Modeling method for single channel of selective catalytic reduction reactor

Abstract

The invention discloses a modeling method for single channels of a selective catalytic reduction reactor, a plurality of SCR single channels are arranged in the reactor, a main channel is surrounded by a catalytic coating, a plurality of pore channels are formed in the catalytic coating, ammonia molecules are adsorbed on active sites of a catalyst, and a selective catalytic reduction reaction is carried out on the active sites of the catalyst. The modeling method comprises the steps that S1, an SCR single-channel mathematical model is established, wherein the SCR single-channel mathematical model comprises a component balance equation, a momentum balance equation and an enthalpy balance equation of a gas phase substance in a main channel, a gas phase component balance equation, an enthalpy balance equation, an NH3 coverage balance equation, a component balance equation of a gas phase-coating interface and a gas enthalpy balance equation; s2, giving an initial condition and a boundary condition, limiting part of unknown parameters, and substituting the parameters into each equation to obtain a closed equation set; the model established by the invention can obtain the nitrogen oxide conversion rate, so that the emission reduction performance of the reactor is evaluated. And the influence of mass transfer limitation and mild aging degree of the catalyst is considered, so that the evaluation is more accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of diesel engine exhaust treatment, and specifically relates to a modeling method for a single channel of a selective catalytic reduction reactor. Background Art

[0002] Heavy-duty commercial vehicles have large loads, long operating hours, high requirements for stable operation quality, and some operating conditions are very harsh. It is difficult for new energy heavy-duty commercial vehicles to meet the needs of the commercial transportation market in a short period of time. Diesel engines have become the main power source in the commercial transportation field due to their high fuel economy, low carbon dioxide emissions and strong torque output. For long-distance transportation and heavy-duty vehicles, diesel engines can significantly reduce operating costs, while reducing carbon emissions while ensuring power, meeting the current dual needs of environmental protection and economy. These advantages have enabled diesel engines to dominate the commercial vehicle market, especially in industries such as logistics, freight and public transportation. However, although the current heavy-duty commercial vehicles such as heavy trucks and large buses account for a small proportion of the total, their pollutants, particulate nitrogen oxides (NO X , nitrogen oxides) emissions account for a high proportion in the transportation sector, up to about 86%. Therefore, heavy-duty commercial vehicles have become the focus of pollution reduction and carbon reduction in the transportation sector.

[0003] Currently, the selective catalytic reduction (SCR) technology based on copper-based molecular sieve catalysts is widely considered to be one of the most effective technologies for reducing particulate matter (PM) and nitrogen oxide (NOx) emissions in diesel exhaust. Hydrothermal stability is considered to be an important criterion for evaluating the durability of SCR catalysts. Hydrothermal aging has an impact on the performance of selective catalytic reduction reactors. Summary of the invention

[0004] In view of the above problems existing in the prior art, the purpose of the present invention is to provide a modeling method for mild hydrothermal aging of a selective catalytic reduction reactor, and to establish a single-channel mathematical model of SCR. The conversion rate of nitrogen oxides can be obtained through the model, so that the emission reduction performance of the reactor can be evaluated or assessed. The single-channel model of SCR takes into account the influence of mass transfer limitation and the degree of mild aging of the catalyst, and the evaluation of the emission reduction performance of the reactor is more accurate. The pore structure in the catalytic coating is simplified to a capillary bundle with a sinusoidal waveform, and the average radius of the pores in the catalytic coating is used as a representative indicator to describe the pore size distribution, so that the mathematical model is simplified while not affecting the evaluation of the reactor performance by the mathematical model finally established. The theoretical model established by the modeling method can be used to capture the mechanism of mild hydrothermal aging and its corresponding influence on catalyst performance, and can more accurately describe the mutual influence between SCR reaction and mass transfer during the mild aging of copper-based molecular sieve catalysts. The mathematical model is a theoretical model, which has low cost and high efficiency for reactor evaluation.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A modeling method for a single channel of a selective catalytic reduction reactor, wherein a plurality of SCR single channels are arranged inside the reactor, wherein the SCR single channel is a cylindrical structure, wherein the side wall of the cylindrical structure is a catalytic coating formed by a catalyst, wherein the channel inside the cylindrical structure surrounded by the catalytic coating is a main channel, wherein there are many pores inside the catalytic coating, and wherein the active sites of the catalyst adsorb ammonia molecules and perform a selective catalytic reduction reaction, wherein the modeling method comprises the following steps:

[0007] Step S1: Establishing a mathematical model of a single channel of SCR, the equation group corresponding to the model includes a component balance equation of gas phase substances in the main channel, a momentum balance equation of gas phase substances in the main channel, an enthalpy balance equation of gas phase substances in the main channel, a gas phase component balance equation in the catalytic coating, a gas phase enthalpy balance equation in the catalytic coating, an NH3 coverage balance equation in the catalytic coating, a component balance equation at the gas phase-coating interface, and an enthalpy balance equation at the gas phase-coating interface;

[0008] Step S2: Given the initial conditions and boundary conditions of the SCR single-channel model, and based on the characteristics of the SCR single-channel, define the values ​​or expressions of some unknown parameters in the equation group in step S1, substitute the values ​​or expressions of the defined parameters into each equation in step S1, and obtain a closed set of equations corresponding to the SCR single-channel model.

