating two-phase flow rates. The nuclear industry has undertaken substantial analysis of critical two-phase flow of steam-water mixtures. The Nuclear Energy Agency (1982) has published a review of four models and summarized available experimental data. Klein (1986) reviews the one-dimensional DEERS model for the design of relief systems for two-phase flashing flow. Three-dimensional models are also available although little published information on their use is available. Additional complexity does not guarantee improved accuracy and can unnecessarily complicate the task of risk analysis. For reactive two-phase discharges, the discharge is driven by the energy created within the fluid due to the exothermic reaction, and the relief analysis is highly coupled to the energy balance of the reactor. This case is discussed in detail by Fisher et al. (1992), Fthenakis (1993), and Boicourt (1995). Two-phase relief design is based on the equation A = m/G^ where is the mass flow rate and G is the mass flux. To insure a conservatively designed relief device, i.e. relief area larger than required, the mass flux or relief discharge model is selected to minimize the mass flux through the relief. A discharge model predicting a smaller mass flux through the relief will ensure a larger relief area and hence

a conservative design. For consequence modeling, the discharge models must be selected to maximize the mass flux. Therefore, the relief mass flux models should not be used as the basis for a consequence model since the conservatism is in the wrong direction. The mass flow rate through the relief is estimated using an energy balance on the reactor vessel. The assumption of a tempered system is made for this analysis. A tempered reactor assumes (1) no external heat losses from the vessel, and (2) that the vessel contains a volatile solvent with the resulting pressure build-up due to the vapor pressure of the solvent as a result of the increasing system temperature from the exothermic reaction. The result is conservative due to the assumption of no heat losses, but not overly conservative for fast runaway reactions. For a tempered reaction system, the heat generated by the reaction is equated to the sensible heat change of the reacting liquid mass as its temperature increases and the heat loss due to the evolution of volatile solvent. The result is (Boicourt, 1995) (2.27)

where Q m Cv T t m V h{g vi%

is the heat generation by reaction (degrees/time) is the mass within the reactor vessel (mass) is the heat capacity at constant volume (energy/mass deg) is the absolute temperature of the reacting material (degrees) is the time (time) is the mass flow rate through the relief (mass/time) is the reactor vessel volume (length3) is the enthalpy difference between liquid and vapor (energy/mass/deg) is the specific volume difference between the liquid and vapor (volume/mass) The closed form solution to Eq. (2.27) is (Leung, 1986b), (2.28)

where q is the average heat release rate (energy/time) and W0 is the initial reaction mass (mass). The assumptions inherent in Eq. (2.28) are (Boicourt, 1995) 1. Homogeneous conditions in the reactor. 2. Constant physical properties.

3. Cp = Cv and Cp is the heat capacity of the liquid. 4. Vapor phase incompressibility; that is, dvjdt is constant during overpressure. 5. The average heat release rate, #, during the overpressure is approximated by (2.29) where the subscripts s and m refer to the set conditions and turnaround conditions, respectively. The set conditions refer to conditions at the set pressure and the turnaround conditions refer to the conditions at the maximum pressure during the relieving process. 6. mis constant during the overpressure. 7. Single component system. Expressions are also available for reactive systems with a variety of vent lines and relief configurations (Boicourt, 1995). Discharge from vessels exposed to fire. Where discharge is from a relief due to fire exposure in a nonreacting system, a long established empirical method for estimating relief rates is that given in the National Fire Protection Association Codes (NFPA, 1987a, b) or the American Petroleum Institute Recommended Practice (API, 1976,1982). A key assumption of these methods is gas only flow. Crozier (1985) provides a summary of the relevant formulas. Certain relief situations (e.g., reacting systems) can give rise to two-phase discharges that will require greater relief area for the same vessel protection assuming gas-only discharges (Fauske et al., 1986; Leung, 1986a). The recent work by AIChE/DIERS provides guidance for vessels subject to runaway reaction or external fire (Fauske et al., 1986). Birk and Dibble (1986) provide a mechanistic, transient discharge model for simulating release rates from pressure vessels exposed to external fire. NFPA 30 (NFPA, 1987a) recommends four heat flux values through the tank wall based on the wetted surface area for nonpressurized tanks. For LPG (pressurized tanks) considered in NFPA 58 (NFPA, 1987b) the heat flux is based on the total tank surface area rather than the wetted surface area although little heat transfer occurs through the nonwetted portion. Experience has indicated that this approach is satisfactory for LPG. However, metal only in contact with vapor may heat rapidly under external fire conditions and lose its strength leading to a BLEVE as pressure builds. Further, in the United States, most LPG installations follow the rules stated in NFPA 58, which are adopted by many regulatory jurisdictions. NFPA 58 basically covers LPG of molecular weight between 30

and 58. NFPA 58 requirements are based on the following equations (implicit in its Appendix D) for predicting heat flux: (2.30)

where Qx is the heat input through the vessel wall due to fire exposure (BTU/hr), A is the total surface area of the vessel (ft2), and F is the environment factor (dimensionless). The area, Ay in this equation is the entire surface area of the vessel, not the wetted surface area that is used in related equations. However, the error introduced by this difference in the calculation for a full tank is small. For water spray protection over the entire surface of the tank (designed according to NFPA15 (1985) with a density of 0.25 gpm/ft2 or more), F = 0.3. For an approved fire-resistant installation, F — 0.3. For an underground or buried tank, F = 0.3 (from NFPA 58, 1987b, Appendix D-2.3.1). For water spray with good drainage F= 0.15. The values for F above are not multiplicative if combined protection systems are in place. The gas discharge rate from the relief valve, m, is then calculated by equating the energy input rate to the rate of energy removal due to vaporization. This results in the following equation: (2.31) where mis the gas discharge rate from relief valve (mass/time) and h{% is the latent heat of vaporization at relief pressure (energy/mass) A detailed discussion of the formulas used in NFPA Codes can be found in Appendix B of the Flammable and Combustible Liquids Code Handbook (NFPA, 1987a). API RP520 (API, 1976) recommends a similar formula applicable to pressurized storage of liquids at or near their boiling point where the liquids have a higher molecular weight than that of butane. All of the recommended heat flux equations in API 520 and NFPA Codes that are used to design relief valves assume that the liquids are not self-reactive or subject to runaway reaction. If this situation arises, it will be necessary to take the heat of reaction and the rate of the reaction into account in sizing the relief device. 2.1.3. EXAMPLEPROBLEMS

Example 1: Liquid Discharge through a Hole Calculate the discharge rate of a liquid through a 10-mm hole, if the tank head space is pressurized to 0.1 barg. Assume a 2-m liquid head above the hole. Data: Liquid density = 490 kg/m3

0.1 bar gauge

Liquid

Hole

FIGURE 2.6. Example 1: Liquid discharge through a hole.

Solution: For liquid discharges, Eq. (2.10) applies. The 2-iCmethod will be used to determine the factional components. A diagram of the process is shown in Figure 2.6. Points 1 and 2 denote the initial and final reference points. For this case there are no pumps or compressors, so Ws - 0. Also, at point 1, V1 = 0. Applying these assumptions, Eq. (2.10) reduces to

Assume NKc > 10,000. Then the excess head loss for the fluid entering the hole is I<^= 0.5. For the exit, I^ = 1.0. Thus, £2Q = 1 5 a n d f r o m % (2-2)

Also, P 1 = 0.10 bar gauge and P 2 = 0 bar gauge. The hole area is

The terms in the above equation are as follows:

Substituting the terms into Eq. (2.10)

Solving gives v2 = 5.7 m/s. Then

This is the maximum discharge rate for this hole. The discharge rate will decrease with time as the liquid head above the hole is decreased. Also, the maximum discharge rate would occur if the hole were located at the bottom of the tank. The solution is readily implemented using a spreadsheet, as shown in Figure 2.7. Example 2: Liquid Trajectory from a Hole Consider again Example 1. A stream of liquid discharging from a hole in a tank will stream out of the tank and impact the ground at some distance away from the tank. In some cases the liquid stream could shoot over any diking designed to contain the liquid.

Example 1: Liquid Discharge through a Hole in a Tank . Input Data: Tank pressure above liquid: Pressure outside hole: Liquid density: Liquid level above hole: Hole diameter: Excess Head Loss Factors: Entrance: Exit: Others: TOTAL: Calculated Results: Hole area: Equation terms: Pressure term: Height term: Velocity coefficient: Exit velocity: Mass flow: Figure 2.7. Spreadsheet output for Example 1: Liquid discharge through a hole in the tank.

Hole

FIGURE 2.8. Tank geometry for Example

(a) If the hole is 3 m above the ground, how far will the stream of liquid shoot away from the tank? (b) At what point on the tank will the maximum discharge distance occur? What is this distance? Solution: (a) The geometry of the tank and the stream is shown in Figure 2.8. The distance away from the tank the liquid stream will impact the ground is given by (2.32)

where s is the distance (length), V2 is the discharge velocity (distance/time), and t is the time (time). The time, £, for the liquid to fall the distance /;, is given by simple acceleration due to gravity, (2.33)

These two equations are implemented in the spreadsheet shown in Figure 2.9. The velocity is obtained from Example 1. The horizontal distance the stream will impact the ground is 4.46 m away from the base of the tank. Solution (b) The solution to this problem is found by solving Eq. (2.10) for V2. The algebraic result is substituted into Eq. (2.32), along with Eq. (2.33). The Example 2a: Liquid Trajectory from a Hole Input Data: Liquid velocity at hole: Height of hole above ground: Calculated Results: Time to reach ground: Horizontal distance from hole:

I

FIGURE 2.9. Spreadsheet output for Example 2a: Liquid trajectory from a hole.

resulting equation for s is differentiated with respect to h. The expression is set to zero to determine the maximum, and solved for h. The result is (2.34)

where H is the total liquid height above ground level (length). Equations (2.33) and (2.34) are then substituted into Eq. (2.32) for s to determine the maximum distance. The result is (2.35)

IfP = 0, i.e. the tank is vented to the atmosphere, then the maximum discharge distance, from Eq. (2.34) occurs when the hole is located at h = H/2. As the tank pressure increases, the location of the hole moves up and eventually reaches the top of the liquid. These equations are conveniently implemented using a spreadsheet, as shown in Figure 2.10. For this case, the hole location for the maximum discharge conditions is at 3.54 m above the ground. The maximum discharge distance is 4.48 m. This example demonstrates the important point that the incident is selected based on the objective of the study. If the objective of the study is to determine the maximum discharge rate from the tank, then a hole is specified at the bottom Example 2b: Maximum Discharge Distance from a Hole in a Tank Input Data: Tank pressure above liquid: Max. liquid height in tank: Density of liquid: Excess Head Loss Factors: Entrance: Exit: Others: TOTAL: Calculated Results: Hole height for max. distance:

Above ground

Actual height: Discharge distance:

Cannot exceed liquid height

FIGURE 2.10. Spreadsheet output for Example 2b: Liquid trajectory from a hole.

of the tank. If the study objective is to determine the maximum discharge distance, then Eq. (2.34) is used to place the location of the hole. Example 3: Liquid Discharge through a Piping System Figure 2.11 shows a transfer system between two tanks. The system is used to transfer a hazardous liquid. The pipe is commercial steel pipe with an internal diameter of 100-mm with a total length of 10 m. The piping system contains two standard, flanged 90° elbows and a standard, full-line gate valve. A 3-kW pump with an efficiency of 70% assists with the liquid transfer. The maximum fluid height in the supply tank is 3 m, and the elevation change between the two tanks is as shown in Figure 2.11. Data: Fluid density (p) = 1600 kg/m3 Fluid viscosity (/<) = 1.8 x 10"3 kg/m s Solution: The postulated scenario is the detachment of the pipe at its connection to the second tank. The objective of the calculation is to determine the maximum discharge rate of liquid from the pipe. Liquid would also discharge from the hole in the tank previously connected to the pipe, but this is not considered in this calculation. The 2-K method, in conjunction with Eq. (2.10) will be used. A trial and error solution method is required, as discussed in the section on liquid discharges. A spreadsheet solution is best, with the output shown in Figure 2.12

Standard Gate Valve

Pump

Pipe Detaches here FIGURE 2.11. Example 3: Liquid discharge through a piping system.

Example 3: Liquid Discharge through a Piping System Input Data: !Guessed discharge velocity:"" Fluid density: Fluid viscosity: Pipe diameter: Pipe roughness: Point 1 pressure: Point 2 pressure: Point 1 velocity: Point 1 height: Point 2 height: Pipe length: Net pump energy: Fittings: Elbows: Valves: Inlet: Exit:

Number 2 1 1 1

K1 800 300 160 0

K-inifinity 0.25 0.1 0.5 1

Calculated Results: Reynolds No: Friction factor: Pipe area: Fittings and pipe K factors: Elbows: Valves: Inlet: Exit: Pipe: TOTAL: Mechanical energy balance terms (m**2/s**2): Pressure: Height: Point 1 velocity: Fittings/pipe: Pump: TOTAL: !Calculated Discharge Velocity: Velocity Difference: [Resulting mass discharge rateT" FIGURE 2.12. Spreadsheet output for Example 3: Liquid discharge through a piping system.

The initial and final reference points are shown in Figure 2.11 by the numbers in the small squares. The pressures at these points are equal. The total elevation change between the two points is 10 + 3 = 13m. The pipe roughness factor is found in Table 2.5. The constants for the fittings are found in Table 2.4. The 3 kW pump is 70% efficient so the net mechanical energy transferred to the fluid is (0.70)(3 kW) = 2 . 1 kW. The pump energy is entered as a negative value since work is going into the system. The calculated results are determined as follows. The Reynolds number is determined from the guessed velocity, the pipe diameter, the fluid density and viscosity. The friction factor is determined using Eq. (2.7). The K^ factors for the elbows and valves are determined using Eq. (2.4). The ^factors for the inlet and exit effects are determined using Eq. (2.6). The pipe K^ factor is found using Eq. (2.3). The excess head loss factors for the complete piping system are summed as shown. The mechanical energy balance terms all have units of m2/s2. The balance term for the fittings and pipe length is computed using Eq. (2.2). The guessed velocity is used here. The pump term in the balance is found from

where v2 is the guessed velocity. The mechanical energy balance terms are summed, as shown, with the difference representing the remaining term, Y2 v\. This represents the calculated velocity in the spreadsheet. The trial-and-error solution is achieved by manually entering velocity values until the guessed and calculated values are nearly identical, or by using a spreadsheet solving function. The resulting mass discharge rate is determined from Pv1A, and has a value of 97.6 kg/s. Example 4: Gas Discharge through a Hole Calculate the discharge rate of propane through a 10-mm hole at the conditions of 25°C and 4 barg (5.01 bar abs). Data: Propane heat capacity ratio = 1.15 (Crane, 1986) Propane vapor pressure at 25°C = 8.3 barg Solution: The steps to determine the discharge rate are: a. Determine phase of discharge. Since the total pressure is less than the vapor pressure of liquid propane, the discharge must be as a vapor. The gas discharge equations must be used. b. Determine flow regime, i.e., sonic or subsonic. The choking pressure is determined using Eq. (2.18).

Since P2= 1.01 bar is less than Pchoked, the flow is sonic through the hole. c. Determine the flow rate. The area of the discharge is

Use Eq. (2.17) to determine the mass flow rate

Assume a discharge coefficient, CD of 0.85. Substituting into Eq. (2.17) ^choked

^choked

^choked

This problem can also be solved using the 2-K method in conjunction with Eq. (2.19). For a hole, the frictional losses are only due to the entrance and exit effects. Thus, X^f = 0-5 4- 1.0 = 1.5. For& = 1.2, from Figure 2.3 (or equations in Table 2.7) (P1 -P2)IP1 = 0.536 and it follows that P 2 = 2.32 bar. Since the ambient pressure is well below this value, the flow will be choked. From Figure 2.4 (or equation in Table 2.7), the expansion factor, Y, is 0.614. The upstream gas density is

Substituting into Eq. (2.19), and using the choked pressure for P 2 ,

Example 4: Gas Discharge through a Hole Input Data: Heat capacity ratio of gas: Hole size: Upstream pressure: Dowstream pressure: Temperature: Gas molecular weight: Excess Head Loss Factors: Entrance: Exit: Others: TOTAL: Calculated Results: Hole area: Upstream gas density: Expansion factor, Y: Actual pressure ratio:

Must be greater than sonic pressure ratio below to insure sonic flow.

Heat capacity ratio, k: Sonic pressure ratios: Choked pressure: Mass flow: !interpolated mass flow: FIGURE 2.13. Spreadsheet output for Example 4: Gas discharge through a hole.

This result is almost identical to the previous result. The method is readily implemented using a spreadsheet, as shown in Figure 2.13. The spreadsheet prints out the mass flows for a range of k values—the user must interpolate to obtain the final result. Example 5: Gas Discharge through a Piping System Calculate the mass flow rate of nitrogen through a 10-m length of 5-mm diameter commercial steel pipe. Assume a scenario of pipe shear at the end of the pipe. The nitrogen is supplied from a source at a pressure of 20 bar gauge and a temperature of 298 K. The piping system includes four 90° elbows (standard, threaded) and two full line gate valves. Calculate the discharge rate by two methods (1) using the orifice discharge equation, Eq. (2.17) and assuming a hole size

equal to the pipe diameter, and (2) using a complete adiabatic flow model. For nitrogen, k = 1.4. Solution: The problem will be solved using two methods (1) a hole discharge and (2) an adiabatic pipe flow solution. Method 1: Hole discharge. Assume a discharge coefficient, CD = 0.85. The cross-sectional area of the pipe is

Also,

Equation (2.17) is used to estimate the mass discharge rate,

^choked

Substituting into Eq. (2.1.17),

Method 2: Adiabatic flow model. For commercial steel pipe, from Table 2.5, e = 0.046 mm and it follows that

Assume fully developed turbulent flow. Then, the friction factor is calculated using Eq. (2.9),

The excess head loss due to the pipe length is given by Eq. (2.3),

For the elbows, at the expected high discharge rates, K^ = K00. Thus, from Table 2.4, IQ = 0.4 for each elbow and for each ball valve Zf = 0.1. The exit effect of the gas leaving the pipe must also be included, that is, K^ = 1.0. Thus, adding up all the contributions,

From Figure 2.4 (or the equations in Table 2.7), for k = 1.4 andi^- = 76.5,

It follows that the flow is sonic since the downstream pressure is less than this. From Figure 2.4 (or Table 2.7), the gas expansion factor, Y = 0.716. The gas density at the upstream conditions is

Substituting into Eq. (2.19),

The mass discharge rate calculated assuming a hole is more than 5 times larger than the result from the adiabatic pipe flow method. Both methods require about the same effort, but the adiabatic flow method produces a much more realistic result. The entire adiabatic pipe flow method is readily implemented using a spreadsheet. The spreadsheet solution is shown in Figure 2.14.

Example 5: Gas Discharge through a Piping System Input Data: Heat capacity ratio, k: Temperature: Molecular weight of gas: Point 1 pressure: Point 2 pressure: Pipe diameter: Pipe length: Pipe roughness: Fittings: Elbows: Valves: Inlet: Exit:

Number

Kjnfinite

Calculated Results: Pipe area: initial gas density: Pipe friction factor: Fittings and pipe K factors: Elbows: Valves: Inlet: Exit: Pipe: TOTAL: Ln(K): Expansion factor: Heat capacity ratio,k (P1 -P2)/P1: P-choked: Mass flow: [Interpolated mass flow: FIGURE 2.14. Spreadsheet output for Example 5: Gas discharge through a piping system.

Example 6: Two-Phase Flashing Flow through a Pipe Propane is stored in a vessel at its vapor pressure of 95 bar gauge and a temperature of 298 K. Determine the discharge mass flux if the propane is discharged through a pipe to atmospheric pressure. Assume a discharge coefficient of 0.85 and a critical pipe length of 10 cm. Determine the mass flux for the following pipe lengths: (a) 0 cm (b) 5 cm (c) 10 cm (d) 15 cm Data: Heat of vaporization: 3.33xl0 5 J/kg Volume change on vaporization: 0.048 m3/kg Heat capacity: 2230 J/kg K Liquid density: 490 kg/m3 Solution: The solution to this problem is accomplished directly using Eqs. (2.23) through (2.26). This is readily implemented using a spreadsheet, as shown in Figure 2.15. The output shown is for a pipe length of 5 cm. The results are Example 6: Two-phase Flashing Flow through a Pipe Input Data: Ambient Temperature: Saturation pressure: Storage pressure: Downstream pressure: Critical pipe length: Pipe length: Discharge coefficient: Heat of vaporization: Volume change on vaporization Heat capacity: Liquid density:

K bar gauge bar gauge bar gauge cm cm

Calculated Results: Total available pressure drop: Non-equilibrium parameter: Subcooled mass flux: Equilibrium mass flux: All liquid discharge thru hole: !Combined mass flux: FIGURE 2.15. Spreadsheet output for Example 6: Two-phase flashing flow through a pipe.

Pipe Length (cm)

Mass Flux (kg/m2 s)

O

82,000

5

11,900

10

8,510

15

8,510

The mass flux at a pipe length of zero is equal to the discharge of liquid through a hole, represented by Eq. (2.12). At a pipe length of 10 cm, the discharge reaches equilibrium conditions and the mass flux remains constant with increasing pipe length. Example 7: Gas Discharge due to External Fire Calculate the gas relief through a relief valve for an uninsulated propane tank with 5 m2 surface area that is exposed to an external pool fire. Data: Surface area = 5 m2 = 53.8 ft2 Environment factor F = 1.0 Latent heat of vaporization hi% = 333 kj/kg (Perry and Green, 1984) 1 Btu/hr = 2.93 x 10"4 kj/s Solution: First use Eq. (2.30) to estimate the heat flux into the vessel due to the external fire: Qf = 34,500EA0 82 = (34,500)(l)(53.8)0'82 Btu/hr = 9.06 XlO5 Btu/hr = 265.4 kj/s Then from Eq. (2.31) the venting rate is Or 265.4 kj/s ™=T^= ^ '/ = 0-797 kg/s hi% 333 kj/kg This rate is higher than would be predicted by the API 520/521 method and, after an initial period, it may not be sustained. The spreadsheet solution to this problem is shown in Figure 2.16. 2.1.4. DISCUSSION

Strengths and Weaknesses Gas and liquid phase discharge calculation methods are well founded and are readily available from many standard references. However, many real releases of pressurized liquids will give rise to two-phase discharges. To handle two-phase

Example 7: Gas Discharge Due to External Fire Input Data: Surface area: Environment factor: Latent heat of vaporization: Calculated Results: Surface area: Heat Flux: Venting Rate: FIGURE 2.16. Spreadsheet output for Example 7: Gas discharge due to external fire.

discharges, the DIERS project developed methods for designing relief systems for runaway reactors or other foaming systems. Other simplified approximate methods have also been developed (e.g., Fauske and Epstein, 1987). For mixtures, the discharge models become considerably more complex and is beyond the scope of the material here. For discharge of liquid and gas mixtures through holes, pipes, and pumps, average properties of the mixture can be used. For flashing discharges through holes, if the thermodynamic path during the discharge is known, then a thermodynamic simulator might be used to determine the final phase splits and compositions. Identification and Treatment of Possible Errors Gas and liquid discharge equations contain a discharge coefficient. This can vary from 0.6 to 1.0 depending on the phase and turbulence of the discharge. The use of a single value of 0.61 for liquids may underestimate the lower velocity discharges through larger diameter holes. Similarly, the value of 1.0 may overestimate gas discharges. All discharge rates will be time dependent due to changing composition, temperature, pressure, and level upstream of the hole. Average discharge rates are case dependent and a number of intermediate calculations may be necessary to model a particular release. The mass flow rate of two-phase flashing discharges will always be bounded by pure vapor and liquid discharges. The 2-K method for both liquid and gas discharges through holes and pipes provides the capability to include entrance and exit effects, pumps and compressors, changes in elevation, changes in pipe size, pipe fittings, and pipe lengths. The discharge coefficient is inherent in the calculation and does not require an arbitrary selection. A method has also been presented to perform a complete adiabatic pipe flow calculation using the 2-K approach. This method produces a much more realistic

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answer than by representing the pipe as a hole, and requires about the same calculational effort.

Utility Gas and liquid phase discharge calculations are relatively easy to use. The DIERS methodology requires the use of commercial computer codes or experimental apparatus and is not easy to apply, needing expert knowledge.

Resources Needed No special skills are required for gas or liquid discharge calculations. Less than 1 hour with an electronic calculator or spreadsheet is usually adequate for a single calculation, with further calculations taking minutes. Two-phase flow analysis requires specialist knowledge and in most cases access to a suitable computer package, unless the simplified methods of Fauske and Epstein (1987) are employed.

Available Computer Codes Pipe flow:

AFT Fathom (Applied Flow Technology, Louisville, OH) Crane Companion (Crane ABZ, Chantilly, VA) FLO-SERIES (Engineered Software, Inc., Lacey, WA) INPLANT (Simulation Sciences Inc., Fullerton, CA) Two-phase flaw:

DEERS Klein (1986) two-phase flashing discharges (JAYCOR Inc.) SAFIRE (AIChE, New York) Spreadsheets from Fauske and Associates for two-phase flow Several integrated analysis packages also contain discharge rate simulators. These include:

ARCHIE (Environmental Protection Agency, Washington, DC) EFFECTS-2 (TNO, Apeldoorn, The Netherlands) FOCUS+ (Quest Consultants, Norman, OK) PHAST (DNV Technica, Temecula, CA) QRAWorks (PrimaTech, Columbus, OH) SAFETI (DNV, Houston, TX) SUPERCHEMS (Arthur D. Little, Cambridge, MA) TRACE (Safer Systems, Westlake Village, CA)

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2 . 2 . Flash a n d E v a p o r a t i o n 2.2.1. BACKGROUND

Purpose The purpose of flash and evaporation models is to estimate the total vapor or vapor rate that forms a cloud, for use as input to dispersion models as shown in Figure 1.3 and Figure 2.1. When a liquid is released from process equipment, several things may happen, as shown in Figure 2.17. If the liquid is stored under pressure at a temperature above its normal boiling point (superheated), it will flash partially to vapor when released to atmospheric pressure. The vapor produced may entrain a significant quantity of liquid as droplets. Some of this liquid may rainout onto the ground, and some may remain suspended as an aerosol with subsequent possible evaporation. The liquid remaining behind is likely to form a boiling pool which will continue to evaporate, resulting in additional vapor loading into the air. An example of a superheated release is a release of liquid chlorine or ammonia from a pressurized container stored at ambient temperature. Case A

Boiling Point

Leak Tank with Liquid

Ambient

Aerosol

Flash Boiling Pool Pool Spread

Case B Leak

Boiling Point

Ambient

Tank with Liquid Evaporating Pool Pool Spread FIGURE 2.17. Two common liquid-release situations dependent on the normal boiling point of the liquid. Aerosol formation is also possible for Case B if the release velocities are high.

If the liquid is not superheated, but has a high vapor pressure (volatile), then vapor emissions will arise from surface evaporation from the resulting pools. The total emission rate may be high depending on the volatility of the liquid and the total surface area of the pool. An example is a release of liquid toluene, benzene or alcohol. For liquids which exit a process as a jet, flow instabilities may cause the stream to break up into droplets before it impacts the ground. The size of the resulting droplets and the rate of air entrainment in the jet, as well as the initial temperature of the liquid, influence the evaporation rate of the droplets while in flight. The time of flight (drop trajectories) influences the fraction of the release which rains out, evaporates, or remains in the aerosol/vapor cloud (DeVaull et al., 1995). Additional references on this subject are the AIChE/CCPS Guidelines for Use of Vapor Cloud Dispersion Models (AIChE/CCPS, 1987a, 1996a), Crowl and Louvar (1990), Fthenakis (1993), the Guidance Manual for Modeling Hypothetical Accidental Releases to the Atmosphere (API, 1996), Understanding Atmospheric Dispersion of Accidental Releases (AIChE/CCPS, 1995a), and several published conference proceedings (AIChE, 1987a, 1991, 1995b). Philosophy If the liquid released is superheated, then the amount of vapor and liquid produced during flashing can be calculated from thermodynamics assuming a suituable path. An isentropic path is assumed if the fluid is accelerated during its release. A constant initial and final enthalpy are assumed if the initial and final states of the fluid are quiescent. During the flash a significant fraction of liquid may remain suspended as a fine aerosol. Some of this aerosol may eventually rain out, but the remainder will vaporize due to air entrained into the cloud. In some circumstances ground boiloff of the rainout may be so rapid that all the discharge may enter the cloud almost immediately. In other cases the quantity of liquid may be so great that it cools the ground enough to sufficiently reduce surface vaporization from the pool. The temperature of the liquid pool that remains may be significantly below the boiling point of the liquid due to evaporative cooling. For cold liquids deposited on warm substrates, a large initial boiloff is followed by lesser vaporization as the substrate cools; eventually heat input may be restricted to atmospheric convection or sunlight. Liquid pool models are primarily dominated by heat transfer effects. If the liquid released is not superheated, but relatively volatile, then the vapor loading is due to evaporation. The evaporation rate is proportional to the surface area of the pool and the vapor pressure of the liquid, and can be significant for large pools. These models are primarily dominated by mass transfer effects. Wind and solar radiation can also affect the evaporation rate.

Both empirical and pseudomechanistic models based on heat and mass transfer concepts are available and are based on the thermodynamic properties of the liquid and, for the boiling pool, on the thermal properties of the substrate (e.g., ground). Vaporization rates may vary greatly with time. The dimensions of the vapor cloud formed over the pool are often required as input to some dense gas dispersion models (Section 2.3.2); this is empirical and is not provided by most models. Applications Spilling of liquids is common during loss of containment incidents in the chemical process industries. Thus, flash and evaporation models are essential in CPQRA. The Rijnmond study (Rijnmond Public Authority, 1982) provides good examples of the use of flash and evaporation models. Wu and Schroy (1979) show how evaporation models may he applied to spills. 2.2.2. DESCRIPTION Description of Technique Flashing. The flash from a superheated liquid released to atmospheric pressure can be estimated in a number of ways. If the initial and final state of the release is quiescent, then the initial and final enthalpies are the same (this does not imply a constant enthalpy process). For pure materials, such as steam, a Mollier entropy-enthalpy diagram or a thermodynamic data table can be used. For liquids that are accelerated during the release, such as in a jet, a common approach is to assume an isentropic path. These calculations can also be performed for pure materials using a Mollier chart or tabulated thermodynamic data. The difference in numerical result between the isentropic and isenthalpic pathways is frequently small for many release situations, but this is not always guaranteed and depends on the thermodynamic behavior of the material. A standard equation for prediction of the fraction of the liquid that flashes can be derived by assuming that the sensible heat contained within the superheated liquid due to its temperature above its normal boiling point is used to vaporize a fraction of the liquid. This isenthalpic analysis leads to the following equation for the flash fraction (Crowl and Louvar, 1990), (2.36) where Cp T

is the heat capacity of the liquid, averaged over T to Th (energy/mass deg) is the initial temperature of the liquid (deg)

Tb is the atmospheric boiling point of the liquid (deg) hi% is the latent heat of vaporization of the liquid at Xb (energy/mass) Fv is the mass fraction of released liquid vaporized (unitless) TNO (1979) provide a flash equation based on the integrated heat balance of a parcel of flashing liquid. Manual treatment of multicomponent mixtures is time consuming. It is easier to use flash capabilities in commercial process simulators (e.g., PRO-n, HY-SYS, ASPEN PLUS, PD-PLUS) or their equivalents available in-house. The fraction of released liquid vaporized (Fv) is a poor predictor of the total mass of material in the vapor cloud, because of the possible presence of entrained liquid as droplets (aerosol). There are two mechanisms for the formation of aerosols: mechanical and thermal. The mechanical mechanism assumes that the liquid release occurs at high enough speeds to result in surface stress. These surface stresses cause liquid droplets to breakup into small droplets. The thermal mechanism assumes that breakup is caused by the flashing of the liquid to vapor. At low degrees of superheat, mechanical formation of aerosols dominates and droplet break-up frequently depends on the relative strength of inertial/shear forces and capillary forces on the drop. This ratio is frequently expressed as the Weber number, and the largest droplets in the jet have a diameter, ^, estimated by a Weber number stability criteria, We = p^d/a, where the effects of surface tension, a, jet velocity, u, and air density, p a , all contribute (DeVaull et al., 1995). Although widely used, the Weber number does not provide a complete answer to the problem and several alternative forms have been presented (Muralidhar et al., 1995). At higher degrees of superheat, a flashing mechanism dominates, usually producing smaller droplets. A study of jet break-up using hydrogen fluoride is provided by Tilton and Farley (1990). To date, no completely acceptable method is available for predicting aerosol formation, although many studies and several experimental tests have been completed (AIChE, 1987,1991,1995b; Fthenakis, 1993)—this area is under continuing study and development at this time. Blewitt et al. (1987) describe experiments with anhydrous hydrofluoric acid spills at the Department of Energy test site in Nevada. In the majority of their tests no liquid accumulated on the test pad although the theoretical adiabatic flash fraction was only 0.2. Wheatley (1987) summarizes seven sets of experiments in Europe and the United States on ammonia. He found that for pressurized releases of ammonia there was no rainout, but that some did occur for semirefrigerated ammonia. It is clear that when materials flash on release, at certain storage pressures and temperatures, all the released mass contributes to the cloud mass, rather than only the vapor fraction.

Aerosol entrainment has very significant effects on cloud dispersion that include • The cloud will have a larger total mass. • There will be an aerosol component (contributing to a higher cloud density). • Evaporating aerosol can reduce the temperature below the ambient atmospheric temperature (contributing to a higher cloud density). • The colder cloud temperature may cause additional condensation of atmospheric moisture (contributing to a higher cloud density). Taken together, these effects tend to significantly increase the actual density of vapor clouds formed from flashing releases. The prediction of these effects is necessary to properly initialize the dispersion models. Otherwise, the cloud's hazard potential may be grossly misrepresented. A common practice for estimating aerosol formation is to assume that the aerosol fraction is equal to some multiple of the fraction flashed, typically 1 or 2. This method has been attributed to Kletz (Lees, 1986). This approach has no fundamental basis, is probably inaccurate, but is still in common practice. Wheatley (1987) suggests this may significantly underestimate the total mass in the cloud because little rainout occurs for superheated releases with flash fractions as low as 10%. The most common means to estimate the aerosol content is to predict droplet size and from this the settling dynamics in the atmosphere. Flashing from releases of superheated liquids has been discussed by several authors including DeVaull et al. (1995), Fletcher (1982), Melhem et al. (1995), Wheatley (1986, 1987), and Woodward (1995). Also, AIChE/CCPS (1989b) contains a model that discusses the atomization due to acceleration (depressurization) as well as superheat of such releases expanding to ambient pressure. One approach is to determine the maximum droplet size from observed, critical droplet Weber numbers, typically in the range 10-20 (Emerson, 1987; Wheatley, 1987). The atmospheric settling velocity of such a droplet may be estimated from Stokes Law or turbulent settling approximation (Clift et al., 1978; Coulson et al., 1978). For example, ammonia droplets must be at least 0.3 mm for the settling velocity to reach 1 m/s. Given the elevation and orientation of the release and the jet velocity, the amount of rainout of aerosol and the resultant mass of material in the cloud can be estimated using the settling velocity. The amount of moisture in the ambient air should be included in these considerations. API (1996) states that, in general, particles of size less than 100 jum will tend to act like a mist or fog, and stay suspended for wind speeds greater than about 2 m/s if released from heights greater than 1 or 2 m. Melhem (Fthenakis, 1993) provides a model for aerosol formation based on the mechanical, or available, energy content of the liquid. The change in available

energy is the difference between the internal and expansion energy of the fluid. The rational is that the mechanical energy contained within the liquid is the energy used to cause the liquid breakup. A modified Weber number, including the available energy, is proposed. Muralidhar et al. (1995) provides a good fit for experimental HF release data using a modified Weber number. An analysis of this modified form, coupled with experimental data, leads them to conclude that for HF releases a good representation of the data is obtained if the initial droplet diameter (in meters) is approximated by D = 0.96a/w, where o is the liquid surface tension (N/m) and u is the release velocity (m/s). It is unclear at present which aerosol formation model is appropriate for risk analysis. Many models provide far too much complexity for risk analysis. At this time, most risk analysts use a model based on a fraction of the total amount flashed. For a conservative result, assume all of the aerosol evaporates. Evaporation. Evaporation from liquid spills onto land and water has received substantial attention. Land spills are better defined as many spills occur into a dike or other retention system that allows the pool size to be well estimated. Spills onto water are unbounded and calculations are more empirical. A number of useful references are available in AIChE/CCPS (1987a) and AIChE/CCPS (1995b). More detailed calculation procedures are given in Cavanaugh, et. al. (1994), Drivas (1982), Fleischer (1980), Kawamura and McKay (1987), MacKay andMatsuga (1973), Shaw and Briscoe (1978), Stiver et al. (1989), TNO (1979), and Webber (1991). Wu and Schroy (1979) handle a second component and Studer et al. (1987) include the dynamics of a deep pool. Vaporization from a pool is determined using a total energy balance on the pool, (2.37)

where m is the mass of the pool (mass) Cp is the heat capacity of the liquid (energy/mass deg) T is the temperature of the liquid in the pool (deg) t is the time (time) H is the total heat flux into the pool (energy/time) L is the heat of vaporization of the liquid (energy/mass ) m is the evaporation rate (mass/time) The heat flux, if, is the net total energy into the pool from radiation via the sun, from convection and conduction to the air, from conduction via the ground, and other possible energy sources, such as a fire.

The modeling approaches using Eq. (2.37) are divided into two classes: low and high volatility liquids. High volatility liquids are those with boiling points near or less than ambient or ground temperatures. For high volatility liquids, the vaporization rate of the pool is controlled by heat transfer from the ground (by conduction), the air (both conduction and convection), the sun (radiation), and other surrounding heat sources such as a fire or flare. The cooling of the liquid due to rapid vaporization is also important. For the high volatility case, Eq. (2.37) can be simplified by assuming steady state, resulting in (2.38) where m is the vaporization rate (mass/time), H is the total heat flux to the pool (energy/time), and L is the heat of vaporization of the pool (energy/mass). The initial stage of vaporization is usually controlled by the heat transfer from the ground. This is especially true for a spill of liquid with a normal boiling point below ambient temperature or ground temperature (i.e., boiling liquid). The heat transfer from the ground is modeled with a simple one-dimensional heat conduction equation given by (2.39) where qg is the heat flux from the ground (energy/area) ks is the thermal conductivity of the soil (energy/length deg) Tg is the temperature of the soil (deg) T is the temperature of liquid pool (deg) as is the thermal diffusivity of the soil (area/time) t is the time after spill (time) Equation (2.39) is not considered conservative. At later times, solar heat fluxes and convective heat transfer from the atmosphere become important. In case of a spill onto an insulated dike floor these fluxes may be the only energy contributions. This approach seems to work adequately for LNG, and perhaps ethane and ethylene. The higher hydrocarbons (C3 and above) require a more detailed heat transfer mechanism. This model also neglects possible water freezing effects in the ground, which can significantly alter the heat transfer behavior. For liquids having normal boiling points near or above ambient temperature, diffusional or mass transfer evaporation is the limiting mechanism. The vaporization rates for this situation are not as high as for flashing liquids or boil-

ing pools, but can be significant if the pool area is large. A typical approach is to assume a vaporization rate of the form (Matthiessen, 1986) (2.40)

where is the mass transfer evaporation rate (mass/time) is the molecular weight of the evaporating material (mass/mole) is the mass transfer coefficient (length/time) is the area of the pool (area) is the saturation vapor pressure of the liquid (force/area) is the ideal gas constant (pressure volume/mole deg) is the temperature of the liquid (abs. deg) This model assumes that the concentration of vapor in the bulk surrounding gas is much less than the saturation vapor pressure. The difficulty with Eq. (2.40) is the need to specify the mass transfer coefficient, kg. There are several procedures to estimate this quantity. The first procedure is to use a reference material and estimate the change in mass transfer coefficient due to the change in molecular weight. This results in an expression of the form (Matthiessen, 1986) (2.41) where kg° is a reference mass transfer coefficient (length/time) and M0 is a reference molecular weight (mass/mole). A typical reference substance used is water, with a mass transfer coefficient of 0.83 cm/s (Matthiessen, 1986). A correlation based on experimental data is provided by MacKay and Matsuga (1973). This correlation assumes neutral atmospheric stability and applies only for a pure component. (2.42)

where k% is the mass transfer coefficient (m/s) Nsc is the Schmidt number (unitless) u is the wind velocity 10 m off the ground (m/s) dp is the diameter of the pool (m) The Schmidt number is given by (2.43)

where JU is the absolute viscosity (force/length time), D1n is the molal diffusivity (moles/length time), and M is the molecular weight of the material (mass/mole), andD is the diffusivity (length/time). Kawamura andMacKay (1987) developed two models to estimate evaporation rates from ground pools of volatile and nonvolatile liquids—the direct evaporation and surface temperature models. Both models are based on steady-state heat balances around the pool and include solar radiation, evaporative cooling, and heat transfer from the ground. Both models agree well with experimental data, typically within 20%, with some differences being as high a 40%. The direct evaporation model is the simpler model, whereas the surface temperature model requires an iterative solution to determine the surface temperature of the evaporating pool. The direct evaporation model includes an evaporation rate due to solar radiation, given by (2.44)

where fhso[ is the evaporation rate (mass/time) Jg601 is the solar radiation (energy/area-time) M is the molecular weight (mass/mole) A is the pool area (area) Hv is the heat of vaporization of the liquid (energy/mole) Equation (2.38) is combined with Eq. (2.44) representing evaporation due to mass transfer. (2.45)

where mtot is the net evaporation rate (mass/time), /J is a parameter which is a function of vapor pressure (dimensionless), andmmass is the mass transfer evaporation rate given by Eq. (2.40) (mass/time) The parameter /J is given by (2.46) where is the dimensionless Schmidt number, given by Eq. (2.43) is the overall heat transfer coefficient of the ground (energy/area-time-deg) is the ideal gas constant (pressure volume/mole deg) is the absolute temperature (deg)

k is the mass transfer coefficient (length/time) P5^ is the saturation vapor pressure (pressure) Hw is the heat of vaporization of the liquid (energy/mole) The value of fi controls the relative contributions of solar and mass transfer evaporation. If (5 is small compared to unity, then solar evaporation dominates, whereas if fi is large, then mass transfer evaporation is dominant. Pool Spread An important parameter in all of the evaporation models is the area of the pool. If the liquid is contained within a diked or other physically bounded area, then the area of the pool is determined from these physical bounds if the spill has a large enough volume to fill the area. If the pool is unbounded, then the pool can be expected to spread out and grow in area as a function of time. The size of the pool and its spread is highly dependent on the level and roughness of the terrain surface—most models assume a level and smooth surface. One approach is to assume a constant liquid thickness throughout the pool. The pool area is then determined directly from the total volume of material. The Dow Chemical Exposure Index (AIChE, 1994) uses a constant pool depth of 1 cm. Wu and Schroy (1979) solved the equations of motion and continuity to derive an equation for the radius of the pool. This equation produces a conservative result, assuming the spill is on a flat surface, the pool growth is not constrained, and the pool growth will be radial and uniform from the point of the spill. The result is (2.47)

where r is the pool radius (length) t is the time after the spill (time) C is a constant developed from experimental data, see below (dimensionless) g is the acceleration due to gravity (length/time2) p is the density of the liquid (mass/volume) Qj^ is the volumetric spill rate after flashing (volume/time) ju is the viscosity of the liquid (mass/length time) /3 is the angle between the pool surface and the vertical axis perpendicular to the ground, see below (degrees) The Reynolds number for the pool spread is given by (2.48)

and the constant, C, has a value of 2 for a Reynolds number greater than 25 and a value of 5 for Reynolds number less than or equal to 25. The pool surface angle is given by (2.49)

(2.50) Clearly, the solution to this model is iterative since several of the parameters in Eq. (2.47) depend on a value of the pool radius, which is the desired result. A more complex model for pool spread has been developed by Webber (1991). This model is presented as a set of two coupled differential equations which models liquid spread on a flat horizontal and solid surface. The model includes gravity spread terms and flow resistance terms for both laminar and turbulent flow. Solution of this model shows that the pool diameter radius is proportional to t in the limit where gravity balances inertia, and as tl/s in the limit where gravity and laminar resistance balance. This model assumes isothermal behavior and does not include evaporation or boiling effects. Some work has been completed on pools on rough surfaces (Webber, 1991). For liquids spilled on water, the treatment is significantly different. For this case the gravity term must be modified in terms of the relative density difference between the released liquid and the water (Webber, 1991). Solutions to these equations result in an early time solution with the pool radius proportional to t1/2 when the resistance is dominated by the displaced water. The asymptotic laminar viscous regime results in a solution with the radius proportional to £1/4. The flow of water beneath the pool is most important in this regime. Logic Diagram A fundamentally based model must solve the simultaneous, time dependent, heat, mass, and momentum balances. A logic diagram is given in Figure 2.18. Theoretical Foundation Equilibrium flash models for superheated liquids are based on thermodynamic theory. However, estimates of the aerosol fraction entrained in the resultant cloud are mostly empirical or semiempirical. Most evaporation models are based on the solution of time dependent heat and mass balances. Momentum transfer is typically ignored. Pool spreading models are based primarily on the opposing forces of gravity and flow resistance and typically assume a smooth, horizontal surface.

Define Factors that Determine the Spill Rate Tank pressure Liquid height Diameter of hole Discharge coefficient Density Define Physical Properties of Materials VLE data Heat capacity Heat of vaporization Liquid density Emissivity Viscosity

Combine Input Data and Calculate Spill rate Pool growth Heat transfer Mass transfer

Results Evaporation rate versus spill time

Define Physical Conditions Ground density and thermal conductivity Ambient temperature Wind speed Solar radiation

FIGURE 2.18. Logic diagram for pool evaporation.

Input Requirements and Availability Flash models require heat capacity, latent heat of vaporization data for the pure materials, normal boiling point temperatures, as well as the initial conditions of temperature and pressure. The AIChE/DIPPR physical properties compilation (Danner and Daubert, 1985) is a useful source of temperature dependent properties. For flashing mixtures a commercial process simulator would normally be used. If droplet size is to be determined to allow estimation of settling velocity, the velocity of discharge must be calculated, along with density and surface tension of the liquid and the density of gas. Evaporation models for boiling pools require definition of the leak rate and pool area (for spills onto land), wind velocity, ambient temperature, pool temperature, ground density, specific heat, and thermal conductivity. Radiation parameters (e.g., incoming solar heat flux, pool reflectivity, and emissivity) are also needed if solar radiation is a significant factor. Most of these data are readily available, but soil characteristics are quite variable. Evaporation models for nonboiling liquids require the leak rate and pool area (for spills onto land), wind velocity, ambient temperature, pool temperature, saturation vapor pressure of the evaporating material, and a mass transfer coefficient.

Pool spreading models require the liquid viscosity and density, and possibly a turbulent friction coefficient. Values for the turbulent friction coefficient have been measured by Webber (1991). Output The output of flash models is the vapor-liquid split from a discharge of a superheated liquid. Aerosol and rainout models provide estimates of the fractions of the liquid that remain suspended within the cloud. The output of evaporation models is the time-dependent mass rate of boiling or vaporization from the pool surface. These models rarely give atmospheric vapor concentrations or cloud dimensions over the pool, which may be required as input to dense gas or other vapor cloud dispersion models. The pool spreading models provide the radius or radial spread velocity of the pool from which the total pool area and depth is determined. Simplified Approaches For evaporation cases, a simplified approach for smaller releases of liquids with normal boiling points well below ambient temperature is to assume all the liquid enters the vapor cloud, either by immediate flash plus entrainment of aerosol, or by rapid evaporation of any rainout. 2.2.3. EXAMPLEPROBLEMS

Example 8: Isenthalpic Flash Fraction Calculate the flash fraction of liquid propane flashed from 10 barg and 25°C to atmospheric pressure. Data: Heat capacity, Cp; 2.45 kj/kg K (average 231-298 K) Ambient temperature, T: 298 K (25°C) Normal boiling point, Th: 231 K (-420C) Heat of vaporization, hfg: 429 kj/kg at -42°C (Perry and Green, 1984) Solution: Using Eq. (2.36)

Experimental results suggest this may seriously underestimate the actual cloud mass, as aerosol droplets will be carried with the dispersing cloud. The spreadsheet output for this problem is shown in Figure 2.19.

