Analysis of the Heat Transfer Performance of a Buried Pipe in the Heating Season Based on Field Testing

Abstract

Ground source heat pump (GSHP) systems have been widely used in the field of shallow geothermal heating and cooling because of their high thermal efficiency and environmental friendliness. A borehole heat exchanger (BHE) is the key part of a ground source heat pump system, and its performance and investment cost have a direct and significant impact on the performance and cost of the whole system. The ground temperature gradient, air temperature, seepage flow rate, and injection flow rate affect the heat exchange performance of BHEs, but most of the research on BHEs lacks field test verification. Therefore, this study relied on the results of a field thermal response test (TRT) based on a distributed optical fiber temperature sensor (DOFTS) and site hydrological, geological, and geothermal data to establish a corrected numerical model of buried pipe heat transfer and carry out the heat transfer performance analysis of a buried pipe in the heating season. The results showed that the ground temperature gradient of the test site was about 3.0 °C/100 m, and the temperature of the constant-temperature layer was about 9.17 °C. Increasing the air temperature could improve the heat transfer performance. The temperature of the surrounding rock and soil mass of the single pipe spread uniformly, and the closer it was to the buried pipe, the lower the temperature. When there is groundwater seepage, the seepage carries the cold energy generated by a buried pipe’s heat transfer through heat convection to form a plume zone, which can effectively alleviate the phenomenon of cold accumulation. With an increase in seepage velocity, the heat transfer of the buried pipe increases nonlinearly. The heat transfer performance can be improved by appropriately reducing the temperature and velocity of the injected fluid. Selecting a backfill material with higher thermal conductivity than the ground body can improve the heat transfer performance. These research results can provide support for the optimization of the heat transfer performance of a buried tube heat exchanger.

1. Introduction

The International Energy Agency (IEA) has confirmed that the increase in fossil fuel consumption has led to a significant increase in CO₂ emissions, and fossil fuel consumption (coal, natural gas, and oil) accounts for more than 80% of global CO₂ emissions [1]. All countries worldwide have begun to implement new energy strategies and gradually convert part or all of their energy supply to renewable energy [2]. In the past decade, renewable energy production in both China and the rest of the world has greatly improved. Geothermal energy is the heat generated and stored in the Earth, which has the characteristics of stability, widespread distribution, and huge reserves, and can be exploited all day long [3].

In recent decades, ground source heat pump (GSHP) systems have been widely adopted for shallow geothermal heating and cooling due to their excellent thermal efficiency and environmental benefits [4]. The vertical buried pipe heat exchange system in a GSHP system utilizes a closed-loop mechanism. This system harnesses the heat from shallow rocks and soil to facilitate building heating. It operates by circulating fluid through a closed borehole heat exchanger (BHE), facilitating heat extraction via conduction or convective heat transfer [5]. The BHE constitutes a critical component of a ground source heat pump system, impacting system performance and cost significantly.

Environmental and geological conditions influence the heat transfer efficiency of BHEs. Variations in air temperature can influence surface soil temperatures, significantly affecting BHE performance, particularly in shallow installations [6]. Sofyan [7] introduced a novel approach to account for seasonal soil temperature fluctuations in horizontal geothermal heat exchangers. This method applies an actual energy balance at the surface and conducts a sensitivity analysis using a validated model to examine the impacts of pipe length, fluid flow rate, inlet fluid temperature, and burial depth on the thermal efficiency of horizontal geothermal heat exchangers. Sofyan [8] introduced a novel internal term approach that incorporates heat movement across various strata, employing an explicit finite difference technique to address the governing equation model, illustrating seasonal variations in ground temperature affecting shallow BHE efficiency. Groundwater infiltration enhances BHE thermal performance in most scenarios. Capozza [9] conducted a simulation exploring the quantitative effects of subterranean water flow on heat exchange, assessing its real impact on optimizing heat pump operations. The findings indicated enhanced thermal efficiency and potential BHE length reduction post-infiltration. Wang [10] defined operational parameters for vertical BHE systems in stratified soils, calculating heat transfer rates via theoretical, experimental, and numerical methods. The outcomes underscored the profound influence of groundwater infiltration velocity on vertical BHE heat transfer characteristics.

In practical engineering applications, BHEs typically traverse various geological strata, where the thermal conductivity of each layer impacts their heat transfer efficiency [11]. At present, the thermal conductivity of layered rock and soil masses is primarily determined through thermal response tests (TRTs) or laboratory experiments [12]. The thermal response test (TRT) entails heating delivered by a circulating fluid within pipes, accompanied by uninterrupted temperature monitoring at both the pipe’s entrance and exit throughout the heating period [13]. The distributed thermal response test (DTRT) involves a similar heating process, utilizing a circulating fluid in the pipes, but it escalates the monitoring process by continuously assessing the temperature at various depths along the length of the borehole heat exchanger (BHE) during the heating stage [14]. Jin [15] introduced a heat transfer model that concurrently addresses multi-layered soil and multiple borehole heat exchangers. This model examines how the thermal properties of geological strata affect the overall thermal performance of multiple BHEs. Comparative analyses using an analytical model highlighted significant thermal efficiency disparities between homogeneous and multi-layered soil formations under specific geological structures. The results indicated that heterogeneous multi-layered rock masses exerted considerable influence on thermal efficiency. For a 4 × 4 borehole configuration, an increase in soil thermal diffusivity by 1 × 10⁻⁷ m²/s resulted in a 4% reduction in operational efficiency. Gong [16] employed the finite volume method to establish and validate a heat transfer model for BHEs in stratified soil, incorporating groundwater seepage considerations. Introducing the thermal interaction coefficient (δ) as an evaluation index for inter-borehole thermal interactions, Gong proposed an empirical method to rapidly calculate the total heat transfer rate in stratified soil BHE fields.

Backfill material serves as the medium for heat transfer between a heat exchange pipe and an underground structure, fulfilling the roles of conducting heat, stabilizing boreholes, and protecting the subsurface environment [17]. Its properties affect the heat extraction efficiency of a BHE. Backfill material is usually prepared as a solid medium with pores, which can transfer heat through the heat conduction of solids or groundwater or the heat convection generated by groundwater flowing through the material [18]. Generally, enhancing the thermal conductivity of backfill materials decreases the thermal resistance between the rock, soil mass, and BHE, thereby improving the heat transfer efficiency [19]. Scholars have studied the thermal conductivity [20], mechanical strength [21], and permeability [22] of common backfill materials such as sand and bentonite [23], and they have studied the effects of adding graphite, cement, slag, steel fiber, and other materials to prepare new backfill materials to obtain better thermal and mechanical properties [24,25,26]. However, considering cost control, it is not cost-effective to use materials such as graphite or a large volume of steel fiber in backfill materials [27].

