CN111028894A - Electrolytic cell optimal efficiency determination method based on two-dimensional steady-state model - Google Patents

Electrolytic cell optimal efficiency determination method based on two-dimensional steady-state model Download PDF

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CN111028894A
CN111028894A CN201911152994.8A CN201911152994A CN111028894A CN 111028894 A CN111028894 A CN 111028894A CN 201911152994 A CN201911152994 A CN 201911152994A CN 111028894 A CN111028894 A CN 111028894A
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electrolytic cell
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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 the 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 the electrolytic cell; s2, inputting a boundary condition into the two-dimensional steady-state model, sequentially selecting one of an operating voltage, the mass fraction of an anode reactant, the flow rate of anode gas and the flow rate of cathode gas in the boundary condition as a variable, keeping the other quantities in the boundary condition unchanged, and taking operating points of the boundary condition as the variable at equal intervals in a certain range; s3, traversing all the operating points of the four variables, and calculating the efficiency of the electrolytic cell; s4, finding the boundary condition corresponding to the optimal efficiency among the results of S3. The method is simulated through the model, is convenient and fast to operate, traverses a plurality of operation points of a plurality of variables, has a wide coverage data range, can obtain more accurate results, and is favorable for application development of the high-temperature proton exchange membrane electrolytic cell in practical engineering.

Description

Electrolytic cell optimal efficiency determination method 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 the 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 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 intelligent transportation.
Proton Exchange Membrane (PEM) electrolyzers are a low temperature electrochemical electrolyzer, 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 a high temperature Proton Exchange Membrane Electrolytic Cell (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.
However, the high temperature condition requires a large cost in the actual process, and in order to save the cost in the actual process, it is necessary to accurately find the working condition with the optimal efficiency of the electrolytic cell 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 practical engineering.
The method comprises the following steps:
s1, establishing a two-dimensional steady-state model of the high-temperature proton exchange membrane electrolytic cell;
s2, interactively inputting boundary conditions into the two-dimensional steady-state model, sequentially selecting one of operating voltage, mass fraction of anode reactants, anode gas flow rate and 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 on the boundary conditions as the variables;
s3, solving all discrete operating points to obtain temperature values and gas velocity values at different operating points in the two-dimensional steady-state model so as to calculate the efficiency of the electrolytic cell;
s4, finding out all boundary conditions corresponding to the optimal efficiency of the electrolytic cell in the result of S3.
In the technical scheme, the efficiencies and the conversion rates 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 electrolytic cell efficiency can be determined. The method is simulated through the model, is convenient to operate, traverses a plurality of operation points of a plurality of variables, has a wide coverage data range, can obtain more accurate results, and is favorable for application development of the high-temperature proton exchange membrane electrolytic cell in practical engineering.
Further, the two-dimensional steady-state model comprises a judging unit and a calculating unit;
a calculation unit: the boundary conditions used for receiving each parameter of interactive input are used as initial values in iterative calculation to start the iterative calculation of finite elements, each iteration obtains result values respectively corresponding to each initial value, and the result values are continuously used as the initial values of the next iteration;
a judging unit: the device is used for storing the relative tolerance of the interactive input, receiving the result value of each iteration and comparing the result value with the result value of the previous iteration, when the difference value of the result values of the two adjacent iterations of all the parameters is less than or equal to the relative tolerance, a stop instruction is formed to stop the calculation of the calculation unit, and after the iteration is stopped, the result value calculated at the last time is the steady-state parameter value of each parameter in the electrolytic cell.
Further, the boundary conditions interactively inputted 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 operating voltage is used as a variable, the interval between two adjacent operating points is 0.1;
when the mass fraction of the anode reactant is taken as a variable, the interval between two adjacent operating points is 0.1;
when the gas flow rate at the anode inlet is taken as a variable, the interval between two adjacent operating points is 0.01;
when the cathode inlet gas flow rate is used as a variable, the interval between two adjacent operating points is 0.01.
Further, the mass and momentum transfer module obtains the pressure value and the mole fraction value of each position through the following formulas:
Figure BDA0002284065860000031
in the formula, NiRepresenting the flux of material transport, P representing the pressure value to be iterated, B0Permeability, which is a physical parameter of the porous electrode, is site dependent, mu denotes the gas viscosity, yiIs the mole fraction value of component i to be iterated;
Figure BDA0002284065860000032
is the total effective diffusion coefficient of component i, obtained by the following formula:
Figure BDA0002284065860000033
Figure BDA0002284065860000034
is the knudsen diffusion coefficient of component i,
Figure BDA0002284065860000035
is the molecular diffusion coefficient of component i;
Figure BDA0002284065860000036
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.
