Matlab

A MATLAB-Based Modelingand Simulation Programfor Dispersion ofMultipollutants From anIndustrial Stack forEducational Use in a Courseon Air Pollution Control

E. FATEHIFAR,1 A. ELKAMEL,2 M. TAHERI3

1Environmental Engineering Research Center, Faculty of Chemical Engineering, Sahand University of Technology,

Tabriz, Iran

2Department of Chemical Engineering, Faculty of Engineering, University of Waterloo, Waterloo, Canada

3Department of Petroleum and Chemical Engineering, School of Engineering, Shiraz University, Shiraz, Iran

Received 1 July 2005; accepted 12 March 2006

ABSTRACT: In this article, a MATLAB program for a three-dimensional simulation ofmultipollutants (CO, NOx, SO2, and TH) dispersion from an industrial stack using a Multiple

Cell Model is presented. The program verification was conducted by checking the simulation

results against experimental data and Gaussian Model and better agreements were obtained in

comparison with the Gaussian model. The effects of meteorological and stack parameters on

dispersion of pollutants like, wind velocity, ambient air temperature, atmospheric stability,

exit temperature, velocity, concentration, and stack height can be easily studied using the

program. Several illustrations for reducing maximum ground level concentrations using the

program are given. The program can simulate all industrial stacks and only needs meteoro-

logical data and stack parameters. The outputs from the program are presented in graphical

form. The program was designed to be user friendly and computationally efficient through

Correspondence to A. Elkamel ([email protected]).

2006 Wiley Periodicals Inc.

300

the use of variable pollution grids, vectorized operations, and memory pre-allocation.

2006 Wiley Periodicals, Inc. Comput Appl Eng Educ 14: 300312, 2006; Published online in WileyInterScience (www.interscience.wiley.com); DOI 10.1002/cae.20089

Keywords: simulation; pollutant dispersion; Multiple Cell Model; industrial stack

INTRODUCTION

Air pollution is caused by emissions from point

sources, area sources, mobile sources, and biogenics.

Substantial evidence has accumulated that air pollu-

tion affects the health of human beings and

animals, damages vegetations, soil and deteriorates

materials, affects climate, reduce visibility and solar

radiation, contributes to safety hazards, and generally

interferes with the enjoyment of life and property

[1].

About 60% of the emissions are from point

sources. Major air pollutants usually considered

include dust, particulates, PM10 (particulate matter

10 microns or less in diameter), and PM2.5 due to

incompletely burned fuel or process byproducts,

nitrogen oxides (mainly due to combination of

atmospheric oxygen and nitrogen at high tempera-

tures), sulfur dioxide (mainly due to the burning of

fuel containing quantities of sulfur), carbon monoxide

(due to incompletely burned fuel), ozone and lead.

Engineering studies of air pollution include: Sources

of Air Pollutants, Air Pollution Control, Dispersion

Modeling, and Effects of Air Pollutants and Air

Quality Monitoring Network Design (AQMN-

Design).

Mathematical diffusion models are most useful

nowadays since they provide useful information for

predicting pollutant concentration and quickly pro-

vide output. Air quality mathematical models repre-

sent unique tools for [2]:

- Establishing emission control legislation; that is,determining the maximum allowable emission

rates that will meet fixed air quality standards

- Evaluating proposed emission control techniquesand strategies; that is, evaluating the impacts of

future controls

- Selecting locations of future sources of pollu-tants, in order to minimize their environmental

impacts

- Planning the control of air pollution episodes;that is, defining immediate intervention strate-

gies (i.e., warning systems and real-time short-

term emission reduction strategies) to avoid

severe air pollution episodes in certain regions

- Assessing responsibility for existing air pollutionlevels

- Designing and optimizing AQMN Mathematicalmodels typically incorporate a plume rise

module which calculates the height to which

pollutants rise due to momentum and buoyancy,

and a dispersion module which estimates how

they spread as a function of wind speed and

atmospheric stability. Figure 1 shows plume

rise and pollution dispersion from an industrial

stack.

