A Multi-Field Coupled Calculation Method for Supercritical Carbon Dioxide Flow in Transversely Isotropic Media

Abstract

This invention relates to a multi-field coupled calculation method for supercritical carbon dioxide seepage in transversely isotropic media, belonging to the field of supercritical carbon dioxide drilling and fracturing in oil and gas development. The method includes: obtaining mechanical and physical parameters; establishing a physical model of supercritical carbon dioxide seepage in the wellbore coordinate system; determining the initial stress and stress boundary conditions of the model; constructing the governing equations for the solid deformation field, seepage field, and temperature field during supercritical carbon dioxide seepage; and simultaneously inputting the boundary conditions, initial conditions, and governing equations for the solid deformation field, seepage field, and temperature field into finite element numerical calculation software to perform fluid-solid-thermal multi-field coupled calculations of supercritical carbon dioxide seepage in transversely isotropic media. This invention treats shale reservoirs as transversely isotropic media and constructs a fluid-solid-thermal multi-field coupled calculation method for supercritical carbon dioxide seepage in transversely isotropic media, providing a theoretical basis for the development of shale gas reservoirs using supercritical carbon dioxide.

Description

Technical Field

[0001] This invention relates to a multi-field coupling calculation method for supercritical carbon dioxide seepage in transversely isotropic media, belonging to the field of supercritical carbon dioxide drilling and fracturing technology in oil and gas development. Background Technology

[0002] Compared to water-based fluids, supercritical carbon dioxide (SCCO) development of shale gas offers advantages such as avoiding reservoir damage, reducing fracturing pressure, generating complex fracture networks, and promoting adsorbed gas desorption. In simulation studies of supercritical carbon dioxide development of shale reservoirs, the multi-field coupled flow mechanism of SCCO in shale reservoirs is fundamental.

[0003] Shale reservoirs have well-developed bedding and exhibit significant anisotropic mechanical properties. Current research on supercritical carbon dioxide flow in shale reservoirs generally simplifies shale reservoirs as isotropic formations, leading to discrepancies between the obtained results and the actual situation. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a multi-field coupled calculation method for supercritical carbon dioxide seepage in transversely isotropic media. By treating shale reservoirs as transversely isotropic media, a fluid-solid-thermal multi-field coupled calculation method for supercritical carbon dioxide seepage in transversely isotropic media is constructed, providing a theoretical basis for the development of shale gas reservoirs using supercritical carbon dioxide.

[0005] The present invention adopts the following technical solution:

[0006] A multi-field coupled calculation method for supercritical carbon dioxide seepage in transversely isotropic media includes the following steps:

[0007] S1. Shale samples were used in the study area. Through indoor physical experiments, the mechanical and physical parameters of the shale samples in the direction parallel to the bedding plane and perpendicular to the bedding plane were tested, including elastic modulus, Poisson's ratio, permeability, coefficient of thermal expansion and thermal conductivity.

[0008] S2. In the wellbore coordinate system, establish a physical model of supercritical carbon dioxide seepage and determine the boundary conditions and initial conditions of pressure and temperature for the physical model.

[0009] S3 transforms the original geostress field from geostress coordinates to wellbore coordinates to determine the initial stress and stress boundary conditions of the supercritical carbon dioxide seepage physical model.

[0010] S4. Construct the solid deformation field control equation, seepage field control equation, and temperature field control equation for supercritical carbon dioxide seepage, so as to perform fluid-solid-thermal multi-field coupling calculations during supercritical carbon dioxide seepage.

[0011] S5 inputs the boundary conditions, initial conditions, and control equations for the solid deformation field, seepage field, and temperature field into the finite element numerical calculation software COMSOL Multiphysics to perform fluid-solid-thermal multi-field coupling calculations of supercritical carbon dioxide seepage in a transversely isotropic medium, and obtains the spatiotemporal distribution laws of the solid deformation field, stress field, pore pressure field, and temperature field during supercritical carbon dioxide seepage.

[0012] Preferably, in step S2, in the finite element numerical calculation software, a cube is first established as the formation, and the side length of the cube is the length, width and height of the formation; a cylinder is dug in the center of the cube to form a cylindrical hollow part, which serves as the well shaft, and the radius of the cylinder is the radius of the well shaft.

[0013] Based on the study of geomechanics and reservoir characteristics of the study area, the pore pressure gradient and geothermal gradient of the regional reservoir are clarified. Combined with the depth of the studied formation, the initial conditions of the pore pressure field and temperature field of the physical model are determined. Based on the distribution characteristics of temperature and pressure of supercritical carbon dioxide in the wellbore, the boundary conditions of the temperature field and pore pressure field in the physical model are determined.

[0014] This physical model can be used to study the spatiotemporal distribution of in-situ stress, pore pressure, and temperature fields in the formation during the process of supercritical carbon dioxide being injected from the wellbore into the transversely isotropic medium. Based on this, further research can be conducted on the wellbore stability or fracturing of supercritical carbon dioxide drilling.

[0015] Preferably, the implementation process of step S3 is as follows:

[0016] S31, the original geostress tensor in the geostress coordinate system is:

[0017] (1)

[0018] In the formula: It is the geostress tensor in the geostress coordinate system; It is the maximum horizontal principal stress; It is the minimum horizontal principal stress; It is the principal stress of the overlying strata;

[0019] S32 transforms the geostress field from the geostress coordinate system to the geographic coordinate system:

[0020] (2)

[0021] In the formula: It is the geostress tensor in the geographic coordinate system; This is the transformation matrix from the geographic coordinate system to the geostress coordinate system, specifically represented as:

[0022] (3)

[0023] In the formula: It is the angle between the direction of the maximum horizontal principal stress and the due north direction; It is the angle between the direction of the principal stress of the overlying strata and the vertical direction of the strata;

[0024] S33 transforms the geostress field from the geographic coordinate system to the wellbore coordinate system:

[0025] (4)

[0026] In the formula: It is the geostress tensor in the wellbore coordinate system; This is the transformation matrix from the geographic coordinate system to the wellbore coordinate system, specifically represented as:

[0027] (5)

[0028] In the formula: It is the wellbore azimuth; It is the well inclination angle.

