Numerical heat transfer model of U-tube ground heat exchanger considering groundwater seepage and its fast solution

Abstract

The application provides a numerical heat transfer model of a middle-deep U-shaped underground pipe considering groundwater seepage and a fast solving method thereof. The heat and seepage coupling heat transfer process in underground rock-soil is analyzed to obtain an energy equation of a porous medium; the energy equation of the middle-deep U-shaped underground pipe heat exchanger in the stage of taking heat from the rock-soil is obtained; the sum of heat capacity and thermal resistance is obtained; the thermal conductivity, the convective heat transfer coefficient, the temperature gradient and the Darcy resistance number are obtained; the control equation set of the middle-deep U-shaped underground pipe heat exchanger in the stage of taking heat considering groundwater seepage is obtained; in order to realize fast solving of the model, a new grid discrete form is provided, so that the calculation efficiency is greatly improved. The application provides a design basis for engineering practice of the middle-deep U-shaped underground pipe heating system in the area with large seepage velocity.

Description

Technical Field

[0001] This invention belongs to the field of medium-deep ground source heat pump technology, specifically relating to a numerical heat transfer model for medium-deep U-shaped buried pipes that considers groundwater seepage and its rapid solution method. Background Technology

[0002] With the development of drilling technology, the depth of geothermal energy extraction has increased from shallow (<200 m) to medium-deep (500-3000 m), and the corresponding systems have evolved from traditional shallow ground source heat pump systems to medium-deep ground source heat pump systems. The medium-deep buried pipe heat exchanger is the core component of the medium-deep ground source heat pump system, and its coupled heat transfer process with the rock and soil affects the system's heat extraction performance. According to their structural form, medium-deep buried pipe heat exchangers can be divided into medium-deep coaxial sleeve type buried pipe heat exchangers and medium-deep U-shaped buried pipe heat exchangers.

[0003] Compared to medium-deep coaxial-cased buried pipe heat exchangers, medium-deep U-shaped buried pipe heat exchangers have a simpler structure, reducing fluid resistance within the pipes and avoiding heat loss between the fluid in the inner pipe and the fluid in the outer annular cavity, thus improving the system's heat exchange efficiency. Furthermore, medium-deep U-shaped buried pipe heat exchangers consist of downcomers, horizontal pipes, and risers. Due to the higher temperature of the soil and rock near the horizontal pipes, heat exchange between the fluid inside the pipes and the surrounding soil and rock is enhanced, improving the ability of medium-deep U-shaped buried pipe heat exchangers to extract geothermal energy. To investigate the long-term heat extraction performance of medium-deep U-shaped buried pipe heat exchangers, existing technology discloses a simplified calculation method that treats the downcomer, horizontal pipe, and riser of the medium-deep U-shaped buried pipe heat exchanger as three independent parts, but ignores the coupled heat transfer between the three pipes. Existing technology also simplifies the heat transfer process of medium-deep U-shaped buried pipe heat exchangers and proposes a semi-analytical heat transfer model. Furthermore, the commercial software Fluent was used to quantify the impact of burial depth and connecting pipe length on the heat exchange of U-shaped deep buried pipes.

[0004] However, none of the aforementioned studies on medium-deep U-shaped buried pipe heat exchangers considered groundwater seepage in the soil and rock. Groundwater seepage adds convective heat transfer to the heat transfer process in the soil and rock, beyond pure conduction. This facilitates the transport of high-grade geothermal energy from distant locations to the vicinity of the medium-deep U-shaped buried pipe heat exchanger, forming a high-temperature heat plume region. Therefore, groundwater seepage enhances heat transfer between the buried pipe and the soil and rock, increasing the heat extraction power of the medium-deep U-shaped buried pipe heat exchanger. Furthermore, when using the commercial software Fluent to study the impact of groundwater seepage in the soil and rock on the heat extraction performance of medium-deep U-shaped buried pipe heat exchangers, it is necessary to establish a physical model, mesh generation, and a solution model. Since the buried depth of medium-deep U-shaped buried pipe heat exchangers often reaches several kilometers, the distance between the downcomer and riser pipes can reach hundreds of meters, and the borehole size is on the millimeter scale, establishing a physical model and mesh generation is difficult and labor-intensive, resulting in high computational costs. Therefore, there is an urgent need to propose a numerical heat transfer model for medium-deep U-shaped buried pipe heat exchangers that considers groundwater seepage, ensures computational accuracy, and enables rapid solution. A careful search of publicly available literature and patents revealed no literature or patent that proposes a numerical heat transfer model for medium-deep U-shaped buried pipe heat exchangers that considers groundwater seepage, nor a rapid solution method. Summary of the Invention

