### 1. Introduction

_{2.5}concentration. Assuming fixed atmospheric parameters, Regland et al. [22] introduced a two-dimensional approach for modeling pollutant emissions from surface emission sources. Nourbakhsh et al. [23] simulated the dispersion patterns of gaseous pollutants (CO, SO

_{2}, and NO

_{2}) emitting from stacks and flares of gas refineries, and observed an acceptable agreement between their CFD model and experimental data. In another study, Issakhov and Baitureyeva developed a 2D and 3D CFD model to numerically investigate the rising pollution from thermal power plants. In addition, they calculated the pollution concentration level at various distances from the emission source [24].

_{x}and O

_{3}by using a large-eddy simulation model and concluded that chemical reaction plays an important role in transmitting pollutants into the street. Similarly, Moradpour et al. [26] assessed the effects of green roofs on reactive pollutant dispersion within an urban street canyon by using a CFD model coupled with NO-NO

_{2}-O

_{3}photochemistry and energy balance models. Additionally, Kitabayashi et al. [27] designed a model based on the Gaussian model to estimate NO

_{x}concentrations by considering the atmospheric chemical reactions. In another study, Tetzlaff et al. [28] modeled the emission of reactive pollutants into the atmosphere from an industrial zone in southern Germany using a large-scale networking model. Baik et al. [29] used the Navier-Stokes equations to model the emission of NO

_{x}and O

_{3}pollutants in urban streets. They found that the chemical transmission of pollutants for O

_{3}was comparable to that of the dispersion and diffusion phenomena, while the magnitude of the chemical reaction term for NO

_{x}is negligible to that of the advection or turbulent diffusion term. Besides, several reduced chemical mechanisms have been presented in the literature to describe the atmospheric chemistry of pollutants. For example, Joelsson et al. [30] presented a reduced mechanism, based on the MCM v3.3.1, for modeling atmospheric chemistry. Their reduction method was a semi-stochastic method based on the heuristic Ant Colony Optimization concept. They showed that their reduced mechanism successfully predicts the concentration of ozone, nitrogen oxides, and other important compounds in simulations of several cases up to five simulated days. As another example, Bright et al. [31] developed a reduced chemical scheme comprising 51 chemical species and 136 reactions, based upon a subset of the MCM v3.1 for the simulation of street canyon atmospheric chemical processing. At the first step, the reduction was achieved by removing night time only chemistry. Then, further reduction was attained by eliminating parent compounds and any unique daughter products, which had little effect on the key chemical intermediates under street canyon conditions.

### 2. Materials and Method

### 2.1. Case Study

^{3}/h on non-rainy days and a maximum of 230 m

^{3}/h on rainy days. The release of extremely volatile pollutants is inevitable since wastewater treatment is usually carried out in outdoor basins. The volatile compounds enter the air through evaporation and air striping processes. Fig. S1 illustrates the schematic flow diagram of the wastewater treatment plant and existing area sources. Moreover, Table S1 displays the characteristics of the entering wastewater such as BTEX concentration, flow rate (Q

_{in}), total suspended solids (TSS), total chemical oxygen demand (TCOD), and biochemical oxygen demand (BOD

_{5}).

### 2.2. Method for Concentration Measurement

### 2.3. Estimating the Emission Rate of BTEX Compounds to the Atmosphere

##### (1)

$${V}_{l}\hspace{0.17em}\left(\frac{d{C}_{l}}{dt}\right)=Q{C}_{l,0}-Q{C}_{l}+{R}_{V}+{R}_{S}+{R}_{ad}+{R}_{ab}+{R}_{b}$$*C*

*and*

_{l,0}*C*

*are the input and output concentrations of the soluble pollutants inside the basin expressed in mg/m*

_{l}^{3}, respectively,

*V*

*indicates the basin volume (m*

_{l}^{3}), and

*Q*shows the volumetric flow rate of wastewater into the basin (m

^{3}/h).

*R*

*,*

_{V}*R*

*,*

_{S}*R*

*,*

_{ad}*R*

*, and*

_{ab}*R*

*are the removal rate of these compounds by evaporation, air stripping, adsorption, liquid absorption, and biological removal (mg/h), respectively. Toxchem is a widely used capable model for predicting contaminants fate and hazardous air pollutants emission within/from wastewater treatment plants [7, 35]. In this study, Toxchem, as a computer-based software including both steady-state and dynamic models, is used to estimate the amount of BTEX emission from a petrochemical wastewater treatment plant [36].*

_{b}_{v}is rate of volatilization (mg/h), K

_{v}is volatilization mass transfer coefficient (m/h), C

_{l}is concentration of volatile compound in the water (mg/m

^{3}), f

_{non}is pH dependent fraction of non-dissociated compound, and V is volume of process vessel (m

^{3}).

_{x}is concentration of contaminant in solid phase (μg/g), K

_{p}is sorption partition coefficient (L/g), and C

_{l}is concentration of contaminant in liquid phase (μg/L).

