Fractured reservoir injection-production parameter optimization method based on reduced-order model retraining

Abstract

The application discloses a kind of based on reduced-order model retraining's fractured reservoir injection-production parameter optimization method, it is related to unconventional oil and gas development technical field, including: establishing fractured reservoir full-order numerical simulation model, setting initial injection-production control parameter, running main, vice training simulation;Snapshot matrix is executed singular value decomposition, and reduced-order basis matrix is constructed;Snapshot matrix and the gradient information of main training simulation are executed reduced-order preprocessing, and reduced-order model is constructed;Based on reduced-order model, injection-production parameter optimization iteration is executed and is dynamically judged, until cumulative adjustment step is not more than pre-set allowable value and has reached pre-set maximum iteration step number, then with current optimal injection-production parameter operation verification, output optimal injection-production parameter and objective function value, otherwise using current optimal injection-production parameter updates main training simulation and retraining reduced-order model.The application is through simulation, reduced-order, optimization, update closed loop process, ensure accuracy while greatly improving the calculation efficiency of fractured reservoir production optimization.

Description

Technical Field

[0001] This invention relates to the field of unconventional oil and gas development technology, and in particular to a method for optimizing injection and production parameters in fractured reservoirs based on retraining a reduced-order model. Background Technology

[0002] Fractured reservoirs, as an important component of unconventional oil and gas resources, are a key and challenging issue in oil and gas development due to their complex internal fracture distribution, strong heterogeneity, and the coupled matrix-fracture characteristics of fluid flow. Optimizing injection and production parameters is a core means to improve the recovery rate and reduce development costs of fractured reservoirs, while accurate reservoir numerical simulation is the fundamental prerequisite for optimizing these parameters; the accuracy of the simulation directly determines the feasibility and effectiveness of the injection and production scheme.

[0003] Currently, numerical simulation modeling methods for fractured reservoirs include embedded discrete fracture models and dual-medium models. Embedded discrete fracture models are widely used in the detailed simulation of fractured reservoirs because they can explicitly characterize fracture geometry and seepage features. However, these full-order models have significant computational bottlenecks: due to the large number and chaotic distribution of fractures in fractured reservoirs, precise meshing of the reservoir is required to accurately characterize the coupled seepage behavior between fractures and the matrix, leading to a sharp increase in the number of meshes and an exponential increase in the computational load of numerical simulation. This severely limits their application in optimizing injection and production parameters in practical engineering, making it difficult to achieve real-time adjustment and dynamic optimization of injection and production schemes. To address the problem of excessively long numerical simulation times, reduced-order modeling techniques have been widely introduced into the field of reservoir numerical simulation. Reduced-order models do not require building massive training datasets or conducting extensive sample training. Instead, they reduce the dimensionality of the original full-order model by projecting the high-dimensional reservoir model into a low-dimensional subspace. While ensuring simulation accuracy meets engineering requirements, this significantly reduces computational complexity and shortens simulation time, meeting the efficiency requirements of injection and production parameter optimization. However, the strong heterogeneity of fractured reservoirs, the complex coupling and seepage characteristics of fractures and matrix, and the dynamic evolution of reservoir state during injection and production have led to the general instability of existing reduced-order models for fractured reservoirs. The prediction results of the reduced-order models deviate too much from those of the full-order models, which cannot provide reliable support for the optimization of injection and production parameters, thus limiting the widespread application of reduced-order models in the optimization of injection and production parameters in fractured reservoirs.

[0004] In summary, the current optimization of injection and production parameters in fractured reservoirs faces challenges such as the time-consuming nature of full-order numerical simulations, which are difficult to apply in practice. While existing reduced-order models do not require a large training dataset, they suffer from insufficient stability. There is an urgent need for an injection and production parameter optimization method that can balance optimization efficiency and simulation stability to address the shortcomings of existing technologies and promote the efficient development of fractured reservoirs. Summary of the Invention

[0005] To address the aforementioned issues, this invention discloses a method for optimizing injection and production parameters in fractured reservoirs based on retraining a reduced-order model. This method employs the Petrove-Galerkin projection method to improve the accuracy and stability of the reduced-order model for fractured reservoirs based on intrinsic orthogonal decomposition-trajectory piecewise linearization (POD-TPWL). Through dynamic update design of primary and secondary training simulations, the reduced-order model is dynamically corrected and progressively improved during the optimization process of injection and production parameters. Ultimately, this achieves the goal of optimizing injection and production parameters for fractured reservoirs with high accuracy and high efficiency, overcoming the technical pain points of long simulation time and unstable reduced-order models in existing technologies.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for optimizing injection and production parameters in fractured reservoirs based on retraining a reduced-order model includes the following steps:

