SOFC electrode poisoning and performance degradation modeling method based on multiple factors

Abstract

The invention provides a modeling method for SOFC electrode poisoning and performance degradation based on multiple factors, and belongs to the technical field of fuel cell numerical simulation. An SOFC three-dimensional geometric model is established, hypothesis conditions of the SOFC three-dimensional geometric model are established, physical parameters and boundary conditions of an SOFC are globally defined, physical field coupling setting is performed on a single cell geometric model of the SOFC, and the SOFC electrode poisoning and performance degradation modeling method based on multiple factors is established. Based on the Ni coarsening numerical model, the carbon deposition numerical model and the chromium poisoning numerical model, finally establishing a mathematical model of SOFC electrode poisoning and performance attenuation with multiple comprehensive factors; carrying out transient solution on different numerical models of the three-dimensional SOFC, and integrating the influence of various poisoning to obtain an SOFC electrode poisoning and performance attenuation rule; and based on the model, solving attenuation data of poisoning on electrochemical and mechanical properties of the SOFC to predict the residual service life of the SOFC.

Description

Technical Field

[0001] The invention proposes a modeling method for SOFC electrode poisoning and performance attenuation based on multiple factors, and relates to the technical field of fuel cell numerical simulation. Background Art

[0002] Solid oxide fuel cell (SOFC) is considered to be a clean energy that may replace traditional fossil fuels in the future due to its high efficiency and low pollutant emissions. SOFC has high energy conversion efficiency and is environmentally friendly; the high temperature operating environment allows it to use a variety of metal and oxide electrode materials, and can directly use various fuels; the operation process is noiseless, without electrolyte leakage and corrosion problems, and its single cell and battery stack have rich and diverse structural design forms; SOFC has a high waste heat temperature and can be operated in conjunction with a steam turbine or for cogeneration. During the operation of SOFC, some elements derived from reactants or battery components (such as C, S or Cr) may cause the electrodes to lose activity and various poisoning phenomena, resulting in a significant decline in battery performance. When SOFC uses reactants derived from fossil fuels such as natural gas, coal gas or liquefied petroleum gas, carbon deposition, sulfur poisoning and nickel particle growth are very likely to occur at the anode and cathode. The poisoning and nickel particle growth inside the battery seriously affect the working efficiency and life of the battery, which is one of the main reasons for the current battery life limit.

[0003] Since the battery stack operates in a high temperature environment for a long time and has a complex structure, the poisoning inside the battery system is affected by many factors, such as temperature field loading, external air flow, fuel gas composition and flow. Therefore, the poisoning inside the fuel cell presents extremely complex distribution characteristics, and the key components of SOFC will inevitably undergo changes in pores, Poisson's ratio, elastic modulus, conductivity, etc. under the long-term effect of poisoning, resulting in current density attenuation and mechanical performance degradation. To study the impact of SOFC single cell poisoning behavior on battery performance degradation, it is necessary to consider the comprehensive effect of multi-physical field coupling such as temperature field, electrochemical field, flow field, concentration field and solid mechanics field. Due to the limitations of experimental costs and laboratory conditions, mathematical modeling and numerical simulation have become increasingly important for the development and research of fuel cells in terms of optimizing battery design and operating parameters, and have even gradually become one of the scientific research methods to replace experimental research.

[0004] At present, most researchers use a combination of computational fluid dynamics software and finite element software to study the distribution of thermal stress and temperature curves inside SOFC. The most common method is a combination of Fluent and ABAQUS. This method first calculates the temperature field generated by the electrochemical reaction of SOFC, and then calculates the stress field based on the temperature field data. Although the distribution law of the stress field inside SOFC can be obtained, this method ignores the reverse effect of the stress field on poisoning, and the poisoning of the anode part of SOFC is more complicated, which is affected by both Ni coarsening and carbon deposition. If the reverse effect of the stress field on poisoning is ignored, the final simulation results will deviate greatly from the actual situation, and it is also impossible to explore the dual effects of poisoning on the electrochemical and mechanical properties of SOFC.

[0005] Therefore, it is necessary to seek a modeling method to establish a poisoning-mechanical coupling unit under the comprehensive effect of multi-field coupling to achieve the mutual coupling of the internal poisoning and stress fields of SOFC. Summary of the invention

[0006] In order to solve the problem that the poisoning and thermal stress inside SOFC cannot be coupled to each other in the traditional simulation process and the reverse effect of the stress field on the poisoning is ignored, the present invention proposes a modeling method for SOFC electrode poisoning and performance degradation based on multiple factors, including the following steps:

[0007] S1. Establish a three-dimensional geometric model of SOFC;

[0008] S2. Assumptions for establishing a three-dimensional geometric model of SOFC;

[0009] S3, globally define the physical parameters and boundary conditions of the SOFC three-dimensional geometric model;

[0010] S4, setting physical field coupling for the SOFC three-dimensional geometric model and performing meshing;

[0011] S5. Based on the numerical model of Ni coarsening, the numerical model of carbon deposition and the numerical model of chromium poisoning, a mathematical model of multi-factor SOFC electrode poisoning and performance degradation is finally established;

[0012] S6. Transiently solve different numerical models of SOFC electrode poisoning and performance degradation, and obtain the law of SOFC electrode poisoning and performance degradation by integrating the influence of various poisonings;

[0013] S7. Based on the model, the attenuation data of the electrochemical and mechanical properties of SOFC after detoxification is calculated to predict the remaining service life of SOFC.

[0014] Furthermore, in step S1, key components of the SOFC three-dimensional geometric model include an anode channel, an anode electrode, an electrolyte, a cathode electrode, a cathode channel and a connector material.

