Optimization design method for middle-deep layer coaxial buried pipe group

Abstract

The invention provides a mid-deep layer coaxial buried pipe group optimization design method which specifically comprises the following steps: S1, according to the structural design of mid-deep layer coaxial buried pipes, establishing a three-dimensional heat transfer model of a mid-deep layer buried pipe heat exchanger based on a bicontinuum finite element method; s2, setting model parameters; s3, inlet temperature, heat extraction power and buried pipe spacing parameters are set, and middle-deep layer coaxial buried pipe group heat extraction amount, adjacent rock-soil temperature or outlet temperature are output; and S4, selecting inlet temperature, heat extraction power and buried pipe spacing parameters as an optimal design scheme of the middle-deep layer coaxial buried pipe group according to the output heat extraction amount of the middle-deep layer coaxial buried pipe group, the adjacent rock-soil temperature or the outlet temperature. According to the method, the medium-deep buried pipe group three-dimensional heat transfer model is established, the influence degree of different pipe group design parameters on the long-term operation heat extraction performance of the system is quantitatively evaluated, and a theoretical basis is provided for actual engineering.

Description

Technical Field

[0001] The present invention relates to the technical field of development and utilization of mid-deep geothermal energy, and in particular to an optimization design method for a mid-deep coaxial buried pipe group. Background Art

[0002] With the global energy transition and the advancement of the "dual carbon" goals, geothermal energy, as a clean, renewable, and abundant energy source, is attracting increasing attention. Research on shallow ground heat exchangers (SGHEs) began early, and the technology is relatively mature. The impact of design parameters such as pipe diameter, pipe spacing, burial depth, circulating medium, and flow rate on heat transfer performance has been extensively studied. However, shallow ground heat exchangers can lead to problems such as heat and cold accumulation, large footprint, and limited heat extraction, making them unsuitable for cold regions or large-scale buildings. In 2012, a research team successfully developed a medium-deep ground heat exchanger (2-3 km deep) to extract mid-depth geothermal energy for building heating. Currently, mid-depth ground source heat pump systems (MDBHEs) are a technology for efficiently utilizing mid-depth geothermal energy. They offer advantages such as high heat transfer efficiency, a small footprint, and minimal environmental impact, and show broad application prospects in building heating and industrial heating.

[0003] With technological advancements, medium- and deep-seated buried heat exchangers have gradually become a research hotspot. Some domestic scholars have studied the effects of depth, circulating medium, and flow rate on the heat transfer performance of medium- and deep-seated buried heat exchangers, exploring their potential applications in cold regions. This has provided important theoretical and technical support for advancing the development and utilization of medium- and deep-seated geothermal resources. Compared with previous studies, the study of pipe group layout (such as well spacing) and operating parameters (such as inlet temperature and heat extraction power) faces more complex multi-parameter coupling and technical barriers. First, pipe group layout involves the nonlinear superposition effect of interwell thermal interference, requiring comprehensive consideration of geological heterogeneity, long-term thermal balance, and optimization of various parameters such as the pipe group. The simulation and experimental costs are significantly higher than those of single-well studies. Second, the optimization of operating parameters requires balancing the system's transient response with the group control strategy. For example, changes in inlet temperature can affect the performance of adjacent wells through thermal short-circuiting, while heat extraction power must be adjusted to avoid efficiency degradation caused by cold / hot accumulation in the formation. The pipe group spacing must be adjusted according to the degree of interference. These dynamic interactions significantly increase the difficulty of experimental design and numerical modeling. In addition, the layout of pipe groups in actual projects is also limited by practical constraints such as site conditions and drilling costs, which further increases the decision-making barriers to large-scale applications.

[0004] However, current research on medium- and deep-layer buried pipe heat exchangers has obvious deficiencies: on the one hand, compared with shallow geothermal energy systems, the medium- and deep-layer geothermal gradient is higher and the formation conditions are more complex, making it difficult to directly apply the existing shallow pipe group design theory; on the other hand, the impact mechanism of key design parameters such as pipe group layout (such as well spacing) and operating parameters (such as inlet temperature and heat extraction power) on the long-term operating performance of the system is still unclear, especially the lack of quantitative sensitivity analysis of different parameters. Summary of the Invention

[0005] The present invention provides a method for optimizing the design of a medium-deep coaxial buried pipe group, the purpose of which is to fill the gap in the prior art in the design of the layout mode and operating parameters of the medium-deep buried pipe group.

[0006] In order to achieve the above-mentioned object, the present invention provides a method for optimizing the design of a medium-deep coaxial buried pipe group, which specifically comprises the following steps:

[0007] S1. Based on the design of the medium-deep coaxial buried pipe structure, a three-dimensional heat transfer model of the medium-deep buried pipe heat exchanger was established using the double-continuum finite element method, and the control equations were listed;

[0008] S2. Setting model parameters of a three-dimensional heat transfer model of a medium-deep buried pipe heat exchanger;

[0009] S3. Set the inlet temperature, heat extraction power, and buried pipe spacing parameters, import the control equations of the three-dimensional heat transfer model of the medium-deep buried pipe heat exchanger, discretize and solve the control equations, and output the heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature, or the outlet temperature;

[0010] S4. According to the output heat of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature, the inlet temperature, heat extraction power and buried pipe spacing parameters are selected as the optimal design scheme for the medium-deep coaxial buried pipe group.

