CN110993035B - Two-dimensional steady-state model establishment method for proton exchange membrane electrolytic cell characteristic analysis - Google Patents

Two-dimensional steady-state model establishment method for proton exchange membrane electrolytic cell characteristic analysis Download PDF

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CN110993035B
CN110993035B CN201911152998.6A CN201911152998A CN110993035B CN 110993035 B CN110993035 B CN 110993035B CN 201911152998 A CN201911152998 A CN 201911152998A CN 110993035 B CN110993035 B CN 110993035B
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李曦
赵东琦
郑依
仲小博
蒋建华
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Abstract

The invention provides a two-dimensional steady-state model establishing method for proton exchange membrane electrolytic cell characteristic analysis, and relates to the technical field of electrolytic cell models. S1, establishing a physical model of the electrolytic cell to simulate electrochemical reaction; s2, establishing a calculation model according to the physical model; s3, inputting boundary conditions into the physical model, starting electrochemical reaction, dividing the physical model into a plurality of grid blocks along the flow channel direction of the physical model, wherein the reactant concentrations in different grid blocks are different, and the reactant concentration in one grid block is regarded as uniform; and S4, the calculation model obtains steady-state parameter values in all grid blocks one by one according to the reactant concentrations in different grid blocks. After the physical model is divided into the grid shape, the distribution consideration of the actual reactant concentration along the flow channel direction is increased, the steady-state parameter value in each grid block is obtained according to the reactivity concentration in each grid block, the local characteristics of the operation of the electrolytic cell can be better reflected, the physical process of the model is more complete, and the accuracy and the application value are improved.

Description

Two-dimensional steady-state model establishment method for proton exchange membrane electrolytic cell characteristic analysis
Technical Field
The invention relates to the technical field of electrolytic cell models, in particular to a two-dimensional steady-state model establishing method for proton exchange membrane electrolytic cell characteristic analysis.
Background
Although renewable energy sources such as tidal energy, wind energy and solar energy are promising energy sources, they are subject to intermittent and regional influences and are not very reliable. In order for renewable energy technologies to be widely and reliably applied, clean and sustainable energy technologies are urgently needed to solve serious environmental problems and meet human needs.
Hydrogen is a promising energy carrier for renewable energy storage, and excess renewable energy can be used to drive an electrolytic cell to generate hydrogen, and also can be converted into electric energy through a fuel cell when the renewable energy is insufficient. In addition, hydrogen is an ideal fuel for fuel cell vehicles to achieve low emissions and smart transportation.
Proton Exchange Membrane Electrolytic Cells (PEMEC) are a low-temperature electrochemical electrolytic cell, and are the most widespread method for producing hydrogen by electrolyzing water. But since the electrolyte membrane requires a high water content to maintain the high proton conductivity of the membrane, the operating temperature is typically below 100 ℃ unless the system is pressurized to maintain the water content of the membrane. However, the energy input to the PEMEC at temperatures below 100 ℃ is electricity, and the contribution of thermal energy is very low. More importantly, the electrode reaction lag requires the use of expensive catalysts, such as Pt, which makes PEMEC very expensive. With the development of alternative electrolyte membranes, PEMECs can be operated at temperatures above 100 ℃, which is highly desirable for hydrogen production. First, electrode kinetics increase with increasing temperature, thereby reducing activation losses of the electrode and enabling the use of lower cost catalysts. Next, when the steam electrolysis was carried out at 130 ℃, the amount of heat (. DELTA.H) required for the water decomposition was 243kJ mol-1Less than the heat required for water splitting at 80 ℃ (284kJ mol)-1). Subsequently, the reversible voltage of the cell can be slightly reduced by increasing the temperature of the cell from 80 ℃ (1.18V) to 130 ℃ (1.16V). In addition, high temperature proton exchange membrane electrolytic cellMore heat energy input is required, indicating that more waste industrial heat can be used for hydrogen production in high temperature proton exchange membrane electrolytic cells.
In engineering practice, the actual electrolytic cell flow channel is usually longer, and due to the consumption of reaction gas during the operation of the electrolytic cell, the concentration of the reaction gas is necessarily reduced along the flow channel direction, so that the reaction rate of the catalytic layer is changed. Therefore, the characteristic analysis in the long-flow-channel electrolytic cell is often not accurate enough, and the application in practical engineering is influenced.
