A method for constructing a nested network model for porous materials

Abstract

This invention relates to the field of porous materials technology, and in particular provides a method for constructing a nested network model of porous materials. The method includes: acquiring the three-dimensional morphology of the porous material; obtaining the solid 3D spatial position and size distribution information of the porous material's catalyst layer based on the 3D morphology, and obtaining the actual porosity of the catalyst layer; constructing a nested network model of the porous material's catalyst layer based on the 3D spatial position and size distribution information of the porous material using a regular network extraction method or an improved MS-RVT algorithm; using equations to describe the mass transport, charge transport, heat transport, and electrochemical reaction processes in the nested network model; solving the equations to obtain the mass concentration of all pores, the temperature of all nodes, and the chemical reaction rate. This invention reflects the true microstructure of porous catalysts and can obtain the mass transport and reaction rate distribution throughout the entire catalyst region.

Description

Technical Field

[0001] This invention relates to the field of porous materials technology, and in particular to a method for constructing a nested network model of porous materials. Background Technology

[0002] Mass transport and chemical reactions in porous catalysts are a key area of ​​fundamental research with significant applications in the energy and environmental fields, such as industrial flue gas treatment systems, wastewater / exhaust gas treatment plants, gas adsorption and storage, pharmaceutical raw material synthesis, fuel cells, and the electrolysis of water and carbon dioxide. As global climate change becomes increasingly severe, carbon neutrality and sustainable development have become a global consensus. Research on porous catalysts is also gradually expanding into emerging technology fields such as the resource utilization of carbon dioxide and hydrogen, geological sequestration and catalytic conversion, and electrochemical energy storage and conversion.

[0003] In recent years, the rapid development of high-resolution X-ray imaging and image processing-based analysis and simulation techniques has driven research and engineering applications of mass transport and chemical reaction mechanisms within porous catalysts. Traditional macroscopic continuity models, relying on mesh generation, physical field discretization, and fundamental conservation laws, can obtain some macroscopic parameters of porous catalysts, but these methods focus on macroscopic processes and cannot describe the details of local spatial structures. In recent years, micro- and mesoscopic scale models capable of efficiently describing the details of microstructures have emerged. Pore network simulations treat porous media as composed of interconnected pores and solids, with pores connected by throats, used to simulate the transport of matter and chemical reaction processes within the porous medium. Compared to the lattice Boltzmann method, the pore network model is computationally faster and is considered the most efficient mesoscopic scale model.

[0004] Although porous network models have been widely applied to mass transport behavior in two-phase flows of porous materials, research on mass transport and chemical reactions in porous catalysts is relatively limited. This is mainly because the study of porous catalysts involves more complex porous networks (gas networks and solid networks that provide sites for electrochemical reactions) and complex mass transport (mass transport within gas networks, mass transport within solid networks, and mass transport between gas and solid networks).

[0005] Therefore, it is necessary to provide a method for constructing nested network models of porous materials to effectively solve the above problems. Summary of the Invention

[0006] This invention provides a method for constructing a nested network model for porous materials.

[0007] The present invention provides a method for constructing a nested network model of porous materials and analyzing mass transport and chemical reactions, comprising the following steps:

[0008] The three-dimensional morphology of the porous material is obtained. Based on the three-dimensional morphology of the porous material, the solid 3D spatial position and size distribution information of the catalyst layer of the porous material are obtained, and the actual porosity of the catalyst layer is obtained. ;

[0009] Based on the 3D spatial location and size distribution information of the porous material, a nested network model of the porous material catalytic layer is constructed by a regular network extraction method or an improved MS-RVT algorithm.

[0010] Equations are used to describe the mass transport, charge transport, heat transport, and electrochemical reaction processes in the nested network model. By solving the equations, the mass concentration in all pores, the temperature of all nodes, and the chemical reaction rate are obtained.

[0011] Preferably, a nested network model of the porous material catalytic layer is constructed using a regular network extraction method, including the following steps:

[0012] The catalytic layer is simplified into a regular network structure. A solid-state network model is constructed in the computational domain, and model parameters are set. Porosity is then calculated based on these parameters. Model parameters include: solid node spacing. Number of solid nodes solid node radius The radius of the cylindrical solid throat connecting the solid nodes. and length Porosity is calculated using the following formula:

[0013] ,

[0014] in, Porosity; For solid node spacing; The number of solid nodes; The radius of the solid node; and These are the radius and length of the cylindrical solid throat connecting the solid nodes, respectively.

[0015] A porous network is constructed within a solid network model to obtain a nested network model.

