Neutrally Buoyant Gas Dispersion

By: Khaldoon AlObaidi

Supervisor: Dr. Simon P. Waldram

Abstract

The main purpose of this project was to investigate the characteristics of dispersion of gases with

a density close to that of air. Specifically, this study focuses on the change in concentration of a

release within a defined geometric space and for specific conditions. The calculations in this

project are based on Pasquill-Gifford model of gas dispersion. For these calculations, the data is

generated using Excel sheets and using the Cave facility that is located at Texas A&M-Qatar.

The results that are obtained from this project give valuable information that is required for risk

assessments in cases of gas release. There is an assumption made that all gases mentioned are

neutrally buoyant gases while in fact that they are not, like Chlorine is heavier than air. Also, all

the cases are worked out when the wind is in the direction of the people (worst case scenario).

Introduction

Gas is a state of matter, consisting of a collection of particles (molecules, atoms, ions,

electrons, etc.) without a definite shape or volume that is in more or less random motion. In

gases, there is a very weak attractive force between the particles. This makes the particles

normally greatly separated. Different gases have different types of intermolecular forces,

different sizes of particles, and different densities. Thus, different gases will diffuse and disperse

at different rates. As it is clear, some gases are toxic that could harm people and/or the

environment. Many industries need to use such gases in their processes. These industries need to

anticipate various types of failures and ensure that their facilities will not create undue risk

during such eventualities. Gas leaks from pressurized containers will be one such failure. So, the

release of toxic gases is an important issue to study because it impacts directly on the lives of

people nearby. Different models have been developed for the study of gas dispersion: all of them

consider the conditions that may have an effect on the dispersion of the gas. These models are

considered as important tools to generate data about the severity of the release and its effect on

personnel and the surrounding environment. By determining the shape and the volume of the

cloud of the release, some risk assessments can be made. Specifically, from these models, the

places with concentration that may cause harm to the people and the environment can be

specified. Also, the direction of evacuation can be determined based on the direction of increase

in the concentration of the cloud. As for the conditions that affect the model predictions, they

are: the atmospheric stability, the buoyancy of the gas, the mass of the release, and the wind

velocity profiles. Model predictions also provide valuable information which, coupled with

results from investigative analysis of previous release incidents, could be used to generate

emergency response plans in case such incidents occur.

One of these models is the Pasquill-Gifford model which is a classic Gaussian plume/puff

model that was generated originally for smokestack emissions2. This model states that: “for

steady emissions of a chemical that has a density close to that of air, over a relatively level

terrain, if there are no chemical sinks in the air (no chemical reactions are degrading the

chemical) and there is unlimited mixing height (no atmospheric inversion exits, and the plume

can be mixed upward indefinitely)”, then the governing equation is:

𝜕 < 𝐶 >

𝜕𝑡+< 𝑢𝑗 >

𝜕 < 𝐶 >

𝜕𝑥𝑗=

𝜕

𝜕𝑥𝑗(𝐾𝑗

𝜕 < 𝐶 >

𝜕𝑥𝑗)

Where: <C> = the average concentration of the chemical in the air.

<uj> = is the average velocity.

Kj = eddy diffusivity with units of area/time

“Although eddy diffusivity approach is useful theoretically, it is no convenient

experimentally and does not provide a useful framework for correlation. Since Kj changes with

position, time, wind velocity, and prevailing weather conditions, new terms were introduced to

solve this difficulty by Sutton”1. These terms are defined as the standard deviation of horizontal

distribution (y) and vertical distribution (z) of pollutant concentration. Both y and z are

themselves functions of x, the distance downwind from the gas release point when the x axis is

aligned with the wind direction. In this project, the release of neutral buoyant gases is studied

and thus the calculations are based on Pasquill-Gifford model of gas dispersion.

Pasquill-Gifford model

Most of the gas dispersion models, the Pasquill-Gifford model is one of them, include a

rank of the atmospheric stability on a scale of 1 to 6 (or letters A through F). In this ranking, “1”

or “A” ranking represents the most unstable air condition (resulting from daytime solar heating

of the ground, and little wind). Rankings 2 and 3 (B and C) represent intermediate daytime

conditions. Ranking 4 or D represents a neutral condition. Ranking 5 or E represents a stable

condition (near sunset or sunrise or at night). Ranking 6 or F represent the most stable condition.

