Method for evaluating the performance degradation of a solid oxide electrolysis cell stack

Abstract

This application discloses a method for evaluating the performance degradation of solid oxide electrolytic cell stacks. The method includes: (1) constructing a structural degradation sub-model of the solid oxide electrolytic cell stack; (2) constructing an electrochemical sub-model; (3) coupling and integrating the structural degradation sub-model of the solid oxide electrolytic cell stack with the electrochemical sub-model through mesoscopic performance parameters to construct a multi-scale degradation model of the solid oxide electrolytic cell; (4) verifying the multi-scale degradation model of the solid oxide electrolytic cell; (5) analyzing the battery voltage degradation sensitivity in the solid oxide electrolytic cell to determine the main factors affecting the stack performance degradation rate; and (6) constructing a formula for the battery voltage degradation rate to monitor the stack operating status and performance degradation trend in real time. According to the technical solution of this application, an effective evaluation method for battery voltage degradation rate is established, which can monitor the stack performance degradation trend and operating status in real time.

Description

Technical Field

[0001] This application relates to the field of solid oxide electrolytic cells, and more specifically, to a method for evaluating the performance degradation of solid oxide electrolytic cell stacks. Background Technology

[0002] Solid oxide electrolyzers (SOECs) are high-temperature electrochemical devices with a structure similar to solid oxide fuel cells (SOFCs), both consisting of a hydrogen electrode, an oxygen electrode, and a dense ceramic electrolyte. SOECs utilize electrical energy to efficiently decompose water vapor or carbon dioxide into hydrogen or carbon monoxide, realizing the conversion and storage of electrical energy into chemical energy. They have broad application prospects in the fields of green hydrogen, syngas production, and renewable energy storage.

[0003] During the operation of SOEC systems, various chemical degradation phenomena occur at the microscopic level within the stack, resulting in a gradual increase in battery voltage at a constant current density. In recent years, domestic and international experts and scholars have conducted in-depth mechanistic elucidation and modeling of the chemical degradation phenomena in SOEC stacks. Research content covers nickel agglomeration in the hydrogen electrode, phase transition in the electrolyte, LSM coarsening in the oxygen electrode, formation of a high-resistivity phase at the oxygen electrode-electrolyte interface, and oxide scale formation on the interconnects. However, existing research lacks effective assessment methods for the long-term performance evolution of SOEC systems, making it difficult to monitor the stack's operating status and predict its service life under complex dynamic scenarios. Consequently, it cannot provide effective guidance for designing safety control strategies for SOEC systems focused on reliability and durability.

[0004] Therefore, how to provide a method for assessing the long-term performance degradation of solid oxide electrolyzers has become a technical problem that needs to be solved in this field. Summary of the Invention

[0005] In view of this, this application proposes a method for evaluating the performance degradation of solid oxide electrolytic cell stacks.

[0006] According to this application, a method for evaluating the performance degradation of a solid oxide electrolytic cell stack is proposed. The method includes the following steps: (1) constructing a structural degradation sub-model of the solid oxide electrolytic cell stack; (2) constructing an electrochemical sub-model; (3) coupling and integrating the structural degradation sub-model of the solid oxide electrolytic cell stack with the electrochemical sub-model through mesoscopic performance parameters to construct a multi-scale degradation model of the solid oxide electrolytic cell; (4) verifying the multi-scale degradation model of the solid oxide electrolytic cell; (5) analyzing the battery voltage degradation sensitivity in the solid oxide electrolytic cell to determine the main factors affecting the stack performance degradation rate; and (6) constructing a formula for the battery voltage degradation rate to monitor the stack operating status and performance degradation trend in real time.

[0007] Preferably, the construction of the solid oxide electrolytic cell stack structure degradation sub-model includes establishing a hydrogen electrode degradation sub-model, an electrolyte degradation sub-model, an oxygen electrode degradation sub-model, and a connector degradation sub-model on the Matlab / Simulink platform.

[0008] Preferably, the calculation formula for the hydrogen electrode degradation sub-model is as follows: in, Let be the radius (m) of the nickel particle. Let be the initial radius of the nickel particle. These are model parameters, where t is the running time. For integrated parameters.

[0009] Preferably, the calculation formula for the electrolyte degradation sub-model is as follows: in, It is the initial conductivity of yttrium-stabilized zirconium oxide. It is the fitting parameter for conductivity. is the time constant (h).

[0010] Preferably, the oxygen electrode degradation sub-model includes a high-resistivity phase model and an LSM coarsening model; The calculation formula for the high-resistivity phase model is as follows: in, The thickness of the zirconate nanoparticle layer, The weight gain (g) of zirconate nanoparticle layer growth 2 ·cm -4 ·h -1 ), This represents the weight fraction of the zirconate nanoparticle layer. The density of the zirconate nanoparticle layer (g·cm) -3 ), The activation energy for the growth of zirconate nanoparticle layers (J·mol⁻¹) -1 ), R The universal gas constant is 8.314 J·mol⁻¹. -1 ·K -1 ), T The stack temperature is K, and t is the operating time; The coarsening of the LSM is characterized by the change in effective TPB length, and the calculation formula of the LSM coarsening model is as follows: in, The initial TPB length of the oxygen electrode (m·m) -3), The length of the TPB at time t (m·m) of the oxygen electrode -3 ), LSM surface diffusion coefficient (cm) 2 ·s -1 ).

[0011] Preferably, the calculation formula for the connector degradation sub-model is as follows: in, The thickness (cm) of the oxide layer on the connector. The growth rate of oxide scale (cm) 2 ·h -1 ), The activation energy for oxide scale growth (J·mol) −1 ).

