Robust optimization method based on integrated optimization algorithm under geological uncertainty

Abstract

The invention relates to the technical field of petroleum and natural gas engineering numerical simulation, in particular to a robust optimization method based on an integrated optimization algorithm under geological uncertainty. According to the method, a control equation of oil-water two-phase underground flow and a productivity model of a well are established, and optimization of an injection-production scheme operation strategy is achieved in combination with the integrated optimization algorithm. In the optimization process, the underground flow state and the oil reservoir production and development dynamic state are predicted and optimized by accurately evaluating key indexes in the target function. And an error measurement mechanism and an overall performance analysis method are introduced, so that the optimization accuracy and robustness are effectively improved. Through the optimization framework based on integrated optimization, robust optimization of oil reservoir management and water-flooding development under geological uncertainty can be rapidly realized, and technical support is provided for efficient decision-making of oil reservoir water-flooding development.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation of petroleum and natural gas engineering, and in particular to a robust optimization method based on an integrated optimization algorithm under geological uncertainty. Background Art

[0002] In the process of oilfield development, production optimization is a key link in achieving efficient resource utilization and maximizing economic benefits. Its core goal is to optimize economic indicators such as net present value (NPV) by adjusting a set of control variables (such as well location, injection rate, etc.). Traditional production optimization methods usually rely on a single reservoir model, which is called nominal optimization. However, due to the complexity and uncertainty of geological conditions, the optimization results based on a single model are often difficult to achieve the expected results in actual oilfields, and may even lead to inaccurate optimization and erroneous reservoir performance predictions. To solve this problem, researchers have proposed multi-model optimization strategies in recent years to deal with the risks brought by geological uncertainty.

[0003] In the current technological context, robust optimization has become an effective solution to geological uncertainties. By simultaneously considering multiple reservoir models, robust optimization methods can maximize expected economic benefits and reduce economic losses due to model errors. Currently, robust optimization algorithms are mainly divided into two categories: gradient-based and gradient-free. Gradient optimization methods use the adjoint equations of the reservoir model to construct gradients to optimize control variables, but in practical applications, they are difficult to integrate with simulators and have high computational costs. In contrast, gradient-free optimization methods such as genetic algorithms and particle swarm optimization algorithms have shown significant advantages in dealing with complex multivariable problems.

[0004] Despite extensive research on production optimization, existing technologies still have some shortcomings. First, optimization methods based on traditional simplified models often lack sufficient accuracy when dealing with complex geological structures. Furthermore, as the uncertainty in oilfield development increases, the number of different simulation scenarios that need to be tested also increases. Summary of the Invention

[0005] The purpose of the present invention is to provide a robust optimization method based on an integrated optimization algorithm under geological uncertainty, so as to solve the problem that optimization methods based on traditional simplified models often cannot provide sufficient accuracy when faced with complex geological structures. In addition, as the uncertainty factors in oil field development increase, the number of different simulation situations that need to be tried also increases.

[0006] To achieve the above object, the present invention provides a robust optimization method based on an integrated optimization algorithm under geological uncertainty, comprising the following steps:

[0007] S1: Establish the governing equations for oil-water two-phase underground flow and the well productivity model;

[0008] S2: Introducing the NPV net present value evaluation method and establishing a robust optimization objective function with the goal of maximizing the net present value of oil field production;

[0009] S3: Introducing and calling external simulators or alternative models to calculate key indicators in the objective function and building a robust optimization computing framework;

[0010] S4: Use the gradient-free linear search method to iteratively optimize variables and seek production well control that maximizes the objective function value.

[0011] In step S1, the reservoir independent variables and dependent variables need to be modeled as follows:

[0012]

[0013] in, represents the output of the simulator or surrogate model, and Represented in three-dimensional space Pressure and saturation calculated or predicted by the simulator or surrogate model, Indicates the mapping relationship of related calculation or prediction process, m represents geological model, w represents well model, Here nb represents the total number of grid blocks, nt represents the number of time steps, and Ns represents the total number of different solutions corresponding to different well controls.