The design of the BHE system itself also has an impact on heat transfer performance and cost [28]. Drilling costs for BHEs are calculated by taking into account the drillability of the rock and soil. Although the deeper the drilling is, the longer the range of heat exchange can be, and the more heat can be exchanged, considering the performance coefficient and cost input, a reasonable length should be designed in combination with the field heat storage conditions [29].

Experimental and numerical simulations are common methods for studying a BHE [30]. Regarding the experimental method, due to the relatively large length and diameter required, it is difficult to perform similar experiments in current laboratory experiments due to the limitations of the test site. Due to the limited monitoring period and high input cost, the in situ thermal response test can only ascertain how fluid temperature evolves during a system’s short-term operation, and it cannot clearly present the evolutionary characteristics and distributional rules of fluid temperature, underground rock, and soil body temperature during the long-term operation of a buried pipe system in the heating season. The traditional thermal response test solely captures temperature data at the inlet and outlet, failing to depict temperature variations along the entire length of a BHE at different depths. Therefore, numerical methods can compensate for these limitations observed in field tests. Numerical techniques predominantly utilize the finite element method (FEM) [31], the finite difference method (FDM) [32], and the finite volume method (FVM) [33], along with other methods [34], using software capable of multi-threading data processing and providing partial differential equation solutions for a large number of elements. Numerical models have been established, including COMSOL Multiphysics, TOUGREACT, FEFLOW, TRYSNS, etc. [35], and the relevant parameters have been analyzed. However, studies based on numerical simulation and analytical solutions lack the verification of actual parameters of temperature evolution or ignore the influence of the geothermal gradient, air temperature conditions, seepage conditions, and temperature changes in the rock and soil mass during heat transfer.

In this study, the finite element numerical simulation method was applied to establish a refined numerical model for heat transfer in buried pipes. This model was developed using field thermal response test results obtained through distributed fiber optic temperature sensing, along with hydrological, geological, and geothermal data from the site. This study examines how the outlet fluid temperature evolution characteristics, velocity, surface temperature fluctuation conditions, seepage velocity, and backfill material properties affect the operation of a heat exchange system. Furthermore, it investigates the heat exchange performance during the buried pipe heating season and analyzes temperature evolution characteristics and thermal disturbances in underground rock and soil masses.

2. Methodology and Materials

2.1. Overview of the Borehole

The research area was located in Changchun, northeast China, and its geographical location is shown in Figure 1. It belonged to the northern temperate zone in the middle latitude of the Northern Hemisphere, with a temperate continental subhumid monsoon climate. According to the climate zone of China, it was a severe region (the coldest monthly average temperature was ≤−10 °C and the daily average temperature was ≤5 °C for more than 145 days per year). The mean yearly temperature in Changchun was 4.5 °C. The temperature changes day by day in the 2022–2023 heating season (from 15 October 2022 to 15 April 2023) are shown in Figure 2. The overall temperature changes were U-shaped, and the average temperature in the heating season was −3.4 °C.

The test hole was located in the northeastern open space of a factory park, and the heating target was the workshop. Based on preliminary drilling data, the strata within 130 m of the test hole could generally be divided into four layers: from 0 to 20 m was a silty clay layer, from 20 to 78 m was a mudstone layer, from 78 to 94 m was a muddy siltstone layer, and from 94 to 130 m was a silty mudstone layer. The groundwater level during the exploration was recorded at a depth of 5.5 m.

2.2. Field Test

The thermal conductivity of the test site was determined through a field test using an improved combined thermal response test system (ICTRTS), as illustrated in Figure 3a. This system comprised TRT and DTRT modules (Figure 3a), with the TRT module divided into two distinct units: a temperature measurement and control chassis and a heating and cycling chassis (Figure 3e). The temperature testing component of the TRT module measured the water inlet and outlet temperatures of the borehole heat exchanger. The DTRT module included a distributed optical fiber temperature sensor (DOFTS) and a host for distributed optical fiber temperature measurement (Figure 3f). To secure the optical fiber during backfilling and testing, it was affixed to the U-shaped pipe wall using a high-temperature-resistant ribbon every 0.2 m (Figure 3b). The temperature-sensing optical fiber spanned the entire length of the U-shaped tube (260 m) (Figure 3a), with a diameter of 62.5 μm, featuring a protective metal armor layer to prevent underground breakage and an outer coating of polyvinyl chloride and acrylic acid (Figure 3d). The integrated optical fiber sensor had a diameter of 3 mm.

Additionally, to safeguard against optical fiber damage at the bottom bend of the U-shaped tube, we utilized a high-temperature and abrasion-resistant hose for wrapping (Figure 3c). The fiber positioning accuracy was 1 m, with a temperature accuracy of 0.1 °C. Temperature probes and recorders were connected separately using two sets of temperature cables shielded by metal hoses. Real-time temperature data from the 130 m segment were transmitted to the temperature measurement host for display and storage. Optical fibers offer several advantages over high-accuracy thermocouples or RTDs. This setup facilitated the establishment of a geothermal profile that captured temporal variations in thermal conductivity. It provided a detailed view of how the heat transfer capacity varied across different geological layers, offering valuable insights into their thermal characteristics.

Utilizing optical time domain reflection technology, a distributed temperature measurement fiber determined spatial positioning, while temperature measurement relied on the Raman scattering temperature sensing principle [36]. During on-site testing, an electric heater applied a thermal load, with the supply voltage’s maximum uncertainty at ±3%. The flow rate of the circulating fluid in a closed loop was measured via an ultrasonic flowmeter, with a maximum measurement uncertainty of ±1%. The TRT module’s temperature probe monitored the temperature of imported and exported fluids, with a maximum uncertainty of ±0.05%. Underground, real-time monitoring of temperature at various depths utilized distributed fiber optic temperature sensors, ensuring a measurement accuracy of ±1 °C and a maximum uncertainty of ±0.5%. The distributed optical fiber achieved a positioning accuracy of ±1 m, with a maximum uncertainty of ±0.4%. Applying error propagation theory, the on-site testing analyzed the uncertainty of thermal conductivity, calculating it as ±3.2% using Equation (1).

