Oil reservoir dynamic efficient proxy modeling method embedded with coarse mesh simulator

Abstract

The invention relates to the field of numerical reservoir simulation, and provides a proxy modeling method for embedding a coarse grid simulator, so as to solve the problems of poor space-time extrapolation performance and unstable long-term prediction. According to the method, a coarse mesh numerical simulator is used as a physical prior module to be embedded into a multi-resolution fusion neural network structure (MNN), and a complex nonlinear relation in the physical prior module is captured by means of a Fourier neural operator (FNO), so that efficient, long-time-sequence and stable prediction of multiple physical fields such as pressure, oil saturation and gas saturation is realized. According to the method, a coarse mesh numerical solution is used as an intermediate drive, multi-scale physical information is fused through a modular MNN network, and the physical consistency and the space-time generalization ability of the proxy model are remarkably improved. In the model, the FNO is utilized to extract global frequency domain characteristics of a coarse grid simulation result field, and through verification of multiple cases, the model shows good space-time extrapolation performance under various coarsening scales and well control conditions. The method has the robustness of numerical simulation and the high efficiency of deep learning.

Description

Technical Field

[0001] This invention relates to the field of reservoir engineering and numerical simulation, and in particular to a method for efficient surrogate modeling of reservoir dynamics embedded in a coarse-grid simulator. Specifically, it relates to a surrogate modeling method using a Fourier neural operator (FNO) embedded in a coarse-grid simulator. Background Technology

[0002] Reservoir numerical simulation is a key technology in oil and gas field development. By solving mathematical models of fluid flow in porous media, it enables the prediction of production and the optimization of development plans. Traditional numerical simulation methods rely on complex physical equations and large amounts of computational resources, making it difficult to meet the needs of real-time decision-making and efficient optimization. In recent years, artificial intelligence technology has provided new solutions for reservoir numerical simulation, significantly improving computational efficiency and prediction accuracy by constructing data-driven surrogate models.

[0003] Purely data-driven neural network surrogate models utilize historical simulation data to establish mapping relationships between inputs and outputs, including different mapping methods such as field-to-field, field-to-sequence, and sequence-to-sequence, and are widely used in reservoir dynamic prediction. For example, Mo et al. proposed a surrogate model for multiphase flow in geological carbon burial processes based on deep convolutional encoder-decoder, proving that it can accurately predict subsurface flow and improve computational efficiency. Wang et al. constructed a theory-guided convolutional neural network (TgCNN) framework to solve the problem of two-phase porous media flow.

[0004] However, these models rely on large amounts of high-quality data and lack physical constraints, which may lead to predictions that violate fundamental physical laws. To overcome this limitation, Physically Constrained Neural Networks (PINNs) were proposed. By embedding the governing equations into the loss function, the model can maintain physical consistency even when data is insufficient, improving generalization ability and interpretability. Bi et al. constructed a dual-driven seepage surrogate model that integrates data-driven and physical-driven approaches, verifying that the robustness of the dual-driven seepage surrogate model is superior to that of the pure data-driven seepage surrogate model. Wang et al. constructed a neural network (TgNN) guided by the theory of the potential problem (e.g., governing equations, other physical constraints, engineering controls, and expertise) for deep learning of groundwater flow, verifying that it has better predictability, reliability, and generalization than deep neural network models.

[0005] Furthermore, operator neural networks (such as DeepONet and Fourier neural operators) can efficiently handle complex partial differential equation problems by directly learning function-to-function mappings, making them suitable for multiphysics coupling and large-scale reservoir simulation. These methods have shown significant advantages in injection-production strategy optimization, history fitting, and geological uncertainty analysis, becoming an important supplement to traditional numerical simulations. For example, Ye et al. used Fourier neural operators (FNO) to construct a surrogate model for geothermal development simulation, accurately predicting reservoir temperature and pressure fields under different production regimes and extraction stages. Jonathan E. Lee et al. developed a nested Fourier-DeepONet to predict CO2 migration paths and pressure distribution during reservoir formation to guide GCS project decisions. Summary of the Invention

[0006] The purpose of this invention is to propose a rapid prediction method for flow state based on a Fourier neural operator embedded in a coarse-grid simulator, so as to achieve rapid prediction of high-resolution pressure and saturation fields during reservoir development, and maintain good simulation accuracy, especially in variable well control and time extrapolation scenarios.

[0007] This method includes the following steps: Based on high-resolution reservoir physical field data from historical time steps, including pressure, oil saturation, and gas saturation.

