v°/EPA
United States
Environmental Protection
Agency
Office of Air Quality
Planning and Standards
Research Triangle Park. NC 27711
EPA-454/R-93-001
January 1993
Air
CONTINGENCY ANALYSIS
MODELING
FOR SUPERFUND SITES
AND OTHER SOURCES
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EPA-454/R-93-001
CONTINGENCY ANALYSIS
MODELING
FOR SUPERFUND SITES
AND OTHER SOURCES
U.S. Environmental Protection Agency
Region 5, Library ;PL-12J)
77 West Jackson Boulevard, 12th Floor
Chicago, IL 60604-3590
Office Of Air Quality Planning And Standards
Office Of Air And Radiation
U. S. Environmental Protection Agency
Research Triangle Park, NC 27711
January 1993
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This report has been reviewed by the Office Of Air Quality Planning And Standards, U. S. Environmental
Protection Agency, and has been approved for publication. Any mention of trade names or commercial
products is not intended to constitute endorsement or recommendation for use.
EPA-454/R-93-001
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TABLE OF CONTENTS
SECTION
1.0 INTRODUCTION AND EXECUTIVE SUMMARY 1-1
2.0 IDENTIFICATION OF A REPRESENTATIVE RANGE 2-1
OF SOURCE TERMS
2.1 Choice of Source Terms 2-1
2.1.1 Telephone Survey 2-1
2.1.2 Outcome of Telephone Survey 2-1
2.2 Range of Possible Accident Scenarios 2-3
2.2.1 Vessel Containing a Liquid 2-9
2.2.2 Accident Scenarios Specifically Relevant to 2-12
Superfund Sites
3.0 COMMUNICATIONS AND HOW TO USE THIS REPORT 3-1
3.1 Concerns Expressed During the Telephone Survey 3-1
3.2 Communications/Flow Charts , .3-1
3.2.1 Accident Sequence Definition- General Discussion 3-1
3.2.2 Accident Sequence Definition - 3-9
Examples for Superfund Sites
3.2.3 Accident Sequence Definition - 3-12
Examples for "Other" Sites
3.2.4 Hydrogen Fluoride - an Interesting Case 3-14
3.3 Other Issues That Must be Addressed 3-15
3.4 Conclusion 3-17
4.0 BRIEF SURVEY OF AVAILABLE DISPERSION MODELS 4-1
4.1 Available Models 4-1
4.2 Why Atmospheric Dispersion Models Give Different Results 4-2
4.3 Choice of Leak Size 4-3
4.4 Generic Issues in Atmospheric Dispersion Modeling 4-4
4.4.1 Atmospheric Stability Categories and Windspeed 4-5
4.4.2 Height at which Windspeed is Measured 4-7
4.4.3 Wind Direction 4-8
4.4.4 AmbientTemperatures 4-8
4.4.5 Relative Humidity 4-8
4.4.6 Surface Roughness Length 4-8
4.4.7 Toxicological Levels of Concern 4-8
4.4.8 Averaging Times 4-10
4.4.9 Aerosolizatton 4-11
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TABLE OF CONTENTS (Continued)
SECTION PAGE
5.0 SPILLAGE OF LIQUIDS ONTO SURFACES 5-1
5.1 Spillage of a Liquid with Above Ambient Boiling Point 5-1
into a Diked Area - Acetone
5.1.1 Description of Scenario 5-1
5.1.2 Rate of Release of Liquid from Vessel 5-1
5.1.3 Behavior of Pool on the Ground 5-2
5.1.4 Calculation of Evaporation Rates 5-3
5.1.5 Equations in TSCREEN 5-5
5.1.6 Duration of Evaporation 5-6
5.1.7 Density of Mixture 5-6
5.1.8 Input to SLAB 5-7
5.1.9 Input to DEGADIS 5-10
5.2 Spillage from Drum 5-15
5.3 Spillage of HF at 60°F 5-15
5.3.1 Description of Scenario 5-15
53.2 Calculation of Release Rate . 5-16
5.3.3 Atmospheric Dispersion Model 5-17
5.4 Spillage of Cryogenic Liquid into a Diked Area 5-17
5.4.1 Choice of Example - Release Rate a Function of Time 5-17
5.4.2 Input to SLAB 5-19
5.4.3 Input to DEGADIS 5-21
5.5 Spillages onto Water 5-23
5.6 Additional Considerations 5-23
5.6.1 Heat Sources 5-23
5.6.2 Spreading Pool 5-24
5.63 Advanced Modeling 5-24
6.0 JETS CONTAINING LIQUID AND VAPOR 6-1
6.1 Emission Rate Formulae - Theory 6-1
6.1.1 Gas Which Partially Condenses on Depressurization 6-2
6.1.2 Saturated Liquid from Pressurized Storage 6-6
6.13 Subcooled Liquid from Pressurized Storage 6-8
6.1.4 Flow Chart 6-10
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TABLE OF CONTENTS (Continued)
SECTION PAGE
6.2 HF at Elevated Temperature and Pressure 6-10
6.2.1 Description of Scenario 6-10
6.2.2 Calculation of Release Rate 6-10
6.2.3 Other Characteristics of the Source Term 6-12
6.2.4 Input to SLAB 6-14
6.2.5 Input to DEGADIS 6-17
6.3 One Ton Cylinder of Chlorine . 6-22
6.3.1 Release Description 6-22
63.2 Input to SLAB 6-22
633 Input to DEGADIS 6-25
6.4 150 Ib Cylinder of Chlorine 6-28
6.5 Miscellaneous 6-29
6.5.1 Jet Directed Downward 6-29
6.5.2 Jet Emerging from a Long Pipe 6-29
6.5.3 Orifice Shape 6-30
7.0 VAPOR JET RELEASES 7-1
7.1 Vapor Release Formulae - Theory 7-1
7.1.1 Release Rate Estimates: Leaks of Gas Directly 7-2
from a Reservoir
7.1.2 Release Rates: Leaks of Gas from a Pipeline 7-7
Attached to a Reservoir
7.1.3 Flow Chart 7-10
7.2 Chlorine Vapor Release 7-10
7.2.1 Description of Scenario 7-10
7.2.2 Input to SLAB 7-12
7.23 Input to DEGADIS 7-15
73 Intermediate Sized Hole in the Vapor Space 7-18
8.0 INSTANTANEOUS (PUFF) RELEASES 8-1
8.1 Description of Release 8-1
8.2 Input to SLAB 8-1
83 Input to DEGADIS 8-4
8.4 Small Cylinder of Chlorine 8-7
ill
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TABLE OF CONTENTS (Continued)
SECTION PAGE
9.0 BUOYANT PLUME RELEASES 9-1
9.1 Introduction 9-1
9.2 Incinerator Plume 9-1
9.2.1 Background 9-1
9.2.2 Specification of Source Term for a Buoyant Plume 9-2
9.23 Example of Source Term 9-7
9.2.4 Atmospheric Dispersion Analysis 9-8
9.3 Fires at Ground Level 9-9
9.3.1 Burning Pool 9-9
9.3.2 Burning Tires 9-13
9.3.3 Atmospheric Dispersion Modeling 9-18
10.0 VAPOR RELEASES FROM MECHANICALLY DISTURBED SOIL 10-1
10.1 Introduction 10-1
10.2 Equations for Emission Rates 10*3
10.2.1 Average Long-Term Emission Rate 10-3
10.2.2 Average Short-Term Emission Rate 10-3
10.23 Simplified Average Short Term Emission Rate 10-5
10.2.4 Worst Case (Instantaneous) Emission Rate 10-5
10.3 Example 10-6
10.3.1 Description of Problem 10-6
10.3.2 Total Emissions Potential for Site 10-6
1033 Average Short-Term Emission Rate 10-6
10.4 Atmospheric Dispersion 10-7
11.0 REFERENCES 11-1
IV
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LIST OF APPEND [CES
APPENDIX A EXAMPLE AND INTERPRETATION OF DEGADIS OUTPUT
APPENDIX B EXAMPLE AND INTERPRETATION OF SLAB OUTPUT
APPENDIX C INTRODUCTION TO BUOYANT PLUME RELEASES
APPENDIX D SIMPLIFIED SOURCE TERMS AND DENSITY CALCULATIONS
FOR FLASHING LIQUID RELEASES
APPENDIX E LIST OF THOSE CONTACTED DURING THE
TELEPHONE SURVEY
APPENDIX F SAFER ANALYSIS OF SCENARIOS FOR
SUPERFUND SITES AND OTHER SOURCES
APPENDIX G HGSYSTEM
APPENDIX H CALCULATION OF MOLECULAR DIFFUSIVITY
FROM BASIC PRINCIPLES
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LIST OF TABLES
TABLE . PAGE
4-1 Meteorological Conditions Defining Atmospheric Stability Categories 4-5
4-2 Relationship Between Atmospheric Stability Category,
Surface Roughness Length z0 and Monin-Obukhov Length L 4-6
4-3 Surface Roughness for Uniformly Distributed Ground Covers 4-9
5-1 SLAB Input - Spillage of Acetone into a Diked Area 5-8
5-2 DEGADIS Input - Spillage of Acetone into a Diked Area 5-11
5-3 Evaporation Rates as a Function of Time 5-19
5-4 SLAB Input - Spillage of Refrigerated Chlorine into a Diked Area 5-20
5-5 DEGADIS Input - Spillage of Refrigerated Chlorine into a Diked Area 5-22
6-1 SLAB Input - Flashing Liquid Release of HF 6-15
6-2 DEGADIS Input - Flashing Liquid Release of HF 6-18
6-3 SLAB Input - Flashing Liquid Release of Chlorine from a One Ton Cylinder 6-23
6-4 DEGADIS Input - Flashing Liquid Release of Chlorine 6-26
from a One Ton Cylinder
7-1 SLAB Input - Vertical Vapor Release of Chlorine 7-13
7-2 DEGADIS Input - Vertical Vapor Release of Chlorine 7-16
8-1 SLAB Input - Puff Release of Chlorine 8-2
8-2 DEGADIS Input - Puff Release of Chlorine 8-5
9-1 Polycyclic Aromatic Hydrocarbon Emission Factors 9-15
from Open Burning Tires
9-2 Particulate Metals Emission Factors from Open Burning Tires 9-16
9-3 Emission Factors for Organic Compounds from Open Burning of Tires 9-17
LIST OF FIGURES
FIGURE PAGE
2-1 Scenario Visualization 2-4
2-2 Some Possible Releases at Super fund Sites 2-7
3-1 Scenarios Identification Flow Chart 3-2
6-1 Liquid Droplet Scenarios - Calculation Flow Chart 6-11
7-1 Vapor Release Rate Calculations Flow Chart 7-11
9-1 Example of a Rotary Kiln Incineration System 9-3
10-1 Idealized Excavation Scenario 10-2
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ACKNOWLEDGEMENTS
This report was prepared by Dina Christensen and Geoffrey Kaiser,
Science Applications International Corporation. Jawad S. Touma was
the Technical Representative for EPA. Dr. E. D. Chikhliwala,
EcoChem Technologies, Inc. provided his own time for preparing
Appendix F.
via
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CONTINGENCY ANALYSIS MODELING
FOR
SUPERFUND SITES AND OTHER SOURCES
1.0 INTRODUCTION AND EXECUTIVE SUMMARY
The purpose of this report is to provide information that will help the Environmental
Protection Agency (EPA) develop guidance on contingency modeling for Superfund sites
and other industrial sources. To this end, the possible range of different kinds of accidental
releases of hazardous vapors that might take place at such sites is first reviewed. These
scenarios are then used to illustrate how atmospheric dispersion models, including dense gas
models, should be applied. There is particular emphasis on the collection and calculation
of the input data that is needed for proper application of the models.
EPA has already developed a considerable amount of information on how to calculate the
characteristics of source terms and how to apply various dispersion models. Early guidance
was given in the "Guideline on Air Quality Models"(l) which describes screening and refined
air quality modeling techniques that focus on the six criteria pollutants (particulate matter,
sulfur dioxide, nitrogen dioxide, carbon monoxide, ozone and lead). Subsequently, it was
recognized that there is an increasing need to provide models that specifically address the
impact of toxic air pollutants. Such models deal with both heavier-than-air (dense) and
passive or neutrally buoyant (non-dense) releases.
To meet this need, EPA published "A Workbook of Screening Techniques for Assessing
Impacts of Toxic Air Pollutants"® and then developed the TSCREEN personal computer
system(3) that utilizes concepts found in expert systems to implement the scenarios described
in the workbook. EPA also co-sponsored the development of the DEGADIS refined dense
gas model(4), conducted a statistical evaluation of seven dense gas models using three
experimental programs(S) and published guidance on how to use the DEGADIS, SLAB,
HEGADAS and AFTOX modeis(6). In addition, guidance has been developed on the
modeling of various specific scenarios, including (but not limited to) incineration at
Superfund sites00, the excavation of contaminated soil(8), the air stripping of contaminated
watert9) and the development of contingency plans using air monitoring(10). The purpose of
1-1
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the present work is to provide information that will help EPA develop further guidance that
supplements existing guidance.
In Section 2.0, there is a discussion of the kinds of release scenarios that are of interest at
Superfund and other industrial sites. In order to help determine this, a telephone survey
of interested EPA personnel was carried out. Those contacted are listed in Appendix E.
The following kinds of scenario were frequently mentioned as being of interest:
o a range of accidents involving drums and cylinders, such as leaks, ruptures and
fires
o accidents involving larger vessels that lead to evaporating pools; and
o accidents involving larger vessels containing gases liquified under pressure.
Section 2 goes on to review the types of release scenarios (source terms) that span the range
of interests expressed above. These scenarios are summarized in Figures 2-1 and 2-2.
In Section 3, the subject of communications is discussed. This was also one of the topics
that was raised during the telephone survey, in which the concerns expressed were far from
uniform. However, there does seem to be an underlying thread of concern running through
what was said, namely how can miscommunication between the person requesting the
analysis (the requestor) and the person performing the analysis (the analyst) be avoided?
Put another way, how can these two individuals communicate in such a way that there is a
clear understanding of the scenario that is to be modeled and the information that the
requestor requires? Other concerns raised included how to ensure that the source term is
realistic and the model is used in such a way as to give credible answers. Section 3 is
intended to address these concerns and also to show how this report should be used.
Section 3 addresses the communications problem by means of a flow chart (Figure 3-1)
which is intended to help the requestor and the analyst accurately define the scenario of
interest. The flow chart also directs the reader to specific sections in this report where
various scenarios are discussed in detail, except in those cases where complex physical
phenomena are involved, such as partial aerosolization, in which case the reader is
recommended to seek expert advice.
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Section 3 also summarizes the scenarios that have been developed as examples for the
purposes of the present report. Specifically, for Superfund sites, the following scenarios
have been chosen:
o spillage of a large quantity of acetone onto the ground. This is meant to
represent cases in which a liquid with a boiling point that is high relative to
the ambient temperature, and a corresponding vapor pressure that is less than
atmospheric, spills onto the ground and evaporates
o spillage of a liquid with a high boiling point from a drum
o various accidents involving cylinders, including vapor releases, liquid releases
and large ruptures
o incineration at Superfund sites
o fire involving the spillage of a liquid pool containing contaminated materials
o emissions from burning tires
o emissions from mechanically disturbed contaminated soil; and
o (for completeness) spillages onto water.
Various scenarios have also been chosen for "other" sites. Note, however, that many of the
phenomena discussed for the following scenarios are relevant to scenarios at Superfund
sites:
o spillage of refrigerated chlorine,onto the ground
o flashing liquid jet releases from chlorine storage, leading to scenarios in which
the plume contains both vapor and liquid droplets (aerosol)
o puff releases from chlorine storage
1-3
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o vapor releases of chlorine driven by high pressure from a storage vessel; and
o some scenarios involving hydrogen fluoride, which is an interesting case in
which complicated thermodynamic and physical properties mean that there is
a particularly wide range of possible source terms, depending on the way in
which the material is released.
Section 3 also provides a check list of items that should be discussed by the requestor and
analyst. These include what the output of the model should be, the choice of toxicological
levels of concern and meteorological considerations that may affect the atmospheric
dispersion.
Section 4 begins with a brief review of available atmospheric dispersion models. Of these,
two were chosen for use in this report, DEGADIS and SLAB. The choice was somewhat
arbitrary. The basis included such factors as the resources available for this study, the
availability of the models and the familiarity of the authors with them. For cases where the
use of the above models is not appropriate (e.g. when the initial source term is not denser
than air) the use of EPA's TSCREEN model is discussed. Subsequently, an arrangement
was made with the authors of the proprietary computer model, SAFER, who ran a limited
number of scenarios as described in Appendix F. Finally, two scenarios were run with the
relatively new model HGSYSTEM, see Appendix G.
Section 4 also discusses issues that are common to all dispersion modeling. These include,
for example, the choice of surface roughness length, the choice of toxicological Levels of
Concern, the weather conditions and averaging times.
Sections 5 through 10 discuss in detail how several scenarios should be modeled in SLAB
and DEGADIS. The expectation is that, by following detailed discussions of the inputs to
each of the computer models, the reader will come to understand what is required to
produce a credible model of a particular scenario. For example, he/she will learn that, even
with widely used models, a great deal of work is required to cast the input into an
appropriate form and that, in some cases, a considerable amount of technical knowledge
about the input data is required. The reader should note that Sections 5 through 10 are not
organized in the sequence of the list of scenarios described above. Instead, they are
organized in groups for which the physical and chemical phenomena are similar:
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o section 5 - vapors evaporating from liquids spilled onto the ground
o section 6 - flashing liquid jets that result in an initial airborne release
containing both vapors and liquid droplets (aerosols)
o section 7 - vapor releases driven out of a vessel by high pressure
o section 8 - puff releases
o section 9 - buoyant plumes; and
o section 10 - emissions from mechanically disturbed soils.
As noted above, Section 5.0 is concerned with the spillage of liquids onto surfaces from
which evaporation subsequently occurs. The first case is that of the spillage of acetone into
a diked area. This scenario has been chosen because it serves as a good introduction to the
topic of evaporating pools, which are the likely mode of release for many high boiling point
liquids at Superfund Sites. A similar case considered is that of the small scale spillage from
a drum. The principal difference from the large scale spill is the relative smallness of the
quantity released.
Another case considered in Section 5 is that of the spillage of hydrogen fluoride from a
storage vessel at an industrial or "other" site. This case is chosen because the information
needed to develop the input data for the computer models is more elaborate for HF.
Finally, the spillage of refrigerated chlorine into a diked area is discussed as an introduction
to the modeling of spillages of cryogenic liquids.
Section 5 continues with a brief "discussion of spillages onto water. These are not treated
in detail but are included for completeness: the most important phenomena are summarized
and the reader is referred to appropriate references. Chapter 5 concludes with discussions
of some additional issues relating to evaporating pools for which this project did not allow
sufficient resources. These include additional sources of heat, spreading pools and advanced
numerical modeling techniques.
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Section 6 is devoted to the subject of flashing liquid jets in which the initial source term
consists of a mixture of vapor and liquid droplets that is released directly from the leaking
vessel or pipework. The first example given is that of a release of HF from an orifice of
diameter 1/2" in a vessel containing HF at elevated temperature and pressure. This is a
release that is very much characteristic of those expected at "other" industrial sites.
However, it is useful to begin with it because, by carefully considering it, the reader will
become familiar with many of the issues that must be addressed if such scenarios are to be
modeled realistically.
The HF example is followed by consideration of a flashing liquid release from a one ton
cylinder of chlorine at ambient temperature. Such one ton cylinders are commonly found
at places such as water treatment facilities. Finally, the specific example of a cylinder
containing 150 Ib of chlorine is examined as being particularly pertinent to the sort of case
that might need to be examined at a Superfund site.
Section 7.0 is devoted to a discussion of releases from the vapor space of a vessel from
which the expected release will be pure vapor. The specific example of chlorine storage is
chosen.
Section 8.0 considers puff releases. The reader is shown how to model the catastrophic
failure of vessels. The specific examples chosen are those of 1 ton and 150 Ib chlorine
cylinders.
Section 9.0 introduces the subject of plume rise. Three examples are chosen, a) the plume
from an incinerator at a Superfund site, b) the plume from a burning pool of liquid
containing toxic materials and c) a stack of burning tires.
Chapter 10 is devoted to a brief discussion of the issues involved in modeling the plume
released when contaminated soil is accidentally disturbed.
Various backup appendices are provided. Appendix A gives an example of an output from
DEGADIS and Appendix B gives an example of an output from SLAB. Appendix C
consists of an introduction to the important elements that must be considered when
calculating the atmospheric dispersion of buoyant plumes. This is meant to be an
introduction for the reader who is interested in pursuing some of the more sophisticated
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issues of plume rise, such as the suppression of lift-off of a buoyant plume initially on the
ground and the termination of plume rise. These issues are often not considered in the
simpler models. Appendix D contains a discussion of some simplified methods of
calculating the densities of mixtures of air and aerosols. Appendix E contains the list of
those contacted during the telephone survey of EPA personnel. Appendix F contains the
outputs of SAFER analyses, which were kindly provided by Dr E.K. Chikhliwala of
EcoChem Technologies, Inc. The subject of Appendix G is the computer model
HGSYSTEM. Finally, Appendix H shows how to calculate molecular diffusivity, a quantity
that is required for the estimation of the rate of evaporation of a pool lying on the ground.
In conclusion, the reader should note that the emphasis in this report is on the source term
and in particular how to prepare inputs for the computer models that credibly represent the
scenarios in question. The SLAB, DEGADIS and HGSYSTEM model Users' Guides
adequately describe the model assumptions and output. For further information on the
proprietary model SAFER, the reader should contact EcoChem Technologies.
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2.0 IDENTIFICATION OF A REPRESENTATIVE RANGE OF SOURCE TERMS
2.1 Choice of Source Terms
2.1.1 Telephone Survey
In order to identify a range of source terms that might be useful to potential readers, a
telephone survey was conducted, encompassing several persons within EPA who had
expressed an interest in this project or who were thought to have relevant skills and
expertise. The people who were contacted are listed in Appendix E. In general, two
subjects were discussed:
(i) What kinds of releases should be included in the potential guidance? This
topic is discussed in Section 2.1.2.
(ii) What communications problems might arise between the person requesting
a contingency analysis (the requestor) and the analyst and how can the
potential for miscommunication be minimized? This topic is discussed in
Section 3.0.
2.1.2 Outcome of the Telephone Survey
In the past there has been no systematic compilation of those kinds of source terms that are
potentially of most use to those who have an interest in contingency modeling at Superfund
sites: this seems to be largely because there is a diversity of concerns arising from the many
different chemicals that are likely to be encountered. During the telephone survey, the
following or similar source terms were discussed (in no particular order):
1. Explosive detonation of HCN cylinder/ or rupture due to polymerization.
2. Transfer of methyl mercaptans from a tank with tank failure or seal failure.
3. Spillage from a tank containing carbon disulfide.
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4. Rupture of cylinders and/or tanks containing gas liquified under pressure such
as chlorine, ammonia and hydrogen fluoride.
5. Contents of a drum catch fire: in general, fires of various types at a Superfund
site
6. Rupture of a 300,000 gallon tank of dichlorobenzene with damage to and
leaks from two adjacent tanks.
7. Acetone spill from a 25,000 gallon tank
8. Abandoned rail cars containing various materials leak.
9. Train derailment
10. Vapors released from disturbed soil; and
11. Incineration at a Superfund site.
As expected, it became apparent that accidents involving drums and cylinders are important
to on-scene coordinators. These are considered in the present document.
Spillage from larger vessels containing materials that are liquid at ambient pressure and
temperature were also frequently mentioned. Therefore, this document contains examples
of evaporation from pools spilled on the ground.
One of the more surprising aspects was how often chlorine and ammonia were mentioned,
not just in the context of small cylinders but also relating to larger vessels and to
transportation accidents. This means that the subject of flashing liquid releases needs to be
addressed. This is an area where the apparent interests of those who are concerned with
Superfund sites overlaps with the concerns of those at "other" sites.
In summary, the discussions with the personnel listed in Appendix E led to the identification
of the need to consider:
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o A range of accidents involving drums and cylinders
o Accidents that lead to evaporating pools; and
o Accidents involving gases liquified under pressure.
The range of possible accident scenarios corresponding to the above categories is discussed
below.
22 Range of Possible Accident Scenarios
One of the first things that a contingency modeler learns is that there is no single source
term and no single atmospheric dispersion model that will cover all of the different kinds
of releases that might take place at a Superfund or other site. The following examples are
intended to serve as surrogates for many of the more likely accident scenarios that might
be encountered at such sites. These examples are organized in relation to the physical and
chemical phenomena that need to be addressed. See Section 3.0 for a discussion of how
they are organized with respect to Superfund or "other" sites.
It is convenient to begin with one simple case that can be used to illustrate many of the
issues that confront a contingency modeler. This is the case of a storage vessel or truck
containing a liquid, together with some associated pipework. For example, there may be a
vessel on a Superfund site containing a liquid that must be transferred into a truck and
transported offsite. There is a possibility that there will be a leak or a rupture during
preparation for transfer itself - for example, the failure of a valve when an operator attempts
to open it or the failure of the vessel or pipework in an area that may have been weakened
by corrosion.
As noted above, it is convenient to begin with the variety of possible leaks from such a
vessel because, in discussing the range of possible source terms, the reader will be
introduced to many of the issues and phenomena that a contingency analyst must consider,
either at a Superfund site or at an industrial site where various liquids are stored and
transferred.
Figure 2-1 contains a summary of the range of possible accident scenarios that might arise
in the context of a vessel containing a liquid. The sections in this report where these
scenarios are discussed are given in parentheses in the third column. Those sections
2-3
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DESCRIPTION OF
RELEASE CASE
VISUALIZATION
APPLICABILITY
(SECTION OF REPORT)
PHENOMENA/ISSUES
ADDRESSED
1 A. Rupture in Vessel Containing
Liquid With Above Ambient
Boiling Point at Low Pressure
a) Spillage Into Diked Area
b) Unconfined Spillage
IB. Rupture in Vessel Containing
Liquid With Above Ambient
Boiling Point at High
Pressure
CONFINED OR
UNCONFINED POOL
Rupture in Vessel or
Pipework While Preparing
to Transfer Contents
Accidents Involving
Vessels Storing High
Boiling Point Liquids on
Industrial Sites
Vessel Standing in Diked
Area
(5.1 and 5.2)
Undiked Vessel
(5.6.2)
Rupture in Pipework While
Transfering Liquid Using
Nitrogen Pad
Truck Unloading
Operations
(4.2.9)
Calculation of Liquid
Release Rales - Static Head
Calculation of Evaporation
Rates From a Pool of Finite
Area
Calculation of Evaporation
Rates From an Unconfincd
Pool
• Definition of Cases in
Which Pressure Driven
Releases Can Form
Aerosols
2. • Rupture in Vessel Containing
Refrigerated Liquids -
Same Cases as 1 A and
1 B Above
Same As Above
Ruptures During Storage
or Transfer of Cryogenic
Liquids
(5.3)
Calculation of the Rate
of Evaporation of Cryogens
Spilled Onto Land
Figure 2-S, Page 1
Scenario Visuafinzaftion
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PESCRIPTION OF
VISUALIZATION
APPLICABILITY
(SECTION OF REPORT)
PHENOMENA/ISSUES
ADDRESSED
to
Oi
3A. Liquid Release From Wall
of Vessel Containing Gas
Liquified Under Pressure
3 B. Liquid Release of Gas
Liquified Under Pressure
From Long Pipe (A or B)
3C. Liquid Release of Gas
Liquified Under Pressure -
Impingement Onto Surface
3D. Catastrophic Failure of
Vessel Containing Gas
Liquified Under Pressure
HIGH PRESSURE
f/////sssr.
Rupture of Short Pipe or
Vessel Containing Gas
Liquified Under Pressure
(6.2 - 6.4)
Rupture of Long Pipe
Containing Gas Liquified
Under Pressure
(6.5.2)
Rupture of Vessel
Containing Gas Liquified
Under Pressure
(6.5.1)
Catastrophic Failures
(8.1)
Rate of Release of Liquids
Driven by High Pressure
Flashing
Flashing-Driven
Aerosoli/ation
Momentum Effects
Flashing in Pipe
Rate of Release of Two
Phase Mixtures
Droplet Recovery, Pool
Formation
• Definition of
Characteristics of Puff
Sources
Figure 2-1, Page 2
Scenario Visuj?Si
-------
DESCRIPTION OF
VISUALIZATION
APPLICABILITY
(SECTION OF REPORT)
PHENOMENA/ISSUES
ADDRESSED
4A. Small Hole in Vapor Space
of Vessel Containing Gas
Liquified Under Pressure
4B. Catastrophic Failure in
Vapor Space
4C. "Intermediate" Sized Hole
in Vapor Space of Vessel
Containing Gas Liquified
Under Pressure
See 3D
2 PHASE
RELEASE
FOAMING
OR
FROTHING
• Rupture in Vapor Space
of Tank During Transfer
Operations
• Leaks in Pipes
• Relief Valve Discharges
(7.2)
See 3D
Intermediate-sized Ruptures
in Vapor Space of
Pressurized Vessels
(7.3)
Rate of Release of
Vapors Driven by
High Pressure
Momentum Effects
See 3D
Two Phase Flow Regimes
(Bubbly Row, Churn
Turbulent Flow, Droplet
Flow)
5. Spillages Onto Water
• Spill From Vessel Into
Diked Area That
Contains Water
• Spillage Adjacent to
Waterway
• Marine Transportation
Accidents
(5.5)
Calculations of Rate of
Evaporation of Liquids
Spilled Onto Water
Figure 2-1, Page 3
-------
DESCRIPTION OF
RELEASE CASE
VISUALIZATION
APPLICABILITY
(SECTION OF REPORT)
PHENOMENA/ISSUES
ADDRESSED
6A. A Drum Containing a Liquid
is ftmctured and the Contents
Full lo (he Ground and
Evaporate
611. A Cylinder Containing a
Gas Liquified Under
Pressure is Punctured
6C. A Cylinder Containing a
Compressed Gas is
Punctured
61). Catastrophic Rupture of
Cylinder
6li. Contents of Drum Burn
FLASHING
LIQUID JET .
INSTANT ANI-OUS. PUFF
/
BUOYANT
VAPOR
CLOUD
.LID
• Drum Removal Activities
at Superlund Site Puncture
Drum
(5.4)
Cylinder Removal
Activities Puncture
Cylinder
(6.4)
Cylinder Removal
Activities Puncture
Cylinder
(7.2)
Cylinder Removal
Activities Cause Large
Rupture in Cylinder
(8.0)
Rupture or Removal of
Lid From Drum Containing
Pyrophoric Material
Evaporation From Small
Pools
Flashing Liquid Jets From
Small Containers
Vapor Jets From Small
Containers
Small Puff Releases
Buoyant Plumes
Figure 2-2, Page 1
Some Possi9>le Releases ;>! Stajperfiind Sites
-------
PESCRIPTIONOF
RELEASE CASE
VISUALIZATION
APPLICABILITY
(SECTION OF REPORT)
PHENOMENA/ISSUES
ADDRESSED
7. Vapor Releases From Soil
VAPOR
CLOUD/ /
f
/SOIL
Activities at Superfund
Site Disturb Contaminated
Soil
(10.0)
• Calculation of Source
Terms From Disturbed
Soil
oo
8. Stack Release From
Incinerator
HI a
lUOYANT
VAPOR
CLOUD
• Incineration Activities
(9.2)
Buoyant Plumes, Elevated
Releases
9. Burning of Spilled
Liquid Pools
Spills of Flammable
Waste From Storage in a
Vessel or Drums
(9.3)
Buoyant Plumes
Burning of Pools
10. Burning Tires
Burning Tires in Waste
Dump or Storage
Building
(9.4)
Buoyant Plumes
Rate of Release of
Heal from Burning
Tires
Figure 2-2, Page 2
Some PosssuiSe ReBeases as Superfund Sines
-------
describe how to calculate the characteristics of the source terms. Figure 2-2 continues with
some additional accident scenarios that might specifically be of interest at a Superfund site.
2.2.1 Vessel Containing a Liquid
Consider the simple case of a vessel that contains a liquid that must be transferred to
another vessel and then shipped off site. The first question to address is whether the liquid
is at or below its atmospheric boiling point, or whether it is a gas liquified under pressure.
2.2.1.1 Liquid Below its Boiling Point
Suppose that there is a liquid in a vessel with a boiling point that exceeds the ambient
temperature. Two cases are considered: a) the driving pressure is insufficient to cause
aerosolization and b) the driving pressure causes aerosolization.
A) Spillage with no Aerosolization (Case 1A, Figure 2-1)
In this case, the liquid spills onto the ground, where it may be confined in a dike or it may
spread over an unconfined area. The principal issue the analyst has to address here is the
rate of evaporation. This depends, among others, on such factors as the wind speed, the
vapor pressure, the area of the dike, the temperature of the ground and the degree of
insolation.
B) Spillage with Aerosolization (Case IB, Figure 2-1)
If the pressure in the vessel is high enough, the jet of liquid may emerge with a high enough
velocity for hydrodynamic forces to cause aerosolization. Thus, there will be an initial
airborne source term consisting of liquid droplets, followed by evaporation from the pool
that remains behind. This scenario will provide an introduction to circumstances in which
aerosolization could be caused by the presence of a high driving pressure, such as might be
present if, for example, nitrogen pressure is being used to effect the transfer from the vessel.
This case will also serve to introduce techniques for calculating the liquid release rate when
driven by high pressures in addition to the pressure arising from its own weight (the static
head).
2-9
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2.2.1.2 Refrigerated Liquid in a Vessel (Case 2, Figure 2-1)
The next case to consider is that of a refrigerated liquid at atmospheric pressure and a
temperature that is lower than ambient, such as refrigerated chlorine or ammonia.
This liquid may also be spilled with or without aerosolization into a dike or into an
unconfined area. The principal difference between this and the foregoing is that the rate
of evaporation of the pool is driven by heat conducted from the surface on which the pool
is lying, rather than by mass transfer into the stream of air flowing above the pool. Thus,
this scenario will introduce the analyst to the modeling required to assess the consequences
of spillages of cryogenic materials.
2.2.1.3 Gas Liquified Under Pressure (Case 3, Figure 2-1)
Case 3 illustrates some of the potential ways in which liquid might be released from a vessel
containing a gas liquified under pressure. For example, Case 3A shows the outcome of a
puncture in the side of the vessel. The liquid will be driven out by a combination of the
vapor pressure and the static head. The key phenomenon to be borne in mind here is that
of flashing. Part of the liquid will immediately flash to vapor. Of the remainder, some will
remain airborne as fine liquid droplets and some will fall onto the ground, the relative
proportions being dependent on such factors as superheat. Thus, this scenario will introduce
the analyst to the key phenomena associated with flashing, liquid jets, including
aerosolization, and the need to take into account momentum effects.
Cases 3B apply when the rupture takes place in a long length of pipework. In that case,
there will likely be some flashing in the pipe. This strongly influences the predicted rate of
release. There will be further flashing and aerosolization once the release emerges into the
atmosphere.
Case 3C applies when the emerging jet is directed at a surface. In this case, there is the
potential for droplet recovery, leading to the formation of a pool on the ground, with only
a fraction of the initially formed aerosol remaining airborne.
If there sh'ould be catastrophic failure of the vessel (Case 3D), there will be immediate bulk
boiling and the formation of vapor and aerosol. The resultant expansion will be highly
2-10
-------
turbulent, so that an initial puff will be formed that will likely contain aerosol, vapor and
air. Thus, this source term can be used to illustrate how the contingency analyst sets about
modeling puff releases.
2.2.1.4 Releases from the Vapor Space of a Pressurized Vessel
One potential case is that of an escape of gas from a small hole in the vapor space of a
pressurized vessel (Case 4A, Figure 2-1). In this context, the definition of a small hole is
that R = a/A « 1, where a is the area of the hole and A is the area of the liquid surface.
For most storage vessels, the shearing off of a valve in the vapor space leads to an orifice
with R «1. In this case, vapor will emerge from the orifice. The flow is likely to be
choked (except for pressures of the order of only 1-2 atmospheres) - that is, the vapor
emerges at the speed of sound. Thus, this case will enable the contingency modeler to
consider jet releases of vapor. It has application also to the case of releases from relief
valves and to releases of lower velocity from stacks. In addition, the vapors in question may
be buoyant or may be denser than air.
If there is a catastrophic failure in the vapor space (Case 4B, Figure 2-1), the consequences
will be the same as for a catastrophic release in the liquid space (Case 3D, Figure 2-1).
There exists a category of intermediate failures such as that illustrated in Case 4C on Figure
2-1, in which the hole can be categorized as neither small nor large. Considerable relevant-
work has been done by the AIChE's DIERS (Design Institute for Emergency Relief
Systems) program. Any one of up to four flow regimes through the orifice is possible.
• Pure vapor - already discussed for a small hole
• Bubbly flow regime in which the liquid phase is continuous with discrete
bubbles
• Churn turbulent flow regime in which the liquid phase is continuous with
coalesced vapor regions of increasing size; or
• Droplet flow regime in which the vapor phase is continuous with discrete
liquid droplets
2-11
-------
The transition between these various flow regimes occurs with increasing volumetric vapor
flux and is also influenced by fluid characteristics and by the presence of impurities. It is
unlikely that, if such a scenario is envisaged, a typical on-scene coordinator or emergency
responder will have access to modelers or resources that will enable a quick atmospheric
dispersion calculation to be done. Hence, in this case, expert assistance should be sought,
and this case will not be discussed in detail in the present work.
2.2.1.5 Spillage onto Water (Case 5, Figure 2-1)
For completeness, the case of spillage onto water will be discussed, which will give guidance
to the analyst on how to calculate rates of evaporation when the important driving forces
are the rate of transfer of heat across the water/substance interface and/or the generation
of heat if the substance is soluble in water.
2.2.2 Accident Scenarios Specifically Relevant to Superfund Sites
The accident scenarios discussed in Figure 2-1 are intended to give the reader guidance on
how to tackle many of the different kinds of releases that might be encountered at
Superfund and other sites. Several accident scenarios that are specific to Superfund sites
are displayed on Figure 2-2.
2.2.2.1 Small Containers
The small containers most likely to be encountered on Superfund Sites are cylinders and
drums. These can generally be treated as small vessels, with the same phenomena being
important as in the case of large vessels, but with the small inventory being the principal
difference. Continuing the numbering scheme that was used on Figure 2-1, it is suggested
that the following scenarios will be useful:
Case 6A A drum containing a liquid is punctured and the contents fall to the ground
and evaporate
Case 6B A cylinder containing a gas liquified under pressure is punctured and the
contents escape through a small hole
2-12
-------
Case 6C A cylinder containing a compressed gas ruptures and the contents escape
through a small hole
Case 6D A cylinder containing compressed gas or a gas liquified under pressure
ruptures catastrophically and the contents escape instantaneously, forming a
puff
Case 6E A drum catches fire and the contents burn.
2.222 Ground Disturbances
Case 7 On a Superfund site, there is the potential for pockets of gas to be uncovered
or for materials to be released from disturbed soils.
2.2.2.3 Stack Releases
Case 8 This case will address how to model stack releases, with the case of an
incinerator being the chosen example.
222A Burning Pools
Case 9 A flammable liquid containing toxic materials is spilled onto the ground and
catches fire. This will serve as an introduction to the calculation of emission
rates from burning pools.
2.2.2.5 Burning Tires
Case 10
A pile of tires catches fire and toxic materials are emitted to the atmosphere.
2-13
-------
-------
3.0 COMMUNICATIONS AND HOW TO USE THIS REPORT
3.1 Concerns Expressed During Telephone Survey
The issues raised by the EPA personnel who were surveyed by telephone were far from
uniform, but there does seem to be an underlying thread of concern running through what
was said, namely how can miscommunication between the person requesting the analysis
(the requestor) and the person performing the analysis (the analyst) be avoided? Put
another way, how can these two individuals communicate in such a way that there is a clear
understanding of the scenario that is to be modeled and the information that the requestor
requires? Other concerns raised included how to ensure that the source term is realistic and
that the model is used in such a way as to give credible answers. The following section is
intended to address these concerns and also to show how this report should be used.
3.2 Communications/Flow Charts
3.2.1 Accident Sequence Definition - General Discussion
The material in this section is intended to help the requestor and the analyst clearly to
define the accident scenario to be modeled. This is done by a series of flow charts (Figure
3-1) which are to be interpreted as follows:
Beginning on Page 1 of Figure 3-1, identify which of the eleven cases displayed in boxes
beneath each other is most applicable to the scenario being investigated. The scenarios are
numbered with reference to Figures 2-1 or 2-2.
Page 1 of Figure 3-1 directs the reader to go to another page, or to go to another section
of this report, or to seek expert advice. On subsequent pages of Figure 3-1, the scenarios
are broken down into more classes, after which the reader is directed to another section in
the report. Once directed into another section of the report, the reader will find there
advice on how either to model the scenario in question or will be recommended to seek
expert advice.
If the reader is advised to seek expert advice, there are two possible reasons for this: either
the scenario is one that was not chosen as part of the present work, because of the
3-1
-------
NEED FOR
CONTINGENCY
ANALYSIS
IDENTIFIED
* Refers to Page No. on Figure 3-1
a) Refers to scenario identification
numbers on Figures 2-1 and 2-2
1 *> SPILLAGE OF
LIQUID WITH
ABOVE
AMBIENT
BOILING POINT
2.a) SPILLAGE
OF
CRYOGENIC
LIQUID
3.»> PRESSURIZED
LIQUID
RELEASES
4.»> PRESSURIZED
VAPOR
RELEASES
5 a) SPILLAGES
ONTO
WATER
6.a> RELEASES
FROM DRUMS
OR
CYLINDERS
7»> VAPOR
RELEASES
FROM SOIL
f SOIL
8 a) STACK
RELEASES
9.
BURNING OF
SPILLED
FLAMMABLE
LIQUID
10. BURNING
TIRES
GO TO SECTION 5 5
GO TO SECTION 10 0
GOTOSECnON-9.2
GO TO SECTION 9.3
GO TO SECTION 9 4
11. OTHER
Figure 3-1, Page 1
Scenario Identification Flow Chart
3-2
-------
a)
b)
c)
d)
e)
0
!.»> SPILLAGE OF
LIQUID WITH
AMBIENT
BOILING POINTW
i
age No. on Figure 3- 1
cnario identification
Figures 2- 1 and 2-2
tilled at a temperature that is
mospheric boiling point
TEMPERATURE
OF LIQUID WELL
BELOW BOILING
POINTc)
TEMPERATURE
OF LIQUID JUST
BELOW BOILING
POINTd>
A STATIC
lltAl)
ONLY
B HIGH
PRESSURE
IN VESSEL
OR PIPE
C STATIC
HEAD
ONLY
D HIGH
PRESSURE
IN VESSEL
OR PIPE
— 1™^>
— \^>
U^>
— 1^>>
/ SEEK \ GOTO |
f EXPERT 1 SECTION 563"=) I
\^AD\ICL^y
/ SEEK \ (jo TO \
1 EXPERT SECTION 4 i 9 0 1
More than five degrees centigrade
l^ss than five degrees centigrade
Expert advice needed on heat balances
Expert advice needed on aerosolizaiion
Figure 3-1, Page 2
Scenario Identification Flow Chart
-------
t
SPILLED LIQUID.
WELL BELOW
BOILING POINT.
STATIC HEAD
ONLY
SPILLED LIQUID.
WELL BELOW
BOILING POINT,
HIGH PRESSURE
A DIKED
AREA
B UNDIKED
AREA
C. DIKED
AREA
D. UNDIKED
AREA
(1)
(0
* Refers 10 Page No. on Figure 3 -1
a) Refers to scenario idenlificauon numbers on Figures 1-1 and 2-2
(I) Key assumption: bigb pressure causes lilUe or no aerosolization
when temperature of liquid is well below boiling point
SCENARIO
! GO TO SECTIONS 5
I OR 5 3
J
SCENARIO lAb)a>
(GOTO SECTION 5 62
SCENARIO I Aa)»)
I GO TO SECTIONS S.I
! OR 5 3
SCENARIO I Ah)*)
GOTO SECTION 5621
Figure 3-1, Page 3
Scenario identification Flow Chart
-------
SPILLAGE OF
CRYOGENIC
LIQUID
STATIC
HEAD
HIGH
PRESSURE
IN VESSEL
* Refers to Page No. on Figure 3-1
a) Refers to scenario identification numbers on Figures 2-1 and 2-2
(1) Fxpert advice required on aero&oli/ation
DIKED
AREA
SCENARIO 2A»)»)
B. UNDIKED
AREA
SCENARIO 2Ab)»)
SCENARIO 2B»
CONFINED OR
IINCONFINED POOL
| GO TO SECTION 4 2 «>
Figure 3-1, Page 4
Scenario Identification Flow Chart
-------
PRESSURIZED
LIQUID
RELEASE
V
O\
* Refers to Page No. on Figure 3-1
a) Refers to scenario identification
numbers on Figures 2-1 and 2-2
(I) More than ten degrees centigrade
(2) Less than ten degrees cenugrade
(3) Expen advice needed on aerosolization
TEMPERATURE
WELL ABOVE
BOILING POINT (»
TEMPERATURE JUST
ABOVE BOILING
POINT(2)
A HORIZONTAL
JET
B. VERTICAL
JET
UP
C. VERTICAL
JET
DOWN
D CATASTROPHIC
FAILURE
E. OTHER
CASIIQUFIED
UNDER PMiSSUIU-
EXPERT | I GO TO SECTION 6 5
ADVICE* >J
SCENARIO 3A/Ba>
GO TO SECTioNS 6;
THROUGH 64
SCENARIO 3B»>
(GO TO SECTIONS 6 ijj
SCENARIO 3C
SCENARIO 3D
i(iOTOSECTIC)N80|
Figure 3-1, Page 5
Scenario Identification Flow Chart
-------
i
—I
VAPOR SPACE
RELEASE - GAS
LIQUIFIED
UNDER
PRESSURE
* Refers to Page No. on Figure 3- 1
a) Refers to scenario identification
numbers on Figures 2- 1 and 2-2
SMALL
B INTERMEDIATE
c LARGE
)
2PIIASE
\\\S f RELEASE
SSH/^
. FOAMING
OR
FROllilNCi
A
SCENARIO 4Aa>
iO TOSECT1ON72|
I GO TO SECTION 7 3JI
! GO TO SECTION 8 1
Figure 3-1, Paged
Scenario Identification Flow Churl
-------
UJ
oo
CYLINDERS
DRUMS
* Refers lo Page No. on Figure 3-1
a) Refers lo scenario identification
numbers on Figures 2-1 and 2-2
A FLASHING
LIQUID
JET
B. VAPOR
JET
C. CATASTROPHIC
RUPTURE
D. SPILLAGE
ONTO GROUND
LIQUID
EVAPORATES
E. PYROPHORIC
MATERIAL
FIRE
F. EXTERNALLY
INITIATED
FIRE
FLASHING
LIQUID JET
c
BUOYANT
VAPt>R
CLOUD
SCI-NARI()6B»)
i GO TO SI-CTJON 6 41
SCENARIO 6C»>
iGOTOSF£T10N72j
SCENARIO6D»)
SCENARIO 6A»>
SCENARIO6E»)
| GO TO SECTION 9 3 jj
SCENARI()6Fa)
Figure 3-1, Page?
Scenario Ideiiiificution Flow Chart
-------
limitations on available resources, or the authors judge that the physical phenomena that
need to be addressed are so complex that they are outside the scope of this document.
3.2.2 Accident Sequence Definition - Examples for Superfund Sites
3.22.1 Spillage of Acetone from a Storage Vessel
In order to illustrate how this section should be used by the reader, assume that a situation
has been identified in which it is known that there is a vessel containing acetone. At a
Superfund site, this may be known, for example, by sampling the contents or by reference
to documentation that has been left behind by a former operator of the site. This
corresponds to scenario #1 on page 1 of Figure (3-1) where a number of variations is
displayed.
The boiling point of acetone is ~ 330 K, which is typically well above the ambient
temperature: the temperature on a hot day might be 305 K. Therefore, the reader chooses
the upper branch on p.2 of Figure (3-1) where the main question is whether the acetone is
under its own static head ( i.e. the pressure is due to its own weight, box A on the figure)
or under an additional pressure from some other source (box B on the figure).
The conditions under which the acetone will be under its static head only will be prior to
its being transferred from the vessel in which it is stored. It will also still be under the static
head in the vessel if it is being withdrawn by a pump. In this case, the reader is directed to
go to "page 3 of Figure (3-1) where the choice is between spillage into a diked or undiked
area. The reader is then directed to Sections 5.1 or 5.3 for spillage into a diked area or to
section 5.6.2 for spillage onto an undiked area. Section 5.1 gives a detailed analysis of how
to calculate the rate of evaporation of acetone spilled into a diked area and how to prepare
inputs for DEGADIS and SLAB. Section 5.6.2 gives guidance on how to model a spreading
pool that is unconfined.
Returning to page 2 of Figure (3-1), the acetone may be under high pressure (box B) - for
example, if a nitrogen pad is being used to transfer it from the vessel. In this case, the
reader proceeds through page 3 of Figure (3-1) and on to various sections of this report just
as was illustrated for the case of the "static head only" as described above. On page 3, boxes
C and D differ from boxes A and B only by there being high pressure. This means that the
3-9
-------
liquid will be driven out of the vessel at a higher rate than it would be for the case of the
static head only. At this point, an important assumption is made, namely that the
temperature of the material is low enough to preclude the formation of small liquid droplets
(aerosol) that arise as the outgoing jet shatters due to the action of hydrodynamic forces.
That is, aerosolization is not expected (see Section 4.2.9 for further discussion). Therefore,
once the pool has formed, there is no difference between the calculations for these cases
(boxes C and D on page 3 of Figure (3-1)) and those for the static head only case and the
reader is directed to the same sections in the report (5.1, 5.3 and 5.6.2).
The methods appropriate for a spill of acetone are also appropriate for many other
materials likely to be found on a Superfund site. For example, the spillage and subsequent
evaporation of dichlorobenzene or methyl mercaptan will follow the same paths through
Figure (3-1). The methods are also appropriate for many high boiling point materials in
abandoned railcars.
3223, Liquid Spillage from a Drum
Assume that there is a drum containing a liquid stored at a Superfund site. By definition,
the liquid has a vapor pressure considerably below one atmosphere (i.e. a boiling point
considerably above ambient). It is not particularly important what the liquid is. The drum
may leak because it has been dropped or punctured in removal operations.
On page 1 of Figure (3-1), the closest scenario is #6. The reader is directed to go to~ page
7, where the lower branch refers to drums and box D is the liquid spillage scenario, which
is discussed in Section 5.2. There the reader will find that the principal difference between
the calculations used for the drum case and those used for a large spill of acetone arise
because the total volume of the spill is much smaller.
3223 Accidents Involving Cylinders
Cylinders are used to supply small amounts of gases that are stored under high pressure,
such as chlorine. Hydrogen fluoride is another example of a gas that is sometimes supplied
in cylinders. The telephone survey identified HCN in a cylinder as a cause for concern.
Thus, it is possible that cylinders will be left behind at Superfund sites and must be
removed, emptied or destroyed.
3-10
-------
150 Ib is a typical size for a cylinder. There are also larger, one ton cylinders such as are
sometimes used to supply chlorine for water treatment or HF for various industrial activities.
On page 1 of Figure 3-1, box #6 identifies releases from drums or cylinders and directs the
reader to p.7 where three alternative cylinder scenarios are shown: A) a flashing, liquid jet;
B) a vapor jet and C) a catastrophic rupture.
Assume that it is known that the cylinder contains chlorine, which will be liquified under
pressure. Therefore, any of the three scenarios A, B or C is possible depending on whether
the rupture is located in the liquid or vapor space and on how big it is. For example, if the
cylinder is upright, the concern might be that valving at the top could fail. In this case,
there would be a vapor jet as discussed in Sections 7.2 and 7.3. If the concern is that the
cylinder might be dropped, then either case A (liquid jet, Section 6.4) or case B (total
rupture, Sections 8.1 and 8.2) would be appropriate.
3.2.2.4 Fires at a Superfund Site
There is a potential for fires at a Superfund site. Suppose, for example, that there is a
storage vessel containing mineral oils in which polychlorinated biphenyls (PCBs) are
dissolved. There is a leak from this vessel and the spilled pool ignites. This corresponds
to Box #9 on page 1 of Figure (3-1). The reader is directed to go to Section 9.3, which
discusses how to calculate the rate of emission of toxic materials from a burning pool.
Fires can also involve drums. Two possible scenarios are shown on page 7 of Figure (3-1).
One consists of the burning of pyrophoric material in a drum. The other is similar to a pool
scenario, except that drums stand in the burning pool. These scenarios are briefly discussed
in Section 9.3.
3.2.2.5 Incineration at a Superfund Site
Incineration is often an option employed at Superfund sites to destroy volatile or
semivolatile organic materials in contaminated waste. Item #8 on page 1 of Figure (3-1)
directs the reader to Section 9.2, which gives an example of how to calculate the emission
rate of toxic materials from an incinerator.
3-11
-------
3.2.2.6 Mechanically Disturbed Soil
Material at a contaminated site must often be excavated prior to remedial treatment. Thus,
excavation itself may cause the release of toxic vapors. Item #7 on page 1 of Figure (3-1)
directs the reader to Section 10.0, which contains a summary of a simple model for
predicting the rates of release during excavation activities.
3.2.2.7 Spillages onto Water
Spillages onto water are not highly probable at Superfund sites, but it is possible to envisage
circumstances in which they might occur if operations are being carried out close to a body
of water. Item #5 on page 1 of Figure (3-1) directs the reader to Section 5.5, where the
issues involved in modeling such spills are discussed.
32.3 Accident Sequence Definition - Examples for "Other" Sites
In order to try to illustrate some of the types of scenarios that may occur at "other"
industrial sites, chlorine has been selected as a vehicle for discussion. Chlorine is often
stored or transported in containers at ambient temperature, in which case it is a liquid at
high pressure (typically ~ 80 - 100 psig). These containers range from 150 Ib cylinders
through 1 ton cylinders up to railcars that contain 80 tons and are sometimes themselves
used as temporary storage vessels. As noted above, 150 Ib or one ton cylinders may also be
found at Superfund sites.
In addition, chlorine is sometimes refrigerated and stored at ambient pressure and a
temperature of ~ 239 K (its boiling point). Very large quantities of chlorine can be found
in refrigerated storage, e.g 10,000 tons.
3.2.3.1 Spillage of Cryogenic Liquid
Assume that a leak occurs in a vessel or its associated pipework in which there is chlorine
refrigerated at ambient pressure. This corresponds to item #2 on page 1 of Figure (3-1).
The reader is directed to page 4 of the figure, where there are two options. Either the
pressure in the vessel is solely that due to the chlorine itself (the static head) or there is
3-12
-------
additional pressure from other sources (e.g. a nitrogen pad for transfer purposes).
For the case of the static head, the liquid may spill into a diked or undiked area. For the
case of a diked area, Section 5.4 shows the reader how to calculate the rate of evaporation.
For the undiked case, Section 5.6.2 discusses the issues involved if the spill is unconfined.
3.2.3.2 Pressurized Releases - Flashing Jets
Imagine the case of a vessel containing chlorine under pressure at ambient temperature in
which leakage occurs from the liquid space. These releases are characterized by partial
flashing to vapor and fragmentation of the liquid jet to form an aerosol. This case
corresponds to item #3 on page 1 of Figure (3-1). The reader is directed to p.5 of the
figure where the first branch concerns whether the temperature is just above its boiling point
(e.g. < 10°C) or well above its boiling point. The issue here is whether the analyst can
assume complete aerosolization or not. For chlorine the atmospheric boiling point is 239
K and a typical ambient temperature may be in the range 0 - 30° C (273 - 303 K).
Therefore, for chlorine, the upper branch on page 5 of Figure (3-1) is appropriate, because
the temperature is in the range 34 - 64 °C above the boiling point and complete
aerosolization is expected.
Five possible cases are considered including three jet cases, horizontal, vertical (up) and
vertical (down). For the horizontal and vertical jet cases, the reader is directed to Sections
6.2 through 6.4 of which Section 6.3 discusses~a flashing jet from a one ton cylinder and
Section 6.4 considers a flashing jet from a 150 Ib cylinder. In addition, Section 8.1 considers
the case in which the rupture in the vessel is so large that the contents are essentially lost
instantaneously.
3.2.3.3 Vapor Releases Driven by High Pressure
For the case of a release from the vapor space of a chlorine vessel at ambient temperature
and high pressure, item #4 on page 1 of Figure (3-1) directs the reader to page 6, where
there are three options, small, medium and large.
A "small" hole is one in which R = a/A « 1, where a is the area of the hole and A is the
area of the liquid surface. For a typical penetration into a vessel (e.g. 1" or 2" in diameter),
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a/A is clearly very small and box A on page 6 of Figure (3-1) applies. The reader is
directed to Section 7.2, which discusses high pressure vapor releases.
If the release is "catastrophic" so that the contents of the vessel are lost almost
instantaneously, the case is that of a puff release, see Section 8.1. For releases of
"intermediate" size, complicated phenomena occur that are difficult to calculate, see Section
7.3.
3.2.3.4 Other Materials
The discussion above for chlorine is also appropriate for other materials such as ammonia,
which may also be found liquified under pressure or refrigerated at ambient pressure with
temperatures well below those of the surrounding atmosphere.
3.2.4 Hydrogen Fluoride - an Interesting Case
Some of the scenarios considered in the present work have to do with the accidental release
of hydrogen fluoride (HF), which has a boiling point of about 20 °C (293 K). HF can be
found in circumstances in which its temperature is well below its boiling point, just below
its boiling point, just above its boiling point or well above its boiling point.
For example, HF storage vessels are sometimes refrigerated so that the temperature is (say)
10 °C below its boiling point. In this case, the methods used to model it are similar to
those used for acetone (Section 3.2.2.1). Following through Figure (3-1) leads the reader
to Section 5.3, which considers a spillage of HF into a diked area.
In some industrial applications, HF may be at a relatively high temperature (say 100 °F) and
any accidental release may take the form of one of the jets shown on page 5 of Figure (3-1).
Specifically, Section 6.2 considers the case of a horizontal flashing jet of HF.
For HF in storage that is directly affected by ambient conditions, its temperature can
fluctuate above and below the boiling point during a single day. If the temperature is just
above the boiling point,.the reader will arrive at the lower branch on page 5 of Figure (3-1).
The reader should seek expert advice because of uncertainty about how much aerosolization
there will be and how much liquid will remain behind as a pool on the ground.
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If the temperature of the HF is slightly below its boiling point, the reader will arrive at the
lower branch of the flow chart on page 2 of Figure (3-1). There is a need to seek expert
advice because a) there is the potential for partial aerosolization and b) sources of heat that
are neglected in some simpler treatments of evaporation (such as that described in Section
5.1) cannot be neglected in this case. An explanation of where to look is given in Sections
5.6.3 and 4.2.9.
3.3 Other Issues that Must Be Addressed
There are a number of other issues that the requestor and the analyst must discuss in order
to ensure that the results are in a useful form for decision making.
o What size of leak should be considered? See Section 4.3.
o What combinations of windspeed and atmospheric stability category should
be considered? For example, the requestor may wish to know the results in
a "worst case" weather condition and also .in a condition that is favorable for
dispersion (i.e. a condition in which an on-scene-coordinator might choose to
perform an operation in order to minimize the consequences should anything
go wrong). The height at which the windspeed is measured should be taken
into account, if known. If not, a height of 10 m should be assumed. See
Section 4.4.1 for further discussion.
o Which wind directions should be considered - see Section 4.4.3.
o What is the ambient temperature? What is the temperature of the ground,
if different? See Section 4.4.4.
o Has the temperature of the material in the vessel prior to release been
specified?
o The issue of site surface roughness is important because, for some heavy
vapor dispersion models, there is an upper bound on the surface roughness
lengths for which the model is valid. For example, the authors of the
computer models SLAB and DEGADIS recommend against using a surface
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roughness length higher than 0.1 m. This is an issue that may have to be
discussed with the model originator. Assuming a smaller roughness length
than is the case at the site in question is likely to lead to some overprediction
of the distances of concern because smaller surface roughness leads to less
rapid dilution as the vapor cloud travels downwind. See Section 4.4.6.
o Should the site be characterized as rural or urban? This question relates to
how the material disperses once the vapor cloud has evolved out of the phase
where initial density or momentum effects are important. In this passive
vapor (non-dense-gas) stage, available heavy vapor models switch to a
traditional Gaussian approach. The parametrizations of the standard
deviations (i.e. plume width and height as a function of downwind distance
and atmospheric stability) differ greatly between rural and urban areas, with
a great deal more dilution occurring in the latter case. The requestor should
be aware that several of the current generation of heavy vapor dispersion
models do not have an easily applicable urban option for the region of passive
dispersion, in which case they-will overestimate distances of concern on urban
sites.
o Which levels of concern (LOCs) are to be considered? This is a controversial
issue. EPA has data bases that are applicable to some of the Superfund
scenarios, such as IRIS and HEAST. Emergency Response Planning
Guidelines (ERPGs) have been issued by the American Industrial Hygiene
Association for some materials. There is the possibility of using the IDLH
(Immediately Dangerous to Life or Health) concentration or some agreed
fraction thereof. It may be necessary to contact experts in the field. See
Section 4.4.7.
o Is the level of concern to be regarded as a maximum concentration to which
people might be exposed, irrespective of the exposure time? For example,
ERPGs are currently defined for exposure times of one hour. What should
be done for shorter durations of plume passage? Should something like
Haber's law be used, which essentially says that the dosage - the product of
exposure time and average concentration - is what causes a given health
effect? This is a controversial issue and the requestor may choose to be safely
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conservative for releases of short duration by assuming the LOG for an
exposure time of one hour. However, this can lead to considerable
overestimates of distances of concern and there may be circumstances in
which the decision maker might wish to try to understand how much
conservatism there is - e.g. if the conservative answer leads to a decision to
evacuate a very large number of people.
o What output does the requestor wish to see? For example, are these simply
distances of concern (DOCs) in each weather condition or are complete
contours of constant LOG desired? At what heights does the requestor wish
to see the DOCs and LOCs?
o What averaging time(s) should be used in the model? See Section 4.4.8 for
a discussion. This is also a subtle question.
o What is the maximum downwind distance to which the calculations should
extend?