$$\mathrm{U}\left({\lambda }_{\mathrm{s}}\right)=\pm {\left\{\left[{\left[{\displaystyle \frac{\partial {\lambda }_{\mathrm{s}}}{\partial Q}}\mathrm{U}\left(Q\right)\right]}^2+{\left[{\displaystyle \frac{\partial {\lambda }_{\mathrm{s}}}{\partial ACV}}\mathrm{U}\left(ACV\right)\right]}^2+{\left[{\displaystyle \frac{\partial {\lambda }_{\mathrm{s}}}{\partial T_{\mathrm{i}\mathrm{n}}}}\mathrm{U}\left(T_{\mathrm{i}\mathrm{n}}\right)\right]}^2+{\left[{\displaystyle \frac{\partial {\lambda }_{\mathrm{s}}}{\partial T_{\mathrm{o}\mathrm{u}\mathrm{t}}}}\mathrm{U}\left(T_{\mathrm{o}\mathrm{u}\mathrm{t}}\right)\right]}^2+{\left[{\displaystyle \frac{\partial {\lambda }_{\mathrm{s}}}{\partial T_{\mathrm{d}\mathrm{t}\mathrm{s}}}}\mathrm{U}\left(T_{\mathrm{d}\mathrm{t}\mathrm{s}}\right)\right]}^2+\left[{\displaystyle \frac{\partial {\lambda }_{\mathrm{s}}}{\partial L}}\mathrm{U}\left(L\right)\right]\right]\right\}}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$$

(1)

First, the initial formation temperature was measured. Following instrument installation completion, the temperature optical fiber was secured on the U-shaped tube’s wall and buried alongside it in the borehole. After the U-shaped pipe was drilled and backfilled, it was filled with water in advance after the water pressure test, and we waited for more than 48 h according to the relevant technical requirements [37]. Then, the initial formation temperature when the testing system was not running was reached, at which point an equilibrium state was reached between the formation temperature and the fluid temperature inside the U-shaped tube. We measured the temperature of the rock and soil at various depths using distributed temperature measurement optical fibers. Next, a thermal response test was conducted by applying a heating load to the circulating water in the water tank. After measuring the initial ground temperature, two 48 h constant-heat-flow tests were conducted. The water in the water tank was heated by an electric heater with heat loads of 12 and 8 kW. During the tests, the heat load applied by the electric heater component and the fluid flow maintained by the circulation pump remained basically constant (within a fluctuation range of ±5%). The TRT module recorded the inlet and outlet temperature evolution data and flow rates of the circulating fluid within the pipeline, while the DTRT module logged temperature changes at different depths. Testing continued until the daily temperature change in the inlet and outlet fluid was less than 0.5 °C, signifying a stable state, warranting further testing and observation.

2.3. Numerical Method

This study employed COMSOL Multiphysics 6.0 software for simulation, a versatile tool utilizing the finite element method, to analyze diverse physical phenomena like electromagnetic fields, structural mechanics, fluid dynamics, and heat conduction [38]. This software is widely applied across the energy, environment, biology, and materials science domains [39]. For the purpose of simulating buried pipe heat transfer, this study utilized modules for heat transfer in porous media (Figure 4a) and non-isothermal pipe flow (Figure 4b). This simulation was based on heat conduction and convective heat transfer models, considering heat transfer and seepage in underground rock and soil, fluid flow and heat transfer in pipelines, and the water thermal coupling simulation of heat transfer between the rock, soil, and pipelines. Custom boundary and initial conditions were set to enhance the accuracy of the buried pipe heat transfer simulation.

Due to the complexity of the actual heat transfer process of buried pipes, certain assumptions were necessary in the numerical model analysis: the pipeline flow model simplified the circulating fluid and pipe wall within a smaller-diameter U-shaped pipe into a one-dimensional heat exchange tube. This tube was processed as a linear grid element and simulated flow and convective heat transfer inside the pipe, along with heat conduction through the pipe wall, employing flow and heat transfer coupling. The heat transfer fluid was assumed to be incompressible and to flow entirely within the tube without loss. All circulating fluids were assumed to be single-phase flows. The U-shaped buried pipe and the surrounding rock and soil layer were treated as homogeneous materials within the same layer. Materials within each layer were assumed to be in close contact, with negligible contact thermal resistance. Heat conduction within the formation was assumed to primarily occur radially. Consequently, the governing equations encompassed equations pertinent to the pipeline fluid, backfill materials, and rock and soil masses, detailed as follows.

The heat balance equation of the fluid in the pipe is the following [40]:

$$\rho A{C}_p{\displaystyle \frac{\partial T}{\partial t}}+\rho A{C}_p{\mathrm{u}}_{et}\cdot {\nabla }_{t}T={\nabla }_t\cdot (A\lambda {\nabla }_{t}T)+{\displaystyle \frac{1}{2}}{f}_D{\displaystyle \frac{\rho A}{2d_h}}|u|u^2+Q_p+Q_{wall}$$

(2)

In this context, ρ denotes the density of the working fluid in kg/m³. The cross-sectional area of the pipeline is represented by A in m². C_p signifies the heat capacity of the fluid, measured in J/(kg∙K). T refers to the temperature of the working fluid in Kelvin (K). The variable t indicates time, in seconds (s). The tangential velocity of the circulating fluid is denoted as u_et, measured in m/s. λ represents the thermal conductivity of the fluid, given in W/(m∙K). The Darcy friction coefficient is represented by f_D. The mean velocity of the fluid is symbolized as u, in m/s. Q_p denotes the heat source or sink within the pipe, in W/m; since this particular pipe lacked an additional heat source, Q_p was set to 0. Finally, Q_wall indicates the heat transferred through the tube wall, also measured in W/m.

The calculation equation for the cross-sectional area of a pipeline is

$$A={\displaystyle \frac{\pi }{4}}{d}_i^2$$

(3)

where d_i is the pipe’s inner diameter, m.

The righthand side of Equation (2) describes the pressure drop caused by internal viscous shear, which includes the Darcy friction factor f_D [41], the calculation equation of which is

$$f_D=8[{\left({\displaystyle \frac{8}{R_e}}\right)}^{12}+{\left(C_A+C_B\right)}^{-1.5}{]}^{{\displaystyle \frac{1}{12}}}$$

(4)

In Equation (4),

$$R_e={\displaystyle \frac{\rho \mathrm{u}{d}_i}{\mu }}$$

(5)

$$C_A={\left[-2.457\mathrm{l}\mathrm{n}({\left({\displaystyle \frac{7}{R_e}}\right)}^{0.9}+0.27\left({\displaystyle \frac{e}{d_i}}\right))\right]}^{16}$$

(6)

$$C_B={\left({\displaystyle \frac{\mathrm{37,530}}{R_e}}\right)}^{16}$$

(7)

where R_e is the Reynolds number and e is the surface roughness.

