Method and system for modeling transient response of a membrane electrode electrolyzer for electroreduction of carbon dioxide

Abstract

The application relates to the technical field of computer simulation, in particular to a membrane electrode electrolyzer transient response modeling method and system for electro-reducing carbon dioxide, which comprises the following steps: obtaining operation parameters and structure parameters of the membrane electrode electrolyzer; establishing a voltage balance equation based on the operation parameters and the structure parameters; establishing a mass conservation equation based on the structure parameters and preset reaction kinetics parameters; performing coupling operation on real-time output variables between a voltage sub-model and a carbon dioxide mass transfer sub-model to generate a coupling model; and performing joint solving on the coupling model according to a set dynamic input condition to obtain a transient response result of the membrane electrode electrolyzer. In this way, the technical problem of insufficient transient response prediction accuracy of the existing modeling technology when dealing with dynamic working conditions driven by fluctuating renewable power is solved, and the accuracy and reliability of performance evolution prediction of the electrolyzer under dynamic operation conditions are improved.

Description

Technical Field

[0001] This invention relates to the field of computer simulation technology, and in particular to a method and system for modeling the transient response of a membrane electrode electrolyzer for the electroreduction of carbon dioxide. Background Technology

[0002] With the continued advancement of global carbon neutrality goals, electrochemical carbon dioxide reduction reactions have become a key pathway for realizing the resource utilization of carbon dioxide and coupling it with the storage of intermittent renewable energy sources. This technology utilizes fluctuating renewable electricity from wind and solar power to drive the conversion of carbon dioxide into high-value-added chemicals such as carbon monoxide, formic acid, and ethylene, which is of significant strategic importance for closing the carbon cycle and mitigating energy fluctuations. To achieve industrial application, current density and energy efficiency need to be significantly improved. Membrane electrode assembly (MEA) electrolyzers, due to their zero-gap structure and direct supply of gaseous reactants, effectively overcome the mass transfer limitations of traditional liquid-phase electrolyzers and have become the current mainstream technology. To optimize the design parameters, operating strategies, and performance prediction of such electrolyzers, constructing accurate and reliable numerical models has become an indispensable research tool. By coupling multi-physics processes such as transport, reaction, and charge balance, these models reveal key internal states that are difficult to measure directly experimentally, such as local pH values, reactant concentrations, and product distributions.

[0003] In the field of numerical modeling for membrane electrode assembly (MEA) electrolyzers, existing technologies have established a certain foundation. Steady-state or multiphysics models are the most common, typically assuming constant operating conditions and using one-dimensional or two-dimensional methods to solve for the concentration field, potential field, and current distribution to predict steady-state performance indicators. For example, many studies have established two-dimensional steady-state models based on commercial software platforms such as COMSOL Multiphysics (COMSOL, an advanced numerical simulation software platform based on the finite element method, specifically designed for modeling, simulating, and analyzing multiphysics phenomena in the real world), successfully analyzing the influence of structural parameters on current efficiency. Furthermore, semi-empirical modeling methods, which construct simplified models by fitting experimental data, have also been applied in engineering pre-research. Currently, to address potential problems such as salt precipitation that may occur during the actual operation of electrolyzers, some studies are beginning to construct more complex multiphysics models to predict related mechanisms. Prior art document 1 (application publication number CN119760944A) discloses a multiphysics modeling method and apparatus for membrane electrode electrolyzers. It constructs a multiphysics numerical model including gas phase concentration field, liquid phase concentration field, potential field, and salting-out field by acquiring device parameters, thereby determining the potential and current density conditions for salting-out and suppressing salting-out by adjusting design parameters or input conditions. This method provides a valuable simulation tool for understanding and mitigating salting-out problems. However, this technical solution essentially still focuses on predicting and avoiding specific failure modes (such as salting-out) under steady-state or quasi-steady-state operating conditions; its model construction and solution primarily serve steady-state analysis.

[0004] While existing technologies have made progress in steady-state performance prediction, their limitations are becoming increasingly apparent in real-world dynamic operating scenarios combined with fluctuating renewable energy sources. Specifically, existing models are mostly based on steady-state assumptions, making it difficult to effectively capture the rapid and continuous changes in operating parameters such as current density, voltage, and material flow rate of the electrolyzer directly caused by fluctuations in wind and solar power. This dynamic input leads to transient processes such as drastic changes in local concentration gradients, pH fluctuations, and water management imbalances within the electrolyzer, resulting in problems such as decreased product selectivity, increased energy consumption, and deterioration of catalyst stability. However, existing technologies lack the ability to accurately describe the transient response of the system under such multivariate dynamic inputs. Even the few models that consider transient effects mostly only address single, specific disturbance scenarios such as "gas depletion," failing to systematically couple multidimensional dynamic inputs such as real-time current fluctuations and temperature changes, and generally neglecting rapid electrochemical kinetic processes occurring on the millisecond scale, such as double-layer charging and discharging. Similarly, the multiphysics models represented in Comparative Document 1, which focus on steady-state mechanism analysis, or the semi-empirical models aimed at simplifying calculations, are unable to accurately characterize and predict the rapid response characteristics such as current overshoot and undershoot that occur when the voltage or current of the electrolyzer changes abruptly under fluctuating power supply conditions, as well as the complex performance evolution paths resulting from these changes. These problems are interconnected, making it difficult for existing modeling techniques to accurately predict the rapid transient response and long-term performance evolution of membrane electrode assembly (MEA) electrolyzers under dynamic operating conditions driven by high renewable energy penetration. This hinders effective guidance for matching and optimizing the electrolyzer with fluctuating power supplies, formulating real-time control strategies, and assessing system lifetime, thus limiting the large-scale commercial application of carbon dioxide electroreduction technology. Therefore, existing modeling techniques for MEA electrolyzers suffer from insufficient transient response prediction accuracy and difficulty in supporting system optimization design and operational control when dealing with dynamic operating conditions driven by fluctuating renewable power supplies. Summary of the Invention

[0005] To address the aforementioned shortcomings or drawbacks, this invention provides a transient response modeling method and system for membrane electrode electrolyzers that electroreduces carbon dioxide. This method can solve the technical problem that existing modeling techniques have insufficient transient response prediction accuracy when dealing with dynamic operating conditions driven by fluctuating renewable power sources.

[0006] This invention provides a method for modeling the transient response of a membrane electrode electrolyzer for the electroreduction of carbon dioxide, comprising: Obtain the operating and structural parameters of the membrane electrode electrolyzer.

[0007] Based on the operating and structural parameters, a voltage balance equation including double-layer capacitance is established to construct a voltage sub-model. The voltage sub-model is configured to describe the relationship between the total voltage, electrode potential, total current, and ohmic resistance of the electrolytic cell.

[0008] Based on structural parameters and preset reaction kinetic parameters, mass conservation equations for gas and liquid phase carbon dioxide concentrations within the cathode catalyst layer are established to construct a carbon dioxide proton transfer model. This model is configured to describe the transport, consumption, and homogeneous reaction process of carbon dioxide from the flow channel to the catalyst surface.

[0009] A coupling operation is performed on the real-time output variables between the voltage sub-model and the carbon dioxide proton transfer model to generate a coupled model containing bidirectional data interaction relationships.

[0010] Based on the bidirectional data interaction relationship, the coupled model is jointly solved according to the set dynamic input conditions to obtain the transient response results of the membrane electrode electrolyzer. The transient response results include the output voltage waveform and the selectivity of the output products.

[0011] According to a second aspect, this invention provides a transient response modeling system for a membrane electrode electrolyzer for the electroreduction of carbon dioxide, comprising: The parameter acquisition module is used to acquire the operating parameters and structural parameters of the membrane electrode electrolyzer.

[0012] The voltage balance equation establishment module is used to establish voltage balance equations including double-layer capacitance based on operating parameters and structural parameters, so as to construct a voltage sub-model. The voltage sub-model is configured to describe the relationship between the total voltage, electrode potential, total current and ohmic resistance of the electrolytic cell.

[0013] The mass conservation equation establishment module is used to establish mass conservation equations for the gas and liquid phase carbon dioxide concentrations within the cathode catalyst layer based on structural parameters and preset reaction kinetic parameters, in order to construct a carbon dioxide proton transfer model. The carbon dioxide proton transfer model is configured to describe the transport, consumption, and homogeneous reaction process of carbon dioxide from the flow channel to the catalyst surface.

[0014] The model coupling module is used to perform coupling operations on the real-time output variables between the voltage sub-model and the carbon dioxide proton transfer model, generating a coupled model that includes bidirectional data interaction relationships.

[0015] The transient response result generation module is used to perform joint solution on the coupled model based on the bidirectional data interaction relationship and the set dynamic input conditions to obtain the transient response results of the membrane electrode electrolyzer. The transient response results include the output voltage waveform and the selectivity of the output products.

[0016] According to a third aspect, the present invention provides a computer device comprising: At least one processor; and a memory communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform any of the transient response modeling methods for electroreduced carbon dioxide membrane electrode electrolyzers in the embodiments of the present invention.

[0017] According to another aspect of the present invention, a non-transient computer-readable storage medium storing computer instructions is provided, wherein the computer instructions are used to cause a computer to execute a transient response modeling method for a membrane electrode electrolyzer for electroreduction of carbon dioxide according to any embodiment of the present invention.

[0018] The present invention provides a transient response modeling method for membrane electrode electrolyzers (MEEs) of electroreduced carbon dioxide. This method is achieved through five core steps: parameter acquisition, voltage sub-model construction, proton transfer model construction, model coupling, and joint solution. Specifically, the operating and structural parameters of the MEEs are acquired to provide basic input for model construction. A voltage balance equation, including double-layer capacitance, is established based on the operating and structural parameters to construct a voltage sub-model, describing the dynamic relationship between voltage, current, and resistance in the electrolyzer. A mass conservation equation for the concentrations of gaseous and liquid carbon dioxide within the cathode catalyst layer is established based on the structural parameters and preset reaction kinetic parameters to construct a carbon dioxide proton transfer model, describing the dynamic processes of carbon dioxide transport, consumption, and reaction. A coupling operation is performed on the real-time output variables between the two sub-models to generate a coupled model containing bidirectional data interaction, enabling dynamic correlation between the electrochemical and mass transfer processes. Based on this bidirectional data interaction, the coupled model is jointly solved according to set dynamic input conditions, ultimately obtaining transient response results including output voltage waveforms and product selectivity.

[0019] In this technical solution, the present invention addresses the technical problem described in the background art that existing models are mostly based on steady-state assumptions and cannot effectively capture the rapid changes caused by fluctuations in renewable energy power. By constructing a voltage sub-model that includes the dynamic effect of double-layer capacitance and a mass conservation equation describing transient concentration changes, the present invention achieves a refined description of the electrical dynamics and mass transport dynamics of the electrolyzer, respectively. This lays the model foundation for simulating rapid transient processes and overcomes the fundamental defect of existing steady-state models in being unable to characterize dynamic behavior. Addressing the problem described in the background art that existing technologies lack the ability to accurately describe the transient response of systems under multivariable dynamic inputs and have insufficient coupling mechanisms between models, the present invention establishes a bidirectional data interaction relationship between the voltage sub-model and the carbon dioxide proton transfer sub-model. During joint solving, the states of both models are updated synchronously based on this relationship, realizing a closed-loop iteration of current-driven mass transfer and concentration feedback to correct voltage. This accurately simulates the complex evolution path of internal states caused by sudden changes in voltage and current under fluctuating power supply, solving the shortcomings of existing models being isolated and unable to predict strongly coupled transient effects. Therefore, the technical solution of the present invention solves the technical problem of insufficient transient response prediction accuracy of existing modeling techniques when dealing with dynamic operating conditions driven by fluctuating renewable power sources by constructing a dynamic sub-model and establishing its bidirectional coupling solution mechanism, thereby improving the accuracy and reliability of predicting the performance evolution of electrolyzers under dynamic operating conditions. Attached Figure Description

[0020] Figure 1 This is a flowchart of a transient response modeling method for a membrane electrode electrolyzer for the electroreduction of carbon dioxide according to an embodiment of the present invention; Figure 2 This refers to another embodiment of the present invention. A schematic diagram of the logical relationship in a semi-empirical model of an electroreduction electrolyzer; Figure 3 This diagram illustrates the relationship between the internal dynamic parameters of the electrolytic cell and the external operating conditions, obtained based on the modeling method described in this invention. Figure 4 This diagram shows the steady-state prediction performance verification of the modeling method described in this invention. Figures 5-8 This is a simulation result verification diagram of the modeling method described in this invention when simulating fluctuating power source input; Figure 9 This is a schematic diagram of the transient response modeling system for a membrane electrode electrolyzer for the electroreduction of carbon dioxide according to an embodiment of the present invention; Figure 10 This is a block diagram of a computer device for implementing embodiments of the present invention. Detailed Implementation

[0021] The following description, in conjunction with the accompanying drawings, illustrates exemplary embodiments of the present invention, including various details to aid understanding. These details should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope of the invention. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0022] During the development of this invention, the inventors, through extensive experiments and data analysis, revealed the inherent relationship between the significant timescale differences and strong coupling contradictions between the electrical response (milliseconds to seconds) and the internal mass transport and reaction response (several seconds to tens of seconds) of an electrolyzer driven by fluctuating power supply: rapid voltage / current fluctuations drastically alter the kinetic state of the reaction interface, while slowly changing reactant concentrations and local pH values ​​significantly influence electrode potential and reaction rate. These two factors mutually constrain each other, and traditional single-timescale models cannot reconcile and describe this contradiction. Based on this contradictory relationship, the inventors innovatively proposed this technical solution. Utilizing a voltage sub-model describing electrical dynamics and a carbon dioxide proton transfer model describing mass transfer reaction dynamics, a real-time, bidirectional data interaction channel is established between the two. Combined with joint numerical solutions of the coupled models based on dynamic input conditions, this achieves accurate simulation of the entire dynamic response from millisecond-level electrical transients to second-level mass transport within a unified framework, embodying the core concept of "decoupling modeling, coupled solution, and coordinating multi-timescale dynamics."