[0008] Spatial downsampling of the high-resolution physics field generates a coarse-grid resolution physical state representation for compatibility with coarse-grid physics simulators, represented as:

[0009] Indicates time step The pressure field, oil saturation field, and gas saturation field. This represents the coarsened pressure field and saturation field results. This represents a downsampling algorithm.

[0010] The coarse-resolution physical field and the well control parameters for the current time step are input into the embedded coarse-grid numerical simulator to obtain the coarse-resolution prediction result for the next time step, as follows: in For embedded coarse-grid simulation operators, For T n Well control parameters for time steps. These represent the values ​​predicted by the coarse-grid numerical simulator at time step T. n+1 The coarse-grid pressure field, coarse-grid gas saturation field, and coarse-grid oil saturation field.

[0011] The output of the coarse-grid simulator is converted into a high-resolution approximation field through an upsampling operation, which is then used as the input to a multi-resolution fusion neural network (MNN). The MNN is constructed based on the Fourier neural operator (FNO) to recover the high-resolution physical field prediction results from the upsampled coarse field and output the pressure P, oil saturation So, and gas saturation Sg at future time steps. Independent sub-network structures (MNN-P, MNN-So, MNN-Sg) are designed for the above three types of physical variables to adapt to the spatial distribution learning of different physical characteristics.

[0012] Where MNN represents a multi-resolution fusion network. These are its learnable parameters. These represent the predictions obtained by the multi-resolution fusion neural network (MNN) at time step T. n+1 High-resolution pressure field, high-resolution gas saturation field and high-resolution oil saturation field.

[0013] Using real high-resolution physical fields as the supervision signal and root mean square error (RMSE) as the loss function, the model is optimized in conjunction with strategies such as regularization and learning rate scheduling. By using the predicted high-resolution physical fields as the input for the next time step and repeating the above steps, autoregressive extrapolation predictions for multiple time steps can be achieved, thereby simulating the long-term dynamic evolution of reservoirs.

[0014] This invention presents a rapid prediction method for flow states based on a Fourier neural operator embedded in a coarse-grid simulator. It focuses on achieving rapid prediction of high-resolution pressure and saturation fields during reservoir development, maintaining good simulation accuracy, especially in scenarios involving variable well control and time extrapolation. By introducing a coarse-grid simulator, it integrates physics-driven and data-driven modeling ideas, introducing interpretable physical constraints while maintaining high efficiency. A multi-resolution fusion neural network (MNN) based on an FNO neural network is constructed, improving spatial recovery accuracy and making it suitable for prediction tasks under complex reservoir geological features. A three-physical-quantity independent prediction mechanism is built, improving the accuracy and stability of multi-physics joint modeling. It also supports variable well control input and has strong time-step extrapolation and operational condition adaptability. By integrating these advanced computational technologies, it advances the cutting-edge development of neural network surrogate models in reservoir numerical simulation, providing a more efficient simulation method for predicting spatiotemporal changes in reservoir physical fields. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is the proxy model framework for the embedded coarse mesh simulator of the present invention.

[0017] Figure 2 This is a flowchart of the neural network model training process of the present invention.

[0018] Figure 3 This is a schematic diagram of the reservoir model of Embodiment 1 of the present invention.

[0019] Figure 4 This is a parameter diagram of a CNN-based multi-resolution neural network structure according to Embodiment 1 of the present invention.

[0020] Figure 5 This is a parameter diagram of the multi-resolution neural network structure based on FNO in Embodiment 1 of the present invention.

[0021] Figure 6 These are the oil-water phase permeation curves and gas-oil phase permeation curves of Embodiment 1 of the present invention.

[0022] Figure 7 This is a basic reservoir parameter diagram of Embodiment 1 of the present invention.

[0023] Figure 8 These are 50 well control sequence samples from six wells in Embodiment 1 of the present invention.

[0024] Figure 9 This is the FNO training loss curve of Embodiment 1 of the present invention (the left horizontal axis represents the training amount, and the right horizontal axis represents the training rounds).

[0025] Figure 10 This is the CNN training loss curve of Embodiment 1 of the present invention (the left horizontal axis represents the training amount, and the right horizontal axis represents the training rounds).

[0026] Figure 11 This is the variation of the validation set loss function with the number of training rounds in Embodiment 1 of the present invention.

[0027] Figure 12 This is a comparison of the numerical simulation calculation costs of reservoir models at different scales in Embodiment 1 of the present invention.

[0028] Figure 13 This is a diagram showing the physical field differences between different coarsening scale models and the original model in Embodiment 1 of the present invention.