[0012] Preferably, the electrochemical sub-model includes a working voltage model, an electrode activation overpotential model, an ohmic overpotential model, and a concentration overpotential model.

[0013] Preferably, the calculation formula for the working voltage model is as follows: in, It is a reversible voltage. T The temperature of the fuel cell stack is K. F It is the Faraday constant (96485.33289 C / mol). The partial pressure of hydrogen gas within the flow channel, The partial pressure of oxygen within the flow channel; This refers to the partial pressure of water vapor within the flow channel.

[0014] Preferably, the calculation formula for the electrode activation overpotential model is as follows: in, This is the electrode activation overpotential. For current density, and These are the exchange current densities for the oxygen electrode and the hydrogen electrode, respectively.

[0015] Preferably, the calculation formula for the ohmic overpotential model is as follows: in, This is an ohmic overpotential. δ and σ These represent the thickness and conductivity of the structure or material, respectively. and This represents the ohmic resistance corresponding to different structural layers in a solid oxide electrolytic cell. and These are the ohmic resistances corresponding to the oxide scale of the connector and the high-resistivity phase at the oxygen electrode-electrolyte interface, respectively.

[0016] Preferably, the calculation formula for the concentration overpotential model is as follows: in, This is due to concentration overpotential. for Partial pressure at the three-phase interface of the hydrogen electrode for Partial pressure at the three-phase interface of the hydrogen electrode for The partial pressure at the three-phase interface of the oxygen electrode.

[0017] Preferably, the mesoscopic performance parameters in step (3) include effective TPB length, electrical conductivity, high-resistivity phase parameter, and effective gas diffusion coefficient.

[0018] Preferably, step (4) involves analyzing the sensitivity of battery voltage changes to stack temperature, current density, fuel utilization rate, and operating time in order to determine the main factors affecting battery voltage degradation rate.

[0019] Preferably, in step (5), a formula for the battery voltage degradation rate is constructed based on the main factors affecting the battery voltage degradation rate determined in step (4); the formula for the battery voltage degradation rate is to construct a functional relationship between the battery voltage degradation rate and the stack temperature and current density; the formula for calculating the battery voltage degradation rate is: in, Battery voltage degradation rate, For current density, It is a pre-factor. For the index, It is the apparent activation energy. R It is the gas constant. T It is the stack temperature (K).

[0020] The solid oxide electrolytic cell stack performance degradation assessment method in this application constructs a multi-scale degradation model by building a stack degradation sub-model, and determines the main factors affecting stack performance degradation based on the multi-scale model, thereby establishing an effective assessment method for battery voltage degradation rate, which can monitor the stack performance degradation trend and operating status in real time.

[0021] Other features and advantages of this application will be described in detail in the following detailed description section. Attached Figure Description

[0022] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application, and the illustrative embodiments and descriptions thereof are used to explain this application. In the drawings: Figure 1 This is a flowchart of the solid oxide electrolytic cell stack performance degradation assessment method according to this application.

[0023] Figure 2 This is a schematic diagram of the microstructure and degradation mechanism of the solid oxide electrolytic cell according to this application.

[0024] Figure 3 This is a graph showing the relationship between the thickness of LZO in the solid oxide electrolytic cell and the stack temperature and time, according to this application.

[0025] Figure 4 This is a schematic diagram illustrating the correlation between the oxide scale resistance and the stack temperature and operating time in a solid oxide electrolytic cell according to this application.

[0026] Figure 5 This is a schematic diagram of the multi-scale degradation model of the solid oxide electrolytic cell according to this application.

[0027] Figure 6 This is a model verification diagram for the mesoscopic performance parameters of the multi-scale degradation model of solid oxide electrolyzers in this application.

[0028] Figure 7 This is a model verification diagram of the macroscopic performance of the multi-scale degradation model of the solid oxide electrolytic cell according to this application.

[0029] Figure 8 This is a graph showing the evolution trend and degradation rate of the battery voltage at different stack temperatures according to this application.

[0030] Figure 9 This is based on the evolution trend and degradation rate of the battery voltage under different current densities in this application.

[0031] Figure 10 This is a graph showing the degradation evolution of the fuel cell stack's thermoelectric properties under different fuel utilization rates, based on the thermoelectric characteristics described in this application.

[0032] Figure 11 This is a surface plot of the degradation rate of the solid oxide electrolytic cell according to this application under different currents and stack temperatures. Detailed Implementation

[0033] The technical solution of this application will now be described in detail with reference to the accompanying drawings and embodiments.

[0034] like Figure 2As shown, a single SOEC in a solid oxide electrolyzer comprises a porous LSM-YSZ (LSM is (La,Sr)MnO3, YSZ is yttrium-stabilized zirconium oxide) oxygen electrode layer, a dense YSZ electrolyte, a porous Ni-YSZ hydrogen electrode functional layer, a porous Ni-YSZ hydrogen electrode support layer, and a Crofer22 APU metal interconnect. During operation, the stack structure undergoes inherent degradation, including Ni agglomeration in the hydrogen electrode, electrolyte phase transition, LSM phase coarsening in the oxygen electrode, high-resistivity phase formation at the oxygen electrode / electrolyte interface, and oxide scale formation in the interconnect. These degradations directly lead to changes in mesoscopic performance parameters, such as electrode and electrolyte conductivity, effective TPB length, and average hydrodynamic porosity radius of the electrodes. These parameter changes are ultimately reflected in the macroscopic evolution of the battery voltage.

[0035] The structural materials and parameters of the SOEC electrolyzer are shown in Table 1.