[0016] Preferably, constructing a solid-state network model in the computational domain and setting the model parameters includes the following steps:

[0017] The actual porosity of the catalyst layer As the target porosity ,Right now ;

[0018] Place the solid nodes regularly in a Cartesian coordinate system and set the radius of the solid nodes. ;

[0019] A cylindrical solid throat is established between all adjacent solid nodes, with the axial direction of the solid throat along the x-axis, y-axis, or z-axis; the length of the solid throat... The radius of the solid throat is the sum of the radii of the two connected solid nodes minus the spacing between the solid nodes. Determined based on the pore-throat volume ratio;

[0020] Obtain the position and size of solid nodes and solid throats, as well as the connection relationships between all solid nodes and solid throats;

[0021] Calculate porosity using the formula. ;

[0022] Adjust the model parameters to obtain the calculated porosity With target porosity Within the set allowable range, the solid network model is constructed.

[0023] Preferably, constructing a porous network in a solid network model includes the following steps:

[0024] Pore ​​nodes are defined, and the positions of all pore nodes in the pore network are the coordinates of the solid nodes. This allows for the uniform nesting of solid-state networks and porous networks;

[0025] Set the pore node spacing of the pore network to the solid node spacing. ;

[0026] Calculate the equivalent radius of the pore node in the pore network using the locations of the solid nodes and pore nodes, as well as the dimensions of the 8 solid nodes and 12 solid throats surrounding the pore node:

[0027] ,

[0028] in, Represents the equivalent radius of pore node i; This represents the proportion of the volume of a pore node in a pore network to the total volume of all pore nodes and all pore throats. Let represent the radius of the j-th solid node surrounding pore node i; k represents the k-th solid throat surrounding pore node i. For solid node spacing; and These are the radius and length of the cylindrical solid throat connecting the solid nodes, respectively.

[0029] The equivalent radius of the pore throat in a porous network is calculated using the following formula:

[0030] ,

[0031] in, This represents the equivalent radius of the pore throat K in the pore network; This refers to the ratio of the volume of a pore node in the pore network to the total volume of all pore nodes and the pore throat. and These are the radii of the first and second pore nodes connected to the pore throat K in the pore network, respectively.

[0032] By setting throats to connect all adjacent pore nodes and solid nodes, the pore network is constructed.

[0033] Preferably, the nested network model of the porous material catalytic layer is constructed using the improved MS-RVT algorithm, including the following steps:

[0034] The maximum sphere algorithm was applied to the pores and solid of the porous material catalyst layer to calculate the computational domain of the porous material catalyst layer.

[0035] The computational domain of the material's catalytic layer is used to perform root-Voronoi space segmentation, and the local connectivity information of the porous material is obtained based on the spatial segmentation information; the local connectivity information includes the position and size of the solid, pores and throats, as well as the connection relationship between the solid, pores and throats.

[0036] Preferably, the maximum sphere algorithm is applied to the pores and solid of the porous material catalyst layer to calculate the computational domain of the material catalyst layer, including the following steps:

[0037] Based on the 3D spatial location and size distribution information of solids, obtain solids, boundaries and pores;

[0038] The largest sphere is grown in the solid and numbered as 1. The generated largest sphere is used as a new pore region. Then, a new largest sphere is grown in the updated solid region until the volume of the largest sphere grown in the solid reaches the set value.

[0039] The largest sphere is grown in the pores and assigned the number 2. The generated largest sphere is used as a new solid region. Then, a new largest sphere is grown in the updated pore region until the volume of the largest sphere grown in the pores reaches the set value; thus, the computational domain of the porous material catalytic layer is obtained.

[0040] Preferably, the root voronoui space is segmented based on the computational domain of the material's catalytic layer, and the local connectivity information of the porous material is obtained based on the spatial segmentation information, including the following steps:

[0041] The actual porosity of the catalyst layer As the target porosity ,Right now ;

[0042] The entire catalytic layer is divided into n polyhedra based on the Genvoronoi space partitioning. The polyhedra are labeled according to the largest sphere to which they belong. The polyhedron to which the largest sphere belongs is labeled as 1, and the polyhedron to which the largest sphere belongs is labeled as 2.

[0043] Add labels to the faces of the polyhedrons; set the common face of the polyhedron labeled 1 to label 1, the common face of the polyhedron labeled 2 to label 2, and the common face of the polyhedrons labeled 1 and 2 to label 3.