Disclosure of Invention
The invention aims to provide a two-dimensional steady-state model establishing method for proton exchange membrane electrolytic cell characteristic analysis, which aims to solve the problem that the electrolytic cell characteristic analysis of a long flow channel is not accurate.
The method comprises the following steps:
s1, establishing a physical model of the proton exchange membrane electrolytic cell, and providing physical parameters of each structure of the electrolytic cell to simulate electrochemical reaction;
s2, establishing a calculation model for calculating relevant steady state parameters in the electrochemical reaction according to the physical model;
s3, inputting boundary conditions into the physical model to start electrochemical reaction, wherein the physical model is divided into a plurality of grid layers along the flow channel direction, each grid layer is divided into a plurality of grid blocks, the reactant concentrations in different grid blocks are different, and the reactant concentration in one grid block is regarded as uniform;
and S4, the calculation model takes the boundary conditions as initial values, calculates in an iterative mode of finite elements, and obtains steady-state parameter values corresponding to the boundary conditions in all the grid blocks one by one according to the reactant concentrations in the different grid blocks.
According to the technical scheme, after the physical model is divided into the grid shape, the distribution consideration of the actual reactant concentration in the flow channel direction is increased, the steady state parameter value in each grid block is obtained according to the reactivity concentration in each grid block, the local characteristics of the operation of the electrolytic cell can be better reflected, the physical process of the model is more complete, the accuracy and the application value are improved, the development of a galvanic pile and a system-level electrolytic cell model is facilitated, the development of the actual application field of the electrolytic cell is promoted, and the prediction of the operation condition of the electrolytic cell is realized.
Further, each structure in the flow channel of the physical model established in S1 sequentially includes, from left to right, a cathode, a gas diffusion electrode, a catalyst layer, an electrolyte membrane, a catalyst layer, a gas diffusion layer, and an anode, where the upper end of the flow channel is a gas inlet and the lower end is a gas outlet;
the physical parameters provided by the physical model comprise the porosity of the catalytic layer, the porosity of the gas diffusion layer, the electrode permeability of the cathode and the anode, and the permeability of the gas diffusion layer; and when the calculation model in the step S4 calculates the steady-state parameter value, corresponding physical parameters are respectively used according to the positions of the different grid blocks.
Furthermore, the grid blocks are rectangular, and the density of the grid blocks is gradually reduced from the middle of the cathode and the anode to two sides respectively.
Further, the boundary conditions input in S3 include an operating voltage, a mass fraction of the anode reactant, an anode gas flow rate, a mass fraction of the cathode reactant, a cathode gas flow rate, an operating pressure, and an operating temperature.
Further, after the iterative calculation of S4 is finished, the obtained steady state parameter values include a current density value corresponding to the operating voltage, a pressure value corresponding to the operating pressure, a mole fraction value corresponding to the mass fraction of the anode reactant and the mass fraction of the cathode reactant, and a temperature value corresponding to the operating temperature.
Further, the calculation model established in S2 includes a mass and momentum transfer module, an electrochemical reaction module, and a heat transfer module, and the calculation order of the calculation model for each steady-state parameter in S4 is:
the method for establishing the two-dimensional steady-state model for the characteristic analysis of the proton exchange membrane electrolytic cell comprises the steps that a mass and momentum transfer module iterates pressure values of all grid blocks from grid block to grid block;
b, iterating the mole fraction values of all the grid blocks by the mass and momentum transfer module according to the pressure values in the grid blocks one by one to obtain the reactant concentration in each grid block;
c, iterating current density values in all cross sections by the electrochemical module according to reactant concentrations in all the grid blocks along the flow channel layer by layer;
and d, the heat transfer module acquires heat change in each grid layer according to the current density value, and iterates the temperature values of all grid blocks one by one.
