Method for predicting gas holdup of porous microstructure flowing PEM hydrogen production device

Abstract

The invention relates to the technical field of proton exchange membrane water electrolysis hydrogen production, and provides a method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device, which comprises the following steps: acquiring basic parameters of a porous flow field; establishing a two-dimensional gas holdup prediction mathematical model for describing the change of gas phase and liquid phase mass flow in unit width of the porous flow field along the flow direction; determining boundary conditions of a flow field inlet and a side wall of the porous flow field to construct a complete two-dimensional boundary value problem; establishing a function relationship between the local gas holdup and the basic parameters; and on the basis of the function relationship and the two-dimensional boundary value problem, carrying out on-way solving calculation so as to output the gas holdup at each differential position in the fluid flowing direction as a two-dimensional gas holdup distribution prediction result of the porous flow field in the length and width directions. The gas holdup prediction method can give consideration to both calculation efficiency and prediction precision, and is easy to couple electrochemical variables.

Description

Technical Field

[0001] This invention relates to the field of proton exchange membrane electrolysis for hydrogen production technology, and in particular to a method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device. Background Technology

[0002] Electrolytic hydrogen production is a technology that uses direct current to decompose water to produce hydrogen. It mainly includes three types of methods: alkaline liquid electrolysis, proton exchange membrane (PEM) electrolysis, and solid oxide electrolysis (SOEC).

[0003] PEM electrolysis for hydrogen production offers advantages such as being clean and pollution-free, producing high-purity hydrogen, and having a fast response speed, making it one of the core technological pathways for large-scale green hydrogen production. On the anode side of the PEM electrolyzer, water undergoes an electrochemical reaction under the action of a catalyst to generate oxygen and protons, accompanied by electron conduction. The generated oxygen, along with unreacted water, needs to be promptly discharged through the porous flow field at the anode.

[0004] The porous anode flow field typically consists of a conductive and corrosion-resistant substrate with a microporous structure (such as porous titanium). Its core function is to uniformly distribute liquid water, efficiently extract gaseous oxygen, and collect current. The gas-liquid two-phase distribution within the flow field, especially the uniformity of the gas holdup (gas phase volume fraction) along the flow path, directly affects the current density distribution, mass transfer resistance, overpotential, and even the overall energy efficiency and operational stability of the electrolyzer. Therefore, accurately predicting the gas holdup distribution within the porous flow field is of great significance for optimizing the flow field structure design, improving electrolysis performance, and extending equipment life.

[0005] Current research on gas-liquid two-phase flow in porous PEM electrolyzers mainly focuses on qualitative analysis of bubble behavior and macroscopic performance effects through experimental methods, or detailed three-dimensional numerical simulations using computational fluid dynamics (CFD) methods. While experimental methods can provide direct observation results, they are limited by measurement methods and equipment scale, making it difficult to comprehensively obtain detailed distribution data of the flow field, especially at the industrial scale. Furthermore, they are costly and time-consuming. Although CFD simulations can reveal local flow and mass transfer details, they consume significant computational resources and involve complex modeling, making them unsuitable for rapid iteration and real-time application in engineering design or operational control systems.

[0006] Therefore, there is a need to develop a gas holdup prediction method that can balance computational efficiency and prediction accuracy and is easy to couple with electrochemical variables. Summary of the Invention

[0007] The main objective of this invention is to provide a method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device, aiming to solve the problems of existing PEM electrolyzer porous flow field gas holdup prediction technology, which suffers from complex calculations, low efficiency, and difficulty in meeting the needs of rapid analysis in engineering design and real-time monitoring during operation.

[0008] To achieve the above objectives, the present invention provides a method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device, comprising the following steps: The basic parameters of the porous flow field in the electrolytic cell are obtained, wherein the basic parameters include the porous flow field structure parameters, electrochemical reaction parameters and operating parameters, the electrochemical reaction parameters include the local current density distribution in the porous flow field, and the operating parameters include the inlet flow distribution and the operating current. Based on the aforementioned basic parameters, a two-dimensional mathematical model for predicting gas holdup is established to describe the variation of gas and liquid phase mass flow rates per unit width along the flow direction in the porous flow field; wherein, the width direction is perpendicular to the flow direction, and the two-dimensional mathematical model for predicting gas holdup includes partial differential equations for gas phase mass balance and partial differential equations for liquid phase mass balance. The boundary conditions of the two-dimensional gas holdup prediction mathematical model at the flow field inlet and sidewall of the porous flow field are determined to construct a complete two-dimensional boundary value problem. Based on the mass conservation relationship and the definition of volume fraction, the gas phase volume flow rate per unit width is correlated with the liquid phase volume flow rate, and a functional relationship between the local gas holdup and the basic parameters is established. Using the gas holdup at the inlet of the flow field as the initial value, the flow path is solved based on the functional relationship and the two-dimensional boundary value problem, thereby outputting the gas holdup at each differential position along the fluid flow direction, which serves as the prediction result of the two-dimensional gas holdup distribution of the porous flow field in the length and width directions.