[0044] Assign a thickness h to all faces of the polyhedron, and calculate the updated volume of the polyhedron based on the face thicknesses:

[0045] ,

[0046] in, For the updated polyhedral volume; The initial volume of the polyhedron. The area of ​​the unlabeled face of the polyhedron;

[0047] The polyhedron formed by stretching the face labeled 1 is still solid, the polyhedron formed by stretching the face labeled 2 is still porous, and the polyhedron formed by stretching the face labeled 3 is half solid and half porous.

[0048] Calculate the updated porosity ;

[0049] The thickness h of the polyhedron is adjusted to achieve the updated porosity. With target porosity If the difference is within the set allowable range, then the thickness h is considered to be set appropriately;

[0050] All polyhedra are updated based on their volume. Equivalent to a sphere, and all the polyhedral throats are equivalent to cylinders with constant length based on the thickness being equal to the length, thus obtaining a nested network model.

[0051] Preferably, equations are used to describe the mass transport, charge transport, heat transport, and electrochemical reaction processes in the nested network model. Solving the equations yields the mass concentration in all pores, the temperature of all nodes, and the chemical reaction rate, including the following steps:

[0052] Given initial conditions, including gas concentration, temperature, and initial electrochemical reaction rate;

[0053] Calculate the gas concentration in all pores and throats of the porous network using the oxygen diffusion law and the oxygen conservation equation:

[0054] ,

[0055] in, This represents the increase in the mass of oxygen in pore i per unit time; under steady-state conditions, this value is zero. This represents the gas conductivity of the throat between pore i and its adjacent pore j; This indicates the oxygen concentration in pore i. This indicates the oxygen concentration in pore j; This indicates that due to the electrochemical reaction, one-eighth of the total oxygen consumed per unit time by the eight aggregates surrounding pore i.

[0056] The electrochemical reaction rates of the solid network nodes are updated by updating the gas concentration, Ohm's law, and the law of conservation of charge:

[0057] ,

[0058] ,

[0059] in, and These represent the current densities of electrons and protons in the throat connected to the aggregate, respectively; and These represent the cross-sectional areas of electron and proton transport in the solid throat, respectively; the surface area of ​​the aggregate is denoted as... The current density on the surface of the aggregate is expressed as: ;

[0060] The current density of electrons and protons can be expressed as:

[0061] ,

[0062] ,

[0063] in, The electron current density; The current density of protons; It is the length of the throat in a solid network; and These represent the electrical conductivity of electrons and protons, respectively. and These represent the potential difference between electrons and protons between two aggregates, respectively;

[0064] The temperatures of the solid network nodes and throats are updated using updated oxygen concentration, electrochemical reaction rate, Fourier's law of heat conduction, and the law of conservation of heat.

[0065] ,

[0066] in, This represents the thermal conductivity of the solid throat between aggregate i and its adjacent aggregate j. Indicates the temperature of aggregate i. The temperature of aggregate j is represented by ; the heat generated per unit time in aggregate i due to electrochemical reactions and overpotential, and the heat loss due to water evaporation, are respectively represented by . and Indicates the ohmic heat dissipation per unit time in the solid throat connecting aggregate i. express.

[0067] Preferably, the method further includes: using the updated results of oxygen concentration in the porous network, electrochemical reaction rate in the solid network, and temperature as initial values, and repeatedly updating them until the difference between the chemical reaction rates of two iterations, the difference between the temperatures of two iterations, or the difference between the oxygen concentrations of two iterations are within a set value. If these values ​​are within the set value, the error is considered to be within the allowable range, and the model is considered to have been successfully solved.

[0068] Preferably, X-ray microtomography is used to scan the yz section of the porous material catalyst layer layer by layer, and the three-dimensional morphology of the porous material catalyst layer is obtained through image recognition and processing.

[0069] Compared with the prior art, the technical solutions of the embodiments of the present invention have beneficial effects.

[0070] For example, the nested network model construction and mass transport and chemical reaction analysis method for porous materials provided by this invention obtains the three-dimensional morphology of the porous material. Based on the three-dimensional morphology of the porous material, the solid 3D spatial position and size distribution information of the catalyst layer of the porous material are obtained, and the actual porosity of the catalyst layer is obtained. Based on the 3D spatial location and size distribution information of the porous material, a nested network model of the porous material catalyst layer is constructed using a regular network extraction method or an improved MS-RVT algorithm. Equations are used to describe the mass transport, charge transport, heat transport, and electrochemical reaction processes in the nested network model. The equations are solved to obtain the mass concentration of all pores, the temperature of all nodes, and the chemical reaction rate. By establishing the nested network model, the influence of the porous catalyst structure on the mass transport and chemical reaction is studied, and the mass concentration and reaction rate distribution are extracted, providing a basis for subsequent optimization of the porous catalyst structure and preparation method. Attached Figure Description

[0071] Figure 1 This is a flowchart illustrating the method for constructing a nested network model of porous materials and analyzing mass transport and chemical reactions according to an embodiment of the present invention.

