A method and device for predicting fracture connectivity in reef limestone using graph neural networks

Abstract

This invention provides a method and device for predicting the connectivity of fractures in reef limestone using a graph neural network, comprising the following steps: Step S1: Using the intersection points of fracture segments in the reef limestone as graph nodes, record the three-dimensional spatial coordinates of each node; using the actual fracture segments between adjacent nodes as edges of the graph, and assigning an edge feature vector to each edge; the edge feature vector includes at least: the fracture azimuth angle, the fracture segment length, the fracture segment curvature, and the minimum angle formed by the fracture segment with all adjacent fracture segments; Step S2: Construct an adjacency matrix and a node feature matrix, and combine them with the edge feature vectors to construct structured graph data describing the geometric morphology and topological connections of the fracture network; Step S3: Input the structured graph data into the graph neural network to obtain a connectivity probability graph. By transforming the reef limestone fracture network into a graph structure and a graph neural network, a synergistic breakthrough is achieved in the accuracy, efficiency, and decision reliability of seepage capacity assessment.

Description

Technical Field

[0001] This invention relates to the field of oil and gas reservoir fracture characterization and seepage prediction technology, specifically to a method and device for predicting fracture connectivity in reef limestone by combining graph neural networks. Background Technology

[0002] Reef limestone reservoirs are important reservoir types in oil and gas exploration and development, and the connectivity of their internal fracture networks directly affects fluid permeability and development effectiveness. A well-connected fracture network provides low-resistance flow channels for oil and gas, increasing production capacity; conversely, poor connectivity restricts permeability and reduces development efficiency. Therefore, accurate prediction and evaluation of fracture connectivity in reef limestone is a crucial foundation for detailed reservoir characterization and optimization of development strategies.

[0003] Traditional methods for assessing fracture connectivity primarily rely on empirical statistical models based on static geometric parameters or computationally expensive numerical simulations. These methods have significant limitations: empirical models struggle to capture the nonlinear effects of the complex topology and spatial configuration of fracture networks on seepage paths; while numerical simulations offer clear physical meaning, they are computationally intensive, failing to meet the demands for efficient evaluation, and often oversimplify the characterization of fracture geometry. Furthermore, existing methods typically lack effective quantification of dynamic interactions between fractures and struggle to predict end-to-end connectivity probabilities, limiting their precise application in engineering decision-making.

[0004] Therefore, there is an urgent need for an intelligent method that can integrate fracture geometry and topological features, balance prediction accuracy and computational efficiency, and output probabilistic connectivity evaluation results, so as to improve the accuracy and engineering applicability of reef limestone reservoir connectivity prediction. Summary of the Invention

[0005] This invention proposes a method and device for predicting the connectivity of fractures in reef limestone by combining graph neural networks, in order to solve the technical problem that existing technologies are unable to output probabilistic connectivity evaluation results while taking into account both prediction accuracy and computational efficiency.

[0006] To address the aforementioned technical problems, this invention provides a method for predicting fracture connectivity in reef limestone using graph neural networks, comprising the following steps:

[0007] Step S1: Use the intersection points of the crack segments in the reef limestone as graph nodes and record the three-dimensional spatial coordinates of each node; use the actual crack segments between adjacent nodes as edges of the graph and assign an edge feature vector to each edge.

[0008] The edge feature vector includes at least: crack orientation azimuth, crack segment length, crack segment curvature, and the minimum angle formed between the crack segment and all adjacent crack segments;

[0009] Step S2: Construct an adjacency matrix and a node feature matrix, and combine them with the edge feature vectors to construct structured graph data describing the geometry and topological connections of the crack network;

[0010] Step S3: Input the structured graph data into the graph neural network to obtain a connected probability graph.

[0011] Preferably, the expression for calculating the minimum included angle in step S1 is:

[0012] ;

[0013] In the formula, Represents a node and nodes The smallest included angle between the sides formed; Represents a node The set of neighbors; Indicates from arrive The direction vector; This represents the inverse cosine function.

[0014] Preferably, the loss function used by the graph neural network during training is... The expression is:

[0015] ;

[0016] ;

[0017] In the formula, This represents the total number of edges in the graph; Represents the weight coefficient of the connected edges; Representing an edge The true connectivity label; Representing an edge The predicted connectivity probability; Indicates the number of disconnected edges; This indicates the number of connected edges.

[0018] Preferably, during training, the graph neural network performs data augmentation on the training dataset, the data augmentation including:

[0019] 1) Random rotation: Increase the azimuth angle of the crack direction by a random quantity uniformly distributed between 0° and 360°;

[0020] 2) Random translation: The node coordinates are uniformly translated within a range of ±10% of the area size;

[0021] 3) Random scale jitter: Multiply the crack segment length by a uniformly distributed random factor of 0.8-1.2.