The mass and momentum transfer module further comprises the following formula for constraining the calculation of the pressure values and obtaining the gas velocity values at different positions:
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, P represents the pressure value to be iterated, mu is the gas viscosity, and T represents the matrix transposition.
Further, the electrochemical reaction module calculates a current density value by the following formula:
V＝E+ηact,an+ηact,ca+ηohmic；
v denotes the operating voltage of the alternating inputs, E denotes the equilibrium voltage of the cell under the current operating conditions, ηact,anIndicates the activation overpotential of the anode, ηact,caIndicates the activation overpotential of the cathode, ηohmicRepresents ohmic overpotential caused by proton and electron conduction;
Figure BDA0002284065860000041
Figure BDA0002284065860000042
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 BDA0002284065860000043
and
Figure BDA0002284065860000044
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 BDA0002284065860000045
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 overpotentials are obtained by ohm's law:
Figure BDA0002284065860000046
Figure BDA0002284065860000047
represents the proton conductivity,. phisRepresents the proton potential, ilIs the current density value to be iterated,
Figure BDA0002284065860000048
represents the proton conductivity,. philRepresents the proton potential; wherein the content of the first and second substances,
Figure BDA0002284065860000049
in an iterative processChange in temperature value,. philVarying with the interactively set operating voltage.
Further, the heat transfer module calculates a temperature value by the following equation:
Figure BDA00022840658600000410
t represents a temperature value to be iterated, and rho represents 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；
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.
Further, the calculation formula of the electrolytic cell efficiency in S3 is:
Figure BDA0002284065860000051
in the formula, L represents the width of the electrolytic cell; t is0Indicating the ambient temperature, Ti,achRepresents the gas temperature value at the anode inlet, Ti,fchRepresents the gas temperature value at the cathode inlet, Cp,g,achDenotes the specific heat capacity of the gas at the anode inlet, Cp,g,fchIndicating the specific heat capacity of the gas at the cathode inlet,
Figure BDA0002284065860000052
indicating a value of the gas flow rate of which the component at the outlet is hydrogen,
Figure BDA0002284065860000053
representing a value of the gas flow rate at which the component at the inlet is hydrogen,
Figure BDA0002284065860000054
indicating a low heating value of hydrogen.
Further, a mole fraction value was also obtained in said S3, which was used to calculate the conversion:
Figure BDA0002284065860000055
Figure BDA0002284065860000056
representing the mole fraction value of the component at the anode inlet as water,
Figure BDA0002284065860000057
representing the mole fraction value of the component in water at the anode outlet.
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 division of grid blocks in the physical model;
FIG. 4 is a diagram illustrating the division of grid blocks in the physical model;
FIG. 5 is a line graph showing the relationship between efficiency and conversion when the operating voltage is used as a variable;
FIG. 6 is a line graph showing the relationship between efficiency and conversion when the anode reactant is used as a variable;
FIG. 7 is a line graph showing the relationship between efficiency and conversion when the anode gas flow rate is used as a variable;
FIG. 8 is a line graph showing the relationship between efficiency and conversion when the cathode gas flow rate is used as a variable;
fig. 9 is a schematic diagram of a discrete process.
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 are not intended to limit 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 the gas flow channel is 1mm, the thickness of the gas diffusion layer is 0.38mm, the thickness of the catalytic layer is 0.05mm, the thickness of the 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 the 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 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, 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, the 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 results of two adjacent calculations 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 the 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 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 judgment 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 calculation 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 equation:
Figure BDA0002284065860000071
in the formula, NiRepresenting the flux of material transport, P representing the pressure value, B0Permeability, which is a physical parameter of the porous electrode, is site dependent, mu denotes the gas viscosity, yiIs 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
is the knudsen diffusion coefficient of component i,
Figure BDA0002284065860000075
is the molecular diffusion coefficient of component i;
Figure BDA0002284065860000076
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 BDA0002284065860000081
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 denotes the operating voltage of the alternating inputs, E denotes the equilibrium voltage of the cell under the current operating conditions, ηact,anIndicates the activation overpotential of the anode, ηact,caIndicates the activation overpotential of the cathode, ηohmicRepresents ohmic overpotential caused by proton and electron conduction;
Figure BDA0002284065860000082
Figure BDA0002284065860000083
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 BDA0002284065860000084
and
Figure BDA0002284065860000085
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 BDA0002284065860000086
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 overpotentials are obtained by ohm's law:
Figure BDA0002284065860000087
Figure BDA0002284065860000088
represents the proton conductivity,. phisRepresents the proton potential, ilThe value of the current density is taken as the value,
Figure BDA0002284065860000089
represents the proton conductivity,. philRepresents the proton potential; wherein the content of the first and second substances,
Figure BDA00022840658600000810
as a function of temperature values in the iterative process,. philVarying with the interactively set operating voltage.
