CN111028894B - Method for determining optimal efficiency of electrolytic cell based on two-dimensional steady-state model - Google Patents

Method for determining optimal efficiency of electrolytic cell based on two-dimensional steady-state model Download PDF

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CN111028894B
CN111028894B CN201911152994.8A CN201911152994A CN111028894B CN 111028894 B CN111028894 B CN 111028894B CN 201911152994 A CN201911152994 A CN 201911152994A CN 111028894 B CN111028894 B CN 111028894B
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李曦
赵东琦
郑依
仲小博
蒋建华
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Huazhong University of Science and Technology
Ezhou Institute of Industrial Technology Huazhong University of Science and Technology
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Abstract

The invention provides a method for determining optimal efficiency of an electrolytic cell based on a two-dimensional steady-state model, and relates to the technical field of electrolytic cells. S1, establishing a two-dimensional steady-state model of an electrolytic cell; s2, inputting boundary conditions into the two-dimensional steady-state model, sequentially selecting one of the operating voltage, the mass fraction of anode reactant, the anode gas flow rate and the cathode gas flow rate in the boundary conditions as a variable, keeping other quantities in the boundary conditions unchanged, and taking operating points at equal intervals in a certain range for the boundary conditions serving as the variable; s3, traversing all operating points of the four variables, and calculating the efficiency of the electrolytic cell; s4, finding out the corresponding boundary condition when the efficiency is optimal in the result of S3. The invention simulates by the model, is convenient to operate, traverses a plurality of operating points of a plurality of variables, has wide coverage data range, can obtain more accurate results, and is beneficial to the application development of the high-temperature proton exchange membrane electrolytic cell in practical engineering.

Description

Method for determining optimal efficiency of electrolytic cell based on two-dimensional steady-state model
Technical Field
The invention relates to the technical field of electrolytic cells, in particular to a method for determining optimal efficiency of an electrolytic cell based on a two-dimensional steady-state model.
Background
Although renewable energy sources such as tidal energy, wind energy, and solar energy are promising energy sources, they are not very reliable due to intermittent and regional effects. In order to allow for widespread and reliable application of renewable energy technologies, clean and sustainable energy technologies are urgently needed to address serious environmental issues and to meet human needs.
Hydrogen is a promising energy carrier for renewable energy storage, and excessive renewable energy can be used for driving an electrolytic cell to produce hydrogen, and can be converted into electric energy by a fuel cell when the renewable energy is insufficient. In addition, hydrogen is an ideal fuel for fuel cell automobiles to achieve low emissions and intelligent transportation.
Proton Exchange Membrane (PEM) cells are one of the most widespread methods for producing hydrogen by electrolysis of water, a low temperature electrochemical cell. But since electrolyte membranes require high water content to maintain 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 high temperature Proton Exchange Membrane Electrolysis Cell (PEMEC) at temperatures below 100 ℃ is electricity and the contribution of thermal energy is very low. More importantly, electrode reaction dullness requires the use of expensive catalysts, such as Pt, which makes PEMEC very expensive. With the development of alternative electrolyte membranes, PEMEC can be operated at temperatures above 100 ℃, a high temperature condition that is highly desirable for hydrogen production.
However, the high temperature condition requires a relatively high cost in the actual engineering, and in order to save the cost in the actual engineering, and other problems, the working condition of the optimal efficiency of the electrolytic cell needs to be found relatively accurately so as to promote the application development of the electrolytic cell.
Disclosure of Invention
The invention aims to provide a method for determining the optimal efficiency of an electrolytic cell based on a two-dimensional steady-state model, so as to solve the problems of low efficiency and high cost of a high-temperature proton exchange membrane electrolytic cell in actual engineering.
The method comprises the following steps:
s1, establishing a two-dimensional steady-state model of a high-temperature proton exchange membrane electrolytic cell;
s2, interactively inputting boundary conditions into the two-dimensional steady-state model, sequentially selecting one of the operating voltage, the mass fraction of anode reactant, the anode gas flow rate and the cathode gas flow rate in the boundary conditions as a variable, keeping other quantities in the boundary conditions unchanged, and taking operating points at equal intervals for the boundary conditions serving as the variable;
s3, solving all discrete operation points to obtain temperature values and gas speed values at different operation points in a two-dimensional steady-state model so as to calculate the efficiency of the electrolytic cell;
s4, finding all boundary conditions corresponding to the optimal cell efficiency in the result of S3.