[0011] Preferably, the medium-deep coaxial buried pipe structure described in S1 is specifically as follows: the medium-deep coaxial buried pipe comprises an inner pipe and an outer pipe which are nested with each other, and backfill material is filled between the outer pipe and the adjacent rock and soil.

[0012] Preferably, the control equation in S1 includes:

[0013] The governing equation for heat transfer of fluid in the outer tube channel is:

[0014]

[0015] The governing equation for heat transfer of fluid in the inner tube channel is:

[0016]

[0017] Heat transfer governing equation for backfill material area:

[0018]

[0019] Comprehensive heat transfer control equation for geotechnical area:

[0020]

[0021] Where ρ is the density, kg / m 3 ; c is specific heat capacity, J / (kg·℃); t is temperature, ℃; τ is time, s; u is the circulating fluid flow rate, m / s; Λ r is the thermal fluid dynamic diffusion tensor; H is the heat source / sink; ε is the porosity; λ is the thermal conductivity, W / (m·K); v is the groundwater seepage velocity, m / s; the subscript r represents the circulating fluid, g represents the backfill material, f represents the groundwater, s represents the rock and soil, i represents the annular channel, and o represents the inner tube channel.

[0022] Preferably, the model parameters in S2 include buried pipe structure parameters and formation rock and soil physical property parameters.

[0023] Preferably, the inlet temperature, heat extraction power, buried pipe spacing parameters and output variables set in S3 are designed by a parameter sensitivity analysis method.

[0024] Preferably, the parameter sensitivity analysis method specifically includes:

[0025] (1) Design the inlet temperature, heat extraction power and buried pipe spacing parameters of the pipe group respectively, and design 4-6 sets of data for each parameter;

[0026] (2) The control variable method is used to import the inlet temperature, heat extraction power and buried pipe spacing parameters of the pipe group into the model, and the heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature are output. The corresponding relationship between the inlet temperature, heat extraction power and buried pipe spacing and one or more of the heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature is studied.

[0027] Preferably, the inlet temperature, heat extraction power and buried pipe spacing parameters of the respective designed pipe groups are designed according to the regional geological conditions, the thermal physical properties of the rock and soil mass and the design operating conditions of the heat pump unit, and the 4-6 groups of data are arranged at intervals;

[0028] The control variable method specifically includes: fixing two of the inlet temperature, heat extraction power and buried pipe spacing parameters, changing the input parameter data of the remaining one, and outputting the corresponding heat extraction of the mid-deep coaxial buried pipe group, adjacent rock and soil temperature or outlet temperature.

[0029] Preferably, the study of the correspondence between one of the inlet temperature, heat extraction power and buried pipe spacing and one or more of the heat extraction of the deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature specifically includes:

[0030] The corresponding relationship between the inlet temperature and the heat taken by the deep coaxial buried pipe group;

[0031] The corresponding relationship between heating power and adjacent rock and soil temperature or outlet temperature;

[0032] The corresponding relationship between the spacing between underground pipes and the heat taken by the coaxial underground pipe group in the middle and deep layers;

[0033] The corresponding relationship between the buried pipe spacing and the adjacent rock and soil temperature or outlet temperature.

[0034] Preferably, the optimization design scheme of the medium-deep coaxial buried pipe group according to the output heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature in S4 specifically includes:

[0035] The heat extraction, adjacent rock and soil temperature or outlet temperature output results of the medium-deep coaxial buried pipe group are ranked by multi-index relative combination, and the inlet temperature, heat extraction power and buried pipe spacing parameters corresponding to the optimal output result are selected as the pipe group optimization design parameters.

[0036] Preferably, after outputting the heat intake of the deep coaxial buried pipe group, the adjacent rock and soil temperature, or the outlet temperature in S4, a curve is drawn according to the output data, namely, the inlet temperature, the heat intake power, and the buried pipe spacing, and the heat intake of the pipe group, the adjacent rock and soil temperature, or the outlet temperature;

[0037] In the multi-index relative combination sorting, when there is a conflict in the sorting of the inlet temperature, heat extraction power, and buried pipe spacing of the medium-deep coaxial buried pipe group, the orthogonal experimental range analysis method is used to calculate the weights of the heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature, or the outlet temperature, and the corresponding design parameters in the multi-index relative combination sorting are selected according to the order of weights;

[0038] The calculation formula of the orthogonal experiment range analysis method is as follows:

[0039] Calculate the range (R), which reflects the degree of influence of factors on the indicator:

[0040]

[0041] Where, is the sum of the indicators of each factor at each level, is the average value of the indicators at each level of each factor;

[0042] Determine the weight of each factor on the indicator based on the range ratio:

[0043]

[0044] Preferably, in the relative combination ranking of the multiple indicators, when there is a conflict in the ranking of the heat output of the deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature, the heat output power of the deep buried pipe is prioritized, followed by the inlet temperature, and finally the buried pipe spacing.

[0045] The above solution of the present invention has the following beneficial effects:

[0046] (1) The present invention establishes a three-dimensional heat transfer model for medium-deep buried pipe groups, comprehensively considering the heterogeneity of the formation, solving the problem that the existing shallow pipe group design theory is difficult to directly apply to the heat exchange model of medium-deep coaxial buried pipe groups, and quantitatively evaluates the impact of different pipe group design parameters on the long-term heat extraction performance of the system, providing a theoretical basis for practical engineering;

[0047] (2) The heat extraction of the deep-layer coaxial buried pipe group, the adjacent rock and soil temperature, or the outlet temperature output by the model can be used to quantitatively evaluate the impact of different pipe group design parameters on the long-term heat extraction performance of the system. Based on the quantitative content, the inlet temperature, heat extraction power, and buried pipe spacing parameters can be selected as the pipe group design parameters, providing a theoretical basis for actual engineering.

