Numerical Investigation on the Intraphase and Interphase Mass Transfer Limitations for NH 3 -SCR over Cu-ZSM-5

: A systematic modeling approach was scrutinized to develop a kinetic model and a novel monolith channel geometry was designed for NH 3 selective catalytic reduction (NH 3 -SCR) over Cu-ZSM-5. The redox characteristic of Cu-based catalysts and the variations of NH 3 , NO x concentration, and NO x conversion along the axis in porous media channels were studied. The relative pressure drop in different channels, the variations of NH 3 and NO x conversion efﬁciency were analyzed. The model mainly considers NH 3 adsorption and desorption, NH 3 oxidation, NO oxidation, and NO x reduction. The results showed that the model could accurately predict the NH 3 -SCR reaction. In addition, it was found that the Cu-based zeolite catalyst had poor low-temperature catalytic performance and good high-temperature activity. Moreover, the catalytic reaction of NH 3 -SCR was mainly concentrated in the upper part of the reactor. In addition, the hexagonal channel could effectively improve the diffusion rate of gas reactants to the catalyst wall, reduce the pressure drop and improve the catalytic conversion efﬁciencies of NH 3 and NO x . Author Contributions: Conceptualization, S.Y. and J.Z.; software, S.Y.; formal analysis, S.Y. and J.Z.; investigation, S.Y. and J.Z.; resources, J.Z.; writing—original draft preparation, S.Y. and J.Z.; writing—review and editing, S.Y. and J.Z.; supervision, J.Z.; funding acquisition, J.Z. authors


Introduction
A diesel engine is widely used in ships and automobiles [1] because of its high thermal efficiency [2], low fuel consumption [3], low emission, and high efficiency [4]. However, the nitrogen oxides (NO x ) and particulate matter (PM) emitted by diesel engines pose a significant threat to human health and the environment [5]. PM is produced by incomplete combustion at low temperature [6], while NO x is produced by combustion at high temperature and oxygen enrichment [7]. The NO x limits for Euro V and Euro VI are 0.18 g/km and 0.08 g/km, respectively [8]. In order to meet this lower limit, when NO x emission exceeds 0.08 g/km, heavy vehicles need to be equipped with aftertreatment devices, such as selective catalytic reduction (SCR) and Lean NO x Trap (LNT). Nowadays, the world environment is becoming worse and worse. The governments and organizations have formulated relevant emission limitation regulations, which are becoming increasingly stringent [9]. At the same time, the International Maritime Organization (IMO) also developed the marine diesel engine MAPPOL 73/78 anti-pollution convention in the bylaw VI of the marine diesel engine NO x emissions to make a strict limit, the by-law and in January 2000 came into force [10]. The 2019 Annual Report on Motor Vehicle Pollution Prevention and Control in China showed that diesel vehicles accounted for a large share of pollution in 2018, with NO x emissions accounting for 70% of total emissions. Facing the problem of global environmental degradation, how to effectively reduce diesel engine emissions has become the main task of sustainable development of human society [11].
Reducing NO x and particulate emissions has become the focus [12]. The SCR has been widely promoted in recent years due to its good technical economy, high reliability, and insensitive to sulfur [13]. However, in the stage of National IV and above emission regulations, NH 3 -SCR is one of the most commonly used aftertreatment technologies for reducing NO x emission of heavy-duty diesel engine [14]. This technology generates Processes 2021, 9,1966 3 of 18 spatial kinetic model of Cu-based molecular zeolite NH 3 -SCR reaction and analyzed the influence of NH 3 -SCR catalytic reaction. They analyzed the fast and standard SCR reaction conversion at each length position in the axial direction. Many accurate and effective experiment data can be obtained by simulating the engine test bench and evaluating catalyst performance by an SCR simulation reaction system. Compared with the engine bench test, it can eliminate the interference of the external environment and is more conducive to the systematic and scientific study of the reaction kinetic model of the catalyst.
Based on above, it is of great significance to study the influence of the Cu-ZSM-5 catalyst reaction kinetic model on the SCR system. Thus, a 3D-computational fluid dynamics model is established and employed to investigate the reaction kinetic model of Cu molecular sieve catalytic. In addition, the relative pressure drop, NH 3 conversion, and NO x conversion efficiency in different channels were analyzed to provide some reference for improving, optimizing, and applying the NH 3 -SCR system. Thus, the work is very interesting.

