A method for predicting remaining oil saturation based on a seepage mechanism-constrained proxy model

Abstract

The present invention provides a method for predicting residual oil saturation based on a seepage mechanism-constrained proxy model, relating to the field of reservoir development technology. The method specifically includes the following steps: using a reservoir numerical simulator to generate a water saturation field dataset for an oil-water two-phase system, and dividing it into a training set and a test set; constructing an end-to-end proxy model based on a three-dimensional convolutional neural network and an informer; training the end-to-end proxy model using the training set under seepage mechanism constraints; and inputting the test set into the trained end-to-end proxy model to obtain a water saturation field prediction result, and plotting an image representing the residual oil saturation distribution. The technical solution of the present invention overcomes the problems of high model computational complexity and low prediction accuracy in the prior art.

Description

Technical Field

[0001] The present invention relates to the field of oil reservoir development, and in particular to a method for predicting residual oil saturation based on a seepage mechanism constraint proxy model. Background Art

[0002] With the continued advancement of waterflooding, most oil reservoirs in my country have entered the high-water-cut development phase. Due to the strong heterogeneity of the underground reservoir, approximately 65% of the crude oil remains after development, representing residual oil. This demonstrates that high-water-cut oilfields still hold significant development potential. Therefore, understanding the distribution of residual oil saturation in reservoirs is crucial for assessing reservoir development potential and formulating and adjusting development strategies.

[0003] A surrogate model is a mathematical model that simulates the behavior of a complex system in a forward fashion, aiming to simplify the original system for subsequent processing. In the field of reservoir development, existing neural network surrogate model studies often target reservoir scenarios in two dimensions, or flatten a three-dimensional plane into a two-dimensional plane for input into the network. This approach neglects the spatial structure of the reservoir, such as complex geological features such as inter- and intra-layer heterogeneity, faults, and inactive grids. The interactions and influences between different layers are difficult to visualize in a two-dimensional unfolded model, resulting in the neural network's inability to accurately capture the reservoir's spatial distribution characteristics and the complexity of fluid flow. Furthermore, entirely data-driven surrogate models lack the support of reservoir development laws and seepage mechanisms, making the model's internal decision-making process difficult to understand and explain. This overreliance on data quality makes the model's prediction accuracy susceptible to data noise, missing data, and bias, limiting its application in critical decision-making scenarios. Furthermore, surrogate models based on recurrent neural networks rely on inferring current predictions based on previous predictions, making parallel computation difficult and resulting in high resource consumption when processing large-scale reservoir scenarios.

[0004] Therefore, there is a need for a method to predict the remaining oil saturation in water-flooded reservoirs that can effectively reduce the computational complexity, introduce the reservoir seepage mechanism, and improve the model prediction accuracy. Summary of the Invention

[0005] The main purpose of the present invention is to provide a method for predicting residual oil saturation based on a seepage mechanism constraint proxy model to solve the problems of high model calculation complexity and low prediction accuracy in the prior art.

[0006] To achieve the above objectives, the present invention provides a method for predicting remaining oil saturation based on a seepage mechanism constraint proxy model, which specifically includes the following steps:

[0007] S1, using a reservoir numerical simulator to generate a water saturation field dataset for the oil-water two-phase system, and divide it into a training set and a test set.

[0008] S2, builds an end-to-end proxy model based on 3D convolutional neural network and Informer.

[0009] S3, under the constraints of the percolation mechanism, uses the training set to train the end-to-end proxy model.

[0010] In step S4, the test set is input into the trained end-to-end proxy model to obtain the water saturation field prediction results and draw an image to represent the remaining oil saturation distribution.

[0011] Furthermore, step S2 specifically includes the following steps:

[0012] S2.1, 3D image features of time steps Input to the input layer, then input to the convolution layer and pooling layer to obtain features:

[0013] ;

[0014] in, Represents depth, height, width, and number of input channels respectively. Indicates that the feature is at position ( ) and output channels The value of Indicates that the input data is at position ( ) and input channels The value of Indicates that the convolution kernel is at position ( ), input channel and output channels The value of Represents the activation function, max Indicates taking the maximum value of all elements in the pooling window.