[0015] Furthermore, in step S2, the assumptions of the SOFC three-dimensional geometric model include:

[0016] a. Assume that the gas mixture consists of ideal gases;

[0017] b. The electrochemical reaction occurs at the boundary interface of the electrode layer;

[0018] c. Assume that the porous electrode is isotropic and macroscopically uniform;

[0019] d. Ignore the ohmic heat generated by the connector;

[0020] e. The heat capacity of a gas mixture is independent of temperature;

[0021] f. SOFC voltage is equal to the voltage difference between anode and cathode;

[0022] g. Ignore the heat transferred by the connector through the radiation mechanism;

[0023] h. Ignore the shrinkage and expansion deformation of the porous medium of SOFC;

[0024] i. Some physical parameters of key components of SOFC do not change with temperature;

[0025] k. The Ni particles of the anode are evenly distributed.

[0026] Furthermore, in step S3, the physical parameters include: density, thermal conductivity, electrical conductivity, thermal expansion coefficient, Poisson's ratio and elastic modulus of the anode, cathode, electrolyte and connector materials, permeability and porosity of porous materials, dynamic viscosity, molar mass, specific heat capacity and thermal conductivity of fuel gas and air; the boundary conditions include: setting the flow field outlet as a pressure outlet boundary, with no slip between the fluid and the wall; using thermal insulation boundaries for the rest of the battery fluid inlet and outlet; the surface of the connector constrains normal displacement, and the entire battery is subject to gravity.

[0027] Furthermore, in step S4, the domain of the physical field involved in the SOFC three-dimensional geometric model is selected, and the parameters of the physical field are set through multi-physical field coupling. The entire SOFC three-dimensional geometric model adopts a structured grid, and a boundary layer grid is added to the anode and cathode flow channel parts and an encrypted grid is used in the part close to the electrolyte.

[0028] Furthermore, in step S6, different numerical models of multi-factor SOFC electrode poisoning and performance degradation are transiently solved to obtain various poisoning effects, including: obtaining a single cell current variation with time curve, a stress field variation with time curve, and an electrode pore variation with time distribution related to the poisoning time; obtaining the relationship between the increase in Ni particle radius and the anode pore and the effect on the anode conductivity, effective elastic modulus and Poisson's ratio; obtaining the effect of carbon deposition on the anode pore distribution and the effect on the effective elastic modulus and Poisson's ratio; and obtaining the relationship between the change in cathode film resistance and the battery current density.

[0029] Furthermore, the effective elastic property model is used to calculate the elastic characteristics after poisoning, including the effective elastic modulus and effective Poisson's ratio:

[0030] The calculation formula of effective elastic modulus is:

[0031]

[0032] The formula for calculating the effective Poisson's ratio is:

[0033]

[0034] α=2ρ+2ρ 2 -ρ 3

[0035] β=4ρ+4ρ 2 +ρ 3

[0036] The relative density ρ of porous materials is:

[0037]

[0038] Among them, E m is the elastic modulus of the matrix material; is the effective elastic modulus of the porous material; ν m is the Poisson’s ratio of the matrix material; is the effective Poisson's ratio of the porous material; α and β are correlation coefficients; is the porosity of the material.

[0039] Furthermore, in the Ni coarsening poisoning model, the Ni particle radius r Ni for:

[0040]

[0041] Among them, k B is the Boltzmann constant, T is the temperature, γ is the surface energy; Ω is the diffusion volume element; δ S is the distance between Ni atoms; D S is the atomic surface diffusion coefficient; rNi0 and r YSZ0 are the initial particle radii of Ni and YSZ respectively; ψ Ni and ψ YSZ are the volume fractions of Ni and YSZ in the anode, respectively; is the average coordination number of Ni and YSZ initial particles, β and λ are two model parameters.

[0042] Furthermore, in the carbon deposition poisoning model,

[0043] r C is the carbon deposition rate:

[0044]

[0045] Among them, c C is the molar concentration of carbon; a is the catalyst activity; R C is the methane cracking rate; R B is the Boudouard reaction rate; the catalyst activity decay rate is:

[0046]

[0047] Among them, k a is the catalyst activity decay constant;

[0048] The porosity change rate caused by carbon deposition in the anode is defined as:

[0049]

[0050] Where ε is the anode porosity; M C and ρ C is the molar mass and density of the deposited carbon;

[0051] The permeability K is defined as:

[0052]

[0053] Among them, K 0 and ε 0 are the initial permeability and porosity of the anode.

[0054] Furthermore, in the chromium poisoning model,

[0055] The Cr poisoning reaction equation is shown as follows:

[0056] 2CrO 2 (OH) 2(g) +6e - →Cr 2 O 3(s) +2H 2 O+3O 2-

[0057] The oxidation rate of Cr is shown in the formula:

[0058]

[0059] Among them, x i is the mole fraction of substance i; 0,D is the exchange current density of Cr oxidation; Defined as CrO in the cathode electrode 2 (OH) 2 The mole fraction of is defined as the mole fraction of water vapor in the chromium source; F is defined as the Faraday constant; η ca is the cathode overpotential; T is defined as the temperature; and R is the universal gas constant.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] (1) The present invention realizes a numerical model under the joint action of multiple physical fields such as mass, momentum, heat, electrochemical reaction, solid mechanics, and domain ordinary differential and differential algebraic equations in the actual operation process of SOFC, which can efficiently obtain the influence of SOFC poisoning on the internal current density and stress distribution of the battery, providing a basis for further optimizing the battery structure and design.

[0062] (2) The present invention can use COMSOL software to establish a multi-physics field finite element model of a solid oxide fuel cell. Based on the physical modules required for studying the thermal stress and poisoning of SOFC, the numerical simulation results of the electrochemical field and the stress field during the poisoning process can be obtained simultaneously within the software, thereby realizing the mutual coupling of the poisoning and stress fields, and considering the influence of the pore changes on the effective elastic modulus and Poisson's ratio at the anode, thereby further improving the accuracy of the calculation.