Example 8: lsenthalpic Flash Fraction Input Data: Ambient temperature: Boiling point temp, at pressure: Heat capacity: Heat of vaporization: Calculated Results: [Flash fraction: FIGURE 2.19. Spreadsheet output for Example 8: lsenthalpic flash fraction.

Example 9: Boiling Pool Vaporization Calculate the vaporization rate due to heating from the ground at 10 s after an instantaneous spill of 1000 m3 of LNG on a concrete dike of 40 m radius. Data: Thermal diffusivity of soil, as: 4.16 X 10~7m2/s Thermal conductivity of soil, ks: 0.92 W/m K Temperature of liquid pool, T: 109 K (-1640C) Temperature of soil, Tg: 293 K (200C) Heat of vaporization of pool, L: 498 kj/kg at -164°C (Shaw and Briscoe, 1978) Solution: The total pool area = Jtr2 = (3.14)(40 m)2 = 5024 m2. The liquid depth in the pool is thus (1000 m3)/(5024 m2) = 0.2 m. Thus, there is more than adequate liquid in the spill to cover the containment area. The heat flux from the ground is given by Eq. (2.39):

Then, the evaporative flux, w, is given by Eq. (2.38)

The total evaporation rate for the entire pool area is

Example 9: Boiling Pool Vaporization Input Data: Thermal diffiusivity of soil: Thermal conductivity of soil: Temperature of the liquid pool: Temperature of the soil: Heat of vaporization: Time: Pool area: Calculated Results: Heat flux from ground: Evaporative flux: Total evaporation rate: FIGURE 2.20. Spreadsheet output for Example 9: Boiling pool vaporization. The spreadsheet output for this problem is shown in Figure 2.20.

Example 10: Evaporating Pool Estimate the evaporation rate for a 100 m2 pool of liquid hexane at a temperature of298 K. Data: M = 86 F a t = 1 5 l m m Hg Solution: This is considered a low volatility pool problem. Equations (2.40) to (2.42) apply. The mass transfer coefficient for the evaporation is estimated using Eq. (2.41):

Equation (2.40) is used to estimate the evaporation rate:

Clearly the evaporation rate from the boiling pool is significantly greater than the evaporation rate from the volatile liquid. The spreadsheet output for this problem is shown in Figure 2.21.

Example 10: Evaporating Pool Input Data: Area of pool: Ambient temperature: Molecular weight of liquid: Saturation vapor pressure: Calculated Results: Mass transfer coefficient: Evaporation rate: FIGURE 2.21. Spreadsheet output for Example 10: Evaporating pool.

Example 11: Pool Evaporation using Kawamura and MacKay (1987) Direct Evaporation Model Determine the evaporation rate from a 10-m diameter pool of pentane at an ambient temperature of 296 K. The pool is on wet sand and the solar energy input rate is 642 J/m2s. Ambient temperature: Wind speed at 10 meters: Physical properties of pentane: Molecular weight: Heat of vaporization: Vapor pressure at ambient temp.: Physical properties of air: Dififusivity: Kinematic viscosity: Heat transfer properties: Solar radiation: Heat transfer coefficient for pentane: Heat transfer coefficient for ground: Solution: The total area of the pool is

The Schmidt number is determined from Eq. (2.43).

The mass transfer coefficient is determined from Eq. (2.42)

The overall ground heat transfer coefficient, £/grd, is a combination of the liquid and ground heat transfer coefficients,

The evaporation rate due to mass transfer effects is given by Eq. (2.40) ^mass

The evaporation rate due to solar energy input is determined from Eq. (2.44) ^SOl

The value of /3 is determined from Eq. (2.46)

The net evaporation rate is determined from Eq. (2.45) *tot

^SOl

* m »

Example 11: Pool Evaporation using Kawamura and MacKay Direct Evaporation Model Input Data: Geometry: Diameter of pool: Physical Properties of Liquid: Molecular weight of liquid: Heat of vaporization of liquid: Vapor pressure of liquid at ambient: Physical Properties of Air: Diffusivity: Kinematic viscosity: Heat Transfer Properties: Solar input: Heat transfer coefficient of liquid: Heat transfer coefficient of ground: Ambient temperature: Wind speed at 10 meters: Calculated Results: Pool area: Schmidt number: Mass transfer coefficient: Overall ground heat transfer coefficient: Evaporation Rates: Mass transfer Solar radiation: Beta: Net evaporation rate: FIGURE 2.22. Spreadsheet output for Example 11: Pool evaporation using Kawamura and MacKay (1987) Direct evaporation model.

It is clear that both mass transfer and solar evaporation contribute to the net result. The spreadsheet implementation of this problem is given in Figure 2.22. Example 12: Pool Spread Estimate the pool radius at 100 s for a continuous spill of liquid water on an unconstrained flat surface. Assume a discharge rate of 1 liter/s (0.001 m3/s) and that the water is at ambient temperature. Data: Liquid density, p: 1000 kg/m3 Liquid viscosity, // 0.001 kg/m-s

Solution: The Wu and Schroy (1979) model presented in Eqs. (2.47) through (2.50) will be used. From Eq. (2.47)

Substituting the known values,

with r having units of meters. The Reynolds number of the spreading pool is given by Eq. (2.48)

The value of B is given by Eq. (2.50)

and the pool spread equation is determined using Eq. (2.49). The entire procedure can easily be solved using a spreadsheet. The output is shown in Figure 2.23. The solution is done iteratively using a manual trial and error procedure. The resulting pool radius is 64.1 m. If a constant pool depth of 1 cm is assumed, the resulting pool diameter is 0.56 m, significantly smaller than the Wu and Schroy (1979) result. A smaller pool diameter would result in a smaller evaporation rate. 2.2.4. DISCUSSION

Resources Needed A process engineer can perform all of the calculations in this section within a short period of time, particularly with the aid of a spreadsheet or a PC-based mathematics package.

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Example 12: Pool Spread via Wu and Schroy (1979) model Input Data: Time: Volumetric spill rate: Liquid density: Liquid viscosity: Calculated Results: Initial estimate of pool diameter: B: Beta:

Trial and Error solution!

Reynolds number: Selected value of C: Recalculated value of pool radius: FIGURE 2.23. Spreadsheet output for Example 12: Pool spread.

Available Computer Codes Wu and Schroy, Monsanto Chemical Co. (St. Louis, MO), available from the Chemical Manufacturers Association under the name of PAVE— Program to Assess Volatile Emissions. Shaw and Briscoe, Safety and Reliability Directorate (Warrington, UK) SPILLS, M. T. Fleischer, Shell Development Company (Houston, TX) Several integrated analysis packages also contain evaporation and pool models. These include:

ARCHIE (Environmental Protection Agency, Washington, DC) EFFECTS-2 (TNO, Apeldoorn, The Netherlands) HGSYSTEM (LPOOL) (Available from EPA Bulletin Board) PHAST (DNV, Houston, TX) QRAWorks (PrimaTech, Columbus, OH) TRACE (Safer Systems, Westlake Village, CA) SAFETI (DNV, Houston, TX) SUPERCHEMS (Arthur D. Little, Cambridge, MA)

2 . 3 . Dispersion Models

Accurate prediction of the atmospheric dispersion of vapors is central to CPQBA consequence estimation. Typically, the dispersion calculations provide an estimate of the area affected and the average vapor concentrations expected. The sim-

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Example 12: Pool Spread via Wu and Schroy (1979) model Input Data: Time: Volumetric spill rate: Liquid density: Liquid viscosity: Calculated Results: Initial estimate of pool diameter: B: Beta:

Trial and Error solution!

Reynolds number: Selected value of C: Recalculated value of pool radius: FIGURE 2.23. Spreadsheet output for Example 12: Pool spread.

Available Computer Codes Wu and Schroy, Monsanto Chemical Co. (St. Louis, MO), available from the Chemical Manufacturers Association under the name of PAVE— Program to Assess Volatile Emissions. Shaw and Briscoe, Safety and Reliability Directorate (Warrington, UK) SPILLS, M. T. Fleischer, Shell Development Company (Houston, TX) Several integrated analysis packages also contain evaporation and pool models. These include:

ARCHIE (Environmental Protection Agency, Washington, DC) EFFECTS-2 (TNO, Apeldoorn, The Netherlands) HGSYSTEM (LPOOL) (Available from EPA Bulletin Board) PHAST (DNV, Houston, TX) QRAWorks (PrimaTech, Columbus, OH) TRACE (Safer Systems, Westlake Village, CA) SAFETI (DNV, Houston, TX) SUPERCHEMS (Arthur D. Little, Cambridge, MA)

2 . 3 . Dispersion Models

Accurate prediction of the atmospheric dispersion of vapors is central to CPQBA consequence estimation. Typically, the dispersion calculations provide an estimate of the area affected and the average vapor concentrations expected. The sim-

plest calculations require an estimate of the release rate of the gas (or the total quantity released), the atmospheric conditions (wind speed, time of day, cloud cover), surface roughness, temperature, pressure and perhaps release diameter. More complicated models may require additional detail on the geometry, discharge mechanism, and other information on the release. Three kinds of vapor cloud behavior and three different release-time modes can be defined: Vapor Cloud Behavior: • Neutrally buoyant gas • Positively buoyant gas • Dense (or negatively) buoyant gas Duration of Release: • Instantaneous (puff) • Continuous release (plumes) • Time varying continuous The well-known Gaussian models describe the behavior of neutrally buoyant gas released in the wind direction at the wind speed. Dense gas releases will mix and be diluted with fresh air as the gas travels downwind and eventually behave as a neutrally buoyant cloud. Thus, neutrally buoyant models approximate the behavior of any vapor cloud at some distance downwind from its release. Neutrally or positively buoyant plumes and puffs have been studied for many years using Gaussian models. These studies have included especially the dispersion modeling of power station emissions and other air contaminants used for air pollution studies. Gaussian plumes are discussed in more detail in Section 2.3.1. Dense gas plumes and puffs have received more recent attention with a number of large-scale experiments and sophisticated models being developed in the past 20 years (Hanna et al., 1990; API, 1992; AIChE/CCPS, 1995b, 1995c). Dense gas plumes are discussed in more detail in Section 2.3.2. Any organization planning to undertake CPQRA must undertake dispersion calculations for both neutral/positive buoyancy and dense gases and for plume and puff releases. Which model to use is usually obvious, but there are no simple published guidelines for model selection (AIChE/CCPS, 1987a, 1995b, 1996a). Borderline cases include moderate sized, dense toxic gas releases or smaller scale dense flammable releases. These may be handled adequately by the simpler neutral buoyancy models. Most dense gas models have an automatic internal transition to neutral Gaussian dispersion when the density effects become negligible, gravity spreading is slowed down to some fraction of wind speed, or Gaussian dispersion predicts more growth (AIChE/CCPS, 1987a). Such models may be used for any release that is initially dense, even if this phase is of short duration.

However, Gaussian models applied to any dense gas release will always produce a conservative result, that is, the computed downwind distances, concentrations and area affected will be much larger than the actual result. In some cases the Gaussian result may be orders of magnitude larger. A large number of parameters affect the dispersion of gases. These include (1) atmospheric stability (2) wind speed (3) local terrain effects (4) height of the release above the ground (5) release geometry, that is, from a point, line, or area source (6) momentum of the material released, and (7) buoyancy of the material released. Atmospheric Stability Weather conditions at the time of the release have a major influence on the extent of dispersion. Some of these effects are shown in Figure 2.24, where the behavior of the plume changes markedly depending on the stability of the atmosphere. Good reviews are available in Hanna et al. (1982), Pasquill and Smith (1983), and Slade (1968). The primary factors are the wind speed and the atmospheric stability. Atmospheric stability is an estimate of the turbulent mixing; stable atmospheric conditions lead to the least amount of mixing and unstable conditions to the most. The atmospheric conditions are normally classified according to six Pasquill stability classes (denoted by the letters A through F) as shown in Table 2.8. The stability classes are correlated to wind speed and the quantity of sunlight. During the day, increased wind speed results in greater atmospheric stability, while at night the reverse is true. This is due to a change in vertical temperature profiles from day to night. Within the stability classes, A represents the least stable conditions while F represents the most stable. Stability is commonly defined in terms of the atmospheric vertical temperature gradient, but Hanna et al. (1982) suggest that a better approach be based on some direct measure of turbulence (e.g., using the Richardson number). In the former, the magnitude of the atmospheric temperature gradient is compared against the adiabatic lapse rate (ALR 0.98°C/100 m), which is the rate of temperature change with height for a parcel of dry air rising adiabatically. In neutral stability the gradient is equivalent to the ALR. Stable conditions refer to a gradient less than the ALR (ultimately to a temperature inversion) and unstable conditions to greater than the ALR. Most people use the Pasquill letter classes because they have produced satisfactory results and are easy to use. In CPQRA, wind speed and stability should be obtained from local meteorological records whenever possible. Where these stability data are not available, Pasquill's simple table (Table 2.8) permits atmospheric stability to be estimated from local sunlight and wind speed conditions.

Stable (Fanning), Stability Classes E, F

Neutral Below, Stable Above (Fumigation)

Unstable (Looping), Stability Classes A, B

Neutral (Coning), Stability Class D

Stable Below, Neutral Aloft (Lofting) FIGURE 2.24. Effect of atmospheric stability on plume dispersion. From Slade (1968).

In the absence of detailed meteorological data for a particular site, two common weather combinations (stability and wind speed) used in many CPQRA studies are D at 5 m/s (11 mph) and F at 2 m/s (4.5 mph). The first is typical for windy daytime situations and the latter for still nighttime conditions. Stability class D is typically the most frequent, while class F is the second most frequent stability condition. A wind speed of from 1.0 to 1.5 m/s is frequently used with F stability since F stability may occur at these low wind speeds. Table 2.8 can be used to select other representative weather conditions.

TABLE 2.8. Meterological Conditions Defining the Pasquill-Gifford Stability Classes (Gifford, 1976) Insolation category is determined from the table below Surface wind speed, m/s

Daytime insolation Strong

Moderate

Slight

Anytime

Nighttime conditions Thin overcast or >4/8 low cloud

A: Extremely unstable conditions B: Moderately unstable conditions C: Slightly unstable conditions

>3/8 cloudiness

Heavy overcast

D: Neutral conditions E: Slighrly stable conditions F: Moderately stable conditions

M e t h o d for estimating insolation category, w h e r e degree of cloudiness is defined as that fraction of the sky above the local apparent horizon that is covered by clouds

Degree of cloudiness 4/8 or less or any amount of high, thin clouds

Solar elevation angle >60°

Solar elevation angle <60° but >35°

Solar elevation angle <35° but >15°

Strong

Slight

Slight

Wind Speed Wind speed is significant as any emitted gas will be diluted initially by passing volumes of air. As the wind speed is increased, the material is carried downwind faster, but the material is also diluted faster by a larger quantity of air. Significant local variations in wind speed and direction are possible due to terrain effects even over distances of only a few miles. Data should be collected on-site with a dedicated meteorological tower. Wind speed and direction are often presented in the form of a wind rose. These show the wind patterns at a particular location. The wind rose is usually presented in compass point form with each arm representing the frequency of wind from that direction (i.e., a north wind blows southward).

Wind data are normally quoted on the basis of 10 m height. Wind speeds are reduced substantially within a few meters of ground due to factional effects. As many smaller discharges of dense materials remain near ground level, wind data should be corrected from 10 m to that relevant for the actual release. An equation for the wind speed profile is given for near-neutral and stable wind profiles in API (1996) and AIChE/CCPS (1996a): (2.51) where u is the wind speed (m/s) u* is the friction velocity constant which is empirically derived (m/s) k is von Karman's constant, with a value of 0.41 z is the height (m) Z0 is the surface roughness length parameter (m) L is the Monin-Obukhov length (m) More complicated expressions are available for other atmospheric stability conditions (Hanna, 1982). The friction velocity, u* is a measure of the frictional stress exerted by the ground surface on the atmospheric flow. It is equal to about 10% of the wind speed at a height of 10 m. The fraction increases as the surface roughness increases or as the boundary layer becomes more unstable. The Monin-Obukhov length, Z, is positive during stable conditions (nighttime) and is negative during unstable conditions (daytime). It is defined by (2.52) where g is the acceleration due to gravity (m/s2), T is the absolute temperature (K), and H is the surface heat flux (J/m2). Values for the length, L, are given in Table 2.9. TABLE 2.9. Relation between the Monin-Obukhov Length, L, and Other Meteorological Stability Conditions (AIChE/CCPS, 1996)

Description Very stable

Time and

Wind speed,

Monin-Obukhov

Pasquill-Gifford

weather

u

length,!/

stability class

Clear night

< 3m/s

10 m

F

Stable

i

2-A m/s

50 m

E

Neutral

Cloudy or windy

Any

> 1100 m |

D

Unstable

I

2-6 m/s

-50 m

B or C

Sunny

<3 m/s

-10 m

A

Very unstable

TABLE 2 . 1 0 . Surface Roughness Parameter, Z0, for Use w i t h Equation (2.1.51)

Terrain classification

Terrain description

Surface roughness, S0, meters

Highly urban

Centers of cities with tall buildings, very hilly or mountainous area

3-10

Urban area

Centers of towns, villages, fairly level wooded country

1-3

Residential

Area with dense but low buildings, wooded area,

1

area

industrial site without large obstacles

Large refineries

Distillation columns and other tall equipment pieces

Small refineries

Smaller equipment, over a smaller area

0.5

Cultivated land

Open area with great overgrowth, scattered houses

0.3

Flat land

Few trees, long grass, fairly level grass plains

0.1

Open water

Large expanses of water, desert flats

0.001

Sea

Calm open sea, snow covered flat, rolling land

0.0001

1

Observed values for the surface roughness, zo, are provided in Table 2.10. It is recommended that the surface roughness length for large refineries be set to 1 m and for small refineries at 0.5 m. According to Eq. (2.51), a plot of (In z) versus u should yield a straight line with intercept (In Z0) and slope u*. This presents an effective method to determine these parameters locally by measurement of wind speeds at different heights. If the second term in Eq. (2.51) containing the Monin-Obukov length is set to zero, then a simple and well-known power law relation is obtained (API, 1996): (2.53)

Equation (2.53) can be simplified further to a power law relation if the velocity is compared to a velocity at a fixed height (Hanna et al., 1982): (2.54)

where p is a power coefficient (unitless). The power coefficient is a function of atmospheric stability and surface roughness. Typical values are given in Table 2.11. Local Terrain Effects. Terrain characteristics affect the mechanical mixing of the air as it flows over the ground. Thus, the dispersion over a lake is considerably dif-

TABLE 2.11. Wind Speed Correction Factor for Equation (2.54J Pasquill-Giffbrd stability

Power law atmospheric coefficient, p —

class

Urban

Rural

A

0.15

0.07

B

0.15

0.07

C

0.20

0.10

D

0.25

0.15

E

0.40

0.35

F

0.60

0.55

ferent from the dispersion over a forest or a city of tall buildings. Most dispersion field data and tests are in flat, rural terrains. Height of the Release above the Ground. Figure 2.25 shows the effect of height on the downwind concentrations due to a release. As the release height increases, the ground concentration decreases since the resulting plume has more distance to mix with fresh air prior to contacting the ground. Note that the release height only affects the ground concentration—the concentration immediately downwind at the release height is unchanged. Release Geometry. An ideal release for Gaussian dispersion models would be from a fixed point source. Real releases are more likely to occur as a line source (from an escaping jet of material), or as an area source (from a boiling pool of liquid). Continuous Release Source Wind Direction

Plume

As Release Height Increases, this Distance Increases. The Increased Distance Leads to Greater Dispersion and a Lower Concentration at Ground Level. FIGURE 2.25. Effect of release height on ground concentration. As the release height increases, the ground concentration decreases.

Momentum of the Material Released and Buoyancy. A typical dense gas plume is shown in Figure 2.26. Dense gases may also be released from a vent stack; such releases exhibit a combination of dense and Gaussian behavior (Ooms et al., 1974), with initial plume rise due to momentum, followed by plume bendover and sinking due to dense gas effects. Far downwind from the release, due to mixing with fresh air, the plume will behave as a neutrally buoyant cloud. Since most releases are in the form of a jet rather than a plume, it is important to assess the effects of initial momentum and air entrainment on the behavior of a jet. Near its release point where the jet velocity differs greatly from the wind velocity, a jet entrains ambient air due to shear (velocity difference), grows in size, and becomes diluted. For a simple jet (neutral buoyancy), its upward momentum remains constant while its mass increases. Therefore, if vertically released, the drag forces increase as the surface area increases and eventually horizontal momentum dominates. The result is that the jet becomes bent over at a certain distance and is dominated by the wind momentum. If the jet has positive buoyancy (buoyant jet), the upward momentum will increase and the initial momentum will become negligible compared to the momentum gained due to the buoyancy. Then, the jet will behave like a plume. The rises of simple or buoyant jets, collectively called plume rises, have been studied by many researchers and their formulas can be found in Briggs (1975, 1984) or most reviews on atmospheric diffusion (including Hanna et al., 1982). For a dense or negatively buoyant jet, upward momentum will decrease as it travels. Finally it will reach a maximum height where the upward momentum disappears and then will start to descend. This descending phase is like an inverted Initial Acceleration and Dilution Wind Dominance of Internal Buoyancy

Dominance of Ambient Turbulence

Transition from Dominance of Internal Buoyancy to Dominance of Ambient Turbulence FIGURE 2.26. The initial acceleration and buoyancy of the released material affects the plume behavior. The release shown is a dense gas release exhibiting initial slumping followed by dispersion to a neutrally buoyant state. Release Source

plume. Simple formulas for the maximum rise, downwind distance to plume touchdown, and dilution at the touchdown were derived by Hoot et al. (1973) and used in the VCDM Workbook (AIChE/CCPS, 1989a). 2.3.1. NEUTRAL AND POSITIVELY BUOYANT PLUME AND PUFF MODELS

2.3.1.1. BACKGROUND Purpose. Neutral and positively buoyant plume or puff models are used to predict average concentration and time profiles of flammable or toxic materials downwind of a source based on the concept of Gaussian dispersion. Plumes refer to continuous emissions, and puffs to emissions that are short in duration compared with the travel time (time for cloud to reach location of interest) or sampling (or averaging) time (normally 10 min). Philosophy. Atmospheric diffusion is a random mixing process driven by turbulence in the atmosphere. The concentration at any point downwind of a source is well approximated by a Gaussian concentration profile in both the horizontal and vertical dimensions. Gaussian models are well established with the original work undertaken by Sutton (1953) and updated by Gifford (1976), Pasquill (1974), and Slade (1968). Applications. The U.S. EPA uses Gaussian models extensively in its prediction of atmospheric dispersion of pollutants. Gaussian models are directly applicable in risk analyses for neutral and positively buoyant emissions as the models have been validated over a wide range of emission characteristics (Hanna et al., 1982) and downwind distances (0.1 to 10 km). They may also be applied to smaller releases of dense gas emissions where the dense phase of the dispersion process is relatively short compared with the neutrally buoyant phase (e.g., smaller releases of toxic materials). Density has to be checked at the touchdown of a dense jet for applicability of Gaussian models. Gaussian models are not generally applicable to larger scale releases of dense materials since the dense gas slumps toward the ground and is not dispersed and transported as rapidly downwind as a neutrally buoyant cloud. For these types of releases a dense cloud model is required. The concentrations predicted by Gaussian models are time averages. Thus, it must be considered that local concentrations might be greater than this average. This result is important when estimating dispersion of highly toxic or flammable materials where local concentration fluctuations might have a significant impact on the consequences. The dispersion models implicitly include an averaging time through the dispersion coefficients, since the experiments to determine the coefficients were characterized by certain averaging times (AIChE/CCPS, 1996a).

AIChE/CCPS (1995c) defines the averaging time as the "user specified time interval over which the instantaneous concentration, mass release rate, or any other variable, is averaged.53 AIChE/CCPS (1995c) further states that with increased averaging time (i.e. increased event duration for an accidental release) the plume from a point source meanders back and forth over a fixed receptor. As the high concentration in an instanteous "snapshot" plume flaps back and forth, the time averaged concentration will decrease on the plume centerline, and increase on the outer fringes of the plume. At the same time, meandering will increase the intensity of concentration fluctuations everywhere across the plume, and produce longer periods of zero concentration intermittancy near the plume centerline. To estimate the probability of exceeding toxic or flammable concentration thresholds these averaging time effects must be accurately predicted. Most Pasquill-Gifford Gaussian models include an implicit 10-min averaging time. 2.3.1.2. DESCRIPTION Hanna et al. (1982), Pasquill and Smith (1983) and Crowl and Louvar (1990) provide good descriptions of plume and puff discharges. Another description, with a hazard analysis orientation, is given by TNO (1979). Plume models are better defined than puff models. This section highlights only the key features of such models; the reader should refer to the references for further modeling details. Gaussian dispersion is the most common method for estimating dispersion due to a release of vapor. The method applies only for neutrally buoyant clouds and provides an estimate of average downwind vapor concentrations. Since the concentrations predicted are time averages, it must be considered that local concentrations might be greater than this average; this result is important when estimating dispersion of highly toxic or flammable materials where local concentration fluctuations might have a significant impact on the consequences. Averaging time corrections can be applied. A complete development of the fundamental equations is presented elsewhere (Crowl and Louvar, 1990). The model begins by writing an equation for the conservation of mass of the dispersing material:

(2.55) where C is the concentration of dispersing material (mass/volume) ;j represents the summation over all three coordinates, x, y, and z (unitless); and u is the velocity of the air (length/time). The difficulty with Eq. (2.55) is that it is impossible to determine the velocity u at every point since an adequate turbulence model does not currently exist.

The solution is to rewrite the concentration and velocity in terms of an average and stochastic quantity: C = (C) + C ; u- — («;) + uj where the brackets denotes the average value and the prime denotes the stochastic, or deviation variable. It is also helpful to define an eddy diffusivity, K1 (with units of area/time) as (2.56) By substituting the stochastic equations into Eq. (2.55), taking an average, and then using Eq. (2.56), the following result is obtained: (2.57)

The problem with Eq. (2.57) is that the eddy diffusivity changes with position, time, wind velocity, prevailing atmospheric conditions, to name a few, and must be specified prior to a solution to the equation. This approach, while important theoretically, does not provide a practical framework for the solution of vapor dispersion problems. Sutton (1953) developed a solution to the above difficulty by defining dispersion coefficients, Ox, oy, andaz defined as the standard deviation of the concentrations in the downwind, crosswind, and vertical (x,y, z) directions, respectively. The dispersion coefficients are a function of atmospheric conditions and the distance downwind from the release. The stability classes are shown in Table 2.8. Pasquill (1962) recast Eq. (2.57) in terms of the dispersion coefficients, and developed a number of useful solutions based on either continuous (plume) or instantaneous (puff) releases. Gifford (1961) developed a set of correlations for the dispersion coefficients based on available data. The resulting model has become known as the Pasquill-Gifford model. Dispersion coefficients oy and oz for diffusion of Gaussian plumes are available as graphs (Figure 2.27). Predictive formulas for these are available in Hanna et al. (1982), Lees (1980), and TNO (1979) and are given in Table 2.12. Use of such formulas allow for easy application of spreadsheets. Puff emissions have different spreading characteristics from continuous plumes and different dispersion coefficients (ay and oz) are required as presented in Figure 2.28, with equations provided in Table 2.13. Experimental data for puff emissions are much more limited than for plumes and thus puff models have greater uncertainty. Also, because of a lack of data, it is often assumed oy = Ox. Hanna et al. (1982) provide some guidance on appropriate values of oy and oz based on the formula of Batchelor (1952). TNO (1979) provides more detailed guidance with formulas to predict oy and az for both continuous and puff emis-

(m) az

<*y (m)

Distance Downwind, km

a z (m)

^y (m)

Distance Downwind, km

Distance Downwind, km Distance Downwind, km FIGURE 2.27. Dispersion coefficients for a continuous release or plume. The top two graphs apply only for rural release conditions and the bottom two graphs apply only for urban release conditions.

sions. The TNO puff oy values are taken to be one half those for continuous plumes, while the oz values are unaltered. Puff Model. The puff model describes near instantaneous releases of material. The solution depends on the total quantity of material released, the atmospheric conditions, the height of the release above ground, and the distance from the release. The equation for the average concentration for this case is (Turner, 1970)

TABLE 2.12. Recommended Equations for Pasquill-Gifford Dispersion Coefficients for Plume Dispersion3 Pasquill-Gifford stability class

oy (m)

oz (m)

Rural Conditions A B C D E F Urban Conditions A-B C D E-F From AIChE/CCPS (1996). The downwind distance, x, has units of meters.

az (m)

ax = ay (m)

a

Distance Downwind, km

Distance Downwind, km

FIGURE 2.29. Dispersion coefficients for an instantaneous release or puff. These apply only for rural release conditions and are developed based o n limited data.

TABLE 2.13. Recommended Equations for Pasquill-Gifford Dispersion Coefficients for Puff Dispersion3 Stability class

oy or Ox

oz

A B C D E F * From AIChE/CCPS (1996). The distance downwind, x, and the dispersion coefficients have units of meters

(2.58)

where is the time average concentration (mass/volume) is the total mass of material released (mass) and oz are the dispersion coefficients in the x^y, and z directions (length) is the cross-wind direction (length) is the distance above the ground (length) is the release height above the ground (length) Equation (2.58) assumes dispersion from an elevated point source with no ground absorption or reaction. Here x is the downwind direction, y is the crosswind direction, and z is the height above ground level. The initial release occurs at a height H above the ground point at (xyyyz) = (0,0,0), and the center of the coordinate system remains at the center of the puff as it moves downwind. The center of the puff is located at x = ut. Notice that the wind speed does not appear explicitly in Eq. (2.58). It is implicit through the dispersion coefficients since these are a function of distance downwind from the initial release and the atmospheric stability conditions.

If the coordinate system is fixed at the release point, then Eq. (2.58) is multiplied by the factor below: (2.59) where u is the wind speed (length/time), t is the time since the release (time), and x is the downwind direction (length). The factor (x-ut) represents the width of the puff. A typical problem is to determine the downwind distance from a release to a fixed concentration. Since the downwind distance is not known, the dispersion coefficients cannot be determined. The solution for this case requires a trial and error solution (refer to the example problem at the end of this section on the puff). Another typical requirement is to determine the cloud boundary at a fixed concentration. These boundaries, or lines, are called isopleths. The locations of these are found by dividing the equation for the centerline concentration, that is, (C)(#,0,0,£), by the general ground level concentration provided by Eq. (2.58). The resulting equation is solved for y to give (2.60) where y is the off-center distance to the isopleth (length), (C)(#,0,0,£) is the downwind centerline concentration (mass/volume), and (C)(.xy,0,£) is the concentration at the isopleth. Equation (2.60) applies to ground level and elevated releases. The procedure to determine an isopleth at any specified time is 1. Specify a concentration, (C)* for the isopleth. 2. Determine the concentrations, (C)(#,0,0,£), along the jv-axis directly downwind from the release. Define the boundary of the cloud along this axis. 3. Set (C)(x,y,0,t) = (C)* in Eq. (2.60) and determine the value ofy at each centerline point determined in step 2. Plot the y values to define the isopleth using symmetry around the centerline. Plume Model. The plume model describes a continuous release of material. The solution depends on the rate of release, the atmospheric conditions, the height of the release above ground, and the distance from the release. This geometry is shown in Figure 2.29. In this case the wind is moving at a constant speed, //, in

FIGURE 2.29. Three-dimensional view of Gaussian dispersion from an elevated continuous emission source. From Turner (1970).

the ^-direction. The equation for the average concentration for this case is (Turner, 1970)

(2.61)

where {C)(x,y,z) is the average concentration (mass/volume), is the continuous release rate (mass/time) and az are the dispersion coefficients in the x, y} and z directions (length) is the wind speed (length/time) is the cross-wind direction (length) is the distance above the ground (length) is the height of the source above ground level plus plume rise (length)

Equation (2.61) assumes dispersion from an elevated point source with no ground absorption or reaction. For releases at ground level, the maximum concentration occurs at the release point. For releases above ground level, the maximum ground concentration occurs downwind along the centerline. The location of the maximum is found using, (2.62) and the maximum concentration is found from (2.63) The procedure for finding the maximum concentration and the downwind distance for the maximum is 1. Use Eq. (2.62) to determine the dispersion coefficient, az, at the maximum. 2. Use Figure 2.28 or Table 2.12 to determine the downwind location of the maximum. 3. Use Eq. (2.63) to determine the maximum concentration. Equations (2.58) and (2.61) are applicable to ideal point sources from which the vapors are released. More complex formulas for other types of sources can be found in Slade (1968). At the source, the simple point-source models have concentration values of infinity and therefore will greatly overpredict concentrations in the near field. To apply them to a real source with given dimensions, the concept of a virtual point source is introduced. The virtual source is located upwind from the real source such that if a plume were originated at the virtual source it would disperse and match the dimensions or concentration at the real source. However, to achieve this, a concentration at a centerline point directly downwind must be known. There are several ways to determine the location of the virtual source for a plume: 1. Assume that all of the dispersion coefficients become equal at the virtual source. Then, from Eq. (2.61) (2.64)

The virtual distances,^, andzv, determined using Eq. (2.64) are added to the actual downwind distance, #, to determine the dispersion coefficients, oy and O2,, for subsequent computations. 2. Assume thatxv = yv = zv. Then, from Eq. (2.61) (2.65) xv is determined from Eq. (2.65) using a trial and error approach. The effective distance downwind for subsequent calculations using Eq. (2.61) is determined from (x + xv). 3. For large downwind distances, the virtual distances will be negligible and the point source models are used directly. The puff and plume model equations can be equated to determine the downwind distance for a transition criteria from the puff to a plume. Logic Diagram. A logic diagram for the calculation of a plume or puff dispersion case using a Gaussian dispersion model is given in Figure 2.30. Theoretical Foundation. Gaussian models represent well the random nature of turbulence. The dispersion coefficients oy and az are empirically based, but results agree as well with experimental data as with other more theoretically based models. They are normally limited to predictions between 0.1 and 10 km. The lower limit allows for flow establishment and overcomes numerical problems, without introducing virtual sources, which can predict concentrations greater than 100% near the source. Input Requirements and Availability. Input requirements for Gaussian plume or puff modeling are straightforward. The source emission in terms of mass rate (plume) or mass (puff) must be defined. Wind speed and atmospheric stability must be specified. Wind speed should be appropriate for the height of the center line. The standard equation assumes a point source with no deposition, reaction, or absorption of vapors. Alternative equations exist for line, area and volume sources, with deposition, reaction or absorption, if relevant (Pasquill and Smith, 1983; Turner, 1970). Output. The output of plume models is the time averaged concentration at specific locations (in the three spatial coordinates: x>y> z) downwind of the source. For toxic or flammable clouds it may be desired to plot a particular isopleth corresponding to a concentration of interest (e.g., fixed by toxic load or flammable concentration). This isopleth usually takes the form of a skewed ellipse. It is usually easiest to computerize the model and determine the contour numerically.

DEFINITION OF SOURCE Release Rate or Total Mass Release Elevation Source Type: Point, Line, Area

LOCAL INFORMATION Wind Speed Atmospheric Stability Urban or Rural Terrain

Specify lsopleth Concentration

Puff

Puff or Plume?

Plume

Specify Time

Specify Location of Interest: x,y,z

Determine Puff Location

Calculate Centerline Concentrations

Calculate Centerline Concentrations

Determine lsopleth Location

Determine lsopleth Locations

No

Determine lsopleth Area

Determine lsopleth Area

More Spatial Steps to Define Cloud Shape?

FIGURE 2.30. Logic diagram for Gaussian dispersion.

Yes

Puff models generate time varying output, and individual puffs can be followed to consider the effects of wind changes. At every point (x, y, z) downwind from the point of release, there will be a unique concentration versus time profile. Simplified Approaches. The Pasquill-Gifford Gaussian models are a simplified approach to dispersion modeling. They are sometimes used to get a first estimate for dense gas dispersion, but the mechanisms differ substantially (Section 2.3.2). Results from one such model are shown in Figures 2.31 and 2.32 for the downwind distance to a specified concentration and the total isopleth area (all dimensionless) as a function of a scaled variable, L*. As evidenced in those figures, the use of dimensionless variables allows plotting the generic physical behavior on a single graph. By defining a scaled length, (2.66) a dimensionless downwind distance, (2.67) and a dimensionless area, (2.68)

X*. Dimensionless Downwind Distance = x/L *

then nomographs can be developed for determining the downwind distance and the total area affected at the concentration of interest, (C)*. Figures 2.31 and 2.32 can be readily curve fit with the resulting equations provided in Table 2.14.

Weather Stabilities F D B

L , Scaled Length (m), L =

/

Q \1/2 ( ^ r )

FIGURE 2.3]. Dimensionless Gaussian dispersion model output for the distance to a particular concentration. This applies for rural release only.

A*, Dimensionless Impact Area = AI(C)

Weather Stabilities F D B / Qm \ 1 / 2 L , Scaled Length (m), L = ^ 5 7 " j

FIGURE 2.32. Dimensionless Gaussian dispersion model output for the impact isopleth area. This applies for rural release only. 2.1.3.3. EXAMPLE PROBLEMS Example 13: Plume Release 1 Determine the concentration in ppm 500 m downwind from a 0.1 kg/s ground release of a gas. The gas has a molecular weight of 30. Assume a temperature of 298 K, a pressure of 1 atm, F stability, with a 2 m/s wind speed. The release occurs in a rural area. TABLE 2.14. Curve Fit Equations for Downwind Reach and Isopleth Area. These Values Are Used in the Equation Form:

Stability class

c

o

c

i

C

2

C

3

B

1.28868

0.037616

-0.0170972

0.00367183

D

2.00661

0.016541

1.42451x10^

0.0029

F

2.76837

0.0340247

0.0219798

0.00226116

B

1.35167

0.0288667

-0.0287847

0.0056558

D

1.86243

0.0239251

-0.00704844

0.00503442

F

2.75493

0.0185086

0.0326708

0.00392425

Solution. This is a continuous release of material and is modeled using Eq. (2.61) for a plume. Assuming a ground level release (JFf = 0), a location on the ground (z = 0) and a position directly downwind from the release (y = 0), then Eq. (2.61) reduces to

For a location 500 m downwind, from either Table 2.12 or Figure 2.28, for F-stability conditions, oy = 19.52 m, and O2 = 6.96 m. Substituting into the above equation

This concentration is 117 mg/m3. To convert to ppm, the following equation is used

The result is 95 ppm. This calculation is readily implemented via spreadsheet. The output is shown in Figure 2.33. The spreadsheet solution enables the user to specify a release height and any location in (x> yy z) space. Furthermore, the spreadsheet prints results for all stability classes. Note that the concentration is reduced to 8 ppm for urban conditions with F-stability. Example 14: Plume Release 2 What continuous release of gas (molecular weight of 30) is required to result in a concentration of 0.5 ppm at 300 m directly downwind on the ground? Also estimate the total area affected. Assume that the release occurs at ground level and that the atmospheric conditions are worst case. Solution. From Eq. (2.61), with H = 0, z = 0, and^ = 0,

Worst case atmospheric conditions are selected to maximize (C). This occurs with minimum dispersion coefficients and minimum wind speed, //, within a stability class. By inspection of Figure 2.27 and Table 2.8, this occurs with F-stability and u = 2 m/s. At 300 m = 0.3 km, from Figure 2.27, oy = 11.8 and

Example 2.13: Plume Release #1 Input Data: Release rate: Molecular weight: Temperature: Pressure: Release height: Distance downwind: Distance off wind: Distance above ground: Calculated Results: RURAL CONDITIONS: Assumed wind speed: Dispersion Coefficients: Sigma y: Sigma z: Downwind concentration:

A

B

Stability Classes C D E

F

PPM: URBAN CONDITIONS: Assumed wind speed: Dispersion Coefficients: Sigma y: Sigma z: Downwind concentration:

A-B

Stability Classes C D

E-F

PPM: FIGURE 2.33. Spreadsheet output for Example 13: Plume Release 1.

O2. = 4.4. The concentration in ppm is converted to kg/m3 by application of the ideal gas law. A pressure of 1 atm and temperature of 298 K are assumed.

Using a molecular weight of 30 gm/gm-mole, the above equation gives a concentration of 0.61 mg/m3. The release rate required is computed directly

This is a very small release rate and demonstrates that it is much more effective to prevent the release than to mitigate it after the fact. The spreadsheet output for this part of the example problem is shown in Figure 2.34. The spreadsheet solution enables the user to specify a release height

and any location in (x,y,z) space. Furthermore, the spreadsheet prints results for all stability classes. The area affected is determined from Figure 2.32. For this case,

From Figure 2.32,^4* = 20 and it follows that

Example 14: Plume Release #2 Input Data: Target concentration: Molecular weight: Temperature: Pressure: Release height: Distance downwind: Distance off wind: Distance above ground: Calculated Results: Target concentration: RURAL CONDITIONS:

Assumed wind speed: Dispersion Coefficients: Sigma y: Sigma z: Release rate:

A

B

Stability Classes C D E

URBAN CONDITIONS:

Assumed wind speed: Dispersion Coefficients: Sigma y: Sigma z: Release rate:

A-B

Stability Classes C D

E-F

FIGURE 2.34. Spreadsheet output for Example 14: Plume Release 2.

F

Example 15: Puff Release A gas with a molecular weight of 30 is used in a particular process. A source model study indicates that for a particular accident outcome 1.0 kg of gas will be released instantaneously. The release will occur at ground level. The plant fence line is 500 m away from the release. a. Determine the time required after the release for the center of the puff to reach the plant fence line. Assume a wind speed of 2 m/s. b. Determine the maximum concentration of the gas reached outside the fence line. c. Determine the distance the cloud must travel downwind to disperse the cloud to a maximum concentration of 0.5 ppm. Use the stability conditions of part b. d. Determine the width of the cloud, assuming a 0.5 ppm boundary, at a point 5 km directly downwind on the ground. Use the stability conditions of part b. Solution a. The time required after the release for the puff to reach the fence line is given by

This leaves very little time for emergency warning or response, b. The maximum concentration will occur at the center of the puff directly downwind from the release. This concentration is given by Eq. (2.58), assuming a release on the ground,

The stability conditions are selected to maximize (C) in the equation above. This requires dispersion coefficients of minimum value. From Figure 2.28, this occurs under F stability with a minimum wind speed of 2 m/s. At a distance downwind of 500 m, from Figure 2.28 or Table 2.13, oy = 6.1 and oz — 2.2 m. Also assume Ox = oy. Substituting into the equation above,

Assuming a pressure of 1 atm and a temperature of 298 K, this converts to 1263 ppm. The spreadsheet output for parts a and b of this problem is provided in Figure 2.35. The spreadsheet provides additional capability for specifying the release height and any downwind location. c. The concentration at the center of the puff is given by the equation above. In this case the dispersion coefficients are not known since the downwind distance is not specified. For this gas, 0.5 ppm = 0.613 mg/m3. Substituting the known quantities,

This equation is satisfied at the correct distance from the release point. The equations for the dispersion coefficients from Table 2.13 are substituted and solved for A;. The result is (0.02K 0 9 2 ) 2 (0.05.x;0-61) = 2.07 x 105. x = 12.2 km This part of the solution is readily implemented via spreadsheet, as shown in Figure 2.36. The solution is achieved by trial and error—the user must adjust the guessed downwind distance until the residual shown below the applicable stability class is zero. The spreadsheet provides additional capability to specify a release height and any downwind location, d. The width of the puff at a specified point downwind can be determined by multiplying the equation above for the centerline concentration by Eq. (2.59), to convert the coordinate system to one that remains fixed at the release point. The resulting equation is

where the quantity # - ut represents the width of the puff. At a downwind distance of 5 km, from Figure 2.29 or Table 2.13, assuming F stability, oy = Ox — 50.6 m

and

Substituting into the above equation,

oz = 9.0 m.

Example 15a,b: Puff Release This part determines the concentration downwind at a specified point (X1Y1Z) Input Data: Total release: Molecular weight: Temperature: Pressure: Release height: Distance downwind: Distance off wind: Distance above ground: Calculated Results: Assumed wind speed: Dispersion Coefficients: Sigma y: Sigma z: Downwind concentration:

A

B

Stability Classes C D E

F

PPM: Arrival time: FIGURE 2.35. Spreadsheet output for Example 15a, b: Puff release. Example 15c: Puff Release This part determines how far cloud must travel to reach a specified concentration at the center. Input Data: Total release: Molecular weight: Temperature: Pressure: Release height: Distance off wind: Distance above ground: Target Concentration: !Guessed downwind distance: Calculated Results: Target concentration: Assumed wind speed: Dispersion Coefficients: Sigma y: Sigma z: Calculated concentration:

A

B

Stability Classes C D

E

F

Residual: NOTE: Adjust GUESSED DOWNWIND DISTANCE above to zero residual in stability class of interest. FIGURE 2.36. Spreadsheet output for Example 15c: Puff release.

The puff thickness is thus 2 X 106 m = 212 m. At a wind speed of 2 m/s, the puff will take 212 m/(2 m/s) = 106 s to pass. The spreadsheet output for this part of the example problem is shown in Figure 2.37. Example 16: Plume with Isopleths Develop a spreadsheet program to determine the location of an isopleth for a plume. The spreadsheet should have specific cells for inputs for: • • • • • • • •

release rate (gm/s) release height (m) spatial increment (m) wind speed (m/s) molecular weight temperature (K) pressure (atm) isopleth concentration (ppm)

The spreadsheet output should include, at each point downwind: Example 15d: Puff Release This part determines the cloud width to a target concentration at a specified point downwind. Input Data: Total release: Molecular weight: Temperature: Pressure: Release height: Distance downwind: Distance off wind: Distance above ground: Target Concentration: Calculated Results: Target concentration:

Assumed wind speed: Dispersion Coefficients: Sigma y: Sigma z:

A

B

Stability Classes C D

Puff width: Time for puff to pass: FIGURE 2.37. Spreadsheet output for Example 15d: Puff release.

E

F

• both y and z dispersion coefficients, Ox and oz (m) • downwind centerline concentrations (ppm) • isopleth locations (m) The spreadsheet should also have cells providing the downwind distance, the total area of the plume, and the maximum width of the plume, all based on the isopleth value. Use the following case for computations, and assume worst case stability conditions: Release rate: Release height: Molecular weight: Temperature: Pressure: Isopleth cone:

50 gm/sec 0m 30 298 K 1 atm 10 ppm

Solution: The spreadsheet output is shown in Figure 2.38. Only the first page of the spreadsheet output is shown. The following notes describe the procedure: 1. The downwind distance from the release is broken up into a number of spatial increments, in this case 10-m increments. The plume result is not dependent on this selection, but the precision of the area calculation is. 2. The equations for the dispersion coefficients (ay and oz) are fixed based on stability class, in this case F-stability. These columns in the spreadsheet would need to be re-defined if a different stability class is required. 3. The dispersion coefficients are not valid at less than 100 m downwind from the release. However, they are assumed valid to produce a complete picture back to the release source. 4. The isopleth calculation is completed using Eq. (2.60) and the procedure indicated. 5. The plume is symmetric. Thus, the plume is located at ±y. 6. The plume area is determined by summing the product of the plume width times the size of each increment. 7. The maximum plume width is determined using the @MAX function in Quattro Pro (or its equivalent function in other spreadsheets). 8. For the maximum plume width and the total area, specific cell numbers must be summed for each run. Example 17: Puff with Isopleths Develop a spreadsheet program to draw isopleths for a puff. The isopleths must be drawn at a user specified time after the release. The spreadsheet should have specific inputs for

Input Data: Release Rate: Release Height: Increment: Wind Speed: Molecular Weight: Temperature: Pressure: lsopleth Cone:

Distance Crosswind m

Example 16: Plume with lsopleths

[Assumed Stability Class: F Calculated Results: Max. plume width: Total Area:

Distance Downwind, m

Dispersion Coeff. Downwind Downwind Downwind Distance Sigma Sigma Centerline Centerline Centerline lsopleth Downwind Z y Concentration Concentration Concentration Location Negative Area (PPm) (m) (m) (gm/m**3) (mg/m**3) (m"2) (m) (m)

FIGURE 2.38. Spreadsheet output for Example 16: Plume with isopleths

• total quantity released (kg) • time after release (s) • distance downwind for center of puff (m) • release height (m) • spatial increment (m) • wind speed (m/s) • molecular weight • temperature (K) • pressure (atm) • isopleth concentration (ppm) The spreadsheet output should include, at each point downwind: • • • •

downwind location, or location with respect to puff center. bothy and z dispersion coefficients, oy and oz (m) downwind centerline concentrations (ppm) isopleth locations (m)

Use the following case for your computations: Release mass: Release height: Molecular weight: Temperature: Pressure: Isopleth cone: Weather stability: Wind speed:

50 kg 0m 30 298 K 1 atm 1.0 ppm F 2 m/s

1. At what time does the puff reach its maximum width? 2. At what time and at what distance downwind does the puff dissipate? Solution: The most direct approach is to use a coordinate system that is fixed on the ground at the release point. Thus, Eq. (2.59) is used in conjunction with Eq. (2.58). The equations for the dispersion coefficients for a puff are obtained from Table 2.13. In order to reduce the number of spreadsheet cells, a spreadsheet grid that moves with the center of the puff is used. In this case 50 cells were specified on either side of the center of the puff. The procedure for the spreadsheet solution is 1. 2. 3. 4. 5. 6. 7.

