Fracture parameter multi-objective optimization method for compressed air energy storage of natural fracture depleted reservoir

Abstract

The invention discloses a fracture parameter multi-objective optimization method for compressed air energy storage of a natural fracture depleted oil reservoir, and belongs to the technical field of oil reservoir engineering and energy storage, and the method comprises the following steps: S1, constructing a double-pore medium numerical model for a matrix-fracture double-pore structure of a natural fracture depleted oil reservoir, analyzing a correlation mechanism of crack parameters and energy storage performance; s2, based on a result of the S1, constructing a multi-target cooperative regulation mathematical model; and S3, solving the multi-target cooperative regulation mathematical model by adopting an adaptive genetic algorithm, and constructing a staged dynamic regulation strategy penetrating through the whole energy storage period in combination with the operation characteristics of the energy storage system. By optimizing the fracture parameters of the natural fracture depleted oil reservoir, efficient and low-loss storage and recovery of air in the fracture oil reservoir are achieved, the air recovery rate and the controllability of operation of the energy storage system are improved, and the stability of the reservoir structure, the safety of the energy storage process, the long-term economy of the system and the utilization efficiency of renewable energy sources are ensured.

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 dual-porosity medium numerical model 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 high-permeability channels (with permeability significantly higher than that of the matrix), and the matrix is ​​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] Where, φ m ρ represents matrix porosity. m S is the matrix fluid density. m v represents matrix saturation. m Let μ be the matrix seepage velocity vector. m p is the matrix viscosity. m For matrix pressure; φ f ρ represents the crack porosity. f S is the density of the fracture fluid. f For the crack gap, v f Let μ be the crack seepage velocity vector. f p is the crack viscosity. f For the crack pressure, q m-f t represents the fluid exchange source term between the matrix and the crack, and t represents time.

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

[0020]

[0021] Where K is the permeability tensor, k f,h k represents the horizontal permeability of the fracture. f,v Vertical permeability of the crack;

[0022] Inter-mesh conductivity is expressed as:

[0023]

[0024] Where T is the inter-mesh conductivity, ΔA is the mesh interface area, and Δx is the mesh gap.

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

[0026] ARF=a+bΔφ f ;

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

[0028] ARF=c+dΔk f ;

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

[0030]

[0031] Where ARF is the air recovery rate, a, b, c, d, e, and f are coefficients, and k is the air recovery rate. f The value represents the crack permeability.

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

[0033] min / maxF(x)=ω1max(ARF)+ω2min(OER)+ω3max(1-RSI);

[0034] Where, x=[φ f ,k f ,S f ], ω1, ω2, ω3 are weighting coefficients, OER is oxidation reaction inhibition, and RSI is 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] Among them, Q in Q is the total amount of air injected. str Q represents the seepage retention loss. ox Q represents the amount of air consumed for oxidation. diff This represents the amount of loss due to diffusion and dissolution.

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

[0045]

[0046] Where, r ox For reaction rate;

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

[0048] max(1-RSI)=1-λ·m pre ;

[0049] Where λ is the congestion coefficient, m pre 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 fractured reservoirs) to improve the optimization efficiency.

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

[0053] F(x)=ω a max(ARF)+ω b min(OER)+ω c max(1-RSI);

[0054] Where, ω a For air recovery rate weighting coefficient, ω b The oxidation reaction inhibition weighting coefficient, ω c 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 operation uses a roulette wheel method, where the probability P of individual i being selected is... i 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 P is adaptively adjusted. c With the probability of mutation Pm , represented as:

[0059]

[0060] Among them, F max F min F avg These represent the maximum fitness, minimum fitness, and average fitness of the current generation population, respectively.

[0061] Preferably, in S3, the phased dynamic control strategy throughout the entire energy storage lifecycle is as follows:

[0062] 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.

[0063] 2) Storage stage regulation: Adjust to a "low permeability + low porosity" strategy, close some high-permeability fractures through temporary plugging technology to reduce the contact efficiency between air and rock and inhibit oxidation reaction; at the same time, monitor changes in reservoir fluid composition and dynamically adjust parameters to maintain stable air composition.