[0009] As a further improvement of the above technical solution:

[0010] In step S2, the defined unknown parameters include: the mass transfer coefficient of any component on the surface of the catalytic coating, the diffusion coefficient of any component in the main channel and in the catalytic coating respectively, the specific surface area of ​​the catalyst in the catalytic coating, the reaction rate expression of each chemical reaction involved in the SCR single channel, and the concentration of catalytic active sites in the catalytic coating; in step S2, when calculating the diffusion coefficient of any component in the catalytic coating, the pore structure of the catalytic coating is simplified to a capillary bundle with a sinusoidal waveform, and the average radius of the pores in the catalytic coating is used as a representative indicator to describe the pore size distribution; the mass transfer in the main channel only considers bulk diffusion, and the mass transfer in the catalytic coating only considers bulk diffusion and Knudson diffusion.

[0011] The component balance equation of the gas phase substance in the main channel is:

[0012]

[0013] Wherein, t represents time; z represents axial direction; ρ represents exhaust density, i.e., gas density in the main channel; v represents exhaust velocity, i.e., gas velocity in the main channel; yi represents mass fraction of component i in the main channel; Di represents diffusion coefficient of component i in the main channel;

[0014] The momentum balance equation of the gas phase in the main channel is:

[0015]

[0016] Where, μ represents dynamic viscosity; p represents pressure;

[0017] The enthalpy balance equation of the gas phase in the main channel is:

[0018]

[0019] Among them, c p represents the specific heat capacity of the gas in the main channel; λg represents the thermal conductivity of the gas in the main channel; Tg represents the gas temperature in the main channel;

[0020] The gas phase component balance equation in the catalytic coating is:

[0021]

[0022] Among them, ρ w is the density of the gas in the catalytic coating; x represents the radial direction; y w,i is the mass fraction of component i in the catalytic coating; D w,i is the diffusion coefficient of component i in the catalytic coating; a c is the specific surface area of ​​the catalyst in the catalytic coating; i,j is the stoichiometric ratio of component i in chemical reaction j; M iis the molar mass of component i; r j is the reaction rate of chemical reaction j;

[0023] Gas phase enthalpy balance equation in catalytic coating:

[0024]

[0025] Among them, T w is the gas temperature in the catalytic coating; w is the thermal conductivity of the gas in the catalytic coating; ΔH m，j is the standard formation enthalpy of chemical reaction j;

[0026] The NH3 coverage balance equation in the catalytic coating is:

[0027]

[0028] Where Ω is the concentration of catalytic active sites; θ NH3 is the coverage of adsorbed NH3 on the reaction surface of the catalytic coating; γ NH3,j is the stoichiometric ratio of NH3 in chemical reaction j;

[0029] The component balance equation at the gas phase-coating interface is:

[0030]

[0031] Among them, k m,i is the mass transfer coefficient of component i on the coating surface;

[0032] The enthalpy balance equation at the gas phase-coating interface is:

[0033]

[0034] Among them, d h is the hydraulic diameter of the main channel, k h is the heat transfer coefficient at the gas-coating interface.

[0035] The initial conditions of the SCR single-channel model are:

[0036]

[0037] The boundary conditions are:

[0038]

[0039] Where L is the main channel length, which is the axial length; δ w is the thickness of the catalytic coating; θ 0 NH3 is the coverage of the initially adsorbed NH3 on the reaction surface of the catalytic coating.

[0040]

[0041] Wherein, L is the main channel length, which is the axial length; Re is the Reynolds number; Sc is the Schmidt number.

[0042] When calculating the diffusion coefficient of any component in the catalytic coating, the pore structure of the catalytic coating is simplified to a capillary bundle with a sinusoidal waveform, then:

[0043]

[0044] Where ε is the porosity, S ⊥ is the normal direction, n is the number of pores per unit area of ​​the catalytic coating, l e is the length of a single pore in the catalytic coating, l is the thickness of the catalytic coating, N is the molar diffusion flux, Δc is the concentration difference between the gas components at the outlet and inlet of the pore structure, and τ is the tortuosity of the coating; τ f is the tortuosity factor.

[0045] or

[0046]

[0047] Among them, V ads is the volume of the adsorbed active component; V m is the molar volume of the adsorbed active component; N A is Avogadro's constant; m is the mass of the catalyst; w is the mass fraction of Cu in the copper-based molecular sieve catalyst; n is the stoichiometric ratio of the active component to Cu, a m is the surface area occupied by each adsorption site on the catalyst surface, M is the catalytic mass per unit volume of the catalytic coating, and a(z) is the distribution function of the copper-based molecular sieve catalyst.

[0048] The ammonia adsorption reaction rate expression is:

[0049]

[0050] The ammonia desorption reaction rate expression is:

[0051]

[0052] The reaction rate expression of nitric oxide oxidation is:

[0053]

[0054] The reaction rate expression of ammonia oxidation is:

[0055]

[0056] The standard SCR reaction rate expression is:

[0057]

[0058] The fast SCR reaction rate expression is:

[0059]

[0060] The slow SCR reaction rate expression is:

[0061]

[0062] The reaction rate expression of NO2 formation is:

[0063]

[0064] Among them, r ads and k ads are the ammonia adsorption reaction rate and rate constant, r des and k des are the ammonia desorption reaction rate and rate constant, respectively; r NO and k NO are the NO oxidation reaction rate and rate constant, respectively; r NH3 and k NH3 are the NH3 oxidation reaction rate and rate constant, respectively; r stand and k stand are the standard SCR reaction rate and rate constant, respectively; r rapid and k rapid are the fast SCR reaction rate and rate constant, respectively; r slow and k slow are the slow SCR reaction rate and rate constant, respectively; r NO2 and k NO2 are the NO2 formation reaction rate and rate constant respectively; c NH3 、c NO、 c NO2 and c O2 are the molar concentrations of NH3, NO, NO2, and O2 respectively; θ NH3，max is the maximum coverage of NH3 on the coating reaction surface; θ* NH3 k is the critical coverage of NH3 on the coating reaction surface; eq is the reaction equilibrium constant.

