A method for calculating the temperature of a multi-layer casing cement sheath

Abstract

The application discloses a temperature calculation method for a multilayer casing cement sheath structure, which comprises the following steps: discretizing a radial heat conduction differential equation in a cylindrical coordinate by using a difference method to calculate the temperature of non-boundary points and non-interface points of a wellbore; calculating the temperature of boundary points and interface points based on the boundary conditions and the temperature and heat flux density continuous conditions of any structure interface; and calculating the radial temperature from the center of the wellbore to the outer boundary of a stratum by using a linear equation group obtained by discretizing the heat conduction differential equation in the cylindrical coordinate and the boundary conditions of the radial temperature of the multilayer structure of the wellbore. According to the structural parameters of the wellbore, the thermal physical property parameters of materials and the boundary temperature parameters, the application can accurately calculate the temperature of the multilayer casing cement sheath structure, solves the radial temperature transmission problem under different structures according to the thermal continuous boundary conditions of different structure contact surfaces, and provides a theoretical basis for the temperature transmission problem of the multilayer structure since the calculation method is accurate and efficient.

Description

Technical Field

[0001] This invention belongs to the field of wellbore heat transfer calculation technology in oil and gas engineering, specifically relating to a method for calculating the temperature of a multi-layer casing cement ring structure. Background Technology

[0002] With the continuous rise in global energy demand, the exploration and development of conventional onshore oil and gas resources has gradually entered a bottleneck period. Reserves and production are insufficient to meet the ever-increasing energy consumption demands. Therefore, the focus of oil and gas resource exploration and development is gradually shifting towards deep-water, ultra-deep-water, and complex oil and gas reservoirs. my country possesses a vast sea area, among which the Bohai Sea contains extremely rich heavy oil resources, with a huge cumulative proven oil and gas equivalent and a steadily increasing annual production, making it a crucial strategic area for ensuring national energy security. The distribution of the wellbore temperature field is a significant factor affecting the mechanical properties of downhole heat source generating devices and surrounding structures such as casing and cement sheaths. Temperature changes cause thermal expansion and contraction of materials, inducing thermal stress, which, when coupled with other loads, significantly affects the structure's load-bearing capacity and stability. Actual wellbore structures are complex multi-layered composite structures composed of nitrogen layers, multiple layers of casing, cement sheaths, and formations. The thermal conductivity of each layer varies greatly, and there is a significant thermal resistance effect at the interlayer interfaces, resulting in a complex radial stratification characteristic in the temperature field distribution. There are several shortcomings in the temperature calculation methods for multi-layered casing cement sheath well structures: traditional methods often simplify the multi-layered structure as a homogeneous medium, ignoring the differences in thermal conductivity of each layer and the thermal continuity of the interlayer interfaces, resulting in a large deviation between the temperature calculation results and the actual operating conditions, making it difficult to accurately reflect the true temperature field distribution; some numerical methods (such as the finite element method) can handle layered structures, but they suffer from complex mesh generation and low computational efficiency, making them less applicable to field operations that require rapid evaluation; existing methods do not adequately describe the heat flow transfer laws at key interfaces such as nitrogen-casing and casing-cement sheath, leading to distortion in the calculation of temperature gradients at the interfaces, which in turn affects the accuracy of structural mechanical performance analysis based on the temperature field.

[0003] Therefore, developing a calculation method that can accurately handle the thermal conduction characteristics of multi-layer interfaces and efficiently solve the radial temperature distribution is of great practical significance for accurately evaluating the mechanical properties of downhole heat source generating devices and surrounding structures and ensuring the safety of offshore heavy oil thermal recovery. Summary of the Invention

[0004] This invention is proposed to address the problems of inaccurate interfacial thermal continuity processing and poor adaptability of traditional methods in the calculation of temperature field distribution of multi-layer heterogeneous wellbore structures in the prior art. Its purpose is to provide a temperature calculation method for multi-layer casing cement sheath structures.