_{b}is biodegradation rate (mg/h), μ

_{m}is maximum specific growth rate (1/h), Y is maximum yield coefficient (g/g), X is volatile fraction of total suspended solids (mg/L), K

_{s}is half saturation constant (mg/L), C

_{l}is contaminant liquid phase concentration (mg/L), and V is vessel volume (L).

### 2.4. Mathematical Dispersion Model and Boundary Conditions

^{3}. Fig. S2 displays a schematic view of the gridded space domain, the origin of the coordinate system, wind direction, and WWTP location in the petrochemical company.

##### (5)

$$\begin{array}{c}\frac{\partial {C}_{g}^{j}}{\partial t}=-\frac{\partial (u{C}_{g}^{j})}{\partial x}-\frac{\partial (v{C}_{g}^{j})}{\partial y}-\frac{\partial (w{C}_{g}^{j})}{\partial z}\\ +\frac{\partial}{\partial x}({K}_{x}\frac{\partial {C}_{g}^{j}}{\partial x})+\frac{\partial}{\partial y}({K}_{y}\frac{\partial {C}_{g}^{j}}{\partial y})+\frac{\partial}{\partial z}({K}_{z}\frac{\partial {C}_{g}^{j}}{\partial z})\\ +{E}^{j}-({k}^{1,j}+{k}^{2,j}){C}_{g}^{j}+{P}^{j}({C}_{g}^{1},{C}_{g}^{2},\mathrm{....},{C}_{g}^{q}),\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j=1,2,\mathrm{.....},q\end{array}$$*x*,

*y*, and

*z*. The next three terms describe the diffusion in the three corresponding directions. E

^{j}shows the amount of emission from the pollutant sources, and the next term (k

^{1,j}+k

^{2,j}) indicates the mathematical equations for dry and wet deposition in the studied area. Finally, the last term (

*P*

^{j}) addresses the pollutants’ reaction.

*u*,

*v*, and

*w*are wind velocity components, and defines the concentrations of the chemical species in the atmosphere. The diffusion coefficients are illustrated by

*K*

_{x},

*K*

_{y},

*K*

_{z}and the number of pollutants is shown by the parameter q.

_{2}, O

_{2}, OH, O

_{3}, are as follows:

##### (6)

$$\text{Initial\hspace{0.17em}condition\hspace{0.17em}}(\text{t}=0)\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}{C}_{g}^{j}=0\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j\ne {N}_{2},{O}_{2},OH,{O}_{3},\dots $$##### (7)

$$\text{B.C}\ne 1\hspace{0.17em}\text{for\hspace{0.17em}x}=0\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}{C}_{g}^{j}=0\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j\ne {N}_{2},{O}_{2},OH,{O}_{3},\dots $$##### (8)

$$\text{B.C}\ne 3\hspace{0.17em}\text{for\hspace{0.17em}y}=0\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}{C}_{g}^{j}=0\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j\ne {N}_{2},{O}_{2},OH,{O}_{3},\dots $$##### (9)

$$\text{B.C}\ne 4\hspace{0.17em}\text{for\hspace{0.17em}y}=\text{W\hspace{0.28em}}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}{C}_{g}^{j}=0\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j\ne {N}_{2},{O}_{2},OH,{O}_{3},\dots $$##### (10)

$$\text{B.C}\ne 5\hspace{0.17em}\text{for\hspace{0.17em}z}=0\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\frac{\partial {C}_{g}^{j}}{\partial z}=0\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j\ne {N}_{2},{O}_{2},OH,{O}_{3},\dots $$##### (11)

$$\text{B.C}\ne 6\hspace{0.17em}\text{for\hspace{0.17em}z}=\text{H\hspace{0.28em}}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\frac{\partial {C}_{g}^{j}}{\partial z}=0\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j\ne {N}_{2},{O}_{2},OH,{O}_{3},\dots $$*W*and

*H*are the width and height of the studied region, respectively. The boundary conditions are obtained based on the following concepts and assumptions:

The wind entering the area is pollution-free (Eq. (7)).

Pollution concentration at

*y*= 0 and*y = W*remains zero; i.e. they are considered as the boundary conditions at infinity (Eqs. (8) and (9)).The pollutants are reflected from the earth (Eq. (10)).

There is no temperature inversion, and the pollutants can move with no limitation in the vertical direction up to the mixing height (Eq. (11)).

Temperature is assumed to be constant (isothermal condition).

