Buried pipe group heat transfer simulation method considering hydraulic-geological boundary geometry mismatch

Abstract

This invention discloses a method for simulating heat transfer in buried pipe systems considering the geometric mismatch between hydraulic and geological boundaries, belonging to the fields of geotechnical engineering and underground energy storage technology. The method includes: identifying the spatial relationship between the groundwater level interface and the geological stratification interface based on a geometric algorithm; performing discretization processing of sub-layers within each layer to generate a sequence of computational sub-layers with hydraulic attribute labels; determining whether geometric mismatch exists by comparing the depth of the top and bottom plates of each geological layer with the groundwater level depth; constructing a composite analytical calculation model to perform full-time and spatiotemporal coupling solution of the transient heat network inside the borehole and the external heterogeneous moving finite line source field; outputting long-term thermal response prediction results, and optimizing and evaluating the layout of the buried pipe system based on the prediction data. This invention accurately characterizes the complex boundary conditions where the groundwater level and the geological stratification interface do not coincide, and achieves fully coupled calculation of transient heat transfer inside the pipe and non-uniform convection-diffusion heat transfer outside the pipe.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering and underground energy storage technology, specifically relating to a method for simulating heat transfer in buried pipe networks considering the geometric mismatch between hydraulic and geological boundaries. This invention is particularly applicable to long-term thermal performance prediction, heat plume migration analysis, and engineering structural design calculations for vertical buried pipe thermal energy storage systems, ground source heat pump systems, and regional geothermal networks under complex hydrogeological conditions (including multi-layered soil structures, groundwater level fluctuations, and scenarios involving geometric mismatch between aquifers and geological stratification). Background Technology

[0002] Ground source heat pumps and borehole thermal energy storage systems utilize shallow geothermal resources for energy peak shaving, exhibiting high efficiency and energy saving. As a core component of the system, the heat exchange performance of the buried pipe heat exchanger (BHE) directly determines the system's operating efficiency and initial investment cost. Therefore, accurately predicting the thermal response of the BHE under long-term operation is crucial during the design phase. Currently, methods for predicting the thermal performance of buried pipe heat exchangers are mainly divided into two categories: numerical simulation and analytical methods, but both have significant limitations.

[0003] 1. Numerical simulation methods (such as finite element method (FEM) and finite volume method (FVM): While existing technologies (such as simulations based on commercial software like COMSOL and ANSYS) can handle complex physical field couplings, they require extremely high-density mesh generation of the borehole and surrounding soil domain. This results in enormous computational costs and extremely long processing times. When facing full lifecycle simulations lasting decades (e.g., 20-30 years) or multi-parameter optimization designs for large-scale pipe network layouts, the computational cost is too high, making it difficult to meet the timeliness and iterative efficiency requirements of engineering design.

[0004] 2. Traditional analytical methods (such as infinite / finite line source models and column source models): These methods are computationally fast, but their theoretical basis is usually based on the assumption of homogeneous soil. They ignore the differences in thermal properties of strata in the vertical direction (i.e., stratification characteristics), resulting in severely insufficient prediction accuracy under real heterogeneous geological conditions.

[0005] 3. Layered stratigraphic modeling techniques considering groundwater flow:

[0006] To address the impact of groundwater seepage on heat transfer performance, existing technologies have attempted to incorporate moving heat source theory or numerical-analytical coupling methods for correction. For example, related patents (such as CN202310990541.2 and CN202511794575.X) disclose rapid calculation models incorporating groundwater convection terms. These technologies, to some extent, solve the problem of pure thermal conductivity models underestimating the heat transfer capacity of water-rich areas, significantly improving computational efficiency. However, existing methods, represented by the aforementioned technologies, still have the following significant drawbacks when dealing with complex hydrogeological conditions:

[0007] (1) The problem of "geometric mismatch" between hydraulic boundaries and geological stratification remains unresolved. The methods described above typically assume that groundwater is uniformly distributed throughout the computational domain, or implicitly assume that the groundwater level interface and the geological stratification interface completely coincide. In actual engineering, geological stratification (based on lithology) and groundwater level (based on hydraulic state) are often non-coincident, frequently resulting in partial submersion of the same geological layer by groundwater level, with "no water in the upper part (pure thermal conductivity) and water in the lower part (convection + thermal conductivity)". Existing technologies lack a mathematical processing mechanism for "discretization of sublayers within the layer", failing to automatically identify and decouple such discontinuous hydraulic boundaries, leading to significant deviations in the thermal response calculation of borehole sections crossing the water level line.

[0008] (2) The homogenization assumption limits the prediction accuracy. In order to maintain the mathematical closure of analytical or semi-analytical solutions, existing fast algorithms often treat soil as a homogeneous porous medium, ignoring the coupling effect of the differences in thermal properties of different soil layers in the vertical direction and the non-uniform distribution of groundwater.

[0009] (3) Insufficient coupling of internal and external heat transfer mechanisms. When introducing groundwater, existing technologies often simplify the transient thermal processes inside the borehole (such as ignoring the thermal short-circuit effect of the U-tube foot or adopting a steady-state assumption), making it difficult to achieve accurate spatiotemporal coupling between the "in-pipe transient thermal network" and the "out-pipe layered non-uniform convection-diffusion field".

[0010] The root cause of these problems lies in the fact that traditional analytical or semi-analytical models, in pursuit of mathematical simplicity and computational speed, inevitably sacrifice the ability to accurately characterize complex boundary conditions (such as discontinuous water levels and abrupt changes in hydraulic properties within layers). While existing high-precision numerical methods can handle such problems, they lose the computational efficiency required for engineering applications. Therefore, there is an urgent need for a new method that can maintain high computational efficiency while accurately characterizing the "geometric mismatch between hydraulic and geological boundaries." Summary of the Invention

[0011] The purpose of this invention is to overcome the deficiencies in the prior art and to provide a method for simulating heat transfer in buried pipe groups that takes into account the geometric mismatch between hydraulic and geological boundaries.

[0012] The specific technical solution adopted in this invention is as follows:

[0013] This invention provides a method for simulating heat transfer in buried pipe groups considering the geometric mismatch between hydraulic and geological boundaries, as detailed below:

[0014] S1. Obtain the geological and engineering parameters of the target site, and construct the initial geological profile model, borehole structure and layout, and operation plan;

[0015] S2. Using the results obtained in S1, the spatial relationship between the groundwater level interface and the geological stratification interface is identified based on a geometric algorithm. The sub-layers within the layer are discretized to generate a computational sub-layer sequence with hydraulic attribute labels. By comparing the depth of the top and bottom plates of each geological layer with the groundwater level depth, it is determined whether there is a geometric mismatch.

