CO2 oil displacement buried pore size simulation method considering swelling viscosity reduction effect

Abstract

The invention discloses a CO2 oil displacement buried pore size simulation method considering a swelling viscosity reduction effect, and belongs to the field of oil and gas exploitation technologies and carbon dioxide storage. According to the method, the mass transfer rate source item is corrected, accurate movement of a phase interface in the CO2 dissolution and diffusion process is simulated, the volume change of crude oil is achieved, and the swelling mechanism in the CO2 injection oil displacement process is fully considered; the viscosity reduction mechanism in the CO2 injection oil displacement process is simulated by combining the CO2 concentration change in the crude oil; the numerical simulation model is established based on the real reservoir pore structure model and the oil gas physical property characteristics of the target block, and simulation of different injection schemes can be repeatedly carried out, so that the optimal injection scheme is efficiently and conveniently analyzed, and a theoretical basis is provided for engineering parameter optimization.

Description

Technical Field

[0001] The present invention belongs to the field of oil and gas production technology and carbon dioxide storage, and specifically relates to a pore-scale simulation method for CO2 oil recovery and storage taking into account the swelling and viscosity reduction effect. Background Art

[0002] Carbon dioxide (CO2) flooding technology is not only an important means of enhancing oil recovery, but also has the potential to sequester carbon and mitigate global climate change. Injecting CO2 into oil reservoirs not only effectively reduces oil viscosity but also increases oil volume through a swelling effect, thereby improving fluidity and enhancing oil recovery. Furthermore, during the oil recovery process, the injected CO2 can be partially retained in the formation pores, achieving carbon sequestration. This technology integrates oil recovery and carbon sequestration, possessing significant economic and social value. Existing numerical simulation methods for CO2 flooding primarily focus on macroscale reservoir simulation. While these methods can effectively assess the overall effectiveness of CO2 flooding, they are unable to describe component mass transfer and phase changes at the oil-gas interface. Accurate characterization and simulation of these microscopic processes, including CO2 dissolution in crude oil, interfacial dynamics, and crude oil swelling and viscosity reduction, have a crucial impact on oil recovery and carbon sequestration efficiency. These processes, including CO2 dissolution in crude oil, interfacial dynamics, and crude oil swelling and viscosity reduction, are key to improving CO2 flooding efficiency and optimizing engineering parameter design. In recent years, with the advancement of computing power, pore-scale numerical simulation methods have rapidly developed. This type of method can directly characterize the reservoir pore structure and reveal the movement mechanism of multiphase fluids in the pores. However, most current pore-scale simulation studies still use basic liquid-liquid two-phase flow methods (such as water flooding), which insufficiently consider the complex physical and chemical phenomena between CO2 and crude oil. This method fails to fully reflect the mechanism of swelling and viscosity reduction effects in oil displacement and storage, making it difficult to provide accurate guidance for practical engineering. Therefore, a pore-scale simulation method for CO2 oil displacement and storage that considers swelling and viscosity reduction effects is proposed. This method not only allows for in-depth study of pore-scale multiphase flow and mass transfer behavior, but also provides theoretical support for optimizing CO2 injection parameters. Summary of the Invention

[0003] In response to the above-mentioned technical problems existing in the prior art, the present invention proposes a rapid simulation method for CO2 oil displacement and storage that takes into account the swelling and viscosity reduction effect and is applicable to different oil reservoir types and different oil and gas phase parameters. It compares the displacement and storage effects of different injection schemes, provides efficient and scientific guidance for the design of actual engineering parameters, and realizes a reasonable integrated design of efficient oil displacement and large-scale storage, overcomes the shortcomings of the prior art, and has good results.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A pore-scale simulation method for CO2 flooding and storage considering the swelling and viscosity reduction effect includes the following steps:

[0006] Step 1: Reservoir structure model construction;

[0007] Step 2: Simulation parameter determination;

[0008] Step 3: Calculation of mass transfer rate source term considering mass transfer and diffusion of CO2 components;

[0009] Step 4: Pore-scale simulation of CO2 flooding and storage considering the swelling and viscosity reduction effect;

[0010] Step 5: Analysis of oil displacement and storage effects.