Specify a time (entered by user). Compute #, the downwind distance, at each cell in grid. Compute the y and z dispersion coefficients (py and az). Compute the centerline concentration at each grid point using Eq. (2.58) Compute the isopleth location at each grid point using Eq. (2.60). Compute both the + and - isopleth to define both sides of puff. Plot the results.

The resulting spreadsheet output is shown in Figure 2.39. Only the first page of the spreadsheet output is shown. To determine the maximum plume width, a trial and error approach is used. Specified times are entered into the spreadsheet and the maximum width is determined manually from the output. The results are shown in Figure 2.40, which shows the puff width as a function of time. Note that the puff increases in width to a maximum of about 760 m, then decreases in size. The maximum width occurs at about t = 13,000 sec, when the puff is 6.5 km downwind from the release. The time for the puff to dissipate is determined by increasing the time until the isopleth disappears. This occurs at about 22,800 s when the puff is 45.5 km downwind.

2.3.1.4. DISCUSSION Strengths and Weaknesses The Gaussian dispersion model has several strengths. The methodology is well defined and well validated. It is suitable for manual calculation, is readily computerized on a personal computer, or is available as standard software packages. Its main weaknesses are that it does not accurately simulate dense gas discharges, validation is limited from 0.1 to 10 km, and puff models are less well established than plume models. The predictions relate to 10 min averages (equivalent to 10 min sampling times). While this may be adequate for most emissions of chronic toxicity, it can underestimate distances to the lower flammable limit where instantaneous concentrations are of interest. More discussion will follow.

Example 17: Puff Model Input Data: Time: Wind Speed: Total Release: Step Increment: Release Height: No. of Increments: Molecular Weight: Temperature: Pressure: lsopleth Cone: !Assumes F-stability Calculated Results: Distance Downwind: lsopleth Cone: Max. Puff Width:

Distance Downwind, m

Distance from Distance Dispersion Coeff. Centerline Center Downwind Sigma y Sigma z Cone. +lsopleth -lsopleth (m) (m) (m) mg/mA3 (m) (m) (m)

FIGURE 2.39 Spreadsheet output for Example 17: Puff with isopleths.

Puff Width (m)

Time after release (s) FIGURE 2.40. Puff width as a function of time for Example 17

Identification and Treatment of Possible Errors Benarie (1987) discusses errors in Gaussian and other atmospheric dispersion models for neutral or positive buoyancy releases. He highlights the randomness of atmospheric transport processes and the importance of averaging time. The American Meteorological Society (1978) has stated that the precision of models based on observation is closely tied to the scatter of that data. At present the scatter of meteorological data is irreducible and dispersion estimates can approximate this degree of scatter only in the most ideal circumstances. As vapors disperse, mixing occurs as turbulent eddies of a spectrum of sizes interact with the plume. Thus, portions of the plume may have local concentrations that deviate above and below the average concentrations estimated by models. In addition, major wind direction shifts may cause a dispersing plume to change direction or meander. While such changes do not have a major effect on the hazard area of the plume relative to its centerline, they do matter with respect to the specific area impacted. Gifford (1975) attempts to account for the effects of averaging time through the following relation: (2.69) (2.70) where is the factor to account for the effect of averaging time (unitless) is the averaging time (time) is the averaging time for the standard Pasquill-Gifford curves, i.e., 600 s is the dispersion coefficient averaged over ta (length) is the standard Pasquill-Gifford dispersion coefficient (length)

Based on limited experimental data, Gifford suggests q = 0.25 to 0.3 for £a of 1 to 100 hr and 0.2 for short averaging times (e.g., 3 min). Because of lack of data, most models use 0.2 for even shorter averaging times. The lower limit of Fy is the value for instantaneous release which TNO (1979) assumes 0.5 (this means their assumption of instantaneous release is about 19 s). Many dispersion cases will give rise to effect zones using Gaussian models of less than 100 m. As this is outside the validation limits (0.1-10 km), such predictions should be treated with caution. Equations (2.69) and (2.70) are essentially identical to the averaging time expression provided by AIChE/CCPS (1996a) (2.71) where (C) is the average gas concentration (mass/volume) and t is the respective averaging time (time). A more detailed discussion of averaging time is provided in AIChE/CCPS (1995c, 1996a).

Utility Gaussian models are relatively easy to use, but plume dispersion is not a simple topic. A wide range of calculation options is available (plume and puff discharges; absorption or reflection at ground level; deposition of material; point, line, and area sources), thus care is required in selecting the right equations for the dispersion parameters and for predicting concentration. Wind velocity should be the average over the plume depth. Resources Needed Dispersion modeling requires some experience if meaningful results are to be obtained. Calculations are quick to perform on a calculator or personal computer. A single dispersion calculation might take 1-2 hr to analyze by an experienced person on a calculator or spreadsheet assuming all meteorological data are available. Collection and analysis of such data may be time consuming (several days depending on availability). Available Computer Codes There are many air pollution models available. Guidelines for Vapor Cloud Dispersion Models (AIChE/CCPS, 1987a; 1996a) reviews these and other computer codes and compares their predictions.

2.3.2. DENSE GAS DISPERSION

2.3.2.1. BACKGROUND Purpose A dense gas is defined as any gas whose density is greater than the density of the ambient air through which it is being dispersed. This result can be due to a gas with a molecular weight greater than that of air, or a gas with a low temperature due to auto-refrigeration during release, or other processes. The importance of dense gas dispersion has been recognized for some time. Early field experiments (Koopman et al., 1984; Puttock et al., 1982; Van Ulden, 1974) have confirmed that the mechanisms of dense gas dispersion differ markedly from neutrally buoyant clouds. When dense gases are initially released, these gases slump toward the ground and move both upwind and downwind. Furthermore, the mechanisms for mixing with air are completely different from neutrally buoyant releases. Reviews of dense gas dispersion and modeling are given by AIChE/CCPS (1987a, 1995b, 1996a), Goyal and Al-Jurashi (1990), Blackmore et al. (1982), Britter andMcQuaid (1988), Havens (1987), Lees (1986,1996), Raman (1986), and Wheatley and Webber (1984). Philosophy Three distinct modeling approaches have been attempted for dense gas dispersion: mathematical, dimensional and physical. The most common mathematical approach has been the box model (also known as top-hat or slab model), which estimates overall features of the cloud such as mean radius, mean height, and mean cloud temperature without calculating detailed features of the cloud in any spatial dimension. Some models of this class impose a Gaussian distribution equating to the average condition. The other form of mathematical model is the more rigorous computational fluid dynamics (CFD) approach that solves the complete three-dimensional conservation equations. These methods have been applied with encouraging results (Britter, 1995; Lee et al. 1995). CFD solves approximations to the fundamental equations, with the approximations being principally contained within the turbulence models—the usual approach is to use the K-e theory. The CFD model is typically used to predict the wind velocity fields, with the results coupled to a more traditional dense gas model to obtain the concentration profiles (Lee et al., 1995). The problem with this approach is that substantial definition of the problem is required in order to start the CFD computation. This includes detailed initial wind speeds, terrain heights, structures, temperatures, etc. in 3-D space. The method requires moderate computer resources.

The dimensional analysis method has been used succesfully by Britter and McQuaid (1988) to provide a simple but effective correlation for modelling dense gas releases. The procedure examines the fundamental equations and, using dimensional analysis, reduces the problem to a set of dimensionless groups. Data from actual field tests are then correlated using these dimensionless groups to develop a nomograph describing dense gas release. A detailed comparison of model predictions with field test data (Hanna et al., 1993) shows that the Britter-McQuaid method produces remarkably good results, with the predictions closely matching test results and outperforming many more complex models. However, this result is expected since the Britter-McQuaid method is based on the test data in the first place. Physical (scale) models employing wind tunnels or water channels have been used for dense gas dispersion simulation, especially for situations with obstructions or irregular terrain. Exact similarity in all scales and the re-creation of atmospheric stability and velocity distributions are not possible—very low air velocities are required to match large scale results. Havens et al (1995) attempted to use a 100-1 scale approach in conjunction with a finite element model. They found that measurements from such flows cannot be scaled to field conditions accurately because of the relative importance of the molecular diffusion contribution at model scale. The use of scale models is not a common risk assessment tool in CPQBA and readers are directed to additional reviews by Meroney (1982), and Duijm et al. (1985). Applications Dense gas mathematical models are widely employed to simulate the dispersion of flammable and toxic dense gas clouds. Early published examples of applications include models used in the demonstration risk assessments for Canvey Island (Health & Safety Executive, 1978, 1981) and the Rijnmond Port Area (Rijnmond Public Authority, 1982), and required in the Department of Transport LNG Federal Safety Standards (Department of Transportation, 1980). While most dense gas models currently in use are based on specialist computer codes, equally good and versatile models are publicly available (e.g., DEGADIS, SLAB). The underlying dispersion mechanisms and necessary validation are more complex than any other area of consequence modeling. For prediction of toxic consequences, two common approaches are the use of either a specific toxic concentration or a toxic dose criterion. Toxic dose is determined as toxic gas concentration for the duration of exposure to determine an effect based on specified probit models (Chapter 4). With flammable releases, the mass of flammable material, as well as the extent of the flammable zone, is important in determining the unconfined vapor

cloud explosion and flash fire potential. The use of the LFL (lower flammable limit) or Vi LFL in determining these parameters is a subject of debate. Some indications of the issues involved are provided below. Most flammable releases do not follow neutral, or Gaussian, behavior since they are almost always heavier than air. As the release continues to mix with air the Gaussian model will eventually apply, but the cloud will no longer be flammable. The basis for specification of Vi LFL (e.g., Department of Transportation, 1980) is to allow for variations in instantaneous cloud concentrations. Pasquill-Gifford Gaussian models have an implicit 10 min averaging time. Benarie (1987) notes that transient concentrations may differ from the average predicted by a factor up to 4 at the 5% confidence level. A problem with using Vi LFL is that hazard zones will be consistently overpredicted; based on the Canvey Study (Health & Safety Executive, 1981), this overprediction is typically about 15-20% in distance. While individual flammable pockets may ignite at the Vi LFL distance, there is a probability that the whole cloud will not. The mass of flammable material in the cloud (i.e., above LFL concentration) based on the Vi LFL isopleth will be overestimated by as much as a factor of two. Consider, for example, a puff release. The mass of flammable material in the cloud is constant (as no transport out of the cloud is permitted), although the total cloud size and mass increase due to dilution. At the Vi LFL concentration not all the mass can be flammable, and the total dimension for the flammable portion of the cloud must be overestimated. Thus flash fire and damage zones from vapor cloud explosions will be consistently overpredicted. However, the energy available in a flammable cloud is based on the average concentration, so the average concentration is the appropriate criterion for the estimation of vapor cloud explosion impacts. Van Buijtenen (1980) developed a number of equations for the amount of gas in the explosive region of a vapor cloud or plume. It was found that, for an instantaneous release, a large fraction of the total amount release (50% for methane) can be in the explosive region, irrespective of source strength and meteorological conditions. For a continuous source, the amount in the explosive region is strongly dependent on source strength and meteorological conditions. Spicer (1995,1996) used the DEGADIS heavy gas computer code to model propane releases. It was determined that cloud concentrations as high as 90% of the LFL could provide "sustained flames.53 Most releases of flammables occur as high pressure or liquefied gas releases. For these types of releases, the primary dilution mechanism is due to entrainment of air by shear as the release jets into the surrounding air. An equation for the

dilution of a turbulent, free jet from a rounded hole is given by Perry and Green (1984) (2.72)

where q is the total jet volumetric flow rate at distance x (volume/time) q0 is the initial jet volumetric flow rate (volume/time) x is the distance from the release point (length) D0 is the opening diameter (length) Equation (2.72) applies only for 7 < (x/D0) < 100. Equation (2.72) shows that entrainment can be substantial. For a 1-cm diameter jet, the total volumetric flow at 1 meter above the discharge will be 32 times the initial volumetric flow. Thus, the initial dilution with air by the jet may reduce the concentrations below the LFL. However, flammable material will accumulate adjacent to the jet eventually resulting in concentrations high enough for ignition. Equation (2.72) is also useful for determining the initial release concentration as an initial starting point for a detailed dense gas dispersion model. Different risk analysts recommend a number of procedures for determining the flammable mass via dispersion: 1. For flammable materials consider four concentrations: UFL, LFL, V2 LFL, 1A LFL. For explosive materials, consider the LFL and 100% concentrations. 2. If the averaging time for the dispersion model is unadjusted, that is, 10 min for Gaussian dispersion, then use Vi LFL as the flash limit. If the averaging time is 20 sec, use the LFL for the flash limit. 2.3.2.2. DESCRIPTION Description of Techniques Detailed descriptions of the mechanisms of dense gas dispersion and the specific implementations for a wide variety of mathematical models are given in AIChE/CCPS (1987a, 1995a,b, 1996a). This is not reproduced here in any detail. The transitional phases in a heavy gas dispersion situation are given in Figure 2.26. Following a typical puff release, a cloud having similar vertical and horizontal dimensions (near the source) may form. The dense cloud slumps under the influence of gravity increasing its diameter and reducing its height. Considerable initial dilution occurs due to the gravity-driven intrusion of the cloud into the ambient air. Subsequently the cloud height increases due to further entrainment of air across both the vertical and horizontal interface. After sufficient dilution

occurs, normal atmospheric turbulence predominates over gravitational forces and typical Gaussian dispersion characteristics are exhibited. Raman (1986) lists typical box model characteristics. The vapor cloud is treated as a single cylinder or box containing vapor at a uniform concentration. Air mixes with the box as it disperses downwind. Box width increases as it spreads due to gravity slumping. The usual assumptions are • The vapor cloud disperses over flat terrain. • The ground has constant roughness. • There are no obstructions. • Local concentration fluctuations are ignored. • The treatment of chemical reactions or deposition is limited. The use ofK-e theory models can relax several of these assumptions. However, validation data are not sufficiently available to verify the models and some numerical problems (pseudodispersion and concentration discontinuities) are unsolved. The Britter and McQuaid (1988) model was developed by performing a demensional analysis and correlating existing data on dense cloud dispersion. The model is best suited for instantaneous or continuous ground level area or volume source releases of dense gases. Atmospheric stability was found to have little effect on the results and is not a part of the model. Most of the data came from dispersion tests in remote, rural areas, on mostly flat terrain. Thus, the results would not be applicable to urban areas, or highly mountainous areas. The model requires a specification of the initial cloud volume, the initial plume volume flux, the duration of release, and the initial gas density. Also required is the wind speed at a height of 10 m, the distance downwind, and the ambient gas density. The first step is to determine if the dense gas model is applicable. If an initial buoyancy is defined as (2.73)

where gQ is the initial buoyancy factor (length/time2) g is the acceleration due to gravity (length/time2) p 0 is the initial density of released material (mass/volume) p a is the density of ambient air (mass/volume) A characteristic source dimension can also be defined dependent on the type of release. For continuous releases, (2.74)

where Dc is the characteristic source dimension for continuous releases of dense gases (length), qQ is the initial plume volume flux for dense gas dispersion (volume/time), and u is the wind speed (length/time) For instantaneous releases, the characteristic source dimension is defined as: (2.75) where D1 is the characterisitic source dimension for instantaneous releases of dense gases (length), V0 is the initial volume of released dense gas material (length3) The criteria for a sufficiently dense cloud to require a dense cloud representation are, for continuous releases, (2.76) and for instantaneous releases, (2.77) If these criteria are satisfied, then Figures 2.41 and 2.42 are used to estimate the downwind concentrations. Table 2.15 provides equations for the correlations in the figures. The criteria for determining whether the release is continuous or instantaneous is calculated using the following group: (2.78)

where Rd is the release duration (time), and A: is the downwind distance in dimensional space (length). If the group has a value greater than or equal to 2.5, then the dense gas release is considered continuous. If the group value is less than or equal to 0.6, then the release is considered instantaneous. If the value lies in-between, then the concentrations are calculated using both continuous and instantaneous models and the minimum concentration result is selected. The Britter and McQuaid model is not appropriate for jets or two-phase plume releases due to the entrainment effect noted earlier. Logic Diagram A brief logic diagram showing the inputs, calculation sequence and outputs from a dense gas model is shown in Figure 2.43.

c m /c 0 X

(q o / u ) 1 / 2 Ful-Scale Data Rego in Passvi e Limit

FIGURE 2.41. Britter-McQuaid dimensional correlation for dispersion of dense cloud plumes. Cm/C0

X v

o Ful-Scale Data Rego in Passvie Limit

FIGURE 2.42. Britter-McQuaid dimensional correlation for dispersion of dense cloud puffs.

TABLE 2.15. Equations Used to Approximate the Curves in the Britter-McQuaid Correlations Provided in Figure 2.41 for Plumes Equation for

Valid range for Concentration ration

CJC0

. =loglo , r x i

^

L( 9 o/«)-J

TABLE 2.16. Equations Used to approximate the Curves in the Britter-McQuaid Correlations Provided in Figure 2.42 for Puffs Valid range for Concentration ration

CJC0

Equation for

fi- 1Og 10 [^]

Theoretical Foundation Neutral buoyancy Gaussian models do not employ correct mechanisms, but, fortuitously, results for many small to medium sized spills are not grossly inaccurate (except for F stability where transition to passive phase takes place further downwind) . As the mechanism is incorrect this generalization may not always be true. Box models employ a simpler theoretical basis than K-e theory models, however, the major mechanisms of gravity slumping, air entrainment, and thermody-

LOCAL INFORMATION

Input Data

CHEMICAL INFORMATION Physical properties: Molecular weight, boiling point, heat capacity, latent heat, LFL1 toxic cone, or toxic dose.

Wind speed Atmospheric stability Surface roughness

Source term calculation (sometimes in the dense model package)

ESTIMATE CLOUD SIZE OR PLUME GENERATION RATE Hole size Phase of release (gas, liquid, 2-phase) Flash fraction Aerosol and ralnout fractions Release duration Pool boiloff (from rainout fraction) Cloud Initial dilution Cloud geometry

RUN DENSE GAS MODEL PACKAGE

Dispersion Calculation

Calculation for initial gravity slumping Entrainment of air Heat transfer to/from cloud Transition to Gaussian dispersion

OUTPUT FROM DENSE GAS MODEL Concentration - distance - time results

FIGURE 2.43. Logic diagram for dense clouds.

namic processes are included. In terms of validation, box models have received substantial attention and good results are claimed by the authors. K-e theory models allow restrictive assumptions of flat terrain and no obstructions to be relaxed, but there are numerical problems and there is a lack of relevant validation data for these cases. Computational fluid dynamics (CFD) is able to account for changes in terrain, buildings, and other irregularities. However, the solution includes simplifi-

cations to the Navier-Stokes equations and requires detailed specification of the initial conditions. The Britter-McQuaid model is a dimensional analysis technique, with a correlation developed from experimental data. However, the model is based only on data taken in flat, rural terrain, and can only be applied to these types of releases. The model is only based on the conditions of the test data and is unable to account for the effects of parameters such as release height, ground roughness, wind speed profiles, etc. Input Requirements and Availability Given the large number and variety of dense gas models, it is not possible to generalize on model input requirements. The model itself or one of the reviews noted above should be consulted for specific details. More detailed dense gas models require additional inputs. These could include ground roughness, physical properties of the spilled material (molecular weight, atmospheric boiling temperature, latent heat of vaporization), wind speed profiles, and the physical properties of the ground (heat capacity, porosity, thermal conductivity). Less straightforward is the definition of the source term: the initial conditions of cloud mass, temperature, concentration, and dimensions (height, width). This is a function of the discharge type (spill or pressurized jet), the rate and duration (or mass if a puff) of release, temperature before and after any flash, the flash fraction, aerosol/fog formation, and initial dilution. Some models include source term models which may not be apparent to the user. Output As with input requirements, specific model output varies greatly. Broadly, the following output would be considered essential for a full analysis: • source term summary (if calculated by model): jet discharge or pool boiloff rate, temperature, aerosol fraction, rainout, initial density, initial cloud dimensions, time variance • cloud dispersion information: cloud radius and height (or other dimensions as appropriate), density, temperature, concentration, time history at a particular location, distance to specified concentrations. • special information: terrain effects, chemical reaction or deposition, toxic load at particular locations, mass of flammable material in cloud. Simplified Approaches Some users employ Gaussian neutral buoyancy models for dense gas releases; however, the mechanisms are incorrect and certain weather conditions are poorly modeled. In the second Canvey Report (Health & Safety Executive, 1981) a

power law correlation of the form R = k2M°A (where R = downwind distance to the lower flammable limit, M = mass of puff emission, and k = constant dependent on material and weather conditions) was suggested for large propane and butane puff emissions as an equation of best fit based on many runs of the DENZ dense gas package. Considine and Grint (1984) have extended this approach substantially with the constant and the power in the above power law expression derived for pressurized and refrigerated releases of propane and butane, over land and onto sea, for instantaneous or continuous releases. The Britter-McQuaid (1988) model is reasonably simple to apply, and produces results which appear to be as good as more sophisticated models. However, detailed specifications on the geometry of the release are required. Furthermore, the model provides only an estimate of the concentration at a fixed point immediately downwind from the release. It does not provide concentrations at any other location, or the area affected. Finally, the model applies only to ground releases. 2.3.2.3. EXAMPLE PROBLEM Example 18: Britter and McQuaid Model Britter and McQuaid (1988) report on the Burro LNG dispersion tests. Compute the distance downwind from the following LNG release to obtain a concentration equal to the lower flammability limit (LFL) of 5% vapor concentration by volume. Assume ambient conditions of 298 K and 1 arm. The following data are available: Spill rate of liquid: 0.23 m3/s Spill duration (Rd): 174 s Windspeed at 10 m above ground (u): 10.9 m/s LNG density: 425.6 kg/m3 LNG vapor density at boiling point of-162°C: 1.76 kg/m3 Solution: The volumetric discharge rate is given by

The ambient air density is computed from the ideal gas law and gives a result of 1.22 kg/m3. Thus, from Eq. (2.73)

STEP 1: Determine if the release is considered continuous or instantaneous. For this case Eq. (2.78) applies and the quantity must be greater than 2.5 for a continuous release. Substituting the required numbers,

and it follows that for a continuous release,* < 758 m. The final distance must be less than this. STEP 2: Determine if a dense cloud model applies. For this case Eqs. (2.74) and (2.76) apply. Substituting the appropriate numbers,

it is clear that the dense cloud model applies. STEP 3: Adjust the concentration for a nonisothermal release. Britter and MacQuaid (1988) provide an adjustment to the concentration to account for nonisothermal release of the vapor. If the original concentration is C*, then the effective concentration is given by

where Tz is the ambient temperature and T0 is the source temperature, both in absolute temperature. For our required concentration of 0.05, the above equation gives an effective concentration of 0.019. STEP 4: Compute the dimensionless groups for Figure 2.41.

and

STEP 5: Apply Figure 2.41 to determine the downwind distance. The initial concentration of gas, C0, is essentially pure LNG. Thus, C0 = 1.0 and it follows that CJC0 = 0.019. From Figure 2.41,

and it follows that A; = (2.25 m)(163) = 367 m. This compares to an experimentally determined distance of 200 m. This demonstrates that dense gas dispersion estimates can easily be off by a factor of 2. A Gaussian plume model assuming worst case weather conditions (F stability, 2 m/s wind speed) predicts a downwind distance of 14 km. Clearly the dense cloud model provides a much better result. A spreadsheet implementing the Britter-McQuaid method is shown in Figure 2.44. Only the first page of the spreadsheet output is provided. The extensive tables used to interpolate the Britter-McQuaid values are not shown. 2.3.2.4. DISCUSSION Strengths and Weaknesses The major strength of most of the dense gas models is their rigorous inclusion of the important mechanisms of gravity slumping, air entrainment, and heat transfer processes. Their primary weakness is related to source term estimation and the high level of skill required of the user. Automatic source term generation models Example 18: Britter - McQuaid Model Input Data: Spill rate: Spill duration: Windspeed at 10 m: Density of liquid: Vapor density at boiling point: Ambient Temperature: Ambient Pressure: Source Temperature: Required concentration: Calculated Results: Ambient air density: Initial buoyancy: Volumetric discharge rate: Char, source dimension: Target concentration: Computed value of Britter-McQuaid X-axis dimensional group: Interpolated value of Britter-McQuaid y-axis dimensional group: [Distance downwind: Continuous release criteria: Dense gas criteria:

Must be greater than 2.5 Must be greater than 0.15

Figure 2.44. Spreadsheet output for Example 18: Britter-McQuaid model.

can improve this situation substantially. Some validation of the models has been provided (Hanna et al., 1990; API, 1992). Identification and Treatment of Possible Errors Errors can arise from four broad sources. Important mechanisms of dense gas dispersion may be omitted for a particular release scenario; model coefficients fitted to limited validation data may be incorrect; the source term may be incorrectly defined; or model assumptions of flat terrain and uniform roughness may be invalid. Errors due to omitted mechanisms or incorrect coefficients can be checked only by reviewing model validation. It is also important to note that few validation data exist for certain release types (e.g., large-scale sudden releases of liquids onto land especially for long distance toxic impacts). Where some doubt exists, users should undertake a range of sensitivity runs to determine the significance of the uncertainty. Utility Some of the computer codes are relatively easy to run, but this can be deceptive. Those models having automatic source term generation are the most straightforward to run, but there may be limits to the cases that may be modeled. Models without source term generation impose a greater load on the user, and some information requested such as initial dilution or initial cloud dimensions may be very difficult to specify. Resources Needed Dense gas dispersion models require a skilled user. In order to obtain such skills the minimum requirements would be extensive reading of dense gas model literature reviews, examination of dense gas trial results, and several practice exercises. Unskilled use of dense gas models can lead to misleading results. One purpose of the CCPS Guidelines for Use of Vapor Cloud Dispersion Models (AIChE/CCPS, 1987a; 1989a; 1996a) is to offer an introduction to dense gas model use. A dense gas computer model is a prerequisite for dispersion analysis. It is possible to develop a model, however, this is a major task due to the number of mechanisms involved and the amount of validation required. One to five man years is required to develop a full capability, adequately validated dense gas model. Most users will obtain a publicly or commercially available model. These can run on personal computers or mainframes. Available Computer Codes AIChE/CCPS (1987a; 1996a) reviews dense and neutral gas codes and provide contact addresses for all of these. The latest edition of the Chemical Engineering Progress software review should be consulted.

3

E x p l o s i o n s

a n d

F i r e s

The objective of this chapter is to review the types of models available for estimation of the consequences of accidental explosion and fire incident outcomes. More detailed and complete information on this subject is provided in Baker et al. (1983), AIChE/CCPS (1994), Lees (1986,1996), andBjerketvedt et al. (1997). A number of important definitions related to fires and explosions follow. Deflagration: A propagating chemical reaction of a substance in which the reaction or propagating front is limited by both molecular and turbulent transport and advances into the unreacted substance at less than the sonic velocity in the unreacted material. Resulting overpressures from a deflagration are typically no more than one or two atmospheres—these are significant enough to cause substantial damage to surrounding structures. Detonation: A propagating chemical reaction of a substance in which the reaction or propagating front is limited only by the rate of reaction and advances into the unreacted substance at or greater than the sonic velocity in the unreacted material at its initial temperature and pressure. Detonations are capable of producing much more damage than deflagrations; overpressures from a detonation can be several hundred psig in value. This, however, is a complex issue and depends on many factors, including geometry, impulse duration, confinement, etc. Flammable Limits: The minimum (lower flammable limit, LFL) and maximum (upper flammable limit, UFL) concentrations of vapor in air that will propagate a flame. Flashpoint Temperature: The temperature of a liquid at which the liquid is capable of producing enough flammable vapor to flash momentarily. There are many ASTM methods, including D56-87, D92-90, D93-90, and

D3828-87 (ASTM, 1992) to determine flashpoint temperatures. The methods are grouped according to two types: open and closed cup. The closed cup methods typically produce values which are somewhat lower. Explosion: Several definitions are available for the word "explosion." AIChE/CCPS (1994) defines an explosion as "a release of energy that causes a blast.55 A "blast55 is subsequently defined as "a transient change in the gas density, pressure, and velocity of the air surrounding an explosion point.55 Crowl and Louvar (1990) define an explosion as "a rapid expansion of gases resulting in a rapidly moving pressure or shock wave.55 NFPA 69 (NFPA, 1986) defines an explosion as "the bursting or rupture of an enclosure or a container due to the development of internal pressure.55 An explosion can be thought of as a rapid release of a high-pressure gas into the environment. This release must be rapid enough that the energy is dissipated as a pressure or shock wave. Explosions can arise from strictly physical phenomena such as the catastrophic rupture of a pressurized gas container or from a chemical reaction such as the combustion of a flammable gas in air. These latter reactions can occur within buildings or vessels or in the open in potentially congested areas. Many types of outcomes are possible for a release. This includes vapor cloud explosions (VCE) (Section 3.1), flash fires (Section 3.2), physical explosions (Section 3.3), boiling liquid expanding vapor explosions (BLEVE) and fireballs (Section 3.4), confined explosions (Section 3.5), and pool fires and jet fires (Section 3.6). Figure 3.1 provides a basis for logically describing accidental explosion and fire scenarios. The output of the bottom of this diagram are various incident outcomes with particular effects (e.g., vapor cloud explosion resulting in a shock wave).

Accidental Release of Materials That Could Burn

Physical Explosions

Confined Explosions

Other Loss of Containment Resulting in Explosions

Figure 3.1a

Figure 3.1b

Figure 3.1c

FIGURE 3.1 Logic diagram for explosion events.

From Figure 3.1

BW P Gas Phase (PV Explosion)

Gas Dispersion Go to Figure 3.1d

Ignition

TR

Liquid Temp. > Boiling Point (BLEVE)

No Ignition or Ignition not flammmable

Fireball with Pool Fire

Flash Fire with Pool _P_ TR Fire Potential BW

VCE with Pool Fire Potential BW

P Projectiles

Gas and Liquid Phase Immediate

Delayed

BW Blast Waves

Physical Explosions

Liquid Temp. < Boiling Point No BLEVE, PV Explosion from Gas Phase Only No Ignition or not flammable BW P

TR Thermal Radiation

BW ~P~

Delayed

BW

Flash Fire BW

TR

TR

VCE

TR

Immediate

Fireball BW P TR

FIGURE 3.1 a. Logic diagram for physical explosions. From Figure 3.1 Combustion within Low Strength Structures

Confined Explosions

Without Explosion Venting BW

With Explosion Venting BW _P_ TR

Combustion, Thermal Decompositions, or Runaway Reaction within Process Vessels/ Equipment

Vent Through Relief System

TR

BW Blast Waves P Projectiles TR Thermal Radiation

Contained Within Relief System

Catastrophic Rupture of Vessels/ Equipment BW

Release to Atmosphere

TR

Goto Figure 3.1c

FIGURE 3.1b. Logic diagram for confined explosions.

Contained Within Process Equipment

BW Blast Waves

From Figure 3.1

P Projectiles Other Loss of Containment Resulting in Explosions Two-Phase

Gas Phase Gas Cloud Dispersion

Gas and Aerosol

Goto Figure 3.1d

Turbulent Free Jet Delayed Ignition

VCE BW

TR Thermal Radiation

Flash

Immediate Ignition

Flash Fire Followed by Pool Fire TR

Liquid Phase Liquid Rain Out Vaporization

No Ignition

Delayed Ignition

Jet Fire

VCE

TR

BW

Immediate Ignition

No Ignition

Flash Fire Followed by Pool Fire TR

FIGURE 3.1c. Logic diagram for other losses of containment.

From Figure 3.1a, b or c

BW Blast Waves P Projectiles

Gas Cloud Dispersion

TR Thermal Radiation Delayed Ignition

Immediate Ignition

Flash Fire

VCE

Flash Fire

TRl

BWj

TR

No Ignition

FIGURE 3. Id. Logic diagram for explosions from gas cloud dispersion.

The major difficulty presented to anyone involved in CPQBA is in selecting the proper outcomes based on the available information and determining the consequences. The consequences of concern in CPQRA studies for explosions in general are blast overpressure effects and projectile effects; for fires and fireballs the consequences of concern are thermal radiation effects. Each of these types of explosions and fires can be modeled to produce blast, projectile and/or thermal radiation effects appropriate for use in CPQRA studies and these techniques are described in the designated sections.

3 . 1 . V a p o r C l o u d Explosions (VCE) 3.1.1. BACKGROUND

Purpose When a large amount of flammable vaporizing liquid or gas is rapidly released, a vapor cloud forms and disperses with the surrounding air. The release can occur from a storage tank, process, transport vessel, or pipeline. Figure 3.1 describes the various failure pathways under which this scenario can occur. If this cloud is ignited before the cloud is diluted below its lower flammability limit (LFL), a VCE or flash fire will occur. For CPQRA modeling the main consequence of a VCE is an overpressure that results while the main consequence of a flash fire is direct flame contact and thermal radiation. The resulting outcome, either a flash fire or a VCE depends on a number of parameters discussed in the next section. Davenport (1977, 1983) and Lenoir and Davenport (1992) have summarized numerous VCE incidents. All (with one possible exception) were deflagrations rather than detonations. They found that VCEs accounted for 37% of the number of property losses in excess of $50 million (corrected to 1991 dollars) and accounted for 50% of the overall dollars paid. Pietersen and Huerta (1985) has summarized some key features of 80 flash fires. Philosophy AIChE/CCPS (1994) provides an excellent summary of vapor cloud behavior. They describe four features which must be present in order for a VCE to occur. First, the release material must be flammable. Second, a cloud of sufficient size must form prior to ignition, with ignition delays of from 1 to 5 min considered the most probable for generating vapor cloud explosions. Lenoir and Davenport (1992) analyzed historical data on ignition delays, and found delay times from 6 s to as long as 60 min. Third, a sufficient amount of the cloud must be within the flammable range. Fourth, sufficient confinement or turbulent mixing of a portion of the vapor cloud must be present.

The blast effects produced depend on whether a deflagration or detonation results, with a deflagration being, by far, the most likely. A transition from deflagration to detonation is unlikely in the open air. A deflagration or detonation result is also dependent on the energy of the ignition source, with larger ignition sources increasing the likelihood of a direct detonation. AIChE/CCPS (1994) also provides the following summary: In the experiments described, no explosive blast-generating combustion was observed if initially quiescent and fully unconfined fuel-air mixtures were ignited by low-energy ignition sources. Experimental data also indicate that turbulence is the governing factor in blast generation and that it may intensify combustion to the level that will result in an explosion. Turbulence may arise by two mechanisms. First, it may result either from a violent release of fuel from under high pressure in a jet or from explosive dispersion from a ruptured vessel. The maximum overpressures observed experimentally in jet combustion and explosively dispersed clouds have been relatively low (lower than 100 mbar). Second, turbulence can be generated by the gas flow caused by the combustion process itself and interacting with the boundary conditions. Experimental data show that appropriate boundary conditions trigger a feedback in the process of flame propagation by which combustion may intensify to a detonative level. These blast-generative boundary conditions were specified as • spatial configurations of obstacles of sufficient extent. • partial confinement of sufficient extent, whether or not internal obstructions were present. Examples of boundary conditions that have contributed to blast generation in vapor cloud explosions are often a part of industrial settings. Dense concentrations of process equipment in chemical plants or refineries and large groups of coupled rail cars in railroad shunting yards, for instance, have been contributing causes of heavy blasts in vapor cloud explosions in the past. Furthermore, certain structures in nonindustrial settings, for example, tunnels, bridges, culverts, and crowded parking lots, can act as blast generators if, for instance, a fuel truck happens to crash in the vicinity. The destructive consequences of extremely high local combustion rates up to a detonative level were observed in the wreckage of the Flixborough plant (Gugan, 1979). Local partial confinement or obstruction in a vapor cloud may easily act as an initiator for detonation, which may propagate into the cloud as well. So far, however, only one possible unconfined vapor cloud detonation has been reported in the literature; it occurred at Port Hudson, Missouri (National Transportation Safety Board, 1972; Burgess and Zabatakis, 1973). In most cases the nonhomogeneous structure of a cloud freely dispersing in the atmosphere probably prevents a detonation from propagating.

Other experimental studies have also demonstrated that there is a minimum mass of flammable material that is required to allow transition from a flash fire to VCE. These estimates range from 1 ton (Wiekema, 1979) to 15 tons (Health & Safety Executive, 1979). Some caution should be exercised in the determination of a minimum value. Gugan (1979) provides a few examples of VCEs with quantities as low as 100 kg for more reactive species such as hydrogen and acetylene. North and MacDiarmid (1988) report on explosions from the release and ignition of approximately 30 kg of hydrogen, although it was partially confined under the roof of a compressor shed. It is also believed that materials with higher fundamental burning velocities, such as hydrogen, acetylene, ethylene oxide, propylene oxide and ethylene are more readily inclined to transition to a VCE for a given release quantity. Flammable vapor clouds may be ignited from a number of sources that may be continuous (e.g., fired heaters, pilot flames) or occasional (e.g., smoking, vehicles, electrical systems, static discharge). Clouds are normally ignited at the edge as they drift. The effect of ignition is to terminate further spread of the cloud in that direction. Flash fires initially combust and expand rapidly in all directions. After the initial combustion, expansion is upward because of buoyancy. As the number of ignition sources increases the likelihood of ignition will generally increase correspondingly. Thus, a site with many ignition sources on or around it would tend to prevent clouds from reaching their full hazard extent, as most such clouds would find an ignition source before this occurs. Conversely, few clouds on such a site would disperse safely before ignition. A more complex CPQRA could take account of the location and probability of surrounding ignition sources. This might be done by considering a number of separate ignition cases applied to a given release. Early ignition, before the cloud becomes fully formed, might result in a flash fire or an explosion of smaller size. Late ignition could result in an explosion of the maximum possible effect. The following approaches have been used to locate the blast epicenter, although no theoretical basis exists at present for any method: 1. at the leading edge of the cloud at the LFL concentration. 2. at the point on the centerline where the fuel concentration is stoichiometric. 3. at the release point of the equipment item. 4. halfway between the equipment item and the LFL at the leading edge of the cloud. 5. at the center of an identifiable congested volume whose vapor concentration is within the flammable range.

Typically, other uncertainties are more important in the analysis. A more detailed analysis would determine the flammable mass in the dispersing cloud (see Section 2.3.2). Applications VCE models have been applied for incident analysis [e.g., Sadee et al. (1977) for the Flixborough explosion] and in risk analysis predictions (Rijnmond Public Authority, 1982). A flash fire model has been developed for risk analysis purposes by Eisenberg et al. (1975). 3.1.2. DESCRIPTION Description of Technique Important parameters in analyzing combustion incidents are the properties of the material: lower and upper flammable limits (LFL and UFL), flash point, auto ignition temperature, heat of combustion, molecular weight, and combustion stoichiometry. Such data are readily available (Department of Transportation, 1978; Perry and Green, 1984; Stull, 1977). The following models of VCEs presented here include: • TNT equivalency model • TNO multi-energy model • Modified Baker model All of these models are quasi-theoretical/empirical and are based on limited field data and accident investigations. TNT Equivalency Models The TNT equivalency model is easy to use and has been applied for many CPQRAs. It is described in Baker et al. (1983), Decker (1974), Lees (1986, 1996), and Stull (1977). The TNT equivalency model is based on the assumption of equivalence between the flammable material and TNT, factored by an explosion efficiency term: (3.1) where is the equivalent mass of TNT (kg or Ib) is an empirical explosion efficiency (unitless) is the mass of hydrocarbon (kg or Ib) is the heat of combustion of flammable gas (kj/kg or Btu/lb) is the heat of combustion of TNT (4437-4765 kj/kg or 1943-2049 Btu/lb).

A typical pressure history at a fixed point at some distance from a TNT blast is shown in Figure 3.2. The important parameters are the peak side-on overpressure (or simply peak overpressure),^0, the arrival time, £a, the positive phase duration time, £d, and the overpressure impulse, ip which is defined as the area under the positive duration pulse, (3.2)

The impulse is an important aspect of damage-causing ability of the blast on structures since it is indicative of the total energy contained within the blast wave. The above parameters can be scaled using the following equations: (3.3)

(3.4)

(3.5)

(3.6)

Pressure

The explosion effects of a TNT charge are well documented as shown in Figure 3.3 for a hemispherical TNT surface charge at sea level. Equations for the functions in Figure 3.3 are provided in Table 3.1. The various explosion parameters in Figure 3.3 are correlated as a function of the scaled range, Z. The scaled

Time FG I URE 3.2. Typical pressure history for a TNT-type explosion. The pressure curv below ambient pressure due to a refraction at time td.

Scaled Overpressure, ps Arrival Time, t a (ms) Impulse, i p (Pa s) Duration, td (ms)

Scaled Distance, Z (m/kg1/3 ) FIGURE 3.3. Shock wave parameters for a spherical TNT explosion on a surface at sea level (Lees, 1996).

range is defined as distance, it, divided by the cube root of TNT mass,TF, with W determined from Eq. (3.1): (3.7)

The peak side-on overpressure is used to estimate the resulting damage using Table 3.2a for general structures and Table 3.2b for process equipment. Tables 3.2a and b do not account for the blast impulse or the particular structure involved. Thus, they should only be used for estimation. Correlations are also available for TNT blasts in free air, without a ground surface (U.S. Army, 1969). This would apply to an elevated blast with the blast receptor very near the source of the blast. Since this is rarely the case in chemical plant facilities, the reflection of a blast wave off of the ground dictates the use of Figure 3.3. Other pressure quanities in blast modeling are the reflected pressure and the dynamic pressure. The reflected pressure is the pressure on a structure perpendicular to the shock wave and is at least a factor of 2 greater than the side-on overpressure. Another quantity is the dynamic overpressure—it is determined by multiplying the density of the air times the square of the velocity divided by 2.

Table 3.1. Equations for the Blast Parameters Functions Provided in Figure 3.3 The functions are tabulated using the following functional form:

where (p is the function of interest; ci} &3b are constants provided in the table below, and Z is the scaled distance (m/kg 1/3 ) Function

Constant

Range

Overpressure^ (kPa)

0

Impulse ip (Pas)

Duration time / d (ms)

Arrival time / a (ms)

NOTE: The number of significant figures is a function of the curve fit method only and not indicative of the accuracy of the method. See Example 19 for application of these equations. (From Lees, 1996.)

TABLE 3.2a. Damage Estimates for Common Structures Based on Overpressure (Clancey, 1972). These values should only be used for approximate estimates. Pressure psig

Damage

kPa

0.02

0.14

0.03

0.21

Occasional breaking of large glass windows already under strain

0.04

0.28

Loud noise (143 dB), sonic boom, glass failure

0.1

0.69

Breakage of small windows under strain

0.15

1.03

Typical pressure for glass breakage

0.3

2.07

"Safe distance" (probability 0.95 of no serious damage below this value); projectile limit; some damage to house ceilings; 10% window glass broken

0.4

2.76

Limited minor structural damage

0.5-1.0

3.4H5.9

Large and small windows usually shattered; occasional damage to window frames

0.7

4.8

Minor damage to house structures

1.0

6.9

Partial demolition of houses, made uninhabitable

1-2

6.9-13.8

Corrugated asbestos shattered; corrugated steel or aluminum panels, fastenings fail, followed by buckling; wood panels (standard housing) fastenings fail, panels blown in

Annoying noise (137 dB if of low frequency 10-15 Hz)

1.3

9.0

Steel frame of clad building slightly distorted

2

13.8

Partial collapse of walls and roofs of houses

2-3

13.8-20.7

Concrete or cinder block walls, not reinforced, shattered

2.3

15.8

Lower limit of serious structural damage

2.5

17.2

50% destruction of brickwork of houses

3

20.7

Heavy machines (3000 Ib) in industrial building suffered little damage; steel frame building distorted and pulled away from foundations

3-4

20.7-27.6

Frameless, self-framing steel panel building demolished; rupture of oil storage tanks

4

27.6

Cladding of light industrial buildings ruptured

5

34.5

Wooden utility poles snapped; tall hydraulic press (40,000 Ib) in building slightly damaged

5-7

34.5^8.2

Nearly complete destruction of houses

7

48.2

Loaded train wagons overturned

7-8

48.2-55.1

Brick panels, 8-12 inches thick, not reinforced, fail by shearing or flexure

9

62.0

Loaded train boxcars completely demolished

10

68.9

Probable total destruction of buildings; heavy machine tools (7000 Ib) moved and badly damaged; very heavy machine tools (12,000 Ib) survive

J500

2068

Limit of crater lip

TABLE 3.2b. Damage Estimates Based on Overpressure for Process Equipment3 Overpressure, psi Equipment Control house steel roof Control house concrete roof Cooling tower Tank: cone roof Instrument cubicle Fire heater Reactor: chemical Filter Regenerator Tank:floatingroof Reactor: cracking Pine supports Utilities: gas meter Utilities: electronic transformer Electric motor Blower Fractionation column Pressure vessel: horizontal Utilities: gas regulator Extraction column Steam turbine Heat exchanger Tank sphere Pressure vessel: vertical Pump • See page 140 for the key to this table.

1-0.

1.5

2.0

4.0

6.0

6.5

7.0

8.0

8.5

10

12

14

16

18

20

Key to Table 3.2b A. B. C. D. E. F. G. H. I. J.

Windows and gauges broken Louvers fall at 0.2- 0.5 psi Switchgear is damaged from roof collapse Roof collapses Instruments are damaged Inner parts are damaged Brick cracks Debris—missile damage occurs Unit moves and pipes break Bracing falls

K. Unit uplifts (half tilted) L. Power lines are severed M. Controls are damaged N. Block walls fall O. Frame collapses P. Frame deforms Q. Case is damaged R. Frame cracks S. Piping breaks T. Unit overturns or is destroyed U. Unit uplifts (0.9 tilted) V. Unit moves on foundation

The overpressure used most frequently for blast modeling in risk analysis is the peak side-on overpressure. The flammable cloud explosion yield is empirical, with most estimates varying between 1 and 10% (Brasie and Simpson, 1968; Gugan, 1979; Lees, 1986). Bodurtha (1980) gives the upper limit on the range of efficiency as 0.2. Eichler and Napademsky (1978) from reviews of historical data conclude the maximum expected efficiency is 0.2 for a symmetric cloud, but could be significantly higher—up to 0.4 for an asymmetric cloud. This factor is based on analysis of many VGE incidents. As doubt exists as to the actual mass involved in many VCE incidents, the true efficiency is uncertain. Prugh (1987) gives a helpful correlation of flammable mass versus VCE probability from historical data. Decker (1974) shows how to link a Gaussian dispersion model with the TNT model. The explosion efficiency depends on the method for determining the contributing mass of fuel. Models based on the total quantity released have lower efficiencies. Models based on the dispersed cloud mass have a higher efficiency. The original reference must be consulted for the details. The following methods for estimating the explosion efficiency are summarized by AIChE (1994): 1. Brasie and Simpson (1968): Use 2% to 5% of the heat of combustion of the total quantity of fuel spilled. 2. Health & Safety Executive (1979 and 1986): 3% of the heat of combustion of the quantity of fuel present in the cloud. 3. Industrial Risk Insurers (1990): 2% of the heat of combustion of the quantity of fuel spilled.