3.4 Conclusion
The requestor who uses the above checklist (Section 3.3) and defines the source term using
Figure (3-1) should avoid most of the potential for miscommunication that can arise
between requestor and analyst.
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4.0 BRIEF SURVEY OF AVAILABLE DISPERSION MODELS
4.1 Available Models
A review of the capabilities, strengths and limitations of all of the models that are available
for modeling accidental releases of toxic or flammable vapors is beyond the scope of this
report. Useful references that review a good deal of relevant material include a recent
comparative study by EPA(5). The models considered there include AIRTOX, CHARM,
DEGADIS, SLAB, TRACE, FOCUS and SAFEMODE. Of these, DEGADIS and SLAB
are available in the public domain and are used in this study.
SLAB treats four types of sources: a) an evaporating pool; b) a horizontal jet release; c) a
vertical stack or jet release and d) an instantaneous (puff) or short duration evaporating
pool release. Thus, SLAB is suitable for all of the denser-than-air releases considered in
this report with the exception that it does not simulate time varying releases, in which case
approximations must be made (such as taking an average rate of release).
DEGADIS is able to simulate elevated jet releases of dense gases, provided that these are
vertically oriented. It can also be used to model heavy vapor releases at ground level,
including continuous releases, varying release rates and puff (instantaneous releases). Thus,
DEGADIS is suitable for all of the source terms modeled below with the exception of
horizontally oriented jets.
In addition, during the course of this work an arrangement was made with the authors of
the proprietary model SAFER, who have analyzed some of the accident scenarios listed in
Section 3. Their results are included in Appendix F. SAFER contains a comprehensive
array of models that can address any of the scenarios described in this report. However, in
Appendix F, examples are given for four scenarios only, a continuous release of flashing
liquid chlorine, a puff release of chlorine, a spillage of refrigerated chlorine onto the ground,
and a spillage of acetone onto the ground.
Finally, HGSYSTEM is a new model that was sponsored by a consortium of industrial
companies with an interest in hydrogen fluoride (HF). It is among the most sophisticated
of publicly available models and was chosen for use with two scenarios, see Appendix G.
The scenarios that HGSYSTEM can model are listed in Table 1 of Appendix G.
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Some of the accident scenarios below do not lead to heavier-than-air releases. In such
cases, the use of models such as TSCREEN or the Industrial Source Complex (ISC)(3S)
model is discussed. .
4.2 Why Atmospheric Dispersion Models Give Different Answers
The user of atmospheric dispersion and contingency models soon discovers that, even when
they are nominally solving the same problem, the answers can be quite different. To explain
in detail all of the differences between SLAB, DEGADIS, SAFER and HGSYSTEM is
beyond the scope of the present report, because the focus of the present work is on the
preparation of input for the models and not on explanation of the output. The calculated
differences may themselves differ from scenario to scenario. However, the following
provides general guidance of which the reader ought to be aware:
i) There is inherent uncertainty in all contingency models and a difference of a
factor of two between the results predicted by different models should not be
surprising. If such differences arise, it is likely that various parameters in the
models have also been assigned different values while remaining within the
bounds of uncertainty.
ii) Unless the input to the different models has been carefully prepared by the
same analyst, there may be input assumptions that lead to large differences
in the answers. A particular example is the choice of LOG - for example,
- whether it has been adjusted for exposure time or not.
iii) The large differences that may arise because of the selection of an urban or
a rural dispersion model have already been discussed above.
iv) Some models can accept time-varying release rates (e.g. DEGADIS,
HGSYSTEM) while others cannot (e.g. SLAB).
v) There are specific modeling differences. For example, for jet releases,
DEGADIS can only accept a vertical orientation whereas SLAB can accept
a vertical or horizontal orientation and HGSYSTEM can accept any
orientation.
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As another example, HGSYSTEM has some sophisticated new features. It
has a new entrainment model for the initial slumping phase of a heavy vapor
release that allows the user to assume higher surface roughness lengths than
the 0.1 m upper bound discussed above for SLAB and DEGADIS. The
higher roughness leads to extra dilution and predicted concentrations in
HGSYSTEM can be as much as a factor of five lower than those in
DEGADIS. In addition, HGSYSTEM has a state-of-the-art algorithm for the
longitudinal spreading of transient releases due to the action of wind shear.
This tends to make HGSYSTEM predict lower peak concentrations together
with larger exposure times for transient or puff releases than do the other
models.
In summary, the user of the models should assess differences in answers as follows:
a) If predicted distances of concern lie within a factor of two, the answers are
within the expected range of uncertainty.
b) Differences in input assumptions should be carefully investigated.
c) If neither a) nor b) proves satisfactory, it will be necessary to make a detailed
study of the differences in the algorithms contained in the computer models.
4.3 Choice of Leak Size
One of the most critical factors among those governing the rate of release is the size of the
leak. The analyst has to decide how large the area is likely to be. Some examples are as
follows:
There may be a gasket rupture, in which case it is conventional to assume the total loss of
gasket material between two bolts. For example, for a flange in a pipe of diameter 2" with
4 bolts, the fraction of the circumference that lies between two bolts has length rd/4 =
1.571". A typical gasket thickness is 1/8" so that A = (1.571)(l/8) = 0.196 in2 - i.e. almost*
equivalent to a hole of diameter 1/2".
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Another rough rule of thumb is that a serious leak from a valve due to loss of valve packing
has an equivalent diameter of about 1/2".
Another potential accident consists of a leak through a pump seal. Conservatively, the total
loss of a seal will leave an annulus around the pump shaft through which material can leak.
For example, a pump shaft of diameter 1" with clearance 0.03" has effective area A =
(T)(l)(0.03) = 0.094 in2, which has an effective diameter of 1/3" (when converted to an
equivalent circular orifice).
Overall, there are a number of potential accident scenarios for which the orifices have
effective diameters in the 1/4" - 1/2" range. A leak diameter of 1/2" is a reasonable
surrogate for these.
The potential for larger leaks can be assessed by looking at vessel penetrations. In many
cases these are 1" or 2" in diameter. For old vessels at Superfund sites, inspection of the
vessel may reveal a corroded area that might fail and A can be estimated from the size of
this area.
4.4 Generic Issues in Atmospheric Dispersion Modeling
Before proceeding to develop atmospheric dispersion modeling input data for each source
term and each atmospheric dispersion model, it is convenient to discuss the choice of certain
parameters or the treatment of certain phenomena that are common to most, if not all,
models and are independent of the source terms. These include:
o Atmospheric stability category
o Windspeed
o Wind direction
o Ambient temperatures
o Relative humidity
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o Surface roughness length
o Toxicological levels of concern
o Averaging times; and
o Aerosolization.
A good basic introduction to many concepts such as atmospheric stability, surface roughness
length and turbulence can be found in Reference (11).
4.4.1 Atmospheric Stability Categories and Windspeed
4.4.1.1 Background
The atmospheric stability category is intended to be a rough indication of the degree of
turbulence in the atmosphere - that is, in the present context, an indication of the
effectiveness of the atmosphere in diluting an accidentally released vapor cloud.
Table 4-1 shows a simple scheme that relates stability category A -F to widely observed
quantities such as the degree of insolation, the cloud cover and the windspeed6
Daytime Insolation
Strong
A
A-B
B
C
C
Moderate
A-B
B
B-C
C-D
D
Slight
B
C
C
D
D
Nighttime
Cloudiness4/8
__
E
D
D
D
<3/8
....
F
E
D
D
a) Fraction of sky covered by clouds
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Atmospheric stability category A corresponds to a hot summer's day when there is a great
deal of convective turbulence in the atmosphere. Atmospheric Stability Category D
generally occurs when there is a brisk windspeed and considerable mechanical turbulence
is present. Atmospheric Stability Category F corresponds to the case where there is little
turbulence of any kind in the atmosphere, such as may occur on a still winter's night.
Atmospheric stability is sometimes expressed in terms of the Monin-Obukhov length,
L = (-PsCpu.3T)/(kgH), where:
o pa is the atmospheric density
o Cp is the specific heat of dry air at constant pressure
o u, is the friction velocity
o T is the surface temperature
o k is Von Karman's dimensionless constant ~ 0.4
o g is the acceleration due to gravity
o H is the vertical flux of sensible heat to the ground. H is negative (upward)
in unstable conditions (A-C), zero in neutral conditions (D) and positive in
stable conditions (E,F).
Some atmospheric dispersion models ask for values of L. There is a simple relationship
between L, the surface roughness length z0 and the atmospheric stability category, taken
from Table V.I of Reference(4):
Table 4-2. Relationship Between Atmospheric Stability Category,
Surface Roughness Length z0 and Monin-Obukhov Length L
Atmospheric Stability Monin-Obukhov
Category Length (m)
A L = -11.4z0ai
B L = -26.0z0an
C L = -123z00'30
D oo
E L = 123z0°-30
F L = 26.0z0°-17
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4.4.1.2 Choice of Weather Conditions
For scenarios in which heavier-than-air effects are not important, it is possible to use
TSCREEN, which has a built-in range of windspeeds with associated stabilities. At each
distance downwind, the model identifies the windspeed and atmospheric stability
combination that gives the maximum predicted concentration for the scenario in question.
For the dense gas models discussed in this report, the worst case weather conditions are not
always obvious and must be determined by trial and error. However, it is generally too
onerous a task to provide runs for the full range of weather conditions that may be
encountered. In general, a useful idea of the range of possible outcomes of accident
scenarios can be obtained by looking at three stability category /windspeed combinations -
A with a low windspeed(e.g. 1.5 m/s), D with a moderate windspeed (e.g. 5 m/s) and F with
a low windspeed (e.g. 1.5 m/s). The category A condition will often give the highest ground
level concentrations for elevated releases where the plume centerline does not return to
ground level, while the category F condition will often be the worst case for ground level
releases. The category D condition, by contrast, is more like an average condition. In the
SLAB and DEGADIS examples given in this report, the case of stability category F with a
windspeed of 1.5 m/s is chosen for illustrative purposes.
The computer models discussed in the present report generally ask the reader to provide
the stability category and windspeed. It is an easy matter to substitute weather conditions
other than those described above if the user wishes to do so.
4.4.2 Height at which Windspeed is Measured
If there is a meteorological station at the site, then the height at which the windspeed is
measured, Z0 should be that of the lowest velocity measurement on the tower. If there are
no local measurements, Zr should take on a default value of 10 m. Again, the computer
models described below specifically request the user to provide a value of this parameter,
which can easily be changed.
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4.4.3 Wind Direction
The models discussed in the present work do not require that the direction of the wind be
specified. After the analysis has been completed, contours of constant concentration can
then be overlaid on maps of the neighborhood in any direction required by the requestor.
Some more sophisticated models may directly plot the contours on maps, in which case the
specific instructions in the model users' manual should be followed.
4.4.4 Ambient Temperatures
There is no one-to-one correspondence between the ambient atmospheric temperature and
the atmospheric stability category. If site specific measurements are available showing
average temperatures for each stability category, these should be used. However, reasonable
default values are as follows: Category A, 305 K; Category D, 288 K; Category F, 278 K.
4.4.5 Relative Humidity
Again, there is no precise correlation between atmospheric stability category and relative
humidity. In the absence of any information, an RH of 50% could be used. More generally,
Category A is usually a dry condition, Category F is often humid and category D can lie
between. Thus, for default values, the following values of RH can be used: Category A,
25%; Category D, 50%; Category F, 75%. Site specific data should be used if available.
4.4.6 Surface Roughness Length
The intensity of mechanical turbulence at a site is dependent on the surface roughness
length, z0. Table (4-3) gives examples of the surface roughness for different surfaces(I2).
similar table appears in Reference (6).
4.4.7 Toxicological Levels of Concern
The atmospheric dispersion analyses result in contours delineating "Levels of Concern"
(LOCs). For short term releases, one of the most recent sources of LOCs are the
Emergency Response Planning Guidelines (ERPGs), which have been made available for
some thirty substances by the American Industrial Hygiene Association/13'
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Table 4-3. Surface Roughness for Uniformly
Distributed Ground Covers
Surface
Roughness (m)
Ground Cover Height (m)
Ice or smooth mud
flats
Snow
Sand
Soils
Short grass
Mowed grass
Long grass
Agricultural crops
4 m high buildings
with lot areas of
2,000 m2 and a
50 m2 silhouette
20 m high buildings
with lot areas of
8,000 m2 and a
560 m2 silhouette
100 m high buildings
with lot areas of
20,000 m2 and a
4,000 m2 silhouette
0.00001
0.00005 - 0.0001
0.0003
0.001 - 0.01
0.003 - 0.01
0.002 - 0.007
0.04 - 0.1
0.04 - 0.2
0.05
0.7
1.0
0.015 - 0.03
0.25 - 1.0
0.40 - 0.2
4
20
100
The ERPG-3 is the maximum-airborne concentration below which it is believed that nearly
all individuals could be exposed for up to one hour without experiencing or developing life-
threatening health effects. The ERPG-2 is the maximum airborne concentration below
which it is believed that nearly all individuals could be exposed for up to one hour without
experiencing or developing irreversible or other serious health effects or symptoms which
could impair an individual's ability to take protective action. The ERPG-1 is the maximum
airborne concentration below which it is believed that nearly all individuals could be
exposed for up to one hour without experiencing other than mild, transient adverse human
health effects or without perceiving a clearly defined objectionable odor.
Note that the ERPGs are defined for a period of one hour. For releases of different
duration, rules such as Haber's law may apply. Haber's law states that a given health effect
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will be observed if the product of exposure time and concentration (i.e. dosage) remains
constant. However, Haber's law may not apply to all chemicals. In seeking to extrapolate
LOCs to exposure times other than those for which they are defined, the advice of an expert
in toxicology should be sought.
Other possibilities for short term LOCs include the IDLH (Immediately Dangerous to Life
or Health) or some fraction thereof, such as one tenth. The National Institute of
Occupational Safety and Health (NIOSH) is the organization that publishes IDLH values.
For more conservative estimates of short-term LOCs, the Occupational Safety and Health
Administration's (OSHA's) Permissible Exposure Limit - Time Weighted Average (PEL-
TWA), or the American Conference of Government Industrial Hygienists' (ACGIH's)
Threshold Limit Value - Time Weighted Average (TLV - TWA), or some fraction thereof
such as a hundredth, are sometimes used, see for example Ref. (8).
If cancer or other effects due to long term exposure are a concern, data on LOCs can be
obtained from EPA's Integrated Risk Information System (IRIS) or EPA's Health Effects
Assessment Summary Tables (HEAST), which are updated quarterly.(14>
4.4.8 Averaging Times
The concept of the averaging time is often one of the most confusing for the user. Here,
two averaging times are discussed, that for meteorological purposes and the exposure time
for toxicological purposes.
In meteorological modeling, the averaging time is used to adjust the effective width of the
plume to take account of meander in the mean wind direction. If a release is of prolonged
duration Tr and the wind direction is nominally unchanging during that period, the action
of large scale turbulent eddies will cause the plume to be broader than it would be for a
release of shorter duration. One of the simplest approaches (valid for the traditional
Gaussian- approach) is to allow the width Wp of the plume to be a function of Tr: Wp is
increased to Wp(Tr/Te)p where Te is the duration of release in the experiments from which
the values of Wp were derived(15). A typical value for p is 0.25 and Tc ~ 3 minutes. This
kind of averaging is usually already incorporated into meteorological models.
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With respect to the LOCs, the averaging time is also important, as has been seen above
where the ERPGs are defined for an exposure time of one hour. If the duration of release
is also one hour, then the averaging times for meteorological and toxicological purposes are
approximately the same. However, if the duration of release and/or the duration of cloud
passage at a particular point are much smaller than one hour, then the meteorological and
toxicological averaging times are not the same. In fact, as was discussed above, the problem
then becomes one of adjusting LOCs for exposure times that differ from those for which
they were defined: expert advice should be sought. Further guidance on how to address this
problem is given in later sections of this report for the specific cases of SLAB and
DEGADIS inputs.
4.4.9 Aerosolization
The problem of aerosolization has received considerable attention in the past few years.
When a flashing liquid jet, or a liquid jet at or just below its boiling point driven by high
pressure, emerge into the atmosphere, liquid droplets may become and remain airborne.
This phenomenon is known as "aerosolization." The fraction of the initial liquid that
aerosolizes is a function both of the degree of superheat and of the pressure in excess of the
vapor pressure in the vessel. The degree of superheat is the difference between the
temperature of the liquid and its atmospheric boiling point.
For the purposes of this report, the examples given in Section 5 fall into the category of
releases that have no associated aerosolization and the examples given in Section 6 fall into
the category of releases for which the assumption of 100% aerosolization is appropriate.
If there is doubt, conservative answers can be obtained by assuming 100% aerosolization.
Alternatively, expert advice should be sought.
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5.0 SPILLAGES OF LIQUIDS ONTO SURFACES
5.1 Spillage of Liquid with Above Ambient Boiling Point into a Diked Area - Acetone
This scenario corresponds to #1A of Figure 2-1. This scenario has been chosen because it
is an example of how to model spillages of high boiling point liquids onto the ground with
subsequent evaporation and formation of a vapor cloud. See Section 3.2.2.1 for a further
discussion.
5.1.1 Description of Scenario
A storage vessel stands in a dike. It contains a liquid at atmospheric pressure and ambient
temperature. The liquid has a boiling point that is higher than the ambient temperature so
that its vapor pressure is below one atmosphere.
Several potential scenarios could lead to a spillage of liquid into the dike. For example, if
the vessel is at a Superfund site, an old and corroded valve could fail when the operator
tries to turn it and the contents will spill into the diked area. Gasket failures could occur
or, if there is a pump, there could be a pump seal leakage. There could be damage if
mechanical equipment being used nearby accidentally collides with pipework or the vessel
itself. In any event, it is assumed that there is a leak and the liquid spills into the dike,
where it lies and evaporates slowly. The driving force for the leak in this example is
assumed to be only a small static head that does not cause aerosolization. The source term
is then that caused by evaporation of the pool. For the purposes of this example, it is
assumed that the dike has an area of 400 m2 (20 m x 20 m). This is not an unusual size for
a diked area at a chemical facility.
5.1.2 Rate of Release of Liquid from Vessel
The rate of release of liquid from an orifice is given by Bernouilli's formula(16>:
Q = c.A.pL (2.(p - Pa)/pL + 2g.h) m (5-1)
where Q is the rate of release (kg/s)
c is a constant, normally set to 0.6
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A is the area of the orifice (m2)
p is the absolute pressure in the vessel (Pa)
pa is the atmospheric pressure (l.OlxlO5 Pa)
g is the acceleration due to gravity (9.81 m/s2)
h is the static head (m), and
PL is the liquid density in the vessel (kg/m3).
The above formula is suitable for calculating the rate of pure liquid flow through a circular
orifice. There are variations on the formula for a non-circular orifice. Eq. (5-1) is
consistent with the corresponding formula that is programmed into TSCREEN(3), which in
turn is derived from work sponsored by the EPA and prepared by Spicer(4I) - see Section
5.1.5 below.
As an example, suppose the static head is h = 3 m. The density of liquid acetone is 791
kg/m3. (Note that a good reference for the standard properties of materials, such as density
and specific heat, is to be found in Reference (46), "Data Compilation - Tables of Properties
of Pure Compounds.") Since there is no additional source of pressure, p = pa. Assume that
there is a leak with an effective diameter 1/2". Then A = (3.142)(l/4)2 = 0.196 in2 =
1.2x10^ m2. Using Eq. (5-1), the initial rate of release is :
Q = (0.6)(1.2xlO^)(791){(2)(9.82)(3)}"2
= 0.437 kg/s.
If the hole has a diameter of 2", the area A is 4.8X10"4 m2 and Q = 1.75 kg/s. See Section
4.3 for guidance on selecting hole sizes.
5.1.3 Behavior of Pool on Ground
As the liquid spills from the vessel, it will spread across the ground. There are several
possibilities - for example:
a) the spill is so rapid that a surrounding diked area is covered almost at once
and the subsequent evaporation takes much longer than the spill from the
vessel
5-2
-------
b) The pool spreads until the rate of evaporation just equals the rate of spillage.
This can happen for a small rate of spill within a diked area, or for any rate
of spill with an undiked area; or
c) The contents of a vessel or drum spill very rapidly and the pool continues to
spread after the spillage from the vessel has ceased.
For simplicity, the case of rapid coverage of a diked area with a subsequent relatively long
period of evaporation is considered below. Discussion of more complex cases is given
below.
5.1.4 Calculation of Evaporation Rates
There is considerable literature on the evaporation rate of liquids from pools on the
ground(16). For slowly evaporating pools, the following approximation is often used:
Q0 = kg.Ap.pvp.M/(R.Tp) (5-2)
where Q0 is the rate of evaporation (kg/s)
Ap is the area of the pool (m2)
Pvp is the vapor pressure (Pa)
M is the molecular weight (kg/kg-mol)
R is the gas constant (8314 J/mol/K), and
Tp is the temperature of the pool (K).
The parameter kg is the mass transfer coefficient, given by the formula
k, = Dm.N3h/d (5-3)
where Dm is the molecular diffusivity of the vapor in air (m2/s)
d is the effective pool diameter (m), and
N3h is the Sherwood number, given by
N,h = 0.037 (kJDJlfl((ud/kjai - 15,200) (5-4)
5-3
-------
where k^ is the kinematic viscosity of air (m2/s), and
u is the windspeed at a height of 10 m (m/s).
Note that this formula neglects other potential sources of heat such as insolation. The
reader should consult standard texts for the treatment of such sources, see Section 5.6.1.
The formula is applied as follows:
i) The temperature of the pool is 278 K (assumed to be a typical ambient temperature
during atmospheric stability category F conditions).
ii) The vapor pressure pvp of the acetone over the pool is given by:
Log10(pvp) = exp(-0.2185A/Tp + B)
from which pvp = l.OSxlO4 Pa. (5-5)
This equation is taken from the Handbook of Chemistry and Physics(I8), which
contains a table of estimates of A and B for a great number of substances.
iii) The area A of the pool is 400 m2 as stated above.
iv) The molecular weight of acetone is 58.
v) As stated above, the gas constant R is 8314 kg/kg-mole
vi) The effective diameter of the pool d is 20 m, the square root of the area.
vii) The windspeed u at a height of 10 m is 1.5 m/s because the calculations here are
being done in atmospheric stability category F with a low windspeed of 1.5 m/s
viii) The kinematic viscosity of air k,,, is l.lxlO"5 m2/s from standard texts, see, for
example, Ref. (17).
ix) Dm.the molecular diffusivity of acetone in air, is l.lxlO"3 m2/s from Reference (17).
5-4
-------
x) Sample Rate of Evaporation in a Windspeed of 1.5 m/s at 278 K
Nsh = 0.037(1. lxlO-5/1.10xlO-5)I/3.X (Eq. (5-4))
X = ((1.5x20/l.lxlO-5)0'8 - 15200)
Nsh = 4646
kg = (l.lxlO'5).(4646)210 = 2.555xlO'3 (Eq. (5-3))
Q0 = (2.555xlO-3).(400).(1.05xl04).(58)/((8314).(278))
= 0.27 kg/s = 38 Ib/min (from Eq. (5-2)).
Note that, from above, the rate of spillage from a 2" hole is predicted to be 1.48 kg/s. This
greatly exceeds the predicted rate of evaporation, 0.27 kg/s, showing that the assumption
that the whole diked area is rapidly covered is a reasonable one.
5.1.5 Equations in TSCREEN
TSCREEN^'40 implements the following equtions:
Q = 6.94xlO'7(l + 0.0043[TP - 273.15]V'73AMpvp/Pvh (5-6)
where Tp is the temperature of the pool (K)
u is the windspeed at a height of 10 m (m/s)
A is the area of the pool (m2)
M is the molecular weight (kg/kg-mol)
pvp is the vapor pressure of the material in the pool, in the present case acetone,
(Pa), and
pvh is the vapor pressure of hydrazine (Pa) (i.e. Eq. (5-6), for reasons of calculational
convenience, calculates the evaporation rates of all materials by comparison with the
rate for hydrazine).
In the above equation, [Tp - 273.15]' is taken to be zero if Tp - 273.15 < 0. pvp is evaluated
using the Clausius - Clapeyron equation:
Pvp = 101325 exp[(XM/R)[(l/Tb) - (1/TP)]] (5-7)
5-5
-------
where X is the latent heat of vaporization of acetone at the normal boiling point (S.OlxlO5
R is the gas constant (8,314 J/kmol/K), and
Tb is the boiling point of the material in the pool (330 K for acetone).
The vapor pressure of hydrazine is given by:
pvh = exp [76.858 - 7245.2/Tp - 8.22 ln(Tp) + 0.0016557TP] (5-8)
Using Eqs (5-6) through (5-8) gives a predicted rate of evaporation for acetone in a 400 m2
diked area at a temperature of 278 K of 0.65 kg/s, 2.4 times that calculated in Section 5.1.4.
Thus, it appears that the equations in TSCREEN are conservative. The reader wishing to
be consistent with other EPA guidance should use these methods.
5.1.6 Duration of Evaporation
Suppose that there is a one long ton - 1,000 kg of acetone left in the vessel. If the spill
were to evaporate at a constant rate of 0.27 kg/s, evaporation would be complete in almost
exactly one hour, assuming that no mitigating measures are available.
In general, the duration of release must be assessed on a case by case basis, taking account
of the quantity released, the rate of evaporation, the availability of mitigating measures and
potential operator actions.
5.1.7 Density of Mixture
As calculated above, the predicted vapor pressure of the acetone at 278 K is about l.OxlO4
N/m2, or about one tenth of one atmosphere. Therefore, each cubic meter above the pool
contains 0.9 m3 of air and 0.1 m3 of acetone. The density of air at 278 K is 1.27 kg/m3.
The density of acetone at 278 K is 2.549 kg/m3. Therefore, the overall density is
(0.1)(2.549) + (0.9)(1.27) = 1.398 kg/m3. Thus, the density difference is (1.398 - 1.27)/1.27
- 10%, sufficient to ensure initial denser-than-air behavior (experience shows that denser-
than-air behavior persists down to density differences as low as 0.1%). That is why it is
appropriate to use SLAB or DEGADIS.
5-6
-------
5.1.3 Input to SLAB
The Users' guide to SLAB is to be found in Ref.(19). The input to SLAB for the acetone
release described above is given in Table (5-1).
Line 1: IDSPL is the spill source type. IDSPL = 1 for an evaporating pool.
Line 2: NCALC is a numerical substep parameter. The code developer recommends using
NCALC = 1. However, NCALC can be increased if numerical stability problems are
encountered.
Line 3: WMS is the molecular weight of acetone in kg/mole WMS; = 0.058.
Line 4: CPS is the specific heat at constant pressure, CPS = 1450 J/kg/K.
Line 5: TBP is the boiling point of acetone, 330 K.
Line 6: CMEDO is the liquid mass fraction in the initial airborne cloud, which in this case
is 0 because only vapor evaporates from the pool on the ground.
Lines 7 - 9: DHE = 5.01E 05 , CPSL = 2,058 and RHOSL = 791 are the heat of
vaporization at 293 K (J/kg), the specific heat of liquid acetone (J/kg/K) and the_ liquid
density (kg/m3) respectively.
Lines 10.11: SPB and SPC are parameters that go into the formula for the saturated vapor
pressure of acetone:
Ps = Pa.exp(SPA - SPB/(T + SPC)) (5-9)
Ps is the saturated vapor pressure, Pa is the ambient pressure (= LOlxlO5 Pa). Table 2 of
the Users' guide contains some values of SPB and SPC, but not for acetone. When these
values are not known, the user's guide recommends default values of SPB = -1 and SPC =
0. T is the ambient temperature, 278 K. The code then uses the Clapeyron equation to
define the value of SPB. When the source is pure vapor, as it is in the present case, and
the temperature of the cloud does not drop below the boiling point, this default is always
5-7 '
-------
Table 5-1. SLAB Input -
Spillage of Acetone into a Diked Area
1
1
0.058
1450.
330.
0.0
5.01E 05
2058.
791.
-1
0.
278.
0.27
400.
3600.
0.
0.0
1800.
l.OE 04
1.
0.
0.
0.
0.1
10.
1.5
278.
75.
6.
-1.
IDSPL
NCALC
WMS
CPS
TBP
CMEDO
DHE
CPSL
RHOSL
SPB
SPC
TS
QS
AS
TSD
QTIS
HS
TAV
XFFM
ZP(1)
ZP(2)
ZP(3)
ZP(4)
zo
ZA
UA
TA
RH
STAB
TER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
5-8
-------
adequate because neither the saturation pressure nor any of the liquid properties will be
used in the SLAB calculation. However, a value for all of these properties must be
specified in the input whether they are used or not.
Lines 12 - 17 specify spill parameters, which have already been discussed in detail above.
TS is the temperature of the released material, 278 K. QS is the rate of release, 0.27 kg/s.
AS is the effective area of the source, 400 m2. TSD is the duration of release, 3600 s. QTIS
is zero except when IDSPL = 4, when it specifies the mass in a puff release. HS.is the
height of release, taken to be Om (close to ground level).
Line 18: TAV is the exposure time. This is set equal to 1800 seconds to be consistent with
the definition of the LOG, in this case assumed to be the IDLH/10 (note - SLAB does not
explicitly ask for this value) which is valid for an exposure time of 30 minutes. See p.52 of
the Users' guide for caveats on the use of this quantity, particularly if TAV > > TSD. '
Line 19: XFFM is the maximum downwind extent of the calculation. It may be necessary
to determine this by trial and error. A value of 10 km (l.OxlO4 m) should be adequate for
many applications.
Lines 20-23: ZP(I) allows the user to specify up to four heights at which the concentration
is calculated as a function of downwind distance. ZP(1) is taken to be 1.6 m (head height).
The remaining ZP(I) are zero, which means that SLAB only considers the first height.
Lines 24 - 29 allow the user to specify meteorological conditions. ZO is the surface
roughness length, which is set to 0.1 m for this example. In the User's Guide, the authors
of SLAB caution against using too high a value of ZO. ZA is the height at which the
windspeed is measured (10 m). UA is the windspeed at height ZA (1.5 m/s). TA is the
ambient temperature (278 K). RH is the relative humidity (75%). STAB is the stability
class (6 or F). The user can easily change the windspeed or atmospheric stability class if
he/she wishes to use different weather conditions..
Line 30: TER < 0 terminates the run.
5-9
-------
Note that SLAB does not have inputs for levels of concern. That is, SLAB does not provide
contours of constant concentration. The user must postprocess the output to obtain the
distances or contours of concern.
5.1.9 Input to DEGADIS
The DEGADIS Users' manual is available as Reference (4), which is the EPA-sponsored
version. An additional source of information on DEGADIS is given in Ref.(20), which was
sponsored by the Gas Research Institute. The input to DEGADIS is described in Table
(5-2), which is the free format input to the module of DEGADIS that models heavy vapor
releases at ground level. The table was generated by using the interactive mode of input
to DEGADIS. References (4) and (5) adequately describe this interactive mode. The
easiest way for a user to become familiar with DEGADIS is to experiment with the
interactive mode of input.
Lines 1-4 of the table allow the user to input four lines of title.
LineJ requests a value of the windspeed UO at a height of ZO m. As in the SLAB example,
these take on values of 1.5 m/s and 10 m. Line 5 also requires a value of the surface
roughness length ZR, which is 0.1 rn for all of the examples in this report. If the user
wishes to use different weather conditions, he/she can readily change UO.
Line 6: ISTAB is the atmospheric stability category, in this case F (6). The user can easily
change ISTAB to 1,2,3,4 or 5 if stability categories A through E respectively are required.
Line 7: OODIST is the distance downwind from the source at which the DEGADIS
calculations start. OODIST is zero for a ground level release. AVTIME is the averaging
time for plume meander, set equal to 3600 seconds because the duration of release is 3,600
seconds, see Section 5.1.6.
Line 8: DELTA and BETA are coefficients in the expression for the horizontal standard
deviation in the passive phase:
5-10
-------
Table 5-2. DEGADIS Input-
Spillage of Acetoue into • Diked Area
tONI INI I) SPILL INTO A DIK ED AREA
STEADY STATE ACETONE SPILL, POOL DIAMETER 10
1000
.10
1.30
6
00 3600.00
7.74E-02 .90 17.52
.17 .97 50.00
278.00 I 00 4.00E-03 75.00
0 278.00
0 .00
0 .00
ACL
L/, 5808 278.00 2.55
~ 1450. 1.00
~ .15 2.00L-05 1.60
2.30E-05
00
4
00 .70 11.20 0.10
1600. .70 11.20 0.10
3601. .00 .0000 0.10
3602. .00 .0000 0.10
I I I I I I
8 MAY-1992 17:24: 7.63
.70 20.00 7.85
278.00
278.00
278.00
278.00
1.00
LOO
1.00
1.00
TITLE I I
TITLE 2 2
TITLE 3 3
TITLE 4 4
UO, ZO, ZR 5
ISTAB 6
OODIST, AVTIME 7
DELTA, BETA, RML 8
SIGX COEFF, SIGX POW, SIGX MIN_DIST 9
TAMB, PAMB, HUMID JO
ISOFL, TSURF 11
I1ITFL, HTCO 12
IWTFL, WTCO 13
GAS_NAME 14
GAS MW, GAS_TEMP, GAS_RHOE 15
GAS CPK.GAS CPP 16
GAS_UFL, GAS_LFL, GAS_ZSP 17
CCLOW 18
GMASSO 19
NT ' 20
PTIME(I), ET(I), RIT(I), PWC(I), PTEMP(I), PFRACV(I) 21
PTIME(2), ET(2), RIT(2), PWC(2), PTEMP(2), PFRACV(2) 22
PTIME(3), ET(3), RJT(3), PWC(3), PTEMP(3), PFRACV(3) 23
PTIME(4), ET(4), RIT(4), PWC(4), PTEMP(4), PFRACV(4) 24
CHECK I, CHECK2, AGAIN, CHECK3.CHECK4.CHECK5 25
TINP 26
ESS, SRCLEN, SRCB 27
-------
cry = DELTA.XBETA (5-10)
where the values of DELTA and BETA are given on p.32 of Ref.(20):
Stability Category DELTA BETA
A
B
C
D
E
F
0.423B
0.3 13B
0.210B
0.136B
0.102B
0.0674B
0.9
0.9
0.9
0.9
0.9
0.9
where B = (AVTIME/600)0'2 accounts for plume meander during prolonged releases. Note
that the above values of DELTA are characteristic of dispersion at rural sites.
RML is the Monin-Obukhov length (see Section 4.2.1.) which is either directly calculated by
the interactive data input module (as is the case here) or input by the user.
Linej? consists of parameters that describe the spreading of the plume along the wind due
to the action of atmospheric turbulence. The x-direction dispersion coefficient SIG-X-MIN-DIST (5-11)
where X is the distance downwind of the source. This expression is explained on p.(34) of
Ref.(20):
5-12
-------
Stability Category SIGX-COEFF SIGX-POW SIG-X-MIN-DIST
Unstable (A,B,C)
Neutral (D)
Stable (E,F)
0.02
0.04
0.17
1.22
1.14
0.97
130m
100m
50m
Line 10: TAMB is the ambient temperature, taken to be 278 K, which lies within the likely
range for atmospheric stability category F. PAMB is the ambient pressure, taken to be one
atmosphere ( the results are not particularly sensitive to this parameter). HUMID consists
of two numbers, the absolute humidity (4.0xlO~3 kg water/kg air) and the relative humidity,
which is set to 75% as being consistent with a cool, relatively humid night such as might
occur under category F weather conditions.
Line 11: TSURF is the surface temperature, set equal to the air temperature in the present
example, 278 K. ISOFL is a number generated by the DEGADIS interactive input routine
in answer to the question, is this an isothermal spill? The answer is no in this case, leading
to ISOFL = 0. "No" here implies that the effect of heat sources, such as heating by the
ground or the heat entering the system as heat is entrained, is taken into account.
Lines 12 and 13: IHTFL, HTCO, IWTFL and WTCO are also generated by the interactive
method of preparing input for DEGADIS. IHTFL is generated in answer to the question,
is heat transfer included? Again, the answer is no in this case and DEGADIS generates
both IHTFL = 0 and HTCO = 0. IWTFL is generated in answer to the question, is water
transfer to be included in the source? The answer is no so that IWTFL = 0 and WTCO
= 0 as generated by DEGADIS.
Line 14: GAS-NAME is a three character identifier chosen by the user.
Line 15: GASMW is the molecular weight of the gas, 58.08. GAS-TEMP is the
temperature of the released gas (278 K) and GAS-RHOE is the density of acetone at that
temperature (2.55 kg/m3).
5-13
-------
Line 16: GAS-CPK and GAS-CPP are parameters in DEGADIS' formula for specific heat
at constant pressure. In the formulation chosen here, 1,450 J/kg/K is the specific heat of
acetone and GAS-CPP = 1 ensures that this value is chosen independent of temperature.
There are more sophisticated options in DEGADIS, allowing temperature dependence of
the specific heat; these options are not discussed here.
Line 17: GAS-UFL is the upper concentration of interest. It is labeled "UFL" because the
model was originally developed to handle flammable vapors. Here, it is arbitrarily set equal
to 0.15. GAS-LFL corresponds to the lower flammable limit or, for a toxic gas, the LOG.
For acetone, the LOG is taken to be 2.0xlO"5 ppm, which in this case is the IDLH/10 and
is valid for an exposure time of 30 minutes. Finally, ZSP is the height at which the
concentration is measured, taken to be 1.6 m (head height).
Line 18: CCLOW is the lowest concentration of interest (in kg/m3). The interactive
module of DEGADIS prints out a suggested value (in this case, 2.3xlO"5 kg/m3). The user
is free to change this value if so desired. It is a lower level of concentration below which
the computer model terminates its calculations.
Line 19: CMASSO ( = 0) is the initial mass over the pool and can be used, for example, for
puff releases. It is zero for a continuous release.
Line 20: NT specifies the number of times at which release parameters are required. For
a release at a constant rate-over a finite duration NT=4, see the discussion of lines 21-24
for an explanation.
Lines 21-24 specify release rate parameters at four times:
PTIME(l) = 0 (release starts): PTIME(2) = 3,600 s. If PTIME (2) = 60,000 s, a steady
state release is assumed). If PTIME(2) < 60,000, a transient release of duration PTIME(2)
is assumed. PTIME(3) and PTIME(4) are always 1 and 2 seconds respectively more than
PTIME(2) and are required by DEGADIS to indicate that the release has terminated.
Thus, for a steady state release or for a release at a fixed rate for a finite time, NT=4. The
array ET contains the rate of release (0.27 kg/s up to 3,600 s and 0 thereafter). The array
RIT contains the radius of the pool, taken to be 11.2 m (the radius of a pool of area 400
m2). The array PTEMP contains the pool temperature (278 K). The array PWC(I) contains
5-14
-------
the initial mole fraction of the released material. In this case, the mole fraction above the
pool is 0.1, see Section 5.1.6.
Lines 25-27 are always generated by the interactive data entry module and are not further
discussed here. Line 27 only appears for the case of a steady state release and gives the
rate of release, source length and source half width (ESS, SRCLEN and SRCB respectively).
5.2 Spillage from Drum
In this case, it is assumed that a drum containing a liquid is punctured and the liquid spills
on the ground. It is unlikely that there will be a dike to contain the spill. A simplified and
likely conservative approach is to assume that the whole contents of the vessel spill at once
and spread to a depth h of one centimeter. If the volume released is V m3, the area A
covered by the spill is then V/0.01 m3 (from the formula V = Ah).
The rate of evaporation Q0 can then be calculated using Equations (5-1) through (5-3). If
the density of the liquid is pL, the liquid regression rate is r = Q0/(/oLA) m/s and the
duration of release td is h/r = 0.01/r. Once these quantities have been determined, input
for the computer models can be generated in exactly the same way as is described in Section
5.1.
5.3 Spillage of HF at 60 °F
5.3.1 Description of Scenario
This example is deliberately chosen to illustrate a case in which finding appropriate values
of input parameters is more difficult. The specific example chosen is one relevant to "other"
sites in which anhydrous hydrogen fluoride is in a refrigerated storage vessel: a brine cooling
loop keeps its temperature at 60 °F, about 10 °F below its boiling point. Note that
anhydrous hydrogen fluoride contains no water and this is how it differs from aqueous
hydrogen fluoride, which is a solution of HF in water. In this hypothetical example, a pump
withdraws the HF from the vessel and transfers it to a reactor where
hydrochlorofluorocarbons (HCFCs) are produced. These are refrigerants that have a small
effect on the ozone layer relative to the chlorofluorocarbons (CFCs), the use of which is to
be phased out by international agreement.
5-15
-------
The vessel and the associated pipework may leak for a number of reasons - e.g. gasket
failure, corrosion or puncture by an external agent such as a fork lift truck or a vessel. The
assumption is that the leak is large enough to fill the diked area quickly.
5.3.2 Calculation of Release Rate
As noted above, the chosen example is one in which there is a leak in a refrigerated storage
vessel containing anhydrous HF. The HF spills into a hypothetical diked area that is
assumed to be 10 mxlO m = 100 m2. Eqs. (5-2) through (5-4) are applied as follows.
i) The temperature of the pool is 60 °F as stated above.
ii) The vapor pressure pvp of the HF over the pool is given by:
pvp = exp(-3030/Tp + 21.9) = 9.1xl04-Pa, see Eq. (5-5).
iii) The area A of the pool is 100 m2 as stated above.
iv) The molecular weight M of HF at 60 °F and atmospheric pressure is about 70 kg/kg-
mol because of the oligomerization effect (that is, it exists as a mixture of HF, (HF)2,
(HF)6 and (HF)8). However, wind tunnel experiments on the evaporation of HF
from pools show that there is very little evidence of heavier-than-air vapor effects.
It is possible, therefore, that the HF evaporates from the pool as a monomer and
does not immediately form (HF)2, (HF)6 and (HF)8. However, for the. sake of
conservatism in Eq. (5-2), where the rate of evaporation of HF is proportional to M,
the molecular weight is taken to be 70. This is an assumption that might require
further consideration at a later date.
v) As stated above, the gas constant R is 8,314 kg/kg-mol
vi) The effective diameter of the pool d is 10 m, the square root of the area.
vii) The windspeed u at a height of 10 m is 1.5 m/s (as above).
viii) The kinematic viscosity of air ^ is l.lxlO"5 m2/s from standard texts.
5-16
-------
ix) Dm, the molecular diffusivitv of HF in air is ~ 10~5 m2/s, see Appendix H or
Reference (46).
x) Sample Rate of Evaporation in a Windspeed of 1.5 m/s
Nsh = 0.037(l.lxlO-5/9.84xlO-6)1/3.X (Eq.(5-4))
X = ((1.5xlO/l.lxlO-5)a8 - 15200)
Nsh = 2520
kg = (9.84xlO-6).(2520)/10 = 2.487xlQ-3 (Eq.(5-3))
Q0 = (2.487xlO-3).(100).(9.1xl04).(70)/((8314).(289))
= 0.66 kg/s = 87 Ib/min (from Eq. (5-2)).
5.3.3 Atmospheric Dispersion Model
As noted above, vapor clouds from HF evaporating from pools in wind tunnels do not
exhibit denser-than-air behavior. Therefore, it is appropriate to use the Gaussian dispersion
model with a line source width of 10 m. Far downwind, this line source becomes
indistinguishable from a point source. TSCREEN would be a suitable atmospheric
dispersion model for this case.
5.4 Spillage of Cryogenic Liquid into Diked Area
5.4.1 Choice of Example - Release Rate a Function of Time
This example will generally be relevant to "other" sites rather than to superfund sites and
consists of the case of a refrigerated chlorine vessel standing within a diked area. There is
a leak for reasons that are similar to those discussed above for acetone or HF. It is
assumed that the leak is large enough to fill the diked area quickly. In this case, the rate
of evaporation is driven by the rate at which heat can be transfered into the liquid from the
surface on which the pool lies. The rate of evaporation is given by:
5-17
-------
Q0 = (k.(Tf - T))/((ast)°-5H,) (5-12)
where ks = thermal conductivity of the material on which the pool lies (W/m/K)
Tg = temperature of the ground (K)
T = temperature of the liquid pool (K)
a, = thermal diffusivity of the soil (m2/s)
t = time after spill (s), and
HL = latent heat of vaporization of spilled material (J/kg).
Thus, this example is one in which the release rate varies as a function of time - it is
proportional to t'1'2.
Eq. (5-14) differs from Eq. (5-2) because two completely different cases are being
considered. Eq. (5-2) refers to the evaporation of a liquid at ambient temperature where
the vapor pressure is less than one atmosphere. In that case, the wind governs the rate of
evaporation. Eq. (5-14) is for a liquid with a temperature that is far below ambient. In this
case, evaporation is driven by the rate at which heat is conducted into the pool from the
surface beneath.
i) The thermal conductivity or, of surfaces such as concrete and soil is generally of the
order of 2 W/m/K. For insulating concrete, this value can be considerably smaller.
ii) The temperature of the ground Tg is 278 K as in all of the examples in this report.
iii) The temperature of the liquid pool T is assumed to be that of chlorine at its boiling
point, 239 K. Therefore, Tg -T = 39 K.
iv) The typical value of the thermal diffusivitv of the underlying surface is 10~6 nr/s.
v) The latent heat of vaporization of chlorine is 2.88x10* J/kg.
vi) The coefficient of f0-3 in Eq. (5-14) is (2)(39)/{(10-6)°'5(2.88xl05). = 16.62. Thus, the
predicted rate of evaporation after 300 seconds is 0.96 kg/s. The rate of release as
5-18
-------
Table 5-4. SLAB Input -
Spillage of Refrigerated Chlorine into a Diked Area
1
1
0.07091
498.1
239.1
0.
287840.
926.3
1574.
1978.34
-27.01
239.1
0.783
100.
1800.
0.
0.
3600.
l.OOE + 04
1.
0.
0.
0.
0.1
10.
1.5
278.
75.
6.
-1.
IDSPL
NCALC
WMS
CPS
TBP
CMEDO
DHE
CPSL
RHOSL
SPB
SPC
TS
QS
AS
TSD
cms
HS
TAV
XFFM
ZP(1)
ZP(2)
ZP(3)
ZP(4)
zo
ZA
UA
TA
RH
STAB
TER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
5-20
-------
Lines 10.11: SPB and SPC are parameters that go into the formula for the saturated vapor
pressure of chlorine:
Ps = Pa.exp(SPA - SPB/(T + SPC))
P3 is the saturated vapor pressure, Pa is the ambient pressure (= l.OlxlO5 Pa), a value for
SPA is specified in the code and the values of SPB (1978.34) and SPC (27.01) are given in
the SLAB Users' Guide. T is the ambient temperature (K).
Lines 12 - 17 specify spill parameters, which have already been discussed in detail above.
TS is the temperature of the released material, 239 K. QS is the rate of release. Note that
SLAB cannot accept a time varying release rate. In principal, SLAB could be rerun for
differing release rates over short periods of time and then the results postprocessed to give
average concentrations over the whole duration of release. This has not been attempted
here, but rather an average value QS = 0.783 kg/s over 1,800 s has been chosen. AS is the
effective area of the source, 100 m2. TSD is the duration of release, 1800 s. HS is the
height of release, 0 m. As described before, QTIS = 0 except for a puff release.
Line 18: TAV is the exposure time. This is set equal to the exposure time corresponding
to the LOC, in this case 3600 seconds because ERPGs are available for chlorine.
5.4.3 Input to DEGADIS
The input to DEGADIS is given in Table (5-5). The following text explains only items that
were not previously explained.
Line 12: IHTFL is one because heat transfer is included.
Lines 14 - 18: give the properties of the gas: CL2 (GAS-NAME), 70 (GAS-MW), 238.7 K
(the assumed temperature of the vapor above the pool), 3.67 kg/m3 (the density of chlorine
vapor at this temperature, calculated using the perfect gas law). The specific heat at
constant pressure is 484 J/kg/K (GAS-CPK) and choosing GAS-CPP to be unity ensures
that CPK remains constant at all temperatures. The GAS-UFL and the GAS-LFL are the
LOCs, in this case the ERPG-3 for C12, 20 ppm and the ERPG-1, 3 ppm. GAS-ZSP is the
5-21
-------
Table 5-5. DEGADIS Input -
Spillage of Refrigerated Chlorlue into a Diked Area
CRYOGENIC LIQUID SPILL ONTO GROUND
CHLORINE SPILL INTO DIKED CONCRETE AREA
TRANSIENT SIMULATION
1.50 10.00
6
.00 1800.00
7.74E-02 .90 1
.17 .97 50.<
278.00 1.00
0 278.00
1 .00
0 .00
CL2
70.91 238.70
484.20 1.00
2.00E-05 3.00E-06
9.32E-06
.00
9
.00000 16.62
300.00 .9600
600.00 .6790
900.00 .5540
1200.0 .4800
1500.0 .4290
1800.0 .3920
1801.0 .0000
1802.0 .0000
F FFFFF
11 -MAY- 1992 18:33:
.10
7.52
X)
4.00E-03
3.67
1.60
5.60
5.60
5.60
5.60
5.60
5.60
5.60
.000
.000
28. 7
75.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
238.70
238.70
238.70
238.70
238.70
238.70
238.70
238.70
238.70
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
TITLE I 1
TITLE 2 2
TITLE 3 3
TITLE 4 4
UO, ZO, ZR 5
ISTAB 6
OODIST, AVTIME 7
DELTA, BETA, RML 8
SIGX_COEFF, SIGX POW, SIGX_MIN_DIST 9
TAMB, PAMB, HUMID 10
ISOFL, TSURF 11
IHTFL, HTCO 12
IWTFL. WTCO 13
GAS_NAME 14
GAS_MW, GAS_TEMP, GAS_RHOE 15
GAS_CPK, GAS_CPP 16
GASJUFL, GAS_LFL, GAS_ZSP 17
CCLOW 18
GMASSO 19
NT 20
PTIME(I), ET(I), RIT(I), PWC(1), PTEMP(l), PFRACV(I) 21
PTIME(2), ET(2), RIT(2), PWC(2), PTEMP(2), PFRACV(2) 22
PTIME(3), ET(3), RIT(3), PWC(3), PTEMP(3), PFRACV(3) 23
PTIME(4), ET(4), RIT(4), PWC(4), PTEMP(4), PFRACV(4) 24
PT1ME(5), ET(5), R1T(5), PWC(5), PTEMP(5), PFRACV(5) 25
PTIME(6), ET(6), RIT(6), PWC(6), PTEMP(6), PFRACV(6) 26
PTIME(7), ET(7), R1T(7), PWC(7), PTEMP(7), PFRACV(7) 27
PTIME(8), ET(8), RIT(8), PWC(8), PTEMP(8), PFRACV(8) 28
PTIME(9), ET(9), RIT(9), PWC(9), PTEMP(9), PFRACV(9) 29
CHECK I, CHECK2, AGAIN, CHECK3.CHECK4.CHECK.5 30
TINP 31
-------
height at which concentrations are calculated, i.e. head height (1.6 m). CCLOW is
calculated by DEGADIS as a recommended input value.
Lines 20 - 29 specify the release rates ET(I) for the times PTIME(I) from Table 5-3. The
radius is taken to be 5.6 m for a diked area of 100 m2. PWC, PTEMP and PFRACV have
already been explained.
5.5 Spillages onto Water
This is one of the source terms for which the available resources did not permit the detailed
development of an example. The models used for calculating the rates of evaporation of
chemicals onto water differ somewhat from those used for releases onto land. The principal
differences arise in the behavior of the chemical immediately after release and in the rate
of evaporation. For example, a cryogenic liquid, such as LNG, released onto water boils
rapidly, at almost a constant rate. Other materials may interact with the water (e.g.
anhydrous ammonia). In such cases, chemical specific models need to be developed.
A review of models for evaporation following spillages onto water has been given by Raj(22).
The specific example of ammonia is covered in Reference (23).
5.6 Additional Considerations
There are additional items to be considered that are not part of the above discussion of
specific source terms. They generally cover areas where the requestor and /or analyst
should seek expert advice.
5.6.1 Heat Sources
The evaporation equation (5-2) contains the assumption that the rate of evaporation is slow
and that the temperature of the pool remains constant. This will certainly not always be so
and a comprehensive model should take account of the following sources of heat:
o the rate of convective heat transfer from the air to the pool in cases where the
temperatures of the pool and the air differ. The rate is proportional to the
temperature difference
5-23
-------
o the rate of radiative heat transfer from the air to the pool. This effect is
proportional to the difference in the fourth power of the temperatures.
o solar radiation
o transfer of heat from the dike walls
o heat lost due to evaporation of the pool; and
o heat added as additional liquid enters the pool from the vessel.
A clear and concise discussion of these heat sources may be found in Ref. (24).
5.6.2 Spreading Pool
The examples given above are all for a confined pool. If there is no diked area, the pool
will spread and the evaporation rate becomes a function of time. The reader is referred to
Reference (22) for further details. An earlier, "classical" reference is that by Shaw and
Briscoe.(25)
5.6.3 Advanced Modeling
The modeling described above is considerably simplified. As noted above, it does not cover
heat sources such as solar radiation or spreading pools. In general, the vaporization rate
is a function of the wind-speed, the pool temperature, the pool size, the properties of the
liquid under consideration and the thermal properties of the environment. The problem
simplifies in two limits: the "boiling cryogen" limit where the vaporization rate is entirely
controlled by the heat flux into the pool and the "evaporation" limit where the pool is
essentially at ambient temperature and mass transfer is controlled by the rate at which the
air streaming over the pool can remove the vapor. In the first case (see Section 5.4) the
vaporization rate is independent of the windspeed. In the second case (see Sections 5.1 and
5.3) it depends strongly on the windspeed.
In general, and in particular for substances which boil close to ambient temperature, neither
of these two limits is appropriate. In that case, there are a number of coupled linear
5-24
-------
differential equations that need to be solved and numerical modeling is required. The issues
involved are discussed in Reference (26).
5-25
-------
6.0 JETS CONTAINING LIQUID AND VAPOR
These releases correspond to the Scenarios labeled #3 in Figure 2-1. They are
characterized by a liquid jet with subsequent flashing to vapor and aerosol. In addition, this
category of releases contains vapor jets in which there is condensation accompanying
expansion from the pressure in the reservoir to atmospheric pressure, see Section (7.1). The
cases considered here differ from the pure vapor releases in Sections 5 or 7 in that the
airborne release consists of both vapor and liquid droplets.
Section (6.1) contains a detailed theoretical discussion of various release formulae. This
discussion follows closely the methods developed by Spicer <36), which were sponsored by the
EPA and have been incorporated into TSCREEN. Sections (6.2) through (6.4) then contain
specific examples, including, first, consideration of an orifice of diameter 1/2" in a vessel
containing HF at elevated temperature and pressure (Section (6.2)). This is a release that
is very much characteristic of those to be expected at "other" industrial sites. However, it
is useful to begin with it because, by carefully considering it, the reader will become familiar
with many of the issues that must be addressed if such scenarios are to be modeled
realistically.
The HF example is followed by a liquid release from a cylinder containing one ton of
chlorine at ambient temperature (Section(6.3)). Such one ton cylinders are commonly found
at such places as water treatment facilities. Next, the specific example of a cylinder
containing 150 Ib of chlorine is examined as being particularly pertinent to the sort of case
that might need to be considered at a Superfund site (Section(6.4)).
6.1 Emission Rate Formulae - Theory
This section is intended to describe how to model the atmospheric dispersion of momentum
jets that contain a mixture of vapor and fine liquid droplets (two-phase leaks). The
following subsections show how to estimate the release rate for three scenarios:
(i) a gas release that partly condenses when depressurized
(ii) a saturated liquid release from pressurized storage; and
(iii) a subcooled liquid release from pressurized storage.
-------
For all of the cases considered in this section, the following assumptions apply: a) any vapor
phase obeys the perfect gas law; b) the pressure and temperature of the reservoir remain
essentially constant; c) for two-phase flows, all released liquid is assumed to travel
downwind with negligible rainout near the source.
6.1.1 Gas which Partially Condenses on Depressurization
The procedure described herein applies to a continuous release of gas that partially
condenses during depressurization. The screening procedures for determining whether
condensation occurs are described in Section (7.1) The required input information is as
follows:
AO area of reservoir hole or opening (m2)
A, flow area representing reservoir conditions (m2). In the case of a leak
from a tank, A, -» oo and j8 ( = Ag/A,) -» 0. In the case of a small leak
from the wall of a pipe, AI is the area of the pipe's cross-section
•Cp specific heat of gas at constant pressure (J/kg/K)
D0 equivalent diameter of hole opening (D0 = (A^/ir)112 )(m)
Dp pipe diameter (as appropriate) (m)
Lp pipe length (as appropriate) (m)
M gas molecular weight (kg/kg-mol)
pa ambient pressure (N/m2 (Pa))
pv vapor pressure (N/m2(Pa))
p pressure in reservoir (N/m2(Pa))
R gas constant (8314 J/kg-mol/K)
Tb boiling point of released material (K)
Tr release temperature (K)
T! temperature in reservoir (K)
7 Cp/Cv, where Cv is the specific heat of the gas at constant volume
hL heat of vaporization at the atmospheric boiling point (J/kg)
pL liquid density (kg/m3)
The calculations of emission characteristics should proceed as follows:
6-2
-------
A. Calculate Choked Flow Pressure p« from:
I: = <_l_)T/cr-i>
PI Y+l
where p. is the choked flow pressure.
B. Choked Flow: for choked flow, estimate the discharge temperature Tr, the discharge
density pr and the emission rate Q, using the following procedures (for subcritical
flow, go to C below):
a) For pure components, estimate T. (the temperature which corresponds to p«)
from the Clausius-Clapeyron equation:
p. = 101325 exp(^(-L-_L)) (6_2)
For multicomponent mixtures, the value of T» can be estimated using the methods
of Sandier (38) (not discussed further here).
b) Estimate Properties at Choked Flow Conditions: assuming isentropic conditions,
estimate the vapor fraction x. at choked flow conditions:
x, = 1 * --(M Cpln(T1/T.)-Rln(p1/p.)) (6-3)
MhL
Using x, from Eq. (6-3), estimate the enthalpy change (H, - H,) and the density p.
as follows:
(H, -H.) = Cp(T,-T.) + hL(l-x.) (6-4)
RT 1-x
P. = [*.(—-rj) - ( -)]•' (6-5)
6-3
-------
c) Estimate Emission Rate: the formula for the emission rate Q is based on work
by Lees(40):
Q=AoP. [2(0.85)( "")]1* (6-6)
where the factor of 0.85 is included to account for irreversibilities in the flow, based
on work by Levitt(39), and the term 4fLp/Dp accounts for the pressure drop between
the reservoir and the hole opening. Use f = 0.0045.
d) Estimate Discharge Temperature and Density: estimate the discharge
temperature Tr after depressurization. If a condensed phase is present, Tr will be
given by:
pt» 101325 exp(^(_L-J-)) (6-7)
Using this estimate of T^ the released vapor fraction xr is given by:
xr = x. + Cp(T. -Tr)/hL (6-8)
If 1 > ^ ^ 0, the above estimate of Tr is valid and the density of the discharged
material is given by:
RT 1-x .,
r P,M PL
If xr < 0 or xr > 1, the condensed contaminant phase that was present at the choked
conditions p. and T. is no longer present and the release now consists of a pure
vapor, without any condensed phase, in which case the discharge temperature and
density are estimated as follows:
T=T. +ht(l-x.)/Cp <6-l0)
p M
(6-H)
r
and XT = 0.