[0029] Preferably, in step S4, before establishing the governing equations for the solid deformation field, the stiffness matrix is ​​first transformed from the bedding plane coordinate system to the wellbore coordinate system. In the bedding plane coordinate system, the stress-strain relationship is:

[0030] (6)

[0031] in, It is the stress tensor in the bedding coordinate system. Let be the stiffness matrix in the bedding plane coordinate system. It is the strain tensor in the bedding plane coordinate system;

[0032] The specific form can be written as:

[0033] (7)

[0034] in, , , It is the normal stress in the bedding plane coordinate system; , , It is the shear stress in the bedding plane coordinate system; , , It is the normal strain in the bedding plane coordinate system. , , It is the shear strain in the bedding coordinate system; , , , , and These are components in the stiffness matrix, specifically represented as:

[0035] (8)

[0036] In the formula: and These are the elastic modulus and Poisson's ratio parallel to the stratification plane, respectively. and These are the elastic modulus and Poisson's ratio perpendicular to the stratification plane, respectively.

[0037] Transform the stiffness matrix in the bedding plane coordinate system to the wellbore coordinate system:

[0038] (9)

[0039] In the formula: It is the stiffness matrix of the wellbore coordinate system; It is the stiffness matrix in the bedding plane coordinate system; It is the stiffness transformation matrix, specifically represented as:

[0040] (10)

[0041] , , , , , , , , The components of the stiffness transformation matrix are specifically represented as follows:

[0042] (11)

[0043] In the formula: It is a wellbore coordinate system. It is a bedding plane coordinate system, specifically represented as:

[0044] (12)

[0045] In the formula: It is a tendency of bedding planes. It is the dip angle of the bedding plane.

[0046] Preferably, the process of establishing the governing equations for the solid deformation field during supercritical carbon dioxide seepage is as follows:

[0047] (1) For transversely isotropic rock media, the constitutive relation is expressed as:

[0048] (13)

[0049] In the formula: These are components of the effective stress tensor; These are the components of the stiffness matrix in the wellbore coordinate system, which is the stiffness matrix of the wellbore coordinate system obtained in step S4. ; These are components of the elastic strain tensor;

[0050] (2) Based on the effective stress principle, the effective stress is obtained:

[0051] (14)

[0052] In the formula: These are the components of the total stress tensor; It is the Biot coefficient; It is pore pressure;

[0053] (3) The stress balance equation is:

[0054] (15)

[0055] In the formula: These are the coordinate components in the i-direction. It is the force per unit volume in the i-direction;

[0056] (4) Elastic strain is expressed as:

[0057] (16)

[0058] In the formula: It is the displacement component in the i-direction; It is the thermal expansion coefficient tensor; This is the current temperature; It is the initial formation temperature; It is elastic strain; It is the Kronecker symbol;

[0059] (5) Obtain the thermal expansion coefficient of the rock in the wellbore coordinate system:

[0060] The coefficient of thermal expansion of rock in the bedding plane coordinate system is

[0061] (17)

[0062] In the formula: The coefficient of thermal expansion of the rock is parallel to the bedding plane. The coefficient of thermal expansion of the rock perpendicular to the bedding plane;

[0063] Transform the rock thermal expansion coefficient from the bedding plane coordinate system to the wellbore coordinate system:

[0064] (18)

[0065] In the formula: The transformation matrix is ​​represented as follows:

[0066] (19)

[0067] By combining equations (13) and (19), the governing equations for the solid deformation field during supercritical carbon dioxide percolation are obtained.

[0068] Preferably, the process of establishing the governing equations for supercritical carbon dioxide seepage is as follows:

[0069] A. The mass conservation equation is:

[0070] (20)

[0071] In the formula: It is the density of supercritical carbon dioxide; It refers to rock porosity; It is time; For Hamiltonian operators; It is the supercritical carbon dioxide percolation velocity; It is a fluid quality source or sink;

[0072] B. The density of supercritical carbon dioxide is:

[0073] (twenty one)

[0074] In the formula: It is the molar mass of carbon dioxide; It is the formation pore pressure; It is reduced density. It is the density of supercritical carbon dioxide. It is the critical density of carbon dioxide; It is the reciprocal of the reduced temperature. That is the critical temperature for carbon dioxide. It is the temperature of the formation; It is a universal gas constant; The remainder of the Helmholtz free energy. ;

[0075] C. The supercritical carbon dioxide seepage velocity is:

[0076] (twenty two)

[0077] In the formula: It is the supercritical carbon dioxide percolation velocity; It is the rock permeability tensor; It is the viscosity of supercritical carbon dioxide; It is the formation pressure gradient; It is an acceleration vector; It is the thermal permeability coefficient; It is the formation temperature gradient;

[0078] D. Obtain the permeability in the wellbore coordinate system.

[0079] The initial permeability of rock in the bedding plane coordinate system is

[0080] (twenty three)

[0081] In the formula: It is the initial permeability tensor of the rock in the bedding plane coordinate system; It is the initial permeability parallel to the bedding plane; It is the initial permeability perpendicular to the bedding plane;

[0082] Rock permeability in bedding plane coordinate system The specific form of the component is:

[0083] (twenty four)

[0084] In the formula: In the bedding plane coordinate system Rock permeability in the direction of direction; In the bedding plane coordinate system Initial permeability of rock in the direction of orientation; It is the effective volume strain. It is the volumetric strain of the rock. It is the formation pore pressure. It is the coefficient of thermal expansion of the rock. It's the temperature difference; It is the initial effective volume strain. It is the initial volumetric strain of the rock. It is the initial formation pore pressure. It is the bulk modulus of the rock matrix; It is the Biot coefficient; It is the initial porosity;