[0036] Table 1. Structural materials and parameters of SOEC electrolyzers According to this application, such as Figure 1 As shown, a method for evaluating the performance degradation of solid oxide electrolytic cell stacks is proposed. The method includes the following steps: (1) constructing a structural degradation sub-model of solid oxide electrolytic cell stacks; (2) constructing an electrochemical sub-model; (3) coupling and integrating the structural degradation sub-model of solid oxide electrolytic cell stacks with the electrochemical sub-model through mesoscopic performance parameters to construct a multi-scale degradation model of solid oxide electrolytic cells; (4) verifying the multi-scale degradation model of solid oxide electrolytic cells; (5) analyzing the battery voltage degradation sensitivity in solid oxide electrolytic cells to determine the main factors affecting the stack performance degradation rate; (6) constructing a formula for the battery voltage degradation rate to monitor the stack operating status and performance degradation trend in real time.

[0037] The solid oxide electrolyzer (SOE) stack performance degradation assessment method in this application constructs a structural degradation sub-model and an electrochemical sub-model for the SOE stack, respectively. Based on mesoscopic performance parameters, these two sub-models are coupled and integrated to construct a multi-scale degradation model, enabling the assessment of stack performance degradation at both microscopic and macroscopic levels. Furthermore, based on this multi-scale model, the main factors affecting stack performance degradation are identified, leading to an effective assessment method for battery voltage degradation rate. This allows for real-time monitoring of stack performance degradation trends and operating status, as well as optimization of the optimal operating strategy for the SOE electrolyzer system. In addition, by combining the steady-state optimal operating point of the SOE electrolyzer system, the degradation rate of the system under different operating power can be determined, and a degradation factor can be constructed to clarify the functional relationship between the actual hydrogen production power and its allocated power, thereby quantifying the actual hydrogen production rate of the system. Simultaneously, based on the multi-scale model and degradation resistance technical indicators, the service life of the system under different operating power can be determined, thus contributing to the development of the system's operating cost function.

[0038] Preferably, in step (1), the construction of the solid oxide electrolytic cell stack structure degradation sub-model includes establishing a hydrogen electrode degradation sub-model, an electrolyte degradation sub-model, an oxygen electrode degradation sub-model, and a connector degradation sub-model on the Matlab / Simulink platform.

[0039] At the hydrogen electrode, the nickel particles agglomerate, leading to an increase in their average size. The change in the average radius of the nickel particles over time is shown in formula (1): in, Let be the radius (m) of the Ni particle. Surface energy (J·m -2 ), For diffusion volume elements, Here is the interatomic spacing (m) of Ni. For Boltzmann constant (1.381 × 10⁻⁶) -23 J.K. -1 ), T The temperature of the fuel cell stack is K. The average coordination number of Ni and YSZ particles, and These represent the volume fractions of Ni particles and YSZ particles in the hydrogen electrode, respectively. and The initial radii of the Ni and YSZ particles are respectively. and Here are the model parameters, where This reflects the initial morphology of the hydrogen electrode, while Depends on , The atomic surface diffusion coefficient (m) related to the stack temperature 2 ·s -1 ), C is the integrated parameter.

[0040] Solving equation (1) yields the calculation formula for the hydrogen electrode degradation sub-model: in, Let be the radius (m) of the nickel particle. Let be the initial radius of the nickel particle. These are model parameters, where t is the running time. For integrated parameters.

[0041] The calculation formula of the hydrogen electrode degradation sub-model shows that... Gradually increasing the value will reduce the effective TPB length and conductivity, and increase the pore radius, thereby affecting the electrode activation overpotential, ohmic overpotential and concentration overpotential.

[0042] According to the first embodiment of this application, when the hydrogen electrode is a Ni-YSZ hydrogen electrode, the effective TPB length per unit volume is as shown in formula (3): in, This represents the contact perimeter (m) between Ni particles and YSZ particles. This indicates the number of Ni particles per unit volume. The coordination number between Ni particles and YSZ particles. This represents the contact angle (rad) between particles. Indicates the porosity of the composite electrode. This represents the average coordination number between Ni particles and YSZ particles; From formulas (3), (4), (5) and (6), the formula for calculating the effective TPB length per unit volume can be modified as shown in formula (7): According to the second embodiment of this application, the effective TPB length of the porous composite electrode is related to the permeability. Therefore, the effective TPB length of the porous composite electrode is as shown in formula (8): in, and These represent the hydrogen electrode. Particles and The probability that particles belong to the same permeation cluster.

[0043] and The formula for calculating probability is shown in formula (9): in, This indicates the coordination number between particles.

[0044] For nickel particles, The calculation formula is shown in formula (10): For YSZ, The calculation formula is shown in formula (11): According to formulas (9), (10) and (11), we can obtain The corresponding maximum value is 0.587 μm, at which point the hydrogen electrode completely fails, and the time to reach this threshold is directly related to the stack temperature.

[0045] For porous composite electrodes, their conductivity is shown in formula (12): in, and These represent the volume fractions of electrode particles and electrolyte particles, respectively. and The effective conductivity of the electrode particles and electrolyte particles are respectively, as shown in formula (13): in, dense solid electrical conductivity (S·cm) -1 ), This represents the volume fraction threshold of the constituent particles in the composite material.