[0008] s1. Establish a full-order numerical simulation model of fractured reservoirs, set initial injection and production control parameters, run the main training simulation and save the state snapshot and gradient information at each time step; run at least one set of sub-training simulations and save the state snapshot at each time step;

[0009] s2. Merge the state snapshots of the main training simulation and the secondary training simulation, construct the stress and saturation snapshot matrices, perform singular value decomposition on the snapshot matrices, and construct the reduced-order basis matrix;

[0010] s3. Using the reduced-order basis matrix, perform reduced-order preprocessing on the snapshot matrix and the gradient information of the main training simulation, project the full-order numerical simulation model to a low-dimensional subspace, and construct a reduced-order model;

[0011] s4. Using the reduced-order model as the prediction model, perform iterative optimization of injection and aspiration parameters to obtain the current optimal injection and aspiration parameters;

[0012] s5. After each iteration, calculate the cumulative adjustment step size of the injection and sampling parameters, and determine: if the cumulative adjustment step size exceeds the preset cumulative step size tolerance value, replace the original injection and sampling parameters of the main training simulation with the current optimal injection and sampling parameters, return to step s1 to re-execute the main training simulation, update the reduced-order basis matrix and the reduced-order model, and continue to execute the optimization iteration; if the cumulative adjustment step size does not exceed the preset cumulative step size tolerance value, further determine whether the preset maximum number of iterations has been reached: if the preset maximum number of iterations has been reached, proceed to step s6; if the preset maximum number of iterations has not been reached, return to step s4 to continue to execute the optimization iteration.

[0013] s6. Run the full-order numerical simulation model with the current optimal injection and extraction parameters for verification, and output the verified optimal injection and extraction parameters and their corresponding objective function values.

[0014] Optionally, in step s1, the full-order numerical simulation model of the fractured reservoir is constructed based on the embedded discrete fracture model EDFM, and the operation adopts a fully implicit discretization method. The nonlinear system at each time step is solved using the Newton-Raphson iteration method, and the solution at each time step is expressed as:

[0015] (1);

[0016] in, This is a flow model for a cracked system derived from the mass conservation equation and Darcy's law. , and These represent cumulative terms, current terms, and source / sink terms, respectively. The solution representing the system is saturation and pressure in an oil-water two-phase system; This represents the injection and sampling control parameters, which are known values ​​and often appear in source and sink entries; and This represents the current time step and the next time step to be solved.

[0017] Optionally, in step s1, the injection and sampling control parameters of the main training simulation are the initial injection and sampling control parameters, such as the median of the upper and lower limits of the injection and sampling control parameters optimization; the injection and sampling control parameters of the secondary training simulation are random variations covering the upper and lower limits of the injection and sampling control parameters. The secondary training simulation is only run once in the initial stage and is not rerun during the optimization iteration process. During the optimization iteration process, only the main training simulation is updated and repeated. The simulation duration of the main training simulation and the secondary training simulation is greater than or equal to the simulation duration of the optimization problem, so as to capture a more comprehensive field evolution behavior.

[0018] Optionally, in step s1, during the training simulation, it is assumed that the main training simulation has a total of At each time step, the sub-training simulation totaled... At each time step, the snapshot matrices are obtained as follows:

[0019] (2);

[0020] (3);

[0021] (4);

[0022] (5);

[0023] in, , , and These are the stress snapshot matrix and saturation snapshot matrix of the main training simulation, and the stress snapshot matrix and saturation snapshot matrix of the sub-training simulation. and Snapshots representing pressure and saturation at each time step:

[0024] (6);

[0025] (7);

[0026] in, and These are the pressures of the matrix mesh and the crack mesh, respectively. and These are the saturation levels of the matrix mesh and the crack mesh, respectively, indicated by superscript. Indicates vector transpose;

[0027] In addition, the main training simulation outputs and saves gradient information at all time steps when solving equation (1). The time steps already saved by the main training simulation are used... It means that the first The gradient information at each time step includes the partial derivative matrix of the residual with respect to the state variables at the current time step. The partial derivative matrix of the current time step residual with respect to the state variables of the previous time step. The partial derivative matrix of the residual with respect to the control variables at the current time step ,in:

[0028] (8).

