Calculation method for temperature response of buried pipes considering groundwater seepage and geothermal gradient

Abstract

This invention discloses a calculation method for the temperature response of buried pipes considering groundwater seepage and geothermal gradients, belonging to the field of building environment and energy application engineering. The method includes: treating the shallow buried pipe heat exchanger as a finite-length heat source model, and treating it as a finite-length heat source seepage model when groundwater seeps through it; establishing an energy control equation that simultaneously includes soil thermal conductivity, groundwater seepage convection, and geothermal gradient correlation terms; setting boundary conditions based on the initial temperature distribution of the geothermal gradient, the constant surface wall temperature, and the finite underground boundary; and finally obtaining an analytical solution expression for the temperature change of any location in the underground soil over time through analytical solving. This invention overcomes the shortcomings of traditional models that ignore key environmental factors, accurately simulates the coupled heat transfer process of conduction and convection, significantly improves the accuracy of temperature field prediction and the reliability of long-term performance evaluation, while avoiding the complexity of numerical calculations and improving computational efficiency.

Description

Technical Field

[0001] This invention belongs to the field of building environment and energy application engineering technology, and in particular relates to a method for calculating the temperature response of buried pipes considering groundwater seepage and geothermal gradient. Background Technology

[0002] Ground source heat pump systems use underground media as heat and cold sources. Due to their significant advantages in energy saving and environmental protection, they have been widely adopted in the fields of building environment and energy application. This system consists of a buried pipe heat exchanger, a heat pump unit, and indoor terminal equipment. The buried pipe heat exchanger is the core component that distinguishes ground source heat pumps from other types of heat pumps, and its heat exchange performance directly determines the overall energy efficiency of the ground source heat pump system. In the current field of buried pipe heat exchanger design, traditional theories are mainly based on pure heat conduction models. These models assume that the underground rock and soil are static, homogeneous solid media, and that heat transfer underground is achieved solely through heat conduction. Among these, the most representative are the line heat source model and the column heat source model developed by Ingersoll et al. in 1954 based on Kelvin's line heat source theory. These models, due to their simple principles and relatively low computational difficulty, have long been the mainstream theoretical basis for the design of buried pipe heat exchangers, providing fundamental technical support for the early promotion and application of ground source heat pump systems.

[0003] However, the actual underground environment has complex multi-factor coupling characteristics. Traditional pure heat conduction models ignore two factors that are crucial to heat transfer performance, leading to significant limitations in their engineering applications. On the one hand, the geothermal gradient is an inherent characteristic formed by the transfer of heat from the Earth's interior to the surface. The ground temperature increases regularly with depth (typically at a rate of about 2-3℃ / 100m). Traditional models that ignore this factor directly lead to an underestimation of the heat transfer capacity at the bottom of the borehole and an overestimation of the heat transfer capacity at the borehole opening, resulting in distorted temperature predictions across the entire length of the buried pipe heat exchanger and affecting the accuracy of system design. On the other hand, groundwater seepage is a common phenomenon in aquifers. When groundwater flows through the pores of soil and rock, it carries heat away rapidly through convection. Its heat transfer efficiency is much higher than that of pure heat conduction. The neglect of this factor in traditional models will seriously underestimate the long-term operating performance of heat exchangers. The flowing groundwater can continuously remove heat (or cold) around the heat exchanger and replenish the undisturbed soil and rock fluids, thereby enhancing the heat exchange effect and reducing the problem of heat and cold accumulation. However, traditional designs often adopt overly conservative pipe length designs because they do not consider this effect, resulting in increased equipment costs and waste of resources, making it difficult to meet the engineering requirements for upgrading ground source heat pump systems to "precision and efficiency". Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a calculation method for the temperature response of buried pipes that considers groundwater seepage and geothermal gradient, thereby resolving the issues present in the prior art.

[0005] To achieve the above objectives, this invention provides a method for calculating the temperature response of buried pipes considering groundwater seepage and geothermal gradients. The buried pipe heat exchanger includes a borehole, a single U-shaped pipe, and backfill material. The method includes:

[0006] The shallow buried pipe heat exchanger is regarded as a finite-length heat source model. When groundwater seeps through the buried pipe heat exchanger, the model is a finite-length heat source seepage model, and a constant wall temperature boundary condition is applied to the surface.

