Dynamic prediction method for permeation condition of long-term storage of CO2 in layered salt rock cavern

Abstract

The invention relates to a dynamic prediction method for the permeation condition of long-term storage of CO2 in a layered salt rock cavern, and the method comprises the steps: S1, setting the rational conditions of the prediction method, and collecting the exploration data of salt rock; s2, on the basis of considering the slippage effect, a permeability equation is obtained by utilizing the relationship between the porosity and the permeability of the salt rock, and the permeability equation represents the relationship between the effective permeability of the gas and the pressure and the temperature of CO2 in the salt rock; s3, determining a seepage velocity formula of the CO2 gas, wherein the seepage velocity formula represents the relationship between the seepage velocity and the effective permeability, pressure and temperature of the CO2 gas in the salt rock; s4, the exploration data are substituted into the permeability equation and the seepage velocity equation which are finally obtained in the two steps, iterative calculation is conducted among the three parameters of the gas pressure, the gas effective permeability and the seepage velocity in the salt rock, and then the condition of the dynamic change process of diffusion and seepage of CO2 in the salt rock cavern to the outside of the cavern is determined in combination with a finite element analysis method.

Description

Technical Field

[0001] The invention belongs to the technical field of carbon dioxide geological storage prediction, and in particular relates to a dynamic prediction method for the permeability of long-term CO2 storage in a layered salt rock karst cavity. Background Art

[0002] Salt rock formation is a resource-based formation, which contains a large amount of salt. Wells can be drilled from the ground into the salt rock, and then water can be injected into the salt rock. The salt in the salt rock dissolves in the water, and then the brine is extracted to the ground. After mining, cavities are formed inside the salt rock. Salt rock has low permeability and good damage self-healing properties. It is a good geological body for CO2 storage. Supercritical CO2 can be injected into the salt rock cavity through industrial technology for long-term storage. However, researchers in this field lack systematic research on the long-term storage of CO2 in salt rock. In addition, for low-permeability porous media such as salt rock, the Klinkenberg effect (slippage effect) has a significant impact on gas permeability, and the salt rock generally contains several layers of mudstone interlayers, which makes the study of long-term storage of CO2 in salt rock more complicated. Summary of the invention

[0003] In view of the above problems, the present invention provides a method for dynamically predicting the permeability of long-term CO2 storage in a layered salt rock cavity, comprising the following steps: S1: Set rational conditions for this dynamic prediction method from the aspects of gas diffusion, storage, migration and the properties of salt rock itself, and collect exploration data of salt rock as the basis for subsequent prediction; S2: On the basis of considering the slippage effect, the relationship between the porosity and permeability of salt rock is used to obtain the permeability equation, which represents the relationship between the effective permeability of gas and the pressure and temperature of CO2 in salt rock; S3: Determine the seepage velocity formula of CO2 gas, which represents the relationship between the seepage velocity and the effective permeability, pressure and temperature of CO2 gas in the salt rock; S4: Substitute the exploration data of step S1 into the permeability equation and seepage velocity equation finally obtained in steps S2 and S3, perform iterative calculations among the three parameters of gas pressure, gas effective permeability and seepage velocity in salt rock, and then combine the finite element analysis method to determine the dynamic change process of CO2 diffusion and seepage from the salt rock cavity to the outside of the cavity.

[0004] Optionally, in step S1, the rational condition includes: (1) Salt rock and mudstone interlayers are abstracted as homogeneous continuous porous media; (2) CO2 only exists in salt rock cavities and follows the ideal gas state equation; (3) In salt rock or mudstone interlayers, the migration of CO2 follows Darcy's law, while taking into account the effects of diffusion, Klinkenberg effect and gravity; (4) The deformation of salt rock and mudstone interlayers conforms to the small deformation hypothesis; (5) Consider the influence of temperature on CO2 migration and deformation of salt rock and mudstone interlayers.

