Simulation of Denitriﬁcation of Vehicle Exhaust over Cu-CHA Bazite Catalyst for a Monolith Reactor

: A CFD model with chemical reaction kinetic and heat and mass transfer for a monolith reactor is established by COMSOL Multiphysics to investigate the inﬂuence of different operating conditions and water on denitriﬁcation efﬁciency for Cu-CHA. At the low temperature range, water has little effect on the denitriﬁcation efﬁciency over the Cu-CHA catalyst while NO conversion is increased by about 30% at the medium temperature. The concentration of O 2 ( C O2 ) has no signiﬁcant effect on the performance of Cu-CHA catalyst. The best ratio of NO 2 to NO x in feed gases may be 1/2, which improves the denitriﬁcation efﬁciency and the yield of N 2 but it produces relatively little N 2 O. The optimal ammonia-nitrogen ratio is 1.1, where Cu-CHA catalyst has fairly great denitriﬁcation efﬁciency and low NH 3 leakage. Increasing inlet ﬂow velocity and cross area of channels have negative effect on NO conversion, while longer channels and thicker substrate have the opposite effect.


Introduction
Due to the high energy consumption, the environmental pollution caused by the use of non-renewable energy needs to be solved urgently. Diesel vehicle exhaust contains a large amount of nitrogen oxide, which poses threats to human health and the environment. As one of the most mature and widest used technology for denitrification, selective catalytic reduction with ammonia (NH 3 -SCR) has been studied in various aspects. According to the different reaction rate, NH 3 -SCR can be divided into three types: standard SCR (Equation (1)), fast SCR (Equation (2)) and NO 2 -SCR (Equation (3)): The reason why the fast SCR has a faster reaction rate than the standard SCR is that the oxidation ability of NO 2 is stronger than that of O 2 . However, the share of NO 2 in diesel exhaust is about 5%, so NO 2 -SCR becomes known as slow SCR. Therefore, the ratio of NO 2 in the feed gases is very important. Also, some researches on the influence of NO 2 on Cu-SSZ-13 [1], Cu-SSZ-39 [2], Cu-T3 [3] etc. indicate that NO 2 can result in the promotion of NO x conversion.
Many kinds of catalysts have been found to be used in NH 3 -SCR because of the active sites on their surface that can adsorb NO x in vehicle exhaust. As so far, catalysts applied to NH 3 -SCR are generally used at medium and high temperature, and have poor water and sulfur resistance, such as commercial V 2 O 5 -TiO 2 . Hence, it is necessary

Effect of the Presence of H 2 O in Reactant Mixture
Figures 1 and 2 compare the NO and NH 3 conversion between simulated and experimental values under various operating conditions. As can be seen from Figures 1 and 2, it reveals that water evidently improves the ability of Cu-CHA to convert NO at medium temperature, with an increase of 30.468% (experiment) and 27.947% (simulation). And it increases NH 3 conversion by 10.341% (experiment) and 29.597% (simulation) at low temperature. Under both operating conditions, NO conversion climbs at low temperature, peaks to maximum at 250 • C, then decline at medium temperature. And Figure 2 shows rapidly rise of NH 3 conversion, followed by a muted growth after 250 • C, and then it reaches approximate 100% eventually. H 2 O also decreases the temperature for Cu-CHA reaching maximum NH 3 conversion. The finding is different from the well-known result that H 2 O would inhibit the NH 3 -SCR reactions over other metals and their oxide catalysts, due to the active sites competition among H 2 O and reactants (NH 3 and NO) or forming nitrate accumulating on the surface of the catalysts [20][21][22]. The special feature of Cu-CHA makes it a very suitable catalyst for NH 3 -SCR, because H 2 O is abundant in diesel vehicle exhaust and it is produced by NH 3 -SCR reaction as well. Actually, this phenomenon is probably due to H 2 O inhibits ammonia oxidation, which occurs at the temperature higher than 300 • C. And at low temperature, this effect may attribute to the enhancement of Cu reducibility and the increase of Bronsted acidity, resulting in more NH 3 to be absorbed [16]. The enhancement of NH 3 conversion means a reduction of the possibility of NH 3 leakage.   Oxygen participates in most reactions in the global kinetic model of NH 3 -SCR, for instance, NH 3 oxidation, NO oxidation, N 2 O decomposition. And it plays an important role in determining the dominant reaction among standard SCR, fast SCR and NO 2 -SCR. So, it is necessary to study the effect of C O2 on denitrification efficiency. Figure 3 shows the simulated results of NO conversion with 0.1%, 2% and 6% O 2 in feed gas. From Figure 3, it can be seen that with the increase of C O2 , NO conversion has little improvement. The more O 2 could stimulate standard SCR (Equation (1)) and promote NO oxidizing to more NO 2 , which is help to fast SCR (Equation (2)). However, because NO and NO 2 have higher oxidation ability than O 2 and the concentration of reactants is low in this model, the difference is not obvious.

