Gas storage surrounding rock elasticoplastic deformation calculation method

Abstract

The invention discloses a gas storage surrounding rock elasticoplastic deformation calculation method, belongs to the technical field of compressed air energy storage, and solves the problems of low calculation efficiency, high parameter dependence and neglected dynamic effect when an existing method depends on numerical simulation calculation. A stress model of the lining gas storage in the inflation and deflation process is constructed, and a stress path of the surrounding rock in the inflation and deflation process is obtained based on the stress model of the lining gas storage in the inflation and deflation process; based on the stress path of the surrounding rock in the inflation and deflation process, a stress field function and a displacement field function of the lining gas storage are obtained, and stress calculation of the lining gas storage in the inflation and deflation process is completed; on the premise of ensuring the calculation precision and accuracy, the problems of long time consumption, slow analysis and calculation, huge calculation amount and the like of numerical simulation are avoided, the calculation efficiency is remarkably improved, and the method is more convenient for engineering technicians to use in site selection and design of the compressed air energy storage lining gas storage.

Description

Technical Field

[0001] The present invention belongs to the technical field of compressed air energy storage, and in particular relates to a method for calculating the elastic-plastic deformation of surrounding rocks of a gas storage reservoir. Background Art

[0002] Compressed air energy storage (CAES) technology, due to its large capacity, long lifespan, and low cost, has become a key technology for peak load regulation in power systems and renewable energy consumption. Underground gas storage, the core of CAES systems, is subject to cyclical dynamic expansion loads during the filling and degassing process. This complicates the stress path and may cause the surrounding rock to enter an elastic-plastic deformation state. Unlike the static or quasi-static loads of traditional underground engineering projects (such as tunnels and mines), the dynamic stress cycles in the surrounding rock of gas storages induce significant plastic zone expansion and creep effects, further exacerbating the deformation complexity.

[0003] Currently, there is little research on the elastic-plastic deformation of gas storage surrounding rocks during the filling and degassing process. Existing methods mostly rely on numerical simulation, but they have the following limitations:

[0004] Low computational efficiency: Traditional numerical models require high-precision meshing for complex geological conditions and dynamic loads, resulting in long calculation times, low analysis efficiency, and huge computational workload, making it difficult to meet real-time engineering needs.

[0005] Strong parameter dependence: The elastic-plastic constitutive relations of surrounding rock (such as the Mohr-Coulomb criterion and the Hoek-Brown criterion) need to rely on the calibration of a large number of geological parameters. However, the spatial variability of rock mass parameters in actual engineering is significant, and traditional methods are difficult to dynamically correct.

[0006] Ignoring dynamic effects: Most existing models are based on quasi-static assumptions and do not fully consider the temperature-stress-seepage multi-field coupling and the cumulative effect of surrounding rock damage during the inflation and deflation process, resulting in a large deviation between the prediction results and the actual working conditions.

[0007] Against the backdrop of the rapid development of CAES technology, there is an urgent need to develop a method that can efficiently and accurately calculate the elastic-plastic deformation of the rock surrounding gas storage reservoirs. This is necessary to ensure the safe and stable operation of CAES systems, promote the large-scale application of renewable energy, and optimize power system operation. To address these issues, we propose a method for calculating the elastic-plastic deformation of the rock surrounding gas storage reservoirs. Summary of the Invention

[0008] The purpose of the present invention is to address the shortcomings of the existing technology and provide a method for calculating the elastic-plastic deformation of the surrounding rock of a gas storage reservoir, which solves the problems of low calculation efficiency, strong parameter dependence and neglect of dynamic effects when the existing method relies on numerical simulation calculation.

[0009] Existing methods rely on numerical simulation calculations, which have the disadvantages of low computational efficiency, strong parameter dependence, and neglect of dynamic effects. To address the above problems, we propose a method for calculating the elastic-plastic deformation of the surrounding rock of a gas storage reservoir. In short, when implementing the method, the basic parameters of the lined gas storage reservoir are first obtained, and a force model of the lined gas storage reservoir during the inflation and deflation process is constructed based on the basic parameters of the lined gas storage reservoir. Then, based on the force model of the lined gas storage reservoir during the inflation and deflation process, the stress path of the surrounding rock during the inflation and deflation process is obtained. Finally, based on the stress path of the surrounding rock during the inflation and deflation process, the stress field function and displacement field function of the lined gas storage reservoir are obtained to complete the force calculation of the lined gas storage reservoir during the inflation and deflation process. In the embodiment of the present invention, by constructing a force model and stress path tracking during the inflation and deflation process, the traditional finite element method's requirement for high-precision meshing of complex geological conditions is avoided, and the calculation time is reduced. At the same time, stress path analysis is introduced to break through the traditional quasi-static assumption and directly obtain the dynamic evolution law of the plastic zone of the surrounding rock without repeated iterative calculations. Through the separate solution of the stress path function and the displacement field function, it is compatible with special geological scenarios such as high-stress soft rock and fractured rock mass, and reduces parameter dependence. While ensuring calculation precision and accuracy, the present invention avoids the problems of long numerical simulation time, slow analysis and calculation, and huge amount of calculation, and significantly improves the calculation efficiency, making it more convenient for engineering and technical personnel to use in the site selection and design of compressed gas energy storage liner gas storage.

[0010] The present invention is achieved by providing a method for calculating the elastic-plastic deformation of surrounding rocks of a gas storage reservoir, the method comprising:

[0011] The basic parameters of the lined gas storage are obtained, and a force model of the lined gas storage during the filling and deflation process is constructed based on the basic parameters of the lined gas storage. The force model of the lined gas storage during the filling and deflation process is:

[0012] The surrounding rock of the lined gas storage reservoir bears the internal pressure of the gas storage a and the ground stress p b work together;

[0013] Loading a force model of the lined gas storage during the filling and deflation process, and obtaining a stress path of the surrounding rock during the filling and deflation process based on the force model of the lined gas storage during the filling and deflation process;

[0014] Based on the stress path of the surrounding rock during the filling and degassing process, the stress field function and displacement field function of the lined gas storage are obtained, and the force calculation of the lined gas storage during the filling and degassing process is completed.