[0029] Optionally, in step s2, singular value decomposition is used to construct reduced-order basis matrices for the pressure field and saturation field from the snapshot matrix, and a complete reduced-order basis matrix is ​​formed by diagonal combination. Assuming there is only one set of sub-training simulations, the pressure snapshot matrix is ​​expressed as:

[0030] (9);

[0031] The saturation snapshot matrix is ​​represented as:

[0032] (10);

[0033] Singular value decomposition was performed on the pressure snapshot matrix and the saturation snapshot matrix respectively:

[0034] (11);

[0035] in, , and These are the left singular matrix, the singular value diagonal matrix, and the right singular matrix, respectively, and the pressure basis matrix. and saturation basis matrix From their respective left singular matrices Columns and front The following is an example:

[0036] (12);

[0037] in, and Representing the left singular matrix respectively The column sum The List, and Determined by the energy loss threshold:

[0038] (13);

[0039] in, , The energy loss thresholds for the pressure basis matrix and the saturation basis matrix are respectively, and are generally less than 10. -8 , and These are singular value diagonal matrices. The A singular value and a singular value diagonal matrix The One singular value;

[0040] Construct the complete basis matrix for:

[0041] (14).

[0042] Optionally, in step S3, the reduced-order model is constructed based on the intrinsic orthogonal decomposition-trajectory piecewise linearization method. Using the reduced-order basis matrix, the snapshot matrix is ​​preprocessed to reduce its order as follows:

[0043] (15);

[0044] in, For the first The full-order high-dimensional state vector at each time step To be The low-dimensional state vector projected onto the low-dimensional basis space;

[0045] Because the reduced-order model stability of fractured reservoirs is worse than that of conventional reservoirs, the Petrove-Galerkin projection method is used to modify the gradient information of the main training simulation. , and Perform order reduction preprocessing to obtain preprocessed gradient information. , and ,as follows:

[0046] (16);

[0047] in, This is the partial derivative matrix of the preprocessed residuals with respect to the state variables at the current time step. This is the partial derivative matrix of the preprocessed residual with respect to the state variables of the previous time step. This is the partial derivative matrix of the preprocessed residuals with respect to the control variables at the current time step;

[0048] Subsequently, the full-order fractured reservoir model is projected onto a low-dimensional subspace to construct a reduced-order model, as follows:

[0049] (17);

[0050] in, This is the low-dimensional state vector at the current time step. Let be the low-dimensional state vector for the next time step to be solved. and These are the low-dimensional state vectors of adjacent time steps after the main training simulation snapshot matrix has been preprocessed to reduce its order. Here, formula (17) represents the reduced-order model. , , , and All of them come from the main training simulation.

[0051] Optionally, in step S4, the reduced-order model is used as the prediction model to perform injection and production parameter optimization iteration. The initial value of the optimization iteration is set to the injection and production control parameters used in the main training simulation, including the bottom hole pressure control regime of each injection well and production well. The optimization process adopts a gradient-based interior-point optimization algorithm and obtains the gradient information of the objective function with respect to the injection and production parameters through the finite difference method.

[0052] Optionally, in step S5, the cumulative adjustment step size is calculated for the new injection-sampling parameters obtained after each iteration by calculating the L2 norm distance between the current injection-sampling parameters and the initial injection-sampling parameters, as follows:

[0053] (18);

[0054] Where L is the cumulative adjustment step size, The new injection and acquisition parameters obtained from the current optimization iteration, These are the initial injection and extraction parameters.

[0055] This invention also proposes a system for optimizing injection and production parameters in fractured reservoirs based on a reduced-order model retraining, which executes the above method, including:

[0056] The model building and simulation module is used to build a full-order numerical simulation model of fractured reservoirs, set initial injection and production control parameters, run the main training simulation and save the state snapshot and gradient information at each time step; and run at least one set of sub-training simulations and save the state snapshot at each time step.

[0057] The reduced-order basis matrix construction module is used to construct pressure and saturation snapshot matrices, perform singular value decomposition on the snapshot matrices, and construct reduced-order basis matrices.

[0058] The order reduction model construction module is used to perform order reduction preprocessing on the snapshot matrix and the gradient information of the main training simulation using the order reduction basis matrix, projecting the full-order numerical simulation model to a low-dimensional subspace to construct the order reduction model;

[0059] The optimization iteration module is used to perform injection and sampling parameter optimization iterations using the reduced-order model as the prediction model.

[0060] The retraining module calculates the cumulative adjustment step size of the injection and sampling parameters after each iteration and determines whether the cumulative adjustment step size exceeds the preset cumulative step size tolerance. If the cumulative adjustment step size exceeds the preset cumulative step size tolerance, the injection and sampling parameters of the original main training simulation are replaced with the current optimal injection and sampling parameters. The module then returns to the model building and simulation module to re-execute the main training simulation, update the reduced-order basis matrix and the reduced-order model, and continue to perform optimization iteration. If the cumulative adjustment step size does not exceed the preset cumulative step size tolerance, the module further determines whether the preset maximum number of iterations has been reached. If the preset maximum number of iterations has been reached, the module enters the verification output module. If the preset maximum number of iterations has not been reached, the module returns to the optimization iteration module to continue performing optimization iteration.