[0085] Transform the permeability in the bedding plane coordinate system to the wellbore coordinate system:

[0086] (25)

[0087] In the formula: It is the permeability tensor in the wellbore coordinate system; It is the transformation matrix, as shown in formula (18); It is the permeability tensor in the bedding plane coordinate system;

[0088] E. The viscosity of supercritical carbon dioxide is:

[0089] (26)

[0090] In the formula: It has zero density viscosity; It is the margin viscosity; It has an unusual viscosity;

[0091] Zero density viscosity is:

[0092] (27)

[0093] In the formula: Represented as

[0094] (28)

[0095] In the formula: It is a constant;

[0096] The remaining viscosity is:

[0097] (29)

[0098] In the formula: It is a constant; The density of supercritical carbon dioxide; , The formation temperature is represented by the ratio of singular viscosity to total viscosity, which is generally less than 0.01 and can be ignored to improve computational efficiency.

[0099] Where a i and d ij The specific values ​​are shown in Table 1 below:

[0100] Table 1 Constants and The value of

[0101]

[0102] F. Porosity is expressed as:

[0103] (30)

[0104] In the formula: It is the initial effective volumetric strain of the rock. It is the initial volumetric strain of the rock. It is the initial formation pore pressure. It is the bulk modulus of the rock matrix; It is the initial formation porosity. It is the Biot coefficient. It is the effective volumetric strain of the rock. It is the volumetric strain of the rock. It is the formation pore pressure. It is the coefficient of thermal expansion of the rock. It's the temperature difference. It is the temperature of the formation. It is the initial formation temperature;

[0105] Substituting formulas (21) and (22) into (20), we get

[0106] (31)

[0107] In the formula: It refers to rock porosity; It is the molecular weight of carbon dioxide; It is the formation pore pressure; It is time; and It is a function of carbon dioxide density and temperature. , , ; It is the density of carbon dioxide; It is the temperature of the formation; It is the rock permeability tensor in the wellbore coordinate system; It is the viscosity of carbon dioxide; It is an acceleration vector; It is the thermal permeability coefficient; It is the Hamiltonian operator;

[0108] According to formula (30), the porosity derivative with respect to time is obtained as follows:

[0109] (32)

[0110] In the formula: It refers to rock porosity; It is time; It is the Biot coefficient; It is the effective volumetric strain of the rock. It is the volumetric strain of the rock. It is the formation pore pressure. It is the bulk modulus of the rock matrix. It is the coefficient of thermal expansion of the rock. It's the temperature difference. It is the temperature of the formation. It is the initial formation temperature;

[0111] Substituting equation (32) into (31), we obtain the governing equation for the seepage of supercritical carbon dioxide in a transversely isotropic medium:

[0112] (33)

[0113] It refers to rock porosity; It is the molecular weight of carbon dioxide; It is the formation pore pressure; It is time; and It is a function of carbon dioxide density and temperature. , , ; It is the Biot coefficient; It is the effective volumetric strain of the rock. It is the volumetric strain of the rock. It is the bulk modulus of the rock matrix. It is the coefficient of thermal expansion of the rock. It's the temperature difference. It is the temperature of the formation. It is the initial formation temperature; It is the density of carbon dioxide; It is the rock permeability tensor in the wellbore coordinate system; It is the viscosity of carbon dioxide; It is an acceleration vector; It is the thermal permeability coefficient; It is the Hamiltonian operator.

[0114] Preferably, the temperature field governing equation for supercritical carbon dioxide percolation is:

[0115] (34)

[0116] In the formula, It is the density of carbon dioxide; It is the specific heat capacity of supercritical carbon dioxide; It refers to rock porosity; It is the density of the rock matrix; It is the specific heat capacity of the rock; It is the temperature of the formation; It is time; It is the supercritical carbon dioxide percolation velocity; It is the thermal permeability coefficient; It is the Hamiltonian operator. It is the temperature of the formation; It is the thermal conductivity of carbon dioxide; It is the thermal conductivity tensor of rock in the wellbore coordinate system; It is the density of the rock matrix;

[0117] The thermal conductivity tensor of the rock in the wellbore coordinate system is obtained by transforming from the bedding plane coordinate system to the wellbore coordinate system:

[0118] (35)

[0119] In the formula: It is the thermal conductivity tensor of rock in the wellbore coordinate system; It is the transformation matrix, as shown in formula (18); It is the thermal conductivity of the rock parallel to the bedding plane in the bedding plane coordinate system; It is the thermal conductivity of the rock perpendicular to the bedding plane in the bedding plane coordinate system;

[0120] The specific heat capacity of supercritical carbon dioxide is:

[0121] (36)

[0122] In the formula: It is the ideal part of the Helmholtz free energy; The specific heat capacity of carbon dioxide. It is the reciprocal of the reduced temperature. That is the critical temperature for carbon dioxide. It is the temperature of the formation. It is a universal gas constant. It is reduced density. It is the density of carbon dioxide. It is the critical density of carbon dioxide. It is the molecular weight of carbon dioxide. For the ideal part of the Helmholtz free energy, , It is the remainder of the Helmholtz free energy. , , ;

[0123] The thermal conductivity of supercritical carbon dioxide is:

[0124] (37)

[0125] In the formula: It has zero density thermal conductivity. It is the margin thermal conductivity. It has unusual thermal conductivity.

[0126] For any details not covered in this invention, please refer to the prior art.

[0127] The beneficial effects of this invention are as follows:

[0128] 1. This invention establishes a multi-field coupling calculation method for supercritical carbon dioxide percolation in transversely isotropic media, filling the gap in the research on multi-field coupling of supercritical carbon dioxide flow in transversely isotropic media.

[0129] 2. In the multi-field coupled evolution process, the physical properties of supercritical carbon dioxide, such as density, viscosity, thermal conductivity and specific heat capacity, evolve with the evolution of the formation temperature field and pressure field, thereby improving the accuracy of simulation calculation.

