A fracture parameter multi-objective optimization method for compressed air energy storage in naturally fractured depleted reservoirs

Abstract

This invention discloses a multi-objective optimization method for fracture parameters in compressed air energy storage in naturally fractured depleted reservoirs, belonging to the fields of reservoir engineering and energy storage technology. The method includes the following steps: S1, constructing a dual-porosity medium numerical model for the matrix-fracture dual-porosity structure of the reservoir, and analyzing the correlation mechanism between fracture parameters and energy storage performance; S2, constructing a multi-objective collaborative control mathematical model based on the results of S1; S3, solving the multi-objective collaborative control mathematical model using an adaptive genetic algorithm, and constructing a phased dynamic control strategy throughout the entire energy storage cycle, combined with the operating characteristics of the energy storage system. This invention optimizes the fracture parameters of naturally fractured depleted reservoirs to achieve efficient and low-loss storage and recovery of air in fractured reservoirs, improving air recovery rate and the controllability of energy storage system operation, while ensuring reservoir structure stability, energy storage process safety, and the long-term economic efficiency and renewable energy utilization efficiency of the system.

Description

Technical Field

[0001] This invention relates to the fields of reservoir engineering and energy storage technology, and in particular to a multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs. Background Technology

[0002] As the global energy structure transitions towards a low-carbon model, the demand for large-scale grid connection of renewable energy sources such as wind and solar power is becoming increasingly urgent. However, their intermittency and volatility pose a severe challenge to the grid's supply and demand balance. Compressed air energy storage (CAES), as a large-scale physical energy storage technology, utilizes excess electricity during off-peak hours to compress air and store it underground. During peak hours, the compressed air is released to drive turbines for power generation, achieving the spatial and temporal transfer of energy. Currently, the underground storage media for CAES mainly include salt caverns, aquifers, and depleted oil and gas reservoirs. Among these, depleted oil and gas reservoirs, due to their natural storage space, developed well networks, and well-defined geological characteristics, have become highly promising energy storage carriers. However, when natural fractured depleted oil reservoirs are used as energy storage media, the fracture network developed within them significantly alters the reservoir's seepage characteristics, leading to multiple challenges during energy storage, including air loss, energy efficiency degradation, and reservoir stability. On the one hand, the presence of fractures increases air transport capacity, but also increases the air-oil-water interface, making it prone to oxidation and dissolution losses. On the other hand, the dissolution and diffusion of gas in the oil-water two phases and the accompanying chemical reactions (such as the formation of precipitates from oxidized pyrite) will affect reservoir properties and gas recovery rate. In the existing technology, the air injection, storage and production process for natural fractured reservoirs is as follows.

[0003] In the existing technology, there is a lack of in-depth analysis and control methods for the impact of fracture parameters (including fracture porosity, permeability, and fracture spacing) on ​​energy storage performance, and it is impossible to effectively predict and control the migration path and diffusion behavior of air in the fracture medium and its actual impact on the air recovery rate.

[0004] Based on the above problems, a multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs is proposed. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs, in order to solve the problems in the background art.

[0006] To achieve the above objectives, this invention provides a multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs, comprising the following steps:

[0007] S1. For the matrix-fracture dual-porosity structure of naturally fractured depleted oil reservoirs, a numerical model of dual-porosity medium is constructed to analyze the correlation mechanism between fracture parameters and energy storage performance; fracture parameters include fracture porosity, fracture permeability, and fracture spacing.

[0008] S2. Based on the results of S1, a multi-objective collaborative control mathematical model is constructed with the objectives of "maximizing air recovery rate, minimizing oxidation reaction inhibition, and maximizing reservoir stability" as the goals.

[0009] S3. An adaptive genetic algorithm is used to solve the mathematical model of multi-objective collaborative regulation. Combined with the operating characteristics of the energy storage system, a phased dynamic regulation strategy that runs through the entire energy storage cycle is constructed.

[0010] Preferably, the specific steps of S1 are as follows:

[0011] S11. The naturally fractured depleted reservoir is divided into discrete grids, and a dual-porosity medium numerical model is constructed using the STARS module of CMG software. The reservoir is divided into discrete grids, and the pore characteristics of the matrix and fractures are defined separately: fractures are used as high-permeability channels (with permeability significantly higher than that of the matrix), and the matrix is ​​used as the main storage unit.

[0012] S12. Set matrix and fracture parameters, and establish the mass conservation equation for fluid exchange between fractures and matrix; simulate the fluid exchange process between fractures and matrix, considering the differences in horizontal and vertical permeability of fractures, as well as the influence of fracture spacing on fluid distribution; the mass conservation equation can accurately characterize its migration law, and the determination of each parameter fully considers the heterogeneity of the reservoir and the fluid flow characteristics. The fluid exchange source term between matrix and fracture is calibrated through laboratory core flow experiments and field production data to ensure that the equation can accurately reflect the fluid migration law under actual working conditions;

[0013] S13. Introduce the permeability tensor to describe the anisotropic characteristics of fracture permeability, and quantify the influence of fracture spacing on fluid distribution through inter-mesh conductivity.