[0072] Figure 2This is a schematic diagram of the nested network model structure obtained by the rule network extraction method in an embodiment of the present invention;

[0073] Figure 3 This is a schematic diagram of the nested network model structure obtained by using the improved MS-RVT algorithm in an embodiment of the present invention;

[0074] Figure 4 This is a schematic diagram of the unit structure of the nested network model obtained by using the improved MS-RVT algorithm in an embodiment of the present invention;

[0075] Figure 5 This is a schematic diagram illustrating the effect of solid network node size on oxygen concentration distribution in a nested network model according to an embodiment of the present invention.

[0076] Figure 6 This is a schematic diagram illustrating the influence of solid network node size on the current density distribution of the porous catalyst layer in the nested network model of this invention.

[0077] Figure 7 This is a schematic diagram illustrating the effect of solid network node size on the temperature distribution of the porous catalyst layer in the nested network model of this invention. Detailed Implementation

[0078] To make the objectives, features, and beneficial effects of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It is to be understood that the specific embodiments described below are merely for explaining the present invention and are not intended to limit the present invention. Furthermore, the same or similar reference numerals may be used in the drawings to refer to the same or similar elements in different embodiments, and descriptions of the same or similar elements in different embodiments, as well as descriptions of prior art elements, features, effects, etc., may be omitted.

[0079] Reference Figures 1 to 4 This invention provides a method for constructing a nested network model of porous materials and analyzing mass transport and chemical reactions.

[0080] Specifically, the method for constructing a nested network model of porous materials and analyzing mass transport and chemical reactions provided in this invention includes the following steps:

[0081] S1: Obtain the three-dimensional morphology of the porous material. Based on the three-dimensional morphology of the porous material, obtain the solid 3D spatial position and size distribution information of the catalyst layer, and obtain the actual porosity of the catalyst layer. ;

[0082] S2: Based on the 3D spatial location and size distribution information of porous materials, a nested network model of the porous material catalytic layer is constructed by using a regular network extraction method or an improved MS-RVT (Radar-assisted View Transformation, RVT) algorithm;

[0083] S3: Equations are used to describe the mass transport, charge transport, heat transport, and electrochemical reaction processes in the nested network model. The equations are solved to obtain the mass concentration in all pores, the temperature of all nodes, and the chemical reaction rate.

[0084] Specifically, equations describing mass transport include the convection-expansion equation and Darcy's law; equations describing charge transport include charge conservation and Ohm's law; equations describing heat transport include the energy conservation equation and Fourier heat conduction equation; and equations describing electrochemical reactions include the Nernst equation and the Butler–Volmer equation.

[0085] In some embodiments, X-ray microtomography is used to scan the yz section of the porous material catalyst layer layer by layer, and the three-dimensional morphology of the porous material catalyst layer is obtained through image recognition and processing.

[0086] Specifically, image processing methods include binarization, MASK-RCNN (Mask Region-based Convolutional Neural Network), etc.

[0087] Specifically, other methods that can obtain the true microstructure of porous materials can be used instead of X-ray microtomography, and no restrictions are placed here.

[0088] In some embodiments, a nested network model of the porous material catalytic layer is constructed using a regular network extraction method, including the following steps:

[0089] S21: The catalyst layer is simplified into a regular network structure. A solid-state network model is constructed in the computational domain, model parameters are set, and porosity is calculated based on the model parameters. The model parameters include: solid node spacing. Number of solid nodes solid node radius The radius of the cylindrical solid throat connecting the solid nodes. and length Porosity is calculated using the following formula:

[0090] ,

[0091] in, Porosity; For solid node spacing; The number of solid nodes; The radius of the solid node; and These are the radius and length of the cylindrical solid throat connecting the solid nodes, respectively.

[0092] S22: Construct a porous network in the solid network model to obtain a nested network model.

[0093] In some embodiments, a solid-state network model is constructed in the computational domain, and model parameters are set, including the following steps:

[0094] S211: The actual porosity of the catalyst layer As the target porosity ,Right now ;

[0095] S212: Regularly place the solid nodes in the Cartesian coordinate system and set the radius of the solid nodes. ;

[0096] S213: A cylindrical solid throat is provided between all adjacent solid nodes, with the axial direction of the solid throat along the x-axis, y-axis, or z-axis; the length of the solid throat... The radius of the solid throat is the sum of the radii of the two connected solid nodes minus the spacing between the solid nodes. Determined based on the pore-throat volume ratio;

[0097] S214: Obtain the position and size of solid nodes and solid throats, as well as the connection relationship between all solid nodes and solid throats;

[0098] S215: Calculate porosity according to the formula. ;

[0099] S216: Correct the model parameters to improve the calculated porosity. With target porosity Within the set allowable range, the solid network model is constructed.