In Equation (2), the calculation equation for the heat transfer of fluid through the pipe wall is [42]

$$Q_{wall}=\left(hZ{)}_{eff}\right(T_{ext}-T)$$

(8)

$$Z=\pi d_i$$

(9)

The effective total thermal resistance of the pipe wall, denoted as (hZ)_eff and measured in W/(m·K), encompasses the thermal resistance contributions from both the pipe itself and the convection layers of its inner and outer walls [43]. The heat transfer coefficient, represented as h and measured in W/(m²∙K), is a key factor in this calculation. Additionally, Z indicates the wetted perimeter of the pipe in meters, and T_ext refers to the exterior temperature outside the pipe in Kelvin.

The following equation [40] describes the heat transfer within porous water-bearing formations:

$$Q_f+Q_{geo}={\left(\begin{array}{c}\rho C_p\end{array}\right)}_{eq}{\displaystyle \frac{\partial T_f}{\partial t}}+\rho C_{p}v\cdot \nabla T_f-\nabla \cdot \left(\begin{array}{c}{\lambda }_{eq}\nabla T_f\end{array}\right)$$

(10)

In the context of geothermal studies, Q_f denotes the thermal source or sink within a geological formation, measured in W/m. Similarly, Q_geo represents the specific geothermal heating function applied to the heat transfer interface within a porous medium, also in W/m. For the purposes of this investigation, no additional heat sources, sinks, or distinct geothermal heating were present in the ground, leading to Q_f and Q_geo being assigned values of zero. The equivalent volumetric heat capacity is denoted by (ρC_p)_eq, with units of J/(m³·K). The groundwater flow rate is indicated by v, measured in m/s, while ∇T_f represents the temperature increment within the formation, in K. Lastly, λ_eq signifies the equivalent thermal conductivity, expressed in W/(m·K).

Using the volume averaging method, the volumetric specific heat of the heat transfer equation in the formation is [44]

$${\left(\begin{array}{c}\rho C_p\end{array}\right)}_{eq}=\sum _i \left({\theta }_i{\rho }_i{C}_{pi}\right)+(1-\sum _i {\theta }_i){\rho }_s{C}_{ps}$$

(11)

In this context, θ_i represents the volume ratio of the ith non-solid within the formation, while ρ_i denotes the density of the ith non-solid material, expressed in kg/m³. Additionally, C_pi refers to the specific heat capacity of the ith non-solid material, measured in J/(kg·K). On the other hand, ρ_s signifies the density of the solid, also in kg/m³, and C_ps indicates the specific heat capacity of the solid, given in J/(kg·K).

The description of equivalent thermal conductivity is the following:

$${\lambda }_{eq}=\sum _i {\theta }_i{\lambda }_i+(1-\sum _i {\theta }_i){\lambda }_{\mathrm{s}}$$

(12)

In this context, λ_i refers to the thermal conductivity of the ith non-solid material, measured in W/(m·K), while λ_s represents the thermal conductivity of the solid, also in W/(m·K).

The equation governing mass conservation for a subterranean hot water system is expressed as the following [45]:

$${\displaystyle \frac{\partial }{\partial t}}\left({\rho }_w\phi \right)+\nabla \cdot \left({\rho }_{w}v\right)={\rho }_q{q}_s$$

(13)

In this context, t represents time in seconds (s), ρ_w indicates the density of groundwater, measured in kg/m³, ϕ denotes the effective porosity, which is dimensionless, v refers to the groundwater flow velocity, given in m/s, ρ_q signifies the density of the source or sink, also in kg/m³, and q_s represents the source or sink term, with units of 1/s.

Darcy’s law describes various permeable flow conditions as the following:

$$v=-{\displaystyle \frac{k\rho g}{\mu }}\nabla H$$

(14)

In this context, k denotes permeability, measured in m², g represents gravitational acceleration, expressed in m/s², µ refers to the dynamic viscosity of groundwater, with units of Pa·s, and H signifies the hydraulic head, given in meters (m).

In the buried pipe heat transfer model, the U-shaped buried pipe heat exchanger (pipe wall and pipe fluid) was generalized into a pipe composed of one-dimensional linear elements, and the backfill material and underground rock and soil body were generalized into a porous medium composed of three-dimensional triangular prism elements, as shown in Figure 5. According to the depth of the LY01 test hole and the length of the U-shaped buried tube heat exchanger used (130 m), the model was generalized to 140 m (depth) × 20 m (radius). The shape, size, and compositional attribute parameters of the U-shaped heat exchanger were consistent with the actual tubes used in field tests, as shown in

Table 1. Parameters of the vertical buried pipe heat transfer model.

Parameter	Value
Vertical depth (m)	140
Thermal conductivity of backfill material (W/(m∙K))	1.2
Thermal conductivity of wall (W/(m∙K))	0.42
Hole diameter (mm)	150
Outer diameter of buried pipe (mm)	32
Inside diameter of buried pipe (mm)	26
Wall thickness (mm)	6
Inlet and outlet pipe spacing (mm)	90

. The average thermal physical property parameters of each layer obtained from the field thermal response test and the basic physical parameters obtained from the laboratory experiment of the drilled rock and soil body core were taken as the basic parameters of the model calculation. In order to improve the reliability and calculation accuracy of the numerical model, the grid of the ground heat exchanger and the stratum around the test hole, which had the most complicated heat transfer process and the highest precision demand, was more finely divided.

The simulation employed formation parameters consistent with the thermal response test conducted in the field. The subsurface down to 140 m comprised layers of silty clay, mudstone, muddy siltstone, and silty mudstone arranged sequentially from top to bottom.

The distribution of ground temperature in the rock and soil mass at a depth of 140 m in the model was derived from field test results (Figure 5). A temperature gradient of 3 °C per 100 m was established, and the constant-temperature layer was set at 9.2 °C (Section 3.1). The flow rate of water in the pipe was 0.68 m/s, which was consistent with the field test, and the flow pattern was turbulent with a Re of 73,886.56. The lithology, density, and pore ratio of each stratified layer of rock and soil were consistent with the parameters obtained from field core measurements. The observed groundwater level was 5.5 m. Based on engineering experience, the permeability coefficient for the clay layer in Changchun ranged from 0.2 to 0.4 m/d, while for the sandstone layer, it was between 1.5 and 3.8 m/d [46]. Groundwater flow was included in the calculation, with the silty clay layer’s permeability coefficient set at 0.3 m/d and that of the silty siltstone layer set at 3 m/d, and the hydraulic gradient was set at 0.1. The model boundary adopted a hot open boundary, and the external temperature conformed to the measured ground temperature gradient, which belonged to the Dirichlet boundary condition. The top temperature adopted the average daily temperature during the heating season in the study area, and the bottom temperature was 11.55 °C. The initial temperature condition of the geometric body was consistent with the measured temperature of the formation.