[0014] S14. Through orthogonal experimental design, the relationship between fracture porosity, fracture permeability, fracture spacing and air recovery rate was qualitatively analyzed. The results showed that: increasing fracture porosity can increase storage space and promote air flow; increasing permeability can optimize injection and production efficiency; reducing spacing can improve air distribution uniformity, but the interaction of the three factors needs to be synergistically regulated.

[0015] In the above process, the pressure response curves of fractures and conventional reservoirs were compared using the TOUGH2-MP / EOS3 simulator to verify the promoting effect of fractures on seepage efficiency. At the same time, the influence of fracture parameters on oxidation reaction and diffusion loss was calibrated using core experimental data.

[0016] Preferably, in S12, the mass conservation equation for fluid exchange between the crack and the matrix is ​​expressed as:

[0017] ;

[0018] in, For matrix porosity, For matrix fluid density, For matrix saturation, Let be the matrix seepage velocity vector. For matrix viscosity, For matrix pressure; For crack porosity, For the density of the fracture fluid, For crack gaps, Let be the crack seepage velocity vector. Crack viscosity, For crack pressure, This is a source term for fluid exchange between the matrix and the fracture. For time.

[0019] Preferably, in S13, the permeability tensor is expressed as:

[0020] ;

[0021] in, For the permeability tensor, The horizontal permeability of the crack. Vertical permeability of the crack;

[0022] Inter-mesh conductivity is expressed as:

[0023] ;

[0024] in, Inter-mesh conductivity, For the area of ​​the grid interface, For grid spacing.

[0025] Preferably, in step S14, the relationship between crack porosity and air recovery rate is expressed as follows:

[0026] ;

[0027] The relationship between crack permeability and air recovery rate is expressed as follows:

[0028] ;

[0029] The relationship between crack spacing and air recovery rate is expressed as follows:

[0030] ;

[0031] in, For air recovery rate, All are coefficients. The value represents the crack permeability.

[0032] Preferably, in S2, the multi-objective collaborative regulation mathematical model is expressed as:

[0033] ;

[0034] in, , , , These are the weighting coefficients. To inhibit the oxidation reaction, For reservoir stability.

[0035] Preferably, the specific steps of S2 are as follows:

[0036] 1) Construct objective functions for air recovery rate, oxidation reaction inhibition, and reservoir stability, respectively;

[0037] 2) Using fracture porosity, fracture permeability, and fracture spacing as decision variables, and geological feasibility, engineering operability, and safety regulations as constraints, a mapping relationship between the parameters and the three objective functions is constructed, expressed as follows:

[0038] ;

[0039] The multi-objective optimization problem is transformed into a single-objective optimization problem by using a weighted summation method, resulting in a multi-objective synergistic regulation mathematical model. The data in the model can be flexibly adjusted according to the actual needs of different stages of the energy storage system. For example, the model reveals that the synergistic improvement of crack porosity and permeability can significantly improve the recovery rate, but the risk of intensified oxidation reaction needs to be considered simultaneously.

[0040] 3) Based on the mechanical properties of reservoir rocks, the range of fracture porosity and fracture permeability is limited, and the fracture spacing adjustment boundary is set in combination with the fracturing technology capability to ensure that the control of fracture parameters is feasible in actual construction.

[0041] Preferably, in step S2, the objective function for air recovery rate is expressed as:

[0042] ;

[0043] in, To the total amount of air injected, This refers to the amount of seepage retention loss. The amount of air consumed for oxidation. This represents the amount of loss due to diffusion and dissolution.

[0044] The objective function for inhibiting oxidation is expressed as:

[0045] ;

[0046] in, For reaction rate;

[0047] The objective function for reservoir stability is expressed as:

[0048] ;

[0049] in, The congestion coefficient is... This represents the amount of precipitate produced during the reaction.

[0050] Preferably, in step S3, the process of solving the multi-objective collaborative regulation mathematical model using an adaptive genetic algorithm is as follows:

[0051] (1) Algorithm encoding and population initialization: The fracture parameters are encoded as binary chromosomes, the population size is set according to the reservoir complexity, and the population is initialized in combination with geological prior knowledge (such as the parameter range of typical fracture reservoirs) to improve the optimization efficiency;

[0052] (2) Construction of dynamic fitness function: A staged weighting coefficient w is introduced, and the target priority is adjusted according to the energy storage cycle (injection, storage, output) to calculate the individual fitness. The calculation formula is expressed as:

[0053] ;

[0054] in, For air recovery rate weighting coefficient, Weighting coefficient for inhibiting oxidation reaction This is the reservoir stability weighting coefficient;

[0055] (3) Iterative optimization mechanism: The population is updated iteratively through selection, crossover and mutation operations. The elite retention strategy is adopted to ensure that the optimal solution is not lost. The algorithm adaptively adjusts the crossover and mutation probabilities, balances global search (finding the optimal parameter combination) and local optimization (refining parameter values), and finally generates the Pareto optimal solution set, providing multiple options for the control scheme;

[0056] The selection process uses a roulette wheel betting method, and the individual... Probability of being selected The calculation formula is:

[0057] ;

[0058] The crossover operation uses a single-point crossover method, while the mutation operation mutates individual genes; to achieve a balance between global search and local optimization, the crossover probability is adaptively adjusted. With the probability of mutation , represented as:

[0059] ;

[0060] ;

[0061] in, , , These represent the maximum fitness, minimum fitness, and average fitness of the current generation population, respectively.

