A hydraulic fracturing timing prediction method based on numerical simulation driving deep learning

Abstract

This invention discloses a time-series prediction method for hydraulic fracturing based on numerical simulation-driven deep learning, relating to the fields of coalbed methane development and rock engineering. The method first establishes a two-dimensional numerical model of hydraulic fracturing in deep coal seams, completing the numerical description of the fluid-structure interaction physical process and verifying it through classical models or physical experiments. Then, based on the numerical simulation results, an original training dataset is constructed, followed by the construction of a small-sample data expansion and time-series prediction model. This achieves small-sample data expansion and model parameter optimization, and finally, based on the trained model, time-series prediction of hydraulic fracturing fracture morphology and stress evolution is realized. This invention combines the physical mechanism description capability of numerical simulation with the computational efficiency of deep learning, achieving rapid and accurate prediction of the entire hydraulic fracturing process under small-sample conditions, improving the model's generalization ability, and is suitable for rapid evaluation and parameter optimization in deep coal seam hydraulic fracturing projects.

Description

Technical Field

[0001] This invention relates to the fields of coalbed methane development and rock mass engineering technology, specifically to a hydraulic fracturing time series prediction method based on numerical simulation-driven deep learning, belonging to the interdisciplinary field of hydraulic fracturing numerical simulation and artificial intelligence. Background Technology

[0002] With the gradual reduction of areas suitable for large-scale development of shallow coal seams, the extension of coalbed methane (CBM) resource development to deeper areas has become an important development direction and an inevitable trend in the industry. However, deep coal seams are typically situated in complex engineering environments characterized by high ground stress, high geothermal temperature, high osmotic pressure, and low permeability, significantly limiting CBM extraction efficiency. To improve coal seam permeability and increase CBM extraction efficiency, hydraulic fracturing technology has been widely applied in deep CBM development projects. This technology injects high-pressure fluid into the target coal seam, creating hydraulic fractures within the seam that further expand into a complex fracture network, thereby significantly improving coal seam permeability and promoting CBM migration and extraction.

[0003] During hydraulic fracturing, as fracturing fluid is continuously injected, the original stress field of the coal seam is disturbed and redistributed under the action of fluid pressure. When the local stress exceeds the strength of the coal body, fracture initiation is induced. The continuous evolution of the stress field further controls the propagation path and deflection direction of the fracture. In this process, the evolution of the stress field and the fracture propagation behavior are coupled and exhibit significant temporal variation characteristics. Therefore, the initiation and propagation behavior of hydraulic fractures and the evolution law of the coal seam stress field directly determine the final effect of hydraulic fracturing, and accurate and efficient prediction of these factors has important engineering significance.

[0004] Currently, it is difficult to directly visualize and monitor the fracture propagation process and stress field evolution under field conditions. Therefore, numerical simulation methods are widely used in hydraulic fracturing research. Commonly used methods include the finite element method, discrete element method, extended finite element method, and finite difference method. These methods can effectively describe the fracture initiation and propagation process and achieve visualized analysis of the dynamic distribution characteristics of the stress field during fracturing. However, they have significant technical drawbacks: numerical simulation methods are usually computationally very expensive, requiring a large number of repetitive calculations under multivariable and multiparameter conditions. This not only results in low computational efficiency but also tends to lead to convergence difficulties, making it difficult to meet the field requirements for rapid prediction and engineering optimization of the hydraulic fracturing process under complex conditions in deep coal seams.

[0005] In recent years, with the rapid development of artificial intelligence technology, deep learning methods have been gradually introduced into the field of hydraulic fracturing effect prediction and evaluation, enabling functions such as predicting fracture propagation behavior, optimizing fracturing parameters, and predicting coalbed methane production. However, the application of existing deep learning methods in this field still has many shortcomings: First, existing algorithms mostly focus on the static prediction of the final fracturing result, lacking the ability to characterize the temporal evolution characteristics of the entire fracturing process, and failing to achieve continuous dynamic prediction of fracture morphology and stress evolution; Second, the model's generalization ability is weak, making it difficult to achieve fast and accurate prediction under complex and changing new working conditions; Third, the field monitoring data for coalbed hydraulic fracturing suffers from strong noise interference and a scarcity of high-quality samples, making it difficult to effectively train purely data-driven deep learning models, and the prediction accuracy cannot be guaranteed, severely limiting the engineering application of deep learning methods in the prediction of the entire hydraulic fracturing process.

[0006] In summary, existing single numerical simulation methods or deep learning methods cannot simultaneously balance computational efficiency in predicting hydraulic fracturing processes with accuracy in representing physical mechanisms, and therefore cannot meet the field application needs of deep coal seam hydraulic fracturing projects. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a hydraulic fracturing time series prediction method based on numerical simulation-driven deep learning. This method solves the technical problems of low computational efficiency and poor convergence in hydraulic fracturing numerical simulation, strong dependence of deep learning models on training data, weak generalization ability under small sample conditions, and insufficient characterization of the time series evolution characteristics of the entire fracturing process in the prior art. It combines the physical mechanism description ability of numerical simulation with the efficient computational ability of deep learning, and realizes rapid and accurate time series prediction of fracture morphology and stress evolution throughout the entire process of hydraulic fracturing in deep coal seams.

