Data physical dual-drive crack propagation prediction method

Abstract

The invention discloses a data and physical dual-drive crack propagation prediction method, which belongs to the field of petroleum engineering and comprises the following steps: step 1, constructing a real observation data set and a sampling data set; step 2, constructing a hybrid architecture fusing a Transform encoder and a graph attention network; 3, three independent and parallel decoders are constructed to map the shared features into the geometric dimensions and mechanical parameters of the cracks; 4, establishing a physical loss function based on linear elastic fracture mechanics and a material balance principle, and combining the physical loss function with a data loss function to construct a mixed loss function for model training; and 5, predicting the geometric dimension and mechanical parameters of the fracturing crack by using the trained model. According to the method, physical priori knowledge is embedded into a multi-task deep learning framework, and physical loss is embedded into a loss function, so that the precision and interpretability of model prediction are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of petroleum engineering, specifically relating to a data-physical dual-driven fracture propagation prediction method based on Transformer and graph attention network. Background Technology

[0002] In the field of oil and gas field exploration and development, large-scale fracturing of unconventional reservoirs has become the main method for developing unconventional oil and gas reservoirs. The geometry of the fractures after fracturing directly determines the effectiveness of the fracturing operation. Accurate prediction of these parameters is crucial for optimizing fracturing operation design, improving recovery rate, and reducing development costs. In order to accurately predict the geometric parameters of fracturing fractures, engineers use mechanism-based numerical simulation methods to predict these fracture parameters. Mechanism-based numerical simulation methods mostly establish a system of partial differential equations based on rock mechanics, fluid mechanics, and fracture mechanics, and then use the finite element method, boundary element method, etc. to solve them. Although this method has clear physical meaning and strong interpretability, it is computationally complex, time-consuming, and cannot meet the needs of rapid prediction in oilfields.

[0003] To address the aforementioned issues, pure data-driven methods based on machine learning have begun to replace numerical simulation for prediction. These methods utilize machine learning models to learn the mapping relationship between input and output parameters from a large amount of historical data. During training, a loss function is first defined to calculate the error between the model's predictions and the actual observations. Then, an optimizer iteratively optimizes the loss function. In each iteration, the backpropagation algorithm is used to update all learnable parameters in the model. After multiple rounds of training, a trained model that can better represent the nonlinear relationship between input and output is obtained. While this method is computationally fast, it is highly dependent on the quality and quantity of historical data, and the model, acting as a "black box," leads to a lack of interpretability in the prediction results and relatively low accuracy. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a data- and physics-driven crack propagation prediction method. It introduces a hybrid network architecture combining a Transformer encoder and a graph attention network to capture complex interactions between features and establish a feature map based on physical priors. Then, three parallel and independent decoders output the geometric parameters of the crack. This model structure accurately quantifies the complex coupling effects between input parameters, improving prediction accuracy. Simultaneously, a hybrid loss function combining data loss and physical loss is introduced to ensure that the prediction results fit the actual observed data while adhering to physical laws, thus solving the problem of poor interpretability in purely data-driven models.

[0005] The technical solution of the present invention is as follows: A data-physical dual-driven crack propagation prediction method includes the following steps: Step 1: Construct a labeled real observation dataset and an unlabeled physical sampling dataset, and perform normalization processing; Step 2: Construct a hybrid architecture that integrates a Transformer encoder and a graph attention network to deeply interact with input features and fuse them with physical priors to generate shared features enhanced with physical information. Step 3: Construct three independent and parallel decoders that share features to map the crack's geometry and mechanical parameters; Step 4: Establish a physical loss function based on linear elastic fracture mechanics and the principle of mass balance, and combine it with the data loss function to construct a hybrid loss function with physical meaning for model training; Step 5: Use the trained model to predict the geometry and mechanical parameters of the hydraulic fracturing cracks.

[0006] Furthermore, the specific process of step 1 is as follows: Step 1.1: Obtain reservoir rock geomechanical parameters, fluid parameters, fracturing operation parameters, and fracturing fracture geometric parameters interpreted through microseismic analysis. After processing missing and outlier values, construct a labeled real observation dataset. Then, the training set and the test set are divided proportionally. Step 1.2: Based on the numerical range of each input feature in the real observation dataset, determine the minimum and maximum values ​​of each feature to define the boundary of the physical parameter space. Then, use Latin hypercube sampling to generate a large number of sampling points in the multidimensional parameter space to establish an unlabeled physical sampling dataset. The entire physical sampling dataset is used as the training set. Step 1.3: Transfer the real observation dataset and physical sampling dataset Geomechanical parameters, fluid parameters, fracturing operation parameters, and fracturing fracture geometric parameters were used as samples to construct a sample set, which was then normalized; specifically: Real observation dataset and physical sampling dataset The geomechanical parameters, fluid parameters, and fracturing operation parameters in the data are processed as samples to obtain two corresponding input feature sample sets. and ; use real observation datasets The geometric parameters of the fracturing fractures in the sample are used as samples to obtain the output sample set. ;in, for The first in Group samples; for The first in Group samples; for The first in Group samples; For each sample group in each sample set, normalization is performed. The two normalized input feature sample sets are respectively , The normalized output sample set is .

