A MATLAB-based modeling and simulation

A MATLAB-Based Modeling and Simulation Program for Dispersion of Multipollutants From an Industrial Stack for Educational Use in a Course on Air Pollution Control E. FATEHIFAR,1 A. ELKAMEL,2 M. TAHERI3 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 three-dimensional simulation of multipollutants (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 meteorological 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]). ß 2006 Wiley Periodicals Inc.

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the use of variable pollution grids, vectorized operations, and memory pre-allocation. ß 2006 Wiley Periodicals, Inc. Comput Appl Eng Educ 14: 300
312, 2006; Published online in Wiley InterScience (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 pollution 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 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: Sources of Air Pollutants, Air Pollution Control, Dispersion Modeling, and Effects of Air Pollutants and Air Quality Monitoring Network Design (AQMNDesign). Mathematical diffusion models are most useful nowadays since they provide useful information for predicting 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 emission rates that will meet fixed air quality standards - Evaluating proposed emission control techniques and strategies; that is, evaluating the impacts of future controls - Selecting locations of future sources of pollutants, in order to minimize their environmental impacts - Planning the control of air pollution episodes; that is, defining immediate intervention strategies (i.e., warning systems and real-time shortterm emission reduction strategies) to avoid severe air pollution episodes in certain regions

- Assessing responsibility for existing air pollution levels - Designing and optimizing AQMN Mathematical models 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 Industrial 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 Atmospheric Turbulence and Diffusion Laboratory, ATDL), Gradient Theory Models, Source-oriented and Receptor-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 ¼ u1zm, Ky ¼ K0zm, and Kz ¼ K1z, 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

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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.] 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 dispersion 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 dispersion 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 comparisons 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 improving the program to include other complications such as multiple stacks, the effect of chemical reactions and complex terrains are discussed.

TREATMENT OF AIR POLLUTION MODELS ON 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 stack’s emission. 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

MATLAB-BASED AIR POLLUTION MODELING

Figure 2

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Mass balance for an unknown cell.

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) vertical transport and diffusion. The mathematical description of these processes leads to a system of partial differential equations: @Cs @ðUx C s Þ @ðUy Cs Þ @ðUz Cs Þ

¼
@x @y @z @t

 @ @Cs @ @C s Kx Ky þ þ @x @y @x @y
 @ @C s Kz þ @z @z  s  s þ E
k1 þ k2s C s þ QðC s Þ;

4. There is no deposition in the system (Ks1 ¼ Ks2 ¼ 0). 5. There is no reaction in the system (Q¼0) By applying the above assumptions, Equation (1) reduces to:

 @ðUx C s Þ @ @Cs @ @Cs ¼ Ky Kz þ þ Es ð2Þ @x @y @z @y @z The following boundary and initial conditions are also used:

ð1Þ

s ¼ 1; 2; . . . ; q 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 coefficients, Es is the emission sources, Ks1 and Ks2 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/@t¼0) 2. Uy ¼ Uz ¼ 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 ¼ 0) [10]

at x ¼ 0; Cð0; j; kÞ ¼ 0 at y ¼ 0;

@C ¼0 @y

at y ¼ W;

@C ¼0 @y

at z ¼ 0;

@C ¼0 @z

at z ¼ mixing length;

ð3Þ

@C ¼0 @z

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 differential element of fluid). Consider a volume of ‘‘fluid’’

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with sides Dx, Dy, and Dz located at a point i þ 1, j, k. Properties at the point i, j, k are known but those in the iþ1 plane are unknown. Conservation of mass for the element of fluid at iþ1, j, k, may be written as:   s s s DyDz þ ðKy Þk DxDz Ciþ1;j;k
Ciþ1;jþ1;k Uxk Ciþ1;j;k =Dy   s s
Ciþ1;j
1;k =Dy þðKy Þk DxDz Ciþ1;j;k   s s
Ciþ1;j;kþ1 =Dz þðKz Þkþ1=2 DxDy Ciþ1;j;k   s s
Ciþ1;j;k
1 = þðKz Þk
1=2 DxDy Ciþ1;j;k s DyDz þ Es DyDz Dz ¼ Uxk Ci;j;k

ð4Þ 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 



Ux

2Kz Dy5 2

þ Dz1 2



ð5Þ

Karman’s constant (k ¼ 0.4), g is the gravitational constant 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 atmosphere 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 is convenient to introduce a drag coefficient, cg, based on the geostrophic wind, ug, such that u ¼ c g ug

The geostrophic drag coefficient is a function of the surface Rossby Number (R0 ¼ ug =fZ0 ) and L, where f is the Coriolis parameter of the earth and Z0 is surface roughness. Lettau suggests the following empirical relationship for a neutral atmosphere [12]: cg ¼

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 Used in the Program Atmospheric conditions are a driving force in the formation, dispersion and transport of pollutant plumes. For solving Equation (4), we need atmospheric 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 atmosphere varies hourly, but for modeling purposes and for short time periods (1
3 h) a constant and representative 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): L¼


u3 Cp rT kgHn

In Equation (6), u* is the friction velocity, Cp is the specific heat of air, T is the air temperature, k is

0:16 log10 ðR0 Þ
1:8

ð8Þ

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 emitted from a stack, they rise above the stack before drifting a significant distance downwind. The effective stack height H is not only the physical stack’s height hs but include also the plume rise (Fig. 3) H ¼ hs þ dh

ð9Þ

The stack height used in the calculations must be the effective stack height. Usually, Brigg’s Equation (10) and Holland’s Equation (1) are used for the prediction of plume rise. Brigg’s and Holland’s equations are given by Equations (10) and (11), respectively. dh ¼

114CF1=3 ; u

F¼

vs gD2 ðTs
Ta Þ ; 4Ta

Dy C ¼ 1:58
41:4 Dz dh ¼

ð6Þ

ð7Þ


 vs D ðTs
Ta Þ 1:5 þ 2:68  10
3 PD u Ts

ð10Þ

ð11Þ

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

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

which is available at www.interscience.wiley.com.] stack gas temperature (K), Ta is atmospheric temperature (8K) and Dy/Dyz is the potential temperature difference (8K/m). The Brigg’s and Holland’s equation 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 Holland’s equation in order to get a better coefficient set. The modification has been done using regression, and the modified equations are: For hs < 35 dh ¼ dh ¼ ðHolland Eq:Þ
32:42þ0:8576  hs For hs < 80 dh ¼ dh ¼ ðHolland Eq:Þ
10:1527þ0:3135hs For hs >¼ 80 dh ¼ dh ¼ ðHolland Eq:Þþ12:39þ0:17  hs

(12)

Figure 3 shows the comparison of modified Holland equation with experimental data and Holland and Brigg’s equations. As shown, there is good agreement between the modified Holland equation and experimental data. The preceding calculations are suitable for neutral conditions. For unstable conditions, Dh should be increased by a factor of 1.1
1.2, and for stable conditions, Dh should be decreased by a factor of 0.8
0.9 [1]. Wind Velocity and Dispersion Coefficients. Wind speed and eddy diffusivities for various stability classes used in this paper are given in Table 1. Mixing Height. The volume available for diluting pollutants in the atmosphere is defined by the mixing

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

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

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

Wind velocity

Eddy diffusivity In surface layer, 0