The heat transfer module includes the following equation:
Figure BDA0002284065860000091
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 mesh layers along the flow channel direction thereof, each mesh layer is divided into a plurality of mesh blocks, the reactant concentrations in 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 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 the formulas (1) to (3), so that the mole fraction values in all the grid blocks can be calculated one by one 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 one grid block by one 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 traversing all the grid blocks one by one according to different positions, and then the distribution of the temperature in the electrolytic cell along the flow channel direction is obtained.
Thirdly, determining the 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, 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.
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 selected as a variable in order, and the other quantities in the boundary condition are kept constant, and the operating points are taken at equal intervals within a certain range for the boundary condition as the variable.
Operating voltage (V)cell) When the variable is used, the interval between two adjacent operating points is 0.1V;
mass fraction of anode reactant
Figure BDA0002284065860000111
As variables, two operating points in proximityThe interval between the two is 0.1;
gas flow velocity at the anode inlet (V)Anode) When the variable is used, the interval between two adjacent operating points is 0.01 m/s;
gas flow velocity (V) at cathode inletCathode) When the variable is used, the interval between two adjacent operating points is 0.01 m/s.
S3, as shown in FIG. 5, solving all discrete operating points of four variables of operating voltage, mass fraction of anode reactant, anode gas flow rate and cathode gas flow rate to obtain temperature values, gas velocity values and mole fraction values at different operating points in a two-dimensional steady-state model, and calculating the electrolytic cell efficiency η and the conversion rate γsyn。
The efficiency calculation formula is as follows:
Figure BDA0002284065860000112
in the formula, L represents the width of the electrolytic cell; t is0Indicating the ambient temperature, Ti,achRepresents the gas temperature value at the anode inlet, Ti,fchRepresents the gas temperature value at the cathode inlet, Cp,g,achDenotes the specific heat capacity of the gas at the anode inlet, Cp,g,fchIndicating the specific heat capacity of the gas at the cathode inlet,
Figure BDA0002284065860000113
indicating a value of the gas flow rate of which the component at the outlet is hydrogen,
Figure BDA0002284065860000114
representing a value of the gas flow rate at which the component at the inlet is hydrogen,
Figure BDA0002284065860000115
indicating a low heating value of hydrogen.
The conversion calculation formula is:
Figure BDA0002284065860000116
Figure BDA0002284065860000117
representing the mole fraction value of the component at the anode inlet as water,
Figure BDA0002284065860000118
representing the mole fraction value of the component in water at the anode outlet.
The efficiencies, conversions at all operating points obtained when the operating voltage was varied in the range of 1.4V to 2V are shown in fig. 6.
The efficiencies, conversions at all operating points obtained when the mass fraction of the anode reactant (i.e., water) was varied from 0.3 to 1.0 are shown in fig. 7.
The efficiencies, conversions at all operating points obtained when the gas flow rate at the anode inlet (i.e. water) was varied from 0.05m/s to 0.15m/s are shown in figure 8.
The efficiencies, conversions at all operating points obtained when the gas flow rate at the cathode inlet (i.e. water) was varied from 0.05m/s to 0.15m/s are shown in fig. 9.
S4, finding out all boundary conditions corresponding to the optimal efficiency of the electrolytic cell in the result of S3:
the operating voltage is 1.76V, the mass fraction of anode water is 0.44, the flow rate of anode gas is 0.03m/s, and the flow rate of cathode gas is 0.11 m/s; the maximum efficiency of 54.5 percent can be achieved.
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 (9)

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 the high-temperature proton exchange membrane electrolytic cell;
s2, interactively inputting boundary conditions into the two-dimensional steady-state model, sequentially selecting one of operating voltage, mass fraction of anode reactants, anode gas flow rate and 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 on the boundary conditions as the variables;
s3, solving all discrete operating points to obtain temperature values and gas velocity values at different operating points in the two-dimensional steady-state model so as to calculate the efficiency of the electrolytic cell;
s4, finding out all boundary conditions corresponding to the optimal efficiency of the electrolytic cell in the result of S3.
2. The method for determining the optimal efficiency of an electrolytic cell according to claim 1, wherein said two-dimensional steady-state model comprises a determining unit and a calculating unit;
a calculation unit: the boundary conditions used for receiving each parameter of interactive input are used as initial values in iterative calculation to start the iterative calculation of finite elements, each iteration obtains result values respectively corresponding to each initial value, and the result values are continuously used as the initial values of the next iteration;
a judging unit: the device is used for storing the relative tolerance of the interactive input, receiving the result value of each iteration and comparing the result value with the result value of the previous iteration, when the difference value of the result values of the two adjacent iterations of all the parameters is less than or equal to the relative tolerance, a stop instruction is formed to stop the calculation of the calculation unit, and after the iteration is stopped, the result value calculated at the last time is the steady-state parameter value of each parameter in the electrolytic cell.