[0015] The stress path of the surrounding rock during the filling and discharge process of the lined gas storage is as follows: during the filling and discharge process, the gas storage internal pressure of the lined gas storage changes cyclically;

[0016] In the initial state, the surrounding rock is in the original rock stress state p a =pb ;

[0017] After excavation, the pressure inside the gas storage drops to 0;

[0018] During the subsequent charging and discharging process, the internal pressure of the gas storage cycles between the maximum internal pressure and the minimum internal pressure. min ≤p a ≤p max ;

[0019] Among them, the surrounding rock meets the MC yield criterion during the filling and degassing process of the lined gas storage, and the MC yield criterion is expressed as:

[0020]

[0021] Considering the isotropic stress state, the surrounding rock is subjected to axial symmetry, radial stress and hoop stress are the maximum and minimum principal stresses, σ1 is the first principal stress, σ3 is the third principal stress, c is the cohesion, is the angle of internal friction;

[0022] When the internal pressure of the lined gas storage is low, the stress state of the surrounding rock meets the low-pressure yield condition, and the yield line equation is:

[0023]

[0024] Among them, the radial direction is the third principal stress, the hoop direction is the first principal stress, and σ r =σ3,σ θ =σ1, when yielding, the stress state of the surrounding rock is located on the low-pressure yield line; if the surrounding rock is loaded on the low-pressure yield line, its stress state moves on the low-pressure yield line;

[0025] When the internal pressure of the lined gas storage is high, the high-pressure yield line is:

[0026]

[0027] Among them, the radial direction is the first principal stress, the hoop direction is the third principal stress, and σ r =σ1,σ θ =σ3, when yielding, the stress state of the surrounding rock is located on the high-pressure yield line; if the surrounding rock is loaded on the high-pressure yield line, its stress state will move on the high-pressure yield line;

[0028] When the internal pressure of the lined gas storage is moderate, the surrounding rock is in an elastic state and the stress is:

[0029]

[0030] Among them, the stress state of the surrounding rock is between the low-pressure yield line and the high-pressure yield line, r a is the radius of the gas storage reservoir, and the internal pressure of the lined gas storage reservoir is judged as small, large, or moderate by a preset pressure threshold;

[0031] When the internal pressure of the lined gas storage changes, the stress increment is:

[0032]

[0033] Among them, the increments of radial stress and hoop stress are inverse to each other, and the surrounding rock stress is along the direction perpendicular to σ r =σ θ Move in the direction.

[0034] When the lined gas storage is loaded and unloaded in the elastic zone, the stress increment is:

[0035]

[0036] When the lined gas storage is loaded and unloaded in the elastic zone, the internal pressure increment of the gas storage is:

[0037]

[0038] The increment of gas storage internal pressure is represented by the coordinates of the points on the stress path. and Respectively represent the i+1th step and the i-th step at r=r a Radial stress at

[0039] When the lined gas storage is loaded on the low-pressure yield line, a plastic zone will appear in the surrounding rock. The stress in the plastic zone can be solved by combining the equilibrium equation, which is:

[0040]

[0041] When the lined gas storage is loaded on the low-pressure yield line, the stress in the plastic zone is:

[0042]

[0043] in, and are the radial stress and hoop stress in the plastic zone at step i+1, r p is the corresponding plastic zone radius;

[0044] Outside the plastic zone is the elastic zone. The stress in the elastic zone is obtained according to the superposition principle. The stress in the elastic zone is:

[0045]

[0046] in, and are the radial stress and hoop stress in the elastic region of step i+1, (σ r ) i ,(σ θ )i are the radial stress and hoop stress calculated in step i, respectively, and Δp ap is the radial stress increment at the plastic zone radius;

[0047] According to the stress continuity condition at the boundary between the elastic and plastic zones, r is solved. p,i+1 and Δp ap,i+1 , r p,i+1 and Δp ap,i+1 The continuous solution is expressed as:

[0048]

[0049] When the lined gas storage is loaded on the high-pressure yield line, a plastic zone will appear in the surrounding rock. The stress in the plastic zone is:

[0050]

[0051] The stress field of the i-th step is:

[0052]

[0053] The recursive relationship of the stress field is:

[0054]

[0055] Among them, σ MC,i+1 Indicates whether plastic loading occurs on the low-pressure yield line or the high-pressure yield line during the process from step i to step i+1;

[0056] If loading is performed on the low-pressure yield line, σ MC,i+1 Take it according to the following formula:

[0057]

[0058] If loading is performed on the high-voltage yield line, σ MC,i+1 Take it according to the following formula:

[0059]

[0060] If it is elastic loading and unloading, then take r p,i+1 =r a , Δp ap,i+1 =Δp a .

[0061] Based on the stress path of the surrounding rock during the filling and releasing process, when obtaining the stress field function and displacement field function of the lined gas storage, the displacement field function is obtained through the stress field function;

[0062] When the surrounding rock is in an elastic state, the displacement is:

[0063]

[0064] During the elastic loading and unloading process, the displacement increment is:

[0065]

[0066] The displacement increment in the elastic region is:

[0067]

[0068] The strain in the axial direction of the gas storage is:

[0069]

[0070] Among them, dσ z is the stress in the axial direction of the gas storage reservoir;

[0071] The radial elastic strain is:

[0072]

[0073] Among them, dε r e is the radial strain increment, dε r is the radial strain increment, dλ is the plastic multiplier, and g is the plastic potential function;

[0074] The plastic potential function is:

[0075]

[0076] Where, φ is the expansion angle of the surrounding rock;

[0077] The radial elastic strain is:

[0078]

[0079] The hoop elastic strain is:

[0080]