[0008] To achieve the above objectives, the technical solution adopted by this invention is: a hydraulic fracturing time series prediction method based on numerical simulation-driven deep learning, specifically including the following steps: S1. Numerical Model Establishment: A two-dimensional hydraulic fracturing numerical model of deep coal seams is established based on finite element analysis software. The coal matrix is ​​meshed, and cohesive elements are inserted between the meshes to simulate the initiation and propagation of fractures. Stress monitoring points are arranged in the model. Combined with the geological and construction parameters of the deep coal seams, multiple sets of variable combinations of input parameters are generated by Latin hypercube sampling, and a unified water injection time is set.

[0009] S2. Description of the physical process of fluid-structure interaction: Based on the fluid-structure interaction theory, the fracture initiation criterion, fracture propagation and evolution law and fluid flow equation in the fracture are defined to complete the numerical description of the physical mechanism of the entire hydraulic fracturing process.

[0010] S3. Numerical Model Verification: Verify the numerical model established in step S1 using a hydraulic fracturing model or physical experiment. Under the same working conditions, compare the fracture opening, fracture length, and pressure evolution laws of the numerical model with those of the hydraulic fracturing model or physical experiment. When the error between the two results is within the preset acceptable range, the numerical model is confirmed to be effective.

[0011] S4. Training Dataset Construction: Extract crack and stress evolution parameters from the numerical simulation results of the effective numerical model, construct input feature vectors and corresponding output variables, normalize the input feature vectors and output variables, and construct the original training dataset.

[0012] S5. Construction and Prediction of Temporal Series Prediction Model: Construct a small sample data expansion and temporal series prediction model. Using the temporal series prediction model as the basic learner, cross-task feature extraction, small sample data expansion and model parameter optimization are completed through small sample data expansion. The model is trained based on the expanded augmented dataset. Finally, the trained temporal series prediction model is used to achieve temporal prediction of fracture morphology and stress evolution in deep coal seam hydraulic fracturing.

[0013] Furthermore, in step S1, the stress monitoring points are arranged as follows: stress monitoring points are set up with the water injection hole as the center, and several stress monitoring points are arranged according to the principle of proximity to the water injection hole, so as to collect stress response information during the crack initiation and propagation process, as well as the disturbance information of crack evolution on the far-field stress field; the process of generating input parameters by Latin hypercube sampling is as follows: elastic modulus E, horizontal stress difference Δσ, permeability k, porosity φ and water injection flow rate Q are selected as sampling variables, and several sets of variable combinations are generated by Latin hypercube sampling. The remaining geological parameters and construction parameters are kept fixed, and the water injection time is unified.

[0014] Furthermore, in step S2, the crack initiation criterion adopts the maximum principal stress criterion, the expression of which is: In the formula, , and These represent the critical normal stress and the first and second tangential stresses at the initial damage of the cohesive element, in MPa; symbol This indicates that the cohesive element is damaged under tensile stress but not under compressive stress.

[0015] Furthermore, in step S2, the crack propagation and evolution law is described by a stiffness degradation model, expressed as: In the formula, The symbol is defined as tensile stress being positive and compressive stress being negative, and the unit is MPa; , and represents the normal stress and two tangential stresses when the cohesive element is undamaged, in MPa; D is the dimensionless damage factor, whose range is determined as follows: in, This represents the displacement of the cohesive element at the initial damage, in meters (m). This represents the displacement when the cohesive element is completely damaged, in meters (m). The maximum displacement during the damage process of the cohesive element is expressed in meters (m), and its expression is: In the formula, , and These represent the normal displacement component and the first and second tangential displacement components at the initial damage of the cohesive element, in meters (m).

[0016] Furthermore, in step S2, the process of constructing the fluid flow equation within the crack is as follows: Assuming the fluid inside the fracture is an incompressible Newtonian fluid, simplifying it to a one-dimensional fluid, its continuity equation is: In the formula, The local average velocity per unit height, in meters (m). 2 / s; The crack width is expressed in meters (m). The fluid filtration rate per unit height, in meters (m). 2 / s.

[0017] Fluid flow within the fracture includes tangential and normal flow, where tangential flow is the flow along the fracture channel and is described by the lubrication equation: In the formula, The permeability coefficient of fluid flowing tangentially within the fracture is expressed in m / s. The viscosity of the fracture fluid is expressed in Pa·s. This represents the pressure gradient of the tangentially flowing fluid.