[0063] The present invention realizes the mutual coupling of electrochemistry and stress field in the SOFC poisoning process in a more convenient and economical way while maintaining high-precision solution.

[0064] What needs to be explained is the coupling principle of electrochemistry: the secondary current and chemical interface and material transfer interface are completed together. The current density of the reaction is closely related to the chemical reaction rate on the electrode surface. The change of current density affects the material transfer of the reactants and the transfer of charge. The principle of electrochemical and thermal coupling: electrochemical reaction is an exothermic reaction, and the heat released by the reaction affects the temperature of the battery. At the same time, the increase in temperature usually increases the reaction rate, but too high a temperature may cause the degradation of the material.

[0065] Principle of coupling between electrochemical and stress fields: Changes in the temperature field caused by electrochemical and thermal coupling will further affect changes in the mechanical field. Long-term electrochemical heat release may cause fatigue and damage to the electrode and electrolyte materials, affecting the service life of the battery. Principle of coupling parameters: Parameters involved in coupling have multi-field sharing characteristics. For example, the porosity of the electrode is shared in the flow field and the heat transfer field. In the calculation process of the multi-field coupling of the model, the porosity between the two fields is called mutually.

[0066] At the same time, the distribution law of effective elastic modulus and Poisson's ratio after considering the porosity change of the anode is obtained, which improves the accuracy of traditional SOFC poisoning simulation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0068] Figure 1 It is a schematic flow chart of the modeling method of SOFC electrode poisoning and performance degradation based on multiple factors of the present invention;

[0069] Figure 2 A three-dimensional geometric model diagram of a SOFC supported by an anode in an embodiment of the present invention;

[0070] Figure 3 It is a single channel side view of the present invention;

[0071] Figure 4 A schematic diagram of a structured grid of a three-dimensional geometric model of an anode-supported SOFC according to an embodiment of the present invention;

[0072] Figure 5 The curve of anode pore change over time after poisoning multi-physics field coupling solution is performed on the three-dimensional geometric model of the anode-supported SOFC in the embodiment of the present invention;

[0073] Figure 6 The current density variation curve over time after the poisoning multi-physics field coupling solution is performed on the three-dimensional geometric model of the anode-supported SOFC in the embodiment of the present invention;

[0074] Figure 7 and Figure 8 The effective elastic modulus and Poisson's ratio change curves over time after the poisoning multi-physics field coupling solution is performed on the three-dimensional geometric model of the anode support SOFC in the embodiment of the present invention;

[0075] Fig. 9 and Fig.10The stress and strain variation curves over time after the poisoning multi-physics field coupling solution is performed on the three-dimensional geometric model of the anode support SOFC in the embodiment of the present invention DETAILED DESCRIPTION

[0076] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0077] In the drawings of the specific embodiments of the present invention, in order to better and more clearly describe the working principles of the various components in the system, the connection relationship of the various parts in the device is shown, which only clearly distinguishes the relative position relationship between the various components, and cannot constitute a limitation on the signal transmission direction, connection sequence and structural size, size and shape of each part within the component or structure.

[0078] The basic principle of the present invention is: according to the actual operation of the flat anode supported SOFC, the physical fields involved in the operation of the SOFC are added to the finite element software and the physical properties and boundary conditions of the materials are given, so as to obtain the distribution of the internal current density and stress field of the SOFC after considering Ni coarsening, carbon deposition and cathode poisoning under the poisoning multi-field coupling interaction.

[0079] like Figure 1 FIG. 1 is a flow chart of a modeling method for SOFC electrode poisoning and performance degradation based on multiple factors of the present invention, which specifically includes the following steps:

[0080] 1. Establish a three-dimensional geometric model of SOFC;

[0081] A geometric model of key components of a three-dimensional SOFC single cell is established, wherein the key components include anode flow channel, anode electrode, electrolyte, cathode electrode, cathode flow channel and interconnect material.

[0082] Figure 2 It is a three-dimensional geometric model diagram of the anode-supported SOFC in an embodiment of the present invention; as shown in the figure, the z direction is the length direction, the x direction is the width direction, and the y direction is the thickness direction. The SOFC stack structure mainly includes a metal connector, a PEN structure, and a sealing frame, wherein the PEN structure is composed of a porous anode, an electrolyte, and a porous cathode. The length L and width W of the metal connector are 70 mm and 64 mm, respectively, and the length l and width w of the PEN structure are 50 mm and 60 mm, respectively. The stack model contains 20 gas flow channels, and the gas flow mode is a one-in-two-out convection form, and the gas flow channels are all rectangular cross-sections.

[0083] 2. Assumptions for establishing the three-dimensional geometric model of SOFC.

[0084] Since the physical fields include mass, momentum, heat, electrochemical reactions, solid mechanics, and domain ordinary differentials and differential algebraic equations, these physical fields are coupled and work together, so the physical fields have an important and complex impact on the changes of physical quantities inside the battery.

[0085] The assumptions of the SOFC 3D geometric model include:

[0086] (1) The gas mixture consists of ideal gases;

[0087] (2) The electrochemical reaction occurs at the boundary interface of the electrode layer;

[0088] (3) The porous electrode is isotropic and macroscopically uniform;

[0089] (4) Ignore the ohmic heat generated by the connector;

[0090] (5) The heat capacity of a gas mixture is independent of temperature;

[0091] (6) SOFC voltage is equal to the voltage difference between anode and cathode;

[0092] (7) Ignore the heat transferred by the connector through the radiation mechanism;

[0093] (8) Ignore the shrinkage and expansion deformation of the porous media of SOFC;

[0094] (9) Some physical parameters of key SOFC components (cathode, anode and electrolyte, etc.) (such as elastic modulus and Poisson's ratio) do not change with temperature;

[0095] (10) The Ni particles of the SOFC anode are evenly distributed.

