CN113420483B - Method for establishing electrochemical model of SOFC/SOEC electrode microstructure - Google Patents

Method for establishing electrochemical model of SOFC/SOEC electrode microstructure Download PDF

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CN113420483B
CN113420483B CN202110736368.4A CN202110736368A CN113420483B CN 113420483 B CN113420483 B CN 113420483B CN 202110736368 A CN202110736368 A CN 202110736368A CN 113420483 B CN113420483 B CN 113420483B
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焦震钧
苏云鹏
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Shenzhen Graduate School Harbin Institute of Technology
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Abstract

The invention provides a method for establishing an electrochemical model of an SOFC/SOEC electrode microstructure, which comprises the following steps: identifying three-phase boundary lines at the intersections of yttria-stabilized zirconia, nickel and gas phases in the anode microstructure grid cells; establishing a coupling relation among gas, ions and electron diffusion equations; and applying constant ion and electron flux boundary conditions on the boundaries of the current collector and the electrolyte, applying constant gas concentration boundary conditions near the current collector, and finally, carrying out steady-state solution by using a separation type solver to obtain the electrochemical characteristics of the microelectrode. By adopting the technical scheme of the invention, an electrochemical model with fully coupled gas, ion and electron diffusion equations is established, and the model calculation result can obtain a series of simulation results such as electrochemical potential distribution, ion flow and electron flow distribution, gas concentration distribution condition, relation between overpotential and input current density and the like in YSZ, and has a certain guiding significance for electrode structure optimization and engineering design.

Description

Method for establishing electrochemical model of SOFC/SOEC electrode microstructure
Technical Field
The invention belongs to the technical field of solid oxide fuel cells, and particularly relates to a method for establishing an electrochemical model of an SOFC/SOEC electrode microstructure.
Background
Solid oxide fuel cells (Solid oxide fuel cell, SOFC)/solid oxide electrolysis cells (solid oxide electrolysis cell, SOEC) have received increasing attention as a promising energy conversion device for efficient use of renewable energy sources, with conventional SOFC/SOEC operating at relatively high temperatures of 600-1000 ℃ to ensure rapid diffusion of oxygen ions in the electrolyte. In order to optimize the operating characteristics of SOFC/SOEC at different operating temperatures and operating conditions, it is very important to understand the reaction kinetics of the SOFC/SOEC electrodes.
The anode/cathode of industrial SOFC/SOEC is mainly composed of submicron-sized nickel (electron conductor and catalyst) and 8YSZ (ion conductor: 8mol% y2o3 doped zirconia) particles, fuel gas is oxidized at the three-phase interface (TPB) where nickel, 8YSZ and gas are combined, such cermet electrode is generally designed to have a microstructure of high volume TPB length connected to the permeation transmission path of electron, ion and gas species, and the three-phase diffusion transmission process and electrochemical reaction coupling occurring on TPB in spatially non-uniform distribution constitute a complex system.
It is desirable to establish a numerical simulation method that quantifies the microstructure of the SOFC/SOEC three-dimensional electrode and simulates the mass transport and reaction inside the electrode to study the effect of the microstructure and operating conditions on the electrode performance. Previously, the LBM method has been used by scholars to simulate, but while the method can predict the electrochemical performance of the electrode relatively accurately, the calculation cost is relatively expensive, and the subsequent coupling of other physical fields can be difficult. The finite element method is a relatively good alternative, however, no scholars can systematically study the electrochemical performance of SOFC/SOEC electrodes using finite element technology at present, mainly because the simulation process encounters the following difficulties: 1) The three-phase boundary TPB at the intersection of yttria-stabilized zirconia, nickel and gas phase cannot be accurately identified, and the software cannot identify the TPB which is ineffective for reaction; 2) When electrochemical coupling of a diffusion equation is processed, error reporting is easy to occur, and the main reason is that the jacobian matrix singular phenomenon is encountered in the iterative calculation process of a solver.
Disclosure of Invention
Aiming at the technical problems, the invention discloses a method for establishing an electrochemical model of an SOFC/SOEC electrode microstructure, which can obtain information such as electrochemical potential distribution in YSZ, ion flow and electron flow distribution in an anode, gas concentration distribution, overpotential and the like, and is helpful for deeply understanding microscopic electrochemical characteristics in a porous electrode during steady-state operation of SOFC/SOEC.