[0081] The governing equation for solving the deformation in the plastic zone is:

[0082]

[0083] Among them, A, B, and Λ are coefficients, and the specific value of the coefficient Λ is determined by the stress path;

[0084] The coefficients A, B, Λ are:

[0085]

[0086] The governing equation for solving the deformation in the plastic zone can be written as follows according to the principle of integration:

[0087]

[0088] Where Δu r I is the radial displacement increment occurring in the plastic zone;

[0089] Each stress increment Δσ r and Δσ θ The corresponding displacement increment Δu r II for:

[0090]

[0091] The displacement boundary conditions are:

[0092]

[0093] The recursive relationship for solving the displacement field is:

[0094]

[0095] Compared with the prior art, the embodiments of the present application have the following beneficial effects:

[0096] In the embodiment of the present invention, by constructing a force model and stress path tracking during the inflation and deflation process, the traditional finite element method's requirement for high-precision meshing of complex geological conditions is avoided, and the calculation time is reduced. At the same time, stress path analysis is introduced to break through the traditional quasi-static assumption and directly obtain the dynamic evolution law of the plastic zone of the surrounding rock without repeated iterative calculations. Through the separate solution of the stress path function and the displacement field function, it is compatible with special geological scenarios such as high-stress soft rock and fractured rock mass, and reduces parameter dependence. While ensuring calculation precision and accuracy, the present invention avoids the problems of long numerical simulation time, slow analysis and calculation, and huge amount of calculation, and significantly improves the calculation efficiency, making it more convenient for engineering and technical personnel to use in the site selection and design of compressed gas energy storage liner gas storage. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 It is a schematic diagram of the implementation process of a method for calculating elastic-plastic deformation of surrounding rocks of a gas storage reservoir provided by the present invention.

[0098] Figure 2 A schematic diagram of the stress path of the surrounding rock during the filling and releasing process of the lined gas storage in Example 1 of the present invention is shown.

[0099] Figure 3 A schematic diagram of the recursive relationship of the stress field during the inflation and deflation process of Example 1 of the present invention is shown.

[0100] Figure 4 A diagram showing the stress model of the surrounding rock of the lined gas storage reservoir for medium-pressure gas energy storage in Example 2 of the present invention is shown.

[0101] Figure 5 This is a diagram showing the change in radial stress of the surrounding rock caused by the internal pressure of the cavern with radial distance during the first inflation and deflation cycle in Example 2 of the present invention.

[0102] Figure 6 This is a graph showing the variation of the annular stress caused by the internal pressure of the cavern with radial distance during the first inflation and deflation cycle in Example 2 of the present invention.

[0103] Figure 7 This is a graph showing the change in radial displacement caused by the internal pressure of the cavern with radial distance during the first inflation and deflation cycle in Example 2 of the present invention.

[0104] Figure 8 This is a graph showing the displacement characteristics of the inner wall of the surrounding rock during the first gas filling and releasing cycle in Example 2 of the present invention.

[0105] Figure 9 This is a diagram showing the changes in the plastic zone of the surrounding rock during the first gas filling and releasing cycle in Example 2 of the present invention.

[0106] Figure 10 The figure shows the displacement characteristic curve of the inner wall of the surrounding rock during 100 gas filling and releasing cycles in Example 2 of the present invention.

[0107] Figure 11 This is a diagram showing changes in the plastic zone of the surrounding rock during 100 gas filling and releasing cycles in Example 2 of the present invention.

[0108] Figure 12 This is a stress path diagram of a point on the inner wall of the surrounding rock of the gas storage reservoir in Example 2 of the present invention. DETAILED DESCRIPTION

[0109] Unless otherwise defined, all technical and scientific terms used herein have the same meanings as commonly understood by those skilled in the art to which this application belongs. The terms used in the specification of the application are only for the purpose of describing specific embodiments and are not intended to limit this application. The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above-mentioned drawings are intended to cover non-exclusive inclusions. The terms "first", "second", etc. in the specification and claims of this application or the above-mentioned drawings are used to distinguish different objects, not to describe a specific order.

[0110] Existing methods rely on numerical simulation calculations, which have the disadvantages of low computational efficiency, strong parameter dependence, and neglect of dynamic effects. To address the above problems, we propose a method for calculating the elastic-plastic deformation of the surrounding rock of a gas storage reservoir. In short, when implementing the method, the basic parameters of the lined gas storage reservoir are first obtained, and a force model of the lined gas storage reservoir during the inflation and deflation process is constructed based on the basic parameters of the lined gas storage reservoir. Then, based on the force model of the lined gas storage reservoir during the inflation and deflation process, the stress path of the surrounding rock during the inflation and deflation process is obtained. Finally, based on the stress path of the surrounding rock during the inflation and deflation process, the stress field function and displacement field function of the lined gas storage reservoir are obtained to complete the force calculation of the lined gas storage reservoir during the inflation and deflation process. In the embodiment of the present invention, by constructing a force model and stress path tracking during the inflation and deflation process, the traditional finite element method's requirement for high-precision meshing of complex geological conditions is avoided, and the calculation time is reduced. At the same time, stress path analysis is introduced to break through the traditional quasi-static assumption and directly obtain the dynamic evolution law of the plastic zone of the surrounding rock without repeated iterative calculations. Through the separate solution of the stress path function and the displacement field function, it is compatible with special geological scenarios such as high-stress soft rock and fractured rock mass, and reduces parameter dependence. While ensuring calculation precision and accuracy, the present invention avoids the problems of long numerical simulation time, slow analysis and calculation, and huge amount of calculation, and significantly improves the calculation efficiency, making it more convenient for engineering and technical personnel to use in the site selection and design of compressed gas energy storage liner gas storage.

