A volume fracturing well EUR prediction method based on improved GAN

Abstract

This invention discloses an improved GAN-based EUR prediction method for volumetric fractured wells, belonging to the interdisciplinary field of oil and gas field development and artificial intelligence technology. The method includes: S1, data acquisition and preprocessing; S2, constructing a generative adversarial network model; S3, introducing Dirichlet mixed noise and back-comparison loss; S4, model adversarial training with multi-loss fusion; and S5, data generation and model evaluation. This invention constructs a single-negative-multiple-positive-sample back-comparison learning mechanism for Dirichlet mixed latent variables, strengthening the consistency of feature structure and parameter correlation between generated and real data, significantly improving EUR prediction accuracy under small sample conditions, and achieving higher SDMetrics and R... 2 The indicators are all superior to traditional methods, and can accurately capture the impact of key fracturing parameters on EUR, providing a reliable basis for the capacity assessment of volumetric fracturing wells and the optimization of development plans, thus helping to improve the efficiency and economic benefits of oil and gas resource extraction.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of oil and gas field development and artificial intelligence technology, and in particular relates to an EUR prediction method for volumetric fractured wells based on an improved GAN. Background Technology

[0002] Ultimate recoverable reserves (EUR) are a key indicator for evaluating the development effectiveness of a single well and are closely related to multiple construction parameters. Current conventional methods for predicting EUR have significant limitations. For example, when using integrated geological and engineering simulation methods, it is necessary to integrate parameters from multiple fields for complex numerical simulations. This modeling process is cumbersome and computationally intensive, not only time-consuming and labor-intensive but also unable to quickly respond to adjustments in development plans. While machine learning-based big data modeling methods possess efficient fitting capabilities, they require extremely large amounts of sample data, relying on large-scale field measurement data to ensure model reliability. In shale oil and gas development, high costs and long development cycles, coupled with a scarcity of effective sample data, make it difficult for existing models to balance efficiency and accuracy.

[0003] Generative Adversarial Networks (GANs), as generative models capable of learning the latent distribution of data, offer new approaches to augmenting small-sample data and fitting distributions. By generating samples with statistical characteristics similar to real data, GANs alleviate the problem of insufficient samples to some extent. However, traditional GANs still suffer from drawbacks in modeling tabular shale oil and gas data, such as reliance on sample size, insufficient preservation of feature correlations, and unstable training, making it difficult to fully reflect the intrinsic relationships between complex parameters. Therefore, an improved GAN method is needed to provide reliable support for optimizing shale oil and gas development strategies. Summary of the Invention

[0004] The purpose of this invention is to provide an improved GAN-based method for predicting the EUR (Effective Urge) of fractured wells. This addresses the problems of existing methods that rely on data obtained from in-situ volumetric fracturing, such as cumbersome simulation processes, high sample size dependence of machine learning models, unstable training of traditional GAN ​​models, and difficulty in capturing the deep correlation between fracturing characteristic parameters and EUR. This invention introduces a more reasonable latent variable modeling method and a reverse contrastive loss to enhance the consistency between generated and real data in terms of feature structure and parameter correlation. This allows for accurate fitting of the intrinsic correlation between construction parameters and EUR under small sample conditions, thereby improving EUR prediction accuracy.

[0005] To achieve the above objectives, this invention provides a method for predicting EUR in volumetric fractured wells based on an improved GAN, comprising the following steps: S1. Construct the target tabular dataset, perform quality screening and cleaning on the original data; use logarithmic transformation to process skewed features and standardize the data to construct a training sample set suitable for neural network input; S2. Construct a generative adversarial network model that includes a generator and a discriminator; S3. Introduce the Dirichlet distribution to perform mixed sampling on the input random noise vector to generate mixed latent variables, and calculate the inverse contrast loss based on the generated sample features and the mixed sample features. S4. Define a comprehensive objective function that includes adversarial loss and reverse contrast loss, and train the discriminator and generator using an alternating optimization strategy; S5. Data is generated through periodic sampling, and then restored to the original numerical space through inverse standardization and inverse transformation. The TabPFN regression model, which has excellent performance in small samples, and statistical similarity are introduced as evaluation indicators. Combined with an early stopping mechanism, the model parameters with the highest scores are backtracked and saved.

[0006] Preferably, the specific content of S1 is as follows: S101. Perform feature distribution detection and transformation on the original data; Traverse all feature columns of the dataset, calculate skewness and numerical range, and perform transformation on long-tailed distribution columns with skewness greater than a preset threshold and large numerical range. S102. Standardize the raw data processed in S201. The Z-Score normalization method is used to map the processed original data to a distribution space with a mean of 0 and a variance of 1, as shown in the following expression: ; In the formula, These are the standardized values; This is the original input; The mean of the sample; Standard deviation; It also records the metadata of integer columns.

[0007] Preferably, the specific content of S2 is as follows: The generator receives dimensions as follows: The noise vector is stacked through multiple linear layers, one-dimensional batch normalization, and ReLU activation function to output a synthetic sample with the same dimension as the real data. The discriminator receives sample data, extracts high-dimensional feature vectors through multiple linear layers and ReLU activation function, and outputs the true and false probabilities through the Sigmoid function. Define the discriminator adversarial loss function To maximize the confidence score of the generated samples and minimize the confidence score of the real samples, the expression is as follows: ; In the formula, This represents the actual distribution of tabular data. For potential spatial noise distribution; This is the expectation operator for sampling the real data distribution; For sampling the expectation operator of the noise distribution; This is the output of the generator; Define the generator adversarial loss function Generate synthetic samples that maximize the deception of the discriminator, as shown in the following expression: .