6-4
-------
C. Subcritical (non-choked) Flow; For subcritical flow, estimate the gas/liquid
discharge temperature T^ the discharge density pr and the emission rate E as follows:
a) Estimate 7/ For pure components, estimate Tr from the Clausius-Clapeyron
equation:
h.M 1 i
Pa = 101325 exp(-L_(JL- _L)) (6.12)
K lb lr
For multicomponent mixtures, Tr can be determined by the methods of Sandler(37)
(not discussed here).
b) Estimate Properties at Discharge Conditions; Assuming isentropic behavior, the
vapor fraction at flow discharge conditions is:
xr = 1 * ^(MCpln(T,/Tr) - Rln(p/pJ) (6-13)
MhL
Using xr from Eq. (6-13), the change in enthalpy (H, - Hr) and the density pr can be
estimated from the following two equations:
(H^H) »Cp(VT,) + hL(l-xr) (6-H)
RT 1 x
Pr = [\(-TJ) + (-^)r' (6-15)
P.M PL
c) Estimate Emission Rate: based on work presented by Lees(40), the emission
rate is given by:
Q - AoPr&(0.8S)()]'fl (6-16)
where the 0.85 is included to account for irreversibilities in the flow, see work by
Levitt(39), and the term 4fLp/Dp is included to account for the pressure drop between
the reservoir and the point of discharge. Use f = 0.0045.
6-5
-------
D. Example: Spicer gives an example of a saturated chlorine vapor leak driven by a
pressure of 2.586xl06 Pa through an orifice of diameter 10.16 cm.
6.1.2 Saturated Liquid from Pressurized Storage
This subsection applies to a continuous release of a pressurized liquid stored under
saturated conditions. The required input information is as follows:
AO area of discharge orifice (m2)
Cp vapor specific heat at constant pressure (J/kg/K)
CpL liquid specific heat (J/kg/K)
DO equivalent diameter of hole or opening (= (Ao/ir)1'2) (m)
Dp diameter of pipe (as appropriate) (m)
Le (empirical) pipe length required to establish equilibrium flow
conditions (0.1 m)
Lp Length of pipe (as appropriate)
M Molecular weight (kg/kg-mol)
pa Ambient pressure (Pa)
p reservoir pressure (Pa)
R gas constant (8314 J/kg-mol/K)
Tb atmospheric boiling point temperature (K)
Tr discharge temperature (K)
T! Temperature in reservoir
hL latent heat of vaporization at the atmospheric boiling point (J/kg) .
pL liquid density at the normal boiling point (kg/m3)
The procedures for estimating emission characteristics are as follows:
A. Estimate Discharge Temperature; the discharge temperature Tr can be estimated
from the Clausius-Clapeyron equation:
htM 1 1
p, = 101325 exp(-L_(JL-JL)) (6-17)
K *b Ar
Note that, for a pressure of one atmosphere = 101,325 Pa, Tr = Tb. For
multicomponent mixtures, the discharge temperature can be calculated using the
6-6
-------
methods of Sandler(37) (not discussed here).
B. Vapor Mass Fraction after Depressurization: the vapor mass fraction after
depressurization is given by:
(6-18)
If 1 S x, > 0, Eq.(7'18) is valid and the reader should proceed to Step C below.
If xr > 1 or xr < 0, seek expert advice - the solution is unphysical.
C. Release Rate: The release rate can be calculated from the formulae of Fauske and
Epstein(34): if VLe ^ 1 (where L, = 0.1 m),
h.Mp T, ..,
Q • V-^*^ (6-19)
pL
where
N =
R(hLMp)2
VL*
Here, C is the discharge coefficient, which takes on a value of 0.6
If Lp /Le > 1:
where F represents the effect of friction in the pipe: F2 = 1/(1 + 4fLp/Dp) with f
0.0015.
6-7
-------
D. Discharge Density: the density after depressurization is:
RT 1 -x
Pr ' W-rrj) + ( -)]" (6-22)
P,M PL
E. Example: Spicer(36) gives an example of a saturated liquid chlorine leak from a
reservoir at pressure 2.586xl06 Pa through an orifice of diameter 10.16 cm.
6.1.3 Subcooled Liquid from Pressurized Storage
This application is similar to that described in Section (7.1.2) except that the liquid is
subcooled -that is, the pressure is less than the saturated vapor pressure at the temperature
of storage. The pressure and temperature in the reservoir are assumed not to change over
the duration of release. The required input information is as follows:
AQ area of discharge orifice (rn)
Cp specific heat of vapor at constant pressure (J/kg/K)
CpL specific heat of liquid at constant pressure (J/kg/K)
D0 equivalent diameter of opening (D0 = (\/ir)m) (m)
Dp diameter of pipe (as appropriate) (m)
Lp length of pipe (as appropriate) (m)
M molecular weight (kg/kg-mol)
pa ambient pressure (Pa)
p pressure in reservoir (Pa)
R gas constant (8314 J/kg/K)
Tb atmospheric boiling point (K)
Tr discharge temperature (K)
TI temperature in reservoir (K)
hL latent heat of vaporization at the atmospheric boiling point (J/kg)
PL liquid density at the atmospheric boiling point (kg/m3)
The calculation is performed as follows:
6-8
-------
A. Estimate the Discharge Temperature T. from the Clausius-Clapeyron equation:
pa = 101325 exp(^l (JL -1)) (6-23)
R Tb Tr
Note that, for pa = one atmosphere = 101,325 N/m2, Tr = Tb. For multicomponent
mixtures, the method of Sandler(37) (not discussed here) should be used.
B. The Vapor Fraction after Depressurization is calculated from the following equation:
(6-24)
If 1 > XT > 0 then Eq. (7-25) is valid and the reader should proceed to step C. If
XT > 1 or xr < 0, seek expert advice, because the solution is unphysical.
C. The Emission Rate O can be calculated using the work of Fauske and Epstein (42):
Q = A [2c2(p-Pl>L + JlL(^Z)2]I/2 (6.25)
where CpL is the specific heat of the liquid at constant pressure and
plv- 101325 exp(^(JL-JL)) (6-26)
and where c = 0.6 is the discharge coefficient. F represents the effect of pipe
friction:
F2 = l/(l+4fL/DJ (6-27)
Here, f = 0.0015.
D. The Discharge Density or is given by:
Pt = l*, + ] (6-28)
P.M PL
6-9
-------
E. Example; Spicer gives an example of a discharge of subcooled liquid chlorine
through an orifice of diameter 10.16 cm from a reservoir in which the pressure is
2.586xl06 N/m2 and the temperature is 298.15 K.
6.1.4 Flow Chart
A flow chart that illustrates the steps outlined above is given on Figure (6-1).
62 HF at Elevated temperature and Pressure
This case is included as an example of a complex scenario from a site other than a
Superfund site and, as noted above, it also illustrates some of the issues that need to be
addressed when the thermodynamics is complex. This case corresponds to scenario #3A
of Figure 2-1.
6.2.1 Description of Scenario
It is assumed that there is a vessel in which there is HF at an elevated temperature of 100
°F and a pressure of 200 psig. The possible failures here are much the same as already
discussed in Section 5.1. For the present case, it is assumed that there is a leak of effective
diameter 0.5".
622 Calculation of Release Rate
The rate of release of liquid from an orifice is given by Bernouilli's formula06':
Q = c.A.pL (2.(p - PJ/pL + 2g.h) "2 (6-29)
where Q is the rate of release (kg/s)
c is a constant, normally set to 0.6
A is the area of the orifice (m2)
p is the absolute pressure in the vessel (Pa)
pa is the atmospheric pressure (l.OlxlO5 Pa)
g is the acceleration due to gravity (9.81 m/s2)
6-10
-------
Vapor Kclease
Scenario from,
Fig. 3-1. p. 6
Scanano 4A
o\
Continue with
Vapor Release
Secc. 7.1
Droplet
Formation?
Sect. 7.1
Calculate
Choked Row
Pressure P *
Eq.(6-l)
Choked How
Source Term
Characteristics
from Eqs (6-2)
through (6-11)
Prepare Source
Term Input for
Vapor Release
Models
Subcruical Row
Source Term
Characteristics
from Eqs (6-12)
through (6-16)
Prepare Input for
Dispersion Models,
wtlh Liquid
Droplets in
Source Term
Liquid Droplet
Release Scenario
from Fig. 3-1. p. 5
Scenario 3A/D
Saturated
Subcoolcd
Source Term
Characteristics
from Eqs (6-17)
through 6-23)
Source Term
Characteristics
from Eqs (6-24)
through (6-29)
Prepare Input
for Dispersion
Models
Figure 6-1
Liquid Droplet Scenarios - Calculation I'loxv Chart
-------
h is the static head, the difference in level between the orifice and the liquid
surface (m), and
pL is the liquid density in the vessel (kg/m3).
The above formula (which is the same as Eq. (5-1)) is suitable for calculating the rate of
pure liquid flow through a circular orifice. It is also the same as Eq. (6-19) for Le/Lp = 0.
There are variations on the formula for a non circular orifice and for cases where there is
flashing in the pipe upstream of the orifice. See Section 6.1.2 for further discussion. Values
to be assigned to the variables in Bernouilli's formula are as follows:
For the case of a half inch orifice, the area A is (3.142)(l/4)2 = 0.196 in2 = 1.2xKT*
m2.
The density of liquid HF is - 1,000 kg/m3
The operating pressure in the vessel is 200 psig = 1.374xl06 Pa. This is well above
the saturated vapor pressure of HF at the operating temperature of 100° F. For
other applications to liquids such as ammonia or chlorine stored under their own
vapor pressure, the pressure in the vessel can be obtained from standard curves of
vapor pressure versus temperature.
The static head h is generally of the order of a few meters (say 5). In the present
case, this makes a very small contribution to the total rate of release.
Applying the above values to Bernouilli's formula gives a rate of release of 3.7 kg/sec ( ~
60 gpm). This rate will persist for some time before there is a significant decrease of
pressure in the vessel.
6.2.3 Other Characteristics of the Source Term
Velocity and Orientation
The velocity of release is given by (Q/A ) = 3.7/1.2x10^/1000 = 30 m/s. For the purposes
of the present example, it is assumed that the release is horizontal in the direction of the
wind (the most conservative assumption).
6-12
-------
Flashing and Vaporization
The liquid will immediately flash and part of it will vaporize. The fraction that flashes to
vapor is given by the formula(16):
Fv = Cp (T, -Tb)/hL (6-30)
where Cp is the heat capacity of the liquid averaged over the temperature range T,
to Tb (J/kg/K)
Tt is the initial temperature of the liquid (K)
Tb is the atmospheric boiling point of the liquid (K)
hL is the latent heat of vaporization of the liquid (J/kg), and
Fv is the fraction of the liquid that is vaporized.
For the present example, the initial temperature of the liquid is 100 °F (310 K). The
atmospheric boiling point of HF is 292.7 K. The heat of vaporization is 208 kJ/kg. The
specific heat of the liquid is - 2500 J/kg/K. Substituting these values into the above
formula gives Fv ~ 0.2.
The balance of the HF (80%) remains liquid at the boiling point of HF. From large scale
HF experiments, it is clear that this liquid does not fall to the ground, but remains airborne
as a fine aerosol. Thus, the initial release consists of 80% liquid droplets and 20% vapor
at the atmospheric boiling point of HF.
Duration of Release
Generically, the duration of the release is hard to predict because it depends on site specific
mitigating equipment and procedures. For example, there may be manual valves that can
be closed in order to isolate the leak. In such a case, the operators would first have to put
on cumbersome protective clothing. It might therefore be 10 - 20 minutes before the
release could be terminated. In the present case, a duration of release of 20 minutes =
1,200 seconds has been assumed.
6-13
-------
6.2.4 Input for SLAB
The input to SLAB for the HF release described above is given in Table (6-1).
Line 1; IDSPL is the spill source type. IDSPL =2 for a horizontal jet.
Line 2: NCALC is a numerical substep parameter. The code developer recommends using
NCALC = 1. However, NCALC can be increased if numerical stability problems are
encountered.
Line 3: WMS is the molecular weight of HF in kg/mol, WMS = 0.02.
Line 4: CPS is the specific heat at constant pressure, taken from a table in the SLAB Users'
manual. CPS = 1450.
Line 5: TBP is the boiling point of HF, 293 K.
Line 6: CMEDO is the liquid mass fraction, which was calculated above to be 0.8.
Lines 7 - 9:DHE = 373,200, CPSL = 2,528 and RHOSL ~ 1,000 are the heat of
vaporization at 293 K (J/kg), the specific heat of liquid HF (J/kg/K) and the liquid density
(kg/m3) respectively. Their values are taken from Table 2 of the SLAB Users' Guide.
Lines 10.11: SPB and SPC are parameters that go into the formula for the saturated vapor
pressure of HF:
Ps = Pa.exp(SPA - SPB/(T + SPC))
Ps is the saturated vapor pressure, Pa is the ambient pressure (= l.OlxlO5 N/m2), a value for
SPA is specified in the code and the values of SPB (3404.51) and SPC( 15.06) are given in
the Users' Guide. T is the ambient temperature (K).
Lines 12 - 17 specify spill parameters, which have already been discussed in detail above.
TS is the temperature of the released material, 293 K. QS is the rate of release, 3.7 kg/s.
AS is the effective area of the source, 0.018 m2. For a flashing liquid jet, the SLAB User's
6-14
-------
Table 6-1. SLAB Input -
Flashing Liquid Release of HF
2
1
0.02
1450.
293.
0.8
3.73E 05
2528.
1000.
3404.51
15.06
293.
3.7
0.018
1200.
0.
5.0
3600.
l.OE 04
1.6
0.
0.
0.
0.1
10.
1.5
278.
75.
6.
-1.
IDSPL
NCALC
WMS
CPS
TBP
CMEDO
DHE
CPSL
RHOSL
SPB
SPC
TS
QS
AS
TSD
QTIS
HS
TAV
XFFM
ZP(1)
ZP(2)
ZP(3)
ZP(4)
zo
ZA
UA
TA
RH
STAB
TER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
6-15
-------
Manual recommends the formula AS = (pL)(A)/(pm) where pL is the liquid density, A is the
orifice area and pm is the density of the vapor/droplet mixture after flashing. Application
of this formula gives AS = 0.018 m2. QTIS = 0 for a release that is not a puff. TSD is the
duration of release, 1200 s. HS is the height of release, 5 m.
Line 18: TAV is the exposure time. This value is conservatively set equal to one hour
because the LOCs for HF are the ERPG-3 and the ERPG-2, which are valid for exposure
times of one hour.
Line 19: XFFM is the maximum downwind extent of the calculation. It may be necessary
to determine this by trial and error. A value of 10 km (1.0xl04m) should be adequate for
many applications.
Lines 20-23: ZP(I) allows the user to specify up to four heights at which the concentration
is calculated as a function of downwind distance.
Lines 24 - 29 allow the user to specify meteorological conditions. ZO is the surface
roughness length, which is here set to 0.1 m. In the User's Guide, the authors of SLAB
caution against using too high a value of ZO. ZA is the height at which the windspeed is
measured (10 m). UA is the windspeed at height ZA (1.5 m/s). TA is the ambient
temperature (278 K). RH is the relative humidity (75%). STAB is the stability class (6 or
F). All of these inputs have been discussed previously.
Line 30: TER < 0 terminates the run.
Note that SLAB does not have inputs for levels of concern. That is, SLAB does not provide
contours of constant concentration. Note also that SLAB does not have the capability of
accepting input such as the ordered triples described below for DEGADIS. Therefore,
SLAB does not take account of the oligomerization of HF. What SLAB does do is to take
account of the initial presence of the liquid droplets of HF and allows separate
evaporation/condensation of both HF and water vapor as the plume dilutes. For many
applications, this will be quite adequate, especially if low levels of concern are being
considered.
6-16
-------
6.2.5 Input to DEGADIS
DEGADIS can be run in one of two modes, a jet release or a pool simulation release. The
table below shows the input to the jet release module of DEGADIS. This differs from the
pool type releases that were described in Section 5 because there are some differences in
the free format input file. The input for DEGADIS is shown on Table (6-2).
Lines 1-4 of the table allow the user to input four lines of title. Note that the second line
above states that the release is being modeled as a vertical jet. This is because DEGADIS
does not allow the user to simulate a horizontal jet. For the present example, it is not
expected that there will be a significant impact on the calculation of contours at low levels
of concentration such as 20 ppm, see the discussion of GASUL, GASLL and NDEN below.
Line 5 requests a value of the windspeed UO at a height of ZO m. For the purposes of the
present example, the category F case is chosen with a windspeed UO = 1.5 m/s. The value
of ZO is 10 m unless specifically stated otherwise.
Line 6 requires a value of the surface roughness length ZR. As noted in previously, the
value has been limited to 0.0.1 m on the advice of the model developers.
Line 7: INDVEL is an index which determines the method of calculation of the velocity
profile in the atmosphere. If INDVEL = 1, the computer program accesses default values
of the profile and of the Monin-Obukhov length based on the stability category ISTAB. In
"the present example, the default mode is chosen by setting INDVEL equal to unity,
choosing the F stability category (ISTAB = 6, see above) and setting the Monin-Obukhov
length RML to 0. RML is then recalculated by the computer program.
Line 8: TAMB is the ambient temperature, taken to be 278 K, which lies within the likely
range for atmospheric stability category F. PAMB is the ambient pressure, taken to be one
atmosphere (the results are not particularly sensitive to this parameter). RELHUM is the
relative humidity, which is set to 75% as being consistent with a cool, relatively humid night
such as might occur under category F weather conditions.
6-17
-------
Table 6-2. DEGADIS Input -
Flashing Liquid Release of HF
FLASHING LIQUID HF RELEASE
VERTICAL JET SIMULATION
1.5 10.
0.1
1 6 0.
278. 1. 75.
278.
HF
20
3600.
293,
4.17E-05 1.7E-05 1.6
0 0.0 0.0
10
0.0 0.0 1.27
0.0125 0.01 1.27
0.025 0.02 1.27
0.125 a. 13 1.44
0.25 0.26 1.55
0.32 0.42 1.69
0.59 1.11 2.21
0.74 1.89 2.83
0.88 3.47 4.16
1.0 13.7 13.7
3.7
5.0 0.106
1200.
50.
TITLE 1
TITLE2
TITLES
TITLE4
UO,ZO
ZR
1
2
3
4
5
6
INDVEL, ISTAB, RML 7
TAMB, PAMB, RELHUM 8
TSURF
GASNAM
GASNMW
AVTIME
TEMJET
GASUL, GASLL, ZLL
INDHT, CPK, CPP
NDEN
ORDERED TRIPLES
ERATE
ELEJET, DIAJET
TEND
DISTMX
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
6.-18
-------
Line 9: TSURF is the surface temperature, set equal to the air temperature in the present
example.
Line 10: GASNAM is a three character identifier chosen by the user.
Line 11: GASMW is the molecular weight of the gas. As has been discussed above, HF
oligomerizes at high concentrations and its molecular weight is effectively much higher than
that of the monomer (20). However, HF oligomerization is taken into account in the
discussion of NDEN below and here it is adequate to set the molecular weight equal to 20.
Line 12: According to the Users' Manual, AVTIME is the averaging time for the
calculation of the width of the cloud. Here it is set equal to the duration of release, 1800
s.
Line 13: TEMJET is the temperature of the release. As described above, this is the
atmospheric boiling point of HF, 293 K.
Line 14: GASUL and GASLL are the upper and lower concentration levels (or "Levels of
Concern" (LOCs)) for which DEGADIS prints out contours of constant concentration. For
the purposes of the present example, the ERPG-3(50 ppm or 4.17xlO"5 kg/m3) and the
ERPG-2 (20 ppm or 1.7xlO"5 kg/m3) are chosen as the levels of concern. Note that the
ERPGs are defined for a period of one hour.
ZLL is the height at which the concentration contours are calculated and is taken to be 1.6
m (head height).
Line 15: INDHT is used to include heat transfer in the DEGADIS computation. Heat
transfer is not included for INDHT = 0. In the present case, INDHT is set equal to zero
because heat transfer is already included under the NDEN entry, see below, by introducing
"ordered triples." In this case, CPP and CPK are not used by the computer program and
so are arbitrarily set to zero. For INDHT = 1, heat transfer is included and the heat
transfer coefficient is calculated by DEGADIS. CPP and CPK are then used to calculate
the heat capacity as a function of temperature according to a correlation that is included in
DEGADIS. If a constant heat capacity is required, set CPP = 0 and CPK to the desired
specific heat at constant pressure (J/kg/K).
6-19
-------
Lines 16 - 26: NDEN is used to specify the contaminant density profile. There are three
alternatives for NDEN. If NDEN = -1, the model treats the contaminant as if it were an
ideal gas with a molal heat capacity equal to that of air. Water condensation effects are
ignored.
If NDEN = 0, the model treats the contaminant as if it were an ideal gas with heat capacity
indicated by CPK and CPP. The effects of condensation of water are taken into account
as appropriate. This option is suitable for use with vapors that do not have complex
thermodynamic properties when mixed with air.
If NDEN > 0, NDEN specifies the number of triples which follow in the next NDEN lines.
The triples are used to specify the contaminant concentration as a function of density, based
on adiabatic mixing with ambient air. The ordered triples represent (in order) the
contaminant mole fraction, the contaminant concentration (kg/m3) and the mixture density
(kg/m3).
Clearly, the ordered triples are intended to be used when the plume has complex
thermodynamic properties, as is the case with HF. However, these properties then have to
be calculated off line. The two key factors to remember as far as HF is concerned is, first,
that it oligomerizes. At high concentrations, it can be represented by a mixture of
monomer, dimer and hexamer and an effective molecular weight close to that of chlorine.
As air is entrained, it disassociates. This is an endothermic reaction and tends to keep the
cloud cold and denser-than air. Second, HF interacts exothermically with water vapor and
forms fine liquid droplets. This effect, in moist air, tends to raise the temperature and
reduce the density of the cloud.
Models that are available for calculating the thermodynamic properties of air/HF mixtures
include those by Clough et al.(30) and Schotte(31). The NDEN array in the table above was
calculated by the authors of this report using the model of Clough et al. Readers are
advised to seek expert help in calculating this NDEN array.
Note that, when the HF mole fraction is unity, the density is very high, 13.72 kg/m3. This
is because of the presence of liquid droplets, as described above. When the mole fraction
is 0.025,which corresponds to an air/HF mass mixing ratio of about 60, the cloud ceases to
be denser than air because of the exothermic reaction with water vapor. For even smaller
6-20
-------
mole fractions, the mixture in fact becomes slightly buoyant, but this has been neglected in
the present work. The slight amount of buoyancy that is generated will not cause the plume
to lift off the ground.
Note also that one recommended way to avoid the labor of having to calculate 10-20
triples for the NDEN array is to provide simply the first and last lines(6). The code then
extrapolates the cloud density linearly between the two. As can be seen, for this particular
example of HF in a humid atmosphere, this would lead to an overestimate of the cloud
density for mole fractions that are less than about 0.025 (equivalently, mass mixing ratios
in excess of 60 or so). Hence, DEGADIS would preserve the denser than air cloud for
greater mass mixing ratios and greater distances downwind than would in fact be the case.
This cautionary note is introduced to encourage the reader to look skeptically at any
approximations that are made in order to ascertain whether they are in fact physically
reasonable.
Line 27: ERATE is the rate of release, which is calculated above to be 3.7 kg/s.
Line 28: ELEJET is the height of release, arbitrarily set to 5 m. DIAJET is the diameter
of the jet. The actual orifice diameter in the present example is only 0.5". However, the
jet immediately expands because of flashing and its density decreases from ~ 1,000 kg/m3
to 13.72 kg/m3. With a mass flow rate of 3.7 kg/s, the volume flow rate is 3.7/13.72 = 0.26
m3/s. Making the simplifying assumption that the velocity remains constant at 30 m/s as
flashing takes place (see above), the effective orifice area increases to 0.26/30 = 0.0089 m2.
This corresponds to an effective diameter of 0.106 m or about 4".
Line 29: TEND is when the release ends, i.e. after 20 min or 1,200 seconds. With TEND
> 0, DEGADIS chooses the transient mode once the initial jet phase is over.
Line 30: DISTMAX is the maximum distance between points in the JETPLU output (m)
and is arbitrarily set to 50 m.
6-21
-------
6.3 One Ton Cylinder of Chlorine
6.3.1 Release Description
One ton cylinders of chlorine are often used at water treatment facilities, where the system
is usually very simple, namely a pipe off the top of the vessel through a regulator and then
through pipework to a station where the chlorine is mixed with water. The types of releases
that can take place might consist of, for example, a shearing off of the regulator, leaving an
unobstructed flow to the atmosphere, or a leak in the vessel itself, perhaps caused by impact
by an external agent. For the purposes of this example, it is assumed again that there is a
hole of diameter 3/8" in the vessel through which liquid emerges at a conservatively
assumed constant rate until the vessel is empty. 3/8" is a typical size for pipework
connected to one ton chlorine cylinders.
Using Eq. (6-29), the release rate calculated for Chlorine at 278 K is 1.96 kg/s. Using
Eq.(6-30), the flash fraction is 0.17 and the liquid aerosol fraction is 0.83. It is assumed that
all of this remains airborne as fine droplets. It is assumed that the resulting aerosol/vapor
mixture is at the atmospheric boiling point of chlorine, 239 K. There is assumed to be 1 ton
~ 1,000 kg in the cylinder, so that the duration of release is 1,000/1.96 -510 seconds.
6.3.2 Input to SLAB
The input for SLAB is contained in Table (6-3).
Line 1: IDSPL is the spill source type. IDSPL =2 for a horizontal jet.
Line 2: NCALC is a numerical substep parameter. The code developer recommends using
NCALC = 1. However, NCALC can be increased if numerical stability problems are
encountered.
Line 3: WMS is the molecular weight of chlorine in kg/mole, WMS = 0.07.
Line 4: CPS is the specific heat at constant pressure, taken from a table in the SLAB Users'
manual. CPS =498
6-22
-------
Table 6-3. SLAB Input -
Flashing Liquid Release of Chlorine from a One Ton Cylinder
2
1
0.07091
498.1
239.1
0.83
287840.
926.3
1574.
1978.34
-27.01
239.1
1.96
0.009
510.
0.
5.
3600.
l.OOE + 04
1.
0.
0.
0.
0.1
10.
1.5
278.
75.
6.
-1.
IDSPL
NCALC
WMS
CPS
TBP
CMEDO
DHE
CPSL
RHOSL
SPB
SPC
TS
QS
AS
TSD
QTIS
HS
TAV
XFFM
ZP(1)
ZP(2)
ZP(3)
ZP(4)
zo
ZA
UA
TA
RH
STAB
TER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
6-23
-------
Line 5: TBP is the boiling point of chlorine, 239.1 K
Line 6: CMEDO is the liquid mass fraction, which was calculated above to be 0.83.
Lines 7 - 9: DHE = 287,840, CPSL = 926.3 and RHOSL ~ 1,574 are the heat of
vaporization at 293 K (J/kg), the specific heat of liquid chlorine (J/kg/K) and the liquid
density (kg/m3) respectively. Their values are taken from Table 2 of the SLAB Users'
Guide.
Lines 10.11: SPB and SPC are parameters that go into the formula for the saturated vapor
pressure of chlorine:
P, = Pa.exp(SPA - SPB/(T + SPC))
Ps is the saturated vapor pressure, Pa is the ambient pressure (= 1.01E 05 N/m2), a value
for SPA is specified in the code and the values of SPB (1978) and SPC (-27.01) are given
in the Users' Guide. T is the ambient temperature (K).
Lines12 ^17 specify spill parameters, which have already been discussed in detail above.
TS is the temperature of the released material, 239 K. QS is the rate of release, 1.96 kg/s.
AS is the effective area of the source, 0.009 m2. TSD is the duration of release, 510 s.
QTIS is zero except in the case of a puff release. HS is the height of release, 5 m.
Line 18: TAV is the exposure time. As recommended in the User's Guide, its value is set
to that which is appropriate for the LOG that is to be considered. In this case, that value
is 1 hr = 3,600 seconds because the LOCs for chlorine are the ERPG-2 and the ERPG-3,
which are defined for an exposure time of one hour.
Line 19: XFFM is the maximum downwind extent of the calculation. It may be necessary
to determine this by trial and error. A value of 10 km (1.0xl04m) should be adequate for
many applications.
Lines 20-23: ZP(I) allows the user to specify up to four heights at which the concentration
is calculated as a function of downwind distance.
6-24
-------
Lines 24 - 29 allow the user to specify meteorological conditions. ZO is the surface
roughness length, which is set to 0.1 m as in previous examples. ZA is the height at which
the windspeed is measured (10 m). UA is the windspeed at height ZA (1.5 m/s). TA is the
ambient temperature (278 K). RH is the relative humidity (75%). STAB is the stability
class (6 or F).
Line 30: TER < 0 terminates the run.
6.3.3 Input to DEGADIS
The input for DEGADIS is given on Table (6-4).
Lines 1 - 4 of the above table allow the user to input four lines of title. Note that the
second line above states that the release is being modeled as a vertical jet. As noted earlier,
this is because DEGADIS does not allow the user to simulate a horizontal jet.
Line 5 requests a value of the windspeed UO at a height of ZO m. As in previous examples,
ZO takes on a value of 10 m. However, the windspeed is 5 m/s, considerably larger than
the 1.5 m/s used in previous examples. This was done after telephone conversations with
the model developer, Dr T. Spicer. DEGADIS could not be made to run at the lower
windspeed and Dr Spicer advised that this is because, when the initial density is initially high
(as when there is a large fraction of liquid droplets), the plume simulated by DEGADIS is
likely to fall back onto the source, in which case it will fail to run. A way of overcoming this
problem is to assume a higher initial windspeed.
Line 6 requires a value of the surface roughness length ZR, which is 0.1 m for all of the
examples in this report.
Line 7: INDVEL is an index which determines the method of calculation of the velocity
profile in the atmosphere. If INDVEL = 1, the computer program accesses default values
of the profile and of the Monin-Obukhov length based on the stability category ISTAB. In
the present example, the default mode is chosen by setting INDVEL equal to unity,
choosing the F stability category (ISTAB = 6, see above) and setting the Monin-Obukhov
length RML to 0. RML is then recalculated by the computer program.
6-25
-------
Table 6-4. DEGADIS Input -
Flashing Liquid Release of Chlorine from a One Ton Cylinder
FLASHING LIQUID CL2 RELEASE
VERTICAL JET SIMULATION
LARGE SCALE: 1,000 kg, 0.5 inch orifice
5. 10.
0.1
1 6 0.
278. 1. 75.
278.
CL2
70
3600
239
2.00E-05 3.0E-06 1.6
0 0.0 0.0
10
0.0 0.0 1.27
0.0125 0.04 1.33
0.025 0.08 1.39
0.125 0.47 1.84
0.25 1.07 2.40
0.32 1.48 2.78
0.59 3.94 5.07
0.74 6.57 7.52
0.88 11.27 11.90
1.0 20.82 20.82
1.96
5.0 0.11
510.
50.
TITLE 1
TITLE 2
TITLE 3
TITLE 4
UO, ZO
ZR
INDVEL, ISTAB, RML
TAMB, PAMB, RELHUM
TSURF
GASNAM
GASMW
AVTIME
TEMJET
GASUL, GASLL, ZLL
INDHT, CPK, CPP
NDEN
ORDERED TRIPLES
ERATE
ELEJET, DIAJET
TEND
DISTMX
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20-
21
22
23
24
25
26
27
28
29
30
6-26
-------
Line 8: TAMB is the ambient temperature, taken to be 278 K, which lies within the likely
range for atmospheric stability category F. PAMB is the ambient pressure, taken to be one
atmosphere (the results are not particularly sensitive to this parameter). RELHUM is the
relative humidity, which is set to 75% as being consistent with a cool, relatively humid night
such as might occur under category F weather conditions.
Line 9: TSURF is the surface temperature, set equal to the air temperature in the present
example, 278 K.
Line 10: GASNAM is a three character identifier chosen by the user.
Line 11: GASMW is the molecular weight of the gas.
Line 1.2: According to the Users' Manual, AVTIME is the averaging time for the
calculation of the width of the cloud, which is taken to be equal to the exposure time for
the chlorine LOCs, 3600 s.
Line 13: TEMJET is the temperature of the release, 239 K.
Line 14: GASUL and GASLL are the upper and lower concentration levels (or "Levels of
Concern" (LOCs)) for which DEGADIS prints out contours of constant concentration.
These are taken to be the ERPG-3 and the ERPG-2, namely 20 ppm and 3 ppm, leading
to mole fractions 2xlO"5 and 3xlO"6 respectively. ZLL is the height at which the
concentration contours are calculated and is taken to be 1.6 m (head height).
Line 15: INDHT is used to include heat transfer in the DEGADIS computation. Heat
transfer is not included for INDHT = 0. In the present case, INDHT is set equal to zero
because heat transfer is already included under the NDEN entry, see below, by introducing
"ordered triples." In this case, CPP and CPK are not used by the computer program and
so are arbitrarily set to zero. For INDHT =1, heat transfer is included and the heat
transfer coefficient is calculated by DEGADIS. CPP and CPK are used to calculate the
heat capacity as a function of temperature according to a correlation that is specified in
DEGADIS. If a constant heat capacity is required, set CPP = 0 and CPK to the desired
specific heat at constant pressure (J/kg/K).
6-27
-------
Lines 16 - 26: NDEN is used to specify the contaminant density profile. There are three
alternatives for NDEN. If NDEN = -1, the model treats the contaminant as if it were an
ideal gas with a molal heat capacity equal to that of air. Water condensation effects are
ignored.
If NDEN = 0, the model treats the contaminant as if it were an ideal gas with heat capacity
indicated by CPK and CPP. The effects of condensation of water are taken into account
as appropriate. This option is suitable for use with vapors that do not have complex
thermodynamic properties when mixed with air.
If NDEN > 0, NDEN specifies the number of triples which follow in the next NDEN lines.
The triples are used to specify the contaminant concentration as a function of density, based
on adiabatic mixing with ambient air. The ordered triples represent (in order) the
contaminant mole fraction, the contaminant concentration (kg/m3) and the mixture density
(kg/m3). For chlorine, these ordered triples have been calculated using the method
described in Section 3 of Appendix D, which contains detailed examples.
Line 27: ERATE is the rate of release, which is calculated above to be 1. 96 kg/s.
Line 28: ELEJET is the height of release, arbitrarily set to 5 m. DIAJET is the diameter
of the jet. The actual orifice diameter in the present example is only 0.5". Here, the
effective diameter is larger because of initial plume expansion during the flashing process.
Line 29: TEND is when the release ends, after 510 seconds. With TEND > 0, DEGADIS
chooses the transient mode once the initial jet phase is over.
Line 30: DISTMAX is the maximum distance between points in the JETPLU output (m)
and is arbitrarily set to 50 m.
6.4 150 Ib Cylinder of Chlorine
The case of the 150 Ib cylinder of chlorine is similar to that for the 1 ton cylinder, with the
exception that the cylinder is predicted to empty in 35 seconds. Therefore, the only change
in the above SLAB input is that AS (line 14) should be reduced to 35 s. In addition, HS
(Line 17) could be set to zero for a cylinder at ground level. In the DEGADIS input,
6-28
-------
TEND (line 29) is reduced to 35 s and ELEJET is reduced to zero. This scenario could
equally well be modeled as a puff release, see Section 8.
6.5 Miscellaneous
The following section is devoted to a discussion of two items that require further study, a
flashing liquid jet that is directed downward and a flashing jet from a long pipe.
6.5.1 Jet Directed Downward
This corresponds to Case 3C on Figure (2-1). When a jet containing an aerosol is directed
downward, there is recovery of a significant fraction of the initially airborne aerosol.
Experiments with ammonia, for example, show that this fraction can be as high as 75%.<32).
Thus the source term will be a mixture of an initial airborne cloud with some remaining
aerosol together with a cloud from an evaporating pool. The reader is advised to seek
expert advice in this case.
6.5.2 Jet Emerging from a Long Pipe
If the pipe from which the liquid jet emerges is long, there will be some flashing before the
material is released to the atmosphere. In this case,~the flow at the outlet will be two phase,
with liquid and vapor in thermal equilibrium. The flow may still -be choked at the outlet,
so further flashing will occur in the atmosphere. Equilibrium flow results in smaller
discharge rates than does pure liquid flow. Therefore, the cases described above may
represent conservatively high flow rates for some release scenarios.
In addition to liquid flow and equilibrium flow, there is a continuum of cases for which flow
at the outlet is two phase but not in thermal equilibrium. These cases have intermediate
flow rates.
The question of rate of release has been addressed by Wheatley (33), whose article constitutes
a useful source of references. Another helpful reference is that by Fauske and Epstein'341,
see Section 6.1.2 and Eqs (6-19) through (6-29) for further discussion.
6-29
-------
6.5.3 Orifice Shape
The shape of the orifice will also influence the predicted rate of release. The work
described above is appropriate for a circular orifice. If the orifice has a different shape -
for example, if it is a long and narrow rectangle, the constant c0 in Eq. (6-1) will be
considerably reduced.
6-30
-------
7.0 VAPOR JET RELEASES
The purpose of this chapter is to describe how to calculate emission characteristics and
atmospheric dispersion model inputs for vapor jets. Section (7.1) contains a detailed
theoretical discussion of various release formulae. Section (7.2) contains a specific example,
that of chlorine released from a small hole in the vapor space of a vessel that contains
chlorine liquified under pressure. The reader who is not interested in theoretical details can
move directly on to Section (7.2), which is self-contained. Section (7.3) contains a brief
discussion of holes in the vapor space that are potentially large enough for there to be two-
phase emissions.
7.1 Vapor Release Formulae - Theory
This chapter is intended to describe how to model the atmospheric dispersion of pure vapors that
are driven through an orifice by internal pressure. This section begins with a discussion of the
issues involved in calculating the release rates and other characteristics of the source term. The
following subsections (7.1.1 and 7.1.2) show how to estimate the release rate of a gas for two
scenarios:
(i) a release of gas from an orifice directly in the wall of a reservoir; and
(ii) a release from a pipe attached to a reservoir.
For all of the releases considered in Section 7.1 it is assumed that (a) the released material is
a vapor under the stated conditions and (b) that the pressure and temperature of the gas in the
reservoir are essentially constant.
Note that the work in Sections (7.1.1) through (7.1.3) draws heavily on the release rate work
that has been performed by Spicer(36> under the sponsorship of EPA and is intended to be
consistent with that work. Spicer's work has been incorporated into the Workbook of Screening
Techniques for Assessing the Impacts of Toxic Air Pollutants (Revised)(3) and the accompanying
TSCREEN model.
7-1
-------
7.1.1 Release Rate Estimates: Leaks of Gas Directly From a Reservoir
This section applies to a release of gas through a hole or opening in the wall of a reservoir in
which the pressure and temperature remain constant. The released material must be an ideal gas
at the reservoir conditions, during the depressurization process and after depressurization.
The above assumptions are clearly simplifications. The assumption that the release rate is
constant is conservative because a) for a vessel containing vapor only, the pressure in the vessel
declines as the release proceeds, thus causing a reduction in the rate of release and b) for a
vessel containing both vapor and liquid, the escaping vapor is replaced as the liquid boils. This
boiling in turn causes the liquid to cool (autorefrigeration) and leads to a corresponding reduction
of pressure in the vapor space. If the assumption that pressure and temperature are constant
leads to predictions of distances of concern that seem overly large (e.g. there may be the
potential need to evacuate large numbers of people) it will be necessary for the requestor to seek
additional advice and/or use a contingency model that can accept a time-varying rate of release.
The ideal gas law states that pV = RT, where V is the volume of one mole of the material at
temperature T and pressure p. R is the gas constant. For a non-ideal gas, the actual behavior
is expressed by a standard text-book equation of the form pV = RT(1 + B/V + C/V2 ).
The quantities B, C, - -, are known as virial coefficients. Values for the second virial
coefficient B can be found for many substances in Reference (44), "Data Compilation - Tables
of Properties of Pure Components," which has been published by the American Institute of
Chemical Engineers (AIChE). If B/V is large compared to unity, the ideal gas assumption
breaks down. In general, for most commonly encountered vapors, contingency modelers do not
question the ideal gas assumption.
If the reservoir contains both vapor and liquid, the hole must be in the vapor space of the tank.
Possible applications include a gas leak from a tank, a small gas leak from the wall of a large
pipe, or a gas discharge from a pressure relief valve mounted on a tank.
The procedures discussed in this subsection show the reader how to calculate the release rate and
the density and temperature after depressurization. The input required for the calculation
includes:
7-2
-------
AQ area of reservoir hole or opening (for guidance on how to choose values
for AO, see Section 4.3).
A, flow area representing reservoir conditions (m2). For a leak from a tank,
AI-* oo (and |8 = 0, see below). For a leak from a pipe, At is the cross
sectional area of the pipe.
Cp the specific heat of the released gas at constant pressure (J/kg/K)
D0 equivalent diameter of reservoir hole or opening (D0 = (Ao/x)"2)
hL the heat of vaporization at the boiling point Tb (J/kg)
M molecular weight of the released gas (kg/mol)
pa ambient pressure (Pa)
pv vapor pressure as a function of temperature (Pa)
p reservoir pressure (Pa)
R gas constant (8314 J/kg-mol/K)
Tb boiling point at atmospheric pressure (K)
Tc critical temperature (K)
Tr discharge temperature (K)
T, reservoir temperature (K)
ft (Ao/A,)1/2
7 Cp/Cv where Cv = Cp - R is the specific heat at constant volume (J/kg/K)
p} density of gas inside reservoir (kg/m3)
The calculational procedure is as follows:
A. Choked Flow Pressure: determine whether the flow is choked or not by first estimating
the choked flow pressure p, from;
p, -
(Y+D
If p, > pa, then the flow is choked or critical (go to B below). If p, < pa, then the
flow is subcritical (go to C below).
B. Choked Flow: for choked flow, estimate a) the gas temperature T,, when the pressure
is p.; b) the emission rate Q (kg/s); and c) the discharge temperature Tr - see paragraphs
a), b) and c) below, respectively.
7-3
-------
a) Estimate T». from the equation:
T.. = 2T,/ (Y+D (7-2)
Before proceeding further, it is necessary to enquire whether condensation will occur by
comparing T., with the (pseudo) critical temperature T0. If T« > Tc, there is no
condensation and Eq. (7-2) applies. If T,. ^ T0, first calculate the vapor pressure of the
gas at -temperature T« using the Clausius Clapeyron equation:
pv = l.OlxlO5 exp{({h,M)/R) (l/Tb-l/T..)) ' (7-3)
If pv(T«) > p,, then condensation does not occur during depressurization arid Eq. (7-2)
is valid. If pv(T«) < p., then the release should be considered as two phase at the
critical pressure and the appropriate procedures are given in Section (6.1). Note that,
for some releases, even if there is liquid present at choked conditions, there may not be
liquid when the final expansion to atmospheric pressure takes place. Section (6.1) shows
the reader how to determine if this is the case.
For multicomponent mixtures, the mixture dewpoint temperature at p, should be
calculated. This can be done using methods described by Sandier*37* (not further
discussed here). If T,. is less than the dewpoint temperature, then condensation occurs
and the reader should proceed to Section (6.1).
b) Estimate the emission rate Q from Perry and Chilton(38):
Q = CQA0[pp1Y(2/ (Y+l))<^1>'CY-D]1/2 (7-4)
Taking into account the ideal gas law, which gives p} = pM/RT, Eq.(7-4) can be
rewritten in a form in which it is frequently found in textbooks(16>17):
Q = G0A0p[(yM/RT) (21 (y*i))
-------
c) Estimate the Discharge Temperature : Spicer recommends the following formula:
Tr = T^l-0.85 ( (Y-l)/ (Y+D )] (7-6)
based on the assumption that the expansion from reservoir to choked conditions occurs
adiabatically and irreversibly. However, the expansion from choked conditions to
atmospheric pressure is assumed to occur adiabatically but not reversibiy. Based on
work by Lewitt^ the irreversible, adiabatic expansion is 85 % efficient. After estimating
Tr, the reader should proceed to step D below.
C. Subcritical Flow
a) Estimate the Emission Rate Q: Perry's handbook gives the rate of discharge for
subcritical flow as:
Q = KYAofep, (p~pa)]1/2 (7-7)
where K = GO (1 - /?*)1/2 (= c0 for 18 = 0) and
Y = l-[(p-p)/ (pY)](0.41 + 0.354) (7-8)
. = l-0.4l[(p-pa)/ (py)] for P = 0
A frequently encountered alternative formulation is(I6'17):
Q = c0A0(2pp(Y/(Y-l)[(p/p)2^-(p/p)(^i)/Y])V2 (7_9)
Spot hand calculations show that Eq.(7-7) is somewhat conservative with respect to
Eq.(7-9)
7-5
-------
b) Estimate Discharge Temperature Tr: the discharge temperature is given by:
(7-10)
where
a = (l/2Cp) (QR/fpMA,,))2 (7-11)
This formula has been taken by Spicer from work by Lees(40).
The above estimate for Tr must be checked to see if there will be condensation. If Tr >
Tc (the (pseudo) critical temperature) Eq. (7-10) is valid. If Tr :£ Tc, the following
procedure for single component parameters should be applied: first calculate the vapor
pressure pv at temperature Tr using the Clausius-Clapeyron equation (7-3). Ifpv(Tr) <
pa, then condensation occurs during the process of depressurization and the release should
be treated as two phase, see Section (6. 1). For multicomponent contaminants, estimate
the dewpoint of the mixture at pressure pa using the methods of Sandier*3^ (not addressed
here). If Tr is less than the dewpoint, there will be condensation and the reader should
proceed to Section (6.1).
D. Discharge Density: pr can be calculated from the discharge temperature using the ideal
gas law:
pr = paM/(RTr)- • (7-12)
E. Examples : Spicer^ gives examples of the applications of steps A through D above to
the following:
Air leak (reservoir pressure of l.OlxlO6 Pa; hole of diameter 5.25 cm; choked
flow)
Air leak (reservoir pressure of 1 .82X105 Pa; hole of diameter 5.25 cm; subcritical
flow), and
Chlorine gas leak (reservoir pressure of 6. 89x10* Pa; temperature 320 K; hole of
diameter 2.8 cm; choked flow).
7-6
-------
The reader is directed to Reference (36) for details. Section 7.2 below contains the case of a
chlorine gas leak from a reservoir at a pressure of 4.3xl05 Pa, with choked flow through a hole
of diameter 3/8" (0.0096 m).
7.1.2 Release Rates: Gas Leaks from a Pipeline Attached to a Reservoir
This section applies to a continuous release of a gas through a long pipe from a reservoir in
which temperature and pressure are assumed to remain constant. The flow through the pipe is
assumed to be adiabatic. The released material must be an ideal gas at the .conditions in the
reservoir, during the depressurization process and after depressurization. If the reservoir
contains vapor and liquid, the pipe must be attached to the vapor space.
The procedure described below provides estimates of the gas release rate and its density and
pressure after depressurization. The input information required is as follows:
AO area of orifice (m2)
DO equivalent diameter of hole (m); D0 = (Ao/T)1/2
Dp pipe diameter (m)
Lp pipe length
M molecular weight (kg/mol)
Ns number of pipe elbows
pa ambient pressure (Pa)
pv vapor pressure (Pa)
p absolute pressure in reservoir (Pa)
R gas constant (8314 J/kg-mol/K)
Tc critical temperature (K)
T, reservoir temperature (K)
7
The procedures to be followed are as follows:
A. Pipe Friction Loss: The frictional loss N is estimated as(38):
4fL
N = - ? + 0.5 + 0.75Ne + (0.5) (7-13
p
7-7
-------
In this equation, the first term represents skin friction losses in the pipe with f — 0.0045. The
second term provides for friction losses in the reservoir to pipe connection. The third term
accounts for frictional losses in any pipe elbows. The fourth term (written in parentheses)
should only be included if D(/DP < 0.2: otherwise, it should be neglected.
B. Discharge for Choked Flow. First, estimate the rate of discharge if the flow is choked
(the validity of this assumption will be checked later), in which case the speed of the gas
at the exit approaches that of sound. For choked flow, the following equations must be
solved simultaneously for the Mach number M2 at the pipe entrance and a dimensionless
parameter Y2:
" Y = 1 + Jl-LlLM2
X2 X + - - - "2 (7-14)
- (JL - I)' + YN - 0
M,2 (7~15
After M2 and Y2 are known, the mass flux G is obtained from:
G = p^CM
RT,
2 (7-16]
The discharge pressure must now be checked to see if it is indeed choked:
RT, 2
P3 = G ( l(_f_))1/2 (7-17)
MY Y + i
If p3 < pa or p3 > p1} then the flow is not choked and the reader should proceed to step
C below. If P] > p3 > pa then the flow is choked and the discharge rate is given by Q
The discharge temperature is given by Tr = 2T,/(7 + 1).
C. Discharge for Subcritical Flow: For subcritical flow, the gas discharge pressure at the
end of the pipe approaches that of the atmosphere. The following eight equations must
be solved simultaneously for the mass flux, G; the Mach numbers at the pipe entrance
and exit, respectively, M2 and M3; the temperature at the pipe entrance and exit, T^ and
Tr; and two dimensionless flow parameters, Y2 and Y3:
7-8
-------
RT,
M = -1 (122)1/2 (7-22)
2 P2 YM
P1/2 (7-23)
p3
(7-24
T1
Tp Y2
(7-25
The above equations have been written into TSCREEN and are solved numerically there.
The solution to these equations must be checked particularly to ensure that M3 < 1 , p
> p2 and T! > T2. If these conditions are not met, seek expert advice.
D. Check Discharge Temperature Tj if Tr is greater than the pseudo-critical temperature
Tc, the equation above used to estimate Tr applies. If not, the following procedure is
recommended. For single component contaminants, evaluate the contaminant vapor
pressure at temperature Tr, pv. If pv < pa, then contaminant condensation occurs during
the process of depressurization and the release is two phase: the reader should proceed
to Section (6.1).
7-9
-------
For multicomponent contaminants, estimate the dewpoint temperature of the mixture at
pressure pa using the method described by Sandier'38'. If Tr is less than the dewpoint
temperature, then condensation occurs during the process of depressurization and the
reader should proceed to section (6.1).
E. Discharge Density: the discharge density p, may be estimated from the equation p{ =
PaM/(RT3)
F. Examples: The following examples are contained in the workbook:
Air leak (reservoir pressure of 1.101x10' Pa, 10 m of pipe of diameter 5.25 cm)
Air leak (reservoir pressure of 1.824xl06 Pa, 10 m of pipe of diameter 5.25 cm)
7.1.3 Flow Chart
Figure 7-1 is a flow chart that summarizes the discussions in Sections (7.1.1) and (7.1.2).
7.2 Chlorine Vapor Release
7.2.1 Description of Scenario
This example is relevant to the case of a gas liquified under pressure. There is a hole in the
vapor space which could be caused for any of the reasons previously discussed - impact from
an external agent, failure at a corroded area, valve or gasket failures, for example.
This corresponds to scenario 4A on Figure 2-1. It is assumed that there is a storage vessel such
as a one ton cylinder containing chlorine at 278 K. For some reason such as the rupture of a
pipe, there is a leak from the vapor space. In this case, it is assumed that the orifice is 3/8" in
diameter because this is a typical size for pipework from a one ton cylinder. Chlorine vapor jets
vertically out of the orifice.
7-10
-------
From
Fig. J-l.p.6
Scenario 4 A^
Emission Kale
Q
b|S(7-4).(7-S)
Discharge
Temperature
anil Density
Eys (76).
(7-7U7 13)
NO
Subcnlicat Discharge
Flow Rale and
Ei)»(7 I9)lhru
<7-26)
\
f1
Corukii-
solion?
Section
(7.1 2D)
l^epare
Iiipul For
Dupersioii
MotleU
fkoplel
Formal ion
Go to Seel (6-1)
Figure 7-1
Vapor Release Rale Calculations Flow Chart
-------
The analyst must first compare p/pa with ((-y+l)/2)'l'/(Y'1), where pa is the ambient pressure,
l.OlxlO5 Pa, p is the absolute pressure in the vessel (Pa) and 7 = CP/CV is the ratio of specific
heats, 1.308 for chlorine. This comparison is the same as that made in Eq. (7-1). For chlorine
at 278 K, the vapor pressure is 4.323X105 Pa (from standard vapor pressure equations) so that
p/pa is equal to 4.32. ((y+l)!2^n equals 1.84, so that p/pa > ((7+l)/2)Y/(-y-') and the flow
is choked.
The quantity T., in Eq. (7.2) is equal to (2)(278)/(2.308) = 240 K. This is well below the
critical temperature Tc of chlorine (450 K) so that T., < Tc. From Eq.(7-3), the vapor pressure
corresponding to temperature T,, is l.OSxlO5 Pa < p.. Therefore, there is condensation and the
reader should proceed to Eq.(6-2), from which the temperature corresponding to the critical
pressure, p, can be calculated to be T, = 261 K. T, and p, are the temperature and pressure at
which the material actual emerges from the orifice. The properties of the gas at these conditions
are as follows: a) The vapor fraction x. is 0.962 (from Eq.(6-3)); b) the density p* is 7.88 kg/m3
(from Eq. (6-5)); and c) the predicted rate of release Q is 0.111 kg/sec (from Eqs (6-4) and
(6-6)).
From Eq. (6-7), the discharge temperature Tr equals the atmospheric boiling point, 239.1 K and
the corresponding released vapor fraction xr is 1.00088 (Eq. (6-9)). Since xr > 1, the solution
is unphysical and Eq. (6-10) applies, giving Tr = 239.6 K. The corresponding density pr is
3.549 kg/m3 from Eq. (6-11).
Thus, from above, the predicted flow rate is 0.111 kg/s. In practice, as noted previously, this
rate of flow would begin to decline immediately because, as vapor escapes, the pressure in the
vessel declines. This causes more vapor to evaporate, cooling the liquid in the vessel, thus
reducing the pressure. This causes the release rate to decrease. However, to illustrate a
conservative calculation, the release rate was assumed to remain constant for 20 minutes. By
this time, in practice, the release rate would have been much reduced. If the results of such a
conservative calculation show unacceptable distances to the LOG, it will be necessary to repeat
the calculation with more careful attention to the variation of release rate as a function of time.
7.2.2 Input to SLAB
The input to SLAB corresponding to the above scenario is contained in Table (7-1).
7-12
-------
Table 7-1. SLAB Input -
Vertical Vapor Release of Chlorine
3
1
0.07091
498.1
239.1
0.
287840.
926.3
1574.
1978.34
-27.01
239.6
0.111
1.6E-04
1,200.
0.
5.
3600
l.OOE + 04
1.6
0.
0.
0.
0.1
10.
1.5
278.
75.
6.
-1.
IDSPL
NCALC
WMS
CPS
TBP
CMEDO
DHE
CPSL
RHOSL
SPB
SPC
TS
QS
AS
TSD
QTIS
HS
TAV
XFFM
ZP(1)
ZP(2)
ZP(3)
ZP(4)
zo
ZA
UA
TA
RH
STAB
TER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
- 16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
7-13
-------
Line 1: IDSPL is the spill source type. IDSPL = 3 for a vertical jet.
Line 2: NCALC is a numerical substep parameter. The code developer recommends using
NCALC = 1. However, NCALC can be increased if numerical stability problems are
encountered.
Line 3: WMS is the molecular weight of chlorine in kg/mole, WMS = 0.07.
Line 4: CPS is the specific heat at constant pressure, taken from a table in the SLAB Users'
manual. CPS = 498 J/K/Kg.
Line 5: TBP is the boiling point of chlorine, 239.1 K.
Line 6: CMEDO is the liquid mass fraction, which is 0 because the release is pure vapor.
Lines 7 - 9: DHE = 287,840, CPSL = 926.3 and RHOSL ~ 1,574 are the heat of
vaporization at 293 K (J/kg), the specific heat of liquid chlorine (J/kg/K) and the liquid
density (kg/m3) respectively. Their values are taken from Table 2 of the SLAB Users'
Guide.
Lines 10,11: SPB and SPC are parameters that go into the formula for the saturated vapor
pressure of HF:
P, = Pa.exp(SPA - SPB/(T + SPC)) (7-26)
P3 is the saturated vapor pressure, Pa is the ambient pressure (= l.OlxlO3 N/m2), a value for
SPA is specified in the code and the values of SPB (1978.34) and SPC(-27.01) are given in
the Users' Guide. T is the ambient temperature (K). Eq.(7-26) with the given values of
SPB and SPC is an empirical fit to the experimental data on chlorine vapor pressure.
Lines 12 - 17 specify spill parameters, which have already been discussed in detail above.
TS is the temperature of the released material, 239.6 K. QS is the rate of release, 0.111
kg/s. AS is the effective area of the source, 1.6x10"* m2. This is derived as follows: the
density at choked conditions (from above) is 7.88 kg/m3. The material exits the hole at this
density and then expands to atmospheric pressure, at which its density is 3.549 kg/m3.
7-14
-------
Therefore, assuming that the exit velocity remains unchanged, the effective area must
increase by the ratio 7.88/3.549 = 2.22. The orifice area is 7.86xlO'5 m2. Therefore, the
effective area is 2.22x7.86xlO'5 = 1.6xl(T* m2. HS is the height of release, 5 m.
Line 18: TAV is the exposure time. As noted previously, it is set equal to the exposure time
for the LOG, 3600 s.
Line 19: XFFM is the maximum downwind extent of the calculation. It may be necessary
to determine this by trial and error. A value of 10 km (l.OE 04 m) should be adequate for
many applications.
Lines 20 - 23: ZP(I) allows the user to specify up to four heights at which the concentration
is calculated as a function of downwind distance.
Lines 24 - 29 allow the user to specify meteorological conditions. ZO is the surface
roughness length, which is set to 0.1 m as in previous examples. ZA is the height at which
the windspeed is measured (10 m). UA is the windspeed at height ZA (1.5 m/s). TA is the
ambient temperature (278 K). RH is the relative humidity (75%). STAB is the stability
class (6 or F).
Line 30: TER < 0 terminates the run.
7.2.3 Input to DEGADIS
The input to DEGADIS corresponding to the above case is contained in Table (7-2).
Lines 1 - 4 of the above table allow the user to input four lines of title.
Line 5 requests a value of the windspeed UO at a height of ZO m. As in previous examples,
these take on values of 1.5 m/s and 10 m.
Line 6 requires a value of the surface roughness length ZR, which is 0.1 m for all of the
examples in this report.
7-15
-------
Table 7-2. DEGADIS Input -
Vertical Vapor Release of Chlorine
CL2 VAPOR RELEASE
VERTICAL JET SIMULATION
LARGE SCALE: 3/8" orifice
1.5 10.
0.1
1 6 0.
278. 1. 75.
278
CL2
70
1200
239.6
2.00E-05 3.00E-06 1.6
0 498.1 0.0
0
0.111
5.0 1.6E-04
1200.
50.
TITLE 1 1
TITLE 2 2
TITLE 3 3
TITLE 4 4
UO, ZO 5
ZR 6
INDVEL, ISTAB, RML 7
TAMB, PAMB, RELHUM 8
TSURF 9
GASNAM 10
GASMW 11
AVTIME 12
TEMJET 13
GASUL, GASLL, ZLL 14
INDHT, CPK, CPP 15
NDEN 16
ERATE 17
ELEJET, DIAJET 18
TEND 19
DISTMX 20
7-16
-------
Line 7: INDVEL is an index which determines the method of calculation of the velocity
profile in the atmosphere. If INDVEL = 1, the computer program accesses default values
of the profile and of the Monin-Obukhov length based on the stability category ISTAB. In
the present example, the default mode is chosen by setting INDVEL equal to unity,
choosing the F stability category (ISTAB = 6, see above) and setting the Monin-Obukhov
length RML to 0. RML is then recalculated by the computer program.
Line 8: TAMB is the ambient temperature, taken to be 278 K, which lies within the likely
range for atmospheric stability category F. PAMB is the ambient pressure, taken to be one
atmosphere ( the results are not particularly sensitive to this parameter). RELHUM is the
relative humidity, which is set to 75% as being consistent with a cool, relatively humid night
such as might occur under category F weather conditions.
Line 9: TSURF is the surface temperature, set equal to the air temperature in the present
example, 278 K.
Line 10: GASNAM is a three character identifier chosen by the user.
Line 11: GASMW is the molecular weight of the gas.
Line 12: According to the Users' Manual, AVTIME is the averaging time for the
calculation of the width of the cloud, which is taken to be equal to the duration of release
in this example.
Line 13: TEMJET is the temperature of the release.
Line 14: GASUL and GASLL are the upper and lower concentration levels (or "Levels of
Concern" (LOCs)) for which DEGADIS prints out contours of constant concentration.