[0064] 3) Production stage control: The combination of "small spacing + medium permeability" is adopted. By adding new fracturing fractures, the air transport 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.

[0065] Preferably, in step 1), the engineering constraints during the process of expanding natural fractures using hydraulic fracturing technology are as follows:

[0066] P inj <P frac ×80%, ensuring that the injection pressure does not exceed 80% of the rupture pressure;

[0067] Among them, P inj To inject pressure;

[0068] P frac The rupture pressure is expressed as:

[0069] P frac =3σ h -σ H +Z+P p ;

[0070] In the formula, σ h For the minimum horizontal principal stress, σ H Where Z is the maximum horizontal principal stress, Z is the tensile strength of the rock, and P is the maximum horizontal principal stress. pPore ​​pressure;

[0071] 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:

[0072]

[0073] In the formula, Let A be the porosity of the i-th crack. i h is the cross-sectional area of ​​the crack. i The height of the crack;

[0074] 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:

[0075]

[0076] Where v is the air velocity and k is the permeability. denoted as pressure gradient, and μ as viscosity.

[0077] 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.

[0078] 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:

[0079] (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.

[0080] (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 clogging pores, and maintain the long-term stability of reservoir permeability.

[0081] (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.

[0082] (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.

[0083] 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

[0084] 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;

[0085] Figure 2 This is a trend diagram showing the influence of crack parameters on air recovery rate in an embodiment of the present invention;

[0086] Figure 3 This is a diagram illustrating the overall architecture of the method according to an embodiment of the present invention.

[0087] Figure 4 This is a flowchart of the adaptive genetic algorithm according to an embodiment of the present invention. Detailed Implementation

[0088] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0089] 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.

[0090] 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.

[0091] Example

[0092] 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:

[0093] 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:

[0094] In the dual-porosity medium model, the crack spacing Sf The spatial spacing of natural fractures in the reservoir is a key parameter characterizing fracture development density; the grid spacing Δx is the size of the computational unit when the numerical model is discretized. In this invention, the two are related through the conductivity formula, but they have different physical meanings.

[0095] S11, Framework for constructing a dual-porosity model:

[0096] 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.

[0097] 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.

[0098] The matrix, serving as the primary fluid storage unit, has a horizontal permeability set to k. m,h Set to 10mD, vertical permeability k m,v The porosity is 0.1 mD and the porosity is φ. m The value is set to 0.11; the cracks serve as high-permeability channels, with a horizontal permeability k. f,h Reaching 500mD, vertical permeability k f,v 50mD, porosity φ f The crack spacing S is 0.001. f Set it to 20ft.

[0099] 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.

[0100] 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:

[0101]

[0102] Where, φ m ρ represents matrix porosity. m S is the matrix fluid density. m v represents matrix saturation. m Let μ be the matrix seepage velocity vector. m p is the matrix viscosity. mFor matrix pressure; φ f ρ represents the crack porosity. f S is the density of the fracture fluid. f For the crack gap, v f Let μ be the crack seepage velocity vector. f p is the crack viscosity. f For the crack pressure, q m-f t represents the fluid exchange source term between the matrix and the crack, and t represents time.

[0103] Boundary conditions:

[0104] (1) Injection well boundary: (Injection pressure is constant at 30MPa) (The gas saturation in the fracture near the injection well is 1);

[0105] (2) Production well boundary: (Constant output);

[0106] (3) Outer boundary: (Closed boundary conditions), initial conditions (Initial reservoir pressure), (Initial oil saturation of the matrix);

[0107] 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.

[0108] S13. To accurately describe the anisotropic characteristics of fracture permeability, a permeability tensor K is introduced, expressed as:

[0109]

[0110] Where K is the permeability tensor, k f,h k represents the horizontal permeability of the fracture. f,v Vertical permeability of the crack;

[0111] The effect of crack spacing on fluid distribution is quantified by the inter-mesh conductivity T, and its calculation formula is as follows:

[0112]

[0113] Where T is the inter-mesh conductivity, ΔA is the mesh interface area, and Δx is the mesh gap.