[0065]

[0066]

[0067] Among them, T a is the aging temperature, ta is the aging time, k a is the Arrhenius kinetic pre-exponential factor; Ea is the activation energy; R is the ideal gas constant, and c is a constant.

[0068] The nitrogen oxides in diesel engine exhaust mainly include nitrogen monoxide and nitrogen dioxide. The nitrogen oxide conversion rate is X NOX The performance indicators of the established model are:

[0069]

[0070] in, is the molar concentration of inlet nitrogen dioxide, c NO,in is the molar concentration of inlet nitric oxide, is the molar concentration of nitrogen dioxide at the outlet, c NO,out is the molar concentration of outlet nitric oxide.

[0071] The beneficial effects of the present invention are:

[0072] (1) A single-channel SCR mathematical model is established by the modeling method, and the nitrogen oxide conversion rate can be obtained through the model, so that the emission reduction performance of the reactor can be evaluated or assessed.

[0073] (2) The SCR single-channel model takes into account the effects of mass transfer limitations and mild aging of the catalyst, and is more accurate in evaluating the emission reduction performance of the reactor.

[0074] (3) The pore structure in the catalytic coating is simplified into a capillary bundle with a sinusoidal waveform, and the average radius of the pores in the catalytic coating is used as a representative indicator to describe the pore size distribution. This simplifies the mathematical model while not affecting the evaluation of the reactor performance by the mathematical model finally established.

[0075] (4) The theoretical model established by the modeling method can be used to capture the mechanism of mild hydrothermal aging and its corresponding impact on catalyst performance, and can more accurately describe the mutual influence between SCR reaction and mass transfer during the mild aging process of copper-based molecular sieve catalysts.

[0076] (5) The mathematical model is a theoretical model, which has low cost and high efficiency in reactor evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 Schematic diagram of the SCR single-channel model of the present invention.

[0078] Figure 2 Schematic diagram of the process of simplifying the catalytic coating into a sinusoidal capillary bundle model.

[0079] Figure 3This is the SCR reaction mechanism diagram of copper-based molecular sieve catalyst. DETAILED DESCRIPTION

[0080] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the present invention, and is not used to limit the present invention.

[0081] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0082] A modeling method for a single channel of a selective catalytic reduction reactor is disclosed. The reactor can be regarded as having multiple SCR single channels inside. When diesel engine exhaust enters the reactor, the exhaust gas as a reactant will pass through the SCR single channel to achieve catalytic reduction, and the generated product will be discharged from the reactor.

[0083] The schematic diagram of the SCR single-channel model is as follows Figure 1 As shown, the SCR single channel is a cylindrical structure, the side wall of the cylindrical structure is a catalytic coating formed by a catalyst, the channel inside the cylindrical structure surrounded by the catalytic coating is the main channel, there are many pores inside the catalytic coating, and ammonia molecules are adsorbed on the active sites of the catalyst. In other words, the SCR single channel includes a main channel and a catalytic coating surrounding the main channel. The mass transfer process of reactants and products in the main channel and the catalytic coating is generally divided into two types: intra-phase mass transfer and inter-phase mass transfer. There is a large amount of NO in the main channel. Xand O2, these components enter the catalytic coating, and this mass transfer process is interphase mass transfer. The ammonia molecules adsorbed on the active sites of the catalyst will react with nitrogen oxides and oxygen. The remaining gas molecules continue to transfer from the gas phase to the inside of the catalytic coating through the diffusion mechanism in the catalytic reactor, and this mass transfer process is intraphase mass transfer. The products generated by the reaction include water and nitrogen, etc. These harmless products are first produced inside the catalytic coating and transported through the porous structure of the coating. The above products diffuse outward from the active sites in the coating through the pores of the catalytic coating, and this mass transfer process is intraphase mass transfer. The pore structure of the coating determines the speed and efficiency of product transfer, ensuring that the products can quickly leave the reaction site and be transferred to the surface of the coating. When H2O and N2 pass through the catalytic coating through intraphase mass transfer and reach the surface, they will enter the interface between the gas phase and the solid phase, that is, the gas phase channel in the reactor. In this process, the products enter the macroscopic channels from the microscopic pores of the coating and enter the gas phase from the solid phase coating through the interphase mass transfer mechanism. The whole process involves complex multiple mass transfer and reaction mechanisms, including axial convection and diffusion in the gas phase, mass transfer on the gas-solid interface, and radial diffusion and catalytic reaction inside the catalytic coating. Each process interacts with each other to ensure that the reactants enter the catalytic coating from the gas phase and effectively complete the chemical conversion in the coating to generate the target product.

[0084] The SCR reactor has the following structural characteristics: small-sized main channels in parallel, large main channel length-to-width ratio, negligible heat loss, and uniform radial flow distribution. It is reasonable to assume that all SCR single channels exhibit consistent flow and reaction behavior in the reactor. This assumption simplifies the analysis of reactor performance and provides a consistent expectation of overall system behavior. Specific assumptions include the following:

[0085] A1) In the model, the axial diffusion effect in the main channel and inside the catalyst coating is neglected. This assumption simplifies the mathematical description of gas transport and reaction processes, because axial diffusion usually contributes less to the overall mass transfer in actual reactors. By ignoring this factor, we can focus more on the analysis of dominant processes, such as convection and radial diffusion, thereby reducing computational complexity.

[0086] A2) The model assumes that the gas flow in the main channel is laminar, which means that there is no significant turbulence in the main channel. Based on the geometry and inlet conditions of the main channel, the laminar flow assumption helps to simplify the fluid dynamics analysis and can provide more accurate mass transfer and reaction calculation results.