In this regard, the invention adopts the following technical scheme:
a method of creating an electrochemical model of SOFC/SOEC electrode microstructure comprising:
step S1, identifying three-phase boundary lines (TPB) at the intersections of Yttria Stabilized Zirconia (YSZ), nickel (Ni) and gaseous phases (Gas) in the electrode microstructure grid cells;
step S2, establishing a coupling relation among gas, ion and electron diffusion equations, wherein the diffusion equations of the gas, the ion and the electron are as follows:
Figure BDA0003140221460000021
/>
Figure BDA0003140221460000022
Figure BDA0003140221460000023
i in reac Is the reaction current, the right-hand terms of the equalities of formulas (1) - (3) respectively represent the source terms of the gas, ion and electron diffusion equations at the three-phase boundary line,
Figure BDA0003140221460000024
is hydrogen molar concentration>
Figure BDA0003140221460000025
And->
Figure BDA0003140221460000026
Ion and electron conductivities, respectively, F representing Faraday constant,>
Figure BDA0003140221460000027
and->
Figure BDA0003140221460000028
The electrochemical potential of ions and electrons, respectively, D being the diffusion coefficient;
the reaction current is represented by the following formula (9):
Figure BDA0003140221460000029
wherein R represents a gas constant and T represents an operating temperature, wherein the current i is exchanged 0 The expression is as follows:
Figure BDA00031402214600000210
local overpotential eta occurring at three-phase boundary line act The following formula (11):
Figure BDA00031402214600000211
wherein, delta G DEG is the standard Gibbs free energy,
Figure BDA00031402214600000212
and->
Figure BDA00031402214600000213
Respectively dividing the three-phase boundary line;
coupling the two diffusion equations by taking the reaction current source terms in the diffusion equation (2) and the reaction current source term in the equation (3) as bridges, compiling a gas diffusion model, and inputting the source term of the equation (1) at the boundary source to realize the full coupling of the diffusion equations (1) - (3);
and S3, applying constant ion and electron flux boundary conditions on the boundaries of the current collector and the electrolyte, applying constant gas concentration boundary conditions near the current collector, and finally, carrying out steady-state solution by using a separation type solver to obtain the electrochemical characteristics of the microscopic anode.
As a further improvement of the present invention, in step S1, three-phase boundary lines at which yttria-stabilized zirconia, nickel, and gas phase meet in the electrode microstructure grid cells are identified using a script program.
As a further improvement of the present invention, in step S1, the divided YSZ, ni and gas three-phase assembly grid is imported using COMSOL finite element software, and the grid node coordinates, node numbers and body element identification numbers are read by the finite element software and the three-phase boundary line identification script program is input to obtain the node number matrix constituting the three-phase boundary line.
As a further improvement of the invention, the face shared between YSZ and Ni subfields is identified as YSZ-Ni interface, and YSZ-Gas interface and Ni-Gas interface are obtained in the same way, and the intersection of the three groups of interface boundary lines is three-phase boundary line.
As a further improvement of the invention, a COMSOL finite element software is utilized to establish a three-phase diffusion and electrochemical reaction full-coupling model; and programming a program to call COMSOL, so as to automatically select the identified TPB boundary and other boundary condition definitions, and batch processing simulation results under different variable conditions.
As a further improvement of the present invention, in step S2, a dust-containing gas model is used for the gas diffusion model, assuming that the total pressure in the electrode is constant, the gas diffusion model formula is as follows:
Figure BDA0003140221460000031
/>
in which y j Is mole fraction, N i Is the molar flow rate, p i Is the partial pressure, where subscripts i and j represent hydrogen and steam, respectively, D i,j And D i,k Binary and knoop diffusion coefficients, respectively.
The diffusion coefficient in formula (1) is:
Figure BDA0003140221460000032
Figure BDA0003140221460000033
binary and knudsen diffusion coefficients are in the form:
Figure BDA0003140221460000034
Figure BDA0003140221460000035
p is the pressure at which the pressure is to be applied,
Figure BDA0003140221460000036
and->
Figure BDA0003140221460000037
Molecular masses of hydrogen and water, respectively, +.>
Figure BDA0003140221460000038
And->
Figure BDA0003140221460000039
The diffusion volumes of hydrogen and water vapor, respectively, and r is the average pore radius, which can be 0.75. Mu.m.
The invention also discloses application of the electrochemical model of the SOFC/SOEC electrode microstructure, the electrochemical model of the SOFC/SOEC electrode microstructure is obtained by adopting the method for establishing the electrochemical model of the SOFC/SOEC electrode microstructure, and the relationship between overpotential and input current density is obtained by solving the electrochemical characteristics of the obtained microelectrode in a steady state and observing the electrochemical potential distribution, ion flow and electron flow distribution and gas concentration distribution conditions in YSZ.
