A pore network structure extraction method based on neighborhood search

Abstract

The present invention discloses a pore network structure extraction method based on neighborhood search, which belongs to the field of porous medium model construction and includes the following steps: Step 1, obtaining a rock image, generating a binary model of the rock porous medium, eliminating isolated pores, and constructing an initial porous medium model; Step 2, randomly determining an initial search point, generating a neighboring element and a neighborhood list of the initial search point; Step 3, determining the pore center of the porous medium model based on the initial search point; Step 4, determining the maximum distance function gradient based on the neighboring element list, thereby determining the central axis element set of the pore network structure; Step 5, combining the central axis element set, finally determining the pore center and pore throat position of the porous medium model, and determining the entire pore network structure based on the pore center and pore throat position. The present invention has high computational efficiency and can achieve efficient extraction of the pore network structure of high-resolution rock images.

Description

Technical Field

[0001] The present invention belongs to the field of porous medium model construction, and in particular relates to a pore network structure extraction method based on neighborhood search. Background Art

[0002] High-resolution rock images lead to low efficiency in extracting pore network structures, so there is an urgent need to develop efficient pore network structure extraction methods.

[0003] Advances in imaging technology and machine learning methods are driving the high-resolution and high-precision imaging of subsurface rock, posing challenges for the efficient extraction of pore network structures from porous media models. Therefore, efficient extraction of pore network structures from highly accurate porous media models is crucial. However, current extraction methods typically process the entire porous media model, requiring computation for every pixel or voxel in the model. This results in low efficiency and high computational resource requirements. Therefore, achieving pore network structure extraction with minimal computational resources is a pressing issue. Summary of the Invention

[0004] To address the problem that existing pore network extraction methods have low computational efficiency for the entire porous media model and are difficult to achieve efficient extraction of high-resolution models, this paper proposes a pore network structure extraction method based on neighborhood search. This method uses a binary image of a rock porous medium to eliminate isolated pores and determine a random initial search point. Based on the search point, the neighboring elements are determined and their neighborhood list is compiled. The pore center of the porous medium is determined by using the principles of gradient descent and neighborhood search, thereby determining the central axis position of the pore network. Combined with the central axis elements, the pore center and pore throat position of the porous medium are finally determined.

[0005] The technical solutions of the present invention are as follows:

[0006] A pore network structure extraction method based on neighborhood search includes the following steps:

[0007] Step 1: Obtain rock images, generate a binary model of rock porous media, remove isolated pores, and construct an initial porous media model;

[0008] Step 2: Randomly determine the initial search point and generate the neighboring elements and neighborhood list of the initial search point;

[0009] Step 3: Based on the initial search point, determine the pore center of the porous media model;

[0010] Step 4: Based on the list of neighboring elements, determine the maximum distance function gradient, thereby determining the central axis element set of the pore network structure;

[0011] Step 5: Combine the central axis element set to finally determine the pore center and pore throat position of the porous medium model. The entire pore network structure can be determined based on the pore center and pore throat position.

[0012] Furthermore, the specific process of step 1 is as follows:

[0013] Step 1.1: Scan the rock image using digital CT technology to obtain the initial raw file. Use Avizo software to denoise and binarize the raw file to generate a binary model of the rock porous medium.

[0014] Step 1.2: Determine the solid phase region and the pore phase region based on the binary model to generate the target porous medium model. The specific generation process is as follows: define the position where the element value is 1 in the binary model as the solid phase, and define the position where the element value is 0 as the pore phase, thereby determining the solid phase and pore phase regions in the target porous medium model, and then generate the target porous medium model.

[0015] Step 1.3: Artificially set the open and closed boundary conditions of the target porous media model to determine connected pores and eliminate isolated pores:

[0016]

[0017] Where V con is a connected pore element; V iso It is an isolated pore element; is the pore element in the target porous media model; {X} is the element set after removing isolated pores;

[0018] Step 1.4: Reconstruct the porous medium model based on the element set after eliminating isolated pores, and define the porous medium model as the initial porous medium model.