[0007] Furthermore, the specific process of step 2 is as follows: Step 2.1: Normalize the two input feature sample sets. , Based on their physical properties, parameters are classified into geomechanical parameters, fluid parameters, and fracturing construction parameters. A fully connected neural network is used to linearly project the classified parameters onto a high-dimensional vector space, resulting in three high-dimensional feature vectors. These high-dimensional feature vectors are then concatenated and a learnable positional code is introduced to form a high-dimensional embedding feature of a unified dimension. Step 2.2: Construct the Transformer encoder to capture the complex relationships between features; Step 2.3: Construct a graph attention network to generate an enhanced feature matrix that combines physical priors and data-driven approaches. The graph attention network includes a first graph attention layer, a dropout layer, a second graph attention layer, and an activation layer. Step 2.4: Concatenate the output of the Transformer encoder with the output of the graph attention network to obtain shared features for physical information enhancement.

[0008] Furthermore, the specific process of step 2.1 is as follows: Step 2.1.1: Combine the two normalized input feature sample sets. , Based on their physical properties, parameters are classified into three subsets: geomechanical parameters, fluid parameters, and fracturing operation parameters. Then, each type of parameter is projected using an independent linear layer. ; ; ; in, , , They are divided into three subsets: geomechanical parameters, fluid parameters, and fracturing operation parameters; , , Here are the learnable weight matrices corresponding to the three subsets; , , These are the high-dimensional feature vectors obtained by linear projection of the three subsets. , , The high-dimensional embedding dimension is the projection of the three subsets; Batch size; Step 2.1.2: Concatenate the high-dimensional feature vectors obtained from the projection to form preliminary fused features, as shown in the following formula: ; in, This represents the initial fusion characteristics. For total embedding dimension; Step 2.1.3: Introduce learnable positional encoding to form a high-dimensional embedding feature with a unified dimension; the formula is as follows: ; in, High-dimensional embedding features; This is a learnable location encoding for embedded features.

[0009] Furthermore, the specific process of step 2.2 is as follows: Step 2.2.1: Embed the high-dimensional features Transformed into a query matrix through linear transformation Key matrix Sum matrix Then through , , The context vector for generating the attention head is calculated using the following formula: ; in, For the first The context vector of each attention head; , , The first The query matrix, key matrix, and value matrix of each attention head; This is a transpose operation; This is the scaling factor; It is the softmax function; Step 2.2.2: Concatenate the context vectors of multiple attention heads and obtain the output of the multi-head attention module through a linear projection matrix. The formula is: ; in, It is a learnable linear projection matrix; For splicing operations; For the first The context vector of each attention head; Step 2.2.3: Combine the output of the multi-head attention module with the high-dimensional embedded features. Perform residual connections and layer normalization to obtain embedded features. : ; in, For layer normalization operation; Step 2.2.4: Based on the feedforward neural network... Perform a nonlinear transformation to obtain the characteristics of the nonlinear transformation. : ; in, It is the ReLU activation function; , These are learnable weights; , For bias; Step 2.2.5, for and Perform the second residual connection and layer normalization operation to obtain the output of the first encoder. : ; Step 2.2.6: Overlay two encoder layers, that is... As Enter step 2.2.1 again until you obtain the final output of the encoder section. .

[0010] Furthermore, the specific process of step 2.3 is as follows: Step 2.3.1: Embed the high-dimensional features obtained in Step 2.1 The input first graph's attention layer undergoes linear transformation, attention calculation, and multi-head attention output; the specific process is as follows: First, perform a linear transformation: ; in, It is a learnable linear transformation matrix; The transformed node features; Then, attention calculation is performed; based on prior knowledge in the field of hydraulic fracturing, the connection relationships between nodes are defined, an adjacency matrix based on physical priors is constructed, and attention weights are calculated based on the adjacency matrix. When a node... With nodes When a physical connection exists, calculate its attention coefficient: ; in, It is an adjacency matrix; ; in, This is the attention weight vector; , Each node With nodes Transformed node features To make nodes With nodes Perform feature splicing; For nodes With nodes Attention coefficient between them; It is a linear rectified function with leakage coefficient; Perform normalization on all neighboring nodes: ; in, For nodes With nodes Attention weights between them; For exponentiation; The adjacency matrix is ​​the first... Line 1 The element of the column, the first Row corresponding node , No. Column corresponding node ; The adjacency matrix is ​​the first... Line 1 Column elements; For nodes With nodes Attention coefficient between them; This represents the number of neighboring nodes. Next, multi-head attention output is performed; two attention heads are used to calculate and integrate the node's neighborhood features respectively: ; ; in, These are the first and second attention head nodes, respectively. The output characteristics; It is a non-linear activation function; These are the first and second attention heads, respectively. With nodes Attention weights between them; The result The final enhanced features are obtained by splicing the data together. ; For nodes Enhanced features; Step 2.3.2, will Input Dropout layer to perform Dropout operation: ; in, To and A random mask matrix with consistent dimensions; This represents the probability of inactivation. Multiply by corresponding elements; This is the node enhancement matrix after the Dropout operation; For Dropout layer; Step 2.3.3, will As input to the attention layer of the second graph, the operations of the attention layer of the first graph are repeated to obtain higher-order node features: ; in, This is the output of the attention layer in the second graph; This is the attention layer of the second graph; Step 2.3.4: Input the output of the attention layer in the second image into the activation layer to obtain the final enhanced feature matrix: ; in, To enhance the feature matrix.

[0011] Furthermore, in step 2.4, the formula for calculating the shared features is: ; in, For shared features.

