Toxic Release And Dispersion Models

Toxic Release and Dispersion
Models
Gausian Dispersion Models

Dispersion Models
Practical and Potential Releases
Pasquil-Gifford Models
Stability classes
Dispersion coefficients
Plume Model
Puff
Integrated dose
Isopleths
Release Mitigation
Example

During an accident process equipment can
release toxic materials very quickly.
Explosive rupture of a process vessel due to
excess pressure
Rupture of a pipeline with material under high
pressure
Rupture of tank with material above boiling point
Rupture of a train or truck following an accident.

Identify the Design basis
What process situations can lead to a release, and
which are the worst situations
Source Model
What are the process conditions and hence what
will the state of the release and rate of release
Dispersion Model
Using prevailing conditions (or worst case)
determine how far the materials could spread

Types of Dispersion Models
Plume models were
originally developed
for dispersion from a
smoke stack.
In an emergency if
there is a leak in a
large tank then a
plume can develop.

Types of Dispersion Models
Puff models are
used when you have
essentially an
instantaneous
release and the
cloud is swept
downwind.
No significant plume
develops

Pasquil-Gifford Dispersion Models
Because of fluctuations and turbulence the
eddy diffusivity is constantly changing and
traditional transport phenomena equations
don’t do a good job of predicting dispersion.

Solution is to assume that the materials
spread out in a normal Gausian-type
distribution.

For a plume the
instantaneous value is
different then the
average.
Develop correlations to
predict the average
concentration profile

As the plume is
swept downwind,
the concentration
profile spreads out
and decreases

Have “dispersion
coefficients” defined in
the direction of the
wind, in a cross wind
direction and with
elevation.
These coefficients are
correlated for six
different stability
classes.

Table 5-2 gives the six stability classes to be
used in the Pasquil-Gifford models.
For a given set of conditions, you can determine
which stability class to use.
Figure 5-10 and Figure 5-11 give the
dispersion coefficients for as a function of
distance downwind from release for Plume
Models

Plume Model Dispersion Coefficients

Puff Model Dispersion Coefficients
σx =σy
Unstable − > log10 σ y = − 0.84403 + 0.992014 log10 ( x )
Neutral − > log10 σ y = 0.006425 + 0.297817 log10 ( x )
Stable − > log10 σ y = − 1.67141 + 0.892679 log10 ( x )

Unstable − > log10 σ z = − 0.27995 + 0.72802 log10 ( x )
Neutral − > log10 σ z = − 0.8174 + 0.698592 log10 ( x )
Stable − > log10 σ z = − 1.33593 + 0.605493log10 ( x )

Plume Model
Assumes plume has developed, hence it
is continuous. Thus there is no
“dispersion coefficient”, σx, in the
direction of flow (direction of the wind)

Plume Model
&
Qm  1  y 2 
< C > ( x, y , z ) = exp  −   
2πσ yσ z u  2 σ y  
   

  1  z − Hr 2   1  z + Hr  2  

× exp  −    + exp  −   

  2 σz  
   2  σ z  
 

Equation 5-49 is complete plume model
Can simplify as needed

Plume Model
Reason for last term
in the expression is
that as the gaseous
plume is dispersed
eventually you get
reflection back off of
the ground

Plume Model - Simplifications
If you a particulate or something that
will react with the ground, then you
remove “reflection” term
&
Qm  1  y 2 
< C > ( x, y , z ) = exp  −   
2πσ yσ z u  2 σ y  
   

  1  z − Hr 2   
× exp  −   

  2  σ z  
 

Plume Model - Simplifications
If your source is at ground level Hr is
zero. Note the two terms add to two.
Results in Eq. 5-46

&
Qm  1  y2 z 2 
< C > ( x, y , z ) = exp  −  2 + 2  
πσ yσ z u  
 2  σ y σ z 


Puff Models
Often in accidents, the releases are
essentially instantaneous and no plume
develops. Need to use a different dispersion
model that is based on a puff.
Now need to have “dispersion coefficient” in
the wind direction. However, assume it is the
same as in the cross wind (y) direction.
Dispersion coefficients only defined for three
stability classes (Unstable, Neutral, Stable).
See bottom of Table 5-2.