These are taken to be the ERPG-3 and the ERPG-2, 20 ppm and 3 ppm, or mole fractions
of 2.0xlO'5 and 3.0xlO~6 respectively. ZLL is the height at which the concentration contours
are calculated and is taken to be 1.1.6 m (head height).
Line 15: INDHT is used to include heat transfer in the DEGADIS computation. Heat
transfer is not included for INDHT = 0. For INDHT = 1, heat transfer is included and the
heat transfer coefficient is calculated by DEGADIS. CPP and CPK are used to calculate
7-17
-------
the heat capacity as a function of temperature according to a correlation that is specified
in DEGADIS. If a constant heat capacity is required, set CPP = 0 and CPK to the desired
specific heat at constant pressure (J/kg/K), 498.1 for chlorine.
Line 16: NDEN is used to specify the contaminant density profile. There are three
alternatives for NDEN. If NDEN = -1, the model treats the contaminant as if it were an
ideal gas with a molal heat capacity equal to that of air. Water condensation effects are
ignored.
If NDEN = 0, the model treats the contaminant as if it were an ideal gas with heat capacity
indicated by CPK and CPP. This option is suitable for use with vapors that do not have
complex thermodynamic properties when mixed with air.
Line 17: ERATE is the rate of release, which is calculated above to be 0.054 kg/s.
Line 18: ELEJET is the height of release, arbitrarily set to 5 m. DIAJET is the diameter
of the jet. The actual orifice diameter in the present example is only 3/8". The orifice
diameter specified above takes account of the initial expansion of the plume, seethe
explanation for line 14 of the SLAB input in Table 7-1.
Line 19: TEND is when the release ends, i.e. after 20 minutes or 1,200 seconds. With
TEND > 0, DEGADIS chooses the transient mode once the initial jet phase is over.
Line 20: DISTMAX is the maximum distance between points in the JETPLU output (m)
and is arbitrarily set to 50 m.
7.3 Intermediate Sized Hole in the Vapor Space
There exists a category of intermediate failures such as that illustrated in #4C, Figure (2-1),
in which the hole can be categorized as neither small nor large. Considerable relevant work
has been done by the AIChE's DIERS (Design Institute for Emergency Relief Systems)
program. Any one of up to four flow regimes through the orifice is possible:
7-18
-------
• Pure vapor - already discussed for a small hole
• Bubbly flow regime in which the liquid phase is continuous with discrete
bubbles
• Churn turbulent flow regime in which the liquid phase is continuous with
coalesced vapor regions of increasing size
• Droplet flow regime in which the vapor phase is continuous with discrete liquid
droplets
The transition between these various flow regimes occurs with increasing volumetric vapor
flux and is also influenced by fluid characteristics and by the presence of impurities. It is
unlikely that, if such a scenario is envisaged, a typical on scene co-ordinator or "emergency
responder will have access to modelers or resources that will enable a quick atmospheric
dispersion calculation to be done. Hence expert assistance should be sought, and this case
is not be discussed in detail in the present work.
7-19
-------
8.0 INSTANTANEOUS (PUFF) RELEASES
8.1 Description of Release
This release corresponds to the catastrophic failure of a vessel containing chlorine under
pressure. The sequence of events in this case is that a major rupture of a vessel or cylinder
occurs, releasing the whole contents almost at once. Some percentage of the chlorine
flashes to vapor, and the remainder is fragmented and remains airborne as fine liquid
droplets. This initial flashing process is highly turbulent and much air is entrained almost
immediately. Experiments and observations of the outcome of actual accidents suggest that
the initial mass of air entrained can equal about ten times the initial mass of chlorine. This
mixture is taken to be the starting point for the SLAB or DEGADIS calculations. The
initial characteristics of the puff are calculated as described in Section 2.1 of Appendix D.
In this particular case, the rupture of a one ton cylinder of chlorine is considered. The
spontaneous rupture of such a vessel is very unlikely: it generally corresponds to a worst-
case scenario. The case of a small ruptured cylinder is discussed in Section 8.4.
8.2 Input to SLAB
The input to SLAB is displayed on Table 8-1. The principal" differences from previous
SLAB inputs are that a) this is a puff release and b) the initial source already has air
entrained into it by assumption.
Line 1: IDSPL is the spill source type. IDSPL =4 for a puff.
Line 2: NCALC is a numerical substep parameter. The code developer recommends using
NCALC = 1. However, NCALC can be increased if numerical stability problems are
encountered.
Line 3: WMS is the molecular weight of the initial chlorine/air mixture in kg/mole. The
reader should remember that the initial puff consists of 1,000 kg of chlorine and 10,000 kg
of air, so that chlorine only takes up 9.1% by mass or 9.1x28.9/70 = 3.76% by volume.
Therefore, the effective molecular weight is WMS = (70)(0.0376) + (28.9)( 1-0.0376) =
30.45.
8-1
-------
Table 8-1. SLAB Input-
Puff Release of Chlorine
4
1
0.03045
954.
239.1
0.
287840.
926.3
1574.
1978.34
-27.01
239.1
0.
444.
0.
11000.
0.
3600
l.OOE + 04
1.
0.
0.
0.
0.1
10.
1.5.
278.
75.
6.
-1.
IDSPL
NCALC
WMS
CPS
TBP
CMEDO
DHE
CPSL
RHOSL
SPB
SPC
TS
QS
AS
TSD
QTIS
HS
TAV
XFFM
ZP(1)
ZP(2)
ZP(3)
ZP(4)
zo
ZA
UA
TA
RH
STAB
TER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
8-2
-------
Line 4: CPS is the effective specific heat at constant pressure. Here again, a composite gas
consisting of 9.1% of C12 and 90.9% of air has an effective specific heat at constant pressure
of (0.091)(498.1) + (0.909)(1,000) - 954 J/Kg/K.
Line 5: TBP is the boiling point of chlorine, 239.1 K. SLAB does not make use of this
quantity because the initial puff has been defined to consist of vapor.
Line 6: CMEDO is the liquid mass fraction, which, for the composite air/chlorine mixture
is zero because all of the chlorine droplets have been evaporated by the air.
Lines 7 - 9: DHE = 287,840, CPSL. = 926.3 and RHOSL ~ 1,574 are the heat of
vaporization at 293 K (J/kg), the specific heat of liquid chlorine (J/kg/K) and the liquid
density (kg/m3) respectively. Their values are taken from Table 2 of the SLAB Users'
Guide. These quantities are not made use of by SLAB because the initial puff is entirely
vapor.
Lines 10.11: SPB and SPC are parameters that go into the formula for the saturated vapor
pressure of chlorine:
P3 = Pa.exp(SPA - SPB/(T + SPC))
Ps is the saturated vapor pressure, Pa is the ambient pressure (= 1.01E 05 N/m2), a value
for SPA is specified in the code and the values of SPB (1978.24) and SPC(-27.01) are given
in the Users' Guide. T is the ambient temperature (K). These quantities are also not used
in the present case.
Lines 12 - 17 specify spill parameters, which have already been discussed in detail above.
TS is the temperature of the released material, 239 K. QS is the rate of release, 0 for a
puff. AS is the effective area of the air/chlorine source, 444 m2 from Eq. (2-2) of Appendix
D. TSD is the duration of release, 0. QTIS is the initial mass in the puff, 11,000 kg, being
made up of 1,000 kg of chlorine and 10,000 kg of air. HS is the effective height of release,
0 m.
Line 18: TAV is the exposure time. As discussed previously for chlorine, it is set equal to
one hour.
8-3
-------
Line 19: XFFM is the maximum downwind extent of the calculation. It may be necessary
to determine this by trial and error. A value of 10 km (1.0xl04m) should be adequate for
many applications.
Lines 20 - 23: ZP(I) allows the user to specify up to four heights at which the concentration
is calculated as a function of downwind distance.
Lines 24 - 29 allow the user to specify meteorological conditions. ZO is the surface roughness
length, which is set to 0.1 m as in previous examples. ZA is the height at which the
windspeed is measured (10 m). UA is the windspeed at height ZA (1.5 .m/s). TA is the
ambient temperature (278 K). RH is the relative humidity (75%). STAB is the stability
class (6 or F).
Line 30: TER < 0 terminates the run.
8.3 Input to DEGADIS
The input for DEGADIS is displayed on Table 8-2.
Lines 1 - 4 of the table allow the user to input four lines of title.
Line 5 requests a value of the windspeed UO at a height of ZO m. As in previous examples,
these take on values of 1.5 m/s and 10 m. Line 5 also requires a value of the surface
roughness length ZR, which is 0.1 m for all of the examples in this report.
Line 6 requests a value for the stability category, 6 (F) in this case.
Line 7: OODIST is the distance downwind of the source at which the DEGADIS
calculations start. AVTIME is the averaging time for plume meander, set equal to the
exposure time for the chlorine LOG, 3600 seconds.
Line 8: DELTA, BETA and RML are explained in Section 5.1.4.
Line 9: consists of parameters that describe the spreading of the plume along the wind due
to the action of atmospheric turbulence. They are described in Section 5.1.4.
8-4
-------
Table 8-2. DEGADIS Input
Puff Release of Chlorine
INSTANTANEOUS PUFF RELEASE
1,000 kg CHLORINE
1.50 10.00
6
.00 3600.00
.10
£
7.74E-02 .90 17.52
.17 .97 50.00
278.00 1.00 4.00E-03 75.00
0 278.00
1 .00
0 .00
CL2
30.44 238.70 3.67
954. 1.00
5.400E-04 8.100E-05 1.60
l.OOOE-04
11000
3
.00 .00 11.89 3.76E-02 239.00
1.00 .00 .00 3.76E-02 239.00
2.00 .00 .00 3.76E-02 239.00
FT F F F F
19-MAY-1992 14:48:50.40
1.00
1.00
1.00
TITLE
TITLE
TITLE
TITLE
SIGX MIN D1ST
UO, ZO, ZR
ISTAB
OODIST, AVTIME
DELTA, BETA, RML
SIGX COEFF, SIGX_POW,
TAMB, PAMB, HUMID
ISOFL, TSURF
IHTFL, HTCO
IWTFL, WTCO
GAS NAME
GAS MW, GAS TEMP, GAS RHOE
GAS CPK, GAS CPP
GAS_UFL, GAS_LFL, GAS_ZSP
CCLOW
GMASSO
NT
PTIME(l), ET(1), R1T(1), PWC(l), PTEMP(l), PFRACV(l)
PTIME(2), ET(2), R1T(2), PWC(2), PTEMP(2), PFRACV(2)
PTIME(3), ET(3), R1T(3), PWC(3), PTEMP(3), PFRACV(3)
CHECK1, CHECK2, AGAIN, dHECK3,CHECK4,CHECK5
TINP
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
-------
Line 10: TAMB is the ambient temperature, taken to be 278 K, which lies within the likely
range for atmospheric stability category F. PAMB is the ambient pressure, taken to be one
atmosphere (the results are not particularly sensitive to this parameter). HUMID consists
of two numbers, the absolute humidity (4.0xlO~3 kg water/kg air) and the relative humidity,
which is set to 75% as being consistent with a cool, relatively humid night such as might
occur under category F weather conditions.
Line 11: TSURF is the surface temperature, set equal to the air temperature in the present
example, 278 K. ISOFL is a number generated by the DEGADIS interactive input routine
as discussed in Section 5.1.4.
Lines 12 and 13: IHTFL, HTCO, IWTFL and WTCO are also generated by the interactive
method of preparing input for DEGADIS as discussed in Section 5.1.4.
Line 1.4: GASNAM is a three character identifier chosen by the user.
UnemJ5: GASMW is the effective molecular weight of the gas/air mixture, 30.44 as
explained in the discussion of the SLAB input. GAS-TEMP is the temperature of the
released gas (239 K) and GAS-RHOE is the density of the air/chlorine mixture at that
temperature (1.56 kg/m3, see Section 2.1 of Appendix D).
Line 16: GAS-CPK and GAS-CPP are parameters in DEGADIS' formula for specific heat
at constant pressure. In the formulation chosen here, 954 J/kg/K is the specific heat of the
initial air-gas mixture as discussed during the development "of the SLAB input. GAS-CPP
= 1 ensures that this value is chosen independent of temperature.
Line 17: GAS-UFL is the upper concentration of interest. It is labeled "UFL" because the
model was originally developed to handle flammable vapors. Here, it corresponds to the
ERPG-3 for chlorine, 20 ppm. However, as noted above, the initial puff consists of 1,000
kg of chlorine and 10,000 kg of air, so that the chlorine only makes up 9.1% of the total by
mass or 9.1x28.9/70 = 3.76% by volume. Therefore, the upper limit should be increased
from 20 ppm to 20/0.037 = 540 pprn = 5.4X10"4 mole fraction. Thus, the input data is being
manipulated to ensure that the model recognizes that, when the concentration of chlorine
is actually 20 ppm, the concentration of the initial composite air/gas mixture is in fact 540
ppm. Similarly, the chlorine LOG of 3 ppm is manipulated to be equivalent to a composite
8-6
-------
LOG of 80 ppm, which is equivalent to a mole fraction of ~ S.lxlO"5. Finally, ZSP is the
height at which the concentration is measured, taken to be 1.6 m (head height).
Line 18: CCLOW is the lowest concentration of interest (in kg/m3). and is taken to be
l.OxlO"4 kg/m3 (-40 ppm), somewhat below the composite ERPG-2 described above.
Line 19: CMASSO ( = 11,000 kg) is the initial mass.
Lines 20-23: NT specifies the number of times at which release parameters are required.
For this puff example, the DEGADIS input requirements are arbitrarily satisfied by 3 points
with release rate zero. Note that the fourth column (PWC) reproduces the initial dilution
over the source. The radius of 11.89 m is that of the source mixture of air and chlorine as
described in Eq. (2-1) of Appendix D.
Lines 24-25 are always generated by the interactive data entry module and are not further
discussed here.
8.4 Small Cylinder of Chlorine
In order to consider a puff release of chlorine, all that is necessary is to replace the initial
mass in the DEGADIS and SLAB outputs above by 150 Ib of chlorine plus 1500 Ib of air,
which comes to a total of 1650 kg (GMASSO, line 19 in the DEGADIS input and QTIS,
line 16 in the SLAB input). In addition, the initial radius (RIT(l) in line 21 of the
DEGADIS input) falls to a fraction (1650/11000)l/3 = 0.53 of its original value. Thus,
RIT(l) in line 21 of the DEGADIS input becomes (11.89)(0.53) = 6.3 m. In addition, AS
(line 14 of the SLAB input) becomes ir(6.3)2 - 125 m.
8-7
-------
9.0 BUOYANT PLUME RELEASES
9.1 Introduction
The purpose of this section is to introduce the reader to ways of calculating the air impacts of
buoyant plumes. This is done by discussing three examples, namely a) an incinerator on a
Superfund site; b) a burning pool containing PCBs; and c) a stack of burning tires. For the
interested reader, Appendix C contains a discussion of the elements of plume rise modeling.
EPA has two models that contain plume rise algorithms, TSCREEN for short term, worst-case
ambient concentration estimates and the Industrial Source Complex Model (ISCLT) for long-term
average concentrations.
9.2 Incinerator Plume
9.2.1 Background
Incineration is frequently employed at Superfund sites in order to destroy Volatile Organic
Compounds (VOCs) in contaminated waste. An incinerator plume (Scenario #8, Figure 2-2) is
one of the simpler cases considered in the present work because it corresponds to an isolated
point source.
The items that are needed to specify the characteristics of the source term for a buoyant plume
from an incinerator are:
o the rate of emission from the stack Q in g/s for each toxic material in the plume
o stack data: a) stack exit temperature (K); b) stack exit velocity (m/s); c) stack
inside diameter (m); d) stack height (m).
Reference (7) contains a detailed discussion of screening procedures for estimating the air
impacts of incineration using a rotary kiln at Superfund sites. For the convenience of the reader,
a summary of the approach taken in Ref. (7) is included.
9-1
-------
9.2.2 Specification of Source Term for a Buoyant Plume
Figure 9-1 shows a schematic drawing of a typical rotary kiln incineration system that is
designed to process soils and liquids that are contaminated by volatile and semivolatile organic
compounds. Organics are volatilized in the kiln and exit with the hot gases into the secondary
combustion chamber (SCC) where destruction is completed. Cyclones upstream of the SCC trap
large paniculate matter. A water quench reduces gas temperature, and a packed tower scrubber
provides primary removal of acid gases. An ejector scrubber removes fine paniculate matter
and additional acid gases before release through the stack.
Figure 9-1 shows typical input rates of liquid and solid (1,000 Ib/hr and 6 tons/hr respectively)
and the rate of heat input (35 mm BTU/hr). The stack height (12 m) and the stack exit
temperature (160°F = 344 K) are also specified. For Superfund site incinerators, a typical
value of stack internal diameter is 0.5 m in a range 0.3 - 1 m and a typical stack exit velocity
is 10 m/s in a range 7-20 m/s. Thus, the stack parameters have already been specified.
Generally, these would be expected to be available from calculations performed during the
design of the incinerator.
The emissions of toxic materials depend, of course, on the nature and quantities of contaminants
in the waste. Waste characterization data are usually obtained from the remedial investigation
(RI) and any treatability studies that may have been conducted. Generally, it is necessary to
consider emissions of organic compounds, metals, acid gases and paniculate matter. In addition,
the organic compounds can be divided into three groups, total hydrocarbons (THCs),
polychlorihated biphenyls (PCBs) and dioxins. THC compounds are considered to consist of
volatile and semivolatile organic compounds that are not PCBs or dioxins. Reference (7)
provides worksheets that enable the user to calculate emission rates for all of the above.
Organic Compounds
If the concentration C0 of one of the group of organic compounds is known in ppm and if the
feed rate of the waste to the incinerator is FR Ib/h, then the feed rate FR,, of the organic
compounds of interest is given by
FR,, = (FR)(C0)(10-6) Ib/h (9-1)
9-2
-------
Stack
Height 12m
Liquid
IQQOlb/hr
Soil
6_Tons/hr
Incinerator
35mm BTU/hr
Rotary Kiln
1400-1 SOOT
T:
o
Clean" Soil
Packed
Tower
Scrubber
Secondary
Combustion
Chamber
2100 - 2400T
Air Pollution
Control System
Figure 9-1. Example of a rotary kiln incineration system.
9-3
-------
In Eq. (9-1), 10~6 is a conversion factor that adjusts units.
Emissions of these organic compounds then depend on the destruction and removal efficiency
(DRE) of the incinerator. The exact DRE depends on the gas residence times and the
temperatures in the incinerator combustion chambers. This is generally measured during trial
bums of the incinerator. However, if this information is not available, RCRA standards require
a DRE of 99.99% for each principal organic hazardous constituent (POHC). POHCs are
organic indicators chosen for the trial burn and are a subset of THCs. Therefore, a 99.99%
DRE may be chosen for THCs. In addition, RCRA standards require a DRE of 99.9999% for
dioxins and the Toxic Substances Control Act (TSCA) standards also require a DRE of
99.9999% forPCBs.
The emission rate from the stack for the organic compounds that are not removed by the
incinerator is ER,, where:
ER,, = (FR0)(1 - DRE0(%)/100)(0.126) g/s (9-2)
where 0.126 is a conversion factor from Ib/hr to g/s.
Metals
Metals may be present with organics in soils or other solid wastes and in liquid waste fuels.
EPA has identified ten toxic metals that may pose a hazard to human health and the environment
when released in incinerator emissions: antimony, arsenic, barium, beryllium, cadmium,
hexavalent chromium, lead, mercury, silver and cadmium. Assume that metal m is present in
the waste in concentration Cm ppm and that the feed rate of the waste is FR Ib/hr. Then the feed
rate of the metal is FRn, where:
= (FR)(CJ(10^) Ib/h. (9-3)
Metals in the feed will either remain with the solids and be discharged in the bottom ash or they
will be carried out of the rotary kiln and SCC by the combustion gases. The percentage that
becomes airborne and travels into the air pollution control device (APCD) is known as the
partitioning factor (PF). EPA has determined conservative values of PFs from experimental
tests. The PFs given in Ref. (7) are as follows: a) if the feed is liquid, PFs = 100% for all ten
9-4
-------
metals at all incinerator temperatures; b) if the feed is solid and the solid temperature (generally
100 °F - 400 °F lower than the combustion gas temperature) is 1600 °F, the PFs are all 100%
except for barium (50%), beryllium (5%) and chromium (5%); c) if the feed is solid and the
solid temperature reaches 2,000 °F, the PFs are all 100% except for beryllium (5%) and
chromium (5%).
It follows that, for metal m, the rate at which the metal leaves the combustion chamber, ER,,,,
is given by:
= (FRJ(PF/100)(0.126) g/s. (9-4)
The fraction of FJR,,, that is removed by the APCD, CEn, is dependent upon the design. EPA
has compiled a table of efficiencies for different APCD devices (Ref. (7), Table 6). CE,,, varies
from as little as 0 up to 99%, depending on the metal and upon the design of the APCD. The
final emission rate of metal m from the stack, ER,,, 3 is given by:
= (ERJd-CEJIOO) g/s. (9-5)
Acid Gases
The presence of halogenated organics and/or sulfur in the waste feed can cause the formation
of acid gases during incineration. The acid gases of primary interest are hydrogen chloride
(HC1), hydrogen fluoride (HF), hydrogen bromide (HBr) and sulfur dioxide (SO2). By knowing
the concentration and molecular weights of the compounds containing acid forming elements in
the waste, the aggregate concentration CA of each element A can be determined by:
CA = EJI, (CA)i)(AWA)/(MWA; ppm (9-6)
where CA ; is the concentration of compound i containing acid forming element A
AWA is the atomic weight of the acid-forming element
MWA>i is the molecular weight of compound i that contains acid-forming element A.
If the ultimate analysis of waste samples has been performed, CA will be available from the data
and Eq.(9-6) need not be used.
9-5
-------
The feed rate FRA of each acid forming element is then given by
FRA = (FR)(CA)(10-6) Ib/h. (9-7)
The rate of formation of acid gases from halogenated waste is calculated by assuming that the
total mass of each acid forming element combines with hydrogen in stoichiometric proportions
to form the acid gases. Likewise, it is assumed that all sulfur compounds combine with oxygen
to form SO2. The mass of gas formed per unit mass of element, RA, is 1.013 for bromine,
1.028 for chlorine, 1.053 for fluorine and 1.998 for sulfur. The rate ERA at which acid gas A
enters the APCD is given by:
ERA = (FRJCRJCO.ne) g/s. (9-8)
Hazardous waste incinerators are equipped with acid gas scrubbers in order to control HC1
emissions. Typical control efficiencies CEA reported for wet scrubbers are 99% for HC1 and
HF, 90%+ for SO2 and unknown for HBr.
The rate of emission of acid gas containing element A from the stack, EA)S is given by:
ERA)S = (ERJO-CE^lOO) g/s. (9-9)
Paniculate Matter
Under existing RCRA standards, the incinerator paniculate matter emissions must not exceed
a stack concentration of 0.08 gr/dcsf (180 mg/dcsf) corrected to 7% oxygen in the stack gas
(50% excess air). Thus, the allowable emission rate of PM, ERpM is calculated by the equation:
ERPM = (0.08 grains/dscf)(Q0)(0.00108) g/s (9-10)
where Q0 is the gas flow rate at 7% oxygen in the stack gas and 0.00108 is the conversion
factor from grains/min to g/s.
9-6
-------
9.2.3 Example of Source Term
Ref. (7) contains a detailed worksheet and an example of the use of the above calculational
techniques. The following is a simplified version of that example.
The site area to be remediated by incineration contains 66,600 tons of soil contaminated with
272 ppm of PCBs, 0.08% (800 ppm) of chlorine (from the ultimate analysis) and 778 ppm of
lead. Emission rates will be calculated based on average feed conditions assuming that soils are
blended before incineration.
The proposed incineration system works at 35 Btu/h with a feed rate capacity of 6 tons/hr for
soils with a moisture content of 10% or less. The APCD and general configuration are shown
in Figure 9-1. The ejector scrubber is considered equivalent to a venturi scrubber with a
pressure drop of 25" of water. The kiln is to be operated at a temperature of 1600 °F and the
SCC at 2200 °F. The system will be operated 24 hours per day for 6 days per week and will
take 540 days to complete the remediation. The stack is to be located 300 meters from the
fenceline and will be 8 meters tall.
The feed rate for PCBs (Eq. (9-1)) is:
FRpcB = (12,000 lb/hr)(272 ppm)(ia6) = 3.264 Ib/h
The PCB emission rate from the stack is (Eq. (9-2)):
= (3.264 lb/h)(l - 99.9999/100)(0.126)
= 4.113xlO-7g/s.
The feed rate for lead (Eq.(9-3)) is:
FRp,, = (12,000 lb/h)(778 ppm)(10^) = 9.336 Ib/h.
The rate at which lead enters the APCD (Eq. (9-4)) is:
= (9.336 lb/h)(100/100)(0. 126) = 1.176g/s
9-7
-------
where, as noted above, the PF for lead is always 100%. According to Table 6 of Ref. (7), a
typical value for the removal efficiency of a venturi scrubber is CEpb = 96%. The rate at which
lead is emitted from the stack is given by (Eq. (9-5)):
ERp,,,, = (1.176 g/s)(l - 96/100) = 0.047 g/s.
The feed rate for chlorine (Eq. (9-7)) is:
FRa = (12,000 lb/h)(800 ppm)(lQ-6) = 9.6 Ib/h.
The rate at which HC1 enters the APCD (Eq. (9-8)) is:
ERHCI = (9.6 Ib/h)(l.028)(0.126) = 1.244 g/s.
As noted above, a wet scrubber will typically remove 99 % of the HC1. The release rate of HC1
from the stack (Eq. (9-9) is:
ERHa,3 = (1-244 g/s)(l - 99/100) = 0.0124 g/s.
Thus, the quantities needed for input to the atmospheric dispersion analysis are 4.113x10~7 g/s
of PCBs, 0.047 g/s of lead and 0.0124 g/s of HC1. As described above, the stack height is 8
m, the stack internal diameter is 0.5 m, the stack exit velocity is 10 m/s and the stack gas exit
temperature is 344 K.
9.2.4 Atmospheric Dispersion Analysis
This case can be run with a Gaussian dispersion model that contains a plume rise option.
TSCREEN is suitable for determining the short-term ambient atmospheric concentrations. The
data given above are sufficient to define the source term. TSCREEN also requires a definition
of terrain (flat in a rural area) and a specification of building dimensions for the calculation of
downwash or wake effects. In this case, there are no buildings nearby. For this particular
problem, TSCREEN predicts a one-hour dispersion factor at 300 m downwind (the fence line)
Of 197.5 /xg/m3 per g/s released.
9-8
-------
Thus, the one hour ambient concentration of PCBs in air at the fenceline is (197.5)(4.113xlO"7)
= 8.12xlO'5 /Ag/m3. Similarly, that for lead is 9.29 ^g/m3 and that for HC1 is 2.46 /xg/m3.
9.3 Fires at Ground Level
In this section, fires at ground level are considered: first, a burning liquid spill of PCB
contaminated waste (Section 9.3.1) and, second, burning tires (Section 9.3.2). Section 9.3.3
describes the use of TSCREEN to model these scenarios, including a discussion of uncertainties.
9.3.1 Burning Pool
In this section, a burning liquid spill of PCB contaminated waste is taken as an example. Ref.
(27) is a source of information on this kind of spill and the work in this section draws heavily
on that reference.
The calculation of the characteristics of the source term requires the following:
a) estimation of the heat of combustion and the liquid density of the mixture that is
spilled
b) determination of the surface area of the spill, the burn rate and the duration of the
fire (see below)
c) calculation of the combustion product rates of formation or the rate at which
unburned toxic materials become airborne (see below); and
d) estimation of the heat output of the fire for the purpose of performing plume rise
calculations.
9.3.1.1 Characteristics of Pool Fires
The Burn Rate
From Ref. (27), the burn rate BR (kg/min) of a pool of area A m2 is given by:
9-9
-------
BR = (A)(pL)(BV)/1000 (9-11)
where PL is the liquid density (kg/m3) and BV is the burn velocity (mm/min.). Note that
conservatisms can be introduced into Eq. (9-11) by choosing conservative burn velocities. Burn
velocities for individual chemicals are given in a publication by the U.S. Coastguard(28). A
weighted average burn velocity can be obtained by multiplying the burn velocities of the
components by their mass fraction in the mixture. A burn velocity of zero may be assumed for
PCBs because they will only burn in the presence of other flammable materials. If data are
unavailable, the following correlation can be used(27):
BV = (0.076)(HC)/(HV) mm/min (9-12)
where Hc is the heat of combustion (J/kg) and 1^ is the latent heat of vaporization (J/kg).
In calculating the burn rate, Ref.(27) considers three cases:
i) Burn rate = release rate
This case is appropriate for an undiked spill or for a case in which the application of
Eq.(9-ll) to a diked area would give a bum rate that exceeds the release or spill rate.
In such cases, it can be assumed that the spilled liquid spreads just far enough for the
burn rate to equal the spill rate. In this case, the area A does not enter into the
calculation. The spill rate equals the burn rate and the duration of release equals the
duration of the spill.
ii) Spillage of a Small Mass of Liquid
If a mass of liquid is spilled that is too small to cover the diked area to a depth of 1 cm,
the assumption is made that the liquid spreads until it has a depth of 1 cm. Thus, if the
mass spilled is M kg, the volume V spilled is simply the mass divided by the density, V
=M/ PL m3- The area occupied by the spill is then the volume divided by the depth, A
= V/0.01 m2. The burn rate can then be calculated from Eq. (9-11) and the duration of
release tR is simply M/BR.
9-10
-------
iii) Rapid Spillage of a Large Mass of Liquid
Assume a rapid spill of liquid M that fills the diked area A to a depth D = M/{(PL)(A)}
m. The burn rate can then be calculated from Eq. (9-11) and the duration of release is
tR = (D)/(1,OOOBV).
Product Rates of Formation
Once the bum rate is known, the product rates of formation can readily be calculated from a
knowledge of what fraction of the burning material forms each kind of product. Ref. (27) comes
to the following conclusions on the basis of a review of the literature on PCB fires:
o PCBs: one weight percent of the PCBs involved in a fire are entrained without
decomposition
o polychlorodibenzofurans (PCDFsV. 0.5 weight percent of the PCBs involved in
a fire are converted to 2,3,7,8-tetrachlorodibenzofuran
o potychlorodibenzodioxins (Peeps'): 0 weight percent of the PCBs involved in a
fire are converted to PCCDs: however, 0.01 weight percent of chlorinated
benzenes (if present as in some commercial products containing PCBs) are
converted to 2,3,7,8-tetrachlorodibenzo-p-dioxin
o phosgene: 0 weight percent of the hepta- or less chlorinated biphenyls involved
in a fire form phosgene; 0.8 weight percent of the octa- or higher chlorinated
biphenyls are converted to phosgene
o hydrogen chloride: the chlorine content of the PCBs that is not entrained and does
not form PCCDs, PCDFs or phosgene is converted to hydrogen chloride in a fire.
The above estimates are intended to be realistic deductions from experiment; the authors of
Reference (27) do not appear to have deliberately sought conservatism.
9-11
-------
Heat Output
The heat output Qh in J/s is given by the product of the burn rate BR in kg/s and the latent heat
of combustion H (j/kg). This quantity can then be used in the plume rise calculations.
9.3.1.2 Example
Consider the case of a commercial product known as Aroclor 1260. This has the following
weight composition of PCBs: 12% C12H5C15, 38% CnH4Cl6, 41% C12H3C17, 8% C12H2C18 and
1 % CijHCL,. Assume that this is present in a mixture of 1 weight percent Aroclor and 99
weight percent transformer oil. This means that the following masses of PCBs are present in
1 Kg of Aroclor: 0.0012 kg C12H5Cl5, 0.0038 kg C12H4C16, 0.0041 kg C12H3C17, 0.0008 kg
C,2H2C18 and 0.0001 kg C^HCL,. Ref.(27) gives a liquid density pL of 788 kg/m3 and a bum
velocity BV of 4.0 mm/min. This mixture is present in an outdoor storage tank that fails
catastrophically, leading to 50 m3 of liquid being spilled over a diked area of 200 m2. The pool
ignites and burns.
From Eq. (9-11), the burn rate BR is given by:
BR = (200)(788)(4)/(1000)
= 10.5 kg/s.
The PCBs are present at 1 weight percent = 0.105 kg/s. According to the rules given above:
o 1% of the PCBs become entrained without decomposition at a rate of 0.00105
kg/s = 1.05 g/s.
o 0.5% of the PCBs are converted to PCDFs at a rate of 0.5 g/s.
o 0.8% of the octa- or higher chlorinated biphenyls are converted into phosgene.
These highly chlorinated PCBs constitute 9% by mass of the total PCBs.
Therefore, the rate of conversion of PCBs to phosgene is (0.09)(0.008)(0.105) =
7.2x10-' kg/s = 0.072 g/s.
9-12
-------
o The total mass M of chlorine that is present in 1 kg of Aroclor can readily be
shown to be 0.006 kg. This follows by taking the above stated masses of PCBs
in 1 kg of Aroclor and multiplying them by the mass fraction of chlorine in each
PCB. The mass fractions are as follows: 0.54 for C12H3C13, 0.59 for C12H4C16,
0.625 for C12H3C17, 0.657 for C12H2C18 and 0.684 for C12HC19. These mass
fractions are calculated as follows: CI2H5C15 has a molecular weight of 12x12 +
5x1 + 5x35 = 324, of which the chlorine makes up 5x35 = 175. Therefore, the
ratio is 175/324 = 0.54. The fractions for the other PCBs are calculated
similarly. The mass of chlorine liberated per kilogram of Aroclor is therefore
0.54x0.0012 + 0.59x0.0038 + 0.625x0.0041 + 0.657x0.0008'+ 0.684x0.0001
= 0.006 kg. This forms (0.006)x(molecular weight of HCl)/(atomic weight of
chlorine) = (36)(0.006)/(35) = 0.00619 kg HCl/kg of Aroclor. The emission rate
of HC1 is therefore (rate of burning of Aroclor = 10.5 kg/s)(mass of HCl/kg of
Aroclor = 0.00619) = (10.5)(0.00619) ~ 65 g/s.
The heat of combustion of oils is typically around 5xl07 J/kg(28), so that the rate of heat
production is predicted to be (rate of burning of Aroclor = 10.5 kg/s)x(heat of combustion) =
(10.5)(5xl07) = 5.25 x 108 J/s.
The total mass spilled is (50 m3)(788 kg/m3) = 39,400 kg. The burn rate calculated above is
10.5 kg/s or (10.5)x(60) = 630 kg/min so that the duration of release is (total mass
spilled)/(burn rate) = 39,400/630 - 62 min.
See Section 9.3.3 for details on how to run this scenario in TSCREEN.
9.3.2 Burning Tires
Considerable concern has been expressed about the topic of burning tires. The following
information is needed in order to generate information for dispersion modeling:
what compounds are emitted when tires burn?
what are the emission factors (mg of compound per kg of tire burned)?
what is the rate of burn (kg/s)?
what is the amount of heat released per unit mass (J/kg)?
9-13
-------
A search has been carried out to determine the best available answers to these questions. The
summary given below shows that there are still considerable uncertainties, particularly in the
calculation of the rate of burn.
9.3.2.1 Compounds and Emission Factors
The EPA publishes and routinely updates a document entitled "Compilation of Air Pollution
Emission Factors" (AP-42). Radian Corporation recently undertook a study<42) of emission
factors for a) open burning of scrap tires; b) open burning of non-agricultural waste; c) open
burning of inorganic agricultural waste; and d) open burning of organic agricultural waste. The
purpose was to provide additional emissions factors for inclusion in (AP-42).
The Radian study found one earlier experimental study of emissions from open air burning of
scrap rubber tires'4^ (steel belted tires were not tested). Experiments were performed for both
large "chunks" of tires and smaller slices or "shredded" tires.
The experimental work indicates that emissions from burning scrap tires are dependent on the
bum rate of the tire, with a greater potential for emissions at a lower bum rate when the tire is
smoldering, rather than when it is burning out of control. Oxygen transport controls the rate
of burn. Gaps between the tires provide the major avenue for oxygen transport.
Compounds emitted from scrap tires burning in the open include particulate matter, aromatic
hydrocarbons, alkenes, dienes, sulfonated compounds and nitrogenated hydrocarbons. These
compounds can conveniently be grouped into the following categories: organic compounds.
polycyclic aromatic hydrocarbons (PAHs) and particulate metals. Tables (9-1) through (9-3)
give the emission factors that were extracted from the experiments in Ref. (43). These factors
are weighted averages over two days of burning and could be higher for a prolonged, slow burn.
9.3.2.2 Heat Release per Unit Mass
Ref.(44) gives the heat of combustion of rubber tires as 34 MJ/kg and makes reference to
"Tire Storage," Loss Prevention Data Sheet 8-3 issued by the Factory Mutual System.
9-14
-------
Table 9-1. Polycyclic Aromatic Hydrocarbon
Emission Factors From Open Burning Tiresa
Emission Factor Rating: D
Pollutant
Acenaphthene
Acenaphthylene
Anthracene
Benzo(A)pyrene
Benzo(B )fluoranthene
Benzo(G,H,I)perylene
Benzo(K)fluoranthene
Benz(A)anthracene
Chrysene
Dibenz(A,H)anthracene
Fluoranthene
Fluorene
Indeno( 1 ,2,3-CD)pyrene
Naphthalene
Phenanthrene
Pyrene
Chunkb»c
mg
kg tire
718.20
570.20
265.60
173.80
183.10
36.20
281.80
7.90
48.30
54.50
42.30
43.40
58.60
0.00
28.00
35.20
Ib
1000
tons tire
1436.40
1140.40
531.20
347.60
366.20
72.40
563.60
15.80
96.60
109.00
84.60
86.80
117.20
0.00
56.00
70.40
Shredded***
mg
kg tire
2385.60
568.08
49.61
115.16
89.07
160.84
100.24
103.71
94.83
0.00
463.35
189.49
86.38
490.85
252.73
153.49
Ib
1000
tons tire
4771.20
1136.17
99.23
230.32
178.14
321.68
200.48
207.43
189.65
0.00
926.69
378.98
172.76
981.69
505.46
306.98
aReference 42.
bO.OO values indicate pollutant was not found.
cValues are weighted averages.
9-15
-------
Table 9-2. Participate Metals Emission
Factors From Open Burning Tiresa
Emission Factor Rating: C
Tire Condition:
Pollutant
Aluminum
Antimony
Arsenic
Barium
Calcium
Chromium
Copper
Iron
Lead
Magnesium
Nickel
Selenium
Silicon
Sodium
Titanium
Vanadium
Zinc
Chunkb
mg
kg tire
3.07
2.94
0.05
1.46
7.15
1.97
0.31
11.80
0.34
1.04
2.37
0.06
41.00
7.68
7.35
7.35
44.96
Ib
1000
tons tire
6.14
5.88
0.10
2.92
14.30
3.94
0.62
23.61
0.67
2.07
4.74
0.13
82.00
15.36
14.70
14.70
89.92
Shredded5
mg
kg tire
2.37
2.37
0.20
1.18
4.73
1.72
0.29
8.00
0.10
0.75
1.08
0.20
27.52
5.82
5.92
5.92
24.75
Ib
1000
tons tire
4.73
4.73
0.40
2.35
9.47
3.43
0.58
15.99
0.20
1.49
2.15
0.40
55.04
11.63
11.83
11.83
49.51
Reference 42.
b Values are weighted averages.
9-16
-------
Table 9-3. Emission Factors For Organic
Compounds From Open Burning Of Tires2
Emission Factor Rating: C
Tire Condition:
Pollutant
1,1 hipheayl, methyl
Ihfluocene
1- methylnaphthalene
2-methyinaphthalene
Acenaphihalene
Benzaldehyde
Benzene
Benzodiazine
BenzoAiran
Benzochiopheao
Benzo(B)thioDhene
Benzsisothiazoie
Bipheoyl
Butadiene
Cyanobenzene
Cyclopentadiene
Dihydroindene
Oiniethyl benzene
Dimethyl hexadiene
Dimelhyl naphthalene
Dimethyldihydro iodene
Ethenyl, dimethyl benzene
Ethenyl, methyl benzene
Ethenyi benzene
Ethenyl cyclobexene
Ethenylmethyl benzene
Ethyenylmethly benzene
Ethyl, methyl benzene
Ethyl benzene
Ethynyl, methyl benzene
Ethynyl benzene
Heptadiene
Hexahydro izepinone
Indene
Ijocyano benzene
Isocyano naphthalene
Limonene
Methyl, ethenyl benzene
Methyl, melhylethenyl benzene
Methyl, methylethyl benzene
Methyl benzaldehyde
Methyl brazeo*
Methylcyclohex«M
Methyl haxadiena
Methyl indene
Methyl, methylethyl benzene
Methyl naphthalene
Methyl, ptcpyi benzene
Methyl thicphene
Methytene indene
Methylethyl benzene
Phenol
Propenyi, methyl benzene
Propenyl naphthalene
Propyl benzene
Styiea*
Tetnmethyl benzene
Thiophene
Tricfalorofluacomethane
Thmethyl benzene
Trimethyl naphthalene
Chunkb
me Ib
kg tire
12.71
191.27
299.20
321.47
592.70
223.34
1526.39
13.12
40.62
10.31
50.37
0.00
. 190.08
117.14
203.91
67.40
9.82
323.58
6.22
35.28
5.02
11.50
12.48
539.72
4.85
103.13
0.00
79.29
138.94
459.31
259.82
6.40
64.35
472.74
283.78
10.75
48.11
21.15
35.57
109.69
0.00
1129.80
3.91
15.59
50.04
11.76
144.78
0.00
4.39
30.37
41.40
337.71
0.00
26.80
19.43
618.77
0.00
17.51
138.10
19SJ9
0.00
1000 tons tire
25.42
382.54
598.39
642.93
1185.39
446.68
3052.79
26.23
81.24
20.62
100.74
0.00
380.16
234.28
407.62
134.80
19.64
647.16
12.44
70.55
10.04
23.01
24.95
1079.44
9.70
206.26
0.00
158.58
277.87
918.62
519.64
12.79
128.69
945.48
567.55
21.51
96.22
42.30
71.13
219.39
0.00
2229.60
7.83
31.18
100.07
23.52
289.56
0.00
8.78
60.75
82.79
675.41
0.00
53.59
38.87
1237.53
0.00
35.02
276.20
391.18
0.00
Shreddedb
ms Ib
kg tire
0.00
315.18
227.87
437.06
549.32
322.05
1929.93
17.43
0.00
914.91
0.00
151.66
329.65
138.97
509.34
0.00
30.77
940.91
73.08
155.28
27.60
196.34
21.99
593.15
89.11
234.59
42.04
223.79
335.12
345.25
193.49
42.12
764.03
346.23
281.13
0.00
2309.57
67.05
393.78
1385.03
75.49
1395.04
33.44
102.20
286.68
114.33
122.68
30.14
10.52
58.91
' 224.23
704.90
456.59
0.00
215.13
649.92
121.72
31.11
0.00
334.80
316.26
1000 tons tire
0.00
630.37
455.73
874.12
1098.63
644.10
3859.86
34.87
0.00
1829.82
0.00
303.33
659.29
277.95
1018.68
0.00
61.53
1881.83
146.15
310.57
55.20
392.68
43.98
1186.31
178.22
469.19
84.07
447.58
670.24
690.50
386.98
84.24
1528.05
69147
562.25
0.00
4619.14
134.10
787.56
2770.07
150.98
2790.08
66.88
204.40
573.36
228.66
245.37
60.28
21.03
117.82
448.46
1409.80
913.18
0.00
430.26
1299.84
243.44
62.22
0.00
669.59
63152
•Reference 42.
D0.00 values indicate (be pollutant was not found.
Values are weighted averages.
9-17
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9.3.2.3 Rate of Burning
Recently, experiments have been carried out at the Lawrence Livermore Laboratory on the
burning of tires(43). There were four tests, with 48, 9, 12 and 12 tests respectively for tests
1 through 4. The average rate of burn was 0.028, 0.021, 0.0214 and 0.02 kg/s respectively.
The peak rate of bum was 0.03, 0.0233, 0.03 and 0.04 kg/s respectively. It is notable that
these numbers are almost independent of the number of tires involved. In discussions with
the person who carried out the experiments, it became apparent that an extensive literature
search had failed to reveal any better data. Clearly, although the above data appear to be
the best that are available, there are still considerable uncertainties, including the need to
confirm whether there is indeed only a week dependence of burn rate on the number of
tires.
9.3.2.4 Example
For the purposes of estimating plume rise, a low rate of heat release is conservative (i.e. a
low rate of burn translates into a low height of rise and relatively high ground level
concentrations. The estimated rate of heat release at a bum rate of 0.02 kg/s is
(0.02)x(34,000,000) = 680,000 J/s = 0.68 MW.
For the purposes of estimating emissions, a higher burn rate is the most conservative. For
example, taking the emission factor for acenaphthene from Table (9-2) gives an emission
rate of (0.04 kg/sec)x(718.2 mg acenapthene/kg) = 28.7 mg/sec = 0.0287 g/s. This release
rate is suitable for the burning of whole tires, as was the case in the experiments. The burn
rate data given above are suitable for chunks of tires, not for shredded tires.
9.3.3 Atmospheric Dispersion Modeling
Both of the above scenarios (burning pool and burning tires) can be approximately modeled
in TSCREEN, because they are similar to a scenario that already exists in TSCREEN,
namely a gaseous release from a flared source (Section 4.2.1 of Reference (3)). That
scenario requires as input the emission rate (e.g 0.072 g/s of chlorine from the burning pool
or 0.0287 g/s of acenapthene from burning tires), the total rate of heat release, Hr (5.25x10*
J/s for the burning pool or 6.8X105 J/s for the burning tires) and the release height above
9-18
-------
the ground, Hs (a nominal 1 m for both scenarios, for example). TSCREEN takes this
information and calculates an effective height of the flare tip Hsl, where:
Hsl = Hs + 4.56xlO-3(Hr/4.1868)a478 (9-13)
The concentrations downwind are then calculated using the elevated Gaussian model with
an allowance for further plume rise.
The use of TSCREEN to model the two ground level scenarios is. a considerable
simplification. Both are area sources, whereas Eq. (9-11) and the subsequent use of the
Gaussian model apply to a point source. This could lead to an overestimation of the height
of rise and therefore to an underestimation of ground level concentrations close in and an
overestimation of ground level concentrations far away from the source. However, the point
source assumption neglects initial dilution by air drawn in over the area source and thus, in
this respect, tends towards conservatism.
The uncertainty in the emission rates is at least as large as the uncertainty in the dispersion
calculations, particularly in the case of the burning tires where the mass being burned is not
known exactly. For the pool case, moisture content is also an important source of
uncertainty.
In summary, the prediction of the dispersion of materials from fires on the ground is
difficult. The method outlined above is a considerable simplification and refinement of the
model may be possible in the future.
9-19
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10.0 VAPOR RELEASES FROM MECHANICALLY DISTURBED SOIL
10.1 Introduction
Excavation and removal of soils contaminated with Volatile Organic Compounds (VOCs)
is a common practice at Superfund sites. Excavation and removal may itself be the
preferred remediation option, or it may be a necessary step in a remediation approach
involving treatment. The purpose of this Section is to acquaint the reader with the methods
that are available with which to estimate the air impacts of the excavation of contaminated
soil.
A description of recent EPA work on this subject is to be found in References (8) or (29).
First, the model assumes an idealized excavation procedure in which soil is scooped out of
a pit in rectangular blocks which retain their shape and are typically of dimension Imx2
mxlm. The scoops are then stacked in rectangular piles. Over a period of one hour, 150
cubic meters of soil may be removed and stacked in a pile of dimensions 5 mxlO mx3 m,
leaving a pit that is 1m deep and of area 15 mxlO m. (Note that Ref. (8) performs sensitivity
studies on some of these variables.) Figure (10-1) displays this idealized excavation
scenario.
Ref.(8) considers emissions from:
o exposed waste in the evacuation pit
o material as it is dumped from the excavation bucket; and
o waste/soil in short-term disposal piles.
There are several approaches to the estimation of the rate of emission of VOCs during
excavation. The best method is to measure the emissions during full-scale or pilot-scale soil
handling activities. The next best method is to estimate the emissions using predictive
equations with site-specific inputs. If site-specific inputs are not available, a conservative
estimate can be made using default values for the parameters. Ref. (8) gives equations for
the following:
10-1
-------
Time Between Scoops is
Approximately 40 Seconds.
Figure 10-1. Idealized Excavation Scenario
10-2
-------
o average long-term emission rate
o short-term emission rate (both detailed and simplified); and
o worst-case (i.e.maximum) instantaneous emission rate.
The equations are derived in Appendix (A) of Ref.(8). They are reproduced below to give
the reader an overview of the variables to which values must be assigned in order to
calculate emission rates.
10.2 Equations for Emission Rates
10.2.1 Average Long-Term Emission Rate
A simple check on the total long term emissions potential of the site can be made by
dividing the total mass of a given contaminant to be removed by the expected duration of
the clean-up:
ER = (Sv)(C)(/3)(l)/tR (10-1)
where ER is the average emission rate (g/s)
Sv is the volume of contaminated soil to be excavated (m3)
C is the average contaminant concentration (/tg/g)
j3 is the bulk density of the soil (g/m3)
1 (unity) is a constant (g/10Vg*106cm3/m3); and
tR is the duration of remediation (s).
10.2.2 Average Short-Term Emission Rate (Detailed Model)
Ref. (8) gives a detailed model for the average emission rate
(ER g/s) from excavation:
ER = ERre + ERDIFF (10-2)
where ERpg is the emission rate from the soil pore space, and ER^^ is the emission rate
from diffusion.
10-3
-------
is given by the following equations.
= (P)(MW)(106)(Ea)(Q)(ExC)/{(R)(T)} (10-3)
where P is the vapor pressure of the contaminant (mm Hg)
MW is the molecular weight of the contaminant (g/g-mol)
Ea is the air-filled porosity (dimensionless)
Q is the excavation rate (m3/s)
106 is a conversion factor from m2 to cm 2
ExC is the soil to gas exchange constant (dimensionless)
R is the gas constant (62,631 mm Hg-cm3/g-rnol/K); and
T is the temperature (K).
Equation (10-3) is based on the assumption that the soil pore gas is saturated with the
compound of interest If this is not the case, then Eq.(10-3) may overpredict the emission
rate. The output of Eq. (10-3) should be multiplied by the duration of release and
compared to the total mass M of contaminants in the soil:
M = (C)(SV)(106) g (10-4)
If Eq. (10-3) gives a value that exceeds M/3, then the following equation should be
substituted for Eq. (10-3):
ERre = (M)(0.33)/(tsv) (10-5)
where tsv is the time in seconds taken to excavate a given volume of soil.
ERDtFF is given by the following equations:
ERD(FF = (C)(10,000)(SA)/(B) (10-6)
B = (EJ/UK^Xk,)} + [(Tt)/{(De)(Keq)}]1/2 (10-7)
where the symbols not already defined above are as follows:
10-4
-------
SA is the area of the emitting surface (m2)
C is the concentration of the contaminant in soil (g/m3)
10,000 is a conversion factor from m2 to cm2
K^ is the equilibrium coefficient (dimensionless)
kg is the gas-phase mass transfer coefficient (cm/s); and
De is the effective diffusivity in air (cm2/s).
10.2.3 Simplified Average Short Term Emission Rate
The equations for ERre and ERDffF can be simplified as follows (as shown in Appendix A
of Ref. (8)):
ERre = (P)(Q)(0.98) (10-8)
where P and Q are defined above and 0.98 is a conversion factor (g/mm Hg/m3): and
ERD(FF = (C')(10,000)(SA)/(B) (10-9)
B = (1.22)(106)(C')/(P) + [(1.79)(109)(C')/(P)]1/2 (10-10)
where the symbols have already been defined above except for C': = (C)/(/3)/(106) /*g/g,
the concentration of the contaminant in soil. 1.22xl06 is a conversion factor (cnr-s-mm
Hg/g) and 1.79xl09 is another conversion factor (s2-cm-mm Hg/g). Note, however, that the
soil concentration term C in this equation is now in /tg/g rather than in g/cm3 as was the
case above.
10.2.4 Worst-Case (Instantaneous) Emission Rate
The worst-case instantaneous emission rate occurs when the exposed surface area is at a
maximum and immediately after a bucket load of soil is dumped onto the storage pile. This
emission rate can be approximated by considering the case in which a pure chemical is
exposed to the atmosphere, in which case the maximum emission rate ER^^ can be shown
to be:
= (kg)(P)(MW)(SA)(10,000)/{(R)(T)} (10-11)
10-5
-------
10.3 Example
The reader is referred to Ref. (8) for detailed discussions of values for the variables above.
However, a brief example follows.
10.3.1 Description of Problem
Assume that 2 m3 of soil are removed per scoop in a block of dimension Imx2 mxlm. 75
scoops per hour are moved (Q = 150 m3/hr = 0.042 m3/s). The excavation pit has
dimensions 10 mxl5 mxl m and, after 1 hour, the storage pile has dimensions 5 mxlO mx3
m. The total surface area exposed (pit plus pile) is 290 m2. See Figure (10-1).
Assume that the site has approximately 10,000 m3 of soil contaminated by chloroform at
concentrations C in soil of 0.1 pg/g. The bulk density of the soil, £, averages 1.5 g/cm3. The
removal is expected to take 20 days (tR = 1.728xl06 s).
10.3.2 Total Emissions Potential for the Site
Using equation (10-1), Sv = 10,000 m3, C =0.1 /*g/g, 0 = 1.5 g/cm3 and tR = 1.728xl06 s:
ER = (10,000)(0.1)(1.5)(l)/(1.728xl06)
= 8.68x10^ g/s
10.3.3 Average Short Term Emission Rate
The rate of emission from the pore space, ERps is calculated from Eq. (10-8) in which the
vapor pressure P of chloroform is 208 mm Hg (p.26 of Ref. (8)) and Q = 0.042 m3/s:
ERps = (208)(0.042)(0.98) = 8.56 g/s
The total amount of chloroform predicted to be emitted over 1 hour (3,600 s) is
(8.56)(3,600) = 30,820 g. However, the total mass of the contaminant present in the soil
is given by the total mass of soil excavated in one hour (150 m3) times the bulk density (1.5
g/cm3 = 1.5xl06 g/m3) times the concentration of the chloroform in soil (0.1 jttg/g = 10"7
g/g): this product is 22.5 g. Therefore, Eq. (10-1) overpredicts and, as described above,
10-6
-------
defaults to Eq.(10-5) in which M is 22.5 g, and tsv is one hour = 3,600 s:
ps = (22.5)(0.33)/(3,600) = 2.08xlQ-3 g/s.
The emission rate due to diffusion is calculated from Eqs (10-9) and (10-10) in which C =
10'7 g/g, SA = 290 m2, and P = 208 mm Hg. Substituting these values into Eqs (10-9) and
(10-10) gives:
ERD1FF = (10-7)(10,000)(290)/B
B = (1.22xl06)(10-7)/(208) + [(1.79xl09)(10-7)/(208)]1/2
ERDIFF = 0.269 g/s
Thus, the total predicted release rate is 0.269 + 0.002 = 0.271 g/s.
10.4 Atmospheric Dispersion
The small rates of release calculated above mean that the scenario should be run with the
Gaussian dispersion model, specifically EPA's TSCREEN model for short-term (1 hour)
worst-case ambient conditions. EPA's Industrial Source Complex (ISCLT) can be used for
long term concentrations.
To run TSCREEN, the following assumptions and input variables are needed:
o The combined emission rate for the excavation pit and the storage pile is
0.271 g/s
o The excavation pit and the pile are sufficiently close together to allow the
user to assume that the area of the emissions source is equal to the combined
horizontal areas of the pit and storage pile
o the terrain is flat without any nearby structures; and
o downwash or building wake effects are not applicable.
10-7
-------
Running TSCREEN for scenarios representing ground level area sources, such as
TSCREEN scenario #2.9, shows that the maximum hourly ambient air concentration at (for
example) a distance of 400 m is approximately 760 ^eg/m3. This can then be compared to
action level ambient air concentrations.
10-8
-------
11.0 REFERENCES
1. U.S. Environmental Protection Agency, "Guidelines on Air Quality Models," EPA-
450-4-78-027R (NTIS PB 86-245248), Research Triangle Park,NC (1988).
2. U.S. Environmental Protection Agency, "A Workbook of Screening Techniques for
Assessing the Impacts of Toxic Air Pollutants," EPA 450/4-87-013 (NTIS PB 87-
227452), Research Triangle Park, NC (1988): "Workbook on Screening Techniques
for Assessing Impacts of Toxic Air Pollutants (Revised)," EPA 454/R-92-024,
Research Triangle Park, NC (1992).
3. U.S. Environmental Protection Agency, "User's Guide to TSCREEN, a Model for
Screening Toxic Air Pollutant Concentrations," EPA 450/4-89-013 (NTIS PB 91-
141820), Research Triangle Park, NC (1988):
4. Spicer, T. and Havens, J.A., " User's Guide for the DEGADIS 2.1 Dense Gas
Dispersion Model," EPA-450/4-89-019, United States Environmental Protection
Agency, Research Triangle Park (November, 1989).
5. U.S. Environmental Protection Agency, "Evaluation of Dense Gas Simulation
Models," EPA 450/4-90-018, Research Triangle Park, NC (1988).
6. U.S. Environmental Protection Agency, "Guidance on the Application of Refined
Dispersion Models for Air Toxics Releases," Source Receptor Analysis Branch,
Technical Support Division, Research Triangle Park, NC (1991).
7. U.S. Environmental Protection Agency, "Screening Procedures for Estimating the Air
Impacts of Incineration at Superfund Sites," EPA Contract No. 68-02-4466 (Work
Assignment No. 91-77) JTN 803770-077-02, Research Triangle Park, NC (1991).
8. U.S. Environmental Protection Agency, "Estimation of Air Impacts for the
Excavation of Contaminated Soil," EPA 450/1-92-004, Research Triangle Park, NC
(1992).
11-1
-------
9. U.S. Environmental Protection Agency, "Estimation of Air Impacts for Air Stripping
of Contaminated Water," EPA 450/1-91-002, Research Triangle Park, NC (1991).
10. U.S. Environmental Protection Agency, "Contingency Plans at Superfund Sites Using
Air Monitoring," EPA 450/1-90-005, Research Triangle Park, NC (1988).
11. "Atmospheric Science and Power Production," (Darryl Randerson, Ed.), DE84005177
(DOE/TIC-27601), published by the National Technical Information Service,
Springfield, VA (1984).
12. Pielke, R.A., "Mesoscale Meteorological Modeling," Academic Press (1984).
13. American Industrial Hygiene Association, "Emergency Response Planning
Guidelines," Akron, Ohio.
14. U.S. Environmental Protection Agency, "Health Effects Assessment Summary
Tables," Washington, D.C. (Updated Quarterly).
15. American Meteorological Society Workshop, "Stability Classification Schemes and
Sigma Curves - Summary of Recommendations," Bulletin of the American
Meteorological Society 58 (1977) pp 1305 - 1309.
16. Useful summaries of some of the basic formulae to be used for calculating release
rates can be found in "Guidelines for Chemical Process Quantitative Risk Analysis,"
Center for Chemical Process Safety of the American Institute of Chemical Engineers,
New York, New York (1989).
17. "Workbook of Test Cases for Vapor Cloud Source Term Dispersion Models," Center
for Chemical Process Safety of the American Institute of Chemical Engineers, New
York (1987).
18. "Handbook of Chemistry and Physics" (Robert C. Wease, Ed.), CRC Press,
Cleveland, OH (54th Edition, 1973 - 1974).
11-2
-------
19. Ermak, D.L. "User's Manual for the SLAB Model, An Atmospheric Dispersion
Model for Denser-than-Air Releases," Lawrence Livermore Laboratories (1989).
20. "LNG Vapor Dispersion Prediction with the DEGADIS Model," Topical Report GRI
89/0242, Gas Research Institute, Chicago, IL (1990).
21. Bird, R.B., W.E. Stewart and E.N. Lightfoot, "Transport Phenomena," John Wiley &
Sons (1960).
22. Phani K. Raj, "Chemical Release/Spill Source Models - A Review," International
Conference and Workshop on Modeling and Mitigating the Consequences of
Accidental Releases of Hazardous Materials (New Orleans, 1991), Published by the
American Institute of Chemical Engineers, New York (1991): "Models for Cryogenic
Liquid Spill Behavior on Land and Water," J. Haz. Mat. 5 (1981) 111 - 130.
23. Raj, P.K., Hagopian, J. and Kalelkar, A.S., "Prediction of the Hazards of Anhydrous
Ammonia Spillage onto Water," CG-D-74-74, prepared for the use of the U.S.
Coastguard by Arthur D.Little, Inc., Cambridge, MA (1974).