[0062] Preferably, in S3, the phased dynamic control strategy throughout the entire energy storage lifecycle is as follows:

[0063] 1) Injection stage control: Using a combination of "high permeability + medium porosity" parameters, natural fractures are expanded through hydraulic fracturing technology to form directional high-permeability channels and shorten the injection time; at the same time, porosity is controlled to reduce air diffusion loss in the initial stage, optimize injection rate and pressure, and avoid reservoir fracturing.

[0064] 2) Storage stage regulation: The strategy is adjusted to "low permeability + low porosity". Some high-permeability fractures are closed by temporary plugging technology to reduce the contact efficiency between air and rock and inhibit oxidation reaction. At the same time, the changes in reservoir fluid composition are monitored and parameters are dynamically adjusted to maintain the stability of air composition.

[0065] 3) Production stage control: The combination of "small spacing + medium permeability" is adopted. By adding new fracturing fractures, the air migration distance is shortened, the production well network deployment is optimized, the air flow is improved, the residual air retention is reduced, and the fracture parameters are adjusted in real time in combination with the production rate and pressure decay to maximize the recovery rate.

[0066] Preferably, in step 1), the engineering constraints during the process of expanding natural fractures using hydraulic fracturing technology are as follows:

[0067] Ensure that the injection pressure does not exceed 80% of the rupture pressure;

[0068] in, To inject pressure;

[0069] The rupture pressure is expressed as:

[0070] ;

[0071] In the formula, For the minimum horizontal principal stress, For the maximum horizontal principal stress, For the tensile strength of rock, Pore ​​pressure;

[0072] In step 2), during the process of temporarily plugging some of the high-permeability fractures, the amount of plugging agent injected is determined based on the fracture volume, which is expressed as:

[0073] ;

[0074] In the formula, For the first Porosity of the crack The cross-sectional area of ​​the crack. The height of the crack;

[0075] In step 3), during the process of shortening the air transport distance by adding new fracturing fractures, the relationship between air velocity, permeability, and pressure gradient is expressed as follows:

[0076] ;

[0077] in, air velocity, For penetration rate, For pressure gradient, It represents viscosity.

[0078] Preferably, in the phased dynamic control process of S3, a real-time monitoring and feedback system is deployed, specifically: deploying a downhole sensor network to collect data such as pressure, temperature, and fluid composition in real time; when an abnormal oxidation reaction is detected (such as a sudden increase in CO2 concentration) or a decrease in recovery rate, the adaptive genetic algorithm in step S3 is triggered to re-optimize the parameters and achieve dynamic correction.

[0079] Therefore, the multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs of the present invention has the following beneficial effects:

[0080] (1) Improve air energy storage efficiency: By modeling the dual-porosity medium and coordinating multi-objective regulation, the injection, storage and production process of air in the reservoir is optimized, and the air recovery rate is significantly improved. When the fracture porosity increases by 0.1 and the permeability increases by 1000mD, the air recovery rate increases by 19% and 16% respectively, providing a high-efficiency operating basis for large-scale compressed air energy storage systems.

[0081] (2) Suppress oxidation reaction and loss: Reduce the contact area between air and rock and residual oil by optimizing parameters, slow down the oxidation reaction rate (the oxidation reaction rate can be reduced by 40% during the storage stage), reduce CO2 generation and solid precipitation to block pores, and maintain the long-term stability of reservoir permeability.

[0082] (3) Ensure reservoir structure safety: Combine rock mechanics constraints with dynamic control strategies to avoid reservoir rupture or permeability decay caused by unreasonable parameters, and ensure the safety and reliability of the energy storage system in long-term operation.

[0083] (4) Promote the consumption of renewable energy: provide large-scale, long-term energy storage solutions for intermittent energy sources such as wind and solar power, improve the economy and controllability of energy storage systems by optimizing crack parameters, and promote the low-carbon transformation of energy structure.

[0084] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0085] Figure 1 This is a schematic diagram of a three-dimensional mesh discretization model of a dual-porosity medium according to an embodiment of the present invention;

[0086] Figure 2 This is a trend diagram showing the influence of crack parameters on air recovery rate in an embodiment of the present invention;

[0087] Figure 3 This is a diagram illustrating the overall architecture of the method according to an embodiment of the present invention.

[0088] Figure 4 This is a flowchart of the adaptive genetic algorithm according to an embodiment of the present invention. Detailed Implementation

[0089] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0090] 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 some embodiments of the present invention, but not all embodiments.

[0091] In the method described in the following embodiments, the correlation mechanism between fracture parameters and energy storage performance is first quantified based on the dual-porosity medium theory. Then, a multi-objective model is established with the goals of maximizing air recovery rate, minimizing oxidation reaction, and maximizing reservoir stability. The optimal parameter combination is solved by using an adaptive genetic algorithm. Finally, a phased dynamic control strategy is formulated in combination with the energy storage cycle characteristics to achieve full-process optimization of fracture parameters.

