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A MATLAB‐based modeling and simulationprogram for dispersion of multipollutants froman industrial stack for educational use in a courseon air pollution control
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COMPUTER APPLICATIONS IN ENGINEERING EDUCATION · JANUARY 2006
Impact Factor: 0.45 · DOI: 10.1002/cae.20089
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A MATLABBased Modelingand Simulation Programfor Dispersion ofMultipollutants From anIndustrial Stack forEducational Use in a Courseon Air Pollution Control
E. FATEHIFAR,
1
A. ELKAMEL,
2
M. TAHERI
3
1
Environmental Engineering Research Center, Faculty of Chemical Engineering, Sahand University of Technology,Tabriz, Iran
2
Department of Chemical Engineering, Faculty of Engineering, University of Waterloo, Waterloo, Canada
3
Department 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 threedimensional simulation ofmultipollutants (CO, NO
x
, SO
2
, and TH) dispersion from an industrial stack using a MultipleCell Model is presented. The program verification was conducted by checking the simulationresults against experimentaldata and Gaussian Modeland betteragreements were obtainedincomparison with the Gaussian model. The effects of meteorological and stack parameters ondispersion of pollutants like, wind velocity, ambient air temperature, atmospheric stability,exit temperature, velocity, concentration, and stack height can be easily studied using theprogram. Several illustrations for reducing maximum ground level concentrations using theprogram are given. The program can simulate all industrial stacks and only needs meteorological data and stack parameters. The outputs from the program are presented in graphicalform. The program was designed to be user friendly and computationally efficient through
Correspondence to A. Elkamel (aelkamel@cape.uwaterloo.ca).
2006 Wiley Periodicals Inc.
300
the use of variable pollution grids, vectorized operations, and memory preallocation.
2006 Wiley Periodicals, Inc. Comput Appl Eng Educ 14: 300
312, 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 pointsources, area sources, mobile sources, and biogenics.Substantial evidence has accumulated that air pollution affects the health of human beings andanimals, damages vegetations, soil and deterioratesmaterials, affects climate, reduce visibility and solarradiation, contributes to safety hazards, and generallyinterferes with the enjoyment of life and property[1].About 60% of the emissions are from pointsources. Major air pollutants usually consideredinclude dust, particulates, PM
10
(particulate matter10 microns or less in diameter), and PM
2.5
due toincompletely burned fuel or process byproducts,nitrogen oxides (mainly due to combination of atmospheric oxygen and nitrogen at high temperatures), 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: Sourcesof Air Pollutants, Air Pollution Control, DispersionModeling, and Effects of Air Pollutants and AirQuality Monitoring Network Design (AQMNDesign).Mathematical diffusion models are most usefulnowadays since they provide useful information forpredicting pollutant concentration and quickly provide output. Air quality mathematical models represent unique tools for [2]:

Establishing emission control legislation; that is,determining the maximum allowable emissionrates 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 pollutants, in order to minimize their environmentalimpacts

Planning the control of air pollution episodes;that is, deﬁning immediate intervention strategies (i.e., warning systems and realtime shortterm emission reduction strategies) to avoidsevere air pollution episodes in certain regions

