Understanding Atmospheric Dispersion of Accidental Releases

Understanding Atmospheric Dispersion of Accidental Releases

A CCPS Concept Book

George E. DeVaull John A. King Ronald J. Lantzy David J. Fontaine

Center for Chemical Process Safety of the American Institute of Chemical Engineers 345 East 47th Street, New York, NY 10017

© Copyright 1995 American Institute of Chemical Engineers 345 East 47th Street New York, New York 10017 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the copyright owner. For more information, a free catalog, or to place an order, call 1-800-242-4363, fax 212-705-8400, or write to AIChExpress Service Center American Institute of Chemical Engineers, 345 East 47th Street, New York, NY 10017. ISBN 0-8169-0681-5 PRINTED IN THE UNITED STATES OF AMERICA DISCLAIMER: It is sincerely hoped that the information presented in this document will lead to an even more impressive safety record for the entire industry; however, the American Institute of Chemical Engineers, its consultants, CCPS subcommittee members, their employers, their employers' officers and directors, and the authors disclaim making or giving any warranties or representations, express or implied, including with respect to fitness, intended purpose, use or merchantability and/or correctness or accuracy of the content of the information presented in this document. As between (1) the American Institute of Chemical Engineers, its consultants, CCPS subcommittee members, their employers, their employers' officers and directors, and the authors and (2) the user of this document, the user accepts any legal liability or responsibility whatsoever for the consequence of its use or misuse.

Preface

As introduction to the subject of this document, dispersion from accidental releases encompasses many different aspects. It includes the methods of classical air pollution modeling used in estimating the dispersion of dilute air pollutants, but also encompasses the more complex physics of dense-vapor and high-momentum releases, boiling and evaporating liquids, multiphase flow, vessel blowdown, and aerosol transport. For the newly initiated, such a broad-based array of topics can be overwhelming. The purpose of this document is to present a basic description of accidental release problems in the context of a technical narrative. The material is intended only as a basic introduction and the interested reader is encouraged to consult the cited references for further information. We also note that, in some aspects of accidental release physics, current understanding is only rudimentary, and further work may be needed toward development of practical engineering models. We also recognize that vapor dispersion modeling does not stand alone in evaluating process hazards. Such analysis must be used within a more comprehensive context of overall risk analysis and risk management. The American Institute of Chemical Engineers (AIChE) has a long history of involvement with loss control and process safety for the petrochemical and chemical industry. Through its strong ties with engineers, operators, safety professionals, and academia, the AIChE has enhanced communication and fostered improvement in the high safety standards of the industry. AIChE publications and symposia have become a prime information resource for the chemical engineering profession on the causes of accidents and means of prevention. The Center for Chemical Process Safety (CCPS) of the AIChE was chartered to develop and disseminate technical information for use in the prevention of major chemical accidents. In pursuit of this charter, the CCPS has published Guidelines, Workbooks, and Conference Proceedings on process safety, risk analysis, hazard evaluation, and vapor dispersion. The CCPS is supported by over 80 world-wide industrial sponsors in the chemical process industry who

provide the necessary funding and professional guidance to its technical committees. A partial list of available CCPS publications is given opposite the title page of this book.

Organization of This Book This volume is intended as a brief introduction to the various topics addressed in accidental releases and atmospheric dispersion. A list of references cited within this text is given at the end of this document for individuals who desire more detailed information. The topics addressed in this primer include a basic introduction in Chapter 1 and a discussion of turbulence and meteorology in Chapter 2. In Chapter 3 the problem of release rate estimates is covered. Following this, in Chapter 4, the problem of liquid pool evaporation is covered. Momentum or buoyancy dominated jet releases are covered in Chapter 5, and the problem of low-momentum heavy-gas releases is covered in Chapter 6. In Chapter 7, the problem of passive dispersion, where ambient turbulence dominates the dilution process, is discussed. Chapter 8 includes discussion a number of special complications that can arise in a dispersion analysis. Chapter 9 is a discussion of toxic vapor hazard levels. Chapter 10 includes information on the availability and use of computer models for accidental release air dispersion modeling. Each chapter is intended as a topical overview of the problem of interest. References are included for further information on the covered subjects.

Acknowledgments This book was authored by George E. DeVaull (Shell Oil Company), John A. King (Shell Oil Company), Ronald J. Lantzy (Rohm & Haas), and David J. Fontaine (Chevron). Significant contributions in content and in technical review by members of the CCPS Vapor Cloud Subcommittee are acknowledged. The committee was co-chaired by Ronald J. Lantzy and Ronald D. Myers (Rohm & Haas), vice-chaired by Gib R. Jersey (Mobil), and, in addition to the authors, included (in alphabetical order), Douglas N. Blewitt (Amoco), Sanford G. Bloom (Martin Marietta), C. K. Cheng (Monsanto), Donald J. Connolley (AKZO Chemicals), Seshu Dharmavaram (du Pont), Ebrahim Esmaili (Exxon), Jerry R. Foster (Union Carbide), David Guinnup (U.S. EPA), William J. Hague (Allied-Signal), Gene K. Lee (Air Products and Chemicals), David McCready (Union Carbide), Malcolm L. Preston (ICI Engineering), Jerry M. Schroy (Monsanto), Kenneth W. Steinberg (Exxon), and David Winegardner (Dow). William J. Minges, Bob G. Perry, Jack Weaver, and Lester H. Wittenberg of

CCPS provided staff support. Comments and suggestions from David J. Wilson (University of Alberta) and John L. Woodward (DNV Technica) are acknowledged. The support and contributions of Larry V. Csengery, Dan C. Baker, A. Bruce Krewinghaus, and Judy C. Moorad of Shell Oil Company in preparation of this book are greatly appreciated.

Nomenclature

Variable names are listed here; they are also defined when first used in the text. A c CD Cp d Dj

cross sectional or surface area pollutant concentration empirical discharge coefficient specific heat liquid droplet diameter jet diameter

Fro initial densimetric Froude number Fro = wj/(Djg Ipj - pool/poo) 2 Fr Froude number Fr = MJ/(Djg) !/ g gravitational constant h vertical height or depth H sensible heat release HQ sensible heat flux k von Karman constant ~ 0.40 (in the atmosphere) L Monin-Obukhov length L = (PaCp^3) / (*g//o), p total pressure q pollutant emission release rate /?WW(T) autocorrelation function of velocity w as a function of time lag T p density pa air density poo ambient density pj jet density s entropy t time TLw, TL,V, TL, w Lagrangian (frame of reference moving with the fluid) integral time scales for w, v, and w

^i,w, Ti,v, ti,w Eulerian (fixed frame of reference) integral time scale for u, v, and w T^C shear stress, normal to z, in x direction T temperature 7a ambient temperature Tas adiabatic saturation temperature 6 initial jet release angle o surface tension Cy, GZ spatial standard deviations of a plume cross-section in the y and z directions, respectively aM, av, (Tw standard deviation of w, v, or w velocity W514 friction velocity WOO ambient velocity wj initial jet velocity w, v, w velocity vectors in the downstream, cross stream, and vertical _ direction, respectively w mean value for w V volumetric flowrate 2 Wed droplet Weber number Wed = pa" d/G x, y, z spatial coordinates in the downstream, cross stream, and vertical direction, respectively Zi inversion height, overall depth of the thermal boundary layer ZO aerodynamic surface roughness height

Contents

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

vii

Nomenclature ......................................................................

xi

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

1

1.1 Purpose ............................................................................

1

1.2 Release/Dispersion Scenario Overview ...........................

1

1.3 Hazards ............................................................................

3

2. Meteorology .................................................................

6

2.1 The Atmosphere ...............................................................

6

2.2 Turbulence in the Atmosphere .........................................

6

2.3 Mechanically Generated Turbulence ................................

8

2.4 Vertical Density Stratification and Buoyancy ....................

8

2.5 Atmospheric Stability Classifications ................................

10

2.6 Similarity Scaling in the Atmospheric Boundary Layer .................................................................................

12

2.7 Changes over Time in the Atmospheric Boundary Layer .................................................................................

13

3. Source Estimates – Leaks and Ruptures ..................

15

3.1 Leaks and Small Holes .....................................................

15

3.2 Phase Changes in Released Fluids .................................

16

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v

vi

Contents 3.3 Aerosol Formation in Liquid or Flashing Liquid Releases ...........................................................................