[0016] If it exists, the geological layer that crosses the waterline will be divided into an upper aquifer sublayer and a lower aquifer sublayer, and each sublayer will be assigned an independent equivalent thermophysical property parameter and hydraulic state label; if it does not exist, S3 will be executed directly.

[0017] S3. Construct a composite analytical calculation model to perform full-time and space-time coupling solution of the transient thermal network inside the borehole and the external heterogeneous moving finite line source field; establish the corresponding heat transfer integral equation for each calculation sub-layer generated in S2; at the same time, use the transient thermal network model to calculate the heat exchange between the fluid inside the borehole and the grouting material; through an iterative time step algorithm, couple the internal and external boundary conditions to calculate the evolution process of the borehole wall temperature field and the fluid outlet temperature throughout the entire simulation cycle.

[0018] S4. Based on the evolution process described in S3, output the long-term thermal response prediction results, and optimize and evaluate the layout of the buried pipe system based on the prediction data; evaluate the degree of thermal interference of different borehole layouts under specific groundwater flow direction according to the prediction results, and recommend the optimal design scheme.

[0019] Preferably, in S1, the geological and engineering parameters include layered data, hydrogeological data, structural layout parameters and operating parameters of the buried pipe heat exchanger from the geological survey report; wherein, the layered data includes the thickness and thermal properties of each layer, the hydrogeological data includes the groundwater level, flow velocity and flow direction, the structural layout parameters include well depth, well diameter, well spacing, U-tube pipe foot spacing and backfill material properties, and the operating parameters include fluid flow rate and inlet temperature.

[0020] Preferably, in step S1, the method for constructing the initial geological profile model is as follows:

[0021] S1-1, Based on the original geological profile model, it is assumed that the site contains a total of Horizontal geological layer, first The depth of the top surface of the layer is denoted as The depth of the bottom surface is denoted as Therefore, its thickness is: The set of thermal property parameters of this layer is denoted as ;in, The first The thermal conductivity, specific heat capacity, density, and thermal diffusivity of the layer;

[0022] S1-2, Define the burial depths of the upper and lower surfaces of the groundwater level as follows: and The groundwater seepage velocity vector is ;in, The Darcy velocity is along the x-axis. The Darcy velocity is along the y-axis.

[0023] S1-3, Set the total number of boreholes , No. The center coordinates of each borehole are The borehole radius is The spacing between the U-shaped pins is 2. The mass flow rate and specific heat of the fluid inside the pipe are respectively and The initial ground temperature The inlet and outlet fluid temperatures as a function of time are respectively and .

[0024] Preferably, the specific method for discretization of sub-layers within the layer in S2 is as follows:

[0025] S2-1, Traverse each geological layer , Let's assume that groundwater flows through layer m, and the groundwater is located on the upper surface of a portion of layer m. and lower surface They are respectively , Then, the positional relationship between each geological layer and the groundwater level was determined:

[0026] like If no groundwater flows through this layer, it is marked as an aquifer.

[0027] like If this layer intersects with the groundwater layer, it is re-divided into two independent calculation sub-layers based on the aquifer and aquifer portions; the thickness of the aquifer sub-layer is: The thickness of the waterless sublayer is: ;

[0028] S2-2, Calculate equivalent thermal properties and flow velocity, without water sublayers inheriting geological layers. thermal properties But forced flow rate However, the equivalent thermal properties of the water layer are taken. And assign an equivalent groundwater flow velocity ;

[0029] S2-3. Generate a calculation sequence by arranging all the geological layers and the cut sublayers according to depth from top to bottom, and dividing each layer into segments with equal thickness within the same layer. Each segment has only two possibilities: water or no water. Using segments as calculation units, a sequence containing multiple calculation units is obtained, with each unit having independent thickness, thermal properties, and hydraulic state labels.

[0030] Preferably, in step S3, when establishing the corresponding heat transfer integral equation, the classical finite line source solution is used for the waterless sublayer, and the moving finite line source solution is used for the water-bearing sublayer.

[0031] Preferably, S3 is as follows:

[0032] S3-1. Determine whether the source section is a water-bearing section;

[0033] If it is a water-bearing section, then the flow velocity will be included. And calculate the equivalent thermal properties when groundwater is present. Thermal properties of groundwater ,in, These are the thermal conductivity, specific heat capacity, density, and porosity of groundwater, respectively; if it is a waterless section, then let , ;

[0034] S3-2. When calculating each segment in S2, it is treated as a finite linear heat source with uniform intensity. Simultaneously, before calculation, the geological layers where the source and target segments are located are divided into primary and secondary layers. When calculating the influence of heat source well j on target segment u on target well i, all segments on the heat source well are traversed. If the source and target segments are located in the same layer, then the calculation... If the source segment and the target segment are not located at the same level, then calculate... Then, by superimposing in step S3-3, the influence of all segments in the main layer and the influence of all segments in the secondary layer above the heat source well are obtained respectively. Then, the influence of all wells in the well group on the target segment is superimposed in the same way.

[0035] S3-3, Traversing the well group for the target segment The influence of the main layer superposition results in the well group for:

[0036] ;

[0037] in, refer to All segments located in the main layer of the well Inoue target section The cumulative effect The total number of sections located in the main layer of the well is ; Indicates the influence of the source segment v in the main layer m above well j on the target segment u in the main layer m above well i. The summation symbol represents the target of all other well pairs in the well group. The cumulative effect of wells, with a total number of wells N in the well group;

[0038] Results of secondary stacking in well groups for:

[0039] ;

[0040] in, refer to All segments in the sub-layer of the well are related to the target segment. The combined effects The total number of all segments located in the sub-layer is ; Indicating well group Well pair When considering the well's influence, the influence of the main layer is removed; n refers to the layer number; the second summation symbol represents the superposition of other layers besides the main layer m). This represents the total impact of N wells in the well group.

[0041] Thermal impact of all wells in the well group on the target section for:

[0042] ;

[0043] in, Indicates the initial ground temperature. This indicates the impact of the main stratigraphic portion of all wells in the well group on the target section. This indicates the impact of all sub-layers of the well group on the target section;

[0044] S3-4. Divide the borehole into several discrete nodes along the depth direction. Each node contains a downflow fluid node. Downstream fluid nodes Grouting nodes and hole wall node There are four main thermal nodes. Then, the heat capacity and thermal resistance parameters are calculated in sequence, the thermal balance equation is established, and the explicit Lax-Wendroff time integration method is used for numerical solution to establish the internal transient thermal network.