[0111] Example 1

[0112] The embodiment of the present invention provides a method for calculating the elastic-plastic deformation of the surrounding rock of a gas storage reservoir. Figure 1 The figure shows a flow chart of a method for calculating the elastic-plastic deformation of surrounding rocks of a gas storage reservoir. The method specifically includes:

[0113] S10, obtaining basic parameters of the lined gas storage reservoir, and constructing a force model of the lined gas storage reservoir during the filling and deflation process based on the basic parameters of the lined gas storage reservoir, wherein the force model of the lined gas storage reservoir during the filling and deflation process is:

[0114] The surrounding rock of the lined gas storage reservoir bears the internal pressure of the gas storage a and the ground stress p b work together;

[0115] Among them, when constructing the stress model of the lined gas storage during the filling and releasing process based on the basic parameters of the lined gas storage, the combined effect of the internal pressure of the gas storage and the ground stress is considered to analyze the stress state changes of the surrounding rock.

[0116] S20, loading a force model of the lined gas storage during the filling and deflation process, and obtaining a stress path of the surrounding rock during the filling and deflation process based on the force model of the lined gas storage during the filling and deflation process, thereby clarifying a stress variation pattern of the surrounding rock under different gas storage internal pressure conditions;

[0117] S30, based on the stress path of the surrounding rock during the filling and degassing process, obtaining the stress field function and displacement field function of the lined gas storage reservoir;

[0118] S40, the stress field function and displacement field function of the lined gas storage are used to complete the force calculation of the lined gas storage during the filling and degassing process.

[0119] Among them, the stress field function and displacement field function of the lined gas storage are derived according to the stress path of the surrounding rock, which is conducive to the quantitative calculation of the elastic-plastic deformation of the surrounding rock.

[0120] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0121] In the embodiment of the present invention, by constructing a force model and stress path tracking during the inflation and deflation process, the traditional finite element method's requirement for high-precision meshing of complex geological conditions is avoided, and the calculation time is reduced. At the same time, stress path analysis is introduced to break through the traditional quasi-static assumption and directly obtain the dynamic evolution law of the plastic zone of the surrounding rock without repeated iterative calculations. Through the separate solution of the stress path function and the displacement field function, it is compatible with special geological scenarios such as high-stress soft rock and fractured rock mass, and reduces parameter dependence. While ensuring calculation precision and accuracy, the present invention avoids the problems of long numerical simulation time, slow analysis and calculation, and huge amount of calculation, and significantly improves the calculation efficiency, making it more convenient for engineering and technical personnel to use in the site selection and design of compressed gas energy storage liner gas storage.

[0122] In an embodiment of the present invention, when obtaining the stress path of the surrounding rock during the inflation and deflation process based on the force model of the lined gas storage during the inflation and deflation process, the stress path of the surrounding rock during the inflation and deflation process of the lined gas storage is: during the inflation and deflation process, the gas storage internal pressure of the lined gas storage changes cyclically;

[0123] In the initial state, the surrounding rock is in the original rock stress state p a =p b ;

[0124] After excavation (similar to the complete deflation process), the pressure inside the gas storage drops to 0;

[0125] During the subsequent charging and discharging process, the internal pressure of the gas storage cycles between the maximum internal pressure and the minimum internal pressure. min ≤p a ≤p max ;

[0126] In order to analyze the elastic-plastic deformation of the surrounding rock during the above process, it is necessary to first analyze the stress path of each point in the surrounding rock during the filling and degassing process. Considering the isotropic stress state, the surrounding rock is subjected to axial symmetry, and the radial stress and hoop stress are the maximum and minimum principal stresses. Among them, the surrounding rock meets the MC yield criterion during the filling and degassing of the lined gas storage. The MC yield criterion is expressed as:

[0127]

[0128] Considering the isotropic stress state, the surrounding rock is subjected to axial symmetry, radial stress and hoop stress are the maximum and minimum principal stresses, σ1 is the first principal stress, σ3 is the third principal stress, c is the cohesion, is the angle of internal friction;

[0129] When the internal pressure of the lined gas storage is low, the stress state of the surrounding rock meets the low-pressure yield condition, and the yield line equation is:

[0130]

[0131] Among them, the radial direction is the third principal stress, the hoop direction is the first principal stress, and σ r =σ3,σ θ =σ1, when yielding, the stress state of the surrounding rock is located on the low-pressure yield line, which is given by formula (2); if the surrounding rock is loaded on the low-pressure yield line, its stress state moves on the low-pressure yield line;

[0132] When the internal pressure of the lined gas storage is high, the high-pressure yield line is:

[0133]

[0134] Among them, the radial direction is the first principal stress, the hoop direction is the third principal stress, and σ r =σ1,σ θ =σ3, the stress state of the surrounding rock is located on the high-pressure yield line when yielding, which is given by formula (3); if the surrounding rock is loaded on the high-pressure yield line, its stress state will move on the high-pressure yield line;

[0135] When the internal pressure of the lined gas storage is moderate, the surrounding rock is in an elastic state and the stress is:

[0136]

[0137] Among them, the stress state of the surrounding rock is between the low-pressure yield line and the high-pressure yield line, r a is the radius of the gas storage reservoir. The internal pressure of the liner gas storage reservoir is judged as small, large, or moderate by a preset pressure threshold. For example, when the internal pressure of the gas storage reservoir is small, the direction of the principal stress of the surrounding rock satisfies the third principal stress in the radial direction and the first principal stress in the circumferential direction. At this time, if the surrounding rock stress state is below the low-pressure yield line (Formula (1)), it is determined to be a low-pressure working condition.

[0138] The stress state of the surrounding rock is between the low-pressure yield line and the high-pressure yield line. When the internal pressure of the lined gas storage changes, the stress increment is:

[0139]

[0140] Among them, it can be seen from formula (5) that the increments of radial stress and hoop stress are opposite to each other. At this time, the surrounding rock stress is along the direction perpendicular to σ r =σ θ Move in the direction.