[0100] In some embodiments, constructing a porous network in a solid network model includes the following steps:

[0101] S221: Set the pore nodes; the positions of all pore nodes in the pore network are the coordinates of the solid nodes. This allows for the uniform nesting of solid-state networks and porous networks;

[0102] S222: Set the spacing between pore nodes in the porous network to the same as the spacing between solid nodes. ;

[0103] S223: Calculate the equivalent radius of a pore node in a pore network using the locations of solid nodes and pore nodes, as well as the dimensions of the 8 solid nodes and 12 solid throats surrounding the pore node.

[0104] ,

[0105] Among them, such as Figure 4 The unit structure shown. Represents the equivalent radius of pore node i; This represents the proportion of the volume of a pore node in a pore network to the total volume of all pore nodes and all pore throats. Let represent the radius of the j-th solid node surrounding pore node i; k represents the k-th solid throat surrounding pore node i. For solid node spacing; and These are the radius and length of the cylindrical solid throat connecting the solid nodes, respectively.

[0106] S224: The equivalent radius of the pore throat in the porous network is calculated using the following formula:

[0107] ,

[0108] in, This represents the equivalent radius of the pore throat K in the pore network; This refers to the proportion of the volume of pore nodes in a pore network to the total volume of all pore nodes and pore throats. and These are the radii of the first and second pore nodes connected to the pore throat K in the pore network, respectively.

[0109] S225: Set throats to connect all adjacent pore nodes and solid nodes to complete the pore network construction.

[0110] In some embodiments, a nested network model of the porous material catalytic layer is constructed using the improved MS-RVT algorithm, including the following steps:

[0111] S21 ， The maximum sphere algorithm is applied to the pores and solid of the porous material catalyst layer to calculate the computational domain of the porous material catalyst layer.

[0112] S22 ， The computational domain of the material catalytic layer is used to perform root voronoi space segmentation, and the local connectivity information of the porous material is obtained based on the spatial segmentation information. The local connectivity information includes the location and size of the solid, pores and throats, as well as the connection relationship between the solid, pores and throats.

[0113] In some embodiments, the maximum sphere algorithm is applied to the pores and solid of the porous material catalyst layer to calculate the computational domain of the material catalyst layer, including the following steps:

[0114] S211 ， Based on the 3D spatial location and size distribution information of solids, the solid, boundary and pores are obtained;

[0115] S212 ， The maximum sphere is grown in the solid and numbered as 1. The generated maximum sphere is used as a new pore region. Then, a new maximum sphere is grown in the updated solid region until the volume of the maximum sphere grown in the solid reaches the set value.

[0116] S213 ， The maximum sphere is grown in the pores and assigned the number 2. The generated maximum sphere is used as a new solid region. Then, a new maximum sphere is grown in the updated pore region until the volume of the maximum sphere grown in the pores reaches the set value; thus, the computational domain of the porous material catalyst layer is obtained.

[0117] Specifically, the setting is eight times the spatial resolution of a CT scan.

[0118] In some embodiments, root voronoi space segmentation is performed based on the computational domain of the material catalytic layer, and local connectivity information of the porous material is obtained based on the spatial segmentation information, including the following steps:

[0119] S221 ， The actual porosity of the catalyst layer As the target porosity ,Right now ;

[0120] S222 ， Based on the Genvoronoi space partitioning, the entire catalytic layer is divided into n polyhedra; according to the largest sphere to which the polyhedron belongs, the polyhedron is labeled as follows: the polyhedron to which the largest sphere belongs is labeled as 1, the polyhedron to which the largest sphere belongs is labeled as 2;

[0121] S223 ， Add labels to the faces of polyhedra; set the common face of polyhedron labeled 1 to label 1, the common face of polyhedron labeled 2 to label 2, and the common face of polyhedrons labeled 1 and 2 to label 3.

[0122] S224 ， : Assign a thickness h to all faces of the polyhedron, and calculate the updated volume of the polyhedron based on the face thicknesses:

[0123] ,

[0124] in, For the updated polyhedral volume; The initial volume of the polyhedron. The area of ​​the unlabeled face of the polyhedron;

[0125] S225 ， The polyhedron formed by stretching the face labeled 1 is still solid, the polyhedron formed by stretching the face labeled 2 is still porous, and the polyhedron formed by stretching the face labeled 3 is half solid and half porous.