[0023] Specifically, the invention team discovered through comparative experiments that traditional numerical modeling methods based on steady-state assumptions have technical defects such as inability to characterize dynamic processes and large prediction deviations: when simulating the fluctuating current output of renewable energy (such as wind power and photovoltaics), the predicted voltage waveform is smooth and the product selectivity is constant, which is seriously inconsistent with the violent oscillations and sudden drop in selectivity measured in experiments. The transient response modeling method for membrane electrode electrolyzers for the electroreduction of carbon dioxide proposed in this invention can improve the accuracy of performance prediction under dynamic operating conditions. By constructing a voltage balance equation including double-layer capacitance as a voltage sub-model, high-fidelity simulation of rapid electrical transients such as current step, fluctuation-induced electrode potential overshoot, and relaxation can be achieved. By constructing a mass conservation equation for gaseous and liquid carbon dioxide concentrations in the cathode catalyst layer as a proton transfer model, accurate tracking of slow processes such as reactant consumption and local concentration redistribution can be ensured. By coupling the two sub-models and performing joint solution, based on real-time interactive current, concentration, and pH data, a complete characterization of the complex closed-loop dynamic process of "electrical disturbance-mass transfer hysteresis-feedback influence" can be achieved, accurately predicting output voltage distortion and product selectivity evolution under fluctuating input.

[0024] Therefore, the present invention provides a transient response modeling method for a membrane electrode electrolyzer for the electroreduction of carbon dioxide, which can be applied to renewable energy-driven processes. The Electrolytic Reduction System Performance Simulation and Optimization System (hereinafter referred to as the "System") can run on industrial control computers, high-performance computing clusters, or cloud computing platforms via local standalone software or cloud computing services to perform dynamic performance prediction, operating parameter optimization, and control strategy verification of electrolytic cells under fluctuating power input. Specifically, this system can be deployed in various hardware environments, including but not limited to: personal computers, engineering workstations, industrial real-time servers, embedded controllers, and cloud server virtual machines. This flexible deployment architecture allows the system to meet the requirements of model accuracy and computational depth in the laboratory R&D stage, while also adapting to the requirements of real-time performance, reliability, and ease of integration in industrial settings.

[0025] like Figure 1 As shown, the method may include: Step S110: Obtain the operating parameters and structural parameters of the membrane electrode electrolyzer.

[0026] Among them, the operating parameters refer to the variable condition parameters of the membrane electrode electrolyzer during actual or simulated operation, including at least the applied current or voltage, the flow rate of the cathode gas inlet, and the temperature of the electrolyzer body; the structural parameters refer to the inherent physical dimensions and properties of the membrane electrode electrolyzer, including at least the cross-sectional area of ​​the membrane electrode, the ohmic resistance, and the porosity and thickness of the cathode catalyst layer.

[0027] Specifically, the system can acquire operating parameters in real time through measuring instruments (such as power supply, mass flow controller, and thermocouples) connected to the experimental electrolytic cell, and read structural parameters from a pre-set material database or design drawings. For example, the operating parameters acquired by the system may include: a current density of 200 mA per square centimeter (…). The cathode carbon dioxide inlet gas flow rate is 50 standard milliliters per minute. The electrolytic cell temperature is 25 degrees Celsius. The obtained structural parameters may include: the cross-sectional area of ​​the membrane electrode is 1.0 square centimeters ( ); The resistance is 0.5 ohms. The cathode catalyst layer has a porosity of 0.4 and a thickness of 20 micrometers.

[0028] Step S120: Based on the operating parameters and structural parameters, establish a voltage balance equation including double-layer capacitance to construct a voltage sub-model.

[0029] The voltage sub-model is configured to describe the relationship between the total voltage, electrode potential, total current, and ohmic resistance of the electrolytic cell. This relationship is defined by an algebraic equation based on Kirchhoff's voltage law and a differential equation containing dynamic terms of double-layer capacitance.

[0030] Specifically, the system can establish the voltage balance equation in the following way: First, based on Kirchhoff's voltage law, establish the first algebraic relationship between the total voltage of the electrolytic cell and the anode electrode potential, cathode electrode potential, total current, and ohmic resistance (corresponding to the following formula). Then, based on the preset cathode and anode double-layer capacitance values, second differential relationships describing the relationship between the cathode electrode potential change rate and the anode electrode potential change rate with the total current and the partial current density of each product are established (corresponding to the following formulas). and Finally, by combining the first algebraic relation with the second differential relation, the voltage balance equation is constructed.

[0031] For example, in the Simscape environment of MATLAB (a graphical environment for simulating and model-based design of multi-domain dynamic systems and embedded systems, enabling users to model, simulate and analyze coupled models of electrochemical systems), the system uses voltage source, resistor, capacitor and controlled current source modules in the electrical component library to build the equivalent circuit model corresponding to the voltage balance equation, thereby constructing the voltage sub-model.

[0032] Step S130: Based on the structural parameters and the preset reaction kinetic parameters, establish the mass conservation equations for the gas phase and liquid phase carbon dioxide concentrations in the cathode catalyst layer to construct a carbon dioxide proton transfer model.

[0033] The carbon dioxide proton transfer model is configured to describe the transport, consumption, and homogeneous reaction of carbon dioxide from the flow channel to the catalyst surface. This process is characterized by two transient mass conservation equations that describe the changes in gaseous and liquid-phase carbon dioxide concentrations over time (corresponding to the following formulas). and ).

[0034] Specifically, the system can be constructed through the following steps: First, based on the pore structure parameters of the cathode catalyst layer, a first mass conservation relationship is established for the change of gas phase carbon dioxide concentration over time. Its balance terms include the gas phase carbon dioxide flux entering the catalyst layer from the flow channel and the gas phase carbon dioxide flux transferred from the gas phase to the liquid phase. Then, based on the pore structure parameters and preset reaction kinetic parameters, a second mass conservation relationship is established for the change of liquid phase carbon dioxide concentration over time. Its balance terms include the carbon dioxide flux transferred from the gas phase to the liquid phase, the carbon dioxide flux consumed by the electrochemical reaction, and the carbon dioxide source term consumed by the homogeneous reaction.

[0035] For example, in the carbon dioxide proton transfer model, the gaseous carbon dioxide flux entering the catalyst layer from the flow channel is expressed by the formula... Calculate the gas phase mass transfer coefficient. The flow rate is 0.5 meters per second (m / s), and the concentration of gaseous carbon dioxide in the flow channel is... 40 moles per cubic meter ( ).

[0036] Step S140: Perform a coupling operation on the real-time output variables between the voltage sub-model and the carbon dioxide proton transfer model to generate a coupled model containing bidirectional data interaction relationships.

[0037] Among them, the real-time output variables refer to the total current and partial current density of each product calculated by the voltage sub-model within a solution time step, and the carbon dioxide concentration and local pH value in the cathode catalyst layer calculated by the carbon dioxide proton model; the two-way data interaction relationship refers to the closed-loop data flow in which the total current and partial current density are input as driving variables to the proton model, while the carbon dioxide concentration and local pH value are input as feedback variables to the voltage sub-model.

[0038] Specifically, the system can achieve coupling operations by establishing a data exchange channel between the two sub-models within each time step of the numerical solver: First, the total current and partial current density of the current step are read from the voltage sub-model and passed to the carbon dioxide proton model to update its internal reaction consumption flux calculation; then, the calculated and updated carbon dioxide concentration and local pH value are read from the carbon dioxide proton model and fed back to the voltage sub-model to dynamically correct its internal electrochemical reaction kinetic parameters and equilibrium potential.

[0039] For example, in Simulink (simulation and model design environment), the system encapsulates the voltage sub-model and the carbon dioxide proton transfer model into two independent modules, and uses "model reference" or S-function (system function) to realize the timed reading, writing and exchange of real-time output variables between the two modules, thereby forming a closed-loop iterative coupled model.

[0040] Step S150: Based on the bidirectional data interaction relationship, perform joint solution on the coupled model according to the set dynamic input conditions to obtain the transient response results of the membrane electrode electrolyzer.

[0041] The transient response results include the output voltage waveform and the selectivity of the output products. The output voltage waveform is the curve of the total voltage of the electrolyzer changing with time, and the product selectivity is characterized by the curve of the partial current density of each electrochemical reaction product changing with time.

[0042] Specifically, the system can load the system of differential-algebraic equations corresponding to the coupled model by calling a preset numerical solver, and perform transient solutions based on the set dynamic input conditions. The solution process includes: setting the simulation time series and initial state; updating the state of the two sub-models synchronously based on the bidirectional data interaction relationship at each internal solution step size; and iteratively calculating until the integral of the entire time series is completed.

[0043] For example, the system employs an implicit variable-step solver ode15s (a numerical integrator suitable for rigid differential equations), setting the initial time step to... Seconds, maximum time step is 0.1 seconds, relative tolerance and absolute tolerance are both 0.1 seconds. The dynamic input condition is set to an amplitude between 100 and 300. The waveform of the current density changes periodically with step changes. After the solution is completed, the system outputs the waveform of the total voltage fluctuation of the electrolyzer under the input current density, as well as the evolution curves of the partial current density of products such as carbon monoxide and formic acid, as the transient response results.

[0044] In other embodiments, such as Figure 2 What is being shown is This diagram illustrates the logical relationships of a semi-empirical model for an electroreduction electrolyzer. It visually represents the entire process from data preparation to model application in a workflow architecture. This architecture comprises multiple sequentially connected logical stages, each containing specific operational steps. Arrows indicate the flow direction of data and logic. In the diagram, the "data preparation" stage refers to the preparatory phase providing input data for model building and parameter determination, specifically including two parallel branches: "experimental data acquisition" and "parameter estimation." The "experimental data acquisition" branch obtains steady-state performance data through actual measurements, while the "parameter estimation" branch obtains physical transport parameters through theoretical calculations or literature reviews. The "model building" stage refers to the phase of constructing a mathematical model based on the prepared data. Its core is the parallel construction of the "voltage model" and the "..." model. "Transmission model". The "voltage model" corresponds to the voltage sub-model in the claims, and its construction involves the establishment and parameter determination of elements such as "voltage equations" and "active impedance"; The "transfer model" corresponds to the carbon dioxide proton transfer model in the claims, and its construction involves establishing mass transfer and reaction equations. The "decoupling and solution" stage refers to the process of coupling and numerically calculating the two constructed sub-models, achieving bidirectional data interaction and state updates between the two models through iterative calculations. The "verification and application" stage refers to the process of using the established complete model for real-world scenario testing and performance prediction, including dynamic response verification in a "wind and solar scenario".

[0045] Specifically, it can be combined with Figure 2The illustrated process demonstrates the complete implementation of this scheme. In the "Data Preparation" stage, the first step is "Experimental Data Acquisition," for example, controlling the membrane electrode electrolyzer at 50, 100, 150, 200, and 300 (…). The system operated at five constant current densities. After reaching steady state, the total voltage of the electrolyzer at each point was recorded, and the product composition was analyzed using gas chromatography to calculate the Faradaic efficiency of each product, thus obtaining a set of steady-state experimental data. Simultaneously, in the "Parameter Estimation" branch, the double-layer capacitance of the cathode and anode was estimated using cyclic voltammetry (CV), for example, yielding a cathode double-layer capacitance of 0.08 farads (F). The ohmic resistance was measured and fitted using electrochemical impedance spectroscopy (EIS), for example, finding to be 0.4 ohms. Physical parameters such as the Henry coefficient and gas-phase mass transfer coefficient of carbon dioxide were determined by consulting materials databases.

[0046] In the "model building" phase, based on the above data, two sub-models were constructed in parallel. For the "voltage model," its mathematical equations, namely the voltage balance equations, were first established based on Kirchhoff's voltage law and the dynamic equations of double-layer capacitance. Then, using the voltage and product distribution under different current densities in the steady-state experimental data, a nonlinear least squares fitting algorithm was used to solve for the key "kinetic and electrical parameters" in the equations. For example, the fitting yielded an exchange current density of 0.012 amperes per square meter (A / m²) for the carbon monoxide generation reaction. For the "… The "transfer model" establishes the mass conservation equations for carbon dioxide gas and liquid phases within the cathode catalyst layer. By utilizing estimated physical transport parameters (such as the gas-liquid phase mass transfer coefficient) and the material balance relationships implicit in steady-state experimental data, parameters such as the homogeneous reaction rate constant are determined.

