Numerical simulation acceleration method based on physical knowledge driven machine learning operator network

Abstract

The invention discloses a numerical simulation acceleration method for driving a machine learning operator network based on physical knowledge. The machine learning operator network specifically adopts a Fourier neural operator network. The method comprises the following steps: constructing a flow equivalent mathematical model of a seepage parameter field; designing a flow equivalent simulation acceleration method based on the Fourier neural operator network; designing a Fourier neural operator network training strategy based on physical knowledge driving; sampling and constructing a permeability field data set, and training and testing a Fourier neural operator network; and deploying the trained Fourier neural operator network on line to assist in real-time flow equivalent calculation. According to the method, label-free training separated from a numerical simulator can be realized, different original grid permeability can be quickly subjected to equivalent processing through a trained model, an equivalent calculation result conforms to physical constraints, and the method has higher equivalent flow simulation solving precision.

Description

Technical Field

[0001] The present invention belongs to the technical field of seepage numerical simulation, and specifically relates to a numerical simulation acceleration method based on physical knowledge-driven machine learning operator networks. Background Art

[0002] In history matching, solution optimization, and uncertainty assessment, it is necessary to repeatedly perform numerical simulations to analyze the seepage process in heterogeneous reservoirs. The simulation calculation cost on the original grid is high and inefficient. In order to reduce the amount of calculation, the industry usually uses "flow equivalence" to convert the original grid model into a post-processing grid model. The "global flow equivalence method" solves the global single-phase flow problem on the original grid, calculates the equivalent conductivity and well index, and ensures that the equivalent model has a global flow state similar to the original model under given boundary conditions. However, the single processing of the global equivalent calculation method has the same order of computational complexity as the original grid simulation; when faced with a large number of random permeability fields, a large-scale linear equation system must be repeatedly solved on the original grid, which has a huge computational cost.

[0003] To improve the efficiency of equivalent calculations, current research is replacing parts of the computational process by establishing surrogate models. These include using neural networks to establish end-to-end surrogate models from "raw grid parameter fields to post-processed grid parameter fields" and numerical simulation surrogate models from "raw grid parameter fields to raw grid flow fields." However, existing data-driven surrogate models rely on large, high-quality data samples for training. Changes to boundary conditions or well patterns require re-running numerous numerical simulations to generate data labels. Existing data-physics hybrid-driven methods still suffer from physical consistency deficiencies. These methods often prioritize minimizing empirical errors and lack strict explicit constraints on Darcy's equations and conservation laws, making them prone to non-conservative or numerically unstable equivalent parameters. Furthermore, existing physically constrained methods often rely on automatic differentiation to construct residuals. In highly heterogeneous media, sensitivity to high-order gradients often leads to error amplification and unstable training. Furthermore, existing surrogate-assisted equivalent calculation methods lack network generalization capabilities. While common neural network methods can learn "field-to-field" mappings, they inadequately extract key patterns, resulting in inaccurate inference and prediction of unknown parameter fields and reduced accuracy in equivalent calculations. Summary of the Invention

[0004] In order to solve the above problems, the present invention proposes a numerical simulation acceleration method based on a physical knowledge-driven machine learning operator network, which can be separated from the numerical simulator as a whole; the control equation is discretized through the finite volume method to strictly maintain the flux continuity and source-sink balance relationship, avoiding the instability and high cost of automatic differentiation in the calculation of high-order spatial derivatives; based on the Fourier neural operator network, linear transformation and frequency domain low-pass filtering are combined in each hidden layer to effectively capture common patterns and improve the model's ability to capture multi-scale heterogeneous fields; physical constraints are strictly followed in neural network training, and the equivalent conductivity and well index of the post-processing grid are calculated strictly according to the flow equivalent analytical formula in post-processing, ensuring physical consistency; under the same computing resources, the present invention can realize parallel rapid flow equivalent processing for batch permeability fields, with prediction accuracy comparable to the original model, and significantly improved computational efficiency compared with existing flow equivalent methods.

[0005] The technical solutions of the present invention are as follows: A numerical simulation acceleration method based on a physical knowledge-driven machine learning operator network, wherein the machine learning operator network specifically adopts a Fourier neural operator network; the method comprises the following steps: Step 1: Construct a flow equivalent mathematical model of the seepage parameter field; Step 2: Design a flow equivalent simulation acceleration method based on Fourier neural operator network; Step 3: Design a Fourier neural operator network training strategy based on physical knowledge; Step 4: Sampling and constructing a permeability field data set, training the Fourier neural operator network, and performing flow equivalent calculation and effect testing assisted by the Fourier neural operator network based on the flow equivalent mathematical model of step 1; Step 5: Deploy the trained Fourier neural operator network online to assist in real-time flow equivalent calculation.