Effect of Concentration of NO 2
In fact, NO accounts for 90-95% of NO x in diesel exhaust due to a high burning temperature inside the internal combustion engine. NO would be partially converted into NO 2 , the reaction equation is given by: This equilibrium is reversible, and Shin, et al. [24] believe that the reaction is thermodynamically controlled above 270 • C and kinetically controlled below 270 • C. The percentage of NO 2 in reactant gases plays an important role in reduction of NO x . Defining x 0 as the ratio of NO 2 to NO x , x 0 varies from 0 to 1.
In this study, five operating conditions were selected to simulate outlet concentration of NO, N 2 and N 2 O. As shown in Table 1, it includes inlet concentrations of components corresponding to different x 0 . Figures 4 and 5 illustrate the outlet concentrations of NO and N 2 , as a function of the reaction temperature and x 0 respectively.    As shown in Figure 4, the outlet C NO reduces to a minimum at 250 • C and then gradually rises under each x 0 . And at the same reaction temperature, with the increase of value of x 0 , the outlet C NO significantly decreases, indicating the presence of NO 2 in feed gas has a positive influence on NO conversion. When x 0 is larger than 0.5, the outlet C NO is close to zero within the range of 200-300 • C, which means that the inlet NO has almost been converted to NO 2 or N 2 . As can be seen from Figure 5, reaction temperature and the value of x 0 greatly influences the yield of N 2 . The outlet C N2 peaks to maximum at 250 • C when x 0 ≤ 0.25 and at 300 • C when x 0 ≥ 0.25, then it decline sharply. Furthermore, as the value of x 0 growing, the yield of N 2 increases and then decreases under the same temperature. Actually, different values of x 0 mean different C NO2 in feed gases and can result in a different selective catalytic reaction. Generally speaking, x 0 = 0-0.5 is the transition period from standard SCR to fast SCR and x 0 = 0.5-0.75 is fast SCR to NO 2 -SCR. The result demonstrates that standard SCR prevails most at 250 • C while fast SCR at 300 • C. Due to the oxidation ability of NO 2 being better than that of O 2 , NO 2 reacts more easily with NH 3 than O 2 at low temperature. Therefore, larger C NO2 can contribute to a higher NO conversion by fast SCR. But, overmuch x 0 make NO 2 -SCR gradually prevail which need more NH 3 to react, and it slows down the fast SCR reaction, resulting in a decrease in yield of N 2 .
Although increasing the value of x 0 can improve NH 3 -SCR, the C N2O in outlet mixture might increase if NO 2 -SCR dominants. N 2 O is formed from ammonium nitrate by thermal decomposition through NO 2 -SCR at low temperature: These two chemical reactions have negative impacts on NO x conversion. On the one hand, the nitrification may cover active sites and cause the devaluation of catalyst activity. On the other hand, N 2 O is one of greenhouse gases and its GWP (global warming potential) is about 298 times than that of CO 2 . Figure 6 shows the outlet C N2O as a function of the reaction temperature and the value of x 0 . As shown in Figure 6, the rise of x 0 causes an overall increase of outlet C N2O , especially in 150-300 • C. It also shows that the outlet C N2O firstly increases and then decreases with the growth of reaction temperature when x 0 > 0.5, however, the concentration slowly falls when x 0 ≤ 0.5. It indicates that N 2 O production being from the decomposition of ammonium nitrate happens at low temperature for Cu-CHA when NO 2 is more, and higher temperature inhibits it.
Based on Figures 4-6, it comes to the conclusion that the balanced point is x 0 = 0.5. Under this operating condition, Cu-CHA catalyst has a high yield of N 2 and quite low outlet concentrations of NO and N 2 O, giving a large NO conversion and better performance.