[0048] (3) The three-dimensional heat transfer model of the medium-deep buried pipe heat exchanger of the present invention has small error and high accuracy. It has been verified that the change trend of the measured curve is highly consistent, and the relative error is always controlled within 8%. This fully verifies that the constructed numerical model can accurately reflect the heat transfer characteristics and dynamic change laws of the medium-deep buried pipe heat exchanger.

[0049] Other beneficial effects of the present invention will be described in detail in the subsequent specific implementation section. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Schematic diagram of the vertical cross-section structure of the heat exchange physical model of the deep buried pipe heat exchanger of the present invention;

[0051] Figure 2 Schematic diagram of the horizontal cross-section structure of the heat exchange physical model of the deep buried pipe heat exchanger of the present invention;

[0052] Figure 3 This is a diagram showing the matching results of the three-dimensional heat transfer model simulation curve and the measured curve of the deep underground heat exchanger in Example 1 of the present invention;

[0053] Figure 4 This is a relationship diagram between the inlet temperature and the heat intake of the buried pipe group obtained by the three-dimensional heat transfer model of the deep buried pipe heat exchanger in Example 1 of the present invention;

[0054] Figure 5 、 6 This is a graph showing the relationship between the heat extraction power and the outlet temperature of the buried pipe group obtained from the three-dimensional heat transfer model of the deep buried pipe heat exchanger in Example 1 of the present invention;

[0055] Figure 7 This is a diagram showing the long-term effect of heat extraction power on the surrounding rock temperature at a depth of 2500 m, obtained from the three-dimensional heat transfer model of the deep buried pipe heat exchanger in Example 1 of the present invention;

[0056] Figure 8 This is a relationship diagram between tube spacing and heat intake obtained from the three-dimensional heat transfer model of the deep underground heat exchanger in Example 1 of the present invention;

[0057] Figure 9 This is a relationship diagram between the tube spacing and the inlet and outlet temperatures obtained from the three-dimensional heat transfer model of the deep underground heat exchanger in Example 1 of the present invention;

[0058] Figure 10 This is a relationship diagram between the tube spacing and the surrounding rock temperature at a depth of 2500m obtained from the three-dimensional heat transfer model of the deep buried tube heat exchanger in Example 1 of the present invention;

[0059] Figure 11 This is a cloud diagram of the surrounding rock temperature at a depth of 2500 m under different pipe spacings in Example 1 of the present invention;

[0060] Figure 12 This is a flow chart of the pipe group optimization design method according to Example 1 of the present invention. DETAILED DESCRIPTION

[0061] To make the technical problems, technical solutions, and advantages to be solved by the present invention more clear, the following is a detailed description with reference to the accompanying drawings and specific embodiments. It is obvious that the embodiments described are only some of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0062] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0063] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood broadly. For example, they may refer to a locking connection, a detachable connection, or an integral connection; they may refer to a mechanical connection or an electrical connection; they may refer to a direct connection or an indirect connection through an intermediate medium; and they may refer to internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0064] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0065] Example 1:

[0066] like Figure 1 、 2 As shown, Figure 1 Schematic diagram of the vertical cross-section structure of the heat exchange physical model of the deep buried pipe heat exchanger of the present invention; Figure 2 Schematic diagram of the horizontal cross-section structure of the heat exchange physical model of the deep buried pipe heat exchanger of the present invention;

[0067] The medium-deep coaxial buried heat exchanger consists of an inner and outer tube, backfill material, and surrounding rock formations. During system operation, the circulating fluid enters through the outer annular cavity, is heated from top to bottom, and then returns through the insulated inner tube to the geothermal well. The returned hot water enters the surface heat pump unit for consumption before returning to the user. The circulating fluid in the heat exchanger flows through the annular space of the casing and out through the central tube, exchanging heat with the surrounding rock and soil during its flow.

[0068] This embodiment provides a method for optimizing the design of a medium-deep coaxial buried pipe group, specifically comprising the following steps:

[0069] S1. Based on the design of the medium-deep coaxial buried pipe structure, a three-dimensional heat transfer model of the medium-deep buried pipe heat exchanger was established using the double-continuum finite element method, and the control equations were listed;

[0070] The structure of a mid- to deep-layer coaxial ground heat exchanger is divided into two parts, bounded by the borehole wall: the heat exchanger and cement sheath within the borehole, and the stratum outside the borehole. Based on the variation of formation temperature with depth, the heat transfer processes in these two parts are calculated separately. The two parts are then coupled using the borehole wall temperature. OpenGeoSys performs numerical simulations based on the laws of conservation of mass and energy, and establishes a three-dimensional heat transfer model of the mid- to deep-layer ground heat exchanger using the bicontinuum finite element method.