[0007] Considering the influence of the geothermal gradient on the underground temperature field, a uniform and stable geothermal heat flow is assumed to exist underground, with the direction of the geothermal heat flow from bottom to top. The lower boundary of the underground region is set as a lower boundary H that is sufficiently far from the bottom of the buried pipe heat exchanger. bound And H bound It is longer than the length of the buried pipe heat exchanger;

[0008] Establish the energy control equation for the soil and rock surrounding the buried pipe heat exchanger. The energy control equation includes soil thermal conductivity, groundwater seepage and convection, and geothermal gradient correlation terms.

[0009] The initial conditions and boundary conditions of the energy control equation are set, wherein the initial conditions are based on the geothermal gradient to determine the initial temperature distribution of the underground soil, and the boundary conditions include surface constant wall temperature conditions and underground finite boundary conditions.

[0010] Based on the energy control equation, initial conditions, and boundary conditions, an analytical solution expression for the temperature change of underground soil at any location over time is obtained through analytical solution.

[0011] Preferably, the energy control equation is a transient energy control equation, the mathematical expression of which includes three variables: soil thermal diffusivity, groundwater seepage velocity, and geothermal gradient.

[0012] Preferably, the initial temperature distribution of the underground soil in the initial conditions is expressed as a linear function of depth based on the geothermal gradient.

[0013] Preferably, the initial condition is expressed as Where t2 represents the temperature at different locations along the depth direction in the soil when there is a geothermal gradient. t 0 For surface temperature, q g For geothermal flow, k The thermal conductivity of the soil, The depth of any point below the ground. H bound The lower boundary is a sufficiently far distance from the bottom of the buried pipe heat exchanger.

[0014] Preferably, the lower boundary of the underground region in the boundary conditions is set as a lower boundary H that is sufficiently far from the bottom of the buried pipe heat exchanger. bound At the location, and apply a uniform geothermal flow. q g .

[0015] Preferably, the analytical solution expression is derived based on the finite-length line heat source model and includes the soil volumetric specific heat capacity, the length of the buried pipe heat exchanger, and the groundwater seepage velocity.

[0016] Preferably, the groundwater seepage direction in the groundwater seepage convection term is along the x-axis.

[0017] Preferably, the single U-shaped pipe includes a downcomer and an upcomer, with circulating fluid flowing in through the downcomer and out through the upcomer, and the backfill material filling the space between the U-shaped pipe and the borehole wall.

[0018] Preferably, the method directly calculates the temperature value at any three-dimensional coordinate point in the underground soil through analytical solution expression, without the need for numerical discretization;

[0019] The analytical solution expression is:

[0020] ;

[0021] in, t 2 represents the temperature at different locations along the depth direction in the soil when there is a geothermal gradient, in °C; t 0 represents the Earth's surface temperature, in degrees Celsius (°C). x、y and z The coordinates of the underground soil are in three dimensions, in meters (m). a Thermal diffusivity of soil medium, unit: m 2 / s; t The time for heat transfer, in seconds. u The seepage velocity of groundwater along the x-direction, in m / s; q g Geothermal heat flow, unit: W / m 2 ; h The depth of the buried pipe heat exchanger, in meters (m). pc Specific heat capacity of underground soil, unit: J / (m³) 3 ·K); k is the thermal conductivity of the underground soil, unit: W / (m·K); t ’ The integral variable representing the heat exchange time of the buried pipe, in seconds; z ’ The integral variable represents the depth of the buried pipe, in meters (m).

[0022] Preferably, the energy control equation, initial conditions, and boundary conditions are all linear. The initial temperature distribution is superimposed onto the solution with zero initial temperature using the superposition principle to handle the problem of variable load.