In the technical scheme, the efficiency and the conversion rate under a plurality of operating points can be obtained by adjusting the boundary conditions input into the two-dimensional steady-state model, so that all the boundary conditions corresponding to the optimal cell efficiency can be determined. The method simulates through the model, is convenient to operate, traverses a plurality of operating points of a plurality of variables, has wide coverage data range, can obtain a more accurate result, and is beneficial to the application development of the high-temperature proton exchange membrane electrolytic cell in actual engineering.
Further, the two-dimensional steady-state model comprises a judging unit and a calculating unit;
a calculation unit: the boundary conditions of the parameters used for receiving interactive input are used as initial values in iterative computation to start iterative computation of finite elements, each iteration obtains result values corresponding to the initial values respectively, and the result values are used as initial values of the next iteration continuously;
a judging unit: and the calculation unit is used for storing the relative tolerance of the interactive input, receiving the result value of each iteration, comparing the result value with the result value of the previous iteration, and forming a stop instruction when the difference value of the result values of two adjacent iterations of all the parameters is smaller than or equal to the relative tolerance, so that the calculation unit stops calculating, and after the iteration is stopped, the result value calculated last time is the steady-state parameter value of each parameter in the electrolytic cell.
Further, the boundary conditions of the interactive input in S2 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, which are used for simulating the electrochemical reaction.
Further, in S2:
when the operation voltage is used as a variable, the interval between two adjacent operation points is 0.1;
when the mass fraction of the anode reactant is taken as a variable, the interval between two adjacent operation points is 0.1;
when the anode inlet gas flow rate is used as a variable, the interval between two adjacent operation points is 0.01;
when the cathode inlet gas flow rate is used as a variable, the interval between two adjacent operation points is 0.01.
Further, the mass and momentum transfer module obtains pressure values and mole fraction values of each position through the following formula:
Figure BDA0002284065860000031
in the formula, N i Representing the flux of the material transport, P representing the pressure value to be iterated, B 0 The permeability of the physical parameter of the porous electrode, which is related to the site, mu represents the gas viscosity, y i Is the mole fraction value of the component i to be iterated out;
Figure BDA0002284065860000032
is the total effective diffusion coefficient of component i, obtained by the following formula:
Figure BDA0002284065860000033
Figure BDA0002284065860000034
the knudsen diffusion coefficient for component i,/>
Figure BDA0002284065860000035
The molecular diffusivity for component i;
Figure BDA0002284065860000036
in the formula, c i Is the molar concentration of component i, i.e. the reactant concentration, and is related to the molar fraction value of component i, ri being the mass source term for component i.
The mass and momentum transfer module further comprises the following formula for restraining the calculation of the pressure value and obtaining the gas velocity values at different points:
Figure BDA0002284065860000037
epsilon is the porosity at the calculated position, tau represents the bending coefficient, rho is the gas density, u is the gas velocity to be iterated out, P represents the pressure value to be iterated out, mu is the gas viscosity, and T represents the matrix transpose.
Further, the electrochemical reaction module calculates the current density value by the following formula:
V＝E+η act,an +η act,ca +η ohmic ；
v represents the operation voltage of the interactive input, E represents the balance voltage of the electrolytic cell under the current running condition, eta act,an Represents the activation overpotential, eta of the anode act,ca Represents the activation overpotential, eta of the cathode ohmic Representing the ohmic overpotential caused by proton and electron conduction;
Figure BDA0002284065860000041
Figure BDA0002284065860000042
is the balance in the standard stateVoltage, R is the universal gas constant, T is the operating temperature of the cell, F is the Faraday constant,/and>
Figure BDA0002284065860000043
and->
Figure BDA0002284065860000044
Respectively represent H at different sites 2 、H 2 O and O 2 Is related to the mass and momentum transfer module obtaining a pressure value;
the activation overpotential of the anode and the activation overpotential of the cathode are both obtained by the following formulas:
Figure BDA0002284065860000045
i represents the operating current density, i 0 Represents the exchange current density, alpha is the charge transport coefficient, n is the number of electrons transferred per mole of electrochemical reaction, gamma is the factor before the index, E act Represents activation energy;
the ohmic overpotential is obtained by ohm's law:
Figure BDA0002284065860000046
Figure BDA0002284065860000047
represents proton conductivity, phi s Represents proton potential, i l For the current density value to be iterated, +.>
Figure BDA0002284065860000048
Represents proton conductivity, phi l Represents proton potential; wherein (1)>
Figure BDA0002284065860000049
Phi varies with the temperature value in the iterative process l And changing with the interactively set operating voltage.