Effect of Ammonia to NO x Ratio (ANR)
ANR is regarded as the ratio of NH 3 to NO x and can be defined as the following formula: ANR = C NH 3 C NOx . According to Equations (1)-(3), standard SCR and fast SCR prevail as ANR = 1. When ANR > 1.0, NH 3 is overmuch and NO 2 -SCR prevails, resulting in weak catalytic ability. However, to ensure high denitrification efficiencies, excessive NH 3 is supplied to SCR equipment to prohibit NH 3 oxidation and inadequate reaction, etc., which has a risk of NH 3 leakage and environment pollution. Thus, four operating conditions are designed to investigate the best ANR value. Table 2 lists four ANR values and corresponding inlet concentrations of mixture gases used for simulation. And Figures 7 and 8 show the outlet concentrations of NO and NH 3 with different values of ANR and reaction temperatures.   It can be seen from Figure 7 that the outlet C NO all declines with the increase of ANR and it falls more obviously at the low and high temperature range, which indicates that the performance of Cu-CHA catalyst is improved with the increasing value of ANR. But the decreasing trend of C NO with ANR rising becomes flat, demonstrating that the influence of NH 3 increase is gradually limited. Especially when ANR ≥ 1.1, the decreasing rate is not greater than 20%, and the temperature influence it more rather than ANR. In addition, at 250 • C and 300 • C, outlet C NO is lowest regardless of ANR value, owing to that reaction temperature is the other major factor to performance of Cu-CHA.
Subsequently, the relationship between ANR and outlet C NH3 at different reaction temperatures is displayed in Figure 8. The change trend of the C NH3 at 150 • C and 200 • C are different from that at the other temperature, which is higher than that at 250-375 • C when ANR ≤ 1.0. This is due to that oxidation of NH 3 and standard SCR mainly occurred at the medium to high temperature range. Besides, the C NH3 is near zero between ANR is 0.8-1.0 when T > 250 • C and it follows by sharply rise as ANR increasing. Therefore, supplying overmuch NH 3 would lead to leakage and is uneconomical.
Combining Figure 7 with Figure 8, it can be concluded that ANR approximately close to 1 is appropriate for Cu-CHA catalyst in NH 3 -SCR. But, considering uncertainties of running status of vehicles, ANR = 1.1 would be more optimal. Under this operating condition, Cu-CHA performs relative lower outlet concentrations of NO and NH 3 , showing higher NO conversion rate and less NH 3 leakage or waste.

Effect of Inlet Velocity
Currently, the common exhaust after-treatment equipment includes DOC (Diesel Oxidation Catalyst), DPF (Diesel Particulate Filter) and SCR. The monolith catalytic reactor used for NH 3 -SCR is usually installed downstream of the exhaust treatment system. Thus, the speed of mixture entering into NH 3 -SCR system has been much retarded. In this study, Reynolds number of mainstream flowing in the channels is 34.8, which can be treated as laminar flow. The change of NO conversion with various inlet flow velocity is shown in Figure 9. Five inlet flow velocities were studied in this study, from 0.1 m/s to 0.9 m/s, gradually increasing by 0.2 m/s. As the inlet velocity increasing, NO conversion decreases significantly from 44.717% to 19.255% from 0.1 m/s to 0.3 m/s, with a reduction of 56.94%. Subsequently, the trend become flatter after 0.3 m/s, indicating that the effect of inlet velocity on the denitrification of Cu-CHA gradually decrease. Due to the length of model is only 20 mm, the negative influence of increasing velocity on NO conversion is limited. Obviously, when other conditions remain unchanged, it can be considered that the contact time between the reactant gases and the catalyst is relatively short as velocity rising, resulting in insufficient reaction and deterioration of denitrification.