SCR Reaction Kinetic Model
The SCR catalytic reactor has many parallel small-sized channels, a large channel length-width ratio, and a large number of channels. In the process of calculation, it is assumed that the flow field of the inlet gas of the SCR reactor is evenly distributed, and the heat transfer loss of the system to the environment is ignored. As shown in Figure 1, the phenomena of SCR mainly involves axial convection and diffusive transport in the gas phase, mass transfer through the gas-solid interface, and radial diffusion and catalytic reactions on the coating. When the NH 3 , NO x , and O 2 in the channel enter the coating (interphase transfer), NH 3 is adsorbed on the catalyst's active sites and subsequently reacts with NO x and O 2 for reduction. The remaining NH 3 , NO x , and O 2 enter the coating (in-phase mass transfer) and continue to react with each other. At the same time, the generated H 2 O, N 2 , and other substances finally diffuse into the channels through the gaps. In the process of establishing the model, the mass transfer at the gas-solid interface adopts Cauchy boundary conditions, and the Hawthorn [34] equation calculates its mass transfer coefficient. At the same time, the model makes the following assumptions: the axial spatial distribution of Cu-based molecular Auvray et al. [32] and establish axial spatial kinetic model of Cu-based molecular zeolite NH3-SCR reaction and ana the influence of NH3-SCR catalytic reaction. They analyzed the fast and standard SC action conversion at each length position in the axial direction. Many accurate and tive experiment data can be obtained by simulating the engine test bench and evalu catalyst performance by an SCR simulation reaction system. Compared with the e bench test, it can eliminate the interference of the external environment and is more ducive to the systematic and scientific study of the reaction kinetic model of the cat Based on above, it is of great significance to study the influence of the Cu-Z catalyst reaction kinetic model on the SCR system. Thus, a 3D-computational flui namics model is established and employed to investigate the reaction kinetic model molecular sieve catalytic. In addition, the relative pressure drop, NH3 conversion NOx conversion efficiency in different channels were analyzed to provide some refe for improving, optimizing, and applying the NH3-SCR system. Thus, the work is interesting.

SCR Reaction Kinetic Model
The SCR catalytic reactor has many parallel small-sized channels, a large ch length-width ratio, and a large number of channels. In the process of calculation, it sumed that the flow field of the inlet gas of the SCR reactor is evenly distributed, an heat transfer loss of the system to the environment is ignored. As shown in Figure  phenomena of SCR mainly involves axial convection and diffusive transport in th phase, mass transfer through the gas-solid interface, and radial diffusion and cataly actions on the coating. When the NH3, NOx, and O2 in the channel enter the coating ( phase transfer), NH3 is adsorbed on the catalyst's active sites and subsequently reacts NOx and O2 for reduction. The remaining NH3, NOx, and O2 enter the coating (inmass transfer) and continue to react with each other. At the same time, the generated N2, and other substances finally diffuse into the channels through the gaps. In the pr of establishing the model, the mass transfer at the gas-solid interface adopts Ca boundary conditions, and the Hawthorn [34] equation calculates its mass transfer c cient. At the same time, the model makes the following assumptions: 1. Ignore the diffusion between the whole channel, the hydrolysis of isocyanat urea. NH3 directly enters the channel. 2. Assuming that the inlet boundary condition of the channel is uniform, the Rideal mechanism is used to calculate the surface catalytic reaction of the Cu m ular sieve. 3. The active catalyst is evenly coated on the coating surface, and the porous me of the coating is evenly distributed.

1.
Ignore the diffusion between the whole channel, the hydrolysis of isocyanate and urea. NH 3 directly enters the channel.

2.
Assuming that the inlet boundary condition of the channel is uniform, the Eley-Rideal mechanism is used to calculate the surface catalytic reaction of the Cu molecular sieve.

3.
The active catalyst is evenly coated on the coating surface, and the porous medium of the coating is evenly distributed.
Processes 2021, 9, 1966 4 of 18 The continuity equation, momentum equation, and enthalpy balance equation of gas-phase components in the channel can be expressed as follows [30]: where ρ is the fluid density, kg/m 3 ; y is the mass fraction of component, %; v is the volume, m 3 ; t is time, s; z is the axial distance, m; D i is the diffusion coefficient of the species i in pores, m 2 /s; µ is the viscosity, Pa·s; c p is the specific heat capacity, J/(kg·K); T is the temperature, K; and λ is the thermal conductivity, W/(m·K). The composition continuity equation, enthalpy balance equation, and NH 3 coverage balance equation of gaseous substances in the coating are as follows [30]: where D w,i is the effective diffusion coefficient of component i, m 2 /s; x is the mole fraction of component, %; y w,i is the mass fraction of component i, %; a c is the geometric surface area m 2 /m 3 ; M i is the molar mass of each i component, g/mol; r j is the reaction rate of reaction j, mol/(s·m 3 ); ∆H m,j is the enthalpy of reaction j, J/mol; Ω is NH 3 storage capacity, mol/m 3 ; θ NH3 is the NH 3 surface site fraction; and γ i,j is the stoichiometric coefficient of the reaction of component i at j. The component continuity equation and enthalpy balance equation between gas and coating are as follows [30]: where k m is the mass transfer coefficient, kg/(m 2 ·s); h T is the heat transfer coefficient, kg/(s·m 2 ); d h is the channel length, m; and k is the reaction constant, S −1 . The main reactions of the NH 3 -SCR catalytic reduction reaction are shown in Table 1. Table 1. Catalytic reaction of Cu molecular sieve.