18

3.4 Transient Vessel Inventory Loss ......................................

18

3.5 Catastrophic Vessel Failures ............................................

19

4. Sources – Liquid Pools ..............................................

20

4.1 Boiling Liquid Pools ..........................................................

20

4.2 Evaporation of Volatile Liquids .........................................

21

4.3 Evaporation of Relatively Nonvolatile Liquids ...................

21

4.4 Multicomponent Mixture Spills ..........................................

22

5. Buoyant and Dense-Gas Jet Releases ......................

23

5.1 Jet Length Scales .............................................................

23

5.2 Momentum and Buoyancy ................................................

24

5.3 The Effect of Wind and Ambient Turbulence ....................

25

6. Low-Velocity Dense-Gas Releases ............................

28

6.1 Source Specification .........................................................

28

6.2 Source Area Region .........................................................

28

6.3 Stably-Stratified Region ....................................................

30

6.4 Passive Dispersion Region ...............................................

30

7. Passive Dispersion .....................................................

31

7.1 The Mechanics of Turbulent Dispersion ...........................

31

7.2 Passive Dispersion from Elevated Releases ....................

32

7.3 Near-Ground Passive Dispersion .....................................

34

7.4 Dispersion Averaging Times .............................................

34

8. Complex Flow Considerations ...................................

35

8.1 Building Wakes and Stack Downwash .............................

35

8.2 Gravity-Driven Flows and the Effects of Terrain ...............

36

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Contents

vii

8.3 Aerosol Rainout ................................................................

36

8.4 Fanning Plumes and Subsidence .....................................

37

9. Hazard Evaluations .....................................................

38

9.1 Chemical Toxicity .............................................................

38

9.2 Flammability .....................................................................

40

10. Computer Models ........................................................

41

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

42

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1

Introduction

1.1. Purpose The purpose of this document is to give a description of the processes involved in an accidental or emergency release and the resulting downwind transport and dilution of gases, vapors, and aerosols. The focus is not on the mechanics of a calculation, but on the physical problem description. This information should give the reader enough background to understand the assumptions and results of an episodic dispersion analysis. It is assumed here that risks associated directly with the cloud concentration—toxicity or flammability—are of primary interest. While succeeding events, such as fire or explosion, can depend on the prior dispersion of a cloud of material and can result in secondary hazards, they are not the primary subject of this document. The cause and probability of a given release are also not discussed here, but can be important in evaluating overall risk. Analysis of accidental releases must be included within the broader context of risk analysis and risk management procedures that are discussed in many CCPS books (as listed inside the front cover) and elsewhere (USEPA, 1991; FEMA, 1989; NRT, 1987; USDOT, 1987; USEPA etal., 1987).

1.2. Release/Dispersion Scenario Overview The analysis of potential accidental releases is useful in developing emergency response plans and as a part of process hazard analysis. It is also a useful tool in assessing methods to prevent these releases and in evaluating proposed mitigation strategies. Estimating and understanding the process requires some knowledge of source behavior and the mechanics of atmospheric transport and dispersion. In a given analysis, parameters governing the release scenario and the environment need to be defined. A number of items that can help in this

definition are listed in Figure 1.1. As shown, these items include a source definition, definition of ambient conditions, release types, and possible release scenarios. From this information, the mechanisms governing the release and dispersion can be identified and used in the analysis. Describing the evolution of a release is best handled by dividing the problem into a series of stages. Basic divisions include (1) an isolated source region, where release rate estimates are nearly independent of environmental conditions; (2) a coupled source/dispersion regime, where both source and environmental parameters are important in estimating the concentration field; and (3) a final region where the ambient wind and weather dominate the dispersion process. As an example, these various problem segments are illustrated for a vessel leak and the subsequent dispersion process in Figure 1.2. In the source region of this figure, the analysis begins with an assumed leak, where we need to calculate a mass release rate and determine the duration of the event through either an inventory estimate or an estimate of the time interval before the problem can be corrected. Estimates of the release phase (liquid, vapor, or aerosol), fluid velocity, and density, as well as the rate of change in mass release rate over time, are needed to determine the next stage in the dispersion process. In the coupled source/dispersion regime, both source and environmental conditions are important. This intermediate region is often within the downwind ftourcg InforrniBitlorr Composition (species and phase) Total Mass Inventory in Storage Thermodynamic Properties of Release (temperature, pressure, enthalpy) Geometry of Leak or Spill

Environmental (Conditions: Air Pressure Wind Speed Atmospheric Stability Ground Temperature

Temperature Relative Humidity Flow Obstructions Ground Slope

Release Types: Liquid, Aqueous Liquid (ionic solutions). Gas, Vapor, Multi-phase, Aerosols Release Duration: Continuous, Transient, Instantaneous Possible Source Scenarios: Evaporation from Soil Leak in a Pipe or Vessel Stack Emission Liquid Spill Evaporation

Runaway Reaction High Momentum Jet Release Two-Phase Jet (Liquid Rainout?) Bare and Combustion Products

Catastrophic Vessel Failure Lighter-than-Air Plume Heavier-tban-Air Plume

Possible Dispersion Mechanisms: Density (heavier-than-air or lighter-than-air): Bouyant/Dense-Gas Elevated Plume Trajectories Gravity Slumping in Ground-Level Heavier-than-Air Releases Stable Density Stratification in Ground-Level Clouds Source Momentum: Dispersion by Ambient Turbulence in: Enhanced Mixing in Elevated Jets Mixing and Surface interactions in Ground-Level Flow

Dilute Plumes Building Wakes

Figure 1.1. Source and environmental parameters that are needed in defining release conditions and in predicting downwind dispersion.

Coupled Source/Dispersion Region Both Source and Environment*] Parameters are Important Need: Source Information, Geometry, Environmental Parameters . Calculate: Trajectory, Dilution Rate, Evaporation Rate

Isolated Source Region Calculations Independent of Environment Chemical Inventory, Composition, Geometry Calculate: Bow Rate, Velocity, Density, Release Phase

Passive Dispersion Ambient Mixing Dominates Need: Source Size Information Wind and Weather Calculate: Trajectory, Dilution Rate

Figure 1.2. Stages in an accidental environmental release and the downwind dispersion process.

range of interest in many accidental releases. In this region the release conditions can affect the wind field and vise versa. Both jet releases and heavy-gas dispersion fall within this regime, where the initial plume velocity and density as well as the ambient wind field will affect the cloud path and dilution rate. This coupled region can also include vapor flow rate estimates, where for example, the evaporation rate from a liquid pool spill can be a function of wind speed. In the final stage of dispersion the concentration of the released gas will be low. The presence of the gas does not alter the ambient wind field or the atmospheric turbulence. Under these conditions the release is dispersed as a passive pollutant by the ambient turbulence. For dilute pollutants or low release rates (such as with fugitive emissions), passive dispersion dominates the dilution process throughout the entire downwind range of interest.

1.3. Hazards If the hazard of concern is a function of concentration, results can be represented by concentration isopleths (lines of constant concentration) on diagrams or maps of the site. Often, since wind direction cannot always be easily estimated a priori, we are interested in a radius of exposure estimate. This is the highest concentration that would be expected at a given radial distance from the release point. Other useful types of concentration plots are shown in Figure 1.3. Of note in this particular figure is the observation that ground-level concentration does not

High Velocity Sulking (a) Jet z Dense Vapor Ground Level Slumping Cloud

Plume Centerline Plane Concentration Isopieths

Concentration Plume Centerline

Ground Level Concentration Isopieths

Ground Level Downwind Distance

Figure 1.3. Plot of distance versus concentration and concentration isopleth maps. This figure shows the concentrations resulting from a particular heavier-than-air vertical jet release, (a) Diagram of the release, where x is the downwind direction, y is in the crosswind direction, and z is the vertical coordinate, (b) Lines of constant concentration in the x-z plane of symmetry, (c) Lines of constant concentration in the x-y ground plane, (d) Concentration levels, as a function of downwind distance, for the plume centerline, as shown in (b), and at ground level.

decrease uniformly with distance for a release from an elevated source. This is because the plume is elevated above the ground; the lower edge of the plume does not contact the ground until the plume has been transported, diluted, and dispersed downwind from the source. All hazards that may arise in an accidental release are not simple functions of the chemical concentration. A list of potential hazards (all of which are not covered in this report) include: • Biological response as a function of concentration, exposure time, and total dose. • Oxygen displacement and the potential for asphyxiation. • Exceeding the flammability limit for local pockets of vapor or light-back of a plume from an ignition point to the leak source. • Visibility limitations within a pollutant cloud. • Temperature extremes resulting from cryogenic liquid spills, flashing flows, hot fluid releases, or chemical reactions. • Entrainment of released material into inlet ducts for surrounding process equipment and ventilation systems. • The thrust and expansion force from high pressure and flashing liquid releases.