[0092] Example

[0093] like Figure 3 As shown, this embodiment relates to a multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs, specifically:

[0094] S1. For matrix-fracture dual-porosity structures in naturally fractured depleted reservoirs, a numerical model of the dual-porosity medium is constructed to analyze the correlation mechanism between fracture parameters and energy storage performance. Fracture parameters include fracture porosity, fracture permeability, and fracture spacing. Specifically:

[0095] In the dual-porosity medium model, the crack spacing The spatial spacing of natural fractures in a reservoir is a key parameter characterizing fracture development density; grid spacing. The two are the size of the computational unit when the numerical model is discretized. In this invention, they are related through the conductivity formula, but their physical meanings are different.

[0096] S11, Framework for constructing a dual-porosity model:

[0097] Using the STARS module of CMG software, the naturally fractured depleted reservoir was discretized into a 5×10×10 three-dimensional mesh. A schematic diagram of the three-dimensional mesh discretization model of the dual-porosity medium is shown below. Figure 1 As shown, a numerical model of a dual-porosity medium is constructed.

[0098] S12. In this model, the matrix and cracks are given different pore characteristic parameters to accurately simulate the complex motion of fluid in a dual-pore system.

[0099] The matrix, serving as the primary fluid storage unit, has a horizontal permeability set at [value missing]. Set to 10mD, vertical permeability The porosity is 0.1 mD. The value is set to 0.11; the cracks act as high-permeability channels, with a horizontal permeability... Reaching 500mD, vertical permeability 50mD, porosity The crack spacing is 0.001. Set it to 20ft.

[0100] The determination of these parameters is based on the survey and analysis of a large amount of actual data from similar reservoirs, as well as rich engineering experience, and can accurately reflect the true geological characteristics of the reservoirs. After the three-dimensional discrete grid system is constructed, based on this three-dimensional discrete grid system and the setting of pore characteristic parameters, and further combined with the theory of dual-porosity media, the exchange mechanism and migration law of fluids between fractures and matrix are explored in depth.

[0101] After completing the construction of the three-dimensional discrete mesh system and setting the pore characteristic parameters, considering the complexity of fluid exchange between the fracture and the matrix, a mass conservation equation for fluid exchange between the fracture and the matrix is ​​established based on the dual-porosity medium theory:

[0102] ;

[0103] in, For matrix porosity, For matrix fluid density, For matrix saturation, Let be the matrix seepage velocity vector. For matrix viscosity, For matrix pressure; For crack porosity, For the density of the fracture fluid, For crack gaps, Let be the crack seepage velocity vector. Crack viscosity, For crack pressure, This is a source term for fluid exchange between the matrix and the fracture. For time.

[0104] Boundary conditions:

[0105] (1) Injection well boundary: (The injection pressure is constant at 30 MPa). (The gas saturation in the fractures near the injection well is 1).

[0106] (2) Production well boundary: (Constant output);

[0107] (3) Outer boundary: (Closed boundary conditions), initial conditions (Initial reservoir pressure). (Initial oil saturation of the matrix);

[0108] The mass conservation equation can accurately characterize its migration law, and the determination of each parameter fully considers the heterogeneity of the reservoir and the fluid flow characteristics. The fluid exchange source term between the matrix and the fracture is calibrated through laboratory core flow experiments and field production data to ensure that the equation can accurately reflect the fluid migration law under actual working conditions.

[0109] S13. To accurately describe the anisotropic characteristics of fracture permeability, a permeability tensor is introduced. , represented as:

[0110] ;

[0111] in, For the permeability tensor, The horizontal permeability of the crack. Vertical permeability of the crack;

[0112] The effect of crack spacing on fluid distribution is quantified by the inter-mesh conductivity T, and its calculation formula is as follows:

[0113] ;

[0114] in, Inter-mesh conductivity, For the area of ​​the grid interface, For grid spacing.

[0115] Research has shown that a 10ft reduction in fracture spacing increases conductivity by approximately 30%, significantly promoting uniform fluid distribution within the reservoir and having a crucial impact on the efficiency of air injection, storage, and production during energy storage.

[0116] S14. Parameter sensitivity analysis method:

[0117] An orthogonal experimental design was employed to systematically investigate the effects of fracture porosity, permeability, and spacing on air recovery rate (ARF). A carefully designed 3... 3 =27 sets of experiments, the specific experimental design is shown in Table 1. During the experiment, only one parameter was changed independently each time: fracture porosity (range 0.001~0.1), fracture permeability (range 10~2000mD), and fracture spacing (range 10~40ft), while keeping other reservoir parameters such as matrix permeability and matrix porosity constant to ensure the accuracy and reliability of the experimental results.

[0118] Table 1 Orthogonal experimental design

[0119]

[0120] In-depth analysis of the experimental results yielded the following conclusion: There is a significant linear relationship between crack porosity and air recovery rate, expressed as follows:

[0121] ,

[0122] That is, for every 0.1 increase in crack porosity, the air recovery rate will increase by 19%;

[0123] The relationship between permeability and air recovery rate is as follows:

[0124] ,

[0125] This means that for every 1000 mD increase in fracture permeability, the air recovery rate increases by 16%;

[0126] The relationship between crack spacing and air recovery rate is as follows:

[0127] ,

[0128] This indicates that for every 10 ft reduction in the crack spacing, the air recovery rate decreases slightly by 0.3%.