[0045] S3-5. In long-term simulations, temperature field snapshots are recorded at each time step to generate three-dimensional temperature cloud maps, which are used to track the migration path and morphological evolution of high-temperature zones with the flow of groundwater.

[0046] Furthermore, in S3-1, a virtual heat source is constructed using the mirror method, that is, for each real heat source located at depth... The source segment is located symmetrically above the ground. A mirror source segment is constructed at the target segment, and the influence on the target segment is the superposition of the temperature fields generated by the real source segment and the mirror source segment.

[0047] Furthermore, in S3-4, the numerical solution employs the explicit Lax-Wendroff time integration method, that is, based on the temperature field at the previous time n, the temperature at the next time n+1 is calculated, and the temperature update formula is as follows:

[0048] ;

[0049] ;

[0050] ;

[0051] The initial conditions are:

[0052] ;

[0053] in, Indicates the initial ground temperature. Indicates the temperature of the fluid inside the pipe. The temperature of the grouting material. Refers to the wellbore temperature; at the initial moment, , , , All four are equal; This represents the inflow temperature of the target segment u located in layer m at the next moment, above well i. This indicates the outflow temperature of target segment u located in layer m at the next time step; if the superscript is n, it corresponds to the temperature at the previous time step, and the subscript... and These correspond to the upper and lower segments of segment u in the depth direction, respectively. It is the product of the time step and the flow rate of the fluid in the well. This represents the thickness of a segment within layer m above well i; if segment u is located in a waterless sublayer, then... If segment u is located in an aquifer, then ; , These are the heat capacity of the fluid in the U-shaped pipe inside the well and the heat capacity of the grouting material inside the well, respectively. The thermal resistance between the fluid inside the pipe and the grouting material in layer m. The thermal resistance between the grouting material and the well wall in layer m. The thermal resistance between the circulating fluids in the two pipes of a U-shaped tube.

[0054] Preferably, in S4, the prediction results include the underground temperature field distribution at different times, the migration trajectory of the thermal plume, the outlet fluid temperature curve of the borehole group, and the system energy efficiency ratio.

[0055] Preferably, S4 is as follows:

[0056] S4-1. Calculate the key performance indicators of the system, including the average outlet temperature-time curve of the well group, the maximum temperature change, and the instantaneous heat injection / extraction rate;

[0057] S4-2. Repeat S1-S4, input different borehole arrangement and spacing parameters, and compare the fluctuation range of the average outlet temperature-time curve under a specific groundwater flow direction for different layouts; select the robust layout scheme with the smallest temperature fluctuation and the lowest thermal interference under uncertain or changing groundwater flow direction.

[0058] S4-3. Generate a technical report containing recommended borehole spacing, optimal arrangement direction, and performance degradation curves over the expected system lifespan as the optimal design scheme to guide on-site construction.

[0059] Compared with the prior art, the present invention has the following advantages:

[0060] 1) This invention breaks through the modeling bottleneck under complex hydrogeological conditions and significantly improves prediction accuracy. This invention pioneered the "intra-layer sub-layer discretization" technique, successfully solving the problem of geometric mismatch between the groundwater level and the geological stratification interface. Compared to existing models that assume the water level coincides with the strata, this invention can accurately depict the real physical scenario of "pure heat conduction in the upper part and convective heat transfer in the lower part within the same soil layer."

[0061] 2) This invention employs a composite analytical algorithm to replace traditional numerical simulation methods (such as FEM / FVM). While maintaining an accurate description of complex mechanisms such as stratification, groundwater, and thermal short-circuiting, it significantly reduces the amount of mesh generation and iterative computation. This achieves an order-of-magnitude improvement in computational efficiency while ensuring high accuracy.

[0062] 3) This invention tightly couples the transient thermal network inside the pipe with the heterogeneous convection field outside the pipe through dynamic boundary conditions, realizing the full-time and space-time coupling of the internal and external heat transfer mechanisms and having a stronger ability to capture details.

[0063] 4) This invention provides a scientific basis for layout optimization, improving the long-term robustness of the system. Based on the high-precision prediction of this invention, the degree of thermal interference of any borehole layout under different groundwater flow directions can be quantitatively evaluated. Attached Figure Description

[0064] Figure 1 A schematic diagram showing the relationship between geological strata and groundwater level;

[0065] Figure 2 Here is a flowchart of the algorithm for identifying hydrated / anhydrous sublayers;

[0066] Figure 3 A schematic diagram of the three-dimensional structure of the borehole in multiple strata and its discretized thermal network;

[0067] Figure 4 This is a schematic diagram of multi-well thermal coupling in a layered aquifer.

[0068] Figure 5 This is a comparison chart of the results of the present invention and experimental data under the condition of groundwater seepage in the embodiment. Detailed Implementation

[0069] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in various embodiments of the present invention can be combined accordingly without mutual conflict.

[0070] This invention provides a method for simulating heat transfer in buried pipe groups considering the geometric mismatch between hydraulic and geological boundaries. This method mainly solves the following technical problems existing in the current methods for predicting the performance of buried pipe heat exchangers through numerical thermal simulation:

[0071] 1. The contradiction between computational efficiency and accuracy: Although existing methods (such as FEM / FVM) can handle complex boundaries, the computation time is too long, making it difficult to meet the timeliness requirements of long-term (decades) operation simulation and multi-parameter optimization design of large pipe groups; while existing analytical methods are computationally efficient, they are often based on the assumption of homogeneous soil or full saturation, resulting in serious inadequacy of prediction accuracy under complex hydrogeological conditions.

[0072] 2. Inability to handle the challenge of "geometric mismatch between hydraulic and geological boundaries": Existing analytical models typically implicitly assume that the groundwater level interface and the geological stratification interface completely coincide, lacking a mathematical mechanism for handling partially submerged conditions where "the same geological layer is cut by the groundwater level into a waterless upper part and a water-bearing lower part." This results in existing models being unable to accurately distinguish between purely thermally conductive zones and convection-thermal coupling zones in borehole sections crossing the water level line, leading to significant calculation biases.

[0073] 3. Errors caused by decoupling of internal and external heat transfer mechanisms: When introducing groundwater terms, existing fast algorithms often simplify the transient thermal processes inside the borehole (such as ignoring thermal short-circuit effects), making it difficult to achieve accurate coupling between the transient thermal network inside the pipe and the non-uniform convection field outside the pipe.