[0046] The conductivity of dense solids in Ni, YSZ, and LSM is related to the stack temperature. Specifically, the formulas for calculating the conductivity are shown in formulas (14), (15), and (16), respectively: It is directly related to the particle radius. Therefore, the volume fraction thresholds of Ni and YSZ particles in the hydrogen electrode are shown in formulas (17) and (18): Furthermore, the aggregation of Ni particles causes a change in the average hydraulic pore radius within the electrode, thereby affecting the transport of reactants in the porous electrode. Therefore, the average hydraulic pore radius is as shown in formula (19): in, The average hydraulic pore radius; Under reducing and high-temperature conditions, due to the diffusion of cations, the YSZ crystal structure will transform from a cubic phase to a tetragonal phase, and the shape of YSZ will change and bands will appear. The changes in YSZ will gradually reduce the ionic conductivity and increase the ohmic resistance.

[0047] Electrolyte degradation can be observed through changes in the conductivity of YSZ.

[0048] Preferably, the calculation formula for the electrolyte degradation sub-model is as follows: in, It is the initial conductivity of yttrium-stabilized zirconium oxide. It is the fitting parameter for conductivity. The time constant (h) is used to characterize the stability of the YSZ structure and is related to the dopant radius. Let be the dopant radius.

[0049] Oxygen electrode degradation is related to the formation of a high-resistivity phase at the oxygen electrode / electrolyte interface and the coarsening of the LSM grains in the LSM electrode of the oxygen electrode. Therefore, the oxygen electrode degradation sub-model includes a high-resistivity phase model and an LSM coarsening model. The high-resistivity phase at the oxygen electrode / electrolyte interface is mainly composed of zirconate nanoparticles La2Zr2O7 formed at the oxygen electrode / electrolyte interface. The high-resistivity phase model can be achieved using the thickness of the LZO layer. The dynamic equations vary with time; preferably, the calculation formula for the high-resistivity phase model is: in, The thickness of the zirconate nanoparticle layer, The weight gain (g) of zirconate nanoparticle layer growth 2 ·cm -4 ·h -1 ), This represents the weight fraction of the zirconate nanoparticle layer. The density of the zirconate nanoparticle layer (g·cm) -3 ), The activation energy for the growth of zirconate nanoparticle layers (J·mol⁻¹) -1 ), R The universal gas constant is 8.314 J·mol⁻¹. -1 ·K -1 ), T The stack temperature is K, and t is the operating time; Figure 3In this context, 'a' represents the correlation between the LZO layer thickness and the stack temperature and operating time, derived from... Figure 3 From 'a', we can know that The layer thickness increases with increasing stack temperature and operating time. Similarly, in other studies, it was found that the LSM oxygen electrode detached after 48 h of testing at 1073 K, and a layer with a thickness of 50–100 nm was observed at the oxygen electrode / electrolyte interface. Layers. Therefore, it is possible to use A layer thickness of 100 nm was used as the threshold for oxygen electrode detachment.

[0050] The relationship between the incubation time for oxygen electrode detachment (the incubation time mentioned above is the time from the start of system operation to oxygen electrode detachment) and the stack temperature is as follows: Figure 3 As shown in b in the figure. Theoretically, at a stack temperature of 1073 K, the incubation time for oxygen electrode detachment is 56.8 h, which is similar to the 48 h in the prior art (Chen, Kongfa. Failure mechanism of (La,Sr)MnO3 oxygen electrodes of solid oxide electrolysis cells. International Journal of Hydrogen Energy 36, no. 17 (2011): 10541-10549.). The above difference stems from (LSM) 0.75 Sr 0.25 ) 0.95 MnO3 / YSZ and LSM 0.8 Sr 0.2 The difference in surface diffusion constants between MnO3 and YSZ.

[0051] The electrical conductivity of the LZO layer is shown in formula (21): in, The electrical conductivity of the LZO layer (S·cm) -1 ), Pre-exponential factor (S·cm) -1 ), T The temperature of the fuel cell stack is K. The activation energy of LZO (J·mol⁻¹) −1 ), R This is the universal gas constant.

[0052] LSM-YSZ phase coarsening (LSM coarsening) refers to the bulk degradation of the LSM-YSZ oxygen electrode, mainly due to the coarsening of LSM phase particles. This is related to Mn... 2+The diffusion is directly related to the loss of active sites, i.e., the length of the TPB. This change increases the activation loss of the oxygen electrode and further increases the battery voltage. Therefore, the normalized TPB length is used to quantify the degradation degree of the LSM-YSZ oxygen electrode body, and its evolution with operating time is shown in formulas (22) and (23): The LSM coarsening is characterized by the change in effective TPB length, and the calculation formula of the LSM coarsening model described in formulas (22) and (23) is as follows: in, The initial TPB length of the oxygen electrode (m·m) -3 ), The length of the TPB at time t (m·m) of the oxygen electrode -3 ), LSM surface diffusion coefficient (cm) 2 ·s -1 ).

[0053] Based on the calculation formula of the LSM coarsening model, it can be inferred that when the operating time is as long as 70376 h, the effective TPB length of the oxygen electrode is theoretically close to 0, at which point it cannot provide reaction sites for electrochemical reactions.

[0054] In a high-temperature, oxygen-rich environment, chromium compounds at the interface between the connector and the oxygen electrode are oxidized, forming a layer of oxide scale (Cr2O3), which increases the contact resistance at the interface. Connector degradation can be represented by the oxide scale thickness. According to Wagner's oxidation theory, the calculation formula for the oxide scale thickness as a function of stack temperature and operating time—that is, the connector degradation sub-model—is as follows: in, The thickness (cm) of the oxide layer on the connector. The growth rate of oxide scale (cm) 2 ·h -1 ), The activation energy for oxide scale growth (J·mol) −1 ).

[0055] The electrical conductivity of the oxide scale is shown in formula (24): in, Pre-exponential factor (S·cm) −1 ), The activation energy of oxide scale (J·mol) −1 ).