[0029] Figure 14 This is the proxy modeling training and prediction process of the embedded coarse mesh simulator in Embodiment 1 of the present invention.

[0030] Figure 15 This is a comparison chart of the time step extrapolation prediction of the pressure field in Embodiment 1 of the present invention.

[0031] Figure 16 This is a comparison chart of time step extrapolation prediction of gas saturation in Embodiment 1 of the present invention.

[0032] Figure 17 This is a comparison chart of time step extrapolation prediction of oil saturation in Embodiment 1 of the present invention.

[0033] Figure 18 This is a diagram showing the relative error of each physical field in the true value prediction of Embodiment 1 of the present invention.

[0034] Figure 19 This is a graph showing the relative error of each physical field in the autoregressive prediction of Embodiment 1 of the present invention.

[0035] Figure 20 This is a flowchart of the reservoir dynamic efficient proxy modeling method embedded in a coarse mesh simulator according to Embodiment 1 of the present invention. Detailed Implementation

[0036] Please see Figures 1-20 This invention provides a fast prediction method for flow state based on a Fourier neural operator embedded in a coarse-grid simulator, comprising the following steps: S100: Establishing a multi-resolution fusion structure for a three-phase proxy model In this embodiment, a proxy modeling method for the three-phase physical quantities of oil, water, and gas is constructed, employing a multi-resolution fusion neural network (MNN). For example... Figure 1 As shown, three sub-MNN networks are constructed based on the FNO network to predict three types of physical fields: pressure, oil saturation, and gas saturation, respectively. Each sub-network structurally embeds a fusion channel with the output of a coarse-grid simulator as input, and a multi-scale feature extraction module is used to fuse and refine the input information.

[0037] This structure learns the coupling relationships between various physical quantities through joint training and enhances its ability to characterize physical laws by utilizing multi-scale information. The fusion structure is as follows: Figure 2 As shown, it includes input fusion at multiple resolutions, cross-channel residual connections, and the final physical field decoding module. S200: Constructing the training dataset and designing exponentially decaying well-controlled sequences. In this embodiment, to construct the multi-temporal dataset required for neural network training, the present invention uses the PUNQ three-dimensional black oil model for data acquisition and numerical simulation. The model is as follows: Figure 3 As shown, see parameters in detail. Figure 7 Fifty different fluid production rate sequences were generated using an exponential decay control strategy. The control logic constructs a well control sequence by randomly sampling the initial rate Q0 and using a bisection method to deduce the decay coefficient 'a' in conjunction with the total production target. The well control is updated every 300 days, for a total of 21 time steps. Each sequence drives a numerical simulation, with a total simulation duration of 6300 days. Ultimately, three-dimensional pressure and saturation data were obtained for 50 sequences × 200 time sections × multi-layer spatial grids, totaling approximately 10,000 samples.

[0038] S300: Comparative Training and Performance Analysis Based on Different Neural Network Architectures In this embodiment, to verify the applicability of the multi-resolution proxy model structure, two mainstream structures are constructed for comparison: proxy networks based on FNO3D (Case 1) and CNN3D (Case 2). The experimental framework is as follows: Figure 4 and Figure 5 As shown, the dataset is divided into a training set: validation set: test set ratio of 8:1:1.

[0039] S400: Research on Coarse Mesh Simulator Embedding and Coarsening Scale Adaptation To further improve simulation efficiency, simulators with different coarsening scales (2x and 3x) are embedded in this embodiment, and their impact on model prediction accuracy and computational performance is explored.

[0040] S500: Time-Domain Autoregressive Extrapolation and Error Assessment under Variable Well Control Conditions In this embodiment, to verify the robustness of the established model in dynamic prediction, an autoregressive extrapolation strategy is used to predict reservoir evolution at 21 time steps. The specific process is as follows: Input the physical field (real or predicted) for the first time step; calculate the next time step using a coarse-grid simulator; upsample to restore the fine scale; feed it into the surrogate model to predict the next time step; iterate repeatedly to complete the prediction for subsequent time steps. Compare and analyze the results. Accurately quantify the prediction error of the model during time-domain extrapolation, and define relative error as an indicator of model performance.

[0041] Example 1 is to simulate and analyze the spatiotemporal variation of the physical field for a three-dimensional (3D) actual three-phase flow reservoir.

[0042] Example 1: The model used in this invention represents a three-dimensional (3D) actual saline reservoir, providing a realistic case for the simulation and analysis of CO2 sequestration. The reservoir domain is discretized into a Cartesian grid, divided into 57×84×5 grid cells along the x, y, and z axes, respectively.