[0008] Preferably, S3 specifically includes: S301. Generating mixed noise based on Dirichlet distribution; S302. Calculate the inverse comparison loss based on the features of the generated samples and the features of the mixed samples.

[0009] Preferably, the specific content of generating mixed noise based on the Dirichlet distribution in S301 is as follows: Define the latent spatial noise set of the input generator. ; Let the batch size for training be... The potential vector dimension is ,but Indicated by The set sequence consisting of independently sampled random noise vectors is expressed as follows: ; In the formula, each All samples were taken from the standard normal distribution. ; For each noise ,exclude All other vectors of itself Assign weights, as expressed below: ; In the formula, It is a dimension of A vector of all 1s; For the concentration parameters of the Dirichlet distribution; For the first The first mixed noise corresponds to the first The noise coefficient satisfies And the coefficient is greater than 0; For each index The sampled coefficients are used to perform a weighted summation of all original vectors except the vector itself to obtain the constrained vector, as shown in the following expression: ; In the formula, For the corresponding Mixed noise; It is the original vector excluding itself; Mixed noise Not including the original noise vector The components, together, constitute a pair of negative samples, mixing noise. Includes raw noise The two components have certain similarities in spatial semantics and can be used as positive samples. All The new set of potential vectors is formed as follows: .

[0010] Preferably, the specific details of calculating the reverse contrast loss based on the generated sample features and the mixed sample features in S302 are as follows: Introducing the concept of contrastive learning; generating samples within the same batch. Its corresponding mixed samples and The feature representation in the feature extraction layer is used as a contrast unit; The generated noise The feature representation calculated at the l-th layer after inputting the generator is denoted as follows. Among them Constitute negative samples Forming positive sample pairs; The generated sample The feature representation computed by the l-th layer of the input discriminator is denoted as: ,by To form negative sample pairs, Construct positive samples, and then calculate the back-contrast loss for each of them. The expression is as follows: ; In the formula, Cosine similarity; Temperature coefficient; It is a natural exponential function.

[0011] Preferably, S4 specifically includes: S401. Construct the discriminator loss function and the generator loss function; S402. The discriminator and generator are trained using an alternating iterative strategy.

[0012] Preferably, the specific details of constructing the discriminator loss function and the generator loss function in S401 are as follows: Adversarial loss based on the discriminator defined in S2 Inverse contrast loss with the discriminator defined in S302 Construct the discriminator loss function The expression is as follows: ; In the formula, Hyperparameters used to balance the contributions of the discriminator's adversarial loss and contrastive learning loss to the total loss; Generator-based adversarial loss defined in S2 Inverse comparison loss with the generator defined in S302 Construct the generator loss function The expression is as follows: ; In the formula, Hyperparameters used to balance the contributions of generator adversarial loss and contrastive learning loss to the total loss.

[0013] Preferably, the specific details of training the discriminator and generator using an alternating iterative strategy in S402 are as follows: S4021, Fixed Generator The parameters enable the discriminator. Gradient calculation is performed to prepare for training the discriminator; S4022. Input the preprocessed real table data samples into the discriminator and calculate the discrimination loss for the real samples; sample random noise vectors from the standard normal distribution, obtain fake samples through the generator, and input them into the discriminator to calculate the discrimination loss for the fake samples; S4023, Using Dirichlet distribution on noise vectors Mixed sampling yields mixed noise. The generated noise and mixed noise are input into the generator to obtain fake samples and mixed samples, respectively. The feature representations of the two in the discriminator are then extracted. Calculate the back contrast loss on the discriminator side. ; Weighted sum of adversarial loss and inverse comparison loss Update the discriminator using the backpropagation algorithm parameter; S4024, Fixed Discriminator Parameters, enable generator Gradient calculation is performed to prepare for training the generator; S4025. Introducing an innovative mechanism to optimize the generator: resampling the noise vector z to generate fake samples. The generator is used to calculate the adversarial loss; simultaneously, a mixed noise is generated again using the Dirichlet distribution, and the generator is used to obtain mixed samples; the feature maps of the generator's intermediate hidden layers for the fake samples and mixed samples are extracted respectively. Calculate the inverse contrast loss on the generator side. ; The adversarial loss and the generator-side inverse contrast loss are weighted and fused together to form the generator's overall objective function. The generator parameters are updated using the backpropagation algorithm; S4026. Repeat S4021-S4025 for iterative training, calculating the coefficient of determination using the TabPFN model every preset number of rounds. The generated data is evaluated using the SDMetrics statistical similarity index. If the overall score meets the early stopping condition, the training is terminated and the optimal model parameters are saved.

[0014] Preferably, the specific content of S5 is as follows: S501. Using the Column Pair Trends module in Python's SDMetrics toolkit, calculate the correlation coefficients between each feature column in the generated data and the correlation coefficients between the generated data and the real training data, and evaluate the consistency of the correlation coefficient matrix. S502. Mix the generated synthetic data with the original training data to construct an enhanced training set, input it into the TabPFN model for training, and validate it on the original test set, calculating the coefficient of determination. ; S503, Constructing the final comprehensive evaluation score function of the model The expression is as follows: ; In the formula, Data generation and training data are processed The library calculates the value of the correlation matrix of the feature columns of the two. for Weight parameters; for Weighting parameters for the evaluation results.