[0005] To quantify the impact of groundwater seepage in soil and rock on medium-deep U-shaped buried pipe heat exchangers, this invention proposes a numerical heat transfer model that considers groundwater seepage and instantaneous coupling between the medium-deep U-shaped buried pipe heat exchanger and soil and rock. Furthermore, to achieve rapid solution of the model, this invention also proposes a grid discretization form. This invention provides a design basis for the engineering practice of medium-deep U-shaped buried pipe heating systems in areas with high seepage velocities.

[0006] This invention is achieved through the following technical solution: A numerical heat transfer model for a medium-deep U-shaped buried pipe considering groundwater seepage, the numerical heat transfer model comprising the following steps. Step 1: Analyze the thermal infiltration coupling heat transfer process in underground rock and soil to derive the energy equation for porous media; Step 2: Based on the energy equation in Step 1, obtain the energy equation for the deep U-shaped buried pipe heat exchanger in the stage of extracting heat from the soil and rock. Step 3: Based on the energy equation in Step 2, obtain the sum of heat capacities and thermal resistance; Step 4: Based on the thermal resistance in Step 3, obtain the thermal conductivity, convective heat transfer coefficient, infinite temperature gradient, and Darcy drag number. Step 5: Based on Steps 1-4, the governing equations for the heat extraction stage of the medium-deep U-shaped buried pipe heat exchanger considering groundwater seepage are obtained, which are used to reveal the impact of groundwater seepage in the soil and rock on the long-term heat extraction performance of the medium-deep U-shaped buried pipe heat exchanger.

[0007] Furthermore, step 1 specifically involves the soil being an isotropic, homogeneous porous medium composed of both solid and fluid components, with a porosity of [missing information]. In porous media, the solid soil and rock portion only undergoes heat conduction, while the fluid portion exhibits both heat conduction and convective heat transfer. The heat conduction process in the soil and rock portion is as follows: (1) The heat conduction and convection heat transfer processes in the fluid are as follows: (2) Based on the premise that porous media satisfy local thermal equilibrium, adding equations (1) and (2) yields the energy equation for porous media as follows: (3) In the formula, It is a vector operator; T The temperature of the porous medium is expressed in °C. t Time, in seconds; The volume of tiny pores in a porous medium V k and the total volume of porous media V The ratio, in units of % The total volumetric specific heat capacity of the porous medium, in J / (m³). 3 K); The total thermal conductivity is expressed in W / (m²). K); q The intensity of the total internal heat source, expressed in W / m². 3 ; It can be calculated using equations (4)-(7) respectively. (4) (5) (6) (7).

[0008] Furthermore, step 2 specifically involves determining the energy equation for the fluid within the downcomer as follows: (8) The energy equation for the fluid inside the horizontal pipe is: (9) The energy equation for the fluid inside the riser pipe is: (10) In the formula: T f1 ,T f2 and T f3 These represent the fluid temperatures inside the downcomer, horizontal pipe, and riser, respectively, in °C. T b11 and T b12 These are the temperatures of the left and right walls of the borehole during the descent, respectively, in °C. T b21 and T b22 These are the temperatures of the upper and lower walls of the horizontal borehole, respectively, in °C. T b31 and T b32 These are the temperatures of the left and right walls of the rising borehole, respectively, in °C. M The flow rate of the circulating working fluid in the pipe is expressed in kg / s. C f The specific heat capacity of the circulating working fluid in the pipe, in kJ / (kg) ℃).

