Monday June 30, 2008 - Vol. VII Issue 5
[Download PDF for Printing]
Gas Dispersion Model in Peac Tool
Occasionally AristaTek will get an inquiry as to what gas
dispersion model is used in the PEAC tool.
Another question is how do the PEAC tool answers compare with answers
from other models in the public domain.
A third question is how does PEAC model algorithms compare with those
used in the ALOHA model. The PEAC tool
already displays the Initial Isolation and Protective Action Distances as
listed in the 2004 (and soon, the 2008) Emergency Response Guidebook, but it
also incorporates a calculator for obtaining a more accurate answer. The calculator gives the PEAC tool user more
control of what he/she wants in terms of the circumstances of the released
chemical, with the PEAC tool displaying the answers using the same format as in
the Emergency Response Guidebook. But
what algorithms do the PEAC tool use?
In answering these questions some technical concepts are
discussed which are difficult to convey in a short summary, and references are
made to other documents for details.
A Brief History of PEAC Tool Development
The current owners of AristaTek were employees of the
University of Wyoming Research Corporation (a.k.a. Western Research Institute),
a not-for-profit research institution that had contracts with the U.S. Department
of Energy (DOE) from 1987 through 1999 to do public safety research relating to
chemical spills. Another major
not-for-profit research organization receiving this funding was the Desert
Research Institute in Reno Nevada. A
major part of this research was to spill chemicals or release toxic gases at
the DOE HazMat Spill Center Test facility near Mercury Nevada in 1993 and
1995. Most of the releases used carbon
dioxide as a toxic gas stimulant, but there were some pan evaporation tests for
measuring the evaporation rate of chlorine and anhydrous ammonia performed in
April 1995 at the DOE site. The summer
1995, gas dispersion release tests called “Kit Fox” simulated releases at a
refinery and were funded by a consortium of 10 industrial entities making up
the Petroleum Environmental Research Forum [PERF], the EPA, and the DOE. A summary of the “Kit Fox” tests is in a
paper S. Bruce King, David Sheesley, Thayne Routh, and John Nordin, “The Kit
Fox Field Demonstration Project and Data Set”, International Conference and
Workshop on Modeling the Consequences of Accidental Releases of Hazardous
Materials, 1999; American Institute of Chemical Engineers, New York,
N.Y. The tests were significant in that
many release tests took place including the near-nighttime, very stable
atmospheric stability condition. In
addition, comparative tests were made for both flat surface terrain releases
and releases where there were structures simulating those at a refinery, both
under daytime “neutral” and near nighttime “stable” atmospheric conditions.
The U.S. Department of Energy (DOE) encouraged information
transfer to emergency responders and others charged with protecting the public
in the event of a toxic chemical release.
The University of Wyoming Research Corporation for several years
maintained a website where non-proprietary data from tests performed at the DOE
HazMat Spill Test facility were freely available. Several papers have been published by different groups on model
development as the result of the DOE HazMat Spill Center Tests. The Lawrence Livermore National Laboratory
SLAB Model was largely developed from earlier tests at that site. The same reference citing the “Kit Fox”
tests published two other papers by different researchers on testing of the HEGADAS
model and DEGADIS model with “Kit Fox” data.
The University of Wyoming Research Corporation employees (S.
Bruce King, David Sheesley, Thayne Routh, John Nordin, and Vern Smith)
approached the problem of information transfer differently. A 1987 University of Wyoming Research
Corporation survey of over 100 industrial chemical spills where people were
evacuated showed that when the accident occurred, none of the existing models
were used to base evacuation distances.
Under the stress of the situation, people were not familiar on how to
run the models. Days after the
incidents occurred, there were sometimes plenty of modelers out there to piece
together what happened. But the
modeling was not done under the stress of the moment of the spill. While the “Kit Fox” and other tests at DOE
HazMat Spill Center Test facility illustrated some modeling deficiencies, the
real problem was rapid communication of information to emergency responders who
must make the decisions.
In 1996 we decided that the best way of information transfer
to emergency responders would be in the form of a small hand-held computer
(PEAC = Palm Emergency Action for Chemicals) which
would contain information on chemicals, personnel protective clothing, and
modeling information for establishing a protective action distance in case of a
spill. The chemical database and
personnel protective clothing information was obtained from consulting many
different sources. We listened to
feedback from emergency responders and other users. We incorporated additional features such as display of the
Emergency Response Guidebook and other data sources intact in addition to the
data sources we had developed, as often responders said that they should
consult three reference sources.