[0012] Furthermore, the specific process of step 3 is as follows: Step 3.1: Construct a physical information attention layer, which incorporates the shared features obtained in Step 2.4. Input physical information into the attention layer to obtain shared physical features. The specific process is as follows: Step 3.1.1: Generate the query matrix Key matrix Sum matrix : ; ; ; in, , , These are three learnable weight coefficients; Step 3.1.2: Calculate the query matrix Bond matrix The similarity is then used to obtain a set of attention weights after passing through the softmax function. : ; Step 3.1.3, Calculation right The weighted sum yields the shared physical characteristics. : ; Step 3.2, Simultaneously, the data is input into three parallel and independent multilayer perceptron decoders, yielding six predicted values: crack area, crack length, crack width, crack height, net pressure, and stress intensity factor. Among these, crack area, crack length, crack width, and crack height are geometric dimensions, while net pressure and stress intensity factor are mechanical parameters.

[0013] Furthermore, the specific process of step 4 is as follows: Step 4.1: Construct the physical loss based on the residuals of the elasticity equation. The specific formula is as follows: ) ; in, Mean square error; This is the predicted value of the stress intensity factor; This is the predicted value for the crack width; This is the predicted value for net pressure; This is the proportionality coefficient; It is the equivalent elastic modulus; Step 4.2: Construct the physical loss based on the crack propagation criterion residual. : ; in, For fracture toughness; Step 4.3: Construct physical loss based on flow equation residuals : ; in, This is the predicted value for the crack length; This is the predicted value for the crack height; For displacement; For time; For shape factor; Step 4.4, the total physical loss is : ; in, , , These are the weighting coefficients for different loss terms; Step 4.5: Calculate data loss : ; in, The number of samples; For the first The first sample One predicted output; For the first The first sample One true value; Step 4.6: Add the data loss and the total physical loss proportionally to obtain the total mixed loss function. : ; in, , These are the weighting coefficients for different losses; Step 4.7: Use the predicted values ​​output from Step 3 to calculate the mixture loss function. The model training process involves minimizing the mixture loss using the Adam optimizer, then performing backpropagation based on the training set to update all learnable parameters in the model, gradually bringing the model's predictions closer to and satisfying the physical constraints.

[0014] Furthermore, the specific process of step 5 is as follows: input the samples in the test set of step 1 and the adjacency matrix in step 2 into the trained model to predict the crack propagation, including crack area, crack length and crack width.

[0015] The beneficial technical effects of this invention are as follows: This invention categorizes input features into three main types: geomechanical parameters, fluid parameters, and fracturing construction parameters. This allows input features to interact within their respective subspaces, capturing strong correlations between features while reducing noise generated between weakly correlated features, thus enhancing the model's generalization ability. Even when faced with previously unseen input data, the model can accurately predict the geometry of fractures. This invention proposes a hybrid model architecture based on Transformer and graph attention networks, employing multiple independent and parallel decoders to output the geometry and physical parameters of fractures. This model structure can capture all possible nonlinear relationships between features and utilizes graph attention networks to give the interactions between features clear physical meaning, enabling the model to improve prediction accuracy while ensuring the learning process conforms to physical laws. This invention embeds multiple physical loss terms into the loss function to construct a physically meaningful hybrid loss function. During training, the model parameters are continuously updated through gradient backpropagation, making the learned laws more physically meaningful and greatly improving the model's interpretability. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the overall design of a data-physical dual-driven crack propagation prediction method according to the present invention.

[0017] Figure 2 This is a structural diagram of the crack propagation prediction model of the present invention.

[0018] Figure 3 This is a loss graph during the training process of the model in this invention.

[0019] Figure 4 This is a comparison chart of the actual and predicted values ​​of the crack area in an embodiment of the present invention.

[0020] Figure 5 This is a comparison chart of the actual and predicted crack length values ​​in an embodiment of the present invention.

[0021] Figure 6 This is a comparison chart of the actual and predicted crack width values ​​in an embodiment of the present invention.

[0022] Figure 7 This is a comparison chart of the losses during the training process between the present invention and the pure data-driven method.

[0023] Figure 8 This invention is an R method that is different from the pure data-driven method. 2 Comparison chart. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: The main process of this invention is as follows: Constructing a sample dataset; building a hybrid architecture integrating Transformer and graph neural networks, deeply interacting with input features and fusing them with physical priors to generate shared features enhanced with physical information; constructing a decoder with three parallel structures to map the shared features to the geometric dimensions and mechanical properties of the crack; based on linear elastic fracture mechanics and the principle of mass balance, constructing a physical residual term and combining it with the mean square error loss of the data-driven prediction results to establish a physically meaningful comprehensive loss function and train the model; after training, the geometric shape and mechanical parameters of the crack can be quickly predicted using geomechanical parameters, fluid parameters, and construction parameters. Figure 1 As shown, a data-physical dual-driven crack propagation prediction method specifically includes the following steps: Step 1: Construct a labeled real observation dataset and an unlabeled sampled dataset, and perform normalization processing; the specific process is as follows: Step 1.1: Obtain reservoir rock geomechanical parameters, fluid parameters, fracturing operation parameters, and fracturing fracture geometric parameters interpreted through microseismic analysis. After processing missing and outlier values, construct a labeled real observation dataset. Then, the training set and the test set are divided in a ratio of 8.5:1.5; Step 1.2: Based on the numerical range of each input feature in the real observation dataset, determine the minimum and maximum values ​​of each feature to define the boundary of the physical parameter space. Then, use Latin Hypercube Sampling (LHS) to generate a large number of sampling points in the multidimensional parameter space to establish an unlabeled physical sampling dataset. The entire physical sampling dataset is used as the training set and is not used in the test. Step 1.3: Transfer the real observation dataset and physical sampling dataset The geomechanical parameters, fluid parameters, fracturing construction parameters, and fracturing fracture geometric parameters in the sample are used as samples to construct a sample set, which is then normalized. Real observation dataset and physical sampling dataset The geomechanical parameters, fluid parameters, and fracturing operation parameters in the data are processed as samples to obtain two corresponding input feature sample sets. and ; use real observation datasets The geometric parameters of the fracturing fractures in the sample are used as samples to obtain the output sample set. ;in, for The first in Group samples; for The first in Group samples; for The first in Group samples; For each sample group in each sample set, normalization is performed using the following formula: ; in, These are the normalized data values; It is the first in the input feature sample set Group samples; It is the minimum value in the original data; It is the maximum value in the original data; The two input feature sample sets after normalization are respectively , The normalized output sample set is .