[0087] A3) In the model, the gas is evenly distributed at the inlet of the SCR single channel, that is, the gas flow, velocity, temperature and concentration at the inlet of each main channel are the same.

[0088] A4) The model assumes that the catalyst active material and the coating are uniformly distributed in all single channels, and the porous medium of the coating is also uniform and isotropic.

[0089] A5) The model divides the catalyst coating area into high permeability and low permeability areas. In the high permeability area, the gas mass transfer process is mainly convection, that is, the gas can pass through the catalyst pores quickly and enter the reaction area; while in the low permeability area, the mass transfer process is mainly diffusion, and the gas molecules move slowly in smaller pores through the diffusion mechanism. Convection mass transfer is not considered in the mass transfer within the copper-based molecular sieve catalyst coating.

[0090] In addition, nuclear magnetic resonance experiments showed that there was no evidence of dealumination of copper-based molecular sieve catalysts at mild aging temperatures, indicating that the performance degradation of copper-based molecular sieve catalysts at mild aging temperatures can be assumed to be due to the reduction of their active sites, and therefore the effect of mild aging can be reflected by changes in the concentration of molecular sieve active sites.

[0091] Based on the above five assumptions, the modeling method includes the following steps:

[0092] Step S1: Establish a single-channel mathematical model of SCR, and the corresponding equation group of the model includes the component balance equation of gas phase substances in the main channel, the momentum balance equation of gas phase substances in the main channel, the enthalpy balance equation of gas phase substances in the main channel, the gas phase component balance equation in the catalytic coating, the gas phase enthalpy balance equation in the catalytic coating, the NH3 coverage balance equation in the catalytic coating, the component balance equation at the gas phase-coating interface, and the enthalpy balance equation at the gas phase-coating interface.

[0093] In this embodiment, each equation of the equation group is as follows:

[0094] 1) Component balance equation of gas phase in the main channel

[0095]

[0096] Wherein, t represents time; z represents axial direction; ρ represents exhaust density, i.e., gas density in the main channel; v represents exhaust velocity, i.e., gas velocity in the main channel; yi represents the mass fraction of component i in the main channel; Di represents the diffusion coefficient of component i in the main channel.

[0097] 2) Momentum balance equation of gas phase in the main channel

[0098]

[0099] Where μ represents dynamic viscosity and p represents pressure.

[0100] 3) Enthalpy balance equation of gas phase substances in the main channel

[0101]

[0102] Among them, c p represents the specific heat capacity of the gas in the main channel; λg represents the thermal conductivity of the gas in the main channel; Tg represents the gas temperature in the main channel.

[0103] 4) Balance equation of gas phase components in catalytic coating

[0104]

[0105] Among them, ρ w is the density of the gas in the catalytic coating; x represents the radial direction; y w,i is the mass fraction of component i in the catalytic coating; D w,i is the diffusion coefficient of component i in the catalytic coating; a c is the specific surface area of ​​the catalyst in the catalytic coating; i,j is the stoichiometric ratio of component i in chemical reaction j; M i is the molar mass of component i; r j is the reaction rate of chemical reaction j.

[0106] 5) Gas phase enthalpy balance equation in catalytic coating

[0107]

[0108] Among them, T w is the gas temperature in the coating; w is the thermal conductivity of the gas in the catalytic coating; ΔH m，j is the standard enthalpy of formation of chemical reaction j.

[0109] 6) NH3 coverage equilibrium equation in catalytic coating

[0110]

[0111] Where Ω is the concentration of catalytic active sites; θ NH3 is the coverage of adsorbed NH3 on the coating reaction surface; γ NH3,j is the stoichiometric ratio of NH3 in chemical reaction j.

[0112] 7) Component balance equation at the gas phase-coating interface

[0113]

[0114] Among them, k m,i is the mass transfer coefficient of component i on the coating surface.

[0115] 8) Enthalpy balance equation at the gas-coating interface

[0116]

[0117] Among them, k h is the heat transfer coefficient at the gas-coating interface.

[0118] Step S2: Given the initial conditions and boundary conditions of the SCR single-channel model, and based on the characteristics of the SCR single-channel, define the values ​​or expressions of some unknown parameters in the equation group in step S1, substitute the values ​​or expressions of the defined parameters into each equation in step S1, and obtain a closed set of equations corresponding to the SCR single-channel model.

[0119] First, the initial conditions and boundary conditions of the SCR single-channel model are given in equations (9) and (10), respectively:

[0120]

[0121] Where L is the main channel length, which is the axial length; δ w is the coating thickness; θ 0 NH3 is the coverage of the initially adsorbed NH3 on the coating reaction surface.

[0122] Then, the values ​​or expressions of some unknown parameters in the equation group in step S1 are defined according to the characteristics of the SCR single channel.

[0123] For the component balance equation of the gas phase-coating interface in formula (7), the mass transfer coefficient km,i of component i on the coating surface can be expressed as:

[0124]

[0125] Among them, d h is the hydraulic diameter of the main channel; Sh is the Sherwood number; D i is the diffusion coefficient of component i in the gas phase. The Sherwood number used in the mass transfer coefficient at the gas-solid interface is calculated from the Hawthorn relationship.

[0126]

[0127] Wherein, L is the main channel length, which is the axial length; Re is the Reynolds number; Sc is the Schmidt number.