[0096] 3. Globally define the physical parameters and boundary conditions of the SOFC 3D geometric model;

[0097] Figure 3 : is a side view of a single-channel SOFC battery geometric model; this single-channel SOFC battery geometric model is a typical single-channel SOFC battery model. ia W is the height of the wall where the upper connector contacts the gas channel; ra H is the width of the wall where the upper connector contacts the gas channel; ib W is the height of the wall where the lower connector contacts the gas channel; rb H is the width of the wall where the lower connector contacts the gas channel; ps is the height of the anode support; H pis the height of the anode; H e is the height of the electrolyte; H n is the height of the cathode; H f is the height of the fuel gas flow channel; H a is the height of the air flow path.

[0098] Physical parameters include: density, thermal conductivity, electrical conductivity, thermal expansion coefficient, Poisson's ratio and elastic modulus of the anode, cathode, electrolyte and interconnect materials; permeability and porosity of porous materials; gas parameters include dynamic viscosity, molar mass, specific heat capacity and thermal conductivity of fuel gas and air;

[0099] The boundary conditions include: setting the flow field outlet as a pressure outlet boundary, and there is no slip between the fluid and the wall; using thermal insulation boundaries for the rest of the battery fluid inlet and outlet; constraining the normal displacement of the surface of the connector, and the entire battery is subject to gravity.

[0100] 4. Carry out physical field coupling modeling and parameter setting for the SOFC three-dimensional geometric model, and perform meshing;

[0101] The specific coupling modeling principle is as follows:

[0102] The coupling principle of electrochemistry: the secondary current, chemical interface and material transfer interface are completed together. The current density of the reaction is closely related to the chemical reaction rate on the electrode surface. The change of current density affects the material transfer of the reactants and the transfer of charges.

[0103] The principle of electrochemical and thermal coupling: Electrochemical reactions are exothermic reactions, and the heat released by the reaction affects the temperature of the battery. At the same time, increased temperature usually increases the reaction rate, but too high a temperature may cause degradation of the material.

[0104] Principle of coupling between electrochemistry and stress field: The change of temperature field caused by electrochemistry and thermal coupling will further affect the change of mechanical field. Long-term electrochemical heat release may cause fatigue and damage of electrode and electrolyte materials, affecting the service life of the battery. The mesh adopts hexahedral units. Since the thickness of each layer in the PEN structure is small, especially the electrolyte and porous cathode, the mesh division is encrypted here. The average quality of the mesh division is 1, which has good convergence and calculation accuracy.

[0105] The domain selection and parameter setting of the physical field involved in SOFC are carried out. These parameters will be called upon each other in the above coupling principle and model, which will make the model more perfect and ensure the accuracy of the results. The mesh of the geometric model uses hexahedral mesh units, which is conducive to the convergence of the model calculation.

[0106] Figure 4The figure is a schematic diagram of the structured grid of the three-dimensional geometric model of the anode-supported SOFC in the embodiment of the present invention; the grid uses hexahedral units with a total of 165,120 units and 176,175 nodes. Since the thickness direction of each layer in the PEN structure is relatively small, especially the electrolyte and the porous cathode, the grid division is encrypted here. It has been tested that the average quality of the grid division is 1, which has good convergence and calculation accuracy. The grid quality uses the system's built-in evaluation method. When the quality value is 1, the grid quality is the best, and when it is 0, the quality is the worst. If the quality is low, it is easy to cause problems such as non-convergence of calculations and inaccurate results.

[0107] 5. Based on the Ni coarsening numerical model, carbon deposition numerical model and chromium poisoning numerical model, a multi-factor mathematical model of SOFC electrode poisoning and performance degradation was finally established.

[0108] 6. Perform transient solutions to different numerical models of SOFC electrode poisoning and performance degradation, and obtain the laws of SOFC electrode poisoning and performance degradation by integrating the influence of various poisonings.

[0109] Different numerical models of SOFC electrode poisoning and performance degradation are transiently solved to obtain various poisoning effects, including: obtaining the time-varying curve of single cell current related to the poisoning time, the evolution law of stress field with time, and the distribution law of electrode pores with time; obtaining the relationship between the increase of Ni particle radius and anode pores, and the influence on anode conductivity, effective elastic modulus and effective Poisson's ratio; obtaining the influence of carbon deposition on anode pore distribution, effective elastic modulus and Poisson's ratio; and obtaining the relationship between the change of cathode film resistance and battery current density.

[0110] By integrating the influence of various poisoning factors, the rules of SOFC electrode poisoning and performance degradation are obtained, as well as the attenuation data of SOFC electrochemical and mechanical properties.

[0111] Figure 5 The curve of anode porosity variation over time after poisoning multi-physics field coupling solution is performed on the three-dimensional geometric model of the anode-supported SOFC in the embodiment of the present invention; the variation data of the anode porosity curve can indicate that poisoning will affect the anode porosity and further affect the material properties of the anode.

[0112] Figure 6 The current density variation curve over time after the poisoning multi-physics field coupling solution is performed for the three-dimensional geometric model of the anode-supported SOFC in the embodiment of the present invention. The current density decay data is collected to predict the trend of electrical performance changes and prepare for the remaining service life assessment.

[0113] Figure 7 and Figure 8The effective elastic modulus and Poisson's ratio of the three-dimensional geometric model of the anode support SOFC in the embodiment of the present invention after the poisoning multi-physics field coupling solution is performed. When the porosity changes, the material properties of the porous electrode will also change. The elastic modulus and Poisson's ratio of the material after the porosity changes can be calculated based on the effective elastic property model.