[0025] Step 2: Construct a hybrid architecture integrating a Transformer encoder and a graph attention network to deeply interact with input features and fuse them with physical priors, generating shared features enhanced with physical information. This hybrid architecture first classifies the normalized sample data, then performs feature embedding and fusion. The Transformer encoder is used to obtain complex nonlinear relationships between features. Based on the adjacency matrix, a feature relationship graph based on physical priors is constructed using a graph attention network. Finally, the outputs of the Transformer encoder and the graph attention network are fused. The model structure is as follows: Figure 2 As shown, the specific working process is as follows: Step 2.1: Normalize the two input feature sample sets. , Based on their physical properties, parameters are classified into geomechanical parameters, fluid parameters, and fracturing operation parameters. A fully connected neural network is used to linearly project each of the classified parameters into a high-dimensional vector space, resulting in three high-dimensional feature vectors. These high-dimensional feature vectors are then concatenated, and learnable positional encoding is introduced to form a unified-dimensional high-dimensional embedding feature. The specific process is as follows: Step 2.1.1: Normalize the input feature sample set (include , ) Based on their physical properties, parameters are classified into three subsets: geomechanical parameters, fluid parameters, and fracturing operation parameters. Then, each type of parameter is projected using an independent linear layer (MLP). ; ; ; in, , , They are divided into three subsets: geomechanical parameters, fluid parameters, and fracturing operation parameters; , , Here are the learnable weight matrices corresponding to the three subsets; , , These are the high-dimensional feature vectors obtained by linear projection of the three subsets. , , The high-dimensional embedding dimension is the projection of the three subsets; The shape factor is the sum of the dimensions of each type of feature; Batch size; Step 2.1.2: Concatenate the high-dimensional feature vectors obtained from the projection to form preliminary fused features, as shown in the following formula: ; in, This represents the initial fusion characteristics. For total embedding dimension; Step 2.1.3: Introduce learnable positional encoding to form a high-dimensional embedding feature with a unified dimension; the formula is as follows: ; in, High-dimensional embedding features; Learnable positional encoding for embedded features; Step 2.2: Construct the Transformer encoder to capture the complex relationships between features; the specific process is as follows: Step 2.2.1: Embed the high-dimensional features Transformed into a query matrix through linear transformation Key matrix Sum matrix Then through , , Generate the context vector of the attention head, as shown in the following formula (for the ...). (Attention) ; in, For the first The context vector of each attention head; , , The first The query matrix, key matrix, and value matrix of each attention head; This is a transpose operation; This is the scaling factor; This is the softmax function, used to normalize the weight matrix; Step 2.2.2: Concatenate the context vectors of multiple attention heads and then project them using a linear projection matrix. Obtain the output of the multi-head attention module The formula is: ; in, It is a learnable linear projection matrix; For splicing operations; For the first The context vector of each attention head; Step 2.2.3: Combine the output of the multi-head attention module with the high-dimensional embedded features. Perform residual connections and layer normalization to obtain embedded features. : ; in, For layer normalization operation; Step 2.2.4: Based on the feedforward neural network... Perform a nonlinear transformation to obtain the characteristics of the nonlinear transformation. : ; in, It is the ReLU activation function; , These are learnable weights; , For bias; Step 2.2.5, for and Perform the second residual connection and layer normalization operation to obtain the output of the first encoder. : ; in, For layer normalization operation, These are the characteristics after nonlinear transformation; High-dimensional embedding features; Step 2.2.6: Overlay two encoder layers, that is... As Enter step 2.2.1 again until you obtain the final output of the encoder section. .

[0026] Step 2.3: Construct a Graph Attention Network (GAT), including a first graph attention layer, a dropout layer, a second graph attention layer, and an activation layer. Based on the adjacency matrix constructed in Step 1.4, the GAT defines the physical connections between feature nodes, then adaptively calculates the weights between nodes based on the attention mechanism, and finally weights and sums the features of neighboring nodes to generate an enhanced feature matrix that combines physical priors and data-driven approaches. The specific process is as follows: Step 2.3.1: Embed the high-dimensional features obtained in Step 2.1 The input first graph's attention layer undergoes linear transformation, attention calculation, and multi-head attention output; the specific process is as follows: Step 2.3.1.1: First, perform a linear transformation: ; in, It is a learnable linear transformation matrix; The transformed node features; Step 2.3.1.2: Perform attention calculation to achieve adaptive weight allocation based on physical adjacency; define the connection relationships between nodes according to prior knowledge in the field of hydraulic fracturing, construct an adjacency matrix based on physical priors, and calculate attention weights based on the adjacency matrix. When a node... With nodes There is a physical connection (i.e.) When ), calculate its attention coefficient: ; in, It is an adjacency matrix; when the node With nodes When strong interactions exist, a physical connection is established, that is... ; ; in, This is the attention weight vector; This is a transpose operation; , Each node With nodes Transformed node features To make nodes With nodes Perform feature splicing; For nodes With nodes Attention coefficient between them; It is a linear rectified function with leakage coefficient; Then, normalization is performed on all neighboring nodes: ; in, For nodes With nodes Attention weights between them; For exponentiation; The adjacency matrix is ​​the first... Line 1 The element of the column, the first Row corresponding node , No. Column corresponding node ; The adjacency matrix is ​​the first... Line 1 Column elements; For nodes With nodes Attention coefficient between them; This represents the number of neighboring nodes. Step 2.3.1.3: Perform multi-head attention output; This invention uses two attention heads to first calculate and integrate the node neighborhood features to obtain... : ; ; in, These are the first and second attention head nodes, respectively. The output characteristics; It is a non-linear activation function; These are the first and second attention heads, respectively. With nodes Attention weights between them; Then get The final enhanced features are obtained by splicing the data together. ; For nodes Enhanced features; Step 2.3.2: To prevent overfitting after multi-head feature concatenation, the concatenated output needs to be... Input Dropout layer to perform Dropout operation: ; in, To and A random mask matrix with consistent dimensions; This represents the probability of inactivation. Multiply by corresponding elements; This is the node enhancement matrix after the Dropout operation; For Dropout layer; Step 2.3.3, will As input to the second attention layer, the operations of the first attention layer are repeated to obtain higher-order node features: ; in, This is the output of the attention layer in the second graph; This is the attention layer in the second graph.