4. Factory Mutual Research Corporation (AIChE/CCPS, 1994): 5%, 10%, and 15% of the heat of combustion of the quantity of fuel present in the cloud, dependent on the reactivity of the material. Higher reactivity gives a higher efficiency. Use the following efficiencies for the highly reactive materials specified: diethyl ether, 10%; propane, 5%; acetylene, 15%. The application of an explosion efficiency represents one of the major problems with the TNT equivalency method. The problem with the TNT equivalency model is that little, if any, correlation exists between the quantity of combustion energy involved in a VCE and the equivalent weight of TNT required to model its blast effects. This result is clearly proven by the fact that, for quiescent clouds, both the scale and strength of a blast are unrelated to fuel quantity present. These factors are determined primarily by the size and nature of the partially confined and obstructed regions within the cloud. TNO Multi-Energy Method This method is described in detail in AIChE (1994), Van den Berg (1985), and Van den Berg et al. (1987). The multi-energy model assumes that blast modeling on the basis of deflagrative combustion is a conservative approach. The basis for this assumption is that an unconfined vapor cloud detonation is extremely unlikely; only a single event has been observed. The basis for this model is that the energy of explosion is highly dependent on the level of congestion and less dependent on the fuel in the cloud. The procedure for employing the multi-energy model to a vapor cloud explosion is given by the following steps (AIChE/CCPS, 1994): 1. Perform a dispersion analysis to determine the extent of the cloud. Generally, this is performed assuming that equipment and buildings are not present. This is due to the limitations of dispersion modeling in congested areas. 2. Conduct a field inspection to identify the congested areas. Normally, heavy vapors will tend to move downhill. 3. Identify potential sources of strong blast present within the area covered by the flammable cloud. Potential sources of strong blast include: • congested areas and buildings such as process equipment in chemical plants or refineries, stacks of crates or pallets, and pipe racks; • spaces between extended parallel planes, for example, those beneath closely parked cars in parking lots, and open buildings, for example, multistory parking garages; • spaces within rubelike structures, for example, tunnels, bridges, corridors, sewage systems, culverts;

• an intensely turbulent fuel-air mixture in a jet resulting from release at high pressure. The remaining fuel-air mixture in the cloud is assumed to produce a blast of minor strength. 4. Estimate the energy of equivalent fuel-air charges. • Consider each blast source separately. • Assume that the full quantities of fuel-air mixture present within the partially confined/obstructed areas and jets, identified as blast sources in the cloud, contribute to the blasts. • Estimate the volumes of fuel-air mixture present in the individual areas identified as blast sources. This estimate can be based on the overall dimensions of the areas and jets. Note that the flammable mixture may not fill an entire blast-source volume and that the volume of equipment should be considered where it represents an appreciable proportion of the whole volume. • Calculate the combustion energy E (J) for each blast by multiplication of the individual volumes of the mixture by 3.5 X 106 J/m3. This value is typical for the heat of combustion of an average stoichiometric hydrocarbon-air mixture (Harris 1983). 5. Estimate strengths of individual blasts. Some companies have defined procedures for this, however, many risk analysts use their own judgment. • A safe and most conservative estimate of the strength of the sources of a strong blast can be made if a maximum strength of 10 is assumed—representative of a detonation. However, a source strength of 7 seems to more accurately represent actual experience. Furthermore, for side-on overpressures below about 0.5 bar, no differences appear for source strengths ranging from 7 to 10. • The blast resulting from the remaining unconflned and unobstructed parts of a cloud can be modeled by assuming a low initial strength. For extended and quiescent parts, assume minimum strength of 1. For more nonquiescent parts, which are in low-intensity turbulent motion, for instance, because of the momentum of a fuel release, assume a strength of 3. 6. Once the energy quantities E and the initial blast strengths of the individual equivalent fuel-air charges are estimated, the Sachs-scaled blast side-on overpressure and positive-phase duration at some distance R from a blast source is read from the blast charts in Figure 3.4 after calculation of the Sachs-scaled distance: (3.8)

combustion energy-scaled distance (R)

Ro P Ro

combustion energy-scaled distance (R)

time

p o = atmospheric pressure c0 = atmospheric sound speed E = amount of combustion energy R 0 » charge radius

FIGURE 3.4. TNO multi-energy model for vapor cloud explosions. The Sachs scaled side-on overpressure and positive-phase duration are provided as a function of the Sachs scaled distance (AlChE/CCPS, 1994).

where R is the Sachs-scaled distance from the charge (dimensionless) R is the distance from the charge (m) E is the charge combustion energy (J) P 0 is the ambient pressure (Pa) The blast peak side-on overpressure and positive-phase duration are calculated from the Sachs-scaled quantities: (3.9) and

(3.10) where Ps is the side-on blast overpressure (Pa) AP5 is the Sachs-scaled side-on blast overpressure (dimensionless) P 0 is the ambient pressure (Pa) td is the positive-phase duration (s) td is the Sachs-scaled positive-phase duration (dimensionless) E is the charge combustion energy (J) C0 is the ambient speed of sound (m/s) If separate blast sources are located close to one another, they may be initiated almost simultaneously. Coincidence of their blasts in the far field cannot be ruled out, and their respective blasts should be superimposed. The most conservative approach to this issue is to assume a maximum initial blast strength of 10 and to sum the combustion energy from each source in question. Further definition of this important issue, for instance the determination of a minimum distance between potential blast sources so that their individual blasts may be considered separately, is a factor in present research. The possibility of unconfined vapor cloud detonation should be considered if (a) environmental and atmospheric conditions are such that vapor cloud dispersion is slow, and (b) a long ignition delay is likely. In that case, the full quantity of fuel mixed within detonable limits should be assumed for a fuel-air charge whose initial strength is maximum 10. The major problem with the application of the TNO multi-energy method is that the user must decide on the selection of a severity factor, based on the degree of confinement. Little guidance is provided for partial confinement geometries. Furthermore, it is not clear how the results from each blast strength should be combined.

Baker-Strehlow Method This method is a modification of the original work by Strehlow et al. (1979), with added elements of the TNO multi-energy method. A complete description of the procedure is provided by Baker et al. (1994). Strehlow's spherical model was chosen because a curve is selected based on flame speed, which affords the opportunity to use empirical data in the selection. The procedures from the TNO multi-energy method were adopted for determination of the energy term. Specifically, confinement is the basis of the determination of the size of the flammable vapor cloud that contributes to the generation of the blast overpressure, and multiple blast sources can emanate from a single release. Baker et al. (1994) state that experimental data suggests that the combined effects of fuel reactivity, obstacle density and confinement can be correlated to flame speed. They describe a set of 27 possible combinations of these parameters based on 1, 2, or 3D flame expansions. Six of the possible combinations lacked experimental data, but they were able to interpolate between the existing data to specify these values. The results are shown in Table 3.3. The flame speeds are

TABLE 3.3. Flame Speed in Mach Number for Soft Ignition Sources (Baker et al., 1994) Obstacle Density ID Flame Expansion Case

Medium

Low

5.2

5.2

5.2

Medium

2.265

1.765

1.029

Low

2.265

1.029

0.294

High Reactivity

High

Obstacle Density 2D Flame Expansion Case

Reactivity

High

Medium

Low

High

1.765

1.029

0.588

Medium

1.235

0.662

0.118

Low

0.662

0.471

0.079

Obstacle Density 3D Flame Expansion Case

Reactivity

High

Medium

Low

High

0.588

0.153

0.071

Medium

0.206

0.100

0.037

Low

0.147

0.100

0.037

expressed in Mach number units. Note that the values in Table 3.3 represent the maximum flame speed for each case and will produce a conservative result. Reactivity is classified as low, average, and high according to the following recommendations of TNO (Zeeuwen and Wiekema, 1978). Methane and carbon monoxide are the only materials regarded as low reactivity, whereas hydrogen, acetylene, ethylene, ethylene oxide, and propylene oxide are considered to be highly reactive. All other fuels are classified as average reactivity. Fuel mixtures are classified according to the concentration of the most reactive component. Confinement is based on three symmetries, as shown in Table 3.4: point-symmetry (3D), line-symmetry (2D), and planar-symmetry (ID). Point-symmetry, also referred to as spherical or unconfmed geometry, has the lowest degree of flame confinement. The flame is free to expand spherically from a point ignition source. The overall flame surface increases with the square of the distance from the point ignition source. The flame-induced flow field can decay freely in three directions. Therefore, flow velocities are low, and the flow field disturbances by obstacles are small. In line-symmetry, that is, a cylindrical flame between two plates, the overall flame surface area is proportional to the distance from the ignition point. Consequently, deformation of the flame surface will have a stronger effect than in the point-symmetry case. In plane-symmetry, that is, a planar flame in a tube, the projected flame surface area is constant. There is hardly any flow field decay, and flame deformation has a very strong effect on flame acceleration. TABLE 3.4. Geometric Considerations for the Baker-Strehlow Vapor Cloud Explosion Model (Baker, 1996) Type

Point Symmetry

Planar Symmetry

Dimension

3-D

2-D

Description "Unconfined volume," almost completely free expansion.

Platforms carrying process equipment; space beneath cars; open-sided multi-story buildings Tunnels, corridors, or sewage systems

Line Symmetry

1-D

Geometry

TABLE 3.5. Confinement Considerations for the Baker-Strehlow Vapor Cloud Explosion Model (Baker, 1996) Type

Obstacle blockage ratio per plane

Low

Pitch for obstacle layers

Geometry

One or two layers of obstacles Less than 10%

Medium

Two or three layers of obstacles Between 10% and 40%

High

Greater than 40%

Three or more fairly closely spaced obstacle layers

Obstacle density is classified as low, medium, and high, as shown in Table 3.5, as a function of the blockage ratio and pitch. The blockage ratio is defined as the ratio of the area blocked by obstacles to the total cross-section area. The pitch is defined as the distance between successive obstacles or obstacle rows. There is normally an optimum value for the pitch; when the pitch is too large, the wrinkles in the flame front will burn out and the flame front will slow down before the next obstacle is reached. When the pitch is too small, the gas pockets between successive obstacles are relatively unaffected by the flow (Baker et al., 1994). Low density assumes few obstacles in the flame's path, or the obstacles are widely spaced (blockage ratio less than 10%), and there are only one or two layers of obstacles. At the other extreme, high obstacle density occurs when there are three or more fairly closely spaced layers of obstacles with a blockage ratio of 40% or greater per layer. Medium density falls between the two categories. A high obstacle density may occur in a process unit in which there are many closely spaced structural members, pipes, valves, and other turbulence generators. Also, pipe racks in which there are multiple layers of closely spaced pipes must be considered high density. Once the flame speed is determined, then Figure 3.5 is used to determine the side-on overpressure and Figure 3.6 is used to determine the specific impulse of the explosion. The curves on these figures are labeled with two flame velocities: Mw and Msxx. M^ denotes the flame velocity with respect to a fixed coordinate system, and is called the "apparent flame speed.33 Msu is the flame velocity with respect to the unburned gas ahead of the flame front. Both of these quantities are

Scaled Overpressure, ps = p0/ pg

Mw

M

su

Scaled Impulse = isa0/ ( P0273E173)

Sachs Scaled Distance, R = R / ( E / P0 )1/3 FIGURE 3.5. Baker-Strehlow model for vapor cloud explosions. The curve provides the scaled overpressure as a function of the Sachs scaled distance [Baker, 1996).

No. Mw

Msu

Sachs Scaled Distance, R = R / (E / PQ )1/3 FIGURE 3.6. Baker-Strehlow model for vapor cloud explosions. The curve provides the scaled impulse as a function of the Sachs scaled distance (Baker, 1996).

expressed in Mach numbers, and are calculated in relation to the ambient speed of sound. Figures 3.5 and 3.6 are based on free air bursts—for a ground or near ground level explosion, the energy is multiplied by a factor of two to account for the reflected blast wave. The procedure for implementing the Baker-Strehlow method is similar to the TNO Multi-Energy method, with the exception that steps 4 and 5 are replaced by Table 3.3 and Figures 3.5 and 3.6. Logic Diagram A logic diagram for the application of the TNT equivalency method is given in Figure 3.7. The main inputs are the mass and dimensions of the flammable cloud and an estimate of explosion efficiency. The main outputs are the peak side-on overpressure or damage levels with distance. Theoretical Foundation The TNT model is well established for high explosives, but when applied to flammable vapor clouds it requires the explosion yield, t], determined from past incidents. There are several physical differences between TNT detonations and VCE deflagrations that limit the theoretical validity. The TNO multi-energy method is directly correlated to incidents and has a defined efficiency term, but the user is required to specify a relative blast strength from 1 to 10. The Baker-Strehlow method uses flame speed data correlated with relative reactivity, obstacle density and geometry to replace the relative blast strength in the TNO method. Both methods produce relatively close results in examples worked. Input Requirements and Availability The following inputs are required for the individual explosion models: • The TNT equivalence, TNO multi-energy and Baker-Strehlow methods require the mass of flammable material in the vapor cloud, and the lower heat of combustion for the vapor. • The TNT equivalent model requires the specification of the explosion efficiency. The TNO multi-energy method requires the specification of the degree of confinement and the specification of a relative blast strength. • The Baker-Strehlow method requires a specification of the chemical reactivity, the obstacle density and the geometry. Baker (1996) provides guidelines to determine the mass of flammable material. For small releases of flammable materials, a typical approach would be to obtain the fuel mass between the flammability limits using a dispersion model.

Release / Dispersion Model Concentration Profiles Estimate Mass and Extent of Flammable Cloud

Estimate TNT Equivalent Weight, Equation (3.1)

Estimate Scaled Distance Parameter for Specified Overpressure

Heat of Combustion, Explosive Efficiency

TNT Scaled Overpressure Curve, Figure 3.3, or Equations from Table 3.1

Estimate Effect Distance, Equation (3.7)

Determine Vapor Cloud Explosion (VCE) Effect Zone FIGURE 3.7. Logic diagram for the application of the TNT equivalency model.

This approach, however, does not work once the flammable portion of the cloud achieves a size that is greater than the confined volume. For this case, the confined volume must be used to estimate the energy term. This can be done by inspecting the process plant and identifying reasonable bounds for confinement and congestion. In most cases, the answer is fairly obvious since equipment is frequently lined up along either side of a pipe rack or alley. Process plants have a

large variety of confinement based on the geometry of the plant. Towers which extend above confined areas are in the open and are normally not considered in the energy estimates. As a result, the upper bound for the volume is usually the upper bound of the congestion above the confined areas. The confined volume for a multi-level unit in a chemical plant is very frequently the volume within the structural steel framework supporting the equipment, with possible exceptions where there are ground level items, such as towers, adjoining a multi-level unit. Frequently, the uppermost level of a multi-level unit has very little equipment, and it is overly conservative to extend the confined volume all the way up to the top of the equipment on the upper deck. A reasonable judgment must be made during a site inspection based on the freedom with which a flame can expand away from a confined zone. Output All three methods predict side-on overpressure and specific impulse with distance. The overpressure is useful to determine the consequence directly, via Table 3.2. The specific impulse is necessary to determine the dynamic loading effects on a structure. Simplified Approaches The TNT, TNO multi-energy and Baker-Strehlow methods are simplified approaches. A further simplification would be to use the initial vapor cloud mass as input without applying a dispersion model, but this might overestimate cloud size after it drifts to an ignition source. 3.1.3. DISCUSSION

Strengths and Weaknesses All of the methods (except the TNT equivalency) require an estimate of the vapor concentration—this can be difficult to determine in a congested process area. The TNT equivalency model is easy to use. In the TNT approach a mass of fuel and a corresponding explosion efficiency must be selected. A weakness is the substantial physical difference between TNT detonations and VCE deflagrations. The TNO and Baker-Strehlow methods are based on interpretations of actual VCE incidents—these models require additional data on the plant geometry to determine the confinement volume. The TNO method requires an estimate of the blast strength while the Baker-Strehlow method requires an estimate of the flame speed. Identification and Treatment of Possible Errors The largest potential error with the TNT equivalency model is the choice of an explosion efficiency. One needs to ensure that the yield corresponds with the correct mass of fuel. An efficiency range of 1-10% affects predicted distances to

selected overpressures by more than a factor of two [from Eq. (3.1), the distance to a particular overpressure is proportional to the cubic root of the calculated TNT equivalent]. Another error is in the estimation of the flammable cloud mass, which is based on flash and evaporation calculations (Section 2.2) and dispersion calculations (Section 2.3), both of which are subject to error. No dispersion model is capable of predicting vapor concentrations in a congested process area. A smaller source of error is the quoted heat of combustion for TNT which varies about 5%. The TNT model assumes unobstructed blast wave propagation, which is rarely true for chemical plants. The TNT equivalency model has the virtue of being easiest to use. Resources Needed TNT equivalency calculations to predict overpressure can be completed in under an hour, given complete dispersion model output for cloud mass and extent. Available Computer Codes Vapor Cloud Explosion Modeling:

AutoReaGas (TNO Prins Maurits Laboratory, The Netherlands) REACFLOW-2D (JRC Safety Technology, Ispra) VCLOUD (W. E. Baker Engineering, San Antonio, TX) Several integrated analysis packages also contain explosion simulators. These include:

ARCHIE (Environmental Protection Agency, Washington, DC) EFFECTS-2 (TNO, Apeldoorn, The Netherlands) uFLACS (DNV Technica, Temecula, CA) PHAST (DNV Technica, Temecula, CA) QRAWorks (PrimaTech, Columbus, OH) SAFER (Safer Systems, Westlake Village, CA) SAFETI (DNV, Houston, TX) SUPERCHEMS (Arthur D. Little, Cambridge, MA) 3.1 A. EXAMPLE PROBLEMS

Example 19: Blast Wave Parameters A 10-kg mass of TNT explodes on the ground. Determine the overpressure, arrival time, duration time, and impulse 10 m away from the blast. Solution: This problem is solved by using Eq. (3.7) to determine the scaled distance.

The required quantities are determined by using Figure 3.3 or Table 3.1. Using Table 3.1, for the overpressure, Then Substituting into the equation provided in Table 3.1, and using the values for the constants,

The procedure is similar for the other quantities required. The entire procedure is easily implemented using a spreadsheet, using the equations found in Table 3.1. The output of this spreadsheet is shown in Figure 3.8. The results are Scaled distance: 4.64 m/kg1/3 Overpressure: 49.3 kPa = 7.14 psia Specific impulse: 63.3 Pa-s PuIs e duration: 3.7ms Arrival time: 7.3 ms Example 20: TNT Equivalency Using the TNT equivalency model, calculate the distance to 5 psi overpressure (equivalent to heavy building damage) of an VCE of 10 short tons of propane. Data: Mass: 10 tons = 20,000 Ib Lower heat of combustion (propane) (Ec): 19,929 Btu/lb (46.350 kj/kg) Assumed explosion efficiency (rj): 0.05 Assumed Ec?TNT: 2000 Btu/lb Solution: From Eq. (3.1),

Example 19: Blast Parameters Input Data: TNT Mass: Distance from blast: Calculated Results: Scaled distance, z: Overpressure Calculation: a+b*log(z): Overpressure:

(only valid for z > 0.0674 and z < 40)

Impulse Calculation: a+b*log(z): Impulse:

(only valid for z > 0.0674 and z < 40)

Duration Calculation: a+b*log(z): Duration:

(only valid for z > 0.178 and z < 40)

Arrival Time Calculation: a+b*log(z): Arrival time:

(only valid for z > 0.0674 and z < 40)

FIGURE 3.8. Spreadsheet output for Example 19: Blast parameters.

The scaled overpressure is 5 psia/14.7 psia = 0.340. From Figure 3.3 the scaled distance is 5.7 m/(kg TNT)1/3. Converting the scaled distance into an actual distance:

The procedure is easily implemented using a spreadsheet, as shown in Figure 3.9. In this case the solution is by trial and error—the distance is modified to achieve the desired overpressure. The results are the same as the numerical calculation above. Example 21: TNO and Baker-Strehlow Methods (Baker et al., 1994) Consider the explosion of a propane-air vapor cloud confined beneath a storage tank. The tank is supported 1 m off the ground by concrete piles. The concentration of vapor in the cloud is assumed to be at stoichiometric concentrations. Assume a cloud volume of 2094 m3, confined below the tank, representing the volume underneath the tank. Determine the overpressure as a function of distance from the blast using: a. the TNO multi-energy method b. the Baker-Strehlow method

Example 20: TNT Equivalency of a Vapor Cloud Input Data: TNT Mass: Distance from blast:

Trial & error distance to get overpress

Calculated Results: Scaled distance, z: Overpressure Calculation: a+b*log(z): Overpressure:

(only valid for z > 0.0674 and z < 40)

Impulse Calculation: a+b*log(z): Impulse:

(only valid for z > 0,0674 and z < 40)

Duration Calculation: a+b*log(z): Duration:

(only valid for z > 0.178 and z < 40)

Arrival Time Calculation: a+b*log(z): Arrival time:

(only valid for z > 0.0674 and z < 40)

FIGURE 3.9. Spreadsheet output for Example 20: TNT equivalency of a vapor cloud.

Solution: (a) The heat of combustion of a stoichiometric hydrocarbon-air mixture is approximately 3.5 MJ/m3 and, by multiplying by the confined volume, the resulting total energy is 7329 MJ. To apply the TNO multi-energy method a blast strength of 7 was chosen. A standoff distance is then specified and the Sachs scaled energy is determined using Eq. (3.8). The curves labeled "7" on Figure 3.4 are then used to determine the overpressure. The procedure is repeated at different standoff distances. The procedure is readily implemented via spreadsheet, as shown in Figure 3.10, for a standoff distance of 30 m. The spreadsheet includes the data digitized from Figure 3.4 (not shown in Figure 3.10). The results are interpolated in the spreadsheet from the digitized data. The results of the complete calculation, as a function of standoff distance, are shown in Figure 3.11. (b) The Baker-Strehlow pressure curves apply to free air blasts. Since the vapor cloud for this example is at ground level, the energy of the cloud is doubled to account for the strong reflection of the blast wave. The resulting total explosion energy is thus 14,600 MJ. The next step is to determine the flame speed using Table 3.3. Because the vapor cloud is enclosed beneath the storage tank the flame can only expand in two

Example 21a: TNO Multi Energy Model Input Data: Heat of combustion: Standoff distance: Ambient pressure: Speed of sound at ambient:

Used for duration only

Enter volume for each blast strength in table below: (Use 7 for a nominal blast and 10 for maximum blast) Blast Volume Strength m**3 1 O 2 O 3 O 4 O 5 O 6

O

7 8 9 10

2094 0 0 0_

2094 Calculated Results:

Blast Strength

Total Energy MJ

Sachs Scaled Scaled Distance Overpressure

Side-on Overpressure kPa psi

Scaled Duration Duration msec

Assumes additive pressures

Overpressure (kPa)

FIGURE 3.10. Spreadsheet output for Example 21a: TNO multi-energy method.

TNO Multi-Energy

Baker - Strehlow Standoff Distance (m) FIGURE 3.11. Comparison of results for Example 2 1 .

directions. Therefore, confinement is 2D. Based on the description of the piles the obstacle density is chosen as medium. The fuel reactivity for propane is average. The resulting flame speed from Table 3.3 is 0.662. Once a standoff distance is specified, the Sachs scaled energy is determined from Eq. (3.8). The final pressure is interpolated from Figure 3.5. The entire procedure is readily implemented using a spreadsheet, shown in Figure 3.12 for a standoff distance of 30 m. The spreadsheet contains data digitized from Figures 3.5 and 3.6 (not shown in Figure 3.12). The results are interpolated by the spreadsheet from the digitized data. The complete results of the procedure, as a function of distance, are shown in Figure 3.11. For this example problem the TNO multi-energy and the Baker-Strehlow methods produce similar results. Based on the uncertainty inherent in these models, the results are essentially identical. Example 21b: Baker-Strehlow Vapor Cloud Explosion Model Input Data: Standoff distance: Flame speed: Explosion energy: Ambient pressure: Ambient speed of sound: Calculated Results: Scaled distance:

Must be less than 10!!

Data interpolated from tables below: Flame OverVelocity, Mw Pressure Mach No. Ps/Po

Flame Velocity, Mw Scaled Mach No. Impulse

Interpolated Scaled Overpressure: Actual Overpressure: Interpolated Scaled Impulse: Specific Impulse: FIGURE 3. ? 2. Spreadsheet output for Example 21b: Baker-Strehlow vapor cloud explosion model.

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3 . 2 . Flash Fires

A flash fire is the nonexplosive combustion of a vapor cloud resulting from a release of flammable material into the open air. Experiments have shown (AIChE51994) that vapor clouds only explode in areas where intensely turbulent combustion develops and only if certain conditions are met. Major hazards from flash fires are from thermal radiation and direct flame contact. The literature provides little information on the effects of thermal radiation from flash fires, probably because thermal radiation hazards from burning vapor clouds are considered less significant than possible blast effects. Furthermore, flash combustion of a vapor cloud normally lasts no more that a few tenths of a second. Therefore, the total intercepted radiation by an object near a flash fire is substantially lower than in the case of a pool fire. Flash fire models—if based on flame radiation—are subject to large error if radiation is estimated incorrectly, because predicted radiation varies with the fourth power of temperature. Typically, the burning zone is estimated by first performing a dispersion model and defining the burning zone from the 1A LFL limit back to the release point, even though the vapor concentration might be above the UFL. Turbulence induced combustion mixes this material with air and burns it. In order to compute the thermal radiation effects produced by a burning vapor cloud, it is necessary to know the flame's temperature, size, and dynamics during its propagation through the cloud. Thermal radiation intercepted by an object in the vicinity is determined by the emissive power of the flame (determined by the flame temperature), the flame's emissivity, the view factor, and an atmospheric-attenuation factor. See Section 3.4 for methods for modeling thermal radiation. Flash fire models are also subject to similar dispersion model errors present in VCE calculations. 3 . 3 . Physical E x p l o s i o n 3.3.1. BACKGROUND

Purpose When a vessel containing a pressurized gas ruptures, the resulting stored energy is released. This energy can produce a shock wave and accelerate vessel fragments. If the contents are flammable it is possible that ignition of the released gas could result in additional consequence effects. Figure 3.1 illustrates possible scenarios that could result. This subsection illustrates calculation tools for both shock wave and projectile effects from this type of explosion.

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3 . 2 . Flash Fires

A flash fire is the nonexplosive combustion of a vapor cloud resulting from a release of flammable material into the open air. Experiments have shown (AIChE51994) that vapor clouds only explode in areas where intensely turbulent combustion develops and only if certain conditions are met. Major hazards from flash fires are from thermal radiation and direct flame contact. The literature provides little information on the effects of thermal radiation from flash fires, probably because thermal radiation hazards from burning vapor clouds are considered less significant than possible blast effects. Furthermore, flash combustion of a vapor cloud normally lasts no more that a few tenths of a second. Therefore, the total intercepted radiation by an object near a flash fire is substantially lower than in the case of a pool fire. Flash fire models—if based on flame radiation—are subject to large error if radiation is estimated incorrectly, because predicted radiation varies with the fourth power of temperature. Typically, the burning zone is estimated by first performing a dispersion model and defining the burning zone from the 1A LFL limit back to the release point, even though the vapor concentration might be above the UFL. Turbulence induced combustion mixes this material with air and burns it. In order to compute the thermal radiation effects produced by a burning vapor cloud, it is necessary to know the flame's temperature, size, and dynamics during its propagation through the cloud. Thermal radiation intercepted by an object in the vicinity is determined by the emissive power of the flame (determined by the flame temperature), the flame's emissivity, the view factor, and an atmospheric-attenuation factor. See Section 3.4 for methods for modeling thermal radiation. Flash fire models are also subject to similar dispersion model errors present in VCE calculations. 3 . 3 . Physical E x p l o s i o n 3.3.1. BACKGROUND

Purpose When a vessel containing a pressurized gas ruptures, the resulting stored energy is released. This energy can produce a shock wave and accelerate vessel fragments. If the contents are flammable it is possible that ignition of the released gas could result in additional consequence effects. Figure 3.1 illustrates possible scenarios that could result. This subsection illustrates calculation tools for both shock wave and projectile effects from this type of explosion.

Philosophy A physical explosion relates to the catastrophic rupture of a pressurized gas filled vessel. Rupture could occur for the following reasons: 1. Failure of pressure regulating and pressure relief equipment (physical overpressurization) 2. Reduction in vessel thickness due to a. corrosion b. erosion c. chemical attack 3. Reduction in vessel strength due to a. overheating b. material defects with subsequent development of fracture c. chemical attack, e.g., stress corrosion cracking, pitting, embrittlement d. fatigue induced weakening of the vessel 4. Internal runaway reaction. 5. Any other incident which results in loss of process containment. Failure can occur at or near the operating pressure of the vessel (items 2 and 3 above), or at elevated pressure (items 1 and 4 above). When the contents of the vessel are released both a shock wave and projectiles result. The effects are more similar to a detonation than a vapor cloud explosion (VCE). The extent of a shock wave depends on the phase of the vessel contents originally present. Table 3.6 describes the various scenarios. There is a maximum amount of energy in a bursting vessel that can be released. This energy is allocated to the following: • vessel stretch and tearing • kinetic energy of fragments • energy in shock wave • "waste55 energy (heating of surrounding air)

TABLE 3.6. Characteristics of Various Types of Physical Explosions Type

Shock Wave Energy

Gas-filled vessel

Expansion of gas

Liquid-filled vessel Liquid temperature < Liquid boiling point

Expansion of gas from vapor space volume; liquid contents unchanged and runs out.

Liquid-filled vessel Liquid temperature > Liquid boiling point

Expansion of gas from vapor space volume coupled with flash evaporation of liquid.

The relative distribution of these energy terms will change over the course of the explosion. Exactly what proportion of available energy will actually go into the production of shock waves is difficult to determine. Saville (1977) in the UK High Pressure Safety Code suggests that 80% of the available system energy becomes shock wave energy for brittle type failure. For the ejection of a major vessel section, 40% of the available system energy becomes shock wave energy. For both cases, the remainder of the energy goes to fragment kinetic energy. In general, physical explosions from catastrophic vessel rupture will produce directional explosions. This occurs because failure usually occurs from crack propagation starting at one location. If the failure were brittle, resulting in a large number of fragments, the explosion would be less directional. However, the treatment of shock waves from this type of failure usually does not consider directionality. 3.3.2. DESCRIPTION Description of Technique Several methods relate directly to calculation of a TNT equivalent energy and use of shock wave correlations as in Figure 3.3 and Table 3.1. There are various expressions that can be developed for calculating the energy released when a gas initially having a volume, F, expands in response to a decrease in pressure from a pressure, P1, to atmospheric pressure, P0. The simplest expression is due to Brode (1959). This expression determines the energy required to raise the pressure of the gas at constant volume from atmospheric pressure, P0, to the initial, or burst, pressure, P 1 , (3.11) where E is the explosion energy (energy), V is the volume of the vessel (volume), and y is the heat capacity ratio for the expanding gas (unitless) If it is assumed that expansion occurs isothermally and that the ideal gas law applies, the following equation can be derived (Brown, 1985): (3.12) where W V P1 P2

is the energy (Ib TNT) is the volume of the compressed gas (ft3) is the initial pressure of the compressed gas (psia) is the final pressure of expanded gas (psia)

P 0 is the standard pressure (14.7 psia) T0 is the standard temperature (492°R) Rg is the gas constant (1.987 Btu/lb-mole-°R) 1.39 X 10"6 is a conversion factor (this factor assumes that 2000 BTU = 1 Ib TNT) Another approach (Crowl, 1992) is to apply the concept of available energy. Available energy represents the maximum mechanical energy that can be extracted from a material as it moves into equilibrium with the environment. Crowl (1992) showed that for a nonreactive material initially at a pressure P and temperature T, expanding into an ambient pressure of P E , then the maximum mechanical energy, E3 derivable from this material is given by (3.13) Note that the first term within the brackets is equivalent to the isothermal energy of expansion. The second term within the parenthesis represents the loss of energy as a result of the second law of thermodynamics. The result predicted by Eq. (3.13) is smaller than the result predicted assuming an isothermal expansion, but greater than the result assuming an adiabatic expansion. The calculated equivalent amount of TNT energy can now be used to estimate shock wave effects. The analogy of the explosion of a container of pressurized gas to a condensed phase point source explosion of TNT is not appropriate in the near field since the vessel is not a point source. Prugh (1988) suggests a correction method using a virtual distance from an explosion center based on work by Baker et al. (1983) and Petes (1971). This method is described below. When an idealized sphere bursts, the air shock has its maximum overpressure right at the contact surface between the gas sphere and the air. Since, initially, the flow is strictly one-dimensional, a shock tube relationship between the bursting pressure ratio and shock pressure can be used to calculate the pressure in the air shock. The blast pressure, Ps, at the surface of an exploding pressure vessel is thus estimated from the following expression (Baker et al., 1983; Prugh, 1988):

(3.14) where Ps is the pressure at the surface of the vessel (bar abs) P b is the burst pressure of the vessel (bar abs)

y is the heat capacity ratio of the expanding gas (Cp/Cv) T is the absolute temperature of the expanding gas (K) M is the molecular weight of the expanding gas (mass/mole) The above equation assumes that expansion will occur into air at atmospheric pressure at a temperature of 25°C. A trial and error solution is required since the equation is not explicit for Ps. Equation (3.14) also assumes that the explosion energy is distributed uniformly across the vessel. In reality this is rarely the case. The procedure of Prugh (1988) for determining the overpressure at a distance from a bursting vessel is as follows: 1. Determine the energy of explosion using Eq. (3.12). 2. Determine the blast pressure at the surface of the vessel, Ps, using Eq. (3.14). This is a trial and error solution. 3. The scaled distance, Z, for the explosion is obtained from Figure 3.3, or the equations in Table 3.1. Most pressure vessels are at or near ground level. 4. A value for the distance, R, from the explosion center is calculated using Eq. (3.7) where the equivalent energy of TNT, W^ has been calculated from Eq. (3.1). 5. The distance from the center of the pressurized gas container to its surface is subtracted from the distance, it, to produce a virtual "distance" to be added to distances for shock wave evaluations. 6. The overpressure at any distance is determined by adding the virtual distance to the actual distance, and then using this distance to determine Z, the scaled distance. Figure 3.3 or Table 3.1 is used to determine the resulting overpressure. AIChE/CCPS (1994) describe a number of techniques for estimating overpressure for a rupture of a gas filled container. These methods are derived mostly from the work of Baker et al. (1983) based on small scale experimental studies. The first method is called the "basic method" (AIChE/CCPS, 1994). The procedure for this method is 1. Collect data. This includes: • the vessel's internal absolute pressure, P 1 • the ambient pressure, P 0 • the vessel's volume of gas filled space, V • the heat capacity ratio of the expanding gas, y • the distance from the center of the vessel to the "target," r • the shape of the vessel: spherical or cylindrical

2. Calculate the energy of explosion, E, using the Brode equation, Eq. (3.11). The result must be multiplied by 2 to account for a surface explosion. __ 3. Determine the scaled distance, R, from the target using (3.15) 4. Check the scaled distance. IfH < 2 then this procedure is not applicable and the refined method described later must be applied. 5. Determine the scaled overpressure, Ps, and scaled impulse, is, using Figures 3.13 and 3.14, respectively. 6. Adjust Ps and is for geometry effects using the multipliers shown in Tables 3.7 and 3.8. 7. Determine the final overpressure and impulse from the definitions of the scaled variables. 8. Check the final overpressure. In the near field, this approach might produce a pressure higher than the vessel pressure, which is physically impossible. If this occurs, take the vessel pressure as the calculated overpressure.

Scaled Overpressure, P8 = ps/ P0 -1

If R < 2, then the above procedure must be replaced by a more detailed approach (AIChE/CCPS, 1994). This approach replaces steps 4 and 5 above in the basic procedure with the following steps:

Scaled Distance, R - r (P0/ E)1/3 FIGURE 3.13. Scaled overpressure curve for rupture of a gas-filled vessel for the basic method.

Scaled Impulse,!= (I8I0V(P^E1*)

Scaled Distance, R = r (Po/E)1/3 FIGURE 3.14. Scaled impulse curve for rupture of a gas-filled vessel for the basic method. The upper and lower lines are error limits for the procedure. TABLE 3.7. Adjustment Factors for P5 and i5 for Cylindrical Vessels as a Function of R (Baker et al., 1975) Multiplier for

TABLE 3.8. Adjustment Factors for P5 and isfor Spherical Vessels as a Function of R (Baker et al., 1975)

Multiplier for R

Scaled variable definitions:

Ps

I

4a. Calculate the initial vessel radius. A hemispherical vessel on the ground is assumed for this calculation. From simple geometry for a sphere, the following equation for the initial vessel radius is obtained: (3.16) where r0 is the initial vessel radius (length) and V is the vessel volume (length3) 4b. Determine the initial starting distance, R0, for the overpressure curve, (3.17)

Scaled Overpressure, P8 - ps/P0 - 1

4c. Calculate the initial peak pressure, Ps, using Eq. (3.14). A trial and error solution is required. 4d. Locate the starting point on the overpressure curves of Figure 3.15 using R0 andPs. The closest curve shown on the figure, or an interpolated curve is appropriate here. 5. DeterminePs at another R from Figure 3.15 using the curve (or interpolated curve) which goes through the starting point of step 4d.

Scaled Distance, R = r (P 0 /E) 1 ' 3 FIGURE 3.15. Scaled overpressure curve for rupture of a gas-filled vessel for the more detailed method.

Tang et al. (1996) present the results of a detailed numerical simulation procedure to model the effects of a bursting spherical vessel. They numerically solved the nonsteady, nonlinear, one-dimensional flow equations. This resulted in a more detailed figure to replace Figure 3.15. AIChE/CCPS (1994) also provides a more detailed method to include the effects of explosively flashing liquids during a vessel rupture. Projectiles When a high explosive detonates, a large number of small fragments with high velocity and chunky shape result (AIChE/CCPS, 1994). In contrast, a BLEVE produces only a few fragments, varying in size (small to large), shape (chunky or disk shaped), and initial velocities. Fragments can travel long distances because large, half-vessel fragments can "rocket53 and disk-shaped fragments can "frisbee." Schulz-Forberg et al. (1984) describe an investigation of BLEVE-induced vessel fragmentation. Baum (1984) also discusses velocities of missiles from bursting vessels and pipes. Baker et al. (1983), Brown (1985,1986) and AIChE/CCPS (1994) provide formulas for prediction of projectile effects. They consider fracture of cylindrical and spherical vessels into 2, 10, and 100 fragments. Typically, for these types of events, only 2 or 3 fragments occur. The first part of the calculation involves the estimation of an initial velocity. Once fragments are accelerated they will fly through the air until they impact another object or target on the ground. The second part of the calculation involves estimation of the distance a projectile could travel. In general, according to Baker et al. (1983), the technique for predicting initial fragment velocities for spherical or cylindrical vessels bursting into equal fragments requires knowledge of the internal pressure (P), internal volume (F 0 ), mass of the container/fragment (Mc), ratio of the gas heat capacities (y), and the absolute temperature of the gas at burst (T0). The results of a parameter study (Baker et al., 1983) were used to develop Figure 3.16, which is used to determine the initial fragment velocity, u. The scaled pressure in Figure 3.16 is given by

(3.18) where P is the scaled pressure (unitless) P is the burst pressure of the vessel (force/area) P 0 is the ambient pressure of the surrounding gas (force/area) V is the volume of the vessel (length3)

Scaled Fragment Velocity = Vj /K ao

Cylindrical

Spherical Cylindrical, n »2

Scaled Pressure, P = (P - F^ ) V / (Mca*) FIGURE 3.16. Scaled fragment velocity versus scaled pressure (Baker et al., 1983). Mc is the mass of the container (mass) a0 is the speed of sound of the initial gas in the vessel (length/time) The speed of sound for an ideal gas is computed from (3.19) where a0 is the speed of sound (length/time) T is the absolute temperature (temperature) Y is the heat capacity ratio of the gas in the vessel (unitless) Rg is the ideal gas constant (pressure - volume/mole deg) M is the molecular weight of the gas in the vessel (mass/mole) Thejy-axis in Figure 3.16 is the dimensionless velocity given by (3.20) where v{ is the velocity of the fragment (length/time), K is a correction factor for unequal mass fragments given by Figure 3.17, and a0 is the speed of sound of the gas in the vessel (length/time) Table 3.9 contains curve fit equations for the fragment velocity correlations presented in Figure 3.16. The data in Figure 3.17 are curve fit by the equation K = 1.306 X (Fragment Mass Fraction) + 0.308446 The procedure for applying this approach is as follows:

(3.21)

Adjustment Factor, K

Fragment Fraction of Total Mass FIGURE 3.J7. Adjustment factor for unequal mass fragments (Baker et al., 1983).

1. Given:

2. 3. 4. 5. 6.

Number of fragments, n Total mass of vessel, Mc Mass fraction for each fragment Internal burst pressure of vessel, P Volume of vessel, V Ambient pressure, P 0 Absolute temperature of gas in vessel, T Heat capacity ratio of gas in vessel, y Molecular weight of gas in vessel, M Determine speed of sound of gas in vessel using Eq. (3.19). Determine scaled pressure using Eq. (3.18). Determine dimensionless velocity from Figure 3.16 or Table 3.9. Determine unequal fragment correction from Figure 3.17 or Eq. (3.21). Determine actual velocity for each fragment using Eq. (3.20).

An empirically derived formula developed by Moore (1967) provides a simplified method to determine the initial velocity, #, of a fragment, (3.22)

where for spherical vessels (3.23)

TABLE 3.9. Curve Fit Equations for the Fragment Velocity Data of Figure 3 . 1 6

Spheres Number of fragments, n

a

Cylinders b

a

b

Variables: vi is the velocity of the fragment (length/time) K is the correction factor for unequal fragments a0 is the speed of sound of the gas in the vessel (length/time) P is defined by Eq. (3.18)

and for cylindrical vessels (3.24)

where u is the initial fragment velocity (m/s) C is the total gas mass (kg) E is the energy (J) Mc is the mass of casing or vessel (kg) Moore's equation was derived for fragments accelerated from high explosives packed in a casing. The equation predicts velocities higher than actual, especially for low pressures and few fragments. For pressurized vessels, a simplified method to determine the initial velocity of a fragment is by the Moore (1967) equation, (3.25) where u P D W

is the initial velocity of the fragment (ft/s) is the rupture pressure of the vessel (psig) is the fragment diameter (inches) is the weight of the fragment (Ib)

The next step is to determine the distance the fragments will fly. From simple physics, it is well-known that an object will fly the greatest distance at a trajectory angle of 45°. The maximum distance is given by (3.26) where rmax is the maximum horizontal distance (length), u is the initial object velocity (length/time), andg is the acceleration due to gravity (length/time2). Kinney and Graham (1985) suggest a very simple formula for estimating a safety distance from a bomb explosion (3.27)

where r is the distance (m) and w is the mass of TNT (kg). Baker et al. (1983) plotted the solutions to a set of differential equations, incorporating the effects of fluid-dynamic forces. The solutions are shown on Figure 3.18. The results assume that the position of the fragment remains the same with respect to its trajectory, that is, that the fragment does not tumble. Figure 3.18 plots scaled maximum range, JR., versus the scaled initial velocity, u. These quantities are given by (3.28)

LAL

Scaled Fragment Range, R = -^JJ—-

C

P0CbADU Scaled Initial Velocity, u = — M,g FIGURE 3.18. Scaled fragment range versus scaled initial distance (Baker et al., 1983).

(3.29) where R is the scaled maximal range (dimensionless) u is the scaled initial velocity (dimensionless) r is the maximal range (length) p 0 is the density of the ambient atmosphere (mass/volume) C D is the drag coefficient, provided in Table 3.10 (unitless) AD is the exposed area in plane perpendicular to the trajectory (area) g is the acceleration due to gravity (length/time2) Mf is the mass of the fragment (mass) Figure 3.18 requires a specification of the lift-to-drag ratio, (3.30) where CL is the lift coefficient (unitless) and^4L is the exposed area in the plane parallel to the trajectory (area). For "chunky" fragments, which are normally expected, the lift coefficient is zero for these objects and the lift-to-drag ratio is thus zero. For thin plates, which have a large lift-to-drag ratio, the "frisbee" effect can occur, and the scaled range more than doubles the range calculated when lift forces are neglected. Refer to Baker et al. (1983, Appendix E, page 688) for a discussion and additional values for the lift coefficient, CL. Table 3.10 contains drag coefficients for various shapes. The procedure for implementing this method is as follows: 1. Given:

2. 3. 4. 5.

Fragment mass, Mf Initial fragment velocity, u Exposed area perpendicular to direction of movement, AD Density of the ambient air, p0 Lift to drag ratio. Determine drag coefficient from Table 3.10. Determine scaled velocity from Eq. (3.29). Determine scaled range from Figure 3.18. Determine actual range from Eq. (3.28)

The dashed line on Figure 3.18 represents the maximum range computed using Eq. (3.26). Brown (1985,1986) provides other methods for fragment prediction. Additional references on projectiles include Sun et al. (1976), TNO (1979), and

TABLE 3.10. Dratj Coefficients for Fragments (Baker et al., 1983) Shape Bight circular cylinder (long rod), side on

Sketch

Cp

Flow

1.20

Sphere

0.47

Flow

Rod, end on

0.82

Flow

Disk, face on

or

1.17

Fbw

Cube, face on

1.05

Flow

0.80

Cube, edge on

Long rectangular member, face on

Flow

Long rectangular member, edge on

Flow

2.05

1.55

Ftow

Narrow strip, face on

1.98

Tunkel (1983). TNO considers that the most likely failure point will be at an attachment to the vessel, so they consider nozzles, manholes, and valves as typical projectiles in their analysis. Fragment distances and sizes are discussed further in Section 3.4 (BLEVE) and Section 4.4 (injuries and damage from projectiles). Applications In general, these types of failures result in risk to in-plant personnel. However, vessel fragments can be accelerated to significant distances. The Canvey Study (Health & Safety Executive, 1978) considered projectile damage effects on other process vessels. Logic Diagram A logic diagram for the modeling of projectile effects due to the explosion of pressure vessels is provided in Figure 3.19. Theoretical Foundation The technology of energy release from pressurized gas containers has been receiving attention for over a century beginning with catastrophic failures of boilers and other pressure vessels. Ultra high pressure systems has also generated interest. Much experimental work has been done, primarily small scale with containers which burst into a large number of fragments, to relate the shock wave phenomena to the well developed TNT relationships. Input Requirements and Availability The technology requires data on container strength. Maximum bursting pressure of the container can be derived from specific information on the metallurgy and design. In accidental releases, pressure within a vessel at the time of failure is not always known. However, an estimate can usually be made (AIChE/CCPS, 1994). If failure is initiated by a rise in initial pressure in combination with a malfunctioning or inadequately designed pressure-relief device, the pressure at rupture will equal the vessel's failure pressure, which is usually the maximum allowable working pressure (MAWP) times a safety factor. For initial calculations, a usual safety factor of four is applied for vessels made of carbon steel, although higher values are possible. In general, the higher the failure pressure, the more severe the effect. Output The output from this analysis is overpressure and impulse versus distance for shock wave effects and the velocity and expected maximum range of projectiles which are generated by the burst vessel.

Rupture of a Pressurized Vessel

Estimate Number of Fragments

Estimate Initial Fragment Velocity

Estimate Maximum Range of Fragment

Assess Impact of Projectiles on Surrounding Areas FIGURE 3.19. Logic diagram for the calculation of projectile effects for rupture of pressurized gas-filled vessels.

Simplified Approaches The techniques presented are basically simplified approaches. It can be conservatively assumed that 100% of the stored energy is converted to a shock wave. 3.3.3. EXAMPLE PROBLEMS Example 22: Energy of Explosion for a Compressed Gas A 1-m3 vessel at 25°C ruptures at a vessel burst pressure of 500 bar abs. The vessel ruptures into ambient air at a pressure of 1.01 bar and 25°C. Determine the energy of explosion and equivalent mass of TNT using the following methods: a. Brode's equation for a constant volume expansion, Eq. (3.11). b. Brown's equation for an isothermal expansion, Eq. (3.12) c. CrowPs equation for thermodynamic availability, Eq. (3.13)

Solution: (a) Substituting the known values into Eq. (3.11)

Since TNT has an explosion energy of 1120 cal/gm = 4.69 X 106 J/kg TNT equiv. mass (b) For this case, Im 3 = 35.3 ft3, T0 = 536°R. Substituting into Eq. (3.12)

Since TNT has an energy of 4.69 x 106 J/kg, this represents 342 MJ of energy, c. Substituting into Eq. (3.13),

The number of moles of gas in the vessel is determined from the ideal gas law. It is 20,246 gm-moles. The total energy of explosion is thus,

This is equivalent to 55.7 kg of TNT.