[0014] In step S1, the establishment of the well productivity model specifically refers to estimating the oil and water production of the production well using the Peaceman formula, and the calculation formula is as follows:

[0015]

[0016] in, is the source-sink mass flow rate of phase j in the i-th well block; P j is the well block pressure; is the bottom hole pressure of well block i; WI i is the well index, which can be expressed as:

[0017]

[0018] Among them, k i is the permeability of the well block corresponding to the i-th well; Δz is the thickness of the well block; the wellbore radius r0 is defined as 0.2Δx; and S represents the skin coefficient of the well.

[0019] In step S2, the definition of the robust optimization objective function for maximizing the net present value of oil field production is as follows:

[0020]

[0021] Where u represents all well control operations in the entire life cycle; n represents the nth control time step; Δt n is the duration of the nth control time step; b is the discount rate; N p and N i Represent the number of production wells and injection wells respectively; c wp represents the treatment cost of produced water; c wi is the water injection cost; and They represent the average oil production rate and average water production rate of the jth production well at the nth time step, respectively, with m 3 / D is the unit; represents the average injection rate at the kth injection well at the nth time step, expressed in m 3 / D is the unit.

[0022] The specific steps of step S3 are:

[0023] Construct a unified input module for simulators and alternative models to calculate or predict key indicators in reservoir production simulations using different setting parameters within the same call interface.

[0024] Construct a unified output module for simulators and alternative models to unify the data format of the same indicators calculated or predicted by different systems;

[0025] The specified optimization objective function is calculated based on the key indicators of reservoir production simulation in a unified data format, and the objective function results are output.

[0026] In step S4, the iterative optimization of variables using the gradient-free linear search method specifically refers to introducing an integrated optimization algorithm to implement an iterative step update strategy in the optimal value search process of reservoir robust optimization, and using the gradient-free linear search method to iteratively optimize the variable x:

[0027]

[0028] Where x l is the estimated value of the optimal variable at the lth iteration; ||·|| ∞ is the infinite norm; α1 is the search step length; C x is the covariance matrix, the specific element C in the covariance matrix x (i,j) can be defined according to the spherical model as follows:

[0029]

[0030] Where Cx (i,j) specifies the correlation coefficient between the well control at the i-th time step and the well control at the i-th time step, which also corresponds to the covariance matrix C x The value of the i-th row and j-th column in the well control sequence; σ is the standard deviation of the well control sequence; T is the maximum relevant well control time step interval set, and at the same time, the search direction vector It can also be expressed as:

[0031]

[0032] Where N e is the total number of well control realizations; Indicates the nth well control implementation; yes The average value of express The calculation results of the NPV objective function of the reservoir robust optimization calculated in the corresponding iterative step; It means The average value of .

[0033] The robust optimization method based on the integrated optimization algorithm under geological uncertainty also includes a termination condition for robust optimization of reservoirs under geological uncertainty, specifically:

[0034] The relative increment of the objective function value of reservoir robust optimization is less than 0.01%;

[0035] The variation of injection rate of the optimized wells during one iteration is less than 1%;

[0036] There is no case where we are forced to reduce the search step size α1 more than three times.

[0037] The steps of constructing the overall framework of the robust optimization algorithm based on the integrated optimization algorithm under geological uncertainty by using the robust optimization method based on the integrated optimization algorithm under geological uncertainty are as follows:

[0038] Establish a function that takes maximizing the net present value of oil field production as its objective;

[0039] An integrated optimization algorithm is introduced as an iterative search step update strategy for reservoir robust optimization;

[0040] Check whether the optimization termination condition is met. If so, the algorithm terminates; otherwise, the search continues.

[0041] This robust optimization method, based on an integrated optimization algorithm under geological uncertainty, significantly improves the overall computational efficiency of oilfield production optimization by combining a simulator, a surrogate model, and an integrated optimization algorithm. While maintaining prediction accuracy, it significantly reduces the computational time complexity of the optimization process, achieving efficient optimization of oilfield operations throughout their lifecycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0043] Figure 1 This is a flowchart of the overall implementation of the robust optimization method based on the integrated optimization algorithm under geological uncertainty provided by the present invention.