[0027] Step 2.3.4: Finally, input the output of the attention layer in the second image into the activation layer, apply a non-linear activation function, and obtain the final enhanced feature matrix: ; in, To enhance the feature matrix.

[0028] Step 2.4: Convert the final output of the Transformer encoder. Enhanced feature matrix output by graph attention network Feature concatenation is performed to obtain shared features with enhanced physical information. : ; Step 3: Construct a physical information attention layer. Use a fully connected neural network to build three independent and parallel decoders that map shared features to the geometric dimensions and mechanical parameters of the crack. The three decoders are: a geometric parameter prediction decoder and a labeled decoder (predicting crack area). Crack length Crack width Geometric parameter prediction decoder without labels (predicting crack height) ), Mechanical state prediction decoder (predicting net pressure) Stress intensity factor The geometric dimensions include crack area, crack length, crack width, and crack height; the mechanical parameters include net pressure and stress intensity factor; the shared features obtained in step 2 are used. The input is fed into the physical information attention layer to obtain shared physical features. Then Simultaneously, the data is fed into three independent decoders, each outputting its own prediction. Using three independent decoders allows the model to select weights and biases that are more suitable for its output parameters. The model structure is as follows: Figure 2 As shown, the specific process is as follows: Step 3.1: Construct a physical information attention layer, which incorporates the shared features obtained in Step 2.4. Input physical information into the attention layer to obtain shared physical features. The specific process is as follows: Step 3.1.1: Generate the query matrix Key matrix Sum matrix : ; ; ; in, , , These are three learnable weight coefficients; Step 3.1.2: Calculate the query matrix Bond matrix The similarity is then used to obtain a set of attention weights after passing through the softmax function. : ; in, This is a transpose operation; This is the scaling factor; It is the softmax function; Step 3.1.3: Calculate the weights right The weighted sum yields the shared physical characteristics. : ; Step 3.2, Simultaneously, the inputs are fed into three parallel and independent multilayer perceptron (MLP) decoders, which respectively obtain six target physical quantities that need to be predicted. , , , , , ) is used to calculate the mixing loss, where The area of ​​the crack. The length of the crack. The width of the crack. The height of the crack. Net pressure, This is the stress intensity factor.

[0029] Step 4: Establish a physical loss function based on linear elastic fracture mechanics and the principle of mass balance, and combine it with the data loss function to construct a physically meaningful hybrid loss function. Use the predicted physical quantities output in Step 3 to calculate the hybrid loss, and use the Adam optimizer to minimize the hybrid loss. Then, perform backpropagation to update all learnable parameters in the model, so that the model's prediction results gradually approach and satisfy the physical constraints, thereby completing the model training. The specific process is as follows: Step 4.1: Construct the residuals of the elasticity equations based on linear elastic fracture mechanics to calculate physical losses. The specific process is as follows: Step 4.1.1: For a medium subjected to uniform internal pressure in an infinitely elastic medium For a two-dimensional (plane strain) crack, the width distribution of the crack surface is calculated using the residuals of the elasticity equation (for a length of...). (cracks) ; in, The width of the crack; The length of the crack is half its length; It is the length coordinate along the crack, from the center ( ) to the tip ( ); The equivalent elastic modulus is given by the formula: ; in, It is the elastic modulus; It is Poisson's ratio; but maximum value for: ; Calculate the stress intensity factor (For cracks subjected to internal pressure): ; United maximum value Formulas and stress intensity factors formula elimination ,get , , The relationship between them: ; Step 4.1.2: Derive the model to more complex three-dimensional cracks. Although the analytical solutions differ, the dimensions are universal. Inevitably and Proportional, only the proportionality coefficient The crack geometry changes accordingly, therefore the three-dimensional crack model is as follows: ; Step 4.1.3: Construct the physical loss based on the residuals of the elasticity equations described above. The specific formula is as follows: ) ; in, Mean square error; This is the predicted value of the stress intensity factor; This is the predicted value for the crack width; This is the predicted value for net pressure; Step 4.2: Construct crack propagation criterion residuals based on linear elastic fracture mechanics to calculate the physical loss based on the crack propagation criterion residuals. The specific process is as follows: Step 4.2.1, Expansion Criterion: When the stress intensity factor at the crack tip... Achieving the fracture toughness of the material Time (i.e.) The cracks expanded. Step 4.2.2: In this model, we assume... Crack propagation occurs, thus introducing physical losses based on the flow equation residuals. This loss ensures that the cracks do not propagate arbitrarily, but are strictly limited by the mechanical properties of the rock: ; Step 4.3: Construct the flow equation residuals based on the principle of mass balance, and use them to calculate the physical losses based on the flow equation residuals. The specific process is as follows: Step 4.3.1: Based on the mass balance relationship between the injected fluid volume, the total fracture volume, and the filtration loss volume, the following formula exists: ; in, For the volume of injected fluid; This represents the total volume of the crack. This is the volume of fluid lost through filtration. ; ; in, For displacement; For time; For shape factor; To simplify the model, we can assume... Setting it to 0 yields a simplified relation: ; Step 4.3.2: Calculate the physical loss based on the flow equation residuals using the simplified model. This loss ensures that the crack size predicted by the network satisfies the basic law of conservation of matter: ; in, This is the predicted value for the crack length; This is the predicted value for the crack height; Step 4.4: Based on the above formula, the total physical loss is... : ; in, , , These are the weighting coefficients for different loss terms; Step 4.5: Calculate data loss : ; in, The number of samples; For the first The first sample One predicted output; For the first The first sample One true value; Step 4.6: Add the data loss and the total physical loss in a certain proportion to obtain the total mixed loss function. : ; in, , These are the weighting coefficients for different losses; Step 4.7: Use the predicted physical quantities output from Step 3 ( , , , , , To calculate the mixed loss function The model training process involves minimizing the mixture loss using the Adam optimizer, then performing backpropagation based on the training set to update all learnable parameters in the model, gradually bringing the model's predictions closer to and satisfying the physical constraints.