[0005] Optionally, step S2 specifically includes the following steps: (a) Considering the influence of slippage effect on gas permeability of salt rock or mudstone interlayer, determine the initial equation of gas effective permeability and the equation of slippage coefficient; (b) There is a cubic theorem between gas permeability and porosity. Combining the initial equation of gas effective permeability with the cubic theorem and the slip coefficient, we can get the gas effective permeability k e and porosity , equations related to pressure p and temperature T; (c) Due to porosity The relationship between the volume strain of the salt rock or mudstone interlayer and the effective gas permeability k obtained in step (b) is e The effective gas permeability k is obtained by combining the equation e Equations related to coal matrix volume strain ε, pressure p, and temperature T; (d) Assuming that the salt rock or mudstone interlayer is isotropic and the pores are filled with CO2 gas, the elastic-plastic constitutive equation is combined with the gas effective permeability k obtained in step (c) e Combined with the equations related to coal matrix volume strain ε, pressure p, and temperature T, the gas effective permeability k is obtained e Equations related to pressure p and temperature T.

[0006] Optionally, in step (a), for low permeability porous media such as salt rock or mudstone interlayers, the slippage effect has a significant impact on its gas permeability, and the initial equation for the effective gas permeability is as follows: (1) Among them, k e is the effective gas permeability of salt rock or mudstone interlayer, in m 2 ; k is the gas permeability of salt rock or mudstone interlayer, unit is m 2 ; p is the CO2 gas pressure in the pores of salt rock or mudstone interlayers, in MPa; b is the slip coefficient, in MPa.

[0007] Further optionally, the slip coefficient b is related to the temperature T (K) of the salt rock or mudstone interlayer, the type of gas sealed and the pore structure of the porous medium, and is determined by the following formula: ; Where c is a constant, c=0.9; μ is the dynamic viscosity of the gas, in Pa·s; R is the molar gas constant, 8.31 J / (mol·K); M g is the molar mass of the gas, in kg / mol; r is the pore radius of the salt rock or mudstone interlayer, in m.

[0008] Regarding the explanation of temperature T, since CO2 seepage is an extremely slow process (measured in years), at a certain moment, the thermal diffusion and thermal convection of the gas temperature and the nearby formation temperature are rapid. Therefore, it is believed that the CO2 gas temperature and the formation temperature are equal in real time. Therefore, the temperature T in the present invention is the formation temperature and also the temperature of the CO2 gas.

[0009] Further optionally, in step (b), the cubic theorem between permeability and porosity is as follows: ; Where k0 is the initial permeability of salt rock or mudstone interlayer, in m 2 ; 0 is the initial porosity of salt rock or mudstone interlayer, in %, k0 and 0 is a known number. From the cubic theorem we get: , substituting this formula and the formula of slip coefficient b into the above formula (1), we get the following formula: (2) From formula (2), we can know that the effective permeability of gas k e and porosity , pressure p, dynamic viscosity μ of gas, and temperature T.

[0010] Further optionally, in step (c), the porosity of the salt rock or mudstone interlayer is Determined by the following formula: (3) Where ε is the volume strain of coal matrix, dimensionless; ΔV s is the change in the skeleton volume of salt rock or mudstone interlayer, in m 3 ; V s0 is the initial skeleton volume of salt rock or mudstone interlayer, in m 3 .

[0011] Further optionally, the ΔV s With V s0 The ratio is determined by the following formula: (4) Among them, Ks is the bulk modulus of the solid skeleton of the salt rock or mudstone interlayer, in MPa; Δp is the change in gas pressure, in MPa; α is the effective stress coefficient of the salt rock or mudstone interlayer, dimensionless; α T is the coefficient of thermal expansion, in K -1 ; ΔT is the temperature change of salt rock or mudstone interlayer, the unit is K (Kelvin); Substituting formula (4) into formula (3), we get: (5) From formula (5) and formula (2), we can know that the effective permeability of gas k e It is related to the coal matrix volume strain ε, pressure p and temperature T.

[0012] Further optionally, in step (d), the elastoplastic constitutive equation considering gas pressure and temperature is as follows: (6) in, is the component of the strain tensor, dimensionless; G is the shear modulus of the salt rock or mudstone interlayer, in MPa; is the component of the stress tensor, in MPa; is the normal stress component, in MPa; K is the bulk modulus of salt interlayer or mudstone, in MPa; is the Kronecker symbol. When i=j, =1, when i≠j, = 0; i and j are the vector subscripts of two directions in the three-dimensional direction. Please note that the bulk modulus K of salt interlayer or mudstone is different from the thermodynamic unit Kelvin.