[0044] Figure 2 This is an algorithm framework diagram of the robust optimization method based on the integrated optimization algorithm under geological uncertainty provided by the present invention.

[0045] Figure 3 It is a schematic diagram of the distribution of several uncertain geological parameters (permeability, porosity) that may exist in the oil reservoir of Example 1 of the present invention.

[0046] Figure 4 Schematic diagram of the well locations and relative permeability curves of Example 1 of the present invention.

[0047] Figure 5 It is a schematic diagram of the well control sequence to be optimized proposed in Example 1 of the present invention.

[0048] Figure 6 Schematic diagram of the geological uncertainty sample of the model of Example 1 of the present invention.

[0049] Figure 7 It is a schematic diagram of the injection rate results of each iterative step during the optimization process of the substitution model of Example 1 of the present invention.

[0050] Figure 8 It is a schematic diagram comparing the final optimization results obtained by optimizing the injection rate under full control time step by substitution and reservoir numerical simulator in Example 1 of the present invention.

[0051] Figure 9 This is a cost diagram comparing the net present value and optimization time using various forward simulation models in Example 1 of the present invention.

[0052] Figure 10 1 is a schematic diagram comparing various performance parameters when implementing the relevant method based on the surrogate model and the reservoir numerical simulator according to Example 1 of the present invention. DETAILED DESCRIPTION

[0053] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0054] See also Figures 1 to 10 The present invention provides a robust optimization method based on an integrated optimization algorithm under geological uncertainty, comprising the following steps:

[0055] S100: Establish the governing equations for oil-water two-phase underground flow and the well productivity model;

[0056] Among them, the reservoir independent variables and dependent variables need to be modeled as follows:

[0057]

[0058] in, represents the output of the simulator or surrogate model, and Represented in three-dimensional space Pressure and saturation calculated or predicted by the simulator or surrogate model, Indicates the mapping relationship of related calculation or prediction process, m represents geological model, w represents well model, Here nb represents the total number of grid blocks, nt represents the number of time steps, and Ns represents the total number of different solutions corresponding to different well controls.

[0059] The establishment of the well productivity model specifically refers to estimating the oil and water production of the production well using the Peaceman formula. The calculation formula is as follows:

[0060]

[0061] in, is the source-sink mass flow rate of phase j in the i-th well block; P j is the well block pressure; is the bottom hole pressure of well block i; WI i is the well index, which can be expressed as:

[0062]

[0063] Among them, k i is the permeability of the well block corresponding to the i-th well; Δz is the thickness of the well block; the wellbore radius r0 is defined as 0.2Δx; and S represents the skin coefficient of the well.

[0064] S200: Construct robust optimization objective function based on NPV;

[0065] Specifically, it refers to the introduction of the NPV net present value evaluation method and the establishment of a robust optimization objective function with the goal of maximizing the net present value of oil field production;

[0066] Furthermore, the definition of the robust optimization objective function with the goal of maximizing the net present value of oil field production is as follows:

[0067]

[0068] Where u represents all well control operations in the entire life cycle; n represents the nth control time step; Δt n is the duration of the nth control time step; b is the discount rate; N p and N i Represent the number of production wells and injection wells respectively; c wp represents the treatment cost of produced water; c wi is the water injection cost; and They represent the average oil production rate and average water production rate of the jth production well at the nth time step, respectively, with m 3 / D is the unit; represents the average injection rate at the kth injection well at the nth time step, expressed in m 3 / D is the unit.

[0069] S300: Build a computational framework for predicting key indicators in the objective function by externally calling numerical simulators or surrogate models;

[0070] The specific steps of step S300 are:

[0071] Construct a unified input module for simulators and alternative models to calculate or predict key indicators in reservoir production simulations using different setting parameters within the same call interface.