[0009] Optionally, the step of establishing a two-dimensional gas holdup prediction mathematical model based on the basic parameters to describe the variation of gas and liquid mass flow rates per unit width along the flow direction in the porous flow field includes: A two-dimensional micro-element control volume is selected in the flow direction and perpendicular to the flow direction of the porous flow field; wherein, the main flow direction is the x-direction; the direction perpendicular to the flow direction is the y-direction, and the gas holdup is uniformly distributed in the y-direction; Based on the fact that the change in gas phase mass along the path of the two-dimensional micro-element control body is equal to the mass of oxygen generated by the electrochemical reaction, a partial differential equation for gas phase mass balance is established. Based on the fact that the change in the mass of the liquid phase within the two-dimensional micro-element control body along the process is equal to the mass of water generated by the electrochemical reaction, a partial differential equation for the liquid phase mass balance is established.

[0010] Optionally, the step of determining the boundary conditions of the two-dimensional gas holdup prediction mathematical model at the inlet and sidewalls of the porous flow field to construct a complete two-dimensional boundary value problem includes: Set the inlet boundary conditions, where the gas phase mass flow rate per unit width at the inlet is zero, and the liquid phase mass flow rate per unit width at the inlet is determined by the inlet flow rate distribution; By substituting the inlet boundary conditions into the partial differential equations for gas phase mass balance and liquid phase mass balance, respectively, and integrating, we obtain the gas phase mass flow rate relationship and the liquid phase mass flow rate relationship describing any position per unit width in the porous flow field plane.

[0011] Alternatively, the partial differential equation for gas phase mass balance is as follows: (1); in, Let be the position coordinates of the two-dimensional micro-element control volume along the main motion direction. Let be the position coordinates of the two-dimensional micro-element control body along the width direction, and let dx be the length of the two-dimensional micro-element control body in the flow direction and dy be the length in the width direction. The gas phase mass flow rate per unit width. for Gas phase mass flow rate per unit width after changing dx; This represents a local current density distribution. is the molar mass of oxygen; F is the Faraday constant; Equation (1) simplifies to: (2).

[0012] Alternatively, the partial differential equation for liquid phase mass equilibrium is as follows: (3); in, The liquid phase mass flow rate per unit width; Let be the molar mass of water.

[0013] Optionally, the inlet boundary conditions are as follows: (4); (5); in, The density of water, The inlet volumetric flow rate per unit width; The gas phase mass flow rate per unit width at the inlet; Let be the liquid mass flow rate per unit width at the inlet; Substitute the inlet boundary conditions (4) and (5) into (2) and (3) respectively and integrate to obtain the gas mass flow rate and liquid mass flow rate relationship describing the unit width at any position in the porous flow field plane; The gas phase mass flow rate relationship is as follows: (6); in, It is a function of local current density; It is a tiny length unit along the flow direction; The formula for liquid phase mass flow rate is as follows: (7).

[0014] Alternatively, the mass flow rates in equations (6) and (7) can be converted into gas phase volumetric flow rates. and liquid volume flow rate : (8); (9); in, The density of the gas phase; The ratio of gas phase volumetric flow rate to liquid phase volumetric flow rate per unit width is defined as the local gas holdup α, thus yielding the basic expression for the two-dimensional gas holdup distribution: (10).

[0015] Alternatively, when the current density is uniformly distributed in the plane, the expression for predicting the two-dimensional gas holdup distribution simplifies to: (11); in, This represents the uniform current density value. When the inlet liquid flow rate is uniformly distributed along the width direction, the model for predicting the gas holdup distribution simplifies to a one-dimensional model: (12); in, The inlet volume flow rate per unit width; When the inlet liquid flow rate is much greater than the amount of liquid consumed, the expression for predicting the gas holdup distribution is further simplified to: (13); The formula for average gas holdup is: (14); in, The average gas holdup, This represents the local gas holdup.

[0016] Optionally, the porous flow field satisfies at least one of the following conditions: The porous flow field is composed of a conductive and corrosion-resistant substrate with a microscale pore structure. The conductive and corrosion-resistant substrate is made of any one of porous titanium, porous graphite, and porous stainless steel. The conductive and corrosion-resistant substrate has a thickness of 100-500 μm, a porosity of 20%-80%, a pore size of 100-300 μm, or a pore density of 20-200 PPI. The cross-sectional shape of the pores in the conductive and corrosion-resistant matrix is ​​any one or more of square, rectangular, rhomboid, and circular.