[0071] During the heat transfer simulation, the rock and soil and the circulating medium are treated as two continuous media and coupled through the heat flow boundary. The relevant control equations follow the third-class boundary conditions on the heat transfer interface. The heat transfer control equations related to the deep coaxial buried pipe heat exchanger and the rock and soil are as follows:

[0072] The governing equation for heat transfer of fluid in the outer tube channel is:

[0073]

[0074] The governing equation for heat transfer of fluid in the inner tube channel is:

[0075]

[0076] Heat transfer governing equation for backfill material area:

[0077]

[0078] Comprehensive heat transfer control equation for geotechnical area:

[0079]

[0080] Where ρ is the density, kg / m 3 ; c is specific heat capacity, J / (kg·℃); t is temperature, ℃; τ is time, s; u is the circulating fluid flow rate, m / s; Λ r is the thermal fluid dynamic diffusion tensor; H is the heat source / sink; ε is the porosity; λ is the thermal conductivity, W / (m·K); v is the groundwater seepage velocity, m / s; the subscript r represents the circulating fluid, g represents the backfill material, f represents the groundwater, s represents the rock and soil, i represents the annular channel, and o represents the inner tube channel.

[0081] S2. Setting model parameters of a three-dimensional heat transfer model of a medium-deep buried pipe heat exchanger;

[0082] The medium in the deep buried heat exchanger is softened water. The established model parameters are shown in Table 1, and the rock and soil physical parameters are shown in Table 2. The geothermal gradient in the study area is 2.45℃ / hm.

[0083] Table 1. Physical parameters required for simulation

[0084]

[0085]

[0086] Table 2 List of thermophysical parameters of core samples

[0087]

[0088] Boundary conditions:

[0089] The annual average surface temperature in Changsha is 19.3°C, so the surface is set to the first type of constant temperature boundary condition with a value of 19.3°C, and the far boundaries around the control body are set to the second type of boundary condition (adiabatic boundary) with a boundary heat flow of 0.

[0090] S3. Set the inlet temperature, heat extraction power, and buried pipe spacing parameters, import the control equations of the three-dimensional heat transfer model of the medium-deep buried pipe heat exchanger, discretize and solve the control equations, and output the heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature, or the outlet temperature;

[0091] The parameter sensitivity analysis method is used to quantitatively evaluate the impact of different pipe group design parameters on the long-term heat extraction performance of the system. The pipe group inlet temperature, heat extraction power and buried pipe spacing parameters are designed according to the regional geological conditions, the thermal physical parameters of the rock and soil, and the design operating conditions of the heat pump unit. The specific steps are as follows: Figure 12 , Figure 12 This is a flow chart of the pipe group optimization design method according to Example 1 of the present invention.

[0092] (1) Influence of inlet temperature on heat extraction

[0093] The heat extraction of deep buried pipes is one of the key indicators to measure the efficiency of regional geothermal energy utilization. As an important parameter affecting the heat extraction, the change of inlet temperature will have a significant impact on the system performance. 3 / h, quantifying the effect of different inlet temperatures (10℃, 12℃, 14℃, 16℃ and 18℃) on the heat extraction of the well group.

[0094] (2) Effect of different heating powers on temperature

[0095] In geothermal energy systems, the arrangement of buried pipes and the heat extraction power are key factors affecting the long-term performance of the system. For 6 buried pipes arranged in a straight line (numbered from left to right as pipes 1, 2, 3, 4, 5 and 6), the spacing is 30m, and the flow rate is set to 23m 3 / h, and analyze the impact of different heating powers (250kW, 275kW, 300kW, 325kW, 350kW) on the surrounding rock and soil temperature during a long-term operation period (15 years).

[0096] (3) Influence of buried pipe spacing on heat extraction

[0097] In geothermal energy systems, well spacing is a key parameter influencing heat extraction efficiency and surrounding rock temperature distribution. Setting appropriate spacing can effectively reduce inter-well thermal interference, optimize the surrounding rock temperature field, and thus improve the long-term operational stability of the system. The effects of different well spacings (5m, 15m, 30m, 45m, and 60m) on well heat extraction and surrounding rock temperature were investigated.

[0098] S4. According to the output heat of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature, the inlet temperature, heat extraction power and buried pipe spacing parameters are selected as the optimal design scheme for the medium-deep coaxial buried pipe group.

[0099] 1. Model verification of the three-dimensional heat transfer model of the medium-deep buried pipe heat exchanger with the parameters of this embodiment:

[0100] Based on the actual engineering parameters of Changsha Huanghua Airport, this project established a numerical model of heat exchange in medium-deep buried pipes.

[0101] By integrating the measured data of the airport's exploration and production wells, the model was verified and analyzed with a focus on the buried pipe water storage temperature as the key indicator. Figure 3 The results of an error analysis comparing simulated and measured outlet water temperatures of medium- and deep-layer buried pipes at Huanghua Airport are presented. The simulated and measured curves show highly consistent trends, with good numerical agreement. Quantitative calculations show that, over the entire system operating cycle, excluding the effects of circuit instability (sudden changes in actual outlet temperature are caused by sudden circuit interruptions or instability), the maximum error is 2.77°C, and the relative error remains within 8%. This fully verifies that the constructed numerical model accurately reflects the heat transfer characteristics and dynamic changes of medium- and deep-layer buried pipe heat exchangers.

[0102] 2. Simulation results and analysis of this embodiment

[0103] (1) Influence of inlet temperature on heat extraction

[0104] The heat extraction of deep buried pipes is one of the key indicators to measure the efficiency of regional geothermal energy utilization. As an important parameter affecting the heat extraction, the change of inlet temperature will have a significant impact on the system performance. 3 / h, quantifying the effect of different inlet temperatures (10℃, 12℃, 14℃, 16℃ and 18℃) on the heat extraction of the well group.