[0013] Further optionally, the shear modulus G is determined by the following formula: G=E / (2+2v) The bulk modulus K is determined by the following formula: K = E / [3 × (1-2v)] Wherein, E is the elastic modulus of the salt rock or mudstone interlayer, in MPa; v is the Poisson’s ratio, dimensionless.

[0014] Alternatively, the effective gas permeability k obtained by substituting formula (6) into step (c) is: e The equation related to the coal matrix volume strain ε, pressure p, and temperature T gives the gas effective permeability k e Equations related to pressure p and temperature T.

[0015] Optionally, in step S3, the seepage velocity of CO2 gas in the salt rock or mudstone interlayer is determined by the following formula: ; Among them, v g is the gas seepage velocity, in m / s; ρ g is the density of gas in salt rock or mudstone interlayer, in kg / m 3 ; g is the acceleration due to gravity, in m / s 2 ; h is the vertical distance of CO2 migration affected by gravity, in meters; Among them, ρ g It is expressed as: ; The final seepage velocity formula is: ; From the above formula, we can know that the seepage velocity v of CO2 gas is g and gas effective permeability k e , pressure p, and temperature T.

[0016] The present invention obtains k through step S2 e =f(p,T), step S3 obtains v g =f'(k e ,p,T), so that k e and v g Linking it to the pressure and temperature of CO2 gas in salt or mudstone interlayers greatly simplifies the complexity of predictions and subsequent calculations.

[0017] Finite element analysis is the simulation of real physical systems (geometry and load conditions) using mathematical approximation methods. Finite element analysis replaces complex problems with simpler ones and then solves them. It regards the solution domain as consisting of many small interconnected subdomains called finite elements, assumes a suitable (simpler) approximate solution for each unit, and then derives the total satisfaction conditions for solving this domain to obtain the solution to the problem.

[0018] In step S4, simulation software (such as COMSOL Multiphysics multi-physics field simulation software) is used to solve the finite element method multi-physics field coupling of the mathematical model of the salt rock cavity. First, the selected salt rock cavity physical model is divided into triangular meshes, and the mesh of the salt rock cavity boundary and the interface between salt rock and mudstone interlayer is encrypted. Then, within the quantitative simulation time range, several cross-sections are selected, and the cross-sections are used as the research objects to obtain the exploration data on the cross-sections. According to step S2, k is obtained. e =f(p,T) and step S3 to get v g =f'(k e,p,T), at gas pressure p, gas effective permeability k e , seepage velocity v g Iterative calculations are performed between the three parameters, and combined with the finite element analysis method, the dynamic permeability of CO2 around the salt rock cavity is determined. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the grid division in step S4 (the circle in the middle is the cavity); Figure 2 It is a schematic diagram of the physical model of the salt rock cavity and the selection of cross-section lines; Figure 3 is the effective permeability curve of mudstone interlayer; Figure 4 is the effective permeability curve of salt rock; Figure 5 is the pore pressure curve of mudstone interlayer; Figure 6 is the pore pressure curve of salt rock layer; Figure 7 It is the curve of CO2 seepage velocity in mudstone interlayer; Figure 8 This is a graph showing the CO2 seepage velocity in salt rock layers. DETAILED DESCRIPTION

[0020] This embodiment provides a method for dynamically predicting the permeability of long-term CO2 storage in a layered salt rock karst cavity, comprising the following steps: S1: Set rational conditions for this dynamic prediction method from the aspects of gas diffusion, storage, migration and the properties of salt rock itself, and collect exploration data of salt rock as the basis for subsequent prediction; S2: On the basis of considering the slippage effect, the relationship between the porosity and permeability of salt rock is used to obtain the permeability equation, which represents the relationship between the effective permeability of gas and the pressure and temperature of CO2 in salt rock; S3: Determine the seepage velocity formula of CO2 gas, which represents the relationship between the seepage velocity and the effective permeability, pressure and temperature of CO2 gas in the salt rock; S4: Substitute the exploration data of step S1 into the permeability equation and seepage velocity equation finally obtained in steps S2 and S3, perform iterative calculations among the three parameters of gas pressure, gas effective permeability and seepage velocity in salt rock, and then combine the finite element analysis method to determine the dynamic change process of CO2 diffusion and seepage from the salt rock cavity to the outside of the cavity.

