SAChE® Certificate Program
Level 2, Course 6a: Atmospheric Dispersion
Unit 3 – Atmospheric Dispersion Models
Narration:
[No narration]
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1
Objectives
Narration (male voice):
This is the third and final unit in the Atmospheric Dispersion course. By the end of this unit,
titled “Atmospheric Dispersion Models,” you will be able to:
•
Identify the strengths and weaknesses of different atmospheric dispersion modeling
approaches;
•
Simulate example chemical releases using Gaussian and Britter-McQuaid models; and
•
Describe how the ALOHA® hazard modeling software can be used for atmospheric
dispersion modeling.
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2
SECTION 1: Overview of Atmospheric Dispersion Models
Narration:
[No narration]
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3
Examples of Atmospheric Dispersion Models
Narration (male voice):
In Section 1, we’ll introduce some examples of atmospheric dispersion models, including:
Passive models;
•
•
•
•
•
Denser-than-air models;
Screening or basic similarity models;
Lumped parameter (computer) models;
Computational Fluid Dynamics (CFD) models; and
Wind tunnel models.
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4
Gas Concentration
Narration (male voice):
Before we look at specific types of models, let’s consider atmospheric dispersion models and gas
concentration.
As the Chemical(s) Other Than (humid) Air (COTA) cloud mixes with ambient air, the conversion
between gas concentration and mole fraction can typically be made with the ideal gas law...
...where...
•
•
•
•
•
•
C is the gas concentration;
yc is the mole fraction;
P is the ambient pressure;
Mc is the COTA molecular weight;
R is the gas constant; and
Tm is the absolute temperature of the gas/air mixture.
If yc is the mole fraction in the gas phase, C is in units of kilograms per cubic meter for R equals
8314 Joules per kmol Kelvin and P is in units of Newtons per square meter. Likewise, if yc is in
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5
parts per million in the gas phase, C is in units of milligrams per cubic meter for R and P of the
same units.
For gases released at ambient temperature, Tm is the ambient temperature. Tm will approach
ambient temperature at low concentrations for releases not at ambient temperature. However,
many release scenarios involve gases and aerosols which are at a significantly different
temperature from ambient, and consequently, Tm would normally be determined by an energy
balance, especially for higher gas concentrations.
[Female voice]
Just like in Unit 2, the equations presented in this unit have been compiled into a single
document for your convenience. Because many of these equations are required to solve this
unit’s Review questions and quiz questions, you are encouraged to click the book icon to open
this reference and save or print it. At any time during this unit, you can also access the equation
document from the Resources tab at the top of the course interface.
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6
Gas Concentration and Density
Narration (male voice):
For mixing of air (as an ideal gas) at ambient conditions with another ideal gas with the same
molar heat capacity as that of air and initially at arbitrary temperature, Ts, the relationship
between gas concentration, C (in units of COTA mass per mixture volume) and density for any
gas/air mixture, ρ (in units of mixture mass per mixture volume), is given by the expression
shown…
…where…
•
•
ρs (=Cs) is the source gas density (and concentration) at Ts; and
ρa is the air density at ambient conditions.
This relationship assumes mixing takes place at ambient pressure and the air is treated as a
pseudo ideal gas mixture (including water vapor), but any potential humidity condensation is
ignored (although it can be important under some circumstances).
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7
Gas Concentration and Density (continued)
Narration (male voice):
Although the relationship shown was derived for ideal gases with equal molar heat capacities, it
provides a useful approximation for gas mixtures with air even when the gas and air heat
capacities are not the same. Furthermore, mixtures of aerosols in air are closely approximated
by this equation provided the initial aerosol density, ρs, reflects the condensed phase. Put
another way, ρs is the total COTA mass divided by the total COTA volume initially present.
The equation shown implies a linear relationship between mixture density and gas
concentration.
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8
Passive Models
Narration (male voice):
Now we’ll look at individual atmospheric dispersion models. We’ll begin with passive models.
Passive models were the first atmospheric dispersion models developed and were based on
visual observations of smoke plumes.
Theoretical analysis dictates that a dispersing plume that does not change the atmospheric flow
field will have a Gaussian spatial distribution in the lateral and vertical directions with length
scales σy and σz. With this perspective, the lateral and vertical extent observed in the
atmosphere can be used to infer the concentration distribution and the maximum centerline
concentration (assuming the total width and depth are multiples of σy and σz).