[0128] For the component balance equation of the gas phase substance in the main channel of formula (1), it is necessary to obtain the diffusion coefficient Di of component i in the main channel; for the component balance equation of the gas phase in the catalytic coating of formula (4), it is necessary to obtain the diffusion coefficient D of component i in the catalytic coating w,i. The reason is as follows: Ignoring the mass transfer resistance caused by diffusion may lead to significant deviations in the prediction of reactor performance. This is because pore diffusion has an important influence on the transport of substances in catalytic reactions, especially inside the catalytic coating. The diffusion process of the reactants through the microporous structure directly affects the reaction rate and overall performance. Therefore, if the influence of pore diffusion is not considered, the mass transfer behavior cannot be accurately described, resulting in distortion of the reactor performance prediction results. Therefore, in the simulation and optimization of reactor performance, it is necessary to reasonably model the pore diffusion process in the catalytic coating to ensure the accuracy and reliability of the prediction.

[0129] The definition of bulk diffusion and Knudson diffusion depends on the relative ratio of collisions between gas molecules and collisions between gas molecules and pore walls. When collisions between gas molecules dominate, the mass transfer process is mainly bulk diffusion; when the frequency of collisions between gas molecules and pore walls is higher, Knudson diffusion is dominant. In addition, the surface roughness and pore structure differences of catalyst particles directly affect their microscopic characteristics, such as specific surface area, pore volume and pore size distribution. These microstructural parameters largely determine the efficiency of catalytic reactions and the speed and path of mass transfer. Increased surface roughness and changes in pore structure may enhance or hinder the diffusion behavior of gases, thereby changing the transfer process of reactants and products. Studies have shown that the microstructural characteristics of catalysts have an important influence on their reaction performance and mass transfer process. The gas diffusion process in the catalyst micropores is significantly affected by the pore size, pore length and pore shape. At the microscopic scale, these structural characteristics determine the movement path and diffusion resistance of gas molecules. In porous media catalysts, there are generally four types of diffusion: bulk diffusion, Knudson diffusion, configurational diffusion and surface diffusion. However, in industrial catalysts, due to their relatively large pore size, the movement of gas molecules in the pores is closer to bulk diffusion, and the influence of configurational diffusion can be ignored. In addition, under high-temperature operating conditions, the kinetic energy of gas molecules increases significantly, causing the contribution of surface diffusion to the overall mass transfer process to become less significant. Therefore, in actual industrial catalytic processes, although the microporous structure will affect the diffusion behavior, under conditions of larger pore size and high temperature, the effects of configurational diffusion and surface diffusion are relatively small and can be ignored. Therefore, in this scheme, mass transfer in the main channel only needs to consider bulk diffusion, and mass transfer in the coating only considers bulk diffusion and Knudson diffusion.

[0130] The bulk diffusion coefficient of multi-component molecules can be calculated using formula (13).

[0131]

[0132] Among them, x i and x j are the concentrations of components i and j respectively. The bulk diffusion coefficient of binary molecules D ijIt can be evaluated by the Chapman-Enskog method. The binary molecular bulk diffusion coefficient refers to the bulk diffusion coefficient of a gas composed of two molecules.

[0133]

[0134] Among them, V i and V j are the molecular volumes of components i and j respectively; M i and M j are the molar masses of components i and j respectively; p is the pressure; Tg is the gas temperature.

[0135] The catalytic coating is a porous medium, and the effective diffusion coefficient in the coating is determined by using a parallel cross-linked pore model, and its calculation formula is shown in formula (15). K The pore size distribution of the coating is an important parameter to characterize its mass transfer characteristics and catalytic performance. To simplify this complex distribution feature, the average radius of uniformly sized pores in the catalytic coating (r p ) as a representative indicator to describe the pore size distribution. Through this method, the complexity of the pore size distribution can be effectively reduced, making it more operational in practical applications. The average radius can not only simplify the pore structure analysis of porous media, but also provide a basis for subsequent mass transfer models and catalytic performance evaluation. By summarizing the pore size distribution of porous media into a single average radius, it is helpful to more clearly understand and predict the diffusion behavior of gases during catalytic reactions and their impact on reaction efficiency. According to the above simplified method, Equation (15) can be restated as Equation (17).

[0136]

[0137] The copper-based molecular sieve catalyst used in this scheme exhibits a unique microporous structure, which is regularly arranged but has certain curvature. This microporous characteristic has an important influence on the mass transfer process of the catalytic reaction. During the catalytic reaction, the reactants NH3, NO, O2 and NO2 need to diffuse from the outer surface of the catalyst into the micropores. This process is called diffusion into the micropores. After the reaction is completed, the generated products such as N2 and H2O diffuse back to the outer surface of the catalyst through the same microporous structure, forming an internal diffusion process. A simplified catalyst coating model (such as Figure 2As shown in the figure, it is specially used to simulate the reaction-diffusion process. This model abstracts the complex physical phenomena by simplifying the coating structure, which facilitates the accurate quantitative analysis of the mass transfer and reaction behavior in the catalytic coating. This simplified model can effectively reduce the computational complexity while maintaining an accurate description of the key mass transfer and reaction mechanisms. In order to further optimize the simulation of the reaction-diffusion process in the catalyst coating, the sinusoidal capillary bundle model (Sinusoidal Capillary Bundle Model) is adopted. This model simplifies the pore structure of the coating into a capillary bundle with a sinusoidal waveform, which not only retains the key features of the actual coating structure, but also greatly simplifies the calculation. The structure highly fits the actual geometric morphology of the coating, and at the same time provides an efficient and accurate calculation method, which helps to simulate the mass transfer process more accurately. The tortuosity is defined as the true length of the radial pore path in the coating (l e ) to the coating thickness (l). Although tortuosity is not an exact geometric parameter, as a numerical parameter, it can effectively describe the degree of curvature of the pores in the coating and its effect on the diffusion process. The definition of tortuosity helps to quantitatively evaluate the diffusion efficiency in the coating, especially in the mass transfer process of porous media, this parameter becomes the core indicator to describe the pore diffusion behavior. Therefore, this scheme calculates the effective diffusion coefficient of the catalyst coating through the sinusoidal capillary bundle model, and further links the porosity with the number of pores per unit area to describe the mass transfer characteristics in the coating. At the same time, the molar diffusion flux formula is used to quantitatively analyze the gas diffusion process in the coating, and the relationship between porosity, effective diffusion coefficient and diffusion flux is established. Assuming that the pores are distributed per unit area and the number is n, the porosity can be expressed as:

[0138]

[0139] Among them, S ⊥ is the normal direction; n is the number of pores per unit area of ​​the catalytic coating.