[0005] This invention is achieved through the following technical solution: A method for calculating the temperature of a multi-layered sleeve cement ring structure includes the following steps: S1. Discretize the radial heat conduction differential equation in cylindrical coordinates using the finite difference method, and calculate the temperature at non-boundary points and non-interface locations in the wellbore: S11. Establish the radial heat conduction differential equation in cylindrical coordinates: The radial heat conduction differential equation in cylindrical coordinates is as follows: In equation (1): r is the radial coordinate, in meters; T is the temperature, in degrees Celsius; k is the thermal conductivity of the material, in cubic meters per second. ; S12. Discretize the radial heat conduction differential equation in cylindrical coordinates established in step S11: Let the radial interval be Dividing the radial interval into N nodes, the node coordinates are: In formula (2): The coordinates are the inner boundary coordinates of the radial interval; Let be the radial coordinate at node j; The ordinal number of the current node; For grid step size, ; S13. At node j, the first derivative is obtained by approximating the derivative of the radial heat conduction differential equation in cylindrical coordinates using the central difference. The discrete derivative; The first derivative The discrete derivative is: In formula (3): For nodes The radial coordinate at the location, in meters; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; For nodes Thermal conductivity of the material at that location, in units of ; The grid step size; S14. The first derivative obtained in step S13 Substituting the discrete derivative (Equation 3) into the radial heat conduction differential equation (Equation 1) in cylindrical coordinates, we obtain the discrete equation: The discrete equation is: In equation (4): For nodes The radial coordinate at the location, in meters; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; The grid step size; S15. Rearrange the discrete equation (Equation 4) obtained in step S14 into a form about the nodes. Temperature at the location The linear equation: The linear equation is: In formula (5): For nodes The radial coordinate at the location, in meters; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; The grid step size; S2. Based on the boundary conditions and the assumption of temperature and heat flux density continuity at the interface of arbitrary structures, calculate the temperature at the boundary points and interface points: S21. The boundary conditions for radial temperature of the multi-layered structure of the wellbore are as follows: the inner boundary temperature of the nitrogen layer is known, the outer boundary temperature of the formation is known, and temperature and heat flux density are continuous at any structural interface. The expression for the boundary conditions for radial temperature of the multi-layered structure of the wellbore is as follows: In formula (6): for Thermal conductivity of the layered structure, in units of ; for Thermal conductivity of the layered structure, in units of ; This is the temperature at the inner boundary of the nitrogen layer, in °C. Temperature at the outer boundary of the formation, in °C; This refers to the A-layer side of the interface; This refers to the b-layer side of the interface. Radial coordinates; Temperature, in °C; S22. Determine the discrete equations for the inner and outer boundaries; Inner boundary Therefore, the discrete equation of the inner boundary is: outer boundary Therefore, the discrete equation of the inner boundary is: When j=N, the node is located at the outer boundary of the formation, and the node temperature is the same as the outer boundary temperature. ; S23. Determine the discrete equations for each interface of the multi-layered structure of the wellbore: The wellbore multi-layer structure includes a nitrogen-inner casing inner wall interface ( ), the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring ( ), the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve ( ), Outer wall of outer sleeve - Inner wall of outer cement ring ( ) and outer cement ring outer wall-stratum ( Five interfaces; S231, Nitrogen-Inner Tube Inner Wall Interface The thermal conductivity of nitrogen is Thermal conductivity of the inner sleeve The heat flow continuity condition at the nitrogen-inner tube wall interface is: The heat flow continuity condition at the nitrogen-inner tube wall interface simplifies to the discrete equation as follows: In equations (9) and (10): This is the thermal conductivity of nitrogen, in units of... ; The thermal conductivity of the inner sleeve is given in units of 1000 ppm. ; The grid step size; Temperature of the grid node at the nitrogen-inner casing wall interface, in °C; This represents the temperature of the preceding grid node on the nitrogen side, immediately adjacent to this interface, in °C. The temperature of the next grid node on the inner sleeve side, immediately adjacent to this interface, is expressed in °C. S232, Interface between outer wall of inner sleeve and inner wall of inner cement ring The thermal conductivity of the inner sleeve is The thermal conductivity of the inner cement ring is The heat flow continuity condition at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring is: The heat flow continuity condition at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring simplifies to the discrete equation as follows: In equations (11) and (12): The thermal conductivity of the inner cement ring is given by [value missing]. ; The thermal conductivity of the inner sleeve is given in units of 1000 ppm. ; The grid step size; Temperature of the grid nodes at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring, in °C; The temperature of the preceding grid node on the outer wall side of the inner sleeve, immediately adjacent to this interface, is expressed in °C. The temperature of the next grid node immediately adjacent to the interface on the inner wall side of the inner cement ring, in °C; S233, Interface between outer wall of inner cement ring and inner wall of outer sleeve The thermal conductivity of the outer tube is The thermal conductivity of the inner cement ring is The heat flow continuity condition at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve is: The heat flow continuity condition at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve is simplified to the discrete equation: In equations (13) and (14): The thermal conductivity of the inner cement ring is given by [value missing]. ; The thermal conductivity of the outer tube is given by [value missing]. ; The grid step size; Temperature of the grid nodes at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve, in °C; The temperature of the preceding grid