[0141] Combining the above formula, the cyclic charging and discharging process can be expressed as (σ θ ,σ r ) is a stress path on the stress plane, Figure 2 The figure shows the stress path of the surrounding rock during the filling and releasing process of the lined gas storage in Example 1 of the present invention, wherein: Figure 2 (a) is the curve of the internal pressure of the lined gas storage changing with time during the cyclic charging and discharging process. Figure 2 (b) represents the stress path of the surrounding rock during the excavation, filling, and subsequent cycles of the lined gas storage, e.g. Figure 2 A0A1A2… in (b). Among them, A0A1A2 represents the stress path during excavation, A2A3A4 represents the stress path during the first inflation process, and A4A5, A4A5,… represent the stress paths during the subsequent inflation and deflation cycles.

[0142] In an embodiment of the present invention, based on the stress path of the surrounding rock during the inflation and deflation process, the stress field function and displacement field function of the lined gas storage are obtained. First, the stress field of the surrounding rock at any stress path point is solved.

[0143] When the lined gas storage is loaded and unloaded in the elastic zone, the internal pressure of the lined gas storage changes, and the stress increment is:

[0144]

[0145] When the lined gas storage is loaded and unloaded in the elastic zone, the increment of the gas storage internal pressure can be expressed by the coordinates of the points on the stress path. The increment of the gas storage internal pressure is:

[0146]

[0147] The increment of gas storage internal pressure is represented by the coordinates of the points on the stress path. and Respectively represent the i+1th step and the i-th step at r=r a Radial stress at

[0148] When the lined gas storage is loaded on the low-pressure yield line, a plastic zone will appear in the surrounding rock. The stress in the plastic zone can be solved by combining the equilibrium equation, which is:

[0149]

[0150] Combining equations (2) and (7), when the lined gas storage is loaded on the low-pressure yield line, the stress in the plastic zone is:

[0151]

[0152] in, and are the radial stress and hoop stress in the plastic zone at step i+1, r p is the corresponding plastic zone radius;

[0153] Outside the plastic zone is the elastic zone. The stress in the elastic zone is obtained according to the superposition principle. The stress in the elastic zone is:

[0154]

[0155] in, and are the radial stress and hoop stress in the elastic region of step i+1, (σ r ) i ,(σ θ ) i are the radial stress and hoop stress calculated in step i, respectively, and Δp ap is the radial stress increment at the plastic zone radius;

[0156] Equations (8) and (9) give the stress distributions in the plastic zone and the elastic zone, respectively. It can be seen that the stress distribution in the plastic zone is independent of the stress history, while the stress distribution in the elastic zone is related to the stress history. Figure 3 The schematic diagram of the recursive relationship of the stress field during the inflation and deflation process of Example 1 of the present invention is shown. Figure 3 It can be seen that the figure shows the recursive relationship between the stress field of step i+1 and the stress field of step i, where r p,i+1 and Δp ap,i+1 These two unknown quantities can be solved based on the stress continuity condition at the junction of the elastic and plastic zones, which is given by formula (10):

[0157] According to the stress continuity condition at the boundary between the elastic and plastic zones, r is solved. p,i+1 and Δp ap,i+1 , r p,i+1 and Δp ap,i+1 The continuous solution is expressed as:

[0158]

[0159] Combining equations (8)-(10) we can get a p,i+1 and Δp ap,i+1 The system of equations can be used to solve r p and Δp ap According to the required r p and Δp ap , and substituting it into equations (8) and (9), the stress field at step i+1 can be obtained.

[0160] When the lined gas storage is loaded on the high-pressure yield line, a plastic zone will appear in the surrounding rock. Combining equations (3) and (7), the stress in the plastic zone is:

[0161]

[0162] The corresponding stress in the elastic zone can be given by combining equations (9) and (10). The stress field of the surrounding rock during elastic loading and unloading as well as plastic loading can be calculated.

[0163] The stress field of the i-th step is:

[0164]

[0165] The recursive relationship of the stress field is:

[0166]

[0167] Among them, σ MC,i+1 Indicates whether plastic loading occurs on the low-pressure yield line or the high-pressure yield line during the process from step i to step i+1; this process can be determined by the stress path. If loading occurs on the low-pressure yield line, σ MC,i+1 According to formula (8), if the load is placed on the high-voltage yield line, σ MC,i+1 According to formula (11), if it is elastic loading and unloading, then take r p,i+1 =r a , Δp ap,i+1 =Δp a .

[0168] If loading is performed on the low-pressure yield line, σ MC,i+1 Take it according to the following formula:

[0169]

[0170] If loading is performed on the high-voltage yield line, σ MC,i+1 Take it according to the following formula:

[0171]

[0172] If it is elastic loading and unloading, then take r p,i+1 =ra , Δp ap,i+1 =Δp a .

[0173] In the embodiment of the present invention, when obtaining the stress field function and displacement field function of the lined gas storage based on the stress path of the surrounding rock during the filling and releasing process, the displacement field function is obtained through the stress field function;

[0174] When the surrounding rock is in an elastic state, the displacement is:

[0175]

[0176] During the elastic loading and unloading process, the displacement increment is:

[0177]

[0178] The displacement increment in the elastic region is:

[0179]

[0180] The strain in the axial direction of the gas storage is:

[0181]

[0182] Among them, dσ z is the stress in the axial direction of the gas storage reservoir;

[0183] The radial elastic strain is:

[0184]

[0185] Among them, dε r e is the radial strain increment, dε r is the radial strain increment, dλ is the plastic multiplier, and g is the plastic potential function.

