1

DCMH.CH4051_Process Safety
Dispersion Models

Prepared by:

Dr. Mardhati Zainal Abidin

Universiti Teknologi PETRONAS

AP Ir. Dr. Risza Rusli

University of Doha for Science & Technology

For:
Ho Chi Minh City University of Technology
Course Learning Outcomes

After completing this chapter, students should be able to do the following:

 Understand air dispersion and the parameters are required to describe it.
 Estimate downwind concentrations of toxic material using dispersion model

 Predict impact/effect due to the released of materials

 Apply hazardous material release prevention and mitigation
 Consequences Analysis Procedure
Loss of containment
•Rupture or break in pipeline
Selection of a Release Incident •Hole in a tank or pipeline
•Runaway reaction
To describe release accident •Fire external to vessel
•Total quantity released Selection of a Source Model
•Release duration
Neutrally buoyant models
•Release rate
Results from the models
Selection of a Dispersion Model
•Downwind concentration
•Area affected
•Duration
Models Flammable/Toxic
•TNT Equivalency Flammable
•Multi-Energy Explosion Toxic •Response vs dose
•Fireball •Probit model
Results Selection of Fire Selection of •Toxic response
•Blast overpressure & Explosion Model Effect Model •No. of individuals affected
•Radiant heat flux •Property damage
•Escape
•Emergency Response Mitigation Factors
•Containment dikes
•PPE
Consequence Model
Introduction

 Dispersion models describe the airborne transport of toxic materials away

from the accident site and into the plant and community.
 After a release, the airborne toxic is carried away by the wind in a
characteristic plume or a puff
 The maximum concentration of toxic material occurs at the release point
(which may not be at ground level).
 Concentrations downwind are less, due to turbulent mixing and dispersion
of the toxic substance with air.

Wind →
 Mixing with fresh air →
 Introduction

Plume Puff

Wind →
Dispersion Model

What?

• Describe how vapors are transported downwind of a release. Valid

between 100 m to 10 km.
• Below 100 m, use ventilation equations Chapter 3.
• Above 10 km → almost unpredictable

Why?

• To estimate the effects of a release on the plant and community

Result

• Downwind concentrations (x,y,z)

• Area affected
• Downwind evacuation distances
Factors Influencing Dispersion

As the wind speed increases, the plume becomes longer and

Wind speed narrower

Vertical temp. profile, primarily a function of wind speed.

Atmospheric During the day the air temperature decreases rapidly with the
stability height, encouraging vertical motions. Oppositely, at night the
air temperature decrease is less

Structure : Affect the mechanical mixing at the surface and

Roughness the wind profile with height. Trees and buildings increase
ground/conditions mixing while lakes (water) and open areas decrease mixing

As the release height increases, the ground level

Height of release concentrations are reduced since the plume must disperse a
above ground level greater distance vertically

Change the effective height of the release. The momentum

Momentum and of a high-velocity jet will carry the gas higher than the point of
buoyancy release, resulting much higher effective release height.
Atmospheric
10
Stability
Atmospheric
11
Stability
Effect of Ground Conditions

Figure 4 Effect of ground conditions on vertical wind gradient

Ground conditions (buildings, water, trees)

• Affect the mechanical mixing at the surface and the wind profile with height
• Trees and buildings increase mixing while lakes and open areas decrease
mixing
Effect of Release Height

Figure 5 Increased release height decreases the ground concentration.

As the release height increases, the ground level concentrations are

reduced since the plume must disperse a greater distance vertically
Release
14
Momentum and Buoyancy
Dispersion Models

 Dispersion models are based on a mass balance.

