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

Abstract

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 O₂ (C_O2) has no significant effect on the performance of Cu-CHA catalyst. The best ratio of NO₂ to NO_x in feed gases may be 1/2, which improves the denitrification efficiency and the yield of N₂ but it produces relatively little N₂O. The optimal ammonia-nitrogen ratio is 1.1, where Cu-CHA catalyst has fairly great denitrification efficiency and low NH₃ 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.

1. 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 (NH₃-SCR) has been studied in various aspects. According to the different reaction rate, NH₃-SCR can be divided into three types: standard SCR (Equation (1)), fast SCR (Equation (2)) and NO₂-SCR (Equation (3)):

$$4\mathrm{N}{\mathrm{H}}_3+4\mathrm{N}\mathrm{O}+{\mathrm{O}}_2\to 4{\mathrm{N}}_2+6{\mathrm{H}}_2\mathrm{O}$$

(1)

$$2\mathrm{N}{\mathrm{H}}_3+\mathrm{N}\mathrm{O}+\mathrm{N}{\mathrm{O}}_2\to 2{\mathrm{N}}_2+3{\mathrm{H}}_2\mathrm{O}$$

(2)

$$8\mathrm{N}{\mathrm{H}}_3+6\mathrm{N}{\mathrm{O}}_2\to 7{\mathrm{N}}_2+12{\mathrm{H}}_{\mathrm{2}}\mathrm{O}$$

(3)

The reason why the fast SCR has a faster reaction rate than the standard SCR is that the oxidation ability of NO₂ is stronger than that of O₂. However, the share of NO₂ in diesel exhaust is about 5%, so NO₂-SCR becomes known as slow SCR. Therefore, the ratio of NO₂ in the feed gases is very important. Also, some researches on the influence of NO₂ on Cu-SSZ-13 [1], Cu-SSZ-39 [2], Cu-T3 [3] etc. indicate that NO₂ can result in the promotion of NO_x conversion.

Many kinds of catalysts have been found to be used in NH₃-SCR because of the active sites on their surface that can adsorb NO_x in vehicle exhaust. As so far, catalysts applied to NH₃-SCR are generally used at medium and high temperature, and have poor water and sulfur resistance, such as commercial V₂O₅-TiO₂. Hence, it is necessary to explore replaceable catalysts. Generally speaking, Cu-zeolite catalyst has better low-temperature performance and higher NH₃-storage capacity [4]. Although a large number of experimental studies aimed to Cu-zeolite catalysts, most of them focused on cations doping, selection of molecular sieve carriers or the comparison of topological structures [5,6,7]. As to the simulation researches, the kinetic models for NH₃-SCR over vanadium-based catalysts only involved standard SCR and ammonia oxidation [8,9]. To zeolite catalyst, however, most researches were concerned about powdered catalysts or reaction in single channel model [10,11,12], which is not in line with the actual situation. Only a few of researches investigated the NH₃-SCR in a monolithic reactor using Cu-zeolite as catalysts [13,14].

Among the zeolites, the chabazite (CHA) has a large surface area and high porosity as a result of microporous topological structure, which makes them one of the most popular NH₃-SCR candidates for the catalyst carrier. Thus, Cu-CHA catalysts are more attractive. Many experimental studies have proved that water has a positive influence on the denitrification efficiency of Cu-CHA [15,16,17] and drawn a common conclusion that Cu-CHA has an excellent hydrothermal stability. Contrary to other metals or their oxide catalysts, water can increase the NO conversion on Cu-CHA, which makes Cu-CHA a quite suitable catalyst for NH₃-SCR. However, few studies have been done on water effect, especially in simulation studies using a global kinetic mechanism. Fahami, et al. [18] explored the effects of gas hourly space velocity (GHSV), NO, O₂, NO₂ and H₂O concentration on NO conversion with a detailed kinetic mechanism for NO oxidation on Cu-CHA at low and medium temperature (150–350 °C). In their studies, the experimental data and simulation results fit well and the parameters of the mathematical model in each chemical reaction step were illustrated. They also found that increasing GHSV and the concentration of H₂O and NO₂ could inhibit NO oxidation, while O₂ could promote it. Active sites may perform diversely at different reaction temperatures. Olsson, et al. [11] established a multi-sites kinetic model containing NH₃ storage, release and oxidation, standard SCR and N₂O formation in 100–600 °C with 5% H₂O in feed gases, but fast SCR and NO₂ SCR were not included. The results showed that different NH₃ adsorption temperatures corresponded to different sites. They also suggested that standard SCR mainly took place on site 1 and NH₃ oxidation was major on site 2. Besides, Gao, et al. [19] built a comprehensive model with two adsorption sites and global kinetic reactions, which was a rare model including low temperature H₂O storage on site 2.