[0114] Fig. 9 and Fig.10 The stress and strain curves over time after the poisoning multi-physics field coupling solution is performed for the three-dimensional geometric model of the anode support SOFC in the embodiment of the present invention. The attenuation data of stress and strain are collected to predict the trend of mechanical energy changes and prepare for the assessment of the remaining service life.

[0115] 7. Based on the model, the attenuation data of the electrochemical and mechanical properties of SOFC caused by detoxification is used to predict the remaining service life of SOFC.

[0116] The present invention is described in further detail below.

[0117] (1) First, in the COMSOL software, the geometry module establishes a single cell model according to the size of the key components of each part of the SOFC. Then, in the "Global Definition" section of the software, the material properties, parameters, variables, names of the various parts of the battery geometry model, and the probes required to solve the average current density are specified.

[0118] Among them, the gas parameters of the solid oxide fuel cell include the gas inlet velocity, mass fraction, diffusion coefficient, pressure at the gas outlet and the initial temperature at the gas inlet; the physical properties of the solid structure (cathode, anode, electrolyte and interconnect material) include the conductivity, exchange current density and initial voltage required in the secondary current density interface, the thermal conductivity and specific heat required in the solid heat transfer interface, the porosity and permeability of the porous medium required in the concentrated species transfer interface, and the density, thermal expansion coefficient, elastic modulus, Poisson's ratio, etc. required in the solid mechanics interface.

[0119] Considering the actual working conditions of SOFC, the initial temperature in the model is set to 800 °C and the pressure is set to 1 atm.

[0120] (2) According to the actual operation of SOFC, the corresponding physical field interfaces are selected for the geometric model in COMSOL software: solid heat transfer interface in the heat transfer module, concentrated species transfer interface in the chemical substance transfer module, secondary current density interface in the electrochemistry module, free and porous media flow interface in the fluid flow module, solid mechanics interface in the structural mechanics module, and domain ordinary differential and differential algebraic equation interface in the mathematics module.

[0121] The "Secondary Current Density Distribution" interface is used for general modeling of electrochemical cells. The relationship between charge transfer and overpotential can be described using arbitrary kinetic expressions (such as Butler-Volmer and Tafel equations). The "Concentrated Species Transport" interface is used for multi-component diffusion, where the diffusion driving force of each species depends on the composition, temperature, and pressure of the mixture. This physics field is used to model the species transfer phenomena between the anode flow channel, cathode flow channel, and porous media (anode, cathode itself) in SOFC. The "Free and Porous Media Flow" interface is used to calculate the fluid velocity and pressure field of single-phase flow, where the free flow is connected to the porous media. In SOFC, the anode is integrated with the fuel channel, the cathode, and the air channel. The "Solid Heat Transfer" interface is used to simulate the conduction heat transfer, convection heat transfer, and radiation heat transfer in the fluid, porous media, and solids in SOFC. The "Solid Mechanics" interface is used to simulate the thermal stresses of key components in SOFC. The Domain ODE and DAE interfaces are used to simulate the poisoning of electrodes in SOFC.

[0122] Solid oxide fuel cells have three main components, namely the electrolyte and two electrodes (cathode and anode), which allow positively charged hydrogen ions (protons) to move between the two sides of the SOFC. At the cathode, the fuel is oxidized, which then produces electrons, which flow from the anode to the cathode through an external load. At the cathode, hydrogen and oxygen ions react to produce water.

[0123] The voltage and current density generated by the electrochemical reaction are calculated using the secondary current distribution model.

[0124] a. Secondary current distribution model

[0125] The transfer control equations of electrons and ions between electrolyte and porous electrode can be expressed as:

[0126]

[0127]

[0128] Among them, ρ l and ρ s are the electron and ion charge densities, respectively; σ l is the effective conductivity of the electrode, and σ s refers to the ionic conductivity of the electrolyte; φ l and φ s are the electron and ion voltages, and Q l and Q s represent the electron and ion charge sources, respectively, is the gradient operator.

[0129] The SOFC current density and voltage distribution can be obtained by coupling and solving the equations of the model.

[0130] The flow rate of the gas in the fuel and air flow channels is calculated using the fluid flow model.

[0131] b. Fluid flow model

[0132] The gas flows freely between the porous electrode and the gas channel, and the fluid flow in the porous electrode and the gas channel can be simulated simultaneously. The Navier-Stokes equation is widely used to describe the flow of gas in the flow channel. Due to the different structures in the porous electrode and the flow channel, the Navier-Stokes equation is modified by introducing the Darcy term, and the porosity of the porous medium is also considered:

[0133]

[0134] Anode S mass :

[0135]

[0136] Cathode S mass :

[0137]

[0138] Where v is the velocity vector, S mass is the mass source term, ε is the porosity, k is the specific permeability, which depends on the geometry of the porous medium, is the molar mass of water, is the molar mass of hydrogen, F is the external force on the fluid, i is the number of species, p is the fluid pressure, and μ is the dynamic viscosity of the fluid.

[0139] The velocity distribution of the gas inside the SOFC can be obtained by coupling and solving the equations of the model.

[0140] The distribution of components in the fuel and air flow paths is calculated using a mass transfer model.

[0141] c. Mass transfer model

[0142] Since the electrochemical reaction occurs near the interface between the electrolyte and the electrode, in order for the gas to reach the reaction site, the gas must diffuse through the pores of the electrode. Considering that the pores in the active anode layer are smaller, which means that the molecules collide with the pore surface more frequently, Knudsen diffusion plays an important role in diffusion. Therefore, the combination of Knudsen diffusion and Fick's law is used in the mass transfer model:

[0143]

[0144] Among them, ω i is the mass fraction of substance i, j iis the mass flux of species i, ε is the volume fraction of pores in the porous medium, M is the total molar mass, is the total diffusion coefficient of the substance.