3. Results and Discussion

3.1. Results of the Field Test

3.1.1. Initial Formation Temperature Distribution

Without heating or water circulation, the temperature measurement data from the DTRT module and the changes in the temperature field from shallow to deep indicated that the lower interior temperature field within 130 m could be categorized into three layers, namely A, B, and C, representing the variable-temperature stratum, the constant-temperature stratum, and the warming stratum, respectively, as illustrated in Figure 6. This process occurs without water circulation, thus excluding additional heat from friction or pump operation. The variable-temperature layer spans from 0 to 25 m, where ground temperatures fluctuated significantly across seasons and locations, influenced by factors like solar radiation, climatic conditions, and surface cover. The constant-temperature stratum extended from 25 to 50 m, maintaining a stable temperature of approximately 9.17 °C, with minimal annual variation. In this layer, a balance was achieved between the Earth’s internal heat conduction and the release of solar radiant heat at the surface. The depth and temperature stability of the constant-temperature layer were primarily influenced by regional geological structures and geotechnical properties, with mudstone being the predominant lithology in the study area, the properties of which were relatively stable. The warming stratum, ranging from 50 to 130 m, exhibited a geothermal gradient of about 3.0 °C/100 m. This section mainly consisted of mudstone and silty mudstone, along with approximately 16 m of argillaceous siltstone. The temperature increase in this stratum was mainly due to heat conduction from the Earth’s interior. Excluding the variable-temperature layer, which was significantly influenced by ambient air temperature and environmental factors, temperature data obtained from distributed temperature optical fiber were used for the calculations. The average formation temperature within the 130 m research depth was determined to be 10.0 °C.

3.1.2. Thermal Conductivity

Figure 7 depicts the evolutionary curve of the inlet and outlet temperatures over time under thermal load conditions. It shows that the temperature of the fluid at the inlet and outlet of the buried pipe increased gradually and stabilized as time progressed. This occurred because the surrounding rock and soil absorbed heat from the buried pipe, causing a temperature rise during the heating operation. Once the heat transfer between the buried pipe and the surrounding geological materials, along with the heat diffusion into these materials, reached an equilibrium, the temperatures at the inlet and outlet stabilized. Using the linear heat source method and plotting the logarithm of temperature against time, the comprehensive thermal conductivity of the rock and soil within the drilled area under thermal load was determined to be 1.859 W/(m∙K). Data on temperature changes over 48 h, recorded by the DTRT module across the entire depth of 130 m under 8 kW heat power, were analyzed, taking into account the weighting coefficient of each section’s thickness. The thermal conductivities of different stratified layers—silty clay, mudstone, muddy siltstone, and silty mudstone—were measured at 1.631 W/(m∙K), 1.888 W/(m∙K), 1.862 W/(m∙K), and 2.144 W/(m∙K), respectively, as illustrated in Figure 8.

3.2. Model Verification

When designing a numerical model, the importance of different parts should be distinguished, and the appropriate grid division strategy should be selected on the premise of ensuring calculation accuracy. According to the key parts and key nodes in the model, the mesh should be refined to improve calculation accuracy. For other areas, rough mesh partitioning can be selected appropriately. In order to ensure the accuracy of the calculation, grid refinement was carried out based on the Grid Convergence Index method (GCI) [47].

The mesh encryption rate φ_i is defined as the following:

$${\phi }_i={\displaystyle \frac{M_{i+1}}{M_i}}, M_{i+1}>M_i$$

(15)

where M_i is the number of grids of the ith model.

The model computation time ratio Φ_i is defined as the following:

$${\Phi }_i={\displaystyle \frac{t_{i+1}}{t_i}}, t_{i+1}>t_i$$

(16)

where t_i is the time consumed to calculate the ith model.

The relative error δ_r of the numerical model is defined by the gap between the numerical results and the test results to reflect the reliability of the numerical calculation results:

$${\delta }_r={\displaystyle \frac{\left|T_{\mathrm{f}}-\right.\left.T_{\mathrm{s}}\right|}{T_{\mathrm{f}}}}$$

(17)

where T_f and T_s are the fluid temperature values in the field test and numerical model results, respectively.

Figure 9 illustrates the relationship between the calculation time ratio and the relative error at various mesh refinement rates. It can be seen that as the number of numerical model grids increased, the computation time also increased, and at the same time, the requirements for the computer CPU performance also increased. In the heat transfer process, especially around heat exchangers and boreholes, the relative error can be reduced by increasing the number of model grids. Although the relative error does not disappear, this degree of error is acceptable in practical engineering applications. Therefore, considering the balance between error control and computational efficiency, the M3 encryption rate of numerical calculation can improve computational accuracy and control computational complexity to a certain extent.

To compare the numerical simulation with the field test results, the model was set with a heating power of 12 kW and an initial circulating fluid temperature of 10.1 °C, matching the thermal response test conditions. The simulation of the thermal response test was conducted for 48 h to analyze the dynamic evolution of fluid temperature within the buried tube, as depicted in Figure 10. The results showed that the trend in the numerical calculations aligned closely with the field test observations of the inlet and outlet temperature changes. In the first 8 h, however, the inlet and outlet temperatures in the numerical model were slightly elevated compared to the on-site test results. This difference arose because the numerical model employed idealized assumptions regarding heat transfer, leading to faster coupling of heat transfer between the idealized one-dimensional pipeline flow and the porous media than observed in the on-site test. As the simulation progressed, the numerical results increasingly aligned with the field test outcomes, indicating that the initial difference in temperature rise had minimal impact on the long-term performance of the numerical model.