[0017] Optionally, the method is constructed based on the following basic assumptions: the porous flow field is a rectangular plane, the gas holdup in the mainstream flow direction varies with position, and the gas holdup perpendicular to the flow direction is uniformly distributed; the anode gas-liquid two-phase flow is homogeneous, and the operating temperature and pressure remain constant; the gas conforms to the ideal gas law; the influence of electroosmosis on the gas-liquid distribution of the flow field is ignored; the reactive area is equal to the projected area of ​​the flow field; there is no gas at the inlet, and the inlet liquid flow rate has a known or measurable distribution.

[0018] In the technical solution of this invention, starting from the two-phase mass transfer characteristics of the porous flow field in an electrolytic cell, a two-dimensional gas holdup prediction mathematical model is established, considering the coupling between the electrochemical reaction source term, fluid flow, and gas-liquid integral number, to guide the design and operation optimization of the flow field structure. This model is based on the principle of mass conservation. Under the simplified homogeneous flow assumption, it establishes a set of partial differential governing equations for the mass flow rates of the gas and liquid phases per unit width along the mainstream direction, and associates them with the definition of local gas holdup, constructing a directly solvable two-dimensional boundary value problem. This model can efficiently calculate the local gas holdup at each point in the flow field plane by inputting porous flow field structure parameters, operating parameters, and electrochemical reaction parameters, thereby predicting the uniformity of the gas-liquid two-phase distribution on the anode side under different design schemes and operating conditions. Therefore, the method of this invention has the following advantages: First, the flow field structure design is based on more scientific and efficient methods: the established two-dimensional gas holdup prediction mathematics significantly simplifies the complexity of traditional three-dimensional CFD simulations while ensuring prediction accuracy. The model can quickly solve the two-dimensional distribution of gas holdup under different combinations of flow field length, width, and inlet conditions, clearly revealing the cumulative law of gas holdup along the flow direction. This provides a direct and reliable theoretical basis for the selection of geometric parameters and pore structure optimization of porous flow fields, accelerating the design iteration process.

[0019] Second, the operational condition analysis and optimization capabilities are significantly enhanced: By using local current density as a key input variable, this model can effectively assess the impact of uneven current distribution on gas-liquid flow in actual operation. Combined with inlet flow rate distribution, it can predict the evolution of gas holdup distribution under different current densities and different inlet water velocities, thereby identifying high-risk areas prone to gas phase blockage and mass transfer deterioration. Based on these prediction results, operating parameters can be optimized in a targeted manner (such as adjusting inlet flow rate distribution and controlling operating current), or the flow field can be zoned to improve overall operational stability and energy efficiency, and reduce experimental trial-and-error costs.

[0020] Third, it has the potential for integration with system control: the method model of this invention is simple and has a fast calculation speed, making it easy to embed into the electrolyzer control system or design software. By acquiring or predicting current density and inlet flow rate data in real time, online monitoring and early warning of gas holdup distribution can be achieved, providing key state variables for the subsequent development of intelligent control strategies based on gas-liquid distribution state feedback (such as adaptive flow regulation), thereby improving the intelligent operation level of the PEM electrolysis hydrogen production system. Attached Figure Description

[0021] Figure 1 This is a flowchart of a first embodiment of the method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to the present invention. Figure 2 This is a flowchart of an embodiment of the construction and performance verification of a PEM electrolysis hydrogen production device with a porous flow field coupling modified transport layer in this invention.

[0022] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0023] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0024] In the following description, the use of suffixes such as "unit," "component," or "element" to denote elements is solely for the purpose of illustrative purposes and has no specific meaning in itself. Therefore, "unit," "component," or "element" may be used interchangeably.

[0025] Please see Figures 1 to 2 The first embodiment of the present invention provides a method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device, comprising the following steps: Step S10: Obtain the basic parameters of the porous flow field in the electrolytic cell. The basic parameters include the porous flow field structure parameters, electrochemical reaction parameters, and operating parameters. The electrochemical reaction parameters include the local current density distribution in the porous flow field, and the operating parameters include the inlet flow distribution and the operating current. Step S20: Based on the basic parameters, establish a two-dimensional gas holdup prediction mathematical model describing the variation of gas and liquid mass flow rates per unit width along the flow direction in the porous flow field; wherein, the width direction is perpendicular to the flow direction, and the two-dimensional gas holdup prediction mathematical model includes partial differential equations for gas phase mass balance and partial differential equations for liquid phase mass balance. Step S30: Determine the boundary conditions of the two-dimensional gas holdup prediction mathematical model at the flow field inlet and sidewall of the porous flow field to construct a complete two-dimensional boundary value problem; Step S40: Based on the mass conservation relationship and the definition of volume fraction, correlate the gas phase volume flow rate per unit width with the liquid phase volume flow rate to establish a functional relationship between the local gas holdup and the basic parameters. Step S50: Using the gas holdup at the inlet of the flow field as the initial value, the flow field is solved along the flow path based on the functional relationship and the two-dimensional boundary value problem, thereby outputting the gas holdup at each differential position along the fluid flow direction, which is used as the prediction result of the two-dimensional gas holdup distribution of the porous flow field in the length and width directions.