[0018] Normal flow is the fluid that filters out from both surfaces of the fracture and enters the formation, described by the flow equations at the top and bottom surfaces of the fracture: In the formula, and These are the flow rates entering the top and bottom crack surfaces, respectively, in m / s; and These are the filtration loss coefficients for the top and bottom crack surfaces, respectively, in m / (Pa·s); and The pore pressure is measured in Pa at the top and bottom crack surfaces. The fluid pressure at the crack is expressed in Pa. This represents the total flow rate along the normal direction of the crack, expressed in m³ / s.

[0019] Furthermore, in step S3, the established hydraulic fracturing numerical model is verified using the KGD classical model. The calculation formula for this verification model under plane strain is: Crack center opening: Half seam length: Net pressure within the hydraulic fracture: In the formula, The opening at the center of the crack, Poisson's ratio, The water injection rate per unit width, For fluid viscosity, Shear modulus For water filling time, It is half the seam length. The pressure inside the crack, It is the minimum principal stress.

[0020] Further, step S4 specifically includes: S401. Extract crack and stress evolution parameters from the numerical simulation results, including crack length. Crack width Stress values ​​at each monitoring point , where i is the number of stress monitoring points arranged.

[0021] S402. Construct the input feature vector: In the formula, E is the elastic modulus, Δσ is the horizontal stress difference, k is the permeability, φ is the porosity, and Q is the injection flow rate.

[0022] S403. Define output variables: S404. Perform min-max normalization on the input feature vector and output variable to eliminate the influence of differences in feature dimensions and value ranges on model training. The normalization formula is: In the formula, The original data, For the normalized data, and These are the maximum and minimum values ​​of the feature in the corresponding dataset, respectively.

[0023] Further, step S5 specifically includes: S501. Construction of the basic learner: The temporal prediction model used is LSTM (Long Short-Term Memory Network). LSTM is used as the basic learner to characterize the temporal features of fracture morphology and stress evolution during hydraulic fracturing. The model parameters are denoted as follows: In the formula, This is the set of all trainable parameters for the model. The weight matrix between the input and the hidden state. The recursive weight matrix between hidden states, These are the bias term parameters.

[0024] S502. Task Partitioning: The small sample data expansion method used is meta-learning, which divides the data corresponding to different fracturing parameter combinations into different meta-learning tasks. Each task is represented as follows: In the formula, Let i be the task corresponding to the i-th numerical simulation sampling group. For the task training set, This is the test set for the task.

[0025] S503, LSTM model parameter optimization based on meta-learning: For each task The gradient of the LSTM is updated using the training set data. The calculation process is as follows: In the formula, These are the initial model parameters. For task learning rate, For the task loss function, For the task Updated parameters.

[0026] In the meta-learning phase, the LSTM model parameters are jointly optimized through multiple tasks. The optimization process is as follows: In the formula, The meta-learning rate, These are the model parameters after joint optimization across multiple tasks. The number of tasks.

[0027] S504. Small Sample Data Expansion: Based on the cross-task shared feature representation obtained through meta-learning, a perturbation mechanism is introduced to expand the data on the original training dataset. The expansion process is as follows: In the formula, For the expanded input variables, For the expanded output variables, It is a perturbation term generated based on task distribution, satisfying... , This is the disturbance intensity parameter, and the disturbance range is constrained by the physical value range of the input variables.

[0028] S505, Construction of Enhanced Training Set: Merge the original training dataset with the extended dataset to construct an enhanced training set: In the formula, The original training dataset, For extended datasets generated based on meta-learning, To enhance the training dataset.

[0029] S506. Model Training and Optimization: Construct a loss function with mean squared error as its core, and use it as the optimization objective function for model training. Use gradient descent to optimize the model parameters, iterate until the loss function converges, and obtain the final trained time series prediction model.

[0030] S507, Time Series Prediction: Input the geological parameters and construction parameters of the target working condition into the trained time series prediction model, and output the time series prediction results of fracture morphology and stress evolution for the entire hydraulic fracturing process.

[0031] Furthermore, in step S501, the LSTM calculation process is as follows: (1) Calculation of the forgetting gate: In the formula, It is the Sigmoid activation function. Let be the input feature vector at time t. Let t be the hidden layer state at time t-1.

[0032] (2) Input gate calculation: (3) Calculation of candidate cell states: In the formula, It is the hyperbolic tangent activation function.

[0033] (4) Cell state renewal: In the formula, This is the element-wise product of Hadamard.

[0034] (5) Output gate calculation: (6) Hidden layer state update: (7) Output layer prediction: .

[0035] Furthermore, in step S5, the task loss function adopts the mean squared error loss, and its expression is: In the formula, The length of the time series sequence. The true value obtained from numerical simulation. These are the model's predicted values.

[0036] The expression for the objective function to be optimized is: In the formula, To increase the number of samples in the training set, For the true value, These are predicted values.

[0037] The parameter update formula for gradient descent is: In the formula, The learning rate for model training. The trainable parameters of the model are obtained by iterative optimization and convergence. The trained model predicts the following output: .