• Thermal radiation estimates from fires or flares. • The effects on people or on the surroundings of the pressure impacts of vapor cloud explosions. Hazard estimates alone are not sufficient for evaluating risks due to a particular release scenario, process unit, or facility. The hazard estimates must be used in conjunction with the postulated probability of a release to develop a more complete evaluation of risk.

2 Meteorology

2.1 The Atmosphere Dispersion of any accidental release in the atmosphere is strongly dependent on wind and weather conditions. This section is intended to cover information important in describing the atmosphere in its lowest regions, within 3000 meters of the ground. This is where all of the accidental releases under discussion could occur, and where the people who may be affected by them live. In investigation of potential hazards from a hypothetical accidental release we are often first interested in the set of atmospheric conditions that result in the highest concentrations at the greatest downwind distance. For ground-level releases this generally consists of calm, low wind speed conditions where turbulent mixing rates are limited. With elevated releases, worst-case weather conditions are those which bring the highest pollutant concentrations down to ground level where they can result in a greater potential for human exposure or creating other hazards. Other considerations, such as the impact of a plume on a building or hillside, may also need to be considered on a site-specific basis. Beyond examining dispersion under worst-case atmospheric conditions, we may also be interested in how often a particular release, if it occurred, would result in a problem. This depends on the full probability distribution of weather conditions, wind speeds, and wind directions expected at the given location.

2.2. Turbulence in the Atmosphere Turbulence is an irregular and random motion present in most fluid flows. It is the dominant mechanism in the mixing and dilution of atmospheric releases. One characteristic of turbulence is the hierarchy of different random fluctuating velocity scales, or eddies. In the atmosphere these scales can range from global patterns down to local and near-instantaneous fluctuations in wind direction and speed.

Different mechanisms are responsible for maintaining turbulent motion at different time scales. Within a 10- to 60-minute time period in the atmosphere, wind speed, wind direction, atmospheric turbulence, and weather conditions can usually be assumed to have relatively constant time averages (while still varying randomly over time). The mean wind velocity, u, and the variance in the mean wind, GM ^ , for instance, are given by

Over longer time periods, the effects of moving weather fronts, storms, and changing solar heat flux must usually be considered. Also, over a longer time duration, pollutants travel farther and the effects of topology are often more important. In accident scenarios that last less than approximately 60 minutes, it is sufficient to proceed using a single set of averaged weather conditions. Longer duration releases can be analyzed with a set of wind and weather data, either as a time series, or alternately as a statistical distribution of different possible conditions and the persistence of these conditions over time. When time periods of approximately 60 minutes or less are considered, the two important mechanisms of turbulent mixing in the atmosphere come from (1) mechanical turbulence generated from wind drag at the ground, and (2) vertical density stratification in the atmosphere. These mechanisms are discussed more completely in the following sections. The "eddies," or random fluid motions, generated by mechanical turbulence have time scales in the range of milliseconds to a minute. Convective thermal cells, associated with daytime density stratification, have time scales that range from one to five minutes. Any time-averages of atmospheric parameters, including concentration averages from dispersing plumes, will become more variable over shorter averaging times, especially at averaging time below 10 minutes where there is a better chance that the averaged sample will be insufficient to capture information from enough random eddies to ensure a consistent value. This idea is captured by the autocorrelation function,

which describes how well velocity (or any relevant variable) correlates with itself as a function of time displacement. The integral time scale, or average correlation time, is given by

Averages taken over time intervals less than TI,M will vary considerably from sample to sample. This variability is much less with averages taken over a time duration greater than Ti,M.

2.3. Mechanically Generated Turbulence As wind passes over the ground, surface friction and internal wind shear retards the flow near the ground. At great heights above the ground, the wind is largely unaffected by surface friction, and acquires a velocity determined primarily by the horizontal pressure gradient of the local weather system and Coriolis forces which result from the rotating earth. The surface obstacles and features that disturb the wind near the ground result in atmospheric turbulence and a net drag force between the ground and the upper atmosphere. This aerodynamic drag, and the associated mechanically generated atmospheric turbulence, increases with higher wind speeds and with greater number, height, and spacing of ground surface features. An aerodynamic surface roughness height, zo, is often used to characterize the averaged effects of surface features on the wind flow. This roughness height may range from less than a millimeter for ice and mud flats to several meters in an urban area. The effect of roughness height on the vertical wind profile is shown in Figure 2.1. Increasing roughness height and greater wind speed generally increase the level of turbulence in the atmosphere. Atmospheric boundary layer wind profiles are discussed in Randerson (1984) and Pasquill and Smith (1983).

2.4. Vertical Density Stratification and Buoyancy Turbulent mixing in the lower atmosphere is strongly affected by changes in air density with height. These changes in air density are driven by the daily variation in radiative heating and cooling of the ground and may result in stable, neutral, or unstable average vertical density and temperature stratification as shown in Figure 2.2. Neutral atmospheric conditions occur when the total enthalpy in the atmosphere is near-constant with height, or when heat transfer between the ground and the atmosphere is very small. Neutral conditions are approached in overcast, windy weather conditions. Because of gas compressibility and the contribution of gravity head, air density and temperature both decrease slightly with height in a neutral atmosphere (near the ground, temperature decreases at a rate of 980C per 100 meters). This is illustrated in Figure 2.2. Unstable conditions occur in daytime as the ground surface is heated by the sun. This warms the atmosphere from below and leads to an unstable density

town outskirts woodland forest

crop land shrubs and trees I

0.1 1.0 0.01 z , Aerodynamic Surface Roughness Height (meters)

short grass

mown grass

I

0.001

Roughness Height

T Vertical Wind Profile Figure 2.1. The effect of surface obstacles and roughness height on vertical wind profiles.

ice, mud falst deser,t cam l sea 0.001 00.001 •i

large urban centers

stratification, with warm, buoyant air underlying a layer of cooler air. Transient thermals result, with the hot air rising and expanding adiabatically in long vertical columns. This rise continues up to a mixing height where the air density inside the thermal is equal to the surrounding air density. This mixing height is also the height of the mean temperature inversion (change in the sign ± ofdT/dz with height) as shown in Figure 2.2. Areas of downward subsidence surround each thermal. Thermal convection in the unstable atmosphere leads to high mixing rates in the vertical direction and rapid dilution of pollutant releases. At night, there is radiative cooling between the ground surface and the night sky. Conduction and convection then cool the atmosphere from below, resulting in a stable vertical temperature and density profile, with density decreasing with increasing height. This stable stratification leads to limited vertical mixing rates in the atmosphere. Dilution rates of pollutants in calm, stably-stratified conditions can be several orders of magnitude less than in an unstable, convective atmosphere. A stable density stratification also occurs above the mean temperature inversion height in unstable atmospheric conditions.

2.5. Atmospheric Stability Classifications There are a number of methods available for quantifying the state of the atmosphere. The best method is often through direct measurements, which can be very useful in estimating dispersion in an actual accidental release, or in dispersion model verification. The most basic method follows the Pasquill-Gifford stability classification scheme. This requires only simple estimates of wind speed, solar insolation (in daytime), and cloud cover (at night). Bounds for this classification scheme are given in Table 2.1. The Pasquill-Gifford stability classes range from A through F. A-stability conditions occur in low winds with high incoming levels of solar radiation. Height

Height Stable

Unstable Mixing Height

Neutral

Stable

Neutral

Unstable

Density,

Unstable p

Unstable Mixing Height

Convective Thermals (in Unstable Conditions) Temperature, T

Figure 2.2. Vertical density and temperature profiles in unstable, neutral, and stable atmospheric conditions. The unstable mixing height is often marked by a inversion, or change in the slope of the vertical density profile.

TABLE 2.1 Definitions ofPasquill Stability Categories in Terms of Wind Speed, Solar Insolation, and Sky Conditions (Pasquill and Smith, 1983) A: extremely unstable conditions B: moderately unstable conditions surface wind speed (m/i)

E: slightly stable conditions F: moderately stable conditions

C: slightly unstable conditions D: neutral conditions

night daytime soiar insolation

thinly overcast, or > 4/8 low clouds

strong

moderate

slight

6

C

D

D

D

D

< 3/8 clouds

(for A-B take average of values for A and B, etc.)