[0126] S226 ， : Calculate the updated porosity ;

[0127] S227 ， : Correct the thickness h of the polyhedron to achieve the updated porosity With target porosity If the difference is within the set allowable range, then the thickness h is considered to be set appropriately;

[0128] S228 ， : All polyhedra are updated based on the volume Equivalent to a sphere, and all the polyhedral throats are equivalent to cylinders with constant length based on the thickness being equal to the length, thus obtaining a nested network model.

[0129] Specifically, porosity The ratio of the sum of the areas of the polyhedra labeled 2 to the total area of ​​the catalyst layer is used.

[0130] In some embodiments, equations are used to describe the mass transport, charge transport, heat transport, and electrochemical reaction processes in the nested network model. Solving the equations yields the mass concentration in all pores, the temperature of all nodes, and the chemical reaction rate, including the following steps:

[0131] S31: Given initial conditions, including gas concentration, temperature and initial electrochemical reaction rate;

[0132] S32: Calculate the gas concentration in all pores and throats of a porous network using the oxygen diffusion law and the oxygen conservation equation:

[0133] ,

[0134] in, This represents the increase in the mass of oxygen in pore i per unit time; under steady-state conditions, this value is zero. This represents the gas conductivity of the throat between pore i and its adjacent pore j; This indicates the oxygen concentration in pore i. This indicates the oxygen concentration in pore j; This indicates that due to the electrochemical reaction, one-eighth of the total oxygen consumed per unit time by the eight aggregates surrounding pore i.

[0135] S33: Update the electrochemical reaction rates of solid-state network nodes by updating the gas concentration, Ohm's law, and the law of conservation of charge.

[0136] ,

[0137] ,

[0138] in, and These represent the current densities of electrons and protons in the throat connected to the aggregate, respectively; and These represent the cross-sectional areas of electron and proton transport in the solid throat, respectively; the surface area of ​​the aggregate is denoted as... The current density on the surface of the aggregate is expressed as: ;

[0139] S34: The current density of electrons and protons can be expressed as:

[0140] ,

[0141] ,

[0142] in, The electron current density; The current density of protons; It is the length of the throat in the solid network (actually a distribution value); and (Siemens per meter) represents the conductivity of electrons and protons, respectively; and These represent the potential difference between electrons and protons between two aggregates, respectively;

[0143] S35: Update the temperature of the solid network nodes and throat by updating the oxygen concentration, electrochemical reaction rate, Fourier's law of heat conduction, and the law of conservation of heat.

[0144] ,

[0145] in, This represents the thermal conductivity of the solid throat between aggregate i and its adjacent aggregate j. Indicates the temperature of aggregate i. The temperature of aggregate j is represented by ; the heat generated per unit time in aggregate i due to electrochemical reactions and overpotential, and the heat loss due to water evaporation, are respectively represented by . and Indicates the ohmic heat dissipation per unit time in the solid throat connecting aggregate i. express.

[0146] In some embodiments, the method further includes: using the updated results of oxygen concentration in the porous network, electrochemical reaction rate in the solid network, and temperature as initial values, and repeatedly updating them until the difference between the chemical reaction rates of two iterations, the difference between the temperatures of two iterations, or the difference between the oxygen concentrations of two iterations are within a set value, then the error is considered to be within the allowable range, i.e., the model is successfully solved.

[0147] Figure 5 This is a schematic diagram illustrating the effect of solid network node size on oxygen concentration distribution in a nested network model according to an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the influence of solid network node size on the current density distribution of the porous catalyst layer in the nested network model of this invention. Figure 7 This is a schematic diagram illustrating the effect of solid network node size on the temperature distribution of the porous catalyst layer in the nested network model of this invention.

[0148] Figures 5-7 The distribution of oxygen concentration, current density, and temperature along the thickness direction of the catalyst layer is shown, calculated using a nested network model.

[0149] Although specific embodiments have been described above, these embodiments are not intended to limit the scope of the invention, even when only a single embodiment is described with respect to a particular feature. The feature examples provided in this disclosure are intended to be illustrative and not limiting, unless otherwise stated. In practice, one or more technical features of the dependent claims may be combined with the technical features of the independent claims as needed and where technically feasible, and may be derived from the technical features of the respective independent claims in any suitable manner rather than solely by the specific combinations listed in the claims.

[0150] While the present invention has been disclosed above, it is not limited thereto. Any person skilled in the art can make various modifications and alterations without departing from the spirit and scope of the invention; therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.