[0022] Preferably, the graph neural network employs DropEdge regularization to prevent overfitting during training: in each training iteration, elements in the adjacency matrix are randomly set to zero and discarded with a set probability.

[0023] Preferably, the graph neural network in step S3 includes: a feature initialization layer, a message passing layer, and an edge prediction layer;

[0024] The feature initialization layer: normalizes the edge feature vectors to obtain initial feature vectors;

[0025] Message passing layer: Based on the adjacency matrix and node feature matrix, a multi-head graph attention mechanism is used to iteratively update node features and generate node embedding vectors;

[0026] Edge prediction layer: The embedding vectors of the two ends of the target edge are concatenated with the initial edge feature vector of the target edge, and then passed through two layers of multilayer perceptron (MLP) and sigmoid function to obtain the connectivity probability of the target edge.

[0027] Preferably, the calculation expression for the message passing layer is:

[0028] ;

[0029] ;

[0030] In the formula, node In the The embedding vector output after layer message passing; σ() represents the activation function; Represents a node The set of neighbors; Represents a node To the neighbors Normalized attention weights; Indicates the first The weight matrix of each attention head; LeakyReLU represents the activation function; Represents the attention mechanism parameter vector; Represents a node The feature embedding vector; Represents a node The feature embedding vector.

[0031] Preferably, the calculation expression for the edge prediction layer is:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] In the formula, Representing an edge fused feature vectors; Representing an edge The connectivity probability; This represents the normalized edge feature vector; For activation functions; This represents the weight matrix of the first layer of a multilayer perceptron; This represents the bias vector of the first layer of a multilayer perceptron; This represents the weight matrix of the second layer of the multilayer perceptron; This represents the bias vector of the second layer of the multilayer perceptron.

[0037] Preferably, the method further includes the following steps:

[0038] Step S4: Binarize the connected probability graph, set a threshold to segment connected components, and extract the largest connected subgraph;

[0039] Step S5: Convert the edge connectivity probability into seepage path weights and assign them to the maximum connected subgraph. Then, use Dijkstra's algorithm to calculate the shortest path between any nodes on the weighted maximum connected subgraph to obtain the main seepage path.

[0040] Step S6: Generate a fracture network heat map based on the fracture connectivity probability and mark the main seepage path for visualization; calculate the global connectivity rate to quantify the reservoir seepage capacity.

[0041] The present invention also provides an electronic device, comprising: a memory, a processor, and a computer program, wherein the computer program is stored in the memory and configured to be executed by the processor to implement the above-described method.

[0042] The beneficial effects of this invention include at least the following: By transforming the fracture network of reef limestone into a graph structure and combining it with a graph neural network, this invention achieves a synergistic breakthrough in the accuracy, efficiency, and reliability of seepage capacity assessment. In terms of accuracy, due to the explicit modeling of geometric topological features such as fracture curvature and dynamic angles, and the use of graph neural networks to capture non-local dependencies, the accuracy of main seepage channel identification is significantly improved compared with traditional numerical simulation. In terms of efficiency, end-to-end graph reasoning replaces physical simulation, which greatly reduces the assessment time of a network of thousands of nodes. In terms of engineering decision-making, probabilistic connectivity output combined with a threshold segmentation mechanism significantly quantifies uncertainty and reduces the misjudgment rate of drilling target areas. At the same time, automated seepage path extraction and heat map rendering greatly reduce manual analysis time, and the intelligentization of the entire process shortens the deployment cycle of the scheme from days to hours. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating an embodiment of the present invention. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0045] Example 1

[0046] like Figure 1 As shown, this embodiment of the invention provides a method for predicting fracture connectivity in reef limestone by combining graph neural networks, including the following steps:

[0047] Step S1: Use the intersection points of the crack segments in the reef limestone as graph nodes and record the three-dimensional spatial coordinates of each node; use the actual crack segments between adjacent nodes as edges of the graph and assign an edge feature vector to each edge.

[0048] Specifically, the core of this step is to abstract the complex network of fissures in the reef limestone into a mathematical graph structure, serving as the input foundation for a graph neural network. First, the intersections of fissure segments are identified as graph nodes, with each node precisely recording its three-dimensional spatial coordinates. Next, the actual fissure segments between adjacent nodes are defined as edges of the graph. Each edge not only represents a connection but is also assigned a multi-dimensional geometric feature vector, including the azimuth angle of the fissure segment, its actual length, curvature, and a key topological indicator—the minimum angle formed between the fissure segment and all adjacent fissure segments. Finally, an adjacency matrix is ​​constructed by defining the Euclidean distance between nodes as less than the connection decision radius, and a node feature matrix is ​​formed by combining the features of each node, thus fully constructing structured graph data describing the geometry and topological connections of the fissure network.