[0015] Therefore, the present invention employs the above-mentioned improved GAN-based EUR prediction method for volumetric fractured wells, which has the following beneficial effects: (1) Construct a single negative sample-multiple positive sample back comparison learning mechanism based on Dirichlet mixed latent variables, the relationship between positive and negative samples is determined by whether the mixed noise contains the target latent variable component; (2) Constructing a reverse contrast loss, which improves the quality of the data generated by the model by bringing the features extracted by the model between positive samples closer to the features extracted by the model between positive and negative samples, thereby improving the EUR prediction effect; (3) The prediction fit was significantly improved in the actual test, and SDMetrics and R 2 The indicators are all superior to traditional methods, and can accurately capture the impact of key fracturing parameters on EUR, providing accurate basis for the capacity assessment of volumetric fracturing wells and the optimization of development plans, and helping to improve resource extraction efficiency and economic benefits.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a flowchart of an improved GAN-based method for predicting EUR in volumetric fractured wells according to the present invention. Figure 2 The fitting effect after generating data from the original GAN; Figure 3 The figure shows the fitting effect after the data is generated by GAN. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0019] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0020] The following is combined Figures 1-3 The embodiments of the present invention will be described in detail below.

[0021] Example 1 A method for predicting EUR in volumetric fractured wells based on an improved GAN includes the following steps: S1. Data Acquisition and Preprocessing Stage: Construct the target tabular dataset, perform quality screening and cleaning on the raw data; In view of the long-tail characteristics of the data distribution, use logarithmic transformation to process the skewed features and standardize the data to construct a training sample set suitable for neural network input; S101. Perform feature distribution detection and transformation on the original data; Traverse all feature columns of the dataset, calculate skewness and numerical range, and perform transformations on long-tailed distribution columns with skewness greater than a preset threshold (e.g., 2.0) and large numerical range to compress the numerical range and make it closer to a normal distribution, thereby reducing the difficulty of model learning. S102. Standardize the raw data processed in S201. The Z-Score normalization method is used to map the processed original data to a distribution space with a mean of 0 and a variance of 1, as shown in the following expression: ; In the formula, These are the standardized values; This is the original input; The mean of the sample; Standard deviation; It also records the metadata of the integer column so that it can be rounded down after generation.

[0022] S2. Construct a generative adversarial network model; construct a generative adversarial network model containing a generator and a discriminator; the generator adopts a structure combining batch normalization and ReLU activation function to stabilize feature output; the discriminator adopts a structure in which fully connected layers are directly mapped to the ReLU activation function.

[0023] The generator receives dimensions as follows: The noise vector is stacked through multiple linear layers, one-dimensional batch normalization, and ReLU activation function to output a synthetic sample with the same dimension as the real data. The discriminator receives sample data, extracts high-dimensional feature vectors through multiple linear layers and ReLU activation function, and outputs the true and false probabilities through the Sigmoid function. Define the discriminator adversarial loss function To maximize the confidence score of the generated samples and minimize the confidence score of the real samples, the expression is as follows: ; In the formula, This represents the actual distribution of tabular data. For potential spatial noise distribution; This is the expectation operator for sampling the real data distribution; For sampling the expectation operator of the noise distribution; This is the output of the generator; Define the generator adversarial loss function Generate synthetic samples that maximize the deception of the discriminator, as shown in the following expression: ; Through the aforementioned adversarial loss, the discriminator minimizes... To improve its discriminative ability, the generator minimizes... To enhance its generation capabilities, the two processes alternately optimize during training, forming an adversarial game. As training progresses, the generator gradually approximates the distribution characteristics of real tabular data, providing the foundational generation capabilities for subsequent introduction of Dirichlet mixture noise and inverse contrastive learning.

[0024] S3. Introducing Dirichlet Mixed Noise and Reverse Comparison Loss; this is the core step of this invention. During the training iteration, a Dirichlet distribution is introduced to mix and sample the input random noise vector, generating mixed latent variables. The reverse comparison loss (RCL Loss) is then calculated based on the features of the generated samples and the mixed samples. This reverse comparison loss does not change the optimization objective of the contrastive learning method, but rather is relative to the traditional contrastive learning method based on sample instance consistency. Specifically, samples generated from a single latent variable are used as anchor samples. Generated samples containing the latent variable component in the mixed latent variable are considered positive samples, while generated samples deliberately excluding the latent variable component are considered negative samples. By guiding the model to narrow the distance between the anchor samples and positive samples and widen the distance between the anchor samples and negative samples in the feature space, potential feature correlation information between samples is mined. This fully utilizes the semantic structural features in the limited fracturing data, improving the model's robustness and EUR prediction adaptability in small sample scenarios.

