Method for constructing nested network model of porous material

Abstract

The invention relates to the technical field of porous materials, in particular to a method for constructing a nested network model of a porous material, which comprises the following steps: acquiring the three-dimensional shape of the porous material, acquiring the solid 3D spatial position and size distribution information of a catalyst layer of the porous material according to the three-dimensional shape of the porous material, and acquiring the actual porosity of the catalyst layer; based on the 3D spatial position and size distribution information of the porous material, constructing a nested network model of a porous material catalyst layer through a regular network extraction method or an improved MS-RVT algorithm; and adopting an equation to describe the material transfer, charge transfer, heat transfer and electrochemical reaction processes in the nested network model, solving the equation, and obtaining the material concentration of all pores, the temperature of all nodes and the chemical reaction rate. By adopting the method, the real microstructure of the porous catalyst can be reflected, and the material transmission and reaction rate distribution in the whole catalyst area can be obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of porous materials, and in particular to a nested network model construction method of porous materials. BACKGROUND

[0002] The mass transport and chemical reaction in porous catalysts, as one of the key common basic researches, have important applications in the fields of energy and environment, such as industrial flue gas treatment systems, sewage / waste gas treatment stations, gas adsorption storage, medical raw material synthesis, fuel cells, and electrolysis of water and carbon dioxide, etc. With the increasingly serious problem of global climate change, carbon neutralization and sustainable development have become the world consensus. The research on porous catalysts has also gradually expanded to emerging technical fields such as resource utilization of carbon dioxide and hydrogen, geological sequestration catalytic conversion, and electrochemical energy storage and conversion.

[0003] In the past few years, high-resolution X-ray imaging and image processing-based analysis and simulation techniques have developed rapidly, promoting the research and engineering applications of the mass transport and chemical reaction mechanisms in porous catalysts. The traditional macroscopic continuity model relying on grid division, physical field discretization, and basic conservation laws can obtain some macroscopic parameters of the porous catalyst, but this method focuses on the macroscopic process and cannot describe the details of the local spatial structure. In recent years, micro-intermediate scale models that can efficiently describe the details of the microstructure have emerged. The pore network simulation regards the porous medium as being composed of connected pores and solids, and the pores are connected through throats for the mass transport and chemical reaction processes in the porous medium. Compared with the lattice Boltzmann method, the pore network model is considered as the most efficient mesoscale model due to its faster calculation speed.

[0004] Although the pore network model has been widely used in the mass transport behavior in the two-phase flow of porous materials, there are few studies on the mass transport and chemical reaction in porous catalysts. The main reason is that the research on porous catalysts involves more complex porous networks (gas network and solid network providing an electrochemical reaction site) and complex mass transport (mass transport in the gas network, mass transport in the solid network, and mass transport between the gas network and the solid network).

[0005] Therefore, it is necessary to provide a nested network model construction method of porous materials to effectively solve the above problems. SUMMARY

[0006] The embodiment of the present application provides a nested network model construction method of porous materials.

[0007] The nested network model construction method of porous materials provided by the embodiment of the present application and the mass transport and chemical reaction analysis method comprise the following steps: The three-dimensional morphology of the porous material is acquired, the solid 3D spatial position and size distribution information of the porous material catalytic layer is obtained according to the three-dimensional morphology of the porous material, and the actual porosity of the catalytic layer is obtained ; 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 equation is used to describe the material transport, charge transport, heat transport and electrochemical reaction process in the nested network model, and the equation is solved to obtain the material concentration of all pores, the temperature and chemical reaction rate of all nodes.

[0008] Preferably, the nested network model of the porous material catalytic layer is constructed by a regular network extraction method, which includes the following steps: The catalytic layer is simplified as a regular network structure, a solid network model is constructed in the calculation domain, model parameters are set, and the 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 the cylindrical solid throat connecting the solid nodes; 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; The pore network is constructed in the solid network model to obtain the nested network model.