[0049] Node coordinates:

[0050] ;

[0051] Represents the spatial coordinate vector of the node; This indicates the node's coordinates in the X direction; This represents the node's coordinate in the Y direction; This represents the node's coordinates in the Z direction; Represents a set of nodes.

[0052] Edge feature vectors:

[0053] ;

[0054] Represents a node and nodes The edge feature vectors that constitute the edges; Indicates the azimuth of the crack direction; Indicates the length of the crack segment; Indicates the crack curvature; This indicates the minimum angle between the crack and the adjacent crack.

[0055] Minimum included angle calculation formula

[0056] ;

[0057] In the formula, Represents a node and nodes The smallest included angle between the sides formed; Represents a node The set of neighbors; Indicates from arrive The direction vector; This represents the inverse cosine function.

[0058] Step S2: Construct the adjacency matrix and node feature matrix, and combine them with edge feature vectors to construct structured graph data describing the geometry and topological connections of the crack network.

[0059] Specifically, the constructed adjacency matrix and feature matrix are shown below.

[0060] Adjacency matrix:

[0061] ;

[0062] Represents the elements of the adjacency matrix; Represents a node and nodes Euclidean distance between them; Indicates the radius of the connection determination.

[0063] Feature matrix:

[0064] ;

[0065] Represents the node feature matrix; Represents a node eigenvectors; This represents the degree of a node, i.e., the number of connected edges.

[0066] Step S3: Input the structured graph data into the graph neural network to obtain the connectivity probability graph.

[0067] Example 2

[0068] This embodiment, building upon Embodiment 1, further provides a training and optimization method for graph neural networks. Label preparation is based on high-precision CT scans or OpenPNM numerical simulations, marking edges in the graph as either truly connected or disconnected. The loss function employs weighted binary cross-entropy, significantly increasing the penalty for prediction errors of sparsely connected edges by introducing weight coefficients, forcing the model to focus more on learning connected samples. Data augmentation strategies include random rotation, random translation, and random scale jittering of the original fracture network to enhance the model's robustness to spatial transformations and its generalization ability. Regularization utilizes the DropEdge technique, randomly discarding some edges in the adjacency matrix during each training iteration. By disrupting partial connectivity, this prevents the model from overfitting to specific graph structures, thereby improving the model's generalization performance.

[0069] 1) Tag preparation: Based on CT scans or numerical simulations such as OpenPNM seepage simulation, real connected paths are labeled, with non-connected edges typically accounting for over 90%;

[0070] 2) The loss function is as follows:

[0071] ;

[0072] ;

[0073] In the formula, This represents the total number of edges in the graph; This represents summing over all edges; Represents the weight coefficient of the connected edges; Representing an edge The true connectivity label; Representing an edge The predicted connectivity probability; Indicates the number of disconnected edges; represents the number of connected edges; log represents the natural logarithm function.

[0074] 3) Data Augmentation: Random rotations (0°-360°), translations (±10% of region size), and scale jitter (0.8-1.2 times) are applied to the original crack network to improve the model's robustness to spatial transformations. The expression is as follows:

[0075] ;

[0076] Indicates the direction and angle of the crack after rotation; This indicates that the random rotation amount follows a uniform distribution; Indicates the coordinates after translation; and This indicates that the random translation amount follows a uniform distribution; Indicates the size of the crack network region; This indicates the scaled crack length; This indicates that the random scaling factor follows a uniform distribution;

[0077] 4) Regularization: The DropEdge technique is used to randomly discard 15% of edges to prevent overfitting.

[0078] ;

[0079] ;

[0080] This represents the adjacency matrix after random discarding; Represents the original adjacency matrix; This represents element-wise multiplication; Represents a random mask matrix; The edge reservation flag (0 / 1); This represents the probability of edge dropping; in this embodiment, the value is 0.15.

[0081] Example 3

[0082] This embodiment provides an improved graph neural network to replace the graph neural network in Embodiment 1, comprising three core processing layers. First, there is a feature initialization layer, which normalizes the multidimensional geometric properties of the input edges, mapping them to initial feature vectors, providing a standardized starting point for subsequent learning. Second, there is the core message passing layer, which employs a graph attention mechanism, dynamically calculating the attention weights of nodes to their neighbors using multi-head attention, and updating the embedding representation of its own nodes by weighted aggregation of the feature information of neighboring nodes. This process uses the LeakyReLU activation function and allows the model to focus on important relationships in different subspaces, effectively capturing nonlocal dependencies and complex interactions in the fracture network. Finally, there is an edge prediction layer, which, for each target edge in the graph, concatenates the final embedding vectors of the nodes at both ends with the normalized initial geometric feature vector of the edge itself. The concatenated fused feature vector is input into a two-layer multilayer perceptron, and finally outputs the probability value of the edge belonging to a connected state through the Sigmoid activation function, thereby generating the probabilistic connected graph of the entire fracture network.