[0025] S301. Generating mixed noise based on Dirichlet distribution; Define the latent spatial noise set of the input generator. ; Let the batch size for training be... The potential vector dimension is ,but Indicated by The set sequence consisting of independently sampled random noise vectors is expressed as follows: ; In the formula, each All samples were taken from the standard normal distribution. ; For each noise ,exclude All other vectors of itself Assign weights, as expressed below: ; In the formula, It is a dimension of A vector of all 1s, controlling the sparsity or smoothness of the weights; For the concentration parameters of the Dirichlet distribution; For the first The first mixed noise corresponds to the first The noise coefficient satisfies And the coefficient is greater than 0; For each index The sampled coefficients are used to perform a weighted summation of all original vectors except the vector itself to obtain the constrained vector, as shown in the following expression: ; in For the corresponding Mixed noise; It is the original vector excluding itself; Mixed noise Not including the original noise vector The components, together, constitute a pair of negative samples, mixing noise. Includes raw noise The two components have certain similarities in spatial semantics and can be used as positive samples. All The new set of potential vectors is formed as follows: .

[0026] S302. Calculate the inverse comparison loss based on the features of the generated samples and the features of the mixed samples.

[0027] To improve the fitting effect, a contrastive learning approach is introduced; within the same batch, samples are generated... Its corresponding mixed samples and The feature representation in the feature extraction layer is used as a contrast unit; The generated noise The feature representation calculated at the l-th layer after inputting the generator is denoted as follows. Among them Constitute negative samples Forming positive sample pairs; The generated sample The feature representation computed by the l-th layer of the input discriminator is denoted as: ,by To form negative sample pairs, Construct positive samples, and then calculate the back-contrast loss for each of them. The expression is as follows: ; In the formula, Cosine similarity; Temperature coefficient; It is a natural exponential function. This loss function forces the model to bring the source noise closer to the sample features generated by its corresponding mixed noise, and to distance it from the sample features generated by other irrelevant noise. It acts on the generator feature space or the discriminator feature space at different training stages according to the optimization objective.

[0028] S4. Adversarial training of the model with multi-loss fusion: Define a comprehensive objective function that includes adversarial loss and back contrast loss, and train the discriminator and generator using an alternating optimization strategy; The discriminator is used to distinguish between real samples and generated samples in adversarial training, and a back contrast constraint is introduced in the feature space to strengthen the consistency of the generated samples and mixed samples in terms of feature structure. The generator aims to deceive the discriminator while minimizing the back contrast loss to ensure the structural fidelity of the generated data.

[0029] S401. Construct the discriminator loss function and the generator loss function; During the discriminator update phase, the discriminator's optimization objective consists of two parts: the discriminator adversarial loss defined in S2 above. Used to distinguish between real samples and generated samples; based on the reverse contrast loss defined in S302. Its input features are derived from the discriminator's feature representations of generated samples and mixed samples. The discriminator loss function is constructed. The expression is as follows: ; In the formula, Hyperparameters used to balance the contributions of the discriminator's adversarial loss and contrastive learning loss to the total loss; During the generator update phase, the generator's optimization objective also consists of two parts: the generator adversarial loss defined in S2 above and the reverse contrast loss defined in S302. Its feature input comes from the feature representations of generated and mixed samples in the generator's intermediate layer, constructing the generator loss function. The expression is as follows: ; In the formula, Hyperparameters used to balance the contributions of generator adversarial loss and contrastive learning loss to the total loss.

[0030] This dual contrast constraint ensures that the generated data not only closely approximates the real data in terms of statistical distribution, but also accurately captures and restores the semantic relationships between the real data.

[0031] S402. The discriminator and generator are trained using an alternating iterative strategy.

[0032] S4021, Fixed Generator The parameters enable the discriminator. Gradient calculation is performed to prepare for training the discriminator; S4022. Input the preprocessed real table data samples into the discriminator and calculate the discrimination loss for the real samples; sample random noise vectors from the standard normal distribution, obtain fake samples through the generator, and input them into the discriminator to calculate the discrimination loss for the fake samples; S4023, Using Dirichlet distribution on noise vectors Mixed sampling yields mixed noise. The generated noise and mixed noise are input into the generator to obtain fake samples and mixed samples, respectively. The feature representations of the two in the discriminator are then extracted. Calculate the back contrast loss on the discriminator side. ; Weighted sum of adversarial loss and inverse comparison loss Update the discriminator using the backpropagation algorithm parameter; S4024, Fixed Discriminator Parameters, enable generator Gradient calculation is performed to prepare for training the generator; S4025. Introducing an innovative mechanism to optimize the generator: resampling the noise vector z to generate fake samples. The generator is used to calculate the adversarial loss; simultaneously, a mixed noise is generated again using the Dirichlet distribution, and the generator is used to obtain mixed samples; the feature maps of the generator's intermediate hidden layers for the fake samples and mixed samples are extracted respectively. Calculate the inverse contrast loss on the generator side. ; The adversarial loss and the generator-side inverse contrast loss are weighted and fused together to form the generator's overall objective function. The generator parameters are updated using the backpropagation algorithm; S4026. Repeat S4021-S4025 for iterative training, calculating the coefficient of determination using the TabPFN model every preset number of rounds. The generated data is evaluated using the SDMetrics statistical similarity index. If the overall score meets the early stopping condition, the training is terminated and the optimal model parameters are saved.

[0033] S5. Data Generation and Model Evaluation: During training, data is periodically sampled and generated, then de-standardized and inversely transformed to restore it to the original numerical space. The TabPFN regression model, known for its excellent performance with small samples, and statistical similarity (SDMetrics) are introduced as evaluation metrics. TabPFN provides the coefficient of determination (R²), and SDMetrics provides the scoring metrics. An early stopping mechanism is incorporated: training terminates when the overall score no longer improves within a preset number of rounds, and the parameters of the model with the highest score are backtracked and saved.

