Multi-input depth operator network stratum fracture pressure prediction method based on physical information double embedding

Abstract

The invention discloses a stratum fracture pressure prediction method of a multi-input depth operator network with double embedding of physical information. Comprising the following steps: acquiring logging data and engineering parameter data of a to-be-predicted well section, then executing target perception mutual information grouping, calculating an input feature mutual information matrix, constructing a mutual information fingerprint vector, weighting and clustering according to the correlation between the mutual information fingerprint vector and fracture pressure, obtaining feature subsets, and respectively inputting the feature subsets into a multi-branch sub-network; a depth operator network is constructed, a backbone network takes well depth as input coding space dependence, a multi-branch sub-network extracts grouping features, an attention module performs adaptive weighted fusion on each branch representation, and adaptive physical constraint is performed through a physical layer; according to the method, the prediction curve of the fracture pressure changing along with the well depth can be output through the physical information double-embedded multi-input depth operator network, the prediction accuracy, the physical consistency and the cross-well-section generalization ability are improved, and the method is suitable for well wall stability analysis and fracturing parameter optimization.

Description

Technical Field

[0001] This invention belongs to the field of petroleum engineering and intelligent drilling and completion technology, and particularly relates to a method for predicting formation fracture pressure based on a multi-input depth operator network with dual embedding of physical information. Background Technology

[0002] Formation fracturing pressure is a key factor in wellbore pressure window design, drilling fluid density determination, wellbore stability analysis, and fracturing operation parameter optimization. Under complex geological structures and heterogeneous formations, fracturing pressure is influenced by multiple factors, including pore pressure, in-situ stress, rock mechanical properties, wellbore trajectory, and seepage coupling, and varies significantly with well depth.

[0003] Existing methods for predicting fracture pressure mainly fall into two categories: model-driven and data-driven. Model-driven methods typically require a complete chain calculation of geostress-wellbore stress distribution-failure criteria, and are sensitive to the accuracy of prior assumptions and parameters. When engineering parameters are incomplete, they are prone to large deviations. Data-driven methods rely on learning mapping relationships from historical samples. Although they have fitting capabilities, they are prone to insufficient generalization when samples are scarce, when there is cross-block migration, or when formation conditions change. They may also produce results that violate physical laws (such as negative fracture pressure or lower than pore pressure).

[0004] Therefore, there is an urgent need for a prediction method that can simultaneously characterize spatial dependence along well depth, integrate multi-source input features, and introduce physical constraints at the training and output levels, so as to improve the accuracy, interpretability, and generalization ability of fracture pressure prediction across well sections. Summary of the Invention

[0005] The present invention aims to provide a formation fracture pressure prediction method based on a multi-input depth operator network with dual embedding of physical information, so as to achieve high-precision prediction of fracture pressure with continuous and physically consistent well depth.

[0006] Step 1: A multi-input dual-physical embedding deep operator network method for predicting formation fracture pressure, including the following steps: Step S10: Obtain logging data and engineering parameter data for the well section to be predicted, and construct a family of multi-source input functions distributed along the well depth using the well depth as the spatial coordinate; the logging and engineering parameters may include, but are not limited to: sonic transit time, density, resistivity, gamma logging curves, wellbore trajectory (inclination angle, azimuth angle), drilling fluid density and wellbore pressure information, pore pressure, geostress-related quantities and rock mechanics parameters, etc. Step S20: Preprocess the data, including at least missing value processing, outlier removal or correction, and normalization; wherein outlier removal or correction can be combined with screening based on the physical boundary of the rupture pressure to avoid data with zero values, negative values, or obvious violations of the physical boundary conditions from entering the training. Step S30: Perform target perception mutual information grouping: Calculate the mutual information between each pair of input features to form a mutual information matrix, and represent each feature as its mutual information fingerprint vector; at the same time, calculate the correlation measure between each feature and the rupture pressure target, and use the correlation to weight the mutual information fingerprint vector; cluster the weighted mutual information fingerprint vector to obtain at least two feature subsets, so as to allocate input information of different types and different contributions to different branch networks for learning; Step S40: Construct and train the multi-input dual physical embedding deep operator network MI-Physical DeepONet, the network including at least: (1) a backbone network: taking well depth as input and outputting backbone features to characterize the spatial dependence of the output function; (2) a multi-branch sub-network: receiving the input function or its sampling sequence corresponding to each feature subset obtained in step S30 respectively, and outputting branch features; (3) an attention fusion module: using backbone features as query vectors and each branch feature as key / value vectors, calculating branch weights and fusion them; (4) an operator output layer: performing inner product operation on the fused branch representation and backbone features to obtain the original rupture pressure output of the neural network; Step S50: Calculate the theoretical rupture pressure based on the physical model of rupture pressure, and adaptively fuse the original output and theoretical output using learnable gating coefficients to output the final rupture pressure. Minimize the data error term and the physical consistency term together. The physical consistency term includes at least the residual of the failure function and the penalty term for the physical constraints of the inequality. Step S50 utilizes the trained network to continuously predict the output fracture pressure of the predicted well section as it changes with well depth, and can be further used for drilling fluid density window design and fracturing parameter optimization.