Further, the heat transfer module calculates the temperature value by the following formula:
Figure BDA00022840658600000410
t represents a temperature value to be iterated out, and ρ represents density; c (C) p Is the heat capacity of the fluid; u is the gas velocity value obtained by the mass and momentum transfer module, lambda eff Is an effective thermal conductivity coefficient; q is a heat source term, representing the amount of heat consumed or generated by an electrochemical reaction or overvoltage loss.
λ eff ＝(1-ε)λ s +ελ l ；
λ eff Is effective heat conductivity coefficient lambda s Representing the solid phase thermal conductivity; lambda (lambda) l Representing the thermal conductivity of the liquid phase, epsilon is the porosity of the physical parameter, and is related to the sites, the effective thermal conductivity of the different sites, and the temperature values at the different sites are obtained.
Further, the calculation formula of the cell efficiency in S3 is as follows:
Figure BDA0002284065860000051
in the formula, L represents electrolysis Chi Kuandu; t (T) 0 Represents the ambient temperature, T i,ach Representing the gas temperature value at the anode inlet, T i,fch Representing the gas temperature value at the cathode inlet, C p,g,ach Represents the specific heat capacity of the gas at the anode inlet, C p,g,fch Representing the specific heat capacity of the gas at the cathode inlet,
Figure BDA0002284065860000052
a gas flow rate value indicating that the component at the outlet is hydrogen,/->
Figure BDA0002284065860000053
A gas flow rate value indicating that the component at the inlet is hydrogen,/->
Figure BDA0002284065860000054
Indicating the low heating value of the hydrogen.
Further, the mole fraction value in S3 is also obtained for calculating the conversion:
Figure BDA0002284065860000055
Figure BDA0002284065860000056
represents the molar fraction of the component at the anode inlet as water,/->
Figure BDA0002284065860000057
Indicating the fraction of water mole at the anode outlet.
Drawings
FIG. 1 is a schematic diagram of a physical model structure 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 schematic diagram of the division of grid blocks in a physical model;
FIG. 4 is a second schematic diagram of the partitioning of grid blocks in a physical model;
FIG. 5 is a plot of operating voltage as a variable versus efficiency, conversion;
FIG. 6 is a plot of anode reactant as a variable versus efficiency, conversion;
FIG. 7 is a plot of anode gas flow rate as a variable versus efficiency and conversion;
FIG. 8 is a plot of cathode gas flow rate as a variable versus efficiency and conversion;
fig. 9 is a schematic diagram of a discrete process.
Detailed Description
In order to make the technical problems, technical schemes and beneficial effects to be solved more clearly apparent, the 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 for purposes of illustration only and are not intended to limit the scope of the invention.
1. Establishing a physical model
Referring to fig. 1 and 2, by constructing the COMSOL software, the flow channel of the electrolytic cell 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, wherein the upper end of the flow channel of the electrolytic cell is a gas inlet, and the lower end of the flow channel of the electrolytic cell is a gas outlet.
The length of the electrolytic cell is 20mm, the height of the gas flow channel is 1mm, the thickness of the gas diffusion layer is 0.38mm, the thickness of the catalyst layer is 0.05mm, the thickness of the electrolyte membrane is 0.1mm, the porosity of the catalyst layer is 0.3, the porosity of the gas diffusion layer is 0.4, and the permeability of the electrode is 2.36 multiplied by 10 -12 m 2 The permeability of the gas diffusion layer was 1.18X10 -11 m 2 . 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 anode, permeability of the gas diffusion layer, for simulating electrochemical reactions.
Boundary conditions are input into the physical model, wherein the boundary conditions comprise an operating voltage, a mass fraction of an anode reactant, an anode gas flow rate, a mass fraction of a cathode reactant, a cathode gas flow rate, an operating pressure and an operating temperature. After inputting the boundary conditions, the electrochemical reaction may be initiated.