node on the outer wall side of the inner cement ring, immediately adjacent to the interface, is expressed in °C. The temperature of the next grid node immediately adjacent to the interface on the inner wall side of the outer casing, in °C; S234, Interface between outer wall of outer sleeve and inner wall of outer cement ring The thermal conductivity of the outer tube is The thermal conductivity of the outer cement ring is The heat flow continuity condition at the interface between the outer wall of the outer jacket and the inner wall of the outer cement ring is: The heat flow continuity condition at the interface between the outer wall of the outer jacket and the inner wall of the outer cement ring simplifies to the discrete equation as follows: In equations (15) and (16): The thermal conductivity of the outer cement ring is given by [value missing]. ; The thermal conductivity of the outer tube is given by [value missing]. ; The grid step size; Temperature of the grid nodes at the interface between the outer wall of the outer jacket and the inner wall of the outer cement ring, in °C; The temperature of the preceding grid node on the outer wall side of the outer casing, immediately adjacent to this interface, is expressed in °C. The temperature of the next grid node immediately adjacent to the interface on the inner wall side of the outer cement ring, in °C; S235, Outer wall of outer cement ring - stratum The thermal conductivity of the outer cement ring is The thermal conductivity of the formation is The heat flow continuity condition at the outer wall of the outer cement sheath-formation interface is: The heat flow continuity condition at the outer cement sheath-formation interface simplifies to the discrete equation: In equations (17) and (18): The thermal conductivity of the outer cement ring is given by [value missing]. ; This is the thermal conductivity of the formation, in units of... ; The grid step size; Temperature of the grid nodes at the interface between the outer wall of the outer cement ring and the formation, in °C; The temperature of the preceding grid node on the outer wall side of the outer cement ring, immediately adjacent to the interface, is expressed in °C. The temperature of the next grid node immediately adjacent to the interface on the formation side, in °C; S24. Discretize the radial heat conduction differential equation (Equation 1) in cylindrical coordinates and the boundary condition expression for the radial temperature of the multi-layered well structure (Equation 6) into a system of linear equations: The system of linear equations is as follows: In equation (19): It is an unknown temperature vector; The coefficient matrix is ​​constructed from discrete governing equations and boundary conditions; The right-hand term vector is determined by the known boundary temperature; S25. Construct the coefficient matrix of the linear equation system (Equation 19) established in step S24. and right end item : S251, Non-interface, Non-boundary node coefficient matrix at For the linear equation (Equation 5) with respect to Coefficients of a linear equation, right-hand side terms The elements of a vector that are not at the interface or boundary are 0. coefficient matrix at non-interface and non-boundary nodes and right end item The expression is: In equation (20): For nodes The radial coordinate at the location, in meters; The grid step size; S252, Set the inner boundary node The coefficients of the inner boundary nodes of the discrete equation (Equation 7) are used as the coefficient matrix. The element in the first row and first column; the right-hand item. The first element of the vector is ; Inner boundary node coefficient matrix at and right end item The expression is: S253, outer boundary node The outer boundary node coefficients of the discrete equation (Equation 8) are used as the coefficient matrix. The element in the Nth row and Nth column; the right-hand term The Nth element of the vector is ; outer boundary node coefficient matrix at and right end item The expression is: S254, Nitrogen-inner tube inner wall interface ( The coefficients of the discrete equation (Equation 10) with respect to T are used as the coefficient matrix. The elements at the nitrogen-inner tube inner wall interface, and the elements at the nitrogen-inner tube inner wall interface of the right-hand term b vector are 0; Nitrogen-inner tube inner wall interface ( The coefficient matrix at ) and right end item The expression is: S255, the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring ( The coefficients of the discrete equation (Equation 12) with respect to T are used as the coefficient matrix. The elements at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring, and the elements at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring on the right end of the vector b are 0; Inner sleeve outer wall - inner cement ring inner wall interface ( The coefficient matrix at ) and right end item The expression is: S256, the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve ( The coefficients of the discrete equation (Equation 14) with respect to T are used as the coefficient matrix. The elements at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve, and the elements at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve of the right-hand term b are 0; Inner cement ring outer wall - outer sleeve inner wall interface ( The coefficient matrix at ) and right end item The expression is: S257, the interface between the outer wall of the outer sleeve and the inner wall of the outer cement ring ( The coefficients of the discrete equation (Equation 16) with respect to T are used as the coefficient matrix. The elements at the interface between the outer wall of the outer tube and the inner wall of the outer cement ring are 0; Outer wall of outer sleeve - inner wall of outer cement ring ( The coefficient matrix at ) and right end item The expression is: S258, the outer wall of the outer cement ring - formation interface ( The coefficients of the discrete equation (Equation 18) with respect to T are used as the coefficient matrix. The elements at the outer wall of the outer cement ring-formation interface, and the elements at the outer wall of the outer cement ring-formation interface of the right-hand term b vector are 0; Outer cement ring outer wall - formation interface ( The coefficient matrix at ) and right end item The expression is: S3. Calculate the radial temperature from the center of the well to the outer boundary of the formation by using the linear equations discretized from the differential equation of heat conduction in cylindrical coordinates and the boundary conditions of the radial temperature of the multi-layer structure of the wellbore. The formula for calculating the radial temperature from the center of the wellbore to the outer boundary of the formation is as follows: .