[0072] Construct a unified output module for simulators and alternative models to unify the data format of the same indicators calculated or predicted by different systems;

[0073] The specified optimization objective function is calculated based on the key indicators of reservoir production simulation in a unified data format, and the objective function results are output.

[0074] S400: Use the gradient-free linear search method to iteratively optimize variables and seek production well control that maximizes the objective function value.

[0075] Specifically, the iterative optimization of variables using the gradient-free linear search method refers to the introduction of an integrated optimization algorithm to implement an iterative step update strategy in the optimal value search process of reservoir robust optimization, and the iterative optimization of variables x using the gradient-free linear search method:

[0076]

[0077] Where x l is the estimated value of the optimal variable at the lth iteration; ||·|| ∞ is the infinite norm; α1 is the search step length; C x is the covariance matrix, the specific element C in the covariance matrix x (i,j) can be defined according to the spherical model as follows:

[0078]

[0079] Where C x (i,j) specifies the correlation coefficient between the well control at the i-th time step and the well control at the i-th time step, which also corresponds to the covariance matrix C x The value of the i-th row and j-th column in the well control sequence; σ is the standard deviation of the well control sequence; T is the maximum relevant well control time step interval set, and at the same time, the search direction vector It can also be expressed as:

[0080]

[0081] Where N e is the total number of well control realizations; Indicates the nth well control implementation; yes The average value of express The calculation results of the NPV objective function of the reservoir robust optimization calculated in the corresponding iterative step; It means The average value of .

[0082] Furthermore, the robust optimization method based on the integrated optimization algorithm under geological uncertainty also includes a termination condition for robust optimization of oil reservoirs under geological uncertainty, specifically:

[0083] The relative increment of the objective function value of reservoir robust optimization is less than 0.01%;

[0084] The variation of injection rate of the optimized wells during one iteration is less than 1%;

[0085] There is no case where we are forced to reduce the search step size α1 more than three times.

[0086] Furthermore, the steps of constructing an overall framework of a robust optimization algorithm based on an integrated optimization algorithm under geological uncertainty by using the robust optimization method based on an integrated optimization algorithm under geological uncertainty are as follows:

[0087] Establish a function that takes maximizing the net present value of oil field production as its objective;

[0088] An integrated optimization algorithm is introduced as an iterative search step update strategy for reservoir robust optimization;

[0089] Check whether the optimization termination condition is met. If so, the algorithm terminates; otherwise, the search continues.

[0090] In this embodiment, the method establishes the control equations of the oil-water two-phase underground flow and the well production capacity model, and combines the integrated optimization algorithm to optimize the well control operation strategy. During the optimization process, the underground flow state and the reservoir production and development dynamics are predicted and optimized by accurately evaluating the key indicators in the objective function. The error measurement mechanism and the overall performance analysis method are introduced to effectively improve the accuracy and robustness of the optimization. Through the optimization framework based on integrated optimization, this technical solution can quickly realize the robust optimization of reservoir management and water injection development under geological uncertainty, providing technical support for efficient decision-making of water injection reservoirs.

[0091] Example 1:

[0092] The reservoir area of ​​the example model is discretized using a Cartesian grid with grid cells of size 60 × 60 × 1 in the x, y, and z directions. Each grid cell has a size of 10 m × 10 m × 4 m. The total number of grid cells is 3600. The reservoir contains 4 injection wells and 9 production wells arranged in a five-point arrangement. The 3D structure of the reservoir and the well locations are shown in Figure 1. Figure 3 The distribution of several uncertain geological parameters (permeability, porosity) that may exist in the reservoir and the relative permeability curve are shown in Figure 4 .