[0019] Furthermore, the specific process of step 2 is as follows:

[0020] Step 2.1. Randomly select an element in the initial porous medium model as the initial search point. The porous medium model is divided into two-dimensional porous medium model and three-dimensional porous medium model. The position coordinates of the initial search points of different dimensional models are defined as follows:

[0021]

[0022] Where, is the position coordinate of the initial search point in the two-dimensional porous media model, are the x-direction and y-direction coordinates of the initial search point in the two-dimensional porous media model; is the position coordinate of the initial search point in the three-dimensional porous media model, are the x-, y-, and z-direction coordinates of the initial search point in the three-dimensional porous media model; random(·) is a random function;

[0023] Step 2.2: Generate a neighboring element list and a solid neighboring domain list based on the initial search point;

[0024] Based on the initial search point, the neighboring element list and solid neighboring domain list of the two-dimensional porous media model are generated. The specific calculation formula is:

[0025]

[0026]

[0027] Among them, N 2D is the list of neighboring elements for the two-dimensional porous media model; Represents the set of solid phase elements within the judgment distance in a two-dimensional porous media model; is the position coordinate of the solid adjacent domain elements in the two-dimensional porous media model, are the x-direction and y-direction coordinates of the solid adjacent domain elements in the two-dimensional porous media model; are the judgment distance values ​​in the x-direction and y-direction in the two-dimensional porous medium model respectively; {S} represents the element set of the entire solid phase; i is the solid adjacent domain element index, and n is the number of solid adjacent domain elements; is the position coordinate of the ith solid adjacent domain element in the two-dimensional porous media model, are the x-direction and y-direction coordinates of the ith solid adjacent domain element in the two-dimensional porous media model; is the neighborhood element set of the initial search point for the solid phase in the two-dimensional porous media model; r represents the cutoff radius;

[0028] Based on the initial search point, a list of neighboring elements and solid neighboring domains of the three-dimensional porous media model is generated. The specific calculation formula is:

[0029]

[0030]

[0031] Among them, N 3D is the list of neighboring elements of the three-dimensional porous media model; It is the set of solid phase elements within the judgment distance in the three-dimensional porous media model; are the position coordinates of the solid adjacent domain elements in the three-dimensional porous media model, are the x-, y-, and z-direction coordinates of the solid adjacent domain elements in the two-dimensional porous media model; are the judgment distance values ​​in the x-direction, y-direction, and z-direction in the three-dimensional porous media model respectively; is the set of neighborhood elements of the initial search point for the solid phase in the three-dimensional porous media model; is the position coordinate of the i-th solid adjacent domain element in the three-dimensional porous media model, are the x-direction, y-direction, and z-direction coordinates of the i-th solid adjacent domain element in the three-dimensional porous media model;

[0032] The specific process of determining the solid adjacent domain list is as follows: first, the preliminary neighborhood range is determined based on the judgment distance values ​​in each direction; then, the center point of the preliminary neighborhood range is used as the center of the circular or spherical area, and r is used as the radius to obtain a circular or spherical area range. All solid phase elements within this range constitute the solid adjacent domain list.

[0033] Furthermore, the specific process of step 3 is as follows:

[0034] Step 3.1: Based on the initial search point and the solid adjacent domain list information, the gradient descent method is used to determine the maximum gradient direction. The calculation formula is:

[0035]

[0036] D(v,S n )=min{dist(v,s),s∈S n ,v∈V N}(11);

[0037]

[0038] Where dist(v,s) is the distance between the pore phase element v and the solid phase element s, the pore phase element is the initial search point, and the solid phase element is the element value in the solid adjacent domain list; x v is the x-direction coordinate of the pore phase element v; s is the x-direction coordinate of the solid phase element s; y v is the y-direction coordinate of the pore phase element v; s is the y-direction coordinate of the solid phase element s; z v is the z-direction coordinate of the pore phase element v; s is the z-direction coordinate of the solid phase element s; D(·) is the gradient of the minimum distance function; V N is the set of pore phase elements; G(·) is the maximum distance function gradient; L is the distance between the initial search point and the adjacent element;