[0006] The beneficial effects of this invention are: This invention provides a method for calculating the temperature of a multi-layer casing-cement sheath structure. By defining multi-layer radial structural parameters and material properties, a layered heat transfer model is established based on the steady-state heat conduction theory in cylindrical coordinates. The control equations are discretized using the finite difference method, and a linear equation set is constructed by combining the interlayer interface heat flow continuity condition. This method enables accurate solving of the radial temperature distribution of the nitrogen-casing-cement sheath-formation multi-layer structure. It can accurately reflect the heat transfer characteristics of the multi-layer structure including nitrogen, casing, cement sheath, and formation, providing a reliable basis for wellbore thermal field analysis and safety assessment, while balancing calculation accuracy and efficiency. Attached Figure Description

[0007] Figure 1 This is a flowchart of the calculation process of the method of the present invention; Figure 2 This is a radial schematic diagram of the well depth structure in Embodiment 1 of the present invention; Figure 3 This is a comparison chart of the calculated temperatures of the multi-layer sleeve cement ring structure in Embodiment 1 of the present invention; Figure 4 This is in Embodiment 1 of the present invention Figure 3 Enlarged view of a section near the wellbore.

[0008] For those skilled in the art, other related figures can be obtained from the above figures without any creative effort. Detailed Implementation

[0009] To enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0010] Example 1 Taking a heavy oil well in the Bohai Sea as an example, its well depth structure is as follows: Figure 2 As shown, the sequence is 9-5 / 8in casing - inner cement sheath - 13-3 / 8in casing - outer cement sheath - formation. The annulus between the 9-5 / 8in casing and the tubing is filled with nitrogen. Multiple rounds of steam injection are performed by injecting heat into the tubing.

[0011] Following the preset steps, first press Figure 1 The process outlines the method for collecting the data required for the calculations.

[0012] For physical properties, the inner radius of the 9-5 / 8in casing is 0.1112m, and the outer radius is 0.1224m; the inner radius of the 13-3 / 8in casing is 0.1602m, and the outer radius is 0.1699m; the outer radius of the outer cement sheath is 0.2223m, and the outer radius of the formation is 15m; the thermal conductivity of nitrogen is 0.025. The thermal conductivity of cement is 0.3. The thermal conductivity of the formation is 1.5. The thermal conductivity of the sleeve is 55. .