E-stability and F-stability conditions arise on clear nights with little wind. D-stability class conditions occur with higher wind speeds and greater cloud cover. A refinement of this method includes surface roughness height in the classification scheme, where increased roughness will shift more cases toward the neutral D-stability class conditions. An analogous method defines "rural" and "urban" classification criteria, where a change from rural to urban conditions has the same effect on stability class as an increase in roughness height (USEPA, 1987). Figure 2.3 shows the trends of Pasquill-Gifford stability class dependence on cloud cover, wind speed, and roughness height. Once the stability class, wind speed, and source release rate are specified in a given scenario, simple dispersion models can be used to predict the downwind concentration field for many types of passive pollutant releases. One item neglected in the Pasquill-Gifford stability class scheme is the overall height of the turbulent boundary layer, or mixing height. This is unspecified but can be important if a dispersing plume reaches this height. It is sometimes included in the class description as a external parameter. Pasquill-Gifford Stability Class

A B

I

Very Unstable Moderately Unstable Slightly Unstable Neutral Slightly Stable Moderately Stable

Increasing Cloud Cover (reduced radiative heat transfer)

(a)

Increasing Wind Speed

Increasing Roughness Height

Increased Turbulent Mixing

(b)

Figure 2.3. Dependence of atmospheric stability class on basic parameters. The arrows for (a), (b), and (c) show a converging trend toward neutral conditions for an increase in the noted parameter. Turbulent mixing, (d), increases through the Pasquill-Gifford stability class range from F to A.

2.6. Similarity Scaling in the Atmospheric Boundary Layer Atmospheric conditions are usually, but not always, classified in terms of Pasquill-Gifford stability class. Alternately, an atmospheric boundary layer analysis can be used (Randerson, 1984). This boundary layer is a turbulent region of air just above the ground surface and below an overlying layer of relatively calm air. The depth of the boundary layer can vary from tens of feet to several thousand feet. Similarity parameters are used to describe the atmospheric boundary layer. Turbulence, wind, and temperature are functions of the similarity parameters, which include friction velocity, the sensible heat flux from the ground, the Monin-Obukhov length, and the mixing height. Their relationship is illustrated and discussed in Figure 2.4.

Unstable Conditions

Turbulence Profile

Wind Profile

Inversion Height

Temperature Profile

B

Sy

Dominate Sensible Heat Flux H0

Stable Conditions

Roughness Height

Friction Velocity

Wind Profile

Mechanical Turbulence Dominates

MoninObukhov Length

Turbulence Profile

Temperature Profile

Mixing Height Suppressed Turbulence

Sensible Heat Flux H0

Roughness Height

Friction Velocity

Mechanical Turbulence Dominates

MoninObukhov Length

Figure 2.4. Similarity scaling parameters in the atmospheric boundary layer. Unstable and stable conditions are shown. Sensible heat flux, //o, is the thermal energy per unit area flowing from/to the ground. The roughness height,zo, is a length scale which characterizes the surface roughness. Friction velocity,u , is the square root of the surface shear stress,!^, divided by the air density, ra, where shear stress has units of force per unit area. The mixing height or inversion height, zi, defines the overall depth of the turbulent boundary layer. The Monin-Obukhov length, L, demarcates the height below which mechanically generated turbulence dominates in the mixing process.

Friction velocity, w* = (t^x/p) /2 , establishes the level of shear stress, T2*, at the ground (drag force per unit area), and the sensible heat flux, HQ (power per unit area), which can be positive or negative, governs the vertical temperature gradient at the ground. The Monin-Obukhov length, L = ~(pCpTau^) I (kgHo), is a parameter for the ratio of the mechanical turbulent energy to that produced by buoyancy. Monin-Obukhov length is negative in unstable conditions, positive for stable conditions, and is infinite in neutral conditions. In unstable atmospheric conditions the inversion height, zi, establishes the overall depth of the thermal convective cells within the boundary layer. Without extensive meteorological measurements, similarity scaling parameters are not easy to estimate and do not always define the state of the atmosphere-4>etter than the simpler Pasquill-Gifford stability class. They can, however, be used to improve certain types of dispersion model predictions, especially for releases near the ground.

2.7. Changes over Time in the Atmospheric Boundary Layer In assessing accidental releases of less than an hour in duration, a dispersion analysis using constant wind and weather conditions is usually sufficient. However, for longer duration releases or pollutant travel times, it sometimes becomes necessary to account for the slower variations in weather conditions over time. Typical variations over a daily cycle in the atmospheric boundary layer are shown in Figure 2.5. From dawn through noon, the solar heat flux to the ground increases as the sun rises into the sky and the depth of the convective mixed layer slowly increases. From noon through late afternoon the mixed depth remains relatively constant. At dusk there is arapid collapse of the daytime solar-driven convective thermals, but aregion of gradually decaying turbulence remains within the depth of the daytime boundary layer. After dusk the surface layer of the atmosphere is gradually cooled from below, with an increasing stable layer growing over time as the effects of the general cooling are felt through a greater depth. By dawn most of the turbulence from the previous day has decayed and the daily cycle begins again. Daily boundary layer growth and collapse is a slow function of time, with few exceptions. Within hour-long blocks of time, the boundary layer can often be described by single value parameters (average wind speed, average solar heat flux, etc.) that are averaged over time and do not depend on weather conditions at earlier time periods. The exceptions for this averaging include the transition periods near dawn or at dusk, when weather fronts or thunderstorms move through an area, or when there is an interruption in the daily temperature cycle.

Height repeating cycle Mixed Layer

Mixed Layer (low turbulence) Vertical Turbulence Profile

Surface Layer Dawn Height

Noon

Surface Layer

Time Dawn

Dusk

Stable Density Profile

Stable

:Density

Profile

Vertical Density Profile

Unstable Density Profile Dawn

Noon

Dusk

Dawn

Time

Figure 2.5. Daily variations in the atmospheric boundary layer. Changes over time in atmospheric turbulence are shown in (a), while changes in the vertical density profile are shown in (b).

3 Source Estimates—Leaks and Ruptures

3.1. Leaks and Small Holes Many types of accidental releases can be analyzed as small holes in tanks or pipes, where the storage pressure decreases slowly with time or is constant. Such a quasi-steady analysis is possible when the fractional change in the vessel inventory is small over the time required for a wave to propagate through the vessel (The wave speed of interest for pressurized vessels is the sonic velocity, or speed of sound, u = [dp/dp \s}/2, while for liquid tanks of depth /z, with a leak below the free surface, the propagation speed of a free surface wave, u = [gh] , is needed). Examples of potential release scenarios from a tank are illustrated in Figure 3.1. Vapor Jet

WIND

Liquid Jet

Vapor Jet Oil Canning?

Siphoning? Pipe With Friction

Flashing Liquid?

Liquid Jet

U^uid

Fragmented Jet?

Figure 3.1. Typical vessel leak scenarios for a pressurized tank.

The level of detail in estimating a flowrate needs to be consistent with the typical information known about a release. Planned episodic releases from a process upset may issue through well characterized pressure relief vents or valves. Conversely, vessel or pipe failures are poorly characterized. These can be long narrow cracks, circular half-moons, star cracks, or circular openings, where the edge of the opening can be an inward dent, a clean crack, or a peeled-back rupture. In many cases, it is sufficient to analyze the release as one-dimensional flow through an ideal hole of equivalent area, Aideal = CoAactual, using an empirical discharge coefficient, CD. This coefficient is always less than one and accounts for multidimensional flow effects and local frictional losses. For a sharp-edged round hole, CD ~ 0.6. Other hole geometries will have different values for CD. With relatively incompressible fluids, momentum conservation, through a Bernoulli-flow assumption, is often used to estimate flow rates. For gases and supercritical fluids, compressibility effects can be important, and must be included in the estimation procedure. With a low enough upstream-to-downstream absolute pressure ratio (usually 2 : 1 or less, and depending on gas composition), gas velocity exiting a leak will be subsonic, or "unchoked." At higher pressure drops, the flow rate will be limited to the sonic velocity of the fluid at the plane of the leak, or "choked." If the discharge is through a vent stack or a section of process piping, frictional losses can be considered. Methodology for estimating the flow rates of liquids and gases through holes, or through sections of process piping are given in Perry's Chemical Engineers' Handbook (Perry et al., 1984), as well as in any introductory text on fluid mechanics. Beyond the plane of the leak, unchoked subsonic flow of liquid or gas will issue from a leak or hole at atmospheric pressure as a gradually growing conical stream, and the jet centerline velocity will decay uniformly with distance from the leak. With choked flow, pressure at the plane of the leak will be greater than atmospheric pressure. This pressure difference causes the jet to expand rapidly beyond the plane of the leak, and accelerate in both the radial and axial direction. At final expansion, the jet dynamic pressure is equal to atmospheric pressure. As a practical matter, liquid releases can also result in choked flow, but this does not often occur since a pressure differential sufficient to choke a liquid release would also be likely to result in a fluid phase change. The geometry of choked and unchoked flows is shown in Figure 3.2.