NO. Reactions
Processes 2021, 9, 1966 5 of 18 In addition, the NH 3 desorption activation energy parameter is modified by Temkin, and the following equation can calculate the NH 3 adsorption and desorption reaction rates: where r des and r ads is the reaction rates of NH 3 desorption and adsorption, mol/(s · m 3 ); k des and k ads is the reaction rate constant of NH 3 desorption and adsorption, s −1 ; c NH3 is the NH 3 molar concentration, mol/m 3 . The NO and NH 3 reaction rates can be obtained by the following equation: where r NH3 and r NO is the reaction rates of NH 3 and NO, mol/(s · m 3 ); k eq , k NH3 and k NO is the reaction rate constants of equilibrium, NH 3 and NO, s −1 ; c NO and c O2 is the NO and O 2 molar concentration, mol/m 3 . The rapid and stand reaction rates can be obtained by the following equation: where r rap and r sta is the rapid and stand reaction rates, mol/(s · m 3 ); k rap and k sta is the rapid and stand reaction rate constants, s −1 ; c NO2 is the NO 2 molar concentration, mol/m 3 , θ * NH3 is the critical NH 3 surface concentration value.

Pore Diffusion Model
Diffusion phenomena in pore media are widely present in external mass transfer and internal mass transfer processes in porous media. The diffusion of components in the diesel exhaust gas in SCR porous media is related to the micropores' pore size, length, and shape [35]. The multi-component diffusion coefficient is obtained by the following equation: The molecular diffusion coefficient of binary bulk can be obtained by the following equation [35]: The Knudsen diffusion coefficient can be obtained by the following equation [36]: The tortuosity square or tortuosity factor enters into the final form of the effective coefficient. In addition, the increase of superficial flux and the additional path length are considered. Based on the residence time of component i in the porous structure, a relation between the effective and pore gas diffusion coefficients is obtained by the following equation [37]: Processes 2021, 9, 1966 6 of 18 where τ is the tortuosity factor; l is the actual length of coating hole, m; l e is the total length of coating, m; ε is the porosity of washcoat. Based on the stationary and not-stationary diffusion, the Equation (18) is also confirmed in Ref. [38]. The porous structure is showed in Figure 2. The porous structure includes many cylindrical pores with the same cross-sectional area S ⊥ . The length of each pore can be obtained by the following equation [39].
where τ is the tortuosity factor; l is the actual length of coating hole, m; le is the total length of coating, m; ε is the porosity of washcoat. Based on the stationary and not-stationary diffusion, the Equation (18) is also confirmed in Ref. [38]. The porous structure is showed in Figure 2. The porous structure includes many cylindrical pores with the same cross-sectional area S┴. The length of each pore can be obtained by the following equation [39].
The above equation is reduce to le = l/cosθ. If there are n such pores per unit surface of the porous material, the porosity ε is obtained by the equation [30]: e l nS l    (20) where S┴ is cross-sectional area, m 2 . The above equation is reduce to l e = l/cosθ. If there are n such pores per unit surface of the porous material, the porosity ε is obtained by the equation [30]: where S ⊥ is cross-sectional area, m 2 . Therefore, the total macroscopic molar diffusion flux in porous media in the sinusoidal capillary model can be calculated by the following equation [38]: where D bulk is the bulk molecular diffusion coefficient; the ∆c is the concentration difference of i component; the equation gives D e f f = ε D bulk (l e /l) 2 , where τ = (l e /l) 2 is the tortuosity factor.
The tortuosity square can be employed to estimate the gas diffusion coefficients. A sudden change of any species concentration is put on the left-hand side in Figure 2, and the concentration on the right-hand side will start to increase after a certain time. The time can be obtained by the following equation [39]: According to the characteristics of the research object, the diffusion coefficients in the mesopores D e f f im is a combination of the bulk and Knudsen diffusivities. Thus, the Processes 2021, 9,1966 7 of 18 multi-component effective gas diffusion coefficient can be calculated by the following equation [38]: According to the conclusions and practical application of Ref. [40], the porosity value selects ε = τ −2/3 [41]. The calculated effective diffusion coefficients of reaction products O 2 , NO and NH 3 are shown in Figure 3. It can be found that the model can accurately calculate the effective diffusion coefficient of each component.
sudden change of any species concentration is put on the left-hand side in Figure 2, and the concentration on the right-hand side will start to increase after a certain time. The time can be obtained by the following equation [39]: According to the characteristics of the research object, the diffusion coefficients in the mesopores eff im D is a combination of the bulk and Knudsen diffusivities. Thus, the multicomponent effective gas diffusion coefficient can be calculated by the following equation [38]: where Dim bulk is the diffusion coefficient of multi-component in the channel, m 2 /s; Dk is Knudsen diffusion coefficient, m 2 /s; Dim eff is the effective diffusion coefficient of multi-component, m 2 /s. According to the conclusions and practical application of Ref. [40], the porosity value selects ε = τ −2/3 [41]. The calculated effective diffusion coefficients of reaction products O2, NO and NH3 are shown in Figure 3. It can be found that the model can accurately calculate the effective diffusion coefficient of each component.