[0026] In the technical solution of this invention, starting from the two-phase mass transfer characteristics of the porous flow field in an electrolytic cell, a two-dimensional gas holdup prediction mathematical model is established, considering the coupling between the electrochemical reaction source term, fluid flow, and gas-liquid integral number, to guide the design and operation optimization of the flow field structure. This model is based on the principle of mass conservation. Under the simplified homogeneous flow assumption, it establishes a set of partial differential governing equations for the mass flow rates of the gas and liquid phases per unit width along the mainstream direction, and associates them with the definition of local gas holdup, constructing a directly solvable two-dimensional boundary value problem. This model can efficiently calculate the local gas holdup at each point in the flow field plane by inputting porous flow field structure parameters, operating parameters, and electrochemical reaction parameters, thereby predicting the uniformity of the gas-liquid two-phase distribution on the anode side under different design schemes and operating conditions. Therefore, the method of this invention has the following advantages: First, the flow field structure design is based on more scientific and efficient methods: the established two-dimensional gas holdup prediction mathematics significantly simplifies the complexity of traditional three-dimensional CFD simulations while ensuring prediction accuracy. The model can quickly solve the two-dimensional distribution of gas holdup under different combinations of flow field length, width, and inlet conditions, clearly revealing the cumulative law of gas holdup along the flow direction. This provides a direct and reliable theoretical basis for the selection of geometric parameters and pore structure optimization of porous flow fields, accelerating the design iteration process.

[0027] Second, the operational condition analysis and optimization capabilities are significantly enhanced: By using local current density as a key input variable, this model can effectively assess the impact of uneven current distribution on gas-liquid flow in actual operation. Combined with inlet flow rate distribution, it can predict the evolution of gas holdup distribution under different current densities and different inlet water velocities, thereby identifying high-risk areas prone to gas phase blockage and mass transfer deterioration. Based on these prediction results, operating parameters can be optimized in a targeted manner (such as adjusting inlet flow rate distribution and controlling operating current), or the flow field can be zoned to improve overall operational stability and energy efficiency, and reduce experimental trial-and-error costs.

[0028] Third, it has the potential for integration with system control: the method model of this invention is simple and has a fast calculation speed, making it easy to embed into the electrolyzer control system or design software. By acquiring or predicting current density and inlet flow rate data in real time, online monitoring and early warning of gas holdup distribution can be achieved, providing key state variables for the subsequent development of intelligent control strategies based on gas-liquid distribution state feedback (such as adaptive flow regulation), thereby improving the intelligent operation level of the PEM electrolysis hydrogen production system.

[0029] The method in this invention is based on the following basic assumptions: the porous flow field is a rectangular plane, the gas holdup in the main flow direction varies with position, and the gas holdup perpendicular to the flow direction is uniformly distributed; the anode gas and liquid phases are homogeneous flow, and the operating temperature and pressure remain constant; the gas conforms to the ideal gas law; the influence of electroosmosis on the gas-liquid distribution of the flow field is ignored; the reactive area is equal to the projected area of ​​the flow field; there is no gas at the inlet, and the inlet liquid flow rate has a known or measurable distribution.

[0030] The method is used to predict the uniformity of gas holdup under different operating parameters during the design phase, or to monitor the gas holdup distribution online based on real-time current density and inlet flow rate during operation. It can be applied to predict the two-dimensional distribution of anode gas holdup under various operating conditions and working states (e.g., different current densities, temperatures, inlet flow rate distributions, or different porous flow field structures and materials). In this embodiment, the method is used to predict the gas holdup distribution along the flow direction of a porous titanium mesh flow field.

[0031] Furthermore, the prediction method of the present invention can be applied to both a single independent electrolytic cell and a stack system composed of multiple electrolytic cells. When applied to a stack, regardless of the electrical connection method used inside the stack, the inlet flow state of each cell can be considered essentially consistent under ideal distribution conditions.

[0032] The local current density distribution is a pre-defined variable or a variable calculated in real time through a coupled electrochemical model. Various methods can be used to obtain the local current density distribution: in-situ, high-resolution measurements can be performed by integrating printed circuit board sensors on the flow field plane of each individual cell; alternatively, overall performance testing can be conducted on multiple parallel cell units, and a representative current density distribution can be obtained by back-calculating through voltage-current characteristics or zonal measurements. The applicability of this method at different scales allows it to support both the fine design and diagnosis of individual cells and to provide an effective tool for the overall performance evaluation and uniformity analysis of the fuel cell stack system.

