Modeling simulation method for solid oxide electrolytic cell containing gradient cathode

Abstract

The invention discloses a modeling simulation method for a solid oxide electrolytic tank containing a gradient cathode. The method comprises the following operation steps: establishing a three-dimensional geometric model of the solid oxide electrolytic cell containing the gradient hole cathode; inputting physical property parameters of materials of all parts of the electrolytic tank and physical property parameters of reaction gas and product gas; according to a binary random filling ball model and a percolation theory, calculating a three-phase interface area in unit volume of the electrode; establishing a three-dimensional multi-physical field coupling model of the solid oxide electrolytic cell containing the gradient hole cathode; carrying out model verification on the three-dimensional multi-physics field coupling model; by solving and analyzing simulation results under different structural parameters of the cathode in an allowable range, key structural parameters influencing the performance of the electrolytic tank are explored, and the structural optimization problem of the cathode is considered. According to the method, the influence rule of the gradient pore structure on the SOEC electrolysis performance can be explored, guidance is provided for SOEC performance improvement, and the method has guiding significance for optimization design of SOEC gradient cathodes.

Description

Technical Field

[0001] The present invention belongs to the field of solid oxide electrolytic cells, and relates to a modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode; specifically, it relates to a modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode structure. Background Art

[0002] Solid Oxide Electrolysis Cell (SOEC) is an all-solid-state energy conversion device that can efficiently convert electrical energy and thermal energy into chemical energy. It can combine renewable energy such as solar energy, wind energy, geothermal energy and industrial waste heat to convert H2O and CO2 into fuels such as H2, CO, and CH4. SOEC has the advantages of high energy conversion efficiency, fast reaction rate, reversible operation model, and low cost, and is a very promising chemical energy storage method.

[0003] The performance of SOEC is limited by various polarization losses, including ohmic polarization, activation polarization and concentration polarization. Under given reaction conditions, these losses depend largely on the materials of the components of the electrolytic cell, the electrode microstructure and the geometric parameters. SOEC can be divided into anode support, electrolyte support and cathode support according to the support type. Since the electrolyte material has a low ionic conductivity, the electrolyte-supported SOEC will have a large ohmic impedance. Therefore, the cathode support structure is often used in SOEC to achieve the thin film of the electrolyte layer and reduce the ohmic loss of SOEC. When using the cathode support structure, it is necessary to consider the mechanical strength, the limitation of mass transport in the electrode and the size of the active reaction area. Therefore, the introduction of a gradient cathode structure can maintain the high specific surface area of ​​the electrode and improve the distribution of active sites. It can also reduce the transmission resistance of the reaction gas and product gas in the porous electrode, reduce the concentration polarization in the SOEC, and improve the overall performance of the SOEC. Summary of the invention

[0004] In view of the above problems, the purpose of the present invention is to address the defects of the prior art and propose a modeling and simulation method for a solid oxide electrolytic cell with a gradient cathode; based on the three-dimensional multi-physics field coupling modeling of SOEC, combined with the binary random filling sphere model and percolation theory, the influence of the gradient pore structure on the performance of SOEC is explored, providing guidance for the cathode structure design of SOEC.

[0005] The technical solution of the present invention is: a modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to the present invention, and its operating steps are as follows:

[0006] Step (1): establishing a three-dimensional geometric model of a solid oxide electrolytic cell including a gradient pore cathode;

[0007] Step (2): inputting the physical property parameters of the materials of each component of the electrolytic cell and the physical property parameters of the reaction gas and the product gas;

[0008] Step (3): Calculate the three-phase interface area per unit volume of the electrode based on the binary random packing sphere model and percolation theory;

[0009] Step (4): setting physical field control equations and boundary conditions to establish a three-dimensional multi-physics field coupling model of a solid oxide electrolytic cell with a gradient hole cathode;

[0010] Step (5): Perform model verification on the above three-dimensional multi-physics field coupling model to ensure the accuracy of the model;

[0011] Step (6): For the verified SOEC three-dimensional multi-physics field coupling model, the simulation results under different cathode structural parameters within the allowable range are solved and analyzed to explore the key structural parameters that affect the performance of the electrolytic cell and consider the optimization problem.