[0023] Compared with the prior art, the present invention has the following advantages and technical effects:

[0024] This invention treats shallow buried pipe heat exchangers as finite-length line heat sources and incorporates soil thermal conductivity, groundwater seepage and convection, and geothermal gradient correlation terms into its energy control equations. This allows the calculation method to fully reflect the coupled heat transfer mechanism of conduction and convection in the actual underground environment. Therefore, this invention can accurately quantify the accelerating effect of groundwater seepage on heat migration and the temperature change along depth caused by the geothermal gradient, thus overcoming the prediction distortion problem caused by traditional pure heat conduction models that neglect these two key factors. This significantly improves the reliability of temperature response calculations under different geological conditions.

[0025] This invention, by setting an initial temperature distribution based on the geothermal gradient and boundary conditions including a finite underground boundary, enables a more realistic simulation of the long-term impact of geothermal heat flow and geological structure on the heat transfer process. Combined with the groundwater seepage effect, this method dynamically reflects the mitigating effect of groundwater flow on the accumulation of hot and cold water around the heat exchanger, thereby accurately assessing the long-term heat transfer performance of buried pipe heat exchangers. This provides a precise basis for optimizing the length and layout of buried pipes, avoiding the risks of conservative design (excessive pipe length) or insufficient performance due to model simplification.

[0026] This invention provides an analytical solution for the temperature variation of underground soil at any location over time. This technical feature eliminates the need for computationally complex numerical discretization methods and the deployment of numerous temperature monitoring devices for long-term monitoring. Engineers can directly input parameters such as soil thermal properties, seepage velocity, and geothermal gradient for calculations, significantly improving computational efficiency, reducing equipment investment and time costs, and providing a powerful tool for engineering design and rapid analysis.

[0027] This invention sets the lower boundary of the underground area as a lower boundary H that is sufficiently far from the bottom of the buried pipe heat exchanger. bound And H bound The length of this method is much greater than that of the buried pipe heat exchanger. This approach avoids the theoretical contradictions caused by the traditional infinite boundary assumption and is more in line with the geological conditions where shallow strata have actual boundaries. At the same time, by clearly defining the buried pipe heat exchanger as a shallow finite-length line heat source model, this method ensures a high degree of fit with the typical application scenario of shallow buried pipe heat exchangers (usually buried at a depth of tens of meters), thereby improving the engineering guidance value of the calculation results. Attached Figure Description

[0028] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0029] Figure 1 This is a schematic diagram of the structure of a buried pipe heat exchanger under the influence of groundwater seepage and geothermal gradient according to an embodiment of the present invention.

[0030] The components are: 1. Downcomer; 2. Ascent pipe; 3. Backfill material; 4. Drill hole; 5. Underground soil. Detailed Implementation

[0031] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0032] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0033] Example 1

[0034] This embodiment provides a method for calculating the temperature response of a buried pipe considering groundwater seepage and geothermal gradient. The buried pipe heat exchanger includes a borehole, a single U-shaped pipe, and backfill material. According to the flow direction of the circulating fluid, the two branches of the U-shaped pipe inside the borehole can be named the downcomer and the riser, respectively. Figure 1 As shown, the borehole contains a downcomer 1, an ascender 2, backfill material 3, a borehole 4, and underground soil 5. In summer, the warmer circulating fluid flows through the two branch pipes of the U-shaped pipe, namely downcomer 1 and ascender 2, transferring heat to these two branch pipes. This heat then travels from the pipes through backfill material 3 to the wall of borehole 4, and from the wall to the surrounding soil. In winter, heat from the surrounding soil is transferred to the wall of borehole 4, and then from the borehole wall through backfill material 3 to the downcomer 1 and ascender 2 of the U-shaped pipe. This heat is then transferred to the circulating fluid, which carries the heat away. Meanwhile, groundwater seeps through borehole 4 containing downcomer 1 and ascender 2. Therefore, the temperature of the surrounding soil is affected by the heat transfer from the borehole-buried pipe heat exchanger and by the convective heat transfer between the groundwater seepage and the buried pipes and soil.

[0035] A method for calculating the temperature response of buried pipes considering groundwater seepage and geothermal gradient, specifically including:

[0036] Step 1: Treat the shallow buried pipe heat exchanger as a finite-length heat source model. When groundwater seeps through the buried pipe heat exchanger, the model is a finite-length heat source seepage model, and a constant wall temperature boundary condition is applied to the surface.