Effects of Structural Parameters 2.4.1. Length of Channels
The internal space of diesel vehicles limits the size of after-treatment equipment and leads to a restriction on the channel length of the monolith catalytic reactor, which will effect on NO conversion, as shown in Figure 10. This section aims to investigate the influence of the length of channels on NO conversion with control variates method. It can be clearly seen from the Figure 10 that NO conversion rises linearly with the increase of the length. When the length is increased by 20 mm, the denitrification efficiency is enhanced by about 10%. The longer channels provide more contact areas to reactant gases and the catalytic substrate. So, it could be predicted that NO conversion could reach a quite high value following this trend, probably 100%. However, it is unrealistic because the space of diesel vehicle and cost of reactor limit it. Hence, it needs more consideration in the practical application.

Cross Area of Channels
Besides, the cross areas of channels also affects NO conversion. Assuming other operating conditions remain constant, Figure 11 described the relationship between NO conversion and the cross area of channels.
In this part, only the side length of square channels varies, from 0.5 mm, 1 mm, 2 mm to 4 mm. And corresponding cross areas of square channels 'A' are 0.25 mm 2 , 1 mm 2 , 4 mm 2 and 16 mm 2 respectively. According to that, the area-volume ratios of single channel are 8, 4, 2 and 1. As shown in Figure 11, from 0.25 mm 2 to 1 mm 2 , NO conversion decreases by 51.849%. After that, the reduction of the denitrification efficiency trends to be flat with the increase of cross area of channels, which means that the influence of cross areas is weaken. From the result described above, larger cross area (amount to smaller surface area) leads to smaller area-volume ratio at the same inlet velocity. The small contact area for reactant and catalyst surface results to the decline of NO conversion. Besides, by Q m = Avρ (here Q m is inlet mass flow rate), the larger A is equal to the higher Q m . WHSV (weight hourly space velocity) is a ration to measure the reactant mass that can be treated by unit mass of catalyst in unit time, which is defined as: WHSV = inlet mass of exhaust gases/mass of Cu-CHA catalyst. Higher Q m leads to larger WHSV, which also shrinks the reaction time and reduces denitrification efficiency.

Wall Thickness of Channels
In general, the monolithic catalysts are prepared by loading the active components on the walls of substrate. The reactants diffuse to surface of Cu-CHA catalyst and a part of them are adsorbed on the active sites. Figure 12 shows the influence of wall thickness of channels on NO conversion with control variates method. In this section, the wall thickness of channels 'a' is set as 50 µm, 100 µm, 150 µm and 200 µm. As can be seen from the Figure 12, it has the maximum average growth rate of NO conversion from 50 to 100 µm. And then, the increasing trend slows down, especially when a varies from 150 to 200 µm, indicating that the influence of wall thickness is limited. On the one hand, from three-dimensional model in Figure 13, the thicker the substrate, the less number of channels and the more mass of Cu-CHA catalyst in per unit area (as setting the total mass of Cu-CHA is constant). On the other hand, due to fixed v and A, Q m of mixture gases is also maintained. So, based on the above two points, the thicker wall leads to more contact between reactants and Cu-CHA catalyst but lower WHSV. In other words, lower WHSV signifies longer residence time of mixture gases which results in more complete NH 3 -SCR reaction and higher NO conversion. However, the effect of WHSV is finite when a varies from 150 to 200 µm, which may because the total mass of Cu-CHA catalyst is fixed.