[0012] Further, in step (1), a three-dimensional geometric model of the SOEC single cell is constructed according to the three-dimensional structural dimensions of an actual solid oxide electrolytic cell, including a porous anode, an electrolyte, a porous cathode containing a gradient structure, and a gas flow channel for transporting reactant gases and generated gases;

[0013] Wherein, in the gradient electrode, the porosity and the radius of the ion / electronic conductor particles increase in a gradient form along the thickness direction of the electrode.

[0014] Furthermore, in step (2), the physical parameters include the physical parameters of the materials of the various components of the electrolytic cell and the physical parameters of the reaction gas on the electrode side, specifically including: electrode effective conductivity, exchange current density, thermal conductivity, constant pressure heat capacity, specific heat, density, dynamic viscosity and gas diffusion coefficient;

[0015] The electrode side reaction gas includes cathode and anode side reaction gases, and the physical property parameters of the cathode and anode side reaction gases can be defined as temperature-dependent functions according to specific components.

[0016] Furthermore, in step (3), the porous electrode can be regarded as the mutual accumulation of ionic conductors and electronic conductors. It is assumed that the electronic conductor and ionic conductor particles in the electrode each account for 50%, and the radius of the two is equal to the average pore radius. According to the binary random packing sphere model and percolation theory, the three-phase interface area S per unit volume of the electrode is TPB It is related to the contact area of ​​the electron conductor and ion conductor particles and the contact probability of the same particles. The calculation formula is:

[0017]

[0018] In the formula, θ represents the contact angle between the electron conductor particles and the ion conductor particles. Assuming that the contact angle between all particles is 15°, represents the average particle radius, n t represents the total number of electron conductor particles and ion conductor particles, n el It represents the percentage of ion conductor particles in all particles, Z el-io represents the average coordination number between ion conductor particles and electron conductor particles, P el represents the probability of ion conductor particle chain, P io represents the probability of electron conductor particle chain.

[0019] Furthermore, the total number of two conductor particles per unit volume of the porous electrode is calculated by the following formula:

[0020] n io =1-n el

[0021] Where ε is the porosity of the electrode, n io It represents the percentage of electron conductor particles in all particles, r el and r io Represent the average radius of ion particles and electron particles respectively; the particle number fraction can be calculated by experimentally measuring the volume fraction of the components in the electrode:

[0022]

[0023] In the formula, φ el It represents the volume fraction of the ion conductor in the porous electrode, and α represents the ratio of the average radius of the electronic conductor particles to the average radius of the ion conductor.

[0024] Furthermore, in step (4), there are multiple reactions in the SOEC that interact with each other and are strongly coupled with the multi-component complex heat and mass transfer process. When establishing the SOEC multi-physics field coupling model, it is necessary to set the corresponding physical field control equations on each calculation domain, including the electrochemical reaction equation, chemical reaction equation, mass conservation equation, momentum conservation equation, energy conservation equation, and charge conservation equation;

[0025] The boundary conditions include flow inlet boundary conditions, pressure outlet boundary conditions, gas component inlet boundary conditions, and temperature boundary conditions, and the coupling of multiple physical fields is achieved by calling equation source terms and common variables.

[0026] Furthermore, in step (5), the three-dimensional geometric model of SOEC is meshed to verify the mesh independence, and the accuracy of the model is verified in combination with the SOEC experimental data to ensure the reliability of the simulation results.

[0027] Furthermore, in step (6), by setting the thickness, porosity, and ion / electron conductor particle diameter of each layer of the gradient hole cathode within the allowable range, the SOEC with different cathode structural parameters is modeled and simulated to obtain the numerical solution related to the model performance and the distribution cloud diagram of the parameters within the model, and through comparative analysis, the key parameters affecting the electrolytic performance of the SOEC and the related optimization schemes are obtained.