Further, the reactant concentrations in the different grid blocks in S3 are obtained from the mole fraction values calculated by the calculation model, and the transfer process of the reactant gas from the previous grid block to the current grid block in the reaction process is expressed by the formula in the mass and momentum transfer module:
Figure GDA0003551330970000041
in the formula, NiRepresenting the flux of mass transport, R representing the universal gas constant, T representing the temperature value, P representing the pressure, B0Permeability of porous electrode, μ represents gas viscosity, yiIs the mole fraction of component i;
Figure GDA0003551330970000042
is the total effective diffusion coefficient of component i, obtained by the following formula:
Figure GDA0003551330970000043
wherein the content of the first and second substances,
Figure GDA0003551330970000044
is the knudsen diffusion coefficient of component i,
Figure GDA0003551330970000045
is the molecular diffusion coefficient of component i;
Figure GDA0003551330970000046
in the formula, ciIs the molar concentration of the component i, and is related to the molar fraction of the component i, and Ri is a mass source item of the component i.
Drawings
FIG. 1 is a first diagram of a physical model of a proton exchange membrane electrolytic cell;
FIG. 2 is a schematic diagram of a physical model structure of a proton exchange membrane electrolytic cell II;
FIG. 3 is a first diagram illustrating the partitioning of grid blocks in the physical model;
FIG. 4 is a diagram of the grid block division in the physical model;
FIG. 5 is a graph showing the pressure distribution on the cathode side of the electrolytic cell in the flow passage direction;
FIG. 6 is a graph showing the pressure distribution of the anode side of the electrolytic cell along the flow passage direction;
FIG. 7 is a graph of mole fraction of water along the flow path on the anode side of the cell;
FIG. 8 is a graph of mole fraction of water along the flow path on the cathode side of the cell;
FIG. 9 is a graph of current density values in the direction of flow channels within an electrolytic cell;
FIG. 10 is a distribution diagram of the temperature in the electrolytic cell in the direction of the flow channels.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not delimit the invention.
Firstly, establishing a physical model
Referring to fig. 1 and 2, the electrolytic cell is constructed by COMSOL software, the electrolytic cell flow channel is rectangular and sequentially comprises a cathode, a gas diffusion electrode, a catalytic layer, an electrolyte membrane, a catalytic layer, a gas diffusion layer and an anode from left to right, the upper end of the electrolytic cell flow channel is a gas inlet, and the lower end of the electrolytic cell flow channel is a gas outlet.
The length of the electrolytic cell is 20mm, the height of a gas flow channel is 1mm, the thickness of a gas diffusion layer is 0.38mm, the thickness of a catalytic layer is 0.05mm, the thickness of an electrolyte membrane is 0.1mm, the porosity of the catalytic layer is 0.3, the porosity of the gas diffusion layer is 0.4, and the permeability of an electrode is 2.36 multiplied by 10-12m2Gas diffusion layer permeability of 1.18X 10-11m2. The physical model provides physical parameters of each structure, including porosity of the catalytic layer, porosity of the gas diffusion layer, electrode permeability of the cathode and the anode, and permeability of the gas diffusion layer, for simulating electrochemical reactions.
Inputting boundary conditions into the physical model, wherein the boundary conditions comprise operation voltage, mass fraction of anode reactant, anode gas flow rate, mass fraction of cathode reactant, cathode gas flow rate, operation pressure and operation temperature. After the boundary condition is input, the electrochemical reaction can be initiated.
Secondly, establishing a calculation model
The embodiment discloses a calculation model of a proton exchange membrane electrolytic cell, which is based on a physical model of the first embodiment, a calculation model is built through COMSOL software, boundary conditions are input into the calculation model, relative tolerance is set, the calculation model performs iterative calculation of finite elements according to the input boundary conditions, iteration is stopped until a difference value between two adjacent calculation results is smaller than or equal to the relative tolerance, and finally a current density value corresponding to an operating voltage, a pressure value corresponding to an operating pressure, a gas velocity value corresponding to an anode gas flow velocity and a cathode gas flow velocity, a mole fraction value corresponding to a mass fraction of an anode reactant and a mass fraction of a cathode reactant, and a temperature value corresponding to an operating temperature are obtained.
The calculation model comprises a calculation unit and a judgment unit, wherein the calculation unit takes the input boundary condition as an initial value to start the iterative calculation of the finite element, each iteration obtains a result value corresponding to the initial value, and then the result value is taken as the initial value of the next iterative calculation.
The judging unit is used for storing the preset relative tolerance of interaction, acquiring the result value of each iteration, comparing the result value with the result value of the previous iteration, and outputting a stop instruction to the calculating module when the difference value between the result values of two adjacent iterations is less than or equal to the relative tolerance, so that the calculation is stopped, and the result value obtained by the last calculation is the steady-state parameter value of the electrolytic cell.
