A method for optimizing design of a medium-shallow coaxial buried pipe group

Abstract

The present application relates to geothermal energy development and utilization technical field, especially relates to a kind of middle-shallow coaxial ground buried pipe group optimization design method.The present application includes the following steps: S1, establish middle-shallow coaxial ground buried pipe group heat transfer model;S2, with pipe depth, heat extraction power and circulation flow as dynamic parameter, substitute into control equation and solve, output middle-shallow coaxial ground buried pipe group surrounding rock minimum temperature and outlet temperature;S3, respectively construct single-variable regression prediction model, determine pipe depth, heat extraction power and circulation flow;S4, based on pipe depth, heat extraction power and circulation flow, dynamically feedback adjustment middle-shallow coaxial ground buried pipe group hardware architecture and control strategy.The present application system analyzes the influence law of three major core parameters of deep pipe depth, circulation flow, heat extraction power on shallow pipe surrounding rock temperature and outlet temperature, and constructs the two-level control system of pre-embedded depth first determining flow / power step control.

Description

Technical Field

[0001] This invention relates to the field of geothermal energy development and utilization technology, and in particular to an optimized design method for a medium-shallow coaxial buried pipe group. Background Technology

[0002] Geothermal resources, as a clean, low-carbon, and sustainable new energy source, have seen advancements in their technological mechanisms. A binary heat accumulation model has been proposed, providing crucial theoretical guidance for the site selection optimization and design upgrades of medium-deep geothermal energy storage systems, thus driving the transformation of geothermal development from resource assessment to technological implementation. With the iterative upgrades of ground source heat pump technology, composite heat exchange systems combining medium-deep and shallow buried pipes are gradually becoming the mainstream form of geothermal development and utilization due to their ability to balance heat exchange efficiency and operational stability. This has also become a research focus for scholars both domestically and internationally.

[0003] Currently, research on medium-deep buried pipe systems focuses on three main areas: design parameter optimization, heat exchange mechanism analysis, and long-term operational characteristic evaluation. Academician Wang Jiyang's "Geothermal+" theory provides a new paradigm for the integrated development of geothermal resources with other renewable energy sources. Wang Guiling points out that to achieve sustainable exploitation of geothermal energy resources, technological breakthroughs should be made in multiple aspects, including geothermal resource exploration, exploitation, and utilization, to develop more heat exchange methods and improve heat exchange efficiency. In terms of international collaborative research, Professor Wang Fenghao's team, in collaboration with the Helmholtz Centre for Environmental Research in Germany and the Technical University of Freiberg, developed a dynamic performance simulation model of a medium-deep U-tube coupled heat pump based on the OpenGeoSys computing platform. Through a combination of engineering measurements and numerical simulations, they elucidated the system load distribution mechanism and long-term performance evolution law. Cai Wanlong, as a core member, focused on the key environmental factor of groundwater seepage, deeply exploring its impact on the long-term heat extraction performance of medium-deep buried pipe groups, quantifying the inter-pipe interaction characteristics and load migration ratio, and improving the detailed understanding of the heat exchange mechanism. Cheng Nan pointed out that when the ratio of cold to heat load in a mixed deep-shallow buried pipe group is 1:2, the heat exchange capacity of a properly designed mixed deep-shallow pipe group is 20% higher than that of a shallow pipe group. Guan Haoran analyzed the influence of various parameters on inter-pipe group thermal interference and system heat exchange performance through experiments, and pointed out that studying the influencing factors and development laws of thermal interference is of great significance for optimizing the heat exchange system and improving heat exchange efficiency. Zhang Fangfang used a deep geothermal energy heating project in a hospital as a case study, and through numerical simulation, gave the design principles for coaxial sleeve heat exchanger design and borehole arrangement.

[0004] Despite the abundant research findings, several shortcomings remain: First, the impact of medium-deep buried pipes on the temperature field of shallow surrounding rock has not been fully quantified, lacking a systematic analysis of its heat transfer path, influence range, and temperature field evolution. Second, the interference mechanism of medium-deep buried pipes on the heat exchange performance of shallow buried pipes has not been thoroughly analyzed, and the intrinsic relationship between its parameters and the outlet temperature and heat exchange efficiency of shallow buried pipes remains unclear. Third, there is a lack of multi-parameter collaborative optimization methods based on the coupling effect between medium and shallow layers, resulting in a lack of systematic multi-parameter matching. Furthermore, engineering design lacks sufficient alignment with relevant technical specifications, such as the clearly defined inlet water temperature threshold requirements for the heating period in the "Technical Specification for Buried Pipe Ground Source Heat Pump Systems" and the "Technical Regulations for Operation and Management of Ground Source Heat Pump Systems," which have not yet been incorporated into targeted design bases for multi-parameter optimization schemes. In addition, the existing dynamic feedback control system does not consider the characteristic that the depth of the deep buried pipe is a fixed parameter pre-embedded in the project; the control link only focuses on flow rate and power, failing to form a step-by-step logic of pre-embedded parameter determination and operational parameter regulation, resulting in a deficiency in the parameter management system. These research gaps often lead to problems in actual engineering projects, such as unbalanced surrounding rock temperature, substandard outlet temperature, and excessive system energy consumption, which limit the efficient and large-scale utilization of medium-deep geothermal resources. Summary of the Invention

[0005] This invention provides an optimized design method for medium-shallow coaxial buried pipe groups. The aim is to systematically analyze the influence of three core parameters—deep buried pipe depth, circulating flow rate, and heat extraction power—on the surrounding rock temperature and outlet temperature of shallow buried pipes through a combination of theoretical modeling, numerical simulation, and orthogonal experiments. Simultaneously, addressing the issue of incomplete parameter control logic in dynamic feedback control, this invention clarifies the attribute classification of deep buried pipe depth as a fixed parameter pre-embedded in the project, and circulating flow rate and heat extraction power as dynamically adjustable parameters during operation. It constructs a two-tiered control system where the pre-embedded depth is determined first, and flow rate / power is controlled step-by-step, thus compensating for the parameter logic deficiencies in the original control links.

[0006] To achieve the above objectives, this invention provides an optimized design method for medium-shallow coaxial buried pipe groups, comprising the following steps: S1. Design a physical model for medium-shallow coaxial buried pipes, establish a heat transfer model for medium-shallow coaxial buried pipe groups, and list the governing equations. S2. Determine the physical parameters of the model, using the buried pipe depth, heat extraction power and circulation flow rate as dynamic parameters, and substitute them into the control equations described in step S1 to solve the problem, outputting the minimum temperature of the surrounding rock and the outlet temperature of the medium-shallow coaxial buried pipe group. S3. Construct univariate regression prediction models for pipe burial depth, heat extraction power, and circulation flow rate with the minimum surrounding rock temperature and outlet temperature, respectively. Based on the data patterns extracted by parameter sensitivity analysis, determine the pipe burial depth mentioned in S2 during the pre-burial stage; and determine the heat extraction power and circulation flow rate mentioned in S2 during the operation stage. S4. Based on the buried pipe depth, heat extraction power, and circulation flow rate determined in S3, dynamically adjust the hardware architecture and control strategy of the medium-shallow coaxial buried pipe group.

[0007] Preferably, the physical model of the medium-shallow coaxial buried pipe in step S1 is as follows: the physical model of the medium-shallow coaxial buried pipe is symmetrical about its central axis and includes an inner pipe of the medium-shallow coaxial buried pipe, an outer pipe of the medium-shallow coaxial buried pipe, backfill material and surrounding rock. The inner pipe of the medium-shallow coaxial buried pipe is connected to the outer pipe of the medium-shallow coaxial buried pipe and circulates fluid.

[0008] Preferably, the establishment of the heat transfer model for the medium-shallow coaxial buried pipe group in step S1, and the listing of the governing equations, specifically includes: Control equations for fluid heat transfer in the outer pipe channel of medium-shallow coaxial buried pipes: (1) Control equations for fluid heat transfer in the inner pipe channel of medium-shallow coaxial buried pipes: (2) Heat transfer control equation for the backfill material zone: (3) Integrated heat transfer control equation for soil and rock regions: (4) In the formula, Density, unit: kg / m³ 3 ; Specific heat capacity, unit: J / (kg·℃); Temperature, in °C; Time, in seconds; The velocity of the circulating working fluid is expressed in m / s. For thermohydrodynamic dispersion tensor; For heat source / heat sink; Porosity; The thermal conductivity is W / (m·K); The groundwater seepage velocity is in m / s; the subscript r represents the circulating medium, g represents the backfill material, f represents the groundwater, s represents the surrounding rock, i represents the outer pipe channel of the medium-shallow coaxial buried pipe, and o represents the inner pipe channel of the shallow coaxial buried pipe.