[0140] The molar diffusion flux can be expressed as:

[0141]

[0142] Where Δc is the difference in gas component concentration.

[0143] The effective diffusion coefficient of porous media can be expressed as:

[0144]

[0145] Where τ is the coating tortuosity; τ f is the tortuosity factor.

[0146] The calculation of the surface reaction rate of the SCR single-channel model is related to the surface area of ​​the active catalyst, as shown in formulas (4) and (5) in the SCR single-channel model. The larger the surface area, the higher the reaction rate. This is because a larger surface area provides more active sites, which promotes the contact and reaction process between the reactants and the catalyst. Therefore, increasing the surface area of ​​the catalyst can effectively increase its surface reaction rate, thereby enhancing the overall catalytic efficiency. Formula (21) represents the calculation result of the active catalyst surface area:

[0147]

[0148] a c is the specific surface area of ​​the active catalyst; V ads is the volume of the adsorbed active component; V m is the molar volume of the adsorbed active component; N A is Avogadro's constant; m is the mass of the catalyst; w is the mass fraction of Cu; and n is the stoichiometric ratio of the active component to Cu. The surface area of ​​the adsorption site refers to the surface area occupied by each adsorption site on the catalyst surface, expressed as a m Or, a c It can also be expressed as formula (22), which is obtained using the easily measurable Cu-based catalyst distribution function a(z).

[0149]

[0150] Wherein, M is the catalytic mass per unit volume of catalytic coating.

[0151] The SCR reaction mechanism is crucial to the reactor model, which is specifically reflected in the SCR single-channel model formulas (4)-(6). Figure 3 The diagram of the reaction mechanism of SCR on Cu-based catalysts shows that copper-based catalysts exhibit complex reaction mechanisms in the selective catalytic reduction (SCR) reaction. This complexity stems from the presence of multiple reaction sites and different metal oxidation states in the catalyst. Although Cu-based catalysts have excellent catalytic performance, the diversity and heterogeneity of their reaction sites lead to multiple reaction pathways and mechanisms in the reaction process. In Cu-based catalysts, the active substances include Cu + , Cu 2+, copper oxide and Bronsted acid sites. These metal oxidation states and acidic sites together constitute a rich reaction environment on the catalyst surface, allowing the reactants to react through different pathways, further increasing the complexity of the reaction mechanism. In order to facilitate the establishment and analysis of the model, a simplified assumption is made, which assumes that the adsorption of ammonia only occurs on a specific type of reaction site. This scheme uses the Temkin relationship to describe the adsorption behavior of ammonia on the catalyst surface. The Temkin relationship takes into account the change in adsorption heat and is applicable to non-uniform adsorption sites. Through this relationship, the desorption process of ammonia at a variety of reaction sites can be better simulated, as shown in Table 1.

[0152] Table 1 Assumptions and expressions of Temkin adsorption equation

[0153]

[0154]

[0155] Where q represents the amount of NH3 adsorbed, P is the partial pressure or concentration of the adsorbed substance, a and c0 are parameter constants measured experimentally; θ NH3 is the coverage of adsorbed NH3 on the coating reaction surface.

[0156] In the NH3-SCR reaction, the Eley-Rideal (ER) mechanism is applied to the SCR kinetic model.

[0157] Among them, it is believed that NH3 is adsorbed on the catalyst surface and NO in the gas phase X A reaction occurs.

[0158] The ammonia adsorption reaction is:

[0159] NH3+S1→NH3-S1 (23)

[0160] The ammonia desorption reaction is:

[0161] NH3-S1→NH3+S1 (24)

[0162] The nitric oxide oxidation reaction is:

[0163]

[0164] The ammonia oxidation reaction is:

[0165] 4NH3-S1+3O2→2N2+6H2O+4S1 (26)

[0166] The standard SCR reaction is:

[0167] 4NH3-S1+4NO+O2→4N2+6H2O+4S1 (27)

[0168] The fast SCR reaction is:

[0169] 2NH3-S1+NO+NO2→2N2+3H2O+2S1 (28)

[0170] The slow SCR reaction is:

[0171] 8NH3-S1+6NO2→7N2+12H2O+8S1 (29)

[0172] The NO2 generation reaction is:

[0173] 2NH3-S1+2NO2→N2+N2O+3H2O (30)

[0174] Among them, S1 represents the catalytic active site. In the adsorption process of NH3, studies have shown that this process belongs to the non-activated adsorption type, which means that its adsorption reaction does not require additional activation energy.

[0175] The Temkin relation takes into account the change in adsorption heat and is applicable to desorption behavior under surface heterogeneity conditions. In the desorption process of NH3, the activation energy (E des ) can be described by Temkin expression (31).

[0176]

[0177] Among them, E 0 des is the initial desorption activation energy; α is the coefficient; θ NH3 is the coverage of adsorbed NH3 on the coating reaction surface.

[0178] The Arrhenius law describes the effect of temperature on the rate of chemical reactions. Specifically, the reaction rate increases with increasing temperature, a phenomenon that can be quantitatively described by the Arrhenius equation. The Arrhenius law states that there is an exponential relationship between the reaction rate and the activation energy and absolute temperature of the reactants. The reaction rate expressions represented by equations (32) to (39) are all expressions that conform to this law for this model.