[0009] Furthermore, the sum of heat capacities in step 3 specifically comprises: C 1. C 2 and C 3 represents the sum of the heat capacities of various materials per unit length within the borehole heat exchanger for each pipe section, in J / (m²). K), calculated using the following formula: (11) (12) (13) In the formula: d b1 , d b2 and d b3 These represent the diameters of the descending, horizontal, and ascending boreholes, respectively, in meters (m). d 1o , d 2o and d 3o These represent the outer diameters of the descending, horizontal, and ascending pipes, respectively, in meters (m). d 1i , d 2i and d 3i These represent the inner diameters of the descending, horizontal, and ascending pipes, respectively, in meters (m). r w cw ,r 1 c 1 ,r 2 c 2 ,r 3 c 3 ,r g1 c g1 ,r g2 c g2 and r g3 c g3 These represent the specific heat capacity of circulating water, the specific heat capacity of the outer pipe, the specific heat capacity of the inner pipe, and the specific heat capacity of the backfill material, respectively, in J / (m³). 3 ·K).

[0010] Furthermore, the thermal resistance in step 3 specifically refers to... R 1. R 2 and R 3 represents the thermal resistance between the circulating water and the borehole wall in the downcomer, horizontal pipe, and riser, respectively, and can be calculated using the following formulas. (14) (15) (16) In the formula: , and These represent the thermal conductivity of the backfill material around the downpipe, horizontal pipe, and uppipe, respectively, in W / (m·K); , and These represent the thermal conductivity of the descending pipe, horizontal pipe, and ascending pipe, respectively, in W / (m·K). h 1. h 2 and h 3 represents the convective heat transfer coefficient between the fluid and the pipe wall in the downcomer pipe, horizontal pipe, and upcomer pipe, respectively, in W / (m²). 2 ·K), step 4 can be calculated using the following formula, (17) In the formula: l The characteristic length of the heat exchange surface, in meters (m). k f Nu represents the thermal conductivity of the heat transfer fluid, in units of W / (m·K); Nu is the Nusselt number.

[0011] Furthermore, the Nusselt number in step 4 is a dimensionless quantity, and its physical meaning is the dimensionless temperature gradient of the fluid on the heat transfer wall surface. The calculation formula is as follows: (18) In equation (18), f For turbulent flow inside the pipe Darcy The drag coefficient is calculated using the following formula: (19) The Reynolds number of a fluid is a measure of the ratio of inertial forces to viscous forces, and its calculation formula is as follows: (20) In the formula: d e The equivalent diameter representing the flow inside the pipe, in meters (m). Represents the kinematic viscosity coefficient, in meters (m). 2 / s; u f Represents the fluid flow velocity, measured in m / s.

[0012] Furthermore, when the medium-deep U-shaped buried pipe heat exchanger stops extracting heat, the circulating fluid within it is in a quiescent state, and the soil and rock subsequently enter a thermal recovery phase. Compared to the governing equations for the heat extraction phase, the fluid governing equations for the thermal recovery phase lack convection terms. This completes the governing equations for both the heat extraction and thermal recovery phases, which can be used to reveal the impact of groundwater seepage in the soil and rock on the long-term heat extraction performance of the medium-deep U-shaped buried pipe heat exchanger.

[0013] A fast solution method for a numerical heat transfer model of a medium-deep U-shaped buried pipe considering groundwater seepage is proposed. The fast solution method adopts a double variable step size meshing form based on unequal differential step size. Specifically, for the soil and rock surrounding the downhole, the left and right walls of the downhole are used as boundaries, and the step size of the soil and rock nodes is a multiple of the node size. and node multiples Growing outwards, the soil and rock on the left side of the descending pipe are at multiples of the nodes. It grows to the boundary position, while the soil and rock on the right side of the downcomer increase by a multiple of the nodes. Increase to half the length of the horizontal pipe (H / 2); For the soil and rock surrounding the riser, the step size of the soil and rock nodes is determined by the left and right walls of the riser borehole, respectively, and is based on multiples of the nodes. and node multiples Growing outwards, the soil and rock on the left side of the riser pipe are at multiples of the nodes. The riser extends to half the length of the horizontal pipe (H / 2), while the soil and rock on the right side of the riser pipe are at multiples of the nodes. Growth to the boundary position; For the soil and rock surrounding the horizontal borehole, the upper and lower walls of the horizontal borehole are used as boundaries, and the step size of the soil and rock nodes is a multiple of the node size. and node multiples Growing outwards, the soil and rock beneath the horizontal pipe increase in multiples of the nodes. As it grows to the boundary position, the soil and rock on the upper side of the horizontal pipe are multiplied by the number of nodes. It grows to the same distance from the bottom wall of the horizontal borehole to the boundary.