[0130] 3. The calculation method of this invention can provide a theoretical basis for subsequent studies on wellbore stability in shale formations during supercritical carbon dioxide drilling, and on the initiation pressure and fracture propagation in shale formations during supercritical carbon dioxide fracturing. Attached Figure Description

[0131] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0132] Figure 1 This is a schematic diagram of the physical model and initial and boundary conditions for supercritical carbon dioxide seepage in this invention;

[0133] Figure 2 Pore ​​pressure distribution;

[0134] Figure 3 Temperature field distribution;

[0135] Figure 4 Radial stress distribution;

[0136] Figure 5 This represents the circumferential stress distribution. Detailed Implementation

[0137] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. However, this is not the only description; all aspects not described in detail herein are based on conventional techniques in the art.

[0138] Example 1

[0139] A multi-field coupled calculation method for supercritical carbon dioxide seepage in transversely isotropic media includes the following steps:

[0140] S1. Shale samples were used in the study area. Through indoor physical experiments, the mechanical and physical parameters of the shale samples in the direction parallel to the bedding plane and perpendicular to the bedding plane were tested, including elastic modulus, Poisson's ratio, permeability, coefficient of thermal expansion and thermal conductivity.

[0141] S2. In the wellbore coordinate system, establish a physical model of supercritical carbon dioxide seepage and determine the boundary conditions and initial conditions of pressure and temperature for the physical model.

[0142] S3 transforms the original geostress field from geostress coordinates to wellbore coordinates to determine the initial stress and stress boundary conditions of the supercritical carbon dioxide seepage physical model.

[0143] S4. After determining the boundary conditions and initial conditions of the physical model, construct the solid deformation field control equation, seepage field control equation, and temperature field control equation for supercritical carbon dioxide seepage, so as to perform fluid-solid-thermal multi-field coupling calculations for supercritical carbon dioxide seepage.

[0144] S5. Boundary conditions, initial conditions, and governing equations for the solid deformation field, seepage field, and temperature field are simultaneously input into the finite element numerical calculation software COMSOL Multiphysics to perform fluid-solid-thermal multi-field coupled calculations of supercritical carbon dioxide seepage in a transversely isotropic medium. This yields the spatiotemporal distribution patterns of the solid deformation field, stress field (including radial and circumferential stress fields), pore pressure field, and temperature field during supercritical carbon dioxide seepage. Figures 2-5 As shown.

[0145] Example 2

[0146] A multi-field coupled calculation method for supercritical carbon dioxide seepage in transversely isotropic media, as described in Example 1, differs in that, in step S2, a cube is first established in the finite element numerical calculation software as the formation, with the cube's side length equal to the formation's length, width, and height; a cylinder is then excavated at the center of the cube to form a hollow cylindrical section, which serves as the wellbore, and the cylinder's radius is the wellbore radius. Figure 1 As shown;

[0147] Based on the study of geomechanics and reservoir characteristics of the study area, the pore pressure gradient and geothermal gradient of the regional reservoir are clarified. Combined with the depth of the studied formation, the initial conditions of the pore pressure field and temperature field of the physical model are determined. Based on the distribution characteristics of temperature and pressure of supercritical carbon dioxide in the wellbore, the boundary conditions of the temperature field and pore pressure field in the physical model are determined.

[0148] This physical model can be used to study the spatiotemporal distribution of in-situ stress, pore pressure, and temperature fields in the formation during the process of supercritical carbon dioxide being injected from the wellbore into the transversely isotropic medium. Based on this, further research can be conducted on the wellbore stability or fracturing of supercritical carbon dioxide drilling.

[0149] Example 3

[0150] A multi-field coupled calculation method for supercritical carbon dioxide percolation in a transversely isotropic medium, as described in Example 2, differs in that the implementation process of step S3 is as follows:

[0151] S31, the original geostress tensor in the geostress coordinate system is:

[0152] (1)

[0153] In the formula: It is the geostress tensor in the geostress coordinate system; It is the maximum horizontal principal stress; It is the minimum horizontal principal stress; It is the principal stress of the overlying strata;

[0154] S32 transforms the geostress field from the geostress coordinate system to the geographic coordinate system:

[0155] (2)

[0156] In the formula: It is the geostress tensor in the geographic coordinate system; This is the transformation matrix from the geographic coordinate system to the geostress coordinate system, specifically represented as:

[0157] (3)

[0158] In the formula: It is the angle between the direction of the maximum horizontal principal stress and the due north direction; It is the angle between the direction of the principal stress of the overlying strata and the vertical direction of the strata;

[0159] S33 transforms the geostress field from the geographic coordinate system to the wellbore coordinate system:

[0160] (4)

[0161] In the formula: It is the geostress tensor in the wellbore coordinate system; This is the transformation matrix from the geographic coordinate system to the wellbore coordinate system, specifically represented as:

[0162] (5)

[0163] In the formula: It is the wellbore azimuth; It is the well inclination angle.

[0164] Example 4

[0165] A multi-field coupled calculation method for supercritical carbon dioxide seepage in transversely isotropic media, as described in Example 3, differs in that, in step S4, before establishing the governing equations for the solid deformation field, the stiffness matrix is ​​first transformed from the bedding plane coordinate system to the wellbore coordinate system. In the bedding plane coordinate system, the stress-strain relationship is:

[0166] (6)

[0167] in, It is the stress tensor in the bedding coordinate system. Let be the stiffness matrix in the bedding plane coordinate system. It is the strain tensor in the bedding plane coordinate system;

[0168] The specific form can be written as:

[0169] (7)

[0170] in, , , It is the normal stress in the bedding plane coordinate system; , , It is the shear stress in the bedding plane coordinate system; , , It is the normal strain in the bedding plane coordinate system. , , It is the shear strain in the bedding coordinate system; , , , , and These are components in the stiffness matrix, specifically represented as:

[0171] (8)

[0172] In the formula: and These are the elastic modulus and Poisson's ratio parallel to the stratification plane, respectively. and These are the elastic modulus and Poisson's ratio perpendicular to the stratification plane, respectively.

