A Cross-Scale Fusion Method for Hole and Slot Networks Based on Graph Coarsening and Link Prediction

Abstract

The present invention discloses a cross-scale fusion method for pore and fracture networks based on graph coarsening and link prediction, comprising the following steps: S1. Establish a ball-and-stick model for the pores and fractures of a digital core, and model a pore and fracture graph network according to the distribution and connectivity relationship of the rock sample; S2. Extract the adjacency matrix and feature matrix of the pore and fracture graph network, construct a graph link prediction model, and perform training; S3. Coarsen the nanoscale isolated connected patches into pore nodes in a pore and fracture graph network according to the porosity distribution and connectivity relationship of the rock sample, and place them into the pore and fracture graph network; S4. Extract a new adjacency matrix and feature matrix according to the new pore and fracture graph network, and use the model to calculate the probability of the existence of gaps between pore nodes, so as to achieve multi-scale fusion. The present invention solves the problems in the prior art that the image scale difference before and after fusion is small, the image resolution is too high after the fusion of the nanoscale image and the micron-scale image, and the computational resources and storage space overhead are too large.

Description

Technical Field

[0001] The present invention relates to a method for cross-scale fusion of pore-fracture networks, mainly a method for cross-scale fusion of pore-fracture networks based on graph coarsening and link prediction. Background Art

[0002] As the oil and gas reservoirs with large structures and simple pore-permeability relationships are decreasing day by day, the development of China's oil and gas industry is constantly breaking through the limits and extending rapidly towards unconventional oil and gas. However, due to the complex rock structure and large physical property changes of unconventional reservoirs, it is difficult to systematically analyze the laws by physical experimental methods. Therefore, there is an urgent need for a more refined analysis of underground cores. As an emerging method, digital cores can visually display the pore-fracture spatial structure of rocks. However, the methods for obtaining digital cores by imaging have obvious defects. One is that the accuracy of common CT scans is at most only on the order of 0.1 um. The pore-fracture scale span of unconventional reservoirs is large, resulting in inaccurate calculation of pore permeability. The other is that the data accuracy obtained by electron microscopy experiments is sufficient but the field of view is small, and the pore-fracture spatial characteristics at larger scales cannot be expressed. The importance of constructing a digital core model containing multi-scale pore information is self-evident.

[0003] At present, the main multi-scale fusion methods are traditional imageology: using two resolutions to collect images of the same core, establishing digital cores respectively, and superimposing and fusing the pore-fracture network models; deep learning methods: reconstructing three-dimensional digital cores with generative adversarial networks, and using the internal micro-pore information extracted by neural networks to superimpose and form multi-scale three-dimensional digital cores. The above multi-scale modeling methods based on image fusion all have the problem of small scale difference between the images before and after fusion, and only the small pore-fracture information is superimposed in the original image. Summary of the Invention

[0004] In view of the above deficiencies in the prior art, a method for cross-scale fusion of pore-fracture networks based on graph coarsening and link prediction provided by the present invention solves the problems of small scale difference between the images before and after fusion in the prior art, too high image resolution after fusion of nano-scale images and micro-scale images, and excessive consumption of computing resources and storage space.

[0005] In order to achieve the above object of the invention, the technical solution adopted by the present invention is a method for cross-scale fusion of pore-fracture networks based on graph coarsening and link prediction, including the following steps:

[0006] S1. For the pores and fractures of the digital core, establish a ball-and-stick model, and model the pore-fracture graph network according to the distribution and connectivity of the rock samples;

[0007] S2. Extract the adjacency matrix and feature matrix of the pore-fracture graph network, construct a graph link prediction model, and perform training;

[0008] S3. According to the porosity distribution and connectivity relationship of the rock sample, coarsen the nanoscale isolated connected patches into pore nodes in a pore-fracture graph network and place them in the pore-fracture graph network;

[0009] S4. According to the new pore-fracture graph network, extract a new adjacency matrix and characteristic matrix, and use the model to calculate the probability of the existence of gaps between pore nodes to achieve multi-scale fusion.

[0010] Further, the step S1 includes the following sub-steps:

[0011] S11. Establish ball-and-stick models for the pores and fractures of the digital core respectively, use methods such as the distance map method to extract the fracture center line, and use the maximum ball method to equivalently transform the fracture space into a dense connected pore space;

[0012] S12. Find the maximum ball corresponding to the contact surface between the pores and fractures, establish the relationship between the throat radius and coordination number distribution of the connectivity between the pores and fractures according to the number and area of the contact surfaces, and select appropriate radii and numbers of throats for the maximum balls of the corresponding pores and fractures at the contact surface to connect the two, and establish the connecting edges of the pore-fracture model.