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9
Passive Models – Elevated and Ground Level Releases
Narration (male voice):
For this discussion, total cloud width and depth are taken to be 4.3σy and 4.3σz, respectively, for
clouds not touching the ground. For ground level releases, the cloud depth is taken to be 2.15σz.
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10
Passive Models – Puffs
Narration (male voice):
Similarly for very short duration releases (“puffs”), theoretical analysis shows that a Gaussian
distribution will also hold along the wind direction, σx, provided that the wind speed is uniform.
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11
Passive Models Continue to Be Used
Narration (male voice):
The most basic (that is, passive) atmospheric dispersion models continue to be used to make
downwind COTA concentration predictions because of their simplicity. When applied to simple
scenarios, more sophisticated dispersion models should agree with predictions of passive
dispersion models.
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12
Denser-than-Air Models
Narration (female voice):
Denser-than-air dispersion models attempt to account for unique aspects of dispersion,
including those shown. Click each image to enlarge the respective illustration.
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13
Displacement (Slide Layer)
[When Image 1 is clicked…]
Displacement of the atmospheric flow field (where the wind is pushed over a cloud);
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14
Suppression (Slide Layer)
[When Image 2 is clicked…]
Suppression of atmospheric turbulence (that is, conditions that suppress mixing with air); and
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15
Density-driven (Slide Layer)
[When Image 3 is clicked…]
Density-driven flows (that cause the cloud to follow the terrain instead of the wind direction and
can enhance mixing with air).
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16
Screening or Basic Similarity Models
Narration (male voice):
Similarity models rely on the correlation of atmospheric dispersion data for characteristic
release types. Two examples of similarity models are the Pasquill-Gifford model (for passive or
neutrally buoyant releases) and the Britter-McQuaid model (for denser-than-air releases), both
of which are described later in this unit.
Similarity models can be useful for the validation of other mathematical models but are limited
to the characteristic release scenarios considered. Similarity models can provide a reasonable
first approximation of the hazard extent for many release scenarios and can be used as
screening tools to indicate which release scenarios are most important to consider with more
detailed modeling approaches.
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17
Lumped Parameter (Computer) Models
Narration (male voice):
Lumped parameter (computer) models typically begin with the basic conservation equations but
make simplifying assumptions (typically related to similarity theory) to reduce the problem to
the solution of simultaneous ordinary differential equations. In the verification process, such
models must also address the relevant physical phenomena as well as be validated for the
application being considered.
These models are typically easily solved on a computer with less user interaction than required
for the solution of partial differential equations, or PDEs.
Simplified mathematical models may also be used as screening tools to identify the most
important release scenarios; other modeling approaches should be considered only if they
address – and have been validated for – the important aspects of the scenario under
consideration.
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18
Computational Fluid Dynamics (CFD) Models
Narration (male voice):
CFD models solve the basic conservation equations for mass and momentum in their form as
PDEs along with some method of turbulence closure and appropriate initial and boundary
conditions.
[Female voice]
While CFD models are now common, there are many potential problems that must be
addressed. Click each numbered dot to learn about these potential problems.
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19
Dot 1 (Slide Layer)
[When Dot 1 is clicked…]
In the verification process, the PDEs being solved must adequately represent the physics of the
dispersion process, especially for processes such as ground-to-cloud heat transfer, phase
changes for condensed phases, and chemical reactions.
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20
Dot 2 (Slide Layer)
[When Dot 2 is clicked…]
Turbulence closure models (and associated boundary and initial conditions) must be appropriate
for the dispersion processes present, especially for denser-than-air COTAs.
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21
Dot 3 (Slide Layer)
[When Dot 3 is clicked…]
Regardless of the algorithm for solving the PDEs, any solution must demonstrate resolution
independence (that is, the numerical solution must be independent of grid spacing or time step).
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22
Dot 4 (Slide Layer)
[When Dot 4 is clicked…]
Models should be validated against relevant information for the scenario considered.
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23
Dot 5 (Slide Layer)
[When Dot 5 is clicked…]
Despite decreased computational costs, such models still require a significant investment for
simulating a release scenario, particularly if dimensions and locations of piping and equipment
are included in the model.