[0173] Transform the stiffness matrix in the bedding plane coordinate system to the wellbore coordinate system:

[0174] (9)

[0175] In the formula: It is the stiffness matrix of the wellbore coordinate system; It is the stiffness matrix in the bedding plane coordinate system; It is the stiffness transformation matrix, specifically represented as:

[0176] (10)

[0177] , , , , , , , , The components of the stiffness transformation matrix are specifically represented as follows:

[0178] (11)

[0179] In the formula: It is a wellbore coordinate system. It is a bedding plane coordinate system, specifically represented as:

[0180] (12)

[0181] In the formula: It is a tendency of bedding planes. It is the dip angle of the bedding plane.

[0182] Example 5

[0183] A multi-field coupled calculation method for supercritical carbon dioxide seepage in transversely isotropic media, as described in Example 4, differs in that the process of establishing the governing equations for the solid deformation field during supercritical carbon dioxide seepage is as follows:

[0184] (1) For transversely isotropic rock media, the constitutive relation is expressed as:

[0185] (13)

[0186] In the formula: These are components of the effective stress tensor; These are the components of the stiffness matrix in the wellbore coordinate system, which is the stiffness matrix of the wellbore coordinate system obtained in step S4. ; These are components of the elastic strain tensor;

[0187] (2) Based on the effective stress principle, the effective stress is obtained:

[0188] (14)

[0189] In the formula: These are the components of the total stress tensor; It is the Biot coefficient; It is pore pressure;

[0190] (3) The stress balance equation is:

[0191] (15)

[0192] In the formula: These are the coordinate components in the i-direction. It is the force per unit volume in the i-direction;

[0193] (4) Elastic strain is expressed as:

[0194] (16)

[0195] In the formula: It is the displacement component in the i-direction; It is the thermal expansion coefficient tensor; This is the current temperature; It is the initial formation temperature; It is elastic strain; It is the Kronecker symbol;

[0196] (5) Obtain the thermal expansion coefficient of the rock in the wellbore coordinate system:

[0197] The coefficient of thermal expansion of rock in the bedding plane coordinate system is

[0198] (17)

[0199] In the formula: The coefficient of thermal expansion of the rock is parallel to the bedding plane. The coefficient of thermal expansion of the rock perpendicular to the bedding plane;

[0200] Transform the rock thermal expansion coefficient from the bedding plane coordinate system to the wellbore coordinate system:

[0201] (18)

[0202] In the formula: The transformation matrix is ​​represented as follows:

[0203] (19)

[0204] By combining equations (13) and (19), the governing equations for the solid deformation field during supercritical carbon dioxide percolation are obtained.

[0205] Furthermore, the process of establishing the governing equations for supercritical carbon dioxide seepage is as follows:

[0206] A. The mass conservation equation is:

[0207] (20)

[0208] In the formula: It is the density of supercritical carbon dioxide; It refers to rock porosity; It is time; For Hamiltonian operators; It is the supercritical carbon dioxide percolation velocity; It is a fluid quality source or sink;

[0209] B. The density of supercritical carbon dioxide is:

[0210] (twenty one)

[0211] In the formula: It is the molar mass of carbon dioxide; It is the formation pore pressure; It is reduced density. It is the density of supercritical carbon dioxide. It is the critical density of carbon dioxide; It is the reciprocal of the reduced temperature. That is the critical temperature for carbon dioxide. It is the temperature of the formation; It is a universal gas constant; The remainder of the Helmholtz free energy. ;

[0212] C. The supercritical carbon dioxide seepage velocity is:

[0213] (twenty two)

[0214] In the formula: It is the supercritical carbon dioxide percolation velocity; It is the rock permeability tensor; It is the viscosity of supercritical carbon dioxide; It is the formation pressure gradient; It is an acceleration vector; It is the thermal permeability coefficient; It is the formation temperature gradient;

[0215] D. Obtain the permeability in the wellbore coordinate system.

[0216] The initial permeability of rock in the bedding plane coordinate system is

[0217] (twenty three)

[0218] In the formula: It is the initial permeability tensor of the rock in the bedding plane coordinate system; It is the initial permeability parallel to the bedding plane; It is the initial permeability perpendicular to the bedding plane;

[0219] Rock permeability in bedding plane coordinate system The specific form of the component is:

[0220] (twenty four)

[0221] In the formula: In the bedding plane coordinate system Rock permeability in the direction of direction; In the bedding plane coordinate system Initial permeability of rock in the direction of orientation; It is the effective volume strain. It is the volumetric strain of the rock. It is the formation pore pressure. It is the coefficient of thermal expansion of the rock. It's the temperature difference; It is the initial effective volume strain. It is the initial volumetric strain of the rock. It is the initial formation pore pressure. It is the bulk modulus of the rock matrix; It is the Biot coefficient; It is the initial porosity;

[0222] Transform the permeability in the bedding plane coordinate system to the wellbore coordinate system:

[0223] (25)

[0224] In the formula: It is the permeability tensor in the wellbore coordinate system; It is the transformation matrix, as shown in formula (18); It is the permeability tensor in the bedding plane coordinate system;

[0225] E. The viscosity of supercritical carbon dioxide is:

[0226] (26)

[0227] In the formula: It has zero density viscosity; It is the margin viscosity; It has an unusual viscosity;

[0228] Zero density viscosity is:

[0229] (27)

[0230] In the formula: Represented as

[0231] (28)

[0232] In the formula: It is a constant;

[0233] The remaining viscosity is:

[0234] (29)

[0235] In the formula: It is a constant; The density of supercritical carbon dioxide; , The formation temperature is represented by the ratio of singular viscosity to total viscosity, which is generally less than 0.01 and can be ignored to improve computational efficiency.