Standard mathematical dispersion models used

for industrial dispersion modeling include the Indus-

trial Source Complex (ISC) developed by the USEPA,

Gaussian Models (Plume, Puff, and Fluctuating

Models), EPA SCREEN model, Regression Models,

Simple Diffusion Models (Box Model and Atmo-

spheric Turbulence and Diffusion Laboratory, ATDL),

Gradient Theory Models, Source-oriented and Recep-

tor-oriented Models and Multiple Cell Model. More

complex models may incorporate more realistic

meteorological treatments, but generally require data

which is more difficult and expensive to obtain.

Examples include Ausmet/Auspuff, Calmet/Calpuff,

LADM, and TAPM. Other models may attempt to

model photochemical reactions between pollutants

like empirical kinetic modeling analysis (EKMA),

while simpler models generally assume that pollutants

are conserved [3,4].

Analytical solutions of the three-dimensional

diffusion equation for an elevated continuous point

source with variable wind and eddy diffusivity have

been obtained only under restricted assumptions.

Smith [5] used power law variations for wind and

diffusivity and assumed the cross-wind variation

always had a Gaussian form. Ragland [6] used power

law variation for y and z diffusivities but held the wind

constant. Gandin and Soloveichik have presented an

important analytical solution which used u u1zm,KyK0zm, and KzK1z, where u is the wind speed,Ky and Kz are the eddy diffusivities in the lateral

and vertical directions, respectively [7]. Peters and

Klinzing [8] have investigated the effect of varying

the value of the power when the wind is held constant.

The maximum ground level concentration agrees

MATLAB-BASED AIR POLLUTION MODELING 301

well with the Gaussian result for neutral atmospheric

stability [7]. Mehdizadeh and Rifai [9] studied

modeling of point source plumes at high altitudes

using a modified Gaussian model. They used two EPA

dispersion models, Screen and ISC and obtained

dispersion of SO2. Shamsijey [4] studied the disper-

sion of Cement particulate emissions and its effects on

the city of Shiraz.

In this article, a MATLAB program for the

simulation of three-dimensional pollution dispersion

from an industrial stack is presented. The program is

designed to be easy to use for educational purposes in

an air pollution control course. It requires few inputs

and presents the results in a visual format using both

two and three-dimensional colorful plots. In the next

section, the governing equations for modeling disper-

sion are briefly reviewed and their mathematical

solution as implemented in MATLAB is discussed.

The atmospheric parameters used in the program are

also listed. Simulation runs to illustrate the use of the

program are presented in a later section where com-

parisons with both experimental data and the Gaussian

model are given. The effect of different parameters

like atmospheric stability, wind velocity, ambient air

temperature, stack gas exit temperature, velocity, and

concentration is illustrated using the program. An

illustration of how to make recommendations using

the program vis-a`-vis abiding to environmental stan-

dards is also given. Finally, future efforts on improv-

ing the program to include other complications such

as multiple stacks, the effect of chemical reactions and

complex terrains are discussed.

TREATMENT OF AIR POLLUTION MODELSON COMPUTERS

The modeling of dispersion of air pollutants from

an industrial source can be broken down into the

following steps:

1. describing the geometry of the domain

2. introducing appropriate boundary conditions

3. introducing sources, sinks and the dispersion

characteristics for the entire domain

4. selection of values for parameters in the model

5. division of the domain into cells and solution of

the finite difference equations

6. visualization of results.

In this study, a Multiple Cell Model was used for

pollution dispersion from an industrial stacks emis-

sion. Figure 2 shows the mass balance for an unknown

cell.

Five major physical and chemical processes are

to be considered when an air pollution model is

Figure 1 Plume rise and pollution dispersion from an Industrial stack. [Color figure can

be viewed in the online issue, which is available at www.interscience.wiley.com.]

302 FATEHIFAR, ELKAMEL, AND TAHERI

developed. These processes are: (i) horizontal trans-

port (advection), (ii) horizontal diffusion, (iii) deposi-

tion (both dry deposition and wet deposition), (iv)

chemical reactions plus emissions, and (v) vertical

transport and diffusion. The mathematical description

of these processes leads to a system of partial differ-

ential equations:

@Cs

@t @UxC

s@x

@UyCs

@y @UzC

s@z

@@x

Kx@Cs

@x

@@y

Ky@Cs

@y

@@z

Kz@Cs

@z

Es ks1 ks2

Cs QCs;

s 1; 2; . . . ; q

1

where Cs is the concentration of the chemical species

involved in the model (CO, NOx, SO2, and TH), U is

wind velocity, Kx, Ky, and Kz are diffusion coeffi-

cients, Es is the emission sources, K1s and K2

s are

deposition coefficients (for the dry deposition and the

wet deposition, respectively) and Q(Cs) represents

chemical reactions. The following assumptions are

employed:

1. Steady state conditions (@C/@t0)2. UyUz 0 (wind velocity in x-direction only

and is a function of z) [10]

3. Transport by bulk motion in the x-direction

exceeds diffusion in the x-direction (Kx 0)[10]

4. There is no deposition in the system

(K1s K2s 0).

5. There is no reaction in the system (Q0)

By applying the above assumptions, Equation (1)

reduces to:

@UxCs@x

@@y

Ky@Cs

@y

@@z

Kz@Cs

@z

Es 2

The following boundary and initial conditions are also

used:

at x 0; C0; j; k 0

at y 0; @C@y

0

at y W ; @C@y

0

at z 0; @C@z

0

at z mixing length; @C@z

0

3

W and mixing height are shown in Figure 3.

Solution of Mathematical Model

For solving the above model, the finite difference

method is used in this article. We divide the air space

into an array of boxes and write an equation of

conservation of mass for each box (as for a differ-

ential element of fluid). Consider a volume of fluid

Figure 2 Mass balance for an unknown cell.


with sides Dx, Dy, and Dz located at a point i 1, j,k. Properties at the point i, j, k are known but those in

the i1 plane are unknown. Conservation of mass forthe element of fluid at i1, j, k, may be written as:

UxkCsi1;j;kDyDz KykDxDz Csi1;j;k Csi1;j1;k

=Dy

KykDxDz Csi1;j;k Csi1;j1;k

=Dy

Kzk1=2DxDy Csi1;j;k Csi1;j;k1

=Dz

Kzk1=2DxDy Csi1;j;k Csi1;j;k1

=

Dz UxkCsi;j;kDyDz EsDyDz4

where values of wind speed and eddy diffusivity are

presumed known. This is an explicit algebraic formula

and may be unstable in some conditions. The stability

condition for this system is [11]:

Dx Ux2Kz

5Dy2 1Dz2 5

More details on the approach we employed to solve

this system of equations will be given later in a

separate section (Program Description). We discuss

first the different atmospheric parameters employed in

the program.

Atmospheric Parameters Usedin the Program

Atmospheric conditions are a driving force in the

formation, dispersion and transport of pollutant

plumes. For solving Equation (4), we need atmo-

spheric parameters like, wind speed, plume rise,

stability category, dispersion coefficients, surface

roughness and other parameters. Required equations

and values for determining these parameters are given

below:

Atmospheric Stability. Stability of the atmospherevaries hourly, but for modeling purposes and for

short time periods (13 h) a constant and representa-tive atmospheric stability was assumed [9]. In the

proposed program, three classes of atmosphere

stability (neutral, stable and unstable) are considered.

Atmospheric stability is calculated by using the

following Equation (6):

L u3CprTkgHn

6

In Equation (6), u* is the friction velocity, Cp is the

specific heat of air, T is the air temperature, k is

Karmans constant (k 0.4), g is the gravitationalconstant and Hn is the net heat that enters the

atmosphere. Hn for a neutral atmosphere is 0, for a

stable atmosphere is 42 and for an unstable atmo-sphere is 175 [4]. We note that L (Monion-Obukhov

length) is simply the height above the ground at which

the production of turbulence by both mechanical and

boundary forces is equal [2] and has the units of

length.

Surface Roughness and Friction Velocity. It isconvenient to introduce a drag coefficient, cg, based

on the geostrophic wind, ug, such that

u cgug 7The geostrophic drag coefficient is a function of the

surface Rossby Number (R0 ug=fZ0) and L, where fis the Coriolis parameter of the earth and Z0 is surface

roughness. Lettau suggests the following empirical

relationship for a neutral atmosphere [12]:

cg 0:16log10R0 1:8

8

For stable and unstable atmosphere it must be

multiplied by 0.6 and 1.2, respectively. Values of

Roughness length (Z0) and friction velocity (u*)

for several different land surfaces are presented in

[10].