[0114] 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.

[0115] S14. Parameter sensitivity analysis method:

[0116] 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 to 0.1), fracture permeability (range 10 to 2000 mD), and fracture spacing (range 10 to 40 ft), while keeping other reservoir parameters such as matrix permeability and matrix porosity constant to ensure the accuracy and reliability of the experimental results.

[0117] Table 1 Orthogonal experimental design

[0118]

[0119]

[0120]

[0121] 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:

[0122] ARF=79+0.19Δφ f ,

[0123] That is, for every 0.1 increase in crack porosity, the air recovery rate will increase by 19%;

[0124] The relationship between permeability and air recovery rate is as follows:

[0125] ARF=79+0.16Δk f ,

[0126] This means that for every 1000 mD increase in crack permeability, the air recovery rate increases by 16%;

[0127] The relationship between crack spacing and air recovery rate is as follows:

[0128]

[0129] This indicates that for every 10 ft reduction in the crack spacing, the air recovery rate increases slightly by 0.3%.

[0130] The trend of the influence of crack parameters on air recovery rate is shown in the figure below. Figure 2As shown, Figure 2 The results show that fracture porosity has the most significant impact on improving air recovery. It leads to a 19% increase in air recovery, followed by fracture permeability which leads to a 16% increase in the air recovery factor.

[0131] 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.

[0132] Perform model validation logic:

[0133] 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.

[0134] 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 k in the numerical model was adjusted. ox By finely adjusting the diffusion coefficient D, the error between the model simulation results and the experimental data is controlled within 5%, effectively ensuring the accuracy and reliability of the model.

[0135] 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.

[0136] 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:

[0137] 1) Objective function design approach:

[0138] The objective function for air recovery rate aims to reduce air loss throughout the entire process of injection, storage, and production. This includes the seepage retention loss Q. str The calculation formula is:

[0139]

[0140] In the formula, μ1 is the aerodynamic viscosity, Q is the daily injection rate of a single well, Δx is the air migration distance, k is the fracture permeability, and A is the fracture cross-sectional area;

[0141] The amount of air consumed by oxidation, Q ox Taking the reaction of oxygen with pyrite as an example, its reaction rate r ox1 Following the Arrhenius equation:

[0142]

[0143] In the formula, k ox Let be the reaction rate constant (taken as 0.02). Where is the oxygen concentration, n is the reaction order (value 0.02), and E is the oxygen concentration. a It is the activation energy;

[0144] Assuming the reservoir is cubic in shape, and considering the fracture porosity in the reservoir as φ f The crack spacing is S f The reservoir volume V can be expressed as:

[0145]

[0146] Diffusion dissolution loss Q diff Following Fick's diffusion law:

[0147]

[0148] In the formula, D is the diffusion coefficient. For concentration gradient;

[0149] If the crack width is w and the length is L, then the diffusion area A = wL, and the diffusion dissolution loss Q can be obtained. diff The calculation formula is:

[0150] Q diff =∫∫J·A dt;

[0151] Total air injected Q in The calculation formula is:

[0152] Q in =V res ·φ f ·S g ;

[0153] In the formula, V res S represents the total reservoir volume. g This represents the gas phase saturation.

[0154] Taking all the above factors into account, the objective function for air recovery rate is constructed as follows:

[0155]

[0156] Among them, Q in Q is the total amount of air injected. str Q represents the seepage retention loss. ox Q represents the amount of air consumed for oxidation. diff This represents the amount of loss due to diffusion and dissolution.