[0061] The verification output module is used to run a full-order numerical simulation model with the current optimal injection and extraction parameters for verification, and outputs the verified optimal injection and extraction parameters and their corresponding objective function values.

[0062] The beneficial effects of this invention are that it effectively overcomes the technical pain points of existing full-order numerical simulations in fractured reservoir injection-production parameter optimization, which are time-consuming and difficult to apply in practice, as well as the insufficient stability and excessive prediction bias of conventional reduced-order models. By using an embedded discrete fracture model (EDFM) to accurately characterize the coupled seepage characteristics of fractures and matrix, and combining the intrinsic orthogonal decomposition-trajectory piecewise linearization (POD-TPWL) method with the Petrove-Galerkin projection method, it significantly reduces the computational complexity and simulation time of numerical simulations, while also significantly improving the accuracy and stability of the reduced-order model. Furthermore, through the collaborative design of primary and secondary training simulations and the retraining mechanism of the reduced-order model, it achieves real-time correction and progressive improvement of the reduced-order model during injection-production parameter optimization. Finally, full-order simulation verification ensures the reliability of the optimal injection-production parameters. The entire method has a closed-loop logic, strong operability, and balances the efficiency and accuracy of injection-production parameter optimization. It can effectively improve the recovery rate of fractured reservoirs and reduce development costs, providing reliable technical support for the efficient development of fractured reservoirs, and has significant engineering application value and promotion prospects. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the process for optimizing injection and production parameters in fractured reservoirs based on a reduced-order model retraining, according to the present invention.

[0064] Figure 2 This is a schematic diagram of well location and fracture distribution in a numerical simulation model of a fractured reservoir, as shown in an embodiment of the present invention.

[0065] Figure 3 The following is a simulation of the bottom pressure control curves of the injection and production wells in a main training exercise according to an embodiment of the present invention, wherein (a) is the bottom pressure curve of the production well and (b) is the bottom pressure curve of the injection well.

[0066] Figure 4 The following is an embodiment of the present invention showing the bottom pressure control curves of the injection-production well in a training simulation, wherein (a) is the bottom pressure curve of the production well and (b) is the bottom pressure curve of the injection well.

[0067] Figure 5 A comparison of the net present value iteration curves optimized based on the traditional no-retraining reduced-order model and the net present value iteration curves optimized based on the full-order numerical simulation model;

[0068] Figure 6 A comparison and verification curve of the production rate of the full-order and reduced-order models under the optimal injection and collection parameters optimized for the traditional non-retraining reduced-order model;

[0069] Figure 7 This is a comparison of the net present value (NPV) optimization iteration curve of the injection-production parameter optimization method for fractured reservoirs based on reduced-order model retraining and the NPV optimization iteration curve based on full-order numerical simulation model.

[0070] Figure 8 This is a verification curve showing the production rate comparison between the full-order model and the retrained reduced-order model under the optimal injection and production parameters of the fractured reservoir injection and production parameter optimization method based on the reduced-order model retraining of the present invention.

[0071] Figure 9 The optimized injection-production well bottom pressure curves are shown in one embodiment of the present invention, wherein (a) is the bottom pressure curve of the production well and (b) is the bottom pressure curve of the injection well. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] A method for optimizing injection and production parameters in fractured reservoirs based on retraining a reduced-order model, such as... Figure 1 As shown, it includes the following steps:

[0074] S1. Establish a full-stage numerical simulation model of fractured reservoirs, set initial injection and production control parameters, and run the main training simulation and the secondary training simulation respectively.

[0075] A full-order numerical simulation model of fractured reservoirs using EDFM was established. The permeability and well location distribution of the model are as follows: Figure 2 As shown, the porosity and permeability follow a Gaussian distribution. Fourteen fractures are included. Other basic parameters of the model are shown in Table 1. The model size is 1600m × 800m × 10m. The matrix is ​​divided into 5000 grids (50 × 25 × 4). The porosity varies randomly within the range of 0.02 to 0.2 and follows a Gaussian distribution. The average permeability of the matrix is ​​65 mD. The matrix permeability and porosity satisfy the Kozeny-Carman equation. The 14 fractures in the model are divided into 874 fracture elements by the matrix grid boundaries. The fracture aperture is 1 mm, and the fracture permeability is 100 D. Four production wells and two injection wells are included. The four production wells are located at both ends of the model, and the two injection wells are located in the middle. Oil and water phases are considered, with oil and water phase densities of 800 kg / m³.3 1000kg / m 3 The viscosities were 5 cp and 1 cp, respectively. The fluid was slightly compressible. The residual oil and bound water saturation were both 0.2. The initial oil saturation was 0.8. The initial reservoir pressure was 25 MPa.