 Two approaches:
The Coordinate System used for Dispersion Models
Dispersion Models

◼ Cases 1 – 10 all depend on the availability of Kj

◼ Kj changes with position, time, wind velocity, and weather conditions. It
is difficult to get the experimental value of Kj
◼ Alternative solution was suggested by Sutton by using a dispersion
coefficient

1
𝜎𝑥2 = ⟨𝐶⟩2 𝑢𝑡 2−𝑛
2

◼ Similar expressions given for σy and σz

◼ Values for the σ are a function of atmospheric conditions and the
distance downwind from the release
◼ The atmospheric conditions are classified according to six different
stability classes as shown in Table 5-1.
◼ The σy and σz for continuous source are given in Table 5-2 or
alternatively available in Figure 5-10 and 5-11.
◼ σx can be assumed as equal to σy
 Dispersion Models - Pasquill-Gifford Models
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Table 5-1 Atmospheric Stability Classes for Use with the Pasquill-
Gifford Dispersion Model (Crowl & Louvar, pg 197)

Wind Day radiation intensity Night cloud cover

speed Calm &
(m/s) Strong Medium Slight Cloudy
clear
<2 A A–B B F F

2–3 A–B B C E E

3–5 B B–C C D E

5–6 C C–D D D D

>6 C D C D D

A : Extremely unstable D : Neutrally stable

B : Moderately unstable E : Slightly stable
C : Slightly unstable F : Moderately stable

Open
Dispersion Models - Pasquill-Gifford Models

(Crowl & Louvar, pg 198)

Dispersion Coefficients for Plume
Dispersion coefficients for plume model for
rural releases.
Dispersion Coefficients for Plume
Dispersion coefficients for plume model for
urban releases
Dispersion Models - Pasquill-Gifford Models
◼ The σ y and σ z for a puff release are given in Table 5-3 (Crowl & Louvar, pg
199).
Dispersion Coefficients for Puff
Dispersion coefficients for puff model
Dispersion Models - Pasquill-Gifford Models

Case 11: Puff with instantaneous point source at ground level, coordinates fixed at
release point, constant wind only in x direction with constant velocity u

 Identical to case 7

∗ 2
𝑄𝑚 1 𝑥 − 𝑢𝑡 𝑦2 𝑧2
𝐶 𝑥, 𝑦, 𝑧, 𝑡 = exp − + 2+ 2
2 𝜋 3/2 𝜎𝑥 𝜎𝑦 𝜎𝑧 2 𝜎𝑥 𝜎𝑦 𝜎𝑧

 Ground level concentration is given at z = 0

∗ 2
𝑄𝑚 1 𝑥 − 𝑢𝑡 𝑦2
𝐶 𝑥, 𝑦, 0, 𝑡 = exp − + 2
2 𝜋 3/2 𝜎𝑥 𝜎𝑦 𝜎𝑧 2 𝜎𝑥 𝜎𝑦

 Ground level concentration along the x-axis, y = z = 0

∗ 2
𝑄𝑚 1 𝑥 − 𝑢𝑡
𝐶 𝑥, 0,0, 𝑡 = exp −
2 𝜋 3/2 𝜎 𝜎 𝜎
𝑥 𝑦 𝑧 2 𝜎𝑥
Dispersion Models - Pasquill-Gifford Models
Case 12: Plume with continuous steady-state source at ground level and
wind moving in x direction at constant velocity u

 Identical to case 9
𝑄𝑚 1 𝑦2 𝑧2
𝐶 𝑥, 𝑦, 𝑧 = exp − +
𝜋 𝜎𝑥 𝜎𝑦 𝑢 2 𝜎𝑦2 𝜎𝑧2

 Ground-level concentration, z = 0
2
𝑄𝑚 1 𝑦
𝐶 𝑥, 𝑦, 0 = exp −
𝜋 𝜎𝑥 𝜎𝑦 𝑢 2 𝜎𝑦

 Concentration along the centerline of the plume directly downwind , y

=z=0

𝑄𝑚
𝐶 𝑥, 0,0 =
𝜋 𝜎𝑥 𝜎𝑦 𝑢
Dispersion Models - Pasquill-Gifford Models
Case 13: Plume with Continuous steady-state source at height Hr above
ground level and wind moving in x direction at constant velocity u