[0083] Specifically, the message passing layer employs a graph attention mechanism (GAT), which dynamically aggregates neighborhood information through multi-head attention weights. The calculation process is as follows:

[0084] ;

[0085] ;

[0086] In the formula, node In the The embedding vector output after layer message passing; σ() represents the activation function; Represents a node The set of neighbors; Represents a node To the neighbors Normalized attention weights; Indicates the first The weight matrix of each attention head; LeakyReLU represents the activation function; Represents the attention mechanism parameter vector; Represents a node The feature embedding vector; Represents a node The feature embedding vector.

[0087] The edge prediction layer predicts each edge Calculate connectivity probability: Initial features of the target edge to be joined and the embedding vectors of the two ends nodes and After inputting into a two-layer MLP, the output probability value is activated by a Sigmoid function. ∈[0,1], forming the full graph connectivity probability matrix, whose expression is:

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] In the formula, Representing an edge fused feature vectors; This represents the normalized edge feature vector; For activation functions; This represents the weight matrix of the first layer of a multilayer perceptron; This represents the bias vector of the first layer of a multilayer perceptron; This represents the weight matrix of the second layer of the multilayer perceptron; This represents the bias vector of the second layer of the multilayer perceptron.

[0093] Example 4

[0094] This embodiment 1, based on embodiment 1, provides a method for probabilistic graph post-processing and engineering applications. It transforms the probabilistic connected graph obtained from model predictions into information and tools that can directly serve engineering decision-making.

[0095] Specifically, the probabilistic graph is binarized by setting a probability threshold, and connected component segmentation identifies connected subgraph components. The largest connected subgraph is extracted as the key seepage main channel. Seepage path analysis converts the connectivity probability of each edge into a path weight; the lower the weight, the more likely the edge is to be connected and the lower the resistance. Dijkstra's algorithm is used to calculate the shortest path between any nodes on the weighted graph, which physically represents the seepage path with the highest probability. The visualization output generates an intuitive heatmap, where the edge colors are rendered using linear interpolation from red to blue, clearly showing the connectivity probability at various points in the network; simultaneously, arrows of the main seepage paths identified by Dijkstra's algorithm are overlaid. Finally, the global connectivity rate, i.e., the proportion of connected edges to the total number of edges, is calculated as a core quantitative indicator for evaluating the seepage capacity of the entire fracture network layer, providing a direct basis for engineering decisions.

[0096] 1) Connected component segmentation: Set a threshold τ, default 0.7, identify connected components after binarizing the probabilistic graph, and extract the largest connected subgraph;

[0097] ;

[0098] This represents the binary connectivity flag, where 1 indicates connectivity and 0 indicates disconnection. Representing an edge The predicted connectivity probability; This represents the probability segmentation threshold, with a default value of 0.7.

[0099] 2) Seepage path analysis: Converting edge probabilities into weights

[0100] ;

[0101] Representing an edge The seepage path weights are assigned to the edges of the maximum connected subgraph. Then, Dijkstra's algorithm is used to calculate the shortest path between any nodes on the weighted maximum connected subgraph, which is physically the main seepage path.

[0102] 3) Visualization Output: Generates a fracture network heatmap, with red for high-probability edges and blue for low-probability edges, overlaid with arrows indicating the main seepage paths, and calculates the global connectivity C to quantify the reservoir's seepage capacity.

[0103] ;

[0104] This represents the global connectivity of the crack network; This represents the total number of connected edges, i.e. The number of =1; This represents the total number of edges in the graph; This indicates a binary connectivity flag.

[0105] When representing colors, the following formula is used for calculation:

[0106] ;

[0107] Representing an edge The rendered color; This represents red-blue color interpolation; the red end indicates the probability of high connectivity. The blue end indicates a low connectivity probability. .

[0108] Example 5

[0109] This embodiment provides an electronic device, including: a memory, a processor, and a computer program, wherein the computer program is stored in the memory and configured to be executed by the processor using any of the methods described in any of the above embodiments or any combination thereof.