3.3. Numerical Simulation Result

When the workshop in the study area was heated by the buried pipe heat exchange system, the system operation time was set to be half a year (from 15 October to 15 April). The temperature of the inlet fluid was equal to the outlet water temperature of the evaporator of the ground source heat pump unit during the operation of the actual buried pipe heat exchange system. Therefore, the inlet fluid temperature was set at a constant 5 °C in the simulation calculation, and the other initial conditions were consistent with the simulated field thermal response test. In order to more obviously compare the influence of different conditions on the heat exchange performance, the heat exchange of the heat exchanger was introduced as a parameter to measure the result:

$$q=c_{\mathrm{p}}\cdot \rho \cdot \pi \cdot r^2\cdot \mu \cdot (T_{\mathrm{i}\mathrm{n}}-T_{\mathrm{o}\mathrm{u}\mathrm{t}})$$

(18)

where q is the heat exchange of the buried pipe, W, C_p is the specific heat capacity of the fluid in the tube, J/(kg∙°C), ρ is the fluid density in the pipe, kg/m³, r is the inner diameter of the buried pipe, m, μ is the fluid injection velocity in the buried tube, m/s, T_in is the fluid temperature at the inlet of the buried pipe end, °C, and T_out is the fluid temperature at the outlet of the buried pipe end, °C.

In this study, both field tests and numerical models used water as the circulating fluid, C_p = 4200 J/(kg∙°C), ρ = 1000 kg/m³.

3.3.1. The Influence of Surface Temperature Fluctuation

The dynamic evolution process of the fluid temperature at the outlet of the buried pipe during the heating season is shown in Figure 11, where temperature conditions A (average annual temperature of 4.5 °C), B (average heating season temperature of −3.4 °C), and C (average daily temperature during the heating season operation period) were applied to the surface of the model. The outlet fluid temperature decreased under all three conditions. Under the A and B conditions, this decline was relatively smooth, whereas, with the C condition, the outlet temperature showed a more variable downward trend. This fluctuation indicates that daily temperature variations affected the heat transfer performance of the buried pipe. The outlet fluid temperature under the A condition was higher than that under the B condition, suggesting that increased temperatures rose the rock mass temperature in the variable-temperature layer, enhancing the buried pipe’s heat transfer efficiency. Taking the 10th–30th-day operation period as an example, on the 12th day of operation, when the temperature was higher than the average annual temperature, the outlet fluid temperature was also higher than the outlet fluid temperature under the A condition; when the temperature was lower than the average temperature of the heating season on the 30th day of operation, the outlet fluid temperature was also lower than the outlet fluid temperature under the B condition. This correlation shows that outlet fluid temperature fluctuations were positively correlated with daily temperature changes, affecting the long-term heat transfer capacity of the buried pipes. We selected the 108th and 174th days with significant temperature differences from the average temperature conditions to compare the heat transfer of the system under three different temperature conditions, as shown in Figure 12. On the 108th day, the heat transfer of the heat exchanger was 61 W less than that under the A condition, while on the 174th day, the heat transfer of the heat exchanger was 31 W more than that under the B condition. In this study area, the depth of the buried pipe was great and the thickness of the variable zone was minimal, so the influence of temperature change on the outlet fluid temperature and heat transfer was relatively small. However, for systems with shallow vertical buried pipes, temperature fluctuations can significantly impact performance. Therefore, an increase in temperature can enhance a heat exchanger’s performance, and temperature variations should be considered when simulating the long-term heat exchange performance of buried pipes. The operational mode of a buried pipe system should be dynamically adjusted according to temperature changes.

3.3.2. The Influence of Groundwater Seepage

Figure 13 illustrates the evolution of the fluid temperature at the outlet of the buried pipe over a 180-day heating season, considering both scenarios with and without seepage in the rock and soil body under daily temperature fluctuations. It is evident that the outlet fluid temperature of the heat exchanger was higher than the inlet temperature in both cases, indicating that the fluid gained heat from the surrounding rock and soil during the operation of the buried pipe heat exchanger. The outlet fluid temperature was higher when seepage was present. As depicted in Figure 14, on the 180th day of operation, the heat exchange capacity of the buried pipe with seepage was approximately 2623 W, significantly greater than the 1198 W observed without seepage, representing an increase of about 118.9%. This is because when there was no seepage, the buried pipe heat exchanger was mainly heated by the surrounding rock and soil through heat conduction. When considering seepage conditions, the heat exchanger was also heated by the surrounding rock and soil through the heat convection generated by groundwater seepage, which enhanced the heat transfer capacity of the buried pipe.

The temperature distribution in the vertical cross-section of the rock and soil surrounding the buried pipe is depicted in Figure 15 and Figure 16, respectively, for the 10th, 30th, 60th, and 180th days of system operation under conditions with and without seepage, as well as with daily temperature fluctuations. It was observed that, under both conditions (non-seepage and seepage), the temperature of the rock and soil surrounding the buried pipe decreased gradually, following a trend similar to the outlet fluid temperature. As the operating time increased, the area affected by heat transfer expanded, indicating that the heat exchanger could extract heat from the rock and soil for heating purposes. Under non-seepage conditions, the temperature around the buried pipe was distributed uniformly, and the temperature decreased as it approached the pipe. There was a distinct stratification in the vertical direction, with the surrounding rock and soil temperature being lower in the regions with mudstone and silty mudstone layers. This occurred because the initial temperatures of these two rock and soil layers were lower, and they had higher thermal conductivity, leading to greater heat exchange with the buried pipe.

For situations involving underground water seepage, the temperature distribution around the buried pipes in the mudstone and silty mudstone layers without seepage was uniform from a vertical viewpoint. The temperature decreased as one approached the buried pipes. In contrast, in the presence of seepage within the silty clay layer and mudstone silty sandstone layer, the temperature field around the buried pipes shifted downstream, with the displacement distance increasing over time and stabilizing eventually. This phenomenon occurred because the fluid temperature at the inlet of the buried pipe was lower than the surrounding formation temperature, creating a cooling effect. Groundwater seepage enhances convective heat transfer, which inhibits upstream cold diffusion and transports it further downstream. Consequently, the temperature of the surrounding rock and soil in the seepage stratum was higher compared to conditions without seepage. Additionally, a vertical temperature gradient formed in the non-seepage layer adjacent to the seepage layer due to interlayer heat transfer, leading to a gradient distribution of the temperature field.