[0015] S2.2, features are obtained after passing the batch normalization layer:

[0016] ;

[0017] in, Indicates that the output feature after batch normalization is at position ( ) and output channels The value of and Respectively represent the output channels calculated in the current batch The mean and variance of and Respectively represent the output channels The scaling and translation parameters.

[0018] S2.3, expand the output features of the batch normalization layer to obtain )-dimensional sequence features, where Represent the depth, height, and width of the output features, respectively, which are determined by the input size, convolution kernel size, stride, and padding:

[0019] ;

[0020] ;

[0021] ;

[0022] in, Represents the filling amount in depth, height and width directions respectively, Represents the stride of the convolution kernel or pooling window in three dimensions respectively.

[0023] Furthermore, step S2 further includes the following steps:

[0024] S2.4, intercept sequence features, and The sequence features of time steps are masked and input into the encoder, where :

[0025] ;

[0026] in, represents the tensor that is input to the encoder after applying the mask, represents element-wise multiplication, Represents A matrix of all ones with the same shape.

[0027] S2.5, the multi-head probabilistic sparse self-attention mechanism in the encoder calculates the input features.

[0028] S2.6, after The feature sequence of time steps is masked, where :

[0029] ;

[0030] in, represents the tensor input to the decoder after applying the mask, Represents a matrix whose elements are either 0 or 1.

[0031] S2.7, the output features of the encoder are combined with the masked The features of each time step are input to the decoder at the same time and calculated using the multi-head probabilistic sparse self-attention mechanism:

[0032] ;

[0033] in, Output features for the decoder, ( ) represents the multi-head probabilistic sparse self-attention mechanism, Indicates calculation of L2 norm.

[0034] S2.8, the decoder output features pass through the fully connected layer to obtain the predicted image.

[0035] Furthermore, step S2.5 specifically includes the following steps:

[0036] S2.5.1, Input Through the weight matrix Convert to query, key, value matrix 、 、 :

[0037] ;

[0038] ;

[0039] .

[0040] S2.5.2, 、 、 Divide Each head calculates attention independently :

[0041] ;

[0042] in, represents the sparse pattern matrix obtained based on the Kullback-Leibler divergence formula, represents the normalized exponential function, Indicates the dimension of the key.

[0043] The calculation formula is:

[0044] ;

[0045] in, Represents the query matrix No. column vectors, Represents the bond matrix No. The transpose of a row vector, Indicates the length of the key vector.

[0046] S2.5.3, concatenate the outputs of all heads and pass them through the weight matrix Project back to the original dimension:

[0047] ;

[0048] in, Indicates a connection operation. Represents a multi-head attention operation.

[0049] Furthermore, step S3 specifically includes the following steps:

[0050] S3.1, standardize the data in the dataset:

[0051] ;

[0052] in, and represent the mean and standard deviation of the data, respectively. represents the water saturation data before normalization, Indicates the standardized .

[0053] S3.2, Loss Function of End-to-End Proxy Model Due to data loss and seepage mechanism losses The two parts are added together, and the formula is:

[0054] .

[0055] S3.3, using the coefficient of determination Quantitatively evaluate the performance of the end-to-end proxy model:

[0056] ;

[0057] in, represents the total number of samples, and Respectively represent The true value of water saturation of samples and the predicted value of the end-to-end proxy model, Represents the mean of the true values.

[0058] Furthermore, the data loss part is constructed using the mean square error function, which is:

[0059] .

[0060] Furthermore, the seepage mechanism loss is calculated , specifically including the following steps:

[0061] S3.2.1, introduce the Oleinik entropy condition constraint to reconstruct the moisture content prediction formula, and define:

[0062] ;

[0063] in, represents the oil-water front saturation, For Find the derivative.

[0064] The dynamic relationship between water content and water saturation is reconstructed according to the Oleinik entropy condition:

[0065] ;

[0066] ;

[0067] in, The reconstructed moisture content prediction formula is: Indicates the moisture content, Indicates water saturation, represents the bound water saturation, Indicates the residual oil saturation, Represents the oil-water viscosity ratio.

[0068] S3.2.2, use the mean square error function to construct the seepage mechanism loss, the formula is:

[0069] ;

[0070] in, and Respectively represent The samples correspond to the true value of moisture content and the predicted value of the end-to-end proxy model.