[0007] Step 2: Based on the multi-input dual-physical embedding deep operator network method for predicting formation fracture pressure described in Step 1, in Step S30, the target-aware mutual information grouping can be implemented as follows: Let the input feature set be... The elements of the mutual information matrix can be represented as The mutual information fingerprint vector of the i-th feature is represented as: ; Represent the dependency structure between this feature and the other features; let... for The correlation measure with the rupture pressure Y (such as the absolute value of the Pearson correlation coefficient or a function thereof) can be used to construct a weighted fingerprint vector as follows: = ; Where α is a hyperparameter, and for { Clustering is performed to obtain feature groups.

[0008] Step 3: Based on the multi-input dual-physical embedding deep operator network method for formation fracture pressure prediction described in Step 1, in step S40, the attention fusion module can use a scalar scoring function to evaluate the importance of branches. Let the backbone feature be q, and the branch feature be... (k=1…N), branch scores can be calculated. =f(q, The weights are then obtained by softmax normalization. The fusion branch is represented as: This fusion method can adaptively allocate branch contributions based on well depth context and input pattern, thereby improving the ability to express complex coupled features.

[0009] Step 4: Based on the photovoltaic power generation prediction method with deep feature fusion under domain knowledge constraints described in Step 1, in Step S50, the dual embedding of physical layer and physical loss can be implemented as follows: Calculate the theoretical fracture pressure based on the pore pressure model, geostress model, wellbore stress distribution model, and fracture criterion. Gating coefficient The output of the gated network is obtained by taking the concatenated vector of [well depth z, input feature X(z)] as input and outputting g∈(0,1); the final output can be expressed as in This is the original output of the operator network.

[0010] The beneficial effects of this invention are as follows: 1. By using a depth operator network to model in the form of "well depth → output function", the spatial dependency relationship along the well depth is explicitly encoded. Compared with the traditional network structure that only makes point predictions, it has stronger continuous prediction and cross-depth generalization capabilities. 2. By grouping multi-source inputs according to "feature-dependent structure + contribution to the target" through target-aware mutual information, the multi-source inputs are clustered and distributed to multi-branch sub-networks. Combined with attention fusion, adaptive weighting is achieved, which helps to improve feature utilization efficiency and noise resistance. 3. By introducing mechanistic information such as pore pressure, geostress, wellbore stress and fracture criteria through a dual embedding method of "physical layer + physical loss", and introducing inequality physical constraint penalty terms, the prediction results meet the basic physical boundaries, improving interpretability and engineering credibility. 4. By adopting gated adaptive fusion and gated regularized adaptive weighting strategies, the contributions of data-driven and physical models can be dynamically balanced under different well sections and different data quality conditions, reducing the dependence on manual parameter tuning and improving robustness. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the overall process of the MI-Physical DeepONet prediction method of the present invention; Detailed Implementation

[0012] The embodiments of the present invention will be described below with reference to the accompanying drawings. It should be noted that the present invention can be implemented in many different ways as defined and covered by the claims. These embodiments are only used to explain the technical solutions of the present invention and are not intended to limit the scope of protection.

[0013] This embodiment takes the prediction of fracture pressure in oil and gas well sections as an example. First, well logging curves and engineering parameters are acquired and cleaned, normalized, and screened for physical boundaries. Then, the input features are grouped according to mutual information and target correlation, and a corresponding branch network is constructed for each group. Subsequently, the backbone network is used to encode spatial dependence with well depth, and multi-branch features are fused through an attention mechanism to output a neural network estimate of fracture pressure. At the same time, the theoretical fracture pressure is calculated based on rock mechanics and wellbore stress models, and the two are adaptively fused through gating coefficients. During the training process, a composite loss function containing data terms, physical residual terms, and inequality constraint terms is used to complete the model training and output continuous prediction results.