[0033] Specifically, the porous flow field satisfies at least one of the following conditions: The porous flow field is composed of a conductive and corrosion-resistant substrate with a microscale pore structure. The conductive and corrosion-resistant substrate is made of any one of porous titanium, porous graphite, and porous stainless steel. The conductive and corrosion-resistant substrate has a thickness of 100-500 μm, a porosity of 20%-80%, a pore size of 100-300 μm, or a pore density of 20-200 PPI. The cross-sectional shape of the pores in the conductive and corrosion-resistant matrix is ​​any one or more of square, rectangular, rhomboid, and circular.

[0034] Optionally, when the porous flow field is composed of porous titanium, its thickness can be 200 μm and its porosity can be 80%; when the porous flow field is composed of porous graphite, its thickness can be 350 μm and its porosity can be 60%.

[0035] According to the first embodiment of the method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device based on the present invention, and in the second embodiment of the method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device based on the present invention, step S20 includes: Step S21: Select a two-dimensional micro-element control volume in the flow direction and perpendicular to the flow direction of the porous flow field; wherein, the main flow direction is the x-direction; the direction perpendicular to the flow direction is the y-direction, and the gas holdup is uniformly distributed in the y-direction. Step S22: Based on the fact that the change in gas phase mass along the path of the two-dimensional micro-element control body is equal to the mass of oxygen generated by the electrochemical reaction, a partial differential equation for gas phase mass balance is established. Step S23: Based on the fact that the change in the mass of the liquid phase within the two-dimensional micro-element control body along the process is equal to the mass of water generated by the electrochemical reaction, a partial differential equation for the liquid phase mass balance is established.

[0036] In a second embodiment of the method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to the present invention, and in a third embodiment of the method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to the present invention, step S30 includes: Step S31: Set the inlet boundary conditions, wherein the gas mass flow rate per unit width at the inlet is zero, and the liquid mass flow rate per unit width at the inlet is determined by the inlet flow rate distribution. Step S32: Substitute the inlet boundary conditions into the partial differential equations for gas phase mass balance and liquid phase mass balance, respectively, and integrate to obtain the gas phase mass flow rate relationship and liquid phase mass flow rate relationship describing any position per unit width in the porous flow field plane.

[0037] Specifically, the partial differential equation for gas-phase mass balance is as follows: (1); in, Let be the position coordinates of the two-dimensional micro-element control volume along the main motion direction. Let be the position coordinates of the two-dimensional micro-element control body along the width direction, and let dx be the length of the two-dimensional micro-element control body in the flow direction and dy be the length in the width direction. The gas phase mass flow rate per unit width. for Gas phase mass flow rate per unit width after changing dx; This represents a local current density distribution. is the molar mass of oxygen; F is the Faraday constant; Equation (1) simplifies to: (2).

[0038] Furthermore, the partial differential equation for liquid phase mass equilibrium is as follows: (3); in, The liquid phase mass flow rate per unit width; Let be the molar mass of water.

[0039] Specifically, the entry boundary conditions are as follows: (4); (5); in, The density of water, The inlet volumetric flow rate per unit width; The gas phase mass flow rate per unit width at the inlet; Let be the liquid mass flow rate per unit width at the inlet; Substitute the inlet boundary conditions (4) and (5) into (2) and (3) respectively and integrate to obtain the gas mass flow rate and liquid mass flow rate relationship describing the unit width at any position in the porous flow field plane; The gas phase mass flow rate relationship is as follows: (6); in, It is a function of local current density; It is a tiny length unit along the flow direction; The formula for liquid phase mass flow rate is as follows: (7).

[0040] Furthermore, the mass flow rates in equations (6) and (7) are converted into gas phase volumetric flow rates. and liquid volume flow rate : (8); (9); in, The density of the gas phase; The ratio of gas phase volumetric flow rate to liquid phase volumetric flow rate per unit width is defined as the local gas holdup α, thus yielding the basic expression for the two-dimensional gas holdup distribution: (10).

[0041] Furthermore, when the current density is uniformly distributed in the plane, the expression for predicting the two-dimensional gas holdup distribution simplifies to: (11); in, This represents the uniform current density value. When the inlet liquid flow rate is uniformly distributed along the width direction, the model for predicting the gas holdup distribution simplifies to a one-dimensional model: (12); in, The inlet volume flow rate per unit width; When the inlet liquid flow rate is much greater than the amount of liquid consumed, the expression for predicting the gas holdup distribution is further simplified to: (13); The formula for average gas holdup is: (14); in, The average gas holdup, This represents the local gas holdup.

[0042] (1) Specifically, taking the local current density distribution as an example, the method for obtaining the current density distribution is as follows: In the laboratory or actual electrolytic cell, the membrane electrode assembly is activated and its performance is tested using a segmented voltage measurement method or a current scanning method. The current density range set for this test should be consistent with the applicable operating conditions of the established model.