[0013] The A matrix is ​​mainly calculated using the radial heat conduction equation in cylindrical coordinates and the boundary condition that the interface temperature and heat flux density are continuous.

[0014] For the right-hand term b, the calculation is performed by setting the inner and outer boundary temperature parameters.

[0015] According to formula (28), the radial temperature distribution of the multi-layer sleeve cement ring structure under different heating temperatures can be calculated. The temperature comparison results are as follows: Figure 3 As shown.

[0016] Depend on Figure 3 It can be seen that the heat injection temperatures of the inner wall boundary conditions are 150℃, 200℃, 280℃, 330℃ and 360℃ respectively. It can be seen that as the temperature increases, the temperature gradient near the wellbore gradually increases, and the radial temperature at the interface gradually decreases.

[0017] Depend on Figure 4 It can be seen that the temperature difference at the nitrogen-casing interface is relatively large, with the nitrogen temperature decreasing from 360℃ to 84℃, indicating that nitrogen has good thermal insulation performance. The casing has a higher thermal conductivity, with the temperature decreasing from 84.61℃ to 84.59℃, so the temperature difference at the casing is smaller. As the temperature increases, the near-wellbore temperature gradient gradually increases, while the change trend is smaller at lower temperatures.

[0018] The applicant declares that the above description is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Those skilled in the art should understand that any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention fall within the protection and disclosure scope of the present invention.

Claims

1. A method for calculating the temperature of a multi-layered sleeve cement ring structure, characterized in that: Includes the following steps: S1. Discretize the radial heat conduction differential equation in cylindrical coordinates using the finite difference method, and calculate the temperature at non-boundary points and non-interfaces in the wellbore. S2. Based on the boundary conditions and the fact that the temperature and heat flux density at the interface of any structure are continuous, calculate the temperature at the boundary point and the interface point. S3. Calculate the radial temperature from the center of the wellbore to the outer boundary of the formation by using a set of linear equations discretized from the differential equation of heat conduction in cylindrical coordinates and the boundary conditions of the radial temperature of the multi-layer structure of the wellbore.

2. The temperature calculation method for the multi-layer sleeve cement ring structure according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Establish the radial heat conduction differential equation in cylindrical coordinates: The radial heat conduction differential equation in cylindrical coordinates is as follows: In equation (1): r is the radial coordinate, in meters; T is the temperature, in degrees Celsius; k is the thermal conductivity of the material, in cubic meters per second. ; S12. Discretize the radial heat conduction differential equation in cylindrical coordinates established in step S11: Let the radial interval be Dividing the radial interval into N nodes, the node coordinates are: In formula (2): The coordinates are the inner boundary coordinates of the radial interval; Let be the radial coordinate at node j; The ordinal number of the current node; For grid step size, ; S13. At node j, the first derivative is obtained by approximating the derivative of the radial heat conduction differential equation in cylindrical coordinates using the central difference. The discrete derivative; The first derivative The discrete derivative is: In formula (3): For nodes The radial coordinate at the location, in meters; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; For nodes Thermal conductivity of the material at that location, in units of ; The grid step size; S14. The first derivative obtained in step S13 Substituting the discrete derivative into the radial heat conduction differential equation in cylindrical coordinates, we obtain the discrete equation: The discrete equation is: In equation (4): For nodes The radial coordinate at the location, in meters; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; The grid step size; S15. Rearrange the discrete equations obtained in step S14 into a form about the nodes. Temperature at the location The linear equation; The linear equation is: In formula (5): For nodes The radial coordinate at the location, in meters; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; For nodes The temperature at that location, expressed in °C; This represents the grid step size.