Claims

1. A method for constructing a nested network model of a porous material, characterized by, The method comprises the following steps: Obtaining a three-dimensional morphology of the porous material, obtaining solid 3D spatial position and size distribution information of the porous material catalytic layer and obtaining actual porosity of the catalytic layer according to the three-dimensional morphology of the porous material ; Based on the 3D spatial position and size distribution information of the porous material, a nested network model of the porous material catalytic layer is constructed by a regular network extraction method or an improved MS-RVT algorithm; the nested network model of the porous material catalytic layer is constructed by the regular network extraction method, including the following steps: the catalytic layer is simplified into a regular network structure, a solid network model is constructed in a calculation domain, model parameters are set, and porosity is calculated according to the model parameters; the model parameters include: solid node spacing , solid node number , solid node radius , radius and length of a cylindrical solid throat connecting the solid nodes and ; the porosity is calculated by the following formula: , wherein, is the porosity; is the solid node spacing; is the solid node number; is the solid node radius; and are the radius and length of the cylindrical solid throat connecting the solid nodes, respectively; a pore network is constructed in the solid network model to obtain the nested network model; The material transport, charge transport, heat transport and electrochemical reaction process in the nested network model are described by equations, and the equations are solved to obtain the material concentration of all pores, the temperature of all nodes and the chemical reaction rate.

2. The method of claim 1, wherein, The solid network model is constructed in the calculation domain, and the model parameters are set, including the following steps: The actual porosity of the catalytic layer is determined by the following equation: The target porosity is 0.

4. That is, ; Placing the solid node rule into the Cartesian coordinate system, setting the solid node radius ; solid throats of connected cylinders are arranged between all adjacent solid nodes, the axial direction of the solid throat is along the x-axis, y-axis or z-axis direction; the length of the solid throat The solid node spacing is reduced by the sum of the radii of the two connected solid nodes, and the radius of the solid throat Determined according to the pore throat volume ratio; The positions and sizes of the solid nodes and solid throats, and the connection relationship between all solid nodes and solid throats are obtained; Porosity was calculated according to the formula ; The model parameters are corrected so that the difference between the calculated porosity and the target porosity is within the set allowed range, and the solid network model construction is completed.

3. The method of claim 1, wherein, The pore network is constructed in the solid network model, including the following steps: setting a pore node, the position of all pore nodes of the pore network being the position coordinates of the solid node so that the solid network and the pore network are uniformly nested; The pore node spacing of the pore network is set to the solid node spacing ; The equivalent radius of the pore node in the pore network is calculated through the positions of the solid nodes and the pore nodes and the sizes of the 8 solid nodes and 12 solid throats around the pore node: ， wherein, represents the equivalent radius of the pore node i; is the ratio of the volume of the pore node to the total volume of all pore nodes and all pore throats in the pore network, represents the radius of the jth solid node around the pore node i; k represents the kth solid throat around the pore node i; is the solid node spacing; and are the radius and length of the cylindrical solid throat connecting the solid nodes, respectively. The equivalent radius of the pore throat in the pore network is calculated by the following formula: ， wherein, represents the equivalent radius of the pore throat k in the pore network; is the ratio of the volume of the pore node in the pore network to the total volume of all pore nodes and the pore throat, and are the radii of the first and second pore nodes connected to the pore throat k in the pore network, respectively. The throat connects all adjacent pore nodes and solid nodes, and the pore network construction is completed.

4. The method of claim 1, wherein, The nested network model of the porous material catalyst layer is constructed by the improved MS-RVT algorithm, including the following steps: The maximum sphere algorithm is used in the pores and solid of the porous material catalyst layer to calculate the calculation domain of the porous material catalyst layer; Based on the calculation domain of the material catalyst layer, the root Voronoi spatial segmentation is performed, and the local connectivity information of the porous material is obtained based on the spatial segmentation information; the local connectivity information includes the positions, sizes of the solid, pores and throats, and the connection relationship between the solid, pores and the throats.

5. The method of claim 4, wherein, The maximum sphere algorithm is used in the pores and solid of the porous material catalyst layer to calculate the calculation domain of the material catalyst layer, including the following steps: Based on the 3D spatial position and size distribution information of the solid, the solid, boundary and pores are obtained; The maximum sphere is grown in the solid, and the maximum sphere is set as No. 1; the generated maximum sphere is taken as a new pore region, and then a new maximum sphere is grown in the updated solid region until the volume of the grown maximum sphere in the solid reaches a set value; The maximum sphere is grown in the pore, and the maximum sphere is set as No. 2; the generated maximum sphere is taken as a new solid region, and then a new maximum sphere is grown in the updated pore region until the volume of the grown maximum sphere in the pore reaches a set value; the calculation domain of the porous material catalyst layer is obtained.