[0056] Figure 4 This is a schematic diagram illustrating the correlation between the oxide scale resistance and the stack temperature and operating time in a solid oxide electrolytic cell. Figure 4 It is known that at a constant stack temperature, the areal resistivity (ASR) gradually increases with operating time. This is because, under constant stack temperature conditions, conductivity remains constant, while oxide thickness increases with operating time. Furthermore, as the stack temperature rises, both oxide thickness and conductivity increase, leading to a further increase in areal resistivity. Oxide scale areal resistivity It exhibits strong sensitivity to changes in stack temperature.

[0057] Preferably, the electrochemical sub-model includes a working voltage model, an electrode activation overpotential model, an ohmic overpotential model, and a concentration overpotential model.

[0058] Preferably, the calculation formula for the working voltage model is as follows: in, It is a reversible voltage. and These represent activation overpotential, ohmic overpotential, and concentration overpotential, respectively. T The temperature of the fuel cell stack is K. F It is the Faraday constant (96485.33289 C / mol). The partial pressure of hydrogen gas within the flow channel, The partial pressure of oxygen within the flow channel; This refers to the partial pressure of water vapor within the flow channel.

[0059] Electrode activation overpotential can be modeled using the Butler-Volmer equation. Preferably, the calculation formula for the electrode activation overpotential model is as follows: in, This is the electrode activation overpotential. For current density, and These are the exchange current densities for the oxygen electrode and the hydrogen electrode, respectively.

[0060] and It is proportional to the effective TPB length at the electrode / electrolyte interface; at the microscale, when the electrode TPB length Decreasing the TPB will lead to an increase in activation loss on a macroscopic scale. Therefore, the exchange current density can be calculated by adding the electrode normalized TPB length parameter to the original exchange current density calculation formula, based on the relationship between activation loss and TPB. Make corrections. and The formulas (26) and (27) are shown respectively: in, and These are the pre-exponential factors of the exchange current density on the hydrogen and oxygen electrodes, respectively. and These are the initial effective TPB lengths for the hydrogen electrode and the oxygen electrode, respectively. and These are the effective TPB lengths for the hydrogen electrode and the oxygen electrode, respectively.

[0061] The deterioration of the microstructure and the formation of high-resistivity phases at the interface ultimately lead to a decrease in the conductivity of the electrodes and electrolytes, as well as an increase in ohmic overpotential.

[0062] Preferably, for a four-layer SOEC, the calculation formula for the ohmic overpotential model is as follows: in, This is an ohmic overpotential. δ and σ These represent the thickness and conductivity of the structure or material, respectively. and This represents the ohmic resistance corresponding to different structural layers in a solid oxide electrolytic cell. and These are the ohmic resistances corresponding to the oxide scale of the connector and the high-resistivity phase at the oxygen electrode-electrolyte interface, respectively. and It has the characteristics of constant thickness and conductivity that changes with microstructure degradation. and Its electrical conductivity is constant, while its thickness varies with the deterioration of its microstructure.

[0063] Concentration overpotential is used to describe the reversible voltage compensation value caused by the diffusion loss of component partial voltage from the channel body to the electrode TPB. Preferably, the calculation formula of the concentration overpotential model is: in, This is due to concentration overpotential. for Partial pressure at the three-phase interface of the hydrogen electrode for Partial pressure at the three-phase interface of the hydrogen electrode for Partial pressure at the three-phase interface of the oxygen electrode and These are the heights of the air passage and the fuel passage, respectively. and The thicknesses of the hydrogen electrode and the oxygen electrode are respectively. gaseous substance Effective diffusion coefficient in porous electrodes.

[0064] It is determined by both binary diffusion and Knudsen diffusion, as shown in equation (31): in, Knudsen diffusion coefficient, and These represent the porosity and tortuosity of the electrode, respectively. and They are gaseous substances The molar mass and diffusion volume.

[0065] For concentration overpotential, Ni particle aggregation will lead to an increase in the average hydraulic pore radius of the porous electrode. The Knudsen diffusion coefficient changes (as shown in formula (19)). This also changes, directly affecting the transport of reactants within the porous electrode, leading to changes in concentration overpotential.

[0066] Preferably, the mesoscopic performance parameters in step (3) include effective TPB length, electrical conductivity, high-resistivity phase parameter, and effective gas diffusion coefficient.

[0067] On the Matlab / Simulink platform, by using the effective TPB length related to activation loss, the conductivity of electrodes and electrolytes related to ohmic loss, the high-resistivity phase parameter, and the effective gas diffusion coefficient related to concentration loss, the microstructure degradation (pile structure degradation sub-model) is correlated with the macroscopic performance (electrochemical sub-model), and a multi-scale degradation model of solid oxide electrolyzers is constructed, such as... Figure 5 As shown.

[0068] In step (4), the existing experimental data is compared with the simulation data of the multi-scale model of the solid oxide electrolyzer to verify the accuracy of the multi-scale model of the solid oxide electrolyzer.

[0069] According to the first embodiment of this application, specifically, existing experimental data of mesoscopic performance parameters are compared with simulation data of solid oxide electrolyzer stack structure degradation sub-model, including the TPB length of oxygen electrode related to LSM coarsening (LSM phase coarsening model), the average radius of nickel particles related to agglomeration (hydrogen electrode degradation sub-model), the YSZ electrolyte conductivity related to phase transition (electrolyte degradation sub-model), and the surface resistivity ASR of connector oxide layer related to oxidation (connector degradation sub-model).