2. 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, wherein a calculation model is built through COMSOL software, boundary conditions are input into the calculation model, relative tolerance is set, the calculation model carries out iterative calculation of finite elements according to the input boundary conditions, iteration is stopped until the difference between the results of two adjacent calculation 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 rate and a cathode gas flow rate, a mole fraction value corresponding to a mass fraction of an anode reactant and a substance fraction of a cathode reactant and a temperature value corresponding to an operating temperature are obtained.
The parameter values obtained through the calculation model are steady-state parameter values of the electrolytic cell, the calculation model comprises a calculation unit and a judgment unit, the calculation unit takes an input boundary condition as an initial value to start iterative calculation of a 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 relative tolerance set in advance, 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 smaller 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 calculation model includes three calculation modules: mass and momentum transfer modules, electrochemical reaction modules, and heat transfer modules.
The mass and momentum transfer module includes the following formula:
Figure BDA0002284065860000071
in the formula, N i Representing the flux of the material transport, P representing the pressure value, B 0 The permeability of the physical parameter of the porous electrode, which is related to the site, mu represents the gas viscosity, y i Is the mole fraction value of component i;
Figure BDA0002284065860000072
is the total effective diffusion coefficient of component i, obtained by the following formula:
Figure BDA0002284065860000073
Figure BDA0002284065860000074
the knudsen diffusion coefficient for component i,/>
Figure BDA0002284065860000075
The molecular diffusivity for component i;
Figure BDA0002284065860000076
in the formula, c i Is the molar concentration of component i, i.e. the reactant concentration, and is related to the molar fraction value of component i, ri being the mass source term for component i.
Figure BDA0002284065860000081
Epsilon is the porosity at the calculated location, 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 comprises the following formula:
V＝E+η act,an +η act,ca +η ohmic ；……(5)
v represents the operation voltage of the interactive input, E represents the balance voltage of the electrolytic cell under the current running condition, eta act,an Represents the activation overpotential, eta of the anode act,ca Represents the activation overpotential, eta of the cathode ohmic Representing the ohmic overpotential caused by proton and electron conduction;
Figure BDA0002284065860000082
Figure BDA0002284065860000083
is the equilibrium voltage in the standard state, R is the universal gas constant, T is the operating temperature of the cell, F is the Faraday constant,/is>
Figure BDA0002284065860000084
And->
Figure BDA0002284065860000085
Respectively represent H at different sites 2 、H 2 O and O 2 Is related to the mass and momentum transfer module obtaining a pressure value;
the activation overpotential of the anode and the activation overpotential of the cathode are both obtained by the following formulas:
Figure BDA0002284065860000086
i represents the operating current density, i 0 Represents the exchange current density, alpha is the charge transport coefficient, n is the number of electrons transferred per mole of electrochemical reaction, gamma is the factor before the index, E act Represents activation energy;
the ohmic overpotential is obtained by ohm's law:
Figure BDA0002284065860000087
Figure BDA0002284065860000088
represents proton conductivity, phi s Represents proton potential, i l Is a current density value>
Figure BDA0002284065860000089
Represents proton conductivity, phi l Represents proton potential; wherein (1)>
Figure BDA00022840658600000810
Phi varies with the temperature value in the iterative process l And changing with the interactively set operating voltage.
The heat transfer module includes the following formula:
Figure BDA0002284065860000091
t represents a temperature value, and ρ represents a density; c (C) p Is the heat capacity of the fluid; u is the gas velocity value obtained by the mass and momentum transfer module, lambda eff Is an effective thermal conductivity coefficient; q is a heat source term, representing the amount of heat consumed or generated by an electrochemical reaction or overvoltage loss.
λ eff ＝(1-ε)λ s +ελ l ；……(10)
λ eff Is effective heat conductivity coefficient lambda s Representing the solid phase thermal conductivity; lambda (lambda) l Representing the thermal conductivity of the liquid phase, epsilon is the porosity of the physical parameter, and is related to the sites, the effective thermal conductivity of the different sites, and the temperature values at the different sites are obtained.