[0034] S501. Using the Column Pair Trends module in Python's SDMetrics toolkit, calculate the correlation coefficients between each feature column in the generated data and the correlation coefficients between the generated data and the real training data, and evaluate the consistency of the correlation coefficient matrix. S502. Considering that the purpose of this GAN data generation is to help improve the fitting accuracy of the TabPFN model, the generated synthetic data is mixed with the original training data to construct an enhanced training set, which is then input into the TabPFN model for training. The model is then validated on the original test set, and the coefficient of determination is calculated. As another key indicator; S503, Constructing the final comprehensive evaluation score function of the model The expression is as follows: ; In the formula, Data generation and training data are processed The library calculates the value of the correlation matrix of the feature columns of the two. for Weight parameters; for Weighting parameters for the evaluation results.

[0035] Example 2 Reference Figure 1 This invention provides a method for predicting EUR (Earning Equivalent to Fluid Volume) in volumetric fractured wells based on an improved GAN. This method comprises five main stages: data acquisition and preprocessing, construction of a generative adversarial network (GAN), introduction of Dirichlet hybrid noise and inverse contrast loss, multi-loss fusion model adversarial training, data generation, and model evaluation and application. The specific implementation details of each stage are as follows: 1. Data Acquisition and Preprocessing Stage: The data comes from field production data of volumetric fracturing wells in a shale gas development block in the Sichuan Basin. These data are all engineering parameters directly collected on-site during fracturing operations and do not include additional geological exploration-derived parameters. A total of 127 complete construction examples of volumetric fracturing horizontal wells were collected from the field. Twenty fracturing construction parameters were identified as key feature columns, covering core parameters such as the number of fracturing stages, cluster number, cluster spacing, stage length, displacement, test length, acid intensity, slickwater intensity, linear gel intensity, and pumped fluid intensity. Using EUR (Effective Urgent Flow Rate) as the target indicator, a complete system was constructed from field volumetric fracturing well data to EUR prediction. The entire research was based entirely on actual construction data.

[0036] During on-site construction, some parameters (such as pumping fluid volume intensity and discharge rate) exhibited significant long-tail distributions due to differences in geological conditions (e.g., some wells required an unconventional increase in fluid volume due to dense reservoirs). For missing values ​​in the data, samples with more than 5% of missing feature columns were directly removed; samples with fewer than 5% missing columns were filled using the median of the same feature column. Ultimately, 112 high-quality samples were retained for subsequent processing.

[0037] The algorithm iterates through all feature columns, calculating the skewness and numerical range for each column. A skewness threshold of 2.0 is set. For columns with a skewness greater than 2.0 and a numerical range exceeding 100, a log1p transformation (formula: x = log(x + 1)) is performed to compress the numerical range and bring it closer to a normal distribution, reducing the learning difficulty of the model. Z-Score normalization is then used to normalize all numerical features, mapping the data to a distribution space with a mean of 0 and a variance of 1. The normalization formula is... ,in The sample mean. The standard deviation is used. Integer column detection functions are used to identify feature columns that are primarily integers (number of fracturing clusters, number of segments, segment length, etc.), and metadata information for these columns is recorded to provide a basis for subsequent reverse rounding processing of generated data.

[0038] The 112 preprocessed samples were divided into a training set (89 sets) and a test set (23 sets) in an 8:2 ratio. The training set was used for adversarial training of the GAN model, and the test set was used to evaluate the quality of the generated data. To verify the fitting potential of the original data, a machine learning model (random forest regression) and a neural network model (TabPFN) were first used to perform regression fitting verification on the original data. The TabPFN model is based on few-shot learning characteristics and is a pre-trained regression model for small-sample tabular data; its network structure has been validated in relevant published literature. Finally, R on the test set... 2 The score is 0.795, which is the best.

[0039] 2. Construct a generative adversarial network model: The generator receives a 100-dimensional random noise vector (sampled from a standard normal distribution N(0,1)) and uses a stacked structure of linear layers + batch normalization + ReLU. The input layer receives a 100-dimensional noise vector, and the output dimension is the same as the first hidden layer. The hidden layer uses a (256,128,64) neuron configuration, with a total of 3 linear layers. Each layer is followed by a BatchNorm1d batch normalization layer (momentum parameter set to 0.9) and a ReLU activation function to stabilize feature output and alleviate the gradient vanishing problem. The output layer is a linear layer with the same number of features as the original data (21 dimensions). It has no activation function and directly outputs the standardized synthetic sample features.

[0040] The discriminator employs a direct mapping structure of a fully connected layer + ReLU, without introducing a batch normalization layer to preserve the original distribution information of the features. The input layer receives 21-dimensional sample features (real or generated samples), and the output dimension is consistent with the first hidden layer. The hidden layer uses a neuron configuration of (256, 128, 64), consisting of three linear layers. Each layer is followed by a ReLU activation function to extract high-dimensional discriminative features. The output layer is a linear layer with one neuron, followed by a Sigmoid activation function, outputting the probability that the sample is real data (range 0-1).