[0070] The parameters in the degradation sub-model of the solid oxide electrolytic cell stack structure in this application are shown in Table 2: Table 2 Parameters of the Degradation Sub-model for Solid Oxide Electrolyte Stack Structure Note: It is the leading factor of the LZO index; This represents the average initial coordination number.

[0071] The experimental parameters and reaction conditions for verifying the nickel particle agglomeration (hydrogen electrode degenerate) model in this application are shown in Table 3.

[0072] Table 3 Experimental parameters and reaction conditions for validating the nickel particle agglomeration (hydrogen electrode degenerate) model. Figure 6 In the figure, 'a' represents the evolution of the normalized TPB length of the oxygen electrode. It can be seen that the prediction results of the LSM phase coarsening model of the oxygen electrode are in high agreement with the experimental data, with an average relative error of less than 1%. Figure 6 In the figure, b represents the evolution of the average radius of nickel agglomerates in the hydrogen electrode. It can be seen that the simulation results of the theoretical model (hydrogen electrode degradation sub-model) of Ni agglomeration in the hydrogen electrode are in good agreement with the experimental data, with an average relative error of less than 1%. Figure 6 In the figure, 'c' represents the evolution of electrolyte conductivity. It can be seen that after 1000 h of testing at 1000 ℃, the conductivity of the YSZ electrolyte decreased from 0.19 S·cm. -1 Gradually decreased to 0.10 S·cm -1 The simulation results are in good agreement with those of the electrolyte degradation sub-model under the same conditions, with an average relative error of less than 5.0%. Figure 6 In the figure, 'd' represents the evolution of the surface resistivity of the oxide layer. It can be seen that the ASR experimental data of the Crofer22APU interconnect tested at 800 °C for 5000 h are consistent with the evolution trend of the interconnect degradation sub-model simulation results, with an average relative error of less than 2.0%. In summary, the multi-scale degradation model of the solid oxide electrolytic cell in this application can predict the changes in mesoscopic performance parameters caused by microstructural degradation, and can provide theoretical support for accurately predicting various parts of voltage drop.

[0073] According to the second embodiment of this application, microscale degradation is ultimately reflected in the evolution of battery voltage at the macroscale through mesoscale performance parameters. Therefore, two sets of experimental data on battery voltage from Risø DTU are used to verify the reliability of the multiscale degradation model at the macroscopic level. These two experimental tests focus on the durability of SOEC at high and low current densities, respectively. Test data A is derived from a stack consisting of six single cells at -0.25 A·cm⁻¹. -2 50% H2O / 50% H2, 666 L·h -1 Fuel and 270 L·h -1 Test data were collected continuously for 830 hours under pure oxygen operating conditions. Test data B, however, was obtained from data collected at -1.5 A·cm. -2 50% H2O / 50% / H 2 24 L·h -1 Fuel flow rate and 20 L·h -1 Experimental data for a single cell were obtained over 700 hours under oxygen flow conditions. The test conditions used in the above two sets of experiments are detailed in Table 4.

[0074] Table 4 Experimental conditions for macroscopic performance verification Note: This represents the mole fraction of oxygen.

[0075] Simulations were performed using an integrated electrochemical degradation submodel, and the results were compared with corresponding experimental data. Figure 7 As shown, the predictions from the electrochemical degradation sub-model agree well with the experimental data. This is achieved at a current density of -0.25 A·cm⁻¹. -2 Under these conditions, the average relative error is less than 1.0%. And at -1.5 A·cm... -2 At current densities of approximately 2.0%, the average relative error is about 2.0%. These errors may stem from differences between the electrochemical degradation submodel and the experiment in terms of microstructure (pile structure) and composition parameters, but are still within acceptable limits.

[0076] According to the solid oxide electrolyzer stack structure degradation sub-model and electrochemical sub-model, the operating variables also affect the stack performance degradation. Preferably, step (4) is to analyze the sensitivity of battery voltage to stack temperature, current density, fuel utilization rate and operating time to determine the main factors affecting the battery voltage degradation rate. Among them, stack temperature, current density and fuel utilization rate are closely related to the thermoelectric characteristics of the solid oxide electrolyzer. Therefore, the battery performance evolution law is analyzed by observing the influence of the above key operating variables on the degradation behavior. The parameters corresponding to the degradation behavior include the average radius of Ni particles in the hydrogen electrode. Normalized TPB length of the electrode Conductivity of the hydrogen electrode ionic conductivity of electrolytes Thickness of LZO layer The surface resistivity of oxide scale and LZO layer and overpotential of electrodes Battery voltage and voltage degradation rate The voltage degradation rate under constant conditions is shown in formula (35): In the formula, and These are the battery voltages at the initial time and time t, respectively.

[0077] 1) Effect of Stack Temperature: The aggregation of Ni particles in the hydrogen electrode, the growth of the LZO layer at the interface between the oxygen electrode and the electrolyte, and the formation of chromium oxide at the interface between the connector and the oxygen electrode are all closely related to temperature. Therefore, by fixing other operating variables besides stack temperature, the evolution of stack degradation behavior at different temperatures was observed. It should be noted that this process only involves the stack structure degradation sub-model, and the simulation analysis is based solely on this sub-model. The operating conditions were set as follows: current density of -0.50 A·cm⁻¹. -2 The fuel composition was 90% H2O / 10% H2, the operating pressure was 1 bar, the fuel utilization rate was 0.6, the excess air ratio was 0.4, the stack temperature varied in the range of 973~1073 K, and the simulation operation time was 20000h. Figure 8 In the figure, 'a' and 'b' represent the changes in battery voltage and degradation rate under different stack temperatures. It can be seen that the higher the stack temperature, the faster the battery voltage increases or decreases, and the higher the degradation rate. For example, at 973 K, the average battery voltage degradation rate is 0.78% / kh; at 1023 K, it is 1.09% / kh; and at 1073 K, it is 1.56% / kh.