[0006] Furthermore, in step 1, the flow equivalent mathematical model includes the control equation, boundary conditions, the discretization format of the control equation, and the flow equivalent equation; the specific construction process is: Step 1.1: Construct the control equation: ; ; in, is the flow velocity; is the spatial position coordinate; is the permeability; is the fluid viscosity; It is a pressure field; represents source and sink terms; is the gradient operator; Step 1.2: Define the boundary condition as the Newman boundary condition with a flow velocity of 0: ; in, It is the Newman boundary location; is the unit normal vector at the boundary position; Step 1.3: Construct the discretization format of the control equation: ; in, and are the serial numbers of two different grids; Indicates the adjacent cells of a grid; Indicates the The control volume of the grid; 、 Respectively grid, The pressure field of a grid; It is the adjacent The grid and The conductivity between the grids is calculated as follows: ; in, and They are The center of the grid and the The normal distance from the center of each mesh to the contact surface; It is the adjacent The grid and The area of ​​the contact surface between the grids; It is the adjacent The grid and The harmonic mean permeability among the grids; The source and sink terms are calculated using the Pisman formula: ; in, is the bottom hole pressure; is the well index, calculated as: ; in, is the equivalent reservoir radius; is the wellbore radius; is the skin factor; is the thickness of the perforated stratum; Step 1.4: Construct the flow equivalent equation of the post-processing grid and the original grid. The flow equivalent equation includes the equivalent conductivity and the equivalent well index. The calculation formulas are: ; ; in, and are the serial numbers of two different post-processing grids; It is the adjacent The post-processing grid and Equivalent conductivity between post-processing grids; It is the adjacent The post-processing grid and The contact surface between the post-processing meshes; It is The equivalent well index of the post-processing grid; For the Well index of each grid; For the A control volume for the post-processing grid; and They are The post-processing grid and The equivalent pressure field of a post-processing grid is calculated as follows: ; ; in, No. A control volume for the post-processing grid; It is The control volume of a grid.

[0007] Furthermore, the specific process of step 2 is as follows: Step 2.1: The mapping formula for constructing the Fourier neural operator network is: ; in, is the permeability field input to the input layer of the Fourier neural operator network; 、 、 Different pressure fields output by the hidden layer of the Fourier neural operator network; is the number of hidden layers of the Fourier neural operator network; is the pressure field output by the output layer of the Fourier neural operator network; is the connection symbol; a fully connected layer is used between the input layer and the hidden layer for dimensionality increase; a fully connected layer is used between the hidden layer and the output layer for dimensionality reduction; the following formula is used for calculation between the hidden layers: ; in, is the hidden layer number of the Fourier neural operator network; It is The pressure field of the first hidden layer input is also the The pressure field output by the hidden layer; It is The pressure field output by the hidden layer; is the Fourier transform; is the inverse Fourier transform; It is a frequency domain low-pass filter; is a linear transformation; is the nonlinear rectifier unit activation function; Step 2.2, referring to the flow equivalent equation, define the flow equivalent analytical formula based on the Fourier neural operator network. The flow equivalent analytical formula includes the equivalent conductivity and the equivalent well index; the calculation formula is: ; ; in, The adjacent first output of the Fourier neural operator network The post-processing grid and Equivalent conductivity between post-processing grids; The output of the Fourier neural operator network The equivalent well index of the post-processing grid; 、 They are the outputs of the Fourier neural operator network. grid, The pressure field of a grid; 、 They are the outputs of the Fourier neural operator network. The post-processing grid and The equivalent pressure field of a post-processing grid is calculated by the following formulas: ; .

[0008] Furthermore, in step 3, the physical knowledge-driven Fourier neural operator network training strategy is trained by a physical constraint loss function based on the finite volume method; the physical constraint loss function based on the finite volume method is: ; in, is the loss value; is the number of grid cells in the original grid model; The governing equation is The residual of a grid is calculated as: .

[0009] Furthermore, the specific process of step 4 is as follows: Step 4.1: Set various parameters, use the spectral domain method to sample a permeability field dataset that obeys a log-normal distribution, and divide it into a training set and a test set; Step 4.2: Based on the physical constraint loss function constructed in step 3, the Fourier neural operator network is trained using the training set. The trained Fourier neural operator network is used to assist in accelerating the flow equivalent calculation, thereby obtaining a neural operator network agent-assisted flow equivalent model. Step 4.3: Use the trained Fourier neural operator network to assist in flow equivalent calculation on the test set to evaluate the equivalent calculation effect assisted by the Fourier neural operator network.

[0010] Furthermore, the specific process of step 4.1 is: setting the size of the grid to ,in yes The number of grids in the direction, yes The number of grids in the direction; set the logarithmic permeability field It obeys the normal distribution; specifically, a spectral domain method based on Monte Carlo wave superposition is used to sample a permeability field data set that obeys the log-normal distribution; the number of samples of the generated data set, the proportion of the training set, the proportion of the test set, the bottom hole pressure of the injection well, and the bottom hole pressure of the production well are pre-set.