[0009] Preferably, 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 taken as the target porosity , that is ; The solid nodes are regularly placed in the Cartesian coordinate system, and the solid node radius is set; The cylindrical solid throat connecting all adjacent solid nodes is set, and the axial direction of the solid throat is along the x-axis, y-axis or z-axis direction; the length of the solid throat is the solid node spacing minus the sum of the radii of the two connected solid nodes, and the radius of the solid throat Determined according to the volume ratio of the pore throat; The position and size of the solid nodes and solid throats, and the connection relationship of all solid nodes and solid throats are obtained; The porosity is 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 allowable range, and the solid network model construction is completed.

[0010] Preferably, the pore network is constructed in the solid network model, including the following steps: Set the pore nodes, and the position of all pore nodes of the pore network is the position coordinates of the solid nodes , so that the solid network and the pore network are uniformly nested; The pore node spacing of the pore network is set as the solid node spacing ; The equivalent radius of the pore node in the pore network is calculated through the position of the solid node and the pore node and the size 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 proportion of the pore node volume in 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 proportion of the pore node volume in the total volume of all pore nodes and the pore throat in the pore network, and are the radius of the first pore node and the second pore node connected with the pore throat K in the pore network, respectively; The throats are set to connect all adjacent pore nodes and solid nodes, and the pore network construction is completed.

[0011] Preferably, the nested network model of the porous material catalytic layer is constructed by the improved MS-RVT algorithm, comprising the following steps: The maximum sphere algorithm is used in the pores and solids of the porous material catalytic layer to calculate the calculation domain of the porous material catalytic layer; Root Voronoi spatial segmentation is performed based on the calculation domain of the material catalytic layer, and 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 solids, pores and throats, and the connection relationship between the solids, pores and the throats.

[0012] Preferably, the maximum sphere algorithm is used in the pores and solids of the porous material catalytic layer to calculate the calculation domain of the material catalytic layer, comprising the following steps: Based on the 3D spatial position and size distribution information of the solids, the solids, boundaries and pores are obtained; The maximum sphere is grown in the solids, 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 pores, 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 catalytic layer is obtained.

[0013] Preferably, root Voronoi spatial segmentation is performed based on the calculation domain of the material catalytic layer, and local connectivity information of the porous material is obtained based on the spatial segmentation information, comprising the following steps: The actual porosity of the catalytic layer is taken as the target porosity , i.e. ; The entire catalytic layer is segmented into n polyhedrons based on the root Voronoi spatial segmentation; the polyhedrons are labeled according to the maximum spheres to which the polyhedrons belong; the polyhedrons belonging to the maximum sphere No. 1 are set as label 1, and the polyhedrons belonging to the maximum sphere No. 2 are set as label 2; The faces of the polyhedrons are labeled; the common faces of the polyhedrons with label 1 are set as label 1, the common faces of the polyhedrons with label 2 are set as label 2, and the common faces of the polyhedrons with label 1 and label 2 are set as label 3, The thickness h is set for all the faces of the polyhedrons, and the volume of the updated polyhedrons is calculated according to the thickness of the faces: , wherein, is the volume of the updated polyhedrons; is the volume of the initial polyhedrons, is the area of ​​the unlabeled face of the polyhedron; 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. Calculate updated porosity ; Modify the thickness h of the polyhedron so that the updated porosity With target porosity If the difference is within the set allowable range, the thickness h is considered to be set appropriately; Set all polyhedra based on the updated volume Equivalent to a sphere, and all polyhedral throats are equivalent to cylinders with constant length according to the thickness equal to the length, to obtain a nested network model.