[0074] In summary, the core technical problem to be solved by this invention is: how to accurately characterize the complex boundary conditions where the groundwater level and the geological stratification interface do not coincide (geometric mismatch) by using an automated intra-layer sub-layer discretization strategy while maintaining the high computational efficiency of analytical methods, and to achieve fully coupled calculation of transient heat transfer inside the pipe and non-uniform convection-diffusion heat transfer outside the pipe, thereby significantly improving the accuracy of long-term thermal response prediction of buried pipe heat exchangers under complex hydrogeological conditions.

[0075] The method of the present invention will now be described in detail.

[0076] S1. Obtain the geological and engineering parameters of the target site, and construct the initial geological profile model, borehole structure and layout, and operation plan; specifically, this includes collecting layered data (thickness of each layer, thermal properties), hydrogeological data (groundwater level, flow velocity, flow direction) and structural layout parameters (well depth, well diameter, well spacing, U-tube pipe spacing, backfill material properties) and operation parameters (fluid flow rate, inlet temperature) of the buried pipe heat exchanger from the geological survey report.

[0077] As a preferred embodiment of the present invention, the method for inputting and initializing multi-source data in constructing the initial geological profile model is as follows:

[0078] S1-1, Geological Layering Data Structure: Assuming the site contains... Horizontal geological layer, first The depth of the top surface of the layer is denoted as The depth of the bottom surface is denoted as Therefore, its thickness is: The set of thermal property parameters of this layer is denoted as (These are thermal conductivity, specific heat capacity, density, and thermal diffusivity, respectively).

[0079] S1-2, Definition of hydraulic boundary parameters: The burial depths of the upper and lower surfaces of the groundwater level are defined as follows: and The groundwater seepage velocity vector is ,in The Darcy velocity is along the x-axis. The Darcy velocity is along the y-axis.

[0080] S1-3, Drilling and Operating Parameter Initialization: Set the total number of boreholes. , No. The center coordinates of each borehole are The borehole radius is The spacing between the U-shaped pins is 2. The mass flow rate and specific heat of the fluid inside the pipe are respectively and The initial ground temperature The inlet and outlet fluid temperatures as a function of time are as follows: , .

[0081] S2. Based on geometric algorithms, the spatial relationship between the groundwater level interface and the geological stratification interface is automatically identified. The "intra-layer sub-layer discretization" process is performed to generate a sequence of calculated sub-layers with hydraulic property labels. By comparing the depth of the top and bottom plates of each geological layer with the groundwater level depth, it is automatically determined whether there is a "geometric mismatch". If there is, the geological layer that crosses the water level line is cut into "upper waterless sub-layer (pure thermally conductive zone)" and "lower water-bearing sub-layer (convection-thermal coupling zone)" and each sub-layer is assigned independent equivalent thermal property parameters and hydraulic state labels (presence or absence of groundwater). If there is no "geometric mismatch", all layers do not need to be further cut into "water-bearing sub-layers" and "waterless sub-layers", and S3 is executed directly.

[0082] As a preferred embodiment of the present invention, the specific geometric algorithm and attribute allocation method for "intra-layer sub-layer discretization" are as follows:

[0083] S2-1, Geometric Mismatch Detection: Traversing every geological layer Let the above and below surfaces of the layer containing the groundwater be: , ,in Indicates the floor number. and Indicate the upper and lower surfaces to determine the positional relationship between the strata and the groundwater level:

[0084] Scenario A (No water at all): If If no groundwater flows through this layer, it is marked as an "aquifer".

[0085] Scenario B (Geometric Mismatch / Partial Immersion): If If this layer intersects with the groundwater layer, it is re-divided into two independent sub-layers based on its aquifer and aquifer components. The thickness of the aquifer sub-layer is:

[0086] ;

[0087] The thickness of the waterless sublayer is:

[0088] ;

[0089] Figure 1 This demonstrates how the groundwater level (blue dashed line) cuts through geological layers, forming "aquifer sub-layers" and "aquifer sub-layers." Each layer is then segmented (each segment is of equal thickness within the same layer). For Duan Hou, ,or This depends on which sub-layer the segment is located in. Subsequent calculations will be performed on a segment-by-segment basis.

[0090] S2-2, Calculate equivalent thermal properties and flow velocity, without water sublayers inheriting geological layers. thermal properties But forced flow rate And the equivalent thermal properties of the water layer. And assign an equivalent groundwater flow velocity .

[0091] The method for calculating equivalent volumetric heat capacity is as follows:

[0092] ;

[0093] in The density of groundwater, The specific heat capacity of groundwater. for Porosity of the layer.

[0094] The calculation methods for equivalent thermal conductivity and equivalent thermal diffusivity are as follows:

[0095] ;

[0096] ;

[0097] in, The thermal conductivity of groundwater.

[0098] Figure 2 The algorithm logic for automatically determining and dividing sub-layers in this invention is described in detail.

[0099] S2-3. Generate a calculation sequence. Arrange all the geological layers and the cut sublayers according to depth from top to bottom, and divide each layer into segments. The segments within the same layer have equal thickness. As shown in S2-2, each segment has only two possibilities: water presence or waterlessness. Using segments as calculation units, obtain a sequence containing multiple calculation units. Each unit has independent thickness, thermal properties, and hydraulic state labels.

[0100] S3. Construct a composite analytical calculation model to perform full-time and space-time coupling solution of the transient thermal network inside the borehole and the external heterogeneous moving finite line source field. For each calculation sublayer generated in S2, establish the corresponding heat transfer integral equation: use the classical finite line source solution for the waterless sublayer and the moving finite line source solution for the water-bearing sublayer. At the same time, use the transient thermal network model to calculate the heat exchange between the fluid inside the borehole and the grouting material. Through an iterative time-stepping algorithm, couple the internal and external boundary conditions to calculate the evolution of the borehole wall temperature field and the fluid outlet temperature throughout the entire simulation cycle.

[0101] As a preferred embodiment of the present invention, the coupled solution and time-stepping algorithm of the composite analytical model is as follows:

[0102] S3-1. Substitute hydraulic properties and, based on step S2-2 above, determine whether the source section is a water-bearing section:

[0103] If it is a water-bearing section, then the flow velocity will be included. And using the thermal properties of groundwater Calculate the equivalent thermal properties of groundwater (thermal conductivity, specific heat capacity, density, porosity). ; In the subsequent calculation of composite thermophysical properties in S3-2, Equivalent thermal properties are used.