The University of Wyoming Research Corporation made a
management decision in the late 1990’s not to pursue public safety research
contracts and concentrate its resources mostly on energy. In 1999 the employees S. Bruce King, David
Sheesley, Thayne Routh, and John Nordin elected to form a for-profit company,
called AristaTek, Inc., to develop and market the PEAC software. The patent rights [U.S. Patent 5724255] to
the PEAC tool which incorporated gas dispersion modeling were initially licensed
to Aristatek and later (December 2000) purchased from the University of Wyoming
Research Corporation. [see http://www.patentstorm.us/patents/5724255.html for
Overview of Input/Output in PEAC Tool for Gas Dispersion Modeling
The basic rules used by AristaTek in selecting models are
(1) the calculations must be rapid and display the results in a format easily
understood, (2) the responder cannot be burdened with a lot of detailed
information required to run the model, (3) the responder should be able to
model different situations to ‘bracket” Protection Action Distances reflecting
possible changing conditions, and (4) the modeling should deliver reasonably
accurate results. In a real world
situation of a chemical release, a first responder does not normally have
information concerning meteorology or other critical details and must make
rough estimates of the situation at hand.
The weather conditions at an airport 15 miles away may be different from
what is happening where the chemical release has occurred.
The display for “Initial Isolation Zone” and “Protective
Action Distance” in the Emergency Response Guidebook is easily understood and
is the basic format chosen for displaying answers in the PEAC tool.
Figure 1: The Display Chosen for the PEAC Tool is
Similar to the Emergency Response Guidebook.
The PEAC tool user may use either English or metric units.
Response Guidebook display
Right: PEAC tool
display of results for an example situation
Notice similarities in format
The Emergency Response Guidebook (ERG) gives the user only
four choices, small or large spills, daytime or nighttime releases. For most chemicals, a small spill is defined
anything less than 55 or 60 gallons, and a large spill is greater than 55 or 60
gallons. For a few highly toxic
chemicals such as chemical warfare agents, a lower quantity is used to
distinguish between small and large spills.
Daytime releases generally have lower protective action zone distances
than nighttime releases because daytime solar heating of the atmosphere creates
a more unstable or turbulent mixing of the air which in turn helps disperse the
chemicals. There is also provision for
chemicals that are water-reactive and release toxic gases. The distances for Initial Isolation and
Protective Action are presented in the form of tables. At the request of PEAC tool users, we have
also provided the user with the option of displaying the same numbers as the
The ERG is updated every four years. The numbers for display of the initial
isolation and protective action distances also are often different for each
update. The two reasons for the changes
are (1) the ERG numbers are modeled to different “Levels of Concern” for
different editions and (2) there are changes in the ERG modeling
methodology. Details of their basis of
modeling are available in a developmental document, published by Argonne
National Laboratories and are available at http://hazmat.dot.gov/pubs/erg/Argonne_Report08042005.pdf
When developing a model for the PEAC tool, the user has the
option of specifying different situations:
total amount of chemical released, either specified as a release rate or
the entire contents released in a very short time (e.g. < 15
seconds). If the release rate or
total amount released is not known, the PEAC tool contains calculators for
meteorological information (wind speed, percent cloud cover, location,
date, time of day). From the
location, latitude and longitude is calculated. This information is used with the date, time of day, percent
cloud cover, and wind speed to calculate the degree to which the chemical
cloud will disperse as it travels downwind.
of three terrains: (1) flat
surface, (2) brush and a few buildings here or there, and (3) urban or
forests. Buildings and trees act
as obstructions to the chemical cloud resulting in a more dispersed cloud,
but at the same time also result in a longer time for the cloud to clear
out of the area.
“Level of Concern” used as the basis for the Protective Action
Distance”. Usually the “Level 2
Emergency Response Planning Guideline” or sometimes the “Immediately
Dangerous to Life and Health” level of concern is selected by the user.
There are several calculators available in the PEAC tool for
estimating the mass released or a release rate if this information is not
known. If rough dimensions of the
container size or if standard transport tanks are used and percent full is
known, the total mass can be calculated.