[0047] In the "decoupling and solution" phase, the constructed "voltage model" and " The "transfer model" is coupled within the numerical solution environment. For example, in the MATLAB / Simulink platform, two models are encapsulated as interconnected subsystems. Dynamic input conditions are set, such as simulating a period of 5 minutes (min) with a current density between 100 and 300. The waveform fluctuates randomly between these values. The ode15s solver is called for transient solution; within each solution step, the current value output by the "voltage model" drives the... "Transfer model" updates concentration field, The concentration and pH value output by the "transfer model" are fed back to the "voltage model" to correct the electrode potential. This process is repeated iteratively until the simulation calculation for all time periods is completed.

[0048] Finally, in the "verification and application" phase, the transient response results predicted by the model (such as voltage fluctuation curves) are compared with the test data of actual electrolyzers under the same dynamic current input to verify the model's accuracy. Furthermore, the verified model can be applied to "wind and solar scenario" analysis. This involves inputting a current density curve obtained from real wind and solar power generation data, and using model simulation to predict key indicators such as hydrogen production selectivity fluctuations and average voltage efficiency of the electrolyzer under this fluctuating power source. This allows for the evaluation of the feasibility and control strategies for direct coupling operation with renewable energy sources. Figure 2 The systematic process shown completes the entire process from data to model and then to simulation application.

[0049] In other embodiments, such as Figure 3 The diagram shows the relationship between the internal dynamic parameters of the electrolyzer and the external operating conditions obtained based on the modeling method described in this invention. The diagram reveals the law of change of the internal environment (pH value) and electrode reaction kinetics (charge transfer resistance) of the electrolyzer with the total current density through model simulation results, providing an intuitive basis for understanding dynamic behavior and calibrating model parameters. Figure 3 It contains two side-by-side coordinate graphs: Figure Simulated curves showing the variation of average pH value of the cathode and anode catalyst layers with total current density are presented; Figure The experimentally measured scatter plots and model-fitted curves of the cathode charge transfer resistance as a function of total current density are presented. Charge transfer resistance is a key kinetic parameter describing the interfacial impedance of electrochemical reactions and is directly related to the electrode reaction rate.

[0050] Specifically, it can be combined with Figure 3 The results shown illustrate the process of obtaining reaction kinetic parameters and validating the model in this scheme. (See Figure...) In the diagram, the red curve represents the average pH value of the cathode catalyst layer, the blue curve represents the average pH value of the anode catalyst layer, and the horizontal axis represents the total current density applied to the electrolyzer, in units of... Simulation results show that as the total current density increases from 0 to approximately 100... The pH value of the cathode catalyst layer rapidly increased from an initial value of approximately 6 to above 14 and then entered a plateau region, which simulates the hydrogen evolution reaction at high current densities at the cathode. Reduction reactions consume protons (or generate) This process leads to localized strong alkalinity; simultaneously, the pH value of the anodic catalyst layer first decreases from approximately 14 to approximately 11, and then slowly rises again with increasing current density. This reflects the complex influence of anodic oxidation reactions (such as water oxidation) on local pH. These pH distributions calculated by the model are key inputs to the reaction equilibrium potential in the subsequent dynamically corrected voltage sub-model.

[0051] In the figure In the diagram, the scatter plots represent the cathode charge transfer resistance values ​​measured by electrochemical impedance spectroscopy (EIS) at different steady-state current densities, expressed in ohms square centimeters. The solid and broken lines represent the theoretical curves calculated based on the dynamic parameters fitted from steady-state experimental data using the modeling method of this invention. The figure clearly shows that the charge transfer resistance decreases significantly with increasing total current density, from approximately 20 ohms per square centimeter (at 50 ohms per square centimeter). (Time) dropped to about 2 (in 800) (Time). This trend aligns with the fundamental principles of Butler-Volmer kinetics, which dictate that higher overpotentials drive faster reaction rates, resulting in lower interfacial resistance.

[0052] For example, the system can utilize graphs In the total current density is The experimental value of charge transfer resistance measured at time (e.g., approximately) This is one of the objectives of the nonlinear fitting. Combining other experimentally measured data at this current density (such as total voltage and Faraday efficiency of each product), the system adjusts kinetic parameters such as exchange current density and charge transfer coefficient in the Butler-Volmer equation to minimize the error between the theoretical value of charge transfer resistance calculated by the model (i.e., the ordinate of the fitted curve at this point) and the experimentally measured value (i.e., the scatter plot). In this way, the values ​​of the charge transfer coefficient and other parameters related to the cathode reaction in the preset reaction kinetic parameters can be accurately calibrated. (Figure) The good agreement between the fitted curve and the experimental scatter points directly verifies the accuracy of the dynamic parameters determined by the method of this invention, as well as the predictive ability of the constructed model.

[0053] In other embodiments, such as Figure 4 This figure displays a verification graph of the steady-state prediction performance of the modeling method described in this invention. By comparing experimental measurement data with model simulation data, the graph intuitively verifies the accuracy of the constructed coupled model in predicting the relationship between the current density of different products and the total current density. The verification graph uses the total current density as the horizontal axis and the product current density as the vertical axis. The graph includes three groups of products (hydrogen gas, hydrogen gas, and so on). Carbon monoxide (CO) and methanol The experimental data scatter plots and corresponding simulated data curves are shown. The experimental data scatter plots are labeled "JH2_exp", "JCO_exp", and "JCH3OH_exp", and the simulated data curves are labeled "JH2_sim", "JCO_sim", and "JCH3OH_sim".

[0054] Specifically, it can be combined with Figure 4The results shown illustrate the prediction accuracy of the model constructed in this scheme. The horizontal axis represents the total current density (unit: ...). The range of values ​​for the product current density is from 0 to 1000, covering the typical operating range from low to high. The vertical axis represents the product current density (also in units of...). The range of variation is from 0 to 500. For hydrogen ( The experimental data scatter plot (JH2_exp) and the simulated curve (JH2_sim) show a high degree of agreement across the entire current density range, for example, at a total current density of 500. At that time, the experimentally measured partial current density was approximately 250. The model predictions are close to the actual values. For carbon monoxide (CO), the experimental data scatter plot (JCO_exp) and the simulated curve (JCO_sim) also show good agreement, for example, at a total current density of 800... At that time, both the experimental and simulated values ​​were close to 400. This indicates that the model accurately captures the current efficiency of the CO generation pathway. For methanol ( The experimental data scatter plot (JCH3OH_exp) and the simulated curve (JCH3OH_sim) also show a high degree of agreement, for example, when the total current density is between 200 and 600. Within the interval, the simulated curve closely passes through the experimental scatter plot.

[0055] For example, select a total current density of The operating conditions were analyzed. Figure 4 From the data, the experimental value of the hydrogen partial current density (JH2_exp) corresponding to this point can be read as approximately 100. The simulated value (JH2_sim) is approximately this value; the experimental value of the carbon monoxide partial current density (JCO_exp) is approximately 260. The simulated value (JCO_sim) almost coincides with it; the experimental value of the methanol partial current density (JCH3OH_exp) is approximately 40. The simulated value (JCH3OH_sim) is also around this range. The experimental and simulated values ​​of the current densities of the three product fractions all show good agreement, with relative errors within an acceptable engineering range (e.g., less than 10%). This result demonstrates that the coupled model constructed and calibrated using the method of this invention can accurately reproduce the product distribution characteristics of the membrane electrode electrolyzer under a wide range of steady-state operation and accurately predict the current distribution of each competing reaction pathway. This provides a solid foundation for verifying the reliability of the model in predicting the selective evolution of products under transient conditions.

[0056] In another embodiment, such as Figures 5-8The display shows a visualization interface for the transient response data of an electrolyzer generated based on a bidirectional coupled semi-empirical transient model. Figure 5 The total current variation curve, Figure 6 The curve showing the change in methanol partial current density. Figure 7 The curve of CO partial current density change Figure 8 This is the curve showing the variation of the partial current density of H2. In practical applications, the host computer control system periodically acquires the total current signal of the anode in the electrolyzer via an analog-to-digital converter and imports it into the transient model as a macroscopic electrical boundary condition. Simultaneously, based on the core algorithm embedded in the data processor, the model synchronously solves the dynamic equations for the charge-discharge of the double layer within the cathode catalyst layer and the CO2 proton transfer mass conservation equation. Through a bidirectional coupling mechanism, the model not only uses the total current to drive mass transport calculations but also provides real-time feedback of the calculated local CO2 concentration and pH value, dynamically correcting the reaction kinetic parameters in the voltage sub-model. Finally, the system outputs the evolution trend of the partial current density of each key product under dynamic operating conditions and, through a visualization module, intuitively presents the complex multi-dimensional electrical and chemical signals as curves, providing operators with visualized data support for evaluating the stability of the electrolyzer and product selectivity under fluctuating power supplies.

[0057] Therefore, according to the above implementation method, the system achieves its purpose through five core steps: parameter acquisition, voltage sub-model construction, proton transfer model construction, model coupling, and joint solution. Specifically, the system acquires the operating and structural parameters of the membrane electrode electrolyzer, providing the basic input for model construction; based on the operating and structural parameters, a voltage balance equation including double-layer capacitance is established to construct a voltage sub-model, which describes the dynamic relationship between voltage, current, and resistance in the electrolyzer; based on the structural parameters and preset reaction kinetic parameters, a mass conservation equation for the concentration of carbon dioxide in the gas and liquid phases within the cathode catalyst layer is established to construct a carbon dioxide proton transfer model, which describes the dynamic process of carbon dioxide transport, consumption, and reaction; a coupling operation is performed on the real-time output variables between the two sub-models to generate a coupled model containing bidirectional data interaction, used to realize the dynamic correlation between the electrochemical process and the mass transfer process; based on this bidirectional data interaction, the coupled model is jointly solved according to the set dynamic input conditions, ultimately obtaining transient response results including output voltage waveform and product selectivity.

[0058] Specifically, in the technical solution of this embodiment, addressing the technical problem mentioned in the background art that existing models are mostly based on steady-state assumptions and cannot effectively capture the rapid changes caused by fluctuations in renewable energy power, a voltage sub-model incorporating the dynamic effects of double-layer capacitance and a mass conservation equation describing transient concentration changes are constructed. This achieves a refined description of the electrical dynamics and mass transport dynamics of the electrolyzer, thus laying the model foundation for simulating rapid transient processes and overcoming the fundamental deficiency of existing steady-state models in being unable to characterize dynamic behavior. Addressing the problem mentioned in the background art of lacking the ability to accurately describe the transient response of a system under multivariable dynamic inputs and insufficient coupling mechanisms between models, a bidirectional data interaction relationship is established between the voltage sub-model and the carbon dioxide proton transfer sub-model. During joint solving, the states of both are updated synchronously based on this relationship, realizing a closed-loop iteration of current-driven mass transfer and concentration feedback to correct voltage. This accurately simulates the complex evolution path of internal states caused by sudden changes in voltage and current under fluctuating power supply, solving the shortcomings of existing models being isolated and unable to predict strongly coupled transient effects. Therefore, the technical solution of this embodiment solves the technical problem of insufficient transient response prediction accuracy of existing modeling techniques when dealing with dynamic operating conditions driven by fluctuating renewable power sources by constructing a dynamic sub-model and establishing its bidirectional coupling solution mechanism, thereby improving the accuracy and reliability of predicting the performance evolution of electrolyzers under dynamic operating conditions.

[0059] In some embodiments, operating parameters include the current or voltage applied to the membrane electrode electrolyzer, and structural parameters include the cross-sectional area and ohmic resistance of the membrane electrode electrolyzer; based on the operating parameters and structural parameters, a voltage balance equation incorporating the double-layer capacitance is established, including: Based on Kirchhoff's voltage law, the first voltage balance relationship is established among the total voltage of the electrolytic cell, the cathode electrode potential, the anode electrode potential, the total current, and the ohmic resistance.

[0060] The first voltage balance relationship is an algebraic equation that describes the total voltage across the electrolytic cell as equal to the anode electrode potential minus the cathode electrode potential, plus the voltage drop across the ohmic resistor caused by the total current.

[0061] Specifically, the system can, based on circuit principles, equate the membrane electrode electrolyzer to a series circuit containing an anode, a cathode, and an ohmic resistor, and write algebraic equations accordingly.

[0062] In some embodiments, the system can calculate a single [item] using the following formula (1). The total voltage applied across the electrolytic cell of the electroreduction membrane electrode : (1) Formula (1) is the expression for the total voltage of the electrolytic cell based on Kirchhoff's voltage law. This indicates the total voltage of the electrolytic cell, measured in volts (V). This represents the anode electrode potential relative to the standard hydrogen electrode, expressed in V. The cathode electrode potential is expressed in V relative to the standard hydrogen electrode; I represents the total current flowing through the electrolyzer in A. This represents the total ohmic resistance of the electrolytic cell, expressed in Ω. This formula establishes the relationship between the total voltage and electrode potential, current, and ohmic losses.