The following are the calculation principles of current density value, pressure value, gas velocity value, mole fraction value and temperature value:
referring to fig. 3 and 4, the physical model is divided into a plurality of mesh layers along the flow path direction thereof, each mesh layer is divided into a plurality of mesh blocks, the reactant concentrations in the different mesh blocks are different, and the reactant concentration in one mesh 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 to the two sides of the anode respectively.
a, firstly calculating the pressure values and the gas velocity values of all grid blocks from the first grid block, and carrying out finite element iterative calculation on the pressure values and the gas velocity values in a single grid block through formulas (1) to (4). Because different grid blocks are positioned at different positions in the electrolytic cell, physical parameters at the positions are used for different positions, 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 direction of the flow channel is obtained.
b, the transfer process of 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 value in all grid blocks can be calculated on a grid block-by-grid block basis 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, physical parameters at the positions are used for different positions, and after all the grid blocks are traversed one by one, 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 the sections layer by layer along the flow channel direction according to the concentration of the reactants in each grid block, performing finite element iterative calculation on the current density values in a single grid layer through formulas (5) to (8), and obtaining the distribution of the current density values in the electrolytic cell along the flow channel after traversing all the grid layers one by one.
And d, obtaining heat change in each grid layer according to the current density value, namely obtaining a heat source item in the formula (9), and iterating out the temperature values of all grid blocks grid block by grid block according to the heat source item. Because different grid blocks are positioned at different positions in the electrolytic cell, physical parameters at the positions are used for different positions, and after all the grid blocks are traversed one by one, the distribution of the temperature in the electrolytic cell along the direction of the flow channel is obtained.
3. Determining optimal efficiency
The method comprises the following steps:
s1, establishing a two-dimensional steady-state model of the high-temperature proton exchange membrane electrolytic cell, wherein the two-dimensional steady-state model comprises a physical model disclosed in the first step and a calculation model disclosed in the second step.
S2, interactively inputting boundary conditions into the two-dimensional steady-state model: the operating voltage, mass fraction of reactant at anode inlet 1, gas flow rate at anode inlet 0.1m/s, mass fraction of reactant at cathode inlet 1, gas flow rate at cathode inlet 0.4m/s, operating pressure 1atm, operating temperature 403.15k. To initiate the electrochemical reaction. Wherein the reactant is water, and the relative tolerance is set to be 0.001.
One of the operating voltage, the mass fraction of the anode reactant, the anode gas flow rate and the cathode gas flow rate in the boundary condition is sequentially selected as a variable, and the other amounts in the boundary condition are kept unchanged, and operating points are taken at equal intervals within a certain range for the boundary condition as a variable.
Operating voltage (V) cell ) When used as a variable, adjacentThe interval between the two operation points is 0.1V;
mass fraction of anode reactant
Figure BDA0002284065860000111
When the variable is used, the interval between two adjacent operation points is 0.1;
gas flow Rate at the anode inlet (V Anode ) When the variable is used, the interval between two adjacent operation points is 0.01m/s;
gas flow Rate at cathode inlet (V Cathode ) As a variable, the interval between two adjacent operating points is 0.01m/s.
S3, as shown in FIG. 5, solving all discrete operation points of four variables of the operation voltage, the mass fraction of the anode reactant, the anode gas flow rate and the cathode gas flow rate to obtain temperature values, gas speed values and mole fraction values at different operation points in a two-dimensional steady-state model so as to calculate the efficiency eta and the conversion rate gamma of the electrolytic cell syn 。
The efficiency calculation formula is:
Figure BDA0002284065860000112
in the formula, L represents electrolysis Chi Kuandu; t (T) 0 Represents the ambient temperature, T i,ach Representing the gas temperature value at the anode inlet, T i,fch Representing the gas temperature value at the cathode inlet, C p,g,ach Represents the specific heat capacity of the gas at the anode inlet, C p,g,fch Representing the specific heat capacity of the gas at the cathode inlet,
Figure BDA0002284065860000113
a gas flow rate value indicating that the component at the outlet is hydrogen,/->
Figure BDA0002284065860000114
A gas flow rate value indicating that the component at the inlet is hydrogen,/->
Figure BDA0002284065860000115
Indicating the low heating value of the hydrogen.
Conversion rateThe calculation formula is as follows:
Figure BDA0002284065860000116
Figure BDA0002284065860000117
represents the molar fraction of the component at the anode inlet as water,/->
Figure BDA0002284065860000118
Indicating the fraction of water mole at the anode outlet.
When the operating voltage was varied in the range of 1.4V to 2V, the efficiency, conversion at all operating points obtained is shown in fig. 6.