[0014] Preferably, equations are used to describe the material transport, charge transport, heat transport, and electrochemical reaction processes in the nested network model, and solving the equations to obtain the material concentrations of all pores, the temperatures of all nodes, and the chemical reaction rates includes the following steps: Given initial conditions, including gas concentration, temperature, and initial electrochemical reaction rate; The gas concentration in all pores and throats in the pore network is calculated using the oxygen diffusion law and the oxygen conservation equation: , in, It represents the increment of oxygen mass in pore i per unit time, and is zero under steady-state conditions; represents the gas conductivity of the throat between pore i and adjacent pore j; represents the oxygen concentration in pore i, represents the oxygen concentration in pore j; represents one eighth of the total oxygen consumed per unit time by the eight aggregates surrounding pore i due to electrochemical reactions; Update the electrochemical reaction rates of the solid network nodes using the updated gas concentration, Ohm's law, and the law of conservation of charge: , , in, and denote the current densities of electrons and protons in the throat connected to the agglomerate, respectively; and are the cross-sectional areas of electron and proton transport in the solid throat, respectively; the surface area of ​​the agglomerates is The current density on the aggregate surface is expressed as ; The current density of electrons and protons can be expressed as: , , where, is the current density of electrons; is the current density of protons; is the length of the throat in the solid network; and represent the conductivity of electrons and protons, respectively; and represent the potential difference of electrons and protons between two agglomerates, respectively; The temperature of the solid network nodes and throats is updated by the updated oxygen concentration, electrochemical reaction rate, Fourier heat conduction law, and heat conservation law: , where, 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 electrochemical reaction and overpotential, and the heat loss caused by water evaporation, are represented by and , respectively; the ohmic heat dissipation per unit time in the solid throat connecting agglomerate i is represented by .

[0015] Preferably, the method further comprises: taking the updated results of the oxygen concentration in the pore network and the electrochemical reaction rate and temperature in the solid network as initial values, repeating the updating until the difference in chemical reaction rate between two iterations, the difference in temperature between two iterations, or the difference in oxygen concentration between two iterations is within a set value, then considering that the error is within an allowable range, i.e. the model solving is successful.

[0016] Preferably, 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.

[0017] Compared with the prior art, the technical scheme of the embodiment of the present application has beneficial effects.

[0018] For example, the method provided by the present application for constructing a nested network model of a porous material and analyzing material transport and chemical reaction obtains the three-dimensional morphology of the porous material, obtains the solid 3D spatial position and size distribution information of the porous material catalytic layer according to the three-dimensional morphology of the porous material, and obtains the actual porosity of the catalytic layer ; 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 rule network extraction method or an improved MS-RVT algorithm; equations are used to describe the material transmission, charge transmission, heat transmission and electrochemical reaction process in the nested network model, the equations are solved, and the material concentration of all pores, the temperature and chemical reaction rate of all nodes are obtained; by establishing the nested network model, the influence of the porous catalyst structure on the material transmission and chemical reaction therein is studied, and the material concentration and reaction rate distribution are extracted, thereby providing a basis for subsequent optimization of the porous catalyst structure and preparation method. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 A flowchart of a nested network model construction and material transmission and chemical reaction analysis method for the porous material of the embodiment of the present application is shown in Figure 1. Figure 2 A nested network model structure schematic diagram obtained by using a rule network extraction method for the embodiment of the present application is shown in Figure 2. Figure 3 A nested network model structure schematic diagram obtained by using an improved MS-RVT algorithm for the embodiment of the present application is shown in Figure 3. Figure 4 A unit structure schematic diagram of the nested network model obtained by using the improved MS-RVT algorithm for the embodiment of the present application is shown in Figure 4. Figure 5 An influence schematic diagram of the solid network node size in the nested network model on the oxygen concentration distribution of the porous catalytic layer for the embodiment of the present application is shown in Figure 5. Figure 6 An influence schematic diagram of the solid network node size in the nested network model on the current density distribution of the porous catalytic layer for the embodiment of the present application is shown in Figure 6. Figure 7 An influence schematic diagram of the solid network node size in the nested network model on the temperature distribution of the porous catalytic layer for the embodiment of the present application is shown in Figure 7. DETAILED DESCRIPTION

[0020] In order to make the purpose, features and beneficial effects of the present application more obvious and easy to understand, the specific embodiments of the present application are described in detail below with reference to the drawings. It can be understood that the following specific embodiments are only used to explain the present application, but not to limit the present application. In the drawings, the same or similar reference numerals may be used to refer to the same or similar elements in different embodiments, and the description of the same or similar elements in different embodiments and the description of prior art elements, features, effects, etc. may be omitted.