[0078] 2) Effect of current density: The operating conditions were set as follows: stack temperature 1023 K, current density -0.25 to -0.75 A·cm. -2 The values ​​vary between the values, while the remaining operating variables are the same as those in 1) regarding the effect of the stack temperature. Figure 9 The effect of different current densities on battery voltage degradation behavior is shown. It is evident that as the current density increases, the battery voltage degradation rate accelerates, and the stack efficiency decreases more rapidly. For example, at -0.25 A·cm⁻¹... -2 At that time, the average voltage decay rate was 0.73% / kh; at -0.50 A·cm -2The value is 1.12% / kh; at -0.75 A·cm -2 The value was 1.43% / kh. Under constant stack temperature and fuel utilization, the increase in electrode activation overpotential, ohmic overpotential, and concentration overpotential was the main reason for the increased voltage degradation rate. The exchange current density on the hydrogen electrode side did not change with the change in current density. In contrast, under constant air flow, the oxygen partial pressure increased due to the increase in current density, leading to an increase in the exchange current density at the oxygen electrode and thus an increase in electrode activation overpotential. Furthermore, the ohmic overpotential was linearly related to the current density, increasing with its increase. Additionally, the gas partial pressure at the TPB changed due to the increase in current density, thus also increasing the concentration overpotential. These effects accelerated the increase in cell voltage and degradation rate.

[0079] 3) Impact of fuel utilization rate: According to the electrochemical sub-model, factors affecting battery voltage also include and These factors not only affect the reversible voltage but also the concentration overpotential. However, under constant operating pressure, and The magnitude depends on the mole fraction of the reactants, which in turn is directly related to fuel utilization, as shown in formula (36): Therefore, we can examine this by changing the fuel utilization rate. and The impact on the performance degradation of the fuel cell stack. Operating conditions were set as follows: operating temperature 1023 K, current density -0.50 A·cm⁻¹. -2 Fuel utilization rate varied between 0.6 and 0.75, and the other operating variables were the same as in 1) and 2). Figure 10 The effects of different fuel utilization rates on the thermoelectric properties of the fuel cell stack (cell voltage and voltage decay rate) are demonstrated. It can be observed that the evolution trend and decay rate of the cell voltage are essentially the same. For example, in... When the value is 0.6, the average voltage decay rate is 1.12% / kh; When it is 0.65, it is 1.10% / kh; in When it is 0.7, it is 1.08% / kh; in At a value of 0.75, the efficiency is 1.04% / kh. Therefore, the impact of changes in fuel utilization rate is negligible in assessing stack performance degradation.

[0080] Therefore, the multi-scale degradation model of solid oxide electrolyzers in this application can predict the voltage loss caused by the degradation of stack performance under different conditions, providing a new approach for battery performance evaluation and remaining lifetime prediction.

[0081] Preferably, in step (6), a formula for the battery voltage degradation rate is constructed based on the main factors affecting the battery voltage degradation rate (pile temperature and current density) in step (5).

[0082] The voltage degradation rate varies under different operating conditions. Therefore, constructing a general model for battery voltage degradation rate can intuitively assess the performance degradation of the battery stack.

[0083] Voltage degradation rate The specific form is usually determined based on empirical knowledge. Among them, the exponential model is often used to describe the degradation rate with temperature. The dependency relationship. Therefore, this section uses the Arrhenius relation to establish the degradation rate. With temperature The exponential relationship between them, while assuming The battery voltage degradation rate is linearly related to the current density i. The formula for the battery voltage degradation rate is to establish a functional relationship between the battery voltage degradation rate and the stack temperature and current density. The formula for calculating the battery voltage degradation rate is as follows: in, Battery voltage degradation rate, For current density, It is a pre-factor. For the index, It is the apparent activation energy. R It is the gas constant. T It is the stack temperature (K). , , These are the fitting parameters.

[0084] To identify the parameters in the above formulas and ensure their accuracy, it is necessary to cover common operating conditions and conduct simulations based on a fuel cell stack degradation sub-model to obtain data on SOEC voltage degradation rates at different current densities and stack temperatures. Specific simulation conditions include current densities ranging from 0.10 to 0.90 A·cm⁻¹. -2 Within the range, at 0.10 A·cm -2 The temperature was selected at 50 K intervals within the range of 923–1173 K. Therefore, 54 simulations were required, with each simulation lasting 20,000 hours. Subsequently, a custom equation was fitted using the Matlab curve fitting toolbox, as shown below. Figure 11 As shown. Among them, In this case, the coefficient of determination The root mean square error is 0.9991. The value is 0.0336. This demonstrates that the fitted equation accurately describes the relationship between voltage degradation rate, current density, and operating temperature under different operating conditions.

[0085] The preferred embodiments of this application have been described in detail above. However, this application is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this application, various simple modifications can be made to the technical solution of this application, and these simple modifications all fall within the protection scope of this application.

[0086] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, this application will not describe the various possible combinations separately.

[0087] Furthermore, various different embodiments of this application can be combined in any way, as long as they do not violate the spirit of this application, they should also be regarded as the content disclosed by this invention.