In summary, most of the research focused on catalysts themselves. However, the structural design of a NH₃-SCR monolith catalyst reactor is lack of the theoretical support. Thus, a global kinetic mechanism is used to simulate the chemical reactions of NO_x over Cu-based monolith catalyst and study the influence of different operating conditions, such as inlet velocity of reactants, the length of channels etc., providing reference for engineering design and evaluating the performance of Cu-CHA monolith catalyst. When the reactant gases flow through the porous monolith catalyst, the selective catalytic reactions occur on the support surface accompanied by heat and mass transfer. Hence, a mathematical model for predicting heterogeneous reactions, flow, mass and heat transfer characteristics of NO_x/NH₃/H₂O/N₂ mixture flowing in a honeycomb cordierite ceramic monolith with Cu-CHA washcoating is established by commercial software COMSOL Multiphysics. And the chemical kinetic model includes ammonia oxidation, nitrogen oxidation, standard, fast and slow SCR reactions, NH₄NO₃ and N₂O formation and decomposition. Also the presence of H₂O in feed gases impacts on the denitrification efficiency of Cu-CHA is studied.

2. Results and Discussion

2.1. Effect of the Presence of H₂O in Reactant Mixture

Figure 1 and Figure 2 compare the NO and NH₃ conversion between simulated and experimental values under various operating conditions. As can be seen from Figure 1 and Figure 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 NH₃ 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 NH₃ conversion, followed by a muted growth after 250 °C, and then it reaches approximate 100% eventually. H₂O also decreases the temperature for Cu-CHA reaching maximum NH₃ conversion. The finding is different from the well-known result that H₂O would inhibit the NH₃-SCR reactions over other metals and their oxide catalysts, due to the active sites competition among H₂O and reactants (NH₃ 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 NH₃-SCR, because H₂O is abundant in diesel vehicle exhaust and it is produced by NH₃-SCR reaction as well. Actually, this phenomenon is probably due to H₂O 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 NH₃ to be absorbed [16]. The enhancement of NH₃ conversion means a reduction of the possibility of NH₃ leakage.

2.2. Effects of Reactant Gas Composition

2.2.1. Effect of Concentration of O₂

Oxygen participates in most reactions in the global kinetic model of NH₃-SCR, for instance, NH₃ oxidation, NO oxidation, N₂O decomposition. And it plays an important role in determining the dominant reaction among standard SCR, fast SCR and NO₂-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% O₂ in feed gas. From Figure 3, it can be seen that with the increase of C_O2, NO conversion has little improvement. The more O₂ could stimulate standard SCR (Equation (1)) and promote NO oxidizing to more NO₂, which is help to fast SCR (Equation (2)). However, because NO and NO₂ have higher oxidation ability than O₂ and the concentration of reactants is low in this model, the difference is not obvious.

2.2.2. Effect of Concentration of NO₂

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 NO₂, the reaction equation is given by:

$$2\mathrm{N}\mathrm{O}+{\mathrm{O}}_2\leftrightarrow 2\mathrm{N}{\mathrm{O}}_2$$

(4)

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 NO₂ in reactant gases plays an important role in reduction of NO_x. Defining x₀ as the ratio of NO₂ to NO_x, x₀ varies from 0 to 1. $x_0=\frac{C_{{NO}_2}}{C_{{NO}_{\mathrm{x}}}}=\frac{C_{{NO}_2}}{C_{NO}+C_{{NO}_2}}$. Here, C_i is the concentration of reactant i.