24. Cavanaugh, T.J., II, J.H. Siegell and K.W.Steinberg, "Simulation of Vapor Emissions
from Liquid Spills," Paper Presented at the 85th Annual Meeting & Exhibition of the
Air and Waste Management Association, Kansas City, Missouri (June, 1992).
25. Shaw, P. and F. Briscoe, "Evaporation from Spills of Hazardous Liquids on Land and
Water," United Kingdom Atomic Energy Authority Report SRD R120 (1978)
26. Webber, D.M. and SJ.Jones, "A Model of Spreading, Vaporizing Pools,"
International Conference on Vapor Cloud Modeling (Boston, 1987): published by the
Center for Chemical Process Safety of the American Institute of Chemical Engineers,
New York (1987).
27. Zamjec, E.R. and Chin C. Chao, "Consequence Analysis of PCB-Containing Liquid
Pool Fires," Presented at the AIChE Spring Meeting, Orlando, FL (March, 1990).
11-3
-------
28. U.S. Coastguard, "Chemical Hazardous Response Information System (CHRIS),
Hazardous Chemical data," Washington, D.C. (1984).
29. Eklund, B., S. Smith, J.F. Durham and J.S. Touma, "Estimation of VOC Emissions,
Ambient Air Concentrations and Health Effects from the Excavation of
Contaminated Soil," Presented at the 85th Annual Meeting & Exhibition of the Air
and Waste Management Association, Kansas City, Missouri (June, 1992).
30. Clough, P.N., D.R. Grist and C.J. Wheatley, "The Mixing of Anhydrous Hydrogen
Fluoride with Moist Air," in the Proceedings of the International' Conference on
Vapor Cloud Modeling, John Woodward, Ed., American Institute of Chemical
Engineers (November 1987).
31. Schotte, W., "Fog Formation of HF in Air," Industrial Engineering Chemical
Research 26(1986)300 .
32. Resplandy, A., "Etude Experimentale des Proprietes de PAmmoniac," Chim. Ind. -
Gen. Chim. 102 (1969) 691.
33. Wheatley, C.J., "Discharge of Liquid Ammonia to Moist Atmospheres - Survey of
Experimental Data and Model for Estimating Initial Conditions in Dispersion
Calculations," United Kingdom Atomic Energy Authority Report SRD/HSE/R4K)
(1987).
34. Fauske, H.K. and M. Epstein, "Source Term Considerations in Connection with
Chemical Accidents and Vapor Cloud Modeling," Presented at the International
Conference on Vapor Cloud Modeling, November 2-4, 1987, (Sponsored by the
Center for Chemical Process Safety, the American Institute of Chemical Engineers
and the U.S. Environmental Protection Agency).
35. U.S. Environmental Protection Agency, "User's Guide for the Industrial Source
Complex (ISC2) Dispersion Models." EPA-450/4-92-008, Research Triangle Park. N'C
(1992).
11-4
-------
36. Spicer, T.O., "Supplement to: A Workbook of Screening Techniques for Assessing
Impacts of Toxic Air Pollutants," Preliminary Report Prepared for the Office of Air
Quality Planning and Standards, U.S. Environmental Protection Agency, Research
Triangle Park, NC (July, 1992).
37. Sandier, S.I., "Chemical and Engineering Thermodynamics," 2nd Edition, John Wiley
and Sons, New York (1989).
38. Perry, R.H., D.W.Green and J.O. Maloney, "Perry's Chemical Engineers' Handbook,"
6th Edition, McGraw-Hill, New York (1984).
39. Lewitt, E.H., "Thermodynamics Applied to Heat Engines," 5th Edition, Sir Isaac
Pitman and Sons, London (1953).
40. Lees, P.P., "Loss Prevention in the Process Industries,", Butterworths, London (1980).
41. Spicer, T.O., "A Screening Procedure to Estimate the Release Rate of Low Volatility
Liquids from Tanks and Pipes," Prepared for the Office of Air Quality Planning and
Standards, U.S. Environmental Protection Agency, Research Triangle Park, NC
(May, 1992).
42. "Emission Factor Documentation for AP-42, Section 2.4, Open Burning," Prepared
by Radian Corporation for EPA under Contract No. 68-DO-0125, Office of Air
Quality and Planning Standards, Research Triangle Park, NC (May, 1992 - Draft).
43. "Characterization of Emissions from the Simulated Open Burning of Scrap Tires,"
Prepared by Acurex Corporation for the EPA, Office of Air Quality and Planning
Standards, Research Triangle Park, NC (1989).
44. Yung, D. and J.R.Mehaffey, "Fire Resistance Requirements for Rubber-Tire
Warehouses," Fire Technology, May 1991, pp 100-112.
45. Hasegawa, H., Lawrence Livermore National Laboratory, Privae Communication
(November 12, 1992).
11-5
-------
46. Design Institute for Physical Property Data, "Data Compilation - Tables of Properties
of Pure Compounds," T.E.Daubert and R.P.Danner (Editors), American Institute of
Chemical Engineers, New York, NY (1985).
11-6
-------
APPENDIX A
EXAMPLE AND INTERPRETATION
OF
DEGADIS OUTPUT
-------
DEGADIS Output File
Example DEGADIS output files are provided for both a transient and steady state release
simulation. Numerically indexed explanatory notes are given for each main section of the
output listings.
A-2
-------
Tha following la • lilting of tha output for a transient ralaaaa aimulation of chlorina.
Output Listing lotea
Vertical Vapor Chlorina Jat Transient Release Simulation
1. Tha data and time tha aimulation wai input and run ia raportad.
2. Tha Input .supplied by tha uaar ia tapaatad for documantation of tha aimulation. Tha tltla block, atmoapharic condition! and adiabatic mixing
of tha contaminant ralaaaa ia shown.
3. Tha contaminant gaa properties, aa apacifiad by tha user, ara documantad.
t
4. Tha input aourca characteristics ara diaplayad. Tha aourca input data point* section liata tha initial mass in tha cloud, tha contaminant mass
rata, aourca radius, contaminant maaa fraction, tamparatura, and anthalpy.
5. Numarical parameters and calculation flags uaad by DEGADIS it liatad. Thaaa valuaa ara aat by tha intaractiva modula of DEGADIS (JETINT) and
tha numaclcal paramatar fllaa Includad with tha coda. Tha latt thraa linaa in this aaction ara »«t by tha uaar and document if tha aimulation
la laotharmal and whathar haat and water tranafar ara includad.
6. A Hating of tha calculatad aourca paramatera aa a function of time ia provldad hara. Includad ara tha aacondary gaa radiua, height, aourca maaa
flux (Q, the contaminant mole fraction (Mole frac C), the
gaa mixture danaity, temperature, and the Richardaon number baaed on the cloud apreading velocity (Rich Ho.). The aource calculation ends when
all the primary and aecondary aource gaa haa been taken up in the atmoapharic flow.
7. Documentation ia provldad to indicate if x-direction diaperalon correction wa» Included in the aimulation. If applied. Identification of the
conatanta uaad in tha x-diraction dlaparaion correction ia diaplayad.
8. Tha concentretion field ia given for different timea after apill initiation. Tha timea given in thla output Hating are default valuea aet by
the numerical parameter file EXAMPLE.ER3. To chooae different timea at which tha concentration field la output, change the appropriate valuea
in HUH_NAME.E83 and execute OEG3 again.
9. For eech time Increment, the downwind portion of the calculations la Hated. Tha eleven columns contain the following information:
Column 1 - Distance downwind of the aource;
Column 2 * Mole fraction;
Column 3 - Contaminant concentration;
Column 4 - Mixture denaity;
Column 5 - Gamma - (p'pt)ICt. where p - contaminant denaity, p. - denaity of tha air, and Cc - contaminant concentration;
Column 6 - Temperature of the mixture on-the centerline of the gas cloud at ground level;
Column 7 - Half width, the contour ahape paramatar b;
Column 8 - S,, a contour shape parameter;
Column 9 - Sr, a contour shape parameter;
Column 10- Width from the centerline to the user apeciflad lower level of Interest at the user specified height; and
Column 11- Width from the centvrllne to the user specified upper level of interest at tha user specified height.
10. A report of the mass of contaminant between the upper and lower level of intereat la provided for each time increment. The mass of contaminant
above the lower level of interest is also given.
A-3
-------
0**e****************
***************
Date input on
Source progrem run on
0 TITLE BLOCK
UOA_DEOADIS MODEL OUTPUT -- VERSION 2.1
*************** 25-JUN-1992 10:59:10.41 ***************
25-JUN-1982 10.58: 8. 0
25-JUN-1992 10:59:10.41
CL2 VAPOR RELEASE
VERICAL JET SIMULATION
LARGE SCALE: 1,000 kg; 2" critic*
«= 1
0
0
0
0
0
Wind velocity «t reference height
Reference height
Surface roughness length
Pa«ijuiU Stability class
Honln-Obukhov length
Gaussian distribution constants
Specified averaging time
Oeltey
Betey
Wind velocity power lew constant Alphs
Friction velocity
Ambient Temperature
Ambient Pressure
Ambient Absolute Humidity
Ambient Relative Humidity
Adlebetlc Mixing: Hole fraction CONCENTRATION
0
.00000
.05568
. 12093
.198*8
.29214
.40753
. 55320
.74286
1.00000
Specified Gas Properties:
Molecular weight:
Release temperature:
kg/m«*3
.00000
. 17086
.37113
.60910
.89654
1.25065
1.69769
2.27973
3.39696
1.50 B/S
10.00 m
.100 B
F
17.5 m
1200.00 s
.07742
.80000
.44905
.07195 m/s
.278.00 K
1.000 atm
4.009E-03 kg/kg BOA
75.00 X
OF C GAS DENSITY
kg/m**3
1.26655
1 . 36690
1.48451
1.62427
1.79308
2.00105
2.26358
2.60541
3.39896
70.000
251.00 K
Enthalpy
J/kg
.00000
.00000
.00000
.00000
. 00000
.00000
.00000
.00000
.00000
Temperature
K
278.00
278.00
278.00
278.00
278.00
276.00
278.00
276.00
251.00
«= 3
A-4
-------
Density at releaae temperature end ambient preaaure:
Average heat capacity:
Upper mole fraction contour:
Lower mole fraction contour:
Height for laopletha:
3.3990 k$/m**3
.00000 J/kg K
2.00000E-05
3.00000E-06
1.6000 m
Source input data point*
Initial meaa in cloud: .00000
«= 4
Time
a
.00000
662.00
663.00
664.00
Contaminant
Maaa Rate
1.5100
1.5100
.00000
.00000
Source Radiua
m
19.686
19.696
.00000
.00000
Contaminant
Maaa Fraction
kg contain/kg mix
3.62986E-03
3.62986E-03
3.62966E-03
3.62986E-03
Temperature
K
278.00
278.00
276.00
278.00
Enthalpy
J/kg
.00000
.00000
.00000
.00000
0 Calculation procedure for ALPHA: 1
0 Entrainment prescription for FBI: 3
0 Layer thickneaa ratio uied for average depth: 2.1300
0 Air entrainnent coefficient uaed: .590
0 Gravity (lumping velocity coefficient uaed: 1.150
0 NOH laothermal calculation
0 Beet tranafer not included
0 * Water tranafer not included
CALCULATED SOURCE PARAMETERS
<= 6
Time
aec
. 000000
3.77626
10.6993
•17.6226
36.9309
56.2382
92.9689
129.699
149.042
168.386
363. 045
Gaa Radlua
m
19.6955
20.0691
21.4156
23.1726
28.6984
34.8794
45.7382
55.5388
59.4749
60.9302
60 0111
Height
m
1.100000E-OS
.792351
2.06330
3.05618
4.64252
5.17819
4.97146
4.14046
3 69906
3.51850
3.46528
Qatar
kg/n>**2/e
2.489397E-04
2.452237E-04
2.329614E-04
2.192248E-04
1.867220E-04
1.650777E-04
1.423013E-04
1.321261E-04
1.301492E-04
1.300341E-04
1.337128E-04
SZU-L/2.)
m
3.35682
3.40271
3.56532
3.77162
4.40255
5.00345
5.96491
6.69385
6.94315
7.02180
6.90624
Mole free C
1.501292E-03
1.477573E-03
1.399892E-03
1.313851E-03
1.115344E-03
9.887324E-04
8.663783E-04
8.264913E-04
8.26B289E-04
8.326102E-04
8.637744E-04
Denaity
kg/m**3
1.26926
1.26922
1.26906
1.26892
1.26856
1.26834
1.26812
1.26804
1.26804
1.26805
1.26811
Temperature
K
276.000
278.000
276.000
278.000
278.000
278.000
278.000
278.000
278.000
278.000
278.000
Rich No
.756144
.756144
.756144
.756144
.756144
.756144
.756144
.756144
.756144
.756144
.756144
A-5
-------
658.484
59 8289
3.45473
1.343098E-04 6.88599
8.686844E-04 1.26812
278.000
.756144
687. 4IU
724.000
7U2.348
708.022
827 591
847. 4U1
857 860
8(>0.0tt2
8UO . 1 50
54. B/67
46.5404
36.0291
24 5/54
13 8486
5.95016
1.58070
.612091
.601683
3.16929
2 68807
2 . 08066
1.41924
.790743
.343585
9.126908E-02
3.454256E-02
3.058242E-02
1
1
9
0
6
6
5
5
5
227504E-04
081975E-04
. 413527E-05
126567E-05
. 997320E-OS
.OB9663E-05
.405815E-05
. 157967E-05
. 148170E-05
6.80812
6.45340
5.72198
4.61030
3.22167
1.84430
.749643
.391354
.386510
7.
5.
4.
3.
3.
2.
2.
2.
2.
403055E-04
980279E-04
794928E-04
861275E-04
149216E-04
642615E-04
296968E-04
179467E-04
175158E-04
1.26789
1.26763
1.26742
1.26725
1.26712
1.26703
1 . 26697
1.26695
1.26695
278.
278.
278.
278.
278.
278
278
278.
278
000
,000
.000
000
.000
.000
.000
.000
.000
.756144
.756144
.756144
.756144
.756144
.756144
.756144
.756144
.756144
8B0.71B .601883 .000000 5.116335E-05
0 Sorted vatuea foi ••ch (pacified tin*.
0 X l>iiaction collection waa applied.
Coefficient: .17000
Power; .97000
Minimum Dl«t«nc»: 50.000 o
.386519
2.166874E-04 1.26694
278.000
.000000
«= 7
Time aftei beginning of apill 171.0000
Mole Cuncentreti
Ki action
(m)
2J5.
2tit>
2UU.
*335.
1 04UE-03 3.21UE-03
7.B82E-04 2 419E 03
4.142E 04 1.271E 03
1 075E-04 3 300E-04
ana 1 ty
f/B**3)
1.2684
1 2680
1.2673
Genraa
.587
.587
.587
Ta
-------
291.
7.518E-04 2.307E-03
1.2679
.587
278.
52.2
4.86
23.0
105.
84.8
326.
363.
401.
441.
483.
5
V
2
1
5
994E-04
364E-04
716E-04
394E-04
178E-05
1.839E-03
1.339E-03
8.336E-04
4.279E-04
1.589E-04
1.2676
1.2673
1.2670
1.2668
1.2666
.587
.587
.587
,587
.587
278.
278.
278.
278.
278.
54.0
53.8
52.0
46.7
23.0
4.94
5.10
5.57
6.52
8.60
27.8
32.0
36.3
40.0
38.0
117.
124.
128.
124.
86.2
104.
108.
109.
100.
58.3
For tha ULC of 2.00000E-03 mola parcant, and th« LLC of 3.00000E-04 nola parcant:
Tha D«a> of contaminant batwaan tha ULC and LLC la: 2.4413 kg.
Th* ma** of contaminant abova tha LLC la: 262.13 kg.
0 Tlma aft-ar baginntng of (pill
0 Dlatanca Mola Concentration
Fraction
(m)
220.
251.
263.
318.
354.
392.
432.
473.
515.
559.
604.
650.
1
9.
a
7.
5.
4
3.
2
1
1
6.
3.
113E-03
827E-04
493E-04
058E-04
711E-04
534E-04
S39E-04
.684E-04
900E-04
212E-04
7S5E-05
101E-05
-------
Tine after beginning of aplll
Distance Hole Concentration
Fraction
(•) (kg/n**3)
2.
2.
2.
2.
2.
2.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
4.
4.
4.
4.
4.
4.
4.
4.
4.
4.
4.
S84E+03
65BE+03
735Et03
8HE+03
888E+03
865E+03
043E+03
122E+03
202E+03
282Et03
362Et03
444E+03
526E+03
608E+03
691E+03
775E+03
859Et03
844Et03
030E+03
116E+03
202E+03
290E+03
377E+03
466E+03
555E+03
644E+03
734E+03
825E+03
916E+03
3
4
4
5
6
6
7
7
a
a
a
a
a
7
7
7
6
6
6
5
5
5
4
4
3
3
3
2
2
. 273E-06
. 008E-06
.763E-06
.498E-06
. 198E-06
. 819E-06
. 342E-06
.731E-06
.016E-06
. 172E-06
.208E-06
. 153E-06
.022E-06
.8176-08
. 583E-06
.280E-06
. 957E-06
.6126-06
.255E-06
.868E-06
. 482E-06
. 074E-06
. 663E-06
.241E-06
.825E-06
.406E-06
.003E-06
. 609E-06
.240E-06
1.
1.
1.
1.
1.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
1.
1.
1.
1.
1.
1.
1.
1.
8.
a.
6.
004E-05
230E-05
462E-OS
687E-05
802E-05
083E-05
253E-05
373E-05
460E-05
508E-05
519E-05
S02E-OS
462E-05
399E-Q5
327E-05
234E-05
135E-05
028E-OS
820E-05
a01E-05
682E-05
557E-05
431E-05
302E-05
174E-05
045E-05
216E-06
007E-06
8736-06
2169.000 aec
Denaity Gamma
(kg/n**3)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.2666
.529
.581
.585
.585
.586
.586
.586
.586
.586
.586
.586
.586
.586
.586
.586
.586
.586
.586
.586
.586
.586
.586
.585
.585
.585
.585
.584
.584
.582
T«np»r«tur«
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
Half
Width
(o)
.000
.000
12.7
37.9
56.9
71.7
83.3
91.5
96.0
96.4
95.4
94.4
93.3
92.3
91.2
90.1
89.0
87.9
86.6
85.4
83.9
81.0
76.4
69.9
61.6
51.0
35.7
14.9
.000
Sz
(a)
46.3
41.2
38.1
37.9
38.1
36.3
38.6
39.0
39.6
40.3
41.1
41.9
42.7
43.5
44.4
45.2
46.0
46.8
47.6
48.4
49.3
50.2
51,2
52.2
53.3
54.4
55.7
57.4
60.5
Sy
128.
151.
178.
200.
216.
229.
240.
249.
256.
261.
265.
270.
275.
279.
284.
288.
293.
297.
302.
306.
310.
314.
317.
318.
318.
316.
311.
301.
287.
Width at t-
3.000E-0
(in)
36.2
80.3
132.
192.
240.
278.
309.
333.
348.
356.
361.
363.
364.
364.
363.
360.
356.
351.
344.
335.
324.
307.
285.
255.
216.
161.
1.60 m to:
2.000E-03moleZ
(m)
For th» ULC of 2.00000E-03 moU percent, and the LLC of 3.00000E-04 mole percent:
kg.
The maia of contaminant betwaen the ULC and LLC la:
The rnaas of contaminant above the LLC ia: 459.65
459.65
kg.
A-8
-------
Output Llatlu* lots*
Acetone Confined Spill Steady State Release Simulation
1. Th« data and tint* tha •inulation waa input and run 1* report ad. >
2. Tha input auppliad by tha uaar la rapaatad for documentation of tha aioulation. Tha title block, aUnoapheric conditiona and adiabatic mixing
of tha contaminant ralaaaa is ahown.
3. Tha contaminant gaa properties, aa apecifled by the uaer, are documented.
4. The input source characteristics are displayed. The source input data points section lists the initial mass in the cloud, the contaminant mass
rate, source radlua, contaminant masa fraction, temperature, and enthalpy. For a ateedy state releaae, there is no initial mass in the cloud
and the source parameters are held constant for an arbitrarily Ions time period.
5. numerical parameters and calculation flags used by DEGADIS is listed. These values ere set by the interactive module of DEGADIS (DE6INP) and
tha numerical parameter files included with the code. The lest three lines in this section are eat by tha user end document if the simulation
is isothermal and whether heat and water transfer are included.
6. A Hating of the calculated source parameters as a function of time ia provided here. Included are tha secondary gas radius, height, source mass
flux (QlUr). the vertical concentretlon distribution parameter at tha downwind edge (SZ(x-L/2)), the contaminant mole fraction (Mole free C), tha
gaa mixture density, temperature, and the Richardson number based on the cloud spreedlng velocity (Rich No.). For e steady state release, the
aource calculations terminate once the parameter* no longer change with time.
7. A summary of tha steady state primary and secondary aource ia provided.
6. The downwind portion of'the calculations is listed. The eleven columns contain tha following information:
Column t ~ Distance downwind of tha source;
Column 2 - Mole fraction;
Column 3 - Contaminant concentration;
Column 4 - Mixture density;
Column 5 - Gamma • (p"P.)/Cc, where p • contaminant density, p. ~ density of the air, and Cc - contaminant concentration;
Column 6 - tempereture of the mixture on tha centerllne of the gas cloud at ground level;
Column 1 - Self width, tha contour shape parameter b;
Column 8 - S,, a contour shape parameter;
Column 9 - S,, e contour shape parameter;
Column 10- Width from the centerline to the uaar apecified lower level of intereat at the user specified height; and
Column 11- Width from tha centeriine to the user specified upper level of interest et the user specified height.
Output continues until the centerline ground level concentration ia below the user specified lower level-of interest.
0. A report of the maas of contaminant between the upper and lower level of interest is provided for each time increment. The mass of contaminant
above the lower level of interest is slso given.
A-9
-------
0*******************
Data input on
Source program tun on
0 TITLE BLOCK
UOA_DEGADIS MODEL OUTPUT
*************** 26-JUH-1982 9:31: 4.60
26-JUH-1982 9:30:52.47
26-JUN-1992 9:31: 4.60
CONFINED SPILL INTO A DIKED AREA
STEADY STATE ACETONE SPILL. POOL DIAMETER 10m
V E 8 S I O H 2.1
*******************
***************
«= 1
Reference height
Surface roughneaa length
Pasqulll Stability claaa
Monin-Obukhov length
Friction velocity
Ambient Temperature
Ambient Pressure
Ambient Absolute Humidity
Ambient Relative Humidity
Adiabatic Mixing:
'erence height
ingth
ilaaa
i
in constants
icified averaging time
Deltay
Betay
law constant Alpha
kidity
lidity
Mole fraction CONCENTRATION
.00000
.00676
.02290
.04689
.08244
.12619
.18301
.25294
.33574
.43037
.54491
.67955
kg/m**3
.00000
.01717
.05776
.11708
.20288
.30510
. 43266
, 58208
.74904
.92777
1.12862
1.34547
1.50
10.00
.100
F
17.5
1200.00
.07742
. 90000
.44905
.07195
278.00
1.000
4.009E-03
75.00
•/a
B
m
m
s
a/a
K
atm
kg/kg BDA
Z
OF C GAS DENSITY
kg/m**3
1.26655
1.27159
1.28349
1.30088
1.32604
1.35602
1.39342
1.43723
1.48618
1.53859
1.S9749
1.66107
Enthalpy
J/kg
.00000.
.00000
.00000
. 00000
. 00000
.00000
. 00000
.00000
.00000
.00000
.00000
.00000
Temperature
K
278.00
278.00
278.00
278.00
278.00
278.00
278.00
278.00
278.00
278.00
278.00
278.00
A-10
-------
.817*1
1.54856
1.72062
.00000
278.00
Specified But Properties:
Molecular weight: 58.080
Release temperature: 278.00 K
Density at releaae temperature and ambient praaaure: 1.7920 kg/m**3
Avactga heat capacity: 59*.97 J/kg K
Upper nole fraction contour: .15000
Lower mole fraction contour: 2.00000E-OS
Height for laoplatba: * .00000 m
Source input data point*
Initial mass in cloud:
«= 4
Time
.00000
60230.
60231.
60232.
Contaminant
Maaa Rata
kg/.
.20100
.20100
.00000
.00000
.00000
Source Radiua
5.0000
S.OOOO
.00000
.00000
Contaminant
Maaa Fraction
kg contain/kg mix
.90000
.90000
.90000
.90000
Temperature
K
278.00
278.00
278.00
278.00
Enthalpy
J/kg
.00000
.00000
.00000
.00000
0 Calculation procedure for ALPHA: 1
0 Enfcrainment prescription for FBI: 3
0 Layer thickness ratio uaad for average depth: 2.1500
0 Air entrainment coefficient uaad: .590
0 Gravity (Lumping velocity coefficient uaed: 1.150
0 NO* laotharmal calculation
0 Heat tranifer not included
0 Water transfer not Included
«= 5
CALCULATED SOURCE PARAMETERS
«= 6
Time
aac
Gaa Radiua
602.300 5.00000
1806.90 5.00000
OSource strength (kg/s) :
Equivalent Primary aource length (m)
Secondary aourca concentretlon (kg/m**3)
Height
m
.000000
.000000
th (m) :
Qatar
kg/m**2/a
2.5592UE-03
2.559211E-03
.20100
10.000
SZU-L/2.)
m
. 528482
.528482
Equivalen
Equivalen
Mole free C
Danaity
kg/m**3
.17518
7.085218E-02 1.31792
7.085218E-02 1.31792
imary source radius (ml :
Equivalent Primary source half-width (m)
Secondary aource SZ (ml :
Temperature
K
278.000
276.000
5.0000
3.9270
.52848
Rich No.
.000000
.000000
A-ll
-------
Contaminant flux rate: 2.55921E-03
Secondary source mate fraction*... contaminant; .132924
Enthalpy: .00000 Denalty: 1.3178
.86361
Secondary aourc* length [•)
10.000
Secondary cource half-width [ml
3.9270
0 Diatanca Ho la Concentration Daniity Temperature Half Sz Sy Width at z- .00 • to:
Fraction ' Width 2.000E-03moleZ 1S.O molaX
(•) (kt/m**3) (k»/o.**3) (K) (m) «n> (m) (n) (a)
«= 8
s.oo
5.10
5.85
8. 02
10.2
13. 5
16.8
23.2
33.7
57.1
80.5
120.
160.
200.
240.
280.
320.
360.
400.
440.
460.
520.
560.
600.
640.
680.
720.
7.
7.
6.
5.
3.
085E-02
046E-02
696E-02
268E-02
806E-02
2.248E-02
1.
5.
3.
1.
6.
3.
2.
1.
1.
9.
7.
6.
5.
4.
4.
3.
3.
3.
2.
2.
2.
402E-02
743E-03
153E-03
160E-03
402E-04
320E-04
126E-04
S16E-04
158E-04
245E-05
618E-OS
430E-05
531E-OS
830E-05
270E-05
814E-05
436E-OS
119E-05
850E-05
619E-05
418E-05
9.
5.
3.
1.
8.
2.
1.
8.
5.
3.
2.
2.
1.
1.
1.
1.
1.
8.
8.
7.
7.
6.
6.
175
174
166
131
538E-02
670E-02
550E-02
4S9E-02
017E-03
853E-03
630E-03
4S2E-04
412E-04
865E-04
850E-04
354E-04
940E-04
637E-04
406E-04
230E-04
067E-04
711E-05
750E-05
942E-05
257E-05
668E-05
157E-05
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
.32
.32
.32
.31
.29
.28
.28
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
.27
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
278.
3.93
3.88
4.64
7.12
9.29
11.9
13.9
17.1
19.1
22.2
23.8
25.1
25.7
25.9
25.6
25.5
25.2
24.8
24.3
23.7
23.1
22.5
21.9
21.2
20.5
IS. 8
19.1
.528
.516
.445
.376
.386
.460
.565
.877
1.20
2.04
2.81
4.00
5.07
6.07
' 7.01
7.91
8.77
9.59
10.4
11.2
11.9
12.6
13.4
14.0
14.7
15.4
16.1
.000
.243
.755
1.63
2.36
3.34
4.24
6.24
7.99
12.1
15,5
20.6
25.1
29.2
33.0
36.6
39.9
43.2
46.3
49.3
52.2
55.0
57.7
60.4
63.0
65.5
68.0
3.93
4.57
6.78
11.7
15.8
20.8
24.7
32.0
37.1
46.5
52.7
59.7
64.3
67.4
69.5
70.8
71.4
71.4
70.9
70.0
68.6
66.7
64.3
61.4
58.0
53.8
48.7
A-12
-------
II
o e
II a
H ~
e a w
S S o
t
i
*• o o>
o o o
X 10 N
ie o ro
sis
i i i
o o o
5* •
§ "
r? s
"I r
.5 I
w M to
•*j ^ -w
ex a cc
o
o
o
e
n
O> ^ CB
ie >i *-
CB -W Ol
o u «j
o
c»
N N>
CO K
-------
APPENDIX B
EXAMPLE AND INTERPRETATION
OF
SLAB OUTPUT
-------
SLAB Output File
The SLAB output file consists of three general categories of information:
• problem description,
instantaneous spatially-averaged cloud properties, and
time-averaged volume fraction.
An example output file is provided to illustrate each category. Numerically indexed
explanatory notes are given for each main section of the output.
B-2
-------
Output Listing tot**
Vertical Vapor Chlorine J«t Release Simulation
1.
2.
3.
5.
6.
A list of tba various user specified input parameters to define th« simulation ia provided. This information
ia organized into six aaetions: problem input, releaaa gas properties, apill eharactariatics, field parameters,
ambient meteorological propartiaa, and additional parameters that describe the ipill scanazio. Hot* that some
of th« problam input paramatars may b« changed by tba cod* in ordar to ba consistant with SLAB modeling
assumptions. Tha valuas listad in tha othar fiva iactions giva tha paramatar valuas actually used in tha
simulation.
Tha Instantaneously spatially averaged cloud parameters giva tha raaults of tha dispersion calculation phase
of tha simulation. Theae intermediate result* axe tha solution* of tha spatially avatagad conservation
equations (plume or puff), tha equation of stata (ideal gas law), and tha length and width equations. Cloud
meander or time-averaging effects are not included. In steady state dispersion mode, during a finite duration
release (t < TSD), apatial averaging is over tha crosswind plan* of tha cloud. • In the puff dispersion mode,
after tha releaae haa terminated (t > TSD), spatial averaging i* over tha entire volume of the cloud. Refar
to the SLAB User's Manual for further discussion.
The instantaneous spatially averaged cloud property reaults are listed in two groupa as a function of downwind
distance and ar* described by tha following cloud parameters:
(Group 1)
(Group 2)
x
zc
h
bb
b
bbx
bz
cv
rho
t
u
ua
cm
cmv
cmda
cmw
ug
w
V
vz
downwind distance (m)
profile center height (m)
cloud height (m)
cloud half-width (m)
half-width parameter (m)
cloud half-length (m)
half-length paramatar (m)
volume fraction of emission
density (kg/or1)
temperature (K)
downwind cloud velocity (m/s)
height averaged ambient wind spaed (m/s)
mass fraction of emission
fraction of emission vapor
fraction of dry air
fraction of water
naas fraction of water vapor
gravity flow velocity, Z-direction (m/s)
grsvity flow velocity, Y-direction (m/s)
gravity flow velocity, X-direction (m/s)
vertical entrainment velocity (m/s)
crosswind horizontal entrainmant velocity (m/s)
downwind horizontal entrainment velocity (m/s)
The time; averaged volume fraction is tha last of tha three general categories of information provided by the
output file and is generally of primary interest to the analyst. From these volume fractions, the time averaged
concentrations of tha modeled release can be determined (volume fraction is converted to concentration in parts
per million by multiplying the volume fraction by one million).
Tha time- averaged volume concentration output is divided into three sections: concentration contour parameters,
concentration in tha z-ip(I) plane, and maximum center Line concentration. All of the reaults presented at a Cram
th« viewpoint of an observer located at tha downwind distance z, crosswind distance y from the mean'cloud
centerline, and height s above tha ground.
Tha equation that should be used for dispersion calculations ia provided. The diapersion calculations can ba
performed in one of three ways: steady state plume made, tranaient puff mode, or a combination of both modes.
Depending on the release type, the time averaged volume concentration is calculated by:
1) steady state plum* mode (x i* independent variable),
e(x,y,z.t) - ec(x) * (erf{x«)-erf(xb)) » (erf(ya)-erf(yb)) • (e*p<-*a*za)+exp(-zb*zb)),
where
c(z,y,z,t)
concentration (volume fraction) at (x.y.x.t)
B-3
-------
x - downwind distance (CD)
y • ccoaswind horizontal distance (m)
z - hal«ht (m)
t • tin* (s)
erf • error function
xa -
xb - (x-xc-bx)/(sr2*batax)
ya • (y+b)/(ar2*betac)
yb -
•xp • exponential function
za • (z-ze)/(sr2*sig>
zb •
-------
problem input
idapl -
ncalc •
«na •
cps
tbp •
cmedO •
dhe •
cpsl •
rhosl »
3pb -
spc
ts -
V
aa •
tsd -
qtii -
ha
tav «
XfflB "
Zp(l> "
zp(2) -
zp(3) -
zp(*> -
zO •
za •
ua -
ta •
rh
stab •
3
1
.070910
498.10
239 . 10
.00
2878*0.
926.30
1374.00
1978.3*
-27.01
251.00
1.51
.00
662.
.00
S.OO
1200.00
10000.00
1.00
.00
.00
.00
. 100000
10.00
1.50
278.00
75.00
6.00
(only displays values to tiro decimal places)
releaae gaa properties
molecular weight of source gaa (kg)
vapor heat capacity, conat. p. (J/kg-k)
teoperature of source gaa (k)
danaity of source gaa (kg/m3)
boiling point temperature
liquid oaaa fraction
liquid heat capacity (j/kg-k)
heat of vaporization (J/kg)
liquid source density (kg/m3)
saturation pressure constant
saturation preasure constant (k)
saturation pressure constant (k)
MDS -
cpa •
ta •
rhos •
tbp •
omedO"
cpal -
dhe •
rhosl-
spa •
spb •
spc -
7.0910E-02
4 . 9810E+02
2.5100E+02
3.4429E+00
2.3910E-H32
0 . OOOOE+00
9.2630E+02
2.8784E-KI3
1.3740E+03
9.3278E-KJO
1.9783E-1-03
-2.7010E+01
spill characteristics
spill type
oaaa source rate (kg/a)
continuous source duration (s)
continuous source oaas (kg)
instantaneoua source m»*t (kg)
source area (o2)
vertical vapor velocity (n/s)
source half width (a)
source height (m)
horizontal vapor velocity (m/s)
- idspl-
tsd
qtca
qtis
as
ws
bs
hs
us
1.5100E+OQ
S. S2QOE-H)2
9.9962E-MJ2
0.OOOOE-MJO
4300E-03
" 9.8338E+01
• 3.3334E-02
- 5.0000E+00
• 0.OOOOE+00
- k.
field paracMters
concentration averaging time (s)
* tav • 1.2000E-K13
B-5
-------
mixing layer height (a)
rn.-r4n.nii downwind diStrSCe (O)
concentration measurement height (a)
- has • 2.60002+02
- xffln - 1.00002+04
- zpU)- 1.00002+00
- zp<2>- O.QOOOE-KIO
- zp<3)- 0.00002+00
- zp(4)- O.OOOOE+00
ambient meteorological properties
molecular weight at ambient
-------
4.282+01
5.07E-MJ1
6.021+01
7 . 182+01
8.392+01
1.03E+02
1.242+02
1.492+02
1.79E+02
2.16E+02
2.61E+02
3 . 15E+02
3 . 82E+02
* . 67E+02
5.73E+02
7 . 09E+02
8.81E+02
1.102+03
1.38E+03
1.742+03
2.19E+03
2.77E+Q3
3.512+03
* . 452+03
S.65E+03
7.16E+03
9.08E+03
1.132+04
1 . 462+04
1.84E+04
z
1 . OOE+00
1.342+00
2.08E+00
2.63E+00
3.172+00
3.712+00
4.232+00
4 . 80E+00
5.342+00
5.88E+00
6.422+00
6 . 56E+00
6.732+00
5.93E+00
7 . 172+00
7.47E+00
7 . 83E+00
8.26E+00
8.79E+00
9.432+00
1.022+01
1.122+01
1.23E+01
1.37E+01
1.54E+01
1.742+01
1.99E+01
2.29E+01
2.632+01
3.09E+01
3.832+01
4.282+01
3.072+01
6.022+01
7.182+01
8.392+01
8.43E-01
4.012-01
3.012-01
2.452-01
2.09E-01
1.83E-01
1.63E-01
1.472-01
1.35E-01
1.24E-01
1.15E-01
1.08E-01
9.96E-02
9.28E-02
8.71E-02
8.242-02
7 . 83E-02
7 . 482-02
7.172-02
6.90E-02
6.652-02
8.432-02
6.232-02
8.03E-02
5.88E-02
5.732-02
5.592-02
5.462-02
5.3*2-02
5.23E-02
em
1. OOE+00
6.44E-01
3.11E-01
1.67E-01
1.012-01
6.7*2-02
*.78E-02
3 . 55E-02
2.74E-02
2.18E-02
1.77E-02
1.77E-02
1.772-02
1.77E-Q2
1.78E-02
1.78E-02
1.73E-02
1.74E-02
1.74E-02
1.732-02
1.72E-02
1.702-02
1.68E-02
1 . S6E-02
1 . 64E-02
1.812-02
1.382-02
1.342-02
1.302-02
1.432-02
1.372-02
1.102-02
7 . 932-03
3. 922-03
4.392-03
3.632-03
2.82E+00
2.37E+00
2.382+00
2.302+00
2.662+00
2.862+00
3 . 10E+00
3.39E+00
3.71E+00
4 . 082+00
4.31E+00
4 . 99E+00
3.822+00
6.39E+00
7.31E+00
8.41E+00
9.892+00
1.122+01
1. 292+01
1.492+01
1.732+01
2.002+01
2.312+01
2.862+01
3 . 07E+01
3.34E+01
4.08E+01
4.70E+01
5.412+01
8.212+01
emv
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1.002+00
-1.002+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
1.77E-02
1.77E-02
1.77E-02
1.77E-02
1.762-02
1.762-02
1.7SE-02
1.74E-02
1.74E-02
1.73E-02
1.722-02
1.70E-02
1.682-02
1.562-02
1.84E-02
1.612-02
1.382-02
1.34E-02
1.302-02
1.432-02
1.372-02
1.102-02
7.932-03
3.922-03
4.392-03
3.632-03
2.40E+01
3.89E+01
3.232+01
6.432+01
7.61E+01
8.74E+01
9.83E+01
1.092+02
1.20E+02
1.312+02
1.43E+02
1.34E+02
1.632+02
1 . 762+02
1.872+02
1.98E+02
2.10E+02
2.222+02
2.332+02
2.48E+02
2.63E+02
2.80E+02
2.992+02
3.202+02
3 . 44E+02
3.71E+02
4 . 03E+02
4 . 38E+02
4 . 792+02
3.26E+02
coda
0 . OOE+00
3.332-01
6.36E-01
8.302-01
3.932-01
9.292-01
9.482-01
9.61E-Q1
9.692-01
9.74E-01
9.78E-01
9.782-01
9.782-01
9. 782-01
9.782-01
9.782-01
9.792-01
9.792-01
9.792-01
9.792-01
9.792-01
9.792-01
9.792-01
9.792-01
9.802-01
9.802-01
9.802-01
9.812-01
9.812-01
9.822-01
9.822-01
9.332-01
9.382-01
9.902-01
9.912-01
9.922-01
2.25E+00
3 . 83E+00
4 . 84E+00
3.94E+00
6 . 97E+00
7.97E+00
8.93E+00
9.87E+00
1.08E+01
1.17E+01
1.26E+01
1.35E+01
1.4*2+01
1.32E+01
1.60E+01
1.682+01
1.73E+01
1.822+01
1.882+01
1.93E+01
2. 012+01
2.082+01
2.14E+01
2.20E+01
2.26E+01
2.322+01
2.37E+01
2.43E+01
2.48E+01
2.33E+01
cam
0 . OQE+QO
1.44E-03
2.78E-03
3. 362-03
3 . 622-03
3 . 762-03
3. 842-03
3 . 89E-03
3 . 92E-03
3.94E-03
3 . 962-03
3.96E-03
3 . 96E-03
3 . 96E-03
3.96E-03
3 . 962-03
3.96E-03
3 . 96E-03
3 . 962-03
3 . 962-03
3.962-03
3.962-03
3.962-03
3.962-03
3 . 962-03
3 . 962-03
3.972-03
3.972-03
3.972-03
3.972-03
3.972-03
3.982-03
4 . 002-03
4.012-03
4.012-03
4.012-03
3.93E+01
4.67E+01
5.37E+01
6.66E+01
7.98E+01
9.38E+01
1.13E+02
1.39E+02
1.67E+02
2.02E+02
2.44E+02
2.95E+02
3.26E+02
3 . 63E+02
4 . 09E+02
4.67E+02
3.38E+02
6.27E+02
7.39E+02
8.79E+02
1.03E+03
1.27E+03
1.34E+03
1 . 38E+03
2.30E+03
2.82E+03
3.46E+03
4.24E+03
3.20E+03
6.37E+03
cmwv
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
-l.OOE+QO
-1.002+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
3.98E-03
3 . 96E-03
3 . 962-03
3.96E-03
3 . 96E-03
3 . 962-03
3 . 962-03
3.96E-03
3.962-03
3.962-03
3 . 962-03
3 . 962-03
3 . 96E-03
3 . 962-03
3 . 962-03
3 . 96E-03
3.972-03
3 . 972-03
3.972-03
3.972-03
3.972-03
3 . 982-03
4.002-03
4.012-03
4.012-03
4.012-03
3.93E+01
4.67E+01
5.372+01
S.66E+01
7.982+01
9.38E+01
1.13E+02
1.392+02
1.672+02
2.02E+02
2.44E+02
2.95E+02
3.00E+02
3.052+02
3 . 082+02
3.12E+02
3.14E+02
3.17E+02
3 . 192+02
3 . 202+02
3.212+02
3.222+02
3.23E+02
3.232+02
3 . 24E+02
3 . 24E+02
3.24E+02
3.24E+02
3 . 25E+02
3.252+02
we
9. 362+01
6.74E+01
3.432+01
4.462+01
3.822+01
2.892+01
2.222+01
1.612+01
1.04E+01
5.06E+00
0 . OOE+00
-8.7QE-03
-1.922-02
-3.19E-02
-4.73E-02
-6.582-02
-8.822-02
-1.15E-01
-1.47E-01
-1.86E-01
-2.332-01
-Z. 882-01
-3.54E-01
-4.32E-01
-5.24E-01
-6.322-01
-7.372-01
-9. 032-01
-1.082+00
-1.292+00
-3.912-01
-4.902-02
-1.332-02
-5.452-03
-2.732-03
-1.372-03
4.312-03
3.232-03
2.422-03
1.882-03
1.492-03
1.20E-03
9.79E-04
7.99E-04
8.322-04
5.332-04
4.352-04
3.332-04
2.662-04
1.972-04
1.432-04
1.032-04
7.332-05
3.162-05
3.592-05
2.46E-05
1.682-05
1.132-03
7 . 362-06
5.01E-06
3.312-06
2.172-06
1.412-06
9.192-07
5. 962-07
3 . 862-07
v«
0. OOE+00
0 . 002+00
0 . 002+00
0.002+00
0.002+00
0 . 002+00
0.002+00
0 . OOE+00
0 . 002+00
0 . 002+00
0 . 002+00
0 . OQE+QO
0 . 002+00
0 . 002+00
0 . OOE+00
0. 002+00
0 . 002+00
0 . 002+00
0 . OOE+00
0 . 002+00
0.002+00
0 . 002+00
0.002+00
0 . 002+00
0 . 002+00
0 . 002+00
0 . 002+00
0 . 002+00
0.002+00
0 . 002+00
2.232+00
1.322+00
1.302+00
9.482-01
7.232-01
3.722-01
1.28E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+OQ
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.272+00
1.27E+00
1.27E+00
u«
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . 002+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0. OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+OQ
0 . 002+00
a . OOE+OO
0 . 002+00
0 . 002+00
0 . 002+00
a . 002+00
0 . 002+00
0 . 002+00
0.002+00
0.002+00
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.782+02
2.782+02
2.782+02
2.78E+02
2.78E+Q2
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.782+02
2.78E+02
2.782+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
2.78E+02
w
-1. OOE+00
- 1 . OOE+00
-1. OOE+00
-1.002+00
-1. OOE+00
-1. OOE+OQ
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
2.09E-02
8.31E-04
6.322-04
6.33E-04
6.33E-04
S.37E-04
S.39E-0*
6.432-04
6.482-04
6.552-04
6.642-04
8.772-04
S.95E-04
7.212-04
7.812-04
8.222-04
9.202-0*
1.102-03
1.502-03
3 . 062-03
3.962-02
3.452-02
3 . 992-02
2.322-02
2.132-02
1.722-02
3.55E-01
8.09E-01
8.03E-01
8.04E-01
8.04E-01
8.06E-01
8.122-01
8.21E-01
8.33E-01
8.49E-01
8.69E-01
8.92E-01
9.23E-01
9.60E-01
1. OOE+00
1.05E+00
1 . 10E+00
1.162+00
1.22E+00
1.28E+00
1.35E+00
1.42E+00
1.49E+00
1 . 56E+00
1.63E+00
1.702+00
1.782+00
1 . 85E+00
1.93E+00
2. OOE+00
V
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1.002+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
-1. OOE+00
3.63E-02
3.62E-02
3.62E-02
3.62E-02
3.62E-02
3.S2E-02
3.62E-02
3 . 62E-02
3.62E-02
3.82E-02
3.62E-02
3.S2E-02
3.62E-Q2
3.S1E-02
3.S1E-02
3.60E-02
3.57E-02
3.46E-02
3.27E-02
2.94E-02
2.11E-02
1.35E-02
1.37E-02
1.292-02
1.222-02
1.172-02
3 41F-01
7 99F-01
7 97E-01
7 97E-01
8.00E-01
8.0AE-01
8.11E-01
3.21E-01
8.34E-01
8.51E-01
3.71E-01
8.94E-01
9.24E-01
9.60E-Q1
1. OOE+00
1.05E+00
1.10E+00
1.18E+00
1.22E*00
1.28E+00
1.35E+00
1.42H-00
1 49E100
1 . 56E+00
1.63E+00
1.70E+00
1.78E+00
1.85E+00
1.93E+00
2. OOE+00
«= 4
vx
0 OOE+00
0. OOE+00
0. OOE+00
0. OOE+00
0. OOE+00
0. OOE+00
0. OOE+00
O.OOE-i-00
0 OOE-M30
0 OOE+OQ
0. OOE+00
3.46E-01
3.46E-01
3.46E-01
3 46E-01
3 46E-01
3.46E-01
3.46E-01
3.46E-01
3.46E-01
3.45E-01
3 45E-01
3.45E-01
3.45E-01
3 44E-01
3.44E-01
3.42E-01
3.39E-01
3.33E-01
3.14E-01
2.34E-01
1. 73E-01
1.61E-01
1.56E-01
1.55E-01
1.572-01
B-7
-------
1.032+02
1.24E+02
1.492+02
1.792+02
2.162+02
2.612+02
3 . 152+02
3 . 822+02
4 . 672+02
5.73E+02
7.092+02
3.812+02
1.10E+03
1.382+03
1.742+03
2.192+03
2.77E+03
3 . 512+03
4 . 452+03
5.652+03
7.162+03
9.082+03
1 . 152+04
1.462+0*
1.8*2+0*
2.952-03
2.402-03
1.962-03
1.602-03
1.312-03
1.072-03
6 . 702-0*
6.532-0*
4.822-0*
3.522-0*
2.53E-0*
1.80E-0*
1.272-0*
8.802-05
6.032-05
*. 112-05
2.772-05
1.852-05
1.232-03
8.112-06
3.322-06
3.472-08
2.262-06
1.462-06
9.472-07
2.952-03
2.402-03
1.962-03
1.602-03
1.312-03
1.072-03
8.702-0*
6.532-04
* . 822-0*
3.522-0*
2.532-0*
1.802-0*
1.27E-0*
8.802-03
6.052-03
4.112-05
2.772-05
1.832-03
1.232-05
8.112-06
3.322-06
3.472-06
2.262-06
1.462-06
9.472-07
9.932-01
9.942-01
9.9*2-01
9.9*2-01
9.932-01
9.932-01
9.932-01
9.952-01
9.952-01
9.962-01
9.962-01
9.962-01
9.962-01
9.962-01
9.962-01
9.962-01
9.962-01
9.962-01
9.962-01
9.962-01
9.962-01
9.962-01'
9.962-01
9.962-01
9.962-01
4.022-03
4.02E-03
4.021-03
4.022-03
4.022-03
4.022-03
4.03E-03
4.032-03
4 . 032-03
4.032-03
4.032-03
4.032-03
4.032-03
4 . 032-03
4.032-03
4 . 032-03
4.032-03
4 . 032-03
4 . 032-03
4.032-03
4.032-03
4.032-03
4.032-03
4 . 032-03
4.032-03
4 . 02E-03
4.02E-03
4 . 022-03
4.022-03
4.022-03
4 . 022-03
4.032-03
4 . 032-03
4.032-03
4 . 032-03
4.03E-03
4.03E-03
4 . 03E-03
4.03E-03
4 . 032-03
4.03E-03
4.03E-03
4 . 032-03
4.03E-03
4.032-03
4 . 032-03
4.032-03
4.032-03
4.032-03
4 . 032-03
-9.622-04
-6.20E-0*
-4.152-0*
-2.862-0*
-2.022-0*
-1.452-0*
-1.072-0*
-9.172-05
-6.262-05
-4.332-05
-3.032-03
-2.152-05
-1.54E-05
-1.122-03
-8.212-06
-6.082-06
-4.532-06
-3.402-06
-2.562-06
-1.9*2-06
-1.472-08
-1.112-06
-8.412-07
-6.352-07
-4.782-07
4.602-01
3.752-01
3.082-01
2.552-01
2.132-01
1.802-01
1.522-01
1.202-01
9.462-02
7.312-02
3.992-02
4.812-02
3.902-02
3.192-02
2.632-02
2.192-02
1.822-02
1.532-02
1.292-02
1.092-02
9.222-03
7.832-03
6.622-03
5.612-03
4.752-03
0 . OOE+00
0 . OOE+00
0 . OOE+00
0. OOE+00
0.002+00
0 . 002+00
7 . 932-02
6.292-02
4 . 972-02
3 . 92E-02
3.08E-02
2.42E-02
1.902-02
1.482-02
1.152-02
8.882-03
6.812-03
5.192-03
3.94E-03
2.98E-03
2.252-03
1.692-03
1.272-03
9.SOE-0*
7 . 12E-0*
1.452-02
1.272-02
1.142-02
1.052-02
9.872-03
9.022-03
8.462-03
7.9*2-03
7.442-03
6.962-03
6.51E-03
6.09E-03
5.70E-03
5.34E-03
5.012-03
4 . 702-03
4.412-03
4.152-03
3 . 902-03
3.662-03
3.442-03
3.222-03
3.022-03
2.812-03
2.622-03
1.132-02
1.Q9E-02
1.06E-02
1.04E-02
1.022-02
1.01E-02
l.OOE-02
l.OOE-02
1.01E-02
1.02E-02
1.04E-02
1.06E-02
1.08E-02
1.10E-02
1.12E-02
1.14E-02
1.1SE-02
1.16E-02
1.17E-02
1.17E-02
1.16E-02
1.142-02
1.12E-02
1.09E-02
1.06E-02
l.SOE-0
1.S4E-0:
1.6SE-01
1.75E-01
1.81E-01
1.382-01
1.96E-01
2.04E-Q1
2.14E-01
2.25E-01
2.36E-01
2.47E-Q1
2.59E-01
2.70E-Q1
2.81E-01
2.91E-01
3.01E-01
3.09E-01
3.17E-01
3.24E- 01
3.3i£ 01
3.36E 01
3.40E- 01
3.42£-01
3.44E-01
«= 5
time «v«Et*«d (tav « 1200. •) voluaw concentration: concentration contour parametera
c - ec(x) • (»rf(xa)-er*(xb)> • («r£.
5.
6.
6.
8.
6.
7.
7.
7.
a.
8.
9.
xc(t)
OOE+00
542+00
082+00
632+00
172+00
71E+00
252+00
302+00
342+00
382+00
422+00
562+00
732+00
932+00
172+00
472+00
332+00
262+00
792+00
432+00
bx(t) betax(t)
0.
S.
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
5.
5.
5.
S.
S.
8.
7.
7.
OOE+00
102-01
022+00
532+00
0*2+00
552+00
062+00
57E+00
062+00
592+00
102+00
222+00
382+00
372+00
802+00
082+00
412+00
822+00
322+00
922+00
0.
t
a.
i.
i.
2.
2,
2.
3.
3.
4.
4.
It.
4.
4.
4,
5.
3.
3,
6.
OOE+00
. 16E-03
.32E-03
.25E-02
, S6E-02
.08E-02
.50E-02
.912-02
.33E-02
. 74E-02
. 16E-02
,27E-02
.39E-02
.55E-02
,73E-02
.96E-02
.24E-02
,57E-02
.98E-02
.47E-02
-------
1.
1.
1.
1.
1.
1.
1.
2.
2.
3.
3.
4.
5.
6.
7.
8.
1.
1.
1.
1.
2.
2.
3.
3.
4.
5.
7.
3.
1.
1.
1.
2.
2.
3.
4.
5.
7.
02E+01
121+01
23E+01
37E+01
54E+01
74E+01
99E+01
29E+01
65E+01
09E+01
63E+01
28E+01
07E+01
02E+01
18E+01
59E+01
03E+02
24E+02
49E+02
79E+02
16E+02
61E+02
1SE+02
82E+02
67E+02
73E+02
09E+02
81E+02
10E+03
38E+03
74E+03
19E+03
77E+03
31E+03
43E+03
65E+03
18E-MJ3
9.08E+03
1.
1.
1.
13E+0*
46E+04
84E+04
2
2
2
2
2
2
2
2
2
2
1
1
7
5
3
3
2
1
1
1
1
a
7
5
4
3
3
2
2
1
1
1
1
1
9
8
7
7
6
5
5
. 13E-02
. 1*E-02
. 13E-02
. 13E-02
. 17E-02
. 18E-02
.20E-02
.23E-02
.26E-02
.30E-02
. 69E-02
. 11E-02
. 30E-03
. 19E-03
. 92E-Q3
. 06E-03
.43E-03
. 98E-03
. 61E-03
.31E-03
.07E-03
. 79E-04
.21E-04
.912-04
. 83E-04
. 99E-04
.31E-04
. 78E-04
.32E-Q4
.98E-04
.69E-04
. *6E-0*
.27E-04
. 12E-0*
. 92E-03
. 33E-03
. 88E-03
.03E-05
.31E-03
. 64E-03
.04E-03
4.
4.
4.
4.
4.
4.
4.
4.
4.
4.
8.
2.
3.
4.
3.
8.
7.
a.
9.
1.
1.
1.
1.
1.
1.
1.
1.
i.
1.
1.
1.
2.
2.
2.
2.
76E-01
76E-01
76E-01
78E-01
76E-01
76E-01
76E-01
76E-01
78E-01
77E-01
81E-01
2SE+00
63E+00
84E+00
9*E+00
97E+00
97E+00
93E+00
87E+00
Q8E+01
17E+01
28E+01
33E+01
44E+01
32E+01
60E+01
68E+01
75E+01
82E+01
88E+01
9SE+01
01E+01
081+01
14E+01
20E+01
2.26E+01
2.
2.
2.
2.
2.
321+01
37E+01
43E+01
48E+01
33E+01
2.
2.
2.
2.
2.
2.
2.
2.
2.
3.
3.
1.
2.
3.
3.
4.
5.
3.
6.
S.
7.
8.
8.
9.
1.
39E+00
42E+00
45E+00
49E+00
54E+00
60E+00
68E+00
78E+00
91E+00
07E+00
34E+00
39E+01
2SE+01
02E+01
72E+01
39E+01
04E+01
69E+01
33E+01
97E+01
61E+01
27E+01
93E+01
83E+01
03E+02
1.11E+02
1.
1.
1.
1.
1.
1.
1.
2.
2.
2.
3.
3.
4.
4.
3.
18E+02
27E+02
37E+02
48E+02
62E+02
78E+02
97E+02
20E+02
49E+02
83E+02
23E+02
70E+02
2SE+02
89E+02
63E+02
1
1
1
1
1
1
1
1
9
8
1
6
4
3
2
2
1
1
1
1
1
1
1
9
9
8
a
7
7
7
6
6
8
6
6
5
3
5
3
3
5
.S1E+01
.S9E+01
.S7E+01
.S4E+01
.49E+01
.43E+01
.33E+01
. 18E+01
. 82E+00
. 19E+00
.62E+00
.43E-01
.01E-01
.01E-01
.4SE-01
.09E-01
.83E-01
.63E-01
.47E-01
. 35E-01
.24E-01
. 13E-01
.08E-01
. 96E-02
.28E-02
. 71E-02
.24E-02
. 83E-02
. 48E-02
. 17E-02
. 90E-02
. 63E-02
. 43E-02
.23E-02
.03E-02
. 88E-02
. 73E-02
. 39E-02
. 46E-02
.34E-02
.23E-02
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
2.
2.
Z.
2.
3.
3.
4.
4.
5.
8.
7.
8.
9.
1.
1.
1.
1.
2.
2.
2.
3.
3.
38E+00
38E+00
38E+00
38E+00
38E+00
38E+00
40E+QO
44E+00
32E+00
69E+00
58E+00
14E+00
13E+00
20E+00
30E+00
42E+00
5SE-H)0
70E+00
87E+00
06E+00
29E+00
34E+00
82E+00
19E+00
63E+00
17E+00
81E+00
53E+00
*2E+00
43E+00
S9E+00
94E+00
13E+01
33E+01
S3E+01
77E+01
04E+01
33E+01
71E+01
12E+01
S8E+01
1.
1.
1.
1.
1.
1.
2.
2.
2.
3.
4.
5.
7.
1.
1.
1.
2.
2.
3.
3.
4.
3.
7.
7.
a.
9.
1.
1.
1.
I.
i.
2.
2.
3.
3.
4.
3.
8.
7.
9.
1.
03E+01
16E+01
29E+01
45E-HU
64E+01
88E+01
16E-M)1
S1E+01
95E+01
53E+01
38E+01
78E+01
69E+01
01E+02
29E+02
84E+02
07E+02
38E+02
20E+02
93E+02
81E+02
83E+02
09E+02
36E+02
25E+02
34E+02
07E+03
23E+03
42E+03
581+03
94E+03
29E+03
71E+03
22E+03
83E+03
58E+03
49E+03
39E+03
93E+03
55E+03
15E+04
1.
1.
1.
1.
1.
1.
1.
2.
2.
3.
3.
4.
5.
6.
7.
8.
1.
1.
1.
1.
2.
2.
3.
3.
4.
3.
7.
8.
1.
1.
1.
2.
2.
3.
4.
5.
7.
9.
1.
1.
1.
02E+01
12E+01
23E-HH
37E+01
54E+01
74E+01
99E+01
29E+01
65E-MJ1
09E+01
63E+01
28E+01
07E-HJ1
02E+01
18E+01
59E+01
03E+02
24E+02
49E+02
79E+02
16E+02
61E+02
13E+02
82E+02
67E+02
73E+02
09E+02
81E-HJ2
10E+03
38E+03
74E+03
19E+03
77E+03
S1E+03
45E+03
65E+03
16E+03
08E+03
13E+04
46E+04
84E+04
8
9,
1.
1.
1,
1.
.85E+00
.34E+00
.06E+01
19E+01
.33E+01
,34E+01
1.77E+01
2.
2.
2.
3.
3.
4.
5.
6.
7.
9.
1.
1.
1.
2.
2.
2.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
.06E+01
40E+01
81E+01
32E+01
93E+01
67E+01
37E+01
86E+01
98E+01
38E+01
15E+02
39E+02
67E+02
02E+02
44Z+02
95E+02
OOE+02
03E-H32
08E+02
12E+02
14E+02
17E+02
19E+02
20E+02
21E+02
22E+02
23E+02
23E+02
24E+02
24E+02
24E+02
24E+02
23E+02
23E+02
7.
7.
3.
9.
1.
1.
1.
1.
1.
2.
2.
3.
3.
4.
5.
6.
7.
9.
1,
1.
1.
1.
2.
7.
1.
1.
2.
2.
3.
3.
4.
5.
7.
8.
1.
1.
1.
1.
2.
3.
3.