[0009] Preferably, the physical parameters of the model in step S2 include well depth, well diameter, inner tube outer diameter, inner tube wall thickness, outer tube outer diameter, outer tube wall thickness, inner tube thermal conductivity, outer tube thermal conductivity, circulating medium thermal conductivity, circulating medium specific heat capacity, circulating medium density, backfill material thermal conductivity, geothermal heat flow, surface temperature, fixed heat extraction power, kinematic viscosity coefficient, and dynamic viscosity coefficient.

[0010] Preferably, the construction of the univariate regression prediction model for the buried pipe depth, heat extraction power, and circulation flow rate with the minimum surrounding rock temperature and outlet temperature in step S3 specifically includes: (1) Construct a nonlinear prediction model for the buried pipe depth H in relation to the minimum temperature of the surrounding rock and the outlet temperature; (2) Construct a linear regression prediction model for heat extraction power P with the minimum surrounding rock temperature and outlet temperature: When the heat extraction power is in the range of 250kW~350kW, the outlet temperature of the shallow pipe satisfies the equation T out = T base -k ×( P -250), the minimum temperature of the surrounding rock meets T rock_min =T r-base -m×( P -250); (3) Construct a piecewise saturation prediction model for the circulating flow rate V in relation to the minimum surrounding rock temperature and the outlet temperature: when V < 48m 3 When V ≥ 48 m, the minimum surrounding rock temperature and the outlet temperature follow a logarithmic growth equation; 3 At / h, the minimum surrounding rock temperature and outlet temperature output are constant saturation values.

[0011] Preferably, the nonlinear prediction model for the buried pipe depth H in relation to the minimum temperature of the surrounding rock and the outlet temperature includes: Nonlinear prediction model for outlet temperature with pipe burial depth: Pipe burial depth outlet temperature of coaxial buried pipes in the middle and shallow layers It satisfies an exponentially saturated nonlinear relationship, and its expression is: ; In the formula: Temperature at the outlet of the buried pipe, unit: °C; The depth of the buried pipe is expressed in meters (m). Nonlinear prediction model of minimum surrounding rock temperature with pipe burial depth: Pipe burial depth With the lowest temperature of the surrounding rock It satisfies an exponentially saturated nonlinear relationship, and its expression is: ; In the formula: Minimum temperature of surrounding rock, unit: °C; The depth of the buried pipe is measured in meters (m).

[0012] Preferably, the piecewise saturation prediction model for the circulating flow rate V in relation to the minimum surrounding rock temperature and the outlet temperature specifically includes: Outlet temperature: when <48m 3 / h time: ; when ≥48m 3 / h time: ; Minimum temperature of surrounding rock: when <48m 3 / h time: ; when ≥48m 3 / h time: ; In the formula: Circulation flow rate, unit: m 3 / h; : Temperature at the outlet of the underground pipe, unit: °C; Minimum temperature of surrounding rock, unit: °C; : Logarithmic fitting coefficient of outlet temperature; Logarithmic fitting coefficients for surrounding rock temperature; The outlet temperature is a constant saturation value. : The minimum constant saturation value of the surrounding rock temperature.

[0013] Preferably, the data patterns extracted based on parameter sensitivity analysis in step S3 specifically include: During the pre-embedding stage, the range of the pipe burial depth H is limited to 2000 m ≤ H ≤ 3000 m; During the operation phase, the minimum inlet water temperature ≥4 ℃ is used as the target constraint and substituted into the prediction model to derive the maximum allowable limit heat extraction power P and the most economical pump flow boundary, outputting the optimal combination of operating parameters: The range of the circulating flow rate V is limited to 38 m³. 3 / h≤V≤48 m 3 / h; The range of heat extraction power P is limited to 250 kW ≤ P ≤ 325 kW.

[0014] Preferably, the hardware architecture of the shallow coaxial buried pipe group in the dynamic feedback adjustment step S4 includes: Sensing unit: Install high-precision water temperature sensors on the outlet branch pipes of the medium-shallow underground pipe group; Execution unit: A variable frequency circulating water pump supporting stepless flow regulation is configured on the medium-shallow circulation pipeline; a variable frequency heat pump unit with variable load is configured on the heat source side of the system; Control unit: A PLC or microprocessor is used as the central controller. The controller stores a univariate regression prediction model of the buried pipe depth, heat extraction power and circulation flow rate with the minimum temperature of the surrounding rock and the outlet temperature, as well as the optimal range of each operating parameter.

[0015] Preferably, the control strategy for the shallow coaxial buried pipe group in step S4, which involves dynamic feedback adjustment, specifically includes: Step 1: Real-time monitoring and deviation analysis by the sensing unit. The central controller reads the actual outlet temperature Treal of the shallow buried pipe in real time and compares it with the safety red line threshold of 4 ℃ required by the regulations and the theoretical operating temperature Tpredict output by the prediction model to determine whether the system has a cold accumulation trend. Step 2: Level 1 Defense Against Circulating Traffic: When the sensing unit detects that Treal is continuously decreasing and approaching the minimum inlet water temperature, the controller determines that preliminary cold accumulation has occurred in the shallow layer. Based on the segmented saturation prediction model of the circulation flow rate V, the minimum surrounding rock temperature, and the outlet temperature, the controller first issues a frequency increase command to the variable frequency circulating water pump to gradually increase the circulation flow rate of the deep buried pipe. If the current flow rate V has not reached the saturation threshold of the interval range, the flow rate is continuously increased until it reaches the saturation threshold to alleviate the temperature drop by increasing convective heat transfer. If the current flow rate is already within the interval range, it is adjusted to the optimal value. Step 3: Secondary defense for heat extraction power: When the circulation flow rate V has reached the saturation threshold, if Treal still falls below the minimum inlet water temperature, it indicates that the system has entered a deep heat deficit state. The control unit triggers the power limiting strategy, which links the variable frequency heat pump unit of the execution unit to reduce the overall heat extraction power of the system step by step according to the set step size, until the shallow surrounding rock temperature sensor reports that the local ground temperature has rebounded, the outlet temperature has recovered to above 4 ℃, and the heat extraction power P is not lower than the lower limit of the range. Step 4: Continuous monitoring and homeostasis maintenance: Once the outlet temperature recovers to above the safe threshold and remains stable, the controller adjusts the flow rate and power to the optimal values ​​to maintain steady-state operation of the system, continuously monitors various parameters, and responds promptly to new temperature deviations.

[0016] The above-described solution of the present invention has the following beneficial effects: (1) This invention establishes a tube group heat exchange model that considers long-term heat conduction effects and surrounding rock characteristics, and reveals the dynamic evolution characteristics of the temperature field under 15 years of continuous operation, making up for the lack of analysis of long-term effects in previous studies. (2) Through a three-factor, five-level orthogonal experiment, the influence weight of each parameter on the system operating characteristics was quantified, the influence law of depth being dominant, power being secondary, and flow being weak was clarified, the research system on the influence of parameters was improved, and a quantitative basis was provided for multi-parameter collaborative optimization. (3) A step-by-step parameter control strategy of pre-embedded fixing and operation regulation was proposed. First, the depth of deep buried pipe was determined in the engineering erection stage, and then the circulation flow and heat extraction power were dynamically adjusted in the system operation stage, so as to make the parameter control logic more complete. (4) A multi-objective optimization scheme that balances performance, cost, and stability was proposed, and the optimal combination of design parameters that is both technically feasible and economically reasonable was determined, providing technical support for the efficient and sustainable exploitation of geothermal energy. The research results can provide theoretical support and technical reference for the optimized design and engineering application of buried pipe network systems. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the heat exchange principle of a shallow to medium-depth buried pipe heat exchanger. Figure 2 The graph shows the effect of the pipe burial depth on the temperature of the surrounding rock (-200m) at the bottom of the shallow pipe in Example 1 (15 years later). Figure 3 The inlet and outlet temperature curves of the shallow pipe 2 corresponding to different depths of the deep pipe in Example 1 (operation for 15 years); Figure 4 This is a graph showing the temperature change trend of the soil and rock at a depth of 200 meters 15 years after the underground pipe group in Example 1 was used for heat extraction. Figure 5 The graph shows the temperature drop of the surrounding rock at the bottom of the shallow buried pipe as a function of power in Example 1 (relative to the original temperature of 24.2℃). Figure 6 This is a graph showing the heat extraction power of the deep buried pipe and the inlet and outlet temperatures of the shallow buried pipe 1 in Example 1. Figure 7 This is a graph showing the relationship between different heat extraction powers of deep buried pipes and the outlet temperature of shallow buried pipes in Example 1 (15 years later). Figure 8 This is a graph showing the effect of different circulation flow rates of deep buried pipes on the surrounding rock temperature of shallow buried pipes in Example 1. Figure 9This is a graph showing the effect of different circulation flow rates of the deep buried pipe on the outlet temperature of the shallow buried pipe 2 in Example 1. Figure 10 This is a flowchart of the optimized design method for the medium-shallow coaxial buried pipe group in Example 1; Figure 11 This is a diagram showing the model matching results in Example 1. Detailed Implementation

[0019] To make the technical problems, solutions, and advantages of this invention clearer, a detailed description will be provided below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0020] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the 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.