In this study, five operating conditions were selected to simulate outlet concentration of NO, N₂ and N₂O. As shown in

Table 1. x₀ and the corresponding inlet concentrations of components used for simulation.

x0	CNH3 (ppm)	CNO (ppm)	CNO2 (ppm)	CO2 (%)	CH2O (%)
0	750	750	0	6	5
0.25	750	562.5	187.5	6	5
0.5	750	375	375	6	5
0.75	750	187.5	562.5	6	5
1	750	0	750	6	5

, it includes inlet concentrations of components corresponding to different x₀. Figure 4 and Figure 5 illustrate the outlet concentrations of NO and N₂, as a function of the reaction temperature and x₀ respectively.

As shown in Figure 4, the outlet C_NO reduces to a minimum at 250 °C and then gradually rises under each x₀. And at the same reaction temperature, with the increase of value of x₀, the outlet C_NO significantly decreases, indicating the presence of NO₂ in feed gas has a positive influence on NO conversion. When x₀ 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 NO₂ or N₂. As can be seen from Figure 5, reaction temperature and the value of x₀ greatly influences the yield of N₂. The outlet C_N2 peaks to maximum at 250 °C when x₀ ≤ 0.25 and at 300 °C when x₀ ≥ 0.25, then it decline sharply. Furthermore, as the value of x₀ growing, the yield of N₂ increases and then decreases under the same temperature. Actually, different values of x₀ mean different C_NO2 in feed gases and can result in a different selective catalytic reaction. Generally speaking, x₀ = 0–0.5 is the transition period from standard SCR to fast SCR and x₀ = 0.5–0.75 is fast SCR to NO₂-SCR. The result demonstrates that standard SCR prevails most at 250 °C while fast SCR at 300 °C. Due to the oxidation ability of NO₂ being better than that of O₂, NO₂ reacts more easily with NH₃ than O₂ at low temperature. Therefore, larger C_NO2 can contribute to a higher NO conversion by fast SCR. But, overmuch x₀ make NO₂-SCR gradually prevail which need more NH₃ to react, and it slows down the fast SCR reaction, resulting in a decrease in yield of N₂.

Although increasing the value of x₀ can improve NH₃-SCR, the C_N2O in outlet mixture might increase if NO₂-SCR dominants. N₂O is formed from ammonium nitrate by thermal decomposition through NO₂-SCR at low temperature:

$$\mathrm{N}{\mathrm{H}}_3+2\mathrm{N}{\mathrm{O}}_2\leftrightarrow \mathrm{N}{\mathrm{H}}_4\mathrm{N}{\mathrm{O}}_3+{\mathrm{N}}_2+{\mathrm{H}}_2\mathrm{O}$$

(5)

$$\mathrm{N}{\mathrm{H}}_4\mathrm{N}{\mathrm{O}}_3\to {\mathrm{N}}_2\mathrm{O}+2{\mathrm{H}}_2\mathrm{O}$$

(6)

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, N₂O is one of greenhouse gases and its GWP (global warming potential) is about 298 times than that of CO₂. Figure 6 shows the outlet C_N2O as a function of the reaction temperature and the value of x₀.

As shown in Figure 6, the rise of x₀ 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 x₀ > 0.5, however, the concentration slowly falls when x₀ ≤ 0.5. It indicates that N₂O production being from the decomposition of ammonium nitrate happens at low temperature for Cu-CHA when NO₂ is more, and higher temperature inhibits it.

Based on Figure 4, Figure 5 and Figure 6, it comes to the conclusion that the balanced point is x₀ = 0.5. Under this operating condition, Cu-CHA catalyst has a high yield of N₂ and quite low outlet concentrations of NO and N₂O, giving a large NO conversion and better performance.