If there is a hole in the side of a container or if there is a
sheared-off pipe, the PEAC tool can estimate a maximum release rate. If the chemical is a liquid and pools on the
ground, the PEAC tool can calculate an evaporation rate.
The ALOHA model used in CAMEO also contains a pool
evaporation calculation methodology.
The algorithms used by ALOHA for pool evaporation have been published
and are in the public domain. During
April 1995, the founders of AristaTek did a few pan evaporation tests using
spilled liquefied anhydrous ammonia and liquefied chlorine (separate tests) in
a wind tunnel at the Nevada HazMat Spill Center Test Facility. As the liquid evaporated in the one-square
meter pan, the remaining liquid auto-chilled to about –70o
temperature achieved was –75.5o
C for anhydrous ammonia). As the liquid temperature decreased, the
evaporation rate (as measured by sensitive scales under the pan) agreed with
what was predicted by the evaporation model for the different temperatures
below the normal chemical boiling point.
The chlorine test was complicated by “hydrate” formation over time,
which could be viewed by remote video, which tended to decrease the evaporation
rate. Nevertheless, we felt that the
evaporation model used in ALOHA was sufficiently accurate to be used in the
PEAC tool. More details on the tests
are at http://www.aristatek.com/newsletter/0602February/TechSpeak.aspx
Links to evaporation rate algorithms in the public domain as
used in ALOHA are at the website, http://www2.arnes.si/~gljsentvid10/doc_evapo.html
. The algorithms were actually not developed
by the ALOHA people but are the result of earlier work developed by Kawamura,
Peter, and Donald Mackay; 1985. The
Evaporation of Volatile Liquids
University of Toronto Depts. Of Chem. Eng. and Applied Chemistry: TIPS Report EE-59, Environmental Canada (54
pages); published in: Hazardous Materials
, vol. 15 (year
1987), pp. 343-364.
All these evaporation rate calculations are handled
internally within the PEAC tool.
PEAC Tool Gas Dispersion Modeling
The PEAC tool follows the same practice of several models in
the public domain (such as ALOHAtm
) of internally selecting an
appropriate category based on user input.
The categories are:
release, Gaussian (Passive) dispersion
release, Dense Gas dispersion
(short duration) release, Gaussian (Passive) dispersion
(short duration) release, Dense Gas dispersion
Within each category, the PEAC tool assigns an atmospheric
stability index (A, B, C, D, E, or F) based on wind speed and solar insolation. The reference citation is Pasquill, F.
(1974), Atmospheric Diffusion,
edition, John Wiley &
Sons (publisher), N.Y., N.Y. The ALOHA
model uses the same methodology. The
SLAB model, developed by Lawrence Livermore National Laboratory, also does
something similar but uses a sliding scale called a “Monin-Obukhov length” or
“Obukhov length” which the user can specify.
Table 1. Pasquill-Gifford Stability Index.
Pasquill Dispersion Class
Surface wind speed and cloud cover
Wind measured at 10 meter height
daytime; strong insolation and wind < 3 m/s or
moderate insolution and wind < 2 m/s
daytime; strong insolation with wind between about 3 and
5 m/s or moderate insolution with wind between 2 and 4 m/s or slight
insolution and wind < 2 m/s
daytime; strong insolation and wind > 5 m/s or
moderate insolution with wind between 4 and about 5.5 m/s or slight
insolution and wind between 2 and 5 m/s
All overcast sky conditions, day or night; daytime and
moderate insolation and wind> 5.5 m/s;
daytime and slight insolation and wind > 5 m/s; nighttime and wind > 5 m/s; nighttime and more than 50% cloud cover or
with thin overcast and wind > 3 m/s
nighttime; thin overcast or > 50% cloud cover and
wind < 3 m/s; < 50% cloud cover
and wind between 3 and 5 m/s
nighttime; < 50% cloud cover and wind < 3 m/s
Strong solar insolation is defined as a solar elevation
angle > 60 degrees.
Moderate solar insolation: solar angle between (and including) 15 and 60 degrees.
Slight solar insolation:
solar angle < 15 degrees.