[0104] If it is a waterless section, then let , ,at this time This is the classical finite line source (FLS) solution. In the subsequent calculations of composite thermal properties in S3-2, Equivalent thermal properties are not used. That is, composite thermal properties are not only related to the sections the path passes through, but also need to take into account the groundwater conditions. When water-bearing sections and water-free sections are combined in the path, their respective equivalent thermal properties and original geological thermal properties are used.

[0105] Figure 3 The diagram shows the structure of a borehole in a layered formation, with a two-dimensional thermal network model on the right, used to illustrate the construction method of the transient thermal network model inside the borehole in this invention.

[0106] S3-2. When calculating each segment in S2, it is treated as a finite linear heat source with uniform intensity. Simultaneously, before calculation, the geological layers where the source and target segments are located are divided into primary and secondary layers. When calculating the influence of heat source well j on target segment u on target well i, all segments on the heat source well need to be traversed. If the source and target segments are located in the same layer, then the calculation... If the source segment and the target segment encountered during traversal are not located at the same level, then calculate... Then, through step S3-3, the influence of all segments in the main layer and the influence of all segments in the secondary layer above the heat source well are obtained respectively. Then, the influence of all wells in the well group on the target segment is superimposed in the same way.

[0107] In addition, to meet the surface temperature boundary conditions, this step uses the mirror method to construct a virtual heat source: for each real source segment (located at depth...) ), at a symmetrical position above the surface (depth) Construct a mirror source segment, and the impact on the target segment is the superposition of the temperature fields generated by the real source segment and the mirror source segment.

[0108] (1) For the source segment located in the main layer Its impact on the target segment is as follows:

[0109] ;

[0110] in, ;

[0111] Where the upper and lower limits of integration represent The depth of the upper and lower boundaries of the segment. and for

[0112] ;

[0113] ;

[0114] In the above formula, For runtime, The coordinate vectors representing the two wells ( Its direction is similar to that of groundwater. The direction is irrelevant. and These represent the path lengths from the real source segment and the mirrored source segment to the target segment, respectively.

[0115] ;

[0116] ;

[0117] in It is the center depth of the target segment. It is the depth of the source segment, in the formula. As given in step 2-2.

[0118] In the formula represent The linear heat source intensity (W / m) on the segment is not a pre-set constant in this invention, but a quantity that changes dynamically with time. It can be set to a constant value at the initial moment or in simplified mode.

[0119] ;

[0120] in, and Drilling lie in layer The temperature of the grouting material and the borehole wall at the section, This refers to drilling. The thermal resistance between the grouting material and the wellbore is calculated using steps S3-4. In the precise coupling mode, this value is determined by the transient thermal network model inside the well at each time step. Real-time calculation yields:

[0121] ;

[0122] At this time, the source segment The impact on the target segment is

[0123] ;

[0124] in, For the index of time steps, Indicates the first time step interval The intensity of the linear heat source within the simulation. It should be noted that although the heat flux changes dynamically with time during the overall simulation, in each discrete time element... Within, this invention assumes By keeping the value constant, this piecewise constant approximation method not only ensures the accurate simulation of long-term variable load operation, but also makes the superposition calculation of analytical solutions mathematically possible.

[0125] (2) For the source segment located in the sub-layer Its impact on the target segment is as follows:

[0126] ;

[0127] in, ;

[0128] in and for:

[0129]

[0130] ;

[0131]

[0132] ;

[0133] These represent the impact of the real source segment and the mirrored source segment, respectively. and These represent the path lengths from the real source segment and the mirrored source segment to the target segment, respectively, calculated using the same method. and :

[0134] ;

[0135] ;

[0136] in It is the depth of the source segment.

[0137] For changes over time The calculation method is the same as described in (1):

[0138] ;

[0139] It should be noted that for segments within the sub-layer, the heat propagation path between them and the target segment passes through multiple geological layers; therefore, the thermal property parameters used are all composite parameters. These are the composite thermal conductivity, composite specific heat capacity, composite density, and composite thermal diffusivity, respectively. In this invention, "composite" refers to the composite along the path between the source and target segments. As mentioned in S3-2 above, this path must pass through two or more geological layers; therefore, the composite parameters are used to describe the thermal effects under this multi-layered condition. The composite thermal properties can be calculated using the following formula:

[0140] ;

[0141] ;

[0142] ;

[0143] ;

[0144] in For the segment index on the heat-affected path, This represents the total number of segments traversed by the path. For the first The thermal properties of the segment itself. The path passes through the first... The length of the segment is This length can be calculated using trigonometric functions. For a mirror segment, the path can simply be understood as the path from the mirror source segment to the target segment.

[0145] S3-3, Traversing the well group for the target segment Due to the influence of the main layers, the stacking results in the well group are as follows:

[0146] ;

[0147] in, refer to All segments located in the main layer of the well (assuming a total of (segment) for the target segment The superposition of the effects, the second summation symbol represents the summation of all other well pairs in the well group. The cumulative effect of wells.

[0148] The result of secondary stacking in the well group is:

[0149] ;

[0150] in, refer to All segments located in the sub-layer above the well (assuming a total of (segment) for the target segment The combined effects Indicates all other well pairs in the well group When the well is affected, the influence generated by the main layer is removed.

[0151] In summary, the thermal impact of all wells in the well group on the target section is as follows:

[0152] ;

[0153] in, Indicates the initial ground temperature. This indicates the impact of the main stratigraphic portion of all wells in the well group on the target section. This indicates the impact of all sub-layers of the well group on the target section;

[0154] S3-4, Establishment of the Internal Transient Thermal Network: This invention divides the borehole into several discrete nodes along the depth direction, each node containing four main thermal nodes: downflow fluid nodes. Downstream fluid nodes Grouting nodes and hole wall node A schematic diagram of the node network is shown below. Figure 3 As shown.

[0155] (1) Calculation of heat capacity and thermal resistance parameters:

[0156] In this invention, the heat capacity of the fluid in the U-shaped pipe inside the drilling rig is:

[0157] ;

[0158] The heat capacity of grouting materials used in drilling is:

[0159] ;

[0160] in, , , , These represent the thermal conductivity and thermal diffusivity of the fluid and the thermal conductivity and thermal diffusivity of the grouting material, respectively. It is the radius of the well. and These are the inner and outer diameters of the U-shaped pipe used in drilling.