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24
Wind Tunnel Models
Narration (male voice):
Wind tunnel models have long been used to study the atmospheric flow around structures, such
as buildings and bridges, to predict pressure loading and local velocities.
Wind tunnel measurement of COTA concentrations for release scenarios can be used to
estimate hazard zones. However, wind tunnel models are generally considered to be incapable
of simultaneously scaling mechanical turbulence and thermally induced turbulence, presenting a
verification issue if both sources of turbulence are important aspects of the problem.
Wind tunnel experiments can be very useful when considering validation of mathematical
models, especially for complex terrain or in the presence of buildings and other structures.
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25
SECTION 2: Screening/Similarity Model Examples
Narration:
[No narration]
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26
Screening/Similarity Model Examples
Narration (male voice):
Now let's look at some of these models in more detail. We’ll begin with passive plume and puff
modeling so you can see the connection to the atmospheric parameters we covered in Unit 2.
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27
Pasquill-Gifford Plume Model
Narration (male voice):
The Gaussian (or Pasquill-Gifford) dispersion model is based on the assumption of a passive
release (that is, the COTA cloud moves at the same speed and direction as the ambient wind
upon release).
Although the Pasquill-Gifford model provides for the prediction of the spatial concentration
distribution, the discussion on the next few slides will be limited to the maximum predicted
concentration since this is most important for hazard assessment purposes. Also, our discussion
will be limited to modeling the release as a point source (where the material is idealized as
being released from a single point in space) for simplicity.
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28
Maximum Average Concentration
Narration (male voice):
At a given downwind distance, x, the maximum (ensemble) average concentration for a
continuous passive plume from a ground-level point source can be determined using the
equation shown:
...where...
•
•
•
•
E is the mass rate at which the COTA becomes airborne;
u is the characteristic wind speed (typically taken to be uᵣ);
σy is the lateral length scale; and
σz is the vertical length scale.
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29
Sources for Pasquill-Gifford Plume Dispersion Coefficients
Narration (male voice):
Pasquill-Gifford plume dispersion coefficients as a function of downwind distance and
atmospheric stability are available from many sources, including:
•
Atmospheric Chemistry and Physics of Air Pollution;
•
Lees’ Loss Prevention in the Process Industries, 4th edition; and
•
“Errors in the Use of the Briggs Parameterization for Atmospheric Dispersion
Coefficients,” Atmospheric Environment.
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30
Dispersion Coefficient Distance
Narration (male voice):
Passive dispersion coefficients are typically not provided for distances less than 100 meters or
greater than a few kilometers because predicted concentrations outside this range must be
viewed with some caution. For example, meteorological conditions may not persist over large
time scales, and at long distances, large-scale meteorological and terrain features may dictate
plume behavior in ways not accounted for by this simple approach.
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31
Briggs Passive Plume Dispersion Coefficients – Tables
Narration (male voice):
The table shown here lists Briggs parameterization of passive plume dispersion coefficients for
rural and urban sites as a function of downwind distance, x, in meters. Note that rural conditions
reflect a surface roughness of approximately 3 centimeters; urban conditions reflect a surface
roughness of approximately 1 meter.
The predicted values of σy and σz are sensitive to the specification of atmospheric stability.
Between D and F stability classes, σy for D stability is roughly three times greater than for F
stability, and σz is roughly two times greater. Since ‹C› is inversely proportional to σy and σz, the
predicted ‹C› for F stability is roughly six times greater than for D stability.
As we noted earlier, F stability occurs at night under low wind speed conditions, so operations
that could involve the loss of containment of airborne materials should be avoided under such
conditions, if possible.
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32
Briggs Passive Plume Dispersion Coefficients – Charts
Narration (female voice):
These charts can be used as a resource to estimate the Briggs lateral and vertical dispersion
coefficient for passive plumes in rural and urban sites.
Click the images to enlarge them.
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33
Pasquill-Gifford Puff Model
Narration (male voice):
Now let’s look at the Pasquill-Gifford puff model.
At a given downwind distance, x, the maximum (ensemble) average concentration for an
instantaneous passive puff from a point source is determined with this equation:
…where…
•
Et is the total material mass that becomes airborne;
•
σx is the wind direction length scale;
•
σy is the lateral length scale; and
•
σz is the vertical length scale.