[0236] Where a i and d ij The specific values ​​are shown in Table 1 below:

[0237] Table 1 Constants and The value of

[0238]

[0239] F. Porosity is expressed as:

[0240] (30)

[0241] In the formula: It is the initial effective volumetric strain of the rock. It is the initial volumetric strain of the rock. It is the initial formation pore pressure. It is the bulk modulus of the rock matrix; It is the initial formation porosity. It is the Biot coefficient. It is the effective volumetric strain of the rock. It is the volumetric strain of the rock. It is the formation pore pressure. It is the coefficient of thermal expansion of the rock. It's the temperature difference. It is the temperature of the formation. It is the initial formation temperature;

[0242] Substituting formulas (21) and (22) into (20), we get

[0243] (31)

[0244] In the formula: It refers to rock porosity; It is the molecular weight of carbon dioxide; It is the formation pore pressure; It is time; and It is a function of carbon dioxide density and temperature. , , ; It is the density of carbon dioxide; It is the temperature of the formation; It is the rock permeability tensor in the wellbore coordinate system; It is the viscosity of carbon dioxide; It is an acceleration vector; It is the thermal permeability coefficient; It is the Hamiltonian operator;

[0245] According to formula (30), the porosity derivative with respect to time is obtained as follows:

[0246] (32)

[0247] In the formula: It refers to rock porosity; It is time; It is the Biot coefficient; It is the effective volumetric strain of the rock. It is the volumetric strain of the rock. It is the formation pore pressure. It is the bulk modulus of the rock matrix. It is the coefficient of thermal expansion of the rock. It's the temperature difference. It is the temperature of the formation. It is the initial formation temperature;

[0248] Substituting equation (32) into (31), we obtain the governing equation for the seepage of supercritical carbon dioxide in a transversely isotropic medium:

[0249] (33)

[0250] It refers to rock porosity; It is the molecular weight of carbon dioxide; It is the formation pore pressure; It is time; and It is a function of carbon dioxide density and temperature. , , ; It is the Biot coefficient; It is the effective volumetric strain of the rock. It is the volumetric strain of the rock. It is the bulk modulus of the rock matrix. It is the coefficient of thermal expansion of the rock. It's the temperature difference. It is the temperature of the formation. It is the initial formation temperature; It is the density of carbon dioxide; It is the rock permeability tensor in the wellbore coordinate system; It is the viscosity of carbon dioxide; It is an acceleration vector; It is the thermal permeability coefficient; It is the Hamiltonian operator.

[0251] Preferably, the temperature field governing equation for supercritical carbon dioxide percolation is:

[0252] (34)

[0253] In the formula, It is the density of carbon dioxide; It is the specific heat capacity of supercritical carbon dioxide; It refers to rock porosity; It is the density of the rock matrix; It is the specific heat capacity of the rock; It is the temperature of the formation; It is time; It is the supercritical carbon dioxide percolation velocity; It is the thermal permeability coefficient; It is the Hamiltonian operator. It is the temperature of the formation; It is the thermal conductivity of carbon dioxide; It is the thermal conductivity tensor of rock in the wellbore coordinate system; It is the density of the rock matrix;

[0254] The thermal conductivity tensor of the rock in the wellbore coordinate system is obtained by transforming from the bedding plane coordinate system to the wellbore coordinate system:

[0255] (35)

[0256] In the formula: It is the thermal conductivity tensor of rock in the wellbore coordinate system; It is the transformation matrix, as shown in formula (18); It is the thermal conductivity of the rock parallel to the bedding plane in the bedding plane coordinate system; It is the thermal conductivity of the rock perpendicular to the bedding plane in the bedding plane coordinate system;

[0257] The specific heat capacity of supercritical carbon dioxide is:

[0258] (36)

[0259] In the formula: It is the ideal part of the Helmholtz free energy; The specific heat capacity of carbon dioxide. It is the reciprocal of the reduced temperature. That is the critical temperature for carbon dioxide. It is the temperature of the formation. It is a universal gas constant. It is reduced density. It is the density of carbon dioxide. It is the critical density of carbon dioxide. It is the molecular weight of carbon dioxide. For the ideal part of the Helmholtz free energy, , It is the remainder of the Helmholtz free energy. , , ;

[0260] The thermal conductivity of supercritical carbon dioxide is:

[0261] (37)

[0262] In the formula: It has zero density thermal conductivity. It is the margin thermal conductivity. It has unusual thermal conductivity.

[0263] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-field coupled calculation method for supercritical carbon dioxide seepage in a transversely isotropic medium, characterized in that, Includes the following steps: S1. Shale samples were used in the study area. Through indoor physical experiments, the mechanical and physical parameters of the shale samples in the direction parallel to the bedding plane and perpendicular to the bedding plane were tested, including elastic modulus, Poisson's ratio, permeability, coefficient of thermal expansion and thermal conductivity. S2. In the wellbore coordinate system, establish a physical model of supercritical carbon dioxide seepage and determine the boundary conditions and initial conditions of pressure and temperature for the physical model. S3 transforms the original geostress field from geostress coordinates to wellbore coordinates to determine the initial stress and stress boundary conditions of the supercritical carbon dioxide seepage physical model. S4. Construct the solid deformation field control equation, seepage field control equation, and temperature field control equation for supercritical carbon dioxide seepage. S5 inputs the boundary conditions, initial conditions, and control equations for the solid deformation field, seepage field, and temperature field into the finite element numerical calculation software to perform fluid-solid-thermal multi-field coupling calculations of supercritical carbon dioxide seepage in a transversely isotropic medium, and obtains the spatiotemporal distribution laws of the solid deformation field, stress field, pore pressure field, and temperature field during supercritical carbon dioxide seepage.