Model Validation
In order to verify the accuracy of the simulation model, the Cu-ZSM-5 molecular sieves catalytic reactor was used to verify the model. The main parameters of the Cu-based molecular sieve catalytic reactor and catalyst are shown in Table 2. The AVL AMAi60 gas analyzer was used for the measurement. The different temperatures, flows, and pressures were measured by the corresponding sensors. The specific test bench is shown in Figure  4. The bench can generate The NH3 of 500 × 10 −6 , NO of 500 × 10 −6 , 2% H2O and 5% O2 (GHSV = 7200 h −1 ) can be generated by the experimental bench and the intake air can be controlled by the adjust valve. Then the gas is heated by a heater, and finally, a catalytic reaction occurs in the SCR catalyst. In order to prevent the cross-contamination of catalysts, all catalysts were first run with 5% O2 and N2 for 20 min at 500 °C to completely

Model Validation
In order to verify the accuracy of the simulation model, the Cu-ZSM-5 molecular sieves catalytic reactor was used to verify the model. The main parameters of the Cu-based molecular sieve catalytic reactor and catalyst are shown in Table 2. The AVL AMAi60 gas analyzer was used for the measurement. The different temperatures, flows, and pressures were measured by the corresponding sensors. The specific test bench is shown in Figure 4. The bench can generate The NH 3 of 500 × 10 −6 , NO of 500 × 10 −6 , 2% H 2 O and 5% O 2 (GHSV = 7200 h −1 ) can be generated by the experimental bench and the intake air can be controlled by the adjust valve. Then the gas is heated by a heater, and finally, a catalytic reaction occurs in the SCR catalyst. In order to prevent the cross-contamination of catalysts, all catalysts were first run with 5% O 2 and N 2 for 20 min at 500 • C to completely remove residual NO x and NH 3 before the experiments were conducted. In addition, the pipes were insulated with glass wool to reduce heat loss.  The SCR reaction kinetic simulation model of Cu molecular zeolite catalyst was established in this paper and included mainly seven steps of the total reaction. The simulation results were optimized by adjusting the kinetic parameters such as pre-factor and activation energy in the model until the experimental results agreed with the simulation results. At the outlet, the experiment and simulation NO and NH3 concentrations in the standard SCR oxidation reaction are shown in Figure 5. It could be seen that the concentration errors of NO and NH3 at the outlet of experimental measurement and simulation calculation were within 5%, which indicated that the model could accurately predict the SCR reaction.  The SCR reaction kinetic simulation model of Cu molecular zeolite catalyst was established in this paper and included mainly seven steps of the total reaction. The simulation results were optimized by adjusting the kinetic parameters such as pre-factor and activation energy in the model until the experimental results agreed with the simulation results. At the outlet, the experiment and simulation NO and NH 3 concentrations in the standard SCR oxidation reaction are shown in Figure 5. It could be seen that the concentration errors of NO and NH 3 at the outlet of experimental measurement and simulation calculation were within 5%, which indicated that the model could accurately predict the SCR reaction.  The SCR reaction kinetic simulation model of Cu molecular zeolite catalyst was established in this paper and included mainly seven steps of the total reaction. The simulation results were optimized by adjusting the kinetic parameters such as pre-factor and activation energy in the model until the experimental results agreed with the simulation results. At the outlet, the experiment and simulation NO and NH3 concentrations in the standard SCR oxidation reaction are shown in Figure 5. It could be seen that the concentration errors of NO and NH3 at the outlet of experimental measurement and simulation calculation were within 5%, which indicated that the model could accurately predict the SCR reaction.

Axial Distribution of SCR Catalytic Reaction
NH 3 with molar concentrations of 500 × 10 −6 , NO with molar concentrations of 500 × 10 −6 , 2% H 2 O, and 5% O 2 were added to the SCR reactor. The NH 3 concentration, NO x concentration, and NO x conversion in the axial direction of the catalyst under inlet conditions were simulated and studied in the steady-state standard SCR reaction, rapid SCR reaction, and NO 2 -SCR reaction [42,43].

Standard SCR Reaction
(1) NH 3 concentration The variation of axial NH 3 concentration under standard SCR reaction condition at a steady state is shown in Figure 6. It can be seen that the concentration of NH 3 changes little at low temperatures. More specifically, with the variation of catalyst position, the effect is not obvious at 180 • C. It is due to the lower low-temperature activity of the Cu zeolite catalyst. When the temperature of the reactor exceeds 280 • C, the NH 3 concentration gradually decreases with the increase of catalyst position. This is due to the higher lowtemperature activity of the Cu zeolite catalyst at high temperatures. Thus, the concentration of NH 3 decreases with the increase of catalyst position. In addition, Komatsu et al. [44] suggested that Cu particles increased the concentration of NO 2 , which reacted with NH 3 and produced N 2 and H 2 O, thus reducing the NH 3 concentration. Thus, the higher the temperature, the more NH 3 concentration decreases. Auvary et al. [32] and Gong et al. [45] have similar conclusions.
10 , 2% H2O, and 5% O2 were added to the SCR reactor. The NH3 concentration, NOx concentration, and NOx conversion in the axial direction of the catalyst under inlet conditions were simulated and studied in the steady-state standard SCR reaction, rapid SCR reaction, and NO2-SCR reaction [42,43].