Compared with the prior art, the invention has the beneficial effects that:
firstly, by adopting the technical scheme of the invention, an electrochemical model of full coupling of a gas, ion and electron diffusion equation is established, and the calculation result of the model can obtain a series of simulation results of electrochemical potential distribution, ion flow and electron flow distribution, gas concentration distribution condition, relation between overpotential and input current density and the like in YSZ, thus having a certain guiding significance for electrode structure optimization and engineering design.
Secondly, by adopting the technical scheme of the invention, the TPB in the electrode microstructure can be accurately identified, the defect that the prior art software automatically identifies the TPB which is easy to select the invalid TPB is overcome, and an important precondition is provided for the establishment of an electrochemical coupling model.
Thirdly, by adopting the technical scheme of the invention, the function of calling the model, automatically selecting TPB boundary and other boundary conditions and processing simulation results in batches by inputting different variables can be realized.
Drawings
Fig. 1 is a program flow chart of a simulation analysis method according to an embodiment of the invention.
Fig. 2 is a schematic diagram of an electrode microstructure grid cell according to an embodiment of the invention.
FIG. 3 shows an input current density of 0.7A/cm according to an embodiment of the present invention 2 Electrochemical in YSZA potential profile and a voltage profile at TPB, wherein (a) is the electrochemical potential profile in YSZ and (b) is the voltage profile at TPB.
Fig. 4 is a graph of ion current and electron current distribution along the current direction for an SOFC anode according to an embodiment of the present invention.
Detailed Description
The following detailed description of the present invention is, but not limited to, embodiments of the invention, and modifications and equivalents of the technical scheme of the invention are included in the scope of protection of the invention without departing from the spirit and scope of the technical scheme of the invention.
In view of the shortcomings of the prior art, the invention provides a method for establishing an electrochemical model of an SOFC/SOEC electrode microstructure, wherein a flow chart is shown in fig. 1, and mainly comprises the following steps:
and S1, importing an electrode microstructure network from outside by adopting COMSOL finite element software, calling a subroutine script to identify TPB, and identifying a three-phase boundary line (TPB) at the intersection of yttria-stabilized zirconia (YSZ), nickel (Ni) and gaseous phase (Gas) in an electrode microstructure grid unit.
And S2, establishing a coupling relation among gas, ions and electron diffusion equations.
And S3, solving a steady state numerical value.
And S4, finally, carrying out result analysis according to the solved result.
The invention aims at autonomously developing a program script capable of accurately identifying TPB, and the main implementation mode is that a node number matrix forming TPB can be obtained by inputting grid node coordinates, node numbers and body element identification numbers. The main implementation mode is that the surface shared between YSZ and Ni subdomains is automatically identified as YSZ-Ni interface, YSZ-Gas interface and Ni-Gas interface can be obtained by the same, TPB is defined as the intersection of three groups of interface boundary lines; establishing a three-phase diffusion and electrochemical reaction full-coupling model by using COMSOL finite element software; and programming a program to call COMSOL, so as to automatically select the identified TPB boundary and other boundary condition definitions, and batch processing simulation results under different variable conditions. The model can obtain the relation between the overpotential and the input current density by analyzing the electrochemical potential distribution, the ion flow and electron flow distribution and the gas concentration distribution in YSZ, and is helpful for deeply understanding the working mode of the microstructure of the porous electrode.
The following detailed description is provided in connection with specific examples.
In this example, a 10 μm x 10 μm x 10 μm electrode microstructure unit was selected for simulation, and the pre-work involved 3D reconstruction of the microelectrodes, followed by meshing with commercial software, the mesh number being about 320 ten thousand, as shown in fig. 2.