[0071] The present invention has the following beneficial effects:

[0072] The present invention incorporates the reservoir seepage mechanism into modeling considerations and integrates a three-dimensional convolutional structure with a probabilistic sparse self-attention mechanism. The three-dimensional convolutional structure is responsible for directly extracting spatial features containing local correlations of the three-dimensional structure from the three-dimensional saturation field; the probabilistic sparse self-attention mechanism is cleverly optimized on the end-to-end proxy model, effectively reducing the computational burden caused by the large number of convolution parameters and the ineffective extraction of inactive grid features in the reservoir. The end-to-end proxy model can output the entire prediction sequence in parallel at one time, overcoming the error accumulation and inefficiency defects of the recursive time series prediction model. The end-to-end proxy model enhances data-driven capabilities by introducing reservoir seepage mechanism constraints, improves the accuracy of reservoir dynamic prediction, enhances the generalization ability of the end-to-end proxy model, and reduces data dependence. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0074] Figure 1 The flowchart of the residual oil saturation prediction method based on the seepage mechanism constraint agent model of the present invention is shown.

[0075] Figure 2 The end-to-end proxy model structure diagram is shown.

[0076] Figure 3 FIG. 4 shows a well location distribution diagram in an embodiment of the present invention.

[0077] Figure 4 A diagram showing the injection and production scheme control details of a three-dimensional conceptual oil reservoir in an embodiment of the present invention is shown.

[0078] Figure 5 The Eclipse calculated water saturation field distribution diagram of the first layer of the three-dimensional conceptual reservoir in an embodiment of the present invention is shown.

[0079] Figure 6 The diagram shows an end-to-end proxy model constrained by the seepage mechanism for predicting the water saturation field distribution of the first layer of a three-dimensional conceptual reservoir in an embodiment of the present invention.

[0080] Figure 7 The absolute error diagram of the water saturation field distribution comparison of the first layer of the three-dimensional conceptual oil reservoir in the embodiment of the present invention is shown.

[0081] Figure 8 The Eclipse calculated water saturation field distribution diagram of the third layer of the three-dimensional conceptual reservoir in an embodiment of the present invention is shown.

[0082] Figure 9 The end-to-end proxy model constrained by the seepage mechanism of the third layer of the three-dimensional conceptual reservoir in the embodiment of the present invention is shown to predict the water saturation field distribution.

[0083] Figure 10 The absolute error diagram of the water saturation field distribution comparison of the third layer of the three-dimensional conceptual oil reservoir in the embodiment of the present invention is shown. DETAILED DESCRIPTION

[0084] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0085] like Figure 1 The remaining oil saturation prediction method based on the seepage mechanism constraint proxy model shown in FIG. includes the following steps:

[0086] S1, using a reservoir numerical simulator to generate a water saturation field dataset for the oil-water two-phase system, and divide it into a training set and a test set.

[0087] S2, builds an end-to-end proxy model based on 3D convolutional neural network and Informer.

[0088] S3, under the constraints of the percolation mechanism, uses the training set to train the end-to-end proxy model.

[0089] In step S4, the test set is input into the trained end-to-end proxy model to obtain the water saturation field prediction results and draw an image to represent the remaining oil saturation distribution.

[0090] The distribution of residual oil saturation is typically determined by water saturation, as the sum of the oil and water saturations in an oil-water two-phase system is 1. Furthermore, reservoir numerical simulators typically directly provide water saturation data when generating training samples. To more efficiently interface with numerical simulators, the present invention employs an end-to-end proxy model to predict the distribution of water saturation, which in turn represents the distribution of residual oil saturation.

[0091] Figure 2 The training process for a single set of samples, spanning N time steps, is demonstrated. To achieve the design requirement of end-to-end prediction, the end-to-end proxy model receives 3D image features, namely, saturation field data for a D×W×H grid. The present invention uses the saturation data from the first n time steps to predict saturation changes over the next Nn time steps.

[0092] First, each N time-step data of the normalized sample is passed through two 3D convolutional layers for position encoding and feature extraction. The stacked convolutional layers adopt a feature pyramid structure, where the resolution of the feature map decreases with increasing network depth, while the number of channels increases. This structure effectively addresses challenges such as variable object shapes and complex backgrounds, providing multi-scale feature information and helping the end-to-end proxy model better learn image details and structure.