[0028] The invention has the following beneficial effects: 1. The use of a gradient electrode can simultaneously meet the requirements of gas transport and electrochemical reaction active area in the cathode, so that the gas distribution in the cathode is more uniform, and the electrolytic performance of the cathode is effectively improved; 2. When modeling SOEC, the actual structure of the battery is accurately restored, the influence of the physical properties of the mixed gas and the ambient temperature is considered, the mutual coupling between different physical fields is considered, and the reaction active area in the cathode is calculated in combination with the binary random stacking model and the percolation theory, so that the model prediction is closer to the actual situation; 3. By establishing a three-dimensional simulation model of SOEC with a gradient cathode of different microstructures, its electrolytic performance is analyzed, and a better cathode structure is obtained, which has guiding significance for the optimal design of the cathode structure of the solid oxide electrolytic cell. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a flow chart of the method of the present invention;

[0030] Figure 2 Schematic diagram of the effect of cathode functional layer thickness on current density in Example 1 of the present invention;

[0031] Figure 3 is a schematic diagram showing the effect of the porosity of the cathode functional layer on the current density in Example 1 of the present invention;

[0032] Figure 4 Schematic diagram of the effect of the thickness of the cathode support layer on the current density in Example 1 of the present invention;

[0033] Figure 5 Schematic diagram of the effect of the porosity of the cathode support layer on the current density in Example 1 of the present invention;

[0034] Figure 6 is a schematic diagram showing the effect of the porosity of the cathode functional layer on the current density in Example 2 of the present invention;

[0035] Figure 7 Schematic diagram of the effect of the particle diameter of the cathode functional layer on the current density in Example 2 of the present invention;

[0036] Figure 8 Schematic diagram of the effect of the porosity of the cathode support layer 1 on the current density in Example 2 of the present invention;

[0037] Fig. 9is a schematic diagram of the relationship between the particle diameter of the cathode support layer 1 and the current density in Example 2 of the present invention;

[0038] Fig.10 is a schematic diagram of the porosity of the cathode support layer 2 versus the current density in Example 2 of the present invention;

[0039] Fig.11 Schematic diagram showing the effect of the particle diameter of the cathode support layer 2 on the current density in Example 2 of the present invention;

[0040] Fig.12 is the molar concentration distribution of CO2 in the cathode in Example 2 of the present invention (mol / m 3 ) schematic diagram. DETAILED DESCRIPTION

[0041] The specific technical scheme of the present invention is further described in detail below with reference to specific examples.

[0042] Example 1

[0043] This example provides a modeling simulation method and an optimization method for a solid oxide electrolytic cell containing a gradient cathode, comprising the following steps:

[0044] Step (1): establishing a three-dimensional geometric model of a solid oxide electrolytic cell comprising two cathode layers, wherein the two cathode layers are a functional layer close to the electrolyte layer and a support layer close to the gas flow duct, the functional layer has a lower porosity and particle radius, and the support layer has a larger porosity and particle radius;

[0045] Step (2): inputting the physical properties of the materials of each component of the electrolytic cell and the physical properties of the reaction gas and the product gas, specifically including: electrode effective conductivity, exchange current density, thermal conductivity, constant pressure heat capacity, specific heat, density, dynamic viscosity, gas diffusion coefficient; wherein the physical properties of the reaction gas on the cathode and anode sides can be defined as temperature-dependent functions according to the specific components;

[0046] Step (3): According to the binary random filling sphere model and percolation theory, the three-phase interface area S per unit volume of the electrode is TPB It is related to the contact area of ​​the electron conductor and ion conductor particles and the contact probability of the same particles. The calculation formula is:

[0047]