[0038] Furthermore, it also includes step S6, which optimizes fracturing operation parameters based on time-series prediction results, specifically as follows: S601. Construct the optimal combination of construction parameters to form an input parameter set: In the formula, E is the elastic modulus, Δσ is the horizontal stress difference, and Q is the water injection flow rate to be optimized.

[0039] S602. Input the input parameter set into the trained time series prediction model to obtain the prediction results: S603. Based on the prediction results, extract the maximum crack propagation length. Define crack propagation efficiency index for: Extract the time-varying stress curve and define the rate of stress change. for: S604. Based on the crack propagation efficiency index and stress change rate, the following definition is made: (1) Definition The critical threshold for fracture propagation capacity under unit water injection flow rate conditions can be selected using historical fracturing data or engineering experience. When the flow rate is high, it indicates that the flow rate can achieve effective fracture propagation and the fracturing effect is good; when If the crack propagation capacity is insufficient and the fracturing effect is poor, then the construction parameters need to be adjusted and optimized.

[0040] (2) Definition This is the critical threshold for the rate of stress change during fracturing, which can be determined based on historical fracturing data statistics or engineering experience. It is used to distinguish between a stable fracture propagation state and an abnormal stress fluctuation state. When When the stress change is gradual during fracturing, the crack propagation is stable; when If the stress changes abruptly during fracturing, it indicates that there may be risks such as localized stress concentration or structural instability.

[0041] Based on the above, the parameter optimization rules are established as follows: When a combination of construction parameters simultaneously meets the above-mentioned parameter optimization rules, the parameter is determined to be the preferred fracturing construction parameter.

[0042] Compared with the prior art, the present invention has the following advantages: 1. The prediction method proposed in this invention constructs a high-quality training dataset of a limited scale through numerical simulation, and introduces a small sample data expansion mechanism to extract shared feature representations between different working conditions. Under small sample conditions, it realizes rapid model learning and adaptive parameter adjustment, effectively improving the model's adaptability to new working conditions. Even with limited training samples, it can still effectively model complex working conditions, overcoming the shortcomings of traditional deep learning methods that rely heavily on large-scale labeled data. It significantly improves the model's generalization ability under multiple working conditions, and is especially suitable for predicting hydraulic fracturing processes under multi-parameter coupling conditions in deep coal seams.

[0043] 2. This invention is based on cross-task feature representations obtained by expanding small sample data. It introduces a perturbation mechanism that conforms to physical constraints to expand the data on the basis of the original small sample data, and constructs an enhanced training dataset, which effectively improves the diversity and representativeness of the data distribution. Under the premise of maintaining the physical mechanism constraints of the original data, it significantly alleviates the problem of scarcity of high-quality samples, reduces the risk of model overfitting, and improves the model's ability to fit the nonlinear relationship of multi-physics coupling in hydraulic fracturing. It further improves the accuracy and stability of predicting the fracture morphology and stress evolution of hydraulic fracturing, and is especially suitable for data-driven modeling under complex geological conditions.

[0044] 3. This invention constructs a time-series prediction model to dynamically model the fracture propagation behavior and stress evolution process during hydraulic fracturing, achieving continuous time-series prediction of the entire fracturing process. Compared with traditional methods that only perform static analysis on the final fracturing result, this invention can accurately characterize the time-series evolution characteristics of the entire fracturing process, providing reliable technical support for rapid assessment, parameter optimization design, on-site dynamic decision-making, and risk warning of the hydraulic fracturing process. It has extremely strong engineering application value and is particularly suitable for hydraulic fracturing projects under deep, high-stress, and low-permeability coal seam conditions. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the overall process of the present invention. Detailed Implementation

[0046] The present invention will be further described below. Example 1:

[0047] This embodiment is a basic implementation of the present invention, and specifically includes the following steps: S1. Numerical Model Establishment: S101. Numerical Model Construction: A two-dimensional hydraulic fracturing model of deep coal seams was established based on ABAQUS finite element analysis software, and the coal matrix was divided into structured meshes. Zero-thickness cohesive elements were inserted between the meshes through a plugin written in the ABAQUS secondary development module to simulate the initiation and propagation process of fractures.

[0048] S102. Stress monitoring point layout: After the cohesive unit is embedded, units at distances of 0m, 25m, 50m, and 100m from the injection hole are selected as stress monitoring points. Among them, 0m is the crack initiation area, used to characterize the stress concentration and release characteristics during the crack initiation stage; 25m and 50m are the intermediate areas on the crack propagation path, used to reflect the stress transmission and disturbance laws during crack propagation; 100m is the far-field area, used to analyze the influence range and attenuation characteristics of the fracturing action on the stress field.

[0049] S103. Input Parameter Acquisition: Based on existing literature and field engineering data, the geological parameters and commonly used construction parameter ranges of deep coal seams are obtained. Elastic modulus E, horizontal stress difference Δσ, permeability k, porosity φ, and water injection flow rate Q are selected as key variables. 120 sets of variable combinations are generated by Latin hypercube sampling. Other parameters (such as Poisson's ratio, cohesive strength, fluid viscosity, etc.) are kept constant, and the water injection time is uniformly set to 300s.