[0039] Step 3.2: Determine the location of the initial pore center:

[0040]

[0041] Where, is the position coordinate of the kth element in the pore space composed of the pore phase element v, are the x-direction coordinate and y-direction coordinate of the kth element in the pore space composed of the pore phase element v; D k 、D k+1 The minimum distance function gradient of the kth element and the k+1th element respectively; {Ini x ,Ini y} is the position coordinate of the initial pore center, Ini x 、Ini y are the x-direction coordinate and y-direction coordinate of the initial pore center, respectively.

[0042] Furthermore, the specific process of step 4 is as follows:

[0043] Step 4.1: Starting from the initial search point, based on the list of neighboring elements, calculate the distance function gradient between the initial search point and each neighboring element according to formula (12), and obtain the maximum distance function gradient;

[0044] Step 4.2: Update the initial search point to the neighboring element corresponding to the maximum distance function gradient;

[0045] Step 4.3: Based on the initial search point updated in step 4.2, repeat steps 4.1 to 4.2 continuously, and store the maximum distance function gradient of the adjacent elements. The set of all updated initial search points generated during the update process is the set of central axis elements starting from the initial search point.

[0046] Furthermore, the specific process of step 5 is as follows:

[0047] Based on the central axis element set obtained in step 4, the local maximum and local minimum in the central axis element set are determined according to formula (14) and formula (15), respectively. The local minimum is the saddle point of the distance function value of the central axis element set, which is the pore throat; the local maximum is the peak value of the distance function value of the central axis element set, which is the pore center. The specific formula is:

[0048]

[0049] Where G k , G k+1 The maximum distance function gradient of the kth element and the k+1th element respectively; {Pore x ,Pore y} is the position coordinate of the pore center, Pore x 、Pore yare the x-direction coordinate and y-direction coordinate of the pore center respectively; x ,Throat y} is the position coordinate of the pore throat, Throat x 、Throat y are the x-direction coordinate and y-direction coordinate of the pore throat, respectively.

[0050] The beneficial technical effects of the present invention are as follows: This method targets a binary model of rock porous media, eliminates isolated pores, determines a random initial search point, identifies neighboring elements based on the search point, and compiles a neighborhood list. This method utilizes gradient descent and neighborhood search to determine the pore center of the porous media, enabling the central axis of the pore network to be determined. Combined with the central axis elements, this method can rapidly determine the pore center and pore throat locations of the porous media, demonstrating its excellent application value. The present invention boasts high computational efficiency and can efficiently extract pore network structures from high-resolution rock images. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of the pore network structure extraction method based on neighborhood search of the present invention.

[0052] Figure 2 It is a schematic diagram of the framework of the pore network structure extraction method based on neighborhood search of the present invention.

[0053] Figure 3 It is a neighborhood determination graph of the pore network structure extraction method based on neighborhood search of the present invention.

[0054] Figure 4 This is a model preprocessing diagram of the pore network structure extraction method based on neighborhood search in an embodiment of the present invention.

[0055] Figure 5 3 is a comparison diagram of the ideas of the method of the present invention and the conventional central axis method in the embodiment of the present invention, wherein (a) is the idea diagram of the method of the present invention, and (b) is the idea diagram of the conventional central axis method. DETAILED DESCRIPTION

[0056] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0057] like Figure 1 and Figure 2 As shown, a pore network structure extraction method based on neighborhood search includes the following steps:

[0058] Step 1: Obtain rock images, generate a binary model of rock porous media, remove isolated pores, and construct an initial porous media model. The specific process is as follows:

[0059] Step 1.1: Scan the rock image using digital CT (computed tomography) technology to obtain the initial raw file, and then use Avizo software to denoise and binarize the raw file to generate a binary model of the rock porous medium.