[0186] The plastic potential function is:

[0187]

[0188] Where, φ is the expansion angle of the surrounding rock;

[0189] Combining equations (17)-(19), the radial elastic strain can be given by equation (20), which is:

[0190]

[0191] The hoop elastic strain is:

[0192]

[0193] Combining equations (20) and (21), the governing equation for deformation in the plastic zone can be given by equation (22). The governing equation for deformation in the plastic zone is:

[0194]

[0195] Among them, A, B, and Λ are coefficients, and the specific value of the coefficient Λ is determined by the stress path;

[0196] Combining equations (2), (3), and (19), the coefficients A, B, and Λ are:

[0197]

[0198] The governing equation for solving the deformation in the plastic zone can be written as follows according to the principle of integration:

[0199]

[0200] Where Δu r I is the radial displacement increment occurring in the plastic zone;

[0201] Each stress increment Δσ r and Δσ θ The corresponding displacement increment Δu r II for:

[0202]

[0203] Combining equations (16), (25), and (26), the displacement boundary condition is:

[0204]

[0205] Combining the differential equation given by formula (25) and the displacement boundary condition given by formula (27), the Runge-Kutta method can be used to solve the problem in the interval [r a ,r p ] to solve Δu by numerical integration r I The displacement increments in both the plastic and elastic zones can be calculated, and the recursive relationship for solving the displacement field is:

[0206]

[0207] Example 2

[0208] In a further preferred embodiment of the present invention, Figure 4The diagram shows the stress model of the surrounding rock of a compressed gas energy storage liner. Before conducting a mechanical response analysis of a liner gas storage, relevant parameters must be determined based on the properties of the surrounding rock. The gas storage radius is 8m, the surrounding rock deformation modulus is 15GPa, the surrounding rock Poisson's ratio is 0.25, the cohesion is 1MPa, the surrounding rock internal friction angle is 30°, the surrounding rock expansion angle is 30°, the in-situ stress is 8MPa, the maximum gas storage internal pressure is 14MPa, and the minimum gas storage internal pressure is 3MPa.

[0209] Based on the above-mentioned parameter values, the stress path, stress field and displacement field of the reservoir surrounding rock are calculated according to the formula derived by this method. The results are as follows: Figure 5-Figure 12 As shown in Figure 2, the mechanical response test results of the reservoir surrounding rock under the benchmark working conditions are shown, where: Figure 5 This is a graph showing the variation of the radial stress of the surrounding rock caused by the internal pressure of the cavern with radial distance during the first inflation and deflation cycle. Figure 6 This is a graph showing the variation of the hoop stress caused by the internal pressure of the cavern with radial distance during the first inflation and deflation cycle. Figure 7 The figure shows the radial displacement caused by the internal pressure of the cavern during the first filling and discharging cycle as a function of radial distance. Figure 5 、 6 It can be seen that the radial stress and hoop stress of the surrounding rock are both compressive stress during the gas filling and degassing process, and approach the ground stress as the radial distance increases. The radial stress of the surrounding rock transitions smoothly from the internal pressure of the cavern to the ground stress as the radial distance increases, while the hoop stress has two obvious stress turning points. Figure 9 It can be seen that the turning point positions correspond to the radii of the two plastic zones formed during the excavation and initial aeration of the cavern. This indicates that at the boundary of the plastic zone of the surrounding rock, the hoop stress undergoes a sudden change, thus forming a stress turning point. Figure 7 is the radial displacement of the cavern. As can be seen from the figure, the surrounding rock always keeps deforming inward during the process of filling and releasing gas, and the deformation of the surrounding rock gradually decreases with the increase of radial distance. Figure 8 This is the displacement characteristic curve of the inner wall of the surrounding rock during the first gas filling and releasing cycle. Figure 9 This is a diagram showing the changes in the plastic zone of the surrounding rock during the first gas filling and degassing cycle.

[0210] Figure 12 The stress path diagram of a point on the inner wall of the gas storage surrounding rock is shown in Figure 8. Point A0 represents the initial stress state. During the excavation phase of the cavern, the surrounding rock stress moves along A0, A1, and A2. When moving from point A0 to point A1, the surrounding rock remains in an elastic state, its radial stress gradually decreases, while the circumferential stress gradually increases, and the radial displacement of the surrounding rock increases linearly (Figure (8) A0A1); when moving to A1, the surrounding rock enters a low-pressure yield state and begins to appear in the plastic zone. pk ( Figure 4(9) A1); As the stress continues to move from point A1 to point A2, the radial stress and hoop stress of the surrounding rock gradually decrease, while the radial displacement increases nonlinearly ( Figure 4 (8) A1A2); when it moves to A2, the radial stress of the surrounding rock drops to 0 MPa, and at the same time, the radius of the plastic zone ( Figure 4 (9)A2,r pk =13.4m) and radial displacement (23.5mm deformation into the tunnel) reached the maximum.

[0211] During the first inflation process, the surrounding rock stress Figure 12 When moving from point A2 to point A3, the surrounding rock remains in an elastic state, its radial stress gradually increases while the hoop stress gradually decreases. The increase in the internal pressure of the cavern has a certain degree of relief on the deformation of the surrounding rock, and the two are in a linear relationship (Figure (8) A2A3); when moving to point A3, the hoop stress of the surrounding rock drops to 0MPa, the surrounding rock enters a high-pressure yield state, and the high-pressure plastic zone begins to appear. ph (Figure (9) A3); As the cavern continues to be inflated, the circumferential stress on the inner wall of the surrounding rock gradually increases (paths A3 and A4), and the radial displacement decreases nonlinearly with the increase of the cavern internal pressure (Figure (8) A3 and A4), while the radius of the high-pressure plastic zone gradually increases with the increase of the pressure; when the cavern internal pressure reaches 14 MPa, the surrounding rock stress moves to point A4, and the radius of the high-pressure plastic zone reaches its maximum (Figure (9) A4, r ph =12.1m), and at the same time, the surrounding rock deformation decreased from 23.5mm in the excavation stage to 11.6mm under the maximum gas storage internal pressure state.