[0161] In this invention, the thermal resistance between the grouting material and the well wall in S3-1 is:

[0162] ;

[0163] in, Let be the equivalent radius of the grouting material in geometric space. , Determined by the drilling radius and the thermophysical properties of the grouting material: , It is the thermal resistance of the grouting material.

[0164] The thermal resistance between the grouting material and the fluid is:

[0165] ;

[0166] in, The equivalent thermal resistance for drilling is calculated by considering both pipe heat conduction and fluid convection heat transfer.

[0167] ;

[0168] in, and These are the thermal resistance of the pipe and the convection thermal resistance (K·m / W), respectively.

[0169] ;

[0170] ;

[0171] in, The convective heat transfer coefficient inside the pipe is determined by the fluid thermal conductivity. Nusselt number Decide:

[0172] ;

[0173] The thermal resistance between the circulating fluid in the two pipes of the U-shaped tube is:

[0174] ;

[0175] in,{ , , , } is a set of dimensionless geometric and thermophysical parameters used to accurately characterize the heat transfer properties of the U-tube configuration and the grout-soil interface, specifically defined as:

[0176] , , , ;

[0177] (2) Establishment of the heat balance equation:

[0178] ;

[0179] ;

[0180] ;

[0181] The four thermal node temperatures are marked in the index. Corresponding to the target segment in step S3-1 above. geological layers Target well . The velocity of the fluid in the U-shaped tube. and These refer to the inflow within the U-shaped tube at segment u in layer m. ) and outflow ( Fluid temperature.

[0182] (3) Numerical solution method:

[0183] This invention employs the explicit Lax-Wendroff time integration method to solve the aforementioned system of differential equations. This method calculates the temperature at the next time step (n+1) based on the temperature field at the previous time step n (indicated by superscripts in the formula). For drilling... Part 1 (the first) Layer, First (number of nodes), and its temperature update formula is as follows:

[0184] ;

[0185] ;

[0186] ;

[0187] The initial conditions for the above equation are:

[0188] ;

[0189] in, Indicates the initial ground temperature. Indicates the temperature of the fluid inside the pipe. The temperature of the grouting material. This refers to the wellbore temperature; initially, all four are equal. This represents the inflow temperature of the target segment u located in layer m at the next moment, above well i. This indicates the outflow temperature of target segment u located in layer m at the next time step, above well i. If the superscript is n, it corresponds to the temperature at the previous time step, and the subscript... and These correspond to the upper and lower segments of segment u in the depth direction, respectively. It is the product of the time step and the flow rate of the fluid in the well. This represents the thickness of a segment within layer m above well i. If segment u is located in a waterless sublayer, "section" refers to a segment, and if it is located in an aquifer, , , These are the heat capacity of the fluid in the U-shaped pipe inside the well and the heat capacity of the grouting material inside the well, respectively. The thermal resistance between the fluid inside the pipe and the grouting material in layer m. The thermal resistance between the grouting material and the well wall in layer m. The thermal resistance between the circulating fluids in the two pipes of a U-shaped tube.

[0190] In summary, using the transient thermal network method constructed in S3-4 above, the wellbore temperature of the target section can be controlled. As boundary conditions for the external moving finite line source method; simultaneously, the external moving finite line source model constructed in steps S3-1 to S3-3 above and the internal transient thermal network model share the wellbore temperature. As a dynamic boundary condition, at each time step The entire spatiotemporal coupling is completed internally. In particular, thanks to the "computation segment sequence" generated in step S2, key parameters in this invention (such as...) It can dynamically adjust according to the actual distribution of geological and hydrological conditions, thus achieving, for the first time, high-precision and high-efficiency simulation of complex working conditions of "hydraulic-geological boundary geometric adaptation" under the analytical framework.

[0191] Figure 4The study demonstrates the thermal interaction mechanisms of multiple boreholes in formations with groundwater flow, including the concepts of real and virtual boreholes.

[0192] S3-5, Calculation of thermal plume migration and long-term effects: In long-term simulations (e.g., 20-30 years), a snapshot of the temperature field is recorded at each time step. This invention can generate a three-dimensional temperature cloud map to track the migration path and morphological evolution of high-temperature areas (thermal plumes) with the flow of groundwater.

[0193] S4. Output long-term thermal response prediction results and optimize the layout of the buried pipe system based on the prediction data. The output includes the underground temperature field distribution at different times, the migration trajectory of the thermal plume, the outlet fluid temperature curve of the borehole group, and the system energy efficiency ratio; based on the prediction results, evaluate the degree of thermal interference of different borehole layouts under specific groundwater flow directions, and thus recommend the optimal design scheme.

[0194] As a preferred embodiment of the present invention, the optimization evaluation method based on the prediction results is as follows;

[0195] S4-1, Performance Indicator Calculation: Calculate the key performance indicators of the system, including:

[0196] (1) Average outlet temperature-time curve of the well group:

[0197] ;

[0198] in Indicates the first Well in The outlet temperature at that moment, This reflects the system's real-time overall heat exchange capacity;

[0199] (2) Maximum temperature change: Reflects the ultimate working load and heat exchange efficiency decay of any single well or well group under different design parameters (such as well spacing and layout). It is defined as the difference between the highest outlet temperature and the initial ground temperature (or inlet temperature) within a specified operating time;

[0200] (3) Instantaneous heat injection / extraction rate:

[0201] ;

[0202] The heat injection / extraction rate P can reflect the actual power output capability of the system at a specific moment.

[0203] S4-2, Layout Scheme Comparison: Repeat S1-S4, inputting different borehole arrangements (e.g., straight, L-shaped, rectangular, quincunx) and spacing parameters. Compare the fluctuation range of the average outlet temperature-time curves of different layouts under specific groundwater flow directions (e.g., parallel to the long side, perpendicular to the long side); select the robust layout scheme with the least temperature fluctuation and lowest thermal interference under uncertain or changing groundwater flow directions.

[0204] S4-3, Output Design Recommendations: Generate a technical report that includes recommended borehole spacing, optimal alignment direction (relative to the dominant groundwater flow direction), and performance degradation curves over the expected system lifespan to guide on-site construction.

[0205] The performance and effects of the method of the present invention will be specifically illustrated through the following examples.

[0206] Example

[0207] This embodiment uses data from a physical experiment as a benchmark. The experiment involved a 48-hour thermal response test conducted in a 123-meter-deep borehole. The borehole traversed five different soil layers: silt (20m), fine sand (30m), clay (20m), gravel (10m), and mudstone (43m), each with varying thermal conductivity and heat capacity. The groundwater level was at a depth of 15m, and the groundwater flow velocity was 5 × 10⁻⁶ m / s². -7 The flow rate is m / s, and groundwater seepage only occurs below 15m.