[0030] Step 5: Use the trained model to predict the geometric dimensions and mechanical parameters of the hydraulic fracturing cracks; input the samples from the test set in Step 1 and the adjacency matrix in Step 2 into the trained model to quickly predict the crack propagation, including crack area, crack length and crack width.

[0031] To demonstrate the feasibility and superiority of the present invention, the following embodiments are provided.

[0032] This embodiment verifies the proposed method and conducts subsequent analysis and discussion. Then, the following steps are followed to perform crack propagation prediction based on a data-physical dual-drive approach. First, real-world observation data (including feature data and label data) is collected. Since real-world data often contains missing and outlier values, it is necessary to detect and process these values. Finally, a real-world observation dataset with 1000 samples and 4000 data points is constructed. By using Latin hypercube sampling, and simultaneously perturbing within the maximum and minimum ranges of each feature, a physical sampling dataset of 1000 samples was obtained. (Unlabeled data), Table 1 shows the input and output parameters of the model.

[0033] Table 1 Model Input / Output Parameters .

[0034] Then, following the process in step 1, the real observation dataset is divided into training and test sets at a ratio of 8.5:1.5, and both the real observation dataset and the physical sampling dataset are normalized. Based on the process in step 2, a hybrid architecture based on a Transformer encoder and a graph attention network is constructed. The normalized samples are then divided into three classes according to their attributes and input into the hybrid model based on the Transformer encoder and graph attention network. Features are mapped to a high-dimensional space, and after feature interaction and fusion, a shared feature is obtained. In step 2, the adjacency matrix between features is manually constructed based on prior physical knowledge. The adjacency matrix is ​​shown below: ; Following the process in step 3, a physical information attention layer and three independent and parallel decoders are constructed. The shared features are input into the physical information attention layer, which outputs a shared physical feature with physical meaning. Then The data is input into three parallel decoders, which map the high-dimensional data into six predicted outputs: crack area, crack length, crack width, crack height, net pressure, and stress intensity factor. A hybrid loss function is constructed based on the process in step 4, including physical and data losses based on the residuals of the elasticity equations, crack propagation criterion residuals, and flow equation residuals. , , and Use output parameters , , calculate Use output parameters and input parameters calculate Using input parameters , and output parameters , , calculate Using tag data , , and output data , , Calculate data loss Ultimately, the total mixed loss is obtained. In this embodiment, , , The Adam optimizer is used to minimize the mixture loss, and then backpropagation is performed to update all learnable parameters in the model, so that the model's predictions gradually approach and satisfy the physical constraints, thus completing model training. During model training, the batch size is set to 64, the learning rate to 0.001, the training epochs to 30, and the random seed to 42. Following the process in step 5, features can be input into the trained model to quickly predict the area, length, and width of cracks.

[0035] Figure 3 The graph shows the model's loss during training. As can be seen from the graph, the model's loss decreases rapidly and converges to a very small value during training, indicating that the model fits the data in the training set very well and is able to learn the patterns within it.

[0036] Figure 4 The graph shows a comparison between the predicted and actual values ​​of the crack area. As can be seen from the graph, the overall trend of the actual and predicted values ​​is consistent, and most of the curves can overlap, indicating that the model can correctly capture the overall pattern of crack area changes and the prediction effect is good.

[0037] Figure 5 The graph shows a comparison between the predicted and actual values ​​of crack length. As can be seen from the graph, the overall trend of the actual and predicted values ​​is consistent, and the peak and trough positions of the two curves are basically corresponding, indicating that the model can correctly capture the overall pattern of crack height change and the prediction effect is good.

[0038] Figure 6 The graph shows a comparison between the predicted and actual values ​​of crack width. As can be seen from the graph, the overall trend of the actual and predicted values ​​is consistent and basically overlaps, indicating that the model can correctly capture the overall pattern of crack width variation and has a good prediction effect.