[0093] The pooling layer uses the max pooling rule to reduce dimensionality and prevent overfitting, highlighting key features and enhancing the robustness of the end-to-end proxy model to variations in feature position. The features then pass through the Batch Normalization layer to maintain a stable distribution. The resulting sequence features are then truncated and fed into the encoder and decoder, respectively.

[0094] The input of the encoder is the features of the first n time steps. The input of the decoder is divided into two parts, one is the output of the encoder, and the other is the features of the last m time steps, where Note that there is overlap when intercepting, that is, the input sequences of the encoder and decoder overlap. This design is mainly to capture the global dependencies of the sequence and improve the generalization ability of the end-to-end proxy model, so that the end-to-end proxy model can achieve better prediction results when dealing with long time series prediction problems.

[0095] The sequence features fed into the encoder / decoder are masked to conceal the values to be predicted. A mask is a binary tensor with the same shape as the input or output tensor, where each element is either 0 or 1. A value of 0 indicates that the feature is the value to be predicted and is masked during training. Therefore, of the m time-step features fed into the decoder, the masked values for the last Nn time-steps are 0. The goal of the end-to-end proxy model is to predict the masked decoder output values. Because of the use of 0-value masking, all values to be predicted can be trained simultaneously with the known values, allowing the end-to-end proxy model to complete predictions in one go.

[0096] By utilizing a multi-head probabilistic sparse self-attention mechanism, the end-to-end proxy model provided by this invention abandons the self-attention distillation mechanism in the original Informer architecture. This is because the core goal of this mechanism is to simplify the end-to-end proxy model by reducing feature dimensions and network parameters, a function that overlaps with the max pooling layer used in end-to-end proxy models. Furthermore, this mechanism is implemented based on one-dimensional convolutions, while the features extracted by three-dimensional convolutions contain both spatial and channel information. Further processing using one-dimensional convolutions would lose key information in the spatial dimension, resulting in a decrease in feature expressiveness.

[0097] Finally, the fully connected layer is used to integrate feature information and complete the mapping of data dimensions, thereby achieving end-to-end learning and outputting the predicted image.

[0098] Specifically, a 3D end-to-end prediction end-to-end proxy model is constructed with low computational complexity to achieve direct input and output prediction of the 3D saturation field and improve application efficiency. Step S2 specifically includes the following steps:

[0099] S2.1, 3D image features of time steps (i.e. water saturation data) is input to the input layer, and then input to the convolution layer and pooling layer to obtain features:

[0100] ;

[0101] in, Represents depth, height, width, and number of input channels respectively. Indicates that the feature is at position ( ) and output channels The value of Indicates that the input data is at position ( ) and input channels The value of Indicates that the convolution kernel is at position ( ), input channel and output channels The value of Represents the activation function, max Indicates taking the maximum value of all elements in the pooling window.

[0102] S2.2, features are obtained after passing the batch normalization layer:

[0103] ;

[0104] in, Indicates that the output feature after batch normalization is at position ( ) and output channels The value of and Respectively represent the output channels calculated in the current batch The mean and variance of and Respectively represent the output channels The scaling and translation parameters.

[0105] S2.3, expand the output features of the batch normalization layer to obtain )-dimensional sequence features, where Represent the depth, height, and width of the output features, respectively, which are determined by the input size, convolution kernel size, stride, and padding:

[0106] ;

[0107] ;

[0108] ;

[0109] in, Represents the filling amount in depth, height and width directions respectively, Represents the stride of the convolution kernel or pooling window in three dimensions respectively.

[0110] Specifically, step S2 further includes the following steps:

[0111] S2.4, intercept sequence features, and The sequence features of time steps are masked and input into the encoder, where :

[0112] ;

[0113] in, represents the tensor that is input to the encoder after applying the mask, represents element-wise multiplication (Hadamard product), Represents For all-1 matrices of the same shape, when the mask matrix value is 1, it means that the value at that position is completely retained.

[0114] S2.5, the multi-head probabilistic sparse self-attention mechanism in the encoder calculates the input features.

[0115] S2.6, after The feature sequence of time steps is masked, where :

[0116] ;

[0117] in, A tensor representing the input to the decoder after applying the mask; Represents a matrix whose elements are 0 or 1; The mask values corresponding to the features of the time step are all 1, and the predicted The mask values corresponding to the features of each time step are all 0, indicating that the value at that position is deleted.