[0076] Table 1 Basic parameters of Example 1

[0077]

[0078] The bottom hole pressure (BHP) settings in the main training simulation are as follows: Figure 3 As shown, the horizontal axis represents simulation time, and the vertical axis represents the BHP value. Figure 3 Figure (a) shows the BHP curves for four production wells, with the bottom hole pressure of all four wells remaining constant at 10 MPa. Figure 3 Figure (b) shows the BHP curves for two injection wells, with a constant injection pressure of 60 MPa for both wells. The simulation lasted 3600 days with a maximum time step of 30 days, generating 169 pressure and saturation snapshots. These 169 pressure and saturation snapshots, along with their corresponding gradient information, were saved. , and The BHP settings for the secondary training simulation are as follows: Figure 4 As shown in (a) and (b), the BHP of the four production wells in the secondary training simulation is randomly selected in the range of 8 to 22 MPa and changes every 200 days. The BHP of the two injection wells is randomly selected in the range of 53 to 67 MPa and changes every 200 days. The other settings are the same as those in the main training simulation. A total of 168 pressure snapshots and saturation snapshots are generated and saved.

[0079] S2. Merge the state snapshots of the main training simulation and the sub-training simulation to construct the pressure and saturation snapshot matrices. Perform singular value decomposition on the snapshot matrices to construct the reduced-order basis matrix.

[0080] Pressure snapshot matrix and saturation snapshot matrix Use separately Perform singular value decomposition (SVD), and let the energy loss threshold formulas for the pressure snapshot matrix and saturation snapshot matrix be... =10 -12 , =10 -8 ,available =124, =138, that is:

[0081] ;

[0082] Use formula Construct the complete basis matrix .

[0083] S3. Using the reduced-order basis matrix, the Petrove-Galerkin projection method is used to perform reduced-order preprocessing on the snapshot matrix and the gradient information of the main training simulation, projecting the full-order numerical simulation model to a low-dimensional subspace to construct a reduced-order model.

[0084] Use 169 of the main training simulations , and Pre-calculation was performed to obtain , and The reduced-order model is now ready to run, with each time step executed via the formula... Perform calculations and updates. This is in contrast to solving the formula for each time step. This formula is not only low-dimensional but also linear, which greatly speeds up the solution process.

[0085] S4. Using the reduced-order model as the prediction model, perform iterative optimization of injection and sampling parameters.

[0086] In this embodiment, the optimization variables are the BHP (Balance of Health) of all wells over 3600 days (changing every 200 days), totaling 108 optimization variables for 4 production wells and 2 injection wells. The optimization upper and lower limits for production wells are 20 MPa and 10 MPa, respectively, and the optimization upper and lower limits for injection wells are 65 MPa and 55 MPa, respectively. The optimization objective is the Net Present Value (NPV), as follows:

[0087] ;

[0088] in, , and These represent the oil production, water production, and water injection volume at time step k, respectively. In this example, the price of crude oil is set to 420 yuan per barrel. For the cost of water treatment, it is set at 98 yuan per barrel. The cost of water injection is set at 49 yuan per barrel. Setting a higher cost for water treatment and injection is to optimize the water production in this simple model and to prevent the final optimization result from being that injection and extraction are only performed at the extreme upper and lower limits of BHP. Let k be the duration of the k-th time step. The discount rate is set to 0.1.

[0089] s5. After each iteration, calculate the cumulative adjustment step size of the injection and sampling parameters, and determine: if the cumulative adjustment step size exceeds the preset cumulative step size tolerance value, replace the original injection and sampling parameters of the main training simulation with the current optimal injection and sampling parameters, return to step s1 to re-execute the main training simulation, update the reduced-order basis matrix and the reduced-order model, and continue to execute the optimization iteration; if the cumulative adjustment step size does not exceed the preset cumulative step size tolerance value, further determine whether the preset maximum number of iterations has been reached: if the preset maximum number of iterations has been reached, proceed to step s6; if the preset maximum number of iterations has not been reached, return to step s4 to continue to execute the optimization iteration.

[0090] In this embodiment, the optimization process employs a gradient-based interior-point optimization algorithm. The gradient information of the objective function with respect to the injection and sampling parameters is obtained through the finite difference method, resulting in an optimization vector composed of 108 optimization variables. , The preset cumulative step size tolerance is 1.2 MPa, that is... .

[0091] s6. Run the full-order numerical simulation model with the current optimal injection and extraction parameters for verification, and output the verified optimal injection and extraction parameters and their corresponding objective function values.