Plume Rise. When the air contaminants are emittedfrom a stack, they rise above the stack before drifting

a significant distance downwind. The effective stack

height H is not only the physical stacks height hs but

include also the plume rise (Fig. 3)

H hs dh 9The stack height used in the calculations must be the

effective stack height. Usually, Briggs Equation (10)

and Hollands Equation (1) are used for the prediction

of plume rise. Briggs and Hollands equations are

given by Equations (10) and (11), respectively.

dh 114CF1=3

u; F vsgD

2Ts Ta4Ta

;

C 1:58 41:4DyDz

10

dhvsDu

1:5 2:68 103PD TsTaTs

11

where vs is stack exit velocity (m/s), D is stack

diameter (m), u is wind velocity (m/s) measured or

calculated at the height, hs, P is pressure (mbar), Ts is


stack gas temperature (K), Ta is atmospheric tem-

perature (8K) and Dy/Dyz is the potential temperaturedifference (8K/m). The Briggs and Hollands equa-tion predictions are compared to the experimental data

of Snyder [13]. It can be seen (Fig. 4) that both

equations do not provide good predictions. Therefore,

we have attempted to modify Hollands equation in

order to get a better coefficient set. The modification

has been done using regression, and the modified

equations are:

For hs < 35 dhdhHolland Eq:32:420:8576 hsFor hs < 80 dhdhHolland Eq:10:15270:3135hsFor hs > 80 dhdhHolland Eq:12:390:17 hs

(12)

Figure 3 shows the comparison of modified Holland

equation with experimental data and Holland and

Briggs equations. As shown, there is good agreement

between the modified Holland equation and experi-

mental data. The preceding calculations are suitable

for neutral conditions. For unstable conditions, Dhshould be increased by a factor of 1.11.2, and forstable conditions, Dh should be decreased by a factorof 0.80.9 [1].Wind Velocity and Dispersion Coefficients. Windspeed and eddy diffusivities for various stability

classes used in this paper are given in Table 1.

Mixing Height. The volume available for dilutingpollutants in the atmosphere is defined by the mixing

Figure 3 Selected domain for simulation. [Color figure can be viewed in the online issue,

which is available at www.interscience.wiley.com.]

Figure 4 Plume rise via stack height. [Color figure can be viewed in the online issue,

which is available at www.interscience.wiley.com.]


Figure 5 Matrix A for 9 grids in y-z face.

Table 1 Wind Velocity and Eddy Diffusivity for Various Stability Categories [3,6,7]

Stability Wind velocity Eddy diffusivity

In surface layer, 0

height. The relation between stability classes and

mixing height is given in Beychok [14].

Program Description

If the following equalities are substituted in Equation

(4):

uDyDz aKyDxDz=Dy eKzDxDy=Dz f

13

We get a system of linear equations that can be written

in compact form as:

AC D 14

where A is a coefficient matrix, C is the matrix of

concentrations and D is the matrix of known

concentrations at a previous face plus the emission

rate into the grid under consideration. Figure 5 shows

the form of matrix A for 9 grids in the y-z face.

Figure 6 shows a flowchart of the computational

procedure employed in the MATLAB program to

obtain the pollution concentration matrix [C]. First the

meteorological data, stack characteristics data and the

domain selection are input to the program through an

interactive user interface. Equation (13) and Table 1

are used to calculate eddy diffusivity and necessary

parameters for the calculation of the elements of

matrix A. The plume rise is calculated using Equation

(12). Finally, the results are provided in an easy to

visualize graphical form. For improving performance

of the program, vector operations and memory pre-

allocation have been employed.

SIMULATION RUNS ANDPROGRAM VERIFICATION

In order to verify the predictions of the program, a

comparison of program output with experimental data

collected from the literature [13] is presented. Table 2

shows the stack parameters that were used to perform

various simulations. Figure 7 shows a comparison

between experimental data, the Gaussian simulation

Figure 6 Flowchart of program.


model and the program results. As can be seen, there

is good agreement between the experimental data and

simulation results of the proposed model in compar-

ison with the Gaussian model. Figure 8 shows

pollution dispersion for the stack under conditions

that we described in Table 2.