3.2. Phase Changes in Released Fluids In releases of subcooled or compressed liquids, a decrease from the storage pressure to atmospheric pressure can cause part of the material to flash to a vapor during the release process. Where gas bubbles form before the fluid exits the

Potential Core

Mixed Zone

Subsonic Unchoked Flow

Oblique Shock Wives A Oscillating Pressure Wave Region

Prandl-Meyer Expansion Waves

Potential Core Mixed Zone

Sonic Choked Flow Figure 3.2. Flow geometry for fluid jets—unchoked and choked flow. In the choked, underexpanded case illustrated, the Prandtl-Meyer waves occur in regions of expanding gases. Shock waves can occur in regions of recompression.

hole or leak, choked flow at the orifice may result, with the orifice pressure greater than ambient pressure, and the fluid velocity at the orifice plane equal to an averaged sonic velocity. Once the two-phase fluid has exited the orifice, rapid expansion to atmospheric pressure occurs. Much as with an underexpanded vapor jet, the flashing fluid will accelerate in both the radial and axial direction. Alternately, a metastable flashing fluid may completely pass the orifice plane as a liquid, with nucleation, bubble growth, and rapid expansion only after the orifice plane. Rapid expansion of a flashing liquid will break up the remaining liquid stream into liquid droplets. A conservative upper bound (overestimate of flowrate) in a flashing liquid accidental release analysis can be found by neglecting vaporization in the fluid as it passes from vessel storage conditions to the orifice (i.e., only liquid passes

through the orifice and all vaporization occurs downstream). Other approximate methods for estimating the mass flowrate of flashing liquids have been introduced by Fauske and Epstein (1987) and Leung and Grolmes (1988). These methods interpolate the upper bound value with a flowrate estimated assuming local thermodynamic equilibrium between the liquid and vapor phases. Such methods are conservative (underestimates of flowrate) when used for sizing pressure relief valves. A summary discussion of these and other methods is given by Fisher etal. (1992).

3.3. Aerosol Formation in Liquid or Flashing Liquid Releases For liquids that exit a vessel 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, influences the evaporation rate of the droplets while in flight. The time of flight (drop trajectories) influences the fraction of the release that rains out, evaporates or remains in the aerosol/vapor cloud. Aerosol breakup occurs typically by either aerodynamic or flashing mechanisms. At low degrees of superheat, aerodynamic mechanisms dominate and droplet break-up depends on the relative strength of inertial/shear forces and capillary forces on the drop. This ratio is expressed as the Weber number, and the largest droplets in the jet have a diameter, d, estimated by a Weber number stability criteria,Wed = paufd/G -13, where the effects of surface tension, a, jet velocity, MJ, and air density, pa, all contribute. At high degrees of superheat, a flashing mechanism dominates, usually producing smaller droplets. Various drop size correlations have been suggested for the flashing mechanism; some of these correlations are functions of the bubble growth rate. The bubble growth rate can depend on the fluid flash fraction, the gas-liquid volumetric expansion ratio, and time.

3.4. Transient Vessel Inventory Loss The flowrate from a finite chemical inventory, with few exceptions, will decrease over time as the vessel pressure or, if applicable, the liquid height in the vessel also decreases over time. Exceptions may include cases where there are exothermic chemical reactions within the stored fluid, or heat transfer to the vessel. Another exception may occur when the hole or vent is in the vapor space of a vessel that contains boiling liquid. Vapor holdup of bubbles within the

boiling liquid will cause the liquid volume to swell and the free surface to rise. The surface may rise above the level of the hole, with a resulting change in the release from vapor to two-phase flow at a higher mass flow rate. The amount of liquid swell and fluid rise in a given scenario depends on the driving force for boiling, either at the vessel walls (due to heat transfer), or throughout the mass of liquid (for chemical reactions or a decrease in storage pressure). Fluid viscosity, surface tension, and the tendency for a liquid to foam also contribute to this potential complication of liquid swell. Analysis procedures for this type of problem have been developed by the AIChE Design Institute for Emergency Relief Systems [DIERS] (Fisher et al., 1992).

3.5. Catastrophic Vessel Failures When a large leak or catastrophic vessel failure occurs, conditions can vary rapidly in time and space. Pressure and gravity waves will propagate from the rupture through the vessel contents, and rapid acceleration of the stored fluid inside the vessel, toward the rupture, occurs as waves pass through the vessel contents. In this type of release a single pressure and temperature cannot be assumed for the contents of the entire vessel, and a transient release analysis is needed. One example of this situation is in the rupture of a long high-pressure pipeline, where a dispersed expansion wave will travel up the pipeline, away from the rupture, at sonic velocity. The release rate from this pipeline will decrease rapidly as a function of time since the rupture, as frictional effects and decreased line pressure just upstream from the rupture increasingly affect the discharge rate. Rupture of a near-symmetrical pressure vessel can result in rapid expansion of the vessel contents. As with the pipeline, transient expansion waves will pass through the vessel contents at high velocity. Initially, this is a nearly isentropic process as the vessel contents expand to atmospheric pressure. This rapid expansion will entrain any vessel liquid fraction (if present) into the vapor cloud. The cloud growth continues as the momentum of the expanding cloud entrains ambient air. Finally, the expanded and partially diluted cloud is often treated as a puff, which is dispersed and diluted as it is convected downwind.

a Sources—Liquid Pools

Liquid spills can result from accidents ranging from a small leak to a vessel failure, and may form a pool on the ground (or on water). The initial transient spreading of this liquid pool is driven by the momentum of the entering liquid stream and the pool depth gravity-head. The approximate radial spreading rate, dr/dt, for an unconfined pool of depth, /z, of relatively in viscid liquid on a smooth surface is limited by the velocity of a free surface wave in the pool, dr/dt ~ (2g/z) . Using mass conservation, a relation can be found that relates pool spreading and spill rate. The actual transient spreading rate is slowed by viscous drag, infiltration into the substrate, evaporation, surface tension, and the wetting factor at the liquid-ground surface. In addition, spreading of a pool can be limited by berms, dikes, or terrain. Several possible situations can occur in liquid pool evaporation. These include (1) a boiling liquid, (2) evaporation of a volatile liquid, or (3) evaporation of a relatively nonvolatile liquid. Each of these items is discussed below. More information on the physics of evaporating pools is given by Webber (1988), Wu and Schroy (1979), and Shaw and Briscoe (1978).

4.1. Boiling Liquid Pools Heat transfer into a liquid pool will occur when the pool is colder than the surroundings. This heat transfer is driven by air convection on the upper liquid pool surface, and by conduction from the substrate below the pool. With some cryogenic fluids, the heat flux into the pool can be great enough to boil the liquid. In this case the pool remains at its normal boiling point and the total mass evaporation rate is equal to the total heat flux into the pool divided by the heat of vaporization for the fluid.

With a cryogenic liquid spilled on land, the heat flux into the pool from the ground will grow smaller over time as the ground surface cools to the liquid boiling point and the penetration depth of cooled soil increases. For floating cryogenic liquids spilled on water, constant convective circulation of the water keeps both the heat transfer per unit area to the pool, and the mass evaporation rate per unit area constant over time. With some boiling cryogenic liquid spills on water, heat transfer occurs through a vapor film (film boiling). Under some conditions, the vapor film can collapse, with a commensurate increase in the heat transfer rate. This is followed by near-homogeneous nucleation in the remaining liquid. The resulting rapidphase-transition can result in violent expansion of the remaining liquid.

4.2. Evaporation of Volatile Liquids For relatively volatile evaporating liquids, as for boiling liquids, heat transfer to the pool is balanced by the heat lost from the pool due to liquid vaporization. However, with a volatile liquid, heat loss from the pool due to boiling or rapid evaporation can be great enough to cause autocooling of the remaining liquid. In this case the pool temperature will decrease below its normal liquid boiling point or below the ambient temperature. A lower limit on the pool temperature is given by the adiabatic saturation temperature, Tas. This temperature is achieved when a saturated air and vapor mixture is produced with an energy balance between the heat of vaporization of the released fluid and the sensible heat of cooling the air from ambient to ras. It is analogous to a thermodynamic wet-bulb temperature for air-water mixtures. The actual dynamic equilibrium pool temperature will be somewhat higher than Tas, depending on the ratio of heat and mass transfer rates for the pool.