2. The multi-field coupling calculation method for supercritical carbon dioxide seepage in transversely isotropic media according to claim 1, characterized in that, In step S2, in the finite element numerical calculation software, a cube is first created as the formation, with the side length of the cube being the length, width, and height of the formation; a cylinder is dug out in the center of the cube to form a cylindrical hollow part, which serves as the well shaft, and the radius of the cylinder is the radius of the well shaft. Based on the study of geomechanics and reservoir characteristics of the study area, the pore pressure gradient and geothermal gradient of the regional reservoir are clarified. Combined with the depth of the studied formation, the initial conditions of the pore pressure field and temperature field of the physical model are determined. Based on the distribution characteristics of temperature and pressure of supercritical carbon dioxide in the wellbore, the boundary conditions of the temperature field and pore pressure field in the physical model are determined.

3. The multi-field coupling calculation method for supercritical carbon dioxide seepage in transversely isotropic media according to claim 2, characterized in that, The implementation process of step S3 is as follows: S31, the original geostress tensor in the geostress coordinate system is: （1） In the formula: It is the geostress tensor in the geostress coordinate system; It is the maximum horizontal principal stress; It is the minimum horizontal principal stress; It is the principal stress of the overlying strata; S32 transforms the geostress field from the geostress coordinate system to the geographic coordinate system: （2） In the formula: It is the geostress tensor in the geographic coordinate system; This is the transformation matrix from the geographic coordinate system to the geostress coordinate system, specifically represented as: （3） In the formula: It is the angle between the direction of the maximum horizontal principal stress and the due north direction; It is the angle between the direction of the principal stress of the overlying strata and the vertical direction of the strata; S33 transforms the geostress field from the geographic coordinate system to the wellbore coordinate system: （4） In the formula: It is the geostress tensor in the wellbore coordinate system; This is the transformation matrix from the geographic coordinate system to the wellbore coordinate system, specifically represented as: （5） In the formula: It is the wellbore azimuth; It is the well inclination angle.

4. The multi-field coupling calculation method for supercritical carbon dioxide seepage in transversely isotropic media according to claim 3, characterized in that, In step S4, before establishing the governing equations for the solid deformation field, the stiffness matrix is ​​first transformed from the bedding plane coordinate system to the wellbore coordinate system. In the bedding plane coordinate system, the stress-strain relationship is: （6） in, It is the stress tensor in the bedding coordinate system. Let be the stiffness matrix in the bedding plane coordinate system. It is the strain tensor in the bedding plane coordinate system; The specific form is written as follows: （7） in, , , It is the normal stress in the bedding plane coordinate system; , , It is the shear stress in the bedding plane coordinate system; , , It is the normal strain in the bedding plane coordinate system. , , It is the shear strain in the bedding coordinate system; , , , , and These are components in the stiffness matrix, specifically represented as: （8） In the formula: and These are the elastic modulus and Poisson's ratio parallel to the stratification plane, respectively. and These are the elastic modulus and Poisson's ratio perpendicular to the stratification plane, respectively. Transform the stiffness matrix in the bedding plane coordinate system to the wellbore coordinate system: （9） In the formula: It is the stiffness matrix of the wellbore coordinate system; It is the stiffness matrix in the bedding plane coordinate system; It is the stiffness transformation matrix, specifically represented as: （10） , , , , , , , , The components of the stiffness transformation matrix are specifically represented as follows: （11） In the formula: It is a wellbore coordinate system. It is a bedding plane coordinate system, specifically represented as: （12） In the formula: It is a tendency of bedding planes. It is the dip angle of the bedding plane.

5. The multi-field coupling calculation method for supercritical carbon dioxide seepage in transversely isotropic media according to claim 4, characterized in that, The process of establishing the governing equations for the solid deformation field during supercritical carbon dioxide seepage is as follows: (1) For transversely isotropic rock media, the constitutive relation is expressed as: （13） In the formula: These are components of the effective stress tensor; These are the components of the stiffness matrix in the wellbore coordinate system, which is the stiffness matrix of the wellbore coordinate system obtained in step S4. ; These are components of the elastic strain tensor; (2) Based on the effective stress principle, the effective stress is obtained: （14） In the formula: These are the components of the total stress tensor; It is the Biot coefficient; It is pore pressure; (3) The stress balance equation is: （15） In the formula: These are the coordinate components in the i-direction. It is the force per unit volume in the i-direction; (4) Elastic strain is expressed as: （16） In the formula: It is the displacement component in the i-direction; It is the thermal expansion coefficient tensor; This is the current temperature; It is the initial formation temperature; It is elastic strain; It is the Kronecker symbol; (5) Obtain the thermal expansion coefficient of the rock in the wellbore coordinate system: The coefficient of thermal expansion of rock in the bedding plane coordinate system is （17） In the formula: The coefficient of thermal expansion of the rock is parallel to the bedding plane. The coefficient of thermal expansion of the rock perpendicular to the bedding plane; Transform the rock thermal expansion coefficient from the bedding plane coordinate system to the wellbore coordinate system: （18） In the formula: The transformation matrix is ​​represented as follows: （19） By combining equations (13) and (19), the governing equations for the solid deformation field during supercritical carbon dioxide percolation are obtained.