[0145] The distribution of gas components inside SOFC can be obtained by coupling and solving the equations of this model.

[0146] The temperature distribution of each component is calculated using the heat transfer model.

[0147] d. Heat transfer model

[0148] The classic heat transfer governing equation is:

[0149]

[0150] Among them C p is the specific heat capacity, and Q is the heat source term in the battery. eff is the effective thermal conductivity, which is determined by the composition of the gas in the gas flow path.

[0151] The λ of the porous electrode eff Calculated as:

[0152] λ eff =(1-ε)λ s +fλ g (9)

[0153] Among them, λ s and λ g is the thermal conductivity of the gas and solid.

[0154] The SOFC temperature distribution can be obtained by coupling and solving the equations of the model.

[0155] The distribution of stress and strain of each component is calculated through the structural mechanics model.

[0156] e. Structural mechanics model:

[0157] Since it is assumed that all the materials of the planar SOFC layers satisfy the linear elastic theory and the deformation caused by thermal stress is very small, the stress-strain relationship of the elastic material under thermal load is:

[0158] σ=Dξ ei +σ 0 (10)

[0159] Where σ is the stress vector, D is the elastic matrix, σ 0 Represents the initial stress magnitude.

[0160] The elastic matrix D of an isotropic material is expressed as:

[0161]

[0162] Among them, E represents the elastic modulus and υ represents the Poisson's ratio. And it satisfies the following relationship with the shear modulus G:

[0163]

[0164] The distribution of SOFC stress and strain can be obtained by coupling and solving the equations of the model.

[0165] Due to the influence of poisoning on the porous electrode, the elastic characteristics after poisoning will change. The effective elastic property model is used to calculate the elastic characteristics after poisoning, mainly including the effective elastic modulus and the effective Poisson's ratio.

[0166] f. Effective elasticity characteristic model

[0167] The calculation formula of effective elastic modulus is:

[0168]

[0169] The formula for calculating the effective Poisson's ratio is:

[0170]

[0171] α=2ρ+2ρ 2 -ρ 3

[0172] β=4ρ+4ρ 2 +ρ 3 (15)

[0173] Relative density of porous materials:

[0174]

[0175] Among them, E m is the elastic modulus of the matrix material; is the effective elastic modulus of the porous material; ν m is the Poisson’s ratio of the matrix material; is the effective Poisson's ratio of the porous material; α and β are correlation coefficients; is the porosity of the material; ρ is the relative density of the porous material.

[0176] Since the electrodes of SOFC are porous materials, the change of porosity during the poisoning process will inevitably lead to the change of effective elastic modulus and Poisson's ratio.

[0177] By coupling and solving the equations of this model, the distribution of elastic characteristics of SOFC electrodes after poisoning can be obtained.

[0178] The Ni coarsening poisoning model can be used to solve the change in the radius of nickel particles, the change in the effective conductivity of the anode, and the change in the porosity of the anode. The equation of this model can be coupled with the effective elastic property model to obtain the elastic characteristics of the nickel particles after coarsening, and the coupling solution with the secondary current can obtain the change in the electrical properties of the nickel particles after coarsening. Finally, the coupling of multiple physical fields can solve the changes in the mechanical and electrochemical properties of SOFC.

[0179] g. Ni coarsening poisoning model

[0180] Nickel particle radius r Ni The growth can be described by a theoretical model.

[0181]

[0182]

[0183] Among them, k B Boltzmann constant, T is temperature, γ(=1.9 J m -2 ) is the surface energy; Ω is the diffusion volume element of Ni is the distance between Ni atoms; D S (=4.8×10 -11 m 2 h, T = 800 ° C) is the atomic surface diffusion coefficient; r Ni0 and r YSZ0 are the initial particle radii of Ni and YSZ respectively; ψ Ni and ψ YSZ are the volume fractions of Ni and YSZ in the anode, respectively; is the average coordination number of Ni and YSZ initial particles. β and λ are two model parameters, β reflects the morphology of the initial anode, and λ depends on the radius of the Ni initial particle.

[0184] Anode effective conductivity equation:

[0185]

[0186] in, is the initial conductivity of Ni material; Anode porosity; The percolation threshold of the anode Ni particles, And the correlation coefficient relationship:

[0187]

[0188] in, is the average coordination number, which also changes with the aggregation of Ni particles.

[0189] The relationship between the average coordination number and the correlation coefficient is:

[0190]

[0191] Among them, Z YSZ,YSZ is the coordination number between YSZ particles, which takes the conventional value of 6.

[0192] The carbon deposition poisoning model can be used to solve the carbon deposition rate and the changes in catalyst activity and anode porosity. The equation of this model can be coupled with the effective elastic property model to obtain the elastic characteristics after carbon deposition, and the coupling with the secondary current can obtain the changes in electrical properties after carbon deposition. Finally, the coupling of multiple physical fields can solve the changes in SOFC mechanical properties and electrochemical properties.

[0193] h. Carbon deposition poisoning model

[0194] r C is the carbon deposition rate, defined as:

[0195]

[0196] Among them, c C is the molar concentration of carbon; a is the catalyst activity; R C is the methane cracking rate; R B is the Boudouard reaction rate. At the initial time t = 0, a = 100%.

[0197] The catalyst activity decay rate is defined as

[0198]

[0199] Among them, k a is the catalyst activity decay constant, calculated as:

[0200]

[0201] Among them, R g is the molar gas constant; T is the temperature.

[0202] The porosity change rate caused by carbon deposition in the anode is defined as:

[0203]

[0204] Where ε is the anode porosity; M C and ρ C is the molar mass and density of the deposited carbon.

[0205] The permeability is defined as:

[0206]

[0207] Among them, K0 and ε 0 are the initial permeability and porosity of the anode.