Standard SCR Reaction
(1) NH3 concentration The variation of axial NH3 concentration under standard SCR reaction condition at a steady state is shown in Figure 6. It can be seen that the concentration of NH3 changes little at low temperatures. More specifically, with the variation of catalyst position, the effect is not obvious at 180 °C. It is due to the lower low-temperature activity of the Cu zeolite catalyst. When the temperature of the reactor exceeds 280 °C, the NH3 concentration gradually decreases with the increase of catalyst position. This is due to the higher low-temperature activity of the Cu zeolite catalyst at high temperatures. Thus, the concentration of NH3 decreases with the increase of catalyst position. In addition, Komatsu et al. [44] suggested that Cu particles increased the concentration of NO2, which reacted with NH3 and produced N2 and H2O, thus reducing the NH3 concentration. Thus, the higher the temperature, the more NH3 concentration decreases. Auvary et al. [32] and Gong et al. [45] have similar conclusions. (2) NOx concentration Figure 7 shows the variation of catalyst axial NOx concentration under standard SCR reaction condition at a steady state. It can be seen that the NOx concentration changes little at low temperatures. With the increase of temperature, the NOx conversion increases due to the increasing gradually activity of the Cu zeolite catalyst. Between 380 °C and 480 °C, NOx on the Cu zeolite catalyst surface can be almost completely converted, resulting in the decrease of NOx concentration. More specifically, at catalyst position of 1.0 cm, the conversion efficiency has reached more than 85%. When the catalyst position is 1.9 cm, 95% of the NOx has been converted. Henry et al. [33] had a similar conclusion. Therefore, the length of the catalyst can be reasonably selected. (2) NO x concentration Figure 7 shows the variation of catalyst axial NO x concentration under standard SCR reaction condition at a steady state. It can be seen that the NO x concentration changes little at low temperatures. With the increase of temperature, the NO x conversion increases due to the increasing gradually activity of the Cu zeolite catalyst. Between 380 • C and 480 • C, NO x on the Cu zeolite catalyst surface can be almost completely converted, resulting in the decrease of NO x concentration. More specifically, at catalyst position of 1.0 cm, the conversion efficiency has reached more than 85%. When the catalyst position is 1.9 cm, 95% of the NO x has been converted. Henry et al. [33] had a similar conclusion. Therefore, the length of the catalyst can be reasonably selected. (3) NOx conversion The variation of axial NOx conversion under standard SCR reaction conditions at a steady state are shown in Figure 8. It can be seen that the concentration of NOx changes little at low temperatures. Only when the temperature in the reactor exceeds 280 °C, the activity of the catalyst increases significantly. More specifically, when the temperature reaches 380 °C, the conversion rate has reached more than 95% at 1.  The variation of axial NO x conversion under standard SCR reaction conditions at a steady state are shown in Figure 8. It can be seen that the concentration of NO x changes little at low temperatures. Only when the temperature in the reactor exceeds 280 • C, the activity of the catalyst increases significantly. More specifically, when the temperature reaches 380 • C, the conversion rate has reached more than 95% at 1.2 cm. Metkar et al. [46] and Xue et al. [47] also proved that the higher the temperature, the higher the NO x conversion efficiency. In addition, it can be found that the SCR reaction is mainly concentrated in the first half part of the reactor, and the influence of the rear section is small. Therefore, the length of the reactor can be reasonably selected to optimize its structure. (3) NOx conversion The variation of axial NOx conversion under standard SCR reaction conditions at a steady state are shown in Figure 8. It can be seen that the concentration of NOx changes little at low temperatures. Only when the temperature in the reactor exceeds 280 °C, the activity of the catalyst increases significantly. More specifically, when the temperature reaches 380 °C, the conversion rate has reached more than 95% at 1.2 cm. Metkar et al. [46] and Xue et al. [47] also proved that the higher the temperature, the higher the NOx conversion efficiency. In addition, it can be found that the SCR reaction is mainly concentrated in the first half part of the reactor, and the influence of the rear section is small. Therefore, the length of the reactor can be reasonably selected to optimize its structure.

Fast SCR Reaction
(1) NH3 concentration The variation of NH3 concentration in the axial direction of the catalyst under fast SCR reaction conditions at a steady state is shown in Figure 9. Compared with standard