When the mass fraction of the anode reactant (i.e., water) was varied in the range of 0.3 to 1.0, the efficiency, conversion at all operating points were obtained as shown in fig. 7.
The efficiency, conversion at all operating points obtained when the gas flow rate at the anode inlet (i.e. water) was varied in the range of 0.05m/s to 0.15m/s is shown in figure 8.
The efficiency, conversion at all operating points obtained when the gas flow rate at the cathode inlet (i.e. water) was varied in the range of 0.05m/s to 0.15m/s is shown in figure 9.
S4, finding all boundary conditions corresponding to the optimal cell efficiency in the result of S3:
the operating voltage is 1.76V, the anode water mass fraction is 0.44, the anode gas flow rate is 0.03m/s, and the cathode gas flow rate is 0.11m/s; the maximum efficiency can be up to 54.5%.
The above is only a few preferred embodiments of the present invention and is not intended to limit the present invention, and various modifications and variations will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. The method for determining the optimal efficiency of the electrolytic cell based on the two-dimensional steady-state model is characterized by comprising the following steps of:
s1, establishing a two-dimensional steady-state model of a high-temperature proton exchange membrane electrolytic cell;
s2, interactively inputting boundary conditions into the two-dimensional steady-state model, sequentially selecting one of the operating voltage, the mass fraction of anode reactant, the anode gas flow rate and the cathode gas flow rate in the boundary conditions as a variable, keeping other quantities in the boundary conditions unchanged, and taking operating points at equal intervals for the boundary conditions serving as the variable;
s3, solving all discrete operation points to obtain temperature values and gas speed values at different operation points in a two-dimensional steady-state model so as to calculate the efficiency of the electrolytic cell;
s4, finding all boundary conditions corresponding to the optimal cell efficiency in the result of S3;
the two-dimensional steady-state model comprises a physical model and a calculation model, and the calculation model comprises a judging unit and a calculation unit;
a calculation unit: the boundary conditions of the parameters used for receiving interactive input are used as initial values in iterative computation to start iterative computation of finite elements, each iteration obtains result values corresponding to the initial values respectively, and the result values are used as initial values of the next iteration continuously;
a judging unit: the method comprises the steps of storing relative tolerance of interactive input, receiving a result value of each iteration, comparing the result value with a result value of the previous iteration, and forming a stop instruction when the difference value of the result values of two adjacent iterations of all parameters is smaller than or equal to the relative tolerance, so that the calculation unit stops calculating, and after the iteration is stopped, the result value calculated last time is a steady-state parameter value of each parameter in the electrolytic cell;
the computing model includes three computing modules: the mass and momentum transfer module obtains pressure values and mole fraction values of all positions through the following formulas:
Figure FDA0004184233730000021
in the formula, N i Representing the flux of material transport, R representing the general gas constant, T representing the temperature value, P representing the pressure value to be iterated, B 0 The permeability of the physical parameter of the porous electrode, which is related to the site, mu represents the gas viscosity, y i Is the mole fraction value of the component i to be iterated out;
Figure FDA0004184233730000022
is the total effective diffusion coefficient of component i, obtained by the following formula:
Figure FDA0004184233730000023
Figure FDA0004184233730000024
the knudsen diffusion coefficient for component i,/>
Figure FDA0004184233730000025
The molecular diffusivity for component i;
Figure FDA0004184233730000026
in the formula, c i Is the molar concentration of component i, i.e. the reactant concentration, which is related to the molar fraction value of component i, ri being the mass source term of component i;
the mass and momentum transfer module further comprises the following formula for restraining the calculation of the pressure value and obtaining the gas velocity values at different points:
Figure FDA0004184233730000027
epsilon is the porosity at the calculated position, tau represents the bending coefficient, rho is the gas density, u is the gas speed to be iterated out, P represents the pressure value to be iterated out, mu is the gas viscosity, and the upper corner mark T represents the matrix transposition.
2. The method according to claim 1, wherein the boundary conditions input in S2 include operating voltage, mass fraction of anode reactant, anode gas flow rate, mass fraction of cathode reactant, cathode gas flow rate, operating pressure, operating temperature, and the like, for simulating electrochemical reaction.