Simulation Methods
The geometric model of honeycomb monolith is established, as shown in Figure 13. In order to reduce running memory and save simulation time, only 1/8 of the reactor is used as the computational domain. And structural physical parameters of Cu-CHA honeycomb cordierite ceramic monolith catalyst is displayed in Table 3. The substrate is a porous media with the porosity of 0.4. The powder Cu-CHA catalyst is washcoated on the walls of small channels. A three-dimension model was used to study the performance of Cu-CHA catalysts in NH 3 -SCR. The model involved fluid flow in honeycomb pores, diffusion of gases, chemical reaction and heat transfer. In general, the standard SCR reaction occurring above 200 • C conforms to Eley-Rideal mechanism. Thus, Eley-Rideal mechanism model is utilized to simulate the SCR reactions of NO over Cu-CHA. Some assumptions are made in order to simplify the calculation and model.

•
The inlet velocity and concentration of mixture, as well as inlet temperature, etc. uniformly distribute; • The reactions in each channel of the Cu-CHA monolithic catalytic reactor are exactly the same; • The mass transfer conforms to Fick's law.
The feed gases flowing in every small channel of the monolith catalyst can be divided into two parts, mainstream flow in central areas and seepage in porous areas near wall. The Naiver-Stokes (N-S) equation is used to describe the mainstream flow and the Brinkman equation is used in porous areas in the meantime: Here, ρ is fluid density, kg/m 3 , u is velocity of fluid, m/s, p is pressure, Pa, µ is dynamic viscosity, N·s/m 2 , ε p is porosity of porous area near wall, I is unit tensor and κ is permeability.
Then, mass transfer equation is written as: In the equation above, D F,j is the diffusion coefficient of the reaction gases, m 2 /s, C i is the concentration of reactant i, mol/m 3 , R i is the rate of chemical reaction. D F,j is a value related to the collision integral Ω D , the characteristic length of the potential σ (m), the minimum potential energy ε/k b (K) and dipole moment µ D (D). These parameters can be got directly in the CHEMKIN.
Heat transfer, chemical reactions and thermal boundary conditions can change the internal temperature of the catalyst. So, the energy equation is given by: In this equation, C P,L is heat capacity of gases, J/(kg·K), k is thermal conductivity, W/(m·K), Q is heat source, W/m 3 .
Some boundary conditions are set as follow. The temperature for inlet feed mixture is in the range of 150-375 • C and ambient temperature is 50 • C. The mixture gases get into the reactor at a flow rate of 3000 mL/min with C NH3 = C NO = 750 ppm, C O2 = 6%, C H2O = 5% and C NO2 = C N2 =0 ppm. The outlet pressure is 1 atm. Also, convective heat transfer around the side and the outlet walls in the model are considered and the convective heat transfer coefficients h are 25 W/(m 2 ·K) and 10 W/(m 2 ·K) respectively.
It is well known that water can affect the catalytic efficiency of catalysts. As mentioned above, some experimental researches have proved that H 2 O has an advantage in NO conversion of NH 3 -SCR on Cu-CHA catalyst. In order to investigate the influence of H 2 O on the NO conversion, two kinds of global kinetic models are built. The model without H 2 O in feed gases comes from De-La-Torre, et al. [25], and the model with H 2 O originates from Metkar, et al. [26]. Both models use one single site and apply Arrhenius to define the rate equations. Tables 4 and 5 show the reactions with related parameters of two models respectively.
Here, in Tables 4 and 5, A if is the forward pre-exponential factor and A ib is the backward pre-exponential factor, E if is the forward activation energy and E ib is the backward activation energy. In Table 4, A 2b = A 2f /(8.61 × 10 −4 m 1.5 ·mol −0.5 ), E 2b = 57.28 kJ/mol. C i means the concentration of reactant i. Besides, K NH3 is equilibrium constant of NH 3 adsorption and desorption while θ NH3 is the adsorption rate of NH 3 . In Table 5, K* is the suppressing co-efficiency of NH 3 adsorption, which is equal to zero in Cu-CHA catalyst.  [25]. 3 1.59 × 10 12 m 6 /(g·h·mol) 108.11 kJ/mol