[0014] The beneficial effects of this invention are: The seepage model proposed in this invention can quantify the impact of groundwater seepage in soil and rock, providing a design basis for the engineering practice of medium-deep U-shaped buried pipe heating systems in areas with high seepage velocities.

[0015] This invention proposes a meshing method based on dual variable step size, which can effectively reduce the number of meshes and abandon the previous invention's assumption that the downcomer, horizontal pipe and riser of the medium-deep U-shaped buried pipe heat exchanger are three independent parts, thus broadening the applicability of the model.

[0016] Under the condition of ensuring the calculation error and using the same equipment, the calculation efficiency of the seepage model proposed in this invention is improved by at least several orders of magnitude compared with the commercial software Fluent. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the grid discretization of the present invention.

[0018] Figure 2 This is a flowchart of the method of the present invention.

[0019] Figure 3 This is a comparison chart of the calculation errors of the model in this invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] A numerical heat transfer model for a medium-deep U-shaped buried pipe considering groundwater seepage, the numerical heat transfer model comprising the following steps. Step 1: Analyze the thermal infiltration coupling heat transfer process in underground rock and soil to derive the energy equation for porous media; Step 2: Based on the energy equation in Step 1, obtain the energy equation for the deep U-shaped buried pipe heat exchanger in the stage of heat extraction from the soil and rock. Step 3: Based on the energy equation in Step 2, obtain the sum of heat capacities and thermal resistance; Step 4: Based on the thermal resistance in Step 3, obtain the thermal conductivity, convective heat transfer coefficient, infinite temperature gradient, and Darcy drag number. Step 5: Based on Steps 1-4, the governing equations for the heat extraction stage of the medium-deep U-shaped buried pipe heat exchanger considering groundwater seepage are obtained, which are used to reveal the impact of groundwater seepage in the soil and rock on the long-term heat extraction performance of the medium-deep U-shaped buried pipe heat exchanger.

[0022] Furthermore, step 1 specifically involves treating the soil and rock as an isotropic, homogeneous porous medium, composed of both solid soil and rock and fluid components, with a porosity of [missing information]. In porous media, the solid portion only involves heat conduction, while the fluid portion involves both heat conduction and convective heat transfer. The heat conduction process in the soil and rock portion is as follows: (1) The heat conduction and convection heat transfer processes in the fluid are as follows: (2) Based on the premise that porous media satisfy local thermal equilibrium, adding equations (1) and (2) yields the energy equation for porous media as follows: (3) In the formula, It is a vector operator; T The temperature of the porous medium is expressed in °C. t Time, in seconds; The volume of tiny pores in a porous medium V k and the total volume of porous media V The ratio, in units of % The total volumetric specific heat capacity of the porous medium, in J / (m³). 3 K); The total thermal conductivity is expressed in W / (m²). K); q The intensity of the total internal heat source, expressed in W / m². 3 .

[0023] It can be calculated using equations (4)-(7) respectively. (4) (5) (6) (7) Furthermore, step 2 specifically involves determining the energy equation for the fluid within the downcomer as follows: (8) The energy equation for the fluid inside the horizontal pipe is: (9) The energy equation for the fluid inside the riser pipe is: (10) In the formula: T f1 , T f2 and T f3 These represent the fluid temperatures inside the downcomer, horizontal pipe, and riser, respectively, in °C. T b11 and T b12 These are the temperatures of the left and right walls of the borehole during the descent, respectively, in °C. T b21 and T b22 These are the temperatures of the upper and lower walls of the horizontal borehole, respectively, in °C. T b31 and T b32 These are the temperatures of the left and right walls of the rising borehole, respectively, in °C. M The flow rate of the circulating working fluid in the pipe is expressed in kg / s. C f The specific heat capacity of the circulating working fluid in the pipe, in kJ / (kg) ℃).