[0013] S13. Represent the balls in the ball-and-stick model as points in the graph structure, the sticks as edges, and represent the pore-fracture graph network as G=(V, E, X);

[0014] where V={v 0 ,…,v n} is the set of pore nodes in the pore-fracture graph network, E={e 0 ,…,e n} is the set of edges in the pore-fracture graph network, is the set of pore node characteristics of the pore-fracture graph network.

[0015] The beneficial effect of the above further solution is: the morphological characteristics of the fracture space are retained to the greatest extent, and the use of the graph structure saves the difficulty of data operation and storage.

[0016] Still further, the step S2 includes the following sub-steps:

[0017] S21. According to the edge set E of the pore-fracture graph network, extract the adjacency matrix A, where A is an n×n matrix, and A i,j is 0 or 1, A i,j =1 indicates that there is a directly connected gap between the pore node v i and the pore node v j , A i,j =0 indicates that there is no directly connected gap between the pore node v i and the pore node v j ;

[0018] Among them, A i,j is determined by E. If e i =<v i , v j > ∈ E, then A i,j = 1. If e i = then A i,j = 0;

[0019] S22. Use the random dropout mask method and the source - point random walk mask method to mask the hole - slit graph network to obtain the masked edge set;

[0020] The implementation process of graph masking based on random dropout is as follows:

[0021] A1. Determine the dropout probability p;

[0022] A2. Randomly select elements in the adjacency matrix according to the dropout probability and set them to 0;

[0023] A3. Repeat A2 multiple times to form the masked adjacency matrix;

[0024] The implementation process of graph masking based on the random walk from the source point is as follows:

[0025] B1. Initialization: Start from the source node s;

[0026] B2. Transition probability: At each step, starting from the current node v, the probability of choosing a neighbor node u to move is where deg(v) represents the degree of node v;

[0027] B3. Iteration: Repeat step B2 multiple times to form a walk path.

[0028] S23. Build a graph link prediction model and use the masked data to train the model;

[0029] Among them, for the encoder part, its neural network architecture is a two - layer graph convolutional neural network GCN, and ReLU is used as the activation function after each layer of GCN;

[0030] The output of the decoder part shows the similarity of the relationships between two terminal nodes at different granularities.

[0031] The beneficial effects of the above further solution are as follows: By using a sampling mask strategy based on uniform distribution, potential central bias can be effectively prevented. The mask breaks the short-term links between pore nodes, forcing the model to learn the underlying semantics to adapt to the masked structure. The graph convolutional encoder can effectively extract the topological structure information of the graph structure. The cross-correlation decoder can effectively simulate the cross-relationships between pore nodes, highlighting the common attributes of the two and the information with inconsistent coefficients, and only the elements highly correlated between two pore nodes will be retained.

[0032] Furthermore, the step S3 includes the following sub-steps:

[0033] S31. Calculate the porosity distribution function of the rock sample at the micron and nanometer scales using the fluid injection experiment method, obtain the morphological characteristics and connectivity relationships of the rock sample at the micron scale using the dual-beam electron microscopy experiment method, and obtain the morphological characteristics and connectivity relationships of the rock sample at the nanometer scale using the scanning electron microscopy experiment method;

[0034] S32. Form nanoscale isolated connected patches according to the various different porosity distribution functions of the rock sample at the nanometer scale obtained by the fluid injection experiment method;

[0035] S33. Coarsen the isolated connected patches in the nanoscale pore-fracture graph network obtained in S32 to obtain pore nodes at the micron scale one by one, and merge them into the pore-fracture graph network.

[0036] The beneficial effects of the above further solution are as follows: By using the fluid injection method and the dual-beam electron microscopy experiment method, the morphological characteristics and connectivity relationships of the rock sample at the micron and nanometer scales can be obtained with sufficient accuracy.

[0037] Furthermore, the step S4 includes the following sub-steps:

[0038] S41. Extract the adjacency matrix and feature matrix of the pore-fracture graph network after fusing the nanoscale isolated connected patches according to the method described in S21;

[0039] S42. Calculate the probability of the existence of gaps between pore nodes according to the model decoder described in S23;

[0040] S43. Set the probability threshold to 70%, and judge whether the probability of the existence of gaps between pore nodes is sufficient to form new connectivity relationships to achieve cross-scale fusion of the pore-fracture network.