[0063] Next, in this embodiment, the system can also calculate the partial current density of the cathode-side generated product k using formula (2). : (2) Formula (2) is the concentration-dependent Tafel kinetic equation describing the cathodic electrochemical reaction (a mathematical model used to describe the relationship between electrode reaction rate and electrode overpotential). The current density representing the product k (such as carbon monoxide, ethylene) is expressed in A / m². This represents the normalized concentration of the oxidized state of a substance in the reaction, and is a dimensionless quantity. This represents the exchange current density corresponding to product k, in A / m². The charge transfer coefficient representing the cathode reaction is dimensionless; F is the Faraday constant, with a value of 96485 coulombs per mole (…). ); The kinetic overpotential of the reaction is expressed in V; R is the gas constant, with a value of 8.314 joules per mole per Kelvin (kJ / L). T represents absolute temperature, measured in Kelvin (K). This formula is used to calculate the current contribution of each reduction reaction path at the cathode.

[0064] Furthermore, in this embodiment, the system can also calculate the partial current density of the oxygen evolution reaction occurring on the anode side using formula (3). : (3) Formula (3) is the kinetic equation describing the anodic electrochemical reaction. Here, k specifically refers to the oxygen evolution reaction (which can be divided into different pH environments). and ). It represents the normalized concentration of the reduced substance (such as water) in the reaction, and is a dimensionless quantity; The charge transfer coefficient representing the anodic reaction is a dimensionless quantity. This represents the overpotential of the anodic reaction. Formulas (2) and (3) together form the basis for calculating the partial current density of all electrochemical reaction products.

[0065] Furthermore, in this embodiment, the system can also calculate the kinetic overpotential of the reaction using formula (4). : (4) Formula (4) defines the overpotential of an electrochemical reaction. The electrode potential representing the reaction occurs is taken as follows: for the cathodic reaction, take For the anodic reaction, take ; This represents the equilibrium potential of the reaction after condition correction, and is expressed in volts (V). Overpotential is the actual driving force propelling an electrochemical reaction.

[0066] In this embodiment, the system can also calculate the corrected reaction equilibrium potential using formula (5). : (5) Formula (5) is the form of the Nernst equation (a basic thermodynamic equation used to calculate the quantitative relationship between the equilibrium potential of the electrode reaction and the concentration and temperature of the reactants) that takes into account the influence of the local environment pH value. The standard equilibrium potential of reaction k is expressed in volts (V); pH represents the local acidity or alkalinity at the site of the reaction, and is a dimensionless quantity. This formula shows that the equilibrium potential undergoes a Nernst shift with changes in local pH, which is key to coupling the chemical environment with electrochemical dynamics.

[0067] In this embodiment, the system can also determine the local pH values ​​of the cathode and anode using formulas (6) and (7), respectively: (6) (7) Wherein, formula (6) is the average pH value within the cathode catalyst layer. With total current density The functional relationship G; Formula (7) is the average pH value in the anode catalyst layer. With total current density The functional relationship F. The total current density is expressed in A / m². Functions G and F can be obtained by establishing a one-dimensional steady-state model using finite element simulation software (such as COMSOL) to simulate ion distribution under different total current densities. Figure 3 As shown. This relationship links macroscopic operating conditions (total current) to the microscopic reaction environment (pH).

[0068] Furthermore, in this embodiment, the system can also establish the relationship between the total current density and the individual current densities and the charging dynamics of the double layer using formulas (8) and (9): (8) (9) Formula (8) describes the current balance on the cathode side. This represents the sum of the current densities of all cathode reactions; This represents the cathode electric double-layer capacitance, measured in F. Represents the cross-sectional area of ​​the membrane electrode, in m². The value represents the rate of change of the cathode electrode potential over time, expressed in V / s. Equation (9) describes the current balance on the anode side. and These represent the fractional current densities of the oxygen evolution reaction under acidic and alkaline conditions, respectively. This represents the anodic double-layer capacitance. These two formulas introduce a term for the rate of change of electrode potential, thus enabling the description of the transient process of current redistribution caused by the charging and discharging of the double layer.

[0069] In this embodiment, the system can also calculate the total ohmic resistance of the electrolytic cell using formula (10). : (10) Formula (10) converts the area ratio resistance into the total resistance. Resistivity per unit area, i.e., the resistance in ohms per unit area, is expressed in units of Ω. or This parameter was obtained by measuring the electrochemical impedance spectroscopy (EIS) of a laboratory-grade membrane electrode assembly electrolyzer with a cross-sectional area of ​​1 cm².

[0070] Furthermore, in this embodiment, the system can also determine the area ratio resistivity using formula (11). With total current density The changing functional relationship: (11) Formula (11) indicates that the area ratio resistivity is a function of the total current density f. This functional relationship is obtained by curve fitting of the ohmic resistance values ​​measured by EIS under different current densities, such as... Figure 3 As shown, this reflects the dynamic changes in ohmic resistance that may occur with operating conditions (such as temperature and wetting conditions).

[0071] Therefore, by combining the above formulas (1) to (11), the system can construct a complete voltage sub-model that includes the dynamic effects of double-layer capacitance. Specifically, in the total voltage of the electrolytic cell... Under certain conditions, the system combines equations (1), (8), and (9) and uses the cathode potential as the equation. Anode potential and total current I (or total current density) The variable to be solved is denoted as , and numerical methods such as Newton's iteration method are used to solve it. During the solution process, formulas (2) and (3) are used to calculate the current density of each component. This depends on the overpotential and equilibrium potential calculated by formulas (4) and (5), and the pH value in formula (5) is determined by formulas (6) and (7) based on the current total current density. Formulas (10) and (11) provide the calculation of ohmic resistance. This method enables dynamic, self-consistent calculation of the voltage, current, potential, and current distribution along each reaction path in the electrolytic cell.

[0072] Based on the preset cathode double layer capacitance and anode double layer capacitance, a second voltage balance relationship is constructed, which includes the total current, the rate of change of cathode electrode potential, the rate of change of anode electrode potential, and the partial current density of each electrochemical reaction product.

[0073] The second voltage balance relationship is an equation that includes a time differential term. It describes the relationship between the current flowing through the electrode double-layer capacitance and the rate of change of the electrode potential. This current is the difference between the total current and the sum of the partial current densities corresponding to each electrochemical reaction.

[0074] Specifically, the system can establish equations for the cathode and anode respectively: the charging current on the cathode double layer capacitor is equal to the total current minus the sum of the partial currents of all electrochemical reactions occurring at the cathode, and this charging current is also equal to the product of the cathode double layer capacitance value and the rate of change of the cathode electrode potential; the same applies to the anode.

[0075] For example, for the cathode, the relationship can be expressed as ,in This represents the preset cathode double-layer capacitance value, in F. The value represents the rate of change of the cathode electrode potential over time, expressed in volts per second (V / s); A represents the cross-sectional area of ​​the membrane electrode, expressed in square meters (m²). This represents the sum of the partial current densities of all cathode products (such as carbon monoxide and ethylene), expressed in A / m². If Given a current of 0.1 F, at a certain moment I is 0.2 amperes and A is 0.0001 m². If the value is 1500 A / m², then the current value can be calculated. It is 0.5V / s.

[0076] By combining the first voltage balance relationship with the second voltage balance relationship, a voltage balance equation can be constructed.

[0077] The voltage balance equation is a system of differential algebraic equations, which consists of the algebraic equation of the first voltage balance relationship and the differential equation of the second voltage balance relationship for the cathode and anode.

[0078] Specifically, the system will describe , , I Algebraic equations describing relations, and and The two differential equations are combined to form a complete system of equations used to solve for or simulate the dynamic behavior of voltage, current, and potential. For example, the final voltage balance equation system contains three equations: , .in, and These represent the partial current densities of each reaction at the cathode and anode, respectively.

[0079] Based on the cross-sectional area and ohmic resistance in the structural parameters, calculate the area ratio resistance in the voltage balance equation.

[0080] Among them, the area resistivity is a parameter that translates the overall ohmic resistance onto a unit area and is used to characterize the ohmic voltage drop in current density-based calculations.

[0081] Specifically, the system divides the ohmic resistance by the cross-sectional area to obtain the area ratio resistance.

[0082] For example, if the cross-sectional area A of the membrane electrode in the structural parameters is 1.0... (i.e., 0.0001m²), ohmic resistance It is 0.5 The calculated area ratio resistivity for In the voltage balance equation, the ohmic voltage drop term... This can be written as current density J (J=I / A and resistivity per square meter) The product form, i.e. ).

[0083] Therefore, according to the above implementation method, the system can gradually construct a complete voltage balance equation describing the dynamic relationship between voltage, current and potential in the membrane electrode electrolyzer based on clear physical laws (Kirchhoff's voltage law) and key component characteristics (electric double layer capacitance), thus laying a precise mathematical foundation for the subsequent construction of the voltage sub-model.

[0084] In some embodiments, the preset reaction kinetic parameters include the electrochemical reaction rate and the homogeneous reaction rate constant; based on the structural parameters and the preset reaction kinetic parameters, a mass conservation equation for the gas phase and liquid phase carbon dioxide concentrations within the cathode catalyst layer is established, including: Based on the pore structure parameters of the cathode catalyst layer, a first mass conservation relationship is established for the change of gas phase carbon dioxide concentration over time. This first mass conservation relationship characterizes the balance between the gas phase carbon dioxide flux entering the cathode catalyst layer from the flow channel and the gas phase carbon dioxide flux transferred from the gas phase to the liquid phase.

[0085] Among them, the pore structure parameters refer to the characteristic parameters describing the morphology of the porous medium in the cathode catalyst layer, including at least the gas phase volume fraction and the liquid phase volume fraction; the first mass conservation relationship is a differential equation that describes the rate of change of gas phase carbon dioxide concentration with time as equal to the net flux of gas phase carbon dioxide entering the catalyst layer per unit volume.

[0086] Specifically, the system can establish a transient mass balance equation for gaseous carbon dioxide within the controlled volume of the cathode catalyst layer based on the law of conservation of mass. The left side of the equation is the accumulation term caused by the change in gaseous carbon dioxide concentration, and the right side of the equation is the difference between the flux entering the channel and the flux transferred to the liquid phase.

[0087] For example, the first mass conservation relation can be expressed as: .in, This represents the gas phase volume fraction in the cathode catalyst layer, for example, a value of 0.6; The volume representing the cathode catalyst layer control volume, for example, for a cross-sectional area of m², thickness is The catalyst layer of rice has a volume of cubic meter; Represents the concentration of gaseous carbon dioxide, in units of ; This represents the cross-sectional area of ​​the membrane electrode, in m². This represents the gaseous carbon dioxide flux entering from the flow channel; This represents the contact area between the gas and liquid phases, expressed in m². This represents the gas phase carbon dioxide flux transferred from the gas phase to the liquid phase.

[0088] Based on the pore structure parameters of the cathode catalyst layer and the preset reaction kinetic parameters, a second mass conservation relationship is established for the change of liquid phase carbon dioxide concentration over time. The second mass conservation relationship characterizes the balance between the carbon dioxide flux transferred from the gas phase to the liquid phase, the carbon dioxide flux consumed by the electrochemical reaction, and the carbon dioxide source term consumed by the homogeneous reaction.

[0089] The second mass conservation relationship is a differential equation that describes the rate of change of liquid phase carbon dioxide concentration over time as equal to the net flux transferred from the gas phase per unit volume of the catalyst layer minus the flux consumed by the electrochemical reaction, and then minus the source term consumed by the homogeneous reaction.

[0090] Specifically, the system can establish a transient mass balance equation for liquid carbon dioxide within the controlled volume of the cathode catalyst layer. The left side of the equation is the accumulation term caused by the change in liquid carbon dioxide concentration, and the right side is the flux term transferred from the gas phase to the liquid phase, minus the flux term consumed by the electrochemical reaction, and then minus the source term consumed by the homogeneous reaction.

[0091] For example, the second mass conservation relation can be expressed as .in, This represents the liquid phase volume fraction in the cathode catalyst layer, for example, a value of 0.4; Represents the concentration of carbon dioxide in the liquid phase, in units of ; This represents the amount of carbon dioxide flux consumed due to electrochemical reactions; This represents the carbon dioxide source term consumed by the homogeneous reaction, expressed in moles per cubic meter per second. ).

[0092] Based on the preset gas phase mass transfer coefficient from the flow channel to the cathode catalyst layer and the gas phase carbon dioxide concentration in the flow channel, the gas phase carbon dioxide flux from the flow channel into the cathode catalyst layer is calculated.

[0093] Among them, the gas phase mass transfer coefficient from the flow channel to the cathode catalyst layer is a parameter describing the ease with which carbon dioxide is transferred from the flow channel bulk to the catalyst layer surface, and the gas phase carbon dioxide concentration in the flow channel is the uniform concentration of carbon dioxide in the flow channel bulk.

[0094] Specifically, the system can calculate this flux using the basic principles of convection-diffusion mass transfer. This flux is proportional to the difference between the gas-phase mass transfer coefficient, the concentration within the flow channel, and the gas-phase concentration at the catalyst layer surface.

[0095] For example, the gaseous carbon dioxide flux entering the cathode catalyst layer from the flow channel. It can be done through formula Calculation. Among them, This represents the preset gas-phase mass transfer coefficient, for example, a value of 0.5 m / s; This represents the concentration of gaseous carbon dioxide within the flow channel, for example, at 1 atmosphere and 25... Under these conditions, the concentration of pure carbon dioxide is approximately .