[0048] In the formula, θ represents the contact angle between the electron conductor particles and the ion conductor particles. Assuming that the contact angle between all particles is 15°, represents the average particle radius, n t represents the total number of electron conductor particles and ion conductor particles, n elIt represents the percentage of ion conductor particles in all particles, Z el-io represents the average coordination number between ion conductor particles and electron conductor particles, P el represents the probability of ion conductor particle chain, P io represents the probability of electron conductor particle chain;

[0049] The total number of two conductor particles per unit volume of the porous electrode is calculated by the following formula:

[0050]

[0051] n io =1-n el

[0052] Where ε is the porosity of the electrode, n io It represents the percentage of electron conductor particles in all particles, r el and r io Represent the average radius of ion particles and electron particles respectively; the particle number fraction can be calculated by experimentally measuring the volume fraction of the components in the electrode:

[0053]

[0054] In the formula, φ el represents the volume fraction of the ion conductor in the porous electrode, and α represents the ratio of the average radius of the electronic conductor particles to the average radius of the ion conductor;

[0055] Step (4): Setting physical field control equations and boundary conditions: It is necessary to set the corresponding physical field control equations on each computational domain, including the electrochemical reaction equation, chemical reaction equation, mass conservation equation, momentum conservation equation, energy conservation equation and charge conservation equation; setting the flow inlet boundary conditions, pressure outlet boundary conditions, gas component inlet boundary conditions and temperature boundary conditions, and realizing the coupling of multiple physical fields by calling the equation source terms and common variables, and completing the construction of the three-dimensional multi-physical field coupling model of the solid oxide electrolytic cell with gradient hole cathode;

[0056] Step (5): for the above three-dimensional multi-physics field coupling model, combined with the volt-ampere characteristic curve obtained from the experiment of the SOEC single cell, the model is verified to ensure the accuracy of the model;

[0057] Step (6): For the calibrated SOEC three-dimensional multi-physics field coupling model, the simulation results of different thicknesses and porosities of the cathode functional layer and the support layer within the allowable range are solved and analyzed to explore the key structural parameters that affect the operating performance of the electrolytic cell and consider optimization issues.

[0058] Table 1 shows the structural parameters of the electrolytic cell.

[0059]

[0060] The parameters within the allowable range of thickness and porosity of the functional layer / support layer were sampled and simulated. The specific working conditions were: operating temperature of 800°C, operating voltage of 1.5V, and CO2 / CO ratio of 1:1. The results are shown in Figure 2. Figures 2 to 5 As shown, the results illustrate that for the electrolytic cell configuration selected in Example 1, with the increase of the thickness and porosity of the functional layer, the electrolytic performance of SOEC shows a trend of first increasing and then decreasing. Therefore, it is more appropriate to select a cathode functional layer thickness of 50-100 μm and a porosity of 0.3-0.4. For the cathode supporting layer, the performance of SOEC decreases with the increase of the thickness of the supporting layer and increases with the increase of the porosity. Therefore, while meeting the strength requirements of SOEC, the supporting layer should be as thin as possible or have a structure with large pores.

[0061] Example 2

[0062] This embodiment provides a modeling simulation method and an optimization method for a solid oxide electrolytic cell having a gradient (three-layer) cathode structure, comprising the following steps:

[0063] Step (1): establishing a three-dimensional geometric model of a solid oxide electrolytic cell including a gradient cathode, wherein the cathode material is SFM, and along the thickness direction of the cathode, the porosity and particle diameter of each layer increase in a gradient form;

[0064] Step (2): inputting the physical properties of the materials of each component of the electrolytic cell and the physical properties of the reaction gas and the product gas, specifically including: effective conductivity of the electrode, porosity of the electrode functional layer and each supporting layer, radius of the ion / electronic conductor particles of the electrode functional layer and each supporting layer, exchange current density, thermal conductivity, constant pressure heat capacity, specific heat, density, dynamic viscosity, gas diffusion coefficient; wherein the physical properties of the reaction gas on the cathode and anode sides can be defined as temperature-dependent functions according to the specific components;