EFFECT OF PARAMETERS

Effects of meteorological parameters like atmospheric

stability, wind velocity, air temperature, surface

roughness and dispersion coefficient on pollutants

dispersion can be easily studied using the program.

The use of the program to study the effect of stack

parameters like exit temperature, exit velocity, stack

height and exit concentration will also be illustrated in

this section.

Effect of atmospheric stability: As Figure 9

shows, distribution of pollutants is better for unstable

conditions and pollutants do not go far from the

stacks.

Effect of exit velocity: When exit velocity

increases, plume rise increases and dispersion of

pollutant increases and finally ground level concen-

tration decreases. Figure 10 shows the effect of exit

velocity on the dispersion of pollutants.

Figure 7 (ac) Vertical concentration as function of stack height measured at 750 mdownwind of stack, (d) longitudinal ground-level concentration profile for stack

height 25 m, KCUHb2/Q and Hb 50 m. [Color figure can be viewed in the onlineissue, which is available at www.interscience.wiley.com.]

Table 2 Stack Parameters

Stack height (m) 75

Stack diameter (m) 6

Exit velocity (m/s) 20

Exit temperature (8K) 418Emission rate (g/s) 1

Wind speed at stack top (m/s) 13.4

Ambient temperature (8K) 298Surface roughness (m) 0.2

Boundary layer height (m) 360

Stability category Neutral


Effect of exit temperature: When exit temperature

increases, density of gases decreases and gases go to

upper layers and ground level concentration decreases.

Effect of wind velocity: Figure 11 shows the effect

of wind velocity on pollutant dispersion. As can be

seen, pollution dispersion decreases when wind

velocity increases and pollutants go far from the

stacks region.

Effect of air temperature: The dispersion of

pollutants increases with increasing temperature and

Figure 8 Effect of atmospheric stability on pollutant dispersion. (1) SO2 concentration

distribution at ground level. (2) CO concentration distribution at Mixing height. (3) NOxconcentration distribution at ground level. (4) TH concentration distribution at ground

level. (5) SO2 concentration distribution at Mixing height. (6) CO concentration

distribution at Mixing height. (7) NOx concentration distribution at X 2 km. (8) THconcentration distribution at X 2 km. (9) SO2 concentration distribution at X 12 km.(10) TH concentration distribution at X 12 km. [Color figure can be viewed in the onlineissue, which is available at www.interscience.wiley.com.]


the pollutants come down near the stack region.

Increase in dispersion happens because, when tempe-

rature increases, the dispersion coefficient increases.

Effect of exit concentration: The ground level

concentration increases with increasing exit concen-

tration.

Effect of stack height: Figure 7 shows the effect

of stack height on pollutant dispersion. The ground

level concentration decreases with increasing stack

height.

The above simulation runs clearly illustrate the

utility of the program in helping decision makers

about air pollution control and the effects of different

variables on pollution dispersion. For instance, the

following observations can be made based on the

simulation runs presented earlier:

Figure 8 (Continued)

Figure 9 Effect of atmospheric stability on pollutant dispersion.


1. Under winter conditions, places that are far

from the stacks observe higher pollutant con-

centrations, while under summer conditions

places near the stack get affected the most.

2. By increasing stack heights, pollutants go up

into the atmospheric layer and pollution gets

dispersed over a wider region and ground level

concentration decreases.

3. Increasing exit velocity and temperature for

stacks emissions causes a decrease in ground

level concentrations.

4. Decreasing exit concentration can also be

obtained by reducing the emission rates. This

can be achieved for instance by installing

control devices and/or redesigning factories by

using new technologies.

CONCLUSION

In this study, a three-dimensional simulation

MATLAB program for multi-pollutants dispersion

from an industrial stack has been presented. This

program is based on a Multiple Cell Model approach.

The program solves a system of partial differential

equations using the finite difference method. Various

simulation runs were conducted using the program

and comparisons with experimental data and Gaussian

model were presented. Several examples on the

effects of meteorological parameters (i.e., wind

velocity, ambient air temperature, atmospheric stabi-

lity and surface roughness) on pollutant dispersion

were illustrated using the program. The effect of stack

parameters like, stack exit temperature, concentration

Figure 11 Effect of wind velocity on pollutant dispersion. [Color figure can be viewed in

the online issue, which is available at www.interscience.wiley.com.]