[0060] Step 1.2: Determine the solid phase region and the pore phase region based on the binary model to generate the target porous medium model. The specific generation process is as follows: define the position where the element value is 1 in the binary model as the solid phase, and define the position where the element value is 0 as the pore phase, thereby determining the solid phase and pore phase regions in the target porous medium model, and then generating the target porous medium model.

[0061] Step 1.3: Artificially set the open and closed boundary conditions of the target porous media model to determine connected pores and eliminate isolated pores:

[0062]

[0063] Where V con is a connected pore element; V iso It is an isolated pore element; is the pore element in the target porous media model; {X} is the element set after excluding isolated pores.

[0064] Step 1.4: Reconstruct the porous medium model based on the element set after eliminating isolated pores, and define the porous medium model as the initial porous medium model.

[0065] Step 2: Randomly determine the initial search point and generate the neighboring elements and neighborhood list of the initial search point. The specific process is as follows:

[0066] Step 2.1: Randomly select an element in the initial porous medium model as the initial search point. In the present invention, the porous medium model can be a two-dimensional space model or a three-dimensional space model. The position coordinates of the initial search points of different dimensional models are defined as follows:

[0067]

[0068] Where, is the position coordinate of the initial search point in the two-dimensional porous media model, are the x-direction and y-direction coordinates of the initial search point in the two-dimensional porous media model; is the position coordinate of the initial search point in the three-dimensional porous media model, are the x-, y-, and z-direction coordinates of the initial search point in the three-dimensional porous media model; random(·) is a random function.

[0069] Step 2.2: Generate a neighboring element list and a solid neighboring domain list based on the initial search point;

[0070] Based on the initial search point, the neighboring element list and solid neighboring domain list of the two-dimensional porous media model are generated. The specific calculation formula is:

[0071]

[0072] Among them, N 2D is the list of neighboring elements for the two-dimensional porous media model; Represents the set of solid phase elements within the judgment distance in a two-dimensional porous media model; is the position coordinate of the solid adjacent domain elements in the two-dimensional porous media model, are the x-direction and y-direction coordinates of the solid adjacent domain elements in the two-dimensional porous media model; are the judgment distance values ​​in the x-direction and y-direction in the two-dimensional porous medium model respectively; {S} represents the element set of the entire solid phase; i is the solid adjacent domain element index, and n is the number of solid adjacent domain elements; is the position coordinate of the ith solid adjacent domain element in the two-dimensional porous media model, are the x-direction and y-direction coordinates of the ith solid adjacent domain element in the two-dimensional porous media model; is the set of neighborhood elements of the initial search point for the solid phase in the two-dimensional porous media model; r represents the cutoff radius.

[0073] Based on the initial search point, a list of neighboring elements and solid neighboring domains of the three-dimensional porous media model is generated. The specific calculation formula is:

[0074]

[0075] Among them, N 3D is the list of neighboring elements of the three-dimensional porous media model; It is the set of solid phase elements within the judgment distance in the three-dimensional porous media model; are the position coordinates of the solid adjacent domain elements in the three-dimensional porous media model, are the x-, y-, and z-direction coordinates of the solid adjacent domain elements in the two-dimensional porous media model; are the judgment distance values ​​in the x-direction, y-direction, and z-direction in the three-dimensional porous media model respectively; is the set of neighborhood elements of the initial search point for the solid phase in the three-dimensional porous media model; is the position coordinate of the i-th solid adjacent domain element in the three-dimensional porous media model, are the x-direction, y-direction, and z-direction coordinates of the i-th solid adjacent domain element in the three-dimensional porous media model;

[0076] The specific process of determining the solid adjacent domain list is as follows: first, the preliminary neighborhood range is determined based on the judgment distance values ​​in each direction; then, the center point of the preliminary neighborhood range is used as the center of the circular or spherical area, and r is used as the radius to obtain a circular or spherical area range. All solid phase elements within this range constitute the solid adjacent domain list.