Puff Model – Puff at height Hr
Eq. 5-58 describes dispersion
Qm  1  y 2 
< C > ( x, y , z ) = exp  −   
 2 σ y  
3
(2π ) 2 σ xσ yσ z    

  1  z − Hr 2   1  z + Hr 2  

× exp  −    + exp  −   

  2 σz  
   2  σ z  
 
 1  x − ut 2 
× exp  −   
 2 σx  
 

Puff Model - Simplification
Ground level source. Eq. 5-38

  x − ut 2  y 2  z 2  
Qm  − 1 
< C > ( x, y , z ) = exp  +   +   
 2  σ x   σ y   σ z   
3
2π 2σ xσ yσ z     

Puff Model-Simplification
Coordinate system moves along with
puff. Eq. 5-54
Qm  1  y 2 
< C > ( x, y , z ) = exp  −   
 2 σ y  
3
(2π ) σ xσ yσ z
2
   

  1  z − Hr 2   1  z + Hr 2  

× exp  −    + exp  −   

  2 σz  
   2  σ z  
 

Integrated Dose
When a person is standing in a fixed
location and a puff passes over, he/she
receives a dose that is the time integral
of the concentration.
∞
Dtid ( x, y , z ) = ∫ < C > ( x, y , z, t )dt
0

Integrated Dose
For person on ground at distance y
cross wind, Eq. 5-43
Qm  1 y2 
Dtid ( x, y ,0) = exp  − 2 
πσ yσ z u  2σ 
 y 

For person on ground at centerline of
flow, Eq. 5-44
Qm
Dtid ( x,0,0) =
πσ yσ z u

Isopleths
An isopleth is a three dimensional
surface of constant concentration.
Calculated by
Specify desired <C>desired, u and t
Find concentration along x axis at that t
<C>(x,0,0,t) to define boundaries and
points along centerline
At each point to be evaluated find y using
equation 5-45.

Isopleths
Equation 5-45 makes more sense if you
write it as follows
 < C > ( x,0,0, t ) centerline 
y =σy 2 ln  
 < C > ( x, y ,0, t ) desired 

Comparison of Plume & Puff Models
Puff model can used for continuous calculations by representing
a plume as a succession of puffs.
Number of Puffs, n
t Continuous Leak
n=
tp Q =Q t&
m m p

Time to form Puff , t p
H eff Instantaneous Leak Into Smaller Puffs
tp =
u (Qm )total
Qm =
Effective Height, H eff n
H eff = (Leak Height) × 1.5

Effective Release Height
Both the Plume and Puff us d  −3  Ts − Ta  
∆H r = 1.5 + 2.68 × 10 Pd  
model utilizes an effective u   Ts  
release height, Hr.
This is caused the ∆H r = additional effective height, m
momentum and buoyancy us = stack velocity, m/s
For release from a stack d = release (stack) diameter, m
u = wind speed, m/s
P = atmospheric pressure, mbar
Ta = air temperature, K
Ts = release gas temperature, K

Release Mitigation
Utilize toxic release
models as a tool for
release mitigation.
Make changes in
process, operations
or emergency
response scenarios
according to results.

Release Mitigation
Inherent Safety Management
Inventory reduction Policies and procedures
Chemical substitution Training for vapor release
Process attentuation Audits & inspections
Engineering Design Equipment testing
Physical integrity of
Routine maintenance
seals and construction
Process integrity Management of change
Emergency control Security
Spill containment

Release Mitigation
Early Vapor Detection Emergency Response
Sensors On-site communications
Personnel Emergency shutdown
Site evacuation
Countermeasures
Safe havens
Water sprays and PPE
curtains
Medical treatment
Steam or air curtains On-site emergency plans,
Deliberate ignition procedures, training &
Foams drills

Solution
Assume point source –plum develops
x = 3 km
Overcast night
u=7 m/s
Table 5.2 -> Stability class D
&
Qm  1  y2 z 2 
< C > ( x, y , z ) = exp  −  2 + 2  
πσ yσ z u  2  σ y σ z 
  

Solution
Ground level concentration, z=0
Centerline, y=0 & Qm
< C > ( x,0,0) =
πσ yσ z u

σ y = 0.128 x.90 = 0.128(3000).9 = 172m
log10 σ z = −1.22 + 1.08log10 x − 0.061(log10 x )2
log10 σ z = −1.22 + 1.08log10 (3000) − 0.061(log10 3000)2
log10 σ z = 1.80
σ z = 63m

Solution

< C > (3000,0,0) =
( s)
3g
= 1.26 × 10−5 g m3
(
π (172m )(63m ) 7 m s )

Toxic Release And Dispersion Models

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