[0041] The beneficial effects of the above further solution are as follows: The cross-correlation decoder can effectively simulate the cross-relationship between pore nodes, highlight the common attributes of the two and the information with inconsistent coefficients, and only the elements highly correlated between two pore nodes will be retained; by effectively simulating the cross-relationship between pore nodes through the cross-correlation decoder, the probability of the existence of gaps in the pore nodes is obtained, realizing the cross-scale fusion of the pore-fracture map network at the nano-scale and micro-scale.

[0042] In summary, the beneficial effects of the present invention are as follows: Compared with the conventional method, it takes into account the problems such as the difficulty in obtaining nano-scale core images, too small field of view, insufficient representativeness, and the too high image resolution after fusion with micro-scale images. The pore-fracture network is used to achieve micro-nano fusion and greatly reduce the calculation amount; using the idea of a masked graph auto-encoder, the model is forced to learn the complete structural information of the pore-fracture graph network by covering the original pore-fracture network path to destroy the topological structure, avoiding overfitting and improving the model effect; the cross-correlation decoder of the neural network uses the k-node feature sequences between two node pairs as input, correlates the neighborhood information of different granularities, highlights their common attributes and dilutes the inconsistent information, and improves the model prediction effect. Brief Description of the Drawings

[0043] Figure 1 It is a flowchart of the pore-fracture network cross-scale fusion method based on graph coarsening and link prediction according to the present invention.

[0044] Figure 2 It is the pore-fracture network cross-scale fusion based on graph coarsening and link prediction. Detailed Embodiment

[0045] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0046] As Figure 1 shown, a pore-fracture network cross-scale fusion method based on graph coarsening and link prediction includes the following steps:

[0047] S1. Model the pore-fracture graph network;

[0048] Step S1 includes the following sub-steps:

[0049] S11. Respectively establish ball-and-stick models for the pores and fractures of the digital core, use methods such as the distance map method to extract the fracture centerlines, and use the maximum sphere method to equivalently represent the fracture space as a dense connected pore space to maximize the retention of the morphological characteristics of the fractures;

[0050] In step S11, the calculation formula for extracting the fracture centerline by the distance map method is:

[0051]

[0052] where C is the fracture centerline, is the set of all paths from point s to point t, v is the pore node, and w(e ij ) is the weight of the edge.

[0053] S12. Find the maximum sphere corresponding to the contact surface between the pores and fractures, establish the relationship between the throat radius and coordination number distribution for the connection between the pores and fractures according to the number and area of the contact surfaces, and select appropriate radii and numbers of throats for the maximum spheres of the corresponding pores and fractures to connect the two, and establish the connecting edges of the pore-fracture model.

[0054] S13. Represent the spheres of the ball-and-stick model as points in the graph structure and the sticks as edges, and represent the pore-fracture graph network as G=(V, E, X);

[0055] where V={v 0 ,…,v n} is the set of pore nodes in the pore-fracture graph network, E={e 0 ,…,e n} is the set of edges in the pore-fracture graph network, is the set of pore node characteristics of the pore-fracture graph network.

[0056] S2. Construct a link prediction model and train it;

[0057] Step S2 includes the following sub-steps:

[0058] S21. According to the edge set E of the pore-fracture graph network, extract the adjacency matrix A, where A is an n×n matrix, and the value of A i,j in the matrix is 0 or 1. A i,j =1 indicates that there is a directly connected gap between the pore node v i and the pore node v j , and A i,j =0 indicates that there is no directly connected gap between the pore node v i and the pore node v j ;

[0059] The calculation formula for extracting the adjacency matrix in step S21 is:

[0060]

[0061] Among them, A i,j indicates whether pore nodes i and j are adjacent, <v i , v j > is the edge representation of pore nodes i and j, and E is the edge set of the pore-fracture graph network.

[0062] S22. Mask the pore-fracture graph network to obtain the masked edge set;

[0063] The calculation formula for graph masking of the pore-fracture graph network by means of random dropout in step S22 is:

[0064]

[0065] Among them, p is the dropout probability, representing that each edge is set to 0 with a probability of p.

[0066] The implementation process is as follows:

[0067] A1. Determine the dropout probability p;

[0068] A2. Randomly select elements in the adjacency matrix and set them to 0 according to the dropout probability;

[0069] A3. Repeat A2 multiple times to form the masked adjacency matrix;

[0070] The implementation process of graph masking of the pore-fracture graph network by means of random walk based on the source node in step S22 is as follows:

[0071] B1. Initialization: Start from the source node s;

[0072] B2. Transition probability: At each step, starting from the current node v, the probability of selecting a neighbor node u to move is where deg(v) represents the degree of node v;

[0073] B3. Iteration: Repeat step B2 multiple times to form a random walk path.