[0129] The trend of the influence of crack parameters on air recovery rate is shown in the figure below. Figure 2 As shown, Figure 2 The results show that fracture porosity has the most significant impact on improving air recovery. It leads to an increase in air recovery by 19%, followed by fracture permeability which leads to an increase in the air recovery factor by 16%.

[0130] Furthermore, increasing fracture porosity has the most significant impact on reducing air recovery rate (ERR), leading to an 11% decrease. Conversely, reducing fracture spacing has a minimal impact on ERR reduction under minimum conditions, resulting in a 0.3% decrease. In summary, this study indicates that NFRs with high fracture porosity and high fracture permeability are more effective. However, these three parameters do not act independently; they have complex interactions that require coordinated regulation to achieve optimal energy storage performance.

[0131] Perform model validation logic:

[0132] The pressure response curves of fractured and conventional reservoirs were simulated using the TOUGH2-MP / EOS3 simulator. Under the same injection conditions (injection rate of 1000 scf / day and injection time of 30 days), the pressure rise rate of the fractured reservoir was 2.3 times faster than that of the conventional reservoir, and the time to reach a stable pressure of 4000 psi was shortened by 40%. These results strongly validate the significant promoting effect of fractures on seepage efficiency.

[0133] The model was calibrated by conducting core experiments. Core samples with different fracture porosity and permeability were selected, and simulated air was injected into the laboratory to monitor key data such as oxygen concentration, carbon dioxide concentration, and air diffusion rate in real time. Experimental results showed that the oxidation reaction rate was positively correlated with fracture permeability and porosity, while diffusion loss was mainly affected by porosity and fracture spacing. Based on the experimental data, the oxidation reaction rate constant in the numerical model was adjusted. With diffusion coefficient Fine-tuning was performed to keep the error between the model simulation results and the experimental data within 5%, effectively ensuring the accuracy and reliability of the model.

[0134] Based on the in-depth analysis of the relationship between fracture parameters and energy storage performance using the above quantitative model, a multi-objective collaborative control mathematical model is further constructed.

[0135] S2. Based on the results of S1, a multi-objective synergistic control mathematical model is constructed with the objectives of "maximizing air recovery rate, minimizing oxidation reaction inhibition, and maximizing reservoir stability"; specifically:

[0136] 1) Objective function design approach:

[0137] The objective function for air recovery rate aims to reduce air loss throughout the entire process of injection, storage, and production. This includes losses due to seepage and retention. The calculation formula is:

[0138] ;

[0139] In the formula, Aerodynamic viscosity, This refers to the daily injection volume of a single well. The distance of air transport. For crack permeability, The cross-sectional area of ​​the crack;

[0140] Air consumption for oxidation Taking the reaction of oxygen with pyrite as an example, its reaction rate Following the Arrhenius equation:

[0141] ;

[0142] In the formula, is the reaction rate constant (taken as 0.02). Oxygen concentration, n This represents the reaction order (value 0.02). Activation energy;

[0143] Assuming the reservoir is cubic in shape, and considering the fracture porosity in the reservoir as follows: The crack spacing is The reservoir volume can be obtained. Represented as:

[0144] ;

[0145] Diffusion Dissolution Loss Following Fick's diffusion law:

[0146] ;

[0147] In the formula, Where is the diffusion coefficient. For concentration gradient;

[0148] If the crack width is , length is Then the diffusion area This allows us to obtain the amount of diffusion and dissolution loss. The calculation formula is:

[0149] ;

[0150] Total amount of air injected The calculation formula is:

[0151] ;

[0152] In the formula, The total volume of the reservoir is... This represents the gas phase saturation.

[0153] Taking all the above factors into account, the objective function for air recovery rate is constructed as follows:

[0154] ;

[0155] in, To the total amount of air injected, This refers to the amount of seepage retention loss. The amount of air consumed for oxidation. This represents the amount of loss due to diffusion and dissolution.

[0156] Oxidation reaction inhibition objective function: Taking the reaction of oxygen with sulfur-containing minerals as the research object, the reaction rate... Contact area with air and rock Proportional, that is:

[0157] ;

[0158] Therefore, an objective function for inhibiting oxidation reactions is constructed:

[0159] ;

[0160] Reservoir stability objective function: reaction precipitation amount Concentration of ions produced by oxidation reaction Reaction equilibrium constant They are closely related, and their relationship expression is:

[0161] ;

[0162] In the formula, Let be the reaction order, taken as 1.2;

[0163] Reservoir permeability decay rate The calculation formula is:

[0164] ;

[0165] in, , The initial fracture permeability, The permeability of the fracture after attenuation. The congestion coefficient is set at 0.4 to 0.6.