[0093] Six representative permeability realizations were prepared for the surrogate models to reflect the uncertainty in the geological model. In addition, 500 well control sequences were generated using Gaussian sampling, with average values ​​uniformly distributed within the optimization constraints. Subsequently, 500 simulations were run for each model with 500 well control sequences, resulting in a total of 25,000 sample sets. 2,500 samples were randomly selected from the sample set to form the reservoir model and constitute the training dataset. The six representative well control sequences are as follows: Figure 5As shown in the figure, the pressure and saturation maps are from the CMG-IMEX reservoir simulator. Pressure and saturation maps for all samples are generated and saved at each time step. The simulation time step is set to 30 days. The total simulation time is 30 days multiplied by 16, with the well rate adjusted every 30 days. There are 16 control steps throughout the simulated production period. These datasets were then used to build a surrogate model for the 3D example reservoir. The model was trained for 50 epochs with a learning rate of 0.001 and a batch size of 8. Training was performed on NVIDIA Tesla A800 GPUs, each with 80GB of memory. The entire training process took 305.7 seconds.

[0094] The technical solution of the present invention is further extended to the prediction ability assessment of the pressure field and saturation field after water flooding in the three-dimensional reservoir model. In order to verify the performance of the model, a systematic comparative analysis was carried out on the simulation results and prediction results under different geological parameter combinations (including boundary well control sequences and random permeability distributions). The alternative model established by the present invention can reconstruct the distribution characteristics of the reservoir parameter field with high precision, providing a reliable input for subsequent production capacity prediction and optimization decisions based on the Peaceman formula. In addition, a uniform initial injection rate of 300 cubic meters per day is set for each well. A range is introduced to adjust the injection volume of each well, and the range is adjusted within the range of 100 cubic meters per day to 500 cubic meters per day.

[0095] In the net present value model, the benchmark crude oil price was set at 3,200 RMB / m³. Additional parameters included a water production cost of 70 RMB / m³ and a water injection cost of 200 RMB / m³. Furthermore, an annual discount rate of 10% was used. The operating strategy for each injection well was adjusted every 30 days, resulting in a total of 16 control time steps. Figure 7 The injection rate for each iteration of the optimization process is also shown as an additional line. As can be seen, the injection rate for most wells improved after optimization using ensemble optimization. Furthermore, the optimized injection rate is relatively stable across the different time steps.

[0096] Figure 8 The final water injection rates optimized using the surrogate model and the full physics simulation are shown. While there are some differences between the water injection plans optimized using the surrogate model and the full physics simulation, these differences are due to the inherent stochastic factors of the integrated optimization algorithm. The optimization trends for the optimal water injection rates based on the surrogate model and the full physics simulator are consistent across all control time steps.

[0097] Comparison of the computational time of various simulation models (e.g. Figure 10(As shown in the figure). Compared to the time required for simulation-based optimization, the surrogate model significantly reduced the optimization computation time from 56,350 seconds to 102 seconds, a 552.5-fold speed-up. The computation time per model run was also reduced from 1,150 seconds to 1.7 seconds. This significant reduction in optimization computational cost highlights the robustness of the optimization algorithm framework that utilizes surrogate models to handle large numbers of forward simulations.

[0098] Using this framework, the algorithm was used to optimize the injection rate under geological uncertainty. The effectiveness of the deep learning-based robust reservoir optimization framework was demonstrated through comparative analysis of full-physics simulations.

[0099] The above disclosure is only a preferred embodiment of the present invention, and certainly cannot be used to limit the scope of the rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiment and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A robust optimization method based on an integrated optimization algorithm under geological uncertainty, characterized by: The steps include: S1: Establish the governing equations for oil-water two-phase underground flow and the well productivity model; S2: Introducing the NPV net present value evaluation method and establishing a robust optimization objective function with the goal of maximizing the net present value of oil field production; S3: Introducing and calling external simulators or alternative models to calculate key indicators in the objective function and building a robust optimization computing framework; S4: Use the gradient-free linear search method to iteratively optimize variables and seek production well control that maximizes the objective function value.

2. The robust optimization method based on an integrated optimization algorithm under geological uncertainty according to claim 1, characterized in that: In step S1, the reservoir independent variables and dependent variables need to be modeled as follows: in, represents the output of the simulator or surrogate model, and Represented in three-dimensional space Pressure and saturation calculated or predicted by the simulator or surrogate model, Indicates the mapping relationship of related calculation or prediction process, m represents geological model, w represents well model, Here nb represents the total number of grid blocks, nt represents the number of time steps, and Ns represents the total number of different solutions corresponding to different well controls.