[0021] REFERENCE Figures 1 to 4 The embodiment of the present application provides a nested network model construction and material transmission and chemical reaction analysis method for a porous material.

[0022] Specifically, the method for constructing a nested network model of a porous material and analyzing material transport and chemical reactions provided by the embodiments of the present application comprises the following steps: S1: obtaining a three-dimensional morphology of the porous material, obtaining solid 3D spatial position and size distribution information of a catalytic layer of the porous material according to the three-dimensional morphology of the porous material, and obtaining an actual porosity of the catalytic layer S2: based on the 3D spatial position and size distribution information of the porous material, constructing a nested network model of the catalytic layer of the porous material by a regular network extraction method or an improved MS-RVT (Radar-assisted View Transformation, RVT) algorithm S3: using equations to describe material transport, charge transport, heat transport and electrochemical reaction processes in the nested network model, solving the equations, and obtaining material concentrations of all pores, temperatures of all nodes and chemical reaction rates.

[0023] Specifically, the equations for describing material transport include convection-diffusion equations, Darcy's law, etc.; the equations for describing charge transport include charge conservation, Ohm's law, etc.; the equations for describing heat transport include energy conservation equations, Fourier heat conduction equations, etc.; and the equations for describing electrochemical reactions include Nernst equations, Butler-Volmer equations, etc.

[0024] In some embodiments, the three-dimensional morphology of the catalytic layer of the porous material is obtained by layer-by-layer scanning of a y-z cross section of the catalytic layer of the porous material using X-ray microtomography, and the three-dimensional morphology of the catalytic layer of the porous material is obtained by image recognition and processing.

[0025] Specifically, the image processing method includes binarization, MASK-RCNN (Mask Region-based Convolutional Neural Network), etc.

[0026] Specifically, other methods that can obtain the real microstructure of the porous material can also be used instead of X-ray microtomography, which is not limited here.

[0027] In some embodiments, the nested network model of the catalytic layer of the porous material is constructed by a regular network extraction method, comprising the following steps: S21: simplifying the catalytic layer into a regular network structure, constructing a solid network model in a calculation domain, setting model parameters, and calculating the porosity according to the model parameters; the model parameters include: solid node spacing , solid node number , and solid node radius ​a radius of a cylindrical solid throat connecting the solid nodes and a length ; the porosity is calculated by the following formula: , wherein, porosity; solid node spacing; solid node number; solid node radius; and are respectively a radius and a length of a cylindrical solid throat connecting the solid nodes; S22: constructing a pore network in the solid network model to obtain a nested network model.

[0028] In some embodiments, the solid network model is constructed in the computational domain, and the model parameters are set, including the following steps: S211: setting an actual porosity of the catalytic layer as a target porosity , i.e. ; S212: placing solid nodes regularly in a Cartesian coordinate system, and setting a solid node radius ; S213: setting a connected cylindrical solid throat between all adjacent solid nodes, and the axial direction of the solid throat is along the x-axis, y-axis or z-axis direction; the length of the solid throat is the solid node spacing minus the sum of the radii of the two connected solid nodes, and the radius of the solid throat is determined according to the pore throat volume ratio; S214: obtaining the positions and sizes of the solid nodes and the solid throats, and the connection relationship of all the solid nodes and the solid throats; S215: calculating the porosity according to the formula; S216: correcting the model parameters so that the difference between the calculated porosity and the target porosity is within the set allowable range, and the solid network model construction is completed.