[0092] In this embodiment, we first attempt to optimize the entire process by constructing a fixed-order reduced model based solely on the initial primary and secondary training samples, without employing the retraining mechanism of this invention. Figure 5 In the figure, the red circled curve represents the NPV iteration curve obtained by optimizing injection and production parameters using a full-order numerical simulation model. The NPV increased from 0.94 billion yuan to 4.32 billion yuan, serving as a benchmark for optimization performance. The blue boxed curve represents the NPV iteration curve obtained by constructing a fixed-order reduction model based solely on the initial primary and secondary training samples without employing the retraining mechanism of this invention. Although this reduced-order model predicted an NPV of 4.50 billion yuan, after substituting the corresponding optimal control parameter BHP into the full-order model for simulation verification, the actual NPV was only 3.10 billion yuan (marked by the red box in the figure), significantly deviating from the optimal value of the full-order simulation optimization. This difference is not primarily due to the pluralistic nature of the optimization problem; the core reason lies in the gradual decrease in accuracy of the fixed-order reduction model during iterative optimization, which fails to provide reliable predictive support for the optimization algorithm, thus leading to distorted optimization results. Figure 6The graphs show the production rate comparison between the full-order model and the reduced-order model, constructed solely based on the initial primary and secondary training samples without employing the retraining mechanism of this invention. The curves represent the oil production, water production, and water injection rates of production wells 1-4 and injection wells 1-2 over time. As can be seen from the graphs, the prediction results of the fixed-order reduced-order model deviate significantly from the full-order numerical simulation results. The production rate curves of some wells show significant differences in both trend and numerical values. This indicates that the fixed-order reduced-order model, without retraining, suffers severe accuracy degradation during optimization and cannot accurately characterize the real production dynamics of fractured reservoirs. This further confirms the necessity and rationality of introducing a dynamic update mechanism for the reduced-order model in this invention.

[0093] Next, the injection and production parameter optimization method for fractured reservoirs based on the reduced-order model retraining method of this invention is used in equation [missing information]. Under given constraints, the optimization process involved 11 iterations of reduced-order model retraining and updating. The optimized BHP was then substituted into a full-order numerical simulation model for verification. Figure 7 The figure shows the NPV optimization iteration curve of the injection-production parameter optimization method for fractured reservoirs based on the reduced-order model retraining mechanism proposed in this invention. The calculated NPV is 412 million yuan, which is basically consistent with the optimal result of the full-order model (432 million yuan), and the accuracy meets the requirements of engineering applications. Although the method of this invention slightly increases the computational load due to retraining, the overall computation time is only 1.5 hours, which is about 73 times faster than the full-order simulation optimization (about 109 hours), significantly improving computational efficiency while ensuring optimization accuracy. Figure 8 This figure shows a comparison of the production rates of the full-order and retrained reduced-order models under the optimal injection-production parameters for the method of optimizing injection-production parameters in fractured reservoirs based on the retrained reduced-order model of this invention. As can be seen from the figure, the curves of the retrained reduced-order model and the full-order model are highly consistent with each other, with minimal numerical deviation. The production dynamics predictions for each well are accurate, fully demonstrating that the method of this invention can effectively maintain the accuracy and stability of the reduced-order model throughout the optimization process through the retraining mechanism, and can provide reliable and accurate predictive support for the optimization of injection-production parameters in fractured reservoirs. Figure 9 The figure shows the optimal injection-production well bottom pressure curves after optimization according to the present invention. (a) is the bottom pressure curve of the production well, and (b) is the bottom pressure curve of the injection well. As can be seen from the figure, the injection-production well bottom pressure regime obtained by retraining and iterative optimization by the method of the present invention is significantly different from the initial main training simulation constant pressure regime. This indicates that the optimization process fully matches the seepage characteristics and development requirements of fractured reservoirs, demonstrating the good adaptability and engineering practical value of the method of the present invention to the optimization problem of complex injection-production parameters.

[0094] This embodiment also proposes a parameter optimization system for fractured reservoirs based on a reduced-order model retraining, which executes the above method, including:

[0095] The model building and simulation module is used to build a full-order numerical simulation model of fractured reservoirs, set initial injection and production control parameters, run the main training simulation and save the state snapshot and gradient information at each time step; and run at least one set of sub-training simulations and save the state snapshot at each time step.

[0096] The reduced-order basis matrix construction module is used to construct pressure and saturation snapshot matrices, perform singular value decomposition on the snapshot matrices, and construct reduced-order basis matrices.

[0097] The order reduction model construction module is used to perform order reduction preprocessing on the snapshot matrix and the gradient information of the main training simulation using the order reduction basis matrix, projecting the full-order numerical simulation model to a low-dimensional subspace to construct the order reduction model;

[0098] The optimization iteration module is used to perform injection and sampling parameter optimization iterations using the reduced-order model as the prediction model.