Example 22: Energy of Explosion for a Compressed Gas Input Data: Vessel volume: Vessel pressure: Final pressure of expanded gas: Ambient pressure: Heat capacity ratio of expanding gas: Temperature of gas: Calculated Results: Brode's equation assuming constant volume expansion: Energy of explosion: 1.25E+08 Joules TNT equivalent: 26.60 kg TNT

t

Brown's equation assuming isothermal expansion: TNT equivalent: 160.68 IbTNT 72.89 kg TNT Energy of explosion: 3.42E+08 Joules Crowl's equationfromthermodynamic availability: Moles of gas in vessel: 20246.36 gm-moles Energy of explosion: 2.61 E+08 Joules TNT equivalent: 55.69 kg TNT FIGURE 3.20. Spreadsheet output for Example 22: Energy of explosion for a compressed gas.

The calculation for all three parts of this example is readily implemented via spreadsheet. The output is shown in Figure 3.20. The three methods do provide considerably different results. Example 23: Prugh's Method for Overpressure from a Ruptured Sphere A 6-ft3 sphere containing high pressure air at 77°F ruptures at 8000 psia. Calculate the side-on overpressure at a distance of 60 ft from the rupture. Assume an ambient pressure of 1 atm and temperature of 77°F. Additional data for air: Heat capacity ratio, y: 1.4 Molecular weight of air: 29 Solution: From Eq. (3.12)

For this particular case,

Substituting into the equation

The pressure at the surface of the vessel is calculated from Eq. (3.14)

where P s is the pressure at surface of vessel, 1.01 bar abs P b is the burst pressure of vessel, 551 bar abs Y = 1.4 T = 2980K M = 29 gm/gm-mole By a trial-and-error solution

Since the vessel is at grade, the blast wave will be hemispherical. The scaled pressure is

From Figure 3.3, and Eq. (3.7)

Since W = 13.8 kg TNT it follows that R = 2.74 m = 8.99 ft. The radius of the spherical container is

The "virtual distance" to be added to distances for blast effects evaluations would be 8.99 - 1.4 = 7.59 feet (2.31 m). Therefore, the blast pressure at a distance of 60 ft (18.28 m) from the center of the sphere would be evaluated using a scaled distance of or

From Figure 3.3 this results in a final overpressure of 18.38 kPa or 2.67 psia. Without the virtual distance, the final overpressure is 3.18 psi. The entire procedure is readily implemented via a spreadsheet, as shown in Figure 3.21. This implementation requires two trial-and-error procedures. The first is used to determine the pressure at the surface of the vessel and the second procedure is used to determine the final overpressure. The user must manually adjust the guessed value until the recomputed value is identical. Example 24: Baker's Method for Overpressure from a Ruptured Vessel Rework Example 23 using Baker's method. Solution: The steps listed in the text are followed. STEP 1: Collect data. The data are already listed in Example 23. STEP 2: Calculate the energy of explosion. The Brode equation, Eq. (3.11) is used.

This result must be multiplied by 2 to use the overpressure curves for an open blast. The effective energy is thus 46.9 MJ. STEP 3: Determine the scaled distance. From Eq. (3.15)

STEP 4: Check if R > 2. This is satisfied in this case. STEP 5: Determine the scaled overpressure from Figure 3.13. The result is 0.098. STEP 6: Adjust the overpressure for geometry effects. Table 3.8 contains the multipliers for spherical vessels. The multiplier is 1.1. Thus, the effective scaled overpressure is (l.l)(0.098) = 0.108.

Example 23: Prugh's Method for Overpressurefroma Ruptured Sphere Input Data: Vessel burst pressure: Distance from vessel center: Vessel volume: Final pressure: Heat capacity ratio: Molecular weight of gas: Gas temperature: Calculated Results: English units equivalents of above data: Vessel burst pressure: Vessel volume: Final pressure: Temperature: Energy of Explosion from Brown's Equation: Trial and error solution to determine surface pressure: Guessed Value: Calculated Value: English Equivalent: Trial and error solution to determine virtual distance: TNT Mass: Distance from blast: Calculated Results: Scaled distance, z: Overpressure Calculation: a+b*log(z): Overpressure:

Adjust until equal to value immediately below

Adjust to match surface pressure above OK value!

(only valid for z > 0.0674 and z < 40) Must match surface pressure above

Radius of vessel: Virtual distance to add: Effective distance from blast: Final overpressure calculation using effective distance: TNT Mass: Distance from blast: Calculated Results: Scaled distance, z: Overpressure Calculation: a+b*log(z): Overpressure:

OK value! (only valid for z > 0.0674 and z < 40)

FIGURE 3.21. Spreadsheet output for Example 23: Prugh's method for overpressure from a ruptured sphere.

STEP 7: Determine the final overpressure. From the definition of the scaled pressure,

STEP 8: Check the final pressure. In this case the final pressure is less than the burst pressure of the vessel. This result is somewhat less than the value of 2.57 psi obtained using Prugh's method. The solution is readily implemented via spreadsheet, as shown in Figure 3.22. Example 25: Velocity of Fragments from a Vessel Rupture A 100-kg cylindrical vessel is 0.2 m in diameter and 2 m long. Determine the initial fragment velocities if the vessel ruptures into two fragments. The fragments represent 3/4 and 1/4 of the total vessel mass, respectively. The vessel is filled with helium at a temperature of 300 K, and the burst pressure of the vessel is 20.1 MPa. For helium, Heat capacity ratio, y: 1.67 Molecular weight: 4 Solution: The procedure detailed in the text is applied. 1. Given: Number of fragments, n = 2 Total mass of vessel, Mc = 100 kg Mass fraction for each fragment: first fragment = 0.75, second fragment = 0.25 Internal burst pressure of vessel, P = 20.1 MPa Volume of vessel, V

Ambient pressure, P 0 = 0.101 MPa Absolute temperature of gas in vessel, T = 300 K Heat capacity ratio of gas in vessel, y = 1.67 Molecular weight of gas in vessel, M = A 2. Determine speed of sound of gas in vessel using Eq. (3.19).

Example 24: Baker's Method for Overpressure from a Ruptured Vessel Input Data: Vessel burst pressure: Distance from vessel center: Vessel volume: Final pressure: Heat capacity ratio: Molecular weight of gas: Gas temperature: Speed of sound in ambient gas: Calculated Results: Energy of explosion using Brode's equation for constant volume expansion: Energy of explosion: TNT equivalent: Effective energy of explosion (x 2): Scaled distance: Interpolated scaled overpressure: Interpolated scaled impulse: Vessel shape: Spherical Overpressure multiplier for vessel shape: Corrected scaled overpressure: Actual overpressure:

Cylindrical

Impulse multiplier for vessel shape: Corrected scaled impulse: Actual impulse: FIGURE 3.22. Spreadsheet from Example 24: Baker's method for overpressure from a ruptured vessel.

3. Determine scaled pressure using Eq. (3.18).

4. Determine the dimensionless velocity from Figure 3.16, or Table 3.9. For n = 2, the dimensionless velocity for spheres is 0.079. 5. Determine the unequal fragment correction from Figure 3.17. For mass fraction = 0.75, K = 1.29 and for mass fraction = 0.25, K = 0.63. 6. Determine actual velocity for each fragment using Eq. (3.20).

For the large fragment,

For the small fragment,

The large fragment has the greater velocity, which is due to the unequal fragment correction. This procedure is readily implemented via a spreadsheet, as shown in Figure 3.23. The spreadsheet must be run for each fragment—the output shown is for the large fragment. Example 26: Range of a Fragment in Air A 100 kg end of a bullet tank blows off and is rocketed away at an initial velocity of 25 m/s. If the end is 2 m in diameter, estimate the range for this fragment. Assume ambient air at 1 atm and 25°C. Example 25: Velocity of Fragments from a Vessel Rupture Input Data: Total mass of vessel: Total volume of vessel: Number of fragments: Mass fraction of total for fragment: Pressure of gas within vessel: Ambient gas pressure: Temperature of gas within vessel: Heat capacity ratio of gas within vessel: Molecular weight of gas within vessel: Calculated Results: Speed of sound of gas within vessel: Adjustment factor for unequal mass: Scaled pressure: Dimensionless velocity for various shapes and numbers: Spheres Cylinders

Sphere Cylinder Interpolated dimensionless velocity for actual number of fragments: Actual velocity of fragment: FIGURE 3.23. Spreadsheet output for Example 25: Velocity of fragments from a vessel rupture.

Solution: The ambient air density is first determined. This is determined using the ideal gas law.

The surface area of the fragment is

We will assume that the fragment flies with its full face area perpendicular to the direction of travel. Other orientations will result in different ranges. For the case where the fragment face is parallel to the direction of travel it is possible that the fragment might "frisbee" as a result of lift: generated during its movement. The drag coefficient, CD is determined from Table 3.10. For a round fragment with its face perpendicular to the direction of travel, CD = 0.47. The scaled velocity is determined from Eq. (3.29),

From Figure 3.18, the scaled fragment range is

The actual range is determined from Eq. (3.28)

The maximum range is determined from Eq. (3.26).

The calculation is readily implemented via a spreadsheet, as shown in Figure 3.24. The data of Figure 3.18 is contained within the spreadsheet, but not shown. Also shown on the output is the maximum distance achieved assuming the presence of lift. This is the maximum range for any of the specified values of the lift to drag ratio. Note that with lift it is possible to exceed the maximum range and, in some cases, the increase can be to more than twice the maximum range.

Example 2.26: Range of a Fragment in Air Input Data: Mass of fragment: Initial fragment velocity: Drag coefficient of fragment: Lift to drag ratio: Exposed area of fragment: Temperature of ambient air: Pressure of ambient air: Calculated Results: Density of ambient air: Scaled velocity of fragment: Interpolated values from figure for various lift to drag ratios: Lift to drag ratio

Scaled Range

Range (m)

Interpolated range: Theoretical max. range (no lift): Max. possible range (with lift): FIGURE 3.24. Spreadsheet output for Example 26: Range of a fragment in air.

3.3.4. DISCUSSION

Strengths and Weaknesses The main strength of these methods is that they are based mostly on experimental data. The weakness is that many of the approaches are empirical in nature, using correlations based on dimensional or dimensionless groups. Extrapolation outside of the range of the correlations provided may lead to erroneous results. For the purposes of this text, the range of validity may be assumed to be the range provided by the figures and tables. The energy of explosion methods assume that the explosion occurs from a point source, which is rarely the case in actual process equipment explosions.

Identification and Treatment of Possible Errors It is very difficult to predict the number of projectiles and where they will be propelled. These methods are more suited for accident investigations, where the number, size and location of the fragments is known. Utility In general, vessels of pressurized gas do not have sufficient stored energy to represent a threat from shock wave beyond the plant boundaries. These techniques find greater application involving in-plant risks. These types of incidents can result in domino effects particularly from the effects of the projectiles produced. Very few CPQRA studies have ever incorporated projectile effects on a quantitative basis. Resources A process engineer should be able to perform each type of calculation in a few hours. Spreadsheet applications are useful. Available Computer Codes. DAMAGE (TNO, Apeldoorn, The Netherlands) SAFESITE (W. E. Baker Engineering, Inc., San Antonio, TX) Several integrated analysis packages contain explosion fragment capability. These include:

QRAWorks (PrimaTech, Columbus, OH) SUPERCHEMS (Arthur D. Little, Cambridge, MA)

3 . 4 . BLEVE a n d F i r e b a l l

3.4.1. BACKGROUND

Purpose This section addresses a special case of a catastrophic rupture of a pressure vessel. A boiling liquid expanding vapor explosion (BLEVE) occurs when there is a sudden loss of containment of a pressure vessel containing a superheated liquid or liquified gas. This section describes the methods used to calculate the effects of the vessel rupture and the fireball that results if the released liquid is flammable and is ignited. Philosophy A BLEVE is a sudden release of a large mass of pressurized superheated liquid to the atmosphere. The primary cause is usually an external flame impinging on the

shell of a vessel above the liquid level, weakening the container and leading to sudden shell rupture. A pressure relief valve does not protect against this mode of failure, since the shell failure is likely to occur at a pressure below the set pressure of the relief system. It should be noted, however, that a BLEVE can occur due to any mechanism that results in the sudden failure of containment, including impact by an object, corrosion, manufacturing defects, internal overheating, etc. The sudden containment failure allows the superheated liquid to flash, typically increasing its volume over 200 times. This is sufficient to generate a pressure wave and fragments. If the released liquid is flammable, a fireball may result. A special type of BLEVE involves flammable materials, such as LPG. A number of such incidents have occurred including San Carlos, Spain (July 11, 1978), Crescent City, Illinois (June 21, 1970), and Mexico City, Mexico (November 19, 1984). Films of actual BLEVE incidents involving flammable materials (NFPA, 1994) clearly show several stages of BLEVE fireball development. At the beginning of the incident, a fireball is formed quickly due to the rapid ejection of flammable material due to depressurization of the vessel. This is followed by a much slower rise in the fireball due to buoyancy of the heated gases. BLEVE and projectile models are primarily empirical. A number of papers review BLEVE modeling, including AIChE (1994), Moorehouse and Pritchard (1982), Mudan (1984), Pitblado (1986), and Prugh (1988). Application BLEVE models are often required for risk analysis at chemical plants (e.g., Rijnmond Public Authority, 1982) and for major accident investigation (e.g., Mexico City, Pietersen and Huerta, 1985). 3.4.2. DESCRIPTION

Description of Technique The calculation of BLEVE incidents is a stepwise procedure. The first step should be pressure and fragment determination, as this applies to all BLEVE incidents (whether for flammable materials or not). For flammable materials the prediction of thermal intensity from fireballs should also be considered. This requires a determination of the fireball diameter and duration. AIChE (1994) provides the most up-to-date reference on modeling approaches for BLEVEs. Blast Effects Blast or pressure effects from BLEVEs are usually small, although they might be important in the near field (such as the BLEVE of a hot water heater in a room).

These effects are of interest primarily for the prediction of domino effects on adjacent vessels. However, there are exceptions. Some BLEVEs of large quantities of nonflammable liquids (such as CO2) can result in energy releases of tons of TNT equivalent. The blast wave produced by a sudden release of a fluid depends on many factors (AIChE, 1994). This includes the type of fluid released, energy it can produce on expansion, rate of energy release, shape of the vessel, type of rupture, and the presence of reflecting surfaces in the surroundings. Materials below their normal boiling point cannot BLEVE. Baker et al. (1983) discuss pressure wave prediction in detail and provides a sample problem in Chapter 2 of their book. TNO (1979) also provide a physical explosion model, which is used by Pietersen and Huerta (1985) in the analysis of the Mexico City incident. Prugh (1988) presents a method for calculating a TNT equivalent that also incorporates the flash vaporization process of the liquid phase in addition to the vapor phase originally present. AIChE (1994) states that the blast effect of a BLEVE results not only from the rapid expansion (flashing) of the liquid, but also from the expansion of the compressed vapor in the vessel's head space. They claim that, in many incidents, head-space vapor expansion produces most of the blast effects. AIChE (1994) describes a procedure developed by Baker et al. (1975) and Tang et al. (1996) for determining both the peak overpressure and impulse due to vessels bursting from pressurized gas. This procedure is too detailed to be described in detail here. The method results in an estimate of the overpressure and impulse due to blast waves from the rupture of spherical or cylindrical vessels located at ground level. The method depends on the phase of the vessel's contents, its boiling point at ambient pressure, its critical temperature, and its actual temperature. An approach is also presented to determine blast pressures in the near-field, based on the results of numerical simulations. These methods are only for the prediction of pressure effects. Fragments The prediction of fragment effects is important, as many deaths and domino damage effects are attributable to fragments. The method of Baker et al. (1983) can be used, but specific work on BLEVE fragmentation hazards has been done by the Association of American Railroads (AAR) (1972, 1973) and by Holden and Reeves (1985). The AAR reports that of 113 major failures of horizontal cylindrical tanks in fire situations, about 80% resulted in projected fragments. Fragments are usually not evenly distributed. The vessel's axial direction receives more fragments than the side directions. Baker et al. (1983) discuss fragment prediction in detail. Figure 3.25 provides data for the number of fragments and the fragment range, based on work by Holden and Reeves (1985). Figure

Range, R (m)

LPG Events

LPG Events Percent Fragments with Range < R

Number of Fragments

No. of Fragments = (Vessel Capacity, m3)

Vessel Capacity, m3 FIGURE 3.25. Correlations for the fragment range and number of fragments. (From Hodlen and Reeves, 1985.)

3.25 shows that roughly 80% of fragments fall within a 300-m (1000-ft) range. Interestingly, BLEVEs from smaller LPG vessels have a history of greater fragment range; one end section at the Mexico City LPG BLEVE incident traveled 1000 m (3300 ft). The total number of fragments is approximately a function of vessel size. Holden and Reeves (1985) suggest a correlation based on seven incidents, as shown in Figure 3.25. Number of fragments = -3.77 + 0.0096[Vessel capacity (m3)] (3.31) Range of validity: 700-2500 m3 Figure 3.25 and the AAR data (Association of American Railroads, 1972, 1973) indicate that a small number of fragments is likely in any BLEVE incident regardless of size. BLEVEs typically produce fewer fragments than high pressure

detonations—between 2 and 10 are typical. BLEVEs usually don't develop the high pressures which lead to greater fragmentation. Instead, metal softening from the heat exposure and thinning of the vessel wall yields fewer fragments. Normally, propane (LPG) storage tanks are designed for a 250-psig working pressure. A normal burst pressure of four times the working pressure is expected for ASME coded vessels, or 1000 psig. BLEVEs usually occur because of flame impingement on the unwetted portion (vapor space) of the tank. This area rapidly reaches 12000F and becomes sufficiently weakened that the tank fails at approximately 300-400 psig (Townsend et al., 1974). Empirical Equations for BLEVE Fireball Diameter, Duration, and Fireball Height Pitblado (1986) lists thirteen published correlations and compares BLEVE fireball diameters as a function of mass released. The TNO formula (Pietersen and Huerta, 1985) gives good overall fit to observed data, but there is substantial scatter in the source data. All models use a power law correlation to relate BLEVE diameter and duration to mass. Useful formulas for BLEVE physical parameters are (AIChE, 1994): Maximum fireball diameter (m): Dmax =5.8 M1/3

(3.32)

Fireball combustion duration (s): (3.33) (3.34) Center height of fireball (m): JJBLEVE = 0.75 Dmax Initial ground level hemisphere diameter (m): D-^31 = 1.3Dmax

(3.35) (3.36)

where M is the initial mass of flammable liquid (kg). The particular formulas for fireball diameter and duration do not include the volume of oxygen for combustion. This, of course, varies and should affect the size of the fireball. The initial diameter is used to describe the initial ground level fireball before buoyancy forces lift it. Radiation Four parameters used to determine a fireball's thermal radiation hazard are the mass of fuel involved and the fireball's diameter, duration, and thermal emissive power (AIChE, 1994). The radiation hazards are then calculated using empirical relations. The problem with a fireball typical of a BLEVE is that the radiation will depend on the actual distribution of flame temperatures, the composition of the gases in the vicinity of the fireball (including reactants and products), the geometry

of the fireball, absorption of the radiation by the fireball itself, and the geometric relationship of the receiver with respect to the fireball. All of these parameters are difficult to quantify for a BLEVE. Johnson et al. (1990) completed experiments with fireballs of butane and propane of from 1000 to 2000 kg size released from pressurised tanks. They found average surface emissive radiation of between 320 to 375 kw/m2, a fireball duration of from 4.5 to 9.2 s and fireball diameters of 56 to 88 m. AIChE (1994) suggests using an emissive power of 350 kW/m2 for large-scale releases of hydrocarbon fuels, with the power increasing as the scale of the release decreases. The emissive radiative flux from any source is represented by the Stefan-Boltzmann law: (3.37) where En^ is the maximum radiative flux (energy/area time); a is the Stefan-Boltzmann constant (5.67 x 10- n kW/m 2 K 4 = 1.71 x 10"9 BTU/hr ft2 0 R); and T{ is the absolute temperature of the radiative source (deg). Equation (3.37) applies only to a black-body and provides the maximum radiative energy flux. For real sources, the emissive power is given by (3.38) where E is emissive energy flux (energy/area time) and e is emissivity (unitless). The emissivity for a black-body radiator is unity, whereas the emissivity for a real radiation source is typically less than unity. For fireballs, Beer's law is used to determine the emissivity (AIChE, 1994). This is represented by the following equation: (3.39) where k is an extinction coefficient (1/length) and D is the fireball diameter (length) Hardee et al. (1978) measured an extinction coefficient of 0.18 m"1 from LNG fires, but AIChE (1994) reports that this overpredicts somewhat the radiation from fireballs. Thermal radiation is usually calculated using surface emitted flux, E^ rather than the Stefan-Boltzmann equation, as the latter requires the flame temperature. Typical energy fluxes for BLEVEs (200-350 kW/m2) are much higher than in pool fires as the flame is not smoky. Roberts (1981) and Hymes (1983) provide a means to estimate surface heat flux based on the radiative fraction of the total heat of combustion. (3.40)

where E is the radiative emissive flux (energy/area time) R is the radiative fraction of the heat of combustion (unitless) M is the initial mass of fuel in the fireball (mass) Hc is the net heat of combustion per unit mass (energy/kg) Dm3X is the maximum diameter of the fireball (length) ^BLEVE iS t n e duration of the fireball (time) Hymes (1983) suggests the following values for it: 0.3 for fireballs from vessels bursting below the relief set pressure 0.4 for fireballs from vessels bursting at or above the relief set pressure. AIChE (1994) combines Eq. (3.40) with the empirical equation by Robert's (1981) for the duration of the combustion phase of a fireball. This results in an equation for the radiation flux received by a receptor, Ex., at a distance L (3.41) where Er is the radiative flux received by the receptor (W/m2) t a is the atmospheric transmissivity (unitless) R is the radiative fraction of the heat of combustion (unitless) Hc is the net heat of combustion per unit mass (J/kg) M is the initial mass of fuel in the fireball (kg) Xc is the distance from the fireball center to the receptor (m) The atmospheric transmissivity, ra, is an important factor. Thermal radiation is absorbed and scattered by the atmosphere. This causes a reduction in radiation received at target locations. Some thermal radiation models ignore this effect, effectively assuming a value of ra = 1 for the transmissivity. For longer path lengths (over 20 m), where absorption could be 20-40%, this will result in a substantial overestimate for received radiation. Useful discussions are given in Simpson (1984) andPitblado (1986). Pietersen andHuerta (1985) recommend a correlation formula that accounts for humidity (3.42)

where ra is the atmospheric transmissivity (fraction of the energy transmitted: 0 to 1); P w is the water partial pressure (Pascals, N/m 2 ); Xs is the path length, distance from the flame surface to the target (m). An expression for the water partial pressure as a function of the relative humidity and temperature of the air is given by Mudan and Croce (1988).

(3.43)

where Pw is the water partial pressure (Pascals, N/m 2 ); (RH) is the relative humidity (percent); Ta is the ambient temperature (K). A more empirically based equation for the radiation flux is presented by Roberts (1981) who used the data of Hasegawa and Sato (1977) to correlate the measured radiation flux received by a receptor at a distance, L, from the center of the fireball, (3.44)

with variables and units identical to Eq. (3.41). The radiation received by a receptor (for the duration of the BLEVE incident) is given by (3.45) where Ex is the emissive radiative flux received by a black body receptor (energy/area time) ra is the transmissivity (dimensionless) E is the surface emitted radiative flux (energy/area time) P21 is a view factor (dimensionless) As the effects of a BLEVE mainly relate to human injury, a geometric view factor for a sphere to a receptor is required. In the general situation, a fireball center has a height, H, above the ground. The distance L is measured from a point at the ground directly beneath the center of the fireball to the receptor at ground level. For a horizontal surface, the view factor is given by (3.46) where D is the diameter of the fireball. When the distance, L, is greater than the radius of the fireball, the view factor for a vertical surface is calculated from (3.47)

More complex view factors are presented in Appendix A of AIChE (1994). For a conservative approach, a view factor of 1 is assumed. Once the radiation received is calculated, the effects can be determined from Section 4.3.

Logic Diagram A logic diagram showing the calculation procedure is given in Figure 3.26. This shows the calculation sequence for determination of shock wave, thermal, and fragmentation effects of a BLEVE of a flammable material.

BLEVE Thermal Radiation Mass of Flammable

Estimate BLEVE Size and Duration Equations (3.32) - (3.36)

Radiant Fraction Emitted

Estimate Surface Emitted Flux Equation (3.40)

Distance to Target

Estimate Geometric View Factor Equations (3.46) - (3.47)

Estimate Atmospheric Transmissivity Equation (3.42)

Estimate Received Thermal Flux Equation (3.45)

Determine Thermal Impact Section 4.3 FIGURE 3.26. Logic diagram for calculation of BLEVE thermal intensity at a specified receptor.

Theoretical Foundation BLEVE models are a blend of empirical correlations (for size, duration, and radiant fraction) and more fundamental relationships (for view factor and transmissivity). Baker et al. (1983) have undertaken a dimensional analysis for diameter and duration which approximates a cube root correlation. Fragmentation correlations are empirical. Input Requirements and Availability BLEVE models require the material properties (heat of combustion and vapor pressure), the mass of material, and atmospheric humidity. Fragment models are fairly simplistic and require vessel volume and vapor pressure. This information is readily available. Output The output of a BLEVE model is usually the radiant flux level and duration. Overpressure effects, if important, can also be obtained using a detailed procedure described elsewhere (AIChE, 1994). Fragment numbers and ranges can be estimated, but a probabilistic approach is necessary to determine consequences. Simplified Approaches Several authors use simple correlations based on more fundamental models. Similarly the Health & Safety Executive (1981) uses a power law correlation to summarize their more fundamental model. Considine and Grint (1984) have updated this to (3.48)

where r50 is the hazard range to 50% lethality (m), t is the duration of BLEVE (s), and M is the mass of LPG in BLEVE (long tons = 2200 Ib). The fragment correlations described for LPG containers are simplified approaches. 3.4.3. EXAMPLE PROBLEMS

Example 27: BLEVE Thermal Flux Calculate the size and duration, and thermal flux at 200 m distance from a BLEVE of an isolated 100,000 kg (200 m3) tank of propane at 200C, 8.2 bar abs (68°F, 120 psia). Atmospheric humidity corresponds to a water partial pressure of 2810 N/m2 (0.4 psi). Assume a heat of combustion of 46,350 kj/kg. Solution. The geometry of the BLEVE are calculated from Eqs. (3.32)(3.36). For an initial mass, M = 100,000 kg, the BLEVE fireball geometry is given by

For the radiation fraction, R, assume a value of 0.3 (Hymes, 1983; Roberts, 1981). The emitted flux at the surface of the fireball is determined from Eq. (3.40),

The view factor, assuming a vertically oriented target, is determined from Eq. (3.47).

The transmissivity of the atmosphere is determined from Eq. (3.42). This requires a value, Xs, for the path length from the surface of the fireball to the target, as shown in Figure 3.27. This path length is from the surface of the fireball to the receptor and is equal to the hypotenuse minus the radius of the BLEVE fireball.

BLEVE Fireball

Path Length

Receptor

FIGURE 3.27 Geometry for Example 27: BLEVE thermal flux.

The transmissivity of the air is given by Eq. (3.42),

The received flux at the receptor is calculated using Eq. (3.45)

This received radiation is enough to cause blistering of bare skin after a few seconds of exposure. An alternate approach is to use Eq. (3.41) or (3.44) to estimate the radiative energy received at the receptor. In this case Xc is the distance from the center of the fireball to the receptor. From geometry this is given by

Substituting into Eq. (3.41)

which is close to the previously calculated value of 34.2 kW/m2. Using Eq. (3.44)

which is a different result, more conservative in this case. This problem is readily implemented using a spreadsheet. The spreadsheet output is shown in Figure 3.28.

Example 28: Blast Fragments from a BLEVE A sphere containing 293,000 gallons of propane (approximately 60% of its capacity) is subjected to a fire surrounding the sphere. There is a torchlike flame impinging on the wall above the liquid level in the tank. A BLEVE occurs and the tank ruptures. It is estimated that the tank fails at approximately 350 psig. Estimate the energy release of the failure, the number of fragments to be expected, and the approximate maximum range of the fragments. The inside diameter of the sphere is 50 ft, its wall thickness is % inch, and the shell is made of steel with a density of 487 lbm/ft3. Assume an ambient temperature of 77°F and a pressure of 1 atm.

Example 27: BLEVE Thermal Flux Input Data: Initial flammable mass: Water partial pressure in air: Radiation Fraction, R Distance from fireball center on ground: Heat of Combustion of fuel:

Pascals

Calculated Results: Maximum fireball diameter: Fireball combustion duration: Center height of fireball: Initial ground level hemisphere diameter. Surface emitted flux: Path length: Transmissivity: Horizontal

Vertical

View Factor: Received flux: FIGURE 3.28. Spreadsheet output for Example 27: BLEVE thermal flux.

Solution. The total volume of the sphere is

The volume of liquid is 0.6 X 65,450 ft3 = 39,270 ft3. The vapor volume is 65,450 ft3 - 39,270 ft3 = 26,180 ft3. If we assume that pressure effects are due to vapor alone, ignoring any effect from the flashing liquid, and if we assume isothermal behavior and an ideal gas, then the energy of explosion due to loss of physical containment alone (i.e., no combustion of the vapor) is given by Eq. (3.12)

W = 3090 Ib TNT The TNT equivalent could be used with Eq. (3.1) and Figure 3.3 to determine the overpressure at a specified distance from the explosion.

The number of fragments is estimated using Eq. (3.31). Number of fragments = -3.77 4- 0.0096 (vessel capacity, m3) = -3.77 + 0.0096 (1854 m3) = 14 fragments The total volume of the %-inch (0.0625 ft) vessel shell is

The mass of the vessel is 246 ft3 X 487 lb/ft3 = 119,700 Ib. If this weight is distributed evenly among 14 fragments, the average weight of each fragment is 119,700 lb/14 = 85471b. A quick estimate of the intial velocity of the fragments is determined from Eq. (3.25):

where u is the intial velocity of the fragment (ft/s) P is the rupture pressure (psig) D is the diameter of the fragment (inch) W is the weight of the fragment (Ib) The average diameter of the fragment is estimated by assuming that each shell fragment is crumbled up into a sphere. Thus, we can determine a fragment diameter by assuming a sphere equal in surface area to the original outer surface area of the fragment. The total surface area of the original vessel is

The fragment surface area is then, 7850 6^/14 = 561 ft2. The equivalent diameter of a sphere with this surface area is

Substituting the numbers provided into Eq. (3.25)

The procedure by Baker is used to calculate the approximate range of a missile under these circumstances

From Table 3.10 select a drag coefficient for a sphere CD

= 0.47

The scaled initial velocity in Figure 3.18 can now be calculated,

If it is assumed that the fragment is "chunky," that is,

then from Figure 3.18, for a scaled initial velocity of 50.4

Solving for R

This is the expected range of the fragments. If the fragments were flatter instead of spherical, then the drag coefficient would be larger and the resulting distance would be less. The spreadsheet implementation of this example is provided in Figure 3.29. 3.4.4. DISCUSSION

Strengths and Weaknesses BLEVE dimensions and durations have been studied by many authors and the empirical basis consists of several well-described incidents, as well as many smaller laboratory trials. The use of a surface emitted flux estimate is the greatest weakness, as this is not a fundamental property. Fragment correlations are subject to the same weaknesses discussed in Section 3.3.4. Identification and Treatment of Possible Errors The two largest potential errors are the estimation of the mass involved and the surface emitted flux. The surface emitted flux is an empirical term derived from

Example 2.28: Blast Fragments from a BLEVE Input Data: Diameter of sphere: Vessel failure pressure: Vessel liquid fill fraction: Vessel wall thickness: Vessel wall density: Temperature: Ambient pressure: Drag coefficient of fragment: Lift to drag ratio: Calculated Results: Diameter of sphere: Vessel failure pressure: Vessel wall thickness: Vessel wall density: Temperature. Total volume of sphere: Liquid volume: Vapor volume: Energy of explosion: Number of fragments: Volume of vessel shell: Total mass of vessel: Average mass of each fragment: Total surface area of sphere: Surface area for each fragment: Average diameter of spherical fragment: !initial velocity of fragment: Density of ambient air: Scaled velocity of fragment:

I

Interpolated values from figure for various lift to drag ratios: Lift to drag Scaled ratio Range

Range (m)

interpolated range: Theoretical max. range (no lift): Max, possible range (with lift): FIGURE 3.29. Spreadsheet output for Example 28: Blast fragments from a BLEVE.

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the estimated radiant fraction. While this is not fundamentally based, the usual value is similar in magnitude (but larger) than that used in API 521 for jet flare radiation estimates. A simplified graphical or correlation approach is a check, but these do not allow for differing materials or atmospheric conditions. Utility BLEVE models require some care in application, as errors in surface flux, view factor, or transmissivity can lead to significant error. Thermal hazard zone calculations will be iterative due to the shape factor and transmissivity which are functions of distance. Fragment models showing the possible extent of fragment flight and damage effects are difficult to use. Resources Needed A process engineer with some understanding of thermal radiation effects could use BLEVE models quite easily. A half-day calculation period should be allowed unless the procedure is computerized in which case much more rapid calculation and exploration of sensitivities is possible. Spreadsheets can be readily applied. Available Computer Codes Several integrated analysis packages contain BLEVE and fireball modeling. These include: ARCHIE (Environmental Protection Agency, Washington, DC) EFFECTS-2 (TNO, Apeldoorn, The Netherlands) PHAST (DNV, Houston, TX) QRAWorks (PrimaTech, Columbus, OH) SUPERCHEMS (Arthur D. Little, Cambridge, MA) TRACE (Safer Systems, Westlake Village, CA)

3 . 5 . C o n f i n e d Explosions 3.5.1. BACKGROUND

Purpose Confined explosions in the context of this section (see Figure 3.1) include deflagrations or other sources of rapid chemical reaction which are constrained within vessels and buildings. Dust explosions and vapor explosions within low strength vessels and buildings are one major category of confined explosion that is discussed in this chapter. Combustion reactions, thermal decompositions, or runaway reactions within process vessels and equipment are the other major category

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the estimated radiant fraction. While this is not fundamentally based, the usual value is similar in magnitude (but larger) than that used in API 521 for jet flare radiation estimates. A simplified graphical or correlation approach is a check, but these do not allow for differing materials or atmospheric conditions. Utility BLEVE models require some care in application, as errors in surface flux, view factor, or transmissivity can lead to significant error. Thermal hazard zone calculations will be iterative due to the shape factor and transmissivity which are functions of distance. Fragment models showing the possible extent of fragment flight and damage effects are difficult to use. Resources Needed A process engineer with some understanding of thermal radiation effects could use BLEVE models quite easily. A half-day calculation period should be allowed unless the procedure is computerized in which case much more rapid calculation and exploration of sensitivities is possible. Spreadsheets can be readily applied. Available Computer Codes Several integrated analysis packages contain BLEVE and fireball modeling. These include: ARCHIE (Environmental Protection Agency, Washington, DC) EFFECTS-2 (TNO, Apeldoorn, The Netherlands) PHAST (DNV, Houston, TX) QRAWorks (PrimaTech, Columbus, OH) SUPERCHEMS (Arthur D. Little, Cambridge, MA) TRACE (Safer Systems, Westlake Village, CA)

3 . 5 . C o n f i n e d Explosions 3.5.1. BACKGROUND

Purpose Confined explosions in the context of this section (see Figure 3.1) include deflagrations or other sources of rapid chemical reaction which are constrained within vessels and buildings. Dust explosions and vapor explosions within low strength vessels and buildings are one major category of confined explosion that is discussed in this chapter. Combustion reactions, thermal decompositions, or runaway reactions within process vessels and equipment are the other major category

of confined explosions. In general, a deflagration occurring within a building or low strength structure such as a silo is less likely to impact the surrounding community and is more of an in-plant threat because of the relatively small quantities of fuel and energy involved. Shock waves and projectiles are the major threats from confined explosions. Philosophy The design of process vessels subject to internal pressure is treated by codes such as the Unfired Pressure Vessel Code (ASME, 1986). Vessels can be designed to contain internal deflagrations. Recommendations to accomplish this are contained in NFPA 69 (1986) andNoronha et al. (1982). The design of relief systems for both low strength enclosures and process vessels, commonly referred to as "Explosion Venting," is covered by Guide for Venting Deflagrations (NFPA 68, 1994). As of this writing both NFPA 68 and NFPA 69 are under revision, with major changes to include updated information from the German standard VDI 3673 (VDI, 1995). Details on the new VDI update are contained in Siwek (1994). Applications There are few published CPQRAs that consider the risk implications of these effects; however the Canvey Study (Health & Safety Executive, 1978) considered missile damage effects on process vessels. 3.5.2. DESCRIPTION Description of the Technique The technique is based on the determination of the peak pressure. Where this is sufficient to cause vessel failure, the consequences can be determined. For most pressure vessels designed to the ASAIE Code, the minimum bursting pressure is at least four times the "stamped" maximum allowable working pressure (MAWP). For a number of reasons (e.g., initial corrosion allowance, use of next available plate thicknesses), vessel ultimate strengths can greatly exceed this value. TNO (1979) uses a lower value of 2.5 times MAWP, as European vessels can have a lower factor of safety. It is possible to be more precise if plate thickness, vessel diameter, and material of construction are known. A burst pressure can be estimated using the ultimate strength of the material and 100% weld efficiency in a hoop stress calculation. Specialist help is desirable for those calculations. Treatments of the bursting and fragmentation of vessels is given in Section 3.3.2. The explosion of a flammable mixture in a process vessel or pipework may be a deflagration or a detonation. Detonation is the more violent form of combustion, in which the flame front is linked to a shock wave and moves at a speed greater than the speed of sound in the unreacted gases. Well known examples of

gas-air mixtures which can detonate are hydrogen, acetylene, ethylene and ethylene oxide. A deflagration is a lower speed combustion process, with speeds less than the speed of sound in the unreacted medium, but it may undergo a transition to detonation. This transition occurs in pipelines but is unlikely in vessels or in the open. Deflagrations can be vented because the rate of pressure increase is low enough that the opening of a vent will result in a lower maximum pressure. Detonations, however, cannot be vented since the pressure increases so rapidly that the vent opening will have limited impact on the maximum pressure. A dust explosion is usually a deflagration. Some of the more destructive explosions in coal mines and grain elevators give strong indications that detonation was approached but efforts to duplicate those results have not been verified experimentally. Certain factors in the combustion of combustible dust are unique and as a result they are modeled separately from gases. Deflagrations. For flammable gas mixtures, Lees (1986) summarizes the work of Zabetakis (1965) of the U.S. Bureau of Mines for the maximum pressure rise as a result of a change in the number of moles and temperature. (3.49) where Pmax is the maximum absolute pressure (force/area) P 1 is the initial absolute pressure (force/area) n is the number of moles in the gas phase T is the absolute temperature of the gas phase M is the molecular weight of the gas 1 is the initial state 2 is the final state Equation (3.49) will provide an exact answer if the final temperature and molecular weight are known and the gas obeys the ideal gas law. If the final temperature is not known, then the adiabatic flame temperature can be used to provide a theoretical upper limit to the maximum pressure. Equation (3.49) predicts a maximum pressure usually much higher than the actual pressure—experimental determination is always recommended. NFPA 68 (NFPA, 1994) also gives a cubic law relating rate of pressure rise to vessel volume in the form (3.50)

where KQ is the characteristic deflagration constant for gases and X51 is the characteristic venting constant for dusts. The "St" subscript derives from the German word for dust, or Staub. The deflagration constant is not an inherent physical property of the material, but simply an observed artifact of the experimental procedure. Thus, different experimental approaches, particularly for dusts, will result in different values, depending on the composition, mixing, ignition energy, and volume, to name a few. Furthermore, the result is dependent on the characteristics of the dust particles (i.e., size, size distribution, shape, surface character, moisture content, etc.). The (dP/dt)max value is the maximum slope in the pressure versus time data obtained from the experimental procedure. ASTM procedures are available (ASTM, 1992). Senecal and Beaulieu (1997) provide extensive experimental values for X 0 and Pmax. Correlations of KQ with flame speed, stoichiometry and fuel autoignition temperature are provided. The experimental approach is to produce nomographs and equations for calculating vent area to relieve a given overpressure. The NFPA 68 guide (NFPA, 1994) also lists tables of experimental data for gases, liquids, and dusts that show Pmax znddP/dt. The experimental data used must be representative of the specific material and process conditions, whenever possible. From these experimental data and from the relations given by Zabetakis, the maximum pressure rise for most deflagrations is typically P2JPi = 8 for hydrocarbon-air mixtures P2JPi = 16 for hydrocarbon-oxygen mixtures where P2 is the final absolute pressure and P 1 is the initial absolute pressure. Some risk analysts use conservative values of 10 and 20, respectively, for these pressures. Detonation. Lewis and von Elbe (1987) describe the theory of detonation, which can be used to predict the peak pressure and the shock wave properties (e.g., velocity and impulse pressure). Lees (1986) says the peak pressure for a detonation in a containment initially at atmospheric pressure may be about 20 bar (a 20-fold increase). This pressure can be many times larger if there is reflection against solid surfaces. Dust Explosions. Bartknecht (1989), Lees (1986), and NFPA 68 (1994) contain a considerable amount of dust explosion test data. The nomographs in NFPA 68 can be used to estimate the pressure within a vessel, provided the related functions of vent size, class of dust (St-I, 2, or 3), or XSt, vessel size, and vent release pressure are known.

Nomographs for three dust classes

are available. In addition, nomographs are provided for specific^ values for the range of 50-600 bar m/s. Empirical equations are also provided that allow the problem to be solved algebraically. In the case of low strength containers, similar estimates can be made using the equations outlined by Swift and Epstein (1987). If the values of peak pressure calculated exceed the burst pressure of the vessel, then the consequences of the resulting explosion should be determined. As in Sections 3.3 and 3.4, the resulting effects are a shock wave, fragments, and a burning cloud. Although the pressure at which the vessel may burst may be well below the maximum pressure that could have developed, it is frequently conservatively assumed that the stored energy released as a shock wave is based on the maximum pressure that could have developed. In chemical decompositions and detonations it is also frequently assumed that the available chemical stored energy is converted to a TNT equivalent. The phenomenon of pressure piling is an important potential hazard in systems with interconnected spaces. The pressure developed by an explosion in Space A can cause pressure/temperature rise in connected Space B. This enhanced pressure is now the starting point for further increase in explosion pressure. This phenomenon has also been seen frequently in electrical equipment installed in areas using flammable materials. A small primary dust explosion may have major consequences if additional combustible dust is present. The shock of the initial dust explosion can disperse additional dust and cause an explosion of considerably greater violence. It is not unusual to see a chain reaction with devastating results. Logic Diagram The logic of confined explosion modeling showing the stepwise procedure is provided in Figure 3.30. Theoretical Foundations Although the fundamentals of combustion and explosion theory have been evolved over the last 100 years, the detailed application to most gases has been more recent. For simple molecules, the theoretical foundation is sound. For more complex species, particularly dust and mists, the treatment is more empirical. Nevertheless, good experimental data have been pooled by the U.S. Bureau of Mines (Zabetakis, 1965; Kuchta, 1973), NFPA 68 (NFPA, 1994), VDI 3673

Flammable Mixture/ Chemical in Process Vessel or Enclosure

Estimate Maximum Pressure Equation (3.49)

Estimate Burst Pressure of Vessel or Enclosure

Is Max. Pressure greater than Burst Pressure of Vessel or Enclosure?

YES

NO

Are Secondary Effects Possible? * Pressure Piling * Secondary Dust Explosion

NO

No Consequence

YES

Estimate Overpressure using Methods in Section 3.5.2

Estimate Projectile Effects using Methods in Section 3.3.2 FIGURE 3.30. Logic diagram for confined explosion analysis.

(VDI, 1995), and Bartknecht (1989). An alternate approach is used in the UK and other parts of Europe as described by Schofield (1984). Input Requirements and Availability The technology requires data on container strengths and combustion parameters. The latter are usually readily available; data on containment behavior are more

difficult. Vessel bursting pressure can be derived accurately only with a full appreciation of the vessel metallurgy and operating history; however, it should be sufficient for CPQRA purposes to refer to the relevant design codes and estimate the bursting pressure based on the safety factor employed. Output This analysis provides overpressure versus distance effects and also projectile effects. Using NFPA 68 (NFPA, 1994), overpressures can be estimated for vented vessels and buildings, which allows estimates to be made of the expected damage levels. Simplified Approaches The peak pressures achieved in confined explosions can be estimated as follows: deflagration is eight times the initial absolute pressure, and detonation 20 times, for hydrocarbon-air mixtures. It can be assumed that pressure vessels fail at about four times the design working pressure. In the cases of dust explosions, the NFPA nomographs can be used for relatively strong vessels and the modified Swift-Epstein equations indicated in NFPA 68 (NFPA, 1994; see also Swift and Epstein, 1987) for low strength structures (such as buildings).

3.5.3. EXAMPLEPROBLEM

Example 29: Overpressure from a Combustion in a Vessel A i m 3 vessel rated at 1 barg contains a stoichiometric quantity of acetylene (C2H2) and air at atmospheric pressure and 25°C. Estimate the energy released upon combustion and calculate the distance at which a shock wave overpressure of 21 kPa can be obtained. Assume an energy of combustion for acetylene of 301 kcal/gm-mole. Solution: The stoichiometric combustion of acetylene at atmospheric pressure inside a vessel designed for 1 barg will produce pressures that will exceed the expected burst pressure of the vessel. The stoichiometric combustion of acetylene requires 2.5 mole of O2 per mole of acetylene: 1 mole of air contains 3.76 mole N 2 and 1.0 mol O2. The starting composition is C2H2 + 2.5O2 + (2.5)(3.76)N2, resulting in the following initial gas mixture,

Compound

Moles

Mole fraction

A 1-m3 vessel at 25°C contains

The amount of acetylene in this volume that could combust is

Therefore the energy of combustion, IJC, is

Since 1 kg of TNT is equivalent to 1120 kcal, then the TNT mass equivalent = 960/1120 = 0.86 kg TNT. This represents the upper bound of the energy. The vessel will probably begin to fail at about 5 barg. However, the rate of pressure rise during the combustion may exceed the rate at which the vessel actually comes apart. The effective failure pressure, therefore, is somewhere between the pressure at which the vessel begins to fail and the maximum pressure obtainable from combustion inside a closed vessel. As in physical explosions (Section 3.3) some fraction of the energy goes into shock wave formation. The most conservative assumption is to assume all of the combustion energy goes into the shock wave. Thus, from Figure 3.3 for P s = 21 kPa, Z = 7.83. Then from Eq. (3.7)

The spreadsheet output for this example is shown in Figure 3.31.

3.5.4. DISCUSSION Strengths and Weaknesses The main strength of these methods is that they are based largely on experimental data. Their main weakness is frequently lack of data, particularly for dusts. Suitable methods for handling gas mixtures and hybrid systems composed of flammable dusts and vapors are lacking.

Example 29: Overpressure from a Combustion in a Vessel Input Data: Mole fraction of fuel: Molecular weight of fuel: Volume of vessel: Energy of combustion of fuel: Initial temperature: Initial pressure: Calculated Results: Total moles in vessel: Total moles of fuel: Total mass of fuel: Total energy of combustion: Equivalent mass of TNT !Distance from blast:

Trial and error to get desired overpressure

Scaled distance, z: Overpressure Calculation: a+b*log(z): Overpressure:

(only valid for z > 0.0674 and z < 40)

FIGURE 331. Spreadsheet output for Example 29: Overpressure from a combustion in a vessel.