[0077] Figure 3 This is the specific process of determining the solid adjacent domain list in the two-dimensional porous media model of the present invention. The left side of the arrow is the initial neighborhood range determined by judging the distance value. x 、P y are the judgment distance values ​​in the x direction and y direction respectively, S p Represents the set of solid phase elements within the judgment distance; the figure to the right of the arrow is the preliminary neighborhood range determined by judging the distance of the neighborhood. Based on the preliminary neighborhood range, a circular area range is obtained with the center point of the preliminary neighborhood range as the center of the circular area and r as the radius. All solid phase elements within this range constitute the solid neighboring domain list. n is the set of neighborhood elements of the initial search point for the solid phase.

[0078] Step 3: Based on the initial search point, determine the pore center of the porous media model;

[0079] Step 3.1: Based on the initial search point and the solid adjacent domain list information, the gradient descent method is used to determine the maximum gradient direction. The calculation formula is:

[0080]

[0081] D(v,S n )=min{dist(v,s),s∈S n ,v∈V N}(11);

[0082]

[0083] Where dist(v,s) is the distance between the pore phase element v and the solid phase element s, the pore phase element is the initial search point, and the solid phase element is the element value in the solid adjacent domain list; x v is the x-direction coordinate of the pore phase element v; s is the x-direction coordinate of the solid phase element s; y v is the y-direction coordinate of the pore phase element v; s is the y-direction coordinate of the solid phase element s; z v is the z-direction coordinate of the pore phase element v; s is the z-direction coordinate of the solid phase element s; D(·) is the gradient of the minimum distance function; VN is the set of pore phase elements; G(·) is the maximum distance function gradient; L is the distance between the initial search point and the adjacent elements.

[0084] Step 3.2: Determine the location of the initial pore center:

[0085]

[0086] Where, is the position coordinate of the kth element in the pore space composed of the pore phase element v, are the x-direction coordinate and y-direction coordinate of the kth element in the pore space composed of the pore phase element v; D k 、D k+1 The minimum distance function gradient of the kth element and the k+1th element respectively; {Ini x ,Ini y} is the position coordinate of the initial pore center, Ini x 、Ini y are the x-direction coordinate and y-direction coordinate of the initial pore center, respectively.

[0087] Step 4: Based on the list of neighboring elements, determine the maximum distance function gradient, thereby determining the central axis element set of the pore network structure; the specific process is:

[0088] Step 4.1: Starting from the initial search point, based on the list of neighboring elements, calculate the distance function gradient between the initial search point and each neighboring element according to formula (12), and obtain the maximum distance function gradient;

[0089] Step 4.2: Update the initial search point to the neighboring element corresponding to the maximum distance function gradient;

[0090] Step 4.3: Based on the initial search point updated in step 4.2, repeat steps 4.1 to 4.2 continuously, and store the maximum distance function gradient of the adjacent elements. The set of all updated initial search points generated during the update process is the set of central axis elements starting from the initial search point.

[0091] Step 5: Combine the central axis element set to finally determine the pore center and pore throat position of the porous media model. The entire pore network structure can be determined based on the pore center and pore throat position. Based on the central axis element set obtained in step 4, the local maximum and local minimum values ​​in the central axis element set are determined according to formulas (14) and (15). The local minimum value is the saddle point of the distance function value of the central axis element set, which is the pore throat; the local maximum value is the peak value of the distance function value of the central axis element set, which is the pore center. The specific formula is:

[0092]

[0093] Where G k , G k+1 The maximum distance function gradient of the kth element and the k+1th element respectively; {Pore x ,Pore y} is the position coordinate of the pore center, Pore x 、Pore y are the x-direction coordinate and y-direction coordinate of the pore center respectively; x ,Throat y} is the position coordinate of the pore throat, Throat x 、Throat y are the x-direction coordinate and y-direction coordinate of the pore throat, respectively.

[0094] In order to demonstrate the feasibility and superiority of the present invention, the following specific examples are given.