[0050] S2. Description of Fluid-Structure Interaction Physical Processes: Based on fluid-structure interaction theory, the fracture initiation criterion, fracture propagation and evolution law, and fluid flow equations within the fracture are defined to complete the numerical description of the physical mechanism of the entire hydraulic fracturing process, as detailed below: S201. Crack Initiation Criterion: The maximum principal stress criterion is selected as the criterion for the initiation of damage in cohesive elements. This criterion determines whether damage has occurred in an element by judging whether the stress in a certain direction reaches the critical stress for damage in that element. The expression is as follows: In the formula, , and These represent the critical normal stress and the first and second tangential stresses at the initial damage of the cohesive element, in MPa; symbol This indicates that the cohesive element is damaged under tensile stress but not under compressive stress.

[0051] S202. Crack Propagation and Evolution Law: After crack initiation, the subsequent crack propagation process is described by a stiffness degradation model, expressed as follows: In the formula, The symbol is defined as tensile stress being positive and compressive stress being negative, and the unit is MPa; , and represents the normal stress and two tangential stresses when the cohesive element is undamaged, in MPa; D is the dimensionless damage factor, whose range is determined as follows: in, This represents the displacement of the cohesive element at the initial damage, in meters (m). This represents the displacement when the cohesive element is completely damaged, in meters (m). The maximum displacement during the damage process of the cohesive element is expressed in meters (m), and its expression is: In the formula, , and These represent the normal displacement component and the first and second tangential displacement components at the initial damage of the cohesive element, in meters (m).

[0052] S203. Fluid Flow Equation within the Crack: Assuming the fluid within the crack is an incompressible Newtonian fluid, and since the crack width is much smaller than the crack length, the fluid within the crack is simplified to a one-dimensional fluid, and its continuity equation is as follows: In the formula, The local average velocity per unit height, in meters (m). 2 / s; The crack width is expressed in meters (m). The fluid filtration rate per unit height, in meters (m). 2 / s.

[0053] Fluid flow within the fracture includes two modes: tangential flow and normal flow; tangential flow refers to the fluid flowing along the fracture channel, described by the lubrication equation: In the formula, The permeability coefficient of fluid flowing tangentially within the fracture is expressed in m / s. The viscosity of the fracture fluid is expressed in Pa·s. This represents the pressure gradient of the tangentially flowing fluid.

[0054] Normal flow refers to the fluid that filters out from the two surfaces of a fracture and enters the formation, described by the flow equations at the top and bottom surfaces of the fracture: In the formula, and These are the flow rates entering the top and bottom crack surfaces, respectively, in m / s; and These are the filtration loss coefficients for the top and bottom crack surfaces, respectively, in m / (Pa·s); and The pore pressure is measured in Pa at the top and bottom crack surfaces. The fluid pressure at the crack is expressed in Pa. This represents the total flow rate along the normal direction of the crack, expressed in m³ / s.

[0055] S3. Numerical Model Verification: To verify the accuracy and reliability of the established numerical model, the classic KGD hydraulic fracturing model was selected for verification. Under plane strain conditions, the core calculation formula of the KGD model is: Crack center opening: Half seam length: Net pressure within the hydraulic fracture: In the formula, The opening at the center of the crack, Poisson's ratio, The water injection rate per unit width, For fluid viscosity, Shear modulus For water filling time, It is half the seam length. The pressure inside the crack, It is the minimum principal stress.

[0056] Under the same working conditions, the calculation results of the established numerical model and the KGD model in terms of fracture aperture, fracture length and pressure evolution were compared. When the numerical simulation results are consistent with the trend of the KGD analytical solution and the numerical error is within 5%, it indicates that the established model can accurately reflect the characteristics of fracture propagation and stress evolution during hydraulic fracturing, thus verifying the effectiveness and reliability of the model.

[0057] S4. Training dataset construction: S401. From the simulation results of the validated numerical model, extract the crack and stress evolution parameters at different times, including crack length. Crack width Stress values ​​at each monitoring point , where i=1,2,3,4, which correspond to stress monitoring points at distances of 0m, 25m, 50m, and 100m from the water injection hole, respectively.

[0058] S402. Construct the input feature vector: In the formula, E is the elastic modulus, Δσ is the horizontal stress difference, k is the permeability, φ is the porosity, and Q is the injection flow rate.

[0059] S403. Define the output variables for the corresponding time: S404. Perform min-max normalization on the input feature vector and output variables to eliminate the impact of differences in feature dimensions and value ranges on model training. The normalization formula is as follows: In the formula, The original data, For the normalized data, and These are the maximum and minimum values ​​of the feature in the corresponding dataset, respectively; after normalization, the original training dataset is constructed.