[0021] Salt rock generally has several layers of mudstone interlayers. The layered salt rock described in the present invention refers to salt rock containing several layers of mudstone interlayers. The permeability of long-term CO2 storage in salt rock and mudstone can be considered separately.

[0022] In step S1, the rational conditions include: (1) Salt rock and mudstone interlayers are abstracted as homogeneous continuous porous media; (2) CO2 only exists in salt rock cavities and follows the ideal gas state equation; (3) In salt rock or mudstone interlayers, the migration of CO2 follows Darcy's law, while taking into account the effects of diffusion, Klinkenberg effect and gravity; (4) The deformation of salt rock and mudstone interlayers conforms to the small deformation hypothesis; (5) Consider the influence of temperature on CO2 migration and deformation of salt rock and mudstone interlayers.

[0023] In step S1, the exploration data includes but is not limited to the shape, size, burial depth, number and properties of salt rock cavities, permeability, porosity, mechanical properties (Poisson's ratio, compressive strength, etc.) of salt rock interlayers and mudstone interlayers, and initial formation temperature.

[0024] Step S2 specifically includes the following steps: (a) Considering the influence of slippage effect on gas permeability of salt rock or mudstone interlayer, determine the initial equation of gas effective permeability and the equation of slippage coefficient; (b) There is a cubic theorem between gas permeability and porosity. Combining the initial equation of gas effective permeability with the cubic theorem and the slip coefficient, we can get the gas effective permeability k e and porosity , equations related to pressure p and temperature T; (c) Due to porosity The relationship between the volume strain of the salt rock or mudstone interlayer and the effective gas permeability k obtained in step (b) is e The effective gas permeability k is obtained by combining the equation e Equations related to coal matrix volume strain ε, pressure p, and temperature T; (d) Assuming that the salt rock or mudstone interlayer is isotropic and the pores are filled with CO2 gas, the elastic-plastic constitutive equation is combined with the gas effective permeability k obtained in step (c) e Combined with the equations related to coal matrix volume strain ε, pressure p, and temperature T, the gas effective permeability k is obtained e Equations related to pressure p and temperature T.

[0025] In step (a), for low-permeability porous media such as salt rock or mudstone interlayers, the slippage effect has a significant impact on its gas permeability. The initial equation for the effective gas permeability is as follows: (1) Among them, k e is the effective gas permeability of salt rock or mudstone interlayer, in m 2 ; k is the gas permeability of salt rock or mudstone interlayer, unit is m 2 ; p is the CO2 gas pressure in the pores of salt rock or mudstone interlayers, in MPa; b is the slip coefficient, in MPa.

[0026] The slip coefficient b is related to the temperature T (K) of the salt rock or mudstone interlayer, the type of gas stored and the pore structure of the porous medium, and is determined by the following formula: ; Where c is a constant, c=0.9; μ is the dynamic viscosity of the gas, in Pa·s; R is the molar gas constant, 8.31 J / (mol·K); M g is the molar mass of the gas, in kg / mol; r is the pore radius of the salt rock or mudstone interlayer, in m.

[0027] The pore radius r of the salt rock or mudstone interlayer is determined by the following formula: ; in, It is the porosity of salt rock or mudstone interlayer, in %.

[0028] In step (b), the cubic theorem between permeability and porosity is as follows: ; Where k0 is the initial permeability of salt rock or mudstone interlayer, in m 2 ; 0 is the initial porosity of salt rock or mudstone interlayer, in %, k0 and 0 is a known number. From the cubic theorem we get: , substituting this formula and the formula of slip coefficient b into the above formula (1), we get the following formula: (2) From formula (2), we can know that the effective permeability of gas k e and porosity , pressure p, dynamic viscosity μ of gas, and temperature T.

[0029] In step (c), the porosity of the salt rock or mudstone interlayer is Determined by the following formula: (3) Where ε is the volume strain of coal matrix, dimensionless; ΔV s is the change in the skeleton volume of salt rock or mudstone interlayer, in m 3 ; V s0 is the initial skeleton volume of salt rock or mudstone interlayer, in m 3 .

