A method for reconstructing and characterizing three-dimensional space network of coal body hydraulic fracturing cracks

Abstract

The application discloses a coal body hydraulic fracturing fracture three-dimensional space network reconstruction and characterization method, which is based on real CT three-dimensional body data, can realize the transformation of fracture structure from geometric visualization to parameterization and evaluation, can directly reflect the real connection relationship of the fracture in the three-dimensional space by identifying and three-dimensionally reconstructing the internal fracture of the coal body before and after fracturing, avoids the connection misjudgment and scale deviation caused by two-dimensional slice inference, improves the authenticity of the evaluation result from the source, and simultaneously adopts skeletonization and node-edge modeling on the fracture network, converts the three-dimensional voxel fracture structure into a node-edge form fracture network model, significantly reduces the calculation complexity under the premise of ensuring the fracture space connection relationship, enables the connectivity and flow conductivity characteristics of the fracture network to be expressed in the form of unified parameters, and is especially suitable for the fracture network characterization of the laboratory true triaxial test and the digital coal rock sample data based on CT scanning.

Description

Technical Field

[0001] This invention relates to a method for reconstructing and characterizing a three-dimensional spatial network of hydraulic fracturing fractures in coal seams. Specifically, it is a method based on CT scanning and three-dimensional reconstruction technology to reconstruct a three-dimensional spatial network model of hydraulic fracturing fractures in coal seams and characterize their connectivity and conductivity. This method can be used for evaluating fracturing effects and optimizing extraction processes, and belongs to the field of coal mine safety and coalbed methane permeability enhancement and extraction technology. Background Technology

[0002] Hydraulic fracturing of coal seams can induce fracture propagation and activate natural cleavage in low-permeability coal seams, thereby improving fracture network connectivity and gas extraction capacity. However, existing evaluation methods mostly rely on fracturing pressure curves, single-hole extraction responses, or qualitative descriptions using two-dimensional slices, making it difficult to obtain the true three-dimensional spatial connectivity structure and flow guideline of the fracture network. Furthermore, a repeatable and quantifiable three-dimensional spatial network model and index system for fractures is lacking. On the other hand, while CT scans and 3D visualization software can extract fracture voxels and 3D geometric features, directly analyzing connectivity and flow paths using voxels or surface models often suffers from high computational burden and difficulty in extracting key flow guidelines. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention provides a method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal bodies. This method can transform the fracture structure from geometric visualization to parameterization and evaluation based on real CT three-dimensional volume data, reflecting the true connectivity of fractures in three-dimensional space and improving the authenticity of evaluation results from the source. It is particularly suitable for fracture network characterization in laboratory true triaxial tests and CT-based digital coal and rock sample data.

[0004] To achieve the above objectives, the method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in this coal seam specifically includes the following steps:

[0005] Step 1: Obtain CT scan data of the coal body before and after fracturing, record the voxel size, scanning direction and sample coordinate system, establish a three-dimensional coordinate reference, and mark the injection hole position;

[0006] Step 2: Denoise and enhance the CT scan data, correct the non-uniform grayscale areas, and finally output a preprocessing parameter record table including filter kernel size, number of iterations and enhancement coefficient, as a basis for experimental repeatability.

[0007] Step 3: Extract cracks based on threshold segmentation, then filter connected components of the cracks to remove suspected noisy connected components. When local crack breaks or discontinuities are found, repair the connection of the crack break area.

[0008] Step 4: Perform 3D skeletonization on the cracks processed in Step 3 to obtain the skeleton centerline, identify the endpoints, bifurcation points and intersection points on the skeleton, and treat them as a set of nodes. Define the skeleton segments between adjacent nodes as edge sets. The initial crack network model is obtained. ;

[0009] Step 5, in the edge set The above defines weights used to characterize the flow-guiding capability. ;

[0010] Step 6, after completing the initial crack network model After construction, the initial crack network model is... Perform topology cleaning and consistency correction to obtain a structurally sound three-dimensional spatial network model of cracks. ,in:

[0011] Node set Represented as

[0012] ;

[0013] In the formula: Indicates the number of nodes;

[0014] The set of edges connecting nodes Represented as

[0015]

[0016] In the formula: Indicates the number of sides;

[0017] Step 7, after topology cleaning, the crack 3D spatial network model Based on this, the connectivity and flow conduction structure characteristics of the fracture network are quantitatively characterized.