[0166] This leads to the reservoir stability objective function:

[0167] ;

[0168] 2) Based on crack porosity Penetration rate ,spacing As a decision variable, a nonlinear mapping relationship is constructed between it and the objective function:

[0169] Represented as:

[0170] ;

[0171] By employing a weighted summation method, the multi-objective optimization problem is transformed into a single-objective optimization problem, resulting in a multi-objective collaborative regulation mathematical model, expressed as:

[0172] ;

[0173] in, , , , This is a weighting coefficient that can be flexibly adjusted according to the actual needs of different stages of the energy storage system.

[0174] 3) Engineering-based setting of constraints:

[0175] Based on the results of reservoir rock mechanics experiments, the reasonable range for porosity is scientifically determined to be 0.001 ≤ ≤0.1, the permeability constraint range is 10≤ The fracture spacing is set to ≤2000mD to avoid damage to the rock structure due to excessively large parameters. Considering the current capabilities of hydraulic fracturing technology, the adjustment boundary for the fracture spacing is set at 10≤ ≤40ft. Simultaneously, the concentration of harmful gases during the oxidation reaction is strictly controlled to ensure that the oxygen concentration decreases by no more than 20%, thereby guaranteeing the safety and environmental friendliness of the construction process.

[0176] Based on the Pareto optimal solution set obtained by the adaptive genetic algorithm, and combined with the operating characteristics of the energy storage system, a phased dynamic control strategy is formulated.

[0177] S3. An adaptive genetic algorithm is used to solve the mathematical model of multi-objective collaborative regulation, such as... Figure 4 As shown, specifically:

[0178] (1) Algorithm encoding and population initialization:

[0179] The fracture porosity, permeability, and spacing are encoded as binary chromosomes. For porosity (range 0.001~0.1), a 10-bit binary encoding is used, achieving an accuracy of (0.1~0.001) / (2). 10 ~1)≈9.77×10 -5The permeability (range 10~2000 mD) uses 12-bit binary encoding, and the spacing (range 10~40 ft) uses 8-bit binary encoding, together forming a 30-bit chromosome structure. Based on the reservoir complexity, the population size is set to 100. During population initialization, combined with prior geological knowledge, initial individuals are randomly generated within the parameter range of typical fractured reservoirs (porosity 0.01~0.05, permeability 100~500 mD, spacing 15~25 ft). This method effectively improves the algorithm's optimization efficiency.

[0180] (2) Construction of dynamic fitness function

[0181] A phased weighting coefficient is introduced to adjust the target priority according to different stages of the energy storage cycle (injection, storage, and output): In the injection stage, a weighting coefficient is set. =0.6, =0.2, =0.2; during the storage phase, adjust to =0.3, =0.5, =0.2; Production stage, set =0.5, =0.2, =0.3. Based on the adjusted weighting coefficients, the fitness of an individual is calculated and expressed as:

[0182] ;

[0183] in, For air recovery rate weighting coefficient, Weighting coefficient for inhibiting oxidation reaction This is the reservoir stability weighting coefficient;

[0184] (3) Iterative optimization mechanism:

[0185] The selection process uses a roulette-style betting method, and the individual... Probability of being selected The calculation formula is:

[0186] ;

[0187] in, For individuals fitness value, The first in the population The fitness value of each individual;

[0188] The crossover operation uses a single-point crossover method, while the mutation operation mutates individual genes; to achieve a balance between global search and local optimization, the crossover probability is adaptively adjusted. With the probability of mutation , represented as:

[0189] ;

[0190] ;

[0191] in, , , These represent the maximum fitness, minimum fitness, and average fitness of the current generation population, respectively.

[0192] Iteration Termination Condition: The algorithm terminates iteration when any of the following conditions are met:

[0193] 1) Maximum number of iterations: The number of iterations reaches 200;

[0194] 2) Optimal solution convergence criterion: The rate of change of the fitness of the optimal solution over 10 consecutive generations is less than 0.1%, i.e.:

[0195] ;

[0196] in, For the first t The fitness of the optimal solution in each generation;

[0197] 3) Criterion for population diversity: The standard deviation of the current generation's population fitness is less than 5%, i.e.:

[0198] ;

[0199] in, Here, N represents the standard deviation of population fitness, and N represents the population size. The mean fitness of the current generation population

[0200] Meanwhile, an elite retention strategy is employed to ensure that the best individuals in each generation are not lost during iteration. Through continuous iteration, a Pareto optimal solution set is ultimately generated, providing diverse options for energy storage system control schemes. This optimization method converges in 200 iterations, achieving a 40% efficiency improvement over traditional genetic algorithms, and providing an efficient solution tool for the engineering control of crack parameters.

[0201] Based on the Pareto optimal solution set obtained by the adaptive genetic algorithm, and combined with the operating characteristics of the energy storage system, a phased dynamic control strategy is formulated, constructing a phased dynamic control strategy that runs through the entire energy storage cycle, specifically as follows:

[0202] 1) Injection phase regulation:

[0203] During the injection phase, a parameter combination of "high permeability + medium porosity" is used to increase the fracture permeability to [a certain level]. =1500mD, porosity adjusted to =0.05. This parameter setting is based on the sensitivity analysis results above. At this point, the air recovery rate can be increased to approximately 89.4%, effectively controlling air diffusion loss while ensuring injection efficiency.