3. The temperature calculation method for the multi-layer sleeve cement ring structure according to claim 1, characterized in that: Step S2 specifically includes the following steps: S21. The boundary conditions for radial temperature of the multi-layered structure of the wellbore are as follows: the inner boundary temperature of the nitrogen layer is known, the outer boundary temperature of the formation is known, and temperature and heat flux density are continuous at any structural interface. The expression for the boundary conditions for radial temperature of the multi-layered structure of the wellbore is as follows: In formula (6): for Thermal conductivity of the layered structure, in units of ; for Thermal conductivity of the layered structure, in units of ; This is the temperature at the inner boundary of the nitrogen layer, in °C. Temperature at the outer boundary of the formation, in °C; This refers to the A-layer side of the interface; This refers to the b-layer side of the interface. Radial coordinates; Temperature, in °C; S22. Determine the discrete equations for the inner and outer boundaries; S23. Determine the discrete equations for each interface of the multi-layered structure of the wellbore; S24. Discretize the radial heat conduction differential equation in cylindrical coordinates and the boundary conditions for radial temperature in the multi-layered structure of the wellbore into a system of linear equations: The system of linear equations is as follows: In equation (19): It is an unknown temperature vector; The coefficient matrix is ​​constructed from discrete governing equations and boundary conditions; The right-hand term vector is determined by the known boundary temperature; S25. Construct the coefficient matrix of the linear equation system established in step S24. and right end item .

4. The temperature calculation method for the multi-layer sleeve cement ring structure according to claim 3, characterized in that: At the inner boundary Therefore, the discrete equation of the inner boundary is: The outer boundary Therefore, the discrete equation of the inner boundary is: 。 5. The temperature calculation method for the multi-layer sleeve cement ring structure according to claim 3, characterized in that: The wellbore multi-layer structure includes five interfaces: nitrogen-inner casing inner wall interface, inner casing outer wall-inner cement sheath inner wall interface, inner cement sheath outer wall-outer casing inner wall interface, outer casing outer wall-outer cement sheath inner wall interface, and outer cement sheath outer wall-formation interface.

6. The temperature calculation method for the multi-layer sleeve cement ring structure according to claim 5, characterized in that: At the nitrogen-inner tube inner wall interface The thermal conductivity of nitrogen is Thermal conductivity of the inner sleeve The heat flow continuity condition at the nitrogen-inner tube wall interface is: The heat flow continuity condition at the nitrogen-inner tube wall interface simplifies to the discrete equation as follows: In equations (9) and (10): This is the thermal conductivity of nitrogen, in units of... ; The thermal conductivity of the inner sleeve is given in units of 1000 ppm. ; The grid step size; Temperature of the grid node at the nitrogen-inner casing wall interface, in °C; This represents the temperature of the preceding grid node on the nitrogen side immediately adjacent to this interface, in °C. The temperature of the next grid node immediately adjacent to the interface on the inner wall side of the inner sleeve, in °C; At the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring The thermal conductivity of the inner sleeve is The thermal conductivity of the inner cement ring is The heat flow continuity condition at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring is: The heat flow continuity condition at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring simplifies to the discrete equation as follows: In equations (11) and (12): The thermal conductivity of the inner cement ring is given by [value missing]. ; The thermal conductivity of the inner sleeve is given in units of 1000 ppm. ; The grid step size; Temperature of the grid nodes at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring, in °C; The temperature of the preceding grid node on the outer wall side of the inner sleeve, immediately adjacent to this interface, is expressed in °C. The temperature of the next grid node immediately adjacent to the interface on the inner wall side of the inner cement ring, in °C; The interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve The thermal conductivity of the outer tube is The thermal conductivity of the inner cement ring is The heat flow continuity condition at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve is: The heat flow continuity condition at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve is simplified to the discrete equation: In equations (13) and (14): The thermal conductivity of the inner cement ring is given by [value missing]. ; The thermal conductivity of the outer tube is given by [value missing]. ; The grid step size; Temperature of the grid nodes at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve, in °C; The temperature of the preceding grid node on the outer wall side of the inner cement ring, immediately adjacent to the interface, is expressed in °C. The temperature of the next grid node immediately adjacent to the interface on the inner wall side of the outer casing, in °C; The interface between the outer wall of the outer sleeve and the inner wall of the outer cement ring The thermal conductivity of the outer tube is The thermal conductivity of the outer cement ring is The heat flow continuity condition at the interface between the outer wall of the outer jacket and the inner wall of the outer cement ring is: The heat flow continuity condition at the interface between the outer wall of the outer jacket and the inner wall of the outer cement ring simplifies to the discrete equation as follows: In equations (15) and (16): The thermal conductivity of the outer cement ring is given by [value missing]. ; The thermal conductivity of the outer tube is given by [value missing]. ; The grid step size; Temperature of the grid nodes at the interface between the outer wall of the outer jacket and the inner wall of the outer cement ring, in °C; The temperature of the preceding grid node on the outer wall side of the outer casing, immediately adjacent to this interface, is expressed in °C. The temperature of the next grid node immediately adjacent to the interface on the inner wall side of the outer cement ring, in °C; The outer wall of the outer cement ring - stratum The thermal conductivity of the outer cement ring is The thermal conductivity of the formation is The heat flow continuity condition at the outer wall of the outer cement sheath-formation interface is: The heat flow continuity condition at the outer cement sheath-formation interface simplifies to the discrete equation: In equations (17) and (18): The thermal conductivity of the outer cement ring is given by [value missing]. ; This is the thermal conductivity of the formation, in units of... ; The grid step size; Temperature of the grid nodes at the interface between the outer wall of the outer cement ring and the formation, in °C; The temperature of the preceding grid node on the outer wall side of the outer cement ring, immediately adjacent to the interface, is expressed in °C. This represents the temperature of the next grid node immediately adjacent to the interface on the formation side, in °C.