[0018] Step 7-1: Analyze the overall scale characteristics of the crack network;

[0019] Step 7-2: Calculate the connectivity index of the fracture network;

[0020] Step 7-3, based on the edge set defined in Step 5 Weight Calculate the weighted average path length of the fracture network. Meanwhile, the betweenness centrality of nodes is calculated. To obtain the betweenness centrality distribution characteristics, and to identify the key nodes that play a dominant role in the flow conduction process of the fracture network using a high quantile threshold, thereby extracting the dominant flow conduction skeleton structure in the fracture network;

[0021] Step 7-4: Calculate the clustering coefficient of the fracture network. To identify whether a crack network has a small-world structure;

[0022] Step 8: Output and visualize the three-dimensional spatial network model of the crack and its representation results.

[0023] Furthermore, in Step 4, the node set The node attributes should at least include the node number and three-dimensional coordinates, and the edge set. The edge attributes must include at least endpoint pairs and geometric length. For edges lacking geometric information, the Euclidean distance between nodes is used. To complete the expression, it is shown below:

[0024]

[0025] In the formula: Represents a node With nodes Euclidean distance in three-dimensional space; For nodes The three-dimensional coordinate components; node The three-dimensional coordinate components.

[0026] Furthermore, the edge weights in Step 5 At least one of the following is included:

[0027] ① Geometric distance type: ;

[0028] ②Flow guiding capacity type: ,in This refers to the equivalent aperture or equivalent hydraulic radius. This is an empirical coefficient.

[0029] Furthermore, the specific process of Step 6 is as follows:

[0030] Self-loop edges in the network are deleted. When there are multiple connecting edges between the same node pair, duplicate edges are merged. Representative connecting edges that satisfy geometric or hydraulic physical constraints and are consistent with the edge weight definition are retained.

[0031] Furthermore, Step 7-1 specifically includes the total number of nodes in the crack network. Total number of sides Node degree and network density ;

[0032] Node degree It is expressed as follows:

[0033]

[0034] In the formula: when node With nodes When there is a connection relationship =1, otherwise =0;

[0035] Crack network density The definition is as follows:

[0036]

[0037] In the formula: The total number of nodes. Let be the total number of edges.

[0038] Furthermore, Step 7-2 is detailed below:

[0039] By identifying connected components in the network Obtain the number of connected components The connected component with the most nodes is extracted as the maximum connected subgraph. And calculate its number of nodes. and its proportion in the entire network ;

[0040] Connected components The definition is as follows:

[0041]

[0042] In the formula: This represents the number of connected components in a crack network; Representing connected components respectively Two different sets of nodes in; Represents connected components The set of edges in the array.

[0043] Maximum connected subgraph The definition is as follows:

[0044]

[0045] In the formula: This represents the maximum number of nodes in a connected subgraph. This represents the percentage of the number of nodes in the largest connected subgraph in the entire crack network.

[0046] Furthermore, in Step 7-3, the weighted average path length It is expressed as follows:

[0047]

[0048] In the formula: The total number of nodes in the crack network; For nodes With nodes The shortest path length between them;

[0049] Betweenness centrality It is expressed as follows:

[0050]

[0051] In the formula: Represents a node and The total number of paths between them; For the nodes passed through in these paths The quantity.

[0052] Furthermore, in Step 7-4, when identifying whether a crack network has a small-world structure, the small-world index is used. The representation is as follows:

[0053]

[0054] In the formula: The average clustering coefficient of the original fracture network; The weighted average path length of the original fracture network; The average clustering coefficient of the randomized control network; This represents the weighted average path length of the randomized control network.