[0096] Based on the preset gas-liquid phase mass transfer coefficient from the gas phase to the liquid phase, the Henry's law coefficient of carbon dioxide, and the concentration of carbon dioxide in the liquid phase, the gas phase carbon dioxide flux transferred from the gas phase to the liquid phase is calculated.

[0097] Among them, the gas-liquid phase mass transfer coefficient from the gas phase to the liquid phase is a parameter describing the rate at which carbon dioxide is transferred across the gas-liquid interface, and the Henry coefficient of carbon dioxide is a thermodynamic constant describing the distribution equilibrium of carbon dioxide between the gas and liquid phases.

[0098] Specifically, the system can calculate this flux based on the two-film theory. This flux is proportional to the gas-liquid phase mass transfer coefficient and the difference between the liquid equilibrium concentration corresponding to the partial pressure of carbon dioxide in the gas phase and the actual liquid concentration. For example, the flux of carbon dioxide transferred from the gas phase to the liquid phase... It can be done through formula Calculation. Among them, This represents the preset gas-liquid phase mass transfer coefficient, for example, a value of [value missing]. m / s; The Henry coefficient, representing carbon dioxide, is 25. The time is approximately 0.034 moles per cubic meter per Pa ( ); This represents the partial pressure of carbon dioxide in the gas phase, and the unit is Pascal (Pa). This refers to the liquid phase carbon dioxide concentration calculated in real time.

[0099] The amount of carbon dioxide consumed by the electrochemical reaction is calculated based on the electrochemical reaction rate in the preset reaction kinetic parameters.

[0100] The electrochemical reaction rate is characterized by the partial current density of each product, and the carbon dioxide flux consumed by the electrochemical reaction refers to the amount of carbon dioxide consumed per unit electrode area per unit time due to all electrochemical reactions.

[0101] Specifically, the system can, according to Faraday's law, convert the partial current density corresponding to each electrochemical reaction, combined with the stoichiometric coefficient and electron transfer number of the reaction, into the flux of carbon dioxide consumed, and then sum over all products. For example, the flux of carbon dioxide consumed by the electrochemical reaction... It can be done through formula Calculation. Among them, This represents the stoichiometric coefficient of carbon dioxide consumed when the k-th product (such as carbon monoxide) is produced; for example, this coefficient is 1 when carbon monoxide is produced. The partial current density representing the generation of the k-th product is expressed in A / m². This represents the number of electrons transferred to form one molecule of the k-th product, for example, 2 for carbon monoxide; F is the Faraday constant, with a value of 96485 coulombs per mole. ).

[0102] Based on the homogeneous reaction rate constant and liquid-phase hydroxide ion concentration in the preset reaction kinetic parameters, the carbon dioxide source term consumed by the homogeneous reaction is calculated.

[0103] Among them, the homogeneous reaction rate constant is a kinetic parameter describing the speed of the reaction between carbon dioxide and hydroxide ions in the liquid phase. The carbon dioxide source term consumed by the homogeneous reaction refers to the amount of carbon dioxide consumed per unit volume of electrolyte liquid per unit time due to the homogeneous reaction.

[0104] Specifically, the system can calculate this source term based on the law of mass action in chemical reaction kinetics. This source term is proportional to the product of the homogeneous reaction rate constant, the liquid-phase carbon dioxide concentration, and the liquid-phase hydroxide ion concentration. For example, the source term for carbon dioxide consumed in the homogeneous reaction. It can be done through formula Calculation. Among them, Represents a pre-defined homogeneous reaction ( The forward reaction rate constant, for example, is a value of When using it, it needs to be converted to cubic meters per mole per second (m / s). ); The activity of carbon dioxide in the liquid phase can be approximated by its concentration. replace; The activity of hydroxide ions in the liquid phase can be approximated by concentration. replace.

[0105] Therefore, according to the above implementation method, the system can gradually construct a complete set of mass conservation equations describing the transient changes in the concentrations of carbon dioxide in the gas and liquid phases within the cathode catalyst layer based on the well-defined principles of mass transfer and reaction kinetics. This allows for a precise characterization of the entire process of carbon dioxide transport and consumption, providing a core mathematical foundation for constructing a high-fidelity carbon dioxide proton transfer model.

[0106] In some embodiments, the system can calculate the transient change in the gas phase carbon dioxide concentration within the cathode catalyst layer using the following formula (12): (12) Formula (12) is the mass conservation equation for gaseous carbon dioxide, which describes the accumulation rate of gaseous carbon dioxide in the control volume as equal to the difference between the inflow flux and the outflow flux. This represents the gas phase volume fraction in the cathode catalyst layer and is a dimensionless quantity (e.g., a value of 0.6). The volume of the cathode catalyst layer control body is represented by m³, which can be obtained by multiplying the cross-sectional area by the thickness. Represents the concentration of gaseous carbon dioxide on the catalyst surface, in units of ; The cross-sectional area of ​​the membrane electrode in the electrolytic cell is represented by m². This represents the gaseous carbon dioxide flux entering the catalyst layer from the cathode channel; This represents the gas-liquid two-phase contact area within the catalyst layer, expressed in m². This represents the gas phase carbon dioxide flux transferred from the gas phase to the liquid phase.

[0107] Next, in this embodiment, the system can also calculate the transient change in the concentration of liquid carbon dioxide in the cathode catalyst layer using formula (13): (13) Formula (13) is the mass conservation equation for liquid carbon dioxide, which describes the accumulation rate of liquid carbon dioxide in the control volume as equal to the flux transferred from the gas phase minus the flux consumed by the electrochemical reaction, and then minus the source term consumed by the homogeneous reaction. This represents the liquid volume fraction in the cathode catalyst layer and is a dimensionless quantity (e.g., a value of 0.4). This represents the concentration of carbon dioxide in the liquid phase participating in the reaction, in units of... ; This represents the amount of carbon dioxide flux consumed due to electrochemical reactions; This represents the carbon dioxide source term consumed by the homogeneous reaction, in units of... .

[0108] Furthermore, in this embodiment, the system can also calculate the gaseous carbon dioxide flux entering the catalyst layer from the cathode channel using formula (14). : (14) Formula (14) describes the convective-diffusion mass transfer process based on concentration difference. The total mass transfer coefficient of gaseous material from the bulk of the flow channel to the surface of the cathode catalyst layer is expressed in m / s. The concentration of gaseous carbon dioxide in the bulk of the cathode flow channel, in units of It can be calculated from the ideal gas law based on the partial pressure of the gas (e.g., at 1 atmosphere and 25°C, pure gas). Concentration is approximately ).

[0109] Furthermore, in this embodiment, the system can also calculate the total mass transfer coefficient using formula (18). : (18) Formula (18) models the total transmission process as three series resistances, whose reciprocals (resistances) are added together. The convective mass transfer coefficient representing the flow of carbon dioxide from the cathode serpentine channel bulk to the surface of the gas diffusion layer (GDL). The equivalent mass transfer coefficient representing the diffusion of carbon dioxide within the pores of the gas diffusion layer; It represents the equivalent mass transfer coefficient of carbon dioxide diffusion within the pores of the cathode catalyst layer.

[0110] In this embodiment, the system can also calculate the convection mass transfer coefficient of the flow channel using formula (19). : (19) Formula (19) is based on the convection-diffusion similarity criterion. θ represents the channel geometry correction factor, which is dimensionless; Sh represents the Sherwood number calculated based on the channel hydraulic diameter and gas properties, which is also dimensionless. This represents the diffusion coefficient of carbon dioxide in a gas mixture, expressed in square meters per second (m² / s). The hydraulic diameter of the serpentine flow channel is represented by meters (m).

[0111] In this embodiment, the system can also calculate the equivalent mass transfer coefficient of the gas diffusion layer using formula (20). : (20) Formula (20) uses the Bruggeman correlation (a semi-empirical formula widely used in porous media transport theory to estimate the relationship between the effective transport coefficient and porosity of fluids in porous structures) to correct the effective diffusion coefficient in porous media. The porosity of the gas diffusion layer is a dimensionless quantity. This represents the thickness of the gas diffusion layer, measured in meters (m).

[0112] In this embodiment, the system can also calculate the gaseous carbon dioxide flux transferred from the gas phase to the liquid phase using formula (15). : (15) Formula (15) describes the mass transfer process at the gas-liquid interface. This represents the mass transfer coefficient of carbon dioxide from the gas phase to the liquid phase, and its unit is m / s; The Henry's coefficient, representing carbon dioxide, is expressed in units of 1000 ppm. , is a function of temperature; This represents the partial pressure of gaseous carbon dioxide within the catalyst layer, expressed in Pa.

[0113] Furthermore, in this embodiment, the system can also calculate the gas-liquid mass transfer coefficient using formula (21). : ;(twenty one) Formula (21) is based on a particle mass transfer model under liquid film coverage. This represents the particle radius of the cathode catalyst layer, measured in meters (m), and can be obtained by averaging the values ​​measured using a transmission electron microscope (TEM). This represents the liquid phase saturation within the catalyst layer. It is a dimensionless quantity and can be obtained through finite element simulation.

[0114] In this embodiment, the system can also calculate the carbon dioxide flux consumed by the electrochemical reaction using formula (16). : (16) Formula (16) sums the consumption of each reaction pathway based on Faraday's law. The stoichiometric coefficient representing the carbon dioxide consumed when the k-th product (such as carbon monoxide) is generated is a dimensionless quantity (e.g., v=1 when CO is generated). The partial current density representing the generation of the k-th product is expressed in A / m². This represents the number of electrons transferred to form one molecule of the k-th product, and is a dimensionless quantity (e.g., n=2 when CO is formed).

[0115] In this embodiment, the system can also calculate the carbon dioxide source term consumed by the homogeneous reaction using formula (17). : (17) Formula (17) is based on the law of mass action in chemical reaction kinetics. This represents a reference concentration, used for dimensional consistency and numerical stability; the unit is... ; Representative reaction The forward reaction rate constant, in units of ; and These represent the activities of carbon dioxide and hydroxide ions in the liquid phase, respectively, and can be approximated by their concentrations.

[0116] Therefore, by combining the above formulas (12) to (17) and formulas (18) to (21), the system can construct a complete CO2 proton transfer model. This model uses the cathode catalyst layer as the control volume and, through the mass conservation equations (12) and (13) of the gas and liquid phases as its core, couples the mass transfer process (14) describing the entry of carbon dioxide into the catalyst layer from the flow channel, the mass transfer process across the gas-liquid interface (15), the electrochemical reaction consumption process (16), and the homogeneous liquid-phase reaction consumption process (17). Among these, the key mass transfer coefficient (…) The calculations are performed using detailed physical sub-models (18) to (21). This series of formulas together provide an accurate mathematical description of the entire dynamic process of carbon dioxide transport, phase change, and reaction consumption in the cathode region, providing a solid foundation for subsequent coupling with the voltage sub-model.

[0117] In some embodiments, the voltage sub-model is configured to output the total current and the partial current density of each product, and the carbon dioxide proton model is configured to output the carbon dioxide concentration and local pH value within the cathode catalyst layer; a coupling operation is performed on the real-time output variables between the voltage sub-model and the carbon dioxide proton model to generate a coupled model containing bidirectional data interaction relationships, including: At each solution time step, the total current and the partial current density of each product are obtained from the voltage sub-model and input as driving variables into the carbon dioxide proton transfer model.

[0118] Among them, the driving variables refer to the key parameters calculated by the voltage sub-model and used to drive or update the internal state of the carbon dioxide proton transfer model. The total current is the core variable that determines the overall rate of the electrochemical reaction, and the current density of each product is the direct input for calculating the carbon dioxide flux consumed by each electrochemical reaction.

[0119] Specifically, at each discrete time point (i.e., time step) during the transient solution process using the numerical solver, the system accesses the output port of the voltage sub-model and reads the calculated total current value and the corresponding partial current density values ​​for each reaction product (such as carbon monoxide, ethylene, and formic acid) at that moment. For example, at solution time t = 1.0 seconds, the system obtains the following output from the voltage sub-model: total current I = 0.2A, and partial current density of carbon monoxide... Partial current density of ethylene These values ​​will be passed as driving variables.

[0120] In the carbon dioxide proton transfer model, based on the total input current and the partial current density of each product, the flux of carbon dioxide consumed by the electrochemical reaction is updated, and the updated carbon dioxide concentration and local pH value in the cathode catalyst layer are obtained.

[0121] Among them, the calculation of the flux of carbon dioxide consumed by the electrochemical reaction is the key source term of the mass conservation equation in the carbon dioxide proton transfer model, and its value depends on the input current density of each component. The updated carbon dioxide concentration and local pH value in the cathode catalyst layer are the new states obtained by the carbon dioxide proton transfer model after solving the mass conservation equation and the charge conservation equation at this time step.