[0105] Figure 4 This is a relationship diagram between the inlet temperature and the heat intake of the buried pipe group obtained by the three-dimensional heat transfer model of the deep buried pipe heat exchanger in Example 1 of the present invention;

[0106] As the inlet temperature increases, the heat production of the well cluster shows a clear upward trend. Specifically, the corresponding heat production for each temperature is shown in Table 3. When the inlet temperature is 10°C, the well cluster heat production is 246.26 MWh. When the inlet temperature rises to 12°C, the heat production increases to 273.72 MWh, an increase of approximately 11.15%. When the inlet temperature further increases to 14°C, the heat production reaches 301.19 MWh, an increase of approximately 10.03% compared to 12°C. When the inlet temperature reaches 16°C, the heat production reaches 328.66 MWh, an increase of approximately 9.11% compared to 14°C. Finally, when the inlet temperature reaches 18°C, the heat production reaches 356.13 MWh, an increase of approximately 8.36% compared to 16°C. Overall, as the inlet temperature increased from 10°C to 18°C, the heat extraction from the well cluster increased from 246.26 MWh to 356.13 MWh, a total increase of approximately 44.62%. With every 2°C increase in temperature, the heat extraction growth rate gradually decreased from 11.14% to 8.36%. This indicates that increasing the inlet temperature can increase the heat extraction of the buried pipe cluster, but the rate of heat extraction growth gradually slows as the temperature rises further. In engineering practice, it is necessary to comprehensively consider geological conditions, system energy consumption, and economic efficiency to select an appropriate inlet temperature.

[0107] Table 3 Heat intake of underground pipe groups corresponding to different temperatures

[0108]

[0109] (2) Influence of heating power on temperature

[0110] In geothermal energy systems, the arrangement of buried pipes and the heat extraction power are key factors affecting the long-term performance of the system. According to relevant literature, the operating life of HVAC systems is 12-15 years, and 15 years is selected as the system operating cycle. The project focuses on 6 buried pipes arranged in a straight line (numbered from left to right as pipes 1, 2, 3, 4, 5 and 6), with a spacing of 30m and a set flow rate of 23m 3 / h, simulating the effects of different heating powers (250kW, 275kW, 300kW, 325kW, 350kW) on the outlet temperature and the surrounding rock and soil temperature during a 15-year operation cycle.

[0111] Figure 5 、 6 This is a relationship diagram of the outlet temperature of the buried pipe group under different heating powers (250kW, 275kW, 300kW, 325kW, and 350kW) obtained from the three-dimensional heat transfer model of the deep buried pipe heat exchanger in Example 1 of the present invention;

[0112] Since the tube group is arranged in a straight line and symmetrically, only tubes 1 to 3 need to be analyzed to reflect the overall situation.

[0113] Figure 5 The focus is on demonstrating the temperature variation of tube 1 at different heat extraction powers. As the heat extraction power increases from 250kW to 350kW, the outlet temperature of tube 1 shows a clear downward trend, and the higher the power, the faster the temperature drop. It is particularly noteworthy that when the heat extraction power reaches 325kW, the inlet temperature drops below 5°C after the sixth year of operation. Engineering practice has shown that this temperature level is no longer economically advantageous, and several scholars have conducted detailed research. Therefore, in engineering, it is necessary to select an appropriate heat extraction power based on geological conditions and system requirements to ensure a balance between long-term stable operation of the system and economic efficiency.

[0114] Figure 6 The temperature changes of tubes 1 to 3 at different heating power levels were compared. The results show that the arrangement of the buried tubes significantly affects the spatial distribution of the outlet temperature: Tube 1 (and the symmetrical tube 6) at the edge maintains a higher outlet temperature and a slower cooling rate due to less thermal interference; while Tubes 2 and 3 at the center experience stronger thermal interference, resulting in lower outlet temperatures and a faster cooling rate. As the heating power increases, this thermal interference effect becomes more pronounced, further widening the temperature difference between the center and edge tubes. This phenomenon demonstrates that the impact of position factors on heat transfer performance must be fully considered in the design of the tube group system.

[0115] (3) Analysis of the effect of heating power on the temperature of the surrounding rock of the pipe group

[0116] Figure 7 This is a diagram showing the long-term effect of heat extraction power on the surrounding rock temperature at a depth of 2500 m, obtained from the three-dimensional heat transfer model of the deep buried pipe heat exchanger in Example 1 of the present invention;

[0117] In the long-term operation of geothermal energy system, the setting of heat extraction power directly affects the temperature variation of the rock formation around the pipe group. Figure 7 As shown in the figure, as the heating power increases, the surrounding rock temperature gradually decreases, and the higher the power, the faster the cooling rate. At high heating power (e.g., 325kW and 350kW), the temperature drop trend is even more pronounced, with the cooling effect of the surrounding rock extending from the near-wellbore area to the far-wellbore area, but the temperature drop in the near-wellbore area is significantly greater than in the far-wellbore area. Furthermore, the surrounding rock temperature changes exhibit temporal and spatial characteristics, with the temperature drop being more dramatic near the wellbore area and less affected in the far-wellbore area. If the system operates for a long time, the temperature drop gradually expands outward, but the cooling rate slows with increasing distance.

[0118] In short, excessively high extraction power can cause the rock temperature near the wellbore to continue to drop, affecting the long-term stability of the system. Therefore, in actual projects, it is necessary to combine geological conditions (such as rock thermal conductivity and initial temperature) with system requirements (such as heating load) to reasonably select the extraction power to balance heat extraction efficiency and the thermal recovery capacity of the surrounding rock to ensure the sustainable operation of the geothermal energy system.