[0055] Clustering coefficient It is expressed as follows:

[0056]

[0057] In the formula: For nodes The number of edges connecting adjacent nodes;

[0058] When constructing the random control network, ensure that the random network has the same total number of nodes as the original crack network. Total number of edges And only connected random networks are retained; repeat. The random network generation and screening processes were performed, and the results were calculated separately. The arithmetic mean of the results was used as the random control baseline, as shown below:

[0059]

[0060] In the formula: , These represent the average clustering coefficient and average path length of each random network, respectively.

[0061] Furthermore, the sample is divided into several sub-volume regions in three-dimensional space as regional units. For each The steps of crack segmentation, network construction, topology cleaning, and connectivity and flow diversion index calculation are repeated to obtain the results. The corresponding network structure and connectivity metrics, through analysis of different... By comparing and analyzing the differences in indicators, the response relationship of fracture network structural parameters with spatial location and scale changes is established, thereby realizing the coupled characterization of fracture network structural evolution and conductivity change under different fracturing conditions.

[0062] Furthermore, the output of Step8 includes a file of crack network node and edge parameters that fully describes the crack network topology, a visualization of the crack network in three-dimensional space, and key indicators of crack network size, connectivity, and flow characteristics.

[0063] Compared with existing technologies, this method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams is based on real CT three-dimensional volume data, enabling the transformation of fracture structure from geometric visualization to parameterization and evaluability. By performing three-dimensional identification and reconstruction of fractures inside the coal seam before and after fracturing, the true connectivity of fractures in three-dimensional space can be directly reflected, avoiding connectivity misjudgments and scale deviations caused by two-dimensional slice inference, thus improving the authenticity of evaluation results from the source. Simultaneously, the fracture network is modeled using skeletonization and node-edge modeling, transforming the three-dimensional voxel fracture structure into a node-edge fracture network model. This significantly reduces computational complexity while ensuring the spatial connectivity of fractures, allowing the scale, connectivity, and conductivity characteristics of the fracture network to be expressed in a unified parameter form. Furthermore, this invention addresses the problems of self-loops, redundant connections, and pseudo-short edges that are easily introduced during CT scan threshold segmentation and skeleton extraction by setting edge weight completion and topology cleaning processes. This ensures the rationality of the network structure and the stability of index calculation, significantly reducing the interference of threshold selection and local fractures on fracture network evaluation. Building upon this foundation, this invention identifies the main connected structure and dominant flow-guiding framework using an index system encompassing indicators such as the proportion of the largest connected subgraph, weighted average path length, and betweenness centrality. This allows the evaluation results to directly correspond to the flow-guiding mechanism and the criteria for judging engineering extraction effectiveness. This invention supports multi-scale comparisons of ROI before and after fracturing, and under different fracturing conditions, such as horizontal stress ratio and injection rate, providing a quantitative basis for optimizing fracturing parameters. Overall, the method of this invention has a clear process, strong repeatability, and a high degree of output standardization. It is suitable for fracture network characterization using laboratory true triaxial tests and CT-based digital coal and rock sample data, and possesses significant engineering application value. Attached Figure Description

[0064] Figure 1 This is a flowchart of the present invention;

[0065] Figure 2 This is a model diagram of a hydraulically fracturing coal sample under true triaxial conditions according to an embodiment of the present invention, wherein... Indicates the vertical principal stress. This represents the horizontal principal stress in direction 1. This represents the horizontal principal stress in direction 2;

[0066] Figure 3 This is a schematic diagram of three-dimensional spatial crack extraction according to an embodiment of the present invention;

[0067] Figure 4 This is a schematic diagram of the reconstruction result of the three-dimensional spatial network model of the crack in an embodiment of the present invention;

[0068] Figure 5 This is a schematic diagram showing the change in probability distribution of fracture network density before and after hydraulic fracturing in an embodiment of the present invention. Detailed Implementation

[0069] The present invention will be further explained below using a hydraulically fracturing coal sample under true triaxial conditions as an example, in conjunction with the accompanying drawings.