[0043] When the electrolyzer reaches electrochemical steady state, the flow field plane can be measured in situ with high resolution using integrated printed circuit board sensors, and the corresponding local current density distribution can be calculated. The current density dataset collected by the data acquisition system is gridded to obtain a data matrix. To evaluate the distribution characteristics of the current density, evaluation metrics including maximum difference, mean, and heterogeneity are introduced. This dataset can be represented as the following two-dimensional matrix: ; in It is a data recording sequence, containing data on the measurement of local current density; This represents the average current density; m represents the number of rows in the matrix, and n represents the number of columns in the matrix. , The average current density can be expressed as: ; Standard deviation It can be calculated as follows: ; For uniform operating conditions or simplified designs, the local current density can be preset to a constant value. Its size is determined based on the design load or rated operating conditions.

[0044] For cases requiring coupling with an electrochemical model, the local current density is obtained by applying the Butler–Volmer equation, which is: ; in, For exchange current density, The anode charge transfer coefficient, The cathode charge transfer coefficient, The local activation overpotential is obtained by solving the electrochemical model using numerical methods (such as the finite element method), which yields the dynamic current density distribution i(x,y) corresponding to the local reaction conditions; z is the number of electrons involved in the electrode reaction, R is the gas constant, and T is the thermodynamic temperature.

[0045] (2) The inlet liquid flow rate distribution q(y) is determined as follows: For design analysis, the inlet flow distribution can be preset based on the flow distributor design theory, for example, assuming a uniform distribution q(y)=q0, or set to a specific function form (such as parabolic distribution) according to the distributor structure.

[0046] For electrolytic cells in experiment or operation, the inlet flow distribution can be measured by arranging multiple micro flowmeters at the inlet section of the flow field to obtain discrete flow data points, and then the continuous distribution function q(y) can be obtained by fitting it through interpolation.

[0047] By substituting the determined local current density distribution i(x,y) and inlet flow distribution q(y) into the two-dimensional boundary value problem constructed in the previous step, and using numerical methods (such as the finite difference method) to perform discrete solution, the predicted result α(x,y) of the two-dimensional gas holdup distribution in the porous flow field can be obtained.

[0048] To achieve the above objectives, the present invention also provides a system for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device, and applies the method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device; the system includes a parameter input module, a calculation and solution module, and a result output module; The parameter input module is used for: The basic parameters of the porous flow field in the electrolytic cell are obtained, wherein the basic parameters include the porous flow field structure parameters, electrochemical reaction parameters and operating parameters, the electrochemical reaction parameters include the local current density distribution in the porous flow field, and the operating parameters include the inlet flow distribution and the operating current. The calculation and solution module is used to: establish a two-dimensional gas holdup prediction mathematical model based on the basic parameters, describing the variation of gas and liquid mass flow rates per unit width along the flow direction in the porous flow field; wherein the width direction is perpendicular to the flow direction, and the two-dimensional gas holdup prediction mathematical model includes partial differential equations for gas phase mass balance and partial differential equations for liquid phase mass balance; determine the boundary conditions of the two-dimensional gas holdup prediction mathematical model at the flow field inlet and sidewalls of the porous flow field to construct a complete two-dimensional boundary value problem; correlate the gas phase volumetric flow rate per unit width with the liquid phase volumetric flow rate according to the mass conservation relationship and the definition of volume fraction, and establish a functional relationship between the local gas holdup and the basic parameters; use the gas holdup at the flow field inlet as the initial value, and perform a flow path solution calculation based on the functional relationship and the two-dimensional boundary value problem; The result output module is used to output the gas holdup at each differential position along the fluid flow direction, as the prediction result of the two-dimensional gas holdup distribution of the porous flow field in the length and width directions.

[0049] The prediction method of this invention can be applied to a variety of operating conditions, such as current density from 0.5 A / cm² to 4.0 A / cm², temperature from 60°C to 90°C, and pressure from 0.1 MPa to 3.0 MPa. For example, the operating current density can be 1.0 A / cm², 2.0 A / cm², or 3.0 A / cm², the temperature can be 70°C or 80°C, and the pressure can be 0.2 MPa, 1.5 MPa, or 2.5 MPa.

[0050] Example 1: Prediction of anode gas holdup distribution in porous flow field at current density of 1.5 A / cm².