[0021] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a locking connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0022] Furthermore, 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.

[0023] In this embodiment of the invention, the structure of the shallow to medium-depth buried pipe heat exchange system includes an inner pipe, an outer pipe, backfill material, and surrounding rock mass. Since this structure is symmetrically distributed along its central axis, to simplify the analysis, any cross-section passing through the axis of the inner pipe can be used for numerical simulation studies of the heat exchange performance. The established physical model is as follows: Figure 1 As shown.

[0024] Example 1: The flowchart of the shallow coaxial buried pipe group optimization design method in Example 1 is as follows: Figure 10 As shown.

[0025] (I) Principles for determining the depth of deep buried pipes and guidance for construction. The depth of deep pipe burial is an irreversible pre-embedded parameter for the project, directly determining the basic performance of the system. It needs to be determined comprehensively by considering three core factors during the underground pipe laying construction phase to complete the burial scheme design and construction implementation. The specific determination principles are as follows: Geological constraint principle: Based on the geological exploration data of the project site, determine the maximum drilling depth of the site. The selected depth shall not exceed the geological bearing capacity limit to avoid engineering risks such as borehole collapse and rock strata fracture. Performance requirements principle: If the project has high requirements for geothermal heat extraction performance (such as heating of large buildings or industrial heating), the depth range of 2500~3000m should be selected first to ensure stable outlet temperature of shallow buried pipes and weak thermal interference effect; if it is a small-scale civil heating project, the economical depth range of 2000~2500m can be selected to balance performance and construction difficulty. Economic budgeting principle: When the budget is sufficient, the optimal depth of 2500m should be selected based on the initial installation and well construction budget of the project; if the budget is limited, the lower limit of 2000m should be selected. At the same time, low power and flow rate operating parameters should be matched in advance to form a defensive design.

[0026] Burial construction guidance process: 1. Site geological exploration to determine the range of drillable depths; 2. Input project performance requirements and economic budget, and screen candidate depth values ​​using the prediction model of this invention; 3. Determine the final burial depth by combining the preferred depth range (2000m≤H≤3000m); 4. Complete the burial of 9 pipe groups according to the array layout (1 deep pipe in the middle, 8 shallow pipes of 200m around it, with a pipe group spacing of 5m); 5. After burial, carry out drilling and cementing, heat exchanger installation and pipeline connection to complete the pre-burial stage construction.

[0027] (II) Model Establishment and Solution of Medium-Deep Coaxial Buried Pipe Heat Exchanger 1. Model Establishment Step 1: Establish a model of a medium-deep coaxial buried pipe heat exchanger. The model is divided into two parts with the borehole wall as the boundary. One part is the heat exchanger and cementing sheath inside the borehole, and the other part is the formation outside the borehole. Based on the change of formation temperature with depth, the heat transfer process of the two parts is calculated separately, and the two parts are coupled together by the borehole wall temperature.

[0028] 2. Solving the formation heat conduction equation Step 2: Solving the formation heat conduction equations: OpenGeoSys uses the laws of conservation of mass and energy for numerical simulation, establishing a three-dimensional numerical model of the medium-deep buried pipe heat exchanger based on the dual-continuous medium finite element method. The circulating working fluid in the heat exchanger flows in from the annulus of the casing and out from the central pipe, exchanging heat with the surrounding soil and rock during the flow. In the heat transfer simulation, the soil and rock and the circulating working fluid are treated as two continuous media, coupled through a heat flow boundary. The relevant governing equations follow the third type of boundary conditions at the heat transfer interface. The relevant heat transfer governing equations for the medium-deep coaxial buried pipe heat exchanger and the soil and rock mass are as follows: Control equations for heat transfer in annular channels: (1) Inner tube channel fluid heat transfer control equation: (2) Heat transfer control equation for the backfill material zone: (3) Integrated heat transfer control equation for soil and rock regions: (4) In the formula, Density, kg / m³ 3 ; Specific heat capacity, J / (kg·℃); Temperature, °C; For time, s; The velocity of the circulating working fluid is m / s; For thermohydrodynamic dispersion tensor; For heat source / heat sink; Porosity; Thermal conductivity, W / (m·K); The groundwater seepage velocity is expressed in m / s; the subscript r represents the circulating working fluid, g represents the backfill material, f represents groundwater, s represents soil and rock, i represents the annular cavity channel, and o represents the inner pipe channel.

[0029] 3. Model parameters and boundary conditions Model parameters: The medium inside the medium-deep buried pipe heat exchanger is softened water. The established model parameters are shown in Table 1, the physical properties of the soil and rock are shown in Table 2, and the geothermal gradient of the study area is 2.45 ℃ / hm.

[0030] Table 1. Physical parameters required for simulation

[0031] Table 2 Summary of thermophysical parameters of core samples

[0032] Boundary conditions: The average annual surface temperature in Changsha is 19.3 ℃, so the surface is set as a type I isothermal boundary condition with a value of 19.3 ℃. The far boundary around the control volume is set as a type II boundary condition (adiabatic boundary) with a boundary heat flux of 0.

[0033] (III) Sensitivity analysis of operating parameters Step 3: Using the parameter sensitivity analysis method, based on the determined deep buried pipe depth, we quantitatively evaluate the impact of two major operating parameters, namely the circulation flow rate and heat extraction power of the deep buried pipe, on the long-term heat extraction performance of the shallow buried pipe system (the influence law of deep buried pipe depth has been analyzed in the pre-buried stage, and the focus here is on analyzing the operating parameters).

[0034] 1. The impact of buried pipe depth on the heat exchange performance of pipe groups (core analysis content in the pre-buried stage) To investigate the fundamental impact of deep buried pipe depth on the heat exchange performance of shallow buried pipes, a group of nine buried pipes arranged in a square array was constructed. One pipe in the center was a deep buried pipe, surrounded by eight shallow buried pipes, each 200m in length, with a spacing of 5m between the pipes. The shallow buried pipes had a flow rate of 0.5 m³ / h and a heat extraction power of 5 kW, while the deep buried pipes had a flow rate of 23 m³ / h and a heat extraction power of 250 kW. The buried pipe depths were successively changed to 1000m, 1500m, 2000m, 2500m, and 3000m. The pipe group operated continuously for 15 years, and the temperature variation of the surrounding rock at a depth of 200m was analyzed.

[0035] (1) Influence of depth on temperature changes of surrounding rock in shallow pipes As the depth of medium-deep buried pipes increases, the distribution of the surrounding rock temperature field (original soil temperature 24.2℃) of shallow buried pipes changes, and the thermal interference effect at 200m underground weakens. When the deep pipe burial depth is 1000m, the surrounding rock temperature curve exhibits a V-shaped distribution, with a sharp temperature drop in the central region (x-axis -10m~10m), reaching a minimum of only 7.1504℃, a temperature difference of 17℃ with the edge region, and a clear temperature abrupt change zone (x-axis ±20m~±50m). When the deep pipe burial depth is 3000m, the surrounding rock temperature curve exhibits a gentle U-shaped distribution, without a clear temperature abrupt change zone, with a minimum temperature of 20.1543℃, and a temperature difference of only 4℃ between the center and the edge. When the deep pipe burial depth is between 1500m, 2000m, and 2500m, the surrounding rock temperature curve shows transitional characteristics. Therefore, in medium-shallow buried pipe systems, as the deep pipe burial depth increases, the shape of the surrounding rock curve gradually changes from V-shaped to U-shaped, and the temperature abrupt change zone disappears. The influence curve of depth on the temperature of the surrounding rock at the bottom (-200m) of shallow buried pipes (15 years later) is shown in the figure. Figure 2 As shown; Table 3. Overview of the effect of deep buried pipe depth on the surrounding rock temperature of shallow buried pipes (15 years later)

[0036] Depend on Figure 2 It is evident that, with other parameters remaining constant, the minimum temperature of the surrounding rock (200m) of shallow buried pipes gradually increases with increasing depth, and the rate of increase gradually decreases, with the minimum temperature growth rate ranging from 77.09% to 9.39%. Beyond 2000m, the increase in the minimum temperature of the surrounding rock is smaller, and the surrounding rock temperature becomes more stable. Simultaneously, the standard deviation of the surrounding rock temperature gradually decreases from 4.1071℃ at 1000m to 1.0335℃ at 3000m, with a decrease of 25%–30% for every 500m increase in depth (see Table 3). This indicates that the uniformity of the surrounding rock temperature field significantly improves with increasing pipe depth. Specifically, when the deep buried pipe is 1000m, the temperature distribution of the surrounding rock of shallow buried pipes fluctuates drastically; the standard deviation of temperature drops below 2℃ at a depth of 2000m, and is <1.5℃ at depths below 2500m. After a depth of 2000m, the rate of decrease in standard deviation remains stable (26.3% decrease from 2000-2500m, 28.4% decrease from 2500-3000m), and the uniformity of the surrounding rock temperature field reaches a good level. This can effectively avoid the risk of surrounding rock cracking caused by excessive temperature gradient, and provide a guarantee for the long-term stable operation of the system. Therefore, under the condition that other parameters remain unchanged, and with appropriate consideration of economic factors, the depth of buried pipe should be greater than 2000m.