[0037] Furthermore, the groundwater seepage direction in the groundwater seepage convection term is along the x-axis.

[0038] Furthermore, the single U-shaped pipe includes a downcomer and an upcomer, with circulating fluid flowing in through the downcomer and out through the upcomer, and the backfill material filling the space between the U-shaped pipe and the borehole wall.

[0039] Specifically, shallow buried pipe heat exchangers are arranged in the underground medium, which is called a finite-length heat source model. When groundwater seeps through the buried pipe heat exchanger, the model is called a finite-length heat source seepage model. A constant wall temperature condition is usually applied to the boundary of the region, i.e., the surface. This is a two-dimensional transient heat conduction in cylindrical coordinates, and its energy control equation can be mathematically described as follows:

[0040] (1)

[0041] in t 1 represents the temperature value at any point in the underground soil without considering the geothermal gradient. x、y and z The coordinates of the underground soil are in three dimensions, in meters (m). a Thermal diffusivity of soil medium, unit: m 2 / s; t The time for heat transfer, in seconds. u The velocity of groundwater seepage along the x-direction is expressed in m / s.

[0042] The initial conditions for this model are:

[0043] (2)

[0044] in t 0 represents the Earth's surface temperature, in °C.

[0045] The boundary conditions for this model are:

[0046] (3)

[0047] in q l The average heat transfer per unit depth of the buried pipe heat exchanger, in W / m; r is the radial coordinate, i.e. Unit: m; t1 is the temperature value at any point in the underground soil without considering the geothermal gradient, in °C.

[0048] Calculations show that, considering only groundwater seepage and not geothermal gradient, the temperature value at any location in the underground soil can be obtained, i.e., the analytical solution expression of equation (1) is:

[0049] (4)

[0050] in t 1 represents the temperature value at any point in the underground soil without considering the geothermal gradient, in °C. t 0 represents the Earth's surface temperature, in degrees Celsius (°C). q l The average heat transfer per unit depth of the buried pipe heat exchanger is expressed in W / m; x, y, and z are the three-dimensional coordinates of the underground soil, expressed in meters; a is the thermal diffusivity of the soil medium, expressed in meters. 2 / s; τ is the heat transfer time, in seconds; u is the seepage velocity of groundwater along the x-direction, in m / s; h The depth of the buried pipe heat exchanger is given in meters (m); ρc is the specific heat capacity of the underground soil in J / (m³). 3 ·K); k τ' is the thermal conductivity of the underground soil, in W / (m·K); τ' is the integral variable of the heat exchange time of the buried pipe, in s; z' is the integral variable of the depth of the buried pipe, in m.

[0051] Step 2: Considering the influence of the geothermal gradient on the underground temperature field, assume the existence of a uniform and stable geothermal heat flow underground, with the direction of the geothermal heat flow from bottom to top. Set the lower boundary of the underground region as a lower boundary H that is sufficiently far from the bottom of the buried pipe heat exchanger. bound And H bound Much longer than the length of a buried pipe heat exchanger;

[0052] Specifically, this study reveals the influence of geothermal gradients on the subsurface temperature field when subsurface soil and rock are horizontally layered, with each layer exhibiting homogeneous properties. Within the discussed area, there exists a uniform and stable geothermal heat flow. q g Unit: W / m 2 The direction is from bottom to top, therefore there is a geothermal gradient in the depth direction within each layer of rock and soil. When the rock and soil are not subjected to any thermal disturbance for a sufficiently long time, the temperature distribution within the rock and soil can be considered to be in a stable state, at which point the temperature distribution of each layer of the medium... t s ( r，z Satisfies the steady-state heat conduction equation:

[0053] (5).

[0054] Step 3: Establish the energy control equation for the soil and rock surrounding the buried pipe heat exchanger. The energy control equation includes soil thermal conductivity terms, groundwater seepage and convection terms, and geothermal gradient correlation terms.

[0055] Furthermore, the energy control equation is a transient energy control equation, and its mathematical expression includes the soil thermal diffusivity, groundwater seepage velocity, and geothermal gradient.