[0118] S2.7, the output features of the encoder are combined with the masked The features of each time step are input to the decoder at the same time and calculated using the multi-head probabilistic sparse self-attention mechanism:

[0119] ;

[0120] in, Output features for the decoder, ( ) represents the multi-head probabilistic sparse self-attention mechanism, Indicates calculation of L2 norm.

[0121] S2.8, the decoder output features pass through the fully connected layer to obtain the predicted image.

[0122] Specifically, step S2.5 includes the following steps:

[0123] S2.5.1, Input Through the weight matrix Convert to query, key, value matrix 、 、 :

[0124] ;

[0125] ;

[0126] .

[0127] S2.5.2, 、 、 Divide Each head calculates attention independently :

[0128] ;

[0129] in, represents the sparse pattern matrix obtained based on the Kullback-Leibler divergence formula, represents the normalized exponential function, Indicates the dimension of the key.

[0130] The calculation formula is:

[0131] ;

[0132] in, Represents the query matrix No. column vectors, Represents the bond matrix No. The transpose of a row vector, Indicates the length of the key vector.

[0133] S2.5.3, concatenate the outputs of all heads and pass them through the weight matrix Project back to the original dimension:

[0134] ;

[0135] in, Indicates a connection operation. Represents a multi-head attention operation.

[0136] Specifically, a loss function is designed based on the seepage mechanism, so that the machine learning end-to-end proxy model can be trained under the constraints of reservoir domain knowledge, thereby improving the generalization and prediction accuracy of the end-to-end proxy model. Step S3 specifically includes the following steps:

[0137] S3.1, standardize the data in the dataset:

[0138] ;

[0139] in, and represent the mean and standard deviation of the data, respectively. represents the water saturation data before normalization, Indicates the standardized .

[0140] S3.2, Loss Function of End-to-End Proxy Model Due to data loss and seepage mechanism losses The two parts are added together, and the formula is:

[0141] .

[0142] S3.3, using the coefficient of determination Quantitatively evaluate the performance of the end-to-end proxy model:

[0143] ;

[0144] in, represents the total number of samples, and Respectively represent The true value of water saturation of samples and the predicted value of the end-to-end proxy model, Represents the mean of the true values.

[0145] Using the coefficient of determination Quantitatively evaluate the performance of the proxy model. It can measure how well the regression model fits the data, and its value range is between 0 and 1. The closer it is to 1, the better the model fitting effect is.

[0146] Specifically, the data loss part is constructed using the mean square error function, and the formula is:

[0147] ;

[0148] in, represents the total number of samples, and Respectively represent The true value of each sample and the predicted value of the end-to-end proxy model; in the present invention, the output of the end-to-end proxy model is a three-dimensional water saturation field.

[0149] Specifically, the seepage mechanism losses are calculated , specifically including the following steps:

[0150] S3.2.1, introduce the Oleinik entropy condition constraint to reconstruct the moisture content prediction formula, and define:

[0151] ;

[0152] in, represents the oil-water front saturation, For Find the derivative.

[0153] The dynamic relationship between water content and water saturation is reconstructed according to the Oleinik entropy condition:

[0154]

[0155] ;

[0156] in, The reconstructed moisture content prediction formula is: Indicates the moisture content, Indicates water saturation, represents the bound water saturation, Indicates the residual oil saturation, Represents the oil-water viscosity ratio.

[0157] At each iteration, the water saturation data of all layers of the coordinate grid of all production wells and the eight grids around them are extracted from the prediction results of the end-to-end proxy model, and the average value is calculated. The corresponding moisture content is obtained from the formula, which is the predicted value of the end-to-end proxy model.

[0158] The water content data of the actual production well is used as a label to calculate the loss of the seepage mechanism:

[0159] ;

[0160] in, is the actual liquid production, The actual oil production.

[0161] The water cut of each production well at each time step is calculated, and this water cut is the true value.

[0162] S3.2.2, the seepage mechanism loss is calculated based on this, and the mean square error function is also used to construct the seepage mechanism loss. The formula is:

[0163] ;

[0164] in, and Respectively represent The samples correspond to the true value of moisture content and the predicted value of the end-to-end proxy model.