[0037] The thermal influence range of the buried pipe depth on the surrounding rock at a depth of 200m was analyzed. Data processing and analysis showed that the thermal influence range decreased progressively from 104.1m at a depth of 1000m (covering an area of ​​±52m along the x-axis) to 94.5m at 1500m, 84.6m at 2000m, 78.6m at 2500m, and finally to 71.1m at 3000m (covering only an area of ​​±35.5m along the x-axis). It is evident that in the medium-shallow buried pipe network system, the thermal influence range of the surrounding rock at a depth of 200m gradually decreases with increasing buried pipe depth. The influence range shows a linear negative correlation with depth, decreasing by 15-20m for every 1000m increase in depth.

[0038] This is primarily due to the increased vertical distance heat must travel from the deep pipe to the surrounding rock 200m underground as depth increases. Since thermal resistance is proportional to distance, this significantly reduces heat transfer efficiency. Simultaneously, the density and thermal conductivity of the rock strata change with depth, with intermediate strata forming a natural insulating layer that further weakens vertical heat transfer. Furthermore, the wider the vertical heat diffusion range, the lower the heat flux density per unit area, resulting in a substantial reduction in the amount of heat reaching the surrounding rock 200m underground. Ultimately, this manifests as a weakened cooling effect, a smaller affected area, and a more uniform temperature field. Therefore, the reasons for the gradual reduction in the thermal impact range can be summarized as the heat transfer path effect, the stratum insulation effect, and the heat diffusion dilution effect. The greater the depth, the weaker the horizontal heat diffusion capacity, resulting in a lower risk of thermal interference to surrounding underground facilities and a significantly improved system environmental compatibility.

[0039] (2) The effect of buried pipe depth on the outlet temperature of shallow buried pipe The depth of deep buried pipes indirectly affects the outlet temperature of shallow buried pipes by changing the heat transfer efficiency, heat influence range, and temperature field gradient between pipe groups. The shallower the depth of the deep buried pipe (e.g., 1000m), the closer its vertical distance to the shallow buried pipe, resulting in lower thermal resistance. The low-temperature effect generated during heat extraction is more easily transferred to the shallow buried pipe area through the surrounding rock, leading to a significant decrease in the temperature of the surrounding rock around the shallow buried pipe, a smaller heat exchange temperature difference, and a corresponding drop in the outlet temperature. Conversely, as the depth of the deep buried pipe increases (e.g., 2500m~3000m), the vertical heat transfer path lengthens, the thermal resistance increases, and the natural insulation effect of the geological rock strata and the vertical diffusion and dilution effect of heat are enhanced. The cooling effect of the deep pipe on the shallow buried pipe area is significantly reduced, the temperature of the surrounding rock around the shallow buried pipe is closer to the original temperature, the heat exchange efficiency remains stable, and the outlet temperature is maintained at a higher level. At the same time, the increase in the depth of the deep buried pipe also reduces the heat influence range and improves the uniformity of the temperature field, avoiding heat exchange efficiency fluctuations caused by local low temperatures in the shallow buried pipe, further ensuring the stability of the outlet temperature. Ultimately, the following influence pattern emerges: "The shallower the deep buried pipe, the lower and more volatile the outlet temperature of the shallow buried pipe; the deeper the depth, the higher and more stable the outlet temperature."

[0040] Since the distance between shallow buried pipes and deep buried pipes plays a significant role in their outlet temperature, we will analyze shallow buried pipe 2, which is closer to the deep buried pipe. Figure 3Table 4 shows that, with other parameters remaining constant, the outlet temperature of shallow buried pipe 2 gradually increases with increasing depth, but the rate of increase decreases, especially after the depth exceeds 2000m, where the temperature rise is relatively small. At a depth of 2000m, after 15 years of operation, the lowest outlet temperature of shallow buried pipe 2 is 4℃. Relevant technical regulations, such as "DB37T5148-2019 FDIS Ground Source Heat Pump System Operation and Management Technical Specifications," indicate that the temperature entering the water source heat pump unit during heating should not be lower than 4℃. Therefore, it is recommended that the depth of the deep buried pipe should exceed 2000m in engineering practice. The inlet and outlet temperature curves of shallow pipe 2 at different depths (after 15 years of operation) are shown below. Figure 3 As shown.

[0041] Table 4. Summary of Temperature Changes at the Outlet of Buried Pipe 2 after 15 Years of Operation

[0042] 2. The impact of heat extraction power on the heat exchange performance of the tube group (core analysis of operating parameters) (1) Morphological characteristics of temperature curves of surrounding rock in shallow buried pipes The actual process of underground pipe heat extraction, based on the fundamental principles of heat transfer, involves the following: As the heat extraction power of deep underground pipes gradually increases (from 250kW to 350kW), the heat absorbed by the pipe network from the soil per unit time increases significantly. This disrupts the original thermal equilibrium in the rock strata, causing a rapid drop in the temperature of the surrounding rock. Due to the large heat capacity of deep soil and the slow heat replenishment, a low-temperature "heat deficit zone" gradually forms around the deep pipes as the heat extraction power continues to increase. This zone acts like a "low-temperature vortex," continuously transferring cold energy to the surrounding area, laying the foundation for subsequent impacts on shallow underground pipes. Figure 4 As shown, due to the symmetry of the underground pipe network layout and the isotropic nature of heat conduction, the temperature distribution curves of the surrounding rock along the distance under different power levels all exhibit a "symmetrical U-shape." In the pipe network layout, the deep pipes are located in the center, and heat is conducted evenly to the surrounding areas, forming a symmetrical temperature distribution. Therefore, the curve, centered at point 0 (the location of the deep pipes), first rapidly decreases to a low temperature trough on both sides, and then slowly rises back to the original temperature. Moreover, the higher the power, the lower the trough value and the wider the trough: at 250kW, the trough width (temperature < 19℃ range) is approximately 10m, and at 350kW, the trough width expands to 20m.

[0043] (2) Temperature variation characteristics of the surrounding rock of shallow buried pipes In the shallow-to-medium-depth buried pipe network system, as the heat extraction power of the deep buried pipes increases, the average temperature of the surrounding rock 200m underground in the shallow pipes decreases linearly, from 23.4759℃ at 250kW to 23.2344℃ at 350kW, a total decrease of 0.2415℃. The lowest temperature of the surrounding rock decreases from 18.4241℃ at 250kW to 16.3504℃ at 350kW, a total decrease of 2.0737℃. It is evident that the response sensitivity of the lowest temperature to power changes is significantly higher than that of the average temperature, being 8.6 times the average temperature decrease. The minimum temperature decrease per unit power remains constant at -0.02074℃ / kW. Simultaneously, the location of the low-temperature core zone expands from ±25~±30m to ±35~±40m, increasing the affected area by 60%.

[0044] Table 5. Temperature Variation of Surrounding Rock (-200m) in Shallow Buried Pipes

[0045] The graph shows the temperature drop of the surrounding rock at the bottom of the shallow buried pipe as a function of power (relative to the original temperature of 24.2℃). Figure 5 As shown, the linear decrease in the average temperature of the surrounding rock stems from the dynamic balance between the heat extraction intensity of the deep-buried pipes and the soil heat supply. Fifteen years of long-term operation has brought the geothermal field to a quasi-steady state. The heat extraction amount increases proportionally with the heat extraction power, leading to a slow depletion of the overall soil heat storage. The drastic change in the minimum temperature of the surrounding rock vividly reflects the "thermal siphon effect" of the deep-buried pipes. The increased heat extraction power creates a stronger low-temperature negative pressure zone around the deep-buried pipes, causing heat to rapidly converge towards them, resulting in a sharp drop in temperature in the central area of ​​the pipe group (the low-temperature core area). The outward expansion of the low-temperature core area is due to the enhanced spatial penetration of the thermal influence under high power, which breaks the original thermal equilibrium boundary, causing the low-temperature zone to continuously spread to the area where the shallow pipes are located. Furthermore, since the shallow pipes themselves are also extracting heat, this further exacerbates the local low-temperature effect.