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34
Sources for Pasquill-Gifford Puff Dispersion Coefficients
Narration (male voice):
Pasquill-Gifford puff dispersion coefficients as a function of downwind distance (or travel time)
and atmospheric stability are available from many sources, such as Air Dispersion Modeling –
Foundations and Applications.
σx can be approximated by σy in puff models, but the correlation proposed by Hanna and
Franzese gives much higher values of σx (σx = 2u ͙t, where t is the travel time).
Just as we saw for passive plumes, passive puff dispersion coefficients are not provided for
distances of less than 100 meters (where near source effects will be important), and predicting
concentrations for distances longer than a few kilometers must be viewed with some caution for
the same reasons cited earlier.
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35
Puff Dispersion Coefficients – Table
Narration (male voice):
This table lists passive puff dispersion coefficients in meters.
Note that the predicted values of σy and σz are sensitive to the specification of atmospheric
stability for puffs as well. Between D and F stability classes, σy for D stability is roughly three
times greater than for F stability, and σz is roughly 10 times greater. Since ‹C› is inversely
proportional to σxσyσz, the predicted ‹C› for F stability is roughly 40 times greater than for D
stability.
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36
Puff Dispersion Coefficients – Charts
Narration (male voice):
These charts can be used as a resource to estimate lateral and vertical dispersion coefficients for
passive puffs. Note that, unlike the passive plume charts, the puff charts do not differentiate
between rural and urban sites.
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37
Britter-McQuaid Correlations
Narration (male voice):
Britter and McQuaid proposed a correlation for estimating the dispersion of denser-than-air
COTAs from area sources for plume and puff releases. Their objective was to produce
correlations which predicted the distance to a given concentration level within a factor of two.
Their analysis identified the dominant independent variables as:
•
Density of released COTA after depressurization to atmospheric pressure, ρs;
•
Volumetric rate, E/ρs (or total volume, Et/ρs), of COTA released;
•
Characteristic wind speed, uᵣ (typically taken to be at 10 meters elevation, zᵣ); and
•
Characteristic source dimension, Ds.
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38
Britter-McQuaid Correlations (continued)
Narration (male voice):
Based in part on the fact that presently available field test data for denser-than-air COTAs do
not clearly indicate the importance of these parameters, Britter and McQuaid considered some
independent variables to be of lesser importance; these parameters were not considered in the
correlation, including:
•
•
•
Surface roughness;
Atmospheric stability; and
Exact source dimensions.
Many models for denser-than-air behavior indicate that these parameters are important.
Other effects were not included in the analysis, including dilution due to source momentum and
condensation of ambient humidity. However, these effects may be of crucial importance for
COTAs that have a molecular weight less than that of air including, for example, liquefied natural
gas (LNG), ammonia, and hydrogen fluoride.
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39
Britter-McQuaid Correlations (continued)
Narration (male voice):
Britter and McQuaid provide correlations for denser-than-air continuous plumes and
instantaneous puffs released at ambient temperature. The Britter-McQuaid correlations are
limited to concentration levels much higher than needed for many toxic materials, but the
correlations can be used to predict the dispersion near the source with subsequent downwind
dispersion predicted using passive dispersion models. This is accomplished by treating the
release as having a virtual source.
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40
Steps to Find Virtual Source
Narration (male voice):
To find the virtual source:
•
Estimate the distance to the lowest concentration predicted by the Britter-McQuaid
model (call this distance xt as the transition to passive behavior).
•
Next, estimate the distance to the same concentration level using the Pasquill-Gifford
model (call this distance xv as the location of the virtual source if the release were
passive).
•
Finally, calculate the distance from the virtual source to the endpoint concentration
using the Pasquill-Gifford model (call this distance xe).
The distance from the real source to the endpoint concentration is xt + (xe - xv).
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41
Ambient Temperature
Narration (male voice):
Since many materials of practical interest are released below ambient temperature, Britter and
McQuaid provide guidance as to how to predict the limiting cases for such releases. Our
discussion will be limited to COTA clouds that are released at ambient temperature (isothermal
releases).