4.3. Evaporation of Relatively Nonvolatile Liquids Evaporation of relatively nonvolatile liquid spills is driven primarily by convective mass transfer at the upper pool surface. Boundary layer similarity arguments for dimensionless viscous and turbulent Schmidt, Nusselt, and Peclet numbers are used to derive a mass transfer coefficient (mass per unit area per unit time) for a particular scenario. This coefficient is a function of the wind velocity, the pool geometry, and several empirical coefficients. Total evaporation rate is a function of the pool area, ambient vapor concentration and vapor pressure of the chemical, and the derived mass transfer coefficient. In this evaporating pool, the heat lost from the pool by liquid vaporization is balanced by heat transfer to the pool plus any net changes in the sensible heat

of the liquid. For relatively nonvolatile liquids, the evaporation rate will be low and once any initial transient differences in the pool and atmospheric temperature are equilibrated, the pool temperature will not deviate much from ambient temperature.

4.4. Multicomponent Mixture Spills In evaporation from multicomponent liquid pools, the more volatile chemical components will evaporate faster, so that pool composition can change over time. The evaporation rate of individual components in the pool is a function of the liquid/vapor partitioning at the pool interface. With the vapor pressure of each component determined just above the pool, the relative evaporation of each component is directly proportional to the molecular weight and diffusivity of that component in air. Overall transport is estimated using the same boundary layer similarity scaling as used for evaporating single-component fluids. With viscous liquids, it is possible for the pool to develop a composition gradient near the liquid-vapor interface which is rich in nonvolatile components. This effect can reduce the overall evaporation rate from the pool.

5 Buoyant and Dense-Gas Jet Releases

Jet momentum in a release can be important when the release velocity is much greater than the wind velocity. When the release density is much different than the air density, buoyancy effects, either lighter-than-air or heavier-than-air, must be considered. The initial velocity and density of a release can significantly affect the near-field trajectory and dilution rate of a plume. The three primary vector forces that can affect plume trajectory include the initial jet momentum, the release buoyancy relative to air, and the ambient wind. These driving forces dominate to different degrees in the various stages of the evolution of a plume. An example of the contributions of these vector quantities to a plume trajectory are illustrated in Figure 5.1. The vector sum of these three components change as a function of initial conditions, the plume dilution rate, and the air/pollutant mixture thermodynamics. The local air entrainment into the jet, or dilution rate, is in turn a function of the same three parameters.

5.1. Jet Length Scales Parametrization helps identify the relative contributions of jet momentum, buoyancy, and ambient wind. For an unobstructed discharge into the ambient atmosphere, the relevant dimensionless groups (Schatzmann, 1979) include: initial densimetric Froude number. initial jet to ambient velocity ratio initial release angle

* momentum

WIND

''wind

Ftotal

release angle ^gravity

Figure 5.1. Balance of forces for an arbitrary initial jet release angle. The jet thrust is oriented in the release direction, the wind force is co-flowing with the wind, and the buoyancy force is parallel to the gravity vector. The vector sum of these forces gives the current plume trajectory.

ambient turbulent intensity vertical ambient density gradient The first three of these groups are vector quantities that help define the forces shown in Figure 5.1. The last two groups help define ambient weather conditions.

5.2. Momentum and Buoyancy Once a release reaches atmospheric pressure (at the leak or hole for a subsonic release or at the expanded jet position for a choked-flow release), the initial jet momentum, or thrust, will dominate the flow behavior. The initial densimetric Froude number, FrD, is a ratio of momentum to buoyancy forces in a release (a type of Richardson number). Papanicolau and List (1988), in study of buoyant jets have found momentum jet behavior buoyant plume behavior so the transition from momentum to buoyancy-dominated behavior occurs is in the range of 1.1 • Fro to 5.6 • Fro jet-diameters along the plume trajectory. In

neutral-density releases, Fro = °°, and buoyancy is not important. In very buoyant releases, Fro is on the order of one. Upstream from the momentum/buoyant transition region (;c < 1.1 • D • Fro), linear growth of the plume diameter and linear decay of the jet velocity and concentration will occur as ambient air is entrained into the plume. The trajectory of the jet will continue in the direction of its initial orientation during this stage and the plume will behave very much like a free jet discharging into a quiescent fluid. As the jet velocity decreases, buoyancy forces can show increasing effects on the plume behavior. Buoyancy effects in a plume become evident where changes are seen in the plume trajectory, or where the average plume diameter and concentration are no longer a linear function of plume travel. Buoyancy forces in a plume are parallel with the gravity vector, and are upwards or downward, respectively, for lighter-than-air or heavier-than-air gases, vapors, or aerosols. The magnitude of this force is proportional to the plume density defect given by (pj - poo)/poo. Buoyancy effects become dominant in a plume at distances x > 5.6 • D • Fro. In cases such as low velocity combustion stack gases or cooling tower plumes, buoyancy forces can dominate during the entire period of plume evolution. With very hot gases, such as with combustion products from a fire or flare, the plume trajectory is also dominated by buoyancy. In such a plume the initial density ratio (pj - poo)/poo, can be effectively quantified by

where HIV is the ratio of the rate of sensible heat release to the volumetric flow rate of combustion products (USEPA, 1988). The thermodynamic properties of air are used in this relation. H is the sensible heat release contributing to heating the plume. It is the difference between the heat of combustion and the radiated heat from the flame. Aerosols, consisting of liquid droplets or solid particles, will also affect the bulk density and the buoyancy of a plume. If the aerosol is composed of small particles (generally 5 jiim or less in diameter), the aerosol will move with the vapor flow, although deposition and diffusion to solid surfaces can occur. With larger particles, gravitational settling will be more significant. More detailed information on aerosol behavior is discussed by Hinds (1982).

5.3. The Effect of Wind and Ambient Turbulence An arbitrary jet release can be at any radial and azimuthal angle with respect to the wind. As the jet progressively dilutes, the tendency is for the wind to bend the jet towards the downwind direction. There are two contributions to this

bent-over region from the ambient wind. The first arises from entrainment of downwind flowing ambient air into the plume, so that total jet momentum gradually tends to the downwind direction. The second contribution is the dynamic pressure force of the wind at the boundary of the jet. This arises because there is a slightly higher dynamic pressure on the upwind side of the plume compared to the lee side. This forces an additional bending of the plume and also initiates internal plume circulation consisting of two counterrotating vortices within the body of the plume as illustrated in Figure 5.2. These vortices are parallel to the curved plume trajectory and enhance the mixing rate in a cross-flowing jet. In a stack release at high wind speeds and lower jet velocities, a low pressure region can develop on the lee side of the stack and the plume can be drawn directly into this wake region. The resulting stack downwash can limit plume rise and result in higher concentrations of pollutant at the ground than expected. In stack releases where this is a problem, a skirt is sometimes added around the

top view

WIND

side view

Figure 5.2. Formation of a vortex pair in a jet discharging into a crosswind. The vortices are shown from both a top and side view. The drawing is idealized. In an actual case the paths of the vortices are often unstable and vary randomly in both time and space.

stack cylinder to prevent the pollutant from traveling directly to ground level in the stack wake. In dilution, the velocity and density of a plume tend toward ambient levels. Eventually, the plume dilution is dominated by passive dispersion. With heavier-than-air releases, it is possible for an elevated plume trajectory to descend to the ground. The vertical forces associated with the plume density and the downward plume velocity will tend to spread the cloud laterally at touchdown. The remaining horizontal cloud velocity will carry the plume further downstream along the ground as it is dissipated by surface friction. A low-momentum heavier-than-air cloud will eventually result. Closed-form equations for predicting the effect of winds on jets and plumes on a plume trajectory are discussed by G. A. Briggs in Randerson (1984), and are implemented in a number of basic dispersion models. With more complicated flow geometries and thermodynamic relations, integral equations that track conserved quantities (mass, momentum, energy) along a curved plume trajectory can be more appropriate for estimating plume dilution and trajectory (Ooms, 1972) than closed-form approximations. A number of numerical computer models use this approach.

6 Low-Velocity Dense-Gas Releases

The release of negatively buoyant, heavier-than-air-gases at ground-level can lead to complications in a dispersion analysis. High molecular weight, low temperatures, aerosol formation, and chemical transformations can all lead to heavier-than-air clouds. Physical processes in dense gas dispersion can be significantly different from passive neutral-density releases, and can lead to higher downwind concentrations. A dense-gas cloud can be split up into several regions that depend on the dominant dispersing mechanism. With increasing distance from the source these include (1) a source specification, (2) a cloud slumping region near the source, (3) a stably-stratified flow region, and (4) a passive dispersion region. These regimes are illustrated in Figure 6.1. More detailed descriptions of heavy-vapor flow are given by Puttock et al. (1983) and McFarlane(1990).