[0046] (3) The effect of heat extraction power on the outlet temperature of shallow pipe As mentioned earlier, when the heat extraction power of deep buried pipes is low, the temperature of the surrounding soil and rock is stable, maintaining a good heat exchange temperature difference with the medium inside the pipe, and the outlet temperature is also relatively stable. However, as the heat extraction power of deep buried pipes increases, the heat deficit zone gradually expands and conducts upwards, causing the temperature of the surrounding soil and rock around the shallow buried pipe to gradually decrease. This leads to a reduction in the temperature difference between the shallow buried pipe and the soil and rock. According to the principle of heat exchange, a decrease in temperature difference will reduce the amount of heat transferred from the soil and rock to the medium inside the pipe per unit time. With a fixed flow rate, the medium inside the pipe will not absorb enough heat, and the outlet temperature will inevitably decrease. Therefore, as the heat extraction power of deep buried pipes further increases, the temperature of the surrounding rock of shallow buried pipes continues to decrease, and thus the downward trend in the outlet temperature will become more pronounced. Figure 6 .

[0047] When the heat extraction power of the deep buried pipe increases from 250kW to 350kW, the heat extraction rate increases by 40%, significantly enhancing the heat extraction intensity on the surrounding soil. This creates a larger and lower-temperature low-temperature heat-affected zone around the deep pipe. This low-temperature zone diffuses into the surrounding soil through heat conduction. The shallow buried pipe is within this heat-affected zone, and due to the thermal interference effect, its outlet temperature decreases synchronously with the decrease in soil temperature. As the heat extraction power of the deep buried pipe gradually increases, the outlet temperature of the shallow buried pipe gradually decreases, showing a perfect linear negative correlation. For every 1kW increase in heat extraction power, the outlet temperature of shallow pipe 1 decreases steadily by approximately 0.0157℃, and that of pipe 2 decreases steadily by approximately 0.0217℃. When the heat extraction power of the deep buried pipe increased from 250kW to 350kW (an increase of 100kW), the outlet temperature of pipe 1 decreased from 7.45582℃ to 5.88218℃ (a decrease of approximately 1.57364℃), while that of pipe 2 decreased from 6.71932℃ to 4.54668℃ (a decrease of approximately 2.17264℃). Furthermore, the temperature difference between the two pipes increased linearly with increasing power, from 0.7365℃ to 1.3355℃. Throughout this process, during 15 years of continuous operation, the temperature remained stable without significant fluctuations, demonstrating quasi-stable characteristics under long-term operation.

[0048] Meanwhile, the 5m spacing between the pipes in the array leads to differences in the degree of interference experienced by shallow buried pipes 1 and 2. Pipe 2, due to its location (in a more heat-sensitive area or closer to the core of heat interference), is more sensitive to power changes, experiencing a larger temperature drop and a continuously widening temperature difference as the power increases. Table 6 shows that when the deep buried pipe heat extraction power is 350kW, after 15 years of system operation, the outlet temperature of shallow buried pipe 2 is relatively low, at 4.55℃. Therefore, to ensure long-term system operation, the deep buried pipe heat extraction power should not be too high; a value below 350kW, with 300-325kW being more suitable, is preferable.

[0049] Table 6. Statistical table of outlet temperatures of shallow buried pipes corresponding to different thermal powers of deep buried pipes.

[0050] Relationship between different heat extraction capacities of deep buried pipes and outlet temperatures of shallow buried pipes (15 years later) Figure 7 As shown.

[0051] 3. The impact of deep-buried pipe circulation flow rate on the operating characteristics of shallow-buried pipes (core analysis of operating parameters) (1) The effect of deep buried pipe flow rate on the surrounding rock temperature of shallow buried pipe Under different circulation flow rates (18-58 m³ / h) in deep buried pipes, the surrounding rock temperature at a depth of 200 m in shallow buried pipes exhibits a radial spatial distribution characteristic of "low at the center, high at the periphery, and decreasing gradient." The central point (0 m) of the deep buried pipes is the cooling core zone, with the lowest temperature, and the lowest temperature is concentrated here for all flow rates. In the near zone (0-10 m), due to the superposition of the temperature fields of the nine pipe groups, the temperature rises rapidly and the gradient change is most significant. In the middle zone (10-50 m), the cooling effect gradually weakens, and the temperature rises slowly, showing a transitional characteristic. Beyond 50 m, the temperature in the far zone tends to stabilize, basically maintaining near the original ground temperature (24.2 ℃), and the influence of heat extraction by the pipe group is negligible. The overall spatial distribution shows good symmetry and regularity. Figure 8 .

[0052] This is because at low circulation flow rates (18-38 m³ / h), the circulating working fluid has a long residence time in the 2500 m deep buried pipe (approximately 5.8 days at 18 m³ / h), resulting in sufficient heat exchange with the deep soil and rock mass, extracting more heat, and forming a high-intensity low-temperature zone in the deep layer. The cold energy is vertically conducted to the shallow layer and then diffuses horizontally in all directions. This, combined with the superposition effect of the only 5 m spacing between the pipe groups, leads to a greater temperature drop in the near-zone. At high flow rates (48-58 m³ / h), the working fluid has a fast flow rate and a short residence time (approximately 2.2 days at 48 m³ / h), resulting in insufficient heat exchange. The intensity of the low-temperature zone in the deep layer weakens, reducing the amount of cold energy conducted to the shallow layer and weakening the cooling effect. Therefore, the above-mentioned characteristic of "low in the center, high in the periphery, and decreasing gradient" is the result of the coupling effect of the flow rate-dominated difference in heat exchange efficiency, the temperature field conduction law of the soil and rock mass, and the system's thermal balance constraints.

[0053] Table 7. Statistical table of relationship between deep buried pipe circulation flow rate and surrounding rock temperature at 200 m underground.

[0054] Analysis of the surrounding rock temperature data revealed that the average near-field temperature gradually increased from 18.747℃ at 18 m³ / h to 19.48℃ at 48-58 m³ / h, with a maximum temperature difference of 0.732℃. The maximum temperature drop calculated based on the original ground temperature (24.2℃) decreased from 6.116℃ to 5.267℃, and the temperature drop rate decreased from 25.273% to 21.764%. The cooling intensity significantly weakened with increasing flow rate (see Table 7). This demonstrates that the influence of deep buried pipe circulation flow rate on surrounding rock temperature exhibits a significant regularity and a clear saturation effect; flow rate is positively correlated with surrounding rock temperature and negatively correlated with cooling intensity. When the flow rate was increased to 48 m³ / h, further increases to 58 m³ / h resulted in all indicators, including the near-zone average temperature, minimum temperature, maximum temperature drop, and temperature drop rate, remaining completely consistent. This indicates that the flow rate's influence has reached its physical limit; further increases in flow rate only increase pump power consumption and cannot alter the surrounding rock temperature distribution characteristics. Deep soil and rock have physical limits to their thermal conductivity; the amount of heat transferred to the buried pipe per unit time is limited. Furthermore, the total heat extraction power of the system remains constant; increasing the flow rate only alters the temperature difference of the working fluid itself and cannot increase the total heat extraction. Therefore, when the circulating working fluid flow rate in the deep buried pipe reaches 48 m³ / h, a flow saturation effect occurs in the surrounding rock temperature change; that is, when the circulating flow rate in the deep buried pipe increases to a certain extent, the surrounding rock temperature no longer changes.

[0055] (2) The effect of deep buried pipe flow rate on shallow buried pipe outlet temperature Under different circulation flow rates in deep buried pipes, the outlet temperature of shallow buried pipes consistently exhibits a three-stage evolution characteristic of "rapid decrease – slow decay – stable equilibrium," as shown in [reference needed]. Figure 9 In the initial stage of the pipe network system operation (0-2 years), due to the high-intensity heat extraction (250 kW) from the deep buried pipes and the rapid superposition of the pipe network temperature field, the outlet temperature of the shallow buried pipes drops rapidly to 10-11 ℃. This stage has the fastest cooling rate, with an average annual temperature drop of 2-3 ℃. In the middle stage of operation (2-10 years), the underground soil and rock gradually form a relatively stable low-temperature zone, the heat exchange gradient decreases, and the temperature drop rate slows significantly, with an average annual temperature drop of 0.1-0.2 ℃. In the later stage of operation (10-15 years), the underground temperature field reaches a dynamic thermal equilibrium state, and the outlet temperature of the shallow buried pipes basically remains near a stable value with slight fluctuations, not exceeding 0.2 ℃, marking the system's entry into a long-term stable operation stage. The relationship between different circulation flow rates of the deep buried pipes and the outlet temperature of the shallow buried pipes is shown in the figure below. Figure 9 As shown.