The PEAC tool modeling uses the same methodology as used by
and other popular gas models in internally calculating a
solar insolation and assigning a stability class based on user input of time of
day, location, date, wind speed, terrain, and cloud cover. The wind speed in the PEAC tool is assumed
to be measured at a 2 meter height, which is corrected to a 10 meter height for
the purpose of table 1. Earlier
versions of ALOHA (version 5.0) did not make this correction for wind speed
height to conform with table 1, but later versions of ALOHA (version 5.2.3 and
beyond) are reported to make this correction.
The calculations are complex, but the methodology for doing this is
available in the open literature.
The model used in the PEAC tool makes the following
assumptions, to keep things simple:
Buoyant gases and toxic cloud liftoff are ignored. The greatest concentration is assumed at ground
Fires are not considered, which may result in liftoff
of toxic gases
Special terrain situations such as a valley with hills
on the side, a street corridor between tall buildings, or a wake behind a large
building are not considered
The protective action distances predicted are for toxic
cloud centerline, ground level locations
The vertical momentum of the source (a jet or
smokestack) is not considered.
The modeling is for gases and vapors; the deposition
aerosols and particulates is not considered
The effect of precipitation is not considered
Atmospheric inversion layers are not considered
Reactions of sunlight and moisture with the airborne
chemical is not considered [However, for some chemicals, a reaction product
with air-water such as hydrochloric acid can be modeled instead of the original
Distances very near the source or very far away (>
10 km) from the source must be viewed with caution. For example, ALOHAtm
and the 2008 Emergency Response will not even display a Protective Action
Distance far from the source. The PEAC®
tool will display distances far from the source, but the emergency responder
must understand that meteorology and terrain will likely not be the same, and
deposition of a toxic chemical might occur.
Distances very near the source will depend upon the circumstances of the
spill, and the PEAC tool assumes a typical release source area for
user-specified release rate or quantity to calculate a distance corresponding
to a downwind concentration.
Gaussian, or passive dispersion methodology is the most
popular model for expressing downwind dispersion of gases. It is used in ALOHA, SLAB, the military D2PC
model, and the PEAC tool. It is
applicable for dispersion of gases roughly the same molecular weight and temperature
of air, or for dilute gases if gas has a higher molecular weight than air. The methodology is not applicable for high
concentrations of dense gases. If a
cross-section of the toxic gas cloud profiles for passive and dense gases were
compared at some distance downwind, it would look like the pictures below.
Figure 2: Difference between
Passive and Dense Gas Cloud Profiles
Analytical expressions for expressing concentrations at any
point downwind for the passive (Gaussian-shaped) cloud are available in any
textbook on Gas Dispersion modeling.
The PEAC tool uses the same analytical expressions as are in the public
domain. The dense gas calculations are
more complex, and straight-forward analytical expressions have not been
published. The simplest dense gas model
assumes a box-shaped profile of “constant height” with Gaussian-shaped
edges. The criteria of whether a dense
gas or passive dispersion model is used is based on something called a
Richardson Number. We will not get into
the mathematical details of the number calculated, except to say that both the
PEAC tool and the ALOHA model use the same Richardson Number concept, and the
details of how the Richardson Number is calculated are available in the open
As the dense gas travels downwind, it mixes in with the
surrounding air. The relative density
between the chemical cloud and surrounding air becomes similar, and the dense
chemical cloud behaves like a passive “Gaussian” cloud as it travels further
So much for similarities.
Why do models differ? The answer
is that different data sets are used to calibrate the models. Also, comparisons may not be made at the
same concentration averaging times for different data sets. The data sets may be outdoor releases or
releases in a wind tunnel using a scale model for the terrain. Model developers also draw heavily on mixing
theory to extend their projections to other circumstances because time and
monetary constrains limit testing to only a few conditions. From these tests, analytical expressions
called “sigma expressions” might be developed to express the degree of
spreading of the chemical cloud as it travels downwind. The spreading results from atmospheric
turbulence due to the wind and solar heating.
During the day, the sun heats up the ground resulting in the air near
the ground becoming less dense. The
warm air rises resulting in mixing and dispersion of the chemical cloud. During a clear night, with little wind, the
ground radiates its heat to space, and the air becomes stable, and there is
little mixing of the chemical cloud with the surrounding air.
Let’s look at an example of a set of analytical expressions
for “sigma expressions” developed from a data set, and see their use in
calculating a downwind concentration.