. 06E-02
. 79E-02
.S7E-02
73E-02
10E-01
26E-01
45E-01
68E-01
96E-01
30E-01
71E-01
21E-01
31E-01
54E-01
44E-01
31E-01
82E-01
*1E-01
13E+QO
37E+00
65E+00
99E+00
41E+00
33E+01
UE+02
55E+02
OOE+02
52E+02
12E+02
35E+02
73E+02
79E+02
11E+02
72E+02
07E+03
32E+03
62E+03
99E+Q3
44E+03
OOE+03
68E+03
tim« averaged (t«v • 1200. »> volvm* concentration: concentration In the z • 1.00 plane.
« 3
downwind
distance
x (m)
l.OOE+00
1.34E+00
2.08E+00
2.S3E+QQ
3 . 17E+00
3.71E+00
4.23E+00
4 . 80E+00
3.34E+00
5.88E+00
8.42E+00
6.36E+00
8.73E+00
S.93E+00
7.17E+00
7.47E+00
7 . 83E+00
3.26E+OQ
3.79E+00
time of
max cone
(s)
3.31E+02
3 . 32E+02
3 . 32E+02
3.33E+02
3.33E+02
3.34E+02
3.34E+02
3.33B+02
3.38E+02
3.38E+02
3.37E+02
3.37E+02
3.37E-MJ2
3.37E+02
3.38E+02
3 . 38E+02
3 . 38E+02
3 . 39E+02
3.39E+02
cloud
duration
6.
8.
8.
8.
8.
8.
8.
8.
8.
8.
6.
8.
8.
8.
8.
8.
8.
8.
a.
(s)
52E+02
62E+02
62E+02
62E+02
S2E+02-
S2E+02
82E+02
82E+02
621+02
821+02
82E+02
82E+02
52E+02
82E+02
82E+02
S2E+02
821+02
S2E+02
82E+02
effective
half width
bbc (m)
3.34E-02
4.29E-01
8.23E-01
1.22E+00
1.62E+00
2.01E+00
2.41E+00
2.81E+00
3.20E+00
3.SOE+00
3 . 99E+00
4 . OOE+00
*.01E+00
4 . 02E+00
4.03E+00
4 . 04E+00
4 . 08E+00
4.07E+00
4 . 10E+00
avera«« concentration (volume fraction) at (x.y.z)
y/bbc-
0.
0.
0.
0.
0.
0.
0.
0.
8.
1.
1.
1.
1.
1.
1.
1.
1.
2.
3.
0.0
OOE+00
OOE+00
OOE+00
OOE+00
OOE+00
OOE+00
OOE+00
OOE+00
01E-43
90E-33
32E-29
33E-29
34E-29
38E-29
44E-29
36E-29
78E-29
19E-29
03E-29
y/bbe-
0.3
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0. OOE+00
0. OOE+00
0. OOE+00
0 . OOE+00
4.13E-43
1.31E-33
9.07E-30
9.13E-30
9.23E-30
9.48E-30
9.91E-30
1.07E-29
1.22E-29
1.30E-29
2.08E-29
y/bbc-
1.0
0 . OOE+00
0. OOE+00
O.OOE+OQ
0 . OOE+00
0 . OOE+00
0 . OOE+00
0. OOE+00
0 . OOE+00
1.33E-43
4.24E-36
2.94E-30
2.96E-30
3.00E-30
3.07E-30
3. 222-30
3.48E-30
3.97E-30
+.39E-30
8.78E-30
y/bbc-
1.5
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0. OOE+00
0 . OOE+00
2.10E-44
6.30E-37
4.31Z-31
4.34E-31
4.60E-31
4.71E-31
4.93E-31
3.34E-31
8.08E-31
7.49Z-31
1.04E-30
y/bbc-
2.0
0. OOE+00
0. OOE+00
0 . OOE+00
O.OOE+00
0 . OOE+00
O.OOE+00
0 . OOE+00
0 . QOE+00
l.*OE-45
4.71E-38
3.27E-32
3.29E-32
3.33E-32
3.41E-32
3.37E-32
3.36E-32
*.<»OE-32
3.42E-32
7.31E-32
y/bbc"
2.5
O.OOE+00
O.OOE+00
O.OOE+00
0. QOE+00
O.OOE+00
O.OOE+00
O.OOE+00
O.OOE+00
O.OOE+00
1.61E-39
1.12E-33
1. 12E-33
1. 14E-33
1.16E-33
1.22E-33
1.32E-33
1.50E-33
1.35E-33
2.57E-33
B-9
-------
9 . 432+00
1.022+01
1. 122+01
1.232+01
1.372+01
1.S4E+01
1.74E+01
1.99E+01
2.292+01
2.652+01
3.092+01
3.632+01
4.282+01
5.072+01
6.022+01
7.182+01
8.592+01
1.032+02
1.242+02
1.492+02
1.792+02
2. 16E-t-02
2.612+02
3 . 152+02
3.32Z-KI2
* . 872+02
5.732+02
7 . 091+02
8.312+02
1. 102+03
1.38E+03
1.74E+03
2.192+03
2.77E-MJ3
3 . 512+03
4.452+03
5 . 852+03
7 . 181+03
9.08E+03
1.132+04
1.462+04
1.842+04
3 . 402+02
3.412+02
3.422+02
3.432+02
3.442+02
3.46E+02
3.48E+02
3.51E+02
3.34E+02
3 . 582+02
3 . 63E+02
3 . 68E+02
3.75E+02
3 . 83E+02
3.93E+02
4.062+02
4.202+02
4 . 38E+02
4 . 80E+02
4 . 87E+02
5.192+02
5.582+02
6.052+02
8.62E+02
7.36E+02
8.232+02
9.34E+02
1.07E+03
1.23E+03
1.42E+03
1.66E+03
1.94E+03
2.29E+03
2.71E+03
3.22E+03
3.83E+03
4 . J8E-MD3
5.492+03
6.592+03
7.93E+03
9.552+03
1.13E+04
8.62Z+02
.82E+02
.822+02
.622+02
.822+02
.82E+02
.822+02
.622+02
.822+02
6.622+02
6.622+02
6.622+02
6.622+02
6 . 622+02
6.622+02
6.622+02
8 . 622+02
6.622+02
6.622+02
6.622+02
6.622+02
6.622+02
6.622+02
6.622+02
7.07E+02
7.37E+02
8.17E+02
8.892+02
9.762+02
1. 082+03
1.212+03
1.372+03
1.562+03
1.802+03
2.082+03
2.422+03
2.832+03
3.312+03
3.89E+03
4 . 382+03
3.402+03
6.382+03
4
4
4
4
4
4
4
4
4
3
3
9
2
3
3
6
7
8
9
1
1
1
i
i
i
i
i
2
2
2
2
2
3
3
3
4
4
3
6
7
8
9
13E+00
17E+00
.212+00
.27E+00
. 34E+00
.42E+00
. 33E+00
. 672+00
. 84E+00
. 06E+00
.34E+00
. 63E+00
.422+01
.912+01
.252+01
.472+01
. 64E+01
. 77E+01
. 89E+01
. 10E+02
.212+02
.322+02
. 44E+02
. 36E+02
. 67E+02
. 80E+02
.922+02
. 06E+02
.202+02
.372+02
. 582+02
. 812+02
. 082+02
.422+02
. 822+02
.312+02
. 902+02
. 60E+02
.41E+02
.372+02
. 482+02
.732+02
4
1
3
1
1
6
7
1
3
6
3
5
4
2
2
1
1
1
9
7
6
5
4
3
2
2
1
1
. 99E-29
. 062-28
.292-28
.742-27
.962-28
.242-23
. 882-23
.122-19
.312-13
.102-10
.262-05
.332-03
.092-03
. 752-03
. 042-03
.612-03
.322-03
. 09E-03
. 092-04
. 572-04
.302-04
.222-04
.312-04
. 552-04
.862-04
.272-04
. 782-04
.372-04
1.042-04
7
3
4
2
1
1
8
5
3
2
1
a
5
. 822-03
.74E-05
. 13E-OS
. 902-05
. 992-05
. 33E-03
. 73E-06
. 62E-06
. 562-06
.242-06
. 402-06
. 69E-07
. 40E-07
3.432-29
7.312-29
2.262-28
1. 192- 27
1.342-26
4.292-25
3.422-23
7.722-20
2.412-15
4.192-10
3.622-05
3.662-03
2.812-03
1.892-03
1.402-03
1.112-03
9.062-04
7.302-04
6.242-04
3.202-04
4.332-04
3.502-04
2.962-04
2.44E-04
1.962-04
1.562-04
1.222-04
9.432-05
7 . 182-05
5.372-03
3.94E-05
2.84E-OS
2.002-03
1.372-05
9.162-06
6.002-06
3.862-06
2.452-06
1.54E-06
9.592-07
5.972-07
3.712-07
1.112-29
2.372-29
7.342-29
3 . 882-28
4.372-27
1.392-25
1.76E-23
2.502-20
7.832-18
1.36E-10
1.17E-03
1.19E-03
9.122-04
6.132-04
4.552-04
3.602-04
2.942-04
2.442-04
2.032-04
1.692-04
1.402-04
1.162-04
9.622-05
7.912-05
6.372-05
5.062-05
3.972-05
3.062-05
2.33E-03
1.742-05
1.282-05
9.222-06
6.482-06
4.442-06
2.97E-06
1.952-06
1.232-06
7.952-07
4 . 992-07
3.112-07 •
1.94E-07
1.212-07
1.712-30
3.54E-30
1.132-29
5.952-29
6.692-28
2.132-26
2.702-24
3.842-21
1.202-16
2.092-11
1.802-06
1.822-04
1.40E-04
9.402-05
6.972-05
5.522-05
4.512-05
.3.732-05
•3.112-05
2.592-05
2.152-05
1.792-05
1.472-05
1.212-05
9.772-06
7.762-06
6.082-06
4.702-06
3.572-06
2.68E-06
1.96E-Q6
1.412-06
9.942-07
6.822-07
4 . 362-07
2.992-07
1.922-07
1.222-07
7.632-08
4.782-08
2.972-08
1.352-08
1.242-31
2.63E-31
8.152-31
4.31E-30
4.85E-29
1.54E-27
1.952-25
2.78E-22
8.702-18
1.312-12
1.30E-07
1.322-05
1.01E-05
6.812-06
5.05E-06
4.002-06
3.27E-06
2.702-06
2.25E-06
1.38E-06
1.562-06
1.292-06
1.072-06
8.79E-07
7.08E-07
3.62E-07
4.40E-07
3.402-07
2.59E-07
1.94E-07
1.422-07
1.022-07
7.202-08
4.942-08
3.30E-08
2.16E-08
1.39E-08
8.332-09
5.54E-09
3 . 462-09
2.15E-09
1.34E-09
4.22/-33
8.9««-33
2.78E-32
1.472-31
1.66E-30
5.28E-29
6.66E-27
9.49E-24
2.972-19
5.172-14
4.462-09
4.522-07
3.46E-07
2.32E-07
1.73E-07
1.362-07
1.122-07
9.25E-08
7 70E-08
6.42E-38
5.33E-08
4.432-08
3.55E-08
3.01E-08
2.422-08
1.922-08
1.512-08
1.162-08
8.86E-C9
5.S3E-09
4.36E-QS
3.50E-OS
2.47E-C";
1.59E 0'.
1. 132-OS
7 42E-10
4.762-10
3.02E-1D
1.892-10
1.182-10
7.36E- ! I
4 57E-1J
tima avaragad (tav - 1200. *) voluma concentration: maxiimm concentration (voluma fraction) along cantatlina.
downwind
diatanea
X (0)
1.002+00
1.3*2+00
2.082+00
2.632+00
3.172+00
3.712+00
4.232+00
4 . 802+00
5.342+00
5.382+00
6.422+00
8.362+00
6.732+00
6.932+00
7.172+00
7.472+00
7.332+00
8.262+00
8.792+00
9.432+00
hvight
x (a)
5.002+00
9.932+00
1.182+01
1.312+01
1.412+01
1. 442+01
1.342+01
1.382+01
1.612+01
1.832+01
1.832+01
1.832+01
1.632+01
1.632+01
1.632+01
1.832+01
1.632+01
1.632+01
1.622+01
1.622+01
majcimum
concentration
e<*,0.*)
8.472-01
4.452-01
1.632-01
7.922-02
4.612-02
3.002-02
2.102-02
1.352-02
1.192-02
9.432-03
7.662-03
7.642-03
7.632-03
7.612-03
7.592-03
7.572-03
7.34E-03
7.302-03
7.432-03
7.402-03
tima of
max cone
(a)
3.312+02
3 . 322+02
3.322+02
3.332+02
3.33E+02
3.34E+02
3.34E+02
3.352+02
3.362+02
3.362+02
3.372+02
3.372+02
3.372+02
3.372+02
3.382+02
3.382+02
3.382+02
3.392+02
3.392+02
3.402+02
cloud
duration
(s)
6 . 322+02
6.322+02
6.622+02
6 . 622+02
6 . 622+02
6.822+02
8.822+02
3 . 322+02
6. 622+02
6.622+02
6.622+02
6.822+02
6.622+02
6.622+02
6.622+02
6.622+02
3.322+02
3.622+02
6.622+02
6.622+02
B-10
-------
1.12E+01
1.23E+01
1.37E+01
1.5*E-M)1
1.74E+01
1.99E+01
2.29E+01
2.65E-t-01
3.09E+01
3.63E+01
4.28E+01
5.07E-MJ1
6.02E+01
7.18E+01
8.59E+01
1.03E+02
1.24E+02
1.49E+02
1.79E-MJ2
2.16E+02
2.81E+02
3 . 15E+02
3 . 82E+02
4 . 67E+02
S.73E-MJ2
7.09E+02
8 . 81E+02
1.10E+03
1.38E+03
1.74E+03
2.19E+03
2.77E-M)3
3.311*03
4.4SE+03
3.652+03
7 . 16E-M)3
9 . 08E+03
1.13E+04
1 . 46E+04
1.84E+04
1.59E+01
1.37B+01
1.3*8+01
1.49E+01
1.43E+01
1.33E+01
1.18E+01
9.62E+00
8.19E-I-00
6.39E-01
O.OOE+00
0 . OOE+00
O.OOE+00
0 . OOE+00
0. OOE+00
0 . OOE+00
0 . OOE+00
0. OOE+00
0 . OOE+00
0. OOE+00
0. OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0 . OOE+00
0. OOE+00
0. OOE+00
0 . OOE+00
0 . OOE+00
0. OOE+00
0. OOE+00
0 . OOE+00
0. OOE+00
0 . OOE+00
0. OOE+00
0. OOE+00
0. OOE+00
0 . OOE+00
0. OOE+00
0. OOE+00
7.23E-03
7 . 16E-03
7.04E-03
6.90E-03
8.73E-03
6.33E-03
8.29E-03
6.01Z-03
5.69E-03
3.33E-03
3.33E-03
3 . 86E-03
2.821-03
2.15E-03
1.88E-03
1.34E-03
1.08E-03
8.73E-0*
7 . 08E-04
3.74E-04
4.66E-04
3.78E-04
3.00E-04
2.36E-04
1.83E-04
1.40E-04
1.06E-04
7.91E-03
3.79E-03
4.16E-OS
2.92E-03
2.00E-03
1.34E-03
8.73E-06
3.63E-06
3.37E-08
2.24E-06
1.40E-06
8.69E-07
3.40E-07
3 . 42E+02
3.43E+02
3 . 44E+02
3.46E+02
3.48E+02
3.31E+02
3.34E+02
3.38E+02
3.63E+02
3 . 88E+02
3.73E+02
3.83E+02
3.93E+02
4.06E+02
4 . 20E+02
4.38E+02
4 . 60E+02
4 . 87E+02
3.19E+02
3.38E+02
8.03E+02
8.62E+02
7.36E+02
8.23E+02
9.34E+02
1.07E+03
1.23E+03
1.42E+03
1.S6E+03
1.94E+03
2.29E+03
2.71E+03
3.22E+03
3 . 83E+03
4.38E+03
3.49E+03
6.39E+03
7 . 93E+03
9.33E+03
1.13E+04
6 . 62E+02
6.62E+02
6 . 82E+02
6 . 62E+02
6 . 62E+02
6.82E+02
8.82E+02
6.S2E+02
S . 62E+02
6 . 82E+02
6.82E+02
6.62E+02
6.62E+02
8.62E+02
6.62E+02
6.S2E+02
6.62E+02
6 . 82E+02
8 . 62E+02
6 . 82E+02
8.62E+02
S.62E+02
7.07E+02
7 . 37E+02
8.17E+02
8 . 89E+02
9.76E+02
1.08E+03
1.21E+03
1.37E+03
1.36E+03
1.80E+03
2.08E+03
2.42E+03
2.83E+03
3.31E+03
3 . 89E+03
4 . 38E+03
3 . 40E+03
8.38E+03
B-ll
-------
APPENDIX C
INTRODUCTION TO BUOYANT PLUME RELEASES
-------
TABLE OF CONTENTS
Section Page
1.0 BACKGROUND C-l
2.0 MODE OF RELEASE C-l
3.0 LIFT-OFF ': C-4
4.0 PLUME TRAJECTORY C-4
5.0 GROUND LEVEL CONCENTRATIONS UNDER A RISING PLUME ... C-6
6.0 TERMINATION OF PLUME RISE C-8
6.1 Termination of Plume Rise in Neutral Conditions C-9
6.2 Termination of Plume Rise in Stable Conditions C-10
7.0 PASSIVE DISPERSION C-10
8.0 REFERENCES C-ll
LIST OF FIGURES
Figure Page
C-l Typical History of Plume Rise C-2
C-2 Some Conceivable Modes of Release of a Buoyant Plume C-3
C-3 Simulation of a Dense Plume in a Water Tank C-7
11
-------
APPENDIX C
INTRODUCTION TO BUOYANT PLUME RELEASES
1.0 BACKGROUND
The purpose of this section is to introduce any reader who may be interested to the subject
of plume rise and to summarize the issues that must be considered by the requestor and the
analyst when a buoyant plume is released into the environment. These are:
(i) Definition of the mode of release,
(ii) "Lift-Off — the behavior of a buoyant plume in a turbulent building wake (if the
plume arises other than from an isolated point source),
(iii) Plume trajectory,
(iv) Ground level concentrations under a rising plume,
(v) Termination of plume rise, and
(vi) Finally, passive dispersion.
As an example, Figure C-l shows a typical history of plume rise for a release into a
turbulent building wake. A good introductory discussion has been compiled by Briggs(1).
(Note: reference numbers refer to Section 8.0 of this Appendix).
2.0 MODE OF RELEASE
Some potential modes of release are shown in Figure C-2. These include an isolated point
source (A - e.g., an incinerator stack). Figure C-2(B) shows two alternatives for a short
stack: a) the plume rises in a low windspeed, and b) the plume is mixed into the turbulent
building wake in a high windspeed. Figure C-2(C) shows direct leakage from the face of
the building into a turbulent wake. Figure C-2(D) shows how a high momentum vertical
jet may escape the wake of the building, while Figure C-2(E) shows that a randomly
C-l
-------
INVERSION LJD
n
RELATIVELY
LOW
CONCENTRATION
HIGHER ^
CONCENTRATION
Figure C-1. Typical History of Plume Rise.
-------
A. TALL STACK - ISOLATED
POINT SOURCE
n
D. VERTICAL JET
B. SHORT STACK
(a) PLUME BEHAVIOUR - LOW
WINDSPEED. (b) WAKE
BEHAVIOUR. BRISK WIND
E. RANDOMLY ORIENTED JET
^
C. LEAKAGE FROM FACE OF
BUILDING INTO TURBULENT
WAKE
r
F. LARGE ARIiA SOURCE AFTER
SPILLAGE ONTO GROUND OR
AFIRE
Figure C-2. Some Conceivable Modes of Release
of a Buoyant Plume
-------
oriented jet may be trapped in the wake. Finally, Figure C-2(F) shows a buoyant plume
evaporating from a spillage on the ground or rising from a fire.
3.0 LIFT-OFF
The question, what happens to a buoyant plume emerging from an area source or one that
is mixed into a turbulent building wake, has not yet been satisfactorily answered and major
uncertainties still remain. However, Briggs(2) has put forward some simple ideas based on
the consideration of a Richardson number
(3-1)
where g is the acceleration due to gravity, H is the depth of the plume, u, is the friction
velocity, pa is the density of the air and Ap = (pa-p), p being the density of the plume. The
quantity gHAp is the square of a buoyancy induced velocity, u., on the other hand, is a
velocity that is typical of the rate of spread of passive plumes. If Lp < 1, it is to be
expected that the dilution of the plume is dominated by atmospheric turbulence and the
plume should behave passively. If, on the other hand, Lp > 1, the plume should rise off the
ground leaving little or no residual gas at ground level. For intermediate values of Lp the
plume should behave in some intermediate fashion.
Briggs(2) used heuristic arguments to obtain a critical value of Lp above which the plume
essentially lifts off cleanly: this was Lp = 2.5. Subsequently, Meroney'3' looked at the rise
of a buoyant plume released at ground level, using smoke visualization in a wind tunnel.
On the basis of these data Lp ~ 20-30 is a more appropriate figure.
4.0 PLUME TRAJECTORY
There are over a hundred plume rise models in the literature. Comprehensive reviews have
been given by Briggs(t) and readers with sufficient stamina may work back from his
references. In neutral conditions, Briggs' formula for the center-line of a buoyant, rising
plume is given by
C-4
-------
Ah = 1.6F1/3x2/3LJ-' m C4"1)
where Ah is the height above the point of release, F is the buoyancy parameter, x is the
distance travelled downwind, and U is the velocity of the plume.
F is given by
F - (gQ/*Cpp.T) mV3 (4-2)
where g is the acceleration due to gravity (9.81 m/s2)
Q is the rate of heat release accompanying the plume (J/s)
Cp is the specific heat of air at constant pressure (J/Kg/K)
pa is the density of air (kg/m3); and
T is the temperature of the air (K).
If Q is in megawatts, it can be shown that
F~8.9QmV3 (4-3)
In the treatment of Briggs, the data used to test Eq. (4-1) are taken from the rise of plumes
from power station chimneys which are 100 m or more in height. The velocity U is either
that at the final height of plume rise or that averaged over the whole of the plume depth
from the source height to the top of the observed plume.
In stable conditions, a rising, bent-over continuous plume follows the trajectory
(4-4)
where z is the height of rise (m)
F is the quanfity defined in Eq.(4-3) (mY3)
i8T is the square of the Brunt-Vaisalla frequency (s2), and is related to the gradient
of potential temperature 9 in the atmosphere by j3T = (g/T)(d0/dz); and
C-5
-------
/?e is the entrainment coefficient (dimensionless)
Eq. (4-4) reduces to Eq. (4-1) for &"\< I When $^\~ jthe plume reaches its final height,
which is given by Briggs as
Ah = 2.6(F/U/3T)I/3 (4-5)
The experimental data are consistent with values of the constant on the right hand side of
Eq. (4-5) being in the range 2.3 to 2.9.. The same comments apply to the height at which
U is measured as for the neutral case.
5.0 GROUND LEVEL CONCENTRATIONS UNDER A RISING PLUME
For a well established plume rising into the atmosphere, there is no doubt that the
concentration beneath it is exceedingly small. Consider the analogy with a salt water plume
falling through a tank of pure water. A reservoir of salt in solution in water was carried on
a trolley which moved above a long trough containing water, see Figure C-3. The relatively
dense salt solution was allowed to flow into the trough through a tube, so simulating a
plume emerging into a cross wind. The salt plume was made visible by shining a light
through it. It was very noticeable that, should a wisp of salt solution attempt to escape from
the plume (as at point A on Figure C-3) it was literally "snatched back" (as at point
B). Caution should be exercised in assuming that this observation applies to the case of a
buoyant plume in the atmosphere, since in that case both the plume itself and the
surrounding atmosphere are turbulent, whereas in Figure C-3 the water is not turbulent.
It is reasonable to assume, however, that as long as the "vigor" of the plume generated
turbulence exceeds that of the atmosphere, the rate of growth of the plume radius r is
entirely determined by the actions of turbulence generated within the plume itself according
to an entrainment law such as r=(3ez, see below.
Returning to Figure C-3, when a salt sensitive probe was moved across the plume, there was
a very sharp concentration boundary: that is, the radial concentration distribution was
nearly "top-hat".
C-6
-------
'/ '/ V '/ V
///./. /. /. .
j^/J^-TURBULENT SALT WATER PLUME" ^ ^
' / ' / / / / /N5
/ / / / / / Xs
/ / / / / / /
x/ x/ ^/ x/ y '/
/ / / /
/- ^ x x
Figure C-3. Simulation of a Dense Plume in a Water Tank.
-------
One simple way of simulating this effect in a conservative way is to assume that the radial
concentration profile of a rising plume x as a function of distance downwind (x), acrosswind
(y), and above ground (z), is Gaussian, with radius r defining the 10% concentration
contour. That is
2ir
-------
(i) The action of atmospheric turbulence - the "vigor" of the turbulence within the
plumes decreases until it is less than the corresponding "vigor" in the atmosphere.
(ii) Stable temperature gradients - the plume rises until its temperature equals that of
the surroundings, give or take a few damped oscillations.
6.1 Termination of Plume Rise in Neutral Conditions
The problem encountered in trying to define a final height of rise in neutral conditions is
that the vast majority of plume rise observations show the plume still rising at the greatest
distances of observation. It follows that terminating plume rise in neutral conditions usually
involves the postulation of some conservative criterion, and since there is an infinite number
of possibilities, it is not surprising that a large number of examples are found in the
literature.
It is the action of atmospheric turbulence that terminates plume rise, and the quantity that
has been described as the "vigor" of the plume turbulence is given a precise meaning by
equating it to the turbulence energy dissipation rate, for which an approximate expression
within the plume is
z (6-1)
where 77 is a constant and w=dz/dt. Outside the plume,
(6-2)
where k is Von Karman's constant. It can be shown that, for plumes rising several hundred
meters into the atmosphere, equating the two quantities gives a final height of rise
Ah~300F/U3 (6-3)
For very buoyant plumes, the quantity Ah may exceed the height of the inversion- lid 1
(Figure C-l). Typical values of 1 vary from a few hundred meters to over a kilometer. If
C-9
-------
the upper edge of the plume touches the inversion lid, its rise can conservatively be
terminated at this point.
For further discussion of the mechanisms for terminating plume rise in unstable and neutral
conditions, consult the reference by Briggs(28).
62 Termination of Plume Rise in Stable Conditions
This has already been discussed and is given in Eq. (4-5). In stable conditions, the plume
rise is effectively terminated directly above the source.
7.0 PASSIVE DISPERSION
The simple picture given on Figure C-l implies that plume rise terminates abruptly and that,
thereafter, the plume behaves passively. A straightforward way of taking this into account
is as follows.
Suppose that plume rise has terminated at a distance xb downwind. The plume will then
have a radius rb, its centre-line will be at a height hb and the spatial distribution of
concentration will be described by Eqs. (5-1) and (5-2) with
Pr -
(7-1)
For distances exceeding xb, the atmospheric dispersion continues to dilute the plume
so that
7) .
where
(7-3)
C-10
-------
^(x-x,) = <£ + ^(x-xj (7-4)
and
Here, ay(x-xb) and
-------
APPENDIX D
SIMPLIFIED SOURCE TERMS AND DENSITY CALCULATIONS
FOR FLASHING LIQUID RELEASES
-------
TABLE OF CONTENTS
Section Page
1.0 PURPOSE D-l
2.0 SIMPLIFIED TREATMENT OF FLASHING LIQUID RELEASES D-l
2.1 Puff Release D-l
2.2 Continuous Release D-2
3.0 SIMPLIFIED CALCULATION OF ORDERED TRIPLES D-3
3.1 Purpose D-3
3.2 Visualization D-3
3.3 Calculations D-4
3.3.1 Initial Density When Mf = 1 D-4
3.3.2 Mole Fraction Me When All Liquid Droplets Just Evaporate . . D-4
3.3.3 Calculations for Mf > Me D-5
3.3.4 Calculations for Mf < Me D-5
u
-------
APPENDIX D
SIMPLIFIED SOURCE TERMS AND DENSITY CALCULATIONS
FOR FLASHING LIQUID RELEASES
1.0 PURPOSE
The purpose of this Appendix is to provide guidance on how to simplify the calculation of
source term parameters and of the density of air/gas/aerosol mixtures in cases where there
might otherwise be the need for complex calculations. The calculations outlined below can
quickly be encoded in a computer program or performed by hand. The methods described
below were used to define the initial conditions for puff releases in Chapter 8 and the
ordered triples for jet releases in Chapter 6.
2.0 SIMPLIFIED TREATMENT OF FLASHING LIQUID RELEASES
The following treatment is suitable for materials such as chlorine or ammonia which are
initially at room temperature with a high degree of superheat:
(i) When such materials flash, it is experimentally observed that they generally remain
completely airborne as a mixture of vapor and droplets.
(ii) It is also known from many experiments that the initial jetting and flashing phase
causes the entrainment of the order of ten times as much air by mass as the initial
release.
(iii) Simplifying Assumption: this air evaporates all of the liquid droplets and leaves a
mixture at the boiling point Tb; this mixture can then be used as a starting point for
the atmospheric dispersion calculations.
2.1 Puff Release
The purpose of this section is to define the initial parameters for a puff release. This
method was used to define the initial conditions for the puff release of chlorine described
in Section 8.1. The following quantities are needed:
D-l
-------
Total mass of material released : M kg
Total mass of air entrained : 10M kg (by assumption)
Temperature of mixture : Tb(K) (boiling point of material - by
assumption)
Density of air at Tb : p^ kg/m3 = pa(Tb)
Density of released material at Tb : pb kg/m3 = pg(Tb)
Assume pab and pb can be obtained from the densities at ambient temperature by using the
perfect gas law, or look them up in an engineering, chemistry, or physics handbook.
It can then easily be shown that:
Initial volume occupied, V : M/pgb + 10M/pab m3
Initial density of puff, p; : 11M/V
Assume air moves with mean velocity u and that the initial mass M is initially stationary.
Initial velocity of puff U; " : 10u/ll (conservation of momentum)
This puff can then be used as initial input to a dispersion modeling code, which will model
the subsequent entrainment of air, and heating by air entrainment and (possibly) by the
ground.
If the initial puff dimensions are needed, a further simplifying assumption is that the puff
is cylindrical with the radius equal to the height.
D-2
-------
r = h =
3V
4x
(2-1)
Which gives the effective area covered by the cylinder as
A = XT'
(2-2)
Example
Chlorine initially at 278 K is released as a puff from a one ton ~ 1,000 kg cylinder in which
it is kept as a liquid under pressure.
Total mass of material released
Total mass of air entrained
Temperature of mixture
Density of air at 239 K
Density of chlorine vapor at 239 K
Initial volume occupied
Initial density of puff
Initial velocity of puff
From Eq. (2-1), r = h = 11.89 m
1,000 kg
10,000 kg (by assumption)
239 K, the boiling point of chlorine
1.477 kg/m3
3.578 kg/m3
1,000/3.578 + 10,000/1.477
7,050 m3
11,000/7,050
1.560 kg/m3
1.36 m/s in a wind of 1.5 m/s.
D-3
-------
From Eq. (2-2), A = T(11.89)2 = 444 m2
These results are used in Section 8.1 as input to the SLAB and DEGADIS models.
22 Continuous Release
The purpose of this section is to define initial volume flow rate, density and velocity of a
continuous flashing release at ground level.
Assume an orifice of diameter A(m2) leading out of a vessel at gauge pressure p (Pa).
Using Bernouilli's formula, the velocity of release V; is
YJ =c/2p/pL m3 (2'3)
(neglecting static head) where c is a constant (~0.6) and pL is the liquid density (kg/m3).
The mass rate of release is M = ApLv-, kg/s (2-4)
As above, assume that air is entrained at a rate 10M so that the initial mass flux is 11M
kg/s, the initial volume flux is V = M /pgb + 10M pab, the initial density is 11M /V (kg/m3)
and the initial temperature is Tb (K).
The initial velocity of the puff uf is given by
U; = (vsta + 10Mu)/llM(m/s) . (2-5)
(which is a simple application of conservation of momentum). This should enable the user
to define the initial starting conditions for a continuous, horizontal, ground level (non-jet)
release. This continuous case has not been used in the present work, but is included for
completeness.
D-4
-------
3.0 SIMPLIFIED CALCULATION OF ORDERED TRIPLES
3.1 Purpose
Suppose that an initial flashing process leads to a proportion fv of vapor and l-fv of liquid
droplets. Assume that fv has been calculated independently, either as a simple flash fraction
or by a more sophisticated model that takes account of droplet rainout. Assume also that
this initial mixture is at temperature Tb.
The object is to calculate "ordered triples" consisting of mole fraction Mf, density p, and
concentration X- These ordered triples are those required by the DEGADIS model, see Table
6-4 of Section 6; lines 17-26 of that table were calculated by the method described below.
3.2 Visualization
X
i
Ta~^
(A)
The above figures show what happens if air is mixed into the vapor/aerosol mixture defined in
Section 3.1. Mf declines from 1 to zero as the amount of air is increased. As shown on Figure
(A) above, small amounts of air evaporate some but not all of the liquid droplets, leaving the
temperature at Tb. At some mole fraction M., all of the liquid droplets have evaporated, but the
temperature is still Tb. For smaller values of Mf (greater amounts of air), the temperature
increases towards that of the surrounding air. Meanwhile, as air is mixed in, the concentration
D-5
-------
X decreases to zero and the density p decreases to that of the ambient air, pa(TJ, see (B) above.
As noted above, the object is to calculate p and x as a function of Mf.
3.3 Calculations
The calculations proceed as follows:
3.3.1 Initial Density When Mf = 1
As described in Section 3.1, every kilogram of material that is initially airborne consists of fv
kg of vapor and (l-fv) kg of liquid. The density of the vapor is pg(Tb) and of the liquid is pL,
so the volume occupied by the vapor is V=fv/pg(Tb) + (l-fv)pL. The overall density is
p(Mf=l)=(fv+l-fv)/V=l/V kg/m3 and the corresponding concentration is x(Mf=l)
=p(Mf=l)= 1/V kg/m3. Mf=l, p(Mf=l), and x(Mf=l) are the "ordered triple."
Example
Chlorine initially at 278 K flashes to vapor and aerosol. From Eq. (6-2) and Section 6.2. 1 of
the main body of this report, fv = 0.17 and l-fv = 0.83. The density of chlorine vapor at its
boiling point is 3.578 kg/m3 (see above). The density of liquid chlorine is 1,574 kg/m3 (see
Table 5-4 in Section 5.4.2 of the main body of this report). The volume occupied by 1 kg of
chlorine is V = 0.17/3.578 + 0.83/1574 = 0.048 m3. The overall density p(Mf=l) is 1/V =
20.82 kg/m3 = x(Mf=l). Therefore, the ordered triple is (1, 20.82, 20.82). This appears as
line 26 on Table 6-4 of Section 6.2.3 of the main report.
3.3.2 Mole Fraction M, When All Liquid Droplets Just Evaporate
Let us assume that mass mK of air just evaporates (l-fv) kg of liquid droplets.
(Ta-Tb)Cp. mae = (l-Oh, (3-1)
where T, is the temperature of the air (K), Cpl is the specific heat at constant pressure of air
(J/Kg/K) and Iv, is the latent heat of vaporization of the liquid droplets (J/kg).
D-6
-------
vv , , r • • /•* o\
m = - kg per kg of emission. (y-^)
(Ta-Tb)Cpa
mae kg/air corresponds to Nae=miie/Mwa moles, where Mwa is the molecular weight of air
(kg/mole). 1 kg of released material corresponds to Ng=l/Mwg moles, where M^ is the
molecular weight of released material (kg/mole). The mole fraction Me (see (A) above) is then
given by
N
Me = - L_ (3-3)
Example
For the case of chlorine initially at 278 K, Eq. (3-2) gives
mae = (0.83)(287,840)/{(278-239)(l,000)} = 6.126 kg
(where 287,840 is the latent heat of vaporization of chlorine from the SLAB User's manual and
1,000 is the specific heat at constant pressure for air). Nae = 6. 125/0.029 = 21 1 moles of air
and Ng = 1/0.07 = 14.2 moles of chlorine. From Eq. (3-3), Me = 14.2/(14.2 + 211) =
0.063.
3.3.3 Calculations for M, > M,
This corresponds to the case where a small amount of air is added (i.e., the mole fraction lies
to the right of M, on Figure (A)).
Let Nf moles of air correspond to a mole fraction Mf on Figure (A) above. An equation similar
to (3-3) applies:
Mf = Ng/(Ng + Nf) (3-4)
Rearranging Eq. (3-4) and remembering that Ng = 1/M,,, it follows that:
D-7
-------
(3-5)
The corresponding mass of air is obtained by multiplying Eq. (3-5) by the molecular weight of
air Mwa:
, (3.6)
The amount of liquid droplets evaporated will be fe (kg) where
all at temperature Tb.
The volume occupied is :
V=myPa(Tb) + (fv+fe)/pg(Tb) + (K-fJ/ft. m3 (3-8)
The density p(Mf) is (1+MJ/V kg/m3
The concentration x(Mf) IS l/v kg/m3
Mf, p(Mf) and X(Mf) give the "ordered triple."
Example
Consider again the case of chlorine initially at 278 K. From Eq. (3-6):
01^ = (0.029)(0.75)/{(0.07)(0.25)} = 1.242 kg.
D-8
-------
From Eq. (3-7):
fe = (278-239)(l,000)(1.242)7(287,840) = 0.168.
From Eq. (3-8):
V = (1.242)7(1.477) + (0.17 + 0.165)7(3.578)
+ (1 - 0.17 - 0.168)7(1,574) = 0.935 m3
so that p(Mf) = 2.242/0.935 = 2.40 kg/m3
and x(Mf) = 1/0.935 = 1.07 kg/m3.
The ordered triple is thus (0.25, 1.07, 2.4) and appears on line 21 of Table 6-4 of Section 6.2.3
of the main body of this report.
3.3.4 Calculations for M, < M.
This corresponds to the case in which a relatively large amount of air is added (i.e., the mole
fraction lies to the left of Me on Figure (A)). Analogous to Eq. (3-6), the mass of air
corresponding to Mf mole fraction is:
maf = -J!! k§ (3'9)
Mwg - Mf
From Section 3.3.2, Eq. (3-2), the mass of air required to evaporate all of the liquid droplets
is
and mae <
D-9
-------
Let the final temperature of the mixture be T, which is found by solving the heat balance
equation
(marmae)Cpa(Ta-T) = (T-Tb)mae Cpa + (T-Tb)Cpg (3-11)
where Cpg is the specific heat at constant pressure of the released material
T - bcp.pg.rp.a (3
KA.+CJ
The volume occupied by the air/material mixture is
V = m>a(T) + l/pg(T) (3-13)
from which jo(Mf) = (1 +mlf)/V and x(Mf) = 1/V. Mf, p(Mf) and x(Mf) then give the "ordered
triple."
Example
Taking once more the case of chlorine at 278 K, consider Mf = 0.025. From Eq. (3-9):
mrf = (0.029)(1 - 0.025)/{(0.07)(0.025)} = 16.16 kg.
Eq. (3-10) has already been solved (see Section 3.3.1 of this appendix) to give m.,c = 6.126 kg.
Eq. (3-12) gives:
T = {(239)[(6.126)(1,000) + 498.1] +
+ [(16.16 - 6.126)(1,000)(278)]}/{(16.16X1,000) + 498.1)}
= 262.5 K
where 498.1 is the specific heat of chlorine at constant pressure from Table 2 of the SLAB
User's guide.
Using the perfect gas law, pa(262.5) = 1.345 kg/m3 and pg(262.5) = 3.258 kg/m3. From Eq.
(3-13):
D-10
-------
V = 16.16/1.345 + 1/3.258 = 12.32 m3
and p(Mf) = 17.16/V = 1.39 kg/m3 and x(Mf) = 1/V = 0.081 kg/m3. Therefore, the ordered
triple is (0.025, 0.08, 1.39) which appears on line 19 of Table 6-4 of Section 6.2.3 of the main
body of this report.
D-ll
-------
APPENDIX E
LIST OF THOSE CONTACTED
DURING THE TELEPHONE SURVEY
-------
APPENDIX E
LIST OF THOSE CONTACTED DURING THE TELEPHONE SURVEY
As was noted in Section 2.1.1, a telephone survey of interested or potentially interested EPA
personnel was conducted in order to obtain advice on the following:
a) Which accident release scenarios would it be most useful to include in the
guidance that EPA is developing on contingency modeling for superfund and
other sites?
b) What potential communications problems may arise between those requesting
a contingency analysis and those performing it?
The following people work for EPA unless otherwise stated.
Kristen Harvey (Roy F. Weston) (908) 906-3484
Bob Cibulski (908) 321-6746
Al Cimorelli (215) 597-6563
Dave Guinnup (919) 541-5368
Jerry Garman (202) 260-7767
Steve Gilrain . (214) 655-6710
Charles Hall (312) 353-2213
Mark Hansen (214) 655-6582
Jerry Heston (215) 597-7915
Norm Huey (303) 293-1760
Steve Jarvela (215) 597-7915
Bill Keffer (913) 551-7000
George Moein (University of Virginia) (804) 982-5252
Jim Mullins (214) 655-2273
Joe Padgett (919) 541-5589
Tom Pritchett (908) 321-6724
Ann Schober (214) 655-6710
Joe Tikvart (919) 541-5562
Joe Touma (919) 541-5381
E-l
-------
Appendix F
Examples of SAFER9 Inputs and Outputs
-------
TABLE OF CONTENTS
No.
1.0
2.0
3.0
4.0
5.0
5.1
5.2
5.3
5.4
5.5
6.0
6.1
7.0
7.1
7.2
7.3
7.4
8.0
8.1
8.2
8.3
9.0
10.0
11.0
TITLE
INTRODUCTION
METHODOLOGY
SCENARIO DESCRIPTION
CHEMICAL AND PHYSICAL PROPERTIES
TOXICOLOGICAL CRITERIA
Concentration
Dose
Toxic load
Lethal exposure potential
Toxicological criteria for chlorine
RELEASE RATE ESTIMATION
Model run and results
SOURCE TERM FOR DISPERSION
Pool evaporation
Aerosol formation
Initial air entrainment
Source term for dispersion for the chlorine cylinder scenario
ATMOSPHERIC DISPERSION
Release scenario inputs
Meteorological data inputs
Results from the dispersion of the chlorine cylinder scenario
SCENARIO 2 - CHLORINE PUFF RELEASE
SCENARIO 3 ~ REFRIGERATED CHLORINE SPILL
SCENARIO 4 - ACETONE SPILL
REFERENCES
PAGE
F-1
F-2
F-3
F-3
F-4
F-5
F-5
F-5
F-5
F-6
F-6
F-9
F-10
F-10
F-10
F-11
F-1 2
F-1 2
F-12
F-1 3
F-1 5
F-1 7
F-1 9
F-26
F-30
F-ii
-------
LIST OF FIGURES
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
TITLE
Sequence of procedures in consequence analysis
Inputs for release rate estimation for the chlorine cylinder scenario
Flow rate as a function of time for the chlorine cylinder scenario
Source term for dispersion
Release scenario definition for the chlorine cylinder scenario
Meteorological data required by the program (for all scenarios)
Centertine values of the lexicological criteria as a function of the
downwind distance for the chlorine cylinder scenario
Release scenario definition for atmospheric dispersion of the
chlorine puff scenario
Centeriine values of the lexicological criteria as a function of
downwind distance for the chlorine puff scenario
Inputs for evaporation rate estimation for the refrigerated chlorine
spill
Evaporation rate for the refrigerated chlorine spill
Release scenario definition for atmospheric dispersion of vapors
for the refrigerated chlorine spill
Centeriine values of the lexicological criteria as a function of
downwind distance for the refrigerated chlorine spill
Inputs for evaporation rate estimation for the acetone spill
Evaporation rates from the acetone pool
Release scenario definition for atmospheric dispersion of the
acetone vapors
Centeriine concentration as a function of downwind distance for
the acetone spill
PAGE
F-2
F-7
F-9
F-10
F-13
F-14
F-15
F-17
F-19
F-20
F-24
F-24
F-25
F-28
F-28
F-29
F-29
LIST OF TABLES
No
1
2
3
4
5
TITLE
Chemical and physical properties of chlorine
Toxicological criteria for chlorine
Summary of downwind distances of the lexicological criteria for the
chlorine cylinder scenario
Chemical and physical properties of acetone
Toxicological criteria for acetone
PAGE
F-4
F-7
F-16
F-26
F-27
F-iii
-------
1.0 INTRODUCTION
In this appendix, we will study how to simulate accidental release scenarios relevant to
Superfiind sites and other sources using the SAFER® model (a chemical hazard analysis
and emergency planning software package available from DuPont SAFER Emergency
Systems, Westlake Village, California). The main document has several scenarios and
extensive discussion regarding the inputs required to model these scenarios. In this
appendix we will simulate the following four scenarios :
Scenario 1 - Chlorine cylinder
A flashing liquid chlorine release occurs from a Vi" orifice in a 1 ton cylinder. It is
assumed that no flashing occurs before the chlorine is released into the
atmosphere. The initial temperature of the vessel is 293 °K.
This release corresponds to the scenario discussed in Section 6.2 of the main
document.
Scenario 2 - Chlorine puff
The catastrophic failure of a 1 ton cylinder results in a puff release. The initial
temperature of the vessel is 293 °K.
This release corresponds to the scenario discussed in Section 8.1 of the main
document.
Scenario 3 - Refrigerated chlorine spill
A refrigerated chlorine leak is large enough to very rapidly fill up a diked area. The
initial temperature of the chlorine is 239 °K. The ground temperature is 278 °K. It
is assumed that the spill occurs on a concrete diked area of 100 m.
This release corresponds to the scenario discussed in Section 5.4 of the main
document.
Scenario 4 - Acetone spill
A large acetone spill from a tank very rapidly fills up a diked area. The initial
temperature of the acetone is 278 °K. The ground temperature is 278 °K. It is
assumed to that the spill occurs on a concrete diked area of 100 m.
This release corresponds to the scenario discussed in Section 5.1 of the mam
document.
Meteorology for all scenarios
For atmospheric dispersion, a stability class of F with a wind speed of 1.5 m/s,
ambient temperature of 278 °K and surface roughness of 0.1m is assumed.
F-l
-------
In order to illustrate the methodology we will discuss scenario 1 in detail. Accompanying
the set up of inputs for this scenario, we will provide discussion regarding variables which
are required by the program. Thus sections 2 through 8 provide general information about
the program and details regarding scenario 1. For the other three scenarios, we discuss
only those aspects of the program which require special attention and lay emphasis on the
inputs required to simulate these scenarios. Thus, sections 9 through 11 provide the inputs
and simulation results for the other three scenarios.
2.0 METHODOLOGY
In order to evaluate the consequences of a hazardous release, several sub-tasks have to be
performed. The sequence of procedures involves obtaining a scenario definition, defining
the physical and chemical properties, the lexicological criteria, estimating the release rates,
calculating the source term for dispersion, atmospheric dispersion and finally calculating
dose, toxic load and lethal exposure potential (see Fig. 1).
The SAFER* program has several modules. Examining the nature of the scenarios and the
basic purpose of the project, it was determined that the TRACE module would be used
for release rate estimation and defining the source term for dispersion. The source term for
dispersion was then used by the Consequence Analysis module for atmospheric dispersion
and subsequent calculations.
0
i
P
Scenario
description
ose, toxic load
Si lethal exposure
otential
^
Physical and
chemical
properties
Atmospheric
dispersion
Toxicologies!
criteria
,
Release
rate
estimates
>
Source t
for atmo
dispersic
r
erm
spheric
m
Fig. 1 : Sequence of procedures in consequence analysis
F-2
-------
3.0 SCENARIO DESCRIPTION
In this stage of the process, we try to obtain a definition of the scenario. Specifications
regarding the containment variables (tank / pipe geometry and process variables) are
defined along with the failure mode (e.g. catastrophic failure or hole rupture etc.). For
some scenarios, additional information regarding diked area may also be available. More
often than not, the scenario definition tends to be fairly general and often the analyst (the
person who interprets a real-life scenario description into a form such that the computer
model can simulate) who runs the scenarios has to make judgments regarding variables.
Usually these judgments are made from past experience, case studies and / or by
conferring with the appropriate plant personnel or emergency responders. During our
simulations for the four scenarios this will become apparent, as the complete scenario
definition will not be supplied and we will make assumptions in order to obtain results
from the models.
A flashing liquid chlorine release occurs
from a Vin orifice in a 1 ton cylinder. It is
assumed that no flashing occurs before the
chlorine is released into the atmosphere.
The initial temperature of the vessel is 293
°K. For atmospheric dispersion, a stability
class of F with a wind speed of 1.5 m/s,
ambient temperature of 278 °K and
surface roughness of O.lm is assumed.
This release corresponds to the scenario discussed in Section 6.2 of the main document.
4.0 CHEMICAL AND PHYSICAL PROPERTIES
In order to run any simulation for a
particular chemical, the program first
requires the user to define specific
chemical/physical properties. The required
chemical and physical properties of
chlorine are defined in Table 1.
F-3
-------
1 Molecular weight (gin/mole)
2 Critical pressure (atm)
3 Critical volume (cmA3/mole)
4 Critical temperature (°K)
5 Normal boiling point (°K)
6 Surface tension of liquid (dyne/cmA2)
7 Liquid viscosity at NBP (cP)
8 Liquid density at NBP (gm/cmA3)
9 Liquid density at 5 °K below NBP
10 Temp when vap press is 400 mmHg (°K)
11 Enthalpy of satd. liquid (cal/mole) at
NBP
10 °K above NBP
20 °K above NBP
12 Cp coefficients (cal/gmol-°K) of gas phase
where Cp=A+B*T+C*TA2+D*TA3
70.91
76.00
124.00
417.00
238.70
25.60
0.49
1.56
1.58
: 225.40
0.00
161.00
327.00
A=6.432 B=0.008
C=-.924e-5 D=0.00
Table 1 : Chemical and physical properties of chlorine
The chemical and physical properties to be defined include the molecular weight, the
critical properties (pressure, volume and temperature), the normal boiling point, surface
tension, liquid viscosity, liquid density, vapor pressure data, enthalpy data and specific
heat of the gas phase. The program comes equipped with a large library of commonly used
chemicals. Additionally, the program has features by which new chemicals can be added.
Several standard references (e.g. [1],[2]) provide the values of the variables which are
required by the program while defining a new chemical.
5.0 TOXICOLOGICAL CRITERIA
To evaluate the consequences of the
release, the program requires the user to
define one or more sets of toxicological
evaluation criteria. These toxicological
criteria relate to the maximum
concentration, dose, toxic load and lethal
exposure potential at a fixed location. The
program evaluates the concentration versus time profile for different receptors and uses
this profile to calculate the other three criteria (i.e. dose, toxic load and lethal exposure
potential).
F-4
-------
5.1 Concentration
The concentration limits are usually determined by the final goal of the study. In order to
evaluate toxicity hazards, concentration limits like IDLH (Immediately Dangerous to Life
and Health), STEL (Short Term Exposure Limits), ERPG (Emergency Response Planning
Guideline) and EEGL (Emergency Exposure Guidance Limit) have been used. Associated
with each one of the concentration limits, there is an averaging time (IDLH - 30 min.,
STEL-15 min. etc.).
5.2 Dose
The dose represents the amount of chemical to which one is exposed over a period of
time. For our application, the dose will be expressed in units of PPM-MIN.
Dose = JCdt
5.3 Toxic load
The toxic load is similar to the dose, but additionally it takes into account the specific
toxicity of the chemical. The toxic load is generally evaluated as :
Toxic load = Jcndt
where n is commonly referred to as the toxic exponent. The value of n has been calculated
for several chemicals (see [3] and [4]). For our application, toxic load will have the units
of PPM -MIN where n is the chemical specific toxic exponent.
5.4 Lethal Exposure Potential
The lethal- exposure potential is evaluated by using the probit model ([5]). The probit
model provides a convenient methodology by which one can evaluate the fraction of an
average population which will have a particular response (e.g. odor, serious toxicity,
lethality) for a specific toxic load exposure. The basic assumption of this model is that the
response plotted against the logarithm of concentration or logarithm of exposure time has
a cumulative normal distribution [4]:
Probit = a + b * Ln(Toxic Load)
.j Probit-5
Lethal Exposure Potential = -_ Jexp (-u2 / 2) du
where a and b are the chemical specific probit constants (usually evaluated by a regression
analysis of the lethality data) and n is the appropriate toxic exponent.
F-5
-------
5.5 lexicological criteria for chlorine
Since chlorine is a very widely used chemical it is possible to define all toxicological
criteria. The concentration limits are defined as ERPG-1, ERPG-2, and ERPG-3. The
ERPGs (Emergency Response Planning Guidelines) are limits which have been defined by
the American Industrial Hygiene Association [6] and are commonly used to assess the
impact of accidental releases. It is to be noted that the ERPG limits represent 1 hour
exposure numbers.
For our specific application (i.e. Superfund sites) the ERPG-2 and the ERPG-3 represent
levels of most interest (i.e. they represent concentration limits where preventive measures
would be activated). However, due to the requirement of 3 levels by the program, we
define the additional third level to be ERPG-1.
The dose limits were defined from the ERPG limits. Thus, the dose limits effectively
represent an equivalent "ERPG dose". The limits are obtained by multiplying each of the
ERPG limits by the exposure duration (i.e. 60 minutes).
The toxic load limits were defined using the methodology for the "Dangerous Toxic Load"
proposed by the Health & Safety Executive, UK [7]. Using the values suggested in [7],
the toxic load medium limit was assigned to be the HSE Dangerous Toxic Load. The low
and high limits are arbitrarily assigned to be some multiple of the HSE Dangerous toxic
load (divided by 5 and multiplied by 5).
There are several references which provide probit constants for chlorine ([4], [8]-[12]).
For this particular simulation, we used the probit constants proposed by Withers and Lees
[8]. Additionally, the lethal exposure potentials were assigned to be 20%, 50% and 80%
(these limits would produce the LC-20, LC-50, LC-80 curves — LC-x represents the
Lethal Concentration for x percent of an average population for a particular exposure
period).
The complete toxicological criteria for chlorine are shown in Table 2.
6.0 RELEASE RATE ESTIMATION
In order to define the release rate as a
function of time from the tank, the
program requires an extensive set of
inputs. These inputs relate the tank
contents, tank geometry and dimensions,
hole geometry and dimensions and the
meteorological conditions. For the
particular chlorine cylinder scenario the
input screen is as illustrated in Fig. 2.
F.-6
-------
CONCENTRATION
Comment
Concentration limit low [PPM]
Concentration limit medium [PPM]
Concentration limit high [PPM]
DOSE
Comment
Dose limit low [PPM-MIN]
Dose limit medium [PPM-MIN]
Dose limit high [PPM-MIN]
TOXIC LOAD
Comment
Toxic load exponent (n)
Toxic load low [PPMAn-MIN]
Toxic load medium [PPMAn-MIN]
Toxic load high [PPMAn-MIN]
PROBITS
Comment
Probit exponent (n)
Probit constant (a)
Probit constant (b)
Lethal exposure potential limit low (%)
Lethal exposure potential limit medium (%)
Lethal exposure potential limit high (%)
Table 2 : Toxicological
Status: ON
ERPGs
1.00
3.00
20.00
Status: ON
ERPG Dose
60.00
180.00
1200.00
. Status: ON
HSE Danger. Toxic Ld
2.00
21600.00
108000.00
540000.00
Status: ON
Withers & Lees
2.00
-8.29
0.92
20.00
50.00
80.00
criteria for chlorine
TnttK KUPTUHE SCEMilHIU : -,
1J : Tank Rupture File; Hame; Tank Rupture Scenario Bescrlptlon;;:: •'••' 1
3 >•.;;..' Chcntitra 1 Mumhuir •:.:,:.•::: v•.:•:,. ;.. ,.•': ,.••;:.''.'."::...-;. :.v..;.:'..:" "...:... '.;:::'.-;;..':.:..
'IJ CJ>en»t c»1 Hamc
5i Temperature: Inside The Tank td
O> Mass Of Chemical top-tlonal*;
7> Liquid Level Inside The Tank {optional}
U} 1'rcssure Inside: The Tank if of gases onlij> •
9> Tank Tyjie ;i -Cl-recta
: £3=cyJ: «jcr-tleal *»si»liertcal: j:
1Q> Tank LeTistliW Cf ti: fr.aQOGei t!3 Tank Hei{jht
12J: TanR: Uidth; (rt)5; O. 13) Tank Dl«metc»
I'll:. Wall: Thielmess: Cf t>::; : :'::.'/Q:.O3;x'-;,:;:. -• .•'•,.:.',.. :..,. . v ,,::.v,: .:..v:..;:
ii>) Hale: Type ll=ctrc:i swootht Z«reet!::;-s«iwothJ';:;.;"':};::;/-'.iv'.;;:;
i : O—eirex jayijed -t—reet. jaifjied} • : : :V
IG> DIscliarcfcs Coci;r - : 0. 17) Hoie ntametcw
18> Holtr Uiath Cft>: Q. ig >•• Hulc Height
:o> Hole Center HeIflh-t ftbove: Tank Bottom
1 TOM CUt CYLIMDEH
••• •::.'• ••. -••••••• &.- • -•• •-.:.-:.
CHLOHINK
Z~cyl- horizontal>s
Jl> Wind Sjieed
22J nmbierit Temp CdegFJ•;
Enter- $>eIection;: number' or HETUMtt? to;- exit
Fig. 2: Inputs for release rate estimation of the chlorine cylinder scenario
F-7
-------
Some of the inputs are self-explanatory. The particular inputs which require special
attention are the following :
Input no. Comment
3,4 Specify the chemical used for the simulation.
For our simulation, chlorine is identified as number 6 by the
program's chemical library.
5 Specifies the tank temperature.
For our simulation this is 68 °F (293 °K).
6-8 Specifies the contents of the tank. Any one of the three inputs is
to be defined. The program estimates the other two variables
depending upon the tank geometry and chemical/physical
properties.
For our simulation we specify the total mass (2000 Ib.) within
the cylinder.
9-14 Geometry and tank dimensions. Depending upon the input 9, one
or more inputs 10-13 should be defined. For example, if input 9 is
selected to be 2 (cylindrical horizontal) then the user should
define input 10 (tank length) and input 13 (tank diameter).
For our simulation \ve choose a standard 1 ton chlorine cylinder
(6.8ft long and 2.5ft diameter).
15-20 Specify the geometry, dimension and location of the hole within
the tank. One or more inputs 17-19 should be defined depending
upon input 15. For example, if input 15 is chosen to be 1
(circular smooth) then the user needs to define input 17 (hole
diameter). If input 16 is left undefined (=0) then the program
assigns a default value of the discharge coefficient (depending
upon input 9). For gas releases, the default value of the discharge
coefficient is 0.61. For liquid releases, the values are 0.65
(circular smooth), 0.622 (circular jagged), 0.625 (rectangular
smooth) and 0.828 (rectangular jagged).
For our simulation we choose a circular smooth hole which is
l/2n (0.04ft) in diameter. Additionally, the hole is located at the
bottom of the tank
21,22 Wind speed and ambient temperature.
For our simulation, the wind speed is 3.35 mph (1.5 m/s) and
ambient temperature is 41 °F (278 °K).
F-8
-------
6.1 Model run and results
When the above release scenario is executed, the program indicates that the "single-phase
liquid flow" and "sonic gas phase" equations were used. Reference [13]-[15] outline the
equations used by the program.
Additionally, the program performs a transient flow rate calculation where the release rate
is estimated as a function of time. This is performed by assuming a sequence of "pseudo-
steady states". Knowing the flow rate at a particular instant, the rate is kept constant for a
time interval which is dependent upon an incremental spilled mass. Subsequently, the new
state of the system (temperature, pressure, liquid/vapor breakup) is calculated and a new
release rate is estimated ([13], [14]).
It is observed that the initial flow rate is 6.97 Ib./s and gradually decays to 5.86 Ib./s after
294 seconds. The complete tank empties in about 341 seconds resulting in an average flow
rate of 5.84 Ib./s. Additionally, the program indicates that the liquid flashes resulting in a
21% vapor fraction and a temperature of-30 °F .
Fig. 3 : Flow rate as a function of time for the chlorine cylinder scenario
F-9
-------
7.0 SOURCE TERM FOR DISPERSION
It is at this stage that the program
calculates the evaporation rate from a
pool, performs flash calculations and
models phenomena close to the source —
aerosol formation and initial air
entrainment (Fig. 4).
R«|«MM rat*
avnmotm
\
(
Initial air entrained
Source term
for
dispersion
Fig 4 : Source term for dispersion
7.1 Pool evaporation
The evaporation rate from the pool is calculated by taking into account the heat
conduction from the ground, mass convection due to the ambient wind and by calculating
the heat input from the solar radiation. Heat conduction from the ground becomes the
driving force for cryogenic liquid spills (refrigerated chlorine, ammonia, LNG etc.). The
convection is important for normal boiling liquids (those that have a boiling point above
typical ambient temperatures). The solar radiation can become an important source of heat
input for low volatility liquid pools. The algorithms used to calculate the evaporation rates
are described in [13] and follow similar approaches outlined in [16]-[20].