[0030] The ΔV s With V s0 The ratio is determined by the following formula: (4) Among them, K s is the bulk modulus of the solid skeleton of the salt rock or mudstone interlayer, in MPa; Δp is the change in gas pressure, in MPa; α is the effective stress coefficient of the salt rock or mudstone interlayer, dimensionless; α T is the coefficient of thermal expansion, in K -1 ; ΔT is the temperature change of salt rock or mudstone interlayer, the unit is K (Kelvin); Substituting formula (4) into formula (3), we get: (5) From formula (5) and formula (2), we can know that the effective permeability of gas k e It is related to the volume strain ε, pressure p and temperature T of the coal matrix. K s ,μ,Mg,α,α T , Δp, and ΔT can all be obtained through exploration. Substituting formula (5) into formula (2) results in a relatively complex formula, which is omitted here, but those skilled in the art can calculate it according to the present invention.

[0031] In step (d), the elastic-plastic constitutive equation considering gas pressure and temperature is as follows: (6) in, is the component of the strain tensor, dimensionless; G is the shear modulus of the salt rock or mudstone interlayer, in MPa; is the component of the stress tensor, in MPa; is the normal stress component, in MPa; K is the bulk modulus of salt interlayer or mudstone, in MPa; is the Kronecker symbol. When i=j, =1, when i≠j, = 0; i and j are the vector subscripts of two directions in the three-dimensional direction. Please note that the bulk modulus K of salt interlayer or mudstone is different from the thermodynamic unit Kelvin.

[0032] The shear modulus G is determined by the following formula: G=E / (2+2v) The bulk modulus K is determined by the following formula: K = E / [3 × (1-2v)] Wherein, E is the elastic modulus of the salt rock or mudstone interlayer, in MPa; v is the Poisson’s ratio, dimensionless.

[0033] Substituting formula (6) into step (c) yields the gas effective permeability k e The equation related to the coal matrix volume strain ε, pressure p, and temperature T gives the gas effective permeability k e An equation related to pressure p and temperature T (because the equation is too complicated, it is omitted here, but those skilled in the art can calculate it according to the present invention).

[0034] In step S3, the seepage velocity of CO2 gas in the salt rock or mudstone interlayer is determined by the following formula: ; Among them, v g is the gas seepage velocity, in m / s; ρ g is the density of gas in salt rock or mudstone interlayer, in kg / m 3 ; g is the acceleration due to gravity, in m / s 2 ; h is the vertical distance of CO2 migration affected by gravity, in meters; Among them, ρ g It is expressed as: ; The final seepage velocity formula is: ; From the above formula, we can know that the seepage velocity v of CO2 gas is g and gas effective permeability k e , pressure p, and temperature T. Both μ and h can be obtained through exploration.

[0035] In step S4, simulation software (such as COMSOL Multiphysics multi-physics field simulation software) is used to perform a finite element method multi-physics field coupling solution on the mathematical model of the salt rock cavity. First, the selected salt rock cavity physical model is divided into triangular meshes, and the mesh of the salt rock cavity boundary and the interface between the salt rock and the mudstone interlayer is encrypted, such as Figure 1Then, within the quantitative simulation time range, select several cross-sections, take the cross-sections as the research objects, obtain the exploration data on the cross-sections, and obtain k according to step S2. e =f(p,T) and step S3 to get v g =f'(k e ,p,T), at gas pressure p, gas effective permeability k e , seepage velocity v g Iterative calculations are performed between the three parameters, and combined with the finite element analysis method, the dynamic permeability of CO2 around the salt rock cavity is determined.

[0036] like Figure 2 As shown, two cross-section lines are selected, both parallel to the x-axis. The position of cross-section line A is the mudstone interlayer, and the position of cross-section line B is the salt rock interlayer.

[0037] The effective gas permeability k obtained in step S2 e The equation related to pressure p and temperature T is related to formula (6). It is difficult for computer software to directly recognize and calculate the equation obtained in step S2. The present invention performs the following transformation.