[0204] Hydraulic fracturing technology is used to expand natural fractures, creating directional high-permeability channels. (Fracturing fluid discharge rate) According to the formula Calculate, where, The width of the crack. The length of the crack. This refers to the fracturing fluid flow rate. This refers to the fracturing time.

[0205] To avoid reservoir fracturing, injection rate and pressure must be strictly controlled, as well as reservoir fracturing pressure. It can be estimated using the following formula:

[0206] ;

[0207] In the formula, The minimum horizontal principal stress is taken as 15~25MPa; The maximum horizontal principal stress is taken as 20~30 MPa; The tensile strength of the rock is taken as 2~5 MPa. The pore pressure is 10~15 MPa.

[0208] The engineering constraints are as follows:

[0209] Injection pressure needs to meet Ensure that the injection pressure does not exceed 80% of the fracture pressure to avoid reservoir rupture.

[0210] By monitoring the injection pressure in real time and comparing it with the calculated rupture pressure, the injection rate is dynamically adjusted to ensure a safe and efficient injection process.

[0211] 2) Storage stage control:

[0212] The strategy was adjusted to "low permeability + low porosity" to reduce fracture permeability to a lower level. =100mD, porosity adjusted to =0.001. This parameter setting can significantly reduce the contact efficiency between air and rock. According to the oxidation reaction inhibition objective function, the oxidation reaction rate can be reduced by approximately 40% under this parameter combination. Partially closing high-permeability fractures using temporary plugging technology, the injection volume of the plugging agent is determined based on the fracture volume. Sure:

[0213] ;

[0214] In the formula, For the first Porosity of the crack The cross-sectional area of ​​the crack. The fracture height was determined; simultaneously, a real-time monitoring system was deployed to perform high-frequency sampling and analysis of reservoir fluid components. When the rate of change in oxygen concentration exceeded the threshold Δ... When the air content reaches 0.05% / d, the parameter adjustment program is immediately initiated to dynamically optimize the crack parameters and maintain the stability of the air composition.

[0215] 3) Output stage regulation:

[0216] The production stage employs a combination of "small spacing + medium penetration rate" to reduce the crack spacing to... =10ft, penetration rate set to =500mD. Based on the sensitivity analysis, this parameter combination can increase the air recovery rate to approximately 92.3%.

[0217] By adding new fracturing fractures, the air transport distance is shortened, and the production well network deployment is optimized. According to Darcy's law, the air velocity... With penetration rate Pressure gradient Related:

[0218] ;

[0219] in, This refers to the air velocity.

[0220] Combined with production rate Adjust crack parameters in real time based on pressure decay. When the pressure decay rate exceeds a set threshold... At psi / d, an adaptive genetic algorithm is triggered to re-optimize the crack parameters and maximize the air recovery rate.

[0221] A real-time monitoring and feedback system is set up during the above process:

[0222] A downhole sensor network is deployed to collect data such as pressure, temperature, and fluid composition in real time. The sensor network employs a distributed deployment to ensure the comprehensiveness and accuracy of data acquisition. The collected data is uploaded to the ground control center in real time via a wireless transmission module, where it is analyzed by the data processing system.

[0223] When abnormal oxidation reactions are detected (such as a sudden increase in CO2 concentration exceeding the threshold) When the recovery rate decreases (below 90% of the target value), an adaptive genetic algorithm is triggered to re-optimize the parameters. After the algorithm is started, it uses the current reservoir state data as the initial condition and combines a multi-objective collaborative control mathematical model to quickly generate a new fracture parameter control scheme, achieving dynamic correction throughout the entire cycle and ensuring the efficient and stable operation of the energy storage system.

[0224] The above method can increase the air recovery rate to 96.3%, improve the energy efficiency of the energy storage system by 25-30%, and reduce the number of fracturing operations through dynamic control, reducing the single-well operation and maintenance cost from 800,000 yuan / year to 640,000-680,000 yuan / year, a reduction of 15-20%. It solves the problems of high air loss, violent oxidation reaction and poor reservoir stability in natural fractured reservoirs, and provides a complete technical path for the large-scale application of compressed air energy storage in depleted reservoirs.

[0225] Therefore, the present invention provides a multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs. By optimizing the fracture parameters of naturally fractured depleted reservoirs, the air recovery rate can be improved, air loss can be reduced, reservoir stability can be enhanced, the economy and safety of compressed air energy storage systems can be improved, and the efficient storage and utilization of renewable energy can be effectively promoted.