7.2 Aerosol formation
Aerosol formation is specified to the program by using two different modes [21]:
OManual mode
The user specifies the aerosol to flash mass ratio
F- 10
-------
ii)Default mode
By using the default option, the program calculates the aerosol fraction. For low-
flashing fraction, the program splits the inlet stream into a flashed vapor and a
liquid pool. For extremely high flashing, the program splits the inlet stream into a
flashed vapor and liquid droplet aerosol. For intermittent flashing fractions, the
program would split the inlet stream into a partial liquid droplet aerosol and
remnant pool liquid.
Let F = Flashing fraction (determined thermodynamically)
A = Liquid droplet (aerosol) fraction
G = Pool liquid fraction
By normalizing with the total inlet stream
F+A+G=1
Define the two cutoff flashing fractions : Fl (=0.05) and F2 (=0.25) where FKF2
ForFF2
A=1-F and G=0
ForFK=F<=F2
A=(1-F2)*(F-F1)/(F2-F1) and G=(1-F1)*(F2-F)/(F2-F1)
Note, the above scheme is approximate and to be used only when other
information is not available. When specific information is available about a release
scenario, it may be better to specify the actual aerosol fraction by using the Manual
mode for Aerosol formation (i.e. Section 7.2, option i).
7.3 Initial air entrainment
The initial air entrainment is associated with the amount of air that is entrained into the
cloud during a catastrophic release or a pressurized release and fairly close to the source.
The program allows two different modes:
OManual mode
In this selection, the user specifies, the air to total chemical mass ratio.
ii) Default mode
In this mode, the program performs a set of iterative calculations and entrains just
sufficient air to evaporate all liquid aerosol droplets. Usually, this is the state at
which the cloud of maximum initial density of and minimum cloud temperature is
produced. The algorithms used for calculating the amount of air entrained are
described in [22] and follow similar work outlined in [23].
F-ll
-------
7.4 Source term for dispersion of the chlorine cylinder scenario
Our particular scenario involves the pressurized release of chlorine resulting in a flash. It is
generally expected that there would be minimal pool formation under such conditions and
even in the case where there was pool formation, the chlorine would evaporate very
rapidly due to heat conduction. Thus for our scenario, it will be assumed that no pool is
formed, there is a flashing vapor stream of 1.23 Ib./sec (21% of 5.84 Ib./sec) and the
remaining 4.61 Ib./sec (79% of 5.84 Ib./sec) will form liquid aerosol droplets. Further, we
use the default initial air entrainment option and entrain just sufficient air to evaporate all
liquid aerosol.
8.0 ATMOSPHERIC DISPERSION
The Consequence Analysis program is
designed for doing detailed planning and
evaluating the consequences of accidental
releases. The atmospheric dispersion
model accounts for dense gas dispersion
and takes into account gravity slumping
followed by subsequent transition to a lean
gas (Gaussian) model. A detailed review of the dispersion algorithms in this program is
beyond the scope of this study but details are provided in [13] and obtainable on request.
The basic dispersion routines have been compared to field test data and evaluated in
independent studies (e.g. [24]).
8.1 Release scenario inputs
In order to run a simulation in the Consequence Analysis module, we have to define a
release scenario. The release scenario was defined using the values developed in Section
6.4. The specific inputs for our scenario are illustrated in Fig. 5.
Some explanations regarding the inputs on the release scenario screen:
Input Comment
1 Type of release, i.e. single-phase or two-phase
For our scenario, we select two-phase.
2 Release rate type, i.e. 1 instantaneous, 2=continuous.
For our scenario we choose continuous.
3 Chemical Identification number.
Chlorine is identified as number 6 in the program's chemical library.
F-12
-------
NOTE:
Duration of the release.
For our scenario this value is calculated to be 341 seconds.
Initial phase of the release (l=liquid, 2=gas or 3=two-phase).
For our scenario we choose two-phase . Note, we choose the two-phase
option because in the following entries we will specify the vapor and
liquid aerosol fractions and ask the program to calculate the initial air
entrained required to just evaporate all liquid aerosol.
Liquid release mass rate - this specifies the aerosol fraction.
For our scenario, this was determined to be 4. 61 Ib./sec.
Gaseous release mass rate — this specifies the initial vapor fraction (may
have originated from flashing).
For our scenario, this was determined to be 1.23 Ib./sec.
Initial release temperature.
For our scenario we choose -30 °F.
We did not explicitly choose an initial air entrainment value (discussed
in Section 6.3). Hence, the program uses the Default mode ii) and
entrains just sufficient air to evaporate all liquid aerosol.
nUDiFY fflHflflETEB UftLUtS
MENU 130 : SCENARIOS
NEXT MENU : BO
ITEtt DESCBIPTION
SELKCTIUM 13 UF <21 =
SELECTION r SUPEH1B
FIELD CODE ; 19
:v U»LUE -:Y;-'.:----:: '•-:-: :- UNITS:
Two-phase madel!V-;.':'S;.il'.: ""•''-.-.
Release rate type- •!!>•:
Chemical ID • number: I'•'.•; • •
Duration • • -,-•••.•.-., •••^•:,.:..''• '!":::,'.'
:.Phase •• •:-.«S :-i-x •^•••-•.'-<:A • ;•;•,••• :;y:™;'>i;.
Lirju id;: release mass:: r*te:>:::
Gaseous: release: mass: rate:
He 1 ease; temperature •:: : ::
.QQQQQQ
2.860000
&.OGQ00Q
341.800000
3.QQQ00Q
4.603898:
1.230G0Q
-3Q.eoooa0
Fig. 5: Release scenario definition for the chlorine cylinder scenario
8.2 Meteorological data inputs
The program requires that data regarding the wind speed, wind direction, ambient
temperature, solar radiation, relative humidity and stability class be defined.
F-13
-------
MENU 2O : STflMDflBD COMBH
NEXT MENU t 1
ITEM UESCHIPTICm
i Manual Met Flag
Man in Obhukhau length
WIND IS FROM
Wind speed
Ambient temperature
» Stability class Umrz 4 uert)
? Surface roughness ;
I- Insolation
» Helntfup TiumifHtii
,^-T-.-^ SELECTION
SELECTION : EPfl
FIELD CODE :
UALUE
,000000
.QQ0Q00
SUBMENU 684
3.345000
•11.000000
&. 000000
.330000
.000000
UNITS
Fig. 6: Meteorological data required by the program (used for all scenarios)
Some comments regarding meteorological inputs are :
Input Comment
1 Type of meteorology (Real-time or Manual mode).
Since we are in the Planning mode \ve use Manual Meteorology (i.e.
the user will input all meteorological variables).
2 Monin-Obhukhov length.
We use the default option, by which the program calculates the Monin-
Obhukhov length as a Junction of surface roughness and stability class.
3 Wind direction
4 Wind speed - the value specified should be the measured value at 10 m
above the ground.
For our simulation, we choose 3.35 mph.
5 Ambient temperature.
For our simulation we specify 41 °F.
6 Stability class (Very Unstable A=l, B=2, C=3, Neutral D=4, E=5, Very
Stable F=6).
For our scenario we specify 6.
1 Surface roughness.
For our scenario we specify a value of 0.33 ft.
% Insolation.
For this scenario we choose no solar radiation. Note, the
meteorological conditions which we specify would most probably occur
at night-time (F stability, 1.5 m/s) and hence this value is chosen to be
zero.
F-14
-------
9 Relative humidity.
For our scenario \ve choose a value of 50%.
8.3 Results from the dispersion of the chlorine cylinder scenario
The program displays the impact of the
release in terms of cloud footprints
(cumulative area swept by the cloud) and
has options to evaluate indoor/outdoor
concentrations and the effect of wind
direction. In this section we will simply
examine the most basic of outputs, i.e.
evaluate the toxicological criteria
(concentration, dose, toxic load and lethal exposure potential) as a function of downwind
distance and also evaluate cloud footprints in terms of the four basic criteria.
In Fig. 7 we illustrate the variation of the centerline values with downwind distance. It is
observed that the ERPG-1 level (1 PPM) reaches 17 miles, the ERPG-2 level (3 PPM)
reaches 10 miles and the ERPG-3 level (20 PPM) reaches 3.7 miles.
i ooe+n
1.00E+10
I.OOEfOl
i.ooE+oa
1.00E-K07
t.OOE + 04
1.00C*09 .
1.0OE + 04
1.00E*03
1.00E + 02
t.OOE + 01
i.ooe»oo
1
LMtMl Cxp<
^^^
OM
mn>
Mnr«
X,
• II
Po
V
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fM -HI
•*»,
-«.
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to
\
\
Ml
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^
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^s
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".
s»
-*.
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too
0«OTHOTM4 DlMWIM 4M«
-------
Dangerous Toxic Load which is primarily defined for land-use planning around industrial
facilities reaches 1.2 miles. Lastly, it is observed that lethal concentration for 50% of an
average population would be achieved approximately 0.5 mile downwind. It should be
emphasized that this simulation creates a theoretical worst-case situation, where people
are not sheltered and do not take mitigating measures. As such, in a real-life situation
depending upon actual circumstances and the course of events different consequences may
be expected.
TOXICOLOGICAL
CRITERION
COMMENT
DOWNWIND
DISTANCE
(MILES)
Concentration (PPM)
1
3
20
ERPG -1 for chlorine [6]
ERPG-2 for chlorine (6]
ERPG -3 for chlorine {6]
17.0
10.1
3.7
Dose (PPM-MIN)
60
180
1200
5.3
2.9
0.9
Toxic load (PPMA2-MIN)
21,600
108,000
540,000
HSE Dangerous Toxic Load for chlorine [7]
2.0
1.2
0.7
Lethal Exposure Potential
20%
50%
80%
LC-20 for scenario using probit constants [8]
LC-50 for scenario using probit constants [8]
LC-80 for scenario using probit constants [8]
0.6
0.5
0.3
Table 3: Summary of downwind distances for different toxicological
criteria for the chlorine cylinder scenario
F-16
-------
9.0 SCENARIO 2 - CHLORINE PUFF RELEASE
SCENARIO DESCRIPTION
The catastrophic failure of a 1 ton cylinder results in a puff release. The initial temperature
of the vessel is 293 °K.
This release corresponds to the scenario discussed in Section 8.1 of the main document.
CHEMICAL AND PHYSICAL PROPERTIES
The properties of chlorine which were defined in section 4.0 are used.
TOXICOLOGICAL CRITERIA
The toxicological criteria for chlorine defined in section 5.5 are used.
RELEASE RATE ESTIMATION
For this scenario, there are no specific calculations which have to be performed to estimate
the release rate / amount. It will simply be assumed that the entire contents of the 1 ton
cylinder is released to form an instantaneous puff.
SOURCE TERM FOR DISPERSION AND RELEASE SCENARIO INPUTS
Since the initial cylinder is at 293 °K and the ambient temperature is 278 °K, there will be a
flashing vapor fraction of'X/21% (see section 7.4). Thus we will specify an amount of 430
Ib. flashed vapor and 1570 Ib. of airborne liquid aerosol (droplets). The entire system will
initially be assumed at the boiling point (-30 °F). Further because of the catastrophic
release, we will use the assumption that just sufficient air is initially entrained to evaporate
all liquid aerosol. The release scenario is defined in Fig. 8. An explanation of the inputs is
as follows:
tlQDlEV PftRftflETER UftLUES
MENU 130 ; SCENARIDS
NEXT MEMU : 8O
ITEW DESCRIPTION
Two-phase nradet : ;
He 1 ease rate type; ; ; : ':;
Chemical ID:^number;
•• Durat-1 onSfVy;-yy.y'-vyy;yy: yyy yyyyy:: • •••;•••;•;•;•;•;
Phase ....••::: • y y" ,..'.'••.- .;•-.-.:, •.':• ;..?.v'..:•''.
Liquid release mass: amount:
Gaseous release mass amount;
Heleaseitemperaturey/yyyyy :;;;;•:
• SELECTION 16 Of 21 '
SELECTION : SUPERZft
FIELD^' CODE ; 13 :.;:;,:'-:T.-:;::
UrtLUE UNITS
.:'::; •. :'•::'::.;::-;-: -.' . QQQGQQ ••: •••• :::.;:v:"
:;oy-:--:-;• -i-;-'-.:: H; Z.OOGQQQ V ;• ': :-:'- "•':-;;:
•. ?!.:.::.::;::; ;•:v •:::;::: &. OQQQQQ : ::3;;;-
•yy:•::•:• yx:';y::::y'•• .QOOQQQCyyySHiy sec;vV*
-v-y:-•-•--.••••:'' 3.QQQQQ&
1578.000000 • 1
439.000000 1
-33,000Q8Q;; i deqF
Fig. 8 : Release scenario definition for atmospheric dispersion of chlorine
puff scenario
F-17
-------
Input Comment
1 Type of release, i.e. single-phase or two-phase
For our scenario, we select two-phase
2 Release rate type, i.e. l=instantaneous, 2=continuous.
For our scenario \ve choose instantaneous.
3 Chemical Identification number.
Chlorine is identified as number 6 in the program's chemical library.
4 Duration of the release.
Since this is an instantaneous release, the duration is set to be 0.
5 Initial phase of the release (l=liquid, 2=gas or 3=two-phase).
For our scenario we choose two-phase. Note, we choose the two-phase
option because in the following entries we will specify the vapor and
liquid aerosol fractions arid ask the program to calculate the initial air
entrained required to just evaporate all liquid aerosol.
6 Liquid release mass amount — this specifies the aerosol fraction.
For our scenario, this was determined to be 1570 Ib.
1 Gaseous release mass amount - this specifies the initial vapor fraction
(may have originated from flashing).
For our scenario, this was determined to be 430 Ib.
8 Initial release temperature.
For our scenario we choose -30 °F.
NOTE: As before, we did not explicitly choose an initial air entrainment value
(discussed in Section 6.3). Hence, the program uses the Default mode
ii) and entrains just sufficient air to evaporate all liquid aerosol.
RESULTS FROM THE DISPERSION OF THE CHLORINE PUFF SCENARIO
The results of the above defined release scenario are illustrated in Fig. 9. Of special
interest, is the fact that the toxic load and dose go through a maximum (fairly close to the
source) while the concentration has a monotonic decreasing behavior. This Is
characteristic of instantaneous heavy gas releases. Qualitatively, this behavior can be
explained as follows. The toxic load and dose are functions of the concentration and the
total exposure time for the release. For instantaneous heavy gas releases, the gravity
slumping adds to the growth of the radial cloud dimensions leading to an increased
exposure time. This increase in the exposure time overrides the decrease in cloud
F-18
-------
concentration which occurs due to dispersion. Hence the resulting product (of
concentration and time) has an increasing - decreasing behavior.
1. OOE* II
r. OOE* 10
1.00£*O9
t.OOE»O8
i.ooe*07
1. OOE* 08
1.0OE.O5
t.OOE»O4
1.0OE»O3
1. OOE* 01
1. OOE tOO
JB— -
^*
*=
^
.••
tf
^
*
•
.-•
-•'
• • •
...
.,-
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Cdfwcntfi
UlhalE
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»m,
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S
•«.
X
(pp
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s
•»
•»
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Pn
V
s
^».
t«ntia
10
I
^
3o.. (PPM-
"\
"-v^
<%>
s
h^^
^«
T
S
x
»»
s
s
0
S
0
>w
^
Lama
^
"•
«.
N
(PPM- 2-1
^
>
.^^
<
\
MM
\
rv
s
s,
•s
V
s
^
s<
S
s
*
sN
^
too tooo loooo 100000
0»»ii»l~< Olxno. (mwt
Fig. 9: Centerline values of the toxicological criteria as a function of
downwind distance for the chlorine puff scenario
10.0 SCENARIO 3 - REFRIGERATED CHLORINE SPILL
SCENARIO DESCRIPTION
A refrigerated chlorine leak is large enough to very rapidly fill up a diked area. The initial
temperature of the chlorine is 239 °K. The ground temperature is 278 °K. It is assumed
that the spill occurs on a concrete diked area of 100 m .
This release corresponds to the scenario discussed in Section 5.3 of the main document.
CHEMICAL AND PHYSICAL PROPERTIES
The properties of chlorine which were defined in section 4.0 are used.
TOXICOLOGICAL CRITERIA
The toxicological criteria for chlorine defined in section 5.5 are used.
F-19
-------
RELEASE RATE ESTIMATION
For this scenario, the precise containment configuration (tank or pipe) is not defined. The
scenario basically requires, that a large release has occurred such that a diked are of 100
m is filled with chlorine liquid. Hence for our simulation, we will assume that an
instantaneous spill of 10,000 Ib. (5 tons) of refrigerated chlorine at -31°F. This amount of
chlorine will spread rapidly and fill up the diked area.
SOURCE TERM FOR DISPERSION
For this scenario, it will be assumed that the complete release amount is "dumped" into the
pool and the evaporation rate from the pool is the source term for dispersion. In order to
model this evaporation process, the program requires inputs which are displayed in Fig.
10.
An explanation of the various inputs is as follows:
1) File name : SUFEB5
REFRIGCLZ SPILL
CHLOHIME
100QQ.
O.
•:: -31,
RELEftSE SCENARIO SETUP 1) File name :
2) Scenario description ; REFRIG Ct
3) Chemical reference number : 6 CHLOHIME
5) Release type tl=cont>: 2=tnst. 3=tranX :; ;;; 2
6): Phase of chemical Temperature of chemical (de^IT) : -3
1O) Elroation of release (ft)
tl) Uertical velocity.-.;..(ft/sec)-.
12) Horizontal velocity (ftxsec)
13) Initial radius (ft>
14) ftir/Chewlcaf woie rvitia Clnltlal dlluttonl
15) Maximum pool area ••:•.. fterosoi air entrainment tll^tlanual J,. 2=Default)
:1) ftip/Chewical mass ratio (ttZO. Manual option only)
:2) Substrate CO=W,1-C,IZ-ftsai11,3=SDso il,4=SMsoiIi
3) Temperature? of;; substrate- (degF): ;: V ;: ; :. :
lommand : •';'.•••! ' -' :"" •'-•'••':•;'•.. ': ' :'.::
,'omment: : Enter Selection number or- BETURH to exit:
1076.39
o.oazaea
Q.1S
(gas)
dig)
dig)
tliq)
tiiq)
tliq)
tliq)
Clltj)
Fig. 10: Inputs for evaporation rate estimation for the refrigerated chlorine
spill
Input no. Comment
1,2 Specifies the file name and an associated description regarding the
scenario
3,4 Specify the chemical used for the simulation.
As mentioned previously, chlorine is identified as number 6 by the
program's chemical library.
F-20
-------
5 Specifies the type of release (1 instantaneous, 2=continuous,
3=transient, i.e. time-varying).
For our simulation we specify an instantaneous release due to the
"dumping" of chlorine into the pool..
6 Specify the phase of release (1 =liquid and 2=gas)
For our simulation, we specify a liquid release.
1 Specify the release size or release rate. Depending upon the selection
made for input 5, we have a release rate (for steady continuous releases)
or the total amount spilled (for instantaneous releases).
For our simulation we will specify the total amount spilled as 10,000
Ib.
8 Specify the duration of release. For instantaneous releases, this variable
is set to be zero. For steady continuous releases, specify the total time
over which the spill occurs.
For our simulation, we specify 0 since we have an instantaneous
release.
9 Specify the temperature of the release.
For our simulation we specify -31 °F.
10-14 Specify the initial source characteristics related to GAS releases. These
variables define the elevation of release, the initial velocity (both
horizontal and vertical), the initial radius (hole size) and the initial
dilution.
For our simulation, we have a liquid amount that is spilled. Thus
variables JO-14 are ignored and set to be 0.
15 Specify the maximum pool area (area contained within the dike).
For our simulation, this is set to be 1076ft2 ( 1-/00 m2 ).
F-21
-------
16 Specify the minimum pool depth.
For our simulation, we choose the default value of 0.032 inch (^1 cm).
NOTE: Variables 15 and 16 are used in conjunction to determine the
dimensions of the pool. The program takes into account the radial
growth of the pool. The pool is allowed to grow until a maximum pool
radius (determined by the maximum allowable pool area) is reached.
Simultaneously, the minimum pool depth constraint should also be
satisfied. Thus the pool keeps on "growing" as long as the minimum
pool depth is maintained and the spill amount/rate exceeds the pool
evaporation rate. In scenarios where the spilling has ceased or in
scenarios where the pool evaporation rate exceeds the spill rate, the
pool may "contract" while maintaining the minimum pool depth.
17 Specify the pool albedo (fraction with a value from 0 to 1). The pool
albedo represents the reflectivity of the pool surface. (1 -albedo)
specifies the fraction of solar radiation that is incident upon the pool
surface and which is absorbed by the pool liquid. The pool albedo is a
function of the pool surface (shiny, dark, transparent, opaque etc.) and
the angle of the incident radiation. By default, the program assumes an
pool albedo of 0.15. Thus in the default mode, 85 % of the incident
solar radiation is actually absorbed by the pool liquid.
The albedo of a plane water surface typically varies as:
Elevation of
sun (degrees) 90 50 30 ' 20 10 5 0
Albedo of water 0.020 0.025 0.060 0.134 0.348 0.584 1.0
For our simulation, we will use the default value ofO. 15.
1 8-2 1 These variables are used to estimate the aerosol liquid fraction and the
initial air entrainment. A detailed discussion of these inputs is given in
section 7.2 and 7.3.
For our simulation we choose default values (2= Default) for inputs 18
and 20. Note, in our case, we specify a temperature slightly less than
the boiling point so that no flashing occurs and the complete spilled
amount is "dumped" into the diked area to form a liquid pool.
F-22
-------
22 Specify the substrate on which the pool is formed. The characteristics of
the substrate (density, specific heat, thermal conductivity, and thermal
diffusivity) are used for calculating the heat conduction flux from the
substrate into the pool. The program has the following options:
# Substrate Density Specific heat Thermal Cond. Thermal Diff.
kg/m3 Joule/kg-°K Watt/m-°K m2/sec
1
2
3
4
Concrete
Average soil
Sandy dry soil
Sandy moist soil
2300
2500
1650
1750
961.4
836.0
794.0
1003.2
0.92
0.96
0.26
0.59
4.16 e-7
4.59 e - 7
1.98e-7
3.36e-7
For our simulation, we choose the substrate to be concrete.
23 Specify the temperature of the substrate. This variable is also used for
calculating the heat conduction flux from the substrate into the pool.
For certain substrates under some meteorological conditions (e.g.
asphalt substrates on a hot summer day, or snow/ice of a "sunny" day)
the temperature of the substrate may be significantly different than the
ambient atmospheric temperature.
For our simulation we will specify the substrate temperature to be
identical to the ambient atmospheric temperature i.e. 41 °F.
When the program simulates the above specified pool evaporation scenario, it produces an
evaporation rate as a function of time. This rate is illustrated in Fig. 11. It is observed that
the rate has a peak value of ^7 Ib./sec initially and then decays to % 0.7 Ib./sec at the end
of an hour. Note, by very definition of the scenario, we have basically "designed" the
scenario such that heat conduction from the ground is the driving force. It is expected that
for such a situation, the heat flux is inversely proportioned to the square-root of the
elapsed time ( Q a 1 /1'/2 where Q is the heat conduction flux and t is the elapsed time).
The Consequence Analysis module of the program does not presently allow the user to
specify a time-varying source term for dispersion. In such a case, one can follow two
different approaches :
OChoose the maximum release rate that occurred over the total evaporation period
as the source term for dispersion. This assumption would lead to the "worst-case"
results for the simulation. In our case, this would result in choosing 7 Ib./sec as the
source term for dispersion.
ii)Choose an average release rate that occurred over the total evaporation period
as the source term for dispersion. In our case, it is observed that within the first 1
F-23
-------
hour, /\/4420 Ib. are evaporated leading to an average evaporation rate of 1.23
Ib./sec for the first hour.
For further simulations, we will choose the latter of the two options (average evaporation
rate) and let 1.23 Ib./sec for 1 hour be the source term for dispersion.
Note: The scenario definition did not specify the total evaporation time associated with
the pool. Often, when an accidental release of chemical occurs that results in a pool,
mitigation measures (such as application of a foam) may be applied to diminish or stop
the vapor emissions. For this particular scenario, we have assumed that within one hour,
mitigation measures would be effective to stop all vapor emissions from the pool.
Fig. 11: Evaporation rate for the refrigerated chlorine spill
Subsequently, we define the inputs which are used for the atmospheric dispersion of the
chlorine vapors from the pool. The inputs are displayed in Fig. 12.
MODIFY PflHflnETER UflLUES
MENU 13O : SCENARIOS
NEXT MENU : QO
ITEtt DESCRIPTION
Single-phase model
ChemicaI ID number r :
Duration
Release rate type
Phase ••-..-.•-.... : -.-.••.••":".'••• ::,'
Total chemical mass rate-
Re lease temperature
SELECTION 13 OF Zl:.=
SELECTION : SUPERS
FIELD CODE : 19
VALUE UNITS
,000000
6.QQQ0QQ
3609.000000
1.000000
2.000000
1.230000
-38.000080
: ib/secs
degF
Fig. 12: Release scenario definition for atmospheric dispersion of vapors
for the refrigerated chlorine spill
F-24
-------
An explanation of these variables is as follows:
Input
1
Comment
Type of release, i.e. single-phase or two-phase
For our scenario, we select single-phase.
Chemical Identification number.
Chlorine is identified as number 6 in the program's chemical library.
Duration of the release.
For our simulation, this is set to be 3600 seconds.
Release rate type, i.e.-l=instantaneous, 2=continuous.
For our scenario we choose continuous. Note, though the initial release was
a instantaneous release (of liquid), the actual source term for dispersion is a
continuous vapor release (due to pool evaporation).
Initial phase of the release (l=liquid, 2=gas or 3=two-phase).
For our scenario we choose gas (to represent the vapors from the
evaporating pool).
Total chemical mass rate.
For our scenario, this was determined to be 1.23 Ib./sec.
Initial release temperature.
For our scenario we choose -30 "F.
RESULTS FROM THE DISPERSION OF THE REFRIGERATED CHLORINE SPILL
The results of the dispersion calculations are illustrated in Fig. 13.
1.00C + 14
1.00C*13
i.ooe-t-tt
LOW 1.11
LOW I- 10
1 OOC+0*
1.00E*07
1.00C-MM
1.00C+0*
l.OOf+M
i.oac*o3
1. ODE +02
1.001+01
1.006*00
^^^
••••MB
••m
•••
^
vg
Nx
= -i
"''^
NJ
"""X
'"^
UtM&m
III
v,
A
•fM-
*•-,
"+,
•ml
k,
"
KM
>•
V
>M
«
•M
S(
•>•
to
''s.
^S
^.^^
'"N^.
SI
"«J
^J
Tort
XI
^
•»•
s
1*
^
• LOM
*.,
^ t
•I,
k"«
100
1 IPTM-?*
''v
"^
"^>J
"l
\
1000
am
"\
Y*i
««*
s
"S
k,
5
r'«
N
^ I
*s
'i.^
10000 1
30000
Fig. 13 : Centerline values of the toxicological criteria as a function of
downwind distance for the refrigerated chlorine spill
F-25
-------
11.0 SCENARIO 4 - ACETONE SPILL
Scenario description
A large acetone spill from a tank very rapidly fills up a diked area. The initial temperature
of the acetone is 278 °K. The ground temperature is 278 °K. It is assumed to that the spill
occurs on a concrete diked area of 100 m .
This release corresponds to the scenario discussed in Section 5.1 of the main document.
Chemical and physical properties
The standard library of chemicals provided with the program had the predefined properties
of acetone. These are outlined in Table 4.
1 Molecular weight (gm/mole) 44.05
2 Critical pressure (atm) 71.00
3 Critical volume (cmA3/mole) 140.00
4 Critical temperature (°K) 469.00
5 Normal boiling point (°K) 283.50
6 Surface tension of liquid (dyne/cmA2) 26.84
7 Liquid viscosity at NBP (cP) 0.28
8 Liquid density at NBP (gm/cmA3) 0.88
9 Liquid density at 5 °K below NBP 0.89
10 Temp when vap press is 400 mmHg (°K) 267.90
11 Enthalpy of satd. liquid (cal/mole) at
NBP 0.00
10 °K above NBP 189.00
20 °K above NBP 403.00
12 Cp coefficients (cal/gmol-°K) of gas phase
where Cp=A+B*T+C*TA2+D*TA3 A=-1.796 B=0.053
C=-0.300e-4 D=0.00
Table 4 : Chemical and physical properties of acetone
TOXICOLOGICAL CRITERIA
Since acetone is comparatively less hazardous than chlorine, it was determined that for the
simulation it would be sufficient to simply examine the concentration levels. ERPG limits
were not available for acetone (as of July, 1992). It was decided to use the IDLH level as
the "concentration limit high". The lexicological criteria are defined in Table 5.
F-26
-------
CONCENTRATION Status: ON
Comment Limit high is EDLH
Concentration limit low [PPM] 10.00
Concentration limit medium [PPM] 100.00
Concentration limit high [PPM] 20000.00
DOSE Status: OFF
Comment
Dose limit low [PPM-MIN] 0.00
Dose limit medium [PPM-MIN] 0.00
Dose limit high [PPM-MIN] 0.00
TOXIC LOAD Status: OFF
Comment
Toxic load exponent (n) . 0.00
Toxic load low [PPMAn-MIN] 0.00
Toxic load medium [PPMAn-MIN] 0.00
Toxic load high [PPMAn-MIN] 0.00
PROBITS Status: OFF
Comment
Probit exponent (n) 0.00
Probit constant (a) 0.00
Probit constant (b) 0.00
Lethal exposure potential limit low (%) 0.00
Lethal exposure potential limit medium (%) 0.00
Lethal exposure potential limit high (%) 0.00
Table 5 : Toxicological criteria for acetone
Note: For this particular scenario, we have turned the status "OFF" for the dose, toxic
load and probits. Thus the program only produces concentration isopleths and does not
calculate the impact with respect to the other toxicological criteria.
RELEASE RATE ESTIMATION
Similar to scenario 3, the precise containment configuration is not defined. Hence we will
assume a large release (10,000 Ib.) that will very rapidly fill up a diked area of 100 m .
Additionally, for this scenario we will assume the initial chemical temperature to be the
ambient temperature (41 °F).
F-27
-------
SOURCE TERM FOR DISPERSION
The release scenario is defined in Fig. 14. The logic for defining the different inputs is
similar to that used for defining the inputs for the refrigerated chlorine spill (see section
10.0).
U File name : SuTEJH
flCETOME LIQ SPILL
ftCETQHE
an)'" :- ••'-' 2 - "•'- ' '• -:
KEL£f)3£ SCLNfllilU SETUP U File name :
2) Scenario description :•••-'• flCETOME LI
31 Chemical reference number : 122 ftCETOME
5J Release type (l=cont, 2=inst, 3=tran) :-••'-/. 2
fr) Phase of cliemicn 1 (1=1 iqi 2=gas) !'•••-.• 1
7) Release size Clbor Ik/sec) : 1000Q
0) Duration of release Csec) : Q
3) Temperature of chemical (dcgF) : 41
10) Elevation of release (ft)
11) Uertical velocity (ft/sec)
12) Horizontal velocity (ft/src)
L3) Initial raaius (ft)
H) rtir/CJiemic«l mole: ratio tinitial dilution)
15) flaxiraum pool area Cft»«2)
l&) tliniraum pool depth (ft>
17) ftlheda {reflectivity] of pool (0.0-1.0)
18) fterosoI formation
-------
- 1-lUDlFV PftHftMETER UftLUES
MENU 130 : SCENARIOS
NEXT MENU : OO
ITEM DESCRIPTION
1 Single-phase model
Chemical ID number :
Duration : :\
Release rate type
• '. ;...• Phase\' '•/'.' •'.- •. • :>;;V: '';;'•
Total chemical mass rate
7 Release temperature ;:;
— SELECTION 18 OF 21 -
SELECTIOM : SUPER*
FiELD CODE;:;.:;-•;.;::••:: ia•,'-:::-^':-^
UALUE UMITS
.GOQQGQ
1ZZ.GQQ000
36Q9.QOOOQO sec
1.000000
2,000000
.26100Q lb/-sec
41.GOQOGO degE
Fig. 16: Release scenario definition for atmospheric dispersion of vapors
from acetone spill
RESULTS FROM THE DISPERSION OF THE ACETONE SPILL
The results of the dispersion calculation are illustrated in Fig. 17. It is observed that the
IDLH concentration of 20,000 PPM is attained
i.ooE+oa
1.00t+05
i.ooe+04
1.00E+03
1.00E + 02
1.00E+01
1.0OE+00
CanCMlVMian (PPM)
100
1000
Fig. 17: Centerline concentration as a function of downwind distance for
the acetone spill
F-29
-------
REFERENCES
[1] Reid, R. C., Prausnitz, J. M. and Poling, R.,The Properties of Gases and Liquids, 4th
edition, McGraw-Hill, New York, New York, 1987.
[2] Daubert, T. E., and Danner, R. P., Data compilation tables for properties of pure
compounds, Design Institute for Physical Property Data, American Institute of Chemical
Engineers, New York, New York, 1985.
[3] Guidelines for Chemical Process Quantitative Risk Analysis, Center for Chemical
Process Safety (CCPS) of the American Institute of Chemical Engineers, New York, New
York, 1989.
[4] ten Berge, W. F. et al, Concentration-Time Mortality Response relationship of irritant
and systematically acting vapors and gases, J. Haz. Matl., 13, 301-309, 1986.
[5] Finney, D. J., Probit Analysis, Cambridge University Press, London, U.K. 1977.
[6] Emergency Response Planning Guidelines for Chlorine, American Industrial Hygiene
Association, Akron, Ohio, 1988.
[7] Toxicology of substances in relation to major hazards, Chlorine, Health and Safety
Executive, London, UK, 1990.
[8] Withers, R. M. and Lees, F. O., The assessment of major hazards: The lethality of
Chlorine. Part 2, Model of toxicity to man, J. Haz. Matl., 12, 283-302, 1985.
[9] Eisenberg et al, Vulnerability model, A simulation for assessing damage resulting from
marine spills, NTIS report AD-A015-245, 1975.
[10] Perry, W. W. and Articola, W. P., A study to modify the vulnerability model of the
risk management system, NTIS report AD-A084-214, 1980.
[11] COVO steering committee, Risk Analysis of six potentially hazardous industrial
objects in the Rijnmond area, A pilot study, Riedel, Dordrecht, 1982.
[12] Marshall V. C., The prediction of human mortality from chemical accidents with
special reference to the lethal toxicity of Chlorine, J. Haz. Matl., 22, 13-56, 1989
[13] Description of modeling techniques for hazardous chemical releases, DuPont SAFER
Emergency Systems, Westlake Village, California, March, 1989.
[14] Belore, R., et al., A computer model for predicting chemical leak rates from damaged
storage tanks, Environment Canada, 1986.
F-30
-------
[15]Delhaye, J. M., Instrumentation in Two-Phase Flow and Heat Transfer in the Power
and Process Industries, Hemisphere Publishing, Washington, 1981.
[16]Bird, R. B. et al, Transport Phenomena, John Wiley, New York, New York, 1981.
[17]Fleisher, M. T., Mitigation of chemical spills, Shell Development Company, Houston,
Texas, 1980.
[18]Mackay, D. and Matsugu, R. S., Evaporation rates of liquid hydrocarbons on land and
water, Canadian J.Chem.Eng., Vol. 51, 434-439, 1980.
[19]Shaw, P. and Briscoe, F., Evaporation rates from spills of hazardous liquids on land
and water, UKAEA-SRD-R100, U. K.,1978.
[20]Treybal, R. E., Mass Transfer Operations, McGraw-Hill, New York, New York,
1968.
[21JTRACE Users Manual, DuPont SAFER Emergency Systems, Westlake Village,
California, 1987.
[22]Chikhliwala, E. D., and Hague, W. J., Specialized techniques for modeling the unique
phenomena exhibited in HF releases, Proceedings of the International Conference on
Vapor Cloud Modeling sponsored by CCPS - AIChE, Boston, 955-973, 1987.
[23]Haddock, S. R. and Williams, R J., J. Chem. Tech. Biotech., Vol. 29, 655, 1979.
[24]Zapert, J. G. et al, Evaluation of Dense Gas Simulation Models, EPA-450/4-90-018,
Research Triangle Park, North Carolina, 1991.
F-31
-------
APPENDIX G
HGSYSTEM
-------
TABLE OF CONTENTS
1.0 INTRODUCTION G-3
2.0 FLASHING LIQUID RELEASE OF HF G-6
2.1 Input for HGSYSTEM . G-6
2.1.1 Input for the HFPLUME Module G-6
2.1.2 Input for the HEGADAS-T Module G-8
2.2 Example of Output G-14
3.0 CHLORINE VAPOR RELEASE G-22
3.1 Input Description : G-22
3.1.1 Input for the PLUME Module G-22
3.1.2 Input for the PGPLUME Module G-24
3.2 Example of Output G-29
4.0 REFERENCES , G-33
LIST OF TABLES
1. Modeling Capabilities of HGSYSTEM G-5
2. HGSYSTEM Input to HFPLUME - Flashing Liquid Release of HF G-ll
3. HGSYSTEM Input to HEGADAS-T - Flashing Liquid Release of HF G-12
4. HEGADAS-T Output - Flashing Liquid Release of HF G-15
5. HGSYSTEM Input to PLUME - Vapor Jet Release of Chlorine G-27
6. HGSYSTEM Input to PGPLUME - Vapor Jet Release of Chlorine G-28
7. PGPLUME Output - Vapor Jet Release of Chlorine G-30
LIST OF FIGURES
1. Available Model Combinations in HGSYSTEM G-4
2.- Sequence of HGSYSTEM models for a pressurized release of HF G-10
3. Sequence of HGSYSTEM models for a pressurized release of non-reactive gas. G-26
G-2
-------
1.0 INTRODUCTION
The computer model HGSYSTEM and its associated manuals(I"3) were generated by the
Industry Cooperative HF Mitigation/Assessment program. This ad-hoc industry program
was started in 1987 in order to study and test techniques for mitigating accidental releases
of hydrogrn fluoride (HF) and alkylation unit acid and to allow better estimation of the
impacts of such releases on the surrounding population.
Because of this focus, HGSYSTEM is a software package of atmospheric dispersion models
with a heavy emphasis on the release and dispersion behavior of hydrogen fluoride.
However, because HGSYSTEM was developed from an existing heavy vapor model,
HEGADAS(4), there are also several models for the release and dispersion of ideal gases.
The models in HGSYSTEM are stand-alone computer programs which may either be run
individually, or alternatively may be linked together to simulate the behavior of an
accidental release of material into the atmosphere. A schematic of the available model
combinations in HGSYSTEM is shown in Figure 1. Note that HGSYSTEM cannot
currently model all of the cases considered in the main body of this report, such as flashing
liquid jets of materials other than HF. The details on HGSYSTEM installation and model
execution is documented in References 1 and 3. For a complete description of the technical
bases underlying each HGSYSTEM model, the reader is directed to the HGSYSTEM
Technical Reference Manual®.
The types of releases HGSYSTEM is capable of modeling are listed in Table 1. Included
in this table are the standard input files, provided with the HGSYSTEM software package,
used to model the desired release type. Two postulated releases were chosen from these
capabilities for comparison with previous DEGADIS and SLAB simulations: 1) flashing
liquid release of HF and 2) chlorine vapor release.
G-3
-------
Source: Reference 3.
Figure 1. Available Model Combinations in HGSYSTEM
G-4
-------
Model
HFSPILL
EVAP
HFFLASH
HFPLUME
PLUME
HEGADAS-S
HEGADAS -T
PGPLUME
HFJET
Standard
Input files
STLIQUID.HLI
STVAPOUR.HLI
STANDST1 . EVI
STANDST2 . EVI
STANDST3 . EVI
STANDTR1 . EVI
STANDTR2 . EVI
STANDTR3 . EVI
SKELETON. HFI
SKELETON. HP I
SKELETON. PLI
STPOOLNO.HSI
STPOOLHF.HSI
STBRKNO.HSI
STBRKHF.HSI
STPOOLNO.HTI
STPOOLHF.HTI
STBRKNO.HTI
STBRKHF.HTI
STANDNO.PGI
STANDHF.PGI
SKELETON. HJ I
Type of problem being analysed
transient spillage of HF liquid
transient spillage of HF vapour
steady-state evaporation of boiling pool on water
steady-state evap. of non-boiling pool on land
steady-state evap. of non-boiling HF pool on land
transient evaporation of boiling pool on water
transient evaporation of non-boiling pool on land
transient evap. of non-boiling HF pool on land
flashing of HF
flashing, jet-flow and near-field dispersion of KF
jet- flow and near- field dispersion of ideal gas
steady HEGADAS run from pool (ideal gas)
steady HEGADAS run from pool (HF gas)
steady HEGADAS run from breakpoint (ideal gas)
steady HEGADAS run from breakpoint (HF gas)
transient HEGADAS run from pool (ideal gas)
transient HEGADAS run from pool (HF gas)
transient HEGADAS run from breakpoint (ideal gas)
transient HEGADAS run from breakpoint (HF gas)
elevated passive dispersion (ideal gas)
elevated passive dispersion (HF-gas)
flashing and jet- flow of HF
Source: Reference 3.
Table 1. Modeling Capabilities of HGSYSTEM
G-5
-------
2.0 FLASHING LIQUID RELEASE OF HF
These releases correspond to the scenarios labeled #3 in Figure 2-1 of the main report.
They are characterized by a liquid jet with subsequent flashing to vapor and aerosol. A
complete description of flashing liquid jets is given in Section 6.0, along with the simulations
made with the DEGADIS and SLAB atmospheric dispersion modeling computer codes. In
this appendix, HGSYSTEM will be used to model this release.
The model combination used to simulate the flashing liquid release of HF in this example
is HFPLUME and HEGADAS-T (refer to Figure 1; HFSPILL was not needed since the
"spill" parameters have already been identified in Section (7.2) of the main report). The
sequence of HGSYSTEM models used for pressurized releases of HF is depicted in Figure
2. From this figure one can see that two HGSYSTEM models are used to describe this type
of release. HFPLUME is the initial model and the subsequent model is determined from
executing the HFPLUME module. In this example, the transition is made from HFPLUME
to HEGADAS-T, which is a model for the dispersion of transient releases of heavy vapors.
This case corresponds to scenario #3A of Figure 2-1 in the main report. It is assumed that
there is a vessel in which there is HF at an elevated temperature of 100 °F (37.78 °C) and
a pressure of 200 psig (14.61 atm). For the present case, it is assumed that there is a leak
of effective diameter 0.5 inches (0.0128 m).
2.1 Input for HGSYSTEM
The input to HGSYSTEM for the HF release described above is given in Tables 2 and 3.
Table 2 is the standard input file (SKELETON.HPI) for the simulation of a flashing liquid
release of HF using the HFPLUME module. An intermediate file is generated from the
execution of HFPLUME and is the subsequent input file for the HEGADAS-T module.
This file is used to model the transition made from HFPLUME to HEGADAS-T stages (see
Figure 2) and is shown in Table 3.
2.1.1 Input for the HFPLUME Module
The input for the HFPLUME module of HGSYSTEM is contained in Table 2. Where
possible, these data are the same as those used for the DEGADIS run in Table (7-2).
Line 1: TRES is the liquid HF storage temperature (C).
Line 2: PRES is the liquid HF (absolute) storage pressure (atm).
Line 3: DMDTHF is the release point mass flow rate (kg/s).
Line 4: DEXTT is the rupture diameter of the vessel or pipe break (m).
G-6
-------
Line 5: ZEXIT is the release height above level ground (m).
Line 6: PHISTK is the release angle to the horizontal, taken to be 90° because the
corresponding DEGADIS run can only handle a vertical release.
Line 7: DURATION is the duration of the release (s).
Line 8: ZO is the height at which the windspeed is measured (m).
Line 9: UO is the ambient wind-speed (m/s). See the note at the end of this list of input
parameters.
Line 10: AIRTEMP is the atmospheric temperature (C).
Line 11: AIRPRESS is the ambient (absolute) pressure at the release height (atm).
Line 12: RHPERC is the atmospheric humidity (%).
Line 13: ZR is the surface roughness (m).
Line 14: PQSTAB is the Pasquill/Gifford classification. See the note at the end of this list
of input parameters.
Line 15: XLST is a termination criterion. The run of HFPLUME is terminated at this
distance downwind.
Lines 16-19: These lines form the far-field transition criteria MATCH datablock. RULST
is the transitional excess velocity ratio; RELST is the last required entrainment ratio;
RGLST is the transitional buoyancy effect; and RNLST is the entrainment ratio for passive
advection. The values given in lines 16 - 19 are all default values provided in the Users'
Manual.
Note: in the course of developing this example, the authors attempted to run a case with
a low windspeed (1.5 m/s) and atmospheric stability category F and obtained several
warning messages. It was concluded, after a number of sensitivity studies, that the
HFPLUME model, as used in the present work, runs into numerical problems with low
windspeeds or very stable weather conditions. To overcome this problem requires a detailed
knowledge of the numerical algorithms in HGSYSTEM. The resources available for this
project did not allow the authors to develop this understanding. If the reader encounters
similar problems, he/she should contact the model developers. For the present case, the
model was run in neutral stability (D)with a moderate windspeed (5 m/s).
G-7
-------
2.12 Input for the HEGADAS-T Module
The input for the HEGADAS-T module of HGSYSTEM is contained in Table 3. Most of
these data were generated by the HFPLUME module.
Lines 1 and 2: These lines are the CONTROL datablock parameters. This block controls
the generation of concentration contour-data by HEGADAS-T. ICNT is the contour control
flag and ISURF is the heat transfer flag. The values ICNT=0 and ISURF = 3 are provided
by the HFPLUME output. ISURF = 3 means that surface heat transfer is included. For
further details on ICONT, ISURF and other control parameters, consult Chapter 8 of the
User's Guide.
Lines 3-8: These lines specify the ambient conditions. ZAIRTEMP is the height of
temperature measurement (m); AIRTEMP is the air temperature (C); ZO is the height of
wind-speed measurements (m); UO is the ambient wind-speed (m/s); RHPERC is the
ambient air humidity (%); and TGROUND is the ground surface temperature (C).
Lines 9-12: This data block contains the data relating the mechanisms of dispersion
appropriate for a given passive limit formulation, and to a specified concentration averaging
time. ZR is the ground surface roughness (m); PQSTAB is the Pasquill/Gifford stability
class; AVTIMC is the concentration averaging time; and CROSSW is the form of sigma-y,
the crosswind standard deviation, see Section 7.3.1 in the technical reference manual for full
details.
Lines 13-18: Define the physical composition of the released anhydrous HF. THERMOD
is a flag implying release of anhydrous HF; CPGAS is the HF monomer (isobaric) specific
heat (J/mol/C); MWGAS is the HF monomer molecular weight (g/mol); TEMPGAS is the
gas temperature (C); and HFLIQFR is the liquid mass-fraction (calculated by HFPLUME).
Line 19: Identified the downwind distance form source to the transition plane from
HFPLUME to HEGADAS-T (m).
Lines 20-22: These lines define the release history as determined by HFPLUME at the
transition point ("breakpoint") between the near-field plume model HFPLUME and the
time-dependent heavy gas dispersion model HEGADAS-T. TSTPOOL identifies the start
time for transition data (s); TSTEPR is the time step between successive BRKDATA
records (s); and BRKDATA contains data at transition points ( the cloud half-width in
meters, the equivalent HF monomer mole-concentration and the mass-flow rate through the
transition plane in kg/s).
Line 23: TSTAR defines the output time (s) to record data for report presentation.
Warning: the user must be aware that the choice of TSTAR is far from trivial. The default
values provided by HFPLUME in this particular case sent the plume far too far downwind:
G-8
-------
effective step lengths were too great to enable the user to make an accurate determination
of where the plume concentration falls below LOCs. It was therefore necessary to rerun the
model with smaller TSTAR steps. This kind of iterative model running is a characteristic
feature of HEGADAS-T and failure to recognize that it is necessary is one of the most
common pitfalls associated with its use. The only way to become confident that the choice
of TSTAR is sensible is to practice with the input.
Lines 24- 27: Comprise the data necessary to control the output listing generated by
HEGADAS-T. XSTEP is the arithmetic progression step-length (m); CU is the inner
contour concentration (kg/m3); CL is the outer contour concentration (kg/m3); the values
given in the current example are the ERPG-3 (inner) and ERPG-2 (outer) for chlorine,
adjusted for a 20 minute exposure time using Haber's law. CAMIN is the last required
mass-concentration (kg/m3).
G-9
-------
-»• wind
HFPLUME
(urborn* plume)
PGPLUUE
(puatre. =i«T»ted plume)
(round
•wind
HFPLUME
HEGADAS
urborae
~FSr'LL
H." source
sc-.l rates
HFPLUME
Jet release.
elevated plume
dispersion.
dense plume
touchdown
and slumping
HFFLASH
HF flash
conditions
on release
•*•
\
PGPLUME
Passive far- field
dispersion of
elevated plume
HEGAOAS-S
HEGAOAS-T
Steady or transient
ground— level
dispersion of
dense/trace gas
Source: Reference 1.
Figure 2. Sequence of HGSYSTEM models for a pressurized release of HF. A transition
is made from HFPLUME to either PGPLUME (elevated dispersion) or HEGADAS (ground-
level dispersion). If HFPLUME is not run, HFFLASH is used to set the flash data needed
by HEGADAS.
G-10
-------
Table 2. HGSYSTEM Input to HFPLUME - Flashing Liquid Release of HF
HFPLUME standard input file SKELETON.HPI
TITLE Flashing HF Release
RESERVOIR
TRES
PRES
PIPE
DMDTHF
DEXIT
ZEXIT
PHISTK
DURATION
37.0
14.61
3.7
0.0128
5
90.00
1200
AMBIENT CONDITIONS
ZO
UO
AIRTEMP
AIRPRESS
RHPERC
DISP
ZR
PQSTAB
TERMINAT
XLST
MATCH
RULST
RELST
RGLST
RNLST
10.0
5
15
1.00
50.
0.1
D
1000.
.1
.3
.3
.1
* RESERVOIR FLUID THERMODYNAMIC STATE
DEG. CELSIUS
ATMOSPHERES
ABSOLUTE TEMPERATURE
ABSOLUTE PRESSURE
* PIPE EXIT-PLANE (CHOKE-FRONT) CONDITIONS
*
* KG/S " DISCHARGE RATE
* M EFFECTIVE ORIFICE DIAMETER
* M HEIGHT ABOVE (LEVEL) GROUND
* DEGREES RELEASE DISCHARGE ANGLE
* S RELEASE DURATION (<0 FOR STEADY)
*
* ATMOSPHERIC AMBIENT CONDITIONS
*
* M REFERENCE HEIGHT
* M/S WIND VELOCITY AT HEIGHT ZO
* CELSIUS AIR TEMPERATURE
* ATMOSPHERES AMBIENT PRESSURE
* PERCENT RELATIVE HUMIDITY
DISPERSION DATA
M
SURFACE ROUGHNESS PARAMETER
PASQUILL STABILITY CLASS
JET/PLUME DEVELOPMENT TERMINATION CRITERIA
M LAST REQD. DOWNWIND DISP.
MATCHING CRITERIA FOR HEGADAS/PGPLUME
LAST REQD. ABS. VALUE OF UJET/UAMB-1
LAST REQD. JET/(JET+HEG) ENTRAINM.
MAX. BUOYANCY EFFECT FOR ADVECTION
MAX. BUOY. EFF. FOR PASS. DISPERSION
9
10
11
12
13
14
15
16
17
18
19
G-ll
-------
Table 3. HGSYSTEM Input to HEGADAS-T - Flashing Liquid Release of HF
TITLE Flashing HF Releasa
Input file for the (transient) heavy gas
advection model HEGADAS-T. The file is
generated by the near field dispersion model
HFPLUME. It incorporates all the breakpoint
data generated by FLUME together with such
additional variables and flags needed to
ensure physical consistency. In addition, the
file contains variables needed to complete a
viable input file suitable for submission to
HEGADAS-T; Such additional data are prefixed
by an asterisk (*) and should be physically
and contextually sensible, but may be changed
at the user's discretion. Such data may also be
overwritten by the addition of keywords to the
HEGADAS-T partial input file under HGSYSTEM.
CONTROL * HEGADAS Control Flags Datablock.
ICNT-
ISURF-
* flag controlling contour generation (-).
* flag indicating plume/ground heat transfer (-).
AMBIENT * Ambient Atmosphere Datablock.
EAIRTEMP-
AIRTEMP-
Z0>
UO-
RHPERO
TGROUND-
14.4
15.0
10.0
5.00
50.0
15.1
height of temperature measurement
ambient (air) temperature (C).
height for wind-speed measurement
ambient wind-speed (m/s).
atmosphere relative humidity (Z).
ground surface temperature (C).
(m).
(m).
DISP * Pasquill/Gifford Dispersion Data.
ZR- 0.100
PQSTAB- D
AVTIMC- 1200.
CROSSW- 2, ,
* surface roughness height (m).
* Pasquill/Gifford stability class.
* concentration averaging time (s).
* type of formula (-).
GASDATA * Released HF-gas Datablock.
THERMOD-
CPGAS-
MWGAS.
WATGAS-
TEMPGAS-
2
29.1
20.0
O.OOOE-01
19.5
HFLIQFR- 0.862
thermodynamie model flag (-).
specific heat HF monomer J/mol/C.
molecular weight HF monomer (g/mol).
fraction water "picked up" from ground (-).
plum* temperature "immediately post flash" (C).
liquid mass-fraction "post flash" (-).
TRANSIT * Location of Transition Datablock.
DISTS-
119.
* downwind distance from release point (m).
9
10
11
12
13
14
15
16
17
18
19
G-12
-------
Table 3. HGSYSTEM Input to HEGADAS-T - Flashing Liquid Release of HF (continued)
TIMEDATA 0,2 * Transient breakpoint Datablock.
NOTE: The TIMEDATA datablock comprises in
addition to the TSTPOOL and TSTEPR keywords
a sequence of BRKDATA records containing
information regarding the transition state at
times TSTPOOL+TSTEPR, TSTPOOL*2*TSTEFR
The source DURATION is here 1.200E+03s; the
time required for flow establishment at the
transition plane is correspondingly 22.7 s.
The data for each BRKDATA record are (in
order of occurrence), the cloud half-width (m),
mole-concentration of (equivalent) HF-monomer,
and the mass-flow of anhydrous HF (kg/s).
TSTPOOL= -1.27
TSTEPR- 48.0
BRKDATA= 12 . 1
BRKDATA" 12 . 1
BRKDATA- 12 . 1
BRKDATA= 12 . 1
BRKDATA= 12 . 1
BRKDATA- 12 . 1
BRKDATA= 12 . 1
BRKDATA- 12 . 1
BRKDATA= 12 . 1
BRKDATA= 12 . 1
BRKDATA- 12 . 1
BRKDATA- 12 . 1
BRKDATA= 12 . 1
BRKDATA- 12 . 1
BRKDATA- 12.1
BRKDATA- 12.1
BRKDATA- 12 . 1
BRKDATA- 12.1
BRKDATA- 12 . 1
BRKDATA- 12 . 1
BRKDATA- 12.1
BRKDATA- 12 . 1
BRKDATA- 12 . 1
BRKDATA- 12.1
BRKDATA- 12 . 1
CALC * Output times
TSTAR= 200 .
TSTAR= 500
TSTAR= 800
TSTAR= 1100
TSTAR= 1400
TSTAR= 1700
TSTAR= 2000
* start time (s; zero breakpoint data).
* time step between BRKDATA records (s).
1.737E-03 3.70 * breakpoint data at 46.7 s.
1.737E-03 3.70 * breakpoint data at 94.7 s.
1.737E-03 3.70 * breakpoint data at 143. s.
1.737E-03 3.70 * breakpoint data at 191. s.
1.737E-03 3.70 * breakpoint data at 239. s.
1.737E-03 3.70 * breakpoint data at 287. s.
1.737E-03 3.70 * breakpoint data at 335. s.
1.737E-03 3.70 * breakpoint data at 383. s.
1.737E-03 3.70 * breakpoint data at 431. s.
1.737E-03 3.70 * breakpoint data at 479. s.
1.737E-03 3.70 * breakpoint data at 527. s.
1.737E-03 3.70 * breakpoint data at 575. s.
1.737E-03 3.70 * breakpoint data at 623. s.
1.737E-03 3.70 * breakpoint data at 671. s.
1.737E-03 3.70 * breakpoint data at 719. s.
1.737E-03 3.70 * breakpoint data at 767. s.
1.737E-03 3.70 * breakpoint data at 815. s.
1.737E-03 3.70 * breakpoint data at 863. s.
1.737E-03 3.70 * breakpoint data at 911. s.
1.737E-03 3.70 * breakpoint data at 959. s.
1.737E-03' 3.70 * breakpoint data at 1.007E+03S.
1.737E-03 3.70 * breakpoint data at 1.055E+03S.
1.737E-03 3.70 * breakpoint data at 1 . 103E+03S .
1.737E-03 3.70 * breakpoint data at 1.151E+03s.
1.737E-03 3.70 * breakpoint data at 1.199E+03s.
Datablock.
* geometric sequence of output times (s)
* geometric sequence of output times (s).
* geometric sequence of output times (s).
* geometric sequence of output times (s).
* geometric sequence of output times (s).
* 'geometric sequence of output times (s).
* geometric sequence of output times (s).
20
21
22
23
GLOUD * Output control datablock.
XSTEP= 50.0
CU- 4.17E-05
CL» 1.S7E-05
CAMIN= l.QE-05
* (fixed) output step-length (m) .
* inner contour concentration (kg/m3).
* outer contour concentration (kg/m3).
* last reouired mass concentration HF (kg/m3)
24
25
26
27
G-13
-------
2.2 Example of Output
The final output generated by the HGSYSTEM modeling effort describing the flashing
liquid release of HF is shown in Table 4. Specifically, this file was obtained from running
the HEGADAS-T module. As can be seen, the first page reproduces the input data from
Table 3 together with some additional default values of control parameters (such as
BLMODEL and ICSCOR). The second page reproduces information on the time
dependence of various parameters at the "breakpoint" (i.e. the point at which the transition
from HFPLUME to HEGADAS-T occurs). The third page of Table 4 begins with reference
to "observers." The observers travel with small portions of the release and begin their travel
at various intervals during the times specified on page 2 of Table 4. They observe the
dispersion of the small portions of the release; the final results are generated by summing
the concentrations seen by each observer. HEGADAS-T chooses the number of observers
to ensure adequate numerical accuracy. The observer concept is used to track transient
releases. The reader who is interested in more details should consult the HGSYSTEM
documentation.
The remainder of the HGSYSTEM output consists of "snapshots" generated at each of the
times generated in the TSTAR array from the input file. At each TSTAR time, the output
consists of a table giving:
The distance x downwind in meters
CONC, the concentration of HF monomer in vol% on the plume axis at x
SZ, the vertical dispersion coefficient at x (m)
SY, the crosswind dispersion coefficient at x (m)
MIDP, the half-width b of the flat portion of the concentration profile at x (m)
YCU, YCL, the crosswind distances to the isoconcentration contours for the upper
and lower levels of concern (m)
ZCU, ZCL, the vertical distances to the isoconcentration contours for the upper and
lower levels of concern (m)
CA, the ground level concentration on the axis at x (kg/m3)
The (YCU,ZCU) and (YCL,ZCL) outputs allow the user to generate snapshots of the
isoconcentration contours for transient releases at different values of TSTAR. The TSTAR
array must include at least one time for which all values of YCU, ZCU, YCL and ZCL are
zero - the user then knows that the plume has travelled far enough downwind for it to have
diluted below the levels of concern. In the current example, TSTAR = 1,400 s was the last
time at which the "snapshot" shows non-zero values of these parameters. For TSTAR =
1,700 and TSTAR = 2,000 (not shown on table 4) the values of ZCU, YCU, ZCL and YCL
were all zero. If the last TSTAR in the input array still has non-zero values of these
variables, the model should be rerun with higher values of TSTAR. More closely spaced
values of TSTAR can also be used to obtain any desired accuracy for the maximum
downwind distance at which levels of concern might be seen.