[0011] Furthermore, the specific process of step 4.2 is as follows: The Adam optimizer is used to train on the training set to optimize the neural network parameters; the mini-batch gradient descent is used, and the loss function of the mini-batch gradient descent is used. for: ; in, is the batch size; is the serial number of the batch; is the neural network parameter, and the update formula is: ; in, 、 Respectively 、 Neural network parameters at the iteration; is the learning rate; No. The bias-corrected estimate of momentum at iteration ; It is The bias-corrected estimate of the second moment at iteration ; is a small constant greater than zero; the total execution Gradient descent training for 1 epoch.

[0012] Furthermore, the specific process of step 4.3 is as follows: the original grid permeabilities of different permeability distributions in the test set are input into the trained Fourier neural operator network in the form of a multidimensional matrix, and the original grid pressure value is output; the equivalent conductivity and equivalent well index of the post-processing grid are calculated based on the flow equivalent analytical formula of step 2.2; and the equivalent calculation effect is evaluated based on the production evaluation indicators of cumulative water injection, cumulative liquid production, and total water cut.

[0013] Furthermore, the specific process of step 5 is: online deployment of the Fourier neural operator network trained by physical knowledge, real-time collection of the latest permeability of the original grid, input of the trained Fourier neural operator network, real-time output of the original grid pressure value, and based on the flow equivalent analytical formula, synchronous calculation and real-time output of the equivalent conductivity and equivalent well index of the post-processing grid.

[0014] The beneficial technical effects of this invention include: Using a trained model, the invention can convert different raw mesh permeabilities into post-processed mesh permeabilities. The equivalent calculation results adhere to physical knowledge constraints and achieve higher accuracy in equivalent flow simulations. Under equivalent parameter settings and computing resources, the invention can perform batch, parallel equivalent processing of permeability fields, achieving prediction accuracy comparable to the original model while significantly improving computational efficiency compared to existing flow equivalence methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flowchart of the numerical simulation acceleration method of the present invention based on physical knowledge-driven machine learning operator networks.

[0016] Figure 2 This is a structural diagram of the physical knowledge-driven agent training and agent-assisted model equivalent processing algorithm provided by the present invention.

[0017] Figure 3 A schematic diagram of defining numerical simulation dimensions, grid division, and well location distribution provided in an embodiment of the present invention.

[0018] Figure 4 Schematic diagram of the logarithmic permeability field of different permeability distributions obtained by sampling based on the spectral domain method provided in an embodiment of the present invention.

[0019] Figure 5 This is a loss reduction curve for the training process of the neural network proxy model provided by an embodiment of the present invention.

[0020] Figure 6 This is the single-phase flow pressure field of the original non-equivalent processing model provided in the embodiment of the present invention.

[0021] Figure 7 The embodiment of the present invention provides a single-phase flow pressure field of a flow equivalent model based on numerical simulation.

[0022] Figure 8 The embodiment of the present invention provides a neural operator network agent-assisted flow equivalent model single-phase flow pressure field.

[0023] Figure 9 This is the two-phase flow pressure field of the original non-equivalent processing model provided in the embodiment of the present invention.

[0024] Figure 10 The embodiment of the present invention provides a two-phase flow pressure field of a flow equivalent model based on numerical simulation.

[0025] Figure 11 The embodiment of the present invention provides a neural operator network agent-assisted flow equivalent model two-phase flow pressure field.

[0026] Figure 12 This is the water saturation field of the original non-equivalently processed two-phase flow model provided in the embodiment of the present invention.

[0027] Figure 13 The present invention provides a two-phase flow water saturation field of a flow equivalent model based on numerical simulation.

[0028] Figure 14 The present invention provides a neural operator network agent-assisted flow equivalent model for a two-phase flow water saturation field.

[0029] Figure 15 This is a comparison chart of the cumulative water injection change curves of two-phase flow before and after equivalent treatment provided by an embodiment of the present invention.

[0030] Figure 16 This is a comparison chart of the cumulative liquid production change curves of two-phase flow before and after equivalent treatment provided by an embodiment of the present invention.