[0043] The total number of grid cells is 23,940, with 19,720 effective grid cells. The reservoir includes 5 production wells. The reservoir model and well location distribution are as follows: Figure 3 As shown, the relative permeability curve is as follows: Figure 6 As shown, detailed reservoir parameters can be found in [link to relevant documentation]. Figure 7 As shown.

[0044] Considering the well control sequence as model input, we used an exponential decay control strategy to generate 50 different fluid production rate sequences for each well. For example... Figure 8 As shown, simulations were performed using 50 generated well control sequences. The simulation time step was set to 30 days, with a total simulation duration of 6300 days. Well control parameters were updated every 300 days, resulting in 21 control time steps throughout the simulation. All simulations were performed using a numerical simulator, and the output included the three-dimensional pressure field and saturation field for each time step, ultimately yielding 10,000 physical field data samples. These simulation data were used to train a surrogate model based on the PUNQ model, establishing independent prediction networks for the pressure field and saturation field respectively to improve the modeling accuracy for different physical quantities.

[0045] Through two comparative cases (Case 1 and Case 2), the modeling performance and applicability of different neural network structures under the same sample were systematically evaluated. The experiments aimed to compare the predictive ability of neural networks for reservoir flow state under purely data-driven conditions. In all cases, the network used the physical field of the previous time step as input to predict the corresponding physical field of the next time step, thereby realizing the stepwise evolution modeling of the temporal physical field.

[0046] Case 1 uses an FNO3d network built with 8000 training samples, and Case 2 uses a CNN network built with 8000 training samples. The datasets for all experiments are divided in a ratio of training set:validation set:test set = 8:1:1 to ensure the stability and comparability of the evaluation results.

[0047] Figure 9 , Figure 10 The curves showing the training loss as a function of training sample size and training epochs are presented for two cases. The results show that in Case 1, because FNO is more sensitive to data preprocessing and Fourier spectrum truncation, its convergence speed is slightly slower than CNN in the early stages of training. However, with the support of large-scale training data, it exhibits stronger learning ability and lower final error. In the later stages of training, FNO's convergence trend is more stable, demonstrating its strong learning ability under fully trained conditions compared to CNN networks. The results for Case 2 show that although CNNs generally have a faster initial convergence speed with the same sample size, their final convergence error is higher than FNO's, and the loss function fluctuates more in the later stages of training, making them prone to overfitting.

[0048] To further evaluate the generalization ability of the two surrogate models during the training process, Figure 11 The results in Case 1 demonstrate the trend of the loss function on the validation set as the training epochs progress. Case 1 shows that as the number of training samples increases, the validation error of FNO steadily decreases and stabilizes at a low level in the later stages, demonstrating good generalization performance. In Case 2, the error trends of the CNN model on the training and validation sets are basically consistent, but the loss fluctuates significantly during training, especially in the later stages, making it less stable than FNO and indicating weaker generalization ability.

[0049] Figure 12 The average simulation time for 30 time steps of numerical simulation using three PUNQ reservoir models with different coarsening scales under the same well control conditions was compared. The results show that the original model (57×84×5) has the highest spatial resolution and can better characterize the physical field features of the reservoir, but its computational cost is significant, with an average time of about 0.4 seconds per time step. The computation time of the double-coarsened model (28×42×5) is only about 0.08 seconds on average. The triple-coarsened model (19×28×5) further reduces this time to 0.041 seconds, showing a significant speed improvement. Figure 13 The diagram illustrates the differences between the reconstructed high-resolution physical fields (showing only the pressure field) from the original model and the physical fields of the two coarsened models after upsampling. It is evident that the differences in the pressure fields are relatively small at the first time step. However, as time steps progress, the differences between the highly coarsened physical fields and the original models become increasingly larger.

[0050] We use a test set to systematically evaluate the time series prediction capability of the constructed model. Specifically, we select the physical field (such as pressure, saturation, etc.) of the first time step in the test sample as the initial input, and then use the model to progressively predict the time series. Each prediction outputs the physical field of the next time step, which is then used as the new input. This process is iterated to complete the inference of the subsequent time evolution.