[0070] like Figure 1 As shown, the method for reconstructing and characterizing the three-dimensional spatial network of fractures in hydraulic fracturing of coal seams uses pre- and post-fracturing CT three-dimensional scan data of the coal seam as input. It sequentially completes the processes of data spatial calibration, preprocessing, fracture segmentation, skeletonization, topology cleaning, and calculation of connectivity and conductivity indicators to obtain a three-dimensional fracture network reconstruction model. Specifically, it includes the following steps:

[0071] Step 1: Obtain CT scan data of the coal body before and after fracturing, record the voxel size, scanning direction and sample coordinate system, establish a three-dimensional coordinate reference, and mark the injection hole position.

[0072] like Figure 2 As shown, the coal sample in the embodiment is a cubic structure of 100mm×100mm×100mm. A unified coordinate system is established and a data calibration record file is generated to ensure that the data results before and after fracturing are traceable.

[0073] Step 2 involves denoising and enhancing the CT scan data, correcting areas of non-uniform grayscale, and finally outputting a preprocessing parameter record table including filter kernel size, number of iterations, and enhancement coefficient, which serves as the basis for experimental repeatability.

[0074] In this embodiment, median filtering is used to suppress random noise and maintain the crack boundary morphology. At the same time, histogram equalization is used to improve the separability between the low gray-scale area of ​​the crack and the high gray-scale area of ​​the matrix, and the gray-scale non-uniform area is corrected to make the crack and the matrix easier to separate in a statistical sense. Finally, a preprocessing parameter record table including the filter kernel size, the number of iterations and the enhancement coefficient is output.

[0075] Step 3: Extract cracks based on threshold segmentation, then filter connected components of the cracks to remove suspected noisy connected components. When local crack breaks or discontinuities are found, repair the connection of the crack break area.

[0076] A schematic diagram of crack extraction in the embodiment is shown below. Figure 3 As shown, when filtering connected components for cracks, isolated noisy connected components with fewer than a set threshold number of voxels are deleted to eliminate the impact of image noise on crack structure recognition. For local crack breaks or discontinuous recognition, connectivity repair is performed, and the differences before and after repair and the repair radius are output to avoid over-connectivity.

[0077] Step 4: Perform 3D skeletonization on the cracks processed in Step 3 to obtain the skeleton centerline, identify the endpoints, bifurcation points and intersection points on the skeleton, and treat them as a set of nodes. Define the skeleton segments between adjacent nodes as edge sets. The initial crack network model is obtained. .

[0078] Step 5, in the edge set The above defines weights used to characterize the flow-guiding capability. It includes at least one of the following:

[0079] ① Geometric distance type: ;

[0080] ②Flow guiding capacity type: ,in This refers to the equivalent aperture or equivalent hydraulic radius. This is an empirical coefficient.

[0081] Step 6, after completing the initial crack network model After construction, the initial crack network model is... Topology cleaning and consistency correction are performed. Specifically, self-loop edges in the network are deleted to eliminate non-physical topology structures caused by nodes repeatedly connecting to themselves. When multiple edges exist between the same pair of nodes, duplicate edges are merged, retaining representative edges that satisfy geometric or hydraulic physical constraints and are consistent with the edge weight definition to avoid redundant representation of network connections. This results in a structurally sound three-dimensional spatial network model of cracks. ,in:

[0082] Node set Represented as

[0083] ;

[0084] In the formula: Indicates the number of nodes.

[0085] The set of edges connecting nodes Represented as

[0086]

[0087] In the formula: Indicates the number of sides.

[0088] Step 7, after topology cleaning, the crack 3D spatial network model Based on this, the connectivity and flow conduction structure characteristics of the fracture network are quantitatively characterized.

[0089] Step 7-1: Analyze the overall scale characteristics of the crack network to reflect its basic structural features, specifically including the total number of nodes in the crack network. Total number of sides Node degree and network density .