[0011] Preferably, step 1 specifically includes the following steps:

[0012] Step 1.1: Select the target block, analyze the oil reservoir and rock type of the target block, determine the reservoir temperature and pressure conditions, and collect relevant geological parameters of the target block, including porosity, permeability, rock mineral composition, and pore size distribution;

[0013] Step 1.2: Build a digital core model; there are two methods:

[0014] Using high-precision imaging technology to directly scan reservoir rocks and construct them using a 3D reconstruction algorithm;

[0015] According to the rock type, random reconstruction is performed using the Monte Carlo method, combined with geological parameter optimization and correction;

[0016] Step 1.3: Based on the digital core model described in step 1.2, coordinate each voxel point and map it to the corresponding structured grid model. That is, the grid point coordinates are consistent with the voxel point coordinates, and the number of grids in the structured grid model is basically equal to the number of voxels in the digital core model.

[0017] Step 1.4: Extract the surface model corresponding to the digital core model described in step 1.2. Using the grid coordinates of the surface model as constraints, move the wall grid point coordinates of the structured grid model described in step 1.3 to obtain a smoothed unstructured reservoir pore grid model.

[0018] Preferably, step 2 specifically includes the following steps:

[0019] Step 2.1: Take oil samples from the reservoir site and measure the physical properties of the crude oil, including density, viscosity, and component content;

[0020] Step 2.2: Design a gas injection plan, identify the gas components, and measure the gas physical properties in the plan. The gas physical properties include the content, density, and viscosity of different gas components.

[0021] Step 2.3: Determine the oil and gas PVT parameters under reservoir temperature and pressure conditions. The oil and gas PVT parameters include contact angle, surface tension, diffusion coefficient of each gas component, solubility, swelling coefficient, and viscosity reduction coefficient.

[0022] Preferably, step 3 specifically includes the following steps:

[0023] Step 3.1: Using the aforementioned oil and gas PVT parameters, calculate the component mass transfer rate As the component concentration c changes, the calculation method is as follows:

[0024]

[0025] c o =Hc g (4);

[0026] Where H is Henry's coefficient, which is obtained by inverse calculation of solubility; D o and D g are the molecular diffusion coefficients of gas components in the oil phase and gas phase, respectively; is the effective diffusion coefficient in the calculation domain after harmonic averaging; Φ is the concentration jump flux at the interface; α o and α g are the oil phase fraction and gas phase fraction in the finite volume method;

[0027] Step 3.2: Based on component mass transfer rate Calculating the mass transfer rate of virtual components The specific steps include:

[0028] Step 3.2.1: Mass transfer rates of components Perform Gaussian diffusion to obtain the smooth component mass transfer rate

[0029] Step 3.2.2: Extracting the mass transfer rate of the smooth component The oil phase side value is based on the mass transfer rate of the components The integration and logarithmic amplification of the virtual component mass transfer rate

[0030]

[0031] Among them, S ns =(C ns Δx) 2 is the numerical smoothing coefficient, which is determined by the grid size Δx of the unstructured reservoir pore grid model and the custom coefficient C ns Calculated; α o,cutis the part of the liquid phase fraction field in the finite volume method with a phase fraction greater than 1.0-cutoff, with a cutoff coefficient of <0.01; A is the magnification factor;

[0032] Step 3.3: The component mass transfer rate source term used in the numerical simulation model includes the component mass transfer rate Virtual component mass transfer rate and the sum of the two

[0033] Preferably, step 4 specifically includes the following steps:

[0034] Step 4.1: Using the viscosity reduction coefficient in the oil and gas PVT parameters, fit the crude oil viscosity function that changes with CO2 concentration Characterize the phenomenon of reduced crude oil viscosity after CO2 dissolution; the viscosity μ of the calculation domain is as follows:

[0035] μ=α o μ o +α g μ g (7);

[0036] Among them, μ o and μ g is the density of the oil phase and the gas phase;

[0037] Step 4.2: Substitute the mass transfer rate source term into the mass conservation equation, phase fraction equation, momentum conservation equation, and concentration control equation. By forming a relative velocity at the phase interface to drive the phase interface to move, the volume expansion of crude oil after CO2 dissolution is simulated; use the finite volume method to solve and obtain the phase fraction, pressure, velocity, and component mass transfer rate in the calculation domain. Changes in component concentration over time; the numerical simulation model is:

[0038]

[0039]

[0040] φ m =u m ·A

[0041]

[0042] Among them, equation (8) is the mass conservation equation. By introducing To realize interface movement and expansion, u is the velocity vector, ρ o and ρ g is the density of the oil phase and the gas phase; Equation (9) is the phase fraction control equation, by introducing To ensure the conservation of phase fractional field mass, the density in the calculation domain ρ=αo ρ o +α g ρ g ,u r is the relative velocity between phases; Equation (10) is the momentum conservation equation, through the capillary force term f ∑ Characterize the surface tension between oil and gas, is the viscosity tensor, g is the gravity vector, and p is the pressure; Equation (11) is the concentration control equation, M is the molar mass of the gas component, c is the concentration of the gas component, where j is the concentration diffusion term, F is the concentration convection term, and u m is the concentration convection correction velocity, which is determined by the convection flux φ m Calculated, C m is the concentration correction factor, is the normal vector of the component mass transfer rate, A is the grid area;

[0043] Step 4.3: Establish a regular structured single-tube model; specifically, the following steps are included:

[0044] Step 4.3.1: Set the fluid phase parameters based on the crude oil physical properties, gas physical properties, and oil and gas PVT parameters, and conduct static swelling simulation in the microscale PVT tube;

[0045] Step 4.3.2: Compare the simulation results with experimental data including viscosity curve, crude oil expansion coefficient, and wall contact angle;

[0046] Step 4.3.3: Modify the viscosity function;

[0047] Step 4.3.4: Adjust physical properties including diffusion coefficient and H coefficient;

[0048] Step 4.3.5: Adjust the smoothing coefficient S ms The custom coefficient C in ns , flux correction factor C m , simulation parameters including magnification A;

[0049] Step 4.3.6: Repeat steps 4.3.1 to 4.3.5 until the simulated viscosity change curve and crude oil volume expansion coefficient have an error of less than 1% compared with the experimentally determined values.

[0050] Preferably, step 5 specifically includes the following steps:

[0051] Step 5.1: Set different gas injection schemes and conduct pore-scale simulations of CO2 flooding considering the swelling and viscosity reduction effect to obtain simulation results for different injection schemes;

[0052] Step 5.2: Compare oil displacement efficiency and CO2 storage efficiency to identify the optimal displacement and storage scheme, providing a theoretical basis for engineering parameter optimization.

[0053] The beneficial technical effects brought about by the present invention are:

[0054] The method proposed in this paper uses a mass transfer rate source term to accurately simulate the movement of the phase interface during CO2 dissolution and diffusion, achieving crude oil volume changes and fully accounting for the swelling mechanism during CO2 injection. The viscosity reduction mechanism during CO2 injection is simulated by utilizing the CO2 concentration variation in crude oil. A numerical simulation model based on a realistic reservoir pore structure model and the physical properties of oil and gas in the target block is established. This allows for repeated simulations of different injection schemes, enabling efficient and convenient analysis of the optimal injection scheme, providing a theoretical basis for optimizing engineering parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a schematic diagram of the static PVT simulation model;

[0056] Figure 2 Schematic diagram of the CO2 concentration change curve and crude oil expansion coefficient change curve;

[0057] Figure 3 Schematic diagram of porous media model;

[0058] Where a is the distance between the centers of the particles, every three particles form an equilateral triangle, that is, the angle between the lines connecting the circles is 60 degrees, and d is the spacing between the particles;

[0059] Figure 4 Build and smooth schematics (local meshes) for structured models;

[0060] Figure 4 (a) is a structured grid model diagram; (b) is an unstructured grid pore model diagram;

[0061] Figure 5 Schematic diagram of the mesh smoothing process;

[0062] Figure 5 (a) is a comparison diagram of the structured grid and the particle surface; (b) is a schematic diagram of the wall grid point calibration; (c) is a schematic diagram of the smoothed unstructured grid;

[0063] Figure 6 Schematic diagram of the change in crude oil saturation and the concentration of CO2 dissolved in crude oil;

[0064] Figure 6 (a) is a graph showing the change of crude oil saturation over time; (b) is a schematic diagram showing the change curve of CO2 component concentration;

[0065] Figure 7Schematic diagram of the mass transfer rate source term. DETAILED DESCRIPTION

[0066] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0067] Case Study 1: Optimization of Simulation Parameters Based on Microfluidic PVT Experiments

[0068] ① Select the target reservoir block, determine the reservoir temperature (50°C) and pressure (30 MPa), obtain the density and viscosity of the crude oil and injected gas, measure the surface tension between the oil and gas, and determine the relationship between crude oil viscosity and dissolved CO2. Conduct microfluidic PVT experiments to determine the wetting angle, CO2 solubility and diffusion coefficient, and expansion coefficient under reservoir temperature and pressure conditions.