[0065] Step (3): According to the binary random filling sphere model and percolation theory, the three-phase interface area S per unit volume of the electrode is TPB It is related to the contact area of ​​the electron conductor and ion conductor particles and the contact probability of the same particles. The calculation formula is:

[0066]

[0067] In the formula, θ represents the contact angle between the electron conductor particles and the ion conductor particles. Assuming that the contact angle between all particles is 15°, represents the average particle radius, n t represents the total number of electron conductor particles and ion conductor particles, n elIt represents the percentage of ion conductor particles in all particles, Z el-io represents the average coordination number between ion conductor particles and electron conductor particles, P el represents the probability of ion conductor particle chain, P io represents the probability of electron conductor particle chain.

[0068] The total number of two conductor particles per unit volume of the porous electrode is calculated by the following formula:

[0069]

[0070] n io =1-n el

[0071] Where ε is the porosity of the electrode, n io It represents the percentage of electron conductor particles in all particles, r el and r io Represent the average radius of ion particles and electron particles respectively; the particle number fraction can be calculated by experimentally measuring the volume fraction of the components in the electrode:

[0072]

[0073] In the formula, φ el represents the volume fraction of the ion conductor in the porous electrode, and α represents the ratio of the average radius of the electronic conductor particles to the average radius of the ion conductor;

[0074] Step (4): Setting physical field control equations and boundary conditions: It is necessary to set the corresponding physical field control equations on each computational domain, including the electrochemical reaction equation, chemical reaction equation, mass conservation equation, momentum conservation equation, energy conservation equation and charge conservation equation; setting the flow inlet boundary conditions, pressure outlet boundary conditions, gas component inlet boundary conditions and temperature boundary conditions, and realizing the coupling of multiple physical fields by calling the equation source terms and common variables, and completing the construction of the three-dimensional multi-physical field coupling model of the solid oxide electrolytic cell with gradient hole cathode;

[0075] Step (5): For the above three-dimensional multi-physics field coupling model, the model is verified in combination with the experimental results to ensure the accuracy of the model;

[0076] Step (6): For the calibrated SOEC three-dimensional multi-physics field coupling model, by solving the simulation results of different porosities and particle diameters of the cathode functional layer and the support layer within the allowable range, a gas distribution cloud map in the cathode is given and analyzed to explore the key structural parameters that affect the performance of the electrolytic cell and consider optimization issues.

[0077] Table 2 shows the structural parameters of the electrolytic cell.

[0078]

[0079] The parameters within the allowable range of particle diameter and porosity of the functional layer / support layer were sampled and simulated. The specific working conditions were: operating temperature of 800°C, operating voltage of 1.5V, and CO2 / CO ratio of 1:1. The results are shown in Figure 2. Figures 6 to 11 As shown; Fig.12 The molar concentration distribution of CO2 in electrodes with gradient pores and electrodes without gradient pores was compared. The results show that in SOECs with gradient pore cathodes, the functional layer should have low porosity and small particle diameter to ensure sufficient active area for electrochemical reactions. For both levels of supporting layers, larger porosity and particle diameter should be selected, and the effect of porosity on gas diffusion in SOECs is greater than that of particle diameter. The presence of gradient pores makes the distribution of the reaction gas CO2 in the cathode more uniform, reduces the gradient of gas components in the cathode, and improves the performance of SOECs.

Claims

1. A modeling and simulation method for a solid oxide electrolytic cell containing a gradient cathode, characterized in that: The operation steps are as follows: Step (1): establishing a three-dimensional geometric model of a solid oxide electrolytic cell including a gradient pore cathode; Step (2): inputting the physical property parameters of the materials of each component of the electrolytic cell and the physical property parameters of the reaction gas and the product gas; Step (3): Calculate the three-phase interface area per unit volume of the electrode based on the binary random packing sphere model and percolation theory; Step (4): setting physical field control equations and boundary conditions to establish a three-dimensional multi-physics field coupling model of a solid oxide electrolytic cell with a gradient hole cathode; Step (5): Perform model verification on the above three-dimensional multi-physics field coupling model to ensure the accuracy of the model; Step (6): For the verified SOEC three-dimensional multi-physics field coupling model, the simulation results under different cathode structural parameters within the allowable range are solved and analyzed to explore the key structural parameters that affect the performance of the electrolytic cell and consider the optimization problem.