Table 1 below shows Pasquill-Gifford stability index.

Pasquill-

Gifford

Dispersion

Class

Description Surface wind speed and cloud cover

Wind measured at 10 meter height

A very unstable Daytime; strong insulation and wind < 3 m/s or

moderate insulation and wind < 2 m/s

B unstable daytime; strong insulation with wind between about 3

and 5 m/s or moderate insulation with wind between 2

and 4 m/s or slight insulation and wind < 2 m/s

C slightly unstable daytime; strong insulation and wind > 5 m/s or

moderate insulation with wind between 4 and about

5.5 m/s or slight insulation and wind between 2 and 5

m/s

D neutral All overcast sky conditions, day or night; daytime

and moderate insulation and wind> 5.5 m/s; daytime

and slight insulation 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

E slightly stable nighttime; thin overcast or > 50% cloud cover and

wind < 3 m/s; < 50% cloud cover and wind between

3 and 5 m/s

F stable nighttime; < 50% cloud cover and wind < 3 m/s

Table 1, Pasquill-Gifford Stability Index.3

Where: 1. Strong solar insulation is defined as solar elevation angle > 60o.

2. Moderate solar insulation: solar angle between (and including) 15o and 60o.

3. Slight solar insulation: solar angle < 15o.

In the original papers for this mode, some graphs were introduced to show the relations

between the parameters of the general equation. Figure 1 below represents the relation between

the distance and the vertical spread and the angular lateral spread for a source in open country.

Figure 1, Tentative estimates of vertical spread (h 2.15z) and angular lateral spread ( = 4.3

y/x) for a source in open country (From Pasquill, 1974).

Another graph that was introduced is figure 2 which shows the relationship between the

downwind distance and the lateral dispersion coefficient y.

Figure 2, Lateral diffusion coefficient, y, versus downwind distance for Pasquill-Gifford

turbulence types (from Gifford, 1976).

The third graph that was introduced in this model represents the relationship between the

downwind distance and the vertical diffusion coefficient.

Figure 3, Vertical diffusion coefficient, z, versus downwind distance for Pasquill-Gifford

turbulence types (from Gifford, 1976).

Additionally, for these parameters a numerical equation was introduced for each atmospheric

stability case to calculate the values of the vertical and lateral diffusion coefficients. These

graphs are available in Crowl/Louvar. Chemical Process Safety Fundamentals with Applications.

The Model of This Project

The model prepared in this project is a simple software model built on concepts utilized

in the Pasquill-Gifford model of neutrally buoyant gas releases. This model helps to determine

the effect of different variables affecting a neutrally buoyant gas release, e.g. of carbon

monoxide, whether the release is a “plume” (i.e. continuous) or a “puff”, (effectively

instantaneous), whether it occurred under daytime or nighttime conditions and whether it was

within an urban or rural area. Concepts used to develop the model were procured from the

Crowl/Louvar Chemical Process Safety Book, utilizing equations from chapters 2 and 5,

especially those related to cases 13 and 15 in chapter 5, which would allow for a generalized

approach to releases of gases with density close to that of air under a wide variety of conditions1.

In addition, the model takes into account the Holland formula for release height correction,

where the additional height resulting from the buoyancy and momentum of the release is

calculated 1.

The most important parameter in the Pasquill-Gifford model is the distance downwind

where the cloud has been diluted enough through mixing, to produce a concentration below the

threshold limit value-time weighted average (TLV-TWA) or the OSHA PEL(permissible

exposure level). This would enable emergency response planners to generate isopleths whose

contours have a concentration below the TLV-TWA and would allow for consideration of the

effects of the atmospheric stability conditions, wind speed and direction, amount of gas released,

the height at which the release occurs and the time dependence of the release system. This would

provide valuable information for engineers interested in determining how far away from urban

areas should a gas handling facility be built, as well as determining the best possible route for

evacuation in case of an emergency.