[0056] Table 8. Statistical table of outlet temperature of shallow buried pipe 2 as a function of flow rate of deep buried pipe.

[0057] As shown in Table 8, when the circulation flow rate of the deep buried pipe gradually increases from 18 m³ / h to 48 m³ / h, the outlet temperature of the shallow buried pipe 2 in the steady-state stage gradually increases from 6.34 ℃ to 7.28 ℃, with a temperature increase of 0.94 ℃. Simultaneously, the temperature drop decreases from 8.53 ℃ to 7.62 ℃, and the temperature drop rate decreases from 57.35% to 51.14%, indicating that increasing the flow rate can effectively slow down the temperature drop amplitude and rate in the shallow buried pipe. However, when the flow rate is further increased from 48 m³ / h to 58 m³ / h, key indicators such as the initial temperature, steady-state temperature, temperature drop, and average temperature in the steady-state stage of the shallow buried pipe remain unchanged. This indicates that at this point, the working fluid flow in the deep buried pipe has reached a fully developed turbulent state, the heat exchange efficiency is approaching its limit, and the influence of the flow rate on the underground temperature field and the temperature of the shallow buried pipe has reached saturation. Further increasing the flow rate can no longer change the system's thermodynamic characteristics; it will only increase pump power consumption. Therefore, there is a significant positive correlation between the circulation flow rate of deep buried pipes and the outlet temperature of shallow buried pipes, and a noticeable flow saturation effect exists. Thus, when the deep buried pipe flow rate is 48 m³ / h, the outlet temperature of the shallow buried pipe remains at 7.28 ℃, resulting in a higher system COP (coefficient of performance). Compared to 58 m³ / h, this reduces pump power consumption, balancing energy efficiency and economy. Therefore, it is recommended that the circulation flow rate of deep buried pipes be selected between 38 and 48 m³ / h.

[0058] (iv) Construction of prediction model Step four: Construct a univariate prediction model for the temperature field of shallow buried pipes. Based on the data patterns extracted from parameter sensitivity analysis, establish a mathematical regression prediction model for the outlet temperature of shallow buried pipes and the minimum temperature of the surrounding rock, specifically including: (1) Constructing a linear regression prediction model for heat extraction power P: When the heat extraction power is in the range of 250kW~350kW, the outlet temperature of the shallow pipe satisfies the equation T out = T base -k ×( P -250), the minimum temperature of the surrounding rock meets T rock_min =T r-base -m×( P -250); (2) Construct a piecewise saturation prediction model for the circulating flow rate V: when V < 48 m 3 When V ≥ 48 m, the temperature follows a logarithmic growth equation; when V ≥ 48 m 3 When / h, the temperature model output is a constant saturation value; Outlet temperature: when <48m 3 / h time: ; when ≥48m 3 / h time: ; Minimum temperature of surrounding rock: when <48m 3 / h time: ; when ≥48m 3 / h time: ; In the formula: Circulation flow rate, unit: m 3 / h; : Temperature at the outlet of the underground pipe, unit: °C; Minimum temperature of surrounding rock, unit: °C; : Logarithmic fitting coefficient of outlet temperature; Logarithmic fitting coefficients for surrounding rock temperature; The outlet temperature is a constant saturation value. : Minimum constant saturation temperature of the surrounding rock; Applicable range: 38m 3 / h≤H≤48m 3 / h.

[0059] (3) Construct a nonlinear prediction model for the buried pipe depth H. (For depth screening in the pre-buried stage).

[0060] The nonlinear prediction models for the pipe burial depth H in relation to the minimum temperature of the surrounding rock and the outlet temperature include: Nonlinear prediction model for outlet temperature with pipe burial depth: Pipe burial depth outlet temperature of coaxial buried pipes in the middle and shallow layers It satisfies an exponentially saturated nonlinear relationship, and its expression is: ; In the formula: Temperature at the outlet of the buried pipe, unit: °C; The buried pipe depth is expressed in meters (m); applicable range: 2000m ≤ H ≤ 3000m. Nonlinear prediction model of minimum surrounding rock temperature with pipe burial depth: Pipe burial depth With the lowest temperature of the surrounding rock It satisfies an exponentially saturated nonlinear relationship, and its expression is: ; In the formula: Minimum temperature of surrounding rock, unit: °C; The depth of the buried pipe is measured in meters (m). Applicable range: 2000m ≤ H ≤ 3000m.

[0061] (V) Parameter optimization and dynamic feedback control system design 1. Parameter optimization Step 5, Parameter Optimization Based on the Prediction Model: In the pre-buried stage, the depth of the buried pipe is determined according to the depth optimization range (2000 m ≤ H ≤ 3000 m); in the operation stage, the minimum inlet water temperature (≥4 ℃) required by the "Technical Specification for Operation and Management of Ground Source Heat Pump Systems" is substituted into the prediction model as the target constraint, and the maximum allowable limit heat extraction power and the most economical water pump flow boundary are derived in reverse, outputting the optimal combination of operating parameters: The optimal range for circulating flow rate (V) is: 38 m³ / h ≤ V ≤ 48 m³ / h; Preferred range for heat extraction power (P): 250 kW ≤ P ≤ 325 kW.

[0062] Step six: Based on the prediction model, set the parameter optimization range and collaborative constraint boundary for the pipeline system engineering design. All operating parameters are optimized within the above range to ensure that the system meets the performance, safety and economic requirements.

[0063] 2. Hardware Architecture of Dynamic Feedback Control System To achieve the dynamic execution and long-term maintenance of the above-mentioned optimized design parameters for the pipe group, this invention proposes a dynamic feedback control system for medium-shallow coaxial buried pipes, the hardware architecture of which mainly includes: (1) Perceptual unit High-precision water temperature sensors are installed on the outlet branch pipes of the shallow buried pipe group; multiple soil temperature sensors are pre-embedded radially in the shallow surrounding rock (about 200m underground) centered on the deep buried pipe; electromagnetic flow meters and heat meters are installed on the main circulation loop of the medium-deep coaxial buried pipe to realize real-time acquisition of outlet temperature, surrounding rock temperature, circulation flow rate and heat extraction.

[0064] (2) Execution unit The medium-deep circulation pipeline is equipped with a variable frequency circulating water pump that supports stepless flow regulation; the system heat source side is equipped with a variable frequency heat pump unit with variable load, which respectively realizes precise regulation of circulation flow and heat extraction power.

[0065] (3) Control unit A PLC or microprocessor is used as the central controller, which stores the "shallow buried pipe temperature field univariate prediction model" of this invention and the optimal range of each operating parameter. The central controller is communicatively connected to the sensing unit and the execution unit, respectively, to receive real-time sensing data and issue dynamic adjustment commands.

[0066] 3. Dynamic feedback control strategy (step-by-step regulation of flow / power during operation) During the actual operation of the pipe network system, based on the pre-determined deep burial depth of the pipes, the central controller executes a hierarchical dynamic closed-loop control strategy of "adjusting flow rate first, then reducing power". The specific steps are as follows: Step 1: Real-time monitoring and deviation analysis. The central controller reads the actual outlet temperature Treal of the shallow buried pipe in real time and compares it with the safety red line threshold required by the regulations (Tsafe=4 ℃) and the theoretical operating temperature Tpredict output by the prediction model to determine whether the system has a cold accumulation trend.

[0067] Step 2: Primary Defense (Adjusting Circulation Flow Rate Using Flow Saturation Effect) When Treal is continuously decreasing and approaching Tsafe, the controller determines that preliminary cold accumulation has occurred in the shallow layer. According to the 'Circulation Flow Rate Segmented Saturation Prediction Model', the controller first issues a frequency increase command to the variable frequency circulating water pump, gradually increasing the circulation flow rate of the deep buried pipe; if the current flow rate V < 48 m³ / s... 3 If the flow rate is / h, then continue to increase it until the saturation threshold of 48 m is reached. 3 / h, to alleviate the temperature drop by increasing convective heat transfer; if the current flow rate is already in the range of 38~48m³ / h, then adjust to the optimal value.