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42
Britter-McQuaid Plume Model
Narration (male voice):
Now that we have discussed the Britter-McQuaid correlations, let’s explore their plume model.
For plume releases, denser-than-air effects can be important if this expression is true…
…where…
•
•
•
•
•
•
ξc is defined as shown;
g is acceleration due to gravity;
E is mass release rate;
ρs is initial density of the released COTA;
uᵣ is wind speed at 10 meters elevation; and
ρa is ambient air density.
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43
Britter-McQuaid Plume Model (continued)
Narration (male voice):
If denser-than-air effects are important, downwind concentration ‹C›/Cs (or ye for an ambient
temperature ideal gas) is correlated in terms of ξc and ψc, defined as shown…
…where…
•
xe is the estimated downwind distance to concentration ‹C›/Cs (or ye for an ambient
temperature ideal gas).
Values for ξc and ψc are provided on the next two slides.
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44
Britter-McQuaid Plume Model – Chart
Narration (male voice):
Curves for Britter-McQuaid correlations for continuous plume releases are shown here.
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45
Britter-McQuaid Plume Model – Table
Narration (male voice):
This table lists values of ψc as a function of ξc and ‹C›/Cs (downwind concentration) for the
Britter-McQuaid plume model.
Values of ξc should be interpolated from values of ψc for particular values of ‹C›/Cs using log-log
interpolation, but linear interpolation is probably sufficient. For ‹C›/Cs values between those in
the table (or figures shown earlier), linear interpolation is recommended.
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46
Denser-than-Air Stratification Effects
Narration (male voice):
For denser-than-air clouds, the importance of the density stratification effects increase with
increasing values of ξc, so denser-than-air stratification effects are most important when the
release rate is large, the wind speed is low, and the density difference with air is large.
Note that the volumetric release rate, Q = E/ρs, and wind speed, ur, are parameters in both ξc
and ψc, but they are raised to different powers.
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47
Fixed Downwind Distance
Narration (male voice):
At a fixed downwind distance, a passive plume model would predict that ‹C›uᵣ/Q would be
constant (all other things equal), and so decreasing Q/uᵣ by a factor of 2 at a fixed downwind
distance would require ‹C› being reduced by a factor of 2, for example.
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48
Fixed Downwind Distance (continued)
Narration (male voice):
In the passive limit, ψc is independent of ξc, so for a given downwind distance, ψc(Q/uᵣ)1/2 is
constant for different endpoint concentrations, and the values in the table shown previously are
consistent with the limit predicted by a passive plume model.
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49
Britter-McQuaid Plume Model – Chart (continued)
Narration (male voice):
Curves for Britter-McQuaid correlations for continuous plume releases are shown here again. All
of the ‹C›/Cs curves have local maxima for values of ξc.
At values of ξc less than the local maximum, increasing Q1/5/uᵣ beyond the passive limit implies
that the distance to the given concentration level will increase at a greater rate than for a
passive release.
At values of ξc greater than the local maximum, increasing Q1/5/uᵣ implies that the distance to
the given concentration level will increase at a lower rate than for a passive release.
If Q1/5/uᵣ is sufficiently large (all other things equal), the predicted distance to a given
concentration level will be less than that predicted using a passive model. So denser-than-air
effects can increase or decrease the distance to a given concentration level when considering
changes in release rate and wind speed (all other things being equal).
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50
Fixed Downwind Distance (continued)
Narration (male voice):
If only wind speed is varied, the downwind distance to a given concentration level can be
expected to go through a local maximum as the wind speed is decreased. As with a passive
plume model, the wind speed cannot be zero, and model performance is expected to be less
reliable as the wind speed approaches zero (for example, in scenarios involving light and
variable winds).
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51
Factors Affecting Denser-than-Air Effects
Narration (male voice):
Finally, note that changes in wind speed, release rate, and density difference have different
impacts on the importance of denser-than air effects (as reflected in a change in ξc) with wind
speed (-1 power) the most important, followed by density difference (+0.4 power) and release
rate (+0.2 power).
So, denser-than-air effects are more important at smaller wind speeds (most important), higher
density differences (less important), and higher release rates (least important).
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52
Averaging Time
Narration (male voice):
Britter and McQuaid report that the averaging time (tplume) for their plume correlation is 10
minutes. The equation shown should be used with p = 0.12 for other averaging times (and
limited to averaging times no shorter than about 20 seconds as for passive releases).