[0095] The present invention uses a two-dimensional porous medium model as an example for testing, and the model size is 20 pixels × 20 pixels. Figure 4 This is a model preprocessing diagram of the pore network structure extraction method based on neighborhood search in an embodiment of the present invention. The porous medium model consists of a solid phase (gray squares) and a pore phase (white squares). Closed boundary conditions are used above and below, and open boundary conditions are used on the left and right to serve as inflow and outflow channels, thereby determining the connected pore space. In addition to the connected pore phase elements, for other isolated pore phase elements, their binary model values ​​are changed from 0 to 1, thereby changing them to solid phase elements. Traversing the solid phase elements, if there are pore phase elements in the neighboring elements of this solid phase element, they are retained as solid phase boundary elements, otherwise they are elements within the solid phase and are eliminated (the binary model value is changed from 1 to 2). In this embodiment, the number of neighboring pixels for each pixel is set to 8, the neighborhood cutoff radius is 5 pixels, the search step is 1 pixel, and the judgment range of the pore center and the pore throat is set to 3 pixels.

[0096] Figure 5 1 is a diagram comparing the ideas of the method of the present invention and the conventional central axis method in an embodiment of the present invention, (a) is a diagram of the idea of ​​the method of the present invention, and (b) is a diagram of the idea of ​​the conventional central axis method. Figure 5 The numbers 1-4 represent the gradient of the distance function between the pore phase element and the solid phase. It can be seen that the conventional central axis method requires calculating the distance function gradient for each pore phase element to obtain the position of the central axis, while the present invention only needs to calculate the neighboring pixels of the search point to obtain the central axis.

[0097] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A pore network structure extraction method based on neighborhood search, characterized in that: The steps include: Step 1: Obtain rock images, generate a binary model of rock porous media, remove isolated pores, and construct an initial porous media model; Step 2: Randomly determine the initial search point and generate the neighboring elements and neighborhood list of the initial search point; Step 3: Based on the initial search point, determine the pore center of the porous media model; Step 4: Based on the list of neighboring elements, determine the maximum distance function gradient, thereby determining the central axis element set of the pore network structure; Step 5: Combine the central axis element set to finally determine the pore center and pore throat position of the porous media model. The entire pore network structure can be determined based on the pore center and pore throat position. The specific process of step 1 is: Step 1.1: Scan the rock image using digital CT technology to obtain the initial raw file. Use Avizo software to denoise and binarize the raw file to generate a binary model of the rock porous medium. Step 1.2: Determine the solid phase region and the pore phase region based on the binary model to generate the target porous medium model. The specific generation process is as follows: define the position where the element value is 1 in the binary model as the solid phase, and define the position where the element value is 0 as the pore phase, thereby determining the solid phase and pore phase regions in the target porous medium model, and then generate the target porous medium model. Step 1.3: Artificially set the open and closed boundary conditions of the target porous media model to determine connected pores and eliminate isolated pores: (1)； Where, is a connected pore element; It is an isolated pore element; is the pore element in the target porous media model; It is the set of elements after removing isolated pores; Step 1.4, reconstructing the porous medium model based on the element set after eliminating isolated pores, and defining the porous medium model as the initial porous medium model; The specific process of step 2 is: Step 2.