[0060] S5. Time Series Forecasting Model Construction and Forecasting: S501. Construction of the basic learner: A Long Short-Term Memory (LSTM) network is used as the basic learner to characterize the temporal features of fracture morphology and stress evolution during hydraulic fracturing. The complete set of trainable parameters of the model is denoted as: In the formula, The weight matrix between the input and the hidden state. The recursive weight matrix between hidden states, These are the bias term parameters.

[0061] The specific calculation process of LSTM is as follows: (1) Calculation of the forgetting gate: In the formula, It is the Sigmoid activation function. Let be the input feature vector at time t. Let t be the hidden layer state at time t-1.

[0062] (2) Input gate calculation: (3) Calculation of candidate cell states: In the formula, It is the hyperbolic tangent activation function.

[0063] (4) Cell state renewal: In the formula, This is the element-wise product of Hadamard.

[0064] (5) Output gate calculation: (6) Hidden layer state update: (7) Output layer prediction: S502, Task Division: Divide the time series data corresponding to different combinations of fracturing parameters in step S1 into different meta-learning tasks. Each task is represented as follows: In the formula, Let i be the task corresponding to the i-th numerical simulation sampling group. For the task training set, This is the task test set; in this embodiment, a total of 120 meta-tasks are divided, of which 96 tasks are used for meta-training and 24 tasks are used for meta-testing.

[0065] S503, LSTM model parameter optimization based on meta-learning: For each task The gradient of the LSTM is updated using the training set data. The calculation process is as follows: In the formula, These are the initial model parameters. The learning rate for the task is set to 0.01 in this embodiment; The task loss function, using mean squared error loss, is expressed as follows: In the formula, The time sequence length is 300 in this embodiment (corresponding to 300s of water injection time, with a time step of 1s). The true value obtained from numerical simulation. These are the model's predicted values; For the task Updated parameters.

[0066] In the meta-learning phase, the LSTM model parameters are jointly optimized through multiple tasks. The optimization process is as follows: In the formula, The learning rate is 0.001 in this embodiment; These are the model parameters after joint optimization across multiple tasks. The number of training tasks is 96 in this embodiment.

[0067] S504. Small Sample Data Expansion: Based on the cross-task shared feature representation obtained through meta-learning, a perturbation mechanism is introduced to expand the data on the original training dataset. The expansion process is as follows: In the formula, For the expanded input variables, For the expanded output variables, It is a perturbation term generated based on task distribution, satisfying... , As a disturbance intensity parameter, this embodiment takes 1% of the range of input variable values. The disturbance range is constrained by the physical range of input variable values ​​to ensure that the expanded data conforms to the actual engineering situation.

[0068] S505, Construction of Enhanced Training Set: Merge the original training dataset with the extended dataset to construct an enhanced training set: In the formula, The original training dataset, For extended datasets generated based on meta-learning, To enhance the training dataset, in this embodiment, the number of expanded samples is increased to 5 times that of the original samples.

[0069] S506, Model Training and Optimization: Construct a loss function based on mean squared error, and use it as the optimization objective function for model training. The expression is: In the formula, To increase the number of samples in the training set, For the true value, These are predicted values.

[0070] The model parameters are optimized using the Adam gradient descent method, and the parameter update formula is as follows: In the formula, The training rate for the model is set to 0.0001 in this embodiment. The trainable parameters of the model are set; the batch size is set to 32, the epoch is set to 200, and the iteration is continued until the loss function converges, resulting in the final trained time series prediction model. The parameters of the converged model are as follows: The model's predicted output is: S507, Time Series Prediction: Input the geological parameters and construction parameters of the target working condition into the trained time series prediction model, and output the time series variation curves of fracture length, fracture width and stress at each monitoring point within 300s of the entire hydraulic fracturing process, thus completing the time series prediction of fracture morphology and stress evolution. Example 2:

[0071] This embodiment, based on Embodiment 1, provides an application for optimizing fracturing construction parameters using the prediction method of this invention. The specific steps are as follows: A deep coal seam is buried at a depth of 1200m. Before fracturing operations, it is necessary to optimize the construction parameters (water injection flow rate). Based on field engineering manuals and sampling experiments, the elastic modulus of the coal seam is determined to be 3.5 GPa, the maximum horizontal principal stress is 29.7 MPa, and the minimum horizontal principal stress is 22.4 MPa. The optimal water injection flow rate Q is within the range of 1~10 m³ / h. 3 / min, the specific optimization steps are as follows: S601. Construct the optimal combination of construction parameters within the range of 1~10m. 3 Within the range of / min, at 1m 3 / min is the step size; construct the input parameter set: In the formula, E = 3.5 GPa, Δσ = 7.3 MPa, and Q are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 m respectively. 3 / min.