6.1. Source Specification The source specification can include the dimension and mass flux from an evaporating or boiling liquid pool. Alternately, it may be the flow from a ground-level low-momentum gas release, or a transition point where an elevated dense-gas release has descended to the ground.

6.2. Source Area Region Very near the source, horizontal spreading or slumping of the gas cloud at the ground predominates. This slumping cloud significantly modifies the ambient wind field. The horizontal spreading of the cloud along the ground is driven by gravity in much the same way as a spreading liquid spill, except the gas density difference relative to air is usually 2 : 1 or 3 : 1 rather than near 1000 : 1 as for a liquid spill in air. The extent and rate of the cloud spreading depends on the

WIND Dense-Vapor Flow

Source Area Region Vapor Cloud Spreading Vapor Cloud Slumping Suppressed Mixing

Stably-Stratified Region Vertical Cloud Density Gradient Present Turbulent Mixing Rate is Reduced Gravity-Driven Slumping Continues

Passive Dispersion Region Low Concentration Levels No Remaining Cloud Density Effects

Figure 6.1. Mechanisms of dilution and transport in a low-velocity dense-gas release.

initial cloud depth, volume, and density. Surface roughness can slow the rate of cloud spreading, and, in combination with the velocity of the slumping cloud, can sometimes enhance the turbulent mixing at the cloud-air interface.

6.3. Stably-Stratified Region The negative vertical density gradient at the top of a heavy-gas cloud inhibits turbulent mixing and reduces the cloud dilution rate. The mixing rate itself is a function of the velocity and density gradients through the cloud-air interface (usually expressed as a Richardson number) and can be 100 to 1000 times less than the dilution rate of a neutrally buoyant cloud released under similar conditions. Very near the source, air-cloud mixing is often suppressed to the point where it can be neglected. Dispersion in this stably-stratified regime can also be sensitive to heat transfer effects from the ground, local obstructions, and topography.

6.4. Passive Dispersion Region As a heavy-gas cloud is carried downwind, concentration levels will gradually decrease and the temperature and density profiles within the cloud will eventually be indistinguishable from the original, unperturbed, values found in the ambient atmosphere. In this final region of dispersion, the presence of the pollutant does not alter the wind field and further mixing can be treated as passive dispersion.

7

Passive Dispersion

Two source conditions need to be met for an atmospheric release to be passively dispersed. These conditions are that (1) the source release velocity is near or below the wind velocity (usually within a factor of 2), and (2) the density difference between the released material and the atmosphere is negligible (usually within ±2% ). In this situation the source flow will not significantly alter the existing wind field, so downwind travel and dispersion of the pollutant will be due only to ambient turbulence and the wind velocity. All atmospheric releases eventually become dilute, with negligible differences in density and velocity from that of ambient air. This means that all releases can be treated as passive dispersion after sufficient downwind dilution.

7.1. The Mechanics of Turbulent Dispersion In a passive release, the dilution problem consists of relating turbulent wind velocity fluctuations to the characteristics of the dispersion. In engineering models of passive atmospheric dispersion, this is accomplished by defining atmospheric dispersion coefficients (that relate atmospheric conditions to the rate of growth for a dispersing plume) based on statistics of the fluctuating turbulent velocities and averaging over many random fluid element trajectories. Since the turbulent eddies associated with the fluctuating velocities in our problem cover a range of sizes from less than a millimeter to several kilometers, the dispersion coefficients are not material properties, but remain functions of atmospheric conditions and the dimensions of the local pollutant cloud size. Turbulent eddy motions that are of smaller scale than the cloud size contribute to dispersion, while eddies of greater size tend to convect the entire pollutant cloud. Most simple engineering models for passive atmospheric dispersion are developed from one of two approaches, using either statistical relations or

gradient-transfer approximations. The Gaussian plume model uses statistical relations between the intensity of wind fluctuations and the rate of cloud growth. Gradient-transfer models assume that turbulence causes a net transport of material down the gradient of pollutant concentration, so the problem can be defined through a diffusion equation. In application to similar problems, both the Gaussian plume model and gradient-transfer model produce similar results. More complicated passive dispersion models are both currently available and under development. All use variations on the statistical Gaussian model-type approach, solutions of the diffusion equation, or a combination of both methods. Many models also include similarity scaling (non-dimensionalization) arguments. Since in passive dispersion the pollutant does not affect the wind field, the total concentration resulting from multiple sources can be represented by superposition of dispersion results from the individual sources. Distributed sources can be represented as a summation or integration over many point pollutant sources of equivalent total strength. This characteristic is often used in routine estimates of dispersion from industrial sites, where the effects of each individual passive source can be summed to find the cumulative concentration field (USEPA, 1987).

7.2. Passive Dispersion from Elevated Releases Far from the ground, wind and turbulent velocities are nearly constant with height. In this situation the atmospheric dispersion coefficients Cfy and Gz are also constant with height. The Gaussian plume model is often appropriate for use in this situation. For a continuous point source of strength, q (mg/s), this is

where c (mass/volume) is concentration, h (length) is the height above the surface, u (velocity) is the wind speed, y (length) is the crosswind distance, and z (length) is the height above the surface. The factors Oy and O^ are the spatial standard deviations (length) of the plume cross-section in they and z directions, respectively. The source is located at (jc, y, z) = (O, O, h). In the above Gaussian plume model equation, the (z + h) term is intended to account for a "reflective" boundary at the ground surface by using a virtual point source located below the ground at a position (jc, y, z) = (O, O, -h). A similar term (z-h- 2zt) is sometimes included to account for plume reflection from an inversion height, z/, or even additional terms at greater downwind distances to account for multiple reflections.

The Gaussian plume model predicts a plume with a Gaussian profile in the vertical and horizontal directions. The vertical and horizontal plume widths, Gy and GZ, may be defined as functions of downwind distance, ;c, and the PasquillGifford stability class (USEPA, 1987), or, based on Taylor (1921), as a function of travel time from the source, t = x/u, the variance in the velocity, GW, and the Lagrangian integral time scale, £L, where, in the vertical direction,

a>(0 = aU,[^- 1+exp^J and a similar equation is valid for the crosswind direction. In a simpler form with the same asymptotic behavior, 0Z(t) = Owt/[l+(t/tL,w)/2]

where the actual source size is small, or the distance of interest is far from the source, the point source assumption is usually adequate. Where the approximation is not suitable, the model can be corrected to a finite source size using an imaginary virtual source located some distance upwind from the actual source. The plume width and source width are constrained to match at the actual source coordinates. Another way to handle arbitrary source geometry is through the gradient-transfer (or diffusion equation) approach. With elevated releases, the highest ground-level concentrations do not occur in calm, stable weather conditions, but during neutral or unstable weather when mixing rates are increased. This problem is illustrated in Figure 7.1. Height

Stable Weather Conditions

Downwind Distance Height

Unstable Weather Conditions

Downwind Distance Figure 7.1. Comparison of two elevated pollutant releases under different meteorological conditions. The release under stable weather conditions persists for a greater downwind distance, but concentrations in the elevated plume do not reach the ground. Dilution is more rapid for the release under unstable weather conditions, but the resulting concentrations at ground level are higher than for the calm weather, stable release case.

Determining the actual maximum expected ground level concentration that would occur in a given elevated release scenario usually involves carrying out calculations for a range of meteorological conditions.

7.3. Near-Ground Passive Dispersion Near the ground, wind shear (change in velocity with height) can be important. In addition, turbulent velocity fluctuations in the vertical plane are restricted by the presence of the ground, and become a strong function of height. The gradient-transfer approach allows the incorporation of these effects into the solution of this problem. Appropriate functions for wind speed and diffusion coefficients are used within either mathematical or numerical solutions of the diffusion equation. These solutions are more often based on boundary-layer similarity parameters rather than on the simpler Pasquill-Gifford stability class information. A summary of these applications is discussed by Gryning et al. (1987).

7.4 Dispersion Averaging Times Concentration estimates made with a dispersion model are specific to the averaging time for which the dispersion coefficients were developed. For instance, the Gaussian dispersion coefficients, Cfy and az, are dependent on the standard deviations in velocity, av and Gw, and the Lagrangian integral time scales, tL,v and tL,\v. The effect of receptor averaging time on av and cw (and thus Cy and az) is weak at time periods longer than both and (greater than a few minutes). Adjustments to model predictions in this range of averaging times is discussed by Hanna et al. (1982). At receptor averaging times shorter than both fL,v and JL,W, there is increasing variability in both measured and predicted concentration values. Statistical methods are required in interpreting these short-term concentration values.