2.2.3. Effect of Ammonia to NO_x Ratio (ANR)

ANR is regarded as the ratio of NH₃ to NO_x and can be defined as the following formula: $\mathrm{A}\mathrm{N}\mathrm{R}=\frac{C_{{\mathrm{N}\mathrm{H}}_3}}{C_{{\mathrm{N}\mathrm{O}}_{\mathrm{x}}}}$. According to Equations (1)–(3), standard SCR and fast SCR prevail as ANR = 1. When ANR > 1.0, NH₃ is overmuch and NO₂-SCR prevails, resulting in weak catalytic ability. However, to ensure high denitrification efficiencies, excessive NH₃ is supplied to SCR equipment to prohibit NH₃ oxidation and inadequate reaction, etc., which has a risk of NH₃ leakage and environment pollution. Thus, four operating conditions are designed to investigate the best ANR value.

Table 2. ANR and the corresponding inlet concentrations of NH₃, NO, O₂ and H₂O.

ANR	CNH3 (ppm)	CNO (ppm)	CO2 (%)	CH2O (%)
0.8	750	937.5	6	5
1	750	750	6	5
1.2	750	625	6	5
1.5	750	500	6	5

lists four ANR values and corresponding inlet concentrations of mixture gases used for simulation. And Figure 7 and Figure 8 show the outlet concentrations of NO and NH₃ 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 NH₃ 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 NH₃ 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 NH₃ 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 NH₃-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 NH₃, showing higher NO conversion rate and less NH₃ leakage or waste.

2.3. 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 NH₃-SCR is usually installed downstream of the exhaust treatment system. Thus, the speed of mixture entering into NH₃-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.

2.4. 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.

2.4.2. 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 mm², 1 mm², 4 mm² and 16 mm² 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 mm² to 1 mm², 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.

2.4.3. 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 NH₃-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.

3. 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. Structural physical parameters of Cu-CHA honeycomb cordierite ceramic catalyst.

Parameter	Value/Unit
Cross sectional area of channel	1 mm2
Wall thickness of substrate	150 μm
Length	20 mm
Radius	20 mm
Volume	6.28 cm3
Porosity	0.4
Washcoat weight	1.08 g
Cu content (related to washcoat)	3.9%

. 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 NH₃-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:

$$\rho (u\cdot \nabla )u=\nabla \cdot (-pI+\mu (\nabla u+{(\nabla u)}^T))$$

(7)

$$\frac{1}{{\epsilon }_{\mathrm{p}}}\rho (u\cdot \nabla )u\frac{1}{{\epsilon }_{\mathrm{p}}}=\nabla \cdot (-pI+\mu \frac{1}{{\epsilon }_{\mathrm{p}}}(\nabla u+{(\nabla u)}^T)-\frac{2}{3}\mu \frac{1}{{\epsilon }_{\mathrm{p}}}(\nabla \cdot u)I)-\mu {\kappa }^{-1}u$$

(8)

Here, ρ is fluid density, kg/m³, u is velocity of fluid, m/s, p is pressure, Pa, μ is dynamic viscosity, N·s/m², ε_p is porosity of porous area near wall, I is unit tensor and κ is permeability.

Then, mass transfer equation is written as:

$$\nabla \cdot (-D_{\mathrm{F},\mathrm{j}}\nabla C_{\mathrm{i}})+u\cdot \nabla C_{\mathrm{i}}=R_{\mathrm{i}}$$

(9)

$$D_{\mathrm{F},\mathrm{j}}=f({\mathsf{\Omega }}_{\mathrm{D}},\sigma ,\epsilon /k_{\mathrm{b}})$$

(10)

$${\mathsf{\Omega }}_{\mathrm{D}}=f({\mu }_{\mathrm{D}},\sigma ,k_{\mathrm{b}},T)$$

(11)

In the equation above, D_F,j is the diffusion coefficient of the reaction gases, m²/s, C_i is the concentration of reactant i, mol/m³, 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:

$$\rho c_{\mathrm{P},\mathrm{L}}u\cdot \nabla T=\nabla \cdot (k\nabla T)+Q$$

(12)

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/m³.

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/(m²·K) and 10 W/(m²·K) respectively.