Identification and Treatment of Possible Errors Schofield (1984) reports that experiments on the behavior of flammable mixtures in large volumes (30 m3 or 1000 ft3) indicate that venting calculations developed from small scale experiments may oversize the vents. Evaluation of container strengths can be a main source of error. Vessels are often stronger than safety factors assume and this factor may be conservative in terms of the frequency or probability of vessel rupture, but conversely, not conservative in terms of calculating the consequences of rupture. Utility The techniques discussed here are straightforward to apply and the data are readily available (provided a simplistic estimate of bursting pressure is acceptable). Resources A process engineer should be able to perform each type of calculation in an hour. Available Computer Codes WinVent (Prcd Engineering, Inc., Palm City, FL)

3 . 6 . P o o l Fires 3.6.1. BACKGROUND

Purpose Pool fires tend to be localized in effect and are mainly of concern in establishing the potential for domino effects and employee safety zones, rather than for community risk. The primary effects of such fires are due to thermal radiation from the flame source. Issues of intertank and interplant spacing, thermal insulation, fire wall specification, etc., can be addressed on the basis of specific consequence analyses for a range of possible pool fire scenarios. Drainage is an important consideration in the prevention of pool fires—if the material is drained to a safe location, a pool fire is not possible. See NFPA 30 (NFPA, 1987a) for additional information. The important considerations are that (1) the liquid must be drained to a safe area, (2) the liquid must be covered to minimize vaporization, (3) the drainage area must be far enough away from thermal radiation fire sources, (4) adequate fire protection must be provided, (5) consideration must be provided for containment and drainage of fire water and (6) leak detection must be provided. Philosophy Pool fire modeling is well developed. Detailed reviews and suggested formulas are provided in Bagster (1986), Considine (1984), Crocker and Napier (1986), Institute of Petroleum (1987), Mudan (1984), Mudan and Croce (1988), and TNO (1979) . A pool fire may result via a number of scenarios. It begins typically with the release of flammable material from process equipment. If the material is liquid, stored at a temperature below its normal boiling point, the liquid will collect in a pool. The geometry of the pool is dictated by the surroundings (i.e., diking), but an unconstrained pool in an open, flat area is possible (see Section 2.2), particularly if the liquid quantity spilled is inadequate to completely fill the diked area. If the liquid is stored under pressure above its normal boiling point, then a fraction of the liquid will flash into vapor, with unflashed liquid remaining to form a pool in the vicinity of the release. The analysis must also consider spill travel. Where can the liquid go and how far can it travel? Once a liquid pool has formed, an ignition source is required. Each release has a finite probability of ignition and must be evaluated. The ignition can occur via the vapor cloud (for flashing liquids), with the flame traveling upwind via the vapor to ignite the liquid pool. For liquids stored below the normal boiling point without flashing, the ignition can still occur via the flammable vapor from the

evaporating liquid. Both of these cases may result in an initial flash fire due to burning vapors—this may cause initial thermal hazards. Once an ignition has occurred, a pool fire results and the dominant mechanism for damage is via thermal effects, primarily via radiative heat transfer from the resulting flame. If the release of flammable material from the process equipment continues, then a jet fire is also likely (see Section 3.7). If the ignition occurs at the very beginning of the release, then inadequate time is available for the liquid to form a pool and only a jet fire will result. The determination of the thermal effects depends on the type of fuel, the geometry of the pool, the duration of the fire, the location of the radiation receiver with respect to the fire, and the thermal behavior of the receiver, to name a few. All of these effects are treated using separate, but interlinked models. Application Pool fire models have been applied to a large variety of combustible and flammable materials. 3.6.2. DESCRIPTION

Description of Technique—Pool Fire Models Pool fire models are composed of several component submodels as shown in Figure 3.32. A selection of these are briefly reviewed here: • burning rate • pool size • flame geometry, including height, tilt and drag • flame surface emitted power • geometric view factor with respect to the receiving source • atmospheric transmissivity • received thermal flux Burning Rate For burning liquid pools, the radiative heat transfer and the resulting burning rate increases with pool diameter. For pool diameters greater than 1 m, radiative heat transfer dominates and the flame's geometric view factor is constant. Thus, a constant burning rate is expected. For pool diameters greater than 1 m, Burgess et al. (1961) showed that the rate at which the liquid pool level decreases is given by (3.51) where ymax is the vertical rate of liquid level decrease (m/s), AH0 is the net heat of

Pool Fire

Estimate Vertical or Mass Burning Rate Equations (3.51), (3.53)

Estimate Flame Height Equation (3.55)

Estimate Maximum Pool Diameter Equation (3.54)

Select Radiation Model

Solid Plume Radiation Model Figure 3.32a

Point Source Radiation Model Figure 3.32b

Estimate Thermal Effect Section 4.3 FIGURE 3.32. Logic diagram for calculation of pool fire radiation effects.

combustion (energy/mass), and AH* is the modified heat of vaporization at the boiling point of the liquid given by Eq. (3.52) (energy/mass). Typical vertical rates are 0.7 X 1(T4 m/s (gasoline) to 2 X IO"4 m/s (LPG). The modified heat of vaporization includes the heat of vaporization, plus an adjustment for heating the liquid from the ambient temperature, T a , to the boiling point temperature of the liquid, TBP. (3.52)

Point Source Radiation Model

Solid Plume Radiation Model

Estimate Radiant Fraction Table 3.11

Estimate Surface Emitted Power Equation (3.59)

Estimate Point Source Location from Flame Height

Estimate Geometric View Factor Equations (3.46), (3.47)

Estimate Point Source View Factor Equation (3.60)

Estimate Trasmissivity Equation (3.42)

Estimate Transmissivity Equation (3.42)

Estimate Incident Radiation Flux Equation (3.62)

Estimate Incident Radiant Flux Equation (3.61)

FIGURE 3.32a. Logic diagram for the solid plume radiation model.

FIGURE 3.32b. Logic diagram for the point source radiation model.

where AHV is the heat of vaporization of the liquid at the ambient temperature (energy/mass) and C is the heat capacity of the liquid (energy/mass-deg). Equation (3.52) can be modified for mixtures, or for liquids such as gasoline which are composed of a number of materials (Mudan and Croce, 1988). The mass burning rate is determined by mutiplying the vertical burning rate by the liquid density. If density data are not available, the mass burning rate of the pool is estimated by (3.53) where mB is the mass burning rate (kg/m2 s).

Equation (3.51) fits the experimental data better than Eq. (3.53), so the procedure using the vertical burning rate and the liquid density is preferred. Typical values for the mass burning rate for hydrocarbons are in the range of 0.05 kg/m2s (gasoline) to 0.12 kg/m2 s (LPG). Additional tabulations for the vertical and mass burning rates are provided by Burgess and Zabetakis (1962), Lees (1986), Mudan and Croce (1988) and TNO (1979). Equations (3.51) to (3.53) apply to liquid pool fires on land. For pool fires on water, the equations are applicable if the burning liquid has a normal boiling point well above ambient temperature. For liquids with boiling points below ambient, heat transfer between the liquid and the water will result in a burning rate nearly three times the burning rate on land (Mudan and Croce, 1988). Pool Size In most cases, pool size is fixed by the size of the release and by local physical barriers (e.g., dikes, sloped drainage areas). For a continuous leak, on an infinite flat plane, the maximum diameter is reached when the product of burning rate and surface area equals the leakage rate. (3.54)

where Dmax is the equilibrium diameter of the pool (length), VL is the volumetric liquid spill rate (volume/time), and y is the liquid burning rate (length/time). Equation (3.54) assumes that the burning rate is constant and that the dominant heat transfer is from the flame. More detailed pool burning geometry models are available (Mudan and Croce, 1988) Circular pools are normally assumed; where dikes lead to square or rectangular shapes, an equivalent diameter may be used. Special cases include spills of cryogenic liquids onto water (greater heat transfer) and instantaneous unbounded spills (Raj and Kalelkar, 1974). Flame Height Many observations of pool fires show that there is an approximate ratio of flame height to diameter. The best known correlation for this ratio is given by Thomas (1963) for circular pool fires. (3.55) where

H is the visible flame height (m) D is the equivalent pool diameter (m) mB is the mass burning rate (kg/m2 s) p a is the air density (1.2 kg/m3 at 200C and 1 atm.) g is the acceleration of gravity (9.81 m/s2) Bagster (1986) summarizes rules of thumb for H/D ratios: Parker (1973) suggests a value of 3 and Lees (1984) lists a value of 2. Moorhouse (1982) provides a correlation for the flame height based on large-scale LNG tests. This correlation includes the effect of wind on the flame length: (3.56) where U10* is a nondimensional wind speed determined using (3.57) where uw is the measured wind speed at a 10 m height (m/s) andp v is the vapor density at the boiling point of the liquid (kg/m3). Flame Tilt and Drag Pool fires are often tilted by the wind, and under stronger winds, the base of a pool fire can be dragged downwind. These effects alter the radiation received at surrounding locations. A number of correlations have been published to describe these two factors. The correlation of Welker and Sliepcevich (1966) for flame tilt is frequently quoted, but the American Gas Association (AGA) (1974) and Mudan (1984) note poor results for LNG fires. The AGA paper proposes the following correlation for flame tilt: (3.58) where u is the nondimensional wind speed given by Eq. (3.57) at a height of 1.6 m and 6 is the flame tilt angle (degrees or radians). Flame drag occurs when wind pushes the base of the flame downwind from the pool, with the upwind edge of the flame and flame width remaining unchanged. For square and rectangular fires the base dimension is increased in the direction of the wind. The thermal radiation downwind increases because the distance to a receiver downwind is reduced. For circular flames, the flame shape

changes from circular to elliptical, resulting in a change in view factor and a change in the radiative effects. Detailed flame drag correlations are provided by Mudan and Croce (1988). Risk analyses can include or ignore tilt and drag effects. Flame tilt is more important; flame drag is an advanced topic, and many pool fire models do not include this effect. A vertical (untilted) pool fire is often assumed, as this radiates heat equally in all directions. If a particularly vulnerable structure is located nearby and flame tilt could affect it, the CPQBA should consider tilt effects (both toward and away from the vulnerable object) and combine these with appropriate frequencies allowing for the direction of tilt. Surface Emitted Power The surface emitted power or radiated heat flux may be computed from the Stefan-Boltzmann equation. This is very sensitive to the assumed flame temperature, as radiation varies with temperature to the fourth power (Perry and Green, 1984). Further, the obscuring effect of smoke substantially reduces the total emitted radiation integrated over the whole flame surface. Two approaches are available for estimating the surface emitted power: the point source and solid plume radiation models. The point source is based on the total combustion energy release rate while the solid plume radiation model uses measured thermal fluxes from pool fires of various materials (compiled in TNO, 1979). Both these methods include smoke absorption of radiated energy (that process converts radiation into convection). Typical measured surface emitted fluxes from pool fires are given by Raj (1977), Mudan (1984), and Considine (1984). LPG and LNG fires radiate up to 250 kW/m2 (79,000 Btu/hr-ft2 ). Upper values for other hydrocarbon pool fires lie in the range 110-170 kW/m2 (35,000-54,000 Btu/hr-ft2), but smoke obscuration often reduces this to 20-60 kW/m2 ( 6300-19,000 Btu/hr-ft2 ). For the point source model, the surface emitted power per unit area is estimated using the radiation fraction method as follows: 1. Calculate total combustion power (based on burning rate and total pool area). 2. Multiply by the radiation fraction to determine total power radiated. 3. Determine flame surface area (commonly use only the cylinder side area). 4. Divide radiated power by flame surface area. The radiation fraction of total combustion power is often quoted in the range 0.15-0.35 (Mudan, 1984; TNO, 1979). See Table 3.11. While the point source model provides simplicity, the wide variability in the radiation fraction and the inability to predict it fundamentally detracts considerably from this approach.

TABLE 3.11. The Fraction of Total Energy Converted to Radiation for Hydrocarbons (Mudan and Croce, 1988) Fuel

Fraction

Hydrogen

0.20

Methane

0.20

Ethylene

0.25

Propane

0.30

Butane

0.30

C5 and higher

0.40

The solid plume radiation model assumes that the entire visible volume of the flame emits thermal radiation and the nonvisible gases do not (Mudan and Croce, 1988). The problem with this approach is that for large hydrocarbon fires, large amounts of soot are generated, obscuring the radiating flame from the surroundings, and absorbing much of the radiation. Thus, as the diameter of the pool fire increases, the emitted flux decreases. Typical values for gasoline are 120 kW/m2 for a 1-m pool to 20 kW/m2 for a 50-m diameter pool. To further complicate matters, the high turbulence of the flame causes the smoke layer to open up occasionally, exposing the hot flame and increasing the radiative flux emitted to the surroundings. Mudan and Croce (1988) suggest the following model for sooty pool fires of high molecular weight hydrocarbons to account for this effect, (3.59) where E^ is the average emissive power (kW/m2) Em is the maximum emissive power of the luminous spots (approximately 140kW/m2) Es is the emissive power of smoke (approximately 20 kW/m2) S is an experimental parameter (0.12 m"1) D is the diameter of the pool (m) Equation (3.59) produces an emissive power of 56 kW/m2 for a 10-m pool and 20 kW/m2 for a 100-m pool. This matches experimental data for gasoline, kerosene and JP-4 fires reasonably well (Mudan and Croce, 1988). Propane, ethane, LNG, and other low molecular weight materials do not produce sooty flames.

Geometric View Factor The view factor depends on whether the point source or solid plume radiation models are used. For the point source model, the view factor is given by (3.60) where FP is the point source view factor (length 2) and A; is the distance from the point source to the target (length). Equation (3.60) assumes that all radiation arises from a single point and is received by an object perpendicular to this. This view factor must only be applied to the total heat output, not to the flux. Other view factors based on specific shapes (i.e., cylinders) require the use of thermal flux and are dimensionless. The point source view factor provides a reasonable estimate of received flux at distances far from the flame. At closer distances, more rigorous formulas or tables are given by Hamilton and Morgan (1952), Crocker and Napier (1986), and TNO (1979). For the solid plume radiation model, the view factors are provided in Figure 3.33 for untilted flames and Figure 3.34 for tilted flames. Figure 3.33 requires an estimate of the flame height to diameter, while Figure 3.34 requires an estimate of the flame tilt. The complete equations for these figures are provided by Mudan and Croce (1988). Both figures provide view factors for a ground level receiver from a radiation source represented by a right circular cylinder. Note that near the source the view factor is almost independent of the flame height since the observer is exposed to the maximum radiation. Received Thermal Flux The computation of the received thermal flux is dependent on the radiation model selected. If the point source model is selected, then the received thermal flux is determined from the total energy rate from the combustion process: (3.61) If the solid plume radiation model is selected, the received flux is based on correlations of the surface emitted flux: (3.62) where Ex is the thermal flux received at the target (energy/area) ra is the atmospheric transmissivity, provided by Eq. (3.42) (unitless)

Maximum View Factor at Ground Level, F21

Height to Radius: Dimensionless Distance from Flame Axis = Distance from Flame Axis / Pool Radius

Maximum View Factor at Ground Level, F21

FIGURE 3.33. Maximum view factors for a ground-level receptor from a right circular cylinder (Mudan and Croce, 1988).

Dimensionless Distance from Flame Axis = Distance from Flame Axis / Pool Radius FIGURE 3.34. Maximum view factors for a ground-level receptor from a tilted circular cylinder (Mudan and Croce, 1988).

is the total energy rate from the combustion (energy/time) is the point source view factor (length2) is the fraction of the combustion energy radiated, typically 0.15 to 0.35 is the mass burning rate, provided by Eq. (3.53) (mass/area-time) is the heat of combustion for the burning liquid (energy/mass) is the total area of the pool (length2) is the solid plume view factor, provided by Eqs. (3.46) and (3.47) Values for the fraction of the combustion energy radiated, 77, are given in Table 3.11. Theoretical Foundation Burning rate, flame height, flame tilt, surface emissive power, and atmospheric transmissivity are all empirical, but well established, factors. The geometric view factor is soundly based in theory, but simpler equations or summary tables are often employed. The Stefan-Boltzmann equation is frequently used to estimate the flame surface flux and is soundly based in theory. However, it is not easily used, as the flame temperature is rarely known. Input Requirements and Availability The pool size must be defined, either based on local containment systems or on some model for a flat surface. Burning rates can be obtained from tabulations or may be estimated from fuel physical properties. Surface emitted flux measurements are available for many common fuels or are calculated using empirical radiation fractions or solid flame radiation models. An estimate for atmospheric humidity is necessary for transmissivity. All other parameters can be calculated. Output The primary output of thermal radiation models is the received thermal radiation at various target locations. Fire durations should also be estimated as these affect thermal effects (Section 4.3). Simplified Approaches Crocker and Napier (1986) provide tables of thermal impact zones from common situations of tank roof and ground pool fires. From these tables, safe separation distances for people from pool fires can be estimated to be 3 to 5 pool diameters (based on a "safe" thermal impact of 4.7 kW/m2). 3.6.3. EXAMPLEPROBLEM

Example 30: Radiation from a Burning Pool A high molecular weight hydrocarbon liquid escapes from a pipe leak at a volumetric rate of 0.1 m3/s. A circular dike with a 25 m diameter contains the leak. If

the liquid catches on fire, estimate the thermal flux at a receiver 50 m away from the edge of the diked area. Assume a windless day with 50% relative humidity. Estimate the thermal flux using the point source and the solid plume radiation models. Additional Data: Heat of combustion of the liquid: Heat of vaporization of the liquid: Boiling point of the liquid: Ambient temperature: Liquid density: Heat capacity of liquid (constant): Solution: Since the fuel is a high molecular weight material, a sooty flame is expected. Equations (3.51) and (3.53) are used to determine the vertical burning rates and the mass burning rates, respectively. These equations require the modified heat of vaporization, which can be calculated using Eq. (3.52):

The vertical burning rate is determined from Eq. (3.51):

The mass burning rate is determined by multiplying the vertical burning rate by the density of the liquid:

The maximum, steady state pool diameter is given by Eq. (3.54),

Since this is larger than the diameter of the diked area, the pool will be constrained by the dike with a diameter of 25 m. The area of the pool is

The flame height is given by Eq. (3.55),

Thus,//= (1.59)(25m) = 39.7 m Point Source Model. This approach is based on representing the total heat release as a point source. The received thermal flux for the point source model is given by Eq. (3.61). The calculation requires values for the atmospheric transmissivity and the view factor. The view factor is given by Eq. (3.60), based on the geometry shown in Figure 3.35. The point source is located at the center of the pool, at a height equal to half the height of the flame. This height is (39.7 m)/2 = 19.9 m. From the right triangle formed,

This represents the beam length from the point source to the receiver. The view factor is determined using Eq. (3.60)

The transmissivity is given by Eq. (3.42) with the partial pressure of water given by Eq. (3.43). The results are

Fire Receptor

Pool FIGURE 3.35. Geometry of Example 30: Radiation from a burning pool.

The thermal flux is given by Eq. (3.61), assuming a conservative value of 0.35 for the fraction of the energy converted to radiation.

Solid Plume Radiation Model. The solid plume radiation model begins with an estimate of the radiant flux at the source. This is given by Eq. (3.59)

Figure 3.33 is used to determine the geometric view factor. This requires the height to pool radius ratio and the dimensionless distance. Since H/D = 1.59, H/R = 2(1.59) = 3.18. The dimensionless distance to the receiver isX/R, where R is the radius of the pool andX is the distance from the flame axis to the receiver, that is, 50 m + 25/2 m = 62.5 m. Thus, X/R = 62.5 m/12.5 m = 5 and from Figure 3.33,P21 = 0.068. The atmospheric transmissivity is given by Eq. (3.42)

The radiant flux at the receiver is determined from Eq. (3.45)

The result from the solid plume radiation model is smaller than the point source model. This is most likely due to consideration of the radiation obscuration by the flame soot, a feature not treated directly by the point source model. The differences between the two models might be greater at closer distance to the pool fire. The spreadsheet output for this example is shown in Figure 3.36. 3.6.4. DISCUSSION

Strengths and Weaknesses Pool fires have been studied for many years and the empirical equations used in the submodels are well validated. The treatment of smoky flames is still difficult.

Example 30: Radiation from a Burning Pool Input Data: Liquid leakage rate: Heat of combustion of liquid: Heat of vaporization of liquid: Boiling point of liquid: Ambient temperature: Liquid density: Constant heat capacity of liquid: Dike diameter: Receptor distance from pool: Relative humidity: Radiation efficiency for point source mode Calculated Results: Modified heat of vaporization: Vertical burning rate: Mass burning rate: Maximum pool diameter: Diameter used in calculation: Area of pool: Flame H/D: Flame height: Partial pressure of water vapor: Point Source Model: Point source height: Distance to receptor: View factor: Transmissivity: !Thermal flux at receptor: Solid Plume Radiation Model: Source emissive power: Distance from flame axis to receptor: Flame radius: Flame H/R ratio: Dimensionless distance from flame axis: lntepolated values from figure: Flame _ H/R

View Factor

Interpolated view factor: Transmissivity: !Thermal flux at receptor" FIGURE 3.36. Spreadsheet output for Example 30:Radiat/on from a burning pool.

A weakness with the pool models is that flame impingement effects are not considered; they give substantially higher heat fluxes than predicted by thermal radiation models. Identification and Treatment of Possible Errors The largest potential error in pool fire modeling is introduced by the estimate for surface emitted flux. Where predictive formulas are used (especially Stefan-Boltzmann types) simple checks on ratios of radiated energy to overall combustion energy should be carried out. Pool size estimates are important, and the potential for dikes or other containment to be overtopped by fluid momentum effects or by foaming should be considered. Utility Pool fire models are relatively straightforward to use. Resources Necessary A trained process engineer will require several hours to complete a pool fire scenario by hand if all necessary thermodynamic data, view factor formulas, and humidity data are available. Available Computer Codes DAMAGE (TNO, Apeldoorn, The Netherlands) PHAST (DNV, Houston, TX) QRAWorks (PrimaTech, Columbus, OH) TRACE (Safer Systems, Westlake Village, CA) SUPERCHEMS (Arthur D. Little, Cambridge, MA)

3 . 7 . J e t Fires 3.7.1. BACKGROUND

Purpose Jet fires typically result from the combustion of a material as it is being released from a pressurized process unit. The main concern, similar to pool fires, is in local radiation effects. Application The most common application of jet fire models is the specification of exclusion zones around flares.

3.7.2. DESCRIPTION

Description of Technique Jet fire modeling is not as well developed as for pool fires, but several review; have been published. Jet fire modeling incorporates many mechanisms, similar tc those considered for pool fires, as is shown on the logic diagram in Figure 3.37 Three approaches are reviewed by Bagster (1986): those of API 521(1996a) Craven (1972), and Hustad and Sonju(1985). The API method is relatively simple, while the other methods are more mechanistic. A more recent review i; provided by Mudan and Croce (1988). The API (1996) method was originally developed for flare analysis, but h now applied to jet fires arising from accidental releases. Flare models apply to ga; releases from nozzles with vertical flames. For accidental releases, the release hole is typically not a nozzle, and the resulting flame is not always vertical. For the modeling approaches presented here, the assumption will be made that th< release hole can be approximated as a nozzle. The assumption of a vertical flame will provide a conservative result, since the vertical flame will provide the largesi radiant heat flux at any receptor point. The API (1996) method is based on the radiant fraction of total combustior energy, which is assumed to arise from a point source along the jet flame path. A graph is provided in API 521 (API, 1996a) that correlates flame length versu! flame heat. The radiant fraction is given as 0.15 for hydrogen, 0.2 for methane and 0.3 for other hydrocarbons (from laboratory experiments). A further modi fying factor of 0.67 should be applied to allow for incomplete combustion. Mudan and Croce (1988) provide a more detailed and recent review of jei flame modeling. The method begins with the calculation of the height of the flame. If we define the break point for the jet as the point at the bottom of the flame, above the nozzle, where the turbulent flame begins, then the flame heigh is given for turbulent gas jets burning in still air by (3.63) where L is the length of the visible turbulentflamemeasured from the break point (m) dj is the diameter of the jet, that is, the physical diameter of the nozzle (m) C x is the fuel mole fraction concentration in a stoichiometric fuel-air mixture (unitless) T¥, Tj are the adiabatic flame temperature and jet fluid temperature, respectively (K)

Jet Fire Estimate Discharge Rate Section 2.1 Estimate Flame Height Equation (3.63) Estimate Point Source Location Estimate Radiant Fraction Table 3.11 Estimate Point Source View Factor Equation (3.60) Estimate Transmissivity Equation (3.42) Estimate Incident Radiant Flux Equation (3.61) Estimate Thermal Effects Section 4.3 FIGURE 3.37. Logic diagram for the calculation of jet fire radiation effects.

aT is the moles of reactant per mole of product for a stoichiometric fuel-air mixture (unitless) Ma is the molecular weight of the air (mass/mole) Mf is the molecular weight of the fuel (mass/mole) For most fuels, CT is typically much less than I 5 aT is approximately I 5 and the ratio TF /TJ varies between 7 and 9. These assumptions are applied to Eq. (3.63) resulting in the following simplified equation:

(3.64) Mudan and Croce (1988) also provide expressions for the flame height considering the effects of crosswind. The radiative flux received by a source is determined using a procedure similar to the point source method described for pool fires in Section 3.6.2. For this case, the radiant flux at the receiver is determined from (3.65) where is the radiant flux at the receiver (energy/area-time) is the atmospheric transmissivity (unitless) is the total energy radiated by the source (energy/time) is the point source view factor, provided by Eq. (3.60) (length"2) is the fraction of total energy converted to radiation (unitless) is the mass flow rate of the fuel (mass/time) is the energy of combustion of the fuel (energy/mass) For this model, the point source is located at the center of the flame, that is, halfway along the flame centerline from the break point to the tip of the flame, as determined by Eqs. (3.63) or (3.64). It is assumed that the distance from the nozzle to the break point is negligible with respect to the total flame height. The fraction of the energy converted to radiative energy is estimated using the values provided in Table 3.11. None of the above methods consider flame impingement. In assessing the potential for domino effects on adjacent hazardous vessels, the dimensions of the jet flame can be used to determine whether flame impingement is likely. If so, heat transfer effects will exceed the radiative fraction noted above, and a higher heat fraction could be transferred to the impinged vessel. Theoretical Foundations The models to predict the jet flame height are empirical, but well accepted and documented in the literature. The point source radiation model only applies to a receiver at a distance from the source. The models only describe jet flames produced by flammable gases in quiescent air—jet flames produced by flammable liquids or two-phase flows cannot be treated. The empirically based radiant energy fraction is also a source of error. Input Requirements The jet flame models require an estimate of the flame height, which is determined from an empirical equation based on reaction stoichiometry and molecular weights. The point source radiant flux model requires an estimate of the total

energy generation rate which is determined from the mass flow rate of combustible material. The fraction of energy converted to radiant energy is determined empirically based on limited experimental data. The view factors and atmospheric transmissivity are determined using published correlations. Simplified Approaches Considine and Grint (1984) give a simplified power law correlation for LPG jet fire hazard zones. The dimensions of the torch flame, which is assumed to be conical, are given by (3.66) (3.67) (3.68) where is the length of torch flame (m) is the jet flame conical half-width at flame tip (m) is the LPG release rate subject to 1 < m < 3000 kg/s (kg/s) is the side-on hazard range to 50% lethality, subject to r > W (m) is the exposure time, subject to 10 < t < 300 s (s)

3.7.3. EXAMPLEPROBLEM

Example 31: Radiant Flux from a Jet Fire A 25-mm hole occurs in a large pipeline resulting in a leak of pure methane gas and a flame. The methane is at a pressure of 100 bar gauge. The leak occurs 2-m off the ground. Determine the radiant heat flux at a point on the ground 15 m from the resulting flame. The ambient temperature is 298 K and the humidity is 50% RH. Additional Data: Heat capacity ratio, k, for methane: Heat of combustion for methane: Flame temperature for methane:

1.32 50,000 kj/kg 2200 K

Solution: Assume a vertical flame for a conservative result and that the release hole is represented by a nozzle. The height of the flame is calculated first

to determine the location of the point source radiator. This is computed using Eq. (3.63)

The combustion reaction in air is

Thus, C x = 1/(1 + 2 + 7.52) = 0.095, T£/T- = 2200/298 = 7.4 anda T = 1.0. The molecular weight of air is 29 and for methane 16. Substituting into Eq. (3.63),

Note that Eq. (3.64) yields a value of 212, which is close to the value of 200 produced using the more detailed approach. Since the diameter of the issuing jet is 25 mm, the flame length is (200)(25 mm) = 5.00 m. Figure 3.38 shows the geometry of the jet flame. Since the flame base is 2 m off the ground, the point source of radiation is located at 2 m + (5.00 m)/2 = 4.50 m above the ground. The discharge rate of the methane is determined using Eq. (2.17) for choked flow of gas through a hole. For this case,

(for choked flow through a hole)

Jet Flame Receptor

FIGURE 338. Geometry for Example 31: Radiant flux from a jet fire.

Substituting into Eq. (2.17)

From Figure 3.38, the radiation path length is the length of the hypotenuse. Thus,

The point source view factor is given by Eq. (3.60)

The transmissivity of the air at 50% RH is determined using Eqs. (3.42) and (3.43). The result is ra = 0.812. The fraction of the total energy that is converted to radiation is found in Table 3.11. For methane this is rj = 0.2. The radiation at the receiver is determined using Eq. (3.65)

A spreadsheet implementation of this problem is shown in Figure 3.39. This example is a bit unrealistic in that the flame will most likely blow out due to the high exit velocity of the jet. As the flow velocity of the jet is increased, the flame moves downstream to a new location where the turbulent burning velocity equals the flame velocity. As the velocity is increased, a point is eventually reached where the burning location is so far downstream that the fuel concentration is below the lower flammability limit due to air entrainment. Mudan and Croce (1988) provide flame blowout criteria. 3.7.4. DISCUSSION

Strengths and Weaknesses Jet flames are less well treated theoretically than pool fires, but simple correlations such as the API or Mudan and Croce (1988) methods allow for adequate hazard estimation. Flame impingement effects are not treated—they give sub-

Example 31: Radiant Flux from a Jet Fire Input Data: Distance from flame: Hole diameter: Leak height above ground: Gas pressure: Ambient temperature: Relative humidity: Heat capacity ratio for gas: Heat of combustion for gas: Molecular weight of gas: Flame temperature: Discharge coefficient for hole: Ambient pressure: Fuel mole fraction at stoichiometric: Moles of reactant per mole of product: Molecular weight of air: Fraction of total energy converted: Calculated Results: Area of hole: Gas discharge rate: L/d ratio for flame: Flame height: Location of flame center above ground: Radiation path length: Point source view factor: Water vapor partial pressure: Atmospheric transmissivity: I Flux at receptor location: FIGURE 3.39. Spreadsheet for Example 31: Radiant flux from a jet fire.

stantially higher heat fluxes than predicted by thermal radiation models. Liquid and two-phase jets cannot be modeled using this approach. The jet flame models presented here assume vertical flames for a conservative result. Identification and Treatment of Possible Errors Jet fire models based on point source radiation approximations will give poor thermal flux estimates close to the jet, and more mechanistic models should be used. The radiant energy fraction is also a source of error. The models presented here do not apply if wind is present, see Mudan and Croce (1988). Resources Necessary A trained process engineer would require several hours to complete a jet fire scenario by hand if all necessary thermodynamic data, view factor formulas, and humidity data are available.

Available Computer Codes EFFECTS (TNO, Apeldoorn, The Netherlands) PHAST (DNV, Houston, TX) QRAWorks (Primatech, Columbus, OH) SUPERCHEMS (Arthur D. Little, Cambridge, MA) TRACE (Safer Systems, Westlake Village, CA)

4

E f f e c t

M o d e l s

The physical models described in Chapter 2 generate a variety of incident outcomes that are caused by release of hazardous material or energy. Dispersion models (Section 2.3) estimate concentrations and/or doses of dispersed vapor; vapor cloud explosions (VCE) (Section 3.1), physical explosion models (Section 3.3), fireball models (Section 3.4), and confined explosion models (Section 3.5) estimate shock wave overpressures and fragment velocities. Pool fire models (Section 3.6), jet fire models (Section 3.7), BLEVE models (Section 3.4) and flash fire models (Section 3.2) predict radiant flux. These models rely on the general principle that severity of outcome is a function of distance from the source of release. The next step in CPQRA is to assess the consequences of these incident outcomes. The consequence is dependent on the object of the study. For the purpose of assessing effects on human beings, consequences may be expressed as deaths or injuries. If physical property, such as structures and buildings, is the object, the consequences may be monetary losses. Environmental effects may be much more complex, and could include impacts on plant or animal life, soil contamination, damage to natural resources, and other impacts. Modeling of environmental impacts is beyond the scope of this book. Many CPQBA studies consider several types of incident outcomes simultaneously (e.g., property damage and exposures to flammable and/or toxic substances). To estimate risk, a common unit of consequence measure must be used for each type of effect (e.g., death, injury, or monetary loss). The difficulty in comparing different injury types has led to the use of fatalities as the dominant criterion for thermal radiation, blast overpressure, and toxicity exposures. One method of assessing the consequence of an incident outcome is the direct effect model, which predicts effects on people or structures based on prede-

termined criteria (e.g., death is assumed to result if an individual is exposed to a certain concentration of toxic gas). In reality, the consequences may not take the form of discrete functions (i.e., a fixed input yields a singular output) but may instead conform to probability distribution functions. A statistical method of assessing a consequence is the dose-response method. This is coupled with a probit equation to linearize the response. The probit (probability unit) method described by Finney (1971) reflects a generalized time-dependent relationship for any variable that has a probabilistic outcome that can be defined by a normal distribution. For example, Eisenberg et al. (1975) use this method to assess toxic effects by establishing a statistical correlation between a "damage load" (i.e., a toxic dose that represents a concentration per unit time) and the percentage of people affected to a specific degree. The probit method can also be applied to thermal and explosion effects. Numerous reference texts are available on toxicology, including Caserett and Doull (1980) and Williams and Burson (1985). These provide more detail on toxicology for risk analysts.

4 . 1 . Dose-Response a n d Probit Functions

4.1.1. DOSE-RESPONSE FUNCTIONS

Toxicologists define toxicity as "the ability of a substance to produce an unwanted effect when the chemical has reached a sufficient concentration at a certain site in the body" (NSC, 1971). Most toxicological considerations are based on the dose-response function. A fixed dose is administered to a group of test organisms and, depending on the outcome, the dose is either increased until a noticeable effect is obtained, or decreased until no effect is obtained. There are several ways to represent dose. One way is in terms of the quantity administered to the test organism per unit of body weight. Another method expresses dose in terms of quantity per skin surface area. With respect to inhaled vapors, the dose can be represented as a specified vapor concentration administered over a period of time. It is difficult to evaluate precisely the human response caused by an acute, hazardous exposure for a variety of reasons. First, humans experience a wide range of acute adverse health effects, including irritation, narcosis, asphyxiation, sensitization, blindness, organ system damage, and death. In addition, the severity of many of these effects varies with intensity and duration of exposure. For example, exposure to a substance at an intensity that is sufficient to cause only

mild throat irritation is of less concern than one that causes severe eye irritation, lacrimation, or dizziness, since the latter effects are likely to impede escape from the area of contamination. Second, there is a high degree of variation in response among individuals in a typical population. Withers and Lees (1985) discuss how factors such as age, health, and degree of exertion affect toxic responses (in this case, to chlorine). Generally, sensitive populations include the elderly, children, and persons with diseases that compromise the respiratory or cardiovascular system. As a result of the variability in response of living organisms, a range of responses is expected for a fixed exposure. Suppose an organism is exposed to a toxic material at a fixed dose and the responses are recorded and classified into a number of response categories. Some of the organisms will show a high level of response while some will show a low level. A typical plot of the results is shown in Figure 4.1. The results are frequently modeled as a Gaussian or "bell-shaped" curve. The shape of the curve is defined entirely by the mean response, /*, and a standard deviation, a. The area under the curve represents the percentage of organisms affected for a specified response interval. In particular, the response interval within one standard deviation of the mean represents 68% of the individual organisms. Two standard deviations represents 95.5% of the total individuals. The entire area under the curve has an area of 1, representing 100% of the individuals. The experiment is repeated for a number of different doses and Gaussian curves are drawn for each dose. The mean response and standard deviation is determined at each dose. A complete dose-response curve is produced by plotting the cumulative mean response at each dose. This result is shown in Figure 4.2. For convenience, the response is plotted versus the logarithm of the dose, as shown in Figure 4.3. Percent or Fraction of Individuals Affected

Average

Low Response

Average Response

High Response

FIGURE 4.1. Typical Gaussian or bell-shaped curve.

Response

Dose

Response (Percent)

FIGURE 4.2. Typical dose-response curve.

Logarithm of the Dose FIGURE 4.3. Typical response versus log(dose) curve.

This form typically provides a much straighter line in the middle of the dose range. The logarithm form arises from the fact that in most organisms there are some subjects who can tolerate rather high levels of the causative variable, and conversely, a number of subjects who are sensitive to the causative variable. 4.1.2. PROBITFUNCTIONS

For most engineering computations, particularly those involving spreadsheets, the sigmoidal-shaped dose-response curve of Figure 4.3 does not provide much utility; an analytical equation is preferred. In particular, a straight line would be ideal, since it is amenable to standard curve fit procedures. For single exposures, the probit (probability unit) method provides a transformation method to convert the dose-response curve into a straight line. The probit variable Y is related to the probability P by (Finney, 1971): (4.1) where P is the probability or percentage, Y is the probit variable, and u is an integration variable. The probit variable is normally distributed and has a mean value of 5 and a standard deviation of 1.

For spreadsheet computations, a more useful expression for performing the conversion from probits to percentage is given by, (4.2)

where "erf is the error function. Table 4.1 and Figure 4.4 also show the conversion from probits to percentages. Probit equations for the probit variable, Y, are based on a causative variable, V (representing the dose), and at least two constants. These equations are of the form, (4.3)

where k1 and k2 are constants. Probit equations of this type are derived as lines of best fit to experimental data (percentage fatalities versus concentration and duration) using log-probability plots or standard statistical packages. Probit equations are available for a variety of exposures, including exposures to toxic materials, heat, pressure, radiation, impact, and sound, to name a few. For toxic exposures, the causative variable is based on the concentration; for Table 4.1. Conversion from Probits to Percentages %

0

1

2

3

4

5

0

—

2.67

2.95

3.12

3.25

3.36

10

3.72

3.77

3.82

3.87

3.92

20

4.16

4.19

4.23

4.26

30

4.48

4.50

4.53

40

4.75

4.77

50

5.00

60

6

7

8

9

3.45

3.52

3.59

3.66

3.96

4.01

4.05

4.08

4.12

4.29

4.33

4.36

4.39

4.42

4.45

4.56

4.59

4.61

4.64

4.67

4.69

4.72

4.80

4.82

4.85

4.87

4.90

4.92

4.95

4.97

5.03

5.05

5.08

5.10

5.13

5.15

5.18

5.20

5.23

5.25

5.28

5.31

5.33

5.36

5.39

5.41

5.44

5.47

5.50

70

5.52

5.55

5.58

5.61

5.64

5.67

5.71

5.74

5.77

5.81

80

5.84

5.88

5.92

5.95

5.99

6.04

6.08

6.13

6.18

6.23

90

6.28

6.34

6.41

6.48

6.55

6.64

6.75

6.88

7.05

7.33

%

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

99

7.33

7.37

7.41

7.46

7.51

7.58

7.65

7.75

7.88

8.09

Probit

Percentage FIGURE 4.4. The relationship between percentage and probit.

explosions, the causative variable is based on the explosive overpressure or impulse, depending on the type of injury or damage. For fire exposure, the causative variable is based on the duration and intensity of the radiative exposure. Probit equations can also be applied to estimate structural damage, glass breakage, and other types of damage. 4.1.3. EXAMPLEPROBLEM

Example 32: Dose-Response Correlation via Probits Eisenberg et al. (1975) report the following data on the effect of explosion peak overpressures on eardrum rupture in humans: Percentage Affected

Peak Overpressure (N/m 2 )

Equivalent Overpressure (psi)

Determine the probit correlation for this exposure. Solution: The percentages are converted to a probit variable using Table 4.1. The results are

Percentage

Probit

1

2.67

10

3.72

50

5.00

90

6.28

Percent Affected

Figure 4.5 is a plot of the percentage affected versus the natural log of the peak overpressure. This demonstrates the classical sigmoid shape of the response versus log dose curve. Figure 4.6 includes a plot of the probit variable (with a linear probit scale) versus the log of the peak overpressure. The straight line confirms the form of Eq. (4.3) and the resulting fit is Y = -16.7 + 2.03 In(P0), where P 0 is the peak overpressure in Pa, or N/m2. The output from the spreadsheet solution to this problem is shown in Figure 4.6. The probit equation is fit using a least-squares line fitting technique supported by the spreadsheet.

In (Overpressure, N/m2 ) FIGURE 4.5. Plot of percentage affected versus the log of the peak overpressure for Example 32: Dose-response correlation via probits.

4 . 2 . Toxic Gas Effects

4.2.1. BACKGROUND

Purpose Toxic effect models are employed to assess the consequences to human health as a result of exposure to a known concentration of toxic gas for a known period of time. Mitigation of these consequences by sheltering or evasive action is discussed in Chapter 5.

Example 32: Dose-Response Correlation via Probits Input Data: Percentage Affected

Peak Peak Overpressure Overpressure Calculated Calculated psi LN(Overpressure) Probit Probit (N/m**2) Percentage

Calculated Results: Regression Output from Spreadsheet follows: Regression Output: Constant StdErrofYEst R Squared No. of Observations Degrees of Freedom

Probit

X Coefficient(s) Std Err of Coef.

In (Overpressure, N/m**2) FIGURE 4.6. Spreadsheet output for Example 32: Dose-response correlation via probits.

This section does not address the release and formation of nontoxic, flammable vapor clouds that do not ignite but pose a potential for asphyxiation. Nontoxic substances can cause asphyxiation due to displacement of available oxygen. Asphyxiant concentrations are typically assumed to be in the range of 50,000-100,000 ppm (5 to 10 volume percent). For CPQRA, the toxic effects are due to short-term exposures, primarily due to vapors. Chronic exposures are not considered here.

Philosophy For toxic gas clouds, concentration-time information is estimated using dispersion models (Section 2.3). Probit models are used to develop exposure estimates for situations involving continuous emissions (approximately constant concentration over time at a fixed downwind location) or puff emissions (concentration varying with time at a downwind location). It is much more difficult to apply other criteria that are based on a standard exposure duration (e.g., 30 or 60 min) particularly for puff releases that involve short exposure times and varying concentrations over those exposure times. The object of the toxic effects model is to determine whether an adverse health outcome can be expected following a release and, if data permit, to estimate the extent of injury or fatalities that are likely to result. For the overwhelming majority of substances encountered in industry, there are not enough data on toxic responses of humans to directly determine a substance's hazard potential. Frequently, the only data available are from controlled experiments conducted with laboratory animals. In such cases, it is necessary to extrapolate from effects observed in animals to effects likely to occur in humans. This extrapolation introduces uncertainty and normally requires the professional judgment of a toxicologist or an industrial hygienist with experience in health risk assessment. Also, many releases involve several chemical components or multiple effects. At this time the cumulative effects of simultaneous exposure to more than one material is not well understood. Are the effects additive, synergistic, or antagonistic in their effect on population? As more information is developed on the characterization of multiple chemical component releases from source and dispersion experimentation and modeling, corresponding information is needed in the toxicology arena. Unfortunately, even toxic response data of humans to single component exposures are inadequate for a large number of chemical species. Finally, there are no standardized toxicology testing protocols that exist for studying episodic releases on animals. This has been in general a neglected aspect of toxicology research. There are experimental problems associated with the testing of toxic chemicals at high concentrations for very short durations in establishing the concentration/time profile. In testing involving fatal concentration/time exposures, the question exists of how to incorporate early and delayed fatalities into the study results. Many useful measures are available to use as benchmarks for predicting the likelihood that a release event will result in injury or death. AIChE (AIChE/CCPS, 1988a) reviews various toxic effects and discusses the use of various established toxicologic criteria. These criteria and methods include

• Emergency Response Planning Guidelines for Air Contaminants (ERPGs) issued by the American Industrial Hygiene Association (AIHA). • Immediately Dangerous to Life or Health (IDLH) levels established by the National Institute for Occupational Safety and Health (NIOSH). • Emergency Exposure Guidance Levels (EEGLS) and Short-Term Public Emergency Guidance Levels (SPEGLs) issued by the National Academy of Sciences/National Research Council. • Threshold Limit Values (TLVs) established by the American Conference of Governmental Industrial Hygienists (ACGIH) including Short-Term Exposure Limits (STELs) and ceiling concentrations (TLV-Cs). • Permissible Exposure Limits (PELs) promulgated by the Occupational Safety and Health Administration (OSHA). • Various state guidelines, for example the Toxicity Dispersion (TXDs) method used by the New Jersey Department of Environmental Protection (NJ-DEP). • Toxic endpoints promulgated by the U.S. Environmental Protection Agency. • Probit Functions. • Department of Energy (DOE) Temporary Emergency Exposure Limits (TEELs) The criteria (ERPGs, IDLHs, etc.) and methods listed above are based on a combination of results from animal experiments, observations of long- and short-term human exposures, and expert judgment. The following paragraphs define these criteria and describe some of their features. ERPGs. Emergency Response Planning Guidelines (ERPGs) are prepared by an industry task force and are published by the American Industrial Hygiene Association (AIHA). Three concentration ranges are provided as a consequence of exposure to a specific substance: • The ERPG-I is the maximum airborne concentration below which it is believed that nearly all individuals could be exposed for up to 1 hr without experiencing any symptoms other than mild transient adverse health effects or without perceiving a clearly defined objectionable odor. • The ERPG-2 is the maximum airborne concentration below which it is believed that nearly all individuals could be exposed for up to 1 hr without experiencing or developing irreversible or other serious health effects or symptoms that could impair their abilities to take protective action. • The ERPG-3 is the maximum airborne concentration below which it is believed that nearly all individuals could be exposed for up to 1 hr without experiencing or developing life-threatening health effects (similar to EEGLs).

ERPG data (AIHA5 1996) are shown in Table 4.2. As of 1996 47 ERPGs have been developed and are being reviewed, updated and expanded by an AIHA peer review task force. Because of the comprehensive effort to develop acute toxicity values, ERPGs are becoming an acceptable industry/government norm. IDLHs. The National Institute for Occupational Safety and Health (NIOSH) publishes Immediately Dangerous to Life and Health (IDLH) concentrations to be used as acute toxicity measures for common industrial gases. An IDLH exposure condition is defined as a condition "that poses a threat of exposure to airborne contaminants when that exposure is likely to cause death or immediate or delayed permanent adverse health effects or prevent escape from such an environment" (NIOSH, 1994). IDLH values also take into consideration acute toxic reactions, such as severe eye irritation, that could prevent escape. The IDLH is considered a maximum concentration above which only a highly reliable breathing apparatus providing maximum worker protection is permitted. If IDLH values are exceeded, all unprotected workers must leave the area immediately. IDLH data are currently available for 380 materials (NIOSH, 1994). Because IDLH values were developed to protect healthy worker populations, they must be adjusted for sensitive populations, such as older, disabled, or ill populations. For flammable vapors, the IDLH is defined as 1/10 of the lower flammability limit (LFL) concentration. EEGLs and SPEGLs. Since the 1940s, the National Research Council's Committee on Toxicology has submitted Emergency Exposure Guidance Levels (EEGLs) for 44 chemicals of special concern to the Department of Defense. An EEGL is defined as a concentration of a gas, vapor, or aerosol that is judged to be acceptable and that will allow healthy military personnel to perform specific tasks during emergency conditions lasting from 1 to 24 hr. Exposure to concentrations at the EEGL may produce transient irritation or central nervous system effects but should not produce effects that are lasting or that would impair performance of a task. In addition to EEGLs, the National Research Council has developed Short-Term Public Emergency Guidance Levels (SPEGLs), defined as acceptable concentrations for exposures of members of the general public. SPEGLs are generally set at 10-50% of the EEGL and are calculated to take account of the effects of exposure on sensitive, heterogenous populations. The advantages of using EEGLs and SPEGLs rather than IDLH values are (1) a SPEGL considers effects on sensitive populations (2) EEGLs and SPEGLs are developed for several different exposure durations, and (3) the methods by which EEGLs and SPEGLs were developed are well documented in National Research Council publications. EEGL and SPEGL values are shown in Table 4.3.