[0208] The steps used in this embodiment are as described above and will not be repeated here.

[0209] Specifically, this invention first executes step S1 to acquire geological parameters, drilling parameters, and other data to construct a geological profile model; then, step S2 analyzes the original 5-layer geological model. The analysis reveals that the groundwater level (15m) is located within layer 1 (silt, 0-20m), indicating a "geometric mismatch." Therefore, according to the S2-1 algorithm, layer 1 is automatically divided into two sub-layers: sub-layer 1a: 0-15m, waterless, treated as purely thermally conductive; sub-layer 1b: 15-20m, water-bearing, treated as a convection-conduction coupling layer.

[0210] The final generated sequence contains six computational sub-layers: [1a, 1b, 2, 3, 4, 5]. According to the S3-1 algorithm, each sequence is further segmented to construct internal and external field models for solution. For this borehole, step S3 is executed to construct a composite analytical computational model; for the above six sub-layers, moving finite line source models are constructed respectively. Sub-layers [1b, 2, 3, 4, 5] consider groundwater seepage terms, while sub-layer 1a does not. Dynamic coupling: through sharing borehole wall temperature... As a dynamic boundary condition, the internal and external fields are solved iteratively within each time step to complete the full spatiotemporal coupling.

[0211] After a 48-hour simulation, step S4 was executed, outputting a curve showing the change in borehole outlet fluid temperature over time. The calculated results of this invention were compared with experimental measurements, and the results are as follows: Figure 5 As shown.

[0212] Comparison with experimental data: The outlet fluid temperature curve predicted by this invention is in high agreement with the experimental data, especially in the steady-state stage where they almost overlap. The calculated root mean square error (RMSE) is 0.163 ℃, the mean absolute error (MAE) is 0.003 ℃, and the mean absolute percentage error (MAPE) is only 0.012%, which fully demonstrates that this invention has extremely high prediction accuracy under complex geological conditions.

[0213] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A method for simulating heat transfer in buried pipe groups considering the geometric mismatch between hydraulic and geological boundaries, characterized in that, Specifically as follows: S1. Obtain the geological and engineering parameters of the target site, and construct the initial geological profile model, borehole structure and layout, and operation plan; S2. Using the results obtained in S1, the spatial relationship between the groundwater level interface and the geological stratification interface is identified based on the geometric algorithm. The sub-layer discretization process within the layer is performed to generate a computational sub-layer sequence with hydraulic attribute labels. By comparing the depth of the top and bottom plates of each geological layer with the depth of the groundwater level, it can be determined whether there is a geometric mismatch. If it exists, the geological layer that crosses the waterline will be divided into an upper aquifer sublayer and a lower aquifer sublayer, and each sublayer will be assigned an independent equivalent thermophysical property parameter and hydraulic state label; if it does not exist, S3 will be executed directly. S3. Construct a composite analytical calculation model to perform full-time and space-time coupling solution of the transient thermal network inside the borehole and the external heterogeneous moving finite line source field; establish the corresponding heat transfer integral equation for each calculation sub-layer generated in S2; at the same time, use the transient thermal network model to calculate the heat exchange between the fluid inside the borehole and the grouting material; through an iterative time step algorithm, couple the internal and external boundary conditions to calculate the evolution process of the borehole wall temperature field and the fluid outlet temperature throughout the entire simulation cycle. S4. Based on the evolution process described in S3, output the long-term thermal response prediction results, and optimize and evaluate the layout of the buried pipe system based on the prediction data; evaluate the degree of thermal interference of different borehole layouts under specific groundwater flow direction based on the prediction results, and recommend the optimal design scheme. In S2, the specific method for discretization of sub-layers within a layer is as follows: S2-1, Traverse each geological layer , Let the upper and lower surfaces of the groundwater be denoted as follows: (The text implies that groundwater flows through the layer.) and The groundwater is located in upper surface in the layer and lower surface They are respectively , Based on the original geological profile model, it is assumed that the site contains a total of Horizontal geological layer, first The depth of the top surface of the layer is denoted as The depth of the bottom surface is denoted as Therefore, its thickness is: Then, the positional relationship between each geological layer and the groundwater level was determined: like If no groundwater flows through this layer, it is marked as an aquifer. like If this layer intersects with the groundwater layer, it is re-divided into two independent calculation sub-layers based on the aquifer and aquifer portions; the thickness of the aquifer sub-layer is: The thickness of the waterless sublayer is: ; S2-2, Calculate equivalent thermal properties and flow velocity, without water sublayers inheriting geological layers. thermal properties But forced flow rate However, the equivalent thermal properties of the water layer are taken. And assign an equivalent groundwater flow velocity ;in, The first The thermal conductivity, specific heat capacity, density, and thermal diffusivity of the layer; the groundwater seepage velocity vector is... ; For equivalent volumetric heat capacity, The density of groundwater, The specific heat capacity of groundwater; S2-3. Generate a calculation sequence by arranging all the geological layers and the cut sublayers according to depth from top to bottom, and dividing each layer into segments with equal thickness within the same layer. Each segment has only two possibilities: water or no water. Using segments as calculation units, a sequence containing multiple calculation units is obtained, with each unit having independent thickness, thermal properties, and hydraulic state labels.

2. The method for simulating heat transfer in buried pipe groups considering the geometric mismatch of hydraulic-geological boundaries according to claim 1, characterized in that, In S1, the geological and engineering parameters include the layered data, hydrogeological data, structural layout parameters and operating parameters of the buried pipe heat exchanger in the geological survey report; among them, the layered data includes the thickness and thermal properties of each layer, the hydrogeological data includes the groundwater level, flow velocity and flow direction, the structural layout parameters include the well depth, well diameter, well spacing, U-tube pipe foot spacing and backfill material properties, and the operating parameters include the fluid flow rate and inlet temperature.