[0069] ② Combined with the physical dimensions of the microfluidic PVT experimental model, a two-dimensional or three-dimensional single tube model was established (e.g. Figure 1 (As shown in the figure), a structured grid was used, and the grid model size and oil-gas phase field distribution were assigned based on the microfluidic PVT experimental model dimensions. In this implementation, the model size was 60 μm × 90 μm, with an initial oil column length of 24.4 μm. The gas phase side was an open boundary, while the oil phase side was a closed boundary.

[0070] ③ Establish a static oil-gas mass transfer and diffusion simulation model: Based on the initial state of the microfluidic PVT experiment, assign initial values ​​to the oil-gas phase field control equations in the grid model, setting the gas phase side as an open boundary and the oil phase side as a closed boundary. Identify the phase interface based on the phase fraction control equation, and set the mass transfer rate source term calculation equation.

[0071] ④ Select the viscosity calculation model, the oil phase viscosity changes with the CO2 component concentration change:

[0072]

[0073] in, is the CO2 injection concentration at the inlet, is the initial CO2 concentration in the oil phase.

[0074] ⑤ Set the simulation equations of the oil phase and gas phase, including the mass conservation equation, phase fraction equation, momentum conservation equation, and concentration control equation, and solve them iteratively in conjunction with the mass transfer rate source term.

[0075] ⑥ Carry out static simulation of CO2-oil considering the swelling and viscosity reduction effect, compare the simulation results with the experimental results, and compare the fitted viscosity change curve with the experimental data; calculate the oil phase volume fraction, and compare the consistency of the oil phase expansion coefficient under the set temperature and pressure conditions with the experimentally measured value.

[0076] ⑦ Modify the viscosity function, adjust the physical parameters and simulation parameters, and repeat the steps until the error between the simulated viscosity and expansion coefficient and the experimentally measured values ​​is less than 1%. The optimized simulation parameters are shown in Table 1:

[0077] Table 1 Simulation parameters

[0078] Crude oil viscosity <![CDATA[4.9×10 -3 Step]]> Gas phase viscosity <![CDATA[1.78×10 -5 Step]]> Crude oil density <![CDATA[830kg / m 3 ]]> Gas phase density <![CDATA[125.54kg / m 3 ]]> Oil-gas interfacial tension 0.02mN / m contact angle <![CDATA[20 ° ]]> Diffusion coefficient <![CDATA[5.5×10 -9 m 2 / s]]> H factor 0.6 <![CDATA[Custom coefficient C ns > 2.0 Magnification A 1.0 <![CDATA[Flux correction factor C m > 0.9 cutoff coefficient 0.001

[0079] ⑧The final simulation results are as follows Figure 2 As shown in the figure, the oil phase viscosity is reduced by 75%, and the oil phase volume expansion coefficient increases from 1.0 to 1.82. The error with the microfluidic experimental data is less than 0.5%. The optimization of the simulation parameters of CO2 flooding at the pore scale considering the swelling and viscosity reduction effect is completed.

[0080] Case Study 2: Pore-scale simulation of CO2 flooding and storage considering swelling and viscosity reduction effects in a regular porous media model;

[0081] ① Assume that the target sandstone reservoir has a reservoir temperature of 50°C and a bottom pressure of 30 MPa, and use the simulation parameters selected in Implementation Case 1.