[0068] Step 3: Secondary Defense (Degrading Heat Extraction and Adjusting Heat Extraction Power for Heat Recovery) When the circulation flow rate has reached the physical limit saturation point (48 m3 / h), if Treal still falls below Tsafe, it indicates that the system has entered a deep "heat deficit" state. The controller triggers a power limiting strategy, linking the variable frequency heat pump unit to reduce the overall system heat extraction power in a set step (e.g., 5 kW) until the shallow surrounding rock temperature sensor reports a local ground temperature rebound, the outlet temperature recovers to above 4 ℃, and the power is not lower than the 250kW lower limit.

[0069] Step 4: Continuous monitoring and steady-state maintenance. Once the outlet temperature recovers to above the safe threshold and remains stable, the controller will adjust the flow rate and power to the optimal values ​​to maintain the steady-state operation of the system and continuously monitor various parameters to respond promptly to new temperature deviations.

[0070] Model validation: Based on actual engineering parameters of Changsha Huanghua Airport, this project established a numerical model for heat transfer in shallow to medium-depth underground pipes. By integrating measured data from the airport's exploration and production wells, and using the outlet water temperature of the underground pipe as a key indicator, the model was validated. The simulated curves and measured curves showed a high degree of consistency in their trends, with good numerical agreement. Specific matching results are shown below. Figure 11 As shown, some specific values ​​are shown in Table 9 below.

[0071] Table 9 Simulated and Measured Values ​​of Water Temperature at the Outlet of Buried Pipes

[0072] Quantitative calculations show that, after eliminating the influence of external factors such as circuit instability, the maximum error of the model is 2.77 ℃, and the relative error is always controlled within 8%, which fully verifies that the established numerical model can accurately reflect the heat transfer characteristics and dynamic change law of the shallow and medium-depth buried pipe heat exchanger.

[0073] Orthogonal experimental design and results analysis 2.1 Orthogonal experimental design and experimental results The depth, circulation flow rate, and heat extraction power of the deep buried pipe were selected as three influencing factors, each with five levels. A three-factor, five-level orthogonal array L was used. 25 (5³) Twenty-five test combinations were designed to comprehensively analyze the effects of various parameters on the temperature of the surrounding rock at a depth of 200m and the outlet temperature of the shallow buried pipe. The test design table and matrix overview are shown in Tables 10 and 11 below. The test results show that the higher the minimum temperature of the surrounding rock, the lower the temperature standard deviation, and the higher the outlet temperature of the shallow buried pipe, the better the system performance. Moreover, all parameter combinations can be quickly predicted through the prediction model.

[0074] Table 10 Orthogonal Experimental Design Table

[0075] Table 11 Overview of Orthogonal Experimental Matrix

[0076] Note: Minimum temperature of surrounding rock (T) min / ℃): The higher the better, as it reflects the strength of the cooling effect on the surrounding rock and avoids low-temperature cracking; Standard deviation of surrounding rock temperature (S / ℃): The lower the better, as it reflects the uniformity of the temperature field, and the smaller the value, the stronger the system stability.

[0077] Shallow buried pipe outlet temperature (T) out / ℃): The higher the better, it must meet the technical requirement of ≥4℃.

[0078] 2.2 Analysis of Orthogonal Experiment Results Based on L25 (5³) Orthogonal arrays were used to conduct range analysis on three factors: the depth of deep buried pipes, the circulation flow rate, and the heat extraction power. By calculating the average value (Kij) and range (R) of each factor at different levels, the influence of factors on the operation characteristics of the deep and shallow pipe group and the order of importance were clarified. See Table 12 for details.

[0079] Table 12 Summary of Range Analysis Results for Each Indicator

[0080] Based on the range analysis results of the three indicators, depth (A) has the largest range and plays a dominant role in all indicators; power (C) has a minor impact on outlet temperature and temperature standard deviation; and flow rate (B) has a weak impact on all indicators, with only a minor effect at high depths. Therefore, the importance ranking of the three factors—depth, circulation flow rate, and heat extraction power—for deep buried pipes is: Depth (dominant factor) > Power (minor factor) > Flow rate (minor impact).

[0081] Based on range analysis, the influence weights of the design parameters were clarified as follows: depth (dominant) > heat extraction power (minor) > circulation flow rate (weak influence), consistent with the parameter influence law of this invention. Depth plays a decisive role in all performance indicators, power has a minor influence on outlet temperature and temperature standard deviation, and flow rate has only a slight effect at high depths, providing experimental basis for the strategy of "pre-buried depth first, and flow rate and power control".

[0082] 2.3 Optimization Range of Core Parameters and Scenario-Based Solution Verification In practical engineering guidance, this application proposes a multi-objective decision-making matching mechanism based on the above-mentioned optimal interval, and the specific design steps are as follows: (1) Step A (Boundary Input): Input the project geological constraints (maximum drillable depth) and economic budget.

[0083] (2) Step B (Matching Decision): ① Scenario 1: Prioritizing overall system performance. If geological conditions permit, prioritize the median optimal value of the depth parameter at 2500m; select the upper limit saturation point of the flow rate at 48m³ / h to maximize heat exchange efficiency; and match a mid-to-high stage heat extraction power of 300kW. This combination can achieve the lowest energy consumption per unit power without degradation during long-term operation.

[0084] ②Scenario 2: Prioritizing initial well construction costs (limited scenario). If the budget is limited or the geology makes deep drilling difficult, the depth should be reduced to the lower limit safety point of 2000m. At this time, the heat extraction power must be reduced to 275kW to prevent shallow heat depletion, and the flow rate should be adjusted to 38m³ / h to form the lowest-cost defensive combination.

[0085] ③Scenario 3: Prioritizing Extreme Heat Extraction Load (Extreme Scenario). If the building's load demand is extremely high and the maximum power of 350kW must be activated, the system will be forced to increase the depth to the upper limit of 3000m or configure a dormant period at a depth of 2500m, maintaining a flow rate of 48m³ / h to offset the severe heat deficit caused by high power.

[0086] (3) Step C (Scheme Output): Output the optimal design parameter table that takes into account economy, technical feasibility and thermal stability, as shown in Table 13 below.

[0087] Table 13 Overview of Multi-Objective Optimization and Candidate Combinations

[0088] Orthogonal experiments verified the rationality of the optimal range of core parameters: 2000m≤H≤3000m, 38 m³ / h≤V≤48 m³ / h, 250 kW≤P≤325 kW. Within this range, the system can meet the requirements of outlet temperature ≥4℃, uniform surrounding rock temperature field, and no risk of cracking. Simultaneously, simulations were conducted to verify combinations of optimal performance (2500m / 48m³ / h / 300kW), optimal cost (2000m / 38m³ / h / 275kW), and high-power verification (2500m / 48m³ / h / 350kW). The results show that the optimal combination (2500m / 48m³ / h / 300kW) can achieve comprehensive benefits such as a stable and uniform surrounding rock temperature field, compliant shallow buried pipe outlet temperature, and the lowest energy consumption per unit power.

[0089] 2.4 Verification of Dynamic Feedback Control Strategy The hierarchical control strategy of "adjusting flow rate first and then reducing power" was verified based on simulation data. The results show that when the shallow outlet temperature approaches 4℃, increasing the flow rate to 48m³ / h can raise the outlet temperature by 0.5~1.0℃. If the temperature still falls below the threshold after the flow rate is saturated, reducing the power by 5~25kW can quickly achieve the recovery of ground temperature and outlet temperature. The control response is fast and the effect is significant, which can effectively avoid system shutdown.

[0090] 3. Conclusions and Recommendations Based on the engineering parameters of Changsha Huanghua Airport, this study systematically explored the influence of three core parameters on the heat transfer performance of shallow buried pipes through a combination of theoretical modeling, numerical simulation, and orthogonal experiments. The study clarified the parameter weights and optimal combinations, and the main conclusions are as follows: The depth of medium-deep underground pipes is the dominant factor affecting the operational characteristics of medium-shallow pipe group systems. 2500m is the optimal depth for the pre-burying stage, which can effectively avoid the risk of low-temperature cracking of the surrounding rock and ensure the foundation for long-term system operation. Heat extraction power is a secondary influencing factor. 300kW is the optimal heat extraction power during operation, which can ensure heat extraction efficiency and avoid the problems of heat exchange efficiency degradation and energy consumption increase caused by excessive power. The circulation flow rate of medium-deep buried pipes exhibits a significant saturation effect. 48 m³ / h is the optimal flow rate during the operation phase, balancing energy efficiency and economy, and enabling the system to maintain a high COP value during the stable operation phase. Orthogonal experiments verified that the parameter influence weights are: depth (dominant) > heat extraction power (minor) > circulation flow rate (weak influence). The optimal parameter combination is 2500m (depth), 48m³ / h (flow rate), and 300kW (power). This combination can achieve comprehensive benefits such as stable and uniform surrounding rock temperature field, compliant shallow buried pipe outlet temperature, and lowest energy consumption per unit power, ensuring 15 years of continuous and stable operation of the system without performance degradation. The two-level strategy of "pre-determining the pre-buried depth - dynamic flow / power regulation" and the hierarchical feedback control logic of "adjusting the flow first and then reducing the power" are scientific, feasible, and in line with engineering practice. They can effectively solve the problems of missing parameter control and unstable system operation in existing technologies, and provide a complete technical solution for the engineering design and operation management of medium-shallow coaxial buried pipe groups.