The computational model includes three computational modules: a mass and momentum transfer module, an electrochemical reaction module, and a heat transfer module.
The mass and momentum transfer module includes the following equations:
Figure GDA0003551330970000061
in the formula, NiRepresenting the flux of material transport, P representing the pressure value, B0Permeability, site dependent, of a physical parameter of the porous electrode, μ denotes gas viscosity, yiIs the mole fraction value of component i;
Figure GDA0003551330970000062
is the total effective diffusion coefficient of component i, obtained by the following formula:
Figure GDA0003551330970000063
Figure GDA0003551330970000064
is the knudsen diffusion coefficient of component i,
Figure GDA0003551330970000065
is the molecular diffusion coefficient of component i;
Figure GDA0003551330970000066
in the formula, ciIs the molar concentration of component i, i.e. the reactant concentration, is related to the mole fraction value of component i, and Ri is the mass source term of component i.
Figure GDA0003551330970000071
ε is the porosity at the calculated position, τ represents the bending coefficient, ρ is the gas density, u is the gas velocity, P represents the pressure value, μ is the gas viscosity, and T represents the matrix transpose.
The electrochemical reaction module includes the following formula:
V＝E+ηact，an+ηact，ca+ηohmic；……(5)
v represents the operating voltage of the alternating input, E represents the equilibrium voltage of the cell under the current operating conditions, etaact,anRepresents the activation overpotential, η, of the anodeact,caRepresents the activation overpotential, eta, of the cathodeohmicRepresents ohmic overpotential caused by proton and electron conduction;
Figure GDA0003551330970000072
Figure GDA0003551330970000073
is the equilibrium voltage in the standard regime, R is the universal gas constant, T represents the operating temperature of the cell, F is the Faraday constant,
Figure GDA0003551330970000074
and
Figure GDA0003551330970000075
each represents H at a different site2、H2O and O2The local partial pressure is related to the pressure value obtained by the mass and momentum transfer module;
the activation overpotential of the anode and the activation overpotential of the cathode are both obtained by the following formulas:
Figure GDA0003551330970000076
i denotes the operating current density, i0Expressing the exchange current density, α is the charge transport coefficient, n is the number of electrons transferred per mole of electrochemical reaction, γ is an exponential pre-factor, EactRepresents activation energy;
ohmic overpotential is obtained by ohm's law:
Figure GDA0003551330970000077
Figure GDA0003551330970000081
represents the proton conductivity,. phisRepresents a proton potential, ilThe value of the current density is used as the value,
Figure GDA0003551330970000082
represents the proton conductivity,. philRepresents the proton potential; wherein the content of the first and second substances,
Figure GDA0003551330970000083
as a function of temperature values in the iterative process,. phi.lVarying with the interactively set operating voltage.
The heat transfer module includes the following formula:
Figure GDA0003551330970000084
t represents a temperature value, ρ represents a density; cpIs the fluid heat capacity; u is the gas velocity value, λ, obtained by the mass and momentum transfer moduleeffIs the effective thermal conductivity; q is a heat source term representing the amount of heat consumed or generated by an electrochemical reaction or overvoltage loss.
λeff＝(1-ε)λs+ελl；……(10)
λeffIs the effective thermal conductivity, λsRepresents a solid-phase thermal conductivity; lambda [ alpha ]lAnd (3) representing the liquid phase thermal conductivity, wherein epsilon is a physical parameter porosity and is related to sites, and the effective thermal conductivity of different sites is used for obtaining temperature values of different sites.