It is well known that water can affect the catalytic efficiency of catalysts. As mentioned above, some experimental researches have proved that H₂O has an advantage in NO conversion of NH₃-SCR on Cu-CHA catalyst. In order to investigate the influence of H₂O on the NO conversion, two kinds of global kinetic models are built. The model without H₂O in feed gases comes from De-La-Torre, et al. [25], and the model with H₂O originates from Metkar, et al. [26]. Both models use one single site and apply Arrhenius to define the rate equations.

Table 4. Kinetic model without H₂O in feed gases [25].

Reactions	Rate Equations	Aif	Eif
$4\mathrm{N}{\mathrm{H}}_3+3{\mathrm{O}}_2\to 2{\mathrm{N}}_2+6{\mathrm{H}}_2\mathrm{O}$	$R_1=A_{1f}{e}^{{(-E}_1/\left(RT\right))}{C}_{{NH}_3}{C}_O{}_{{}_2}{/(1+C}_{{NH}_3}{K}_{{NH}_3})$	1.59 × 1012 m6/(g·h·mol)	108.11 kJ/mol
$2\mathrm{N}\mathrm{O}+{\mathrm{O}}_2\leftrightarrow 2\mathrm{N}{\mathrm{O}}_2$	$R_2{=A}_2{}_f{e}^{{(-E}_{2f}/\left(RT\right))}{C}_{NO}{C}_{O_2}^{0.5}{-A}_{2b}{e}^{{(-E}_{2b}/\left(RT\right))}{C}_{{NO}_2}$	6.81 × 105 mol/(m3·s)	12.39 kJ/mol
$4\mathrm{N}{\mathrm{H}}_3+4\mathrm{N}\mathrm{O}+{\mathrm{O}}_2\to 4{\mathrm{N}}_2+6{\mathrm{H}}_2\mathrm{O}$	$R_3{=A}_{3f}{e}^{{(-E}_{3f}/\left(RT\right))}{C}_{{NH}_3}{C}_{NO}{C}_{O_2}{/(1+C}_{{NH}_3}{K}_{{NH}_3})$	1.09 × 1012 m9/(g·h·mol2)	91.45 kJ/mol
$2\mathrm{N}{\mathrm{H}}_3+\mathrm{N}\mathrm{O}+\mathrm{N}{\mathrm{O}}_2\to 2{\mathrm{N}}_2+3{\mathrm{H}}_2\mathrm{O}$	$R_4{=A}_{4f}{e}^{{(-E}_{4f}/\left(RT\right))}{C}_{{NH}_3}{C}_{NO}{C}_{{NO}_2}{/(1+C}_{{NH}_3}{K}_{{NH}_3})$	9.40 × 109 m9/(g·h·mol2)	41.98 kJ/mol
$8\mathrm{N}{\mathrm{H}}_3+6\mathrm{N}{\mathrm{O}}_2\to 7{\mathrm{N}}_2+12{\mathrm{H}}_2\mathrm{O}$	$R_5{=A}_{5f}{e}^{{(-E}_{5f}/\left(RT\right))}{C}_{{NH}_3}{C}_{{NO}_2}{/(1+C}_{{NH}_3}{K}_{{NH}_3})$	3.07 × 1012 m6/(g·h·mol)	118.10 kJ/mol
$6\mathrm{N}{\mathrm{H}}_3+8\mathrm{N}{\mathrm{O}}_2\to 7{\mathrm{N}}_2\mathrm{O}+9{\mathrm{H}}_2\mathrm{O}$	$R_6{=A}_{6f}{e}^{{(-E}_{6f}/\left(RT\right))}{C}_{{NH}_3}{C}_{{NO}_2}{/(1+C}_{{NH}_3}{K}_{{NH}_3})$	4.48 × 1018 m6/(g·h·mol)	152.34 kJ/mol
$2{\mathrm{N}}_2\mathrm{O}\to 2{\mathrm{N}}_2+{\mathrm{O}}_2$	$R_7{=A}_{7f}{e}^{{(-E}_{7f}/\left(RT\right))}{C}_{N_{2}O}{C}_{{NO}_2}$	2.45 × 1028 m6/(g·h·mol)	257.92 kJ/mol
$K_{N{H}_3}$	$K_{N{H}_3}{=A}_{N{H}_3}{e}^{{(-E}_{N{H}_3}/\left(RT\right))}$	7.66 × 10−7 m3/mol	−99.19 kJ/mol

and

Table 5. Kinetic model with H₂O in feed gases [26].