[0029] In some embodiments, the pore network is constructed in the solid network model, including the following steps: S221: setting a pore node, and the position of all the pore nodes of the pore network is the solid node position coordinate , so that the solid network and the pore network are uniformly nested; S222: setting the pore node spacing of the pore network as the solid node spacing ; S223: Calculates the equivalent radius of a pore node in a pore network using the positions of the solid and pore nodes and the dimensions of the 8 solid nodes and 12 solid throats surrounding the pore node: , Among them, such as Figure 4 The unit structure shown, represents the equivalent radius of pore node i; is the ratio of the volume of pore nodes 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; S224: The equivalent radius of the pore throat in the pore network is calculated using the following formula: , in, represents the equivalent radius of the pore throat K in the pore network; is the ratio of the volume of pore nodes to the total volume of all pore nodes and pore throats in the pore network, and are the radii of the first and second pore nodes connected to the pore throat K in the pore network, respectively; S225: Set throats to connect all adjacent pore nodes and solid nodes to complete the pore network construction.

[0030] In some embodiments, a nested network model of a porous material catalytic layer is constructed using an improved MS-RVT algorithm, comprising the following steps: S21 ， :The maximum sphere algorithm is applied to the pores and solids of the porous material catalytic layer to calculate the computational domain of the porous material catalytic layer; S22 ， : Root-Voronoi space segmentation is performed based on the computational domain of the material catalytic layer, 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 solids, pores and throats, as well as the connection relationship between solids, pores and throats.

[0031] In some embodiments, a maximum sphere algorithm is applied to the pores and solids of a porous material catalyst layer to calculate a computational domain of the material catalyst layer, including the following steps: S211 ， : Based on the solid 3D spatial position and size distribution information, obtain solids, boundaries and pores; S212 ， : Grow the largest sphere in the solid and set the largest sphere as No. 1, take the generated largest sphere as the new pore region, then grow the new largest sphere in the updated solid region, until the volume of the largest sphere grown in the solid reaches a set value; S213 ， : Grow the largest sphere in the pore and set the largest sphere as No. 2, take the generated largest sphere as the new solid region, then grow the new largest sphere in the updated pore region, until the volume of the largest sphere grown in the pore reaches a set value; obtain the calculation domain of the porous material catalytic layer.

[0032] Specifically, the set value is eight times the spatial resolution of the CT scan.

[0033] In some embodiments, based on the calculation domain of the material catalytic layer, root Voronoi spatial segmentation is carried out, and based on the spatial segmentation information, local connectivity information of the porous material is obtained, including the following steps: S221 ， : Set the actual porosity of the catalytic layer as the target porosity , that is ; S222 ， : Divide the entire catalytic layer into n polyhedrons based on the root Voronoi spatial segmentation; according to the maximum sphere to which the polyhedron belongs, set a label for the polyhedron, and set the label as 1 for the maximum sphere numbered 1 to which the polyhedron belongs, and set the label as 2 for the maximum sphere numbered 2 to which the polyhedron belongs. S223 ， : Label the faces of the polyhedron; set the common faces of the polyhedrons with label 1 as label 1, set the common faces of the polyhedrons with label 2 as label 2, and set the common faces of the polyhedrons with label 1 and label 2 as label 3, S224 ， : Set the thickness h of all the faces of the polyhedron, and calculate the volume of the updated polyhedron according to the thickness of the face: , wherein, is the volume of the updated polyhedron; is the volume of the initial polyhedron, is the area of the face without label of the polyhedron; S225 ， : 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; S226 ， : Calculate the updated porosity ; S227 ， : revise the thickness h of the polyhedron so that the updated porosity is within the set tolerance from the target porosity ; if so, the thickness h is considered to be set properly; S228 ， : equivalent all the polyhedrons into spheres according to the updated volume , and equivalent all the polyhedron throats into constant-length cylinders according to the thickness equal to the length, to obtain a nested network model.