[0024] Furthermore, the sum of heat capacities in step 3 specifically comprises: C 1. C 2 and C 3 represents the sum of the heat capacities of various materials per unit length within the borehole heat exchanger for each pipe section, in J / (m²). K), calculated using the following formula. (11) (12) (13) In the formula: d b1 , d b2 and d b3 These represent the diameters of the descending, horizontal, and ascending boreholes, respectively, in meters (m). d1o , d 2o and d 3o These represent the outer diameters of the descending, horizontal, and ascending pipes, respectively, in meters (m). d 1i , d 2i and d 3i These represent the inner diameters of the descending, horizontal, and ascending pipes, respectively, in meters (m). r w c w ,r 1 c 1 ,r 2 c 2 ,r 3 c 3 ,r g1 c g1 ,r g2 c g2 and r g3 c g3 These represent the specific heat capacity of circulating water, the specific heat capacity of the outer pipe, the specific heat capacity of the inner pipe, and the specific heat capacity of the backfill material, respectively, in J / (m³). 3 ·K); Further, the thermal resistance in step 3 specifically refers to, R 1. R 2 and R 3 represents the thermal resistance between the circulating water and the borehole wall in the downcomer, horizontal pipe, and riser, respectively, in units of (m·K) / W, which can be calculated using the following formulas. (14) (15) (16) In the formula: , and These represent the thermal conductivity of the backfill material around the downpipe, horizontal pipe, and uppipe, respectively, in W / (m·K); , and These represent the thermal conductivity of the descending pipe, horizontal pipe, and ascending pipe, respectively, in W / (m·K). h 1. h 2 and h3 represents the convective heat transfer coefficient between the fluid and the pipe wall in the downcomer pipe, horizontal pipe, and upcomer pipe, respectively, in W / (m²). 2 ·K), step 4 can be calculated using the following formula, (17) In the formula: l The characteristic length of the heat exchange surface, in meters (m). k f The thermal conductivity of the heat transfer fluid, expressed in W / (m²). 2 ·K); Nu is the Nusselt number.

[0025] Furthermore, the Nusselt number in step 4 is a dimensionless quantity, and its physical meaning is the dimensionless temperature gradient of the fluid on the heat transfer wall surface. The calculation formula is as follows: (18) In equation (18), f For turbulent flow inside the pipe Darcy The drag coefficient is calculated using the following formula: (19) The Reynolds number of a fluid is a measure of the ratio of inertial forces to viscous forces, and its calculation formula is as follows: (20) In the formula: d e The equivalent diameter representing the flow inside the pipe, in meters (m). Represents the kinematic viscosity coefficient, in meters (m). 2 / s; u f Represents the fluid flow velocity, measured in m / s.

[0026] Furthermore, when the medium-deep U-shaped buried pipe heat exchanger stops extracting heat, the circulating fluid within it is in a quiescent state, and the soil and rock subsequently enter a thermal recovery phase. Compared to the governing equations for the heat extraction phase, the fluid governing equations for the thermal recovery phase lack convection terms. This completes the governing equations for both the heat extraction and thermal recovery phases, which can be used to reveal the impact of groundwater seepage in the soil and rock on the long-term heat extraction performance of the medium-deep U-shaped buried pipe heat exchanger.