TABLE 4.2. Emergency Response Planning Guidelines, ERPGs (AIHA, 1996). All values are in ppm unless othenvise noted. Values are updated regularly. Chemical

ERPG-I

ERPG-2

ERPG-3

Acetaldehyde Acrolein Acrylic Acid Acrylonitrile AUyI Chloride

10 0.1 2 NA 3

200 0.5 50 35 40

1000 3 750 75 300

Ammonia Benzene Benzyl Chloride Bromine 1,3-Butadiene

25 50 1 0.2 10

200 150 10 1 50

1000 1000 25 5 5000

»-Butyl Acrytate »-Butyl Isocyanate Carbon Disulfide Carbon Tetrachloride Chlorine

0.05 0.01 1 20 1

25 0.05 50 100 3

250 1 500 750 20

0.1 0.1 NA 2 mg/m3 20

1 1 0.2 10 mg/m3 100

10 10 3 30 mg/m3 300

Crotonaldehyde Diborane Diketene Dimethylamine Dimethylchlorosilane

2 NA 1 1 0.8

10 1 5 100 5

50 3 50 500 25

Dimethyl Disulfide Epichlorohydrin Ethylene Oxide Formaldehyde Hexachlorobutadiene

0.01 2 NA 1 3

50 20 50 10 10

250 100 500 25 30

Hexafluoroacetone Hexafluoropropylene Hydrogen Chloride Hydrogen Cyanide Hydrogen Fluoride

NA 10 3 NA 54

1 50 20 10 20

50 500 100 25 50

Chlorine Trifluouride Chloroacetyl Chloride Chloropicrin Chlorosulfonic Acid Chlorotrifluoroethylene

(continued)

Table 4.2. (continued) Chemical

ERPG-I

ERPG-2

ERPG-3

0.1 10 NA 25 /xgm/m3 200

30 50 0.1 100 /Agm/m3 1000

100 200 1 500 jugm/m3 5000

Methyl Chloride Methylene Chloride Methyl Iodide Methyl Isocyanate Methyl Mercaptan

NA 200 25 0.025 0.005

400 750 50 0.5 25

1000 4000 125 5 100

Methykrichlorosilane Monomethylamine Perfluoroisobutylene Phenol Phosgene

0.5 10 NA 10 NA

3 100 0.1 50 0.2

15 500 0.3 200 1

Hydrogen Sulfide Isobutyronitrile 2-Isocyanatoethyl Methacrylate Lithium Hydride Methanol

Phosphorus Pentoxide Propylene Oxide Styrene Sulfonic Acid (Oleum, Sulfur Trioxide, and Sulfuric Acid) Sulfur Dioxide

5 mg/m3 50 50

25 mg/m3 250 250

100 mg/m3 750 1000

2 mg/m3 0.3

10 mg/m3 3

30 mg/m3 15

Tetrafluoroethylene Titanium Tetrachloride Toluene Trimethylamine Uranium Hexafluoride

200 5 mg/m3 50 0.1 5 mg/m3

1000 20 mg/m3 300 100 15 mg/m3

10,000 100 mg/m3 1000 500 30 mg/m3

Vinyl Acetate

5

75

500

TLV-STEL. Certain American Conference of Governmental Industrial Hygienists (ACGIH) criteria may be appropriate for use as benchmarks (ACGIH 5 1996). In particular, the ACGIH's threshold limit values-short-term exposure limits (TLV-STELs) and threshold limit values-ceiling limits (TLV-C) are designed to protect workers from acute effects resulting from exposure to chemicals; such effects include, among others, irritation and narcosis. TLV-STELS are the maximum concentration to which workers can be exposed for a period of up to 15 minutes without suffering (1) intolerable irritation (2) chronic or irreversible

TABLE 4.3. Emergency Exposure Guidance Levels (EEGLs) from the National Research Council (NRC). All values are in ppm unless otherwise noted. Compound

1-Hr. EEGL

24-Hr. EEGL

Source

Acetone

8,500

1,000

NRCI

Acrolein

0.05

0.01

NRCI

100

NRCIV

3

Aluminum oxide

15 mg/m

Ammonia

100

Arsine

1

0. 1

NRCI

Benzene

50

2

NRCVI

Bromotrifluoromethane

25,000

NRC III

Carbon disulfide

50

NRCI

Carbon monoxide

400

50

NRCIV

Chlorine

3

0.5

NRCII

Chlorine trifluoride

1

Chloroform

100

30

NRCI

Dichlorodifluoromethane

10,000

1000

NRCII

Dichlorofluoromethane

100

3

NRCII

Dichlorotetrafluoroethane

10,000

1000

NRCII

1,1 -Dimethylhydrazine

0.24"

0.01"

NRCV

Ethanolamine

50

3

NRCII

Ethylene glycol

40

20

NRCIV

Ethylene oxide

20

1

NRCVI

Fluorine

7.5

Hydrazine

0.12"

Hydrogen chloride

20/l

NRC VII

NRCII

NRCI

a

Hydrogen sulfide Isopropyl alcohol Lithium bromide Lithium chromate

400

0.005"

NRCV

20/1"

NRCVII

10

NRCIV

200 3

15 mg/m

3

100/xg/m

NRCII 3

7 mg/m

NRCVII

3

50/Ag/m

NRCVIII 3

Mercury (vapor)

0.2 mg/m

NRCI

Methane

5000

NRCI

10

NRCIV

Methanol

200

TABLE 4.3. (continued) Compound

1-Hr. EEGL

24-Hr. EEGL

Source

Methylhydrazine

0.24"

0.01*

NRCV

Nitrogen dioxide

1"

0.04*

NRCIV

Nitrous oxide

10,000

Ozone

1

0. 1

NRCI

Phosgene

0.2

0.02

NRCII

Sodium hydroxide

2 mg/m3

Sulfur dioxide

10

NRCIV

NRCII 5

3

NRCII

Sulfuric acid

1 mg/m

Toluene

200

100

NRCVII

Trichloroethylene

200 ppm

10 ppm

NRCVIII

Trichlorofluoromethane

1500

500

NRCII

Trichlorotrifluoroethane

1500

500

NRCII

10

NRCII

100

NRCII

Vinylidene chloride Xylene

200

NRCI

a SPEGL value.

tissue change (3) narcosis of sufficient degree to increase accident proneness, impair self-rescue, or materially reduce worker efficiency, provided that no more than four excursions per day are permitted, with at least 60 minutes between exposure periods, and provided that the daily TLV-TWA is not exceeded. The ceiling limits (TLV-Cs) represent a concentration which should not be exceeded, even instantaneously. Use of STEL or ceiling measures may be overly conservative if the CPQRA is based on the potential for fatalities; however, they can be considered if the study is based on injuries. PEL. The Permissible Exposure Limits (PELs) are promulgated by the Occupational Safety and Health Administration (OSHA) and have force of law. These levels are similar to the ACGIH criteria for TLV-TWAs since they are also based on an 8-hr time-weighted average exposures. OSHA-cited "acceptable ceiling concentrations," "excursion limits," or "action levels" may be appropriate for use as benchmarks.

TXDS Acute Toxic Concentration. Some states have their own exposure guidelines. For example, the New Jersey Department of Environmental Protection (NJ-DEP) uses the Toxic Dispersion (TXDS) method of consequence analysis for the estimation of potentially catastrophic quantities of toxic substances as required by the New Jersey Toxic Catastrophe Prevention Act (TCPA) (Baldini and Komosinsky, 1988). An acute toxic concentration (ATC) is defined as the concentration of a gas or vapor of a toxic substance that will result in acute health effects in the affected population and one fatality out of 20 or less (5% or more) during a 1 hr exposure. ATC values as proposed by the NJ-DEP are estimated for 103 "extraordinarily hazardous substances," and are based on the lowest value of one of the following: • the lowest reported lethal concentration (LCLO) value for animal test data • the median lethal concentration (LC50) value from animal test data multiplied by 0.1 • the IDLH value. Refer to Baldini and Komosinsky (1988) for a listing of the ATC values for the 103 "extraordinarily hazardous substances," or contact the NJ-DEP. Toxic Endpoints. The EPA (1996) has promulgated a set of toxic endpoints to be used for air dispersion modeling of toxic gas releases as part of the EPA Risk Management Plan (RMP). The toxic endpoint is, in order of preference: (1) the ERPG-2, or (2) the Level of Concern (LOC) promulgated by the Emergency Planning and Community Right-to-Know Act. The Level of Concern (LOC) is considered "to be the maximum concentration of an extremely hazardous substance in air that will not cause serious irreversible health effects in the general population when exposed to the substance for relatively short duration" (EPA, 1986). Toxic endpoints are provided for 77 chemicals under the RMP rule (EPA, 1996). In general, the most directly relevant toxicologic criteria currently available, particularly for developing emergency response plans, are ERPGs, SPEGLs, and EEGLs. These were developed specifically to apply to general populations, and to account for sensitive populations and scientific uncertainty in toxicologic data. For incidents involving substances for which no SPEGLs or EEGLs are available, IDLHs provide an alternative criteria. However, because IDLHs were not developed to account for sensitive populations and because they were based on a maximum 30-min exposure period, U.S. EPA suggests that the identification of an effect zone should be based on exposure levels of one-tenth the IDLH (EPA, 1987). For example, the IDLH for chlorine dioxide is 5 ppm. Effect zones resulting from the release of this gas would be defined as any zone in which the

concentration of chlorine dioxide is estimated to exceed 0.5 ppm. Of course, the approach is very conservative and gives unrealistic results; a more realistic approach is to use a constant-dose assumption for releases less than 30 min using the IDLH. The use of TLV-STELs and ceiling limits may be most appropriate if the objective of a CPQRA is to identify effect zones in which the primary concerns include more transient effects, such as sensory irritation or odor perception. Generally, persons located outside the zone that is based on these limits can be assumed to be unaffected by the release. For substances that do not have IDLHs, Levels of Concern (LOCs) are estimated from median lethal concentration (LC50) or median lethal dose (LD50) levels reported for mammalian species (EPA, 1987). LC50S and LD50S are concentration or dose levels, respectively, that kill 50% of exposed laboratory animals in controlled experiments. These can also be estimated from lowest reported lethal concentration or lethal dose levels (LC50 and LDLO, respectively). Inhalation data (LC50 or LCLO) are preferred over other data (LD50 or LDLO). Using these data, the level of concern is estimated as follows (EPA, 1986):

Because the "level of concern5' derived from an LD50 or LDLO represents a "specific" dose in units of mg/kg body weight, it is necessary to convert this "specific35 dose to an equivalent 30-min exposure to an airborne concentration of material as follows: (level of concern)

(4.4)

where 70 kg is the assumed weight of an adult male and 0.4 m3 is the approximate volume of air inhaled in 30 min. The estimated IDLH, whether derived from LC50 or LD50 data, is divided by a factor of 10 to identify consequence zones. The Department of Energy's Subcommittee on Consequence Assessment and Protective Action (SCAPA) (Craig et al., 1995) provide a hierarchy of alternative concentration guidelines in the event that ERPG data are not available. These interim values are known as Temporary Emergency Exposure Links (TEELs). This hierarchy is shown in Table 4.4. These methods may result in some inconsistencies since the different methods are based on different concepts—good judgment should prevail.

Table 4.4. Recommended Hierarchy of Alternative Concentration Guidelines (Craig etal., 1995) Hierarchy of Alternative Guideline

Guidelines

ERPG-I

AIHA EEGL (30-minute)

NAS

IDLH

NIOSH

ERPG-2

AIHA EEGL (60 minute)

NAS

LOC

EPA/FEMA/DOT

PEL-C

OSHA

TLV-C

ACGIH

5 x TLV-TWA

ACGIH

ERPG-3

AIHA: NAS: NIOSH: EPA: FEMA. DOT: OSHA: ACGIH:

Source of Alternative

AIHA PEL-STEL

OSHA

TLV-STEL

ACGIH

3 x TLV-TWA

ACGIH

American Industrial Hygiene Association National Academy of Sciences Committee on Toxicology National Institutes for Occupational Safety and Health Environmental Protection Agency Federal Emergency Management Agency U. S. Department of Transportation U.S. Occupational Safety and Health Administration American Conference of Governmental Industrial Hygienists

Application of Probit Equations For about 20 commonly used substances, there is some information on dose-response relationships that can be applied to a probit function to quantify the number of fatalities that are likely to occur with a given exposure. Where sufficient information exists, use of the probit function can refine the hazard assessment; however, despite the appearance of greater precision, it is important to remember that probit relationships for specific substances are typically extrapolated experimental animal data and, therefore, uncertainty surrounds these risk estimates when they are applied to human populations. Many probit models are the result of the combination of a wide range of animal tests involving different animal species producing widely varying responses. There has been little effort to

try to utilize those studies and data that represent the greatest similarity to human exposure. There is also a standard error associated with the use of the probit function and if only a few data points are available the confidence limits of the resulting correlation can be very broad. The probit method is a statistical curve fitting method. Furthermore, the results are often extrapolated beyond the experimental data range. This presents a difficult problem for higher doses since the toxicity mechanisms might change. Probit equations for a number of different vapor exposures are provided in Table 4.5. Fatality probit coefficients are also available for approximately 10 materials in Tsao and Ferr (2979). Withers and Lees (19S5) provide a review of acute chlorine toxicity, and Withers (1986) presents a similar review of acute ammonia toxicity. Rijnmond Public Authority (1982) provides probits for four chemicals (chlorine, ammonia, hydrogen sulfide, and acrylonitrile): however, the Withers and Lees reviews are more recent. Prugh (1995) presents a compilation of probit equations for 28 materials, showing widely differing results from different investigators. Schubach (1995) performs a comparison between CCPS (AIChE, 1988a) and TNO (1992) probit equations. He demonstrates the sensitivity of risk assessment results to differences in probit equations. Franks et al. (1996) provides a summary of probit data and how these data are related to LC50 values. 4.2.2. DESCRIPTION

Description of Technique To determine the possible health consequences of a toxic release incident outcome, dispersion models are used to develop a contour map describing the concentration of gas as a function of time, location, and distance from the point of release. This is a reasonably simple process for a continuous release since the concentration is constant at a fixed point. However, this approach is more difficult for an intermittent or instantaneous release since concentration-time information is required. Once the concentration-time information are developed from the dispersion models it is relatively straightforward to use established toxicologic criteria (e.g., ERPG, EEGL, SPEGL, or IDLH) to assess the likelihood of an adverse outcome. Effects zones can be identified that represent areas in which the concentration of gas and duration of exposure exceed these criteria. All humans exposed within the consequence zone are assumed to be at risk of experiencing the adverse effects associated with exposure to the material. In some cases adjustments might be necessary due to sensitive populations. Once the concentration-time information are determined, the next step is to determine the toxic dose. Toxic dose is usually defined in terms of concentration

TABLE 4.5. Probit Equation Constants for Lethal Toxicity The probit equation is of the form Y = a + b ln(C%) where Y is the probit a, b, n are constants C is the concentration in ppm by volume tc is the exposure time in minutes U.S. Coast Guard (1980) Substance Acrolein

a

b

n

a

b

n

-9.931

2.049

1

-9.93

2.05

1.0

-9.82

0.71

2.00

0.54

1.01

0.5

-5.3

0.5

2.75

-21.76

2.65

1.00

-26.4

3.35

1.0

-19.92

5.16

1.0

-19.27

3.69

1.0

Acrylonitrile

-29.42

3.008

1.43

Ammonia

-35.9

1.85

2

Benzene

-109.78

5.3

2

Bromine

-9.04

0.92

2

-37.98

3.7

1

Carbon Monoxide Carbon Tetrachloride

-6.29

0.408

2.50

Chlorine

-8.29

0.92

2

Formaldehyde

-12.24

1.3

2

Hydrogen Chloride

-16.85

2.00

1.00

Hydrogen Cyanide

-29.42

3.008

1.43

Hydrogen Fluoride

-25.87

3.354

1.00

Hydrogen Sulfide

-31.42

3.008

1.43

Methyl Bromide

-56.81

5.27

1.00

1.637

0.653

Methyl Isocyanate

-5.642

Nitrogen Dioxide

-13.79

1.4

2

Phosgene

-19.27

3.686

1

0.509

2.00

2.10

1.00

0.408

2.50

Propylene Oxide Sulfur Dioxide Toluene

World Bank (1988)

-7.415 -15.67 -6.794

per unit time of exposure raised to a power multiplied by duration of exposure (CM£), with n typically ranging from 0.5 to 3 (Lees, 1986). This relationship is an expansion of the original Haber law developed in 1924 which states that, for a given physiological effect, the product of the concentration times the time is equal to a constant. For continuous releases, toxic dose may be calculated directly, since the concentration is constant. For instantaneous, time-varying (puff) releases, the toxic dose is estimated by integration or summation over several time increments. toxic dose

(4.5)

where C is the concentration (usually ppm or mg/m3) n is the concentration exponent (dimensionless) t is the exposure time (min) i is the time increment (dimensionless) Although there are various criteria that can be applied for the determination of effect zones beyond the plant boundary there is no concensus within industry on which criteria to apply. This same problem exists for local, state, and federal regulatory bodies as well. Because such wide variation exists, judgment of trained toxicologists should be utilized.

Theoretical Foundation Probit equation parameters for individual gases are usually derived from animal experiments. Accurate concentrations and duration values are rarely available for historical toxic accidents, but approximate estimates may be derived in some cases to complement the animal data. Probit equation parameters for gas mixtures are not currently available. The probit method is simply a statistical curve-fitting approach to handle the nonlinear experimental data from exposures. Extrapolation outside the range of the applicable data is unreliable. Animal experiments are usually done on groups of rats or mice, but other species are also used. The variability in toxic effect (concentration and time) between animal species can be substantial. No definitive correlation is available to relate human and animal responses, for example, the relationship between species often depends on the substance to which the relevant species are exposed; substance specific conversion models are sometimes required. Therefore, species-specific methods need to be defined for converting animal data to human effects or for using animal data directly. Anderson (1983) suggests that an equiv-

alent dose for humans can be estimated based on mouse data taking into account LC50 data, air intake, weight, target organs, and other factors. A further consideration is that probit data are developed using mean exposure concentrations. It is not known whether the approach is applicable to time varying concentrations as would be expected from a moving puff. Probit data are available from a number of sources (US Coast Guard, 1980; WorldBank, 1988;Prugh, 1995;Lees, 1996). These data are shown in Table 4.5. Prugh (1995) provides a concise summary of probit models for 28 chemicals. His summary shows a wide variability in coefficient and exponent values between different investigators. Schubach (1995) demonstrates that this results in a great variability in the predicted consequences. Ten Berge et al. (1986) discuss the applicability of Haber's law and conclude that a concentration exponent of 1 does not fit the available data. Prugh (1995) also performs a detailed analysis for chlorine, demonstrating that Eq. (4.5), with a fixed exponent #, fits the available data at high concentrations, but not at low. This implies that the probit equation and Eq. (4.5) does not fit the data over wide concentration ranges. He concludes that this might be true for other chemical species. Input Requirements and Availability The analysis of toxic effects requires input at two levels 1. Predictions of toxic gas concentrations and durations of exposure at all relevant locations. 2. Toxic criteria for specific health effects for the particular toxic gas. Predictions of gas cloud concentrations and durations are available from neutral and dense gas dispersion models (Section 2.3). IDLH and other acute toxic criteria are available for many chemicals and are described by AIChE/CCPS (1988b). Probit equations are readily applied using spreadsheet analysis, but are not as readily available. Output The usual output of toxicity effect analysis is the identification of populations at risk of death or serious harm and the percentage of the population that may be affected by a given toxic gas exposure. Simplified Approaches The use of established toxicity measures (e.g., ERPGs, EEGLs, SPEGLs, ACGIH TLV-STELs, TLV-Cs) is usually a simpler approach than the probit model. However, when the release is of longer or shorter duration than the published criteria time durations the results are more difficult to interpret.

4.2.3. EXAMPLEPROBLEMS

Example 33: Percent Fatalities from a Fixed Concentration-Time Relationship Determine the likely percentage of fatalities from a 20-min exposure to 400 ppm of chlorine. Solution: Use the probit expression for chlorine fatalities found in Table 4.5:

Substituting for this exposure, Table 4.1, Figure 4.4, or Eq. (4.2) is used to convert from the probit to percentages. The result is 69%. The spreadsheet output for this example is shown in Figure 4.7. The spreadsheet has been generalized so that the user can specify as input any general probit equation form. Example 34: Fatalities Due to a Moving Puff A fixed mass of toxic gas has been released almost instantaneously from a process unit. The release occurs at night with calm and clear conditions. If the gas obeys the probit equation for fatalities

where C has units of ppm and T has units of minutes. a. Prepare a spreadsheet to determine the percent fatalities at a fixed location 2000-m downwind as a result of the passing puff. Vary the total Example 33: Percent Fatalities from a Fixed Concentration-Time Relationship Input Data: Concentration: Exposure Time: Probit Equation:

minutes

k1: k2: Exponent: Calculated Results: Probit Value: Percent: FIGURE 4.7. Spreadsheet output for Example 33: Percent fatalities form a fixed concentration-time relationship.

release quantity and plot the percent fatalities vs. the total release quantity. b. Change the concentration exponent from n = 2.75 to n = 2.50 in the probit equation and determine the percent fatalities for a 5-kg release. How does this compare to the previous result? Additional data: Molecular weight of gas: Temperature: Pressure: Release height: Wind speed:

30 298 K 1 atm Ground level 2 m/s

Solution: (a) A diagram of the release geometry is shown in Figure 4.8. The material is released instantaneously at the release point to form a puff, and the puff moves downwind toward the receptor target. As the puff moves downwind, it mixes with fresh air. The most direct approach is to use a coordinate system for the puff that is fixed on the ground at the release point. Thus, Eq. (2.59) is used in conjunction with Eq. (2.58). Since the release occurs at ground level, Hr = 0, and the resulting working equation is (4.6) For a night release, with clear conditions and a wind speed of 2 m/s, the stability class is F. Thus, from Table 2.13 and* = 2000 m downwind:

Wind Direction

Instantaneous Release Point

Moving Puff

Fixed Receptor Location

FIGURE 4.8. Geometry for Example 34: Fatalities due to a moving puff.

The spreadsheet output for this example is shown in Figure 4.9. The most versatile approach is to design the spreadsheet cell grid to move with the center of the puff, rather than assigning each cell to a fixed location in space with respect to the release. This reduces the total number of spreadsheet cells required. The spreadsheet includes 50 cells on either side of the puff center. The cell width is

Probit Equation: Exponent: k1: Y2:

Puff Concentration Profile Concentration, ppm

Example 34: Fatalities Due to a Moving Puff Input Data: TlTTTeI Wind Speed: Total Release: Step Increment: Release Height: No. of Increments: Molecular Weight: Temperature: Pressure:

Distance from Puff Center, m

Calculated Results: Distance Downwind: Time Increment: Max. cone, in puff: Results: Probit: Percent fatalities: Tables for Dispersion Calculation: Distance from Distance Dispersion Coeff. Centerline Center Downwind Sigma y Sigma z Cone. Cone, Causative (m) (m) (m) mg/mA3 (m) ppm Variable -75 1925 16.6 5.0 0.020022 0.0 0.0 -73.5 1926.5 16.8 5.0 0.030113 0.0 0.0 -72 1928 16.8 5.0 0.04488 0.0 0.0 -70.5 1929.5 16.8 5.0 0.066284 0.1 0.0 -69 1931 16.8 5.1 0.097014 0.1 0.0 -67.5 1932.5 16.8 5.1 0.140718 0.1 0.0 -66 1934 16.8 5.1 0.202287 0.2 0.0 -64.5 1935.5 16.8 5.1 0.288208 0.2 0.0 -63 1937 16.8 5.1 0.406986 0.3 0.0 -61.5 1938.5 16.9 5.1 0.569645 0.5 0.0 -60 1940 16.9 5.1 0.790307 0.6 0.0 -58.5 1941.5 16.9 5.1 1.086849 0.9 0.0 -57 1943 16.9 5.1 1.48163 1.2 0.0 -55.5 1944.5 16.9 5.1 2.002272 1.6 0.0 -54 1946 16.9 5.1 2.682467 2.2 0.1 FIGURE 4.9. Spreadsheet output for Example 34: Fatalities due to a moving puff.

assumed to be small enough that the concentration is approximately constant within each cell. The width of each cell can be varied at the top of the spreadsheet to adjust the total distance encompassed. This value can be adjusted so that the full concentration profile of the passing puff is included by the cells. The rigorous solution to the problem would vary the time at the top of spreadsheet and track the concentration at x = 2000 m as the puff passed. However, the puff has a small enough diameter and the puff passes relatively quickly so that the concentration profile will not change much in shape as it passes. Thus, the concentration profile centered around x = 2000 m can be used to approximate the actual concentration profile as a function of time. The procedure for this approach is 1. Compute x at each cell in the grid (first column) 2. Compute centerline concentration at each point using Eq. (4.6). 3. Compute C2 75 T at each point on the grid. The concentration must have units of ppm and the time has units of minutes. 4. Form the sum ^ C 2 7 5 T . 5. Calculate the probit using the results of step 4 and the probit equation. 6. Convert the probit to percentage.

Percent Fatalities

The spreadsheet output for a 5 kg release is shown in Figure 4.9. Figure 4.9 includes a plot of the puff concentration at x = 2000 m when the puff is centered at that point. The spreadsheet is executed repeatedly using differing values of the total release quantity. The percent fatalities are recorded for each run. The total results are plotted in Figure 4.10. These results show that a relatively small change in total release (from about 3 to 7 kg) changes the percent fatalities from 3 to 98 percent.

Total Release, kg FIGURE 4.10. Total fatalities versus total quantity released for Example 34: Fatalities due to a moving puff.

(b) For this case, the spreadsheet is executed with n = 2.50 with a total release of 5 kg. The percent fatalities in this case is 48.3%. Thus, a small change in the exponent in the probit results in a large change in the effects. The fixed downwind distance with 10% fatalities changes from 2912 m to 2310 m with a change in n from 2.75 to 2.50. 4.2.4. DISCUSSION

Strengths and Weaknesses A strength of the probit method is that it provides a probability distribution of consequences and it may be applicable to all types of incidents in CPQEA (fires, explosions, toxic releases). It is generally the preferred method of choice for CPQBA studies. A weakness of this approach is the restricted set of chemicals for which probit coefficients are published. Probit models can be developed from existing literature information and toxicity testing. EBJPG, EEGL, IDLH, or other fixed concentration methods are available for many more chemicals, but these do not allow comparisons that differ in duration form the exposure time used to establish the guidelines. Identification and Treatment of Possible Errors The potential for error arises both from the dispersion model and the toxicity measures. Errors in dispersion modeling are addressed in Section 2.3. Interpretation of animal experiments are subject to substantial error due to the limited number of animals per experiment and imprecise applicability of animal data to people. The probit method is only a statistical data fitting technique. The data are also developed based on a constant mean exposure to animals—the approach assumes that the probit equations can be applied to varying concentrations. For far field effects, that is, effects at large distances downwind from the release, the predicted consequences are highly sensitive to the dispersion and toxic effects models. As the distance from the release increases, the area impacted increases as the square of the distance. This increases the sensitivity of the consequences. For instance, Example 34 demonstrates that a change in probit concentration exponent from n = 2.75 tow = 2.50 changes the predicted consequence dramatically—this is well within the variability range for published probit equations. Wide variability exists in published probit equations. Currently, no heuristics are available to assist in the selection of an appropriate equation. If the ERPG-3 concentration is used with a probit equation assuming a one hour exposure, the results should predict a low percentage of fatalities. For many chemicals this is not the case.

Another factor to consider is the degree of exertion likely to be present in the affected population. The inhalation rate in humans varies from 6 liters/min at rest to about 43 liters/min during slow running. One means for quantifying the error is to validate the combined dispersion results and probit effects against known historical accidents, although these data are rare. Finally, since the area increases as the square of the distance from the release, the population impact increases in the far field. This increases the sensitivity of the probit method to lower concentrations. Utility Toxicology is a specialized area and few engineers and scientists have a good understanding of the underlying basis for the various toxicity criteria. Once a criterion has been selected, whether probit or a fixed value system (EBJPG, EEGL, etc.), the application is straightforward. Fixed values for toxicity measures are easier to apply than probits, especially for plume emissions. It is always preferable to use data for which there is sufficient documentation about how the data were obtained, rather than to use reference values where little or no supporting information is available. Resources Needed Some understanding of toxic effects is important because such effects are highly variable; generalizing or uncritically applying formulas can yield very misleading results. Probit equations should be developed from experimental animal data only in collaboration with a skilled industrial hygienist or toxicologist trained in health risk assessment techniques. Regardless of the method used to estimate the potential health consequences of an incident outcome (i.e., use of toxicity measures or probit functions), a toxicologist should be called to provide input to this aspect of a CPQRA. Available Computer Codes DAMAGE (TNO, Apeldorn, The Netherlands) PHAST (DNV, Houston, TX) TRACE (Safer Systems, Westlake Village, CA) 4 . 3 . T h e r m a l Effects 4.3.1. BACKGROUND

Purpose To estimate the likely injury or damage to people and objects from thermal radiation from incident outcomes.

Philosophy Thermal effect modeling is more straightforward than toxic effect modeling. A substantial body of experimental data exists and forms the basis for effect estimation. Two approaches are used: • simple tabulations or charts based on experimental results • theoretical models based on the physiology of skin burn response. Continuous bare skin exposure is generally assumed for simplification. Shelter can be considered if relevant (Chapter 5). Applications Thermal effect modeling is widely used in chemical plant design and CPQRA. Examples include the Canvey Study (Health & Safety Executive, 1978, 1981), Rijnmond Public Authority (1982) risk assessments, and LNG Federal Safety Standards (Department of Transportation, 1980). The API 521 (1996a) method for flare safety exclusion zones is widely used in the layout of process plants. 4.3.2. DESCRIPTION

Description of Techniques API (1996a) BJP 521 provides a short review of the effects of thermal radiation on people. This is based on the experiments of Buettner (1957) and Stoll and Green (1958). The data on time for pain threshold is summarized in Table 4.6 (API, 1996a). It is stated that burns follow the pain threshold "fairly quickly." The values in Table 4.6 may be compared to solar radiation intensity on a clear, hot summer day of about 320 Btu/hr ft2 (1 kW/m2). Table 4.6. Exposure Time Necessary to Reach the Pain Threshold (API, 1966a) Radiation intensity 2

(Btu/hr/ft )

Time to pain kW/m

2

threshold (s)

500

1.74

60

740

2.33

40

920

2.90

30

1500

4.73

16

2200

6.94

9

3000

9.46

6

3700

11.67

4

6300

19.87

2

Based on these data, API suggests thermal criteria (Table 4.7), excluding solar radiation, to establish exclusion zones or determine flare height for personnel exposure. Other criteria for thermal radiation damage are shown in Table 4.8. Mudan (1984) summarizes the data of Eisenberg et al. (1975) for a range of burn injuries, including fatality, and of Mixter (1954) for second-degree burns (Figure 4.11). Eisenberg et al. (1975) develop a probit model to estimate fatality levels for a given thermal dose from pool and flash fires, based on nuclear explosion data. (4.7)

where Y is the probit (Section 4.1), t is the duration of exposure (sec), and/is the thermal radiation intensity (W/m2). Lees (1986) summarizes the data from which this relationship was derived. The probit method has found less use for thermal injury than it has for toxic effects. Mathematical models of thermal injuries can be based on a model detailed description of the skin and its heat transfer properties. Experiments have shown that the threshold of pain occurs when the skin temperature at a depth of 0.1 mm TABLE 4.7. Recommended Design Flare Radiation Levels Excluding Solar Radiation (API, 1996a) Permissible design level (K)

a

Btu/hr/ft2

kW/m2

5000

15.77

3000

9.46

Value of K at design flare release at any location to which people have access, for example, at grade below the flare or on a service platform of a nearby tower. Exposure must be limited to a few seconds, sufficient for escape only

2000

6.31

Heat intensity in areas where emergency actions lasting up to 1 min may be required by personnel without shielding but with appropriate clothing

1500

4.73

Heat intensity in areas where emergency actions lasting several minutes may be required by personnel without shielding but with appropriate clothing

500

1.58

Value of K at design flare release at any location where personnel are continuously exposed

Conditions* Heat intensity on structures and in areas where operators are not likely to be performing duties and where shelter from radiant heat is available, for example, behind equipment

On towers or other elevated structures where rapid escape is not possible, ladders must be provided on the side away from the flare, so the structure can provide some shielding when K is greater than 200 Btu/hr/ft2 (6.31 kW/m2).

TABLE 4.8. Effects of Thermal Radiation (World Bank, 1985) Radiation intensity (kW/m2)

Observed effect

37.5

Sufficient to cause damage to process equipment

25

Minimum energy required to ignite wood at indefinitely long exposures (nonpiloted) Minimum energy required for piloted ignition of wood, melting of plastic tubing

12.5 9.5

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

4

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

1.6

Will cause no discomfort for long exposure

Near 100% fatalities Mean 50% fatalities

TIME, s

1% Fatalities

Significant injury threshold Data of Mixter (1954)

INCIDENT THERMAL FLUX, kW/M2 FIGURE 4.11. Serious injury/fatality levels for thermal radiation (Mudan, 1984).

is raised to 45°C. When the skin surface temperature reaches about 55°C blistering occurs. Mehta et al. (1973) describe a thermal energy model to predict damage levels above 55°C. Lees (1994) provides a detailed analysis of fatal injuries from burns, including a review of probit equations. He also considers the effects of clothing and buildings on the resulting injuries.

Schubach (1995) provides a review of thermal radiation targets for risk analysis. He concludes that (1) the method of assuming a fixed intensity of 12.6 kW/m2 to represent fatality is inappropriate due to an inconsistency with probit functions and (2) a thermal radiation intensity of 4.7 kW/m2 is a more generally accepted value to represent injury. This value is considered high enough to trigger the possibility of injury for people who are unable to be evacuated or seek shelter. That level of heat radiation would cause injury after 30 s of exposure. Schubach (1995) also suggests that the fatality probit data of Eisenberg et al. (1975) applies to lightly clothed individuals, and that the type of clothing would have a significant effect on the results. The effect of thermal radiation on structures depends on whether they are combustible or not and the nature and duration of the exposure. Thus, wooden materials will fail due to combustion, whereas steel will fail due to thermal lowering of the yield stress. Many steel structures under normal load will fail rapidly when raised to a temperature of 500-6000C, whereas concrete will survive for much longer. Flame impingement on a structure is more severe than thermal radiation. Theoretical Foundation Thermal effects models are solidly based on experimental work on humans, animals, and structures. A detailed body of theory has been developed in the area of fire engineering of structures. Input Requirements and Availability The inputs to most thermal effect models are the thermal flux level and duration of exposure. Thermal flux levels are provided by one of the fire consequence models (Section 3.4 or 3.6), and durations by either the consequence model (e.g., for BLEVEs) or by an estimate of the time to extinguish the fire. More detailed models use thermal energy input after a particular skin temperature is reached. Data for these models are more difficult to provide. Output The primary output is the estimated level of injury from a specified exposure. Simplified Approaches The use of a fixed thermal exposure criteria, resulting in a fixed injury or fatality level, without accounting for duration of exposure is a simplified approach. This allows the consequence models to be used to predict a standard thermal exposure level, without reference to the specific details of each incident in terms of duration. The fixed criteria may be based on an implicit exposure time. The LNG Federal Safety Standards (Department of Transportation, 1980) use a fixed criteria of 5 kW/m2 for defining limiting thermal flux levels for people.

4.3.3. EXAMPLEPROBLEMS

Example 35: Thermal Flux Estimate Based on 50% Fatalities Determine the thermal flux necessary to cause 50% fatalities for 10 and 100 s of exposure. Solution: From Figure 4.11, the flux levels corresponding to 50% fatalities for 10 and 100 s are 90 and 14 kW/m2, respectively. Using the Eisenberg probit method, Eq. (4.7) is rearranged to solve for the thermal radiation intensity I:

For 50% fatality, the probit variable, Y = 5.0 (Table 4.1) For t = 10 s, 7 = 6 1 kW/m2 For t = 100 s, I= 11 kW/m2 These results differ from those of Figure 4.11 by about 30%. It is unlikely that much greater accuracy can be achieved. This example demonstrates the importance of the duration of exposure, especially for short duration incidents such as BLEVEs (on the order of 10-20 s). A fixed criterion, suitable for prolonged exposures, may be inappropriate for such incidents. The spreadsheet output for this problem is provided in Figure 4.12. The data of Figure 4.11 have been digitized and are included in the spreadsheet. The Example 35: Thermal Flux Estimate Input Data: Exposure time: Percent Fatalities: Calculated Results: Thermal Flux Estimate for: Significant injury threshold: Percent Fatalities:

Interpolated Flux for Specified Percent: Thermal Flux Estimate Based on Eisenberg Fatality Probit: Probit: Thermal Flux: FIGURE 4.12. Spreadsheet output for Example 35: Thermal flux estimate based on 50% fatalities.

spreadsheet will determine the thermal flux based on any specified exposure time and percent fatalities. Example 36: Fatalities Due to Thermal Flux from a BLEVE Fireball Estimate the fatalities due to the thermal flux from a BLEVE based on the release of 39,000 kg of flammable material. Assume that 400 workers are distributed uniformly from a distance of 75 m to 1000 m from the ground location of the fireball center. Solution: The incident radiant flux from a BLEVE fireball is estimated using Eq. (3.44) and the fireball duration is estimated from Eq. (3.34). The fireball center height, ^LEVE* *s given by Eq. (3.35). The solution will assume that the fireball stays fixed at the fireball center height during the entire exposure duration. The receptor distance from the fireball center height to the receptor is given from geometry as Receptor Distance where L is the distance on the ground from the fireball center. The probit equation for fireball fatalities is given by Eq. (4.7). The procedure is to divide the distance from 75 to 1000 m into a number of small shells of equal thickness. Assume that the shell thickness is small enough that the incident thermal flux at the center of each cell is approximately constant throughout the cell thickness. The procedure at each shell is as follows: 1. Compute the distance from ground zero to the center of the current shell. 2. Compute the receptor distance from the fireball center to the current shell. 3. Compute the incident heat flux at the shell center using Eq. (3.44). 4. Compute the probit for fatality using Eq. (4.7). 5. Convert the probit to a percentage using Eq. (4.2). 6. Calculate the total shell area. 7. Determine the total number of workers in the shell. 8. Multiply the total number of workers by the percent fatalities to determine the total fatalities. 9. Sum up the fatalities in all shells to determine the total. The output of the spreadsheet solution is shown in Figure 4.13. A total of 16.2 fatalities is predicted. A shell size thickness of 5-m was selected, with a total of 185 shells. The results are essentially independent of this value. The fatalities drop to zero at about 270 m from the BLEVE.

Example 36: Fatalities due to Thermal FluxfromBLEVE Fireball Input Data: Total people: Inner radius: Outer radius: Total flammable: Distance increment: Calculated Results: Total Fatalities: Total Area: People/m**2: Total increments: Time duration: Max. fireball diam.: Height of fireball: Ground Receptor Heat Distance Distance FluxA m m kW/m 2

Probit

Percent

Area m**2

People People Cumulative in area Fatalities People

FIGURE 4.13. Spreadsheet output for Example 36: Fatalities due to thermal flux from a BLEVE fireball.

tering is discussed in Chapter 5). Also, in hot sunny climates, it may be necessary to add solar radiation intensity to that estimated by consequence models to determine total radiation exposure from an incident. In general, error in thermal effects is likely to be less than errors in estimating explosion and toxic effects. Utility Thermal effect models are easy to apply for human injury. The issue of duration of exposure may be difficult to resolve where shelter is available, but limited. Thermal effects on steel structures are more difficult to calculate, as an estimate of temperature profiles due to the net radiation balance (in and out of the structure) and conduction through the structure may be necessary. Resources Needed A process engineer using a hand calculator can predict thermal effects with little special training. Effects on structures require sophisticated thermal modeling. Available Computer Codes DAMAGE (TNO, Apeldorn, The Netherlands) PHAST (DNV, Houston, TX) TRACE (Safer Systems, Westlake Village, CA)

4 . 4 . E x p l o s i o n Effects 4.4.1. BACKGROUND

Purpose Explosion effect models predict the impact of blast overpressure and projectiles on people and objects. Philosophy Most effect models for explosions are based on either the blast overpressure alone, or a combination of blast overpressure, duration, and/or specific impulse. The blast overpressure, impulse and duration are determined using a variety of models, including TNT equivalency, multi-energy and Baker-Strehlow methods. See Section 3.1 for details on these models. Applications Virtually all CPQRAs of systems containing large inventories of flammable or reactive materials will need to consider explosion effects. Some analyses may also need to consider condensed phase explosions or detonations of unstable materi-

als. Examples include the Canvey Study (Health & Safety Executive, 1978, 1981) and Rijnmond Public Authority (1982) risk assessments. However, in the case of very large explosions, or for explosions or sites near off-site structures, significant offsite damage could result. Many accident investigations have employed explosion effect models (e.g., Sadee et al., 1977). Since the blast overpressure decreases rapidly as the distance from the source increases, significant offsite damage from blasts is not expected. Most studies are directed toward on-site damage. 4.4.2. DESCRIPTION

Description of the Technique Explosion effects have been studied for many years, primarily with respect to the layout and siting of military munitions stockpiles. Baker et al. (1983) and Lees (1986,1996) provide extensive reviews of explosion effects and the effects of projectiles. Explosion effects are classified according to effects on structures and people. Structures. Overpressure duration is important for determining effects on structures. The positive pressure phase of the blast wave can last from 10 to 250 ms, or more, for typical VCEs. The same overpressure level can have markedly different effects depending on the duration. Therefore, some caution should be exercised in application of simple overpressure criteria for buildings or structures. This criteria can in many cases cause overestimation of structural damage. If the blast duration is shorter than the characteristic structural response times it is possible the structure can survive higher overpressures. Baker et al. (1983) discuss design issues relating to the response of structures to explosion overpressures. AIChE/CCPS (1996b) provides an extensive review of risk criteria and risk reduction methods for structures exposed to explosions, and a discussion of blast resistant building design. Eisenberg et al. (1975) provide a simple probit model to describe the effects on structures. (4.8)

where Y is the probit and P 0 is the peak overpressure (Pa) The probit, Y, can be converted to a percentage using Eq. (4.1). The percentage here represents the percent of structures damaged. More detailed effect models for structures are based on both the peak overpressure and the impulse (Lees, 1996; AIChE/CCPS, 1996b). Tables 3.2a and 3.2b provide an estimate of damage expected as a function of the overpressure.

The interpretation of these data is clear with respect to structural damage, but subject to debate with respect to human casualties. The Rijnmond (1982) study equates heavy building damage to a fatal effect, as those inside buildings would probably be crushed. People. People outside of buildings or structures are susceptible to 1. direct blast injury (blast overpressure) 2. indirect blast injury (missiles or whole body translation) Relatively high blast overpressures (> 15 psig) are necessary to produce fatality (primarily due to lung hemorrhage). Eisenberg et al. (1975) provides a probit for fatalities as a result of lung hemorrhage due to the direct effect of overpressure, (4.9)

where Y is the probit and P0 is the peak overpressure (Pa). It is generally believed that fatalities arising from whole-body translation are due to head injury from decelerative impact. Baker et al. (1983) present tentative criteria for probability of fatality as a function of impact velocity. They also provide correlations for determining impact velocity as a function of the incident overpressure and the ratio of the specific impulse over the mass of the human body to the % power. Lees (1996) provides probit equations for whole body translation and impact. Injury to people due to fragments usually occurs either because of penetration by small fragments or blunt trauma by large fragments. Baker et al. (1983) review skin penetration and suggest that it is a function of A/M where A is the cross-sectional area of the projectile along its trajectory and M is the mass of the projectile. Injury from blunt projectiles is a function of the fragment mass and velocity. Very limited information is available for this effect. TNO (1979) suggest that projectiles with a kinetic energy of 100 J can cause fatalities. Theoretical Foundation The probit models are simply a convenient method to fit the limited data. Most effect models, particularly for human effects, are based on limited, and sometimes indirect data. The basis for explosion effect estimation is experimental data from TNT explosions. These data are for detonations and there may be differences with respect to longer duration deflagration overpressures.

Input Requirements and Availability The primary input is the blast overpressure (defined as the peak side-on overpressure), although for structural damage analysis, an estimate of the duration is also necessary. Projectile damage analysis requires an estimate of the number, velocity, and spatial distributions of projectiles, and is more difficult than overpressure analysis. Output The output is the effect on people or structures of blast overpressure or projectiles. Simplified Approaches For explosion effects, some risk analysts assume that structures exposed to a 3 psi peak side-on overpressure, or higher, will suffer major damage, and assume 50% fatalities within this range (corresponding to a probit value of 5). 4.4.3. EXAMPLEPROBLEM

Example 37: 3-psi Range for a TNT Blast 100 kg of TNT is detonated. Determine the distance to the 3-psi limit for structures and 50% fatalities. Solution: The solution is by trial and error. The procedure to determine the blast overpressure is described in Section 3.1 (see Example 19). The procedure is as follows: 1. Guess a distance. 2. Calculate the scaled distance using Eq. (3.7). 3. Use Figure 3.3 or the equations in Table 3.1 to determine the overpressure. 4. Check if the overpressure is close to 3 psi. The procedure is repeated until an overpressure of 3 psi is obtained. The result is 36.7 m. A spreadsheet implementation of this problem is provided in Figure 4.14. 4.4.4. DISCUSSION

Strengths and Weaknesses The strength of explosion and projectile effect models is their base of experimental data and general simplicity of approach. A weakness relates to the difference

Example .37: 3 psi Range for a TNT Blast Input Data: Mass of TNT: Calculated Results: Trial and Error Solution for 3 psi range: Guessed distance:

Trial and Error to get pressure!

Scaled distance, z: Overpressure Calculation: a+b*log(z): Overpressure:

(only valid for z > 0.0674 and z < 40) Must be 3 psi.

FIGURE 4.14. Spreadsheet output for Example 37: 3 psi range for a TNT blast.

between indoor and outdoor effects. People may be killed indoors due to building collapse at lower overpressure than outdoors due to overpressure alone. A rigorous treatment of projectile effects is difficult to undertake. Explosions in built-up areas are rarely uniform in effects. VCEs are often directional and this effect is not accounted for in current effect models. Identification and Treatment of Possible Errors The relationship between overpressure and damage level is well established for TNT5 but this relationship may be in error when applied to VCEs. Utility Explosion effect models are easy to use. Projectile effect models are more difficult to apply. Resources Needed Given quantitative results from explosion overpressure models and projectile analysis, effects can be determined by reference to published data on damage or injury level. No special computational resources are required. Available Computer Codes SAFESITE (W. E. Baker Engineering, San Antonio, TX) HEXDAM, VASDIP, VEXDAM (Engineering Analysis, Inc., Huntsville, AL) Several integrated computer codes also include explosion effects. These include,

DAMAGE (TNO, Apeldoorn, The Netherlands) QRAWorks (Primatech, Inc., Columbus, OH)

5

E v a s i v e

5.1.