### 2.5. Numerical Solution

##### (12)

$$\frac{\partial {C}_{g}^{j,1}}{\partial t}=-\frac{\partial (u{C}_{g}^{j,1})}{\partial x}-\frac{\partial (v{C}_{g}^{j,1})}{\partial y}$$##### (13)

$$\frac{\partial {C}_{g}^{j,2}}{\partial t}=+\frac{\partial}{\partial x}({K}_{x}\frac{\partial {C}_{g}^{j,2}}{\partial x})+\frac{\partial}{\partial y}({K}_{y}\frac{\partial {C}_{g}^{j,2}}{\partial y})$$##### (14)

$$\frac{\partial {C}_{g}^{j,3}}{\partial t}=-({k}^{1,j}+{k}^{2,j}){C}_{g}^{j,3}(x,y,{z}_{0},t)$$##### (15)

$$\frac{\partial {C}_{g}^{j,4}}{\partial t}=+{E}^{j}(x,y,{z}_{0},t)+{P}^{j}({C}_{g}^{1,4},{C}_{g}^{2,4},\mathrm{....},{C}_{g}^{q,4}),\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j=1,2,\mathrm{.....},q$$##### (16)

$$\frac{\partial {C}_{g}^{j,5}}{\partial t}=-\frac{\partial (w{C}_{g}^{j,5})}{\partial z}+\frac{\partial}{\partial z}({K}_{z}\frac{\partial {C}_{g}^{j,2}}{\partial z})$$### 2.6. Reaction Description and Method of Mechanism Reduction

*t*= 0 called the initial condition (Eq. (17)).

*C*indicates the concentration of the components,

*k*shows rate constants, and

*C*

*is the initial concentration of components.*

_{0}_{3}, (b) the photolysis of nitrous acid HNO

_{2}, and (c) indirectly from the photolysis of formaldehyde HCHO [1, 46]. These reactions are illustrated as follows:

_{x}to react with the OH radical in the troposphere. The hydroxyl radical reacts with the VOC when the VOC concentration is high. On the other hand, the NO

_{x}wins the competition when the NO

_{x}ratio is higher. Finally, OH reacts with both proportionally when the ratio of NO

_{x}/VOC is a certain value [47].

^{8}ODEs must be handled at every time step for a space domain including 1,000 × 1,000 × 100 grid-points. Therefore, employing a helpful method for eliminating the ineffective reactions is necessary. Reducing the number of reactions not only decreases the computational time but also helps to easily describe the degradation of BTEX compounds, and identify effective components in the final BTEX concentrations.

The initial concentration of components is assigned.

One-dimensional reactive dispersion simulation is conducted considering a system of equations involving 339 ODEs for a given time.

The final concentration of the BTEX is calculated (

*j*= benzene, toluene, ethylbenzene, and xylene).The first reaction (

*i*= 1) is selected.The

*i*^{t}^{h}reaction is eliminated from ODEs, and a new 1D simulation is conducted Then, the final concentration of the BTEX is recalculated.-
The value of the objective function (

*O.F*), which represents the percentage of change in the concentration of the BTEX before and after eliminating*i*^{th}reaction, is calculated using Eq. (25).where*n*represents the number of BTEX compounds. If

*O.F*> 1%, the*i*^{th}reaction is selected as an effective reaction. Otherwise, it is discarded. It should be noted that the minimum of*O.F*can be altered optionally depending on the accuracy of the calculation.The Next reaction is selected (

*i = i+*1), and steps (5) to (7) are repeated until checking

### 3. Results and Discussions

### 3.1. Fate of BTEX

### 3.2. 1-D Reactive Transmission Analysis

_{1D}, HONO, HO

_{2}, and NO through reactions 17, 21, and 22. However, as a serious competitor for BTEX, the existing reactants in reactions 14, 25, and 26 react with OH and limit BTEX consumption. Furthermore, some reactions such as 13, 18, 23, and 24 are considered as the competitors for OH because they consume O

_{1D}and NO components, which are regarded as some of the main sources of OH production. The adverse or favorable effect of other reactions on hydroxyl production can be similarly explained. The selected reactions and corresponding species are employed to participate in the 3D mathematical model and calculate the spatial concentration distribution.

### 3.3. 3-D model results

^{3}over the WWTP for 10 min after the emission (Fig. 5(b)). When the time increases, benzene travels farther distances, pollutes more spaces, and reaches the maximum value of 53 mg/m

^{3}(Fig. 5(c)). Finally, for 12 h simulation time, no significant changes are observed for the distances less than 5 km, and consequently, pollution transfer occurs under the steady-state condition up to 5 km for the simulation times of more than 12 h (Fig. 5(d)). It should be noted that the high concentration of benzene over the WWTP is a serious threat to the life of the worker or people nearby. However, its concentration is less than 1 mg/m

^{3}for distances between 1,000 and 2,000 m far from the emission sources. In addition, its value is lower than 0.05 mg/m

^{3}for a distance greater than 3,000 m.

^{3}, respectively. In addition, their values are less than 0.01 mg/m

^{3}for distances longer than 1,000 m far from emission points.

^{3}in distances greater than 4,000 m in x-direction, which is less than the recommended annual thresholds for ambient air benzene in several Asian countries [50]. Thus, pollutants cannot travel long distances from sources, and considerable ground-level concentrations are found up to 4,000 m in the x-direction.

### 4. Conclusions

_{2}compounds. However, a greater space domain should be highlighted. Among the BTEX compounds, benzene accounts for about 75% of pollutants, this is not affected significantly by the reaction. Thus, special attention should be paid to avoid its adverse effects. In conclusion, the Toxchem and presented 3D dispersion model give realistic results and can be used for similar cases.