[0119] (4) Influence of buried pipe spacing on heat extraction

[0120] In geothermal energy systems, well spacing is a key parameter influencing heat extraction efficiency and surrounding rock temperature distribution. Proper well spacing can effectively reduce inter-well thermal interference, optimize the surrounding rock temperature field, and thus improve the long-term operational stability of the system. This study analyzed how different well spacings (5m, 15m, 30m, 45m, and 60m) affect well heat extraction and surrounding rock temperature.

[0121] (4.1) Analysis of outlet temperature changes of tube groups with different spacing

[0122] (4.1.1) Relative combination ranking of multiple indicators

[0123] The heat extraction, adjacent rock and soil temperature or outlet temperature output results of the medium-deep coaxial buried pipe group are ranked by multi-index relative combination, and the inlet temperature, heat extraction power and buried pipe spacing parameters corresponding to the optimal output result are selected as the pipe group optimization design parameters.

[0124] (4.1.2) Use orthogonal experimental range method to analyze:

[0125] 1. Orthogonal experimental design:

[0126] Factors and levels:

[0127] Inlet temperature (A): 10℃, 12℃, 14℃, 16℃, 18℃

[0128] Heat extraction power (B): 250kW, 275kW, 300kW, 325kW, 350kW

[0129] Pipe group spacing (C): 5m, 15m, 30m, 45m, 60m

[0130] Orthogonal array selection: using L 25 (5 6 ) orthogonal table (25 groups of experiments), covering all parameter combinations.

[0131] 2. Range analysis steps

[0132] (1) Calculate the average level of each factor

[0133] For the five levels of each factor (A, B, C), calculate the mean of Y1, Y2, and Y3 respectively.

[0134] Example: Calculation of the mean value of the outlet temperature (Y1)

[0135] A1 (at 10℃):

[0136] B1 (250kW):

[0137] C1 (5m):

[0138] (2) Calculate the range (R)

[0139] The degree of influence of the extreme difference reflection factor on the indicator:

[0140]

[0141] Example: For Y1:R A =Y A5 -Y A1 , R B , R C Same thing.

[0142] (3) Weight distribution

[0143] Determine the weight of each factor on the indicator based on the range ratio:

[0144] 3. Results Analysis

[0145] (1) Outlet temperature (Y1)

[0146] Primary and secondary factors: heating power (B) > inlet temperature (A) > spacing (C)

[0147] Basis: The increase in heat extraction power leads to a significant decrease in outlet temperature (e.g., to below 5°C at 350kW), while the spacing has little effect (it tends to be stable after 30m).

[0148] Range ratio: close to 50% (B): 30% (A): 20% (C).

[0149] (2) Heat intake (Y2)

[0150] Primary and secondary factors: inlet temperature (A) > spacing (C) > heating power (B)

[0151] Basis: When the inlet temperature rises from 10℃ to 18℃, the heat intake increases by 44.6%, while when the distance exceeds 30m, the increase is only 0.6%.

[0152] Range ratio: close to 60% (A): 25% (C): 15% (B).

[0153] (3) Surrounding rock temperature (Y3)

[0154] Primary and secondary factors: heating power (B) > spacing (C) > inlet temperature (A)

[0155] Basis: High heating power (350kW) causes the surrounding rock temperature to drop rapidly, and increasing the spacing can alleviate thermal interference.

[0156] Range ratio: close to 50% (B): 35% (C): 15% (A).

[0157] 4. Comprehensive Weight Table

[0158]

[0159] 5. Engineering optimization suggestions

[0160] Heat power priority control (highest overall weight):

[0161] Avoid exceeding 300kW (recommended value for Changsha area) to prevent sudden drop in outlet temperature and thermal exhaustion of surrounding rock.

[0162] The inlet temperature is next:

[0163] Select 12-14℃ (for a 10-11% heat increase and a higher COP).

[0164] Spacing optimization:

[0165] Use a spacing of 30m (the balance point between thermal interference and heat extraction).

[0166] Figure 8 This is a relationship diagram between tube spacing and heat intake obtained from the three-dimensional heat transfer model of the deep underground heat exchanger in Example 1 of the present invention;

[0167] Figure 9 This is a relationship diagram between the tube spacing and the inlet and outlet temperatures obtained from the three-dimensional heat transfer model of the deep underground heat exchanger in Example 1 of the present invention;

[0168] Figure 8This figure shows the heat extraction of well clusters at different spacings during short-term geothermal energy system operation. As the spacing increases from 5m to 60m, the heat extraction initially increases and then stabilizes. When the spacing is small (≤5m), thermal interference between wells is significant, resulting in low heat extraction. As the spacing increases (≥15m), thermal interference decreases, and heat extraction gradually increases. When the spacing exceeds a certain range (≥30m), the increase in heat extraction significantly decreases. Specific data shows that when the well cluster spacing is 5m, the heat extraction is 219.57MWh, at which point thermal interference between well clusters is significant and heat exchange efficiency is low. When the well cluster spacing increases to 15m, the heat extraction increases to 233.03MWh, a 6.1% increase, and thermal interference is significantly reduced. Further increasing the spacing to 30m, the heat extraction reaches 235.02MWh, but the increase has dropped to 0.9%. When the spacing is further expanded to 45m and 60m, the heat extraction reaches 236.51MWh and 235.13MWh, respectively, with increases of only 0.6% and -0.6%, respectively. This indicates that heat extraction growth reaches saturation or even shows a downward trend after spacing exceeds 30m. Based on these data characteristics, it is recommended that the well cluster spacing be controlled within the range of 15-30m in actual projects. This range can effectively reduce thermal interference between wells while ensuring high heat extraction efficiency.