[0122] Specifically, the system substitutes the received partial current densities into a preset dynamic formula (such as a conversion formula based on Faraday's law). The system then recalculates the flux consumption. Using this updated flux value as a known condition, it numerically solves the mass conservation equations describing the changes in carbon dioxide concentrations in the gas and liquid phases, as well as the charge conservation relationship related to hydroxide ion concentrations. Finally, it calculates the new carbon dioxide concentration and pH distribution within the catalyst layer at the end of the current time step. For example, based on the input partial current density, the system calculates the current time step... Substituting this value into the differential equations of the carbon dioxide proton transfer model, and solving it using the Newton-Raphson method, yields the updated liquid-phase carbon dioxide concentration. The local pH value, pH=10.5, was calculated from the hydroxide ion concentration.

[0123] The updated carbon dioxide concentration and local pH value within the cathode catalyst layer are obtained from the carbon dioxide proton transfer model and input as feedback variables into the voltage sub-model.

[0124] Among them, the feedback variable refers to the key state quantity calculated by the carbon dioxide proton transfer model and used to correct the internal parameters of the voltage sub-model. The carbon dioxide concentration in the cathode catalyst layer directly affects the activity of electrochemical reactants, and the local pH value directly affects the equilibrium potential and kinetics of the electrochemical reaction.

[0125] Specifically, after the carbon dioxide proton transfer model completes the solution for the current time step, the system accesses its output port to read the calculated carbon dioxide concentration (e.g., the concentration at the catalyst surface) and the corresponding local pH value at a representative location within the cathode catalyst layer. For example, the feedback variable read by the system from the carbon dioxide proton transfer model is: pH=10.2. These values ​​will be passed as feedback variables.

[0126] In the voltage sub-model, the electrochemical reaction kinetic parameters and reaction equilibrium potential are dynamically corrected based on the input carbon dioxide concentration and local pH value within the cathode catalyst layer.

[0127] Dynamic correction refers to adjusting the calculation parameters within the voltage sub-model in real time based on feedback variables at each solution time step. Electrochemical reaction kinetic parameters include at least the pH-related exchange current density, and the reaction equilibrium potential is the thermodynamic equilibrium potential in the Nernst equation related to reactant concentration and pH.

[0128] Specifically, the system substitutes the received carbon dioxide concentration and local pH value into a preset parameter correction formula. For example, the carbon dioxide concentration is substituted into the Nernst equation to correct the equilibrium potential of the corresponding reaction. Substituting the local pH value into the kinetic formula corrects the exchange current density. Or the reaction rate constant. For example, for a reaction that produces carbon monoxide, its equilibrium potential... It can be corrected according to the Nernst equation as follows: ,in Related to carbon dioxide concentration. (If the reference potential...) The gas constant R = 8.314 Temperature T = 298 K, Faraday constant F = 96485 The calculated carbon dioxide activity partial pressure of carbon monoxide Atmospheric pressure (atm), then the corrected .

[0129] A real-time data exchange channel is established between the voltage sub-model and the carbon dioxide proton transfer model to form a closed-loop iterative coupled model.

[0130] In this context, a data exchange channel refers to a software interface or memory sharing mechanism that enables data reading, writing, and transfer between two independent models (or modules) at specific points in time within a simulation software or computing environment. A closed-loop iterative coupled model refers to a cyclical data flow formed through this channel, where the voltage model output drives the mass transfer model, and the mass transfer model outputs feedback to correct the voltage model. This process is repeated at each time step, resulting in a co-evolution of the model states as a whole model.

[0131] Specifically, in a simulation platform (such as MATLAB / Simulink), the system encapsulates the voltage sub-model and the carbon dioxide proton transfer model as two independent modules (e.g., using Simulink's "Model" block or S-function). By configuring the module's input and output ports and using the solver's "data storage read / write" or "global variable" functions, the aforementioned driving variable transfer, feedback variable transfer, and model state update operations are automatically executed within each time step determined by the solver. For example, in the Simulink environment, two "Model Reference" modules are used to encapsulate the two sub-models respectively, and a structured data format is defined using the "Simulink.Bus" object. The input and output ports of the two modules are connected via signal lines. The solver is set to ode15s, and in each internal step of the solution, data is automatically exchanged via signal lines, thus forming a coupled system model that is solved in a closed-loop time iteration.

[0132] Therefore, according to the above implementation method, the system can achieve real-time, bidirectional data interaction between two physical process sub-models by establishing a clear driving and feedback mechanism, and tightly couple electrochemical dynamics with mass transport dynamics, thereby constructing a closed-loop simulation model that can accurately simulate complex interactive effects under fluctuating conditions. This is the key to achieving high-precision transient response prediction.

[0133] In some embodiments, the dynamic input conditions include time-varying current density, cathode inlet gas flow rate, and electrolyzer temperature; based on the bidirectional data interaction relationship, the coupled model is jointly solved according to the set dynamic input conditions to obtain the transient response results of the membrane electrode electrolyzer, including: Set the current density input waveform, cathode inlet gas flow rate change curve, and temperature change curve that include a time series.

[0134] Here, the time series refers to discretizing the entire simulation period into a series of sequentially arranged time points; the current density input waveform is a function of current density changing with time; the cathode inlet gas flow rate curve is a function of gas volume flow rate entering the cathode changing with time; and the temperature change curve is a function of electrolytic cell operating temperature changing with time. These curves collectively define the dynamic changes in external operating conditions.

[0135] Specifically, the system allows users to define three time-dependent functions or data sequences via programming or a graphical interface. These functions describe the preset variations in current density, airflow rate, and temperature throughout the simulation duration. For example, to simulate photovoltaic power fluctuations, a simulation duration of 100 seconds can be set. The current density input waveform is defined as: 150 for 0-20 seconds. A jump to 300 in 20-40 seconds It linearly decreases to 200 in 40-60 seconds. Maintain 200 for 60-100 seconds. The cathode carbon dioxide inlet flow rate variation curve was set to a constant 50%. The temperature change curve of the electrolytic cell was set to start from... Start at 0.1 degrees Celsius per second ( The rate of increase is slow.

[0136] The preset numerical solver is invoked to perform transient solution on the coupled model based on the set current density input waveform, cathode inlet gas flow rate change curve and temperature change curve.

[0137] The preset numerical solver refers to a library of computational algorithms or software modules used to solve dynamic systems described by a system of differential-algebraic equations. Transient solution refers to the process of calculating the gradual evolution of system state variables (such as voltage and concentration) from the initial moment over time.

[0138] Specifically, after configuring the coupled model in a simulation environment (such as MATLAB / Simulink), the system selects and calls a suitable numerical integrator for solving rigid differential-algebraic equation systems, using the set dynamic input conditions as external inputs to the model, and initiates the numerical integration process from the initial time to the final time. For example, the system calls the ode15s solver in Simulink (a variable-order, variable-step numerical integrator suitable for rigid systems). The initial time is specified in the solver settings. seconds, end time Seconds, maximum step size MaxStep = 0.1 seconds, relative tolerance absolute tolerance Connect the defined current density, intake airflow rate, and temperature curves as outputs of the "From Workspace" or "Signal Builder" module to the corresponding input ports of the coupled model.

[0139] Within each solution time step, the state variables of the voltage sub-model and the carbon dioxide proton transfer model are updated synchronously based on the two-way data interaction relationship.

[0140] The solution time step is a discrete time interval that is adaptively determined by the numerical solver during integration or set by the user. State variables are the smallest set of variables describing the dynamic behavior of the system; for the voltage sub-model, this includes electrode potentials, and for the carbon dioxide proton transfer model, it includes gas and liquid phase carbon dioxide concentrations.

[0141] Specifically, at each internal calculation step of the solver (which may be smaller than the user-defined maximum step size), the system automatically performs data transfer and model updates based on the data exchange channels established in the coupled model. The specific process is as follows: First, based on the dynamic input and model state at the current time point, the solver calculates the output (total current, partial current density) of the voltage sub-model within this step size. Then, these output values ​​are immediately transmitted to the carbon dioxide proton model via the data channel as input to calculate the state changes of this sub-model. Next, the new state (carbon dioxide concentration, pH value) calculated by the carbon dioxide proton model is fed back to the voltage sub-model via the data channel for calculation correction within this step size or the next step size. For example, at the solver's internal step size of t=25.3 seconds, the input current density of the coupled model is 250... The solver first calls the voltage sub-model and calculates I = 0.25A. A / m². These values ​​are immediately passed to the carbon dioxide proton transfer model, which updates the reaction consumption flux accordingly and solves for the desired value. The pH value is 9.8. This pH value is fed back to the voltage sub-model to correct the reaction equilibrium potential in the next long calculation. This process is completed synchronously within this time step.

[0142] The coupled model is solved iteratively until the full-time simulation of the time series is completed.

[0143] Iterative execution refers to the numerical solver performing multiple internal iterative calculations at each time point according to a "prediction-correction" or similar algorithm to achieve convergence accuracy, and gradually advancing from one time point to the next until the entire set simulation time range is covered.

[0144] Specifically, the system drives the numerical solver from the initial time... Begin by calculating the next time point based on the current model state and input. The state. From arrive During the process, the solver may internally attempt multiple substeps and perform iterative calculations to meet tolerance requirements. Then, with Starting from, calculate This process repeats until the current time reaches or exceeds the set termination time. .

[0145] For example, the ode15s solver can be used to simulate a coupled model from 0 to 100 seconds. The solver starts at 0 seconds and adaptively selects the first step size based on the model's stiffness and rate of change. The first step is to calculate the state at 0.01 seconds. After that, the step size may be dynamically adjusted to 0.05 seconds, 0.1 seconds or smaller, and the state at time points of 0.02 seconds, 0.07 seconds, 0.12 seconds, etc. is calculated step by step. After thousands of iterative calculations with internal step sizes, the state calculation at the 100-second time point is finally completed, marking the end of the full-time simulation.

[0146] Record and output the total voltage waveform of the electrolyzer and the partial current density waveforms of each electrochemical reaction product throughout the entire solution time series of the coupled model as transient response results.

[0147] Among them, the total voltage waveform of the electrolytic cell is the total voltage of the electrolytic cell. Sequence data pairs changing with time t The curves formed in the coordinate system. The partial current density waveforms of each electrochemical reaction product are the partial current densities of each product (such as carbon monoxide, ethylene, and hydrogen). Sequence data pairs changing with time t The resulting sets of curves are key results for evaluating the performance evolution of the electrolyzer under dynamic input.

[0148] Specifically, during the solver's operation, at each successful output time point (determined by the solver step size or user-specified recording interval), the system records the current time, the total electrolyzer voltage value read from the coupled model, and the partial current density values ​​of each product read from the voltage sub-model to an array or data file. After the simulation is complete, the system outputs these data in the form of a numerical list or graphical curve. For example, after the simulation, the system outputs a MATLAB structure or a CSV (Comma-Separated Values) file. The file contains data columns such as "Time", "Total Voltage", "j_CO", "j_C2H4", and "j_H2". The time column ranges from 0 seconds to 100 seconds, with a data point approximately every 0.1 seconds (set by the output recording interval), totaling approximately 1000 rows. Based on this data, waveforms can be plotted showing the instantaneous voltage drop and subsequent relaxation of the total voltage at a current density step, as well as the fluctuations in the carbon monoxide partial current density. These waveforms represent the transient response results and can be directly used to analyze dynamic performance.

[0149] Therefore, according to the above implementation method, the system can drive a tightly coupled voltage-mass transfer model to perform high-fidelity transient numerical simulation by accepting dynamic input conditions that match the actual fluctuating power supply. Finally, it outputs key waveform data that can reveal the evolution law of voltage stability and product selectivity of the electrolyzer during dynamic operation, thereby providing quantitative basis for the dynamic characteristic analysis of the electrolyzer, the verification of control strategies, and the matching optimization with renewable energy.

[0150] In some embodiments, a preset numerical solver is invoked to perform transient solutions on the coupled model based on a set current density input waveform, cathode inlet gas flow rate variation curve, and temperature variation curve, including: Set the initial time step and the maximum time step for transient solutions.

[0151] The initial time step is the initial time interval used by the numerical solver to begin integration, while the maximum time step is the upper limit of the time interval allowed by the solver during adaptive propagation. Setting these two parameters helps to achieve a balance between computational efficiency and numerical stability.

[0152] Specifically, before invoking the numerical solver, the system specifies a suggested initial time step size and an upper limit for the time step size through a configuration interface or script command. For example, setting the initial time step. Set the maximum time step This means that the solver will start its calculations with a step size of 0.0001 seconds, and in subsequent calculations, no matter how slowly the model changes, the single-step time interval will not exceed 0.1 seconds.

[0153] Invoke the preset implicit variable step size solver and load the system of differential-algebraic equations of the coupled model.

[0154] Implicit variable-step solvers are a type of numerical algorithm that uses implicit integration and can dynamically adjust the calculation step size according to the rate of change of the solution. They are suitable for solving stiff differential-algebraic equation systems. Differential-algebraic equation systems refer to the collective mathematical form of coupled models, which simultaneously include differential equations describing the rate of change of state variables and algebraic equations describing the constraint relationships between variables.

[0155] Specifically, in the simulation environment, the system selects an implicit variable-step-size solver (such as a backward differential formula BDF-type algorithm) suitable for rigid systems from the available solver library, and loads a set of mathematical equations (differential and algebraic equations) obtained after compiling or transforming the coupled model into the solver, preparing it for solution. For example, in the MATLAB / Simulink environment, "ode15s" (a variable-order, variable-step-size solver based on numerical differential formulas) is selected from the solver list. The system compiles the Simulink block diagram or Model file representing the coupled model, generates a representation of the internal differential-algebraic equations that the solver can recognize and process, and completes the loading.