Assessing responsibility for existing air pollutionlevels

Designing and optimizing AQMN Mathematicalmodels typically incorporate a plume risemodule which calculates the height to whichpollutants rise due to momentum and buoyancy,and a dispersion module which estimates howthey spread as a function of wind speed andatmospheric stability. Figure 1 shows plumerise and pollution dispersion from an industrialstack.Standard mathematical dispersion models usedfor industrial dispersion modeling include the Industrial Source Complex (ISC) developed by the USEPA,Gaussian Models (Plume, Puff, and FluctuatingModels), EPA SCREEN model, Regression Models,Simple Diffusion Models (Box Model and Atmospheric Turbulence and Diffusion Laboratory, ATDL),Gradient Theory Models, Sourceoriented and Receptororiented Models and Multiple Cell Model. Morecomplex models may incorporate more realisticmeteorological treatments, but generally require datawhich is more difﬁcult and expensive to obtain.Examples include Ausmet/Auspuff, Calmet/Calpuff,LADM, and TAPM. Other models may attempt tomodel photochemical reactions between pollutantslike empirical kinetic modeling analysis (EKMA),while simpler models generally assume that pollutantsare conserved [3,4].Analytical solutions of the threedimensionaldiffusion equation for an elevated continuous pointsource with variable wind and eddy diffusivity havebeen obtained only under restricted assumptions.Smith [5] used power law variations for wind anddiffusivity and assumed the crosswind variationalways had a Gaussian form. Ragland [6] used powerlaw variation for
y
and
z
diffusivities but held thewindconstant. Gandin and Soloveichik have presented animportant analytical solution which used
u
¼
u
1
z
m
,
K
y
¼
K
0
z
m
, and
K
z
¼
K
1
z
, where
u
is the wind speed,
K
y
and
K
z
are the eddy diffusivities in the lateraland vertical directions, respectively [7]. Peters andKlinzing [8] have investigated the effect of varyingthe value of the power when the wind is held constant.The maximum ground level concentration agrees
MATLABBASED AIR POLLUTION MODELING 301
well with the Gaussian result for neutral atmosphericstability [7]. Mehdizadeh and Rifai [9] studiedmodeling of point source plumes at high altitudesusing a modified Gaussian model. They used two EPAdispersion models, Screen and ISC and obtaineddispersion of SO
2
. Shamsijey [4] studied the dispersion of Cement particulate emissions and its effects onthe city of Shiraz.In this article, a MATLAB program for thesimulation of threedimensional pollution dispersionfrom an industrial stack is presented. The program isdesigned to be easy to use for educational purposes inan air pollution control course. It requires few inputsand presents the results in a visual format using bothtwo and threedimensional colorful plots. In the nextsection, the governing equations for modeling dispersion are brieﬂy reviewed and their mathematicalsolution as implemented in MATLAB is discussed.The atmospheric parameters used in the program arealso listed. Simulation runs to illustrate the use of theprogram are presented in a later section where comparisons with bothexperimental data and the Gaussianmodel are given. The effect of different parameterslike atmospheric stability, wind velocity, ambient airtemperature, stack gas exit temperature, velocity, andconcentration is illustrated using the program. Anillustration of how to make recommendations usingthe program visa`vis abiding to environmental standards is also given. Finally, future efforts on improving the program to include other complications suchas multiple stacks, the effect of chemical reactions andcomplex terrains are discussed.
TREATMENT OF AIR POLLUTION MODELSON COMPUTERS
The modeling of dispersion of air pollutants froman industrial source can be broken down into thefollowing steps:1. describing the geometry of the domain2. introducing appropriate boundary conditions3. introducing sources, sinks and the dispersioncharacteristics for the entire domain4. selection of values for parameters in the model5. division of the domain into cells and solution of the ﬁnite difference equations6. visualization of results.In this study, a Multiple Cell Model was used forpollution dispersion from an industrial stack’s emission. Figure 2 shows the mass balance for an unknowncell.Five major physical and chemical processes areto be considered when an air pollution model is
Figure 1
Plume rise and pollution dispersion from an Industrial stack. [Color ﬁgure canbe viewed in the online issue, which is available at www.interscience.wiley.com.]
302 FATEHIFAR, ELKAMEL, AND TAHERI
developed. These processes are: (i) horizontal transport (advection), (ii) horizontal diffusion, (iii) deposition (both dry deposition and wet deposition), (iv)chemical reactions plus emissions, and (v) verticaltransport and diffusion. The mathematical descriptionof these processes leads to a system of partial differential equations:
@
C
s
@
t
¼
@
ð
U
x
C
s
Þ
@
x
@
ð
U
y
C
s
Þ
@
y
@
ð
U
z
C
s
Þ
@
z
þ
@ @
x K
x
@
C
s
@
x
þ
@ @
y K
y
@
C
s
@
y
þ
@ @
zK
z
@
C
s
@
z
þ
E
s
k
s
1
þ
k
s
2
C
s
þ
Q
ð
C
s
Þ
;
s
¼
1
;
2
;
...
;
q
ð
1
Þ
where
C
s
is the concentration of the chemical speciesinvolved in the model (CO, NO
x
, SO
2
, and TH),
U
iswind velocity,
K
x
,
K
y
, and
K
z
are diffusion coefficients,
E
s
is the emission sources,
K
1
s
and
K
2
s
aredeposition coefficients (for the dry deposition and thewet deposition, respectively) and
Q
(
C
s
) representschemical reactions. The following assumptions areemployed:1. Steady state conditions (
@
C
/
@
t
¼
0)2.
U
y
¼
U
z
¼
0 (wind velocity in
x
direction onlyand is a function of
z
) [10]3. Transport by bulk motion in the xdirectionexceeds diffusion in the xdirection (
K
x
¼
0)[10]4. There is no deposition in the system(
K
1
s
¼
K
2
s
¼
0).5. There is no reaction in the system (
Q
¼
0)By applying the above assumptions, Equation (1)reduces to:
@
ð
U
x
C
s
Þ
@
x
¼
@ @
y K
y
@
C
s
@
y
þ
@ @
z K
z
@
C
s
@
z
þ
E
s
ð
2
Þ
The following boundary and initial conditions are alsoused:at
x
¼
0
;
C
ð
0
;
j
;
k
Þ ¼
0at
y
¼
0
; @
C
@
y
¼
0at
y
¼
W
; @
C
@
y
¼
0at
z
¼
0
; @
C
@
z
¼
0at
z
¼
mixinglength
; @
C
@
z
¼
0
ð
3
Þ
W
and mixing height are shown in Figure 3.
Solution of Mathematical Model
For solving the above model, the ﬁnite differencemethod is used in this article. We divide the air spaceinto an array of boxes and write an equation of conservation of mass for each box (as for a differential element of ﬂuid). Consider a volume of ‘‘ﬂuid’’
Figure 2
Mass balance for an unknown cell.
MATLABBASED AIR POLLUTION MODELING 303