[0038] According to the small deformation hypothesis, the relationship between the mechanical equilibrium equation of salt rock or mudstone interlayer and the strain component satisfies the following formula: (7) The relationship between the mechanical equilibrium equation and the displacement component satisfies the following formula: (8) in, is the divergence of the stress tensor (partial derivative in the direction of spatial coordinate j), in N / m³; F i is the body force component, in N / m³; μ ij is the displacement gradient tensor, dimensionless; μ ji is the transposed component of the displacement gradient tensor, dimensionless.

[0039] Formula (7) represents the body force component F i With internal stress Since the deformation is slow, the two should be equal in quantity and opposite in direction. Formula (8) is the relationship between strain and displacement, that is, a strain variable is represented by unique components in two directions, which is equivalent to vector decomposition.

[0040] Substituting formula (7) and (8) into formula (6), we obtain the following formula: (9) Among them, e i,jj or e j,jiIt is in tensor form, e can represent variables μ, T, p, where the first subscript is the i-direction component of the variable, the second subscript is the partial derivative in the i direction, and the third subscript is the partial derivative in the j direction.

[0041] Formula (9) can be directly recognized and calculated by computer software. Substituting formula (9) into step (c) yields the gas effective permeability k e The equation related to the coal matrix volume strain ε, pressure p, and temperature T gives the gas effective permeability k e Equations related to pressure p and temperature T.

[0042] In addition, according to the mass m of gas per unit volume of salt rock or mudstone interlayer g The expression is: ; From the above formula, we can know that pressure p and m g and porosity About, and m g is a variable, and the present invention determines m by the following method g : Considering the conservation of mass, Darcy's law, slippage effect and gravity influence, the CO2 migration and diffusion equation in salt rock or mudstone interlayer is determined as follows: (10) Among them, Q g is the gas mass exchange rate, in kg / (m 3 ·s); D g is the dynamic diffusion coefficient of the gas, in m 2 / s; t is time, unit is s; From formula (10), we can know that m g With Q g It is related to time t, to be precise , that is, the mass at time t+a = the mass at time t + the integral of the gas exchange amount over time. Therefore, during the iterative calculation of step S4, formula (10) is included in the calculation range.

[0043] The relationship equations obtained in steps S2 and S3 are all related to the temperature T. The present invention calculates the temperature T using the following method: The energy conservation equation is established. The solid skeleton and gas of the salt rock or mudstone interlayer satisfy the energy conservation law respectively. The energy conservation equation of the solid skeleton is obtained as follows: ; The energy conservation equation for a gas is: ; in, is the density of the solid skeleton of salt rock or mudstone interlayer, in kg / m 3 ;c s and c g are the specific heat capacities of the solid skeleton and gas, respectively, in J / (kg·K); and are the thermal conductivity of the solid skeleton and gas, respectively, in W / (m·K); Q s and Q g are the heat source sinks of the solid skeleton and gas, respectively, in W / m 3 ; T s and T g are the temperatures of the solid skeleton and gas, respectively, in K; Assuming that the solid and the gas are always in thermal equilibrium and taking deformation energy into account, the following total energy conservation equation is determined from the above two energy conservation equations: (11) Where T0 is the common absolute temperature of the solid skeleton and the gas in thermal equilibrium in the initial state, in K; Q eq is the heat source sink of the porous medium filled with CO2 gas, in W / m 3 ; is the density of the porous medium filled with gas, in kg / m 3 ;c eq is the specific heat capacity of the porous medium filled with gas, in J / (kg·K); is the thermal conductivity of the porous medium filled with gas, in W / (m·K); is the specific heat capacity of the gas, in J / (kg·K); represents the velocity vector, dimensionless; is the volume strain, dimensionless; γ is the coefficient of the relationship between the heat released or absorbed due to volume change and the temperature change and volume strain rate, with the unit of (W·s) / (K·m 3 );n is the proportion of solid skeleton in the porous medium filled with gas, dimensionless.

[0044] Among them, the heat source sink term Q of the porous medium filled with CO2 gas is eq Determined by the following formula: ; The specific heat capacity of the gas-filled porous medium is determined by the following formula: ; The thermal conductivity of the porous medium filled with gas Determined by the following formula: ; Formula (11) and its subsequent subordinate formulas are incorporated into the iterative calculation of step S4.