[0156] Set the relative and absolute tolerances for numerical solutions for the implicit variable step size solver.

[0157] The relative tolerance is a parameter that controls the solution accuracy, defined as the upper limit of the allowable ratio of the error estimate to the magnitude of the state variable; the absolute tolerance is another parameter that controls the solution accuracy, defined as the upper limit of the absolute value of the error estimate. Together, they determine the convergence criterion of the solver at each time step.

[0158] Specifically, the system specifies the values ​​for relative tolerance and absolute tolerance in the solver's parameter settings. Smaller tolerance values ​​generally mean higher computational accuracy, but may also increase computation time. For example, setting the relative tolerance... Set absolute tolerance This means that the solver controls the local truncation error in each iterative calculation step, ensuring that the ratio of the error to the state value is less than [a certain value]. or the absolute value of the error is less than .

[0159] Based on the current density input waveform, the cathode inlet gas flow rate change curve, and the temperature change curve, the initial state of the coupled model at the starting point of the solution time series is configured.

[0160] The initial state refers to the set of initial values ​​that all state variables (such as electrode potential and carbon dioxide concentration) must possess at the start time of the simulation (t=0). A correct initial state is a prerequisite for initiating the transient solution. Specifically, the system determines the dynamic input values ​​(current density, flow rate, temperature) at the simulation start time (t=0) based on user-defined or default rules. Using this as a basis, it calculates the initial values ​​of all state variables for the coupled voltage sub-model and carbon dioxide proton transfer model by solving a set of steady-state equations or by directly assigning a set of reasonable preset values. For example, at t=0, the current density input waveform is J=150mA / cm², the cathode inlet flow rate is 50sccm, and the temperature is 25°C. Using this as input and assuming an initial steady state, the system calculates the initial cathode potential. Initial anode potential Initial liquid phase carbon dioxide concentration This is used to configure the initial state of the entire coupled model.

[0161] The implicit variable-step solver is driven to start from the beginning of the time series solution and execute adaptive solution step size advancement based on the initial time step size, maximum time step size, relative tolerance, and absolute tolerance.

[0162] The adaptive solution step size advancement refers to the process by which the solver intelligently determines the step size for the next time step based on the rate of change of the current solution and the set accuracy tolerance. When the solution changes drastically, the step size is automatically reduced to ensure accuracy, and when the solution changes gradually, the step size is automatically increased to improve efficiency.

[0163] Specifically, the system initiates the solver's integration loop. Starting from the configured initial state, the solver first attempts to perform calculations using the set initial time step. Then, it compares the truncation error estimate obtained from each step with the relative and absolute tolerances. If the error meets the tolerance requirements, the result of that step is accepted, and the step size for the next step may be appropriately increased (not exceeding the maximum step size); if not, the result of that step is rejected, the step size is reduced, and the calculation is recalculated until the accuracy requirements are met or an error is reported due to an excessively small step size. For example, the solver starts from t=0 and first attempts to perform calculations using the set initial time step. The calculation step size is 0.0001 seconds. After successful calculation, because the solution changes gradually in the initial stage, the solver may automatically increase the step size to 0.001 seconds. When the simulation reaches a moment when the current density changes abruptly (e.g., t=20 seconds), the model state changes drastically, and the solver will automatically shrink the step size to a very small value (e.g., ...). The step size is set to 1 second to capture transient details, and then gradually increases as the system approaches a new "steady state".

[0164] At each internal solution step, the rate of change of state variables of the voltage sub-model and the carbon dioxide proton transfer model is monitored, and the iterative convergence process of the implicit variable step size solver is controlled based on the monitoring results.

[0165] Here, the rate of change of the state variable refers to the derivative of the state variable with respect to time (e.g., ...). Monitoring these rates of change helps the solver determine the system's rigidity and whether the current step size is appropriate. The iterative convergence process refers to the multiple prediction-correction calculation cycles performed by the solver within each step to obtain a solution that meets the required accuracy.

[0166] Specifically, within each step of the solver's attempts, it calls functions of the coupled model to calculate the derivatives of the state variables. If the derivatives are very large (indicating drastic changes), the solver determines that the current step size may be too large, and thus adopts a more stringent convergence strategy during iterative correction, or directly reduces the step size and retryes. This is a key mechanism for handling rigid systems and ensuring numerical stability. For example, at the instant of a current step change at t=20 seconds, when the solver tries a step size, it finds that the calculated rate of change of the cathode potential... The voltage suddenly reached the level of 105V / s, which is much higher than the level during the plateau phase. On the order of V / s. Based on this monitoring result, the solver will immediately reduce the trial step size and perform multiple correction iterations using Newton's method within this small step size to ensure that the obtained solution is on the order of V / s. and Only after the state values ​​precisely satisfy the system of differential-algebraic equations will the result of this step be accepted and the process continue.

[0167] In response to the implicit variable step size solver completing the integral calculation of the entire solution time series, a signal indicating that the transient solution is complete is generated.

[0168] The signal indicating the completion of the transient solution is a marker, message, or event that signifies the normal termination of the simulation process. It notifies the system or user that the numerical integration has successfully progressed from the initial time to the termination time, and that the states at all time points have been calculated.

[0169] Specifically, when the solver's internal clock reaches or exceeds the user-defined simulation termination time, and the final integration calculation is successfully completed, the solver will exit the main integration loop and return a success status code or trigger a completion event. The system can capture this signal and trigger subsequent result processing and output. For example, if the simulation termination time is set to 100 seconds, after the solver successfully calculates the system state at t=100 seconds, MATLAB's ode15s solver will exit normally and display "Simulation complete" in the command-line window. Simultaneously, the system can set an internal variable named "simulation_status" to "completed" or generate a completion message box as a signal that the transient solution is complete.

[0170] Therefore, according to the above implementation method, the system can drive the implicit variable step size solver to perform efficient and stable numerical integration of strongly coupled, multi-time-scale differential-algebraic equations by finely configuring solver parameters and monitoring the solution process, thereby reliably completing the transient solution task of the coupled model under the full dynamic input time series, and providing computational guarantee for obtaining accurate transient response results.

[0171] In some embodiments, the step of obtaining the preset reaction kinetic parameters includes: Experimental measurement data of the membrane electrode electrolyzer under multiple steady-state operating conditions were obtained. The experimental measurement data included the total voltage of the electrolyzer, the total current density, and the Faraday efficiency of each electrochemical reaction product.

[0172] Steady-state operating conditions refer to the state in which the electrolyzer operates for a sufficient time under constant current density, inlet gas flow rate, and temperature, and its output voltage and product distribution no longer change significantly. Multiple different steady-state operating conditions cover a representative range of current densities. Faraday efficiency is the ratio of the amount of charge actually transferred to produce a specific product to the total charge, used to calculate the partial current density of that product.

[0173] Specifically, the system can control the experimental platform to operate the electrolyzer sequentially at 5, 10, or more pre-set constant current densities. After each steady state is reached, the composition of the outlet gas is measured using online or offline analysis methods such as gas chromatography. Combined with the measured total current, the Faraday efficiency of each product (e.g., carbon monoxide, ethylene, hydrogen) is calculated, and the total voltage of the electrolyzer at that steady state is recorded. For example, the electrolyzer can be controlled at total current densities of 50, 100, 150, 200, and 300... Steady-state experiments were conducted under five conditions. The current density was 150... At that time, the total voltage of the electrolyzer was measured to be 2.9V, the Faraday efficiency of carbon monoxide was 85%, the Faraday efficiency of ethylene was 5%, and the Faraday efficiency of hydrogen was 10%. These data constitute a set of experimental measurements.

[0174] Based on experimental measurement data under multiple different steady-state operating conditions, the exchange current density and charge transfer coefficient corresponding to each electrochemical reaction were calculated using a fitting algorithm.

[0175] Here, the exchange current density is the reaction rate density of the electrochemical reaction at the equilibrium potential, and it is a key parameter in the Butler-Volmer kinetic equation. The charge transfer coefficient is a symmetry factor describing the influence of electrode potential on the activation energy of the reaction. A fitting algorithm is a mathematical optimization method that minimizes the error between the calculated model values ​​and the experimental measurements by adjusting the model parameters; for example, the least squares method.

[0176] Specifically, the system can utilize the Butler-Volmer equation for electrochemical reactions (corresponding to the formula above). and The partial current density of each product is expressed as a function of electrode overpotential, exchange current density, and charge transfer coefficient. Subsequently, the partial current density of each product and the corresponding electrode overpotential data obtained from experiments at different steady-state points are used as known inputs. A nonlinear least squares fitting algorithm is employed to fit the Butler-Volmer equations for multiple reactions (such as carbon monoxide formation, ethylene formation, and hydrogen evolution) to solve for the exchange current density and charge transfer coefficient of each reaction that minimizes the overall error between the model's predicted current and the experimental current.

[0177] For example, for the reaction that produces carbon monoxide, its Butler-Volmer equation is set to the following form: ; The data obtained from the five steady-state experimental data Substituting the η value, the exchange current density of the reaction is obtained through a fitting algorithm. Charge transfer coefficient .

[0178] Based on experimental measurement data under multiple different steady-state operating conditions, the reaction rate constant corresponding to the consumption of carbon dioxide in the homogeneous reaction was calculated by a fitting algorithm.

[0179] The rate constant corresponding to the consumption of carbon dioxide in a homogeneous reaction refers to the reaction between carbon dioxide and hydroxide ions in the liquid phase. kinetic rate constant This parameter is used to calculate the rate at which each side responds to carbon dioxide consumption.

[0180] Specifically, the system can deduce this parameter by combining the mass conservation relationship under steady-state conditions with pH estimation. Under steady-state conditions, the rate of change of liquid-phase carbon dioxide concentration is zero, and the accumulation term in the liquid-phase mass conservation equation of the proton transfer model is zero. By substituting the liquid-phase carbon dioxide consumption flux (current-dependent) calculated at different steady-state current densities, and the hydroxide ion concentration estimated based on steady-state pH and material balance, into this steady-state equation, a parameter related to... The system of equations is then solved using a fitting algorithm to find the optimal solution. Value. For example, at a current density of 200 The steady-state point is obtained by calculating the electrochemical consumption based on the current and Faraday efficiency. The net rate, and simultaneously estimated based on the steady-state pH value measured at that point (e.g., pH=10). Assuming the liquid phase is in this steady state... If the concentration is approximately constant, then the consumption rate should equal the formation rate. By fitting data from multiple such steady-state points, the homogeneous reaction rate constant can be obtained. .

[0181] The calculated exchange current density, charge transfer coefficient, and reaction rate constant are set as preset reaction kinetic parameters.

[0182] Among them, the preset reaction kinetic parameters refer to a set of values ​​that are pre-stored in the model parameter database or configuration file, and are used to initialize the corresponding parameter variables in the voltage sub-model and the carbon dioxide proton transfer model.

[0183] Specifically, after completing the parameter fitting calculation, the system will obtain... as well as The system writes these parameter values ​​to a parameter file in a specified format (such as JSON, MAT, or Excel). When performing transient response modeling, the system reads these values ​​from this file during the initialization phase and assigns them to the corresponding variables in the model. For example, the system generates a text file named "kinetic_parameters.json" containing key-value pairs: “j0_CO”:0.012,“alpha_CO”:0.5,“j0_C2H4”:0.001,“alpha_C2H4”:0.3,“j0_H2”:0.1,“alpha_H2”:0.5,“kf”:2500.0. The modeling program loads this file upon startup and sets these values ​​as the preset kinetic parameters for the corresponding reactions.

[0184] Therefore, according to the above implementation method, the system can accurately determine the key reaction kinetic parameters required for the voltage quantum model and the carbon dioxide proton transfer model based on real and reliable steady-state experimental data and through a rigorous mathematical fitting process. This ensures that the subsequently constructed transient model has a solid experimental foundation and high prediction accuracy, fundamentally solving the problem of transient response prediction distortion caused by inaccurate model parameters.

[0185] Figure 9 This is a structural block diagram of a transient response modeling system for a membrane electrode electrolyzer for the electroreduction of carbon dioxide according to an embodiment of the present invention.

[0186] like Figure 9 As shown, the transient response modeling system for the membrane electrode electrolyzer for the electroreduction of carbon dioxide includes: The parameter acquisition module 210 is used to acquire the operating parameters and structural parameters of the membrane electrode electrolyzer.

[0187] The voltage balance equation establishment module 220 is used to establish voltage balance equations including double-layer capacitance based on operating parameters and structural parameters, so as to construct a voltage sub-model. The voltage sub-model is configured to describe the relationship between the total voltage, electrode potential, total current and ohmic resistance of the electrolytic cell.

[0188] The mass conservation equation establishment module 230 is used to establish the mass conservation equations for the gas phase and liquid phase carbon dioxide concentrations in the cathode catalyst layer based on structural parameters and preset reaction kinetic parameters, so as to construct a carbon dioxide proton transfer model. The carbon dioxide proton transfer model is configured to describe the transport, consumption and homogeneous reaction process of carbon dioxide from the flow channel to the catalyst surface.