[0090] Node degree It is the most basic topological quantity in a network, representing the relationship between nodes. The number of connected edges is represented as follows:

[0091]

[0092] In the formula: when node With nodes When there is a connection relationship =1, otherwise =0.

[0093] Crack network density The definition is as follows:

[0094]

[0095] In the formula: The total number of nodes. Let be the total number of edges.

[0096] Step 7-2: Calculate the connectivity index of the fracture network by identifying the connected components in the network. Obtain the number of connected components The connected subgraph with the most nodes is then extracted as the maximum connected subgraph. Calculate its number of nodes and its proportion in the entire network This is used to characterize the overall connectivity of the fracture system. The above index is defined as follows:

[0097] Connected components crack networks A subgraph in which all nodes are reachable from each other, but have no connection to any external nodes of that component, is defined as follows:

[0098]

[0099] In the formula: This represents the number of connected components in a crack network; Representing connected components respectively Two different sets of nodes in; Represents connected components The set of edges in; Represents the entire crack network The set of nodes.

[0100] Maximum connected subgraph This refers to the subgraph with the largest number of nodes among all connected components in a fracture network. This subgraph represents the largest connected structure in the network, with the largest number of nodes. It can be used to measure the scale characteristics of the dominant connectivity structure in a fracture network. The definition is as follows:

[0101]

[0102] In the formula: This represents the maximum number of nodes in a connected subgraph. This represents the percentage of the number of nodes in the largest connected subgraph in the entire crack network.

[0103] Step 7-3, based on the edge set defined in Step 5 Weight Calculate the weighted average path length of the network. This is used to measure the global reachability and fluid transport efficiency between nodes in a fracture network. Simultaneously, the betweenness centrality of the nodes is calculated. The betweenness centrality distribution characteristics were obtained, and the key nodes that play a dominant role in the flow guidance process of the fracture network were identified by using a high quantile threshold, thereby extracting the dominant flow guidance skeleton structure in the fracture network. and The definition is as follows:

[0104] Weighted average path length Defined as the average of the shortest paths between any two nodes in the network, it is expressed as follows:

[0105]

[0106] In the formula: The total number of nodes in the crack network; For nodes With nodes The shortest path length between them.

[0107] Betweenness centrality The degree to which a node acts as a "bridge" or "critical passage" in a network is expressed as follows:

[0108]

[0109] In the formula: Represents a node and The total number of paths between them; For the nodes passed through in these paths The quantity.

[0110] Step 7-4: To quantitatively determine whether the internal fracture network of the coal body exhibits small-world characteristics before and after hydraulic fracturing, the small-world index is used. The representation is as follows:

[0111]

[0112] In the formula: The average clustering coefficient of the original fracture network; The weighted average path length of the original fracture network; The average clustering coefficient of the randomized control network; This is the weighted average path length of the random control network.

[0113] Clustering coefficient This represents the degree of interconnection between a node and its neighboring nodes, reflecting the local clustering of cracks in the crack network, as shown below:

[0114]

[0115] In the formula: For nodes The number of edges connecting adjacent nodes.

[0116] When calculating whether a crack network has small-world characteristics, it is necessary to construct a random control network and ensure that the random network has the same total number of nodes as the original crack network. Total number of edges Considering that disconnected random networks can lead to unstable average path length calculations and introduce systematic biases, only connected random networks are retained. To improve the robustness of the statistical results, the calculation is repeated. The random network generation and screening processes were performed, and the results were calculated separately. The arithmetic mean of the results was used as the random control baseline, as shown below:

[0117]

[0118] In the formula: , These represent the average clustering coefficient and average path length of each random network, respectively.

[0119] In the embodiments Using 200, that is, after repeating the random network generation and screening process 200 times, the results are calculated and their arithmetic mean is taken as the random control baseline, as shown below:

[0120]

[0121] In the formula: , These represent the average clustering coefficient and average path length of the 200 selected random networks, respectively.