7. The temperature calculation method for the multi-layer sleeve cement ring structure according to claim 3, characterized in that: The coefficient matrix of the linear equation system established in construction step S24 and right end item Specifically, it includes: S251, Coefficient matrix at non-interface and non-boundary nodes For the linear equation with respect to Coefficients of a linear equation, right-hand side terms The elements of a vector that are not at the interface or boundary are 0. coefficient matrix at non-interface and non-boundary nodes and right end item The expression is: In equation (20): For nodes The radial coordinate at the location, in meters; The grid step size; S252. Use the coefficients of the inner boundary nodes of the discrete equations of the inner boundary nodes as the coefficient matrix. The element in the first row and first column; the right-hand item. The first element of the vector is ; coefficient matrix at inner boundary nodes and right end item The expression is: S253. The coefficients of the outer boundary nodes in the discrete equations of the outer boundary nodes are used as the coefficient matrix. The element in the Nth row and Nth column; the right-hand term The Nth element of the vector is ; coefficient matrix at outer boundary nodes and right end item The expression is: S254. The coefficients of the discrete equations of the nitrogen-inner casing interface with respect to T are used as a coefficient matrix. The elements at the nitrogen-inner tube inner wall interface, and the elements at the nitrogen-inner tube inner wall interface of the right-hand term b vector are 0; Coefficient matrix at the nitrogen-inner tube wall interface and right end item The expression is: S255. The coefficients of the discrete equations for the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring with respect to T are used as a coefficient matrix. The elements at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring, and the elements at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring on the right end of the vector b are 0; Coefficient matrix at the interface between the outer wall of the inner sleeve and the inner wall of the inner cement ring and right end item The expression is: S256. The coefficients of the discrete equations of the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve with respect to T are used as the coefficient matrix. The elements at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve, and the elements at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve of the right-hand term b are 0; Coefficient matrix at the interface between the outer wall of the inner cement ring and the inner wall of the outer sleeve and right end item The expression is: S257. The coefficients of the discrete equations for the interface between the outer wall of the outer sleeve and the inner wall of the outer cement ring with respect to T are used as a coefficient matrix. The elements at the interface between the outer wall of the outer tube and the inner wall of the outer cement ring are 0; Coefficient matrix at the interface between the outer wall of the outer tube and the inner wall of the outer cement ring and right end item The expression is: S258. The coefficients of the discrete equations of the outer cement sheath-formation interface with respect to T are used as a coefficient matrix. The elements at the outer wall of the outer cement ring-formation interface, and the elements at the outer wall of the outer cement ring-formation interface of the right-hand term b vector are 0; Coefficient matrix at the outer wall of the outer cement ring-formation interface and right end item The expression is: 。 8. The temperature calculation method for the multi-layer sleeve cement ring structure according to claim 1, characterized in that: The formula for calculating the radial temperature from the center of the wellbore to the outer boundary of the formation is as follows: 。

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