Reactions	Rate Equations	Aif	Eif
$4\mathrm{N}{\mathrm{H}}_3+3{\mathrm{O}}_2\to 2{\mathrm{N}}_2+6{\mathrm{H}}_2\mathrm{O}$	$R_1=A_{1f}{e}^{{(-E}_1/\left(RT\right))}{C}_O{}_{{}_2}{\theta }_{{NH}_3}$	5.56 × 1016 mol/(m3·s)	178.8 kJ/mol
$2\mathrm{N}\mathrm{O}+{\mathrm{O}}_2\leftrightarrow 2\mathrm{N}{\mathrm{O}}_2$	$R_2{=A}_2{}_f{e}^{{(-E}_{2f}/\left(RT\right))}{C}_{NO}{C}_{O_2}^{0.5}{-A}_{2b}{e}^{{(-E}_{2b}/\left(RT\right))}{C}_{{NO}_2}$	5.10 × 107 mol/(m3·s)	56.0 kJ/mol
$4\mathrm{N}{\mathrm{H}}_3+4\mathrm{N}\mathrm{O}+{\mathrm{O}}_2\to 4{\mathrm{N}}_{\mathrm{2}}+6{\mathrm{H}}_2\mathrm{O}$	$R_3{=A}_{3f}{e}^{{(-E}_{3f}/\left(RT\right))}{C}_{NO}{/(1+C}_{{NH}_3}{K}^{*})$	7.08 × 1013 mol/(m3·s)	89.1 kJ/mol
$2\mathrm{N}{\mathrm{H}}_3+\mathrm{N}\mathrm{O}+\mathrm{N}{\mathrm{O}}_2\to 2{\mathrm{N}}_2+3{\mathrm{H}}_2\mathrm{O}$	$R_4{=A}_{4f}{e}^{{(-E}_{4f}/\left(RT\right))}{C}_{NO}{C}_{{NO}_2}{\theta }_{{NH}_3}$	1.00 × 1018 mol/(m3·s)	77.1 kJ/mol
$8\mathrm{N}{\mathrm{H}}_3+6\mathrm{N}{\mathrm{O}}_2\to 7{\mathrm{N}}_2+12{\mathrm{H}}_2\mathrm{O}$	$R_5{=A}_{5f}{e}^{{(-E}_{5f}/\left(RT\right))}{C}_{{NO}_2}{\theta }_{{NH}_3}$	1.96 × 1017 mol/(m3·s)	136.3 kJ/mol
$2\mathrm{N}{\mathrm{H}}_3+2\mathrm{N}{\mathrm{O}}_2\to {\mathrm{N}}_2+\mathrm{N}{\mathrm{H}}_4\mathrm{N}{\mathrm{O}}_3+{\mathrm{H}}_2\mathrm{O}$	$R_6{=A}_{6f}{e}^{{(-E}_{6f}/\left(RT\right))}{C}_{{NO}_2}{\theta }_{{NH}_3}$	2.28 × 108 mol/(m3·s)	43.0 kJ/mol
$\mathrm{N}{\mathrm{H}}_4\mathrm{N}{\mathrm{O}}_3\to {\mathrm{N}}_2\mathrm{O}+2{\mathrm{H}}_2\mathrm{O}$	$R_7{=A}_{7f}{e}^{{(-E}_{7f}/\left(RT\right))}{C}_{{NH}_{4}N{O}_3}$	1.25 × 108 mol/(m3·s)	41.5 kJ/mol

show the reactions with related parameters of two models respectively.

Here, in Table 4 and Table 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 NH₃ adsorption and desorption while θ_NH3 is the adsorption rate of NH₃. In Table 5, K* is the suppressing co-efficiency of NH₃ adsorption, which is equal to zero in Cu-CHA catalyst.