[0056] Specifically, when groundwater seeps in, and a temperature gradient exists, the lower boundary of the area can be set at... z = H bound >>h, where h is the depth of the buried pipe heat exchanger, H bound Let the lower boundary be sufficiently far from the bottom of the buried pipe heat exchanger. This is to avoid the boundary temperature tending to infinity, which has no substantial impact on solving the temperature distribution problem. z The positive direction of the coordinates is from the surface to the depth. In this case, the boundary condition of the lower boundary of the region can be written as:

[0057] (6)

[0058] in, q g Geothermal heat flow, unit: W / m 2 ; k Let be the thermal conductivity of the underground soil, in W / (m·K). Compared to the unsteady-state problem above, the other two boundary conditions remain unchanged. The boundary conditions at that point are changed to:

[0059] (7)

[0060] If the given surface temperature is t 0. If this temperature is the same as the initial temperature of the soil, then for the problem of a homogeneous medium throughout the region, we have:

[0061] (8)

[0062] in, t 2 represents the temperature at different locations along the depth direction in the soil when there is a geothermal gradient, in °C; q g For geothermal flow, W / m 2 Applying the same approach to the finite-length heat source model, when considering the geothermal gradient, the governing equations and boundary conditions are the same as in the previous problem, except that the lower boundary is moved from infinity to a finite distance sufficiently far from the heat source, where there is a uniform heat flow at the boundary. q g .

[0063] When there is groundwater seepage and the geothermal gradient is considered, the energy control equation is as shown in equation (9):

[0064] (9)

[0065] Step 4: Set the initial conditions and boundary conditions of the energy control equation, wherein the initial conditions are based on the geothermal gradient to determine the initial temperature distribution of the underground soil, and the boundary conditions include the surface constant wall temperature condition and the underground finite boundary condition.

[0066] Furthermore, the initial temperature distribution of the underground soil in the initial conditions is expressed as a linear function of depth based on the geothermal gradient.

[0067] Furthermore, the lower boundary of the underground region in the boundary conditions is set as a lower boundary H that is sufficiently far from the bottom of the buried pipe heat exchanger. bound At the location, and apply a uniform geothermal flow. q g .

[0068] Specifically, the initial conditions for the energy governing equations are:

[0069] (10)

[0070] Where t2 represents the temperature at different locations along the depth direction in the soil when there is a geothermal gradient. For surface temperature, q g For geothermal flow, The thermal conductivity of the soil, The depth of any point below the ground. H bound The lower boundary is a sufficiently far distance from the bottom of the buried pipe heat exchanger.

[0071] The boundary conditions for this model are:

[0072] (11)

[0073] in, H bound The lower boundary is the distance sufficiently far from the bottom of the buried pipe heat exchanger, in meters (m).

[0074] Step 5: Based on the energy control equation, initial conditions, and boundary conditions, obtain the analytical solution expression for the temperature change of the underground soil at any location over time through analytical solution.

[0075] Furthermore, the analytical solution expression is derived based on the finite-length line heat source model and includes the soil volumetric specific heat capacity, the length of the buried pipe heat exchanger, and the groundwater seepage velocity.

[0076] This embodiment directly calculates the temperature value at any three-dimensional coordinate point in the underground soil using analytical expression, without the need for numerical discretization;

[0077] When groundwater seepage and geothermal gradient are taken into account, the temperature value at any location in the underground soil can be obtained. The analytical solution expression for this problem is:

[0078] (12)

[0079] in, t 2 represents the temperature at different locations along the depth direction in the soil when there is a geothermal gradient, in °C; t 0 represents the Earth's surface temperature, in degrees Celsius (°C). x、y and z The coordinates of the underground soil are in three dimensions, in meters (m). a Thermal diffusivity of soil medium, unit: m 2 / s; t The time for heat transfer, in seconds. u The seepage velocity of groundwater along the x-direction, in m / s; q g Geothermal heat flow, unit: W / m 2 ; h The depth of the buried pipe heat exchanger, in meters (m). pc Specific heat capacity of underground soil, unit: J / (m³) 3 ·K); k is the thermal conductivity of the underground soil, unit: W / (m·K); t ’ The integral variable representing the heat exchange time of the buried pipe, in seconds; z ’ The integral variable represents the depth of the buried pipe, in meters (m).