[0165] In order to verify the method provided by the present invention, the following simulation experiments were performed:

[0166] The grid number of the 3D conceptual reservoir is set to 51×51×3, the grid size is 20m×20m×4m, and a five-point well pattern is used. Figure 3 As shown. The open source package SGeMS is used to generate 100 random permeability fields that conform to the log-normal distribution with a mean of 5 and a variance of 0.5. Considering the engineering constraints of injection-production balance, three groups of randomly changing injection-production schemes are set, each time step is set to 30 days, and a total of 10 time steps are output. Figure 4 One of the injection-production plans is shown.

[0167] Simulations were performed using the Eclipse reservoir simulator, and a saturation field dataset (300, 15, 51, 51, 3) was extracted from the results. Here, 300 represents the number of samples, which is the product of 100 permeability fields and three injection-production schemes. 15 represents the total number of time steps, and (51, 51, 3) represents the number of three-dimensional reservoir grids. 70% of the samples in the dataset were used as a training set for surrogate model training, and 30% were used as a test set for generalization performance testing.

[0168] An end-to-end surrogate model constrained by percolation predicts the next five time steps based on the first five time steps. The overlap between the encoder and decoder input time steps is set to 2, resulting in m = 7. The Adam algorithm is used to optimize the model's trainable parameters, with an initial learning rate of 0.001. Training iterations are set to 10, with a batch size of 50. The model is built using Python 3.12.7 and PyTorch 2.5.1 on an Intel Core i5-10500 processor with 32GB of RAM. Across 10 repeated experiments, the average training time for the model was 1705 seconds.

[0169] Table 1 Performance of the end-to-end proxy model constrained by flow mechanism on conceptual reservoirs

[0170]

[0171] After completing the iterative training, the average performance indicators of the end-to-end proxy model constrained by the percolation mechanism on the training set and the test set are shown in Table 1. As can be seen from Table 1, the average values of the mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE) of the training set and the test set are very low, proving that the model has high prediction accuracy. The performance of these three indicators on the test set is slightly worse than that on the training set, but the gap is small, which shows that the model has good generalization ability. The average values are slightly lower than those in the training set, but are very close to 1, indicating that the model fits well and can explain a large proportion of the variability in the target variable.

[0172] Figure 5-Figure 7 and Figures 8-10 The prediction results for the first and third layers of a randomly selected set of samples from the test set are shown and compared with the Eclipse calculation results (labels). The production times of the images from left to right are 180 days, 210 days, 240 days, 270 days, and 300 days, respectively.

[0173] from Figure 5 and Figure 8 As can be seen in the figure, the water saturation is obviously high in the center of the injection well (blue), and the overall distribution pattern reflects the complex flow behavior in the reservoir. Figure 6 and Figure 9 Shown with Figure 5 and Figure 8 The similar distribution trend better captures the main characteristics of the Eclipse calculation results. Figure 7 and Figure 10 The absolute error between the predicted value and the labeled value is shown, with yellow indicating higher error and blue indicating lower error. The error is concentrated at the boundaries of the saturation variation region, indicating that the proxy model has some inaccuracy in predicting locations with drastic saturation changes. Nevertheless, judging by the color distribution and numerical performance of the image, the prediction results of the end-to-end proxy model constrained by the percolation mechanism are generally highly reliable.

[0174] Furthermore, the proposed percolation-constrained end-to-end proxy model avoids the common drawback of traditional serial prediction architectures, namely the accumulation of prediction errors as the prediction time step moves away from the training data. This is because the generative decoder in the model can output the entire prediction sequence in parallel at once, replacing the inefficient architecture that relies on the output of the previous step to predict the current step.