4. Grid Independence and Validation Test of Method

4.1. 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 H₂O in feed gases.

Table 6. The variation results of calculation with grid number.

Grid Number	Outlet CNO	Relative Variation	NO Conversion	Relative Variation	Outlet CNH3	Relative Variation
5346	5.860 × 10−4	/	0.21867	/	6.958 × 10−4	/
11,040	6.151 × 10−4	4.7340%	0.17984	17.7561%	7.053 × 10−4	1.3413%
22,260	6.217 × 10−4	1.0600%	0.17105	4.8858%	7.074 × 10−4	0.3025%
29,070	6.291 × 10−4	0.0318%	0.16119	0.1654%	7.099 × 10−4	0.0099%
32,300	6.290 × 10−4	0.0127%	0.16129	0.0661%	7.099 × 10−4	0.0028%
44,980	6.289 × 10−4	0.0014%	0.16141	0.0743%	7.098 × 10−4	0.0183%

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.

4.2. 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].

Table 7. The results with relative errors of NO conversion between experiment and simulation under two operating conditions.

Temperature (°C)	NO Conversion (Without H2O)			NO Conversion (With 5% H2O)
	Experiment	Simulation	Relative Error	Experiment	Simulation	Relative Error
150	15.000%	16.092%	7.280%	16.500%	18.055%	9.424%
200	66.200%	72.744%	9.885%	66.700%	72.813%	9.165%
250	98.000%	99.057%	1.079%	99.300%	98.580%	0.725%
300	90.100%	84.164%	6.588%	91.700%	95.101%	3.709%
350	45.060%	50.912%	12.987%	68.920%	77.745%	12.805%
375	21.200%	26.717%	26.024%	38.000%	54.664%	30.484%
average	/		10.641%	/		11.052%

and

Table 8. The results with relative errors of NH₃ conversion between experiment and simulation under two operating conditions.

Temperature (°C)	Without H2O			With 5% H2O
	Experiment	Simulation	Relative Error	Experiment	Simulation	Relative Error
150	13.200%	15.336%	16.182%	16.830%	17.852%	6.072%
200	44.340%	42.516%	4.114%	55.460%	72.113%	30.027%
250	78.030%	74.300%	4.780%	80.820%	98.289%	21.615%
300	98.210%	96.317%	1.928%	98.600%	100.000%	1.420%
350	100.000%	99.999%	0.001%	100.000%	100.000%	0.000%
375	100.000%	100.000%	0.000%	100.000%	100.000%	0.000%
average	/		4.501%	/		9.856%

list relative errors of NO and NH₃ conversion between experimental and simulated results under different operating conditions to show the validation of the numerical model.

From these tables, it is apparent that a very good agreement has been obtained, the average errors of NO conversion are only 10.641% (without H₂O) and 11.052% (with H₂O) between the experimental data and simulated outcomes. Simultaneously, the average errors of NH₃ conversion are 4.501% (without H₂O) and 9.856% (with H₂O) respectively. The average errors with 5% H₂O are a little higher than that without H₂O. The maximum deviations is 30.484% (at T = 375 °C with 5% H₂O, in NO conversion), while the minimum is close to 0% (at T = 350 °C and 375 °C for with and without H₂O, in NH₃ conversion). The results obtained, thus far, have clearly indicated that the catalytic reactor model presented in this study predicts well the catalyst’s global performance, and it can readily be employed for further simulation studies.

5. 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 NH₃-SCR system were researched respectively to investigate the influence on the performance of Cu-CHA catalyst.

The presence of H₂O in feed gases can increase the denitrification efficiency of Cu-CHA catalyst at medium temperature range (250–375 °C) and improves the NH₃ conversion especially at low temperature range (150–250 °C). It inhibits NH₃ 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 NO₂ in reactant have higher oxidation ability than O₂ and concentration of reactants is low. By ascending the ratio of NO₂ 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 x₀ = 0.5, where fast SCR prevails and Cu-CHA catalyst performs high NO conversion and yield of N₂, extremely low output of N₂O as well. With the ratio of NH₃ 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 NH₃ 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.