[0169] Figure 9 The inlet and outlet temperature curves of each pipe when the well cluster spacing is 5m. As shown in the figure, when the well cluster spacing is 5m, the heat transfer performance of each pipe varies significantly, and the impact of inter-well thermal interference on the heat transfer performance of the buried pipe shows a clear spatial distribution. The central pipes (Nos. 3 and 4) are most severely affected by thermal interference, with a significant drop in inlet and outlet temperatures, indicating a significant impact on heat transfer efficiency. Pipes Nos. 2 and 5, as intermediate transition points, experience a more moderate temperature drop and exhibit moderate heat transfer performance. Pipes Nos. 1 and 6, located at the edge, maintain optimal inlet and outlet temperatures due to their distance from the core thermal interference zone, demonstrating the best heat transfer stability. This temperature distribution pattern intuitively reflects that when densely distributed wells are deployed, thermal interference in the central area is prominent, leading to a significant deterioration in heat transfer performance, while the peripheral pipes are less affected and can maintain good heat transfer efficiency. This phenomenon provides an important basis for optimizing well cluster layout.

[0170] (4.2) Analysis of rock and soil temperature changes after 15 years of operation of pipe groups with different spacing

[0171] Figure 10 This is a relationship diagram between the tube spacing and the surrounding rock temperature at a depth of 2500m obtained from the three-dimensional heat transfer model of the deep buried tube heat exchanger in Example 1 of the present invention;

[0172] Figure 11 This is a cloud diagram of the surrounding rock temperature at a depth of 2500 m under different pipe spacings in Example 1 of the present invention;

[0173] Figure 10 The curves showing the effect of different pipe group spacings (5m, 15m, 30m, 45m, 60m) on the surrounding rock temperature change after the system has been running for 15 years are shown. Figure 7 As shown in the figure, the spacing between pipe groups has a significant impact on the range of surrounding rock temperature variation and temperature gradient. Specifically, as the spacing increases, the range of surrounding rock temperature variation expands, but the temperature gradient decreases, and the temperature drop rate slows down accordingly. When the spacing between pipe groups is small (such as 5m and 15m), the thermal interference effect between pipe groups is significant, resulting in a large surrounding rock temperature gradient and a faster temperature drop. However, when the spacing increases (such as ≥30m), the thermal interference between pipe groups decreases, and the surrounding rock temperature distribution tends to be more uniform. Figure 11 The temperature cloud chart further confirms this pattern: when the spacing between underground pipes is 5m or 15m, thermal interference is severe. When the spacing is 30m or greater, while some interference still exists, this level of interference is acceptable, as analyzed above. Combined with the aforementioned observation that heat generation increases saturate and even decreases after spacing exceeds 30m, 30m is a suitable spacing for underground pipes in the Changsha Airport area.

[0174] Therefore, in actual engineering, it is recommended to comprehensively consider geological conditions, heat storage characteristics and system requirements, and reasonably select the spacing between pipe groups to optimize the distribution of surrounding rock temperature field and ensure the long-term stable operation of the system.

[0175] 3. Conclusion

[0176] Based on the typical geological conditions of Changsha Huanghua Airport, this paper established a numerical model of a medium-deep coaxial buried pipe group. The effects of inlet temperature, heat extraction power, and pipe group spacing on heat extraction efficiency were studied, and the variation of surrounding rock temperature after long-term operation of the system was analyzed. The main conclusions are as follows:

[0177] 3.1. Increasing the pipe group inlet temperature promotes heat extraction to a certain extent. While appropriately increasing the pipe group inlet temperature can increase heat extraction to a certain extent, it is important to consider geological conditions, system energy consumption, and economic efficiency. Excessively high temperatures may lead to decreased efficiency, so the inlet temperature should be optimized within a reasonable range. The inlet temperature in the Changsha Airport area should ideally be 12-14°C. This range offers optimal energy efficiency (high COP and a 10-11% increase in heat extraction). Above 14°C, the benefits diminish (increase ≤ 9% and increased energy consumption). This also helps avoid soil thermal imbalance (the local constant temperature layer is approximately 19°C). Dynamic adjustment (e.g., 14°C → 12°C) can better balance system stability and economic efficiency.

[0178] 3.2. Increasing the heat extraction power will accelerate the decrease in the tube group outlet temperature and the surrounding rock temperature. The rate of decrease increases with operating time. The heat extraction power and the temperature decrease rate are positively correlated. In the Changsha Huanghua Airport area, it is recommended to select a moderate heat extraction power (e.g., 300kW) to balance heat extraction efficiency and long-term stability of the surrounding rock temperature.

[0179] 3.3 Tube group spacing significantly affects surrounding rock temperature distribution and interwell thermal interference. Increasing tube group spacing can reduce thermal interference and achieve a more uniform temperature distribution. However, excessive spacing may limit the heat extraction range of a single tube. In the Changsha area, a moderate spacing (e.g., 30m) is recommended to balance thermal interference suppression and heat extraction efficiency.