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53
Britter-McQuaid Puff Model
Narration (male voice):
For puff (short duration) releases, Britter and McQuaid recommend that denser-than-air effects
can be important if this expression is true…
…where…
•
Et is the total COTA mass released.
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54
Britter-McQuaid Puff Model (continued)
Narration (male voice):
If denser-than-air effects are important, downwind concentration ‹C›/Cs (or ye for an ambient
temperature ideal gas) is correlated in terms of ξᵢ and this equation…
…where…
•
xe is the estimated downwind distance to concentration ye.
Values for ξᵢ and ψᵢ are provided in the table on the next slide.
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55
Britter-McQuaid Puff Model – Table
Narration (male voice):
This table lists values of ψᵢ (table entries) as a function of ξᵢ and ‹C›/Cs for the Britter-McQuaid
puff model.
Values of ξᵢ should be interpolated from values of ψᵢ for particular values of ‹C›/Cs using log-log
interpolation, but linear interpolation is probably sufficient. For ‹C›/Cs values between those in
the table, linear interpolation is recommended.
Britter and McQuaid report that the averaging time for their puff correlation is “several seconds.”
Copyright ©American Institute of Chemical Engineers 2019. All rights reserved.
56
Britter-McQuaid Puff Model – Chart
Narration (male voice):
Curves for Britter-McQuaid correlations for instantaneous puff releases are shown here.
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57
Denser-than-Air Stratification Effects
Narration (male voice):
For denser-than-air puffs, the importance of the density stratification effects increase with
increasing values of ξᵢ, so denser-than-air stratification effects are most important when the
release volume is large, the wind speed is low, and the density difference with air is large.
Note that the total volume released (V = Et/ρs) is a parameter in both ξᵢ and ψᵢ, but they are
raised to different powers.
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58
Fixed Downwind Distance
Narration (male voice):
At a fixed downwind distance, a passive puff model would predict that ‹C›/V would be constant
(all other things equal), and so decreasing V by a factor of 2 would result in ‹C› being reduced by
a factor of 2, for example.
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59
Britter-McQuaid Puff Model (continued)
Narration (male voice):
Only the ‹C›/Cs curves with values less than 0.005 do not have local maxima for values of ξᵢ.
At values of ξᵢ less than the local maximum, increasing V beyond the passive limit implies that
the distance to the given concentration level will increase at a greater rate than for a passive
release.
At values of ξᵢ greater than the local maximum, increasing V implies that the distance to the
given concentration level will increase at a lower rate than for a passive release.
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60
Britter-McQuaid Puff Model (continued)
Narration (male voice):
Note that if ξᵢ is sufficiently large, the predicted distance to a given concentration level will
always be greater than that predicted using a passive model for concentration levels above 0.01
(typical of hydrocarbon lower flammability limit [LFL] values). For concentration levels less than
0.002, the predicted distance to a given concentration level will always be less than that
predicted by a passive dispersion model.
So, denser-than-air effects can increase or decrease the distance to a given concentration level
depending on the concentration level under consideration.
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61
Factors Affecting Denser-than-Air Effects
Narration (male voice):
Finally, note that changes in wind speed, release volume, and density difference have different
impacts on the importance of denser-than air effects (as reflected in change in ξᵢ) with wind
speed (-1 power) the most important followed by density difference (+0.5 power) and release
volume (+0.16 power) consistent with the plume model parameterization.
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SECTION 3: Dispersion Modeling with ALOHA
Narration
[No narration]
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Introduction to ALOHA®
Narration (male voice):
In this last section, we’ll introduce the ALOHA® hazard modeling program which can be used to
model plume and puff scenarios. ALOHA® was developed jointly by the U.S. National Oceanic
and Atmospheric Administration (NOAA) and U.S. Environmental Protection Agency (EPA).
The program can estimate how quickly a chemical will escape from a tank, puddle, or gas
pipeline and form a hazardous gas cloud. The software can then model how that cloud will
travel downwind, including both neutrally buoyant and heavy gas dispersion. ALOHA® also
models pool fires, boiling liquid expanding vapor explosions (BLEVEs), vapor cloud explosions
(VCEs), jet fires, and flammable gas clouds (where flash fires might occur).