G-14
-------
Table 4. HEGADAS-T Output - Flashing Liquid Release of HF
HTMAIN
DATE 17/11/92
HEGADAS-T PROGRAM C VERSION NOV90 )
STANDARD REPORT FILE
PAGE 0
TIME 09-32
«« Flashing HF Release
HEGADAS-T INPUT DATA
OUTPUT CODE ICNT
SURFACE-TRANSFER CODE ISURF
GAS-BLANKET FORMULATION BLMODEL
CLOUD-SHAPE CORRECTION CODE ICSCOR
AIR TEMP.AT HEIGHT ZAIRTEMP AIRTEMP = 15.000
REF. HEIGHT FOR AIR TEMP. ZAIRTEMP = 14.400
RELATIVE HUMIDITY RHPERC = 50.000
WIND VELOCITY AT HEIGHT ZO UO - 5.0000
REFERENCE HEIGHT FOR WIND VEL. ZO = 10.000
EARTH-S SURFACE TEMPERATURE TGROUND - 15.100
SURFACE ROUGHNESS PARAMETER
PASQUILL STABILITY CLASS
AVERAG. TIME FOR CONC.MEAS.
MONIN - OBUKHOV LENGTH
TYPE OF FORMULA FOR SIGMA_Y
with parameters:
CONST. IN GRAV. SPREADING LAW
CONST. IN GRAV. SPREADING LAW
TYPE OF FORMULA FOR SIGMA_X
with parameters:
ZR
PQSTAB
AVTIMC
OBUKL
MODSY
DELTA
BETA
CE
CD
MODSX
ASIGX
BSIGX
0.10000
D
1200.0
l.OOOOOE+05
2
9.18959E-02
l.OOOOOE-04
1.1500
5.0000
3
10.000
0.10000
> CONTROL data block: control parameters
(no output of cumulative cloud data)
(only heat transfer, no water vapor)
(new, non-oscillatory formulation)
(correction included)
> AMBIENT data block: ambient data
CELSIUS
M
Z
M/S
M
CELSIUS
> DISP data block: dispersion data
M
SECONDS
M
(Briggs formula)
M**(-l)
(Chatwin/WilsonX
TEMPERATURE OF EMITTED GAS TEMPGAS - 19.500
SPECIFIC HEAT OF EMITTED GAS CPGAS - 29.100
MOLECULAR WEIGHT OF EM. GAS MWGAS » 20.000
.?ICKED-UP WATER BY EM. GAS WATGAS = O.OOOOOE-01
HEAT GROUP IN HEAT FLUX QH HEATGR = 24.000
THERMODYNAMIC MODEL THERMOD.= 2
::NITIAL LIQUID IN HF HFLIQFR = 0.35200
TIME-DEPENDENT RECORD DATA: ITYPBR = 2
- skip increment for reading INCRT = 0
- start time for data TSTPOOL = -1.2700
- time step between read records DT = 48.000
- number of records read NTYD = 25
OUTPUT STEP LENGTH XSTEP - 50.000
CA AT WHICH CALC. IS STOPPED CAMIN = l.OOOOOE-05
UPPER CONCENTRATION LIMIT CU = 4.17000E-05
LOWER CONCENTRATION LIMIT CL = 1.67000E-05
PSTS OF TIME FOR CLOUD CALC. TSTAR = 200.00
500.00
800.00
1100.0
1400.0
1700. 0"
2000.0
SEC
SEC
SEC
SEC
SEC
SEC
SEC
rULL BREAKPOINT AT DISTS = 119.00
HND PROFILE EXPONENT ALPHA = 0.28820
•RICTION VELOCITY USTAR * 0.44413
JR TEMP AT GROUND LEVEL TAP = 15.000
> GASDATA data block: gas data
CELSIUS
J/MOLE/CELSIUS
KG/KMOLE
(MOLAR FRACTION)
(hydrogen fluoride)
(MASS FRACTION)
>TIMEDATA data block: source/breakpoint data
(breakpoint data: B_aff, CONC, GSFLOW)
S
S
(see list of breakpoint data below for record data read)
> CLOUD data block: control of cloud output
M
KG/M3
KG/M3
KG/M3
> CALC data block, control of output times
>TRANSIT data block(s): breakpoint data
M
M/S
CELSIUS
G-15
-------
Table 4. HEGADAS-T Output - Flashing Liquid Release of HF (continued)
HTMAIN
DATE 17/11/92
HEGADAS-T PROGRAM ( VERSION NOV90 )
STANDARD REPORT FILE
PAGE i
TIME 09:32
«« Flashing HF Release »»
TIME-DEPENDENT
TIME -
TSTPOOL
(S)
7.70
69.3
131.
193.
254.
316.
377.
439.
501.
562.
624.
686.
747.
309.
871.
932.
994.
1.055E+03
1.117E+03
1.179E+03
1.240E+03
CONC CLOUD
(Z VOL.) HALF -WIDTH
2.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0,
0,
0,
0,
0
0
0,
2
788E-02
174
174
174
174
174
174
,174
,174
,174
,174
,174
.174
.174
,174
.174
.174
.174
.174
.174
. 788E-02
(M)
1.94
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
12.1
1.94
CLOUD
HEIGHT
(M)
82.2
19.8
19.8
19.8
19.8
19.8
19.8
19.8
19.8
19.8
19.8
19.8
19.3
19.8
19.8
19.8
19.8
19.8
19.8
19.8
32.2
DATA AT FULL
GAS
FLOW
BREAKPOINT X - 119.
SZ
(M)
RIB
M
TMP
(C)
CA
(KG/M3)
(KG/S)
0.594
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
0.
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
.70
594
88.9
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
88.9
2.96
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.44
2.97
14.
14.
14.
14.
14,
14,
14.
14
14.
14,
14
14.
14
14
14
14
14
14
14
14
14
,7
3
,3
,3
.3
.3
,3
.3
.3
.3
.3
.3
.3
.3
.3
.3
.3
.3
.3
.3
.7
2.362E-04
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
1.474E-03
2.362E-04
Observer-dispersion data set at breakpoint; total CPU
15 seconds
G-16
-------
Table 4. HEGADAS-T Output - Flashing Liquid Release of HF (continued)
HTMAIN
DATE 17/11/92
HEGADAS-T PROGRAM ( VERSION NOV90 )
STANDARD REPORT FILE
«« Flashing HF Release »»
PAGE
TIME 09'
•32
Observer-release frequency • 32; maximum value over all times of [mean error in observer concentration]/[peak cone.] = 0.516
Observer-release frequency = 16; maximum value over all times of [mean error in observer concentration]/[peak cone.] = 0.152
Observer-release frequency = 8; maximum value over all times of [mean error in observer concentration]/[peak cone.] = 0.139
Observer-release frequency = 4; maximum value over all times of [mean error in observer concentration]/[peak cone.] = 3.426E-02
Convergence tolerance OBSEPS = 5.000E-02 is satisfied
Cloud shape correction performed
Observer-dispersion data set for 41 observers; total CPU = 313 seconds
DISPERSION DATA AT TIME = 200.0
DISTANCE
(M)
150.
200.
250.
300.
350.
400.
450.
500.
550.
600.
650.
700.
750.
800.
850.
900.
950.
l.QOOE-t-03
1.050E+03
1.100E+03
1.150E+03
1.200E+03
1.250E+Q3
1.300E+03
1.350E+03
1.400E+03
CONC
(%
3
0
0
0.
9.
8.
7.
6,
5.
4.
4.
3.
3,
2.
2.
2.
1.
1.
1.
9,
7.
5,
3.
2.
1.
6.
VOL.)
. 190E-02
.145
.135
.116
.896E-02
.668E-02
. 476E-02
.373E-02
,505E-02
. 855E-02
.286E-02
.763E-02
.297E-02
. 887E-02
.514E-02
. 165E-02
. 834E-02
.520E-02
.226E-02
. 557E-03
.151E-03
, 085E-03
.399E-03
. 108E-03
.198E-03
168E-04
SZ
(M)
14.
15.
13.
12.
11.
12.
12.
13.
13.
14.
15.
16.
17.
18.
19.
20.
22.
24.
27.
29.
39.
50.
62.
73.
75.
77.
9
2
9
7
8
3
7
2
8
6
4
2
2
4
6
8
7
9
1
4
5
3
0
3
7
9
SY
(M)
12.3
19.2
26.4
33.6
40.5
46.3
52.1
58.0
63.4
68.4
73.4
78.4
34.8
93.5
102.
111.
117.
122.
128.
133.
135.
137.
139.
141.
147.
153.
MIDP
(M)
6.11
6.57
7.04
7.51
7.86
7.69
7.53
7.36
6.91
6.02
5.13
4.25
3.32
2.32
1.31
0.313
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.QOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
YCU
(M)
22.9
42.0
55.1
67.2
78.1
86.2
93.6
100.
105.
110.
113.
116.
120.
127.
132.
135.
134.
130.
122.
108.
82.6
24.6
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
SEC
ZCU
(M)
24.2
39.1
35.3
31.1
27.7
27.8
27.7
27.3
27.3
27.7
28.0
28.1
28.3
28.6
28.6
28.2
28.1
27.3
25.3-
21.3
18.4
3.51
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
YCL
(M)
26.6
46.5
61.4
75.3
88.0
97.8
107.
115.
123.
128.
134.
139.
146.
155.
164.
172.
175.
175.
172.
167.
153.
134.
103.
36.4
O.OOOE-01
O.OOOE-01
ZCL
(M)
33.0
47.0
42.7
37.9
34.1
34.5
34.6
34.6
35.0
36.0
36.8
37.5
38.3
39.5
40.4
40.9
42.3
43.4
43.3
41.9
48.1
48.7
38.7
8.92
O.OOOE-01
O.OOOE-01
CA
(KG/M3)
2.708E-04
1.232E-03
1.147E-03
9.842E-04
8.404E-04
7.359E-04
6.345E-04
5.406E-04
4.663E-04
4.116E-04
3.633E-04
3.189E-04
2.794E-04
2.446E-04
2.130E-04
1.834E-04
1.553E-04
1.287E-04
1.038E-04
8.092E-05
6.054E-05
4.306E-05
2.878E-05
1.785E-05
1.014E-05
5.222E-06
G-17
-------
Table 4. HEGADAS-T Output - Flashing Liquid Release of HF (continued)
DISPERSION DATA AT TIME - 500.0
DISTANCE
CM)
150.
200.
250.
300.
350.
400.
450.
500.
550.
600.
650.
700.
750.
800.
850.
900.
950.
l.OOOE+03
1.050E+03
1.100E+03
1.150E-KI3
1.200E+03
1.250E+03
1.300E+03
1.350E+03
1.400E+03
1.450E+03
1.500E+03
1.550E+03
1.600E+03
1.650E+03
1.700E-HJ3
1.750E+03
1.800E+03
1.850E+03
1..900E+03
1.950E-H)3
2.000E-HJ3
2.050E+03
2.100E-H33
2.150E+03
2.200E+03
2.250E+03
2.300E-1-03
2.350E+03
2.400E+03
2.450E+03
2.500E+03
2.550E+03
2.500E+03
2.650E+03
2.700E+03
CONC
(Z
0,
0,
0,
0,
9,
8,
7,
6.
5,
4
3,
3,
3.
2
2,
2,
1.
1.
1.
1.
1.
9,
8.
3.
7
6.
6,
5,
5.
4,
4
4.
3.
3.
3,
3
3
2
2
2
2
2
2
2
1
1
1.
1
1
1
1,
1
VOL.)
.155
.147
.135
.114
.875E-02
. 409E-02
.085E-02
.086E-02
.301E-02
.594E-02
. 984E-02
.490E-02
.077E-02
. 710E-02
.380E-02
.085E-02
.824E-02
.597E-02
. 404E-02
.243E-02
. 108E-02
.941E-03
.964E-03
, 124E-03
.394E-03
.759E-03
.201E-03
.709E-03
.273E-03
.885E-03
.538E-03
.226E-03
. 946E-03
.692E-03
. 463E-03
.253E-Q3
.063E-03
. 888E-03
. 728E-03
. 581E-Q3
. 446E-03
.320E-03
.204E-03
.096E-03
. 995E-03
. 900E-03
. 810E-03
.725E-03
.642E-03
.562E-03
.484E-03
. 406E-03
SZ
(M)
19.
16.
14.
12.
12.
12.
12.
13.
14.
14.
15.
16.
17.
18.
20.
21.
23.
24.
26.
28.
29.
31.
32.
34.
36.
37.
39.
40.
42.
43.
45.
47.
48.
50.
51.
53.
54.
56.
57.
59.
60.
62.
63.
65.
66.
63.
69.
71.
72.
74.
75.
77.
4
7
0
0
2
4
7
3
1
9
7
8
8
8
0
6
3
9
5
1
7
3
9
5
1
7
2
a
4
9
5
0
6
1
7
2
7
3
3
3
3
3
8
3
3
3
3
2
7
2
6
1
SY
(M)
8.37
17.6
26.9
35.7
42.6
49.6
56.5
62.9
69.0
75.2
81.3
88.4
95.6
103.
109.
115.
121.
127.
133.
139.
145.
151.
156.
162.
168.
174.
179.
185.
191.
196.
202.
207.
213.
218.
224.
229.
235.
240.
246.
251.
257.
262.
267.
273.
278.
283.
288.
294.
299.
304.
309.
314.
MIDP
(M)
9.36
8.69
8.03
7.55
7.74
7.93
8.12
7.63
6.82
6.01
5.20
3.80
2.39
0.983
O.OOOE-01
O.OOOE-01
O.OQOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
YCU
(M)
24.9
41.2
57.0
70.8
81.6
91.4
100.
107.
113.
118.
123.
128.
132.
135.
137.
139.
139.
138.
136.
134.
130.
126.
121.
115.
107.
97.7
86.0
71.1
49.7
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
-O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
SEC
ZCU
(M)
50.8
43.2
35.6
29.1
28.7
28.0
27.2
27.2
27.6
27.9
27.9
28.2
28.5
28.5
28.5
28.8
28.7
28.2 '
27.5
26.5
25.3
23.8
22.1
20.1
17.9
15.4
12.5
9.24
5.26
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
YCL
(M)
26.9
45.3
63.4
79.4
92.1
104.
115.
124.
132.
139.
146.
154.
161.
167.
173.
177.
181.
184.
187.
189.
190.
192.
192.
193.
193.
193.
192.
191.
189.
187.
184.
181.
177.
173.
168.
182.
156.
148.
140.
130.
119.
105.
89.0
67.0
29.0
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
ZCL
(M)
61.0
52.0
43.0
35.5
35.2
34.8
34.2
34.6
35.6
36.4
37.0
38.0
39.0
39.8
40.7
42.1
43.3
44.2
44.7
45.1
45.4
45.5
45.4
45.2
44.8
44.3
43.6
42.8
41.8
40.7
39.5
38.1
36.6
34.9
33.1
31.1
28.9
26.6
24.1
21.4
18.4
15.2
- 11.6
7.39
2.01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-Q1
O.OOOE-01
CA
(KG/M3)
1.320E-03
1.246E-03
1.150E-03
9.667E-04
8.388E-04
7.139E-04
6.011E-04
.5.162E-04
4.495E-04
3.894E-04
3.377E-04
2.957E-04
2.607E-04
2.296E-04
2.016E-04
1.766E-04
1.545E-04
1.353E-04
1.189E-04
1.053E-04
9.384E-05
8.417E-05
7.589E-05
6.878E-05
6.260E-05
5.722E-05
5.249E-05
4.833E-05
4.464E-05
4.135E-05
3.841E-05
3.578E-05
3.340E-05
3/125E-05
2.931E-05
2.754E-05
2.592E-05
2.445E-05
2.309E-05
2.185E-05
2.070E-05
1.964E-05
1.866E-05
1.774E-05
1.688E-05
1.608E-05
1.532E-05
1.460E-05
1.390E-05
1.322E-05
1.256E-05
1.190E-05
G-18
-------
Table 4. HEGADAS-T Output - Flashing Liquid Release of HF (continued)
DISPERSION DATA AT TIME - 800.0
DISTANCE
CM)
200.
250.
300.
350.
400.
450.
500.
550.
600.
650.
700.
750.
800.
850.
900.
950.
l.OOOE+03
1 . 050E+03
1 . 100E+03
1.150E+03
1.200E+03
1.250E+03
1.300E+03
1.350E+03
1.400E+03
1.450E+03
1.500E+03
1.550E+03
1.600E+03
1.650E+03
1.700E+03
1.750E+03
1.800E-K13
1.350E+03
1.900E+03
1.950E+03
2.000E+03
2.050E+03
2.100E+03
2.150E-H33
2.200E+03
2.250E+03
2.300E+03
2.350E+03
2.400E+03
2.450E+03
2.500E+03
2.550E+03
2.500E-H33
2.650E+03
2.700E+03
2.750E+03
2.800E+03
2.850E-HJ3
2.900E+03
2.950E+03
:i.OOOE-K)3
:i . 050E-HJ3
3 . 100E-HJ3
CONC
(2
VOL.)
2.756E-07
9.045E-02
0.114
9.727E-02
8.189E-02
7.023E-02
6.074E-02
5.204E-02
4.478E-02
3.916E-02
3.452E-02
3.036E-02
2.661E-02
2.331E-02
2.040E-02
1.787E-02
1.570E-02
1.
1.
1.
9.
8.
8.
7.
6.
6.
5.
5.
4,
4.
4.
3.
- 3.
3.
3.
3.
2.
2.
2.
2.
2.
2.
2.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
.3871-02
.232E-02
. 100E-02
874E-03
907E-03
074E-03
.352E-03
722E-03
168E-03
681E-03
247E-03
862E-03
517E-03
208E-03
929E-03
577E-03
449E-03
241E-03
052E-03
878E-03
720E-03
573E-03
438E-03
314E-03
199E-03
092E-03
993E-03
901E-03
315E-03
735E-03
660E-03
590E-03
524E-03
462E-03
404E-03
350E-03
298E-03
250E-03
204E-03
160E-03
119E-03
080E-03
SZ
(M)
10.9
12.7
12.5
12.4
12.2
12.7
13.5
14.2
15.0
15.9
16.9
17.8
19.0
20.5
22.0
23.4
25.0
26.6
28.2
29.3
31.4
33.0
34.6
36.2
37.8
39.3
40.9
42.5
44.0 .
45.6
47.1
48.7
50.2
- 51.8
53.3
54.8
56.4
57.9
59.4
BO. 9
62.4
63.9
65.4
66.9
68.4
69.3
71.3
72.8
74.3
75.7
77.2
78.7
80.1
81.6
83.0
84.5
85.9
87.4
38.8
SY
(M)
22.1
28.6
36.0
43.4
50.3
57.6
64.2
70.8
77.3
83.2
89.2
95.1
101.
108.
115.
121.
128.
134.
139.
145.
151.
157.
163.
168.
174.
180.
185.
191.
197.
202.
208.
213.
219.
224.
230..
235.
241.
246.
251.
257.
262.
268.
273.
278.
283.
289.
294.
299.
304.
309.
315.
320.
325.
330.
335.
340.
345.
350.
355.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,
0
MIDP
(M)
6.12
6.68
7.25
7.81
8.37
8.11
7.50
6.88
6.20
4.91
3.63
2.34
1.36
.960
.561
.162
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
. OOOE-Q1
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
YCU
(M)
0. OOOE-01
55.5
71.1
82.8
93.5
102.
109.
116.
121.
125.
128.
131.
133.
136.
137.
138.
137.
136.
133.
130.
126.
121.
114.
107.
97.0
85.2
70.0
48.0
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
O.QOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
SEC
ZCU
(M)
0. OOOE-01
29.0
30.5
28.9
27.3
27.2
27.5
27.6
27.7
28.0
28.3
28.4
28.5
28.8
28.8
28.5
28.0
27.3
26:4
25.2
23.7
22.0
20.0
17.8
15.2
12.4
9.02
4.98
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
YCL
(M)
0. OOOE-01
62.7
79.8
93.5
106.
117.
126.
135.
143.
149.
154.
160.
165.
171.
176.
180.
184.
186.
189.
190.
192.
193.
193.
193.
193.
192.
191.
189.
187.
184.
181.
177.
173.
168.
162.
155.
148.
139.
130.
118.
105.
88.0
66.0
28.0
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
ZCL
(M)
0. OOOE-01
35.9
37.2
35.6
34.0
34.2
35.0
35.6
36.2
37.2
38.2
38.9
39.9
41.3
42.4
43.3
44.0
44.7
45.1
45.4
45.5
45.4
45.1
44.8
44.2
43.5
42.7
41.8
40.6
39.4
38.0
36.5
34.8
32.9
30.9
28.8
26.5
23.9
21.2
18.2
15.0
11.4
7.23
1.89
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
O.OOQE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
CA
(KG/M3)
2.340E-09
7.685E-04
9.711E-04
8.259E-04
6.950E-04
5.959E-04
. 5.152E-04
4.413E-04
3.796E-04
3.319E-04
2.925E-04
2.572E-04
2.255E-04
1.975E-04
1.728E-04
1.513E-04
1.329E-04
1.174E-04
1.043E-04
9.315E-05
8.360E-05
7.541E-05
6.835E-05
6.224E-05
5.690E-05
5.222E-05
4.809E-05
4.442E-05
4.115E-05
3.824E-05
3.562E-05
3.326E-05
3.113E-Q5
2.919E-05
2.743E-05
2.583E-05
2.436E-05
2.302E-05
2.178E-05
2.064E-05
1.958E-05
1.861E-05
1.771E-05
1.687E-05
1.609E-05
1.536E-05
1.469E-05
1.405E-05
1.346E-05
1.290E-05
1.238E-05
1.189E-05
1.142E-05
1.099E-05
1.058E-05
1.019E-05
9.822E-Q6
9.475E-06
9.145E-06
G-19
-------
Table 4. HEGADAS-T Output - Flashing Liquid Release of HF (continued)
DISPERSION DATA AT TIME - 1100.
DISTAHCE
(M)
' 150.
200.
250.
300.
350.
400.
450.
500.
550.
600.
650.
700.
750.
800.
850.
900.
950.
1.000E-HJ3
1.050E+03
1.100E+03
1.150E+03
1.200E+03
1.250E+03
1.300E+03
1.350E+03
1.400E+03
1.450E+03
1.500E+03
1.550E+03
1.600E+03
1.650E+03
1.700E+03
1.750E+03
_1.800E+-03
1 . 850E+03
1.900E+03
1.950E+03
2.000E+03
2.050E+03
2.100E+03
2.150E+03
2.200E+03
2.250E+03
2.300E+03
2.350E+03
2.400E+03
2.450E+03
2.500E+03
2.550E+03
2.600E-I-03
2.650E+03
2.700E+03
2.750E+03
2.800E+03
2.850E+03
2.900E-I-03
2.950E+03
3 . OOOE+03
3.0SOE+03
(Z
1
7
0
0
9
8
7
6
5
4
3
3
2
2
2
2
1
1
1
1
1
9
8
3
7
6
6
5
5
4
4
4
3
3
3
3
3
2
COHC
VOL. )
.365E-12
.185E-02
.136
.114
.599E-02
.237E-02
.095E-02
.026E-02
.136E-02
.463E-02
.907E-02
.413E-02
.981E-02
.611E-02
.289E-02
.007E-02
.762E-02
.553E-02
.375E-02
.221E-02
.090E-02
.781E-03
.828E-03
.006E-03
.293E-03
.669E-03
. 122E-03
.639E-03
.211E-03
.830E-03
.•488E-03
. 182E-03
.906E-03
.656E-03
.429E-03
.223E-03
.035E-03
.863E-03
2.705E-03
2
.560E-03
2.427E-03
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
.303E-03
. 189E-03
.083E-03
. 985E-03
.893E-03
. 808E-03
.728E-03
.654E-03
. 584E-03
.519E-03
.457E-03
.399E-03
.345E-03
.294E-03
.246E-03
.200E-03
.157E-03
. 116E-03
SZ
(M)
11.3
14.1
13.4
12.7
12.1
12.2
12.8
13.5
14.1
15.0
16.0
16.9
18.0
19.3
20.7
22.0
23.5
25.1
26.7
28.4
30.0
31.5
33.1
34.7
36.3
37.9
39.5
41.1
42.6
44.2
45.7
47.3
48.3
50.4
51.9
53.4
55.0
56.5
58.0
59.5
61.0
62.5
64.0
65.5
67.0
68.5
70.0
71.4
72.9
74.4
75.9
77.3
78.8
80.2
81.7
83.1
34.6
36.0
87.5
SY
(M)
14.1
20.6
28.3
36.1
43.8
51.0
57.9
64.8
71.6
77.9
84.1
90.3
96.7
103.
110.
116.
122.
128.
134.
140.
146.
152.
157.
163.
169.
174.
180.
186.
191.
197.
203.
208.
214.
219.
225.
230.
236.
241.
247.
252.
257.
263.
268.
273.
279.
284.
289.
294.
300.
305.
310.
315.
320.
325.
330.
335.
341.
346.
351.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
MIDP
(M)
5.42
6.14
6.85
7.56
8.28
8.31
7.95
7.59
7.16
6.00
4.34
3.67
2.66
1.36
1.06
.252
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
YCU
(M)
0. OOOE-01
39.9
58.5
71.5
33.8
93.9
103.
110.
117.
122.
126.
129.
132.
135.
137.
138.
138.
137.
136.
133.
130.
125.
120.
114.
106.
96.1
34.0
68.4
45.4
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01 '
0. OOOE-01
0. OOOE-01
0. OOOE-01
o.oooE-ai
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
SEC
ZCU
(M)
0. OOOE-01
30.3
34.1
31.0
28.1
27.3
27.5
27.5
27.4
27.8
28.1
28.2
28.4
28.8
28.8
28.6
28.4
28.0
27.3
26.3
25.1
23.5
21.8
19.8
17.6
15.0
12.1
8.69
4.57
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
TCL
(M)
0. OOOE-01
45.2
65.2
80.2
94.6
107.
118.
127.
137.
144.
150.
156.
162.
168.
173.
177.
181.
184.
187.
189.
191.
192.
193.
193.
193.
193.
192.
190.
189.
186.
184.
181.
177.
172.
167.
161.
155.
147.
139.
129.
117.
103.
86.4
63.7
21.7
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
ZCL
(M)
0. OOOE-01
38.0
41.1
37.8
34.7
34.0
34.6
35.0
35.3
36.4
37.4
38.1
39.1
40.4
41.5
42.3
43.2
44.1
44.3
45.2
45.4
45.5
45.4
45.1
44.7
44.2
43.5
42.6
41.7
40.5
39.3
37.9
36.3
34.6
32.8
30.8
28.6
26.2
23.7
21.0
18.0
14.7
11.0
6.82
1.27
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
a. OOOE-OI
0. OOOE-01
0. OOOE-01
0. OOOE-01
CA
(KG/M3)
1.159E-14
6.101E-04
1.157E-03
9.649E-04
8.149E-04
6.992E-04
6.020E-04
5.111E-04
•'4.355E-04
3.783E-04
3.312E-04
2.892E-04
2.525E-04
2.212E-04
1.939E-04
1.700E-04
1.493E-04
1.316E-04
1.164E-04
1.034E-04
9.227E-05
8.281E-05
7.474E-05
6.778E-05
6.174E-05
5.646E-05
5.183E-05
4.774E-05
4.411E-05
4.088E-05
3.799E-05
3.540E-05
3.306E-05
3.095E-05
2.903E-05
2.728E-05
2.569E-05
2.424E-05
2.290E-05
2.167E-05
2.054E-05
1.950E-05
1.S53E-05
1.763E-05
1.680E-05
1.602E-05
1.530E-05
1.463E-05
1.400E-05
1.341E-05
1.285E-05
1.233E-05
1.184E-05
1.139E-05
1.095E-05
1.054E-05
1.016E-05
9.791E-06
9.447E-06
G-20
-------
Table 4. HEGADAS-T Output - Flashing Liquid Release of HF (concluded)
DISPERSION DATA AT TIME « 1400.
DISTANCE
(M)
l.OOOE+03
1.050E+03
1.100E+03
1.150E+03
1.200E-H)3
1.250E-HJ3
1.300E-HJ3
1.350E+03
1.400E-HJ3
1.450E-H33
1.500E+03
1.550E+03
1.600E+Q3
1.650E+03
1.700E+03
1.750E+03
1.800E+03
1.850E+03
1.900E-H)3
1.950E+03
2.000E-I-03
2.050E+03
2.100E+03
2.150E+03
2.200E+03
2.250E+03
2.300E+03
2.350E+03
2.400E+03
2.450E+03
2.500E+03
2.550E+03
2.600E+03
2.S50E+03
2.700E+03
2.750E+03
2.800E+03
2.850E-I-03
2 . 900E+03
2.950E+03
3.QOOE+03
3.Q50E+03
3.100E+03
CONC
(*
1.
1.
2.
3.
It.
5.
5.
5.
5.
5.
5.
4.
4.
4.
4.
3.
3.
3.
3.
3.
2.
2.
2.
2.
2.
2.
2.
1.
1.
1.
I.
1.
1.
-1
1.
1.
1.
1.
I.
1.
1.
1.
1.
VOL. }
132E-03
912E-03
842E-03
788E-03
612E-03
221E-03
582E-03
716E-03
S75E-03
511E-03
272E-03
992E-03
698E-03
405E-03
125E-03
863E-03
620E-03
398E-03
195E-03
010E-03
840E-03
684E-03
540E-03
408E-03
286E-03
173E-03
068E-03
971E-03
881E-03
796E-03
717E-03
643E-03
574E-03
510E-03
449E-03
391E-03
338E-03
287E-03
239E-03
193E-03
151E-03
110E-03
072E-03
SZ
(M)
65.0
67.2
59.1
50.9
42.7
35.7
36.7
37.7
38.7
39.7
41.3
42.8
44.4
46.0
47.5
49.1
50.6
52.1
53.7
55.2
56.7
58.2
59.7
61.2
62.7
64.2
65.7
67.2
68.7
70.2
71.7
73.1
74.6
76.1
77.5
79.0
80.5
81.9
83.4
84.8
86.3
87.7
39.1
SY
(M)
111.
117.
127.
137.
146.
156.
162.
168.
175.
181.
187.
192.
198.
204.
209.
215.
220.
226.
231.
237.
242.
247.
253.
258.
263.
269.
274.
279.
285.
290.
295.
300.
305.
311.
316.
321.
326.
331.
336.
341.
346.
351.
356.
MIDP
(M)
0,
0
0.
0
0
0
0
0
0
0
0.
0.
0.
0
0,
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.
0.
0.
0.
0,
0,
0
0
0
0
0
0
0
. OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
. OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
.OOOE-01
YCU
(M)
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
37.5
57.3
65.0
65.8
60.6
48.6
22.2
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0, OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
0. OOOE-01
O.OOOE-01
0. OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
SEC
zcu
(M)
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
3.93
7.30
8.59
8.48
7.26
5.11
1.50
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-31
O.OOOE-01
O.OOOE-01
O.OOOE-01
TCL
(M)
O.OOOE-01
O.OOOE-01
76.7
110.
135.
154.
165.
174,
180.
183.
185.
185.
184.
182.
180.
176.
171.
166.
160.
154.
146.
137.
127.
115.
101.
83.6
59.5
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
0. OOOE-01
O.QOOE-01
O.OOOE-01
O.OOOE-Q1
ZCL
(M)
O.OOOE-01
O.OOOE-01
27.0
36.5
37.6
35.0
37.8
39.5
40.3
40.5
40.7
40.4
39.8
38.8
37.5
36.0
34.3
32.5
30.5
28.3
25.9
23.3
20.5
17.5
14.2
10.5
6.14
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
O.OOOE-01
CA
(KG/M3 )
9.586E-06
1.619E-05
2.406E-05
3.207E-05
3.904E-05
4.420E-05
4.725E-05
' 4.839E-05
'4.804E-05
4.665E-05
4.463E-05
4.226E-05
3.977E-05
3.729E-05
3.492E-05
3.270E-05
3.064E-Q5
2.876E-05
2.704E-05
2.548E-05
2.404E-05
2.272E-05
2.150E-05
2.038E-05
1.935E-05
1.839E-05
1.751E-05
1.668E-05
1.592E-05
1.520E-05
1.453E-05
1.391E-05
1.332E-05
1.278E-05
1.226E-05
1.178E-05
1.132E-05
1.089E-05
1.048E-05
1.010E-05
9.739E-06
9.396E-06
9.071E-06
Xloud data set; total CPU
337 seconds
G-21
-------
3.0 CHLORINE VAPOR RELEASE
These releases correspond to the scenarios labeled #4 in Figure 2-1 of the main report.
They are characterized by a gas liquified under pressure. A complete description of vapor
releases is given in Section 7.0, along with the simulations made with the DEGADIS and
SLAB atmospheric dispersion modeling computer codes. In this appendix, HGSYSTEM will
be used to model this release.
The model combination used to simulate the vapor release of chlorine in this example is
PLUME and PGPLUME (refer to Figure 1). The sequence of HGSYSTEM models used
for pressurized releases of non-reactive gases such as chlorine is depicted in Figure 3. From
this figure one can see that two HGSYSTEM models are used to describe this type of
release. PLUME is the initial model and the subsequent model is determined from
executing the PLUME module. In this example, the transition is made from PLUME to
PGPLUME.
This case corresponds to scenario #4 A of Figure 2-1 in the main report. It is assumed that
there is a storage vessel containing chlorine at 278 K (-34 °C). For some reason such as the
rupture of a pipe, there is a leak from the vapor space. In this case, it is assumed that the
orifice is 0.01 m in diameter. Chlorine vapor jets vertically out of the orifice.
3.1 Input Description
The input to HGSYSTEM for the chlorine release described above is given in Tables 5 and
6. Table 5 is the standard input file (SKELETON.PLI) for the simulation of a jet vapor
release of an ideal gas, chlorine in this case, using the PLUME module. An intermediate
file is generated from the execution of PLUME and is the subsequent input file for the
PGPLUME module. This file is used to model the transition made from PLUME to
PGPLUME stages (see Figure 3) and is shown in Table 6.
3.1.1 Input for the PLUME Module
The input for the PLUME module of HGSYSTEM is contained in Table 5.
Line 1: TEMPGAS is the initial temperature of the chlorine at the point of release.
Line 2: MFGAS is the mole fraction of the pollutant, in this case 100% because the chlorine
is released as a pure vapor.
Line 3: MFH20 is the mole fraction of water vapor in the release, taken to be zero.
Line 4: MWGAS is the molecular weight of the released gas in g/mol (70 for chlorine).
Line 5: CPGAS is the specific heat of chlorine at constant pressure, 34.86 J/mol/C.
G-22
-------
Line 6: DMDT is the discharge rate of 0.054 kg/s, see Section (7.2).
Line 7: DEXTT is the actual diameter of the orifice, 3/8" = 0.01 m.
Line 8: ZEXTT is the discharge height, arbitrarily taken to be 5 m.
Line 9: PHISTK is the orientation of the release, assumed to be vertical for the purposes
of comparison with the DEGADIS input in Table (7-2).
Line 10: DURATION is the duration of release, taken to be 20 minutes (see Section (7.2)).
Line 11: ZO is the reference height at which the windspeed is measured (10 m).
Line 12: UO is the windspeed, 5 m/s.
Line 13: AIRTEMP is the ambient temperature, 5 °C.
Line 14: AIRPRESS is the ambient pressure, 1 atmosphere.
Line 15: RHPERC is the ambient relative humidity, assumed to be zero in this example.
Line 16: ZR gives the surface roughness length of 0.1 m as assumed for all applications in
this report.
Line 17: PQSTAB gives the stability category, D in this case.
Lines 18 through 23: these give user-supplied criteria for terminating the PLUME
calculation. Negative values imply that the criteria are ignored. Any keywords that are
omitted are assigned the notional value -1. SLST is the distance along the plume axis at
which the plume calculations are terminated. DLST specifies the maximum plume diameter
of interest (e.g. when the plume touches the ground). ZLSY specifies the maximum height
of interest (e.g. when the plume encounters an inversion lid). DXLST is the maximum
distance downwind at which PLUME calculations are desired. ULST is a plume velocity
at which calculations will be terminated. BETLST is the lowest concentration of interest
(in volume percent). The values of the variables in lines 18 through 23 are default values
from the PLUME standard input file.
Lines 24 through 27 contain default criteria for transition to the passive dispersion model
PGPLUME or to the heavy vapor model HEGADAS. RULST examines the difference
between the plume's velocity and the ambient windspeed. RELST examines the relative
values of entrainment velocities for jet dispersion versus those for heavy gas entrainment
and/or entrainment in the passive mode. RGLST compares the relative magnitude of
buoyancy induced velocities and advection velocities. RNLST is another parameter that
G-23
-------
compares entrainment rates prior to transition to passive advection. See Reference (3),
Appendix 2 for further details.
The output from the PLUME model defines the input for the PGPLUME model, which
follows.
3.1.2 Input for the PGPLUME Module
The input for the PGPLUME module of HGSYSTEM is contained in Table 6.
Line 1: CPGAS is the specific heat of chlorine vapor at constant pressure, 34.9 J/mol/K.
Line 2: MWGAS is the molecular weight of chlorine (70 g/mol).
Line 3: GASFRAC is the released mole fraction of chlorine (1.0).
Line 4: WATFRAC is the released mole fraction of water vapor (0).
Line 5: DXPLUME is the horizontal distance at which the transition from PLUME to
PGPLUME took place (m).
Line 6: ZPLUME is the height of the plume center-line at the point of transition (m).
Line 7: DPLUME is the plume diameter at the point of transition (m).
Line 8: PHIPLUME is the orientation of the plume at the transition point (2.96°).
Line 9: UREL is the difference between the plume's speed and the windspeed on the axis
at the transition point.
Line 10: CMASS is the average concentration across the plume at the transition point
(kg/m3).
Line 11: RREL is the difference in density between the plume and its surroundings (kg/m3).
Line 12: DURATION is the effective duration of release (i.e. the time taken for the plume
to pass through a vertical plane at the transition point).
Line 13: AIRTEMP is the ambient temperature (°C).
Line 14: AIRPRESS is the ambient pressure (1 atmosphere).
Line 15: PHPERC is the ambient relative humidity (%).
G-24
-------
Line 16: UATM = 4.63 m/s is the windspeed on the plume axis at the transition point.
Line 17: RATM is the ambient atmospheric density (kg/m3).
Line 18: ZR is the surface roughness length (0.1 m).
Line 19: PQSTAB is the atmospheric stability category (D).
Line 20: AVTTMC is the concentration averaging time, set equal to the duration of release
(1,200 s.).
Line 21: XFIRST is the downwind distance at which PGPLUME calculations start (set equal
to DXPLUME).
Line 22: STEP is the length of successive arithmetical steps at which PGPLUME performs
calculations.
Line 23: NSTEP is the number of steps of length STEP that PGPLUME takes.
Line 24: FACTOR is the scale factor for taking steps after NSTEP equal steps have been
taken (i.e. if the arithmetic sequence of stepping ends at distance XN downwind, the next
step is to a distance 1.2xN ).
Line 25: XLAST is the greatest downwind distance of interest to the analyst (m).
Line 26: VFLAST is the lowest concentration of interest to the analyst (ppm).
G-25
-------
PGPLUME
crouad
HEGADAS
— "I
(round
PLUME
J«'. release.
elevated plume
dispersion.
dense plume
touchdown
and slumping
PGPLUME
Passive far-field
dispersion of
elevated plume
HEGAOAS-S
HEGAOAS-T
Steady or transient
ground—level
dispersion of
dense/trace gas
Source: Reference 1.
Figure 3. Sequence of HGSYSTEM models for a pressurized release of non-reactive gas.
A transition is made from PLUME to either PGPLUME (elevated dispersion) or HEGADAS
(ground-level dispersion).
G-26
-------
Table 5. HGSYSTEM Input to PLUME - Vapor Jet Release of Chlorine
PLUME standard input file SKELETON.PLI
TITLE Vapor chlorine release
GASDATA
TEMPGAS =
MFGAS
MFH20
MWGAS
CPGAS
PIPE
DMDT
DEXIT
ZEXIT
PHISTK
DURATION -
-34.0
100.0
0.0
70.0
34.86
0.054
0.01
5.00
90.00
1200
AMBIENT CONDITIONS
ZO
UO
AIRTEMP =
AIRFRESS -
RHPERC
DISP
ZR
PQSTAB
TERMINAT
SLST
DLST
"ZLST
DXLST
ULST
BETLST =•
MATCH
RULST
RELST
RGLST
RNLST
10.0
5.0
5.00
1.00
0.00
0.10
D
-1
-1E6
-.35
-500
-0.1
IE- 7
.1
.3
.3
.1
* PHYSICAL PROPERTIES OF GAS
*
* CELSIUS TEMPERATURE OF POLLUTANT
* PERCENT MOLE FRACTION OF POLLUTANT
* PERCENT MOLE FRACTION OF WATER
* s/mol MOLECULAR WEIGHT POLLUTANT
* J/mol/C ISOBARIC SPECIFIC HEAT
*
* PIPE EXIT-PLANE (CHOKE-FRONT) CONDITIONS
•ft
* KG/S DISCHARGE RATE
* M EFFECTIVE ORIFICE DIAMETER
* M HEIGHT ABOVE (LEVEL) GROUND
* DEGREES RELEASE DISCHARGE ANGLE
* S RELEASE DURATION (<0 FOR STEADY)
* ATMOSPHERIC AMBIENT CONDITIONS
* M
* M/S
* CELSIUS
* ATMOSPHERES
* PERCENT
REFERENCE HEIGHT
WIND VELOCITY AT HEIGHT ZO
AIR TEMPERATURE
AMBIENT PRESSURE
RELATIVE HUMIDITY
* DISPERSION DATA
*
* M SURFACE ROUGHNESS PARAMETER
* PASQUILL STABILITY CLASS
*
* JET/PLUME DEVELOPMENT TERMINATION CRITERIA
*
* M LAST REQD. DOWNWIND DISP.
* M LAST REQD. PLUME DIAMETER
* M LAST REQD. PLUME CENTROID RISE HI.
* M LAST REQD. HORIZONTAL DISPLACEMENT
* M/S LAST REQD. (MEAN) PLUME VELOCITY
* PERCENT LAST REQD. POLLUTANT CONCENTRATION
*
* MATCHING CRITERIA FOR HEGADAS / PGPLUME
*
* LAST REQD. ABS. VALUE OF UJET/UAMB-1
* LAST REQD. JET/(JET+HEG) ENTRAINM.
* MAX. BUOYANCY EFFECT FOR ADVECTION
* MAX. BUOY. EFF. FOR PASS. DISPERSION
g
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
G-27
-------
Table 6. HGSYSTEM Input to PGPLUME - Vapor Jet Release of Chlorine
TITLE Vapor chlorine release
Input file for the (steady-state) passive
adveotion model PGPLUME. The file is
generated by the near field dispersion model
PLUME. It incorporates all the breakpoint
data generated by PLUME together with such
additional variables and flags needed to
ensure physical consistency. In addition, the
file contains variables needed to complete a
viable input file suitable for submission to
PGPLUME; Such additional data are prefixed
by an asterisk (*) and should be physically
and contextually sensible, but may be changed
at the user's discretion. Such data may also be
overwritten by the addition of keywords to the
PGPLUME partial input file under HGSYSTEM.
GASDATA * released gas composition datablock.
CPGAS= 34.9 * pollutant specific heat (J/mol/C).
MWGAS= 70. Q * pollutant molecular weight (g/mol).
GASFRAO 1.00 * release mole-fraction pollutant (-).
WATGAS- O.OOOE-01 * release mole-fraction watar-vapor (-).
GEOMETRY * plume geometry at matching datablock.
DXPLUME= 7.34 * matching plane displacement (m) .
ZPLUME= 7,11 * oenttoid height above ground (m) .
DPLUME= 3.04 * near-plume (effective) diameter (m).
PHIPLUME= 2.96 * plume axis orientation (degrees).
STATE * plume dynamic/thermodynamic state.
UREL- -6.251E-02 * plume relative velocity (m/s).
CMASS- 1.632E-03 * nearfield mass-concentration (kg/m3).
RREL» 9.583E-04 * plume (mean) excess density (kg/m3).
DURATION- 1.200E+03 * (steady) release duration (s).
AMBIENT * ambient atmosphere datablock.
AIRTEMP- 5.03 ambient (air) temperature (C) .
AIRPRESS- 1.000 ambient (absolute) pressure (atm).
RHPERO O.OOOE-01 ambient (relative) humidity (Z).
UATM- 4.63 wind-speed at centroid height (m/s).
RATM* 1.27 ambient atmosphere density (kg/ra3).
DISP * Pasquill/Gifford dispersion data.
ZR" 0.100 * ground surface roughness (m) .
PQSTAB- D * Pasquill/Gifford stability class (-).
AVTIMC=» 1200. * concentration averaging time (s).
TERMINAT * output control datablock.
XFIRST- 7.34 first required downwind distance (m) .
STEP- 100. arithmetic series step- length (m).
HSTEP" 10 maximum number of (arithmetic) steps (-).
FACTOR- 1.20 scale factor for geometric series (-).
XLAST- 1.001E+04 last required downwind distance (m).
VFLAST- 1.00 last required mole concentration (mm).
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
G-28
-------
3,2 Example of Output
The final output generated by the HGSYSTEM modeling effort describing the vapor jet
release of chlorine is shown in Table 7. Specifically, this file was obtained from running the
PGPLUME module. The output is in the form of tables of mole-concentration at several
heights above the ground and distances off-axis, repeated for a number of distances
downwind (a few examples only are shown). On each page of the output, the downwind
displacement is given immediately under the heading "cross-section data".
G-29
-------
Table 7. PGPLUME Output - Vapor Jet Release of Chlorine
Output from PGPLUME Version HOV90
Cross-Section Data:
downwind displacement: 7.340E-03km;
peak mole-concentration gas: 2.86E-02 Z;
plume averaging time: 20. mins;
transverse plume "width": 2.3 m;
maximum concentration height: 7.1 m;
Title: Vapor chlorine release
Cross-Section Data:
peak excess-velocity: -4.6
peak excess-density: 0.51
peak mass-concentration: 0.87
vertical plume "height": 0.93
section centroid height: 7.1
Date: 17/11/92 Time: 08:26
Virtual Source Data:
cm/s; downwind displacement: -15.
g/m3; height above ground: 7.1
g/n>3; source mass-flux gas: 5.41E-02
m; release duration: 20.
m; matching achieved: "Perfect" match
m;
m;
kg/s;
mins ;
! Table of Mole-Concentration gas (ppm) at several !
!heights (z)(m) above (level) ground, and at several!
! distances (y)(m) measured horizontally off-axis: !
i !
! O.OOOE-01 0.458
i
! O.QOOE-01! 1.124E-10 1.102E-10
i i
! 6.18 ! 173. 170.
i i
! 6.41 ! 216. 211.
i ;
! 6.65 ! 252. 247.
i ;
' 6.88 ! 277. 272.
i
! 7.11 ! 286. 280.
! 7.34 ! 277. 272.
i i
! 7.57 ! 252. 247.
t ;
! 7.81 ! 216. 211.
i i
! 8.04 ! 173. 170.
i i
!
! height (m) above !
! (level) ground. !
i t
Near-field Matching Data:
nean plume velocity-excess: -6.2
nean plume density-excess: 0.96
nean plume concentration gas: 1.6
affective plume "diameter": 3.0
ilume downwind displacement: 7.3
>lume centroid height: 7.1
flume cross-sectional area: 7.3
lean plume inclination: 3.0
0.917
1.038E-10
160.
199.
233.
256.
264.
256.
233.
199.
160.
1.38 1.83 2.29
9.388E-11 8.162E-11 6.817E-11 5
145. 126. 105.
180. 157. 131.
211. 183. 153.
231. 201. 168.
239. 208. 173.
231. 201. 168.
211. 183. 153.
180. 157. 131.
145. 126. 105.
2.75
.471E-11
84.4
105.
123.
135.
139.
135.
123.
105.
84.4
3.21 3.67 4.13 !
!
4.218E-11 3.125E-11 2.224E-11!
!
65.1 48.2 34.3 '
i
81.0 60.0 42.7 !
!
94.7 70.; 49.9 !
i
104. 77.0 54.8 !
i
107. 79.5 56.5 !
104. 77.0 54.8 !
!
94.7 70.1 49.9 '
i
81.0 60.0 42.7 '
i
65.1 48.2 34.3 !
i
t
t
r
t
t
r
t
t
!
i
i
t
t
i
i
t
i
i
i
i
t
! horizontal off-axis !
! displacement (m). !
cm/s;
g/m3;
g/m3;
tn;
m;
in;
ra2;
degrees
Atmosphere Conditions:
atmosphere density: 1.3
atmosphere temperature: 5.2
atmosphere pressure: 1.0
relative humidity: O.OOE-01
ambient wind-speed: 4.6
surface roughness: 0.10
Pasquill/Gifford class: D
kg/m3;
C;
atm;
Z;
m/s;
m;
(-);
!
Pasquill/Gifford Matching Data:
peak excess-velocity: -4.6
peak density-excess: 0.51
peak concentration gas: 0.87
peak mole concentration gas- 2.86E-02
peak concentration height: 7 1
plume averaging time : 20 .
transverse plume "width": 2.3
vertical plume "height" : 0 . 93
i
cm/s ;
g/m3,
g/m3;
I;
m;
mins :
m;
m.
G-30
-------
Table 5. PGPLUME Output - Vapor Jet Release of Chlorine (continued)
Output from PGPLUME Version HOV90
Title: Vapor chlorine release
Date: 17/11/92
Time: 08:26
Cross-Section Data:
downwind displacement: 8.808E-03km;
peak mole-concentration gas: 2.54E-02 Z;
plume averaging time: 20. mins;
transverse plume "width": 2.4 m;
maximum concentration height: 7.1 m;
Cross-Section Data:
peak excess-velocity: -4.1
peak excess-density: 0.46
peak mass-concentration: 0.78
vertical plume "height": 0.98
section centroid height: 7.1
Virtual Source Data:
cm/s; downwind displacement: -15. m;
g/m3; height above ground: 7.1 m;
g/m3; source mass-flux gas: 5.41E-02 kg/s;
m; release duration: 20. nuns;
m;
matching achieved: "Perfect" match
! Table of Mole-Concentration gas (ppm) at several !
Iheights (z)(m) above (level) ground, and at several!
! distances (y)(m) measured horizontally off-axis: !
i
i
! O.OOOE-01!
t
! 6.13
!
! 6.37
r
! 6.62
!
! 6.36
i
! 7.11
I
! 7.36
I
! 7.60
!
! 7.85
i
! 8.09
i
!
i
T
t
!
i
!
i
I
i
i
I
i
1
i
i
!
!
!
!
O.OOOE-01
2.280E-09
154.
192.
224.
246.
254.
246.
224.
192.
154.
0.487
2.235E-09
151.
188.
220.
242.
249.
242.
220.
188.
151.
0.974
2.105E-09
142.
177.
207.
227 .
235.
227.
207.
177.
142.
1.46
1.905E-09
129.
160.
187.
206.
212.
206.
187.
160.
129.
1.95
1.656E-09
112.
139.
163.
179.
185.
179.
163.
139.
112.
2.44
1.383E-09
93.5
116.
136.
149.
154.
149.
136.
116.
93.5
2.92
1.110E-09
75.0
93.4
109.
120.
124.
120.
109.
93.4
75.0
3.41
8.559E-10
57.9
72.0
84.2
92.5
•
95.4
92.5
84.2
72.0
57.9
! height (m) above !
! (level) ground. !
i
i
3.90
6.340E-10
42.9
53.3
62.4
68.5
70.7
68.5
62.4
53.3
42.9
4.38 !
) i
4.513E-10! !
t ,
30.5 i '
i i
38.0 ! !
I 1
44.4 ' '
t t
48.8 ! !
i t
50.3 t !
i t
48.8 ' !
i t
44 .4 ' !
i i
38,0 ' '
t t
30.5 ! i
t i
i
! horizontal off-axis !
! displacement (m) '
!
t
Near-field Matching Data:
mean plume velocity-excess: -6.2
mean plume density-excess: 0.96
mean plume concentration gas: 1.6
effective plume "diameter": 3.0
plume downwind displacement: 7.3
plume centroid height: 7.1
plume cross-sectional area: 7 3
mean plume inclination: 3.0
Atmosphere Conditions:
cm/s; atmosphere density: 1.3 kg/m3;
g/m3; atmosphere temperature: 5.2 C;
g/m3; atmosphere pressure: 1.0 atm;
m; relative humidity O.OOE-01 %;
m; ambient wind-speed: 4.6 m/s;
m; surface roughness: 0.10 m;
m2; Pasquill/Gifford class: D (-);
degrees;
Pasquill/Gifford Matching Data:
peak excess-velocity: -4.6 cm/s;
peak density-excess: 0.51 g/m3;
peak concentration gas: 0.87 g/m3.
peak mole concentration gas- 2.36E-02 7,,
peak concentration height: 71 m;
plume averaging time: 20. mins:
transverse plume "width": 2.3 m;
vertical plume "height": 0.93 m.
G-31
-------
Table 5. PGPLUME Output - Vapor Jet Release o£ Chlorine (concluded)
Output from PGPLUME Version NOV90
Cross-Section Data:
downwind displacement: 0.598 km;
peak mole-concentration gas: l.OOE-04 Z;
plume averaging time: 20. mins;
transverse plume "width": 50. m;
maximum concentration height: O.OOE-01 m;
Title: Vapor chlorine
Cross-Section Data:
release
peak excess-velocity: -0.28 cm/s;
peak excess-density: 1.79E-03 g/m3;
peak mass-concentration: 3.05E-03 g/m3;
vertical plume "height": 19. m;
section centroid height: 16. m;
Date: 17/11/92 Time: 08:26
Virtual Source Data:
downwind displacement: -15.
height above ground: 7.1
source mass-flux gas: 5.41E-02
release duration: 20.
matching achieved: "Perfect" match
m;
m;
kg/s;
nuns ;
! Table of Mole-Concentration gas (ppm) at several !
'.heights (z)(m) above (level) ground, and at several!
! distances (y)(m) measured horizontally off -axis: !
i i
! O.OOOE-01 10.00 20.0
i
! O.OOOE-01! 1.00 0.980 0
i I
! 2.37 ! 0.993 0.974 0
i i
! 4.74 ! 0.974 0.954 ' 0
i t
! 7.11 ! 0.942 0.923 0
t t
! 11.9 ! 0.846 0.829 0
I j
! 16.6 ! 0.720 0.706 0
i t
'21.4 ! 0.580 0.568 0
i i
! 26.2 ! 0.442 0.433 0
I j
! 31.0 ! 0.319 0.312 0
; !
! 35.7 ! 0.217 0.213 0
! ! -
i
! height (m) above !
! (level) ground. !
i i
Near-field Matching Data:
mean plume velocity-excess: -95.
mean plume density-excess: 0.96
mean plume concentration gas: 1.6
effective plume "diameter": 3.0
plume downwind displacement: 7.3
plume centroid height: 7.1
plume cross-sectional area: 7.3
mean plume inclination: 3.0
.923
.917
.899
.869
.781
.664
.535
.408
.294
.200
30.0 40.0 50.0
0.835 0.726 0
0.830 0.721 0
0.813 0.707 0
0.787 0.684 0
0.707 0.614 0
0.601 0.523 0
0.484 0.421 0
0.369 0.321 0
0.266 0.231 0
0.181 0.158 0
.607
.603
.591
.571
.513
.437
.352
.268
.193
.132
60.0
0.487
0.484
0.474
0.458
0.412
0.350
0.282
0.215
0.155
0.106
70.0 80.0 90.0 !
i
0.375 0.278 0.198 !
i
0.373 0.276 0.197 '
I
0.365 0.271 0.193 !
i
0.354 0.262 0.186 !
i
0.318 0.235 0.167 !
i
0.270 0.200 0.142 \
i
0.218 0.161 0.115 !
i
0.166 0.123 8.745E-02!
i
0.120 8.858E-02 6.305E-02!
t
8.147E-02 6.036E-02 4.296E-02!
r
-
i
'
;
!
1
1
1
1
1
1
1
1
1
1
1
I
1
r
i
!
1
1
! horizontal off-axis
' displacement (m) .
cm/s;
g/m3;
g/m3;
m;
m;
ro;
m2;
degrees:
Atmosphere Conditions :
atmosphere density:
atmosphere temperature:
atmosphere pressure:
relative humidity:
ambient wind-speed:
surface roughness:
Pasquill/Gifford class:
1.3
: 5.2
1.0
O.OOE-01
5.5
0.10
: D
kg/m3 ;
C;
atm;
%;
m/s;
m;
(-);
!
Pasquill/Gifford Matching Data:
peak excess-velocity: -93.
peak density- excess: 0.51
peak concentration gas : 0 87
peak mole concentration gas: 2.86E-02
peak concentration height: 7.1
plume averaging time: 20.
transverse plume "width": 2.3
vertical plume "height". 1.1
cm/s ;
g/m3,
S/m3,
• ;
m;
nuns ;
m;
m.
G-32
-------
4.0 REFERENCES
1. Witlox, H.W.M., "HGSYSTEM: Dispersion Models for Ideal Gases and Hydrogen
Fluoride, Tutorial and Quick-Reference Guide", External Report TNER.90.007,
Thornton Research Centre, Shell Research, Chester, England (May, 1991).
2. McFarlane, K., Prothero, A., Puttock, J.S., Roberts, P.T., and Witlox, H.W.M.,
"Development and Validation of Atmospheric Dispersion Models for Ideal Gases and
Hydrogen Fluoride, Part I: Technical Reference Manual", External Report
TNER.90.015, Thornton Research Centre, Shell Research, Chester, England
(November, 1990).
3. Witlox, H.W.M., McFarlane, K., Rees, F.J., and Puttock, J.S., "Development and
Validation of Atmospheric Dispersion Models for Ideal Gases and Hydrogen
Fluoride, Part II: HGSYSTEM Program User's Manual", External Report
TNER.90.016, Thornton Research Centre, Shell Research, Chester, England
(November, 1990).
4. Colenbrander, G.W. and J.S. Puttock, "Decription of the HEGADAS Model for
Dense Gas Releases," External Report TNER.90.022, Thornton Research Centre,
Shell Research, Chester, England (1989).
G-33
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APPENDIX H
CALCULATION OF MOLECULAR DIFFUSIVITY
FROM BASIC PRINCIPLES
-------
APPENDIX H
CALCULATION OF MOLECULAR DIFFUSIVITY
FROM BASIC PRINCIPLES
The equation for the rate of evaporation of a liquid with an above ambient boiling point
from a pool lying on the ground contains the molecular diffusivity Dm of the diffusing species
in air, see Eq. (5-3) in Section 5.1.3 of the main body of the report. If D,,, is not available
from data compilations, it can be calculated by using the Chapman-Enskog kinetic theory
of gases as explained by Bird et al.(21) (the reference is to be found in Section 11):
Dm = 0.001853.((Tb)3(l/Ma + l/Mb))ai/B cm2/s (1)
B = Pa(Sab)2.Oab . (2)
The following is an example for a pool of HF spilled on the ground at a temperature Tb of
60 °F = 298 K (see Section 5.3). Ma is the molecular weight of air (28.9). Mb( = M) is the
molecular weight of HF, taken here to be 70 because HF vapor oligomerizes (associates into
(HF)2, (HF)6 and possibly (HF)8). pa is the atmospheric pressure, l.OlxlO5 Pa = 1
atmosphere.
The quantity S^ is expressed as the arithmetic mean of two other quantities: Sab = (sa +
sb)/2, measured in angstroms. For air, Bird et al. give a value of sa equal to 3.617. For HF,
sb is not tabulated by Bird et al. and has to be calculated from the critical temperature Tc
(K) and the critical pressure Pc(atmospheres) using a formula that is also given by Bird et
al.:
sb = 2.44(TC/PC)"3 (3)
For HF, T0 = 461 K and Pc = 64 atmospheres so that sb = 2.44(461/64)1/3 = 4.712
angstroms. Hence, Sab = (3.617 + 4.712)/2 = 4.16 angstroms.
The quantity Oab is a complicated function of another quantity eab/k which in turn is the
geometrical mean of two other quantities ea/k and eb/k, where k is Boltzmann's constant.
e^/k = (e,eb)°-Vk (4)
For air, Bird et al. assign a value of 97 to ea/k. For HF, eb/k = 355. Therefore eab/k =
(355x97)a5 = 186.
There is a table in Bird et al. (Table B-2) that relates O^ to kTb/ert. For kJJs^ = 289/186
HI
-------
= 1.557, the table gives Oab - 1.180. Combining all of the above gives B = (1)(4.16)2(1.180)
= 20.46 and Dm = (0.001853)((2893)( 1/28.9 + 1/70))0-5 = 0.0984 cm2/s = 9.84xlO'6 m2/s.
The above method is applicable when Dm is not available from data sources. A typical
default value for Dm for many materials is ~ 10"3 m2/s.
H2
-------
TECHNICAL REPORT DATA
(Please read Instructions on reverse before completing)
1. REPORT NO.
EPA-454/R-93-001
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Contingency Analysis Modeling for Superfund
Sites and Other Sources
5. REPORT DATE
January 1993
6. PERFORMING ORGANIZATION CODE
7. AUTHOR
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