To use the model, the user needs to initially input the release characteristics, represented

by the letters PD for plume release during day, PN for plume release during night, FD for puff

release during day, and FN for puff release during night. The model uses SI units in its

calculations. The next step for the user is to determine the distance downwind, represented by the

x direction if a one-dimensional model is required, or input the distance in the y direction, and z

direction if a higher-dimensional model is required. The user is then required to specify the

height at which the release occurs, the wind speed, and the mass flow rate of the release in the

case of a plume release, or the mass of gas released in the case of a puff release. For the puff

case, the user has to input the time period over which the release is expected to occur, which is

usually in the order of seconds to a few minutes. For all cases, the pressure and temperature of

the release area have to be specified and added to the model. The model will directly determine

the atmospheric stability case, calculate the Pasquill-Gifford dispersion coefficients as a function

of x distance, and determine the concentration at a given point for rural and urban areas. Other

variables that could be investigated by the model involve the calculation of the probability of

causing harm or death at a specific location (e.g. in a hospital, school or shopping mall) under

different conditions. The model is capable of accepting a rough estimate of the number of people

in a given region, as well as the time of exposure to the gas. The model will directly calculate the

probit variable (Y), probability of death (or toxic effect), and the number of people expected to

die as a result of a specific gaseous release. Of course the two constants for a specific form of

probit equation have to be specified.

The model has several characteristics that help to make it user friendly. The yellow colored

boxes represent user specified inputs, while the orange colored boxes represent model generated

outputs. Rural and urban releases are represented in their own columns, height correction

parameters are accounted for. The following are some picture of the model direct.

The Input Parameters

To simplify working with the model, the boxes that are shaded with yellow color are those that

have to be specified by the user. There is a guideline in the upper part of the first Excel sheet (the

model direct). The units of parameters are specified between parentheses.

Figure 4, Parameters that have to be specified by the user.

Figure 5, Types of materials that can chosen by the user.

Figure 6, The correction of height based on Holland formula.

The Outputs Parameters

Figure 7, The results of the model.

Figure 8, The ground level isopleth for a plume release during the day with Qm= 2 kg/s, TLV-

TWA = 1.5 mg/m3, urban conditions, stability case B, wind speed of 3.5 m/s.

Figure 9, The isopleth of puff day case with Q*m= 2 kg for 300 s release, stability case D, TLV-

TWA = 1.5 mg/m3, and wind speed of 3.5 m/s.

Figure 10, The isopleth of plume night case with Qm= 0.8239 kg/s, urban conditions, stability

case B, TLV-TWA = 3 mg/m3, and wind speed of 4.1666 m/s.

Figure 11, The isopleth of puff night case with Q*m= 0.8239 kg for 300 s release stability case

D, TLV-TWA = 3 mg/m3, and wind speed of 4.1666 m/s.

Types of Calculations and Cave Facility

The release models of neutral buoyant gases are considered as significant tools for

studying the behavior of plume or puff clouds that are formed as a result of release incidents

during production, transportation or storage. The releases of neutrally buoyant gases may occur

as a result of a wide variety of factors, most of which are leaks, damage to storage equipment,

faulty valves or handling errors. The goal of the model that was prepared during this project,

shown in its Excel representation and Cave representation, was used to determine several

characteristics of a release cloud for gases with a density close to that of air. This model is based

on the Pasquill-Gifford model for neutrally buoyant gas releases. There are three kinds of

calculations that can be performed with this model:

1. Calculating the cloud properties at a specific point. In this case the user has to enter a

number of parameters: the case of release (plume day, plume night, puff day, or puff

night), the coordinates (x,y,z) for the point of study, the wind speed, the mass of the

release (or the mass flow rate of the release), the people in that area, the time of

exposure, the height of the release, , the duration of the release for the case of a puff,

the temperature of the atmosphere , the pressure, the molecular weight of the gas, and

the gas that is released. From these specified parameters the user can get the

following results: the atmospheric stability case, the concentration in ppm and mg/m3,

the probit variable, the predicted number of fatalities that would occur at that

location.