[0027] A rapid solution method for a numerical heat transfer model of a medium-deep U-shaped buried pipe considering groundwater seepage is provided. The rapid solution method utilizes the aforementioned numerical heat transfer model of a medium-deep U-shaped buried pipe considering groundwater seepage. The rapid solution method proposes a double-variable step size meshing form based on unequal differential step size. This meshing form takes into account the differences in soil and rock gradients, and the double-variable step size effectively reduces the number of computational grids, thereby improving the model's computational efficiency. Specifically, for the soil and rock surrounding the downhole, the left and right walls of the downhole are used as boundaries, and the step size of the soil and rock nodes is a multiple of the node size. and node multiples Growing outwards, the soil and rock on the left side of the descending pipe are at multiples of the nodes. It grows to the boundary position, while the soil and rock on the right side of the downcomer increase by a multiple of the nodes. The length increases to half the length of the horizontal pipe (H / 2). For the soil and rock surrounding the riser, the step size of the soil and rock nodes is determined by multiples of the node length, using the left and right walls of the riser borehole as boundaries. and node multiples Growing outwards, the soil and rock on the left side of the riser pipe are at multiples of the nodes. The riser extends to half the length of the horizontal pipe (H / 2), while the soil and rock on the right side of the riser pipe are at multiples of the nodes. Growth to the boundary position. For the soil and rock surrounding the horizontal borehole, the upper and lower walls of the horizontal borehole are used as boundaries, and the step size of the soil and rock nodes is a multiple of the node size. and node multiples Growing outwards, the soil and rock beneath the horizontal pipe increase in multiples of the nodes. As it grows to the boundary position, the soil and rock on the upper side of the horizontal pipe are multiplied by the number of nodes. It grows to the same distance from the bottom wall of the horizontal borehole to the boundary.

[0028] (1) Import the basic parameters into the model, including the pipe size, borehole size, backfill material thermal properties, and soil thermal properties. (2) Due to the thermal resistance during the heat extraction and soil thermal recovery stages... R Heat capacity C Unlike other methods, it is set as a global variable during the calculation process. (3) The appendix proposed in this invention is used. Figure 2 The grid is divided into grids as shown, and the soil and fluid temperature fields are initialized. (4) The soil and fluid temperature fields are determined based on whether there is seepage in the soil and fluid. The soil and fluid heat conduction control equation and porous medium model are used. (5) In addition, during system operation, the deep U-shaped buried pipe heat exchanger is in the stage of heat extraction from the soil and fluid. After the system is shut down, the soil and fluid temperature is in the stage of heat recovery. Therefore, the fluid control equations are used in different stages according to the system operation stage. (6) The ADI differential format is used to establish the equations of each node. (7) Variables are created to distinguish between longitudinal and transverse alternating solutions. (8) The TDMA algorithm can be used to solve the discretized soil and fluid node equations. However, the fluid node equations in the pipe do not satisfy the tridiagonal equation form. Therefore, the fluid node equations in the pipe can be solved using the Gaussian elimination method. (9) The node equations are solved alternately in the longitudinal and transverse directions. Finally, it is determined whether the soil and fluid temperature fields converge and the results are output.

[0029] To verify the accuracy of the seepage model proposed in this invention, a model considering groundwater seepage was established using commercial CFD software, and the simulation data from Fluent was compared with the simulation data from this model. The basic parameters used in the simulation are listed in Table 1. Figure 3 As can be seen, the simulated outlet water temperature decrease trend using the model proposed in this invention is the same as that of Fluent, and the outlet water temperature is in a quasi-steady-state stage when the operating time is greater than 200 h. Compared with the outlet water temperature simulated by Fluent, the maximum relative error of this model is less than 6%, and the root mean square error is 0.53 ℃, indicating that the seepage model proposed in this invention can be used to simulate the impact of groundwater seepage on the heat extraction performance of medium-deep U-shaped buried pipe heat exchangers.

[0030] Based on the parameters listed in Table 1, and assuming the same computational accuracy and equipment (AMD Ryzen 9 5900X 12-Core Processor), the simulation computation using the model proposed in this patent takes approximately 12 minutes per year, while using the commercial CFD software Fluent takes at least 40 hours (computation time is related to the number of grids). The computational efficiency of the model proposed in this patent is improved by several orders of magnitude.