[0099] The retraining module calculates the cumulative adjustment step size of the injection and sampling parameters after each iteration and determines whether the cumulative adjustment step size exceeds the preset cumulative step size tolerance. If the cumulative adjustment step size exceeds the preset cumulative step size tolerance, the injection and sampling parameters of the original main training simulation are replaced with the current optimal injection and sampling parameters. The module then returns to the model building and simulation module to re-execute the main training simulation, update the reduced-order basis matrix and the reduced-order model, and continue to perform optimization iteration. If the cumulative adjustment step size does not exceed the preset cumulative step size tolerance, the module further determines whether the preset maximum number of iterations has been reached. If the preset maximum number of iterations has been reached, the module enters the verification output module. If the preset maximum number of iterations has not been reached, the module returns to the optimization iteration module to continue performing optimization iteration.

[0100] The verification output module is used to run a full-order numerical simulation model with the current optimal injection and extraction parameters for verification, and outputs the verified optimal injection and extraction parameters and their corresponding objective function values.

[0101] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for optimizing injection and production parameters in fractured reservoirs based on retraining a reduced-order model, characterized in that, Includes the following steps: s1. Establish a full-order numerical simulation model of fractured reservoirs, set initial injection and production control parameters, run the main training simulation and save the state snapshot and gradient information at each time step; run at least one set of sub-training simulations and save the state snapshot at each time step; In step s1, the injection and sampling control parameters of the main training simulation are the initial injection and sampling control parameters, and the injection and sampling control parameters of the sub-training simulation are random variation values ​​covering the upper and lower limits of the injection and sampling control parameters. The sub-training simulation is only run once in the initial stage and is not run again during the optimization iteration process. During the optimization iteration process, only the main training simulation is updated and repeated. In step s1, it is assumed that the main training simulation has a total of At each time step, the sub-training simulation totaled... At each time step, the snapshot matrices are obtained as follows: ； ； ； ； in, , , and These are the stress snapshot matrix and saturation snapshot matrix of the main training simulation, and the stress snapshot matrix and saturation snapshot matrix of the sub-training simulation. and Snapshots representing pressure and saturation at each time step: ； ； in, and These are the pressures of the matrix mesh and the crack mesh, respectively. and These are the saturation levels of the matrix mesh and the crack mesh, respectively, indicated by superscript. Indicates vector transpose; s2. Merge the state snapshots of the main training simulation and the secondary training simulation, construct the stress and saturation snapshot matrices, perform singular value decomposition on the snapshot matrices, and construct the reduced-order basis matrix; In step s2, assuming there is only one set of secondary training simulations, the merged stress snapshot matrix is ​​represented as follows: ； The merged saturation snapshot matrix is ​​represented as follows: ； Singular value decomposition was performed on the merged pressure snapshot matrix and saturation snapshot matrix respectively: ； in, , and These are the left singular matrix, the singular value diagonal matrix, and the right singular matrix, respectively, and the pressure basis matrix. and saturation basis matrix From their respective left singular matrices Columns and front The following is an example: ； in, and Representing the left singular matrix respectively The column sum The List, and Determined by the energy loss threshold: ； in, , These are the energy loss thresholds for the pressure basis matrix and the saturation basis matrix, respectively. and These are singular value diagonal matrices. The A singular value and a singular value diagonal matrix The One singular value; Construct the complete basis matrix for: ； s3. Using the reduced-order basis matrix, perform reduced-order preprocessing on the snapshot matrix and the gradient information of the main training simulation, project the full-order numerical simulation model to a low-dimensional subspace, and construct a reduced-order model; s4. Using the reduced-order model as the prediction model, perform iterative optimization of injection and aspiration parameters to obtain the current optimal injection and aspiration parameters; s5. After each iteration, calculate the cumulative adjustment step size of the injection and sampling parameters, and determine: if the cumulative adjustment step size exceeds the preset cumulative step size tolerance value, replace the original injection and sampling parameters of the main training simulation with the current optimal injection and sampling parameters, return to step s1 to re-execute the main training simulation, update the reduced-order basis matrix and the reduced-order model, and continue to execute the optimization iteration; if the cumulative adjustment step size does not exceed the preset cumulative step size tolerance value, further determine whether the preset maximum number of iterations has been reached: if the preset maximum number of iterations has been reached, proceed to step s6; if the preset maximum number of iterations has not been reached, return to step s4 to continue to execute the optimization iteration. s6. Run the full-order numerical simulation model with the current optimal injection and extraction parameters for verification, and output the verified optimal injection and extraction parameters and their corresponding objective function values.