The simplified equation for a ground level (continuous)
release, Gaussian (passive) distribution is
C/q = (p U sy
where C = ground level concentration at the cloud
release rate (continuous release, no dense gas effects)
U = wind
= standard deviation of the plume/cloud concentration in the cross-wind
direction [“sigma expression”]
= standard deviation of the plume/cloud concentration in the vertical direction
downwind direction, y = crosswind direction, z = height above ground; Release
point at x = y = z = 0.
In formulating this equation, it is assumed that the plume
cloud is free to expand in all directions constrained only by the ground. Therefore there are no atmospheric mixing
heights, valleys, or corridors to put a cap on the expansion.
One of the most
commonly used and well known expressions for “sigma expressions” are those
published by Gary Briggs in 1973, using a data set for low-level sulfur dioxide
releases in a southwestern Kansas field.
The paper citation is Briggs, G.A., 1973, “Diffusion Estimation
for Small Emissions, ATDL Contribution File No. 79, Atmospheric Turbulence and
Diffusion Laboratory. The ALOHA model
and the PEAC tool uses these expressions for continuous releases:
Table 2. Analytical Briggs Sigma Expressions for
(x in meters)
0.22x(1 + 0.0001x)-1/2
0.16x(1 + 0.0001x)-1/2
0.11x(1 + 0.0001x)-1/2
0.08x(1 + 0.0002x)-1/2
0.08x(1 + 0.0001x)-1/2
0.06x(1 + 0.0015x)-1/2
0.06x(1 + 0.0001x)-1/2
0.03x(1 + 0.0003x)-1
0.04x(1 + 0.0001x)-1/2
0.016x(1 + 0.0003x)-1
These sigma expressions are valid for a concentration
averaging time of 3 minutes and for a surface roughness z0
meters. However, the same expressions
have been used in models with a surface roughness of 0.3 meters and a 10 minute
concentration averaging time. There are
also some minor differences in how the PEAC tool handles the expressions for
urban situation, which result in a slightly more conservative prediction of
protective action distance for a given downwind concentration.
For the instantaneous (short duration) release, Gaussian
(passive) dispersion mode, the PEAC tool and ALOHA use different sigma
expressions, but both methodologies are published in the open literature. The expressions for the PEAC tool “sigma
expressions” (passive dispersion mode, instantaneous release) came from the
DEGADIS manual, cited below:
Spicer, T.O., and J.A. Havens, (1989). “Users Guide for
the DEGADIS 2.1 Dense Gas Dispersion Model”, Environmental Protection Agency,
Report EPA-450/4-89-019. [comment: the manual also includes passive (Gaussian)
The PEAC tool uses the same concentration averaging times
] as used in the DEGADIS manual, as follows:
Atmospheric Stability A, B,
= 18.4 seconds
Stability D. tave
Stability E. tave
= 11.4 seconds
Stability F. tave
The DEGADIS manual did not originally develop this work
but compiled it from earlier publications, with modifications.
For the dense gas mode, the PEAC tool did not follow the
DEGADIS manual. However, the ALOHA
model did incorporate the DEGADIS methodology for their dense gas mode. The PEAC tool more closely mimics the SLAB
Model developed by Lawrence Livermore National Laboratory, but is not
SLAB. The reference citation for SLAB
model development is
1990. User’s Manual for
SLAB: An Atmospheric Dispersion Model
for Denser-Than-Air Releases
Livermore National Laboratory, Livermore CA.
The PEAC tool dense gas modeling uses a one-minute
concentration averaging time for continuous releases, and 10 seconds averaging
time for instantaneous (short duration) releases.
The developers of
the DEGADIS model (Tom Spicer and Jerry Havens) examined the results of 1995
Kit Fox Dispersion tests performed at the Nevada DOE HazMat Spill Center. They concluded that the DEGADIS predictions
were consistent with what was observed from the Kit Fox dispersion tests. The reference citation is Spicer,
T.O., and J.A. Havens, “Description and Analysis of Atmospheric Dispersion
Tests Conducted by EPA at the DOE HazMat Spill Center”, International
Conference and Workshop on Modeling the Consequences of Accidental Releases of
American Institute of Chemical Engineers, New York, N.Y. [comment:
EPA was only one of several participants providing funding for the tests
or providing direction for the tests].