[0074] S23. Construct a graph link prediction model, with a graph autoencoder as the basic structure, consisting of an encoder and a decoder;

[0075] Among them, for the encoder part, its neural network architecture is a two-layer graph convolutional neural network GCN, and ReLU is used as the activation function after each layer of GCN;

[0076] The output of the decoder part shows the similarity of the relationships between two terminal nodes at different granularities.

[0077] The process of constructing the graph link prediction model in step S23 is as follows:

[0078] A1. Use the K-layer graph convolutional neural network GCN as the encoder to calculate the node embedding representation. The formula for updating the node embedding by GCN is as follows;

[0079]

[0080] Among them, X (l+1) is the feature matrix of the (l + 1)-th layer, is the degree matrix plus the identity matrix, is the adjacency matrix plus the identity matrix, X (;l) is the feature matrix of the l-th layer, W (l) is the weight matrix of the l-th layer, and σ is the activation function;

[0081] A2. Use the cross-correlation decoder to calculate the edge representation between node pairs using the K embedding representations of the pore nodes obtained in the previous step. The formula for the edge representation is as follows;

[0082]

[0083] Among them is the cross-representation between pore nodes i and j, means concatenating the results of the following expressions, ⊙ represents element-wise multiplication, is the embedding information of the a-th hop subgraph of pore node i, is the embedding information of the b-th hop subgraph of pore node j;

[0084] A3. Use the multi-layer perceptron MLP to calculate the edge representation obtained in the previous step to obtain the probability that there is a gap between pore node pairs.

[0085] S3. Coarsen the isolated connected components into pore nodes and fuse them with the original pore-fracture map;

[0086] Step S3 includes the following sub-steps:

[0087] S31. Use the fluid injection experiment method to calculate the porosity distribution function of the rock sample at the microscale and nanoscale, use the dual-beam electron microscope experiment method to obtain the morphological characteristics and connectivity relationship of the rock sample at the microscale, and use the scanning electron microscope experiment method to obtain the morphological characteristics and connectivity relationship of the rock sample at the nanoscale;

[0088] S32. According to the various porosity distribution functions of the rock sample at the nanoscale obtained by the fluid injection experiment method, form nanoscale isolated connected components;

[0089] S33. Coarsen the isolated connected components in the nanoscale pore-fracture map network obtained in S32 to obtain pore nodes at the microscale, and merge them into the pore-fracture map network.

[0090] S4. The new pore-fracture map obtains a new connectivity relationship through the model;

[0091] Step S4 includes the following sub-steps:

[0092] S41. Extract the adjacency matrix and feature matrix of the pore-fracture map network after fusing nano-scale isolated connected components according to the method described in S33;

[0093] S42. Calculate the probability that there is a gap between pore nodes according to the model decoder described in S23;

[0094] S43. Set the probability threshold to 70%, and determine whether the probability that there is a gap between pore nodes is sufficient to form a new connectivity relationship, so as to realize the cross-scale fusion of the pore-fracture network.

[0095] In the above embodiments, the graph link prediction model is as Figure 2 shown in the upper part. The adjacency matrix A and feature matrix X of the micro-scale pore-fracture map network are extracted and input into the model for training. After passing through two layers of graph convolutional neural networks GCN in the encoder, X(1) and X(2) are output, representing the feature matrices output by each layer of GCN. The feature sequence is input into the decoder, and the probability of the existence of a gap edge between pore nodes is obtained through cross-correlation operation. If this probability is greater than the set 70% threshold, it is determined that there is a gap edge. The model application is as Figure 2 shown in the lower part. The porosity distribution and pore-fracture morphology parameter distribution of the rock sample are obtained through fluid injection experiments and electron microscopy experiments, and then isolated connected components are generated by resampling. After graph coarsening, pore nodes are formed, which are fused with the original pore-fracture map, and then the above model is used for link prediction on it to form a new connectivity relationship and realize multi-scale fusion.