 Identical to case 10
2
𝑄𝑚 1 𝑦
𝐶 𝑥, 𝑦, 𝑧 = exp − ×
2𝜋 𝜎𝑦 𝜎𝑧 𝑢 2 𝜎𝑦
2 2
1 𝑧 − 𝐻𝑟 1 𝑧 + 𝐻𝑟
exp − + exp −
2 𝜎𝑧 2 𝜎𝑧

 Ground level concentration, z = 0

2 2
𝑄𝑚 1 𝑦 1 𝐻𝑟
𝐶 𝑥, 𝑦, 0 = exp − −
𝜋𝜎𝑦 𝜎𝑧 𝑢 2 𝜎𝑦 2 𝜎𝑧
Dispersion Models - Pasquill-Gifford Models

Case 13: Plume with continuous steady-state source at height Hr above

ground level and wind moving in x direction at constant velocity, u.
 Simplified Cases - Plume
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 Maximum Concentrations - Plume
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Dispersion Models - Pasquill-Gifford Models

Case 14: Puff with instantaneous point source at height Hr above ground
level and a coordinate system on the ground that moves with the puff

 The center of the puff is found at x = u t.

∗ 2
𝑄𝑚 1 𝑦
𝐶 𝑥, 𝑦, 𝑧, 𝑡 = exp − ×
2𝜋 3/2𝜎𝑥 𝜎𝑦 𝜎𝑧 2 𝜎𝑦
2 2
1 𝑧 − 𝐻𝑟 1 𝑧 + 𝐻𝑟
exp − + exp −
2 𝜎𝑧 2 𝜎𝑧

 Ground level concentration, z = 0

∗ 2 2
𝑄𝑚 1 𝑦 1 𝐻𝑟
𝐶 𝑥, 𝑦, 0, 𝑡 = exp − −
2𝜋 3/2 𝜎𝑥 𝜎𝑦 𝜎𝑧 2 𝜎𝑦 2 𝜎𝑧
Dispersion Models - Pasquill-Gifford Models
Case 14: Puff with instantaneous point source at height, Hr above ground
level and a coordinate system on the ground that moves with the puff.

 Ground level centerline concentration, y = z = 0

∗ 2
𝑄𝑚 1 𝐻𝑟
𝐶 𝑥, 0,0, 𝑡 = exp −
2𝜋 3/2 𝜎𝑥 𝜎𝑦 𝜎𝑧 2 𝜎𝑧

 The total integrated dose at ground level

∗ 2 2
𝑄𝑚 1 𝑦 1 𝐻𝑟
𝐷𝑡𝑖𝑑 𝑥, 𝑦, 0 = exp − −
𝜋𝜎𝑦 𝜎𝑧 𝑢 2 𝜎𝑦 2 𝜎𝑧
Dispersion Models - Pasquill-Gifford Models
Case 15: Puff with instantaneous point source at height Hr above ground level
and a coordinate system fixed on the ground at the release point

 The center of the puff is found at x = u t.

∗ 2
𝑄𝑚 1 𝑦
𝐶 𝑥, 𝑦, 𝑧, 𝑡 = exp − ×
2𝜋 3/2 𝜎𝑥 𝜎𝑦 𝜎𝑧 2 𝜎𝑦
2 2 2
1 𝑧 − 𝐻𝑟 1 𝑧 + 𝐻𝑟 1 𝑥 − 𝑢𝑡
exp − + exp − × exp −
2 𝜎𝑧 2 𝜎𝑧 2 𝜎𝑥

 Ground level concentration, z = 0

∗ 2 2 2
𝑄𝑚 1 𝑦 1 𝐻𝑟 1 𝑥 − 𝑢𝑡
𝐶 𝑥, 𝑦, 0, 𝑡 = exp − − × exp −
2𝜋 3/2 𝜎𝑥 𝜎𝑦 𝜎𝑧 2 𝜎𝑦 2 𝜎𝑧 2 𝜎𝑥
 Dispersion Models - Pasquill-Gifford Models