Fast SCR Reaction
(1) NH 3 concentration The variation of NH 3 concentration in the axial direction of the catalyst under fast SCR reaction conditions at a steady state is shown in Figure 9. Compared with standard SCR reaction (Seen Figure 6), the NH 3 concentration of fast SCR reaction is also significantly transformed at low temperatures. Moreover, the NH 3 concentration decreases faster in the first half of the catalyst. In addition, the concentration of NH 3 is lower than that of NO x . This is due to the reduction of NH 3 concentration due to the existence of an NH 3 oxidation reaction. Metkar et al. [48] and Lu et al. [49] have similar experimental conclusions. SCR reaction (Seen Figure 6), the NH3 concentration of fast SCR reaction is also significantly transformed at low temperatures. Moreover, the NH3 concentration decreases faster in the first half of the catalyst. In addition, the concentration of NH3 is lower than that of NOx. This is due to the reduction of NH3 concentration due to the existence of an NH3 oxidation reaction. Metkar et al. [48] and Lu et al. [49] have similar experimental conclusions. (2) NOx concentration Figure 10 shows the catalyst axial NOx concentration variation under the fast SCR reaction condition in a steady state. Compared with the standard SCR, NOx in the first half of the reactor is also significantly converted in the fast SCR reaction, and the speed of (2) NO x concentration Figure 10 shows the catalyst axial NO x concentration variation under the fast SCR reaction condition in a steady state. Compared with the standard SCR, NO x in the first half of the reactor is also significantly converted in the fast SCR reaction, and the speed of the fast SCR reaction is faster. This is because the NO x conversion activity of the zeolite catalyst gradually increases with the increase of temperature under the fast reaction. Activity has been greatly improved. Meanwhile, the concentration of NO x in the reactor is higher than that of NH 3 due to an NH 3 oxidation reaction (Figure 9). (2) NOx concentration Figure 10 shows the catalyst axial NOx concentration variation under the fast SCR reaction condition in a steady state. Compared with the standard SCR, NOx in the first half of the reactor is also significantly converted in the fast SCR reaction, and the speed of the fast SCR reaction is faster. This is because the NOx conversion activity of the zeolite catalyst gradually increases with the increase of temperature under the fast reaction. Activity has been greatly improved. Meanwhile, the concentration of NOx in the reactor is higher than that of NH3 due to an NH3 oxidation reaction (Figure 9). (3) NOx conversion Figure 11 shows the catalyst axial NOx conversion variation under the fast SCR reaction condition in a steady state. It can be seen that the NOx conversion rate of the fast SCR (3) NO x conversion Figure 11 shows the catalyst axial NO x conversion variation under the fast SCR reaction condition in a steady state. It can be seen that the NO x conversion rate of the fast SCR reaction increases gradually at all temperatures. It is because the presence of NO 2 in the reaction improves the NO x conversion efficiency and the reaction is much faster than the standard SCR reaction. In addition, with the increase of catalyst position, the conversion increases gradually. This shows that the activity of Cu-based catalysts is enhanced under fast reaction. At the same temperature, the position dependence of the rapid SCR reaction on the catalyst decreases (after 0.9 cm, the effect is small), which may be due to the higher total conversion caused by the mixed reaction control. reaction increases gradually at all temperatures. It is because the presence of NO2 in the reaction improves the NOx conversion efficiency and the reaction is much faster than the standard SCR reaction. In addition, with the increase of catalyst position, the conversion increases gradually. This shows that the activity of Cu-based catalysts is enhanced under fast reaction. At the same temperature, the position dependence of the rapid SCR reaction on the catalyst decreases (after 0.9 cm, the effect is small), which may be due to the higher total conversion caused by the mixed reaction control.

NO 2 -SCR Reaction (1) NO x concentration
The variation of catalyst axial NO 2 concentration under NO 2 -SCR reaction condition in a steady state are shown in Figure 12. It can be seen that more NO 2 will be produced at 180-280 • C, and the concentration of NO 2 increases with the increase of reactor location. However, there is less NO 2 in the high-temperature stage. This is because the oxidation reaction of NO is reversible. At low temperature, the reaction rate is controlled by reaction kinetics, while at high temperature, the reaction is controlled by reaction equilibrium, and NO 2 decomposes to produce NO. For example, Shi et al. [50] reached a similar conclusion. In addition, it can be found that the concentration of NO 2 remains unchanged when the reactor position is 0.6 cm at high temperatures (380-480 • C).

NO2-SCR Reaction
(1) NOx concentration The variation of catalyst axial NO2 concentration under NO2-SCR reaction condition in a steady state are shown in Figure 12. It can be seen that more NO2 will be produced at 180-280 °C, and the concentration of NO2 increases with the increase of reactor location. However, there is less NO2 in the high-temperature stage. This is because the oxidation reaction of NO is reversible. At low temperature, the reaction rate is controlled by reaction kinetics, while at high temperature, the reaction is controlled by reaction equilibrium, and NO2 decomposes to produce NO. For example, Shi et al. [50] reached a similar conclusion. In addition, it can be found that the concentration of NO2 remains unchanged when the reactor position is 0.6 cm at high temperatures (380-480 °C).  (2) NO x conversion The variation of catalyst axial NO x conversion under NO 2 -SCR reaction condition in a steady state are shown in Figure 13. It can be seen that the presence of NO 2 improves the overall conversion of NO x . However, NO 2 -SCR reaction is faster than standard SCR but slower than the fast SCR. In addition, NO 2 -SCR reaction is mainly concentrated in the first half of the catalytic reactor, and there is only a slight increase in the second half. Moreover, at 280-480 • C, the NO x conversion rate is relatively high. This shows that the catalytic activity increases gradually with the increase of temperature. NO x reacts from 280 • C, and the conversion rate increases gradually with the increase of the position of the catalyst. Finally, it tends to be stable. In addition, it can be seen from Figure 13 that the conversion efficiency of NO x is the best at the position of 1.2 cm. (2) NOx conversion The variation of catalyst axial NOx conversion under NO2-SCR reaction condition in a steady state are shown in Figure 13. It can be seen that the presence of NO2 improves the overall conversion of NOx. However, NO2-SCR reaction is faster than standard SCR but slower than the fast SCR. In addition, NO2-SCR reaction is mainly concentrated in the first half of the catalytic reactor, and there is only a slight increase in the second half. Moreover, at 280-480 °C, the NOx conversion rate is relatively high. This shows that the catalytic activity increases gradually with the increase of temperature. NOx reacts from 280 °C, and the conversion rate increases gradually with the increase of the position of the catalyst. Finally, it tends to be stable. In addition, it can be seen from Figure 13 that the conversion efficiency of NOx is the best at the position of 1.2 cm.