[0179] The ammonia adsorption reaction rate expression is:

[0180]

[0181] The ammonia desorption reaction rate expression is:

[0182]

[0183] The reaction rate expression of nitric oxide oxidation is:

[0184]

[0185] The reaction rate expression of ammonia oxidation is:

[0186]

[0187] The standard SCR reaction rate expression is:

[0188]

[0189] The fast SCR reaction rate expression is:

[0190]

[0191] The slow SCR reaction rate expression is:

[0192]

[0193] The reaction rate expression of NO2 formation is:

[0194]

[0195] Among them, r ads and k ads is the ammonia adsorption reaction rate and rate constant; r des and k des is the ammonia desorption reaction rate and rate constant; r NO and k NO is the NO oxidation reaction rate and rate constant; r NH3 and k NH3 is the NH3 oxidation reaction rate and rate constant; r stand and k stand is the standard SCR reaction rate and rate constant; r rapid and k rapid is the fast SCR reaction rate and rate constant; r slow and k slow is the slow SCR reaction rate and rate constant; r NO2 and k NO2 is the NO2 generation reaction rate and rate constant; c NH3 、c NO、 c NO2 and c O2 are the molar concentrations of NH3, NO, NO2, and O2 respectively; θ NH3，max is the maximum coverage of NH3 on the coating reaction surface; θ* NH3 k is the critical coverage of NH3 on the coating reaction surface; eq is the reaction equilibrium constant.

[0196] The reactor model is based on the assumption that the mild hydrothermal aging process can be considered as a chemical reaction, as shown in Eq. (40), and the rate of the reaction can be expressed by Arrhenius kinetics. In mathematical terms, the extent of mild hydrothermal aging is calculated by using the loss of catalytic active sites to calculate the hydrothermal aging rate, which is the aging temperature (T a ) and aging time (t a ) function.

[0197]

[0198] Where Ω is the concentration of catalytic active sites in equation (6), indicating the secondary deactivation mechanism of catalytic active site loss. a is the Arrhenius kinetic pre-exponential factor; Ea is the activation energy; R is the ideal gas constant.

[0199] The integral form of the mild hydrothermal aging calculation function is as follows:

[0200]

[0201] Where c is a constant.

[0202] Equation (41) can be used to estimate the change in the concentration of catalytic active sites with aging time and temperature.

[0203] Substituting equation (41) into equation (6) in the model, we can obtain the concentration of catalytic active sites Ω and the coverage of adsorbed NH3 on the coating reaction surface θ after continuous mild aging. NH3 .

[0204] The nitrogen oxides in diesel engine exhaust mainly include nitrogen monoxide and nitrogen dioxide. The nitrogen oxide conversion rate is X NOX is the performance index of this model, which can be expressed as:

[0205]

[0206] in, is the molar concentration of inlet nitrogen dioxide, c NO,in is the molar concentration of inlet nitric oxide, is the molar concentration of nitrogen dioxide at the outlet, c NO,out is the molar concentration of outlet nitric oxide.

[0207] From the above, after obtaining the closed equation group corresponding to the SCR single-channel model, the nitrogen oxide concentration at the outlet can be calculated, and then the nitrogen oxide conversion rate can be obtained. The above conversion rate reflects the emission reduction performance of the reactor.

[0208] Finally, it is necessary to explain here that the above embodiments are only used to further illustrate the technical solution of the present invention in detail and cannot be understood as limiting the scope of protection of the present invention. Some non-essential improvements and adjustments made by technicians in this field based on the above content of the present invention all fall within the scope of protection of the present invention.

Claims

1. A modeling method for a single channel selective catalytic reduction reactor, characterized in that: The reactor is provided with a plurality of SCR single channels inside, the SCR single channels are cylindrical structures, the sidewalls of the cylindrical structures are catalytic coatings formed by catalysts, the channels inside the cylindrical structures surrounded by the catalytic coatings are main channels, the catalytic coatings have many pores inside, the active sites of the catalysts adsorb ammonia molecules and perform selective catalytic reduction reactions, and the modeling method comprises the following steps: Step S1: Establishing a mathematical model of a single channel of SCR, the equation group corresponding to the model includes a component balance equation of gas phase substances in the main channel, a momentum balance equation of gas phase substances in the main channel, an enthalpy balance equation of gas phase substances in the main channel, a gas phase component balance equation in the catalytic coating, a gas phase enthalpy balance equation in the catalytic coating, an NH3 coverage balance equation in the catalytic coating, a component balance equation at the gas phase-coating interface, and an enthalpy balance equation at the gas phase-coating interface; Step S2: Given the initial conditions and boundary conditions of the SCR single-channel model, and based on the characteristics of the SCR single-channel, define the values ​​or expressions of some unknown parameters in the equation group in step S1, substitute the values ​​or expressions of the defined parameters into each equation in step S1, and obtain a closed set of equations corresponding to the SCR single-channel model.

2. The modeling method according to claim 1, characterized in that: In step S2, the defined unknown parameters include: the mass transfer coefficient of any component on the surface of the catalytic coating, the diffusion coefficient of any component in the main channel and in the catalytic coating respectively, the specific surface area of ​​the catalyst in the catalytic coating, the reaction rate expression of each chemical reaction involved in the SCR single channel, and the concentration of catalytic active sites in the catalytic coating; in step S2, when calculating the diffusion coefficient of any component in the catalytic coating, the pore structure of the catalytic coating is simplified to a capillary bundle with a sinusoidal waveform, and the average radius of the pores in the catalytic coating is used as a representative indicator to describe the pore size distribution; the mass transfer in the main channel only considers bulk diffusion, and the mass transfer in the catalytic coating only considers bulk diffusion and Knudson diffusion.