[0034] Specifically, the porosity is represented by the ratio of the sum of the areas of the polyhedrons with label 2 to the total area of the catalyst layer.

[0035] In some embodiments, the material transport, charge transport, heat transport, and electrochemical reaction processes in the nested network model are described by equations, and the equations are solved to obtain the material concentrations of all the pores, the temperatures of all the nodes, and the chemical reaction rates, including the following steps: S31 : given initial conditions, including gas concentrations, temperatures, and initial electrochemical reaction rates; S32 : calculate the gas concentrations of all the pores and throats in the pore network by the oxygen diffusion law and the oxygen conservation equation: , where represents the increment of the oxygen mass in pore i per unit time, which is zero under steady-state conditions; represents the gas conductance of the throat between pore i and adjacent pore j; represents the oxygen concentration in pore i, represents the oxygen concentration in pore j; represents one-eighth of the total amount of oxygen consumed per unit time by the eight agglomerates surrounding pore i due to electrochemical reactions; S33 : update the electrochemical reaction rates of the solid network nodes by the updated gas concentrations, Ohm's law, and the charge conservation law: , , where and represent the current densities of electrons and protons in the throats connected to the agglomerates, respectively; and represent the cross-sectional areas of electron and proton transport in the solid throats, respectively; the surface area of the agglomerate is denoted as ; the current density on the surface of the agglomerate is represented as ; S34: The current densities of electrons and protons can be expressed as: , , where, is the current density of electrons; is the current density of protons; is the length of the throat in the solid network (in fact, a distribution value); and represent the conductivities of electrons and protons, respectively (in Siemens per meter); and represent the potential differences of electrons and protons between two agglomerates, respectively; S35: Update the temperatures of the solid network nodes and the throats by the updated oxygen concentration, electrochemical reaction rate, Fourier heat conduction law, and heat conservation law: , where, 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 .

[0036] In some embodiments, further comprising: repeating the updating with the updated results of the oxygen concentration in the pore network, the electrochemical reaction rate and the temperature in the solid network as initial values until the difference of the chemical reaction rates of two iterations, the difference of the temperatures of two iterations, or the difference of the oxygen concentrations of two iterations is within a set value, then considering that the error is within an allowable range, i.e. the model solving is successful.

[0037] Figure 5 is a schematic diagram showing the influence of the solid network node size on the oxygen concentration distribution of the porous catalytic layer in the nested network model of the embodiments of the present application; Figure 6 is a schematic diagram showing the influence of the solid network node size on the current density distribution of the porous catalytic layer in the nested network model of the embodiments of the present application; Figure 7 is a schematic diagram showing the influence of the solid network node size on the temperature distribution of the porous catalytic layer in the nested network model of the embodiments of the present application.

[0038] Figures 5 to 7The distribution of oxygen concentration, current density and temperature along the thickness direction of the catalyst layer calculated by the nested network model is shown.

[0039] Although specific embodiments have been described above, these embodiments are not intended to limit the scope of the present disclosure, even if only a single embodiment is described with respect to a particular feature. The examples of features provided in the present disclosure are intended to be illustrative rather than limiting, unless expressly stated otherwise. In practice, one or more technical features of a dependent claim can be combined with technical features of an independent claim, and technical features from corresponding independent claims can be combined in any appropriate manner rather than only through the specific combinations listed in the claims, provided that such combinations are technically feasible.

[0040] Although the present disclosure has been described as above, the present disclosure is not limited thereto. Any person skilled in the art can make various modifications and changes without departing from the spirit and scope of the present disclosure, and the scope of protection of the present disclosure should be defined by the scope defined by the claims.

Claims

1. A method for constructing a nested network model of porous materials, characterized in that: The steps include: Obtain the three-dimensional morphology of the porous material, and based on the three-dimensional morphology of the porous material, obtain the solid 3D spatial position and size distribution information of the porous material catalyst layer, and obtain the actual porosity of the catalyst layer ; 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 rule network extraction method or an improved MS-RVT algorithm; 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 of all nodes, and the chemical reaction rate.