[0189] The model coupling module 240 is used to perform coupling operations on the real-time output variables between the voltage sub-model and the carbon dioxide proton transfer model to generate a coupled model containing bidirectional data interaction relationships.

[0190] The transient response result generation module 250 is used to perform joint solution on the coupled model based on the bidirectional data interaction relationship and the set dynamic input conditions to obtain the transient response results of the membrane electrode electrolyzer. The transient response results include the output voltage waveform and the selectivity of the output products.

[0191] The specific functions and examples of each module and submodule of the device in this embodiment of the invention can be found in the relevant descriptions of the corresponding steps in the above method embodiments, and will not be repeated here.

[0192] According to embodiments of the present invention, the above-described method of the present invention can be applied to a computer device and a readable storage medium.

[0193] Figure 7 A schematic block diagram of an example computer device 600 that can be used to implement embodiments of the present invention is shown. The computer device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The computer device can also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0194] like Figure 10 As shown, the computer device 600 includes a computing unit 601, which can perform various appropriate actions and processes based on a computer program stored in a read-only memory (ROM) 602 or a computer program loaded from a storage unit 608 into a random access memory (RAM) 603. The RAM 603 may also store various programs and data required for the operation of the computer device 600. The computing unit 601, ROM 602, and RAM 603 are interconnected via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0195] Multiple components in computer device 600 are connected to I / O interface 605, including: input unit 606, such as keyboard, mouse, etc.; output unit 607, such as various types of monitors, speakers, etc.; storage unit 608, such as disk, optical disk, etc.; and communication unit 609, such as network card, modem, wireless transceiver, etc. Communication unit 609 allows computer device 600 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0196] The computing unit 601 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 601 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 601 performs the various methods and processes described above, such as a transient response modeling method for an electroreduced carbon dioxide membrane electrode electrolyzer. For example, in some embodiments, a transient response modeling method for an electroreduced carbon dioxide membrane electrode electrolyzer can be implemented as a computer software program tangibly contained in a machine-readable medium, such as storage unit 608. In some embodiments, part or all of the computer program can be loaded and / or installed on the computer device 600 via ROM 602 and / or communication unit 609. When the computer program is loaded into RAM 603 and executed by the computing unit 601, one or more steps of the transient response modeling method for an electroreduced carbon dioxide membrane electrode electrolyzer described above can be performed. Alternatively, in other embodiments, the computing unit 601 may be configured, by any other suitable means (e.g., by means of firmware), to perform a transient response modeling method for electroreduced carbon dioxide membrane electrode electrolyzers.

[0197] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0198] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0199] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0200] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0201] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0202] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact via communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other. Servers can be cloud servers, servers in distributed systems, or servers incorporating blockchain technology.

[0203] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0204] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for modeling the transient response of a membrane electrode electrolyzer for the electroreduction of carbon dioxide, characterized in that, include: Obtain the operating parameters and structural parameters of the membrane electrode electrolyzer; Based on the aforementioned operating parameters and structural parameters, a voltage balance equation including double-layer capacitance is established to construct a voltage sub-model. The voltage sub-model is configured to describe the relationship between the total voltage, electrode potential, total current, and ohmic resistance of the electrolytic cell. The voltage sub-model is also configured to output the total current and the current density of each product. Based on the structural parameters and preset reaction kinetic parameters, a mass conservation equation for the gas phase and liquid phase carbon dioxide concentration in the cathode catalyst layer is established to construct a carbon dioxide proton transfer model. The carbon dioxide proton transfer model is configured to describe the transport, consumption and homogeneous reaction process of carbon dioxide from the flow channel to the catalyst surface. The carbon dioxide proton transfer model is configured to output the carbon dioxide concentration and local pH value in the cathode catalyst layer. A coupling operation is performed on the real-time output variables between the voltage sub-model and the carbon dioxide proton transfer model to generate a coupled model containing bidirectional data interaction. Specifically, this includes: at each solution time step, obtaining the total current and the partial current density of each product from the voltage sub-model and inputting them as driving variables into the carbon dioxide proton transfer model; in the carbon dioxide proton transfer model, updating the flux calculation of carbon dioxide consumed by the electrochemical reaction based on the input total current and the partial current density of each product, and solving for the updated carbon dioxide concentration and local pH value within the cathode catalyst layer; obtaining the updated carbon dioxide concentration and local pH value within the cathode catalyst layer from the carbon dioxide proton transfer model and inputting them as feedback variables into the voltage sub-model; in the voltage sub-model, dynamically correcting the electrochemical reaction kinetic parameters and reaction equilibrium potential based on the input carbon dioxide concentration and local pH value within the cathode catalyst layer; and establishing a real-time data exchange channel between the voltage sub-model and the carbon dioxide proton transfer model to form a closed-loop iterative coupled model. Based on the bidirectional data interaction relationship, the coupled model is jointly solved according to the set dynamic input conditions to obtain the transient response results of the membrane electrode electrolyzer. The transient response results include the output voltage waveform and the selectivity of the output products. The dynamic input conditions include the time-varying current density and the cathode inlet gas flow rate.

2. The method according to claim 1, characterized in that, The operating parameters include the current or voltage applied to the membrane electrode electrolyzer, and the structural parameters include the cross-sectional area and ohmic resistance of the membrane electrode electrolyzer; the step of establishing a voltage balance equation including the double-layer capacitance based on the operating parameters and structural parameters includes: Based on Kirchhoff's voltage law, a first voltage balance relationship is established among the total voltage of the electrolytic cell, the cathode electrode potential, the anode electrode potential, the total current, and the ohmic resistor. Based on preset cathode double layer capacitance and anode double layer capacitance, a second voltage balance relationship is constructed, which includes the total current, the cathode electrode potential change rate, the anode electrode potential change rate, and the partial current density of each electrochemical reaction product. By combining the first voltage balance relationship with the second voltage balance relationship, the voltage balance equation is constructed. Based on the cross-sectional area and the ohmic resistance in the structural parameters, calculate the area ratio resistance in the voltage balance equation.

3. The method according to claim 2, characterized in that, The preset reaction kinetic parameters include the electrochemical reaction rate and the homogeneous reaction rate constant; the establishment of the mass conservation equations for the gas and liquid phase carbon dioxide concentrations within the cathode catalyst layer based on the structural parameters and the preset reaction kinetic parameters includes: Based on the pore structure parameters of the cathode catalyst layer, a first mass conservation relationship is established for the change of gas phase carbon dioxide concentration over time. This first mass conservation relationship characterizes the balance between the gas phase carbon dioxide flux entering the cathode catalyst layer from the flow channel and the gas phase carbon dioxide flux transferred from the gas phase to the liquid phase. Based on the pore structure parameters of the cathode catalyst layer and the preset reaction kinetic parameters, a second mass conservation relationship is established for the change of liquid phase carbon dioxide concentration over time. The second mass conservation relationship characterizes the balance between the carbon dioxide flux transferred from the gas phase to the liquid phase, the carbon dioxide flux consumed by the electrochemical reaction, and the carbon dioxide source term consumed by the homogeneous reaction. Based on the preset gas phase mass transfer coefficient from the flow channel to the cathode catalyst layer and the gas phase carbon dioxide concentration in the flow channel, the gas phase carbon dioxide flux from the flow channel into the cathode catalyst layer is calculated. Based on the preset gas-liquid phase mass transfer coefficient from gas phase to liquid phase, the Henry's law coefficient of carbon dioxide, and the concentration of carbon dioxide in the liquid phase, the gas phase carbon dioxide flux transferred from the gas phase to the liquid phase is calculated. The amount of carbon dioxide consumed by the electrochemical reaction is calculated based on the electrochemical reaction rate in the preset reaction kinetic parameters. Based on the homogeneous reaction rate constant and liquid-phase hydroxide ion concentration in the preset reaction kinetic parameters, the carbon dioxide source term consumed by the homogeneous reaction is calculated.

4. The method according to claim 1, characterized in that, The dynamic input conditions also include the electrolyzer temperature. The process of jointly solving the coupled model based on the bidirectional data interaction relationship and the set dynamic input conditions to obtain the transient response results of the membrane electrode electrolyzer includes: Set the current density input waveform, cathode inlet gas flow rate change curve, and temperature change curve that include a time series; The preset numerical solver is invoked to perform transient solution on the coupled model based on the set current density input waveform, the cathode inlet gas flow rate change curve and the temperature change curve; Within each solution time step, the state variables of the voltage sub-model and the carbon dioxide proton transfer model are updated synchronously based on the bidirectional data interaction relationship. The solution calculation of the coupled model is performed iteratively until the full-time simulation of the time series is completed; Record and output the total voltage waveform of the electrolyzer and the partial current density waveforms of each electrochemical reaction product of the coupled model throughout the entire solution time series as the transient response result.

5. The method according to claim 4, characterized in that, The step of calling a preset numerical solver to perform a transient solution on the coupled model based on the set current density input waveform, the cathode inlet gas flow rate change curve, and the temperature change curve includes: Set the initial time step and the maximum time step for the transient solution; Invoke the preset implicit variable step size solver and load the system of differential-algebraic equations of the coupled model; Set the relative and absolute tolerances for numerical solutions for the implicit variable step size solver; Based on the current density input waveform, the cathode inlet gas flow rate change curve, and the temperature change curve, configure the initial state of the coupled model at the starting point of the solution time series; The implicit variable step size solver is driven to perform adaptive solution step size advancement starting from the beginning of the solution time series, based on the initial time step size, the maximum time step size, the relative tolerance, and the absolute tolerance. At each internal solution step, the rate of change of state variables of the voltage sub-model and the carbon dioxide proton transfer model is monitored, and the iterative convergence process of the implicit variable step size solver is controlled based on the monitoring results. In response to the implicit variable step size solver completing the integral calculation of the entire solution time series, a signal indicating that the transient solution is complete is generated.

6. The method according to claim 1, characterized in that, The steps for obtaining the preset reaction kinetic parameters include: The experimental measurement data of the membrane electrode electrolyzer under multiple different steady-state operating conditions were obtained. The experimental measurement data included the total voltage of the electrolyzer, the total current density, and the Faraday efficiency of each electrochemical reaction product. Based on the experimental measurement data under the various steady-state operating conditions, the exchange current density and charge transfer coefficient corresponding to each electrochemical reaction were calculated by a fitting algorithm. Based on the experimental measurement data under the various steady-state operating conditions, the reaction rate constant corresponding to the consumption of carbon dioxide in the homogeneous reaction was calculated by a fitting algorithm. The calculated exchange current density, charge transfer coefficient, and reaction rate constant are set as the preset reaction kinetic parameters.

7. A transient response modeling system for a membrane electrode electrolyzer for the electroreduction of carbon dioxide, characterized in that, include: The parameter acquisition module is used to acquire the operating parameters and structural parameters of the membrane electrode electrolyzer. The voltage balance equation establishment module is used to establish a voltage balance equation including double-layer capacitance based on the operating parameters and structural parameters, so as to construct a voltage sub-model. The voltage sub-model is configured to describe the relationship between the total voltage, electrode potential, total current and ohmic resistance of the electrolytic cell. The voltage sub-model is configured to output the total current and the current density of each product. The mass conservation equation establishment module is used to establish mass conservation equations for the gas phase and liquid phase carbon dioxide concentrations in the cathode catalyst layer based on the structural parameters and preset reaction kinetic parameters, so as to construct a carbon dioxide proton transfer model. The carbon dioxide proton transfer model is configured to describe the transport, consumption and homogeneous reaction process of carbon dioxide from the flow channel to the catalyst surface. The carbon dioxide proton transfer model is configured to output the carbon dioxide concentration and local pH value in the cathode catalyst layer. The model coupling module is used to perform coupling operations on the real-time output variables between the voltage sub-model and the carbon dioxide proton model, generating a coupled model containing bidirectional data interaction relationships. Specifically, this includes: at each solution time step, obtaining the total current and the partial current density of each product from the voltage sub-model and inputting them as driving variables into the carbon dioxide proton model; in the carbon dioxide proton model, updating the flux calculation of carbon dioxide consumed by the electrochemical reaction based on the input total current and the partial current density of each product, and solving for the updated carbon dioxide concentration and local pH value within the cathode catalyst layer; obtaining the updated carbon dioxide concentration and local pH value within the cathode catalyst layer from the carbon dioxide proton model and inputting them as feedback variables into the voltage sub-model; in the voltage sub-model, dynamically correcting the electrochemical reaction kinetic parameters and reaction equilibrium potential based on the input carbon dioxide concentration and local pH value within the cathode catalyst layer; and establishing a real-time data exchange channel between the voltage sub-model and the carbon dioxide proton model, forming a closed-loop iterative coupled model. The transient response result generation module is used to perform joint solution on the coupled model based on the bidirectional data interaction relationship and according to the set dynamic input conditions to obtain the transient response result of the membrane electrode electrolyzer. The transient response result includes the output voltage waveform and the selectivity of the output products. The dynamic input conditions include the time-varying current density and the cathode inlet gas flow rate.

8. A computer device, characterized in that, include: At least one processor; and a memory that is communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-6.

9. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, in, Computer instructions are used to cause a computer to perform the method according to any one of claims 1-6.

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