[0041] 3. Introduce Dirichlet mixed noise and inverse contrast loss: In each round of training, the batch size is set to 32, and 32 100-dimensional noise vectors are independently sampled from the standard normal distribution N(0,1) to form the basic noise set. Sampling the mixing coefficient matrix from the Dirichlet distribution The concentration parameter (Dirichlet Alpha) of this distribution is set to 1.0, and the generated mixing coefficient matrix has a dimension of 32×32, with diagonal elements padded with 0 (to avoid self-mixing) to ensure the diversity of mixed noise. First, through the formula... Generation coefficient Subsequently, the mixed noise was calculated, generating 32 mixed latent variables with the same dimensions as the base noise. .

[0042] Randomly select either the hidden layer in the generator or the discriminator as the feature extraction layer to obtain the feature representation of the generated samples from the base noise, respectively. (where l represents the feature representation of the sample generated by the mixed noise in the l-th layer) Within the same batch, with Construct positive sample pairs; Its corresponding Negative sample pairs are constructed. Then, the positive and negative sample pairs are substituted into the back-contrast loss expression to calculate the back-contrast loss. This loss forces the model to narrow the feature distance of positive sample pairs and widen the feature distance of negative sample pairs, thereby improving the structural fidelity of the generated data.

[0043] 4. Adversarial training of models using multi-loss fusion: (1) Training parameter configuration: The total number of training epochs is set to 1000, the batch size is 32, the generator learning rate is 5e-4, the discriminator learning rate is 2e-4, and the optimizer uses the Adam algorithm. The momentum parameter is set to... =0.5、 =0.99. Back-comparison loss weights of the generator. =0.5, the back-comparison loss weight of the discriminator =0.5, used to balance the optimization priority of adversarial loss and inverse contrast loss.

[0044] (2) Alternating combat training process: Building upon the Dirichlet mixture latent variables and reverse contrastive loss introduced in S3, this invention employs an alternating adversarial training strategy to jointly optimize the discriminator and generator. Let the generator be G and the discriminator be D.

[0045] ① Discriminator training phase: In each training iteration, the generator parameters are fixed first, and the discriminator is updated.

[0046] Sample real data from the real data distribution. And sample noise vectors from the potential noise distribution. , Simultaneously, mixed latent variables are generated according to the method described in S3. .Will and The generated samples and mixed samples obtained by inputting them into the generator are represented as follows: , Then, the real sample x and the fake sample x were compared. Input the discriminator adversarial loss expression to calculate the discriminator adversarial loss. Building upon this, a reverse contrastive loss is introduced to regularize the discriminator's feature space. Specifically, feature representations of generated samples and mixed samples are extracted from the discriminator: ,in Indicates the i-th generated sample In the discriminator Features extracted from layers, This indicates that the i-th generated mixed sample In the discriminator Features extracted from layers. As anchor features, the corresponding original generated features Treating all features within a batch as the only negative sample and the rest as positive samples, we substitute these features into the inverse contrast loss expression to calculate the loss. ,Will , Hyperparameters Substituting 0.5 into the discriminator loss expression, we calculate the total discriminator loss. Then, we update the discriminator parameters based on backpropagation.

[0047] ② Generator training phase: After completing the discriminator update, fix the discriminator parameters and update the generator.

[0048] Sample noise vectors from the potential noise distribution. , Similarly, a mixed sample is generated based on S3. ,Will and After merging, the generator adversarial loss is calculated based on the generator adversarial loss expression. To enhance the structural consistency of generated samples across multiple feature spaces, a layer is randomly selected from multiple intermediate feature layers of the generator or discriminator, and the generated sample features and mixed sample features of the corresponding layer are extracted. ,in This indicates that the i-th noise z is in the generator at the i-th position. Features extracted from layers, Then it represents the i-th mixed noise. In the generator Features extracted from layers. As anchor features, the corresponding original generated features Treating all features within a batch as the only negative sample and the rest as positive samples, we substitute these features into the inverse contrast loss expression to calculate the generator contrast loss. ,Will , Hyperparameters Substituting 0.5 into the discriminator loss expression, we calculate the generator's total loss. Then, we update the generator parameters based on backpropagation.

[0049] 5. Data Generation and Model Evaluation: During the iterative training of the model adversarial training, a comprehensive quality assessment is performed on the synthetic data (500 data points) generated by the generator every 50 epochs (iteration rounds). To ensure that the assessment results reflect both the statistical authenticity of the data and its practical value in downstream regression tasks, the system monitors the comprehensive score in real time. If the comprehensive score does not increase within three consecutive assessment periods (i.e., three consecutive 50-epoch intervals), an early stopping mechanism is triggered, automatically ending the training and backtracking to save the model parameters at the moment with the highest comprehensive score in the historical record.

[0050] like Figure 2 As shown, this experimental group did not introduce reverse contrast loss and kept other parameters consistent; the model was trained solely on the basic adversarial loss. The generated fracturing data failed to fully reflect the actual field engineering situation and could not accurately reproduce the engineering correlation logic between construction parameters such as the number of fracturing segments, cluster spacing, and pumping fluid intensity and EUR (Earnings Evidence). The 500 generated data points and the original data were evaluated using SDMetrics (a Python library function) to assess the correlation coefficient matrix between the feature parameters of the original data and the generated data. The final evaluation results were: SDMetrics (column-pair trend) score 0.8251 (reflecting the consistency of parameter correlation between the generated data and the actual field fracturing data), and the coefficient of determination (R²) for EUR prediction... 2 0.853 (reflecting the fitting accuracy between the EUR predicted value and the actual measured value), in this experiment and All scores are 0.5. Based on the final comprehensive evaluation score expression, the comprehensive score is calculated to be 0.8391.