Case 15: Puff with instantaneous point source at height Hr above ground level
and a coordinate system fixed on the ground at the release point

 Ground level centerline concentration, y = z = 0

∗ 2 2
𝑄𝑚 1 𝐻𝑟 1 𝑥 − 𝑢𝑡
𝐶 𝑥, 0,0, 𝑡 = exp − × exp −
2𝜋 3/2𝜎𝑥 𝜎𝑦 𝜎𝑧 2 𝜎𝑧 2 𝜎𝑥

Open
34 Puff
35 Simplified Cases - Puff
Location of Puff

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 Maximum Concentration - Puff
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Guidelines
Puff and  If release given in mass / time → Plume

Plume  If release given as a fixed mass → Puff

 If mass is released over a period of time
equal to or less than 10 minutes → Puff
 Plume Cmax = release position
 Puff Cmax = centre of cloud
 If atmosphere conditions not known,
assume worst case for highest C.
 Most chemical plants are located in the
country, so default condition is rural.
Example 5-1

10 kg/s of H2S is released 100 m off of ground. Estimate the

concentration 1 km downwind on ground? It is a clear, sunny day,
1 PM, wind speed = 3.5 m/s. Assume rural conditions. Find the
maximum concentration of the release.

39
Applies to ground concentration directly downwind of release, Eq 5-51

2
𝑄𝑚 1 𝐻𝑟
𝐶 0,0,0 = exp −
𝜋𝜎𝑦 𝜎𝑧 𝑢 2 𝜎𝑧
2
10 kg/s 1 100𝑚
𝐶 0,0,0 = exp −
𝜋 130𝑚 (120𝑚)(3.5𝑚/𝑠) 2 120𝑚

𝐶 0,0,0 = 41.2 𝑥10 − 6 g/m3

Use Equation 2-7 to get 29.7 ppm. TLV-TWA is 10 ppm.

40
Where is max. concentration?

Use Equation 5-53:

𝐻𝑟 100 m
(𝜎𝑧 )𝑚𝑎𝑥 = = = 70.7 m
2 2

Use equation in Table 5-3 to determine downwind distance:

𝜎𝑧 = 0.12𝑥
70.7𝑚 = 0.12𝑥
𝑥=589.12 m

At this location, from Figure 5-10:

𝜎𝑦 = 92 𝑚
Equation 5-52 to calculate max. concentration:
What is max. discharge to result in 10 ppm?
 Example 5-2

10 kg of H2S is released instantly on the ground. What is concentration

at fence line 100 m away? Same conditions as before.

44
Example 5-2

45
 Example 5-2

How long does it take for puff to reach fenceline?

What size release will result in 10 ppm at fenceline?

Same procedure as for plume.
Answer is 0.175 kg = 175 gm.
Conclusion about releases:
Don’t release it in the first place!
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 Pasquill-Gifford Models

◼ Limitations to Pasquill-Gifford Model or Gaussian dispersion

◼ Applies only to neutrally buoyant dispersion of gases in which the
turbulent mixing is the dominant feature of the dispersion.
◼ Typically valid for a distance of 0.1-10 km from the release point.
◼ The predicted concentrations are time average.
◼ It is possible for instantaneous local concentrations to exceed the
average values predicted and may vary as much as a factor of 2
compared to Gaussian models
◼ The models presented here assumed 10-minute time average
 Toxic Effect Criteria

The dispersion calculation are completed & hence: What concentration is

considered dangerous?

TLV-TWA is for worker exposures, and not design for short- term exposures
under emergency conditions.