[0031] Figure 17 This is a comparison diagram of the water content change curves of the two-phase flow before and after the equivalent treatment provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0032] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: like Figure 1 and Figure 2As shown, the present invention proposes a numerical simulation acceleration method based on a physical knowledge-driven machine learning operator network. The physical knowledge-driven method in the present invention means that in a flow equivalent mathematical model, the equivalent calculation of the model is driven by the flow equivalent based on physical equations, so that the equivalent results conform to physical laws. The machine learning operator network specifically adopts a Fourier neural operator network; the method of the present invention specifically includes the following steps: Step 1: Construct a flow equivalent mathematical model of the seepage parameter field; the flow equivalent mathematical model of the seepage parameter field is a single-phase flow equivalent mathematical model based on Darcy's law, including a control equation, boundary conditions, a discretization format of the control equation, and a flow equivalent equation. The specific construction process is as follows: Step 1.1: Construct the governing equations of the flow equivalent mathematical model: ; ; in, is the flow velocity; is the spatial position coordinate; is the permeability; is the fluid viscosity; It is a pressure field; represents source and sink terms; is the gradient operator; Step 1.2: Define the boundary conditions of the flow equivalent mathematical model as the Newman boundary conditions with a flow velocity of 0: ; in, It is the Newman boundary location; is the unit normal vector at the boundary position; Step 1.3: Construct the discretization format of the control equation: ; in, and are the serial numbers of two different grids; Indicates the adjacent cells of a grid; Indicates the The control volume of the grid; 、 Respectively grid, The pressure field of a grid; It is the adjacent The grid and The conductivity between the grids is calculated as follows: ; in, and They are The grid center and the The normal distance from the center of each grid to the contact surface; It is the adjacent The grid and The area of ​​the contact surface between the grids; It is the adjacent The grid and The harmonic mean permeability among the grids; The source and sink terms are calculated using the Peaceman formula: ; in, is the bottom hole pressure; is the well index, calculated as: ; in, is the equivalent reservoir radius; is the wellbore radius; is the skin factor; is the thickness of the perforated stratum; Step 1.4: Construct the flow equivalent equation between the post-processed grid and the original grid. The flow equivalent processing method can make the equivalent model and the non-equivalent model have good physical consistency. The flow equivalent equation includes the equivalent conductivity and the equivalent well index. The calculation formulas of the equivalent conductivity and the equivalent well index are: ; ; in, and are the serial numbers of two different post-processing grids; It is the adjacent The post-processing grid and Equivalent conductivity between post-processing grids; It is the adjacent The post-processing grid and The contact surface between the post-processing meshes; It is The equivalent well index of the post-processing grid; For the Well index of each grid; and They are The post-processing grid and The equivalent pressure field of a post-processing grid is calculated as follows: ; ; in, and They are The post-processing grid and A control volume for the post-processing grid; It is The control volume of a grid.

[0033] Step 2: Design a flow equivalent simulation acceleration method based on a Fourier neural operator network. The Fourier neural operator network is used to construct a highly generalized neural network proxy model for mapping the permeability field to the pressure field, thereby avoiding repeated pressure field solutions based on numerical simulations and accelerating equivalent calculations. The specific process is as follows: Step 2.1: The mapping formula for constructing the Fourier neural operator network is: ; in, is the permeability field input to the input layer of the Fourier neural operator network; 、 、 Different pressure fields output by the hidden layer of the Fourier neural operator network; is the number of hidden layers of the Fourier neural operator network; is the pressure field output by the output layer of the Fourier neural operator network; is the connection symbol; Use fully connected layers for dimensionality increase; Use fully connected layers for dimensionality reduction; arbitrary hidden layer mapping The calculation is done using the following formula: ; in, is the hidden layer number of the Fourier neural operator network; It is The pressure field of the first hidden layer input is also the The pressure field output by the hidden layer; It is The pressure field output by the hidden layer; is the Fourier transform; is the inverse Fourier transform; It is a frequency domain low-pass filter; is a linear transformation; is the nonlinear rectifier unit activation function; Step 2.2, referring to the flow equivalent equation, define the flow equivalent analytical formula based on the Fourier neural operator network. The flow equivalent analytical formula also includes the equivalent conductivity and equivalent well index; the calculation formula is: ; ; in, The adjacent first output of the Fourier neural operator network The post-processing grid and Equivalent conductivity between post-processing grids; The output of the Fourier neural operator network The equivalent well index of the post-processing grid; 、 They are the outputs of the Fourier neural operator network. grid, The pressure field of a grid; 、 The calculation is performed by a highly generalized neural network, which can avoid repeated numerical simulation calculations, and the process can be processed in batches; 、 They are the outputs of the Fourier neural operator network. The post-processing grid and The equivalent pressure field of the post-processing grid is calculated by the following formulas: ; ; Step 3. Design a Fourier neural operator network training strategy driven by physical knowledge; the physical knowledge-driven Fourier neural operator network training strategy refers to training through a physical constraint loss function based on the finite volume method to achieve physical consistency embedding; this training strategy eliminates the need to generate "label data" through numerical simulation (this label data-based approach is data-driven, which is different from the method of the present invention), and ensures that the output of the Fourier neural operator network conforms to physical laws.