[0051] like Figure 3 As shown, this experimental group adopted the improved strategy proposed in this invention. While maintaining consistent basic model parameters, it introduced a reverse comparison loss and set the weight coefficients of the reverse comparison loss for both the generator and discriminator to 0.5. This strategy strengthens the constraint on the correlation between fracturing operation parameters and EUR (Earnings Evidence) characteristics. The generated data not only statistically closely matches the actual fracturing operation data from the Sichuan Basin shale gas field, but also more accurately captures the engineering impact of core operation parameters such as displacement and acid intensity on EUR, adapting to the EUR prediction needs of small-sample fracturing data from the field. The model generation quality and engineering practicality are significantly improved. The 500 generated data points and the original data were evaluated using SDMetrics (a Python library function) to assess the correlation coefficient matrix between the feature parameters of the original data and the correlation coefficient matrix between the feature parameters of the generated data. The final evaluation results show that the SDMetrics (feature column trend) score reached 0.8743, and the coefficient of determination (R²) for EUR prediction was [missing information]. 2 The value was increased to 0.906 in this experiment. and All scores are 0.5. Based on the final comprehensive evaluation score expression, the comprehensive score is calculated to be 0.8902.

[0052] In summary, compared to the scheme that does not introduce reverse contrast loss ( Figure 2 ), Improvement strategy of this invention ( Figure 3 The SDMetrics index improved by approximately 0.0492 (reflecting a significant improvement in the engineering fit between the generated data and the field fracturing data), and the EUR predicted R 2 The indicator improved by approximately 0.053 (meaning a significant improvement in the fitting accuracy between the EUR prediction and the actual field measurement), and the overall score improved by approximately 0.0511. This fully verifies that the innovative design of this invention, through Dirichlet hybrid noise and inverse correlation loss, can ensure the consistency of parameter correlation between the generated data and the actual field fracturing data in small-sample engineering scenarios of shale oil and gas volumetric fracturing, while also significantly improving the accuracy of EUR prediction, providing more reliable technical support for field fracturing scheme optimization, single-well production capacity assessment, and development benefit calculation.

[0053] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting EUR in volumetric fractured wells based on an improved GAN, characterized in that, Includes the following steps: S1. Construct the target tabular dataset, perform quality screening and cleaning on the original data; use logarithmic transformation to process skewed features and standardize the data to construct a training sample set suitable for neural network input; S2. Construct a generative adversarial network model that includes a generator and a discriminator; S3. Introduce the Dirichlet distribution to perform mixed sampling on the input random noise vector to generate mixed latent variables, and calculate the inverse contrast loss based on the generated sample features and the mixed sample features. S4. Define a comprehensive objective function that includes adversarial loss and reverse contrast loss, and train the discriminator and generator using an alternating optimization strategy; S5. Data is generated through periodic sampling, and then restored to the original numerical space through inverse standardization and inverse transformation. The TabPFN regression model, which has excellent performance in small samples, and statistical similarity are introduced as evaluation indicators. Combined with an early stopping mechanism, the model parameters with the highest scores are backtracked and saved.

2. The method for predicting EUR in volumetric fractured wells based on an improved GAN according to claim 1, characterized in that, The specific content of S1 is as follows: S101. Perform feature distribution detection and transformation on the original data; Traverse all feature columns of the dataset, calculate skewness and numerical range, and perform transformation on long-tailed distribution columns with skewness greater than a preset threshold and large numerical range. S102. Standardize the raw data processed in S201. The Z-Score normalization method is used to map the processed original data to a distribution space with a mean of 0 and a variance of 1, as shown in the following expression: ； In the formula, These are the standardized values; This is the original input; The mean of the sample; Standard deviation; It also records the metadata of integer columns.

3. The EUR prediction method for volumetric fractured wells based on an improved GAN according to claim 2, characterized in that, The specific details of S2 are as follows: The generator receives dimensions as follows: The noise vector is stacked through multiple linear layers, one-dimensional batch normalization, and ReLU activation function to output a synthetic sample with the same dimension as the real data. The discriminator receives sample data, extracts high-dimensional feature vectors through multiple linear layers and ReLU activation function, and outputs the true and false probabilities through the Sigmoid function. Define the discriminator adversarial loss function To maximize the confidence score of the generated samples and minimize the confidence score of the real samples, the expression is as follows: ； In the formula, This represents the actual distribution of tabular data. For potential spatial noise distribution; This is the expectation operator for sampling the real data distribution; For sampling the expectation operator of the noise distribution; This is the output of the generator; Define the generator adversarial loss function Generate synthetic samples that maximize the deception of the discriminator, as shown in the following expression: 。 4. The EUR prediction method for volumetric fractured wells based on an improved GAN according to claim 3, characterized in that, S3 specifically includes: S301. Generating mixed noise based on Dirichlet distribution; S302. Calculate the inverse comparison loss based on the features of the generated samples and the features of the mixed samples.