6. The method of claim 5, wherein, Based on the calculation domain of the material catalyst layer, the root Voronoi spatial segmentation is performed, and the local connectivity information of the porous material is obtained based on the spatial segmentation information, including the following steps: The actual porosity of the catalytic layer is determined by the following equation: The target porosity is 0.

4. i.e. ; Based on the root Voronoi spatial segmentation, the entire catalyst layer is segmented into n polyhedrons; according to the maximum sphere to which the polyhedron belongs, the polyhedron is labeled; the polyhedron belonging to the maximum sphere numbered 1 is labeled as 1, and the polyhedron belonging to the maximum sphere numbered 2 is labeled as 2; The faces of the polyhedron are labeled; the common faces of the polyhedron with label 1 are labeled as 1, the common faces of the polyhedron with label 2 are labeled as 2, and the common faces of the polyhedron with label 1 and label 2 are labeled as 3, The thickness h of all faces of the polyhedron is set, and the volume of the updated polyhedron is calculated according to the thickness of the face: ， wherein, is the updated polyhedral volume; is the initial polyhedral volume, is the area of the untagged face of the polyhedron. The polyhedron stretched by the face with label 1 is still solid, the polyhedron stretched by the face with label 2 is still pore, and the polyhedron stretched by the face with label 3 is half solid and half pore; Computing an updated porosity ; The thickness h of the modified polyhedron is corrected so that the updated porosity differs from the target porosity by an amount within a set allowable range, and it is determined that the thickness h is set appropriately. All polyhedra are converted to updated volumes Equivalent to spheres and all polyhedron throats are equivalent to constant length cylinders with thickness equal to length, resulting in a nested network model.

7. The method of claim 1, wherein, The equations are used to describe the material transport, charge transport, heat transport and electrochemical reaction processes in the nested network model, the equations are solved to obtain the material concentration of all pores, the temperature and chemical reaction rate of all nodes, including the following steps: Given initial conditions, including gas concentration, temperature and initial electrochemical reaction rate; The gas concentration of all pores and throats in the pore network is calculated by the oxygen diffusion law and the oxygen conservation equation: ， wherein, represents the increment of oxygen mass in the pore i per unit time, which value is zero in steady state conditions; represents the gas conductance of the throat between the pore i and the adjacent pore j; represents the oxygen concentration in the pore i, represents the oxygen concentration in the pore j; represents one eighth of the total amount of oxygen consumed per unit time by the eight agglomerates surrounding the pore i due to the electrochemical reaction; The electrochemical reaction rate of the solid network nodes is updated by the updated gas concentration, Ohm's law and the charge conservation law: ， ， where and denote the current density of electrons and protons, respectively, connected to the throat of the agglomerate; and denote the cross-sectional area for the transport of electrons and protons, respectively, in the solid throat; the surface area of the agglomerate is denoted by ; the current density at the surface of the agglomerate is denoted by ; The current density of electrons and protons can be represented as: ， ， wherein, is the current density of electrons; is the current density of protons; is the length of the throat in the solid network; and denote the conductivity of electrons and protons, respectively; and denote the potential difference of electrons and protons between the two agglomerates, respectively. The temperature of the solid network nodes and the throats is updated by the updated oxygen concentration, electrochemical reaction rate, Fourier heat conduction law and heat conservation law: ， wherein represents the thermal conductivity of the solid throat between agglomerate i and its adjacent agglomerate j, represents the temperature of agglomerate i, represents the temperature of agglomerate j; the heat generated in agglomerate i per unit time due to the electrochemical reaction and overpotential, and the heat loss due to water evaporation, are represented by and respectively. The ohmic heat dissipation per unit time in the solid throat connecting agglomerate i is represented by .

8. The method of claim 7, wherein, Also including: The updated results of the oxygen concentration in the pore network, the electrochemical reaction rate and the temperature in the solid network are taken as the initial values, and the updating is repeated until the difference in the chemical reaction rate between two iterations, the temperature difference between two iterations or the oxygen concentration difference between two iterations is within the set value, then it is considered that the error is within the allowable range, that is, the model solving is successful.

9. The method of claim 1, wherein, The y-z cross section of the porous material catalytic layer is scanned layer by layer by X-ray microtomography, and the three-dimensional morphology of the porous material catalytic layer is obtained by image recognition and processing.

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