3. The method for simulating heat transfer in buried pipe groups considering the geometric mismatch of hydraulic-geological boundaries according to claim 1, characterized in that, In S1, the method for constructing the initial geological profile model is as follows: S1-1, Based on the original geological profile model, it is assumed that the site contains a total of Horizontal geological layer, first The depth of the top surface of the layer is denoted as The depth of the bottom surface is denoted as Therefore, its thickness is: The set of thermal property parameters of this layer is denoted as ;in, The first The thermal conductivity, specific heat capacity, density, and thermal diffusivity of the layer; S1-2, Define the burial depths of the upper and lower surfaces of the groundwater level as follows: and The groundwater seepage velocity vector is ;in, The Darcy velocity is along the x-axis. The Darcy velocity is along the y-axis. S1-3, Set the total number of boreholes , No. The center coordinates of each borehole are The borehole radius is The spacing between the U-shaped pins is 2. The mass flow rate and specific heat of the fluid inside the pipe are respectively and The initial ground temperature The inlet and outlet fluid temperatures as a function of time are respectively and .

4. The method for simulating heat transfer in buried pipe groups considering the geometric mismatch of hydraulic-geological boundaries according to claim 1, characterized in that, In S3, when establishing the corresponding heat transfer integral equation, the classical finite line source solution is used for the waterless sublayer, and the moving finite line source solution is used for the water-bearing sublayer.

5. The method for simulating heat transfer in buried pipe groups considering the geometric mismatch of hydraulic-geological boundaries according to claim 1, characterized in that, S3 is specifically as follows: S3-1. Determine whether the source section is a water-bearing section; If it is a water-bearing section, then the flow velocity will be included. And calculate the equivalent thermal properties when groundwater is present. The thermal properties of groundwater are ,in, These are the thermal conductivity, specific heat capacity, density, and porosity of groundwater, respectively; if it is a waterless section, then let , ; S3-2. When calculating each segment in S2, it is treated as a finite linear heat source with uniform intensity. Simultaneously, before calculation, the geological layers where the source and target segments are located are divided into primary and secondary layers. When calculating the influence of heat source well j on target segment u on target well i, all segments on the heat source well are traversed. If the source and target segments are located in the same layer, then the calculation... If the source segment and the target segment are not located at the same level, then calculate... Then, by superimposing in step S3-3, the influence of all segments in the main layer and the influence of all segments in the secondary layer above the heat source well are obtained respectively. Then, the influence of all wells in the well group on the target segment is superimposed in the same way. S3-3, Traversing the well group for the target segment The influence of the main layer superposition results in the well group for: ； in, refer to All segments located in the main layer of the well Inoue target section The cumulative effect The total number of sections located in the main layer of the well is ; Indicates the influence of the source segment v in the main layer m above well j on the target segment u in the main layer m above well i. The summation symbol represents the target of all other well pairs in the well group. The cumulative effect of wells, with a total number of wells N in the well group; Results of secondary stacking in well groups for: ； in, refer to All segments in the sub-layer of the well are related to the target segment. The combined effects The total number of all segments located in the sub-layer is ; Indicating well group Well pair When considering the well's influence, the influence of the main layer is removed, where n refers to the layer number, and the second summation symbol indicates the superposition of other layers besides the main layer m. This represents the total impact of N wells in the well group; Thermal impact of all wells in the well group on the target section for: ； in, Indicates the initial ground temperature. This indicates the impact of the main stratigraphic portion of all wells in the well group on the target section. This indicates the impact of all sub-layers of the well group on the target section; S3-4. Divide the borehole into several discrete nodes along the depth direction. Each node contains a downflow fluid node. Downstream fluid nodes Grouting nodes and hole wall node There are four main thermal nodes. Then, the heat capacity and thermal resistance parameters are calculated in sequence, the thermal balance equation is established, and the explicit Lax-Wendroff time integration method is used for numerical solution to establish the internal transient thermal network. S3-5. In long-term simulations, temperature field snapshots are recorded at each time step to generate three-dimensional temperature cloud maps, which are used to track the migration path and morphological evolution of high-temperature zones with the flow of groundwater.

6. The method for simulating heat transfer in buried pipe groups considering the geometric mismatch of hydraulic-geological boundaries according to claim 5, characterized in that, In S3-1, a virtual heat source is constructed using the mirror method, that is, for each real heat source located at depth... The source segment is located symmetrically above the ground. A mirror source segment is constructed at the target segment, and the influence on the target segment is the superposition of the temperature fields generated by the real source segment and the mirror source segment.

7. The method for simulating heat transfer in buried pipe groups considering the geometric mismatch of hydraulic-geological boundaries according to claim 5, characterized in that, In S3-4, the numerical solution employs the explicit Lax-Wendroff time integration method, which calculates the temperature at the next time n+1 based on the temperature field at the previous time n. The temperature update formula is as follows: ； ； ； The initial conditions are: ； in, Indicates the initial ground temperature. Indicates the temperature of the fluid inside the pipe. The temperature of the grouting material. Refers to the wellbore temperature; at the initial moment, , , , All four are equal; This represents the inflow temperature of the target segment u located in layer m at the next moment, above well i. This indicates the outflow temperature of target segment u located in layer m at the next time step; if the superscript is n, it corresponds to the temperature at the previous time step, and the subscript... and These correspond to the upper and lower segments of segment u in the depth direction, respectively. It is the product of the time step and the flow rate of the fluid in the well. This represents the thickness of the segment in layer m above well i; if segment u is located in a waterless sublayer, then... If segment u is located in an aquifer, then ; , These are the heat capacity of the fluid in the U-shaped pipe inside the well and the heat capacity of the grouting material inside the well, respectively. The thermal resistance between the fluid inside the pipe and the grouting material in layer m. The thermal resistance between the grouting material and the well wall in layer m. The thermal resistance between the circulating fluid in the two pipes of a U-shaped tube.

8. The method for simulating heat transfer in buried pipe groups considering the geometric mismatch of hydraulic-geological boundaries according to claim 1, characterized in that, In S4, the prediction results include the underground temperature field distribution at different times, the migration trajectory of the thermal plume, the outlet fluid temperature curve of the borehole group, and the system energy efficiency ratio.

9. The method for simulating heat transfer in buried pipe groups considering the geometric mismatch of hydraulic-geological boundaries according to claim 1, characterized in that, S4 is specifically as follows: S4-1. Calculate the key performance indicators of the system, including the average outlet temperature-time curve of the well group, the maximum temperature change, and the instantaneous heat injection / extraction rate; S4-2. Repeat S1-S4, input different borehole arrangement and spacing parameters, and compare the fluctuation range of the average outlet temperature-time curve under a specific groundwater flow direction for different layouts; select the robust layout scheme with the smallest temperature fluctuation and the lowest thermal interference under uncertain or changing groundwater flow direction. S4-3. Generate a technical report containing recommended borehole spacing, optimal arrangement direction, and performance degradation curves over the expected system lifespan as the optimal design scheme to guide on-site construction.

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