The temperature distribution at the intermediate depth (z = 86 m) within the muddy siltstone layer, both with and without seepage, after 10, 30, 60, and 180 days of operation, is depicted in Figure 17 and Figure 18, respectively. Under the condition of no seepage flow, the temperature field around the buried pipe shows uniform diffusion. The closer the rock and soil were to the pipe, the lower their temperature, indicating that the buried pipe’s heat exchange absorbed heat from the surrounding rock and soil. The thermal influence of the buried pipe extended progressively with longer operation times. Under seepage conditions, groundwater flow shifted the temperature field in the flow direction, reducing the upstream thermal influence and expanding the downstream area into a plume. This plume grew with continued operation and eventually stabilized. Compared to non-seepage conditions, groundwater seepage facilitates the dispersal of cold capacity, preventing its accumulation near a buried pipe and maintaining higher temperatures in the surrounding rock and soil. This process enhances the heat transfer efficiency of the buried pipe. Therefore, when designing and simulating systems, the improved heat transfer performance due to groundwater seepage, especially over long-term operation, should be considered. This consideration can lead to more accurate system designs and potentially lower initial investment costs.

3.3.3. The Influence of Seepage Velocity

As discussed in the above section, groundwater seepage can improve the efficiency of a buried pipe heat exchanger, but it also causes the surrounding rock and soil temperature field to develop a plume zone. Thus, assessing the impact of seepage velocity on the heat exchanger’s performance and the surrounding environment was crucial. For the simulation, the seepage velocities in the muddy siltstone layer were set at 0.1, 0.2, 0.3, and 0.4 m/d. Figure 19 illustrates the temperature changes in the outlet fluid during the heating season. It shows that, regardless of seepage velocity, the outlet fluid temperature declined over time, consistent with the initial trend under constant seepage. At any given time, a higher seepage velocity resulted in a higher outlet fluid temperature, with the difference becoming more pronounced during prolonged operation. This effect occurred because a greater seepage velocity enhanced convective heat transfer, thereby increasing the heat exchanger’s capacity. However, this rise in fluid temperature was not proportional to the increase in seepage velocity, as the contact area between the pipeline and the backfill material limited performance gain. Figure 20 depicts the heat exchange rates at different seepage velocities after extended operation. Compared to a seepage velocity of 0.3 m/d, which resulted in a heat exchange rate of 2623 W, increasing the velocity to 0.4 m/d raised the rate to 2639 W, a 0.61% increase. Conversely, reducing the seepage velocity to 0.2 m/d decreased the heat exchange rate to 2531 W, a 3.5% reduction, and further decreased it to 0.1 m/d resulted in a rate of 2457 W, a 6.3% reduction. Thus, the heat transfer rate increased with higher seepage velocity, but the rate of increase diminished.

The temperature distribution at the mid-depth (z = 86 m) of the muddy siltstone layer after 180 days of system operation, under seepage velocities of 0.1, 0.2, 0.3, and 0.4 m/d, is shown in Figure 21. It is evident that the seepage velocity significantly impacted the temperature distribution of the surrounding rock and soil near the buried pipe. As the seepage velocity increased, the temperature of the surrounding rock and soil rose, and the temperature influence range upstream became narrower. Similarly, the downstream temperature influenced the range and the feather-shaped zone formed were smaller. This suggests that higher groundwater seepage velocities more effectively mitigate the cold accumulation caused by heat exchange in buried pipes. Additionally, the size of the feather-shaped region did not decrease linearly with increasing seepage velocity, which aligns with the relationship between outlet fluid temperature and seepage velocity due to the limited heat transfer area of the pipeline. In conclusion, groundwater seepage in rock and soil can reduce cold accumulation around a buried pipe, maintain higher temperatures in the surrounding rock and soil, and transport cold downstream to create a feather-shaped zone, thereby enhancing the heat transfer efficiency of the buried pipe. Moreover, increasing the seepage velocity to a certain level can further improve the heat exchanger’s performance.

3.3.4. The Influence of Inlet Fluid Temperature

The temperature of the inlet fluid is a critical factor influencing the heat exchange efficiency of a buried pipe heat exchange system. Generally, a lower inlet fluid temperature results in a greater temperature differential with the underground heat reservoir, thereby enhancing heat exchange. However, in practical applications, the inlet water temperature cannot be reduced indefinitely; it should remain above 4 °C in winter without antifreeze. Therefore, to assess the impact of inlet fluid temperature on heat exchange performance during the heating season, four different temperatures were set as the following: 1 °C, 3 °C, 5 °C, and 7 °C. The evolution of the outlet fluid temperature over a 180-day heating season is shown in Figure 22. The results indicated that as the inlet fluid temperature rose, the outlet temperature also increased, but the temperature difference between them diminished. Figure 23 illustrates the significant differences in heat exchange performance under various inlet temperature conditions over the 180 days. For instance, compared to the heat exchange at an inlet temperature of 5 °C (2623 W), the heat exchange at an inlet temperature reduced by 2 °C (3569 W) increased by 36%. Conversely, increasing the inlet fluid temperature by 2 °C resulted in a 39% decrease in heat transfer (1594 W). This demonstrated that the heat transfer efficiency of the buried pipe system increased as the inlet fluid temperature decreased. From a heat transfer perspective, a lower inlet water temperature increased the temperature difference between the fluid in the pipe and the surrounding underground rock and soil, thereby extracting more heat from the subsurface.

Figure 24 shows the temperature distribution at a mid-depth of 86 m in the muddy siltstone layer after 180 days of operation, with varying inlet fluid temperature conditions. Under consistent seepage conditions, an increase in inlet fluid temperature led to higher temperatures in the surrounding rock and soil near the buried pipe. This resulted in less cold accumulation but also reduced the thermal influence range, thereby decreasing the heat transfer efficiency. To optimize heat transfer performance during the heating season, it is advisable to lower the inlet fluid temperature of a buried pipe heat exchange system, as this enhances heat exchange with the surrounding rock and soil.

3.3.5. The Influence of Fluid Injection Speed

The injection speed of fluid affects the heat transfer between a buried pipe heat exchanger and the surrounding rock and soil. It also exerts pressure on the pipeline and connected components, leading to energy consumption during the operation of the circulating pump. Thus, selecting an appropriate injection flow rate can enhance the heat transfer performance of the buried pipe while ensuring the safety and longevity of the heat exchanger system. Figure 25 illustrates the evolution of outlet fluid temperature over a 180-day heating season at different fluid injection velocities (0.3, 0.5, 0.68, 0.9, and 1.1 m/s). As the injection flow rate increased, the outlet fluid temperature decreased. This occurred because, although a higher flow velocity improved convective heat transfer between the fluid inside the pipe and the surrounding rock and soil, the increased velocity reduced the time available for heat exchange per unit time, resulting in less efficient heat transfer and, consequently, lower outlet temperatures. Figure 26 shows the heat transfer performance of the buried tube heat exchanger at different fluid injection speeds over 180 days. At an injection flow rate of 0.68 m/s, the heat transfer was 2623 W; when the flow rate was increased by approximately 0.2 m/s, the heat transfer dropped to 2001 W, a decrease of 23.7%. Conversely, when the flow rate decreased by approximately 0.2 m/s, the heat transfer increased by 15.4%. These data indicate that increasing the injection flow rate significantly impacts the long-term heat transfer of buried pipes, with a general trend of decreasing heat transfer as the flow rate increases.