[0014] Step 1: As Figure 1 As shown, the method includes the following steps: Step S10, Data Acquisition and Input Function Construction: Collect multi-source data sampled along the well depth of the well section to be predicted, treat the well depth z as a continuous spatial coordinate, and represent each type of input feature as an input function that varies with the well depth. This forms a family of input functions. ; Step S20, Data Preprocessing: Missing value imputation, outlier detection and processing are performed on the raw data, and features of different dimensions are normalized. Outlier processing can be combined with physical boundary conditions, for example: the rupture pressure should be non-negative and usually not lower than the pore pressure; when samples that clearly violate the boundary conditions appear, they can be removed or corrected. Step S30, Target Perception Mutual Information Grouping: Calculate the mutual information matrix The mutual information fingerprint vectors are constructed and then clustered after being weighted according to the target relevance. Clustering methods can include K-means, spectral clustering, or hierarchical clustering; the number of clusters can be determined using the silhouette coefficient or elbow method. After grouping, each feature subset is input into the corresponding branch network to reduce interference from cross-type features and highlight information that contributes significantly to the target. Step S40, Network Construction and Training: Input well depth z into the backbone network to obtain backbone features. The k-th branch network receives the k-th feature subset as input to obtain the branch representation. ;by For query, {} Calculate attention weights for key / value pairs { } and obtain fusion characterization Operator output layer for t(z) and Performing the inner product operation yields ; Step S41, Physical layer calculation and gating fusion: Calculate the theoretical fracture pressure based on pore pressure models (e.g., Eaton method), horizontal geostress models (e.g., Huang's geostress model), deviated wellbore stress distribution models, and fracture criteria such as the maximum tensile stress criterion. Gated network output Final output ; Step S42, Composite Loss Function: Minimize during training ; ; Mean square error can be used; It can be derived from the residual of the failure function under critical failure conditions. Physical inequalities can be penalized using ReLU forms: nonnegativity constraint ReLU(−Y) and lower bound constraint ReLU(Pp−Y). To avoid gating saturation, the weight of the gating regularization term... The loss level can be adaptively set at the beginning of training and gradually decreased as training progresses; Step S43, Output and Application: Use the trained model to infer the target well section at any well depth, output the continuous fracture pressure curve, and further use it for drilling fluid density window design, wellbore stability analysis and fracturing construction parameter optimization.

[0015] The above description represents only embodiments of the present invention and is not intended to limit the scope of protection of the invention. Any equivalent structural or procedural modifications based on the description in the specification and drawings of this invention, as well as direct or indirect applications in other related technical fields, fall within the scope of protection of this invention.

Claims

1. A method for predicting formation fracture pressure based on a multi-input depth operator network with dual embedding of physical information, characterized in that, Includes the following steps: Step S10: Obtain logging and engineering parameter data of the well section to be predicted, and construct a family of multi-source input functions distributed along the well depth, using the well depth as the spatial coordinate for predicting fracture pressure. Step S20: Calculate the mutual information between each input feature and form a mutual information fingerprint vector. Simultaneously, introduce correlation weights between the input features and the rupture pressure target to weight the mutual information fingerprint vector. Then, use a clustering method to group the rupture pressure input features. Step S30: Construct a multi-input deep operator network (MI-DeepONet), including a backbone network that processes well depth information, takes well depth as input, and outputs backbone features to characterize the spatial dependence of the output function. Multiple branch networks process the input features after clustering and grouping respectively. An attention mechanism is implemented on the outputs of the backbone network and each branch network to perform weighted fusion output of the rupture pressure prediction. Step S40: Introduce a physical layer into the network structure. Calculate the theoretical fracture pressure at the corresponding well depth based on the fracture pressure physical model. Adaptively fuse the original neural network prediction and the theoretical fracture pressure using learnable gating coefficients to output the final fracture pressure. Construct a composite loss function that includes data-driven loss and fracture pressure physical-driven loss, and train the model. Use the trained model to predict the fracture pressure of the well section to be predicted.

2. The method for predicting formation fracture pressure using a deep operator network with mutual information grouping input and physical information embedding as described in claim 1, characterized in that, The mutual information matrix between each pair of input features of rupture pressure is calculated, and the correlation measure between each input feature and the rupture pressure target is calculated. The weight outputs of the backbone network and branch network sets are fused through dot product operation to achieve spatial dependency modeling of input features. The expression for the rupture pressure prediction output target is: in, It is the target output, output by well depth. definition, Represents the dimension of the input function. Represents the output dimension of the neural network. These are the branch network group weight coefficients. Represents the number of inputs. Represents the output of the branch network. Represents the backbone network output For input data, The weight matrix represents m n-dimensional input data. This is the network bias vector.

3. The method for predicting formation fracture pressure using a deep operator network with mutual information grouping input and physical information embedding as described in claim 1, characterized in that: In step S40, a physical layer is introduced to limit the prediction of fracture pressure based on the universal physical law of formation fracture pressure. The gating coefficient of the physical layer is output by a gating network. The gating network takes the concatenated vector of well depth and input features as input and learns the gating coefficient through training. The gating coefficient represents the credibility of the output of the physical model. The physical loss function based on the formation fracture pressure physical model is also included. The physical consistency loss is characterized by including at least: the residual of the failure function constructed by the maximum tensile stress criterion or equivalent fracture criterion, the non-negativity constraint penalty for fracture pressure ≥ 0, and the lower bound constraint penalty for fracture pressure ≥ pore pressure. The total loss function is expressed as follows: in Represents the total loss function. Represents data loss. Represents the physical loss of rupture pressure. Represents the gating regularization term. This serves as a balance factor between physics-driven loss and data-driven loss. This is the gating coefficient balancing factor. The data loss expression is: in, These are the model's predicted values. This is the actual value. The expression for the physical loss due to rupture pressure is: in Let be the residual of the j-th physical equation.

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