[0180] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for optimizing the design of a medium-deep coaxial buried pipe group, characterized in that: The specific steps include: S1. Based on the design of the medium-deep coaxial buried pipe structure, a three-dimensional heat transfer model of the medium-deep buried pipe heat exchanger was established using the double-continuum finite element method, and the control equations were listed; S2. Setting model parameters of a three-dimensional heat transfer model of a medium-deep buried pipe heat exchanger; S3. Set the inlet temperature, heat extraction power, and buried pipe spacing parameters, import the control equations of the three-dimensional heat transfer model of the medium-deep buried pipe heat exchanger, discretize and solve the control equations, and output the heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature, or the outlet temperature; S4. According to the output heat of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature, the inlet temperature, heat extraction power and buried pipe spacing parameters are selected as the optimal design scheme for the medium-deep coaxial buried pipe group.

2. The pipe group optimization design method according to claim 1, characterized in that: The medium-deep coaxial buried pipe structure described in S1 is specifically as follows: the medium-deep coaxial buried pipe includes an inner pipe and an outer pipe that are nested with each other, and backfill material is filled between the outer pipe and the adjacent rock and soil.

3. The pipe group optimization design method according to claim 2, characterized in that: The control equations described in S1 include: The governing equation for heat transfer of fluid in the outer tube channel is: The governing equation for heat transfer of fluid in the inner tube channel is: Heat transfer governing equation for backfill material area: Comprehensive heat transfer governing equations for geotechnical areas: Where ρ is the density, kg / m 3 ; c is specific heat capacity, J / (kg·℃); t is temperature, ℃; τ is time, s; u is the circulating fluid flow rate, m / s; Λ r is the thermal fluid dynamic diffusion tensor; H is the heat source / sink; ε is the porosity; λ is the thermal conductivity, W / (m·K); v is the groundwater seepage velocity, m / s; the subscript r represents the circulating fluid, g represents the backfill material, f represents the groundwater, s represents the rock and soil, i represents the annular channel, and o represents the inner tube channel.

4. The pipe group optimization design method according to claim 1, characterized in that: The model parameters in S2 include the buried pipe structure parameters and the physical property parameters of the stratum rock and soil.

5. The pipe group optimization design method according to claim 1, characterized in that: The parameters of the inlet temperature, heat extraction power, buried pipe spacing and output variables set in S3 are designed by parameter sensitivity analysis method.

6. The pipe group optimization design method according to claim 5, characterized in that: The parameter sensitivity analysis method specifically includes: (1) Design the inlet temperature, heat extraction power and buried pipe spacing parameters of the pipe group respectively, and design 4-6 sets of data for each parameter; (2) The control variable method is used to import the inlet temperature, heat extraction power and buried pipe spacing parameters of the pipe group into the model, and the heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature are output. The corresponding relationship between the inlet temperature, heat extraction power and buried pipe spacing and one or more of the heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature is studied.

7. The pipe group optimization design method according to claim 6, characterized in that: The inlet temperature, heat extraction power and buried pipe spacing parameters of the respective designed pipe groups are designed according to the regional geological conditions, the thermal physical parameters of the rock and soil mass and the design operating conditions of the heat pump unit. The 4-6 groups of data are arranged at intervals. The control variable method specifically includes: fixing two of the inlet temperature, heat extraction power and buried pipe spacing parameters, changing the input parameter data of the remaining one, and outputting the corresponding heat extraction of the mid-deep coaxial buried pipe group, adjacent rock and soil temperature or outlet temperature.

8. The pipe group optimization design method according to claim 6, characterized in that: The study of the correspondence between one of the inlet temperature, heat extraction power and buried pipe spacing and one or more of the heat extraction of the deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature specifically includes: The corresponding relationship between the inlet temperature and the heat taken by the deep coaxial buried pipe group; The corresponding relationship between heating power and adjacent rock and soil temperature or outlet temperature; The corresponding relationship between the spacing between underground pipes and the heat taken by the coaxial underground pipe group in the middle and deep layers; The corresponding relationship between the buried pipe spacing and the adjacent rock and soil temperature or outlet temperature.

9. The pipe group optimization design method according to claim 8, characterized in that: The optimization design scheme for the medium-deep coaxial buried pipe group as described in S4 is to select the inlet temperature, heat extraction power and buried pipe spacing parameters as parameters based on the output heat extraction of the medium-deep coaxial buried pipe group, the adjacent rock and soil temperature or the outlet temperature, and specifically includes: The heat extraction, adjacent rock and soil temperature or outlet temperature output results of the medium-deep coaxial buried pipe group are ranked by multi-index relative combination, and the inlet temperature, heat extraction power and buried pipe spacing parameters corresponding to the optimal output result are selected as the pipe group optimization design parameters.

10. The pipe group optimization design method according to claim 9, characterized in that: After outputting the heat intake of the deep coaxial buried pipe group, the adjacent rock and soil temperature, or the outlet temperature in S4, a curve is drawn corresponding to the inlet temperature, the heat intake power, and the buried pipe spacing, respectively, and the heat intake of the pipe group, the adjacent rock and soil temperature, or the outlet temperature, based on the output data; In the relative combination ranking of multiple indicators, when there is a conflict in the ranking of the heat intake of the deep coaxial buried pipe group, the adjacent rock and soil temperature, or the outlet temperature, the orthogonal experimental range analysis method is used to calculate the weights of the heat intake of the deep coaxial buried pipe group, the adjacent rock and soil temperature, or the outlet temperature, and the corresponding design parameters in the relative combination ranking of multiple indicators are selected according to the order of weights; The calculation formula of the orthogonal experiment range analysis method is as follows: Calculate the range (R), which reflects the degree of influence of factors on the indicator: Where, is the sum of the indicators of each factor at each level, is the average value of the indicators at each level of each factor; Determine the weight of each factor on the indicator based on the range ratio:

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