Under the “D” atmospheric stability condition, the DEGADIS
model, SLAB, and model used in the PEAC tool, as well as the Kit Fox data
generally gave similar results, at least within a factor of two. There were greater differences for the E
stability condition and even more for the F stability condition.
Concentration Averaging Times and Toxic Cloud Duration
Some important concepts are (1) how long will the toxic
cloud last and (2) what is the concentration averaging time. This might be best illustrated by looking at
data obtained from the tests at the DOE HazMat Spill Center in Nevada. In these tests, various chemicals were
released and resulting toxic cloud characteristics measured. During August-September 1995, for example,
the series of over 70 tests identified as “Kit Fox” used carbon dioxide as a
surrogate for more toxic chemicals. The
carbon dioxide releases were done at ground level with carbon dioxide released
at a specific rated for finite periods of time ranging from 15 seconds to 6
minutes. Chemical sensors were placed
at approximately 90 different locations downwind in order to estimate the cloud
centerline locations, cloud width and height, and concentrations as a function
of distance downwind. The sensors
recorded carbon dioxide concentrations every second. For the example illustrated below (figure 3), the carbon dioxide
release rate was 1.722 kg/s for exactly 180 seconds and the sensor was located
at the centerline just above ground level, 25 meters downwind. The surface roughness was 0.02 meters, the
wind speed at the 2 meter height was 2.1 m/s, and the calculated Monin-Obukhov
length was 5.6 meters (indicative of a F atmospheric stability). The release was done after sunset under
cloudless skies. The sensor in figure 1
measured carbon dioxide concentrations as a function of time at one-second
intervals. A one-minute running average
concentration was calculated from the sensor measurements and also graphed on
figure 3. Some general observations from
the tests were
In figure 3, based on a 2.1 m/s wind speed and sensor
placed 25 m downwind, the carbon dioxide cloud should have arrived at the
sensor 12 seconds after the start of the release but it actually arrived at the
sensor 24 seconds after the start of the release. Even though the release was 180 seconds, the cloud lingered for
almost 220 seconds before it completely passed over the sensor.
All data taken regardless of the test or sensor showed
peak one-second concentrations higher than the peak one-minute average. Obviously the peak 10-minute average would
be even less. For the example in figure
3, the peak one-second sensor reading was 37,000 ppm but the peak one-minute
average was 30,000 ppm.
Even though the release start and finish had a sharp
cutoff, the concentrations as seen by the sensor increased with time, leveled
off, and then decreased. The parameter sx
[“sigma x” ] is used in models to measure
the cloud spread in the downwind direction.
3: Example Ground-level Carbon Dioxide Sensor Measurement for a 3-Minute
Release (Kit Fox)
The point to be made that a
chemical release even under controlled conditions produce complex downwind
behavior that is usually not accounted for with gas dispersion models in the
public domain, and the emergency responder should keep this in mind when using
a gas dispersion model to predict a public evacuation distance. If the release rate is small under
conditions of a “D” atmospheric stability, the wind speed at the cloud level
should fairly accurately predict the time that the cloud will arrive at some
downwind receptor. The cloud will still
spread out in the downwind and crosswind directions and increase with
height. However, if the release is
large such that dense gas effects occur, the cloud will tend to slow down. Also, under more stable atmospheric
conditions the cloud will linger longer and take more time to clear out. One of the tests under the Kit Fox series
involved a six-minute release of carbon dioxide under a far F nighttime atmospheric
stability, wind speeds on order of 1 m/s; it took the cloud over 45 minutes to
clear out from many downwind sensor locations.
If the spill occurs in an urban setting, the downwind wake behind
buildings may contain higher concentrations and take longer for the toxic cloud
to clear out.
Gas dispersion models are
derived from experimental data where chemicals are released under field or wind
tunnel conditions. The cloud shape and
spread are measured as a function of distance downwind for different meteorological
conditions. The raw data for the
various tests have different concentration averaging times. Most data has been taken under a “D”
atmospheric stability condition, and very little (until “kit Fox”) has been
taken under the stable, nighttime (“F” stability) condition. Some models in the public domain allow the
user to specify a concentration averaging time, and then correct sy
= lateral dispersion in the crosswind
direction using the user-specified averaging time t and sy,ref
dispersion in the crosswind direction based on a reference time under which the
model was originally formulated. The
SLAB model contains a slightly modified expression that avoids the anomaly of sy
approaching zero as t approaches zero.
problem is that gas dispersion models in the public domain especially under the
“F” stability condition do not agree with each other because they are
formulated differently. Another issue
is that minor changes in wind speed and degree of atmospheric stability in the
“F” stability condition can greatly affect the behavior and dispersal of the
toxic cloud. The PEACtm
uses the models as discussed earlier but it should not be surprising that
models in the public domain predict differently, especially under the “F”
stability condition. While some models
predict cloud arrival time and duration, data such as taken at Kit Fox can show
serious disagreement under certain conditions.