Figure 10 Effect of exit velocity on pollutant dispersion. [Color figure can be viewed in

the online issue, which is available at www.interscience.wiley.com.]


and velocity and stack height was also illustrated

using the program. The program can be used as a

training tool in an air pollution course to study the

effects of air temperature, dispersion coefficients, exit

temperature, stack height, exit velocity, wind velocity

and exit concentration on pollution dispersion.

REFERENCES

[1] H. S. Peavy, D. R. Rowe, and G. Tchobanoglous,

Environmental engineering, McGraw-Hill, New York,

1985.

[2] J. H. Seinfeld and S. N. Pandis, Atmospheric chemistry

and Physics, John Wiley & Sons, New York, 1998.

[3] P. Zanneti, Air pollution modeling theories, computa-

tional methods and available software, Computational

Mechanics Publications, New York, 1990.

[4] M. Shamsijey, Simulation of Pollutant Emitted from

Cement Factory Over the City of Shiraz , M.Sc. Thesis,

Shiraz University, Shiraz, Iran, 2004.

[5] F. B. Smith, The Diffusion of Smoke from a continuous

elevated point source into a turbulent atmosphere,

J Fluid Mech 2 (1957), 4976.[6] K. W. Ragland, Multiple box model for dispersion of

air pollutants from area sources, Atmos Environ 7

(1973), 10171032.

[7] K. W. Ragland and R. L. Dennis, Point source

atmospheric diffusion model with variable wind

and diffusivity profiles, Atmos Environ 9 (1975),

175189.[8] G. E. Klinzing and L. K. Peters, The effect of

variable diffusion coefficients and velocity on the

dispersion of pollutants, Atmos Environ 5 (1971),

497504.[9] F. Mehdizadeh and H. S. Rifai, Modeling point source

plumes at high altitudes using a modified gaussian

model, Atmos Environ 38 (2004), 821831.[10] R. J. Heinsohn and R. Kabel, Sources and control of air

pollution, Prentice Hall, New York, 1999.

[11] A. Constantinides and N. Mostoufi, Numerical meth-

ods for chemical engineers with Matlab applications,

Prentice Hall, New York, 1999.

[12] H. H. Lettau, Wind profile, surface stress, geos-

trophic drag coefficients in the atmospheric surface

layer, Advances in geophysics, Vol. 6 Atmospheric

diffusion and air pollution, Academic Press, New York,

1959, pp 241256.[13] W. Snyder, Downwash of plumes in the vicinity of

buildings, Kluwer Academic Publishers, Netherlands,

1994.

[14] M. R. Beychok, Fundamentals of stack gas dispersion,

M. R. Beychok (Ed.), 3rd ed., 1995, p 9.

BIOGRAPHIES

Esmaeil Fatehifar is an assistant professor of

chemical engineering at Sahand University of

Technology, Tabriz, Iran, where is also

presently head of the Environmental Engi-

neering Research Center (EERC). He

received his PhD and MS from the Depart-

ment of Chemical Engineering at Shiraz

University and his BS from Sahand University

of Technology. Dr. Fatehifar was also a

visiting scholar in the Department of Chemical Engineering at the

University of Waterloo. Dr. Fatehifar research interests are in air

pollution modeling and control, environmental engineering, and

mathematical modeling and simulation. He is the author of several

publications in these fields.

Ali Elkamel is a faculty member in the

Department of Chemical Engineering at the

University of Waterloo. Prior to joining

the University of Waterloo, he served at

Purdue University, Procter and Gamble,

Kuwait University, and the University of

Wisconsin. His research has focused on the

applications of systems engineering and

optimization techniques to pollution pro-

blems and sustainable development.

Mansoor Taheri is a professor of chemical

engineering at the University of Shiraz,

Shiraz, Iran. He received his PhD from

Pennsylvania State University. His research

has focused on air pollution control, energy

saving, and transport phenomena. He is

author of Environmental Engineering,

Volume 1: Heating and Air Conditioning.

He has published more than 30 papers in

these fields. Professor Taheri has supervised

several masters and PhD students. He was selected as a Chemical

Engineer of the Year 2002 by the Iranian Society of Chemists &

Chemical Engineers. He was also a Distinguished Professor of

Shiraz University in 2002.


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