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64
Threat Zone Estimate
Narration (male voice):
ALOHA® produces a visual threat zone estimate which shows the area where a hazard (such as
toxicity or thermal radiation) is predicted to exceed a user-specified level for that hazard.
The threat zone estimates can be plotted on maps in:
•
•
•
MARPLOT®;
Ersi’s ArcMap (using the ALOHA® ArcMap Import Tool); and
Google Maps and Google Earth (using ALOHA’s KML Export).
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Accessing ALOHA®
Narration (female voice):
Before continuing, you are encouraged to learn more about ALOHA® by clicking the link shown.
From that web page, you can download the free software and try it out.
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66
Steady-state Plume Example
Narration (male voice):
Let’s begin with a steady-state plume example.
In this scenario, a large chlorine vessel is estimated to be leaking 0.4 kilograms per hour. We will
estimate downwind distances to the ERPG-2 and ERPG-1 concentration levels (3 parts per
million and 1 part per million, respectively).
The leak is sufficiently slow so that it can be assumed to be at ambient temperature; without
intervention, the leak could last several hours based on the vessel inventory.
For the purposes of this estimate, atmospheric conditions are based on 2 meters per second
wind speed at an elevation of 10 meters. The atmospheric stability is assumed to be D (worst
case during the day) and F (typically worst case at night).
In the vicinity of the release, the terrain is open and relatively flat.
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67
Steady-state Plume Example (continued)
Narration (male voice):
Let’s consider the information we know about this scenario.
Because the release duration could be several hours, plume behavior is appropriate to describe
this release.
Because the hazards under consideration (ERPG-1 and ERPG-2 with an averaging time of 60
minutes for both) are based on an averaging time much greater than tplume (with an averaging
time of 10 minutes), no averaging time adjustment will be made. Therefore, the equation
presented near the end of Unit 2, used to determine the correction factor for plume model
predictions, is not needed.
Because chlorine has a molecular weight greater than air, this release could require the use of a
denser-than-air dispersion model. The left hand side of this expression (shown earlier in this
unit)…
…is evaluated to be 0.19 so the use of a passive plume model is justified.
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68
Steady-state Plume Example (continued)
Narration (male voice):
Continuing our analysis of what we know, using rural terrain (3 centimeter surface roughness),
this equation…
…is used to predict concentrations as a function of distance as shown in this table (reported to 2
significant digits).
In both of the ERPG level cases, the downwind distance to the concentration levels considered
are roughly three times longer for F stability in comparison to D stability.
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Steady-state Plume Example (continued)
Narration (male voice):
Now suppose that in a subsequent scenario evaluation the estimated release rate is much
higher: 4.0 kilograms per hour. Despite the larger release rate, the release could still continue
for several hours.
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Steady-state Plume Example (continued)
Narration (male voice):
As in the previous example, plume behavior would be recommended for this release because of
the long release duration, and no averaging time adjustment is required because of the end
points of ERPG-1 and ERPG-2.
The left hand side of this equation…
…is evaluated to be 0.30, so use of a denser-than-air COTA model is now appropriate.
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Steady-state Plume Example (continued)
Narration (male voice):
However, the Britter-McQuaid plume model only predicts concentrations to as low as a mole
fraction of 0.002 (2000 parts per million). Using ξc = 0.30, the (ensemble average) chlorine
concentration of 2000 parts per million is predicted to extend to 6.2 meters downwind of the
source using the table.
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Steady-state Plume Example (continued)
Narration (male voice):
To predict the distance to the desired endpoint concentrations, the virtual source distance to
2000 parts per million must be calculated using a passive plume model.
For D stability, the passive plume model distance to reach 2000 parts per million would be 2.5
meters, and 6.8 meters for F stability. This indicates that denser-than-air behavior is predicted
to cause concentrations to be higher near the source than would be predicted by a passive
plume model.
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Steady-state Plume Example (continued)
Narration (male voice):
The virtual source distances of 2.5 meters and 6.8 meters will be used to determine the final
endpoint distance once the passive plume model estimate of distance to the ERPG levels are
determined. The results are shown in the table.