[0051] In this embodiment, the anode of the electrolytic cell uses a porous titanium flow field with a thickness of 200 μm. The flow field is a rectangular plane with a length L of 0.05 m and a width W of 0.05 m. The operating temperature is set to 80℃, the operating pressure to 0.2 MPa, the deionized water volumetric flow rate to 100 mL / min, and the inlet flow rate to be uniformly distributed along the width direction. The current density is uniformly distributed in the plane and set to 1.5 A / cm². The oxygen density ρ under the operating conditions is calculated according to the ideal gas law. g The density of liquid water is ρ = 1.09 kg / m³. l The value is 972 kg / m³. Based on the prediction model of this invention, the simplified formula (12) for uniform current density is used to calculate the gas holdup distribution along the flow direction. The prediction results show that the gas holdup increases from 0 at the inlet to 0.46 at the outlet, and the average gas holdup of the entire flow field is 0.28.

[0052] Example 2: Prediction of anode gas holdup distribution in porous flow field at current density of 2 A / cm².

[0053] In this embodiment, the anode of the electrolytic cell uses a porous titanium flow field with a thickness of 350 μm. The flow field is a rectangular plane with a length L of 0.1 m and a width W of 0.1 m. The operating temperature is set to 80℃, the operating pressure to 0.2 MPa, the deionized water volumetric flow rate to 200 mL / min, and the inlet flow rate to be uniformly distributed along the width direction. The current density is uniformly distributed in the plane and set to 2 A / cm². The oxygen density ρ under the operating conditions is calculated according to the ideal gas law. g The density of liquid water is ρ, which is 2.18 kg / m³. l The value is 972 kg / m³. Based on the prediction model of this invention, the simplified formula (12) for uniform current density is used to calculate the gas holdup distribution along the flow direction. The prediction results show that the gas holdup increases from 0 at the inlet to 0.69 at the outlet, and the average gas holdup of the entire flow field is 0.48.

[0054] Example 3: Prediction of anode gas holdup distribution in porous flow field at current density of 2.5 A / cm².

[0055] In this embodiment, the anode of the electrolytic cell uses a porous titanium flow field with a thickness of 350 μm. The flow field is a rectangular plane with a length L of 0.1 m and a width W of 0.1 m. The operating temperature is set to 80℃, the operating pressure to 0.5 MPa, the deionized water volumetric flow rate to 200 mL / min, and the inlet flow rate to be uniformly distributed along the width direction. The current density is uniformly distributed in the plane and set to 2.5 A / cm². The oxygen density ρ under the operating conditions is calculated according to the ideal gas law. g The density of liquid water is ρ = 5.45 kg / m³. l The value is 972 kg / m³. Based on the prediction model of this invention, the simplified formula (12) for uniform current density is used to calculate the gas holdup distribution along the flow direction. The prediction results show that the gas holdup increases from 0 at the inlet to 0.53 at the outlet, and the average gas holdup of the entire flow field is 0.33.

[0056] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a computer-readable storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to enter the methods described in the various embodiments of the present invention.

[0057] In the description of this specification, references to terms such as "one embodiment," "another embodiment," "other embodiments," or "first embodiment to Xth embodiment," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, method steps, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0058] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0059] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0060] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device, characterized in that, Includes the following steps: The basic parameters of the porous flow field in the electrolytic cell are obtained, wherein the basic parameters include the porous flow field structure parameters, electrochemical reaction parameters and operating parameters, the electrochemical reaction parameters include the local current density distribution in the porous flow field, and the operating parameters include the inlet flow distribution and the operating current. Based on the aforementioned basic parameters, a two-dimensional mathematical model for predicting gas holdup is established to describe the variation of gas and liquid phase mass flow rates per unit width along the flow direction in the porous flow field; wherein, the width direction is perpendicular to the flow direction, and the two-dimensional mathematical model for predicting gas holdup includes partial differential equations for gas phase mass balance and partial differential equations for liquid phase mass balance. The boundary conditions of the two-dimensional gas holdup prediction mathematical model at the flow field inlet and sidewall of the porous flow field are determined to construct a complete two-dimensional boundary value problem. Based on the mass conservation relationship and the definition of volume fraction, the gas phase volume flow rate per unit width is correlated with the liquid phase volume flow rate, and a functional relationship between the local gas holdup and the basic parameters is established. Using the gas holdup at the inlet of the flow field as the initial value, the flow path is solved based on the functional relationship and the two-dimensional boundary value problem, thereby outputting the gas holdup at each differential position along the fluid flow direction, which serves as the prediction result of the two-dimensional gas holdup distribution of the porous flow field in the length and width directions.

2. The method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to claim 1, characterized in that, The steps of establishing a two-dimensional gas holdup prediction mathematical model based on the basic parameters to describe the variation of gas and liquid mass flow rates per unit width along the flow direction in the porous flow field include: A two-dimensional micro-element control volume is selected in the flow direction and perpendicular to the flow direction of the porous flow field; wherein, the main flow direction is the x-direction; the direction perpendicular to the flow direction is the y-direction, and the gas holdup is uniformly distributed in the y-direction; Based on the fact that the change in gas phase mass along the path of the two-dimensional micro-element control body is equal to the mass of oxygen generated by the electrochemical reaction, a partial differential equation for gas phase mass balance is established. Based on the fact that the change in the mass of the liquid phase within the two-dimensional micro-element control body is equal to the mass of water generated by the electrochemical reaction, a partial differential equation for the liquid phase mass balance is established.