[0208] The chromium poisoning model can be used to solve the increase in the area specific resistance of the cathode. The model can be coupled with the secondary current to obtain the change in electrical properties after chromium poisoning. Finally, the coupling of multiple physical fields can be used to solve the changes in the mechanical and electrochemical properties of SOFC.

[0209] i. Chromium poisoning model

[0210] The Cr poisoning reaction equation is shown as follows:

[0211] 2CrO 2 (OH) 2(g) +6e - →Cr 2 O 3(s) +2H 2 O+3O 2- (27)

[0212] The oxidation rate of Cr is shown in the formula:

[0213]

[0214] Among them, x i is the mole fraction of substance i; 0,D is the exchange current density of Cr oxidation; Defined as CrO in the cathode electrode 2 (OH) 2 The mole fraction of is defined as the mole fraction of water vapor in the chromium source; F is defined as the Faraday constant; η ca is the cathode overpotential; T is defined as the temperature; and R is defined as the universal gas constant.

[0215] The chromium poisoning reaction will affect the increase of the cathode area specific resistance.

[0216] The size of the area specific resistance can be defined in the electrode film resistance of the secondary current module.

[0217] Specifically, the operations to achieve poisoning are as follows:

[0218] 1. Ni particle coarsening model: The main dependent variable involved is the effective anode conductivity. The only independent variables of the entire coarsening equation are the initial radius of the Ni particle and the initial conductivity of the anode.

[0219] First, the equations are programmed into COMSOL.

[0220] r Ni In the equation, if r is known Ni0, then the equation is a function of time. So r Ni The equations and the various known parameters involved in the equations are defined as a set of variables in the component definition. Ni The equation can become a new variable that changes over time.

[0221] Then r Ni The equation combined The average coordination number equation and its coefficient equation can be used to derive the Ni particle radius and Further, we can deduce a mathematical relationship that varies with the radius of Ni particles. The new variable.

[0222] Once the above variables are known, the effective conductivity of the anode can be defined directly at the model interface.

[0223] 2. Carbon deposition model:

[0224] In the carbon deposition model, the main dependent variable is the anode porosity.

[0225] Since the differential equations involved in the carbon deposition model are in the same format as the Domain ODEs and PDEs interface, the carbon deposition equations can be incorporated into the interface to solve the porosity balance problem. In addition, the initial values ​​of the Domain ODEs and PDEs interface are set to the initial porosity of the anode, so the porosity data of the anode can be directly referenced.

[0226] 3. Chromium poisoning model:

[0227] In the chromium poisoning model, the main dependent variable is the cathode area specific resistance.

[0228] The area specific resistance is defined in the Film Resistance - Surface Resistance section of the Secondary Current interface.

[0229] After the numerical model is established, the model needs to be verified. The specific steps are as follows:

[0230] Firstly, the data of the decay of the real stack current density over time is obtained;

[0231] The decay data of current density is calculated through simulation;

[0232] Adjust the model parameters and boundary conditions to ensure that the error between the simulated current density data and the actual current density data is within a reasonable range.

[0233] The specific steps to predict the remaining service life of the battery stack based on attenuation data are as follows:

[0234] First, data collection and preprocessing are performed;

[0235] The data was collected as follows:

[0236] Collection of electrical performance data, mechanical performance data, environmental conditions, operating time and other data;

[0237] The data prediction process is as follows:

[0238] First, remove noise and outliers. Second, extract useful features from the raw data, such as maximum Mises stress, average current density, etc.

[0239] The decay model is constructed as follows:

[0240] Prediction model of performance degradation:

[0241] Performance degradation refers to the degradation of electrical properties and mechanical properties. The performance degradation of the Ni particle coarsening model, carbon deposition model and chromium poisoning model includes the degradation of electrical properties and mechanical properties.

[0242] Electrical performance decay: Linear regression, exponential decay model, etc. can be used to fit the decay trend of electrical performance data;

[0243] Mechanical property decay: Analyze the changes in stress and strain data and construct a mechanical property decay model.

[0244] Remaining life prediction method:

[0245] The performance standards of the fuel cell stack are set as follows:

[0246] Set electrical performance thresholds: minimum voltage threshold (set a minimum voltage threshold based on the design specifications and operating requirements of the fuel cell stack. When the voltage is lower than this threshold, it indicates that the performance of the fuel cell stack has significantly declined), maximum impedance threshold (set a maximum allowable impedance value. Exceeding this value may indicate that there are serious problems inside the fuel cell stack), power density decay rate (set a power density decay rate threshold to monitor whether the fuel cell stack is decaying at too fast a rate).

[0247] Set mechanical property thresholds: maximum allowable stress (set a maximum stress threshold, exceeding this value may cause material fatigue or damage), strain limit (set the maximum allowable strain value, exceeding this value may indicate that the structure has been deformed), temperature limit (set a maximum operating temperature threshold and temperature difference threshold, exceeding these thresholds may cause material and component degradation).

[0248] Based on machine learning methods: Use machine learning algorithms such as decision trees, random forests, and support vector machines (SVM) to train models to predict the remaining life of the battery stack.

[0249] The input parameters of the machine learning model are the attenuation data of electrical and mechanical properties, and the electrical and mechanical performance thresholds are used to determine whether the current performance is in a safe state.

[0250] Finally, real-time monitoring of electrical and mechanical properties can be achieved, performance changes can be captured in a timely manner, and the remaining service life can be predicted based on performance degradation.