2. The method for constructing a nested network model of porous materials according to claim 1, characterized in that: The nested network model of the porous material catalytic layer is constructed using a 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 the calculation domain, model parameters are set, and the porosity is calculated based on the model parameters; the model parameters include: solid node spacing , the number of solid nodes , solid node radius , the radius of the cylindrical solid throat connecting the solid nodes and length ; The porosity is calculated by the following formula: ， in, is the porosity; is the solid node spacing; is the number of solid nodes; is the solid node radius; and are the radius and length of the cylindrical solid throat connecting the solid nodes; A pore network is constructed in the solid network model to obtain a nested network model.

3. The method for constructing a nested network model of porous materials according to claim 2, wherein: Constructing a solid network model in the computational domain and setting model parameters include the following steps: The actual porosity of the catalytic layer As the target porosity ,Right now ; Place the solid nodes regularly in the Cartesian coordinate system and set the solid node radius ; A cylindrical solid throat is set between all adjacent solid nodes, and the axial direction of the solid throat is 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 distance between the solid nodes. Determined based on the pore-throat volume ratio; Obtain the positions and sizes of solid nodes and solid throats, as well as the connection relationships between all solid nodes and solid throats; Calculate the porosity according to the formula ; Modify the model parameters so that the calculated porosity With target porosity The difference is within the set allowable range, and the solid network model is constructed.

4. The method for constructing a nested network model of porous materials according to claim 1, wherein: Constructing a pore network in a solid network model involves the following steps: Set the pore nodes. The positions of all pore nodes in the pore network are the solid node position coordinates. , so that the solid network and the pore network are evenly nested; Set the pore node spacing of the pore network to the solid node spacing ; The equivalent radius of the pore node in the pore network is calculated by the positions of the solid nodes and pore nodes and the sizes of the 8 solid nodes and 12 solid throats around the pore node: ， in, represents the equivalent radius of pore node i; is the ratio of the volume of pore nodes 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; The equivalent radius of the pore throat in the pore network is calculated by the following formula: ， in, represents the equivalent radius of the pore throat K in the pore network; is the ratio of the volume of pore nodes in the pore network to the total volume of all pore nodes and the pore throats, and are the radii of the first and second pore nodes connected to the pore throat K in the pore network, respectively; Set the throat to connect all adjacent pore nodes and solid nodes to complete the pore network construction.

5. The method for constructing a nested network model of porous materials according to claim 1, characterized in that: The nested network model of the porous material catalytic layer is constructed using the improved MS-RVT algorithm, including the following steps: The maximum sphere algorithm is applied to the pores and solids of the porous material catalytic layer to calculate the computational domain of the porous material catalytic layer. Root Voronoi space segmentation is performed based on the calculation domain of the material catalytic layer, and local connectivity information of the porous material is obtained based on the space segmentation information; the local connectivity information includes the position and size of the solid, pore and throat, and the connection relationship between the solid, pore and throat.

6. The method for constructing a nested network model of porous materials according to claim 5, characterized in that: The maximum sphere algorithm is applied to the pores and solids of the porous material catalytic layer to calculate the computational domain of the material catalytic layer, including the following steps: Obtain solids, boundaries, and pores based on the solid 3D spatial position and size distribution information; Grow a maximum sphere in the solid and set the maximum sphere to 1. Use the generated maximum sphere as a new pore area, and then grow a new maximum sphere in the updated solid area until the volume of the maximum sphere grown in the solid reaches the set value. A maximum sphere is grown in the pores and numbered 2. The generated maximum sphere is used as a new solid region, and 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; the calculation domain of the porous material catalytic layer is obtained.