The temperature distribution in the mid-depth section (z = 86 m) of the muddy siltstone layer after 180 days of system operation under different fluid injection rates is shown in Figure 27. The results indicated that under the same seepage conditions, as the injection flow rate increased, cold accumulation strengthened, and the temperature of the surrounding rock and soil around the buried pipe gradually decreased. However, when the flow rate exceeded 0.5 m/s, the size of the feather-shaped area formed by the cold diffusion did not increase significantly, so the heat transfer performance of the system gradually decreased. Therefore, appropriately reducing the injection flow rate during the operation of buried pipe heat exchangers can improve heat transfer performance and reduce pipeline pressure and circulating pump power consumption, but the flow rate should not be too low in order to ensure that the fluid inside the pipes is constantly in a turbulent state.

3.3.6. The Influence of Backfill Materials

Figure 28 displays the temperature evolution of the outlet fluid in the heat exchange system with different backfill materials, while

Table 2. Thermal conductivity coefficients of backfill material [48,49].

Code	Material	Thermal Conductivity (W/(m∙K))
A	Bentonite	0.75
B	Fine sand, bentonite	1.2
C	Waste materials of silica	2.0
D	Aluminum shavings, cement, fine sand	3.0

provides the thermal conductivity values of these materials. The data revealed that as the thermal conductivity of the backfill material increased, the outlet fluid temperature rose accordingly. However, when the thermal conductivity of the backfill material surpassed that of the surrounding rock and soil near the buried pipe, the rate of increase in fluid temperature diminished, thereby reducing the influence of the backfill material on the heat transfer efficiency of the buried pipe. Figure 29 compares the long-term heat transfer performance of buried pipe heat exchangers utilizing various backfill materials. Compared with using the B backfill heat exchanger (2623 W), using the A backfill heat exchanger (2098 W) reduced heat transfer by 20%, using the C backfill heat exchanger (2737 W) increased heat transfer by 4.4%, and using the D backfill heat exchanger (2850) increased heat transfer by 8.7%. When A was used as the backfill material, the heat exchange performance of the heat exchanger was considerably lower compared to using the other three materials. The differences in heat transfer among the other three backfill materials, excluding bentonite, were relatively minor. This is due to the fact that the higher thermal conductivity of backfill material generally improves heat transfer efficiency by allowing for more effective heat conduction from the surrounding rock and soil to a buried pipe. Conversely, if the thermal conductivity of the backfill is lower than that of the surrounding rock and soil, it impedes heat transfer. Although a higher thermal conductivity does not hinder heat transfer, the benefits are not infinite. The effectiveness of the backfill material is constrained by its filling range, meaning that heat transfer does not increase indefinitely with higher conductivity. Additionally, excessive backfill material can lead to thermal short circuits between buried pipes.

Figure 30 illustrates the temperature distribution at the mid-depth section (z = 86 m) of the muddy siltstone layer over 180 days of operation with various backfill materials for the buried pipe heat exchanger. The data showed that, under consistent seepage conditions, a higher thermal conductivity of the backfill material led to a greater deviation in the temperature field around the buried pipe and enhanced heat exchange with the surrounding rock and soil. As the thermal conductivity of the backfill material increased from 0.75 W/(m∙K) to 1.2 W/(m∙K), and then to 2.0 W/(m∙K), the extent of heat transfer’s influence around the buried pipe increased substantially. However, when the thermal conductivity rose from 2.0 W/(m∙K) to 3.0 W/(m∙K), the increase in the heat transfer range was minimal. This suggests that once the thermal conductivity of backfill material surpasses that of the surrounding rock and soil, its impact on heat transfer performance becomes relatively minor. In conclusion, for backfilling around buried pipes, selecting a backfill material with a thermal conductivity slightly higher than that of the surrounding rock and soil is advisable to enhance heat transfer performance and maintain cost efficiency.

4. Conclusions

In this study, a numerical model of the heat transfer of a shallow vertical buried pipe considering surface temperature fluctuations, rock and soil stratification, and groundwater seepage conditions was established. The reliability of the model was verified based on temperature data from field tests, and the heat transfer performance of buried pipe heat transfer systems under different conditions was studied. The research results mainly drew the following conclusions:

• The shallow geothermal field of a testing site can be divided into a variable-temperature layer (0–25 m), a constant-temperature layer (25–50 m, 9.17 °C), and a warming layer (50–130 m), with a geothermal gradient of approximately 3.0 °C/100 m. The layered thermal conductivities were the following: the silty clay layer, 1.631 W/(m∙K); the mudstone layer, 1.888 W/(m∙K); the muddy siltstone layer, 1.862 W/(m∙K); and the silty mudstone layer, 2.144 W/(m∙K).
• Higher air temperatures can enhance heat transfer performance. Daily temperature fluctuations positively correlate with heat transfer efficiency, and the heat transfer can be 61 W less than under annual average temperature conditions. Therefore, when modeling the long-term heat transfer performance of buried pipes, it is crucial to account for temperature variations and dynamically adjust the operating mode of the system.
• Without groundwater seepage, the temperature around a buried pipe is uniformly distributed, with lower temperatures near the pipe; with groundwater seepage, the cold energy generated by the underground pipe’s heat transfer through thermal convection migrates and diffuses to form a feather-shaped area, which can effectively alleviate the phenomenon of cold accumulation, keep the surrounding rock and soil at a high temperature, and improve the heat transfer performance of the heat exchanger by about one-fold. As the seepage velocity increases, the heat transfer of buried pipes shows a nonlinear increase.
• Properly reducing the temperature and velocity of injected fluid can improve heat transfer performance by 30%. Lowering the temperature of the injected fluid can increase the temperature difference in heat transfer, but it can lead to a severe cold accumulation phenomenon. Increasing the injection flow rate will increase the area of the feather-shaped zone formed by cold diffusion, and it will also increase pipeline pressure and circulating pump power consumption. Choosing backfill materials with thermal conductivities higher than that of the geological soil can improve heat transfer performance by 20%.

Future research should consider the potential effects of temperature waves more carefully; for example, it should focus on fluid flow behavior and temperature changes by establishing three-dimensional pipeline and fluid models.