[0045] This embodiment carries out numerical simulation of CO2 storage in salt rock karst cavity under the condition of slip effect, with simulation time intervals (i.e. storage time) of 1 year, 5 years, 10 years, 20 years, 30 years and 40 years, and gas injection pressure of 15MPa. The original salt rock formation pressure is taken as the initial condition, the set salt rock karst cavity gas storage pressure is taken as the inner boundary condition, and the outer boundary condition is set as the constant pressure boundary condition considering that the maximum radius of the salt rock karst cavity is much smaller than the extension width of the salt rock layer. The key parameters used in the simulation process are shown in Table 1.

[0046] Table 1 Key parameters of numerical simulation .

[0047] After the software operation iteration and finite element analysis in step S4, the effective permeability curve, pore pressure curve, and seepage velocity curve of the salt rock and mudstone interlayer are obtained, such as Figure 3-Figure 8 shown.

Claims

1. A dynamic prediction method for the permeability of long-term CO2 storage in layered salt rock karst cavities, characterized in that: The following steps are involved: S1: Set rational conditions for this dynamic prediction method from the aspects of gas diffusion, storage, migration and the properties of salt rock itself, and collect exploration data of salt rock as the basis for subsequent prediction; S2: On the basis of considering the slippage effect, the relationship between the porosity and permeability of salt rock is used to obtain the permeability equation, which represents the relationship between the effective permeability of gas and the pressure and temperature of CO2 in salt rock; S3: Determine the seepage velocity formula of CO2 gas, which represents the relationship between the seepage velocity and the effective permeability, pressure and temperature of CO2 gas in the salt rock; S4: Substitute the exploration data of step S1 into the permeability equation and seepage velocity equation finally obtained in steps S2 and S3, perform iterative calculations among the three parameters of gas pressure, gas effective permeability and seepage velocity in salt rock, and then combine the finite element analysis method to determine the dynamic change process of CO2 diffusion and seepage from the salt rock cavity to the outside of the cavity.

2. The dynamic prediction method according to claim 1, characterized in that: In step S1, the rational conditions include: (1) Salt rock and mudstone interlayers are abstracted as homogeneous continuous porous media; (2) CO2 only exists in salt rock cavities and follows the ideal gas state equation; (3) In salt rock or mudstone interlayers, the migration of CO2 follows Darcy's law, while taking into account the effects of diffusion, Klinkenberg effect and gravity; (4) The deformation of salt rock and mudstone interlayers conforms to the small deformation hypothesis; (5) Consider the influence of temperature on CO2 migration and deformation of salt rock and mudstone interlayers.

3. The dynamic prediction method according to claim 2, characterized in that: Step S2 specifically includes the following steps: (a) Considering the influence of slippage effect on gas permeability of salt rock or mudstone interlayer, determine the initial equation of gas effective permeability and the equation of slippage coefficient; (b) There is a cubic theorem between gas permeability and porosity. Combining the initial equation of gas effective permeability with the cubic theorem and the slip coefficient, we can get the gas effective permeability k e and porosity , equations related to pressure p and temperature T; (c) Due to porosity The relationship between the volume strain of the salt rock or mudstone interlayer and the effective gas permeability k obtained in step (b) is e The effective gas permeability k is obtained by combining the equation e Equations related to coal matrix volume strain ε, pressure p, and temperature T; (d) Assuming that the salt rock or mudstone interlayer is isotropic and the pores are filled with CO2 gas, the elastic-plastic constitutive equation is combined with the gas effective permeability k obtained in step (c) e Combined with the equations related to coal matrix volume strain ε, pressure p, and temperature T, the gas effective permeability k is obtained e Equations related to pressure p and temperature T.

4. The dynamic prediction method according to claim 3, characterized in that: In step (a), the initial equation for gas effective permeability is as follows: （1） Among them, k e is the effective gas permeability of salt rock or mudstone interlayer, in m 2 ; k is the gas permeability of salt rock or mudstone interlayer, unit is m 2 ; p is the CO2 gas pressure in the pores of salt rock or mudstone interlayers, in MPa; b is the slip coefficient, in MPa.