7. The method for constructing a nested network model of porous materials according to claim 6, characterized in that: Performing root Voronoi space segmentation based on the computational domain of the material catalytic layer, and obtaining local connectivity information of the porous material based on the space segmentation information, including the following steps: The actual porosity of the catalytic layer As the target porosity ,Right now ; The entire catalytic layer is divided into n polyhedrons based on the root-Voronoi space partitioning. The polyhedrons are labeled according to the largest sphere to which they belong. The label of the polyhedron whose largest sphere number is 1 is 1, and the label of the polyhedron whose largest sphere number is 2 is 2. Label the faces of the polyhedron; set the common face of the polyhedron with label 1 to label 1, set the common face of the polyhedron with label 2 to label 2, and set the common face of the polyhedron with labels 1 and 2 to label 3. Set the thickness h for all faces of the polyhedron, and calculate the volume of the updated polyhedron based on the thickness of the faces: ， in, is the updated polyhedron volume; is the initial polyhedron volume, is the area of ​​the unlabeled face of the polyhedron; 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. Calculate updated porosity ; Modify the thickness h of the polyhedron so that the updated porosity With target porosity If the difference is within the set allowable range, the thickness h is considered to be set appropriately; Set all polyhedra based on the updated volume Equivalent to a sphere, and all polyhedral throats are equivalent to cylinders with constant length according to the thickness equal to the length, to obtain a nested network model.

8. The method for constructing a nested network model of porous materials according to claim 1, wherein: Equations are used to describe the material transport, charge transport, heat transport, and electrochemical reaction processes in the nested network model. Solving the equations to obtain the material concentrations of all pores, the temperatures of all nodes, and the chemical reaction rates includes the following steps: Given initial conditions, including gas concentration, temperature, and initial electrochemical reaction rate; The gas concentration in all pores and throats in the pore network is calculated using the oxygen diffusion law and the oxygen conservation equation: ， in, It represents the increment of oxygen mass in pore i per unit time, and is zero under steady-state conditions; represents the gas conductivity of the throat between pore i and adjacent pore j; represents the oxygen concentration in pore i, represents the oxygen concentration in pore j; represents one eighth of the total oxygen consumed per unit time by the eight aggregates surrounding pore i due to electrochemical reactions; Update the electrochemical reaction rates of the solid network nodes using the updated gas concentration, Ohm's law, and the law of conservation of charge: ， ， in, and denote the current densities of electrons and protons in the throat connected to the agglomerate, respectively; and are the cross-sectional areas of electron and proton transport in the solid throat, respectively; the surface area of ​​the agglomerates is The current density on the surface of the aggregate is expressed as ; The current density of electrons and protons can be expressed as: ， ， in, is the electron current density; is the current density of protons; is the length of the throat in the solid network; and represent the conductivity of electrons and protons, respectively; and represent the potential differences of electrons and protons between the two aggregates, respectively; Update the temperatures of the solid network nodes and throats using the updated oxygen concentration, electrochemical reaction rate, Fourier's law of heat conduction, and the law of conservation of heat: ， in, represents the thermal conductivity of the solid throat between aggregate i and its adjacent aggregate j, represents the temperature of aggregate i, represents the temperature of aggregate j; the heat generated in aggregate i per unit time due to electrochemical reaction and overpotential, as well as the heat loss due to water evaporation, are expressed as and The ohmic heat dissipation per unit time in the solid throat connecting the aggregate i is expressed as express.

9. The method for constructing a nested network model of porous materials according to claim 8, characterized in that: Also includes: The updated results of the oxygen concentration in the pore network, the electrochemical reaction rate and the temperature in the solid network are used as the initial values ​​and are updated repeatedly until the difference between the chemical reaction rate of two iterations, the temperature difference of two iterations or the oxygen concentration difference of two iterations is within the set value. The error is considered to be within the allowable range, that is, the model solution is successful.

10. The method for constructing a nested network model of porous materials according to claim 1, characterized in that: The yz cross-section of the porous material catalytic layer is scanned layer by layer by using X-ray microtomography, and the three-dimensional morphology of the porous material catalytic layer is obtained through image recognition and processing.

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