[0082] ② Gaussian distribution function is used to obtain a two-dimensional porous medium model with random distribution of rock particles. The particle distribution rule is: in is the average particle radius, λ is the standard deviation of particle radius distribution, and the model is as follows Figure 3 The detailed parameters are as follows:

[0083]

[0084] ③ Such as Figure 4 As shown in the figure, a structured grid model a is constructed, and the surface of the circular particles is stepped. The model is smoothed and the positions of all the structural grid corner points on the particle surface are corrected to obtain the corresponding unstructured grid pore model b. The circular particle surface of model b uses an unstructured quadrilateral grid. Compared with model a, the grid smoothness is improved and the calculation stability is higher.

[0085] ④ Set the gas injection parameters, assuming that the injected fluid is pure CO2 gas, the injection velocity is 5e-3m / s, and the injection direction is the X-axis direction.

[0086] Figure 5 (a) is a comparison diagram of the structured grid and the particle surface; (b) is a schematic diagram of the wall grid point calibration; (c) is a schematic diagram of the smoothed unstructured grid;

[0087] ⑤ Carry out pore-scale simulation of CO2 flooding and storage considering the swelling and viscosity reduction effect, evaluate the flooding and storage effect, and analyze the changes in crude oil saturation and the concentration of dissolved CO2 in crude oil during the gas flooding process (such as Figure 6 As shown in the figure, the oil recovery rate and CO2 storage rate are analyzed. The source term change curve of the component mass transfer rate at the phase interface is shown in the figure. Figure 7 shown.

[0088] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A pore-scale simulation method for CO2 flooding and storage considering the swelling and viscosity reduction effect, characterized in that: The steps include: Step 1: Reservoir structure model construction; Step 2: Simulation parameter determination; Step 3: Calculation of mass transfer rate source term considering mass transfer and diffusion of CO2 components; Step 4: Pore-scale simulation of CO2 flooding and storage considering the swelling and viscosity reduction effect; Step 5: Analysis of oil displacement and storage effects.

2. The pore-scale simulation method for CO2 flooding and storage considering the swelling and viscosity reduction effect according to claim 1 is characterized in that: Step 1 specifically includes the following steps: Step 1.1: Select the target block, analyze the oil reservoir and rock type of the target block, determine the reservoir temperature and pressure conditions, and collect relevant geological parameters of the target block, including porosity, permeability, rock mineral composition, and pore size distribution; Step 1.2: Build a digital core model; there are two methods: Using high-precision imaging technology to directly scan reservoir rocks and construct them using a 3D reconstruction algorithm; According to the rock type, random reconstruction is performed using the Monte Carlo method, combined with geological parameter optimization and correction; Step 1.3: Based on the digital core model described in step 1.2, coordinate each voxel point and map it to the corresponding structured grid model. That is, the grid point coordinates are consistent with the voxel point coordinates, and the number of grids in the structured grid model is basically equal to the number of voxels in the digital core model. Step 1.4: Extract the surface model corresponding to the digital core model described in step 1.

2. Using the grid coordinates of the surface model as constraints, move the wall grid point coordinates of the structured grid model described in step 1.3 to obtain a smoothed unstructured reservoir pore grid model.

3. The pore-scale simulation method for CO2 flooding and storage considering the swelling and viscosity reduction effect according to claim 1 is characterized in that: Step 2 specifically includes the following steps: Step 2.1: Take oil samples from the reservoir site and measure the physical properties of the crude oil, including density, viscosity, and component content; Step 2.2: Design a gas injection plan, identify the gas components, and measure the gas physical properties in the plan. The gas physical properties include the content, density, and viscosity of different gas components. Step 2.3: Determine the oil and gas PVT parameters under reservoir temperature and pressure conditions. The oil and gas PVT parameters include contact angle, surface tension, diffusion coefficient of each gas component, solubility, swelling coefficient, and viscosity reduction coefficient.