[0034] The physical constraint loss function based on the finite volume method is: ; in, is the loss value; is the number of grid cells in the original grid model; The governing equation is The residual of a grid is calculated as: ; pass Physically driven training can make the output of the neural network have good physical consistency; Step 4: Sampling and constructing a permeability field data set, training the Fourier neural operator network, and performing flow equivalent calculation and effect testing assisted by the Fourier neural operator network based on the flow equivalent mathematical model of step 1. The specific process is as follows: Step 4.1: Set various parameters and use the spectral domain method to sample a permeability field dataset that obeys a log-normal distribution and divide it into a training set and a test set. The specific process is as follows: Set the grid size to ,in yes The number of grids in the direction, yes The number of grids in the direction; Set up the log permeability field It follows a normal distribution with a mean of , the variance is ; Specifically, a spectral domain method based on Monte Carlo wave synthesis is used to sample a permeability field dataset that follows a log-normal distribution. Monte Carlo wave synthesis obtains the energy spectral density by Fourier transforming the variogram. A radial spectral cumulative distribution function is established in the spectral domain, and the frequency modulus is randomly sampled and inversely transformed. Random directions and phases are sampled. Finally, wave superposition, normalization, and exponential transformation are performed to obtain the permeability field. This method can be implemented using readily available tools. The variogram model is: ; in, is the range value; is the gold nugget value; is the spatial lag distance; is the variation function value; is an exponential function with base e; Set the number of samples in the generated dataset to indivual; Set the training set ratio , the test set ratio ; Set the injection well bottom hole pressure to , the bottom hole pressure of the production well is ; Step 4.2: Based on the physical constraint loss function constructed in step 3, the Fourier neural operator network is trained using the training set. The trained Fourier neural operator network is used to assist in accelerating the flow equivalent calculation, thereby obtaining a neural operator network agent-assisted flow equivalent model. The training parameters are set as follows: Use Adam optimizer to train on the training set to optimize the neural network parameters; set the learning rate to ; Using small batch gradient descent, the loss function of small batch gradient descent for: ; in, is the batch size; is the serial number of the batch; is the neural network parameter, and its update formula is: ; in, 、 Respectively 、 Neural network parameters at the iteration; is the learning rate; No. The bias-corrected estimate of momentum at iteration ; It is The bias-corrected estimate of the second moment at iteration ; is a small constant greater than zero; the total execution Gradient descent training for epochs; Step 4.3: Use the trained Fourier neural network to assist in flow equivalent calculation on the test set and evaluate the equivalent calculation effect assisted by the Fourier neural network. The specific process is as follows: the original grid permeability of different permeability distributions in the test set is input into the trained Fourier neural network in the form of a multi-dimensional matrix, and the original grid pressure value is output; the equivalent conductivity and well index of the post-processing grid are calculated based on the flow equivalent analytical formula in step 2.2; the equivalent calculation effect is evaluated based on the cumulative water injection volume, cumulative liquid production volume, and total water content production evaluation indicators. The specific process is as follows: The simulation accuracy loss of single-phase flow before and after the Fourier neural operator network equivalent processing was tested, and the numerical simulation accuracy loss of slightly compressible oil-water two-phase flow problem before and after the Fourier neural operator network equivalent processing was simultaneously tested; three models were selected for testing and comparison, including the original non-equivalent processing model, the flow equivalent model based on numerical simulation, and the neural operator network agent-assisted flow equivalent model established by the present invention, and the simulation results of these three models for the three production evaluation indicators of cumulative water injection volume, cumulative liquid production, and total water content were compared.

[0035] The original unprocessed model refers to the original model that has not undergone any processing. This model is usually constructed using a very fine grid and has high computational accuracy, but the simulation speed is very slow when directly used for numerical simulation. This is the model to be compared with the method of the present invention.

[0036] A flow equivalent model based on numerical simulation (processed using existing systematic methods) is a model derived from numerical simulation to solve for pressure, followed by flow equivalent calculations. This model reduces the number of meshes, resulting in faster simulation speeds when used in numerical simulations. It offers accuracy very close to that of the original, non-equivalent model. However, the equivalence process requires repeated numerical simulations of the original, non-equivalent model, resulting in slower calculation speeds.

[0037] The neural operator network agent-assisted flow equivalent model has the same accuracy as the "numerical simulation flow equivalent model" and does not require repeated numerical simulation calculations, which is very slow. It also reduces the number of grids, further improving the simulation speed when used in numerical simulations.

[0038] Cumulative water injection The calculation formula is: ; in, It’s time; is the time sequence number; is the initial moment; is the time step; are all injection wells; For the Injection rate of water injection wells in each grid; Cumulative fluid production volume The calculation formula is: ; in, It is all producing wells; It is Liquid production rate of production wells in each grid; Total moisture content The calculation formula is: ; in, For the The water production rate of the production wells in each grid.

[0039] Step 5: Deploy the trained Fourier neural network online to assist in real-time flow equivalent calculations. The specific process involves deploying the trained Fourier neural network online, collecting the latest permeability of the original grid in real time, inputting the trained Fourier neural network, and outputting the original grid pressure value in real time. Based on the flow equivalent analytical formula, the equivalent conductivity and equivalent well index of the post-processing grid are simultaneously calculated and output in real time.