[0122] To reveal the differences in crack network structures across spatial scales and operating conditions, the sample can be divided into several sub-volume regions in three-dimensional space as regional units. For each The steps of crack segmentation, network construction, topology cleaning, and connectivity and flow diversion index calculation are repeated to obtain the results. The corresponding network structure and connectivity metrics, through analysis of different... By comparing and analyzing the differences in indicators, the response relationship of fracture network structural parameters with spatial location and scale changes is established, thereby realizing the coupled characterization of fracture network structural evolution and conductivity change under different fracturing conditions.

[0123] Step 8: After completing the above analysis, output and visualize the three-dimensional spatial network model of the crack and its characterization results.

[0124] The output may include a file containing the node and edge parameters of the crack network to fully describe its topology, a visualization of the crack network in three-dimensional space, and key metrics reflecting the scale, connectivity, and flow characteristics of the crack network.

[0125] A schematic diagram of the reconstruction result of the three-dimensional spatial network model of the crack in the embodiment is shown below. Figure 4 As shown in the figure. A schematic diagram illustrating the change in the probability distribution of fracture network density of the coal sample before and after hydraulic fracturing is shown in the example. Figure 5 As shown.

[0126] This method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams uses raw CT data as input. It sequentially completes preprocessing, fracture identification, skeleton extraction, model construction, edge weight definition, topology cleaning, and connectivity and conductivity index calculation, thereby reconstructing a three-dimensional spatial network model of fractures and outputting visualized results. This method can improve the authenticity of evaluation results and is particularly suitable for fracture network characterization in laboratory true triaxial tests and CT-based digital coal and rock sample data.

Claims

1. A method for reconstructing and characterizing a three-dimensional spatial network of hydraulic fracturing fractures in coal seams, characterized in that, Specifically, the following steps are included: Step 1: Obtain CT scan data of the coal body before and after fracturing, record the voxel size, scanning direction and sample coordinate system, establish a three-dimensional coordinate reference, and mark the injection hole position; Step 2: Denoise and enhance the CT scan data, correct the non-uniform grayscale areas, and finally output a preprocessing parameter record table including filter kernel size, number of iterations and enhancement coefficient, as a basis for experimental repeatability. Step 3: Extract cracks based on threshold segmentation, then filter connected components of the cracks to remove suspected noisy connected components. When local crack breaks or discontinuities are found, repair the connection of the crack break area. Step 4: Perform 3D skeletonization on the cracks processed in Step 3 to obtain the skeleton centerline, identify the endpoints, bifurcation points and intersection points on the skeleton, and treat them as a set of nodes. Define the skeleton segments between adjacent nodes as edge sets. The initial crack network model is obtained. ; Step 5, in the edge set The above defines weights used to characterize the flow-guiding capability. ; Step 6, after completing the initial crack network model After construction, the initial crack network model is... Perform topology cleaning and consistency correction to obtain a structurally sound three-dimensional spatial network model of cracks. ,in: Node set Represented as ； In the formula: Indicates the number of nodes; The set of edges connecting nodes Represented as In the formula: Indicates the number of sides; Step 7, after topology cleaning, the crack 3D spatial network model Based on this, the connectivity and flow conduction characteristics of the fracture network are quantitatively characterized. Step 7-1: Analyze the overall scale characteristics of the crack network; Step 7-2: Calculate the connectivity index of the fracture network; Step 7-3, based on the edge set defined in Step 5 Weight Calculate the weighted average path length of the fracture network. Meanwhile, the betweenness centrality of nodes is calculated. To obtain the betweenness centrality distribution characteristics, and to identify the key nodes that play a dominant role in the flow conduction process of the fracture network using a high quantile threshold, thereby extracting the dominant flow conduction skeleton structure in the fracture network; Step 7-4: Calculate the clustering coefficient of the fracture network. To identify whether a crack network has a small-world structure; Step 8: Output and visualize the three-dimensional spatial network model of the crack and its representation results.