Claims

1. A method for evaluating the performance degradation of a solid oxide electrolytic cell stack, characterized in that, The method includes the following steps: (1) Construct a sub-model of the degradation structure of the solid oxide electrolytic cell stack; (2) Construct an electrochemical sub-model; (3) The structural degradation sub-model of solid oxide electrolytic cell is coupled and integrated with the electrochemical sub-model through mesoscopic performance parameters to construct a multi-scale degradation model of solid oxide electrolytic cell; (4) Verify the multi-scale degradation model of the solid oxide electrolytic cell; (5) Analyze the battery voltage degradation sensitivity in solid oxide electrolyzers to determine the main factors affecting the performance degradation rate of the stack; (6) Construct a formula for the battery voltage degradation rate to monitor the stack operation status and performance degradation trend in real time.

2. The method for evaluating the performance degradation of a solid oxide electrolytic cell stack according to claim 1, characterized in that, The construction of the solid oxide electrolytic cell stack structure degradation sub-model includes establishing hydrogen electrode degradation sub-model, electrolyte degradation sub-model, oxygen electrode degradation sub-model and connector degradation sub-model on the Matlab / Simulink platform.

3. The method for evaluating the performance degradation of a solid oxide electrolytic cell stack according to claim 2, characterized in that, The calculation formula for the hydrogen electrode degradation sub-model is as follows: in, Let be the radius (m) of the nickel particle. Let be the initial radius of the nickel particle. These are model parameters, where t is the running time. For integrated parameters.

4. The method for evaluating the performance degradation of a solid oxide electrolytic cell stack according to claim 2, characterized in that, The calculation formula for the electrolyte degradation sub-model is as follows: in, It is the initial conductivity of yttrium-stabilized zirconium oxide. It is the fitting parameter for conductivity. is the time constant (h).

5. The method for evaluating the performance degradation of a solid oxide electrolytic cell stack according to claim 2, characterized in that, The oxygen electrode degradation sub-model includes a high-resistivity phase model and an LSM coarsening model; The calculation formula for the high-resistivity phase model is as follows: in, The thickness of the zirconate nanoparticle layer, The weight gain (g) of zirconate nanoparticle layer growth 2 ·cm -4 ·h -1 ), This represents the weight fraction of the zirconate nanoparticle layer. The density of the zirconate nanoparticle layer (g·cm) -3 ), The activation energy for the growth of zirconate nanoparticle layers (J·mol⁻¹) -1 ), R The universal gas constant is 8.314 J·mol⁻¹. -1 ·K -1 ), T The temperature of the fuel cell stack is K, and t is the operating time. LSM coarsening is characterized by changes in effective TPB length, and the calculation formula for the LSM coarsening model is as follows: in, The initial TPB length of the oxygen electrode (m·m) -3 ), The length of the TPB at time t (m·m) of the oxygen electrode -3 ), LSM surface diffusion coefficient (cm) 2 ·s -1 ).

6. The method for evaluating the performance degradation of a solid oxide electrolytic cell stack according to claim 2, characterized in that, The calculation formula for the connector degeneration sub-model is as follows: in, The thickness (cm) of the oxide layer on the connector. The growth rate of oxide scale (cm) 2 ·h -1 ), The activation energy for oxide scale growth (J·mol) −1 ).

7. The method for evaluating the performance degradation of a solid oxide electrolytic cell stack according to claim 1, characterized in that, The electrochemical sub-models include the working voltage model, the electrode activation overpotential model, the ohmic overpotential model, and the concentration overpotential model.

8. The method for evaluating the performance degradation of a solid oxide electrolytic cell stack according to claim 7, characterized in that, The calculation formula for the working voltage model is as follows: in, It is a reversible voltage. T The temperature of the fuel cell stack is K. F It is the Faraday constant (96485.33289 C / mol). The partial pressure of hydrogen gas within the flow channel, The partial pressure of oxygen within the flow channel; The partial pressure of water vapor within the flow channel; The calculation formula for the electrode activation overpotential model is as follows: in, This is the electrode activation overpotential. For current density, and These are the exchange current densities of the oxygen electrode and the hydrogen electrode, respectively. The calculation formula for the ohmic overpotential model is as follows: in, This is an ohmic overpotential. δ and σ These represent the thickness and conductivity of the structure or material, respectively. and This represents the ohmic resistance corresponding to different structural layers in a solid oxide electrolytic cell. and These are the ohmic resistances corresponding to the oxide scale of the connector and the high-resistivity phase at the oxygen electrode-electrolyte interface, respectively. The calculation formula for the concentration overpotential model is as follows: in, This is due to concentration overpotential. for Partial pressure at the three-phase interface of the hydrogen electrode for Partial pressure at the three-phase interface of the hydrogen electrode for The partial pressure at the three-phase interface of the oxygen electrode.

9. The method for evaluating the performance degradation of a solid oxide electrolytic cell stack according to claim 1, characterized in that, The mesoscopic performance parameters mentioned in step (3) include effective TPB length, electrical conductivity, high-resistivity phase parameters, and effective gas diffusion coefficient. Step (5) involves analyzing the sensitivity of battery voltage to stack temperature, current density, fuel utilization rate, and operating time in order to determine the main factors affecting battery voltage degradation rate.

10. The method for evaluating the performance degradation of a solid oxide electrolytic cell stack according to claim 1, characterized in that, In step (6), a formula for the battery voltage degradation rate is constructed based on the main factors affecting the battery voltage degradation rate in step (5); The formula for the battery voltage degradation rate is to establish a functional relationship between the battery voltage degradation rate and the stack temperature and current density. The formula for calculating the battery voltage degradation rate is as follows: in, Battery voltage degradation rate, For current density, It is a pre-factor. For the index, It is the apparent activation energy. R It is the gas constant. T It is the stack temperature (K).

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