The method for establishing the electrochemical model of the SOFC/SOEC electrode microstructure by using the simulation analysis method comprises the following steps of:
step one: starting COMSOL finite element software through a main program, and inputting an instruction to import the divided three-phase (comprising YSZ, ni and gas) assembly grids into the software;
step two: and calling an autonomously developed subroutine to identify a three-phase boundary line (TPB), and obtaining a node number matrix forming the TPB by inputting grid node coordinates, node numbers and body element identification numbers. The main implementation mode is that the surface shared between YSZ and Ni subdomains is automatically identified as YSZ-Ni interface, YSZ-Gas interface and Ni-Gas interface can be obtained by the same, TPB is defined as the intersection of three groups of interface boundary lines;
step three: establishing a coupling relationship between gas, ion and electron diffusion equations, assuming YSZ and Ni are ideal ion and electron conductors, the gas, ion and electron diffusion equations can be written as:
Figure BDA0003140221460000061
Figure BDA0003140221460000062
Figure BDA0003140221460000063
i in reac Is the reaction current, the right-hand terms of (1) - (3) equal signs represent the source terms of the gas, ion and electron diffusion equations at the three-phase boundary line, and for non-TPB the source term is zero,
Figure BDA0003140221460000064
is hydrogen molar concentration>
Figure BDA0003140221460000065
And->
Figure BDA0003140221460000066
Ion and electron conductivity, respectively, < >>
Figure BDA0003140221460000067
And->
Figure BDA0003140221460000068
The electrochemical potential of the ions and electrons, respectively, F is the faraday constant, the gas diffusion model uses a Dusty Gas Model (DGM), assuming a constant total pressure in the electrode, the DGM formula is as follows:
Figure BDA0003140221460000069
in which y j Is mole fraction, N i Is the molar flow rate, p i Is the partial pressure, where subscripts i and j represent hydrogen and steam, respectively, D i,j And D i,k The binary and Knudsen diffusion coefficients, respectively, and T is the operating temperature.
Figure BDA00031402214600000610
Figure BDA00031402214600000611
Binary and knudsen diffusion coefficients are in the form:
Figure BDA00031402214600000612
Figure BDA00031402214600000613
p is the pressure at which the pressure is to be applied,
Figure BDA00031402214600000614
and->
Figure BDA00031402214600000615
Molecular masses of hydrogen and water, respectively, +.>
Figure BDA00031402214600000616
And->
Figure BDA00031402214600000617
The average pore radius r was taken to be 0.75 μm for the hydrogen and water vapor diffusion volumes, respectively.
The reaction current is given by the Butler-Volmer equation as follows:
Figure BDA00031402214600000618
wherein R represents a gas constant and T represents an operating temperature, wherein the current i is exchanged 0 The expression is as follows:
Figure BDA00031402214600000619
local overpotential η occurring at TPB act The formula is as follows:
Figure BDA0003140221460000071
Δg° is the standard gibbs free energy,
Figure BDA0003140221460000072
and->
Figure BDA0003140221460000073
The partial pressures at TPB, respectively.
Step four: in COMSOL software, the reaction current source term in the diffusion equations (2) and (3) is taken as a bridge, the two diffusion equations are coupled by using a weak form operation, a PDE module is used for compiling a gas diffusion model, and the source term of the equation (1) is input into a boundary source so as to realize the full coupling relation of the diffusion equations (1) - (3). Applying constant ion and electron flux boundary conditions (Newman conditions) of 0.7A/cm at the current collector and electrolyte boundary 2 Applying a constant gas concentration boundary condition (Diels-Alder boundary condition) of 9.46mol/m near the current collector 3 And finally, carrying out steady state solving by using a separated solver.
Step five: the important electrochemical characteristics of the micro-electrode can be obtained through the simulation result, the electrochemical potential distribution and the voltage distribution at the TPB in YSZ which cannot be obtained through experiments can be observed as shown in figure 3, and the anode ion flow and electron flow distribution curves are shown in figure 4.
In addition, the gas concentration distribution can be obtained, and the relationship between the overpotential and the input current density can also be obtained.
By adopting the technical scheme, the three-phase diffusion and electrochemical reaction full-coupling model is established by identifying the TPB and utilizing the COMSOL finite element software, and the COMSOL is compiled and called by a program, so that the simulation results under the condition of automatically selecting the identified TPB boundary and other boundary condition definitions and processing different variables in batches can be realized. The model can obtain the relation between the overpotential and the input current density by analyzing the electrochemical potential distribution, the ion flow and electron flow distribution and the gas concentration distribution in YSZ, and is helpful for deeply understanding the working mode of the microstructure of the porous electrode.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.