[0080] Therefore, considering groundwater seepage and geothermal gradient, the expression for the temperature response at any point in the soil is shown in equation (13):

[0081] (13)

[0082] in, , is the excess temperature value at any point in the underground soil, in °C; x , y and z τ represents the three-dimensional coordinates of the underground soil, in meters (m), and τ represents the heat transfer time, in seconds (s). t 2 represents the temperature at different locations along the depth direction in the soil when there is a geothermal gradient, in °C; t 0 represents the Earth's surface temperature, in degrees Celsius (°C). a Thermal diffusivity of soil medium, unit: m2 / s; t The time for heat transfer, in seconds. u The seepage velocity of groundwater along the x-direction, in m / s; q g Geothermal heat flow, unit: W / m 2 ; h The depth of the buried pipe heat exchanger, in meters (m). pc Specific heat capacity of underground soil, unit: J / (m³) 3 ·K); k is the thermal conductivity of the underground soil, unit: W / (m·K); t ’ The integral variable representing the heat exchange time of the buried pipe, in seconds; z ’ The integral variable represents the depth of the buried pipe, in meters (m).

[0083] In this embodiment, for a shallow buried pipe heat exchanger, if the initial temperature of the ground is... T If 0, then the initial soil temperature at a certain depth on the ground is no longer considered to be... T 0 instead T s ,Right now T s The initial soil temperature at a certain depth below the ground surface is taken into account, considering the influence of groundwater seepage. Under the combined influence of groundwater seepage and geothermal gradient, the temperature response value at any point in the underground soil can be obtained during the comprehensive heat exchange process between the shallow surface pipe heat exchanger and the underground soil and groundwater.

[0084] Furthermore, the energy control equation, initial conditions, and boundary conditions are all linear, allowing the initial temperature distribution to be superimposed onto the solution at zero initial temperature through the superposition principle, in order to handle variable load effects.

[0085] Specifically, under the condition that the governing equations and all boundary conditions are linear, if the initial temperature distribution satisfies the corresponding boundary conditions, the influence of the initial temperature distribution on the temperature response can be realized by superimposing the initial temperature distribution onto the solution with the corresponding zero initial temperature. Under the same conditions, this conclusion also applies to the superposition of porous temperature fields in space and the superposition of variable loads in time. Therefore, the research results on shallow ground source heat pump heat transfer without considering the geothermal gradient can be easily extended to situations where the influence of the geothermal gradient needs to be considered.

[0086] The beneficial effects of this embodiment:

[0087] This invention eliminates the need for deploying a large number of temperature monitoring elements, reducing equipment investment costs. It also avoids the manpower and time consumption of long-term temperature monitoring, thereby reducing the implementation cost and complexity of temperature response calculation for buried pipe heat exchangers.

[0088] This invention can obtain the specific changes in temperature at any location in the underground soil over time, clearly understand the dynamic changes in the soil temperature field around the shallow buried pipe heat exchanger, and provide accurate temperature data support for the design of buried pipe heat exchangers.

[0089] This invention incorporates the effects of groundwater seepage and geothermal gradient, correcting the misjudgment of heat exchange capacity in different areas (bottom and opening) of boreholes by the traditional pure heat conduction model, improving the accuracy of temperature response prediction for buried pipe heat exchangers, and avoiding design deviations caused by temperature prediction distortion.

[0090] This invention can accurately reflect the promoting effect of groundwater seepage on heat migration, avoid the problem of traditional models underestimating the long-term performance of heat exchangers by ignoring this factor, reduce overly conservative pipe length design, and improve the economy and resource utilization efficiency of ground source heat pump system design.

[0091] This invention provides technical support for the transformation of ground source heat pump systems from the traditional design mode of "rough estimation" to the refined simulation design of "precise and efficient", helping to improve the overall energy efficiency and operational reliability of ground source heat pump systems.