2. The modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to claim 1, characterized in that: In step (1), the three-dimensional geometric model of the SOEC single cell is constructed according to the three-dimensional structural dimensions of the actual solid oxide electrolytic cell. The invention comprises a porous anode, an electrolyte, a porous cathode with a gradient structure, and a gas flow channel for transporting reaction gas and generated gas.

3. The modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to claim 2, characterized in that: in, In the gradient electrode, the porosity and the radius of the ion / electronic conductor particles increase in a gradient form along the thickness direction of the electrode.

4. The modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to claim 1, characterized in that: In step (2), the physical parameters include the physical parameters of the materials of the various components of the electrolytic cell and the physical parameters of the reaction gas on the electrode side, specifically including: electrode effective conductivity, exchange current density, thermal conductivity, constant pressure heat capacity, specific heat, density, dynamic viscosity and gas diffusion coefficient.

5. The modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to claim 4, characterized in that: in, The electrode side reaction gas includes cathode side and anode side reaction gas, and the physical property parameters of the cathode side and anode side reaction gas can be defined as temperature-dependent functions according to specific components.

6. The modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to claim 1, characterized in that: In step (3), according to the binary random packing sphere model and percolation theory, the three-phase interface area S per unit volume of the electrode is TPB It is related to the contact area of ​​the electron conductor and ion conductor particles and the contact probability of the same particles. The calculation formula is: In the formula, θ represents the contact angle between the electron conductor particles and the ion conductor particles. Assuming that the contact angle between all particles is 15°, represents the average particle radius, n t represents the total number of electron conductor particles and ion conductor particles, n el It represents the percentage of ion conductor particles in all particles, Z el-io represents the average coordination number between ion conductor particles and electron conductor particles, P el represents the probability of ion conductor particle chain, P io represents the probability of electron conductor particle chain.

7. The modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to claim 1, characterized in that: In step (3), the total number of the two conductor particles per unit volume of the porous electrode is calculated by the following formula: n io =1-n el Where ε is the porosity of the electrode, n io It represents the percentage of electron conductor particles in all particles, r el and r io Represent the average radius of ion particles and electron particles respectively; the particle number fraction can be calculated by experimentally measuring the volume fraction of the components in the electrode: In the formula, φ el It represents the volume fraction of the ion conductor in the porous electrode, and α represents the ratio of the average radius of the electronic conductor particles to the average radius of the ion conductor.

8. The modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to claim 1, characterized in that: In step (4), when establishing the SOEC multi-physics field coupling model, it is necessary to set the corresponding physical field control equations on each calculation domain, including the electrochemical reaction equation, the chemical reaction equation, the mass conservation equation, the momentum conservation equation, the energy conservation equation and the charge conservation equation.

9. The modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to claim 1, characterized in that: In step (4), the boundary conditions include flow inlet boundary conditions, pressure outlet boundary conditions, gas component inlet boundary conditions, and temperature boundary conditions, and the coupling of multiple physical fields is achieved by calling equation source terms and common variables.

10. The modeling and simulation method of a solid oxide electrolytic cell containing a gradient cathode according to claim 1, characterized in that: In step (6), the thickness, porosity, and ion / electron conductor particle diameter of each layer of the gradient hole cathode are set within an allowable range, and a SOEC with different cathode structural parameters is modeled and simulated to obtain a numerical solution related to the model performance and a cloud diagram of the parameter distribution in the model. Through comparative analysis, the key parameters and optimization schemes affecting the electrolytic performance of the SOEC are obtained.

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