For this reason, the PEAC tool does not predict the cloud arrival time
More information on this subject is presented in an
earlier AristaTek newsletter article, which is available at http://www.aristatek.com/Newsletter/03%2011%20November/Technical%20Dialogue.htm
Atmospheric Stability Index vs Monin-Obukhov Length
Both the PEAC tool and ALOHA assign stability classes A, B,
C, D, E, and F based on solar insolation and wind speed. But some models such as SLAB allow the user
to specify stability on a sliding scale called “Monin-Obukhov Length”
(sometimes called “Obukhov length”, which is an indicator of the degree of
mixing of the air due to solar heating or nighttime cooling and the wind. The Monin-Obukhov length can be obtained
from sonic anemometer measurements through a complex process, or approximated
if accurate measurements of wind speed and temperature are available at least
two different heights above the ground.
A basic observation made during the “Kit Fox” tests was that meteorology
did not fit exactly into C, D, or F conditions but instead there was “D
borderline C”, “D near E”, “E changing into F”, “far F”, and if the winds died
down at night and the air became very stable, sometimes “undefined” terms such
as “G” stability or “H” stability were invented for the purpose of
conversation. Gary Briggs, representing
the EPA and author of the some of the “sigma formations” cited earlier, was
present during the Kit Fox tests. He
used these terms when the winds died down and the carbon dioxide cloud remained
stationary during the night.
The SLAB model allows the user to input different
Monin-Obukhov conditions. A
hypothetical chlorine continuous release was modeled for several Monin-Obukhov
lengths representing stable atmospheric conditions. All computer runs were done at a surface roughness = 0.1 meters
and the wind speed of 1 m/s measured at the 2 meter height. The chlorine
release rate was 0.126 kg/s (continuous) at 0.1 meter height.
Table 3. Calculated Downwind Distance (meters) for a
Chlorine Level of Concern = 3 ppm, calculated using the SLAB Model
28 (F near E stability)
10 (somewhat far F stability)
5 (far F or “G” stability)
A Monin-Obukhov length of 5 meters represents a far-F
stability condition or maybe what some might call a “G” condition.
When comparing models in the public domain, the comparison
for say an F stability may not be at the same Monin-Obukhov length, or the data
set used for calibration of “sigma expressions may not be at the same
Monin-Obukhov length, or be based on data sets taken under a different
stability condition and extrapolated to a F stability condition.
For dense gas modeling, the corresponding Monin-Obukhov
lengths as used in the PEAC tool are listed in table 4
Table 4. PEAC Tool Monin-Obukhov Lengths (L) for
Atmospheric Stability (units: meters).
(1/L = 0)
(1/L = 0)
(1/L = 0)
Example Comparisons of PEAC Tool Modeling Results With
The PEAC tool model and several other models were run for
several hypothetical situations. Lists
of protection action distances were tabulated and then graphed for different
concentrations representing Levels of Concern.
Anhydrous Ammonia Spill, mid afternoon, wind 5 m/s at 2 meter height
Denver Colorado, outdoor temperature 70o
F. The pooled liquid evaporates from a pool at 2.5 kg/s. (we will not do the evaporation rate
calculator here but simply enter a release rate for ammonia).
Figure 4: Ammonia Release at 2.5
kg/sec, wind 5 m/s at 2 meter height
In this example, a “D” stability is computed internally by
the PEAC tool and by ALOHA. At
distances greater than 200 meters, the cloud behaves passively, ALOHA and PEAC
use the same algorithms, and essentially the same answers are obtained.
Example 2: 10 kg Instantaneous
(short duration) Ammonia Release, D Stability
In this example, 10 kilograms of anhydrous ammonia is
released instantaneously (10 seconds).