[0039] This invention will be compared with purely data-driven machine learning prediction methods. Figure 7The graph shows a comparison of the training losses of the pure data-driven method and the data-physical dual-driven method proposed in this invention. It can be seen that the method proposed in this invention has a faster convergence speed and a smaller training loss.

[0040] Figure 8 R is a pure data-driven method and a data-physical dual-driven method proposed in this invention. 2 (The closer the model's fitting ability is to 1, the better the effect.) Comparison chart: As can be seen from the chart, the method R proposed in this invention... 2 All are above 0.9, and all are greater than the R of purely data-driven methods. 2 value.

[0041] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A data-physical dual-driven crack propagation prediction method, characterized in that, Includes the following steps: Step 1: Construct a labeled real observation dataset and an unlabeled physical sampling dataset, and perform normalization processing; Step 2: Construct a hybrid architecture that integrates a Transformer encoder and a graph attention network to deeply interact with input features and fuse them with physical priors to generate shared features enhanced with physical information. Step 3: Construct three independent and parallel decoders that share features to map the crack's geometry and mechanical parameters; Step 4: Establish a physical loss function based on linear elastic fracture mechanics and the principle of mass balance, and combine it with the data loss function to construct a hybrid loss function with physical meaning for model training; Step 5: Use the trained model to predict the geometry and mechanical parameters of the hydraulic fracturing cracks.

2. The data-physical dual-driven crack propagation prediction method according to claim 1, characterized in that, The specific process of step 1 is as follows: Step 1.1: Obtain reservoir rock geomechanical parameters, fluid parameters, fracturing operation parameters, and fracturing fracture geometric parameters interpreted through microseismic analysis. After processing missing and outlier values, construct a labeled real observation dataset. Then, the training set and the test set are divided proportionally. Step 1.2: Based on the numerical range of each input feature in the real observation dataset, determine the minimum and maximum values ​​of each feature to define the boundary of the physical parameter space. Then, use Latin hypercube sampling to generate a large number of sampling points in the multidimensional parameter space to establish an unlabeled physical sampling dataset. The entire physical sampling dataset is used as the training set. Step 1.3: Transfer the real observation dataset and physical sampling dataset Geomechanical parameters, fluid parameters, fracturing operation parameters, and fracturing fracture geometric parameters were used as samples to construct a sample set, which was then normalized; specifically: Real observation dataset and physical sampling dataset The geomechanical parameters, fluid parameters, and fracturing operation parameters in the data are processed as samples to obtain two corresponding input feature sample sets. and ; use real observation datasets The geometric parameters of the fracturing fractures in the sample are used as samples to obtain the output sample set. ;in, for The first in Group samples; for The first in Group samples; for The first in Group samples; For each sample group in each sample set, normalization is performed. The two normalized input feature sample sets are respectively , The normalized output sample set is .

3. The data-physical dual-driven crack propagation prediction method according to claim 2, characterized in that, The specific process of step 2 is as follows: Step 2.1: Normalize the two input feature sample sets. , Based on their physical properties, parameters are classified into geomechanical parameters, fluid parameters, and fracturing construction parameters. A fully connected neural network is used to linearly project the classified parameters onto a high-dimensional vector space, resulting in three high-dimensional feature vectors. These high-dimensional feature vectors are then concatenated and a learnable positional code is introduced to form a high-dimensional embedding feature of a unified dimension. Step 2.2: Construct the Transformer encoder to capture the complex relationships between features; Step 2.3: Construct a graph attention network to generate an enhanced feature matrix that combines physical priors and data-driven approaches. The graph attention network includes a first graph attention layer, a dropout layer, a second graph attention layer, and an activation layer. Step 2.4: Concatenate the output of the Transformer encoder with the output of the graph attention network to obtain shared features for physical information enhancement.

4. The data-physical dual-driven crack propagation prediction method according to claim 3, characterized in that, The specific process of step 2.1 is as follows: Step 2.1.1: Combine the two normalized input feature sample sets. , Based on their physical properties, parameters are classified into three subsets: geomechanical parameters, fluid parameters, and fracturing operation parameters. Then, each type of parameter is projected using an independent linear layer. ； ； ； in, , , They are divided into three subsets: geomechanical parameters, fluid parameters, and fracturing operation parameters; , , Here are the learnable weight matrices corresponding to the three subsets; , , These are the high-dimensional feature vectors obtained by linear projection of the three subsets. , , The high-dimensional embedding dimension is the projection of the three subsets; Batch size; Step 2.1.2: Concatenate the high-dimensional feature vectors obtained from the projection to form preliminary fused features, as shown in the following formula: ； in, This represents the initial fusion characteristics. For total embedding dimension; Step 2.1.3: Introduce learnable positional encoding to form a high-dimensional embedding feature with a unified dimension; the formula is as follows: ； in, High-dimensional embedding features; This is a learnable location encoding for embedded features.

5. The data-physical dual-driven crack propagation prediction method according to claim 4, characterized in that, The specific process of step 2.2 is as follows: Step 2.2.1: Embed the high-dimensional features Transform into a query matrix through linear transformation Key matrix Sum matrix Then through , , The context vector for generating the attention head is calculated using the following formula: ； in, For the first The context vector of each attention head; , , The first The query matrix, key matrix, and value matrix of each attention head; This is a transpose operation; This is the scaling factor; It is the softmax function; Step 2.2.2: Concatenate the context vectors of multiple attention heads and obtain the output of the multi-head attention module through a linear projection matrix. The formula is: ； in, It is a learnable linear projection matrix; For splicing operations; For the first The context vector of each attention head; Step 2.2.3: Combine the output of the multi-head attention module with the high-dimensional embedded features. Perform residual connections and layer normalization to obtain embedded features. : ； in, For layer normalization operation; Step 2.2.4: Based on the feedforward neural network... Perform a nonlinear transformation to obtain the characteristics of the nonlinear transformation. : ； in, It is the ReLU activation function; , These are learnable weights; , For bias; Step 2.2.5, for and Perform the second residual connection and layer normalization operation to obtain the output of the first encoder. : ； Step 2.2.6: Overlay two encoder layers, that is... As Enter step 2.2.1 again until you obtain the final output of the encoder section. .