6. The multi-field coupling calculation method for supercritical carbon dioxide seepage in transversely isotropic media according to claim 4, characterized in that, The process of establishing the governing equations for supercritical carbon dioxide seepage is as follows: A. The mass conservation equation is: （20） In the formula: It is the density of supercritical carbon dioxide; It refers to the porosity of the rock; It is time; For Hamiltonian operators; It is the supercritical carbon dioxide percolation velocity; It is a fluid quality source or sink; B. The density of supercritical carbon dioxide is: （21） In the formula: It is the molar mass of carbon dioxide; It is the formation pore pressure; It is reduced density. It is the density of supercritical carbon dioxide. It is the critical density of carbon dioxide; It is the reciprocal of the reduced temperature. That is the critical temperature for carbon dioxide. It is the temperature of the formation; It is a universal gas constant; The remainder of the Helmholtz free energy. ; C. The supercritical carbon dioxide seepage velocity is: （22） In the formula: It is the supercritical carbon dioxide percolation velocity; It is the rock permeability tensor; It is the viscosity of supercritical carbon dioxide; It is the formation pressure gradient; It is an acceleration vector; It is the thermal permeability coefficient; It is the formation temperature gradient; D. Obtain the permeability in the wellbore coordinate system. The initial permeability of rock in the bedding plane coordinate system is （23） In the formula: It is the initial permeability tensor of the rock in the bedding plane coordinate system; It is the initial permeability parallel to the bedding plane; It is the initial permeability perpendicular to the bedding plane; Rock permeability in bedding plane coordinate system The specific form of the component is: （24） In the formula: In the bedding plane coordinate system Rock permeability in the direction of direction; In the bedding plane coordinate system Initial permeability of rock in the direction of orientation; It is the effective volume strain. It is the volumetric strain of the rock. It is the formation pore pressure. It is the coefficient of thermal expansion of the rock. It's the temperature difference; It is the initial effective volume strain. It is the initial volumetric strain of the rock. It is the initial formation pore pressure. It is the bulk modulus of the rock matrix; It is the Biot coefficient; It is the initial porosity; Transform the permeability in the bedding plane coordinate system to the wellbore coordinate system: （25） In the formula: It is the permeability tensor in the wellbore coordinate system; It is the transformation matrix, as shown in formula (18); It is the permeability tensor in the bedding plane coordinate system; E. The viscosity of supercritical carbon dioxide is: （26） In the formula: It has zero density viscosity; It is the margin viscosity; It has an unusual viscosity; Zero density viscosity is: （27） In the formula: Represented as （28） In the formula: It is a constant; The remaining viscosity is: （29） In the formula: It is a constant; The density of supercritical carbon dioxide; , The value represents the formation temperature; the ratio of exotic viscosity to total viscosity is less than 0.01 and is negligible. F. Porosity is expressed as: （30） In the formula: It is the initial effective volumetric strain of the rock. It is the initial volumetric strain of the rock. It is the initial formation pore pressure. It is the bulk modulus of the rock matrix; It is the initial formation porosity. It is the Biot coefficient. It is the effective volumetric strain of the rock. It is the volumetric strain of the rock. It is the formation pore pressure. It is the coefficient of thermal expansion of the rock. It's the temperature difference. It is the temperature of the formation. It is the initial formation temperature; Substituting formulas (21) and (22) into (20), we get （31） In the formula: It refers to the porosity of the rock; It is the molecular weight of carbon dioxide; It is the formation pore pressure; It is time; and It is a function of carbon dioxide density and temperature. , , ; It is the density of carbon dioxide; It is the temperature of the formation; It is the rock permeability tensor in the wellbore coordinate system; It is the viscosity of carbon dioxide; It is an acceleration vector; It is the thermal permeability coefficient; It is the Hamiltonian operator; According to formula (30), the porosity derivative with respect to time is obtained as follows: （32） In the formula: It refers to the porosity of the rock; It is time; It is the Biot coefficient; It is the effective volumetric strain of the rock. It is the volumetric strain of the rock. It is the formation pore pressure. It is the bulk modulus of the rock matrix. It is the coefficient of thermal expansion of the rock. It's the temperature difference. It is the temperature of the formation. It is the initial formation temperature; Substituting equation (32) into (31), we obtain the governing equation for the seepage of supercritical carbon dioxide in a transversely isotropic medium: （33） It refers to the porosity of the rock; It is the molecular weight of carbon dioxide; It is the formation pore pressure; It is time; and It is a function of carbon dioxide density and temperature. , , ; It is the Biot coefficient; It is the effective volumetric strain of the rock. It is the volumetric strain of the rock. It is the bulk modulus of the rock matrix. It is the coefficient of thermal expansion of the rock. It's the temperature difference. It is the temperature of the formation. It is the initial formation temperature; It is the density of carbon dioxide; It is the rock permeability tensor in the wellbore coordinate system; It is the viscosity of carbon dioxide; It is an acceleration vector; It is the thermal permeability coefficient; It is the Hamiltonian operator.

7. The multi-field coupling calculation method for supercritical carbon dioxide seepage in transversely isotropic media according to claim 6, characterized in that, The temperature field governing equation for supercritical carbon dioxide seepage is: （34） In the formula, It is the density of carbon dioxide; It is the specific heat capacity of supercritical carbon dioxide; It refers to the porosity of the rock; It is the density of the rock matrix; It is the specific heat capacity of the rock; It is the temperature of the formation; It is time; It is the supercritical carbon dioxide percolation velocity; It is the thermal permeability coefficient; It is the Hamiltonian operator. It is the temperature of the formation; It is the thermal conductivity of carbon dioxide; It is the thermal conductivity tensor of rock in the wellbore coordinate system; It is the density of the rock matrix; The thermal conductivity tensor of the rock in the wellbore coordinate system is obtained by transforming from the bedding plane coordinate system to the wellbore coordinate system: （35） In the formula: It is the thermal conductivity tensor of rock in the wellbore coordinate system; It is a transformation matrix; It is the thermal conductivity of the rock parallel to the bedding plane in the bedding plane coordinate system; It is the thermal conductivity of the rock perpendicular to the bedding plane in the bedding plane coordinate system; The specific heat capacity of supercritical carbon dioxide is: （36） In the formula: It is the ideal part of the Helmholtz free energy; The specific heat capacity of carbon dioxide. It is the reciprocal of the reduced temperature. That is the critical temperature for carbon dioxide. It is the temperature of the formation. It is a universal gas constant. It is reduced density. It is the density of carbon dioxide. It is the critical density of carbon dioxide. It is the molecular weight of carbon dioxide. For the ideal part of the Helmholtz free energy, , It is the remainder of the Helmholtz free energy. , , ; The thermal conductivity of supercritical carbon dioxide is: （37） In the formula: It has zero density thermal conductivity. It is the margin thermal conductivity. It has unusual thermal conductivity.

Images