Claims (3)

1. The method for establishing the electrochemical model of the SOFC/SOEC electrode microstructure is characterized by comprising the following steps of: it comprises the following steps:
step S1, importing partitioned YSZ, ni and gas three-phase assembly grids by adopting COMSOL finite element software, reading grid node coordinates, node numbers and body element identification numbers through the finite element software, and inputting a three-phase boundary line identification script program to obtain a node number matrix forming a three-phase boundary line; identifying three-phase boundary lines at the intersections of yttria-stabilized zirconia, nickel and gas phases in the electrode microstructure grid cells;
step S2, establishing a coupling relation among gas, ion and electron diffusion equations, wherein the diffusion equations of the gas, the ion and the electron are as follows:
Figure FDA0004126875110000011
Figure FDA0004126875110000012
Figure FDA0004126875110000013
i in reac Is the reaction current, the right-hand terms of the equalities of formulas (1) - (3) respectively represent the source terms of the gas, ion and electron diffusion equations at the three-phase boundary line,
Figure FDA0004126875110000014
is hydrogen molar concentration>
Figure FDA0004126875110000015
And->
Figure FDA0004126875110000016
Ion and electron conductivities, respectively, F representing Faraday constant,>
Figure FDA0004126875110000017
and->
Figure FDA0004126875110000018
The electrochemical potential of ions and electrons, respectively, D being the diffusion coefficient;
in step S2, the gas diffusion model uses a dust-containing gas model, and the total pressure in the electrode is set to be constant, and the gas diffusion model formula is as follows:
Figure FDA0004126875110000019
in which y j Is mole fraction, N i Is the molar flow of hydrogen, N j Is the molar flow rate of steam, p i Is the partial pressure, where subscripts i and j represent hydrogen and steam, respectively, D i，j And D i，k Binary and knudsen diffusion coefficients, respectively;
the diffusion coefficient in formula (1) is:
Figure FDA00041268751100000110
Figure FDA00041268751100000111
binary and knudsen diffusion coefficients are in the form:
Figure FDA0004126875110000021
Figure FDA0004126875110000022
p is the pressure at which the pressure is to be applied,
Figure FDA0004126875110000023
is the mole fraction of hydrogen, +.>
Figure FDA0004126875110000024
And->
Figure FDA0004126875110000025
Molecular masses of hydrogen and water, respectively, +.>
Figure FDA0004126875110000026
And->
Figure FDA0004126875110000027
The diffusion volumes of hydrogen and water vapor are respectively, and r is the average pore radius; />
The reaction current is represented by the following formula (9):
Figure FDA0004126875110000028
wherein R represents a gas constant and T represents an operating temperature, wherein the current i is exchanged 0 The expression is as follows:
Figure FDA0004126875110000029
local overpotential eta occurring at three-phase boundary line act The following formula (11):
Figure FDA00041268751100000210
wherein, delta G DEG is the standard Gibbs free energy,
Figure FDA00041268751100000211
is the partial pressure of water at the boundary line of three phases, +.>
Figure FDA00041268751100000212
Is the partial pressure of hydrogen at the three-phase boundary line;
establishing a three-phase diffusion and electrochemical reaction full-coupling model by using COMSOL finite element software; calling COMSOL finite element software to automatically select the identified TPB boundary and other boundary condition definitions, and processing simulation results under different variable conditions in batches;
coupling the two diffusion equations by taking the reaction current source terms in the diffusion equation (2) and the reaction current source term in the equation (3) as bridges and using weak form operation, compiling a gas diffusion model by using a PDE module, and inputting the source terms of the equation (1) at a boundary source to realize the coupling of the diffusion equations (1) - (3);
step S3, applying constant ion and electron flux boundary conditions on the boundaries of the current collector and the electrolyte, applying constant gas concentration boundary conditions near the current collector, and finally, carrying out steady-state solution by using a separation type solver to obtain the electrochemical characteristics of the microscopic anode; the ion and electron flux boundary condition is 0.7A/cm 2 The method comprises the steps of carrying out a first treatment on the surface of the The boundary condition of the gas concentration is 9.46mol/m 3 。
2. The method for establishing an electrochemical model of an SOFC/SOEC electrode microstructure according to claim 1, wherein the method comprises the following steps: the face shared between the YSZ and Ni subfields is identified as YSZ-Ni interface, and YSZ-Gas interface and Ni-Gas interface are obtained in the same way, and the intersection of the three sets of interface boundary lines is a three-phase boundary line.
3. An application of an electrochemical model of an SOFC/SOEC electrode microstructure, characterized by: the electrochemical model of the SOFC/SOEC electrode microstructure is obtained by adopting the method for establishing the SOFC/SOEC electrode microstructure electrochemical model according to any one of claims 1-2, and the relationship between overpotential and input current density is obtained by solving the electrochemical characteristics of the obtained microelectrode in a steady state, observing the electrochemical potential distribution, ion flow and electron flow distribution and gas concentration distribution in YSZ.
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