2. The ground level isopleths (contours of constant concentration equal to the TLV-

TWA) of the clouds for the four cases: plume day, plume night, puff day, and puff

night. For this calculation, the parameters that have to be specified by the user are: the

mass of the release (or the mass flow rate of the release), the TLV-TWA value, and

the wind speed. The model will perform the calculation for the dispersion coefficients

from both the value of TLV-TWA and the from the stability case. Then the

downwind, ground level locations at which the concentration equals the TLV-TWA

are calculated using the solver equate the locations at which the dispersion

coefficients that are obtained from the two calculations are equal Also, the model will

directly draw two dimensional graphs of ground level isopleths’showing the

geographical locations from which people should be excluded.

3. Calculating and drawing a 3-D cloud of the release. This is performed by determining

the concentration at different points (x,y,z). This type of calculation was performed

with the help of the Cave.

The Cave is a new facility at Texas A&M-Qatar that allows a user to see a 3-D shape and to

move in, out and around it by using special optical goggles. This facility works on the basis of

using three projectors that project the picture at small different time intervals which allow the

eyes to distinguish between them and see the third dimension of it. There are only certain types

of file formats that the Cave facility can read to show such 3-D pictorial representations. Thus,

the data that were obtained from the Excel sheets were saved as csv and txt files in order to

ensure that the Cave facility would accept them. For the third type of calculation, one case of

study was specified. This case was arbitrarily assumed to be a 10% release from any company in

Qatar that has a production of 260,000 ton/yr of a neutrally buoyant gas. The average wind speed

in Qatar is about 4.2226 m/s. The volume of study was 1.5 km in each direction from the point of

release. This volume was divided to intervals of 30 m in each direction. Thus, the Excel sheets

were used to specify the concentration at different x,y,z points in that volume and then the

generated files were converted to the formats that can be accepted by the Cave facility in order to

generate the 3-D visualization of the release. There were two cases studied in the Cave: these

were a continuous plume release and a puff release. The plume release is a steady state problem

and one file is required since the mass release is constant at all times. For the puff case, 60 files

were generated with a time intervals of 5 s between each thus generating a study of the cloud

over the first 5 minutes after its release.

Recommendations

1. It is recommended that further studies should be performed using this model to investigate

the release of gases that are more dense than air.

2. Also, as an aid to risk assessments, detailed maps can be used to project the release over a

specific geographical region.

3. The model works for specified gases for which the probit equations for specific causative

variables have been defined. Other gases and their causative variable probit laws can be

added to the Excel Sheets.

Acknowledgments

This work was supported by Chemical Engineering Department at Texas A&M with Dr. Simon

P. Waldram, Senior Professor, as supervisor. Use of the Cave Facility in the IT Department was

facilitated through the help and work of Mr. Ali Sheharyar.

This research project was used as a CHEN elective course substitute.

References

1. Crowl/Louvar. Chemical Process Safety Fundamentals with Applications. 2nd. Edition.

Prentice Hall PTR: New Jersey; 2002.

2. Hemond/Fechner-Levy. Chemical Fate and Transport in the Environment.2nd. Edition.

Academic Press; 2000. Available at:

http://books.google.com.qa/books?id=dcOGQ6CNraUC&pg=PA336&lpg=PA336&dq=P

asquill-

Gifford+model&source=bl&ots=Lu2StCV4cg&sig=WpqY7X2nLmgFB0dBYjzoWLBV

vlc&hl=ar&ei=ONXoSYSfD82OjAfgqeSeCg&sa=X&oi=book_result&ct=result&resnu

m=3#PPA336,M1. Accessed. March 20, 2009.

3. Till/Grogan. Radiological Risk Assessment and Environmental Analysis. Oxford

University Press: US; 2008. Available at:

http://books.google.com.qa/books?id=QUmazo6y26sC&pg=PA95&lpg=PA95&dq=Pasq

uill+Gifford++model&source=bl&ots=4knTRVI_gB&sig=0XLqlZytwX7ZAMIpt_RNiH

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um=3#PPA98,M1. Accessed. April 12, 2009.

4. Authority Civil Aviation, Qatar Weather Website. Available at:

http://www.qatarweather.net/. Accessed. January 2, 2009.