[0072] S602. Input each set of input parameters into the time-series prediction model trained in Example 1 to obtain the time-series prediction results of crack morphology and stress evolution corresponding to each set of parameters: S603. Based on the prediction results, extract the maximum crack propagation length corresponding to each set of parameters. Define crack propagation efficiency index for: Extract the time-varying stress curves corresponding to each set of parameters and define the stress change rate. for: S604. Based on engineering experience and historical fracturing data, determine the critical threshold for fracture propagation capacity under unit injection flow rate conditions. Critical threshold of stress change rate during fracturing Establish parameter optimization rules: The calculation results of each set of parameters are evaluated. When the combination of construction parameters simultaneously meets the above parameter optimization rules, the parameter is determined to be the preferred fracturing construction parameter. In this embodiment, the injection flow rate Q = 6.4 m³ / h. 3 / min , Since the optimal selection rule is met, 6.4m is determined. 3 / min is the optimal water injection flow rate parameter for this coal seam.

[0073] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A hydraulic fracturing time series prediction method based on numerical simulation-driven deep learning, characterized in that, Includes the following steps: S1. Numerical Model Establishment: A two-dimensional hydraulic fracturing numerical model of deep coal seams is established based on finite element analysis software. The coal matrix is ​​meshed, and cohesive elements are inserted between the meshes to simulate the initiation and propagation of fractures. Stress monitoring points are arranged in the model. Combined with the geological and construction parameters of the deep coal seams, multiple sets of variable combinations of input parameters are generated by Latin hypercube sampling, and a unified water injection time is set. S2. Description of the physical process of fluid-structure interaction: Based on the fluid-structure interaction theory, the fracture initiation criterion, fracture propagation and evolution law and fluid flow equation in the fracture are defined to complete the numerical description of the physical mechanism of the entire hydraulic fracturing process. S3. Numerical model verification: The numerical model established in step S1 is verified by using a hydraulic fracturing model or physical experiment. Under the same working conditions, the fracture opening, fracture length and pressure evolution laws of the numerical model and the hydraulic fracturing model or physical experiment are compared. When the error between the two results is within the preset acceptable range, the numerical model is confirmed to be effective. S4. Training Dataset Construction: Extract crack and stress evolution parameters from the numerical simulation results of the effective numerical model, construct input feature vectors and corresponding output variables, normalize the input feature vectors and output variables, and construct the original training dataset. S5. Construction and Prediction of Temporal Series Prediction Model: Construct a small sample data expansion and temporal series prediction model. Using the temporal series prediction model as the basic learner, cross-task feature extraction, small sample data expansion and model parameter optimization are completed through small sample data expansion. The model is trained based on the expanded augmented dataset. Finally, the trained temporal series prediction model is used to achieve temporal prediction of fracture morphology and stress evolution in deep coal seam hydraulic fracturing.

2. The method according to claim 1, characterized in that, In step S1, the stress monitoring points are arranged as follows: stress monitoring points are set up with the water injection hole as the center, and several stress monitoring points are arranged according to the principle of proximity to the water injection hole. These points are used to collect stress response information during the crack initiation and propagation process, as well as information on the disturbance of the far-field stress field by crack evolution. The process of generating input parameters through Latin hypercube sampling is as follows: elastic modulus E, horizontal stress difference Δσ, permeability k, porosity φ, and water injection flow rate Q are selected as sampling variables. Several sets of variable combinations are generated through Latin hypercube sampling. The remaining geological parameters and construction parameters are kept fixed, and the water injection time is unified.

3. The method according to claim 1, characterized in that, In step S2, the crack initiation criterion adopts the maximum principal stress criterion, the expression of which is: In the formula, , and These represent the critical normal stress and the first and second tangential stresses at the initial damage of the cohesive element, in MPa; symbol This indicates that the cohesive unit is damaged under tensile stress.

4. The method according to claim 1, characterized in that, In step S2, the crack propagation and evolution law is described by a stiffness degradation model, expressed as: In the formula, The sign convention is defined as positive for tensile stress and negative for compressive stress; , and Here, represents the normal stress and two tangential stresses when the cohesive element is undamaged; D is the dimensionless damage factor, whose value range is determined as follows: in, This represents the displacement of the cohesive element at the initial damage stage. This represents the displacement when the cohesive element is completely damaged. The maximum displacement during the damage process of the cohesive element is expressed as: In the formula, , and These represent the normal displacement component and the first and second tangential displacement components at the initial damage of the cohesive element.

5. The method according to claim 1, characterized in that, In step S2, the process of constructing the fluid flow equation within the crack is as follows: Assuming the fluid inside the fracture is an incompressible Newtonian fluid, simplifying it to a one-dimensional fluid, its continuity equation is: In the formula, The local average velocity per unit height; The width of the crack; The fluid loss rate per unit height; Fluid flow within the fracture includes tangential and normal flow, where tangential flow is the flow along the fracture channel and is described by the lubrication equation: In the formula, Let be the permeability coefficient of the fluid flowing tangentially within the fracture. The viscosity of the crack fluid is... The pressure gradient of the tangentially flowing fluid; Normal flow is the fluid that filters out from both surfaces of the fracture and enters the formation, described by the flow equations at the top and bottom surfaces of the fracture: In the formula, and These represent the flow rates entering the top and bottom crack surfaces, respectively. and These are the filtration loss coefficients for the top and bottom crack surfaces, respectively. and For the pore pressure on the top and bottom crack surfaces, The fluid pressure at the crack. This represents the total flow rate along the normal direction of the crack.