8 Complex Flow Considerations

Most dispersion cases discussed thus far are applicable in simple, flat terrain where near-constant weather conditions are assumed over the release period. The following are cases that need consideration in special situations, where local effects or changes can be important in an analysis.

8.1. Building Wakes and Stack Downwash As wind blows across buildings, hills, or structures, a low-pressure separatedflow region can develop on their downwind side. Plumes traveling adjacent to such a structure can be drawn into the wake region. This is illustrated in Figure 8.1. While this effect can improve turbulent mixing, it also brings elevated plumes back down to the ground where people, and possibly building ventilation intakes, are present.

WIND

plume

lowpressure wake region Figure 8.1. Building wake influence on an elevated plume.

The effect can also occur with stack releases at high wind speeds and low stack exit velocities. Under these conditions, the pollutant plume can be drawn into the wake region of the stack itself. The resulting stack down wash can reduce the effective release height, with pollutant sometimes traveling directly to ground level within the downwash region (R. P. Hosker in Randerson, 1984).

8.2. Gravity-Driven Flows and the Effects of Terrain All of the discussion of meteorology and dispersion in this primer has focused on flat terrain. A flat terrain analysis usually works well when the depth of the pollutant cloud is the same as, or greater than, the height of the roughness elements on the ground. When a dispersion analysis is extended into complex terrain where this criteria is not met, the problem can be much more complicated. However, the two dominant transport and dilution mechanisms of mechanical turbulence and vertical density stratification are still important. In complex flow situations, heavier-than-air fluids tend to flow downhill and remain in low spots. Heavier-than-air gases will tend to go around obstacles, rather than over them. Turbulence in complex flows is initiated wherever there is a gradient in fluid velocity and will tend to locally increase the fluid mixing rate. Turbulence can arise at any solid interface, or at a shear layer between two streams flowing at different velocities or in different directions. For the turbulent, obstructed flow of a heavy-gas cloud through an industrial environment, the detailed dispersion problem can be extremely complicated, and is necessarily simplified in analysis.

8.3. Aerosol Rainout Accidental releases can include aerosol clouds, usually consisting of liquid droplets, vapor, and air. The aerosols can originate from multiphase releases, combustion or reaction products, or in condensation of pollutants or water vapor after mixing with air. When the aerosol particles are small (5 u,m in air or less), they will follow the fluid motion of the plume with little settling due to gravity. Differences in the bulk cloud trajectory and the individual particle trajectories can become significant only when the velocity of the settling aerosol particles is much greater than the downward velocity or slumping of the bulk cloud. Under such conditions, the liquid aerosol fraction of the release can "rain-out" of the cloud to form an evaporating liquid pool.

8.4. Fanning Plumes and Subsidence In simple dispersion scenarios, we assume steady weather conditions (constant wind speed, stability class, etc.), Sometimes releases and dispersion can occur where changes in weather over time can significantly affect downwind concentrations and the potential for exposure. For purposes of hazard analysis, one of the most significant of these cases is for an elevated or buoyant release in nighttime stable meteorological conditions. With this type of release, a narrow, elevated plume can extend a considerable distance downwind, and under stable weather conditions would present little potential for exposure at ground level. However, at dawn, a mixing layer will begin to form and grow in depth (as shown in Figure 2.5). As the morning progresses and the mixing depth grows past the plume height as shown in Figure 8.2, the elevated plume is brought to ground level by the subsidence within the convective boundary layer. This transient event can result in ground-level concentrations much greater than expected from a simple analysis of steady weather conditions. A similar situation can arise for an elevated release near the shoreline of a large body of water with an offshore-to-onshore breeze. In this case, during the morning period, a thermal internal boundary layer can develop over land. This well-mixed boundary layer grows in height with distance from the shoreline. At the onshore position where the elevated plume intercepts the surface boundary layer, the elevated pollutants will be drawn to ground level. WIND

WIND

morning inversion height growth

Stable Plume at Dawn

Fanning Plume in Morning

Figure 8.2. Generation of a "fanning" plume from an elevated release in the transition from nighttime stable conditions to daytime convective conditions.

9 Hazard Evaluations

The primary hazard concerns of accidental vapor releases include chemical toxicity and flammability.

9.1. Chemical Toxicity Acute health effects of chemical exposure can include irritation, narcosis, asphyxiation, sensitization, blindness, organ system damage, and death. The severity of these effects varies both with concentration levels and the duration of exposure. There is a great deal of variation in individual sensitivity to chemical exposure, and a general dearth of data on toxic responses to human exposure. Much of the available data is based on studies of laboratory animals. This data is extrapolated from observed effects in animals to anticipated effects in humans. Many established criteria are available for judging toxic effects. Some of these criteria are concisely summarized in Table 9.1, and are discussed in more detail in the Guidelines for Safe Storage and Handling of Toxic Materials (AIChE/CCPS, 1988). The reader is encouraged to consult this book and the other cited references (Rusch, 1993; Fairhurst and Turner, 1993; ACGIH, 1992; FEMA, 1989; NRT, 1987) for more complete definitions, and to find the specific toxicity limits for the chemicals of interest. The concentration-based levels in Table 9.1 define a concentration level, an exposure duration, and a defined effect on a specified population. The Dangerous Toxic Load (DTC) concept combines the effect of concentration level and exposure duration in a Probit distribution. This is useful in accounting for the non-linear effects of varying exposure duration and concentration level.

Table 9.1

Available Acute Toxicity Criteria and Their Basis of Definition.

measure

organization population

time

criteria below which:

ERPG-I

AIHA

nearly all individuals

lhr

[exposure] ... without experiencing other than mild transient adverse health effects or perceiving a clearly defined objectionable odor

ERPG-2

AIHA

nearly all individuals

1 hr

[exposure] ... without experiencing or developing irreversible or other serious health effects or symptoms that could impair their ability to take protective action

ERPG-3

AIHA

nearly all individuals

1 hr

[exposure] ... without developing life-threatening health effects

IDLH

NIOSH

healthy adult 30 min escape without loss of life or irreparable organ system damage, including acute effects which could impair escape (severe eye irritation) male workers

EEGL

NRC

DoD

SPEGL

NRC

general public

1 to 24 hr

may have transient irritation, central nervous system effects; system effects; no impairment in performance of a task

ItO

criteria are the same as EEGL

24 hr 15 min, 4 times/ day

acute effects such as irritation and narcosis. Not a separate criteria from the 8 hr workday and 40 hr workweek TLV-TWA

TLV-STELACGIH

all workers

PEL-STEI .OSHA

all workers

15 min criteria are the same as TLV

DTL

general population

dose/ limit for fatalities responsea

HSE

Notes: ERPG, Emergency Response Planning Guidelines; IDLH, Immediately Dangerous to Life or Health; EEGL, Emergency Exposure Guidelines; SPEGL, Short-Term Public Emergency Guidance Levels; TLV-STEL, Threshold Limit Value Short-Term Exposure Limit; TLV-TWA, Threshold Limit Value Time Weighted Average; PEL, Permissible Exposure Limits; DTL, Dangerous Toxic Load. AIHA, American Industrial Hygiene Association; NIOSH, National Institute for Occupational Safety and Health; NRC, National Research Council / National Academy of Sciences; DoD, Department of Defense; ACGIH, American Conference of Industrial Hygienists; OSHA, Occupational Safety and Health Administration; HSE, Health and Safety Executive of Great Britain.

9.2. Flammability Flammable chemicals in air will ignite and burn only within mixture limits defined by the Lower Flammability Limit (LFL) and the Upper Flammability Limit (UFL). Since flammability is governed by instantaneous concentration levels, evaluation criteria for flammability in accidental releases are often set at a fraction of the LFL, such as LFL/2 or LFL/4.

10 Computer Models

There are a wide number of public-domain and proprietary models available for estimating the effects of accidental chemical releases. Evaluation of a selection of these models against field dispersion data (Hanna and Chang, 1992a, b) has shown that the best of these models can predict downwind concentrations relative to experimentally measured concentrations within a factor of two in about 50% of model/data comparisons. Given a model with this degree of accuracy, the validity and usefulness of predicted results will depend on the applicability of the model to the particular release scenario and the selected model input parameters. Examples in applying a range of models to specific release scenarios have been addressed in a number of reports and guideline documents (USEPA, 1993; USEPA, 1991; AIChE /CCPS, 1989; AIChE/CCPS, 1987). Brief descriptions of model features are given in each of the above references. These models and descriptions will become outdated with time, of course, as existing models are revised and new models are developed. Additional information on the features and availability of accidental release air dispersion modeling software, as well as other environmental-related software, are periodically published in an Environmental Software Survey (Johnson, 1992,1993).

References

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