[0031] Table 1 Simulation Parameters

Claims

1. A method for constructing a numerical heat transfer model for a medium-deep U-shaped buried pipe considering groundwater seepage, characterized in that, Constructing the numerical heat transfer model includes the following steps: Step 1: Analyze the thermal infiltration coupling heat transfer process in underground rock and soil to derive the energy equation for porous media; Step 2: Based on the energy equation in Step 1, obtain the energy equation for the deep U-shaped buried pipe heat exchanger in the stage of heat extraction from the soil and rock. Step 3: Based on the energy equation in Step 2, obtain the sum of heat capacities and thermal resistance; Step 4: Based on the thermal resistance in Step 3, obtain the thermal conductivity, convective heat transfer coefficient, infinite temperature gradient, and Darcy drag number. Step 5: Based on Steps 1-4, the governing equations for the heat extraction stage of the medium-deep U-shaped buried pipe heat exchanger considering groundwater seepage are obtained, which are used to reveal the impact of groundwater seepage in soil and rock on the long-term heat extraction performance of the medium-deep U-shaped buried pipe heat exchanger. Step 1 specifically involves the soil and rock being an isotropic, homogeneous, porous medium composed of both solid and fluid components, with a porosity of [missing information]. ; In porous media, the solid soil and rock portion only undergoes heat conduction, while the fluid portion exhibits both heat conduction and convective heat transfer. The heat conduction process in the soil and rock portion is as follows: （1） The heat conduction and convection heat transfer processes in the fluid are as follows: （2） Based on the premise that porous media satisfy local thermal equilibrium, adding equations (1) and (2) yields the energy equation for porous media as follows: （3） In the formula, It is a vector operator; T The temperature of the porous medium is expressed in °C. t Time, in seconds; The volume of tiny pores in a porous medium V k and the total volume of porous media V The ratio, in units of % The total volumetric specific heat capacity of the porous medium, in J / (m³). 3 ·K); The total thermal conductivity is expressed in W / (m·K). q The intensity of the total internal heat source, expressed in W / m². 3 ; It can be calculated using equations (4)-(7) respectively. （4） （5） （6） （7）。 2. The method for constructing a numerical heat transfer model for a medium-deep U-shaped buried pipe considering groundwater seepage, as described in claim 1, is characterized in that... Step 2 specifically involves determining the energy equation for the fluid within the downcomer. （8） The energy equation for the fluid inside the horizontal pipe is: （9） The energy equation for the fluid inside the riser pipe is: （10） In the formula: T f1 , T f2 and T f3 These represent the fluid temperatures inside the downcomer, horizontal pipe, and riser, respectively, in °C. T b1l and T b1r These are the temperatures of the left and right walls of the borehole during the descent, respectively, in °C. T b2t and T b2b These are the temperatures of the upper and lower walls of the horizontal borehole, respectively, in °C. T b3l and T b3r These are the temperatures of the left and right walls of the rising borehole, respectively, in °C. M The flow rate of the circulating working fluid in the pipe is expressed in kg / s. C f Specific heat capacity of the circulating working fluid inside the pipe, in kJ / (kg·℃).

3. The method for constructing a numerical heat transfer model for a medium-deep U-shaped buried pipe considering groundwater seepage, as described in claim 2, is characterized in that... The sum of heat capacities in step 3 is specifically as follows: C 1. C 2 and C 3 represents the sum of the heat capacities of various materials per unit length within the borehole heat exchanger for each pipe section, in J / (m²). K), calculated using the following formula. （11） （12） （13） In the formula: d b1 , d b2 and d b3 These represent the diameters of the descending, horizontal, and ascending boreholes, respectively, in meters (m). d 1o , d 2o and d 3o These represent the outer diameters of the descending, horizontal, and ascending pipes, respectively, in meters (m). d 1i , d 2i and d 3i These represent the inner diameters of the descending, horizontal, and ascending pipes, respectively, in meters (m). ρ w c w ρ 1 c 1 ρ 2 c 2 ρ 3 c 3 ρ g1 c g1 ρ g2 c g2 and ρ g3 c g3 These represent the specific heat capacity of circulating water, the specific heat capacity of the outer pipe, the specific heat capacity of the inner pipe, and the specific heat capacity of the backfill material, respectively, in J / (m³). 3 ·K).