4. The pore-scale simulation method for CO2 flooding and storage considering the swelling and viscosity reduction effect according to claim 1, characterized in that: Step 3 specifically includes the following steps: Step 3.1: Using the aforementioned oil and gas PVT parameters, calculate the component mass transfer rate As the gas component concentration c changes, the calculation method is as follows: Where H is Henry's coefficient, which is obtained by inverse calculation of solubility; D o and D g are the molecular diffusion coefficients of gas components in the oil phase and gas phase, respectively; is the effective diffusion coefficient in the computational domain after harmonic averaging; Φ is the concentration jump flux at the interface; α o and α g are the oil phase fraction and gas phase fraction in the finite volume method; Step 3.2: Based on component mass transfer rate Calculating the mass transfer rate of virtual components The specific steps include: Step 3.2.1: Mass transfer rates of components Perform Gaussian diffusion to obtain the smooth component mass transfer rate Step 3.2.2: Extracting the mass transfer rate of the smooth component The oil phase side value is based on the mass transfer rate of the components The integration and logarithmic amplification of the virtual component mass transfer rate Among them, S ns =(C ns Δx) 2 is the numerical smoothing coefficient, which is determined by the grid size Δx of the unstructured reservoir pore grid model and the custom coefficient C ns Calculated; α o,cut is the part of the liquid phase fraction field in the finite volume method with a phase fraction greater than 1.0-cutoff, with a cutoff coefficient of cutoff < 0.01; A is the magnification factor; Step 3.3: The component mass transfer rate source term used in the numerical simulation model includes the component mass transfer rate Virtual component mass transfer rate and the sum of the two 5. The pore-scale simulation method for CO2 flooding and storage considering the swelling and viscosity reduction effect according to claim 1, characterized in that: Step 4 specifically includes the following steps: Step 4.1: Using the viscosity reduction coefficient in the oil and gas PVT parameters, fit the crude oil viscosity function that changes with CO2 concentration Characterize the phenomenon of reduced crude oil viscosity after CO2 dissolution; the viscosity μ of the calculation domain is as follows: μ = a o m o +a g m g (7); Among them, μ o and μ g is the density of the oil phase and the gas phase; Step 4.2: Substitute the mass transfer rate source term into the mass conservation equation, phase fraction equation, momentum conservation equation, and concentration control equation. By forming a relative velocity at the phase interface to drive the phase interface to move, the volume expansion of crude oil after CO2 dissolution is simulated; use the finite volume method to solve and obtain the phase fraction, pressure, velocity, and component mass transfer rate in the calculation domain. Changes in component concentration over time; the numerical simulation model is: Among them, equation (8) is the mass conservation equation, by introducing To realize interface movement and expansion, u is the velocity vector, ρ o and ρ g is the density of the oil phase and the gas phase; Equation (9) is the phase fraction control equation, by introducing To ensure the conservation of phase fractional field mass, the density in the calculation domain ρ=α o ρ o +α g ρ g ,u r is the relative velocity between phases; Equation (10) is the momentum conservation equation, through the capillary force term f ∑ Characterize the surface tension between oil and gas, is the viscosity tensor, g is the gravity vector, and p is the pressure; Equation (11) is the concentration control equation, M is the molar mass of the gas component, c is the concentration of the gas component, where j is the concentration diffusion term, F is the concentration convection term, and u m is the concentration convection correction velocity, which is determined by the convection flux φ m Calculated, C m is the concentration correction factor, is the normal vector of the component mass transfer rate, A is the grid area; Step 4.3: Establish a regular structured single-tube model; specifically, the following steps are included: Step 4.3.1: Set the fluid phase parameters based on the crude oil physical properties, gas physical properties, and oil and gas PVT parameters, and conduct static swelling simulation in the microscale PVT tube; Step 4.3.2: Compare the simulation results with experimental data including viscosity curve, crude oil expansion coefficient, and wall contact angle; Step 4.3.3: Modify the viscosity function; Step 4.3.4: Adjust physical properties including diffusion coefficient and H coefficient; Step 4.3.5: Adjust the smoothing coefficient S ns The custom coefficient C in ns , flux correction factor C m , simulation parameters including magnification A; Step 4.3.6: Repeat steps 4.3.1 to 4.3.5 until the simulated viscosity change curve and crude oil volume expansion coefficient have an error of less than 1% compared with the experimentally determined values.

6. The pore-scale simulation method for CO2 flooding and storage considering the swelling and viscosity reduction effect according to claim 1, characterized in that: Step 5 specifically includes the following steps: Step 5.1: Set different gas injection schemes and conduct pore-scale simulations of CO2 flooding considering the swelling and viscosity reduction effect to obtain simulation results for different injection schemes. Step 5.2: Compare oil displacement efficiency and CO2 storage efficiency to identify the optimal displacement and storage scheme, providing a theoretical basis for engineering parameter optimization.

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