2. The method for optimizing injection and production parameters in fractured reservoirs based on retraining a reduced-order model as described in claim 1, characterized in that, In step s1, the full-order numerical simulation model of the fractured reservoir is constructed based on an embedded discrete fracture model. The simulation is run using a fully implicit discretization method, and the nonlinear system at each time step is solved using the Newton-Raphson iteration method. The solution formula for each time step is as follows: ； in, This is a flow model for a cracked system derived from the mass conservation equation and Darcy's law. , and These represent cumulative terms, current terms, and source / sink terms, respectively. The solution representing the system is saturation and pressure in an oil-water two-phase system; This indicates the injection control parameters, which are known values. and This represents the current time step and the next time step to be solved.

3. The method for optimizing injection and production parameters in fractured reservoirs based on retraining a reduced-order model as described in claim 1, characterized in that, In step s1, the main training simulation outputs and saves the gradient information at all time steps when solving the solution formula for each time step. The gradient information at each time step includes the partial derivative matrix of the residual with respect to the state variables at the current time step. The partial derivative matrix of the current residual with respect to the state variables of the previous time step The partial derivative matrix of the residual with respect to the control variables at the current time step ,in: 。 4. The method for optimizing injection and production parameters in fractured reservoirs based on retraining a reduced-order model as described in claim 3, characterized in that, In step S3, the snapshot matrix is ​​preprocessed by reducing its order using the reduced basis matrix, as follows: ； in, For the first The full-order high-dimensional state vector at each time step To be The low-dimensional state vector projected onto the low-dimensional basis space; The Petrove-Galerkin projection method is used to extract gradient information from the main training simulation. , and Perform order reduction preprocessing to obtain preprocessed gradient information. , and ,as follows: ； in, This is the partial derivative matrix of the preprocessed residuals with respect to the state variables at the current time step. This is the partial derivative matrix of the preprocessed residual with respect to the state variables of the previous time step. This is the partial derivative matrix of the preprocessed residuals with respect to the control variables at the current time step; Subsequently, the full-order fractured reservoir model is projected onto a low-dimensional subspace to construct a reduced-order model, as follows: ； in, This is the low-dimensional state vector at the current time step. Let be the low-dimensional state vector for the next time step to be solved. and These are the low-dimensional state vectors of adjacent time steps after the main training simulation snapshot matrix has been preprocessed by reducing its order.

5. The method for optimizing injection and production parameters in fractured reservoirs based on retraining a reduced-order model as described in claim 4, characterized in that, In step S5, the cumulative adjustment step size is calculated based on the new injection and sampling parameters obtained after each iteration, as follows: ； in, To accumulate adjustment step size, The new injection and acquisition parameters obtained from the current optimization iteration, These are the initial injection and extraction parameters.

6. A parameter optimization system for injection and production in fractured reservoirs based on a reduced-order model retraining, characterized in that, The method of any one of claims 1 to 5 comprises: The model building and simulation module is used to build a full-order numerical simulation model of fractured reservoirs, set initial injection and production control parameters, run the main training simulation and save the state snapshot and gradient information at each time step; and run at least one set of sub-training simulations and save the state snapshot at each time step. The reduced-order basis matrix construction module is used to construct pressure and saturation snapshot matrices, perform singular value decomposition on the snapshot matrices, and construct reduced-order basis matrices. The order reduction model construction module is used to perform order reduction preprocessing on the snapshot matrix and the gradient information of the main training simulation using the order reduction basis matrix, projecting the full-order numerical simulation model to a low-dimensional subspace to construct the order reduction model; The optimization iteration module is used to perform injection and sampling parameter optimization iterations using the reduced-order model as the prediction model. The retraining module calculates the cumulative adjustment step size of the injection and sampling parameters after each iteration and determines whether the cumulative adjustment step size exceeds the preset cumulative step size tolerance. If the cumulative adjustment step size exceeds the preset cumulative step size tolerance, the injection and sampling parameters of the original main training simulation are replaced with the current optimal injection and sampling parameters. The module then returns to the model building and simulation module to re-execute the main training simulation, update the reduced-order basis matrix and the reduced-order model, and continue to perform optimization iteration. If the cumulative adjustment step size does not exceed the preset cumulative step size tolerance, the module further determines whether the preset maximum number of iterations has been reached. If the preset maximum number of iterations has been reached, the module enters the verification output module. If the preset maximum number of iterations has not been reached, the module returns to the optimization iteration module to continue performing optimization iteration. The verification output module is used to run a full-order numerical simulation model with the current optimal injection and extraction parameters for verification, and outputs the verified optimal injection and extraction parameters and their corresponding objective function values.

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