The meteorology is deliberately chosen to get a “D stability”. The PEAC tool is set to “cropland”, and the
other models were set to 0.1 m surface roughness.
Figure 5: Instantaneous release of 10 kilograms of
Anhydrous Ammonia, “D” stability
In this mode, both DEGADIS and the PEAC tool give the same
answers because the same algorithms were used.
The answers were also similar to those predicted by the military D2PC
model, which is a Gaussian (passive) model but uses different sigma
expressions. The ALOHA model sigma
expressions result in a different answer.
Information including algorithms on the military D2PC model
is in the following document:
Whitacre, C.G., J. H. Griner III, M.M.
Myirski, and D.W. Sloop. 1987. Personal Computer Program for Chemical
Hazard Prediction (D2PC)
Research Development & Engineering Center, U.S. Armaments Munitions
Chemical Command, Aberdeen Proving Ground, MD.
Example 3: 10 kg
Instantaneous (short duration) Ammonia Release, F Stability
In this example, 10 kilograms of anhydrous ammonia is
released instantaneously (10 seconds).
The meteorology is deliberately chosen to get a “F stability”. The PEAC tool is set to “cropland”, and the
other models were set to 0.1 m surface roughness.
Figure 6: Instantaneous release of 10 kilograms of
Anhydrous Ammonia, “F” stability
In this mode, both DEGADIS and the PEAC tool give the same
answers because the same algorithms were used.
Both answers were a little less conservative than those predicted by the
military D2PC model, which is a Gaussian model but uses different sigma
expressions. The ALOHA model sigma
expressions result in less conservative answer.
Example 4: Sarin Release.
In this example we
will compare the PEAC tool results with the military D2PC model. This is a passive (Gaussian) model designed
for modeling chemical warfare agent releases.
For the PEAC tool, we will deliberately choose parameters to get a D
Stability condition, and model for a 0.0003 kg/sec release of Sarin as from an
evaporating pool. We do not have the
D2PC model itself to run, but we do have the algorithms for this model, which
were programmed in an Excel spreadsheet.
The comparison is in Figure 7.
The comparisons were repeated for conditions deliberately
chosen to get an F stability condition (figure 8, note change in release rate
and wind speed):
In this example, the D2PC model and the PEAC model give
Example 5: 2 kg/sec Chlorine
Release at Ground Level.
In this example, chlorine is released at ground level at
continuous release rate of 2 kg/sec. At
this release rate, the chlorine cloud is a dense gas, at least near the
source. The passive model D2PC does not
apply. In figure 9, meteorological
conditions were deliberately chosen to get a D stability (overcast, wind 5 m/s
at 2 meter height). In figure 10,
meteorological conditions were deliberately chosen to get a F stability (clear
nighttime, wind 1 m/s at 2 meter height).
For the SLAB modeling comparisons, we set the SLAB Monin-Obukov length
to the same value as used in the PEAC tool.
Figure 9. 2 kg/s Chlorine Release, D Stability, Wind 5
m/s at 2 m height
Figure 10. 2 kg/s
Chlorine Release, F Stability, Wind 1 m/s at 2 meter height
Example 6: A Terrorist blows
up a 90-ton Rail Car Containing Chlorine, and all of the Chlorine is Released
to the Atmosphere at Once.
For this situation, the models were set to a D stability
condition using a wind speed of 5 m/s at a 2 meter height, urban setting for
the PEAC tool (or 1 meter surface roughness for SLAB), and 50oF
ambient temperature (Figure 11). For
the F Stability, a clear nighttime sky was specified using a 1.5 m/s wind speed
at a 2 meter height.
For the SLAB model, the user must specify an effective cross
sectional area after the explosion. No
guidelines are provided with the SLAB model on how to do this, so two extreme
situations were modeled (dispersed over a wide area or a more narrow area). The maximum cloud centerline concentrations
are plotted near ground level.
The PEAC model methodology compares favorably with
established models in the public domain.
Generally, the available models give similar result for the “D”
stability condition, but have some differences when the F stability is modeled.
The PEAC modeling methodology uses fairly short concentration averaging times
and therefore presents a more conservative distance corresponding to a given
Level of Concern than if a longer averaging time were used. The “Kit Fox” tests showed a wide variance
in results for the “F stability” depending upon the degree of air stability,
and this is a major reason why models can differ considerably when a F
stability is specified.