4. The method for constructing a numerical heat transfer model for a medium-deep U-shaped buried pipe considering groundwater seepage, as described in claim 3, is characterized in that... The thermal resistance in step 3 is specifically as follows: R 1. R 2 and R 3 represents the thermal resistance between the circulating water and the borehole wall in the downcomer, horizontal pipe, and riser, respectively, in units of (m·K) / W, which can be calculated using the following formulas. （14） （15） （16） In the formula: , and These represent the thermal conductivity of the backfill material around the downpipe, horizontal pipe, and uppipe, respectively, in W / (m·K); , and These represent the thermal conductivity of the descending pipe, horizontal pipe, and ascending pipe, respectively, in W / (m·K). h 1. h 2 and h 3 represents the convective heat transfer coefficient between the fluid and the pipe wall in the downcomer pipe, horizontal pipe, and upcomer pipe, respectively, in W / (m²). 2 ·K), step 4 can be calculated using the following formula, （17） In the formula: l The characteristic length of the heat exchange surface, in meters (m). k f Nu represents the thermal conductivity of the heat transfer fluid, in units of W / (m·K); Nu is the Nusselt number.

5. The method for constructing a numerical heat transfer model for a medium-deep U-shaped buried pipe considering groundwater seepage according to claim 4, characterized in that, The Nusselt number in step 4 is a dimensionless quantity, which physically represents the dimensionless temperature gradient of the fluid on the heat transfer wall surface. The calculation formula is as follows. （18） In equation (18), f For turbulent flow inside the pipe Darcy The drag coefficient is calculated using the following formula: （19） The Reynolds number of a fluid is a measure of the ratio of inertial forces to viscous forces, and its calculation formula is as follows: （20） In the formula: d e The equivalent diameter representing the flow inside the pipe, in meters (m). Represents the kinematic viscosity coefficient, in meters (m). 2 / s; u f Represents the fluid flow velocity, measured in m / s.

6. The method for constructing a numerical heat transfer model for a medium-deep U-shaped buried pipe considering groundwater seepage according to claim 5, characterized in that, When the medium-deep U-shaped buried pipe heat exchanger stops extracting heat, the circulating fluid inside the medium-deep U-shaped buried pipe heat exchanger is in a static state. In the following time, the soil and rock are in the heat recovery stage. Compared with the governing equation of the heat extraction stage, the fluid governing equation of the heat recovery stage has no convection term. Thus, the complete governing equations of the heat extraction stage and the heat recovery stage are formed, which can be used to reveal the impact of groundwater seepage in the soil and rock on the long-term heat extraction performance of the medium-deep U-shaped buried pipe heat exchanger.

7. A rapid solution method for a numerical heat transfer model of a medium-deep U-shaped buried pipe considering groundwater seepage, characterized in that, The fast solution method utilizes the numerical heat transfer model of a medium-deep U-shaped buried pipe considering groundwater seepage as described in any of claims 1-6. The fast solution method proposes a novel mesh generation method with double variable step size based on unequal differential step size. Specifically, for the soil and rock surrounding the downhole, the left and right walls of the downhole are used as boundaries, and the step size of the soil and rock nodes is a multiple of the node size. and node multiples Growing outwards, the soil and rock on the left side of the descending pipe are at multiples of the nodes. It grows to the boundary position, while the soil and rock on the right side of the downcomer increase by a multiple of the nodes. Increase to half the length of the horizontal pipe (H / 2); For the soil and rock surrounding the riser, the step size of the soil and rock nodes is determined by the left and right walls of the riser borehole, respectively, and is based on multiples of the nodes. and node multiples Growing outwards, the soil and rock on the left side of the riser pipe are at multiples of the nodes. The riser extends to half the length of the horizontal pipe (H / 2), while the soil and rock on the right side of the riser pipe are at multiples of the nodes. Growth to the boundary position; For the soil and rock surrounding the horizontal borehole, the upper and lower walls of the horizontal borehole are used as boundaries, and the step size of the soil and rock nodes is a multiple of the node size. and node multiples Growing outwards, the soil and rock beneath the horizontal pipe increase in multiples of the nodes. As it grows to the boundary position, the soil and rock on the upper side of the horizontal pipe are multiplied by the number of nodes. It grows to the same distance from the bottom wall of the horizontal borehole to the boundary.

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