5. The EUR prediction method for volumetric fractured wells based on an improved GAN according to claim 4, characterized in that, The specific details of generating mixed noise based on the Dirichlet distribution in S301 are as follows: Define the latent spatial noise set of the input generator. ; Let the batch size for training be... The potential vector dimension is ,but Indicated by The set sequence consisting of independently sampled random noise vectors is expressed as follows: ； In the formula, each All samples were taken from the standard normal distribution. ; For each noise ,exclude All other vectors of itself Assign weights, as expressed below: ； In the formula, It is a dimension of A vector of all 1s; For the concentration parameters of the Dirichlet distribution; For the first The first mixed noise corresponds to the first The noise coefficient satisfies And the coefficient is greater than 0; For each index The sampled coefficients are used to perform a weighted summation of all original vectors except the vector itself to obtain the constrained vector, as shown in the following expression: ； In the formula, For the corresponding Mixed noise; It is the original vector excluding itself; Mixed noise Not including the original noise vector The components, together, constitute a pair of negative samples, mixing noise. Includes raw noise The two components have certain similarities in spatial semantics and can be used as positive samples. All The new set of potential vectors is formed as follows: 。 6. The EUR prediction method for volumetric fractured wells based on an improved GAN according to claim 4, characterized in that, The specific details of calculating the reverse contrast loss based on generated sample features and mixed sample features in S302 are as follows: Introducing the concept of contrastive learning; generating samples within the same batch. Its corresponding mixed samples and The feature representation in the feature extraction layer is used as a contrast unit; The generated noise The feature representation calculated at the l-th layer after inputting the generator is denoted as follows. Among them Constitute negative samples Forming positive sample pairs; The generated sample The feature representation computed by the l-th layer of the input discriminator is denoted as: ,by To form negative sample pairs, Construct positive samples, and then calculate the back-contrast loss for each of them. The expression is as follows: ； In the formula, Cosine similarity; Temperature coefficient; It is a natural exponential function.

7. The EUR prediction method for volumetric fractured wells based on an improved GAN according to claim 6, characterized in that, S4 specifically includes: S401. Construct the discriminator loss function and the generator loss function; S402. The discriminator and generator are trained using an alternating iterative strategy.

8. The method for predicting EUR in volumetric fractured wells based on an improved GAN according to claim 7, characterized in that, The specific details of constructing the discriminator loss function and generator loss function in S401 are as follows: Adversarial loss based on the discriminator defined in S2 Inverse contrast loss with the discriminator defined in S302 Construct the discriminator loss function The expression is as follows: ； In the formula, Hyperparameters used to balance the contributions of the discriminator's adversarial loss and contrastive learning loss to the total loss; Generator-based adversarial loss defined in S2 Inverse comparison loss with the generator defined in S302 Construct the generator loss function The expression is as follows: ； In the formula, Hyperparameters used to balance the contributions of generator adversarial loss and contrastive learning loss to the total loss.

9. The volumetric fracturing well EUR prediction method based on an improved GAN according to claim 7, characterized in that, The specific details of training the discriminator and generator using an alternating iterative strategy in S402 are as follows: S4021, Fixed Generator The parameters enable the discriminator. Gradient calculation is performed to prepare for training the discriminator; S4022. Input the preprocessed real table data sample into the discriminator and calculate the discrimination loss for the real sample; Random noise vectors are sampled from a standard normal distribution, fake samples are obtained through a generator, and the samples are input into a discriminator to calculate the discrimination loss for the fake samples; S4023, Using Dirichlet distribution on noise vectors Mixed sampling yields mixed noise. The generated noise and mixed noise are input into the generator to obtain fake samples and mixed samples, respectively. The feature representations of the two in the discriminator are then extracted. Calculate the back contrast loss on the discriminator side. ; Weighted sum of adversarial loss and inverse comparison loss Update the discriminator using the backpropagation algorithm parameter; S4024, Fixed Discriminator Parameters, enable generator Gradient calculation is performed to prepare for training the generator; S4025. Introducing an innovative mechanism to optimize the generator: resampling the noise vector z to generate fake samples. The generator is used to calculate the adversarial loss; simultaneously, a mixed noise is generated again using the Dirichlet distribution, and the generator is used to obtain mixed samples; the feature maps of the generator's intermediate hidden layers for the fake samples and mixed samples are extracted respectively. Calculate the inverse contrast loss on the generator side. ; The adversarial loss and the generator-side inverse contrast loss are weighted and fused together to form the generator's overall objective function. The generator parameters are updated using the backpropagation algorithm; S4026. Repeat S4021-S4025 for iterative training, calculating the coefficient of determination using the TabPFN model every preset number of rounds. The generated data is evaluated using the SDMetrics statistical similarity index. If the overall score meets the early stopping condition, the training is terminated and the optimal model parameters are saved.

10. The method for predicting EUR in volumetric fractured wells based on an improved GAN according to claim 9, characterized in that, The specific details of S5 are as follows: S501. Using the Column Pair Trends module in Python's SDMetrics toolkit, calculate the correlation coefficients between each feature column in the generated data and the correlation coefficients between the generated data and the real training data, and evaluate the consistency of the correlation coefficient matrix. S502. Mix the generated synthetic data with the original training data to construct an enhanced training set, input it into the TabPFN model for training, and validate it on the original test set, calculating the coefficient of determination. ; S503, Constructing the final comprehensive evaluation score function of the model The expression is as follows: ； In the formula, Data generation and training data are processed The library calculates the value of the correlation matrix of the feature columns of the two. for Weight parameters; for Weighting parameters for the evaluation results.

Images