The calculation principles of the current density value, the pressure value, the gas velocity value, the mole fraction value and the temperature value are as follows:
referring to fig. 3 and 4, the physical model is divided into a plurality of grid layers along the flow path direction thereof, each grid layer is divided into a plurality of grid blocks, the reactant concentrations in different grid blocks are different, and the reactant concentration in one grid block is regarded as uniform. The grid blocks are rectangular, and the density of the grid blocks is gradually reduced from the middle of the cathode and the anode to the two sides of the cathode and the anode respectively.
and a, calculating the pressure values and the gas velocity values of all grid blocks from the first grid block to grid block, wherein the pressure values and the gas velocity values in a single grid block are obtained by carrying out finite element iterative calculation through formulas (1) to (4). Because different grid blocks are positioned at different positions in the electrolytic cell, aiming at different positions, physical parameters at the positions are used, and after all the grid blocks are traversed one by one, the distribution of the pressure and the gas speed in the electrolytic cell along the flow passage direction is obtained.
b, the transfer process of the reactant gas from the previous grid block to the current grid block in the reaction process is expressed by formulas (1) to (3), so that the mole fraction values in all the grid blocks can be calculated one grid block by one grid block according to the pressure value in each grid block, and the reactant concentration in each grid block is obtained. Because different grid blocks are positioned at different positions in the electrolytic cell, the physical parameters at the positions are used for traversing all the grid blocks one by one according to different positions, and then the distribution of the reactant concentration in the electrolytic cell along the flow channel direction is obtained.
And c, iterating the current density values in all cross sections in the grid layer by grid layer mode along the flow channel direction according to the reactant concentrations in all the grid blocks, carrying out finite element iterative calculation on the current density values in a single grid layer through formulas (5) to (8) to obtain the current density value distribution in the electrolytic cell along the flow channel after traversing all the grid layers one by one.
And d, obtaining the heat change in each grid layer according to the current density value, namely obtaining a heat source item in the formula (9), and then iterating the temperature values of all grid blocks from grid block to grid block according to the heat source item. Because different grid blocks are positioned at different positions in the electrolytic cell, the physical parameters at the positions are used for different positions, and the distribution of the temperature in the electrolytic cell along the flow channel direction is obtained after all the grid blocks are traversed one by one.
Thirdly, the method is used for analyzing the characteristics of the electrolytic cell
The method comprises the following steps:
and S1, establishing a physical model disclosed in the specification, and providing physical parameters of each structure in the electrolytic cell, wherein the physical parameters comprise the porosity of the catalytic layer, the porosity of the gas diffusion layer, the electrode permeability of the cathode and the anode and the permeability of the gas diffusion layer.
S2, establishing the calculation model disclosed in the second step according to the physical model in the S1.
S3, inputting boundary conditions into the physical model of S1: the operating voltage was 1.4V, the mass fraction of the reactant at the anode inlet was 1, the gas flow rate at the anode inlet was 0.1m/s, the mass fraction of the reactant at the cathode inlet was 1, the gas flow rate at the cathode inlet was 0.4m/s, the operating pressure was 1atm, and the operating temperature was 403.15 k. To initiate the electrochemical reaction. Wherein the reactant is water and the relative tolerance is set to 0.001.
S4, calculating by using the boundary conditions input in S1 as initial values through the calculation model disclosed in the second embodiment, collecting and sorting data of each grid block, and respectively obtaining distribution diagrams of the pressure in the electrolytic cell along the flow direction as shown in FIGS. 5 and 6; the reactant mole fraction profile along the flow path for the anode side of the cell as shown in figure 7; a plot of the mole fraction of reactants at the cathode side of the cell along the direction of the flow channel as shown in FIG. 8; the distribution of the current density values in the direction of the flow channels within the electrolytic cell as shown in FIG. 9; the distribution of the temperature in the electrolytic cell in the direction of the flow channel is shown in FIG. 10.
By the method, the performance of the proton exchange membrane electrolytic cell in different working states and the distribution of each steady-state parameter in the flow channel direction are solved. Due to the consumption of reaction gas during the operation of the electrolytic cell, the concentration of the reaction gas is inevitably reduced along the flow channel direction, so that the reaction rate of the catalytic layer is changed, which is shown in that the current density of each node of the electrolytic cell along the flow channel direction is different. In engineering practice, the actual flow channel of the single electrolytic cell is a long flow channel, and the influence of the length of the flow channel and the structure of the flow channel on the cell is often significant. The method considers the actual reaction gas concentration distribution along the flow passage direction, improves the accuracy and application value of a two-dimensional steady-state model, is particularly beneficial to the development of a system-level electrolytic cell model and the research of an electrolytic cell dynamic model, promotes the development of the actual application field of the proton exchange membrane electrolytic cell, and realizes the prediction of the operation condition of the electrolytic cell.