[0212] During the first degassing process, the surrounding rock stress moves along A4, A5, and A6 in Figure (12). In the A4 and A5 stages, the surrounding rock maintains an elastic state, its radial stress gradually decreases, and its circumferential stress gradually increases. The radial displacement of the surrounding rock decreases linearly with the decrease in the internal pressure of the cavern (Figure (8) A4 and A5); when it moves to point A5, the surrounding rock enters a low-pressure yield state and begins to appear in a low-pressure plastic zone. pl (Figure (9) A5); As the cavern continues to deflate, the radial stress and hoop stress of the surrounding rock wall gradually decrease (paths A5 and A6), while the radial displacement (Figure (8) A5 and A6) and the radius of the low-pressure plastic zone (Figure (9) A5 and A6) increase nonlinearly as the cavern internal pressure decreases; when the cavern internal pressure drops to 3 MPa (point A6), the radius of the low-pressure plastic zone of the surrounding rock reaches its maximum (Figure (9) A6, r pl =8.3m), and at the same time, the surrounding rock deformation increases from 11.6mm under the maximum gas storage internal pressure to 19.1mm under the minimum gas storage internal pressure.

[0213] During the second inflation process, the surrounding rock was initially in an elastic stress state (paths A6 and A7). When the internal pressure of the cavern increased to 12.46 MPa, the surrounding rock began to enter a high-pressure yield state (paths A7 and A4). The surrounding rock stress path during the second deflation process was the same as that during the first deflation (paths A4, A5, and A6). In all subsequent inflation and deflation cycles (excluding special operating conditions such as shutdowns for maintenance), the surrounding rock stress path moved along A6, A7, A4, A5, and A6.

[0214] Figure 10 The displacement characteristic curve of the inner wall of the surrounding rock during 100 cycles of gas filling and degassing is shown. Figure 10 As can be seen from the figure, the surrounding rock has accumulated plastic deformation under the action of long-term inflation and deflation cycles. After 100 inflation and deflation cycles, the radial deformation of the surrounding rock at the maximum and minimum gas storage internal pressures increased to 17.3mm and 24.7mm, respectively. Compared with the first inflation and deflation cycle, both increased by approximately 5.6mm, with an average increase of 0.056mm per single inflation and deflation cycle. This shows that under the baseline scheme, the surrounding rock deformation continues to advance into the cavern with the increase in inflation and deflation cycles. Moreover, the surrounding rock deformation at the minimum gas storage internal pressure within 100 cycles has exceeded the deformation during the cavern excavation stage. The surrounding rock deformation becomes more severe with the increase in inflation and deflation cycles.

[0215] Figure 11 It is a diagram showing the changes in the plastic zone of the surrounding rock during 100 cycles of inflation and deflation. As can be seen from the figure, except for the cavern excavation stage, the plastic zone of the surrounding rock shows periodic changes during multiple inflation and deflation cycles, in which high-pressure and low-pressure plastic zones are formed in the inflation stage and deflation stage respectively. Under the benchmark calculation scheme, the radii of the high-pressure and low-pressure plastic zones of the surrounding rock are stable at 8.5m (excluding the plastic zone that appears during the first inflation process) and 8.3m respectively. It is worth noting that although the high-pressure and low-pressure plastic zones of the surrounding rock cycle and appear alternately with the inflation and deflation process of the cavern, the range of the plastic zone does not accumulate, and the maximum plastic zone radius still appears in the cavern excavation stage (r pk =13.4m).

[0216] Under the baseline operating conditions derived from the formula derived in this example, the surrounding rock experiences cumulative plastic deformation during the cyclic inflation and deflation process. While cavern inflation mitigates this inward deformation to a certain extent, the surrounding rock continues to deform inward under cyclic inflation and deflation conditions, even exceeding the deformation observed during cavern excavation. Furthermore, the radius of the surrounding rock's plastic zone exhibits periodic variation during long-term inflation and deflation cycles, but its maximum plastic zone still occurs when cavern excavation is complete.

[0217] In summary, the present invention provides a method for calculating the elastic-plastic deformation of the surrounding rock of a gas storage reservoir. In an embodiment of the present invention, by constructing a force model and stress path tracking during the gas filling and degassing process, the traditional finite element method's requirement for high-precision meshing of complex geological conditions is avoided, and the calculation time is reduced. At the same time, stress path analysis is introduced to break through the traditional quasi-static assumption and directly obtain the dynamic evolution law of the plastic zone of the surrounding rock without repeated iterative calculations. Through the separate solution of the stress path function and the displacement field function, it is compatible with special geological scenarios such as high-stress soft rock and fractured rock mass, and reduces parameter dependence. Under the premise of ensuring calculation precision and accuracy, the present invention avoids the problems of long numerical simulation time, slow analysis and calculation, and huge amount of calculation, and significantly improves the calculation efficiency, making it more convenient for engineering and technical personnel to use in the site selection and design of compressed gas energy storage liner gas storage.

[0218] It should be noted that for the aforementioned embodiments, for simplicity of description, they are all expressed as a series of action combinations. However, those skilled in the art should be aware that the present invention is not limited by the order of the actions described, because according to the present invention, certain steps may be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present invention.

[0219] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the scope of protection of the invention. Obviously, the embodiments described are only some embodiments of the present invention, rather than all embodiments. Based on these embodiments, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in this field can still combine, add, delete or make other adjustments to the features in the various embodiments of the present invention according to the circumstances without conflict, without making creative work, so as to obtain different other technical solutions that do not deviate from the concept of the present invention in essence, and these technical solutions also fall within the scope of protection of the present invention.

Claims

1. A method for calculating elastic-plastic deformation of surrounding rock of a gas storage reservoir, characterized in that: The method comprises: The basic parameters of the lined gas storage are obtained, and a force model of the lined gas storage during the filling and deflation process is constructed based on the basic parameters of the lined gas storage. The force model of the lined gas storage during the filling and deflation process is: The surrounding rock of the lined gas storage bears the internal pressure of the gas storage p a and the ground stress p b work together; Loading a force model of the lined gas storage during the filling and deflation process, and obtaining a stress path of the surrounding rock during the filling and deflation process based on the force model of the lined gas storage during the filling and deflation process; Based on the stress path of the surrounding rock during the filling and degassing process, the stress field function and displacement field function of the lined gas storage are obtained, and the force calculation of the lined gas storage during the filling and degassing process is completed.