2. The method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams according to claim 1, characterized in that, In Step 4, the node set The node attributes should at least include the node number and three-dimensional coordinates, and the edge set. The edge attributes must include at least endpoint pairs and geometric length. For edges lacking geometric information, the Euclidean distance between nodes is used. To complete the expression, it is shown below: In the formula: Represents a node With nodes Euclidean distance in three-dimensional space; For nodes The three-dimensional coordinate components; node The three-dimensional coordinate components.

3. The method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams according to claim 2, characterized in that, Edge weights in Step 5 At least one of the following is included: ① Geometric distance type: ; ②Flow guiding capacity type: ,in This refers to the equivalent aperture or equivalent hydraulic radius. This is an empirical coefficient.

4. The method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams according to claim 3, characterized in that, Step 6 involves the following steps: Self-loop edges in the network are deleted. When there are multiple connecting edges between the same node pair, duplicate edges are merged. Representative connecting edges that satisfy geometric or hydraulic physical constraints and are consistent with the edge weight definition are retained.

5. The method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams according to claim 4, characterized in that, Step 7-1 specifically includes the total number of nodes in the crack network. Total number of sides Node degree and network density ; Node degree It is expressed as follows: In the formula: when node With nodes When there is a connection relationship =1, otherwise =0; Crack network density The definition is as follows: In the formula: The total number of nodes. Let be the total number of edges.

6. The method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams according to claim 5, characterized in that, Step 7-2 is as follows: By identifying connected components in the network Obtain the number of connected components The connected component with the most nodes is extracted as the maximum connected subgraph. And calculate its number of nodes. and its proportion in the entire network ; Connected components The definition is as follows: In the formula: This represents the number of connected components in a crack network; Representing connected components respectively Two different sets of nodes in; Represents connected components The set of edges in the array. Maximum connected subgraph The definition is as follows: In the formula: This represents the maximum number of nodes in a connected subgraph. This represents the percentage of the number of nodes in the largest connected subgraph in the entire crack network.

7. The method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams according to claim 6, characterized in that, In Step 7-3, the weighted average path length It is expressed as follows: In the formula: The total number of nodes in the crack network; For nodes With nodes The shortest path length between them; Betweenness centrality It is expressed as follows: In the formula: Represents a node and The total number of paths between them; For the nodes passed through in these paths The quantity.

8. The method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams according to claim 7, characterized in that, In Step 7-4, when identifying whether a crack network has a small-world structure, the small-world index is used. The representation is as follows: In the formula: The average clustering coefficient of the original fracture network; The weighted average path length of the original fracture network; The average clustering coefficient of the randomized control network; This represents the weighted average path length of the randomized control network. Clustering coefficient It is expressed as follows: In the formula: For nodes The number of edges connecting adjacent nodes; When constructing the random control network, ensure that the random network has the same total number of nodes as the original crack network. Total number of edges And only connected random networks are retained; repeat. The random network generation and screening processes were performed, and the results were calculated separately. The arithmetic mean of the results was used as the random control baseline, as shown below: In the formula: , These represent the average clustering coefficient and average path length of each random network, respectively.

9. The method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams according to claim 8, characterized in that, The sample is divided into several sub-volume regions in three-dimensional space as regional units. For each The steps of crack segmentation, network construction, topology cleaning, and connectivity and flow diversion index calculation are repeated to obtain the results. The corresponding connectivity and diversion metrics, through different By comparing and analyzing the differences in indicators, the response relationship of fracture network structural parameters with spatial location and scale changes is established, thereby realizing the coupled characterization of fracture network structural evolution and conductivity change under different fracturing conditions.

10. The method for reconstructing and characterizing the three-dimensional spatial network of hydraulic fracturing fractures in coal seams according to claim 8, characterized in that, The output of Step 8 includes a file of crack network node and edge parameters that fully describes the crack network topology, a visualization of the crack network in three-dimensional space, and key indicators of crack network size, connectivity, and flow characteristics.

Images