[0157] Oxidation reaction inhibition objective function: Taking the reaction of oxygen with sulfur-containing minerals as the research object, the reaction rate r ox Contact area A with air and rock contact Proportional, that is:

[0158]

[0159] Therefore, an objective function for inhibiting oxidation reactions is constructed:

[0160]

[0161] Reservoir stability objective function: reaction precipitation amount m pre The concentration of ions produced by the oxidation reaction, C ion , reaction equilibrium constant K eq They are closely related, and their relationship expression is:

[0162]

[0163] In the formula, m is the reaction order, which is taken as 1.2;

[0164] The formula for calculating the reservoir permeability decay rate (RSI) is:

[0165]

[0166] Where, k1=k0·(1-λ·m pre ), k0 is the initial fracture permeability, k1 is the fracture permeability after attenuation, and λ is the plugging coefficient, which is taken as 0.4 to 0.6;

[0167] This leads to the reservoir stability objective function:

[0168] max(1-RSI)=1-λ·m pre ;

[0169] 2) Using crack porosity φ f Penetration rate k f Spacing S f As a decision variable, a nonlinear mapping relationship is constructed between it and the objective function:

[0170] Represented as:

[0171]

[0172] 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:

[0173] min / maxF(x)=ω1max(ARF)+ω2min(OER)+ω3max(1-RSI);

[0174] Where, x=[φ f ,k f ,S f ], ω1, ω2, ω3 are weighting coefficients that can be flexibly adjusted according to the actual needs of different stages of the energy storage system.

[0175] 3) Engineering-based setting of constraints:

[0176] Based on the results of reservoir rock mechanics experiments, the reasonable range for porosity is scientifically determined to be 0.001 ≤ φ. f ≤0.1, the permeability constraint range is 10≤k f 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≤S. f ≤40ft. At the same time, 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 ensuring the safety and environmental friendliness of the construction process.

[0177] 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.

[0178] S3. An adaptive genetic algorithm is used to solve the mathematical model of multi-objective collaborative regulation, such as... Figure 4 As shown, specifically:

[0179] (1) Algorithm encoding and population initialization:

[0180] 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.

[0181] (2) Construction of dynamic fitness function

[0182] 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, ω is set... a =0.6, ω b =0.2, ω c =0.2; during storage phase, adjust to ω a =0.3, ω b =0.5, ω c =0.2; During the production phase, set ω a =0.5, ω b =0.2, ω c =0.3. Based on the adjusted weighting coefficients, the fitness of an individual is calculated and expressed as:

[0183] F(x)=ω a max(ARF)+ω b min(OER)+ω c max(1-RSI);

[0184] Where, ω a For air recovery rate weighting coefficient, ω b The oxidation reaction inhibition weighting coefficient, ω c This is the reservoir stability weighting coefficient;

[0185] (3) Iterative optimization mechanism:

[0186] The selection operation uses a roulette wheel method, where the probability P of individual i being selected is... i The calculation formula is:

[0187]

[0188] Among them, F i F represents the fitness value of individual i. j Let be the fitness value of the j-th individual in the population;

[0189] 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 P is adaptively adjusted. c With the probability of mutation P m , represented as:

[0190]

[0191] Among them, F max F min F avg 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, Let be the fitness of the optimal solution in generation t;

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

[0198]

[0199] Where σ is the standard deviation of population fitness, N is the population size, and F avg 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 k.f =1500mD, porosity adjusted to φ f =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, forming directional high-permeability channels. The fracturing fluid displacement Q is calculated using the formula... The calculation is performed, where w is the fracture width, L is the fracture length, t is the fracturing fluid velocity, and t is the fracturing time.

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

[0206] P frac =3σ h -σ H +Z+P p ;

[0207] In the formula, σ h The minimum horizontal principal stress is σ, which ranges from 15 to 25 MPa. H The maximum horizontal principal stress is denoted as Z, which is taken as 20–30 MPa; Z is the tensile strength of the rock, which is taken as 2–5 MPa; P p The pore pressure is taken as 10–15 MPa.

[0208] The engineering constraints are as follows:

[0209] The injection pressure needs to meet P inj <P frac ×80%, ensuring that the injection pressure does not exceed 80% of the fracture pressure to avoid reservoir fracture.