5. The dynamic prediction method according to claim 4, characterized in that: The slip coefficient b is related to the temperature T (K) of the salt rock or mudstone interlayer, the type of gas stored and the pore structure of the porous medium, and is determined by the following formula: ； Where c is a constant, c=0.9; μ is the dynamic viscosity of the gas, in Pa·s; R is the molar gas constant, 8.31 J / (mol·K); M g is the molar mass of the gas, in kg / mol; r is the pore radius of the salt rock or mudstone interlayer, in m.

6. The dynamic prediction method according to claim 5, characterized in that: In step (b), the cubic theorem between permeability and porosity is as follows: ； Where k0 is the initial permeability of salt rock or mudstone interlayer, in m 2 ; From the cubic theorem we get: , substituting this formula and the formula of slip coefficient b into the above formula (1), we get the following formula: （2） Formula (2) shows the effective permeability k of the gas e and porosity , pressure p, and temperature T.

7. The dynamic prediction method according to claim 6, characterized in that: In step (c), the porosity of the salt rock or mudstone interlayer is Determined by the following formula: （3） Where ε is the volume strain of coal matrix, dimensionless; ΔV s is the change in the skeleton volume of salt rock or mudstone interlayer, in m 3 ; V s0 is the initial skeleton volume of salt rock or mudstone interlayer, in m 3 ; The ΔV s With V s0 The ratio is determined by the following formula: （4） Among them, K s is the bulk modulus of the solid skeleton of the salt rock or mudstone interlayer, in MPa; Δp is the change in gas pressure, in MPa; α is the effective stress coefficient of the salt rock or mudstone interlayer, dimensionless; α T is the coefficient of thermal expansion, in K -1 ; ΔT is the temperature change of salt rock or mudstone interlayer, unit is K; Substituting formula (4) into formula (3), we get: （5） From formula (5) and formula (2), we can know that the effective permeability of gas k e It is related to the coal matrix volume strain ε, pressure p and temperature T.

8. The dynamic prediction method according to claim 7, characterized in that: In step (d), the elastic-plastic constitutive equation considering gas pressure and temperature is as follows: （6） Among them, ε ij is the component of the strain tensor, dimensionless; G is the shear modulus of the salt rock or mudstone interlayer, in MPa; σ ij is the component of the stress tensor, in MPa; σ hh is the normal stress component, in MPa; K is the bulk modulus of salt interlayer or mudstone, in MPa; δ ij is the Kronecker symbol. When i=j, δ ij =1, when i≠j, δ ij =0; i and j are the vector indices of two directions in three dimensions respectively; Substituting formula (6) into step (c) yields the gas effective permeability k e The equation related to the coal matrix volume strain ε, pressure p, and temperature T gives the gas effective permeability k e Relationship with pressure p and temperature T.

9. The dynamic prediction method according to claim 8, characterized in that: In step S3, the seepage velocity of CO2 gas in the salt rock or mudstone interlayer is determined by the following formula: ； Among them, v g is the gas seepage velocity, in m / s; ρ g is the density of gas in salt rock or mudstone interlayer, in kg / m 3 ; g is the acceleration due to gravity, in m / s 2 ; h is the vertical distance of CO2 migration affected by gravity, in meters; Among them, ρ g It is expressed as: ； The final seepage velocity formula is: 。 10. The dynamic prediction method according to claim 9, characterized in that: In step S4, a finite element method multi-physics field coupling solution of a mathematical model of the salt rock cavity is performed using simulation software, and firstly, a triangular mesh is performed on the selected physical model of the salt rock cavity; Then, within the quantitative simulation time range, several cross-sections are selected, and the cross-sections are taken as the research objects to obtain the exploration data on the cross-sections. According to step S2, the relationship between the effective gas permeability and the pressure and temperature of CO2 in the salt rock is obtained, and the relationship between the seepage velocity and the effective gas permeability, pressure and temperature of CO2 in the salt rock is obtained in step S3. Under the conditions of gas pressure p, gas effective permeability k e , seepage velocity v g Iterative calculations are performed between the three parameters, and combined with the finite element analysis method, the dynamic permeability of CO2 around the salt rock cavity is determined.

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