Grid Independence Verification
Generally speaking, the denser the mesh is, the smaller the error generated in the calculation. However, the mesh cannot be infinitely refined due to the finite computational ability. To ensure the accuracy of the calculation results, it is necessary to find a suitable grid, which can reduce the calculation error and speed up the calculation. In our study, several different grids with number of 5346, 11,040,22,260,24,225,29,070,32,300,44,980 are used to verify the independence of grid density, with the inlet temperature T = 150 • C and being without H 2 O in feed gases. Table 6 shows the results of grid independence test, which presents the variation of C NO and C NH3 at outlet and NO conversion, respectively. It can be seen from the Table 6, with the increase of grid number, the relative variations of C NO , C NH3 and NO conversion become smaller. Actually, if comparing the variation between the Grid 5 (32,300) and 6 (44,980), it can be found that although the number of grid is increased by nearly 40%, the relative variations of outlet C NO , C NH3 and NO conversion is small, being 0.001%, 0.018% and 0.074% respectively. Therefore, Grid 5 (32,300) is used in this investigation to ensure balances between the accuracy and the grid density.

Validation against Experimental Results
In order to demonstrate the accuracy of the present developed model, two sets of experimental data are selected as the verification benchmarks. These experimental data are acquired from De-La-Torre's work [23], because the boundary conditions, the structure and physicochemical properties of catalyst they used for SCR and other operating conditions are the most similar to ours. More details of the reactor's dimension and operating condition refer to the reference [23].
Tables 7 and 8 list relative errors of NO and NH 3 conversion between experimental and simulated results under different operating conditions to show the validation of the numerical model.

Conclusions
A three dimensionally numerical model including global kinetic chemical reactions, fluid dynamics, heat and mass transfer was built for a Cu-CHA catalyst reactor by COMSOL Multiphysics with 32,300 grid numbers. And several structural and operating conditions of NH 3 -SCR system were researched respectively to investigate the influence on the performance of Cu-CHA catalyst.
The presence of H 2 O in feed gases can increase the denitrification efficiency of Cu-CHA catalyst at medium temperature range (250-375 • C) and improves the NH 3 conversion especially at low temperature range (150-250 • C). It inhibits NH 3 oxidation, increases Cu reducibility and Bronsted acidity, causing higher NO conversion for Cu-CHA than that without water.
The C O2 has almost no influence on catalytic performance of Cu-CHA catalyst, possibly because the existence of NO and NO 2 in reactant have higher oxidation ability than O 2 and concentration of reactants is low. By ascending the ratio of NO 2 to NO x , the outlet C NO declines, C N2 firstly increases and then decreases and C N2O continues to rise. The balanced point is x 0 = 0.5, where fast SCR prevails and Cu-CHA catalyst performs high NO conversion and yield of N 2 , extremely low output of N 2 O as well. With the ratio of NH 3 to NO x (ANR) increase, outlet C NO gradually declines while C NH3 rapidly grows when ANR > 1. The appropriate value of ANR is approximately 1.1, where Cu-CHA catalyst has great denitrification efficiency and low NH 3 escape.
Increasing inlet flow velocity leads to worse denitrification performance of Cu-CHA catalyst, which may be due to insufficient react time between feed gases and catalyst. As the length of channels increases by 20 mm, the denitrification efficiency is enhanced by about 10% evenly, owing to providing more contact areas. In addition, the change of cross area of channels and wall thickness have great influence on NO conversion by affecting WHSV in reaction system. Bigger cross area causes larger WHSV, resulting in lower NO abatement efficiency. In contrast, thicker wall of channels brings lower WHSV, leading to longer residence time of exhaust gases and higher NO conversion of the reactor. However, the effect of WHSV is finite which may because the total mass of Cu-CHA catalyst is fixed.
Author Contributions: Validation, writing-review & editing, Y.L.; Conceptualization, methodology, software, formal analysis, investigation, resources, data curation, visualization, writing-original draft, Y.Z. and N.Z.; Project administration, funding acquisition Y.L. and Z.L. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by Beijing Natural Science Foundation (3192008) and the National Key R&D Program of China (No. 2017YFB0504000).