[0040] The physics-driven proxy-assisted seepage parameter field flow equivalence method provided in this embodiment can be separated from the entire process of training, prediction, and equivalent calculation of the numerical simulator; the control equation is discretized through the finite volume method to strictly maintain the flux continuity and source-sink balance relationship, avoiding the instability and high cost of automatic differentiation in the calculation of high-order spatial derivatives; based on the Fourier neural operator network, linear transformation and frequency domain low-pass filtering are combined in each hidden layer to effectively capture common patterns and improve the model's ability to capture multi-scale heterogeneous fields; physical constraints are strictly followed in neural network training, and the equivalent conductivity and well index of the post-processing grid are calculated strictly according to the flow equivalent analytical formula in post-processing, ensuring physical consistency; under the same computing resources, the present invention can replace the numerical simulation part of the existing equivalent calculation process, and can also realize parallel processing of batch permeability fields, with significantly improved computing efficiency compared with the existing flow equivalent method, and has a prediction accuracy comparable to the original model.

[0041] To demonstrate the feasibility of the present invention, a specific example is given for single-phase flow in heterogeneous porous media based on the Darcy equation. The specific process of constructing a physics-driven proxy model, auxiliary equivalent processing, and evaluating the equivalent calculation effect in the example is as follows: First, a numerical simulation model is constructed; the size, grid division and well location distribution are as follows Figure 3 As shown, the model size is 675m×675m, the grid is divided into 45×45 Cartesian grids, and the size parameter of each grid is 15m×15m; all boundaries are closed Newman boundary; there are 7 injection wells I1, I2, I3, I4, I5, I6, and I7, and 18 production wells P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12, P13, P14, P15, P16, P17, and P18. The overall well network layout adopts the five-point method and the constant flow pressure injection and production method.

[0042] Then, the permeability distribution obtained by sampling using the spectral domain method is as follows: Figure 4 As shown in the figure, the sampled logarithmic permeability field obeys a normal distribution with a mean of 0 and a variance of 0.3. The nugget value of the variogram model is 0, the range value is 75m, the generated permeability field range is 0.0028mD to 153.34mD, and the permeability difference range is 118.39 to 14172.09. A total of 200 different permeability field samples were sampled, 100 of which were taken as the training set, and the remaining 100 samples were taken as the test set.

[0043] Then, the Fourier neural operator network is set to include one input layer, three hidden layers, and one output layer. The mapping order is input layer, first hidden layer, second hidden layer, third hidden layer, and output layer. The neural network is trained on the training set. The learning rate of the Adam optimizer is set to 0.001, the batch size of the small batch gradient descent is 2, and a total of 10,000 generations of training are set. The logarithmic loss value decrease curve during the training process is as follows: Figure 5 shown.

[0044] Finally, a global flow simulation is performed on the original non-equivalent processed model; a global flow equivalent calculation assisted by a digital model is performed to obtain a flow equivalent model based on numerical simulation as a control group; the trained Fourier neural operator network model is batch inferenced on the test set to obtain the batch pressure field of the original grid, and post-processing calculations are performed according to the flow equivalent analytical formula to obtain the neural operator network agent-assisted flow equivalent model.

[0045] In this embodiment, single-phase flow simulation is performed on the original non-equivalent processing model, the flow equivalent model based on numerical simulation, and the neural operator network agent-assisted flow equivalent model. The single-phase flow pressure field before and after the equivalent processing is compared as shown in FIG. Figure 6 、 Figure 7 、 Figure 8 shown; from Figure 6 、 Figure 7 、 Figure 8 It can be seen that the pressure field distribution of single-phase flow is similar before and after the equivalent treatment, and has good consistency in single-phase flow pressure prediction.