6. The data-physical dual-driven crack propagation prediction method according to claim 5, characterized in that, The specific process of step 2.3 is as follows: Step 2.3.1: Embed the high-dimensional features obtained in Step 2.1 The first image's attention layer undergoes linear transformation, attention calculation, and multi-head attention output; the specific process is as follows: First, perform a linear transformation: ； in, It is a learnable linear transformation matrix; The transformed node features; Then, attention calculation is performed; based on prior knowledge in the field of hydraulic fracturing, the connection relationships between nodes are defined, an adjacency matrix based on physical priors is constructed, and attention weights are calculated based on the adjacency matrix. When a node... With nodes When a physical connection exists, calculate its attention coefficient: ； in, It is an adjacency matrix; ； in, This is the attention weight vector; , Each node With nodes Transformed node features To make nodes With nodes Perform feature splicing; For nodes With nodes Attention coefficient between them; It is a linear rectified function with leakage coefficient; Perform normalization on all neighboring nodes: ； in, For nodes With nodes Attention weights between them; For exponentiation; The adjacency matrix is ​​the first... Line number The element of the column, the first Row corresponding node , No. Column corresponding node ; The adjacency matrix is ​​the first... Line 1 Column elements; For nodes With nodes Attention coefficient between them; This represents the number of neighboring nodes. Next, multi-head attention output is performed; two attention heads are used to calculate and integrate the node's neighborhood features respectively: ； ； in, These are the first and second attention head nodes, respectively. The output characteristics; It is a non-linear activation function; These are the first and second attention heads, respectively. With nodes Attention weights between them; The result The final enhanced features are obtained by splicing the data together. ； For nodes Enhanced features; Step 2.3.2, will Input Dropout layer to perform Dropout operation: ； in, To and A random mask matrix with consistent dimensions; This represents the probability of inactivation. Multiply by corresponding elements; This is the node enhancement matrix after the Dropout operation; For Dropout layer; Step 2.3.3, will As input to the attention layer of the second graph, the operations of the attention layer of the first graph are repeated to obtain higher-order node features: ； in, This is the output of the attention layer in the second graph; This is the attention layer of the second graph; Step 2.3.4: Input the output of the attention layer in the second image into the activation layer to obtain the final enhanced feature matrix: ； in, To enhance the feature matrix.

7. The data-physical dual-driven crack propagation prediction method according to claim 6, characterized in that, In step 2.4, the formula for calculating the shared features is: ； in, For shared features.

8. The data-physical dual-driven crack propagation prediction method according to claim 7, characterized in that, The specific process of step 3 is as follows: Step 3.1: Construct a physical information attention layer, which incorporates the shared features obtained in Step 2.

4. Input physical information into the attention layer to obtain shared physical features. The specific process is as follows: Step 3.1.1: Generate the query matrix Key matrix Sum matrix : ； ； ； in, , , These are three learnable weight coefficients; Step 3.1.2: Calculate the query matrix Bond matrix The similarity is then used to obtain a set of attention weights after passing through the softmax function. : ； Step 3.1.3, Calculation right The weighted sum yields the shared physical characteristics. : ； Step 3.2, Simultaneously, the data is input into three parallel and independent multilayer perceptron decoders, yielding six predicted values: crack area, crack length, crack width, crack height, net pressure, and stress intensity factor. Among these, crack area, crack length, crack width, and crack height are geometric dimensions, while net pressure and stress intensity factor are mechanical parameters.

9. The data-physical dual-driven crack propagation prediction method according to claim 1, characterized in that, The specific process of step 4 is as follows: Step 4.1: Construct the physical loss based on the residuals of the elasticity equation. The specific formula is as follows: ) ； in, Mean square error; This is the predicted value of the stress intensity factor; This is the predicted value for the crack width; This is the predicted value of net pressure; This is the proportionality coefficient; It is the equivalent elastic modulus; Step 4.2: Construct the physical loss based on the crack propagation criterion residual. : ； in, For fracture toughness; Step 4.3: Construct physical loss based on flow equation residuals : ； in, This is the predicted value for the crack length; This is the predicted value for the crack height; For displacement; For time; For shape factor; Step 4.4, the total physical loss is : ； in, , , These are the weighting coefficients for different loss terms; Step 4.5: Calculate data loss : ； in, The number of samples; For the first The first sample One predicted output; For the first The first sample One true value; Step 4.6: Add the data loss and the total physical loss proportionally to obtain the total mixed loss function. : ； in, , These are the weighting coefficients for different losses; Step 4.7: Use the predicted values ​​output from Step 3 to calculate the mixture loss function. The model training process involves minimizing the mixture loss using the Adam optimizer, then performing backpropagation based on the training set to update all learnable parameters in the model, gradually bringing the model's predictions closer to and satisfying the physical constraints.

10. The data-physical dual-driven crack propagation prediction method according to claim 9, characterized in that, The specific process of step 5 is as follows: input the samples in the test set of step 1 and the adjacency matrix in step 2 into the trained model to predict the crack propagation, including crack area, crack length and crack width.

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