Reaction Conditions of Different SCR Channel Cross-Sections
In order to further improve the heat and mass transfer of the SCR channel, three different structures of SCR channels were designed and then calculated and simulated to optimize the performance of each SCR channel. The first structure is a square channel, the

Reaction Conditions of Different SCR Channel Cross-Sections
In order to further improve the heat and mass transfer of the SCR channel, three different structures of SCR channels were designed and then calculated and simulated to optimize the performance of each SCR channel. The first structure is a square channel, the second structure is a rectangular channel, and the third structure is a hexagonal channel. The wall thickness C of the three channels is 0.7 mm, and the length A and width B are shown in Figure 14. Under the same boundary condition, the effects of different length-width ratio structures on SCR channel performance are studied using the verified simulation model in term of pressure drop, NH 3 conversion, and NO x conversion are discussed.

Reaction Conditions of Different SCR Channel Cross-Sections
In order to further improve the heat and mass transfer of the SCR channel, three different structures of SCR channels were designed and then calculated and simulated to optimize the performance of each SCR channel. The first structure is a square channel, the second structure is a rectangular channel, and the third structure is a hexagonal channel.
The wall thickness C of the three channels is 0.7 mm, and the length A and width B are shown in Figure 14. Under the same boundary condition, the effects of different lengthwidth ratio structures on SCR channel performance are studied using the verified simulation model in term of pressure drop, NH3 conversion, and NOx conversion are discussed.  It can be seen that with the increase of length-width ratio, the relative pressure drop, relative NO conversion, and relative NH 3 conversion all show a decreasing trend. When the length-width ratio is greater than 5, the length-width ratio has little effect on the relative pressure drop, relative NO conversion, and NH 3 conversion. This also shows that when selecting rectangular or square channels, the interval with a length-width ratio of 1-5 is a range worthy of consideration. For example, compared with square (A = 4.0), when the length-width ratio is 2, the relative pressure drop, relative NH 3 conversion, and relative NO conversion ratio of the rectangle (A = 3.2) are reduced by 6.8%, 0.15%, and 0.12%, respectively. Meanwhile, with the increase of width A, the relative pressure drop, relative NO conversion, and relative NH 3 conversion decreased.
A significant disadvantage of square and rectangular channels is that the adjacent edges intersect at a right angle. It is unfavorable for gas flow. Thus, the gas pressure drop is increased, and the reduction efficiency of nitrogen oxides is reduced in the channel. In addition, sharp right-angle edges are easy to be block, resulting in the failure of SCR porous media channel. In order to overcome this deficiency, this paper changes the rectangular channel with 90 • edge to the hexagonal channel with 120 • edge. The chemical reaction of gas will be improved due the improvement of gas flow. The velocity cross-section distribution of gas passing through the rectangular and hexagonal channels under the same boundary conditions is shown in Figure 16. It can be seen that the gas flow field distribution in the hexagonal channel is more uniform than that in the rectangular channel. At the corner of the rectangular channel, the flow rate of a large part of the reaction gas is very low or even stagnant. Therefore, more dead zones of gas reaction with catalyst are formed at the corner of the rectangular channel. Among them, the area where the cross-section velocity of the rectangular channel is less than 5 m/s accounts for 38%. Compared with rectangular channel, the area where the cross-section velocity of the hexagonal channel is less than 5 m/s accounts for 33%. Thus, the hexagonal channel can effectively increase the diffusion rate of gas reactants to the catalyst wall to improve the catalytic conversion efficiency.
tained, as shown in Figure 15a-c.
It can be seen that with the increase of length-width ratio, the relative pressure drop, relative NO conversion, and relative NH3 conversion all show a decreasing trend. When the length-width ratio is greater than 5, the length-width ratio has little effect on the relative pressure drop, relative NO conversion, and NH3 conversion. This also shows that when selecting rectangular or square channels, the interval with a length-width ratio of 1-5 is a range worthy of consideration. For example, compared with square (A = 4.0), when the length-width ratio is 2, the relative pressure drop, relative NH3 conversion, and relative NO conversion ratio of the rectangle (A = 3.2) are reduced by 6.8%, 0.15%, and 0.12%, respectively. Meanwhile, with the increase of width A, the relative pressure drop, relative NO conversion, and relative NH3 conversion decreased. A significant disadvantage of square and rectangular channels is that the adjacent edges intersect at a right angle. It is unfavorable for gas flow. Thus, the gas pressure drop is increased, and the reduction efficiency of nitrogen oxides is reduced in the channel. In addition, sharp right-angle edges are easy to be block, resulting in the failure of SCR porous media channel. In order to overcome this deficiency, this paper changes the rectangular channel with 90° edge to the hexagonal channel with 120° edge. The chemical reaction of gas will be improved due the improvement of gas flow. The velocity cross-section distribution of gas passing through the rectangular and hexagonal channels under the same boundary conditions is shown in Figure 16. It can be seen that the gas flow field distribution in the hexagonal channel is more uniform than that in the rectangular channel. At the corner of the rectangular channel, the flow rate of a large part of the reaction gas is very low or even stagnant. Therefore, more dead zones of gas reaction with catalyst are formed at the corner of the rectangular channel. Among them, the area where the cross-section velocity of the rectangular channel is less than 5 m/s accounts for 38%. Compared with rectangular channel, the area where the cross-section velocity of the hexagonal channel is less than 5 m/s accounts for 33%. Thus, the hexagonal channel can effectively increase the diffusion rate of gas reactants to the catalyst wall to improve the catalytic conversion efficiency. The relative NO conversion, relative NH3 conversion, and relative pressure drop for the rectangular and hexagonal channels relative to the square channel are shown in Figure  17a-c. It can be found that the hexagonal channel further enhances the heat and mass transfer between the gas and the catalyst wall and reduces the pressure drop of the gas in the channel when the length-width ratio and wall thickness are constant. For example, compared with the square channel (A = 4.0), the relative pressure drop of the designed hexagonal channel is reduced by 9.6%, and the relative NO conversion and relative NH3 The relative NO conversion, relative NH 3 conversion, and relative pressure drop for the rectangular and hexagonal channels relative to the square channel are shown in Figure 17a-c. It can be found that the hexagonal channel further enhances the heat and mass transfer between the gas and the catalyst wall and reduces the pressure drop of the gas in the channel when the length-width ratio and wall thickness are constant. For example, compared with the square channel (A = 4.0), the relative pressure drop of the designed hexagonal channel is reduced by 9.6%, and the relative NO conversion and relative NH 3 conversion are increased by 0.51% and 0.48%. Therefore, a reasonable selection of structural parameters of SCR catalysts can effectively optimize the SCR catalyst system. The relative NO conversion, relative NH3 conversion, and relative pressure drop for the rectangular and hexagonal channels relative to the square channel are shown in Figure  17a-c. It can be found that the hexagonal channel further enhances the heat and mass transfer between the gas and the catalyst wall and reduces the pressure drop of the gas in the channel when the length-width ratio and wall thickness are constant. For example, compared with the square channel (A = 4.0), the relative pressure drop of the designed hexagonal channel is reduced by 9.6%, and the relative NO conversion and relative NH3 conversion are increased by 0.51% and 0.48%. Therefore, a reasonable selection of structural parameters of SCR catalysts can effectively optimize the SCR catalyst system.