2. The method for calculating elastic-plastic deformation of surrounding rock of a gas storage reservoir according to claim 1, characterized in that: The stress path of the surrounding rock during the filling and discharge process of the lined gas storage is as follows: during the filling and discharge process, the gas storage internal pressure of the lined gas storage changes cyclically; In the initial state, the surrounding rock is in the original rock stress state p a =p b ; After excavation, the pressure inside the gas storage drops to 0; During the subsequent charging and discharging process, the internal pressure of the gas storage cycles between the maximum internal pressure and the minimum internal pressure. min ≤p a ≤p max ; Among them, the surrounding rock meets the MC yield criterion during the filling and degassing process of the lined gas storage, and the MC yield criterion is expressed as: Considering the isotropic stress state, the surrounding rock is subjected to axial symmetry, radial stress and hoop stress are the maximum and minimum principal stresses, σ1 is the first principal stress, σ3 is the third principal stress, c is the cohesion, is the angle of internal friction; When the internal pressure of the lined gas storage is low, the stress state of the surrounding rock meets the low-pressure yield condition, and the yield line equation is: Among them, the radial direction is the third principal stress, the hoop direction is the first principal stress, and σ r =σ3,σ θ =σ1, when yielding, the stress state of the surrounding rock is located on the low-pressure yield line; if the surrounding rock is loaded on the low-pressure yield line, its stress state moves on the low-pressure yield line; When the internal pressure of the lined gas storage is high, the high-pressure yield line is: Among them, the radial direction is the first principal stress, the hoop direction is the third principal stress, and σ r =σ1,σ θ =σ3, when yielding, the stress state of the surrounding rock is located on the high-pressure yield line; if the surrounding rock is loaded on the high-pressure yield line, its stress state will move on the high-pressure yield line; When the internal pressure of the lined gas storage is moderate, the surrounding rock is in an elastic state and the stress is: Among them, the stress state of the surrounding rock is between the low-pressure yield line and the high-pressure yield line, r a is the radius of the gas storage reservoir, and the internal pressure of the lined gas storage reservoir is judged as small, large, or moderate by a preset pressure threshold; When the internal pressure of the lined gas storage changes, the stress increment is: Among them, the increments of radial stress and hoop stress are inverse to each other, and the surrounding rock stress is perpendicular to σ r =σ θ Move in the direction.

3. The method for calculating elastic-plastic deformation of surrounding rock of a gas storage reservoir according to claim 1, characterized in that: When the lined gas storage is loaded and unloaded in the elastic zone, the stress increment is: When the lined gas storage is loaded and unloaded in the elastic zone, the internal pressure increment of the gas storage is: The increment of gas storage internal pressure is represented by the coordinates of the points on the stress path. and Respectively represent the i+1th step and the i-th step at r=r a Radial stress at When the lined gas storage is loaded on the low-pressure yield line, a plastic zone will appear in the surrounding rock. The stress in the plastic zone can be solved by combining the equilibrium equation, which is: When the lined gas storage is loaded on the low-pressure yield line, the stress in the plastic zone is: in, and are the radial stress and hoop stress in the plastic zone at step i+1, r p is the corresponding plastic zone radius; Outside the plastic zone is the elastic zone. The stress in the elastic zone is obtained according to the superposition principle. The stress in the elastic zone is: in, and are the radial stress and hoop stress in the elastic region of step i+1, (σ r ) i ,(σ θ ) i are the radial stress and hoop stress calculated in step i, respectively, and Δp ap is the radial stress increment at the plastic zone radius; Solve r according to the stress continuity condition at the boundary between the elastic and plastic zones p,i+1 and Δp ap,i+1 , r p,i+1 and Δp ap,i+1 The continuous solution is expressed as: When the lined gas storage is loaded on the high-pressure yield line, a plastic zone will appear in the surrounding rock. The stress in the plastic zone is: The stress field of the i-th step is: The recursive relationship of the stress field is: Among them, σ MC,i+1 Indicates whether plastic loading occurs on the low-pressure yield line or the high-pressure yield line during the process from step i to step i+1; If loading is performed on the low-pressure yield line, σ MC,i+1 According to the following formula: If loading is done on the high-voltage yield line, σ MC,i+1 According to the following formula: If it is elastic loading and unloading, then take r p,i+1 =r a , Δp ap,i+1 =Δp a .

4. The method for calculating elastic-plastic deformation of surrounding rock of a gas storage reservoir according to claim 2, characterized in that: Based on the stress path of the surrounding rock during the filling and releasing process, when obtaining the stress field function and displacement field function of the lined gas storage, the displacement field function is obtained through the stress field function; When the surrounding rock is in an elastic state, the displacement is: During the elastic loading and unloading process, the displacement increment is: The displacement increment in the elastic region is: The strain in the axial direction of the gas storage is: Among them, dσ z is the stress in the axial direction of the gas storage reservoir; The radial elastic strain is: Among them, dε r e is the radial strain increment, dε r is the radial strain increment, dλ is the plastic multiplier, and g is the plastic potential function.

5. The method for calculating elastic-plastic deformation of surrounding rock of a gas storage reservoir according to claim 4, characterized in that: The plastic potential function is: Where, φ is the expansion angle of the surrounding rock; The radial elastic strain is: The hoop elastic strain is: The governing equation for solving the deformation in the plastic zone is: Among them, A, B, Λ are coefficients, and the specific value of the coefficient Λ is determined by the stress path; the coefficients A, B, Λ are: The governing equation for solving the deformation in the plastic zone can be written as follows according to the integration principle: Where Δu r I is the radial displacement increment occurring in the plastic zone; Each stress increment Δσ r and Δσ θ The corresponding displacement increment Δu r II for: The displacement boundary conditions are: The recursive relationship for solving the displacement field is:

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