[0226] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A fracture parameter multi-objective optimization method for compressed air energy storage in naturally fractured depleted reservoirs, characterized in that, Includes the following steps: S1. For the matrix-fracture dual-porosity structure of naturally fractured depleted oil reservoirs, a numerical model of dual-porosity medium is constructed to analyze the correlation mechanism between fracture parameters and energy storage performance; fracture parameters include fracture porosity, fracture permeability, and fracture spacing. S2. Based on the results of S1, a multi-objective synergistic regulation mathematical model is constructed with the objectives of "maximizing air recovery rate, minimizing oxidation reaction inhibition, and maximizing reservoir stability" as its goals. The specific steps are as follows: 1) Construct objective functions for air recovery rate, oxidation reaction inhibition, and reservoir stability, respectively; the objective function for air recovery rate is expressed as: ； wherein, is the air recovery rate for air, is the total amount of air injected, is the amount of seepage detention loss, is the amount of air consumed by oxidation, is the amount of diffusion and dissolution loss; The objective function for inhibiting oxidation is expressed as: ； wherein is the oxidation reaction inhibition, is the reaction rate; The objective function for reservoir stability is expressed as: ； wherein, is the reservoir stability, is the plugging coefficient, is the reaction precipitation amount; 2) Using fracture porosity, fracture permeability, and fracture spacing as decision variables, and geological feasibility, engineering operability, and safety standards as constraints, a mapping relationship between parameters and three objective functions is constructed. The weighted summation method is then used to transform the multi-objective optimization problem into a single-objective optimization problem, resulting in a multi-objective collaborative control mathematical model. 3) Based on the mechanical properties of reservoir rocks, the range of fracture porosity and fracture permeability is limited, and the fracture spacing adjustment boundary is set in combination with the fracturing technology capability to ensure that the control of fracture parameters is feasible in actual construction. S3. An adaptive genetic algorithm is used to solve the multi-objective collaborative regulation mathematical model. Combined with the operating characteristics of the energy storage system, a phased dynamic regulation strategy spanning the entire energy storage lifecycle is constructed. The phased dynamic regulation strategy spanning the entire energy storage lifecycle is as follows: 1) Injection stage control: Using a combination of "high permeability + medium porosity" parameters, natural fractures are expanded through hydraulic fracturing technology to form directional high-permeability channels and shorten the injection time; 2) Storage stage regulation: Adjust to a "low permeability + low porosity" strategy, using temporary plugging technology to close some high permeability fractures, reduce the contact efficiency between air and rock, and inhibit oxidation reaction; 3) Production stage control: The combination of "small spacing + medium permeability" is adopted to shorten the air migration distance by adding new fracturing fractures, optimize the deployment of production well network, improve air flow and reduce residual air retention.

2. The fracture parameter multi-objective optimization method for compressed air energy storage in natural fractured depleted reservoirs according to claim 1, characterized in that: The specific steps of S1 are as follows: S11. Divide the naturally fractured depleted reservoir into a discrete grid and construct a numerical model of a dual-porosity medium. S12. Set the matrix parameters and fracture parameters, and establish the mass conservation equation for fluid exchange between the fracture and the matrix. S13. Introduce the permeability tensor to describe the anisotropic characteristics of fracture permeability, and quantify the influence of fracture spacing on fluid distribution through inter-mesh conductivity. S14. Through orthogonal experimental design, qualitatively analyze the relationship between crack porosity, crack permeability, crack spacing and air recovery rate.

3. The fracture parameter multi-objective optimization method for compressed air energy storage in naturally fractured depleted reservoirs according to claim 2, characterized in that: In S12, the mass conservation equation for fluid exchange between the crack and the matrix is ​​expressed as: ； in, For matrix porosity, For matrix fluid density, For matrix saturation, Let be the matrix seepage velocity vector. For matrix viscosity, For matrix pressure; For crack porosity, For the density of the fracture fluid, For crack gaps, Let be the crack seepage velocity vector. Crack viscosity, For crack pressure, This is a source term for fluid exchange between the matrix and the fracture. For time.

4. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs according to claim 3, characterized in that: In S13, the permeability tensor is expressed as: ； in, For the permeability tensor, The horizontal permeability of the crack. Vertical permeability of the crack; Inter-mesh conductivity is expressed as: ； in, Inter-mesh conductivity, For the area of ​​the grid interface, For grid spacing.

5. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs according to claim 4, characterized in that: In step S14, the relationship between crack porosity and air recovery rate is expressed as follows: ； The relationship between crack permeability and air recovery rate is expressed as follows: ； The relationship between crack spacing and air recovery rate is expressed as follows: ； in, For air recovery rate, All are coefficients. The value represents the crack permeability.

6. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs according to claim 5, characterized in that: In S2, the multi-objective collaborative regulation mathematical model is expressed as follows: ； in, , , , These are the weighting coefficients. To inhibit the oxidation reaction, For reservoir stability.

7. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs according to claim 6, characterized in that: In step 1) of S3, the engineering constraints during the process of expanding natural fractures using hydraulic fracturing technology are as follows: ， in, To inject pressure; The rupture pressure is expressed as: ； In the formula, For the minimum horizontal principal stress, For the maximum horizontal principal stress, For the tensile strength of rock, Pore ​​pressure; In step 2) of S3, during the process of temporarily plugging the high-permeability fractures, the amount of plugging agent injected is determined based on the fracture volume, which is expressed as: ； In the formula, For the first Porosity of the crack The cross-sectional area of ​​the crack. The height of the crack; In step 3) of S3, during the process of shortening the air transport distance by adding new fracturing fractures, the relationship between air velocity, permeability, and pressure gradient is expressed as follows: ； in, air velocity, For penetration rate, For pressure gradient, It represents viscosity.

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