6. The method according to claim 1, characterized in that, In step S3, the KGD model is used to verify the accuracy and reliability of the established numerical model. The calculation formula for this verification model under plane strain conditions is as follows: Crack center opening: Half seam length: Net pressure within the hydraulic fracture: In the formula, The opening at the center of the crack, Poisson's ratio, The water injection rate per unit width, For fluid viscosity, Shear modulus For water filling time, It is half the seam length. The pressure inside the crack, It is the minimum principal stress.

7. The method according to claim 1, characterized in that, Step S4 specifically includes: S401. Extract crack and stress evolution parameters from the numerical simulation results, including crack length. Crack width Stress values ​​at each monitoring point , where i is the number of stress monitoring points arranged; S402. Construct the input feature vector: In the formula, E is the elastic modulus, Δσ is the horizontal stress difference, k is the permeability, φ is the porosity, and Q is the injection flow rate; S403. Define output variables: S404. Normalize the input feature vector and output variable to eliminate the impact of differences in feature dimensions and value ranges on model training.

8. The method according to claim 1, characterized in that, Step S5 specifically includes: S501. Construction of the basic learner: The time-series prediction model used is LSTM, which is used as the basic learner to characterize the temporal features of fracture morphology and stress evolution during hydraulic fracturing. The model parameters are denoted as: In the formula, This is the set of all trainable parameters for the model. The weight matrix between the input and the hidden state. The recursive weight matrix between hidden states, For bias term parameters; S502. Task Partitioning: The small sample data expansion method used is meta-learning, which divides the data corresponding to different fracturing parameter combinations into different meta-learning tasks. Each task is represented as follows: In the formula, Let i be the task corresponding to the i-th numerical simulation sampling group. For the task training set, For the task test set; S503, LSTM model parameter optimization based on meta-learning: For each task The gradient of the LSTM is updated using the training set data. The calculation process is as follows: In the formula, These are the initial model parameters. For task learning rate, For the task loss function, For the task Updated parameters; In the meta-learning phase, the LSTM model parameters are jointly optimized through multiple tasks. The optimization process is as follows: In the formula, The meta-learning rate, These are the model parameters after joint optimization across multiple tasks. Number of tasks; S504. Small Sample Data Expansion: Based on the cross-task shared feature representation obtained through meta-learning, a perturbation mechanism is introduced to expand the data on the original training dataset. The expansion process is as follows: In the formula, For the expanded input variables, For the expanded output variables, It is a perturbation term generated based on task distribution, satisfying... , This is a disturbance intensity parameter, and the disturbance range is constrained by the physical value range of the input variables; S505, Construction of Enhanced Training Set: Merge the original training dataset with the extended dataset to construct an enhanced training set: In the formula, The original training dataset, For extended datasets generated based on meta-learning, To enhance the training dataset; S506. Model Training and Optimization: Construct a loss function with mean squared error as the core, use it as the optimization objective function for model training, use gradient descent to optimize the model parameters, iterate until the loss function converges, and obtain the final trained time series prediction model. S507, Time Series Prediction: Input the geological parameters and construction parameters of the target working condition into the trained time series prediction model, and output the time series prediction results of fracture morphology and stress evolution for the entire hydraulic fracturing process.

9. The method according to claim 8, characterized in that, In step S5, the task loss function adopts the mean squared error loss, and its expression is: In the formula, The length of the time series sequence. The true value obtained from numerical simulation. These are the model's predicted values; The expression for the objective function to be optimized is: In the formula, To increase the number of samples in the training set, For the true value, This is a predicted value; The parameter update formula for gradient descent is: In the formula, The learning rate for model training. The trainable parameters of the model are obtained by iterative optimization and convergence. The trained model predicts the following output: 。 10. The method according to claim 1, characterized in that, It also includes step S6, which optimizes fracturing operation parameters based on time-series prediction results, specifically: S601. Construct the optimal combination of construction parameters to form an input parameter set: In the formula, E is the elastic modulus, Δσ is the horizontal stress difference, and Q is the water injection flow rate to be optimized; S602. Input the input parameter set into the trained time series prediction model to obtain the prediction results: S603. Based on the prediction results, extract the maximum crack propagation length. Define crack propagation efficiency index for: Extract the time-varying stress curve and define the rate of stress change. for: S604. Establish parameter optimization rules based on crack propagation efficiency index and stress change rate: In the formula, The critical threshold for crack propagation capacity under unit water injection flow rate conditions. This is the critical threshold for the rate of stress change during fracturing; When a combination of construction parameters simultaneously meets the above-mentioned parameter optimization rules, the parameter is determined to be the preferred fracturing construction parameter.

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