[0092] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for calculating the temperature response of a ground heat exchanger, which takes into account the groundwater seepage and the geothermal gradient, the ground heat exchanger comprising a borehole, a single U-tube and backfill material, characterized in that, The method comprises: The shallow ground heat exchanger is regarded as a finite length line heat source model, and when the underground water seepage passes through the ground heat exchanger, the model is a finite length line heat source seepage model, and a fixed wall temperature boundary condition is adopted for the ground surface; Considering the influence of the geothermal gradient on the underground temperature field, it is assumed that there is a uniform and stable geothermal flow in the underground, the direction of the geothermal flow is from bottom to top, and the lower boundary of the underground area is set as a lower boundary H far away from the bottom of the ground heat exchanger bound , and H bound is greater than the length of the ground heat exchanger; An energy control equation of the rock and soil around the ground heat exchanger is established, and the energy control equation comprises a soil heat conduction term, an underground water seepage convection term and a ground temperature gradient correlation term; The energy control equation is: ； wherein a is the thermal diffusivity of the soil medium, unit: m 2 / s; t2is the temperature of different positions along the depth direction in the soil with the ground temperature gradient, unit: ℃; τ is the time of heat transfer, unit: s; x, y and z are the three-dimensional coordinates of the underground soil, unit: m; r is the radial coordinate, unit: m; H bound is the lower boundary far enough from the bottom of the ground heat exchanger, unit: m; Initial conditions and boundary conditions of the energy control equation are set, wherein the initial conditions determine the initial temperature distribution of the underground soil based on the ground temperature gradient, and the boundary conditions comprise a fixed wall temperature condition of the ground surface and a finite boundary condition of the underground; The initial conditions of the energy control equation are: ； wherein t0 is the ground temperature, unit: ℃; q g is the terrestrial heat flow, unit: W / m 2 ; k is the soil thermal conductivity, W / (m·K); z is the depth of any point below the ground, unit: m; The boundary conditions of the model are: ； wherein q l is the average heat exchange per unit depth of the ground heat exchanger, in W / m; Based on the energy control equation, the initial conditions and the boundary conditions, an analytical solution expression of the temperature at any position of the underground soil changing with time is obtained by analytical solution; The method directly calculates the temperature value at any three-dimensional coordinate point in the underground soil through the analytical solution expression without numerical discretization. The analytical solution expression is: ； Wherein, u is the seepage velocity of groundwater along the x direction, unit: m / s; h is the depth of the ground heat exchanger, unit: m; pc is the volumetric specific heat capacity of the underground soil, unit: J / (m3·K); τ ’ is the integral variable of the ground heat exchanger time, unit: s; z ’ is the integral variable of the ground heat exchanger depth, unit: m.

2. The computational method of claim 1, wherein, The energy control equation is a transient energy control equation, and the mathematical expression comprises a soil heat diffusion coefficient, an underground water seepage velocity and a ground temperature gradient.

3. The computational method of claim 1, wherein, The initial temperature distribution of the underground soil in the initial conditions is expressed as a linear function of the depth based on the ground temperature gradient.

4. The computational method of claim 1, wherein, The lower boundary of the underground region in the boundary condition is set to a lower boundary H far enough from the bottom of the ground heat exchanger bound at the location, and a uniform terrestrial heat flow q is applied g .

5. The computational method of claim 1, wherein, The analytical solution expression is derived based on the finite length line heat source model and comprises a soil volumetric heat capacity, a ground heat exchanger length and an underground water seepage velocity.

6. The computational method of claim 1, wherein, The underground water seepage direction in the underground water seepage convection term is along the x-axis direction.

7. The computational method of claim 1, wherein, The single U-shaped pipe comprises a descending pipe and an ascending pipe, circulating liquid flows into the descending pipe and flows out of the ascending pipe, and the backfill material is filled between the U-shaped pipe and the borehole wall.

8. The computational method of claim 1, wherein, The energy control equation, the initial conditions and the boundary conditions are all linear, and the initial temperature distribution is superimposed on the solution of zero initial temperature by the superposition principle to process variable load action.

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