3. The method of claim 2, wherein the boundary conditions interactively inputted 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, and operating temperature for simulating electrochemical reaction.
4. The method for determining the optimum efficiency of an electrolytic cell according to claim 3, wherein in said S2:
when the operating voltage is used as a variable, the interval between two adjacent operating points is 0.1;
when the mass fraction of the anode reactant is taken as a variable, the interval between two adjacent operating points is 0.1;
when the gas flow rate at the anode inlet is taken as a variable, the interval between two adjacent operating points is 0.01;
when the cathode inlet gas flow rate is used as a variable, the interval between two adjacent operating points is 0.01.
5. The method of claim 3, wherein the mass and momentum transfer module obtains the pressure value and the mole fraction value at each position by the following formula:
Figure FDA0002284065850000021
in the formula, NiRepresenting the flux of material transport, P representing the pressure value to be iterated, B0Permeability, which is a physical parameter of the porous electrode, is site dependent, mu denotes the gas viscosity, yiIs the mole fraction value of component i to be iterated;
Figure FDA0002284065850000022
is the total effective diffusion coefficient of component i, obtained by the following formula:
Figure FDA0002284065850000023
Figure FDA0002284065850000024
is the knudsen diffusion coefficient of component i,
Figure FDA0002284065850000025
is the molecular diffusion coefficient of component i;
Figure FDA0002284065850000026
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.
The mass and momentum transfer module further comprises the following formula for constraining the calculation of the pressure values and obtaining the gas velocity values at different positions:
Figure FDA0002284065850000031
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, P represents the pressure value to be iterated, mu is the gas viscosity, and T represents the matrix transposition.
6. The method of claim 5, wherein the electrochemical reaction module calculates the current density value by the following formula:
V＝E+ηact,an+ηact,ca+ηohmic；
v denotes the operating voltage of the alternating inputs, E denotes the equilibrium voltage of the cell under the current operating conditions, ηact,anIndicates the activation overpotential of the anode, ηact,caIndicates the activation overpotential of the cathode, ηohmicRepresents ohmic overpotential caused by proton and electron conduction;
Figure FDA0002284065850000032
Figure FDA0002284065850000033
is flat in the standard stateEquilibrium voltage, R is the universal gas constant, T represents the operating temperature of the cell, F is the Faraday constant,
Figure FDA0002284065850000034
and
Figure FDA0002284065850000035
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 FDA0002284065850000036
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 overpotentials are obtained by ohm's law:
Figure FDA0002284065850000037
Figure FDA0002284065850000038
represents the proton conductivity,. phisRepresents the proton potential, ilIs the current density value to be iterated,
Figure FDA0002284065850000039
represents the proton conductivity,. philRepresents the proton potential; wherein the content of the first and second substances,
Figure FDA00022840658500000310
as a function of temperature values in the iterative process,. philVarying with the interactively set operating voltage.
7. The method of claim 6, wherein the heat transfer module calculates the temperature value by the following equation:
Figure FDA0002284065850000041
t represents a temperature value to be iterated, and rho represents 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；
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.
8. The method for determining the optimal cell efficiency based on a two-dimensional steady-state model according to claim 7, wherein the calculation formula of the cell efficiency in S3 is as follows:
Figure FDA0002284065850000042
in the formula, L represents the width of the electrolytic cell; t is0Indicating the ambient temperature, Ti,achRepresents the gas temperature value at the anode inlet, Ti,fchRepresents the gas temperature value at the cathode inlet, Cp,g,achDenotes the specific heat capacity of the gas at the anode inlet, Cp,g,fchIndicating the specific heat capacity of the gas at the cathode inlet,
Figure FDA0002284065850000043
indicating the exitThe component is a gas flow rate value of hydrogen,
Figure FDA0002284065850000044
representing a value of the gas flow rate at which the component at the inlet is hydrogen,
Figure FDA0002284065850000045
indicating a low heating value of hydrogen.
9. The method for determining the optimum efficiency of an electrolytic cell according to claim 5, wherein said S3 further comprises obtaining mole fraction values for calculating the conversion:
Figure FDA0002284065850000046
Figure FDA0002284065850000051
representing the mole fraction value of the component at the anode inlet as water,
Figure FDA0002284065850000052
representing the mole fraction value of the component in water at the anode outlet.
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