[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 phase regulation:

[0212] The strategy was adjusted to "low permeability + low porosity" to reduce the fracture permeability to k. f =100mD, porosity adjusted to φ f =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 high-permeability fractures are closed using temporary plugging technology; the injection volume of the plugging agent is based on the fracture volume V. fracture Sure:

[0213]

[0214] In the formula, Let A be the porosity of the i-th crack. i h is the cross-sectional area of ​​the crack. i 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 a threshold... Immediately initiate the parameter adjustment program to dynamically optimize crack parameters and maintain stable 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 S. f =10ft, permeability set to k f =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 v is related to the permeability k and the pressure gradient. Related:

[0218]

[0219] Where v is the air velocity.

[0220] Combined with production rate Q prod Adjust crack parameters in real time according to pressure decay. When the pressure decay rate exceeds the set threshold ΔP... decay At 50 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 multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted oil 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 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. 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.

2. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally 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 multi-objective optimization method for fracture parameters in compressed air energy storage of 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: Where, φ m ρ represents matrix porosity. m S is the matrix fluid density. m v represents matrix saturation. m Let μ be the matrix seepage velocity vector. m p is the matrix viscosity. m For matrix pressure; φ f ρ represents the crack porosity. f S is the density of the fracture fluid. f For the crack gap, v f Let μ be the velocity vector of the crack seepage. f p is the crack viscosity. f For the crack pressure, q m-f t represents the fluid exchange source term between the matrix and the crack, and t represents time.

4. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs according to claim 2, characterized in that: In S13, the permeability tensor is expressed as: Where K is the permeability tensor, k f,h k represents the horizontal permeability of the fracture. f,v Vertical permeability of the crack; Inter-mesh conductivity is expressed as: Where T is the inter-mesh conductivity, ΔA is the mesh interface area, and Δx is the mesh gap.

5. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs according to claim 2, characterized in that: In step S14, the relationship between crack porosity and air recovery rate is expressed as follows: ARF=a+bΔφ f ; The relationship between crack permeability and air recovery rate is expressed as follows: ARF=c+dΔk f ; The relationship between crack spacing and air recovery rate is expressed as follows: Where ARF is the air recovery rate, a, b, c, d, e, and f are coefficients, and k is the air recovery rate. f 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 1, characterized in that: In S2, the multi-objective collaborative regulation mathematical model is expressed as follows: min / maxF(x)=ω1max(ARF)+ω2min(OER)+ω3max(1-RSI); Where, x=[φ f ,k f ,S f ], ω1, ω2, ω3 are weighting coefficients, OER is oxidation reaction inhibition, and RSI is 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: The specific steps of S2 are as follows: 1) Construct objective functions for air recovery rate, oxidation reaction inhibition, and reservoir stability, respectively; 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.

8. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs according to claim 7, characterized in that: The objective function for the air recovery rate is expressed as: Among them, Q in Q is the total amount of air injected. str Q represents the seepage retention loss. ox Q represents the amount of air consumed for oxidation. diff This represents the amount of loss due to diffusion and dissolution. The objective function for inhibiting oxidation is expressed as: Where, r ox For reaction rate; The objective function for reservoir stability is expressed as: max(1-RSI)=1-λ·m pre ; Where λ is the congestion coefficient, m pre This represents the amount of precipitate produced during the reaction.

9. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs according to claim 1, characterized in that: In S3, the phased dynamic control strategy that runs through the entire energy storage cycle 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, and close some high permeability fractures through temporary plugging technology to 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.

10. The multi-objective optimization method for fracture parameters in compressed air energy storage of naturally fractured depleted reservoirs according to claim 8, characterized in that: In step 1), the engineering constraints during the process of expanding natural fractures using hydraulic fracturing technology are as follows: P inj <P frac ×80%, Among them, P inj To inject pressure; P frac The rupture pressure is expressed as: P frac =3σ h -σ H +Z+P p ; In the formula, σ h For the minimum horizontal principal stress, σ H Where Z is the maximum horizontal principal stress, Z is the tensile strength of the rock, and P is the maximum horizontal principal stress. p Pore ​​pressure; 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: In the formula, Let A be the porosity of the i-th crack. i h is the cross-sectional area of ​​the crack. i The height of the crack; 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: Where v is the air velocity and k is the permeability. denoted as pressure gradient, and μ as viscosity.

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