Claims

1. A cross-scale fusion method of slot networks based on graph coarse-graining and link prediction, characterized in that: The following steps are involved: S1. A ball-and-stick model is established for the holes and fractures of the digital core, and a hole-and-fracture graph network is modeled based on the distribution and connectivity of the rock samples; S2, extract the adjacency matrix and feature matrix of the hole-seam graph network, build a graph link prediction model, and train it; The step S2 comprises the following sub-steps: S21, extracting an adjacency matrix A according to an edge set E of the hole-slit graph network; S22, masking the hole graph network using a random discarding masking method and a source point random walk masking method to obtain a masked edge set; S23, building a graph link prediction model, and using the masked data to train the model; The graph link prediction model in step S23 is: The neural network architecture of the encoder part is a two-layer graph convolutional neural network GCN, and ReLU is used as the activation function after each layer of GCN; The decoder part calculates the input gap node representation sequence to obtain edge representation, and then uses the multi-layer perceptron MLP to calculate the probability of gaps between nodes; The update formula of the graph convolutional neural network GCN in the encoder is as follows: Among them, X (l+1) is the feature matrix of the l+1th layer, Add the identity matrix to the degree matrix, Add the identity matrix to the adjacency matrix, X (l) is the feature matrix of the lth layer, W (l) is the weight matrix of the lth layer, σ is the activation function; The formula for calculating the probability of gaps between nodes in the decoder is: Where P i,j represents the probability that there is a gap between pore nodes i and j, It means to concatenate the results of the following formulas, ⊙ represents element-by-element multiplication, is the embedding information of the a-th hop subgraph of the pore node i, is the embedding information of the b-th hop subgraph of the pore node j, and MLP is a multi-layer perceptron; S3, according to the porosity distribution and connectivity of the rock sample, the nanoscale isolated connected pieces are coarse-grained into pore nodes in the pore-fracture graph network, and placed in the pore-fracture graph network; S4. Based on the new pore-slit graph network, a new adjacency matrix and feature matrix are extracted, and the model is used to calculate the probability of the existence of gaps between pore nodes to achieve multi-scale fusion.

2. According to claim 1, the cross-scale fusion method of slot network based on graph coarse-graining and link prediction is characterized in that: The step S1 comprises the following sub-steps: S11, using the distance map method and the maximum ball method to establish ball-and-stick models for the holes and seams of the digital core respectively; S12, establishing the connection edge of the hole and seam model according to the throat parameters of the maximum ball; S13. The ball-and-stick model is represented as a graph structure, called a hole-slot graph network.

3. The cross-scale fusion method of slot network based on graph coarse-graining and link prediction according to claim 2 is characterized in that: The calculation formula for extracting the crack centerline using the distance graph method in step S11 is: Where C is the crack centerline, is the set of all paths from point s to point t, v is the pore node, w(e ij ) is the weight of the edge.

4. The cross-scale fusion method of aperture network based on graph coarse-graining and link prediction according to claim 2 is characterized in that: The method of establishing the hole-slit graph network in step S13 is: The balls of the ball-and-stick model are represented as points in the graph structure, the sticks are represented as edges, and the hole-and-slot graph network is represented as G = (V, E, X); where V = {v0,…,v n } is the set of pore nodes in the pore-fracture graph network, E = {e0,…,e n } is the edge set of the hole-slot graph network, X=[x1,x2,…,x n ]∈R n×f is the pore node feature set of the pore-fracture graph network, where n is the number of x and f is the length of x.

5. The cross-scale fusion method of slot network based on graph coarse-graining and link prediction according to claim 1 is characterized in that: The formulas based on the random discard mask method and the source point random walk mask method in step S22 are: The formula based on the random drop mask method is: Among them, p is the drop probability, which means that each edge is set to 0 with a probability of p; The walk probability formula based on the source point random walk mask method is: Where deg(v) represents the degree of node v, v is the current node, and u is the neighbor node.

6. The cross-scale fusion method of slot network based on graph coarse-graining and link prediction according to claim 1 is characterized in that: The step S3 comprises the following sub-steps: S31, obtaining the morphological characteristics and connectivity of the rock sample; S32, forming nanoscale isolated connected sheets according to the porosity distribution function of the rock sample at the nanoscale obtained in S31; S33. Coarse-grain the isolated connected pieces to obtain micron-scale pore nodes, which are then merged into the pore-slit graph network.

7. The cross-scale fusion method of aperture network based on graph coarse-graining and link prediction according to claim 6 is characterized in that: The porosity definition and porosity distribution function of step S32 are: Where K(r,L) is a cube with a side length of L and a center of point r inside the porous medium. is the porosity definition of K(r,L), V(G) is a set is the volume of , m is the number of K(r,L) in the system, and δ(x) is the Dirac distribution function.

8. The cross-scale fusion method of aperture network based on graph coarse-graining and link prediction according to claim 1 is characterized in that: The step S4 comprises the following sub-steps: S41, extracting the adjacency matrix and feature matrix of the fused hole-seam graph network; S42, calculating the probability of the existence of gaps between the gap nodes through the graph link prediction model described in S23; S43, setting the probability threshold to 70%, judging whether the probability of the existence of gaps between pore nodes is sufficient to form a new connectivity relationship, and realizing the cross-scale fusion of the pore-fracture network.

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