The above description is only a few preferred embodiments of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. The method for establishing the two-dimensional steady-state model for the characteristic analysis of the proton exchange membrane electrolytic cell is characterized by comprising the following steps of:
s1, establishing a physical model of the proton exchange membrane electrolytic cell, and providing physical parameters of each structure of the electrolytic cell to simulate electrochemical reaction;
s2, establishing a calculation model for calculating relevant steady state parameters in the electrochemical reaction according to the physical model; the computational model comprises a mass and momentum transfer module, an electrochemical reaction module, and a heat transfer module;
s3, inputting boundary conditions into the physical model to start electrochemical reaction, wherein the physical model is divided into a plurality of grid layers along the flow channel direction, each grid layer is divided into a plurality of grid blocks, the reactant concentrations in different grid blocks are different, and the reactant concentration in one grid block is regarded as uniform;
and S4, the calculation model takes the boundary conditions as initial values, calculates in an iterative mode of finite elements, and obtains steady-state parameter values corresponding to the boundary conditions in all the grid blocks one by one according to the reactant concentrations in the different grid blocks. The calculation order of the calculation model in S4 for each steady-state parameter is:
a, iterating the pressure values of all grid blocks by the mass and momentum transfer module one grid block by one grid block;
b, iterating the mole fraction values of all the grid blocks by the mass and momentum transfer module according to the pressure values in the grid blocks one by one to obtain the reactant concentration in each grid block;
c, iterating current density values in all cross sections by the electrochemical module according to reactant concentrations in all the grid blocks along the flow channel layer by layer;
and d, the heat transfer module acquires the heat change in each grid layer according to the current density value, and iterates the temperature values of all grid blocks from grid block to grid block.
2. The method for establishing the two-dimensional steady-state model for the proton exchange membrane electrolytic cell characteristic analysis according to claim 1, wherein each structure in the flow channel of the physical model established in S1 sequentially comprises a cathode, a gas diffusion electrode, a catalyst layer, an electrolyte membrane, a catalyst layer, a gas diffusion layer and an anode from left to right, the upper end of the flow channel is a gas inlet, and the lower end of the flow channel is a gas outlet;
the physical parameters provided by the physical model comprise the porosity of the catalytic layer, the porosity of the gas diffusion layer, the electrode permeability of the cathode and the anode, and the permeability of the gas diffusion layer; and when the calculation model in the step S4 calculates the steady-state parameter value, corresponding physical parameters are respectively used according to the positions of the different grid blocks.
3. The method according to claim 2, wherein the grid blocks are rectangular, and the density of the grid blocks gradually decreases from the middle of the cathode and the anode to the two sides.
4. The method according to claim 1, wherein the boundary conditions inputted in S3 include operating voltage, mass fraction of anode reactant, anode gas flow rate, mass fraction of cathode reactant, cathode gas flow rate, operating pressure, and operating temperature.
5. The method according to claim 4, wherein the steady state parameter values obtained after the iterative calculation of S4 are determined to include a current density value corresponding to an operating voltage, a pressure value corresponding to an operating pressure, a mole fraction value corresponding to a mass fraction of the anode reactant and a mass fraction of the cathode reactant, and a temperature value corresponding to an operating temperature.
6. The method according to claim 5, wherein the reactant concentrations in different grid blocks in S3 are obtained from mole fraction values calculated by the calculation model, and the transfer process of reactant gas from a previous grid block to a current grid block in the reaction process is expressed by a formula in the mass and momentum transfer module:
Figure FDA0003551330960000021
in the formula, NiRepresenting the flux of mass transport, R representing the universal gas constant, T representing the temperature value, P representing the pressure, B0Permeability for porous electrodes, μ denotes gas viscosity, yiIs the mole fraction of component i;
Figure FDA0003551330960000031
is always of component iThe effective diffusion coefficient is obtained by the following formula:
Figure FDA0003551330960000032
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003551330960000033
is the knudsen diffusion coefficient of component i,
Figure FDA0003551330960000034
is the molecular diffusion coefficient of component i,. epsilon.is the porosity at the calculated position,. tau.represents the bending coefficient;
Figure FDA0003551330960000035
in the formula, ciIs the molar concentration of the component i, and is related to the molar fraction of the component i, and Ri is a mass source item of the component i.
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