[0051] Figure 14 This demonstrates the data preparation and model training process: Data Collection: The pressure and saturation fields at 21 time steps under a fine-grid design are obtained using a traditional numerical simulator (denoted as ①). The high-resolution physical field at the current time step is downsampled to match the input format of the coarse-grid simulator (denoted as ②). Combining the well control sequence, which changes every time step, the coarse-grid simulator is invoked to progressively predict the physical field for the next time step (denoted as ③). The coarsened result is upsampled back to the high-resolution grid (denoted as ④). The upsampled result is fed into the surrogate model to predict the high-resolution physical field (denoted as ⑤). The physical field predicted by the network is repeated 20 times using operations ②-⑤ to obtain the predicted physical fields for 20 time steps, which are then compared with the corresponding real data from ①, i.e., autoregressive prediction (denoted as ⑥).

[0052] Figure 15 , Figure 16 and Figure 17 This paper compares the predicted results and simulator solutions for the first layer of the reservoir at three different time points, along with their error distributions. The two methods show a very similar overall spatial distribution, with errors mainly concentrated at the boundaries and in highly variable regions, further demonstrating the model's ability to capture dynamic evolution trends effectively. To verify the model's prediction accuracy, we compare the prediction results with the actual physical fields calculated by traditional numerical simulators. To accurately quantify the prediction error during time-domain extrapolation, we compare the relative error indices of autoregressive and true value predictions, see [link to relevant documentation]. Figure 18 and 19 The results show that this method exhibits good time-domain extrapolation capability under variable well control conditions, with an error range within an acceptable range, and can effectively predict the evolution trend of the physical field within several future time steps.

[0053] Experiments show that this method has strong spatiotemporal generalization in reservoir numerical simulation surrogate model problems.

[0054] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A method for dynamic and efficient surrogate modeling of reservoirs embedded in a coarse-grid simulator, characterized in that, Includes the following steps: Data preparation and downsampling: Acquire high-resolution reservoir physical field data for the current time step, including pressure, oil saturation, and gas saturation; perform spatial downsampling on the high-resolution physical field data to generate the corresponding coarse-resolution physical field; Coarse-grid simulation: The coarse-resolution physical field and the well control parameters of the current time step are input into the embedded coarse-grid numerical simulator to obtain the coarse-resolution prediction results of the next time step; High-resolution field reconstruction: The coarse-resolution prediction result of the next time step is input into a multi-resolution fusion neural network (MNN). This module, based on Fourier neural operators, is used to restore the coarse-resolution prediction result to the high-resolution physical field prediction result of the next time step. The high-resolution physical field prediction result includes pressure, oil saturation, and gas saturation. Autoregressive extrapolation: The high-resolution physical field prediction result of the next time step is used as the input to the new current time step, and the above steps are repeated to achieve prediction of the physical field evolution for multiple subsequent time steps.

2. The method for efficient reservoir dynamic proxy modeling embedded in a coarse-grid simulator as described in claim 1, characterized in that, The multi-resolution fusion neural network (MNN) includes three independent subnetworks based on Fourier neural operators, which are used to predict pressure, oil saturation and gas saturation, respectively.

3. The method for efficient reservoir dynamic proxy modeling embedded in a coarse-grid simulator as described in claim 1, characterized in that, The spatial downsampling process is represented as follows: ; Indicates time step The pressure field, oil saturation field, and gas saturation field. This represents the coarsened pressure field and saturation field results. This represents a downsampling algorithm.

4. The method for efficient reservoir dynamic proxy modeling embedded in a coarse-grid simulator as described in claim 1, characterized in that, The simulation process of the embedded coarse-grid numerical simulator is represented as follows: ; in For embedded coarse-grid simulation operators, For T n Well control parameters for time steps. These represent the values ​​predicted by the coarse-grid numerical simulator at time step T. n+1 The coarse-grid pressure field, coarse-grid gas saturation field, and coarse-grid oil saturation field.

5. The method for efficient reservoir dynamic proxy modeling embedded in a coarse-grid simulator as described in claim 1, characterized in that, The prediction process of the multi-resolution fusion neural network (MNN) is represented as follows: ; MNN stands for Multi-resolution Fusion Network. These are its learnable parameters. These represent the predictions obtained by the multi-resolution fusion neural network (MNN) at time step T. n+1 High-resolution pressure field, high-resolution gas saturation field and high-resolution oil saturation field.

6. The method for efficient reservoir dynamic proxy modeling embedded in a coarse-grid simulator as described in claim 1, characterized in that, An autoregressive extrapolation strategy is used for multi-time-step prediction, specifically: The high-resolution physical field prediction result of the next time step obtained by the steps described in claim 1 is used as the high-resolution reservoir physical field data of the current time step. The steps described in claim 1 are repeated, and this process is repeated in a loop to achieve prediction of the physical field evolution for multiple subsequent time steps.

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