3. The method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to claim 2, characterized in that, The step of determining the boundary conditions of the two-dimensional gas holdup prediction mathematical model at the inlet and sidewalls of the porous flow field to construct a complete two-dimensional boundary value problem includes: Set the inlet boundary conditions, where the gas phase mass flow rate per unit width at the inlet is zero, and the liquid phase mass flow rate per unit width at the inlet is determined by the inlet flow rate distribution; By substituting the inlet boundary conditions into the partial differential equations for gas phase mass balance and liquid phase mass balance, respectively, and integrating, we obtain the gas phase mass flow rate relationship and the liquid phase mass flow rate relationship describing any position per unit width in the porous flow field plane.

4. The method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to claim 3, characterized in that, The partial differential equation for gas phase mass equilibrium is as follows: （1）； in, Let be the position coordinates of the two-dimensional micro-element control volume along the main motion direction. Let be the position coordinates of the two-dimensional micro-element control body along the width direction, and let dx be the length of the two-dimensional micro-element control body in the flow direction and dy be the length in the width direction. The gas phase mass flow rate per unit width. for Gas phase mass flow rate per unit width after changing dx; This represents a local current density distribution. is the molar mass of oxygen; F is the Faraday constant; Equation (1) simplifies to: (2)。 5. The method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to claim 4, characterized in that, The partial differential equation for liquid phase mass equilibrium is as follows: (3)； in, The liquid phase mass flow rate per unit width; Let be the molar mass of water.

6. The method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to claim 5, characterized in that, The entry boundary conditions are as follows: (4)； (5)； in, The density of water, The inlet volumetric flow rate per unit width; The gas phase mass flow rate per unit width at the inlet; Let be the liquid mass flow rate per unit width at the inlet; Substitute the inlet boundary conditions (4) and (5) into (2) and (3) respectively and integrate to obtain the gas mass flow rate and liquid mass flow rate relationship describing the unit width at any position in the porous flow field plane; The gas phase mass flow rate relationship is as follows: (6)； in, It is a function of local current density; It is a tiny length unit along the flow direction; The formula for liquid phase mass flow rate is as follows: (7)。 7. The method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to claim 6, characterized in that, Convert the mass flow rates in equations (6) and (7) into gas phase volumetric flow rates. and liquid volume flow rate : (8)； (9)； in, The density of the gas phase; The ratio of gas phase volumetric flow rate to liquid phase volumetric flow rate per unit width is defined as the local gas holdup α, thus yielding the basic expression for the two-dimensional gas holdup distribution: (10)。 8. The method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to claim 7, characterized in that, When the current density is uniformly distributed in the plane, the expression for predicting the two-dimensional gas holdup distribution simplifies to: (11)； in, This represents the uniform current density value. When the inlet liquid flow rate is uniformly distributed along the width direction, the model for predicting the gas holdup distribution simplifies to a one-dimensional model: (12)； in, The inlet volume flow rate per unit width; When the inlet liquid flow rate is much greater than the amount of liquid consumed, the expression for predicting the gas holdup distribution is further simplified to: (13)； The formula for average gas holdup is: (14)； in, The average gas holdup, This represents the local gas holdup.

9. The method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to any one of claims 1 to 8, characterized in that, The porous flow field satisfies at least one of the following conditions: The porous flow field is composed of a conductive and corrosion-resistant substrate with a microscale pore structure. The conductive and corrosion-resistant substrate is made of any one of porous titanium, porous graphite, and porous stainless steel. The conductive and corrosion-resistant substrate has a thickness of 100-500 μm, a porosity of 20%-80%, a pore size of 100-300 μm, or a pore density of 20-200 PPI. The cross-sectional shape of the pores in the conductive and corrosion-resistant matrix is ​​any one or more of square, rectangular, rhomboid, and circular.

10. The method for predicting the gas holdup of a porous microstructure flow PEM hydrogen production device according to any one of claims 1 to 8, characterized in that, The method is based on the following basic assumptions: the porous flow field is a rectangular plane, the gas holdup in the main flow direction varies with position, and the gas holdup perpendicular to the flow direction is uniformly distributed; the anode gas and liquid phases are homogeneous flows, and the operating temperature and pressure remain constant; the gas conforms to the ideal gas law; the influence of electroosmosis on the gas-liquid distribution of the flow field is ignored; the reactive area is equal to the projected area of ​​the flow field; there is no gas at the inlet, and the inlet liquid flow rate has a known or measurable distribution.

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