3. The modeling method according to claim 1 or 2, characterized in that: The component balance equation of the gas phase in the main channel is: Wherein, t represents time; z represents axial direction; ρ represents exhaust density, i.e., gas density in the main channel; v represents exhaust velocity, i.e., gas velocity in the main channel; yi represents mass fraction of component i in the main channel; Di represents diffusion coefficient of component i in the main channel; The momentum balance equation of the gas phase in the main channel is: Where, μ represents dynamic viscosity; p represents pressure; The enthalpy balance equation of the gas phase in the main channel is: Among them, c p represents the specific heat capacity of the gas in the main channel; λg represents the thermal conductivity of the gas in the main channel; Tg represents the gas temperature in the main channel; The gas phase component balance equation in the catalytic coating is: Among them, ρ w is the density of the gas in the catalytic coating; x represents the radial direction; y w,i is the mass fraction of component i in the catalytic coating; D w,i is the diffusion coefficient of component i in the catalytic coating; a c is the specific surface area of ​​the catalyst in the catalytic coating; i,j is the stoichiometric ratio of component i in chemical reaction j; M i is the molar mass of component i; r j is the reaction rate of chemical reaction j; Gas phase enthalpy balance equation in catalytic coating: Among them, T w is the gas temperature in the catalytic coating; w is the thermal conductivity of the gas in the catalytic coating; ΔH m，j is the standard formation enthalpy of chemical reaction j; The NH3 coverage balance equation in the catalytic coating is: Where Ω is the concentration of catalytic active sites; θ NH3 is the coverage of adsorbed NH3 on the reaction surface of the catalytic coating; γ NH3,j is the stoichiometric ratio of NH3 in chemical reaction j; The component balance equation at the gas phase-coating interface is: Among them, k m,i is the mass transfer coefficient of component i on the coating surface; The enthalpy balance equation at the gas phase-coating interface is: Among them, d h is the hydraulic diameter of the main channel, k h is the heat transfer coefficient at the gas-coating interface.

4. The modeling method according to claim 3, characterized in that: The initial conditions of the SCR single-channel model are: The boundary conditions are: Where L is the main channel length, which is the axial length; δ w is the thickness of the catalytic coating; θ 0 NH3 is the coverage of the initially adsorbed NH3 on the reaction surface of the catalytic coating.

5. The modeling method according to claim 3, characterized in that: Wherein, L is the main channel length, which is the axial length; Re is the Reynolds number; Sc is the Schmidt number.

6. The modeling method according to claim 3, characterized in that: When calculating the diffusion coefficient of any component in the catalytic coating, the pore structure of the catalytic coating is simplified to a capillary bundle with a sinusoidal waveform, then: Where ε is the porosity, S ⊥ is the normal direction, n is the number of pores per unit area of ​​the catalytic coating, l e is the length of a single pore in the catalytic coating, l is the thickness of the catalytic coating, N is the molar diffusion flux, Δc is the concentration difference between the gas components at the outlet and inlet of the pore structure, and τ is the tortuosity of the coating; τ f is the tortuosity factor.

7. The modeling method according to claim 3, characterized in that: or Among them, V ads is the volume of the adsorbed active component; V m is the molar volume of the adsorbed active component; N A is Avogadro's constant; m is the mass of the catalyst; w is the mass fraction of Cu in the copper-based molecular sieve catalyst; n is the stoichiometric ratio of the active component to Cu, a m is the surface area occupied by each adsorption site on the catalyst surface, M is the catalytic mass per unit volume of the catalytic coating, and a(z) is the distribution function of the copper-based molecular sieve catalyst.

8. The modeling method according to claim 3, characterized in that: The ammonia adsorption reaction rate expression is: The ammonia desorption reaction rate expression is: The reaction rate expression of nitric oxide oxidation is: The reaction rate expression of ammonia oxidation is: The standard SCR reaction rate expression is: The fast SCR reaction rate expression is: The slow SCR reaction rate expression is: The reaction rate expression of NO2 formation is: Among them, r ads and k ads are the ammonia adsorption reaction rate and rate constant, r des and k des are the ammonia desorption reaction rate and rate constant, respectively; r NO and k NO are the NO oxidation reaction rate and rate constant, respectively; r NH3 and k NH3 are the NH3 oxidation reaction rate and rate constant, respectively; r stand and k stand are the standard SCR reaction rate and rate constant, respectively; r rapid and k rapid are the fast SCR reaction rate and rate constant, respectively; r slow and k slow are the slow SCR reaction rate and rate constant, respectively; r NO2 and k NO2 are the NO2 formation reaction rate and rate constant respectively; c NH3 、c NO、 c NO2 and c O2 are the molar concentrations of NH3, NO, NO2, and O2 respectively; θ NH3，max is the maximum coverage of NH3 on the coating reaction surface; θ* NH3 k is the critical coverage of NH3 on the coating reaction surface; eq is the reaction equilibrium constant.

9. The modeling method according to claim 3, characterized in that: Among them, T a is the aging temperature, t a is the aging time, k a is the Arrhenius kinetic pre-exponential factor; Ea is the activation energy; R is the ideal gas constant, and c is a constant.

10. The modeling method according to claim 3, characterized in that: The nitrogen oxides in diesel engine exhaust mainly include nitrogen monoxide and nitrogen dioxide. The nitrogen oxide conversion rate is X NOX The performance indicators of the established model are: in, is the molar concentration of inlet nitrogen dioxide, c NO,in is the molar concentration of inlet nitric oxide, is the molar concentration of nitrogen dioxide at the outlet, c NO,out is the molar concentration of outlet nitric oxide.

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