1. Randomly select an element in the initial porous medium model as the initial search point. The porous medium model is divided into two-dimensional porous medium model and three-dimensional porous medium model. The position coordinates of the initial search points of different dimensional models are defined as follows: (2)； (3)； Where, is the position coordinate of the initial search point in the two-dimensional porous media model, 、 are the initial search points in the two-dimensional porous media model. direction, Direction coordinates; is the position coordinate of the initial search point in the three-dimensional porous media model, 、 、 are the initial search points in the three-dimensional porous media model. direction, direction, Direction coordinates; is a random function; Step 2.2: Generate a neighboring element list and a solid neighboring domain list based on the initial search point; Based on the initial search point, the neighboring element list and solid neighboring domain list of the two-dimensional porous media model are generated. The specific calculation formula is: (4)； (5)； (6)； in, is the list of neighboring elements for the two-dimensional porous media model; Represents the set of solid phase elements within the judgment distance in a two-dimensional porous media model; is the position coordinate of the solid adjacent domain elements in the two-dimensional porous media model, 、 They are the solid adjacent domain elements in the two-dimensional porous media model. direction, Direction coordinates; 、 In the two-dimensional porous media model, direction, The judgment distance value in the direction; The collection of elements that represents the solid phase as a whole; is the solid adjacent domain element index, is the number of solid adjacent domain elements; The first The position coordinates of adjacent domain elements of solids, 、 They are the first solid adjacent domain elements direction, Direction coordinates; is the set of neighborhood elements of the initial search point for the solid phase in the two-dimensional porous media model; represents the cutoff radius; Based on the initial search point, a list of neighboring elements and solid neighboring domains of the three-dimensional porous media model is generated. The specific calculation formula is: (7)； (8)； (9)； in, is the list of neighboring elements of the three-dimensional porous media model; It is the set of solid phase elements within the judgment distance in the three-dimensional porous media model; are the position coordinates of the solid adjacent domain elements in the three-dimensional porous media model, 、 、 They are the solid adjacent domain elements in the two-dimensional porous media model. direction, direction, Direction coordinates; 、 、 In the three-dimensional porous media model direction, direction, The judgment distance value in the direction; is the set of neighborhood elements of the initial search point for the solid phase in the three-dimensional porous media model; The first The position coordinates of adjacent domain elements of solids, 、 、 They are the first solid adjacent domain elements direction, direction, Direction coordinates; The specific process of determining the solid adjacent domain list is as follows: first, determine the preliminary adjacent domain range based on the judgment distance values ​​in each direction; then, take the center point of the preliminary adjacent domain range as the center of the circular or spherical area, and As the radius, a circular or spherical region is obtained, and all solid phase elements within the region constitute the solid adjacent domain list; The specific process of step 3 is: Step 3.1: Based on the initial search point and the solid adjacent domain list information, the gradient descent method is used to determine the maximum gradient direction. The calculation formula is: (10)； (11)； (12)； Where, Pore ​​phase elements Solid phase elements The pore phase element is the initial search point, and the solid phase element is the element value in the solid adjacent domain list; Pore ​​phase elements of Direction coordinates; Solid phase elements of Direction coordinates; Pore ​​phase elements of Direction coordinates; Solid phase elements of Direction coordinates; Pore ​​phase elements of Direction coordinates; Solid phase elements of Direction coordinates; is the gradient of the minimum distance function; is the collection of pore phase elements; is the maximum distance function gradient; is the distance between the initial search point and the adjacent element; Step 3.2: Determine the location of the initial pore center: (13)； Where, Pore ​​phase elements The pore space composed of The position coordinates of the elements, 、 The pore phase elements The pore space composed of elements Direction coordinates, Direction coordinates; 、 Respectively Elements, The minimum distance function gradient of elements; is the position coordinate of the initial pore center, 、 The initial pore center Direction coordinates, Direction coordinates; The specific process of step 4 is as follows: Step 4.1: Starting from the initial search point, based on the list of neighboring elements, calculate the distance function gradient between the initial search point and each neighboring element according to formula (12), and obtain the maximum distance function gradient; Step 4.2: Update the initial search point to the neighboring element corresponding to the maximum distance function gradient; Step 4.3: Based on the initial search point updated in step 4.2, repeat steps 4.1 to 4.2 continuously, while storing the maximum distance function gradient of the neighboring elements. The set of all updated initial search points generated during the update process is the set of central axis elements starting from the initial search point; The specific process of step 5 is as follows: Based on the central axis element set obtained in step 4, the local maximum and local minimum in the central axis element set are determined according to formula (14) and formula (15), respectively. The local minimum is the saddle point of the distance function value of the central axis element set, which is the pore throat; the local maximum is the peak value of the distance function value of the central axis element set, which is the pore center. The specific formula is: (14)； (15)； Where, 、 Respectively Elements, The maximum distance function gradient of elements; is the position coordinate of the pore center, 、 The pore center Direction coordinates, Direction coordinates; is the position coordinate of the pore throat, 、 The pore throat Direction coordinates, Direction coordinates.

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