[0110] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; only preferred embodiments of the present invention are illustrated. The descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. As long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0111] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for predicting fracture connectivity in reef limestone using graph neural networks, characterized in that: Includes the following steps: Step S1: Use the intersection points of the crack segments in the reef limestone as graph nodes and record the three-dimensional spatial coordinates of each node; use the actual crack segments between adjacent nodes as edges of the graph and assign an edge feature vector to each edge. The edge feature vector includes at least: crack orientation azimuth, crack segment length, crack segment curvature, and the minimum angle formed between the crack segment and all adjacent crack segments; Step S2: Construct an adjacency matrix and a node feature matrix, and combine them with the edge feature vectors to construct structured graph data describing the geometry and topological connections of the crack network; Step S3: Input the structured graph data into a graph neural network to obtain a connectivity probability graph; The graph neural network described in step S3 includes: a feature initialization layer, a message passing layer, and an edge prediction layer; The feature initialization layer: normalizes the edge feature vectors to obtain initial feature vectors; Message passing layer: Based on the adjacency matrix and node feature matrix, a multi-head graph attention mechanism is used to iteratively update node features and generate node embedding vectors; Edge prediction layer: After concatenating the embedding vectors of the two ends of the target edge with the initial edge feature vector of the target edge, the connection probability of the target edge is obtained by passing it through two layers of multilayer perceptron (MLP) and the sigmoid function. The method further includes the following steps: Step S4: Binarize the connected probability graph, set a threshold to segment connected components, and extract the largest connected subgraph; Step S5: Convert the edge connectivity probability into seepage path weights and assign them to the maximum connected subgraph. Then, use Dijkstra's algorithm to calculate the shortest path between any nodes on the weighted maximum connected subgraph to obtain the main seepage path. Step S6: Generate a fracture network heat map based on the fracture connectivity probability and mark the main seepage path for visualization; calculate the global connectivity rate to quantify the reservoir seepage capacity.

2. The method for predicting fracture connectivity in reef limestone using graph neural networks according to claim 1, characterized in that: The expression for calculating the minimum included angle in step S1 is: ； In the formula, Represents a node and nodes The smallest included angle between the sides formed; Represents a node The set of neighbors; Indicates from arrive The direction vector; Indicates from arrive The direction vector; This represents the inverse cosine function.

3. The method for predicting fracture connectivity in reef limestone using graph neural networks according to claim 1, characterized in that: The loss function used by the graph neural network during training The expression is: ； ； In the formula, This represents the total number of edges in the graph; Represents the set of edges; Represents the weight coefficient of the connected edges; Representing an edge The true connectivity label; Representing an edge The predicted connectivity probability; Indicates the number of disconnected edges; This indicates the number of connected edges.

4. The method for predicting fracture connectivity in reef limestone combined with graph neural networks according to claim 1, characterized in that: During training, the graph neural network performs data augmentation on the training dataset, including: 1) Random rotation: Increase the azimuth angle of the crack direction by a random quantity uniformly distributed between 0° and 360°; 2) Random translation: The node coordinates are uniformly translated within a range of ±10% of the area size; 3) Random scale jitter: Multiply the crack segment length by a uniformly distributed random factor of 0.8-1.

2.

5. The method for predicting fracture connectivity in reef limestone using graph neural networks according to claim 1, characterized in that: During training, the graph neural network employs DropEdge regularization to prevent overfitting: in each training iteration, elements in the adjacency matrix are randomly set to zero and discarded with a set probability.

6. The method for predicting fracture connectivity in reef limestone using graph neural networks according to claim 1, characterized in that: The calculation expression for the message passing layer is: ； ； In the formula, Represents a node In the The embedding vector output after layer message passing; σ() represents the activation function; Represents a node The set of neighbors; Represents a node To the neighbors Normalized attention weights; Indicates the first The weight matrix of each attention head; LeakyReLU represents the activation function; Represents the attention mechanism parameter vector; Represents a node The feature embedding vector; Represents a node The feature embedding vector.

7. The method for predicting fracture connectivity in reef limestone combined with graph neural networks according to claim 6, characterized in that: The calculation expression for the edge prediction layer is: ； ； ； ； In the formula, Representing an edge fused feature vectors; Indicates the concatenation function; Representing an edge The connectivity probability; This represents the normalized edge feature vector; For activation functions; This represents the weight matrix of the first layer of a multilayer perceptron; This represents the bias vector of the first layer of a multilayer perceptron; This represents the weight matrix of the second layer of the multilayer perceptron; This represents the bias vector of the second layer of the multilayer perceptron.

8. An electronic device, comprising: A memory, a processor, and a computer program, characterized in that: the computer program is stored in the memory and configured to be executed by the processor to implement the method of any one of claims 1 to 7.

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