3. The method for determining optimal efficiency of an electrolytic cell based on a two-dimensional steady-state model according to claim 2, wherein in S2:
when the operation voltage is used as a variable, the interval between two adjacent operation points is 0.1;
when the mass fraction of the anode reactant is taken as a variable, the interval between two adjacent operation points is 0.1;
when the anode inlet gas flow rate is used as a variable, the interval between two adjacent operation points is 0.01;
when the cathode inlet gas flow rate is used as a variable, the interval between two adjacent operation points is 0.01.
4. A method of determining the optimal efficiency of an electrolytic cell based on a two-dimensional steady-state model according to claim 3, wherein the electrochemical reaction module calculates the current density value by the formula:
V＝E+η act,an +η act,ca +η ohmic ；
v represents the operation voltage of the interactive input, E represents the balance voltage of the electrolytic cell under the current running condition, eta act,an Represents the activation overpotential, eta of the anode act,ca Represents the activation overpotential, eta of the cathode ohmic Representing the ohmic overpotential caused by proton and electron conduction;
Figure FDA0004184233730000031
Figure FDA0004184233730000032
is the equilibrium voltage in the standard state, F is Faraday constant,/>
Figure FDA0004184233730000033
And->
Figure FDA0004184233730000034
Respectively represent H at different sites 2 、H 2 O and O 2 Is related to the mass and momentum transfer module obtaining a pressure value;
the activation overpotential of the anode and the activation overpotential of the cathode are both obtained by the following formulas:
Figure FDA0004184233730000035
i represents the operating current density, i 0 Represents the exchange current density, alpha is the charge transport coefficient, n is the number of electrons transferred per mole of electrochemical reaction, gamma is the factor before the index, E act Represents activation energy;
the ohmic overpotential is obtained by ohm's law:
η ohmic ＝i l R l +i s R s ，
Figure FDA0004184233730000041
Figure FDA0004184233730000042
represents electron conductivity, phi s Representing electron potential, i l For the current density value to be iterated, +.>
Figure FDA0004184233730000043
Represents proton conductivity, phi l Represents proton potential; wherein (1)>
Figure FDA0004184233730000044
Phi varies with the temperature value in the iterative process l And changing with the interactively set operating voltage.
5. The method of determining optimal efficiency of an electrolytic cell based on a two-dimensional steady-state model of claim 4, wherein the heat transfer module calculates the temperature value by the formula:
Figure FDA0004184233730000045
t represents a temperature value to be iterated out, and ρ represents density; c (C) p Is the heat capacity of the fluid; u is the gas velocity value obtained by the mass and momentum transfer module, lambda eff Is an effective thermal conductivity coefficient; q is a heat source term representing heat consumed or generated by an electrochemical reaction or overvoltage loss;
λ eff ＝(1-ε)λ s +ελ l ；
λ eff is effective heat conductivity coefficient lambda s Representing the solid phase thermal conductivity; lambda (lambda) l Representing the thermal conductivity of the liquid phase, epsilon is the porosity of the physical parameter, and is related to the sites, the effective thermal conductivity of the different sites, and the temperature values at the different sites are obtained.
6. The method for determining the optimal efficiency of an electrolytic cell based on a two-dimensional steady-state model as set forth in claim 5, wherein the calculation formula of the electrolytic cell efficiency in S3 is:
Figure FDA0004184233730000046
in the formula, L represents electrolysis Chi Kuandu; t (T) 0 Represents the ambient temperature, T i,ach Representing the gas temperature value at the anode inlet, T i,fch Representing the gas temperature value at the cathode inlet, C p,g,ach Represents the specific heat capacity of the gas at the anode inlet, C p,g,fch Representing the specific heat capacity of the gas at the cathode inlet,
Figure FDA0004184233730000051
a gas flow rate value indicating that the component at the outlet is hydrogen,/->
Figure FDA0004184233730000052
A gas flow rate value indicating that the component at the inlet is hydrogen,/->
Figure FDA0004184233730000053
Indicating the low heating value of the hydrogen.
7. A method of determining the optimal efficiency of an electrolytic cell based on a two-dimensional steady-state model according to claim 3, wherein in S3 a mole fraction value is also obtained for calculating the conversion:
Figure FDA0004184233730000054
Figure FDA0004184233730000055
represents the molar fraction of the component at the anode inlet as water,/->
Figure FDA0004184233730000056
Indicating the fraction of water mole at the anode outlet.
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