Conclusions
With the increasingly stringent emission regulations due to energy crisis [51][52][53][54][55][56][57] and environmental problems [58][59][60][61][62][63][64][65][66][67][68], how to effectively reduce NOx emission from a diesel engine has become a concern [69]. In order to reduce the NOx emission, the kinetic model of NH3-SCR reaction over Cu-ZSM-5 catalyst was established in this paper. Firstly, the NH3 concentration, NOx concentration, and NOx conversion rate variation laws along the axis were analyzed. Secondly, the relative pressure drops, relative NH3 conversions, and relative NOx conversion efficiencies of different SCR channels were studied. Finally, the main conclusions were as follows: (1) The improved model can better predict the catalytic reaction of the diesel SCR system.
(2) The Cu-based zeolite catalyst is of poor low-temperature characteristics and good high-temperature activity. (3) NH3-SCR catalytic reaction is mainly concentrated in the first half of the reactor, and the influence of the second half is little. (4) The hexagonal channel can effectively increase the diffusion rate of gas reactants to the catalyst wall, reduce the pressure drop and improve the catalytic conversion efficiencies of NH3 and NOx.

Conclusions
With the increasingly stringent emission regulations due to energy crisis [51][52][53][54][55][56][57] and environmental problems [58][59][60][61][62][63][64][65][66][67][68], how to effectively reduce NO x emission from a diesel engine has become a concern [69]. In order to reduce the NO x emission, the kinetic model of NH 3 -SCR reaction over Cu-ZSM-5 catalyst was established in this paper. Firstly, the NH 3 concentration, NO x concentration, and NO x conversion rate variation laws along the axis were analyzed. Secondly, the relative pressure drops, relative NH 3 conversions, and relative NO x conversion efficiencies of different SCR channels were studied. Finally, the main conclusions were as follows: (1) The improved model can better predict the catalytic reaction of the diesel SCR system.
(2) The Cu-based zeolite catalyst is of poor low-temperature characteristics and good high-temperature activity. (3) NH 3 -SCR catalytic reaction is mainly concentrated in the first half of the reactor, and the influence of the second half is little. (4) The hexagonal channel can effectively increase the diffusion rate of gas reactants to the catalyst wall, reduce the pressure drop and improve the catalytic conversion efficiencies of NH 3 and NO x . Data Availability Statement: All data used to support the findings of this study are included within the article.

Conflicts of Interest:
The authors declare that they have no conflict of interests regarding the publication of this paper.