[0175] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for predicting residual oil saturation based on a seepage mechanism constraint proxy model, characterized in that: The specific steps include: S1, using a reservoir numerical simulator to generate a water saturation field dataset for the oil-water two-phase system and divide it into a training set and a test set; S2, builds an end-to-end proxy model based on a 3D convolutional neural network and Informer; S3, trains the end-to-end proxy model using the training set under the constraints of the percolation mechanism; S4, input the test set into the trained end-to-end proxy model to obtain the water saturation field prediction results, and draw an image to represent the remaining oil saturation distribution; Step S3 specifically includes the following steps: S3.1, standardize the data in the dataset: ； in, and represent the mean and standard deviation of the data, respectively. represents the water saturation data before normalization, Indicates the standardized ; S3.2, Loss Function of End-to-End Proxy Model Due to data loss and seepage mechanism losses The two parts are added together, and the formula is: ； S3.3, using the coefficient of determination Quantitatively evaluate the performance of the end-to-end proxy model: ； in, represents the total number of samples, and Respectively represent The true value of water saturation of samples and the predicted value of the end-to-end proxy model, represents the mean of the true values; The data loss part is constructed using the mean square error function, and the formula is: ； Calculating seepage mechanism losses , specifically including the following steps: S3.2.1, introduce the Oleinik entropy condition constraint to reconstruct the moisture content prediction formula, and define: ； in, represents the water saturation at the oil-water front, For Derivative; The dynamic relationship between water content and water saturation is reconstructed according to the Oleinik entropy condition: ； ； in, The reconstructed moisture content prediction formula is: Indicates the moisture content, Indicates water saturation, represents the bound water saturation, Indicates the residual oil saturation, It represents the oil-water viscosity ratio; S3.2.2, use the mean square error function to construct the seepage mechanism loss, the formula is: ； in, and Respectively represent The samples correspond to the true value of moisture content and the predicted value of the end-to-end proxy model.

2. The method for predicting residual oil saturation based on a seepage mechanism constraint proxy model according to claim 1, characterized in that: Step S2 specifically includes the following steps: S2.1, 3D image features of time steps Input to the input layer, then input to the convolution layer and pooling layer to obtain features: ； in, Represents depth, height, width, and number of input channels respectively. Indicates that the feature is at position ( ) and output channels The value of Indicates that the input data is at position ( ) and input channels The value of Indicates that the convolution kernel is at position ( ), input channel and output channels The value of Represents the activation function, max Indicates taking the maximum value of all elements in the pooling window; S2.2, features are obtained after passing the batch normalization layer: ； in, Indicates that the output feature after batch normalization is at position ( ) and output channels The value of and Respectively represent the output channels calculated in the current batch The mean and variance of and Respectively represent the output channels The scaling and translation parameters of ; S2.3, expand the output features of the batch normalization layer to obtain )-dimensional sequence features, where Represent the depth, height, and width of the output features, respectively, which are determined by the input size, convolution kernel size, stride, and padding: ； ； ； in, Represents the filling amount in depth, height and width directions respectively, Represents the stride of the convolution kernel or pooling window in three dimensions respectively.

3. The method for predicting residual oil saturation based on a seepage mechanism constraint proxy model according to claim 2, characterized in that: Step S2 also includes the following steps: S2.4, intercept sequence features, and The sequence features of time steps are masked and input into the encoder, where : ； in, represents the tensor input to the encoder after applying the mask, represents element-wise multiplication, Represents All-1 matrices of the same shape; S2.5, the multi-head probabilistic sparse self-attention mechanism in the encoder calculates the input features; S2.6, after The feature sequence of time steps is masked, where : ； in, A tensor representing the input to the decoder after applying the mask, Represents a matrix whose elements are 0 or 1; S2.7, the output features of the encoder are combined with the masked The features of each time step are input to the decoder at the same time and calculated using the multi-head probabilistic sparse self-attention mechanism: ； in, Output features for the decoder, ( ) represents the multi-head probabilistic sparse self-attention mechanism, Indicates calculation of L2 norm; S2.8, the decoder output features pass through the fully connected layer to obtain the predicted image.

4. The method for predicting residual oil saturation based on a seepage mechanism constraint proxy model according to claim 3, characterized in that: Step S2.5 specifically includes the following steps: S2.5.1, Input Through the weight matrix Convert to query, key, value matrix 、 、 : ； ； ； S2.5.2, 、 、 Divide Each head calculates attention independently : ； in, represents the sparse pattern matrix obtained based on the Kullback-Leibler divergence formula, represents the normalized exponential function, Represents the dimension of the key; The calculation formula is: ； in, Represents the query matrix No. column vectors, Represents the bond matrix No. The transpose of a row vector, Indicates the length of the key vector; S2.5.3, concatenate the outputs of all heads and pass them through the weight matrix Project back to the original dimension: ； in, Indicates a connection operation. Represents a multi-head attention operation.

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