A c t i o n s

Background

Purpose In the event of a major incident, the consequences to people will probably be less serious than predicted by the release and incident outcome models described in Chapters 2 and 3 and the effect models in Chapter 4. This is not only because of uncertainties in modeling incident outcomes or modeling limitations that may lead to conservative assumptions and results but also because of topographical and physical obstruction factors, and because of evasive actions taken by people. Evasive actions can include evacuation, escape, sheltering, and heroic medical treatment. This chapter addresses the impact of evasive actions as mitigating factors to a CPQRA study. Escape from a vapor cloud release is primarily associated with toxic releases. Flammable clouds exist within shorter distances from the source and if ignited present thermal and blast effects beyond the initial cloud dimensions. There is usually very little reaction time in flammable releases that ignite. This chapter applies to toxic releases only. In the event of an incident, some (all) people in the effects zone may be indoors (i.e., shelter) or may seek shelter. These people may or may not be in a "safe" shelter depending on whether the shelter provides total or partial isolation from the incident outcome. Others (including some of the people in "safe" shelters) may move outside of the affected area (i.e., escape or evacuate) if there is sufficient warning. By these evasive actions, the number of potential casualties may be reduced. Thus, consideration of evasive actions—shelter, escape, and/or evacuation—may achieve a more realistic estimate of consequences. Following an incident, the effects on people able to escape to or remain in a shelter differ from those for people in the open. Davies and Purdy (1986) dis-

cussed this in relation to building types and human behavior. For CPQRA, each incident outcome must be considered separately because consequences depend on • The nature of the hazard considering both intensity and duration. Shelters vary in the degree of protection provided-for thermal and toxic hazards, shelters can have a beneficial effect, but for explosions, the hazard may be greater indoors because of the possibility of the building collapsing. Table 5.1 summarizes the important factors for each type of hazard. • The nature of the hazard considering its degree of toxicity and its warning properties. A release of carbon monoxide provides no warning while a release of tri-methyl amine normally provides a strong odor at concentrations well below harmful levels. Other gases such as phosgene produce harmful effects at extremely low concentrations, below the odor threshold. • The nature of the surrounding population. The distribution of the population indoors varies depending on the time of day and season, the overall health of the population (senior citizens, infirm, etc.), and the type of clothing being worn by personnel exposed to possible heat radiation—cotton, wool, polyester, etc. • The types of buildings and their construction—ventilation rates, resistance to blast effects, the ability of overhead fixtures to remain intact, etc. • The effectiveness of training and the availability of equipment for emergency response and medical treatment-both within the plant and among emergency response services. Trained personnel, obviously can improve the chance of survival for those exposed. • The prevailing weather conditions, topography, and physical obstructions. • The intensity and duration to which a toxic gas incapacitates exposed personnel. Technology In the nuclear industry radiation exposure and resultant evacuation actions have been investigated in comprehensive detail. The EPA (Hans and Sell, 1974) made a study of evacuation to determine the risks of rapidly moving large segments of population. Prugh (1985) provides correlations of evacuation effectiveness as a function of the area to be evacuated, the population density, and the warning time. The probability of escape or escape to a shelter for a sudden release of a large toxic cloud such as from the bursting of a vessel is very low because it is impossible to determine an escape direction. A structure will provide a shelter for toxic releases. The maximum concentration that develops is a function of the air infiltration rate, which is a function of

TABLE 5.1. Benefits of Evasive Actions3

Hazard effect Thermal radiation

In shelter

Escape

Escape to shelter (after occurrence)

Evacuation* (after occurrence)

Very beneficial

Very beneficial

Very beneficial

Very beneficial

Very beneficial

Very beneficial

Very beneficial

Very beneficial

Very beneficial if shelter is far enough away from blast effects

Limited benefit (escape time limited)

Limited benefit (escape time too limited) fireball may exceed escape speed

N o benefit (no evacuation time)

Very beneficial if shelter is far enough away from blast effects

Beneficial

Beneficial

Limited benefit (limited evacuation time, e.g., 10-30 min)

Limited benefit (due to vapor ingress)

Limited benefit (flame may exceed escape speed)

Limited benefit (flame may exceed escape speed)

No benefit (no evacuation time)

Overpressure

Increased risk of collapse of structure at lower overpressure (rather than direct fatality)

Very limited benefit(no escape time)

Very limited benefit (no escape time)

N o benefit (no evacuation time)

Missiles

Limited benefit (protection from primary missiles but secondary missiles may be generated)

N o benefit (no escape time)

N o benefit (no escape time)

N o benefit (no evacuation time)

Very beneficial (if forced ventilation is not used)

Beneficial if escape is rapid (depends on size of cloud and wind speed)

Beneficial if escape is rapid (depends on size of cloud and wind speed)

Benefits uncertain during a release

Pool fire Fet fire BLEVE At instant BLEVE takes place

Pre-BLEVE

Flash fire

Explosion

Toxic exposure

a

b c

The type of clothing (wool, polyester, cotton, etc.) being worn by exposed personnel influences the impact of heat radiation on the individual Escape prior to an incident is equivalent to being in shelter. Evacuation is beneficial prior to an incident where warning is given and escape time is available (but impact of rapid evacuation must be considered against possible benefits

the tightness of the structure (normal air changes) and the wind speed. Correlations for this effect are provided by Prugh (1985). Escape to a structure will result in lower maximum concentrations but the integrated dose in terms of concentration time will be the same. Most toxic materials have hazardous effects that are related to some power of the concentration greater than one and therefore, safe shelters can be especially effective. In addition, exposure to lower concentrations should result in less chance of disability or disorientation so that additional evasive actions can be considered. Nuclear studies consider evasive actions such as shelter and evacuation. Appendix E of the PRA Procedures Guide (NUREG, 1983) provides a useful overview of nuclear evacuation models. Section 4.3 discusses the maximum allowable levels of thermal exposure from flares, which would indicate when a shelter or a shield to block heat radiation is necessary.

5.2. Description Description of Technique There are many possible aspects of evasive actions that can be considered. In studies where evasive action is considered the type of evasive action will many times be dictated by the established emergency response plans. This may include evacuation or sheltering in place depending on the quantity and hazardous properties of the material which could be released. Figure 5.1 (Prugh, 1985) addresses evacuation effectiveness. The percentage of people not evacuated during the specified warning time is plotted as a function of warning time, area to be evacuated, and population density, based on data developed by EPA (Hans and Sell, 1974). This chart could be used to establish effectiveness of evacuation for various large scale release scenarios where sheltering in place is less desirable. An approach to establish a baseline for the fraction of population who are in some form of shelter could be the following: Of the total population let x = fraction of total population already in a shelter y = fraction of total population outside initially who eventually reach shelter \y < (1-x)] The fraction of people in a shelter is P = x + y and not in a shelter is P = 1 - (x + y). In this simple model there is no consideration of people already in a shelter who attempt to escape. This model could easily produce widely varying results depending on whether daytime or nighttime populations are considered.

EVACUATION FAILURE (%) WARNING (h) FIGURE 5.1. Prediction of evacuation failures (Prugh, 1985).

Additional calculations would normally be required first to show that for given specific air infiltration rates people are "safe" in their shelter. If harmful levels are possible then it is necessary to calculate the fraction of population in shelters that would likely be exposed. Theoretical Foundation The analysis of evasive actions is empirical, and is based primarily on historical information from past incidents. These rates may be pessimistic because increased attention is now being given to emergency response plans for CPI facilities. These response plans should improve the scope and response to evasive actions [e.g., CMA3S CAER (Community Awareness and Emergency Responses) program]. Input Requirements and Availability The most important inputs are those concerning the emergency response systems in place, community types and population densities. General information on population and types of communities may be obtained from census data, and county and state records offices. Detailed information may only be available by

on-site observations and surveys. Even then, the analyst will have to make a number of simplifying assumptions. Technical input will also be required on the effectiveness of sheltering for each hazard type as summarized in Table 5.1. Output The outputs are probability factors used to modify the predicted number of casualties following an incident to reflect the appropriate evasive actions. Simplified Approaches The above techniques are a simple approach to assessing possible evacuation actions. Further simplification can be attained by reducing the level of detail of the site-data gathered; this requires making broader assumptions and relying on general rather than site-specific data.

5.3. Example Problem

Example 38: Estimation of Evacuation Failure Assume that the nearest population center to an industrial plant is 1 mile downwind. Assume also that the population density is 2000 people per square mile and that the worst case accidental release scenario occurs under a wind speed of 1 mph and that an area of 5 square miles must be evacuated. What fraction of the population would not be successfully evacuated!1 Solution. Figure 5.1 is used to determine the failure rate. The required parameters are A = 5 square miles Warning time = 1 hr (1 mile divided by 1 mile per hour wind speed). D = 2000 people/square mile ^0.33^0.40 = (i.7i)(20.9) = 35.6 From Figure 5.1, for a warning time of 1 hr, evacuation failure is estimated to be 58%. A spreadsheet implementation of this problem is shown in Figure 5.2.

5 . 4 . Discussion

Strengths and Weaknesses The omission of evasive actions in a CPQRA will lead to an overestimation of the numbers of casualties. Obviously, as shown in the sample problem, there are

Example 38: Estimation of Evacuation Failure Input Data: Total Area: Population density: Warning time:

5 Square miles 2000 People/square mile 1 Hour

Calculated Results: A**0.33 * D**0.4

3537

Data table for interpolation: Evacuation Failure %

!Percentage of people not evacuated in warning time: FIGURE 5.2. Spreadsheet output for Example 38: Estimation of evacuation failure.

uncertainties in estimating the factors that account for evasive actions. The main disadvantages are the element of judgment required and the quality of the input data. For these reasons, many analysts do not consider evasive actions in their studies. Identification and Treatment of Errors The technique is empirically based, and there are very limited data. The reader is reminded that with empirical methods, the worst scenario may not yet have occurred and, thus, may not be properly modeled. However, omission of evasive actions usually results in an overestimation of the number of casualties in a CPQRA. Utility and Resources The resources needed are dependent on the level of detail necessary for estimation of evasive actions. Often, a scientist or engineer with some experience in human factors is needed. For an in-depth analysis, several days may be required for site visits to obtain local population data, to conduct interviews with local emergency planning personnel, and to complete questionnaires to determine the level of public preparedness. At the simplest level, once base population data are gathered, the factors required may be quickly estimated by expert judgment and discussion.

Available Computer Codes Nuclear safety codes (e.g., CRAC2) usually include evacuation and sheltering factor considerations. The EVAS computer code (Hesel and Schnadt, 1982) simulates evacuation movements for large areas, and also gives an estimate of evacuee exposure to chemicals or to radiation. This code is used to advise authorities in Germany about emergency planning optimization. The UK Health & Safety Executive has developed a risk assessment computer model for toxic incidents, BJSKBAT. This includes the consideration of evasive actions (while not presently available publicly, it is described by Pape and Nussey, 1985). VASDIP, HEXDAM and VEXDAM (Engineering Analysis, Inc., Huntsville, AL) can be used to estimate the effects of sheltering due to vapor cloud explosions. Tatom andTatom (1996) provide detail on the use of this software for determining the explosive effects on the human body.

6

M o d e l i n g

S y s t e m s

Complete systems of source, dispersion, consequence, and effect analysis models are now available for relatively convenient use. The reader is directed to the Chemical Engineering Progress Annual Software Review for more information. These models are fully integrated, supporting a thermodynamic database, seamless transfer of data from one model to another, and a full graphical output capability. A short list of the more popular models is provided below: PHAST (DNV, Houston, TX) QRAWorks (Primatech, Columbus, OH) SAFETI (DNV, Houston, TX) SUPERCHEMS (Arthur D. Little, Cambridge, MA) TRACE (Safer Systems, Westlake Village, CA)

Appendix: CD-ROM

This is Version 1.04 of the CD-ROM disk for the book Guidelinesfor Consequence Analysis of Chemical Releases

June 1, 1999 Copyright © 1999, American Institute of Chemical Engineers The software spreadsheets contained in this disk are implementations of the examples worked in this book. These spreadsheets must be used in conjunction with this text and are not designed as a stand alone product. This disk contains several subdirectories: • Bibliography: This directory contains ProCite compatible files containing all of the reference citations listed in the bibliography. • Sprdshts: This directory contains the spreadsheets for the example problems. The Sprdshts directory contains two subdirectories: -Excel: The examples implemented via Microsoft Excel. -Q-Pro: The examples implemented via Quattro-Pro. The Excel or Q-Pro subdirectories also contain a file titled "Index," with an extension of either cc.xls" for Excel or cc.wb3" for Quattro-Pro. These files contain a spreadsheet index of the example problems. This includes the example problem number and the problem title. Also included is a table of input parameters, calculated results, and the units for both input and output. To select a problem, first go to either the Excel or Q-Pro subdirectories, depending on your spreadsheet. Select the applicable problem. For instance, if you wish to select the spreadsheet for Example 14, select file "EX-14." The file extension will be cc.xls" for Excel and cc.wb3" for Quattro-Pro.

The entire Excel or Q-Pro subdirectories can be copied to a hard drive directory using the Windows Explorer. Or, individual spreadsheets can also be copied to a hard drive. The spreadsheet implementation was done as directly and as simply as possible. Thus, solver and other complex capabilities were not utilized. Most of the functions used are simple—mostly log and exp. A number of the spreadsheets use linear interpolation functions (see note below). Some of the spreadsheets use curve-fitting capability—available least squares or other functions are used to achieve this. For iterative solutions, the user must perform a trial-and-error type procedure by manually inputting guessed values. For the Excel spreadsheets, a number of the effect models use probit equations. The conversion from probit to percentage is accomplished, in some examples, using the EBJF function. This function is only avalable to Excel if the analysis tookpack is loaded. For many of the examples, a figure is used for obtaining necessary values. For these cases, the figure was scanned and digitized using a commercial package called UNSCAN-IT to extract the data from the scanned figure. The resulting values are included in a data table contained within the spreadsheet (but not shown in the spreadsheet figures with the text). The values required by the spreadsheet are interpolated from the data table. The spreadsheets were originally implemented in Quattro-Pro and are compatible with versions 6/7/8 of that software. The outputs shown in the text are from Quattro-Pro. Considerable effort was required to convert the spreadsheets to Microsoft Excel format. The major problem was in the implementation of the Quattro-Pro LINTERP function, which does not have an identical function in Excel. This function provides a linear interpolation from an X-T data table. An equivalent interpolation was implemented in the Excel spreadsheets, but this required additional cell coding. As a result, the Excel version of the spreadsheet will have some differences from the Quattro-Pro versions shown in the text. It is also suspected that the interpolation implemented in Excel is not as general as the function in Quattro-Pro. For the Microsoft Excel spreadsheets, a file format from an earlier version of Excel before Microsoft Office 97 was used, if possible. This was done to provide maximum import capability for Excel users since the more recent versions can read earlier versions. Unfortunately, some of the features used were not supported by the earlier Excel versions, necessitating moving forward to a more recent version. Thus, the actual file version might vary from example to example depending on features supported.

The spreadsheets are provided without support or guarantee. The only statement that can be made about the spreadsheets is that the manual solutions provided agree with the spreadsheet results. It is highly recommended that the user carefully evaluate any results generated by the spreadsheets for validity. Problems or suggestions related to the spreadsheets should be sent to: AICHE/CCPS, 3 Park Avenue, New York, New York 10016-5991. It is sincerely hoped that the spreadsheets presented here will lead to a better understanding of process safety concepts among engineers and an even more impressive safety record for the entire chemical industry. However, neither the American Institute of Chemical Engineers, its consultants, CCPS Subcommittee members, their employers, their employer's officers and directors, nor CCPS contractors, warrant or represent, expressly or implied, the correctness or accuracy of the content of the spreadsheets presented here. As between the American Institute of Chemical Engineers, its consultants, CCPS Subcommittee members, their employers, their employer's officers and directors, nor CCPS contractors, and the users of this document, the user accepts any legal liability or responsibility whatsoever for the consequence of its use or misuse.

VERSION NOTES: 1.0 Original Release, February 1998 1.01 June 10, 1998 Corrected friction factor error in Example 3, both Quattro Pro and Excel. 1.02 September 10, 1998 Corrected problems in Excel solutions: Example 16—Reformatted to Arial 10 for consistency. Example 19—Corrected Excel crash problem. Example 33—Corrected probit equation. Corrected problems in Quattro-Pro solutions: Example 24—Changed underline in heading to bold. 1.03 December 1,1998—Peer review copy Example 17: Corrected wayward cells, Excel and Quattro-Pro versions. Improved graph format, Excel version. 1.04 June 1,1999: Original book release version Example 22: Corrected conversion to kg. Example 23: Corrected temperature from 492 to 537 R, redid trial-and-error solution. Example 36: Corrected distance calculation to use hypotenuse.

G l o s s a r y

Absolute application (of CPQRA): The application of CPORA in which the results of the analysis are compared against predetermined risk targets. Adiabatic Lapse Rate (ALR): See Dry Adiabatic Lapse Rate. Aerosol: Liquid droplets small enough to be entrained in a vapor stream. Aerosolfraction:The fraction of liquid phase which, when flashed to the atmosphere, remains suspended as an aerosol. Analysis data base: A data base that contains all input data for a CPOBA, including the System Description, as well as environmental data (e.g., land use and topography, population and demography, meteorological data). Arrival time: The time required for a blast or pressure wave to arrive at a specified distance from a blast. Atmospheric dispersion: The low momentum mixing of a gas or vapor with air. The mixing is the result of turbulent energy exchange, which is a function of wind (mechanical eddy formation) and atmospheric temperature profile (thermal eddy formation). Atmospheric stability: A measure of the degree of atmospheric turbulence and resulting gas dispersion. The stability classes are defined in terms of the wind speed and thermal input from the sun. Aggregate risk: Societal risk for on-site workers in occupied buildings (API 752). Average aggregate risk: Average societal risk for on-site workers in occupied buildings (API 752). Average individual risk: There are three Average Individual Bisks introduced in this book: A. Average Individual Risk (exposedpopulation) is the individual risk averaged

over the population which is exposed to risk from the facility.

B. Average Individual Risk (total population) is the individual risk averaged over a predetermined population, without regard to whether or not all people in that population are actually exposed to the risk. C. Average Individual Risk (Exposed hours/worked hours). The individual risk for an activity may be calculated for the duration of the activity or may be averaged over the working day. Average Rate of Death (ROD): The average number of fatalities that might be expected per unit time from all possible incidents. Averaging time: The length of time in atmospheric dispersion testing over which concentration data are averaged to produce the concentration-time series. Availability: The fraction of time a system is fully operational, or, in thermodynamics, the maximum mechanical energy extractable from a system with respect to the environment. Auto-ignition temperature: The lowest temperature at which a fuel/oxidant mixture will spontaneously ignite. Baker-Strehlow Model: An explosion model based on the effect of confinement on the flame speed. Basic event: A fault tree event that is sufficiently basic that no further development is necessary (e.g., equipment item failure, human failure, or external event). See also Undeveloped Event. BLEVE: A "Boiling Liquid Expanding Vapor Explosion," which occurs from the sudden release of a large mass of pressurized liquid to the atmosphere. A primary cause is an external flame impinging on the shell of a vessel above the liquid level, weakening the shell and resulting in sudden rupture. Boolean algebra: A branch of mathematics describing the behavior of linear functions of variables which are binary in nature: on or off, open or closed, true or false. All coherent fault trees can be converted into an equivalent set of Boolean equations. Boundinggroup (ofincidents): A small number of incidents selected to bracket the spectrum of possible incidents, which may include those catastrophic incidents sometimes referred to as the Worst Credible Incident and Worst Possible Incident. Britter-McQuaid Model: A model for dense gas dispersion using dimensional analysis coupled with actual dense gas release data. Catastrophic incident: An incident with an outcome effect zone that extends off site into the surrounding community.

Cause consequence diagrams: A method for illustrating the possible outcomes arising from the logical combination of selected input events or states. Cell (in study cube): One of the 27 different categories of CPQRA, defined by a unique value for each axis of the study cube. Coherent: A coherent fault tree uses only "AND" and "OR" gates to represent the failure logic. Time delay gates, inhibit conditions, or CCNOR" gates are not permitted. Common Cause Failure (CCF): The failure of more than one component, item, or system due to the same cause. Component technique: One member of the roster of methods that collectively form the complete CPQRA procedure. Condensed phase explosion: An explosion that occurs when the material is present in the form of a liquid or solid. Conditional probability: Probability of occurrence given that a precursor event has occurred. Confidence interval: A range of values of a variable with a specific probability that the value of the variable lies within the range. Confidence limits: The upper and lower endpoints of a confidence interval. Confined explosions: An explosion of a fuel-oxidant mixture inside a closed system (e.g., vessel or building). Consequence analysis: The analysis of the expected effects of incident outcome cases independent of frequency or probability. Consequences: A measure of the expected effects of an incident outcome case. Conservative result, model, or design: A procedure where small or large values are assigned to unknowns duing consequence modeling. This ensures that the resulting engineering design to mitigate or remove the hazard is overdesigned. Continuous release: Emissions that are long in duration compared with the travel time (time for cloud to reach location of interest) or averaging or sampling time. CPQRA: The acronym for Chemical Process Quantitative Bisk Analysis. It is the process of hazard identification followed by numerical evaluation of incident consequences and frequencies, and their combination into an overall measure of risk when applied to the chemical process industry. It is particularly applied to episodic events. It differs from, but is related to, a Probabilistic Risk Assessment (PRA), a quantative tool used in the nuclear industry.

Deflagration: The chemical reaction of a substance in which the reaction front advances into the unreacted substance at less than sonic velocity. Where a blast wave is produced that has the potential to cause damage, the term explosive deflagration may be used.

Deflagration constant: An experimental value for explosion characterization which is indicative of the maximum rate of pressure increase during an explosion. Defined by Equation (3.50). Dense gas: A gas with density exceeding that of air at ambient temperature. Depth of study: A measure of the level of review, degree of complexity, and extent of detail involved in a CPQRA. Detonation: A release of energy caused by the extremely rapid chemical reaction of a substance in which the reaction front advances into the unreacted substance at greater than sonic velocity. Directional probability: Probability in a given wind direction. Directional incident outcome: An incident outcome whose consequences produce an effect zone determined by a given wind direction. Discharge rate model: Models used to estimate the mass release rate or total quantity released during the discharge of material from a process. Dispersion coefficient: The standard deviation sigma in a specified direction of the gaussian distribution model used in atmospheric dispersion. The dispersion coefficient is normally expressed as a function of distance for a given weather stability. Dispersion model: A mathematical model describing how material is transported and dispersed downwind of a release. Domino effects: The triggering of secondary events, such as toxic releases, by a primary event, such as an explosion, such that the result is an increase in consequences or area of an effect zone. Generally only considered when a significant escalation of the original incident results. Dry Adiabatic Lapse Rate (DALR): The negative of the temperature gradient established as dry air ascending in the atmosphere. For air with a molecular weight of 29 and a specific heat ratio of 1.41 the DALR = 0.995°C/100 m. Duration: The time required for the blast overpressure pulse to return to ambient pressure. Effect models: Models that predict effects of incident outcomes usually with respect to human injury or fatality or property damage. Effect zone: For an incident that produces an incident outcome to toxic release, the area over which the airborne concentration equals or exceeds some level of

concern. For a flammable release, the area over which a particular incident outcome case produces an effect based on a specified criterion. For a loss of containment incident producing thermal effects, the area over which a particular incident outcome case produces an effect based on a specified radiative heat stress limit. Emergency Response Planning Guideline (ERPG): Concentration limits (ERPGs 1, 2, and 3) established by the American Industrial Hygiene Association which are intended to provide estimates of concentration ranges where one might reasonably anticipate observing adverse effects as a consequence of exposure to the specific substance for up to one hour. Emissivity: The ratio of the radiant energy emitted by a surface to that emitted by a black body at the same temperature. Entrainment: The suspension of liquid as an aerosol in the atmospheric dispersion of a two-phase release or the aspiration of air into a jet discharge. Episodic release: A release of limited duration, usually associated with an accident. Equipment reliability: The probability that, when operating under stated environment conditions, process equipment will perform its intended function adequately for a specified exposure period. Event: An occurrence involving equipment performance or human action, or an occurrence external to the system that causes system upset. In this book, an event is associated with an incident either as the cause or a contributing cause of the incident or as a response to the initiating event. Event sequence: A specific unplanned sequence of events composed of initiating events and intermediate events that may lead to an incident. Event tree (analysis): A graphical logic model that identifies and quantifies possible outcomes following an initiating event. Expansion factor: A factor in compressible fluid flow which accounts for changes in fluid properties due to expansion of the fluid. Explosions: A release of energy that causes a pressure discontinuity or blast wave. External event: Event caused by (1) a natural hazard—earthquake, flood, tornado, extreme temperature, lightning, etc; or (2) man-induced events—aircraft crash, missile, nearby industrial activity, sabotage, etc. Failurefrequency:The number of failure events that occur divided by the total elapsed calendar time during which those events occur or by the total number of demands, as applicable. Failure mode: A symptom, condition, or fashion in which hardware fails. A mode might be identified as a loss of function; premature function (function with-

out demand); an out-of-tolerance condition; or a simple physical characteristic such as a leak (incipient failure mode) observed during inspection. Failure mode and effects analysis: A hazard identification technique in which all known failure modes of components or features of a system are considered in turn and undesired outcomes are noted. Failure probability: The probability—a value from 0 to 1—that a piece of equipment will fail on demand (not to be confused with fractional dead time) or will fail in a given time interval. Failure rate: The number of failure events that occur divided by the total elapsed operating time during which these events occur or by the total number of demands, as applicable. Failure severity: The degree of function degradation of equipment usually noted through deficient performance; categorized by the terms "catastrophic," "degraded," and "incipient." Fatal Accident Rate (FAR): The estimated number of fatalities per 108 exposure hours (roughly 1000 employee working lifetimes). Fault tolerant: A control system configuration that inherently provides auto selection of alternate or redundant signal paths to effect uninterrupted operations. Fault tree: A method for representing the logical combinations of various system states which lead to a particular outcome (Top Event). Fault tree analysis: Estimation of the hazardous incident (Top Event) frequency from a logic model of the failure mechanisms of a system. Fireball: The atmospheric burning of a fuel-air cloud in which the energy is mostly emitted in the form of radiant heat. The inner core of the fuel release consists of almost pure fuel whereas the outer layer in which ignition first occurs is a flammable fuel-air mixture. As buoyancy forces of the hot gases begin to dominate, the burning cloud rises and becomes more spherical in shape. Flammable limits: The minimum (lower flammable limit, LFL) and maximum (upper flammable limit, UFL) concentration of combustible vapor in air that will propagate a flame. Flammable mass: The mass of flammable vapor within a vapor cloud that will burn on ignition. Flashfire:The combustion of a flammable vapor and air mixture in which flame passes through that mixture at less than sonic velocity, such that negligible damaging overpressure is generated.

Flashpoint temperature: The temperature at which a liquid is capable of producing enough flammable vapor to flash momentarily. Fractional Dead Time (FDT): The mean fraction of time in which a component or system is unable to operate on demand. (Also known as Unavailability.) Frequency: Number of occurrences of an event per unit of time. F-N curve: A plot of cumulative frequency versus consequences (expressed as number of fatalities). Gaussian model: A dispersion model based on the concept that atmospheric diffusion is a random mixing process driven by turbulence in the atmosphere. The concentration at any point downwind of a release source is approximated by a Gaussian concentration profile in both the horizontal and vertical dimensions. Generic data: Data that are built using inputs from all of the plants within a company or from various plants within the CPI, from literature sources, past CPQRA reports, and commercial data bases. Gravity slumping: The decrease in elevation from the atmospheric dispersion of a dense gas due to the effects of gravity. Hazard rate: Also known as the Time-Related Equipment Failure Rate, is an Instantaneous Failure Rate function of time. Hazard: A chemical or physical condition that has the potential for causing damage to people, property, or the environment. Hazard and Operability Study (HAZOP): A technique to identify process hazards and potential operating problems using a series of guide words to study process deviations. Human error probability: The ratio between the number of human errors and the number of opportunities for human error. Human factors: A discipline concerned with designing machines, operations, and work environments so that they match human capacities and limitations. Human reliability: The study of human errors. Human reliability analysis (HRA): A method by which the probability of a person successfully performing a task is estimated. Impulse: The area under the overpressure-time curve for explosions. The area can be calculated for the positive phase or negative phase of the blast. Incident: The loss of containment of material or energy. Incident enumeration: The identification and tabulation of incidents without regard to significance or other biases.

Incident outcome: The physical manifestation of an incident. Incident outcome case: The quantitative definition of a single result of an incident outcome through specification of sufficient parameters to allow distinction of this case from all others for the same incident outcome. Individual Hazard Index (IHI): The Fatal Accident Rate (FAR) for a particular hazard, with the exposure time defined as the actual time that a person is exposed to a hazard of concern. Individual risk: The risk to a person in the vicinity of a hazard. This includes the nature of the injury to the individual, the likelihood of the injury occurring, and the time period over which the injury might occur. Initial list (of incidents): A list containing all the incidents identified by the enumeration methods chosen. Initiating event: The first event in an event sequence. Instantaneous release: Emissions that are short in duration compared with the travel time (time for cloud to reach location of interest) or sampling (or averaging) time. Intermediate event: An event that propagates or mitigates the initiating event during an event sequence. Isopleth: A line of constant vapor concentration downwind from a release. Jet discharge: The release of a vapor and/or liquid at sufficient pressure such that significant air entrainment results. Jet fire: Fire type resulting from fires from pressurized release of gas and/or liquid. Kawamura and MacKay model: A model used to represent pool evaporation. Level of concern: The concentration of an airborne chemical above which there may be adverse human health effects experienced as a result of a short-term exposure during an episodic release. Likelihood: A measure of the expected probability or frequency of occurrence of an event. Localized incident: An incident whose effect zone is limited to a plant area (e.g., pump fire, small toxic release), and does not extend into the off-site surrounding community. Major incident: An incident whose effect zone, while significant, is still limited to site boundaries (e.g., major fire, spill). Maximum individual risk: The individual risk to the person(s) exposed to the highest risk in an exposed population.

Maximum potential quantity: The maximum amount of a chemical that can be released from a process containment system. Such a system may be an isolated pressure vessel and associated piping or two or more interconnected and communicating vessels without isolation capability. This quantity is different from and often much greater than both the typical chemical inventory and design maximum inventory for a containment system. Median lethal concentration/dose: Concentration or dose levels, respectively, that kill 50% of exposed laboratory animals in controlled experiments. Mitigation factors: Systems or procedures, such as water sprays, foam systems, and sheltering and evacuation, which tend to reduce the magnitude of potential effects due to a release. Monim-Obukhov length: A value used in gas dispersion, defined by Equation (2.52). Mortality index: An index based on the observed average ratio of casualties to the mass of material or energy released, as derived from the historical record. It is used to characterize the potential hazard of toxic material storage. Negatively buoyant gas: A gas with density greater than that of air at ambient temperature. Neutral buoyant gas: A gas with density approximately equal to that of air at ambient temperature. Overpressure: The pressure above ambient pressure due to a blast wave. Pasquill^Gifford model: A modeling approach for gas dispersion that develops a set of dispersion coefficients to represent the eddy diffusivity in the dispersion equation. Peak side-on overpressure: The maximum pressure incident to an object exposed to a blast wave. Physical models: Models that provide quantitative information on source rate and extent of damage (thermal radiation, explosion overpressure, concentration of dispersing vapor clouds). Physical explosion: The catastrophic rupture of a pressurized gas-filled vessel. Plant-specific data: Failure rate-data generated from collecting information of equipment failure experience at a specific plant. Point source model: A thermal energy model based on representing the total heat release as a point source. Pool Fire: The combustion of material evaporating from a layer of liquid at the base of the fire.

Programmable Logic Controller (PLC): Intelligent electronic models to perform the tasks of sequential control and process logic solution. Positively buoyantgas: A gas with density less that of air at ambient temperature Probabilistic Risk Assessment (PRA): A commonly used term in the nuclear industry to describe the quantitative evaluation of risk using probability theory. Probability: The expression for the likelihood of occurrence of an event or an event sequence during an interval of time or the likelihood of the success or failure of an event on test or on demand. By definition, probability must be expressed as a number ranging from 0 to 1. Probit: A random variable with a mean of 5 and a variance of 1 which is used in various effect models. Propagating factors: Human, process, and environmental actions and influences that contribute to guiding, sustaining, continuing, transmitting, spreading, and extending the sequence of events following the initiating event. Protective system: Systems such as pressure vessel relief valves, that function to prevent or mitigate the occurrence of an incident. Puff model: A mathematical model used to represent the dispersion of gas from an instantaneous release. Puff release: See Instantaneous Release. Rain out: When a superheated liquid is released to the atmosphere, a fraction of it will flash into vapor. Another fraction may remain suspended as an aerosol. The remaining liquid, as well as portions of aerosol, may "rain out" on the ground. Raw plant data: Untreatedfield-equipment-specificfailure information often collected as part of plant operating and maintenance records, required as input for preparing plant-specific failure rate data. Reflected pressure: The pressure on a structure perpendicular to the shock wave. Relative Application (of CPQRA): A comparison and ranking of various risk estimates to prioritize risk reduction strategies based on their competitive effectiveness. Risk: A measure of human injury, environmental damage or economic loss in terms of both the incident likelihood and the magnitude of the loss or injury. Risk analysis: The development of a quantitative estimate of risk based on engineering evaluation and mathematical techniques for combining estimates of incident consequences and frequencies.

Risk assessment: The process by which the results of a risk analysis (i.e., risk estimates) are used to make decisions, either through relative ranking of risk reduction strategies or through comparison with risk targets. Risk contour: Lines that connect points of equal risk around the facility (cciso-risk" lines). Risk estimation: Combining the estimated consequences and likelihood of all incident outcomes from all selected incidents to provide a measure of risk. Risk management: The systematic application of management policies, procedures, and practices to the tasks of analyzing, assessing, and controlling risk in order to protect employees, the general public, and the environment as well as company assets while avoiding business interruptions. Risk measures: Ways of combining information on likelihood with the magnitude of loss or injury (e.g., risk indices, individual risk measures, and societal risk measures). Risk targets: Objective-based risk criteria established as goals or guidelines for performance. Sachs scaled distance: A dimensionless distance used in blast modeling, defined by Equation (3.8) Sampling time: The length of time in atmospheric dispersion testing over which concentration data are sampled. Sampling time is normally synonymous with averaging time. Sensitivity: The sensitivity of a measure to a parameter is defined as the change in the measure per unit change in that parameter. Sheltering: Physical protection (such as an enclosed building) against the outcome of an incident. Side-on pressure: The pressure that would be recorded on the side of a structure parallel to the blast. Societal risk: A measure of risk to a group of people. It is most often expressed in terms of the frequency distribution of multiple casualty events. Solid plume radiation model: A thermal radiation model that assumes that the entire visable volume of the flame emits thermal radiation, and the non-visable gases do not. Source model or term: A model used to determine the rate of discharge, the total quantity released (or total time) of a discharge of material from a process, and the physical state of the discharged material.

Time to failure: The time period measured from the moment when equipment installation is complete to the equipment's inability to perform its duty or intended function. Time-varying continuous release: A subset of continuous release (see Continuous Release) that the release rate varies significantly with time. Time-in-service: Time from that moment when equipment installation is complete, the time period for equipment commissioning, and the operating time thereafter. TNO multi-energy model: A blast model based on the theory that the energy of explosion is highly dependent on the level of congestion and less dependent on the fuel in the cloud. TNT equivalency model: An explosion model based on the explosion of a thermodynamically equivalent mass of TNT. Top event: The unwanted event or incident at the "top" of a fault tree that is traced downward to more basic failures using logic gates to determine its causes and likelihood. Toxic dose: The combination of concentration and time for inhalation of a toxic gas that produces a specific harmful effect. Transmissivity: The fraction of radiant energy that is transmitted from the radiating object through the atmosphere to a target. The transmissivity is reduced due to the absorption and scattering of energy by the atmosphere itself. Unavailability: The probability the fault event exists at a specified time. Uncertainty: A measure, often quantitative, of the degree of doubt or lack of certainty associated with an estimate of the true value of a parameter. Unconfined Vapor Cloud Explosion (UVCE): A term often found in the literature referring to a vapor cloud explosion. It is now generally accepted that some degree of confinement is necessary for a vapor cloud explosion. Undeveloped event: A base event that is not developed because of insufficient consequence or because information is unavailable. Vapor Cloud Explosion (VCE): When a flammable vapor is released, its mixture with air will form a flammable vapor cloud. If ignited, the flame speed may accelerate to high velocities and produce significant blast overpressure. Virtual source: The offset in distance to the specified source of a gas or vapor release that results in a maximum concentration of 100% at the source using a gaussian dispersion model. Weber number: A number representing the relative strength of inertial/shear forces and capillary forces in the drop. Used to model aerosol formation.

Wind rose: A plan view diagram that shows the percentage of time the wind is blowing in a particular direction. Worst credible incident: The most severe incident, considering only incident outcomes and their consequences, of all identified incidents and their outcomes, that is considered plausible or reasonably believable. Worst possible incident: The most severe incident, considering only incident outcomes and their consequences, of all identified incidents and their outcomes. Wu and Schroy model: A model used to represent pool spread.

Index

Index terms

Links

A Atmospheric stability, dispersion models

78

B Baker method, physical explosion models

178

Baker method (modified) example problems

154

vapor cloud explosion models

145

Baker-Strehlow method example problems

154

vapor cloud explosion models

145

Blast wave parameters, vapor cloud explosion models

152

BLEVE and fireball models

185

applications of

186

blast effects

186

computer codes for

201

equations for fireball

189

errors

199

example problems

194

201

fragments

196

200

thermal flux calculations

194

197

fragments

187

input requirements and availability

194

logic diagram

193

output

194

philosophy of

185

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319

320

Index terms

Links

BLEVE and fireball models (Continued) purpose of

185

radiation

189

resources for

201

simplified approaches

194

strengths and weaknesses of

199

techniques described

186

theoretical foundation

194

thermal effect models

268

utility of

201

Boiling pool vaporization, flash and evaporation models Britter and McGuaid model, dense gas dispersion model, example problems

70 122

C Chemical process quantitative risk analysis (CPQRA). See also Consequence analysis; Source models definitions

6

overview

1

purpose of

1

steps in

3

Compressed gas, physical explosion models

174

Computer codes BLEVE and fireball models

201

confined explosion models

209

dense gas dispersion model

125

discharge rate models

56

evasive action techniques

282

explosion effect models

274

flash and evaporation models

76

jet fire models

233

neutral and positively buoyant plume and puff models

110

physical explosion models

185

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321

Index terms

Links

Computer codes (Continued) pool fire models

225

resources for

283

thermal effect models

270

toxic gas effect models

262

Confined explosion models

201

applications of

202

computer codes for

209

errors

209

example problems

207

input requirements and availability

206

logic diagram

205

outputs

207

philosophy of

202

purpose of

201

resources for

209

simplified approaches

207

strengths and weaknesses of

208

technique description

202

deflagrations

203

detonation

204

dust explosions

204

theoretical foundation

205

utility of

209

Consequence analysis. See also Chemical process quantitative risk analysis (CPQRA); Source models chemical process quantitative risk analysis (CPQRA)

1

overview

8

Conservative result, consequence analysis for

12

D Deflagration confined explosion models

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203

301

206

322

Index terms

Links

Deflagration (Continued) defined

127

Dense gas dispersion model

111

applications of

112

computer codes for

125

errors

125

example problems

122

input requirements and availability

121

logic diagram

116

output

121

philosophy of

111

purpose of

111

resources for

125

simplified approaches

121

strengths and weaknesses of

124

technique description

114

theoretical foundation

119

utility of

125

Detonation confined explosion models

204

defined

127

Discharge rate models

15

applications of

18

background

15

computer codes for

56

equations

22

errors

55

example problems

40

gas discharge due to fire

54

gas discharge through hole

47

gas discharge through piping system

49

liquid discharge through hole

40

liquid discharge through piping system

45

This page has been reformatted by Knovel to provide easier navigation.

120

323

Index terms

Links

Discharge rate models (Continued) liquid trajectory from hole

42

two-phase flashing flow through pipe

53

fire exposure

39

gas discharges

29

two-phase discharge

35

liquid discharges

26

resources for

56

strengths and weaknesses of

54

technique description

18

hole size

21

leak duration

22

release phase

18

special issues

22

thermodynamic path and endpoint

20

utility of Dispersion models atmospheric stability dense gas dispersion model

56 76 78 111

See also Dense gas dispersion model neutral and positively buoyant plume and puff models

85

See also Neutral and positively buoyant plume and puff models overview

76

wind speed

80

height effects

83

momentum and buoyancy

84

release geometry

83

terrain effects on

82

Dose-response functions effect models

236

243

sample problem

240

242

Drainage, pool fire models

210

Dust explosions, confined explosion models

204

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324

Index terms

Links

E Effect models dose-response functions

235 236

240

243 explosion effect models

270

See also Explosion effect models methods

235

probit functions

238

thermal effect models

262

242

See also Thermal effect models toxic gas effect models

241

See also Toxic gas effect models Emergency Exposure Guidance Levels (EEGLs), toxic gas effect models

245

248

244

246

Emergency Response Planning Guidelines (ERPGs), toxic gas effect models Endpoint, thermodynamic path and, discharge rate models

20

Environmental concerns. See Effect models Equations, discharge rate models

22

Errors BLEVE and fireball models

199

confined explosion models

209

dense gas dispersion model

125

discharge rate models

55

evasive action techniques

281

explosion effect models

274

jet fire models

232

neutral and positively buoyant plume and puff models

109

physical explosion models

185

pool fire models

225

thermal effect models

269

toxic gas effect models

261

vapor cloud explosion models

151

This page has been reformatted by Knovel to provide easier navigation.

201

325

Index terms Evacuation failure, evasive action techniques

Links 280

281

See also Evasive action techniques Evaporating pool direct evaporation model, flash and evaporation models

72

flash and evaporation models

71

Evaporation, flash and evaporation models

62

Evaporation models. See Flash and evaporation models Evasive action techniques

275

benefits of

277

computer codes for

282

errors

281

example problem

280

input requirements and availability

279

output

280

purpose of

275

simplified approaches

280

strengths and weaknesses of

280

technique description

278

technology

276

theoretical foundation

279

utility and resources

281

Explosion, defined

128

Explosion effect models

270

applications of

270

computer codes for

274

errors

274

example problem

273

input requirements and availability

273

output

273

philosophy of

270

purpose of

270

resources for

274

simplified approaches

273

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281

278

274

326

Index terms

Links

Explosion effect models (Continued) strengths and weaknesses of

273

technique description

271

theoretical foundation

272

utility of

274

Explosions and fires BLEVE and fireball models

127 185

See also BLEVE and fireball models confined explosion models

201

See also Confined explosion models definitions

127

flash fires

158

jet fire models

225

See also Jet fire models outcomes

128

See also Effect models physical explosion models

158

See also Physical explosion models pool fire models

210

See also Pool fire models vapor cloud explosion models

131

See also Vapor cloud explosion models

F Fanning friction factor, discharge rate models

25

Fireball. See BLEVE and fireball models Fire exposure, discharge rate models

39

Fires and explosions. See Explosions and fires Flammable limits, defined Flash and evaporation models

127 57

applications of

59

computer codes for

76

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327

Index terms

Links

Flash and evaporation models (Continued) description

59

flashing

59

input requirements and availability

68

logic diagram

67

output

69

pool spread

66

simplified approaches

69

theoretical foundation

67

example problems

69

boiling pool vaporization

70

evaporating pool

71

evaporating pool with direct evaporation model

72

isenthalpic flash fraction

69

pool spread

74

philosophy of

58

purpose of

57

resources for

75

Flash fire models, generally Flashing, flash and evaporation models Flashpoint temperature, defined

68

158 59 127

Fragments and projectiles BLEVE and fireball models

187

196

200 projectiles, physical explosion models

166

range in air, physical explosion models

182

velocities of, physical explosion models

180

G Gas discharges, discharge rate models

29

Gases, heat capacity ratios

31

Geometric view factor, pool fire models

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218

219

328

Index terms

Links

H Heat capacity ratios, gases

31

Height effects, wind speed, dispersion models

83

Hole size, discharge rate models

21

I Incident outcome models. See Effect models Isenthalpic flash fraction, flash and evaporation models

69

Isopleths plume releases with, example problems

104

puff releases with, example problems

105

J Jet fire models

225

applications of

225

computer codes for

233

errors

232

example problem

229

input requirements

228

purpose of

225

resources for

232

simplified approaches

229

strengths and weaknesses of

231

technique description

226

theoretical foundation

228

L Leak duration, discharge rate models

22

Liquid discharges, discharge rate models

26

M McGuaid and Britter model, dense gas dispersion model, example problems This page has been reformatted by Knovel to provide easier navigation.

122

232

329

Index terms

Links

Modified Baker method example problems

154

vapor cloud explosion models

145

Moody friction factor, discharge rate models

25

N Neutral and positively buoyant plume and puff models applications of computer codes for described

85 85 110 86

plume model

91

puff model

88

errors

109

example problems

97

plume releases

97

plume with isopleths

104

puff releases

100

puff with isopleths

105

input requirements and availability

94

logic diagram

94

95

output

94

96

philosophy of

85

purpose of

85

resources for simplified approaches strengths and weaknesses of theoretical foundation utility of

110 96 108 94 110

O Outcomes, explosions and fires See also Effect models

This page has been reformatted by Knovel to provide easier navigation.

128

330

Index terms

Links

P Permissible Exposure Limits (PELs), toxic gas effect models

249

Physical explosion models

158

applications of

173

computer codes for

185

errors

185

example problems

174

Baker’s method

178

energy for compressed gas

174

fragment range in air

182

fragment velocities

180

Prugh’s method

176

input requirements and availability

173

logic diagram

173

output

173

philosophy of

159

projectiles

166

purpose of

158

resources for

185

simplified approaches

174

strengths and weaknesses of

184

technique description

160

theoretical foundation

173

utility of

185

Plume model, described

91

See also Neutral and positively buoyant plume and puff models Plume releases example problems with isopleths, example problems

97 104

Pool fire models

210

applications of

211

burning rate

211

computer codes for

225

This page has been reformatted by Knovel to provide easier navigation.

174

331

Index terms

Links

Pool fire models (Continued) errors

225

example problem

220

flame height

214

flame tilt and drag

215

geometric view factor

218

input requirements and availability

220

logic diagrams for

212

output

220

philosophy of

210

pool size

214

purpose of

210

received thermal flux

218

resources for

225

simplified approaches

220

strengths and weaknesses of

223

surface emitted power

216

technique description

211

theoretical foundation

220

utility of

225

Pool spread, flash and evaporation models

224

219 213

220

225

66

Probit functions effect models

238

sample problem

240

242

toxic gas effect models, equations

252

254

Projectiles. See Fragments and projectiles Prugh’s method, physical explosion models Puff model, described

176 88

See also Neutral and positively buoyant plume and puff models Puff releases example problems

100

with isopleths, example problems

105

This page has been reformatted by Knovel to provide easier navigation.

332

Index terms

Links

R Radiated heat flux jet fire models

229

pool fire models

216

Radiation, BLEVE and fireball models

189

Received thermal flux, pool fire models

218

Release geometry, wind speed, dispersion models

83

Release phase, discharge rate models

18

Reynolds number, discharge rate models

25

Risk, definitions of

6

Risk analysis, chemical process quantitative risk analysis (CPQRA)

3

Risk assessment, chemical process quantitative risk analysis (CPQRA)

3

Risk management, chemical process quantitative risk analysis (CPQRA)

3

220

27

S Short-Term Public Emergency Guidance Levels (SPEGLs), toxic gas effect models

245

Software. See Computer codes Source models

15

See also Chemical process quantitative risk analysis (CPQRA); Consequence analysis discharge rate models

15

See also Discharge rate models dispersion models

76

See also Dispersion models flash and evaporation models

57

See also Flash and evaporation models Surface emitted power, pool fire models

216

T Terrain effects, wind speed, dispersion models This page has been reformatted by Knovel to provide easier navigation.

82

248

333

Index terms Thermal effect models

Links 262

applications of

263

computer codes for

270

errors

269

example problems

267

BLEVE fireball

268

thermal flux estimation

267

input requirements and availability

266

output

266

philosophy of

263

purpose of

262

resources for

270

simplified approaches

266

strengths and weaknesses of

269

technique description

263

theoretical foundation

266

utility of

270

Thermal flux calculations BLEVE and fireball models

194

thermal effect models

267

Thermodynamic path, endpoint and, discharge rate models

197

20

Threshold Limit Values-Short-Term Exposure Limits (TLV-STEL), toxic gas effect models

247

TNO multi-energy method example problems

154

physical explosion models

173

vapor cloud explosion models

141

TNT equivalency model example problems

153

physical explosion models

160

vapor cloud explosion models

134

Toxic Dispersion (TXDS) acute toxic concentration, toxic gas effect models

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250

249

334

Index terms

Links

Toxic endpoints, toxic gas effect models

250

Toxic gas effect models

241

computer codes for

262

EEGLs and SPEGLs

245

248

ERPGs

244

246

errors

261

example problems

257

fixed concentration-time relationship

257

moving puff

257

input requirements and availability

256

output

256

PELs

249

philosophy of

243

probit equations

252

purpose of

241

resources for

262

simplified approaches

256

strengths and weaknesses of

261

technique description

253

theoretical foundation

255

TLV-STEL

247

Toxic Dispersion (TXDS) acute toxic concentration

250

toxic endpoints

250

utility of

262

Toxicology. See Effect models Two-K method, discharge rate models

23

Two-phase discharge, gas discharges, discharge rate models

35

V Vapor cloud explosion models

131

applications of

134

computer codes for

152

errors

151

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254

255 249

335

Index terms

Links

Vapor cloud explosion models (Continued) example problems

152

Baker-Strehlow method

154

blast wave parameters

152

TNO equivalency model

154

TNT equivalency model

153

input requirements and availability

149

logic diagram

149

output

151

philosophy of

131

purpose of

131

resources for

152

simplified approaches

151

strengths and weaknesses of

151

technique description

134

Baker-Strehlow method

145

TNO multi-energy method

141

TNT equivalency model

134

theoretical foundation

149

W Wind speed, dispersion models

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References

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