[0251] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0252] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A modeling method for SOFC electrode poisoning and performance degradation based on multiple factors, characterized in that: The steps include: S1. Establish a three-dimensional geometric model of SOFC; S2. Assumptions for establishing a three-dimensional geometric model of SOFC; S3, globally define the physical parameters and boundary conditions of the SOFC three-dimensional geometric model; S4, setting physical field coupling for the SOFC three-dimensional geometric model and performing meshing; S5. Based on the numerical model of Ni coarsening, the numerical model of carbon deposition and the numerical model of chromium poisoning, a mathematical model of multi-factor SOFC electrode poisoning and performance degradation is finally established; S6. Transiently solve different numerical models of SOFC electrode poisoning and performance degradation, and obtain the law of SOFC electrode poisoning and performance degradation by integrating the influence of various poisonings; S7. Based on the model, the attenuation data of the electrochemical and mechanical properties of SOFC after detoxification is calculated to predict the remaining service life of SOFC.

2. The modeling method according to claim 1, characterized in that: In the step S1, key components of the SOFC three-dimensional geometric model include an anode flow channel, an anode electrode, an electrolyte, a cathode electrode, a cathode flow channel and a connector material.

3. The modeling method according to claim 2, characterized in that: In step S2, the assumptions of the SOFC three-dimensional geometric model include: a. Assume that the gas mixture consists of ideal gases; b. The electrochemical reaction occurs at the boundary interface of the electrode layer; c. Assume that the porous electrode is isotropic and macroscopically uniform; d. Ignore the ohmic heat generated by the connector; e. The heat capacity of a gas mixture is independent of temperature; f. SOFC voltage is equal to the voltage difference between anode and cathode; g. Ignore the heat transferred by the connector through the radiation mechanism; h. Ignore the shrinkage and expansion deformation of the porous medium of SOFC; i. Some physical parameters of key components of SOFC do not change with temperature; k. The Ni particles of the anode are evenly distributed.

4. The modeling method according to claim 1, characterized in that: In step S3, the physical parameters include: the density, thermal conductivity, electrical conductivity, thermal expansion coefficient, Poisson's ratio and elastic modulus of the anode, cathode, electrolyte and connector materials, the permeability and porosity of porous materials, the dynamic viscosity, molar mass, specific heat capacity and thermal conductivity of fuel gas and air; the boundary conditions include: setting the flow field outlet as a pressure outlet boundary, and there is no slip between the fluid and the wall; thermal insulation boundaries are used for the rest of the battery fluid inlet and outlet; the surface of the connector constrains the normal displacement, and the entire battery is subject to gravity.

5. The modeling method according to claim 1, characterized in that: In step S4, the domain of the physical field involved in the SOFC three-dimensional geometric model is selected, and the parameters of the physical field are set through multi-physical field coupling. The entire SOFC three-dimensional geometric model adopts a structured grid, and a boundary layer grid is added to the anode and cathode flow channel parts, and an encrypted grid is used in the part close to the electrolyte.

6. The modeling method according to claim 1, characterized in that: In step S6, different numerical models of multi-factor SOFC electrode poisoning and performance degradation are transiently solved to obtain various poisoning effects, including: obtaining a single cell current variation with time curve, a stress field variation with time curve, and an electrode pore variation with time distribution related to the poisoning time; obtaining the relationship between the increase in Ni particle radius and the anode pore and the effect on the anode conductivity, effective elastic modulus and Poisson's ratio; obtaining the effect of carbon deposition on the anode pore distribution and the effect on the effective elastic modulus and Poisson's ratio; and obtaining the relationship between the change in cathode film resistance and the battery current density.

7. The modeling method according to claim 6, characterized in that: The effective elastic property model is used to calculate the elastic characteristics after poisoning, including the effective elastic modulus and effective Poisson's ratio: The calculation formula of effective elastic modulus is: The formula for calculating the effective Poisson's ratio is: a=2ρ+2ρ 2 -r 3 β=4ρ+4ρ 2 +r 3 The relative density ρ of porous materials is: Among them, E m is the elastic modulus of the matrix material; is the effective elastic modulus of the porous material; ν m is the Poisson’s ratio of the matrix material; is the effective Poisson's ratio of the porous material; α and β are correlation coefficients; is the porosity of the material.

8. The modeling method according to claim 6, characterized in that: In the Ni coarsening poisoning model, the radius of the nickel particle r Ni for: Among them, k B is the Boltzmann constant, T is the temperature, γ is the surface energy; Ω is the diffusion volume element; δ S is the distance between Ni atoms; D S is the atomic surface diffusion coefficient; r Ni0 and r YSZ0 are the initial particle radii of Ni and YSZ respectively; ψ Ni and ψ YSZ are the volume fractions of Ni and YSZ in the anode, respectively; is the average coordination number of Ni and YSZ initial particles, β and λ are two model parameters.

9. The modeling method according to claim 6, characterized in that: In the carbon deposition poisoning model, r C is the carbon deposition rate: Among them, c C is the molar concentration of carbon; a is the catalyst activity; R C is the methane cracking rate; R B is the Boudouard reaction rate; the catalyst activity decay rate is: Among them, k a is the catalyst activity decay constant; The porosity change rate caused by carbon deposition in the anode is defined as: Where ε is the anode porosity; M C and ρ C is the molar mass and density of the deposited carbon; The permeability K is defined as: Where K0 and ε0 are the initial permeability and porosity of the anode.

10. The modeling method according to claim 6, characterized in that: In the chromium poisoning model, The Cr poisoning reaction equation is shown as follows: 2CrO2(OH) 2(g) +6e - →Cr2O 3(s) +2H2O+3O 2- The oxidation rate of Cr is shown in the formula: Among them, x i is the mole fraction of substance i; 0,D is the exchange current density of Cr oxidation; It is defined as the mole fraction of CrO2(OH)2 in the cathode electrode; is defined as the mole fraction of water vapor in the chromium source; F is defined as the Faraday constant; η ca is the cathode overpotential; T is defined as the temperature; and R is the universal gas constant.

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