[0046] Two-phase flow simulations were performed on the original unequivalent model, the flow equivalent model based on numerical simulation, and the neural operator network agent-assisted flow equivalent model. The two-phase flow pressure fields before and after the equivalent treatment were compared. Figure 9 、 Figure 10 、 Figure 11 As shown in the figure, the saturation field of the two-phase flow before and after the equivalent treatment is compared as shown in the figure. Figure 12 、 Figure 13 、 Figure 14 As shown in the figure, the comparison of the two-phase flow cumulative injection curves before and after the equivalent treatment is shown in the figure. Figure 15 As shown in the figure, the comparison of the two-phase flow cumulative liquid production curves before and after the equivalent treatment is shown in the figure. Figure 16 As shown in the figure, the two-phase flow moisture content curves before and after the equivalent treatment are compared as shown in the figure. Figure 17 As shown. Figure 12 、 Figure 13 、 Figure 14It can be seen that the saturation field distribution of the two-phase flow is similar before and after the equivalent treatment, and has good consistency in the prediction of the two-phase flow saturation, proving that the neural operator network agent-assisted flow equivalent model has a prediction accuracy comparable to that of the original model. Figure 15 It can be seen that the cumulative water injection curves of the two-phase flow are close before and after the equivalent treatment, and have good consistency in injection flow prediction, proving that the neural operator network proxy-assisted flow equivalent model has a prediction accuracy comparable to the original model; among them, the results of the neural operator network proxy-assisted flow equivalent model are more consistent with the original non-equivalent treatment model, proving that the neural operator network proxy-assisted flow equivalent model has a higher equivalent flow simulation solution accuracy. Figure 16 It can be seen that the cumulative liquid production curves of the two-phase flow are close before and after the equivalent treatment, and have good consistency in output flow prediction, proving that the neural operator network proxy-assisted flow equivalent model has the same prediction accuracy as the original model; among them, the results of the neural operator network proxy-assisted flow equivalent model are more consistent with the original non-equivalent treatment model, proving that the neural operator network proxy-assisted flow equivalent model has higher equivalent flow simulation solution accuracy. Figure 17 It can be seen that the moisture content curves of the two-phase flow are close before and after the equivalent treatment, and have good two-phase flow prediction consistency, which proves that the neural operator network agent-assisted flow equivalent model has a prediction accuracy comparable to the original model; among them, the results of the neural operator network agent-assisted flow equivalent model are more consistent with the original non-equivalent treatment model, which proves that the neural operator network agent-assisted flow equivalent model has higher equivalent flow simulation solution accuracy.

[0047] The time consumption comparison between the flow equivalent calculation based on numerical simulation and the flow equivalent calculation assisted by the neural operator network agent is shown in Table 1.

[0048] Table 1 Time consumption comparison results .

[0049] As can be seen from Table 1, the neural operator network agent-assisted flow equivalence has significantly less computational time in both 500 and 1000 equivalent calculations, proving that the neural operator network agent-assisted flow equivalence method has significantly improved computational efficiency compared with existing flow equivalence methods.

[0050] 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 numerical simulation acceleration method based on physical knowledge-driven machine learning operator networks, characterized in that: The machine learning operator network specifically adopts a Fourier neural operator network; the method comprises the following steps: Step 1: Construct a flow equivalent mathematical model of the seepage parameter field; Step 2: Design a flow equivalent simulation acceleration method based on Fourier neural operator network; Step 3: Design a Fourier neural operator network training strategy based on physical knowledge; Step 4: Sampling and constructing a permeability field data set, training the Fourier neural operator network, and performing flow equivalent calculation and effect testing assisted by the Fourier neural operator network based on the flow equivalent mathematical model of step 1; Step 5: Deploy the trained Fourier neural operator network online to assist in real-time flow equivalent calculation.

2. The numerical simulation acceleration method based on physical knowledge-driven machine learning operator network according to claim 1 is characterized in that: In step 1, the flow equivalent mathematical model includes the control equation, boundary conditions, the discretization format of the control equation, and the flow equivalent equation; the specific construction process is: Step 1.1: Construct the control equation: ； ； in, is the flow velocity; is the spatial position coordinate; is the permeability; is the fluid viscosity; It is a pressure field; represents source and sink terms; is the gradient operator; Step 1.2: Define the boundary condition as the Newman boundary condition with a flow velocity of 0: ； in, It is the Newman boundary location; is the unit normal vector at the boundary position; Step 1.3: Construct the discretization format of the control equation: ； in, and are the serial numbers of two different grids; Indicates the adjacent cells of a grid; Indicates the The control volume of the grid; 、 Respectively grid, The pressure field of a grid; It is the adjacent The grid and The conductivity between the grids is calculated as follows: ； in, and They are The center of the grid and the The normal distance from the center of each mesh to the contact surface; It is the adjacent The grid and The area of ​​the contact surface between the grids; It is the adjacent The grid and The harmonic mean permeability among the grids; The source and sink terms are calculated using the Pisman formula: ； in, is the bottom hole pressure; is the well index, calculated as: ； in, is the equivalent reservoir radius; is the wellbore radius; is the skin factor; is the thickness of the perforated stratum; Step 1.4: Construct the flow equivalent equation of the post-processing grid and the original grid. The flow equivalent equation includes the equivalent conductivity and the equivalent well index. The calculation formulas are: ； ； in, and are the serial numbers of two different post-processing grids; It is the adjacent The post-processing grid and Equivalent conductivity between post-processing grids; It is the adjacent The post-processing grid and The contact surface between the post-processing meshes; It is The equivalent well index of the post-processing grid; For the Well index of each grid; For the A control volume for the post-processing grid; and They are The post-processing grid and The equivalent pressure field of a post-processing grid is calculated as follows: ； ； in, No. A control volume for the post-processing grid; It is The control volume of a grid.