Recommended method by Environmental Protection Agency (EPA) is by

using emergency response planning guidelines (ERPGs) for air
contaminants issued by the American Industrial Hygiene Association (AIHA)
Emergency Response Planning Guidelines (ERPGs)
Three concentration ranges are provided as a consequence of exposure to a specific
substance:

Maximum airborne concentration below which it is

believed nearly all individuals could be exposed for up
ERPG-1 to 1 hr without experiencing effects other than mild
transient adverse health effects or perceiving a clearly
defined objectionable odor.

Maximum airborne concentration below which it is

believed nearly all individuals could be exposed for up
ERPG-2 to 1 hr without experiencing or developing irreversible
or other serious health effects or symptoms that could
impair their abilities to take protective action.

Maximum airborne concentration below which it is

believed nearly all individuals could be exposed for up
ERPG-3 to 1 hr without experiencing or developing life-
threatening health effects.
Examples of ERPGs in unit ppm

ERPG-1 ERPG-2 ERPG-3

Acetaldehyde 10 200 1000
Acrolein 0.1 0.5 3
Vinyl Acetate 5 75 500
Realistic and Worst-Case Releases

 Realistic releases represent the incident outcomes with a high

probability of occurring

 Worst-case releases are those that assume almost catastrophic failure

of the process, resulting in near instantaneous release of the entire
process inventory or release over a short period of time
 The worst-case releases must be used to determine the consequences
study required by EPA Risk Management Plan

 Table 4-5 lists a number of realistic and worst-case releases.

Realistic and Worst-Case Releases
Realistic and Worst-Case Releases
 Release Mitigation

The purpose of the toxic release model is to provide a tool for performing
release mitigation.
Release mitigation is defined as “lessening” the risk of a release incident by
acting on the source (at the point of release) either:
1. in a preventive way by reducing the likelihood of an event which could
generate a hazardous vapour cloud; or
2. in a protective way by reducing the magnitude of the release and/or
the exposure of local persons or property.

Open
 Release Mitigation
The release mitigation design procedure is shown as below:

Open
 Release Mitigation

Best: prevent the accident leading to the release.

In the event of an accident. Release mitigation involves -
1. Detecting the release as quickly as possible;
2. Stopping the release as quickly as possible; and
3. Invoking a mitigation procedure to reduce the impact of the release on the
surroundings.
Once a release is in vapour form, the resulting cloud is nearly impossible to
control. Thus, an emergency procedure must strive to reduce the amount of
vapour formed.
Table 4 provides additional methods and detail on release mitigation
techniques.

Open
 Release Mitigation

Table 4 Release mitigation approaches

Major Area Examples

Inventory reduction: Less chemicals
inventoried or less in process vessels.
Chemical substitution: Substitute a less
Inherent Safety hazardous chemical for one more
hazardous.
Process attenuation: Use lower temperatures
and pressures.
Plant physical integrity: Use better selas or
materials of construction.
Process integrity: Insure proper operating
Engineering Design conditions and material purity.
Process design features for emergency
control : Emergency relief systems.
Spill containment: Dikes and spill vessels.

Open
 Release Mitigation

Table 4 Release mitigation approaches

Major Area Examples

Operating policies and procedures.
Training for vapor release prevention and
control.
Audits and inspections.
Management Equipment testing.
Maintenance program.
Management of modifications and changes to
prevent new hazards.
Security.
Early Vapor Detection Detection by sensors.
and Warning Detection by personnel.

Open
 Release Mitigation

Table 4 Release mitigation approaches

Major Area Examples

Water sprays.
Water curtains.
Steam curtains.
Countermeasures Air curtains.
Deliberate ignition of explosive cloud.
Dilution.
Foams.
On-site communications.
Emergency shutdown equipment and
procedures.
Site evacuation.
Emergency Response Safe havens.
Personal protective equipment.
Medical treatment.
On-site emergency plans, procedures,
training and drills.

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Reference

Crowl, D. A. and Louvar, J. F., Chemical Process Safety: Fundamentals with

Applications, Prentice Hall, 3rd Edition, 2011.