3. The robust optimization method based on an integrated optimization algorithm under geological uncertainty according to claim 2, characterized in that: In step S1, the establishment of the well productivity model specifically refers to estimating the oil and water production of the production well using the Peaceman formula, which is calculated as follows: in, is the source-sink mass flow rate of phase j in the i-th well block; P j is the well block pressure; is the bottom hole pressure of well block i; WI i is the well index, which can be expressed as: Among them, K i is the permeability of the well block corresponding to the i-th well; Δz is the thickness of the well block; the wellbore radius r0 is defined as 0.2Δx; and S represents the skin coefficient of the well.

4. The robust optimization method based on an integrated optimization algorithm under geological uncertainty according to claim 3, characterized in that: In step S2, the definition of the robust optimization objective function with the goal of maximizing the net present value of oil field production is as follows: Where u represents all well control operations in the entire life cycle; n represents the nth control time step; Δt n is the duration of the nth control time step; b is the discount rate; N p and N i Represent the number of production wells and injection wells respectively; c wp represents the treatment cost of produced water; c wi is the water injection cost; and They represent the average oil production rate and average water production rate of the jth production well at the nth time step, respectively, with m 3 / D is the unit; represents the average injection rate at the kth injection well at the nth time step, expressed in m 3 / D is the unit.

5. The robust optimization method based on an integrated optimization algorithm under geological uncertainty according to claim 4, characterized in that: The specific steps of step S3 are: Construct a unified input module for simulators and alternative models to calculate or predict key indicators in reservoir production simulations using different setting parameters within the same call interface. Construct a unified output module for simulators and alternative models to unify the data format of the same indicators calculated or predicted by different systems; The specified optimization objective function is calculated based on the key indicators of reservoir production simulation in a unified data format, and the objective function results are output.

6. The robust optimization method based on an integrated optimization algorithm under geological uncertainty according to claim 5, characterized in that: In step S4, the variable is iteratively optimized using the gradient-free linear search method. Specifically, an integrated optimization algorithm is introduced to implement the iterative step update strategy in the optimal value search process of reservoir robust optimization, and the variable x is iteratively optimized using the gradient-free linear search method: Where x l is the estimated value of the optimal variable at the lth iteration; ||·|| ∞ is the infinite norm; α1 is the search step length; C x is the covariance matrix, the specific element C in the covariance matrix x (i,j) can be defined according to the spherical model as follows: Where C x (i,j) specifies the correlation coefficient between the well control at the i-th time step and the well control at the i-th time step, which also corresponds to the covariance matrix C x The value of the i-th row and j-th column in the well control sequence; σ is the standard deviation of the well control sequence; T is the maximum relevant well control time step interval set, and at the same time, the search direction vector It can also be expressed as: Where N e is the total number of well control realizations; Indicates the nth well control implementation; yes The average value of express The calculation results of the NPV objective function of the reservoir robust optimization calculated in the corresponding iterative step; It means The average value of .

7. The robust optimization method based on an integrated optimization algorithm under geological uncertainty according to claim 6, characterized in that: It also includes the termination conditions for reservoir robust optimization under geological uncertainty, specifically: The relative increment of the objective function value of reservoir robust optimization is less than 0.01%; The variation of injection rate of the optimized wells during one iteration is less than 1%; There is no case where we are forced to reduce the search step size α1 more than three times.

8. The robust optimization method based on an integrated optimization algorithm under geological uncertainty according to claim 7, characterized in that: The steps of constructing the overall framework of the robust optimization algorithm based on the integrated optimization algorithm under geological uncertainty using the robust optimization method based on the integrated optimization algorithm under geological uncertainty are as follows: Establish a function that takes maximizing the net present value of oil field production as its objective; An integrated optimization algorithm is introduced as an iterative search step update strategy for reservoir robust optimization; Check whether the optimization termination condition is met. If so, the algorithm terminates; otherwise, the search continues.

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