3. The numerical simulation acceleration method based on physical knowledge driven machine learning operator network according to claim 2 is characterized in that: The specific process of step 2 is: Step 2.1: The mapping formula for constructing the Fourier neural operator network is: ； in, is the permeability field input to the input layer of the Fourier neural operator network; 、 、 Different pressure fields output by the hidden layer of the Fourier neural operator network; is the number of hidden layers of the Fourier neural operator network; is the pressure field output by the output layer of the Fourier neural operator network; is the connection symbol; a fully connected layer is used between the input layer and the hidden layer for dimensionality increase; a fully connected layer is used between the hidden layer and the output layer for dimensionality reduction; the following formula is used for calculation between the hidden layers: ； in, is the hidden layer number of the Fourier neural operator network; It is The pressure field of the first hidden layer input is also the The pressure field output by the hidden layer; It is The pressure field output by the hidden layer; is the Fourier transform; is the inverse Fourier transform; It is a frequency domain low-pass filter; is a linear transformation; is the nonlinear rectifier unit activation function; Step 2.2, referring to the flow equivalent equation, define the flow equivalent analytical formula based on the Fourier neural operator network. The flow equivalent analytical formula includes the equivalent conductivity and the equivalent well index; the calculation formula is: ； ； in, The adjacent first output of the Fourier neural operator network The post-processing grid and Equivalent conductivity between post-processing grids; The output of the Fourier neural operator network The equivalent well index of the post-processing grid; 、 They are the outputs of the Fourier neural operator network. grid, The pressure field of a grid; 、 They are the outputs of the Fourier neural operator network. The post-processing grid and The equivalent pressure field of a post-processing grid is calculated by the following formulas: ； 。 4. The numerical simulation acceleration method based on physical knowledge driven machine learning operator network according to claim 3 is characterized in that: In step 3, the physical knowledge-driven Fourier neural operator network training strategy is trained by a physical constraint loss function based on the finite volume method; the physical constraint loss function based on the finite volume method is: ； in, is the loss value; is the number of grid cells in the original grid model; The governing equation is The residual of a grid is calculated as: 。 5. The numerical simulation acceleration method based on physical knowledge driven machine learning operator network according to claim 4 is characterized in that: The specific process of step 4 is as follows: Step 4.1: Set various parameters, use the spectral domain method to sample a permeability field dataset that obeys a log-normal distribution, and divide it into a training set and a test set; Step 4.2: Based on the physical constraint loss function constructed in step 3, the Fourier neural operator network is trained using the training set. The trained Fourier neural operator network is used to assist in accelerating the flow equivalent calculation, thereby obtaining a neural operator network agent-assisted flow equivalent model. Step 4.3: Use the trained Fourier neural operator network to assist in flow equivalent calculation on the test set to evaluate the equivalent calculation effect assisted by the Fourier neural operator network.

6. The numerical simulation acceleration method based on physical knowledge driven machine learning operator network according to claim 4 is characterized in that: The specific process of step 4.1 is: set the size of the grid to ,in yes The number of grids in the direction, yes The number of grids in the direction; Set up the log permeability field It obeys the normal distribution; specifically, a spectral domain method based on Monte Carlo wave superposition is used to sample a permeability field data set that obeys the log-normal distribution; the number of samples of the generated data set, the proportion of the training set, the proportion of the test set, the bottom hole pressure of the injection well, and the bottom hole pressure of the production well are pre-set.

7. The numerical simulation acceleration method based on physical knowledge driven machine learning operator network according to claim 4 is characterized in that: The specific process of step 4.2 is as follows: The Adam optimizer is used to train on the training set to optimize the neural network parameters; the mini-batch gradient descent is used, and the loss function of the mini-batch gradient descent is used. for: ； in, is the batch size; is the serial number of the batch; is the neural network parameter, and the update formula is: ； in, 、 Respectively 、 Neural network parameters at the iteration; is the learning rate; No. The bias-corrected estimate of momentum at iteration ; It is The bias-corrected estimate of the second moment at iteration ; is a small constant greater than zero; the total execution Gradient descent training for 1 epoch.

8. The numerical simulation acceleration method based on physical knowledge driven machine learning operator network according to claim 7 is characterized in that: The specific process of step 4.3 is as follows: the original grid permeabilities of different permeability distributions in the test set are input into the trained Fourier neural operator network in the form of a multidimensional matrix, and the original grid pressure value is output; the equivalent conductivity and equivalent well index of the post-processing grid are calculated based on the flow equivalent analytical formula of step 2.2; and the equivalent calculation effect is evaluated based on the production evaluation indicators of cumulative water injection volume, cumulative liquid production, and total water cut.

9. The numerical simulation acceleration method based on physical knowledge driven machine learning operator network according to claim 8, characterized in that: The specific process of step 5 is as follows: online deployment of the Fourier neural operator network trained by physical knowledge, real-time collection of the latest permeability of the original grid, input of the trained Fourier neural operator network, real-time output of the original grid pressure value, and synchronous calculation and real-time output of the equivalent conductivity and equivalent well index of the post-processing grid based on the flow equivalent analytical formula.

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