Note that the final predicted distances are in the last two columns and reported to 2 significant
digits (but calculations were carried out to 3 significant digits). As we can see, the impact of the
denser-than-air effects are marginal for the low concentration levels considered here.
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74
Puff Example
Narration (male voice):
Now let’s consider a puff scenario.
In this scenario, sudden failure of a small propane vessel (1.234 cubic meters) occurs. The vessel
is estimated to contain 480 kilograms (20% ullage). For this scenario, we want to estimate
downwind distances to the LFL and ½ LFL concentration levels (2.1% and 1.05% in air on a molar
basis, respectively).
When released, the propane will expand and cool (as in a BLEVE), but for this example, the
depressurized cloud will be assumed to be at ambient temperature (a limiting case where all of
the heat transfer to the cloud occurs at the source).
For the purposes of this estimate, atmospheric conditions are based on 2 meters per second
wind speed at 10 meters elevation. The atmospheric stability level is assumed D (worst case
during the day) and F (typically worst case at night).
In the vicinity of the release, the terrain is open and relatively flat.
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75
Puff Example (continued)
Narration (male voice):
Like we did for the plume example, let’s consider what we know about this scenario.
Because the release duration is instantaneous (sudden failure of the vessel), puff behavior is
appropriate to describe this release (despite this being a relatively large cloud).
The hazards under consideration (LFL and ½ LFL) are based on a short averaging time
comparable to tpuff, so – like the plume example – predicted concentrations will not need to be
corrected for averaging time inconsistencies.
Because propane has a molecular weight greater than air, this release could require the use of a
denser-than-air dispersion model. The left hand side of this expression…
…is evaluated to be 2.9, so the use of the Britter-McQuaid puff model is justified.
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Puff Example (continued)
Narration (male voice):
Along with the table and figure shown for ψᵢ as a function of ξᵢ, the equation shown…
…is used to predict the distance to LFL and ½ LFL as 130 meters and 200 meters, respectively
(reported to 2 significant digits).
As mentioned previously, the Britter-McQuaid correlations were developed without
consideration of atmospheric stability, so the predictions are independent of atmospheric
stability.
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Puff Example (continued)
Narration (male voice):
If the passive puff model had been used, the distances to LFL and ½ LFL are shown in the table
for atmospheric stabilities D and F (to two significant digits). Note that accounting for denserthan-air effects reduces the predicted downwind distance of the flammable gas extent.
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Unit 3 Summary
Narration (male voice):
We’ve reached the end of the third and final unit in the Atmospheric Dispersion course. Having
completed this unit, titled “Atmospheric Dispersion Models,” you should now be able to:
•
Identify the strengths and weaknesses of different atmospheric dispersion modeling
approaches;
•
Simulate example chemical releases using Gaussian and Britter-McQuaid models; and
•
Describe how the ALOHA® hazard modeling software can be used for atmospheric
dispersion modeling.
On the next slide, we’ll take a brief look back at the main topics we covered in this course.
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Course Summary
Narration (male voice):
We covered many topics in this Atmospheric Dispersion course.
In Unit 1, titled “Introduction to Atmospheric Dispersion”…
•
•
•
We defined “atmospheric dispersion;”
We explained why atmospheric dispersion models are useful; and
We identified how atmospheric dispersion is related to familiar topics in chemical
engineering (such as fluid flow, heat transfer, and influence of turbulence on mixing).
In Unit 2, titled “Characterizing the Atmosphere, Release Conditions, and Important Properties
of the Chemical Released,” you learned…
•
•
…how to identify important factors that characterize atmospheric flow and describe
how these parameters impact the dispersion of a Chemical(s) Other Than (humid) Air
(COTA) cloud;
…how to identify characteristics of the material hazard and type of release that are
important to atmospheric dispersion modeling; and
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•
…how to determine the dispersion model averaging time appropriate to assess the
hazard under consideration.
And, as we just summarized on the previous slide, in this final unit you learned…
•
•
•
…how to Identify the strengths and weaknesses of different atmospheric dispersion
modeling approaches;
…how to simulate example chemical releases using Gaussian and Britter-McQuaid
models; and
…how the ALOHA® hazard modeling software can be used for atmospheric dispersion
modeling.
Before closing the course, please take the Unit 3 quiz. The quiz introduction is on the next slide.
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