[0091] In summary, the present invention has the following core technical advantages: The long-term thermal effect analysis system has been improved: a pipe group heat transfer model considering long-term heat conduction effect and soil stratification characteristics has been established, and the dynamic evolution characteristics of temperature field under 15 years of continuous operation have been revealed for the first time. This makes up for the shortcomings of previous studies in the analysis of long-term effects and provides theoretical support for the long-term stable operation of the system. The influence weights and patterns of parameters were quantified: through a three-factor, five-level orthogonal experiment, the influence patterns of parameters with depth as the dominant factor, power as the secondary factor, and flow rate as the weak factor were clarified, the parameter influence research system was improved, and a precise quantitative basis was provided for multi-parameter collaborative optimization. A complete parameter control logic has been constructed: an innovative two-level control strategy of "pre-determining the pre-buried depth - dynamic adjustment of flow / power" has been proposed. The deep buried pipe depth is clearly defined as a fixed parameter for pre-buried engineering. The burial design and construction are completed during the erection stage, and only the flow and power are dynamically adjusted during the operation stage. This makes up for the parameter deficiency in the original control link and makes the parameter control logic more in line with the actual engineering. An efficient prediction model was established: it delves into the microscopic thermal interference mechanism, extracts the linear prediction equation for heat extraction power and the piecewise saturation equation for circulation flow, and for the first time achieves the technical effect of quickly and accurately guiding the matching of shallow and deep buried pipe parameters through empirical formulas without the need for complex three-dimensional numerical reconstruction, which greatly improves design efficiency and scientificity. A closed-loop dynamic feedback control system has been formed: a closed-loop system has been constructed for the entire process of pre-embedded design, buried construction, operation monitoring and feedback regulation. Based on the flow saturation effect, the system first adjusts the flow and then reduces the power, which completely solves the system shutdown problem caused by local thermal deficit and ensures the system's continuous and stable operation for 15 years. A multi-scenario adaptive optimization scheme is proposed: combining geological constraints, performance requirements and economic budget, three scenarios can be divided into performance priority, cost priority and extreme load priority, and the corresponding optimal parameter combination can be matched, which solves the problem that the single parameter combination of traditional design methods is difficult to adapt to complex engineering boundaries.

Claims

1. A method for optimizing the design of medium- to shallow coaxial buried pipe groups, characterized in that, Includes the following steps: S1. Design a physical model for medium-shallow coaxial buried pipes, establish a heat transfer model for medium-shallow coaxial buried pipe groups, and list the governing equations. S2. Determine the physical parameters of the model, using the buried pipe depth, heat extraction power and circulation flow rate as dynamic parameters, and substitute them into the control equations described in step S1 to solve the problem, outputting the minimum temperature of the surrounding rock and the outlet temperature of the medium-shallow coaxial buried pipe group. S3. Construct univariate regression prediction models for pipe burial depth, heat extraction power, and circulation flow rate with the minimum surrounding rock temperature and outlet temperature, respectively. Based on the data patterns extracted by parameter sensitivity analysis, determine the pipe burial depth mentioned in S2 during the pre-burial stage; and determine the heat extraction power and circulation flow rate mentioned in S2 during the operation stage. S4. Based on the buried pipe depth, heat extraction power, and circulation flow rate determined in S3, dynamically adjust the hardware architecture and control strategy of the medium-shallow coaxial buried pipe group.

2. The method for optimizing the design of medium-shallow coaxial buried pipe groups as described in claim 1, characterized in that, The physical model of the medium-shallow coaxial buried pipe mentioned in step S1 is as follows: the physical model of the medium-shallow coaxial buried pipe is symmetrical about the central axis and includes the inner pipe of the medium-shallow coaxial buried pipe, the outer pipe of the medium-shallow coaxial buried pipe, backfill material and surrounding rock. The inner pipe of the medium-shallow coaxial buried pipe is connected to the outer pipe of the medium-shallow coaxial buried pipe and circulates fluid.

3. The method for optimizing the design of medium-shallow coaxial buried pipe groups as described in claim 1, characterized in that, Step S1, which involves establishing a heat transfer model for a medium-shallow coaxial buried pipe group and listing the governing equations, specifically includes: Control equations for fluid heat transfer in the outer pipe channel of medium-shallow coaxial buried pipes: （1） Control equations for fluid heat transfer in the inner pipe channel of medium-shallow coaxial buried pipes: （2） Heat transfer control equation for the backfill material zone: （3） Integrated heat transfer control equation for soil and rock regions: （4） In the formula, Density, unit: kg / m³ 3 ; Specific heat capacity, unit: J / (kg·℃); Temperature, in °C; Time, in seconds; The velocity of the circulating working fluid is expressed in m / s. For thermohydrodynamic dispersion tensor; For heat source / heat sink; Porosity; The thermal conductivity is W / (m·K); The groundwater seepage velocity is in m / s; the subscript r represents the circulating medium, g represents the backfill material, f represents the groundwater, s represents the surrounding rock, i represents the outer pipe channel of the medium-shallow coaxial buried pipe, and o represents the inner pipe channel of the shallow coaxial buried pipe.

4. The method for optimizing the design of medium-shallow coaxial buried pipe groups as described in claim 3, characterized in that, The physical parameters of the model mentioned in step S2 include well depth, well diameter, inner tube outer diameter, inner tube wall thickness, outer tube outer diameter, outer tube wall thickness, inner tube thermal conductivity, outer tube thermal conductivity, circulating medium thermal conductivity, circulating medium specific heat capacity, circulating medium density, backfill material thermal conductivity, geothermal heat flow, surface temperature, fixed heat extraction power, kinematic viscosity coefficient, and dynamic viscosity coefficient.

5. The method for optimizing the design of medium-shallow coaxial buried pipe groups as described in claim 1, characterized in that, Step S3, which involves constructing a univariate regression prediction model for the buried pipe depth, heat extraction power, and circulation flow rate in relation to the minimum surrounding rock temperature and outlet temperature, specifically includes: (1) Construct a nonlinear prediction model for the buried pipe depth H in relation to the minimum temperature of the surrounding rock and the outlet temperature; (2) Construct a linear regression prediction model for heat extraction power P with the minimum surrounding rock temperature and outlet temperature: When the heat extraction power is in the range of 250kW~350kW, the outlet temperature of the shallow pipe satisfies the equation T out = T base -k ×( P -250), the minimum temperature of the surrounding rock meets T rock_min =T r-base -m×( P -250); (3) Construct a piecewise saturation prediction model for the circulating flow rate V in relation to the minimum surrounding rock temperature and the outlet temperature: when V < 48 m 3 When V = 48 m, the minimum surrounding rock temperature and the outlet temperature follow a logarithmic growth equation; when V ≥ 48 m 3 At / h, the minimum surrounding rock temperature and outlet temperature output are constant saturation values.

6. The method for optimizing the design of medium-shallow coaxial buried pipe groups as described in claim 5, characterized in that, The nonlinear prediction model for the buried pipe depth H in relation to the minimum temperature of the surrounding rock and the outlet temperature includes: Nonlinear prediction model for outlet temperature with pipe burial depth: Pipe burial depth outlet temperature of coaxial buried pipes in the middle and shallow layers It satisfies an exponentially saturated nonlinear relationship, and its expression is: ； In the formula: Temperature at the outlet of the buried pipe, unit: °C; The depth of the buried pipe is expressed in meters (m). Nonlinear prediction model of minimum surrounding rock temperature with pipe burial depth: Pipe burial depth With the lowest temperature of the surrounding rock It satisfies an exponentially saturated nonlinear relationship, and its expression is: ； In the formula: Minimum temperature of surrounding rock, unit: °C; The depth of the buried pipe is measured in meters (m).

7. The method for optimizing the design of medium-shallow coaxial buried pipe groups as described in claim 5, characterized in that, The piecewise saturation prediction model for the circulating flow rate V in step S3, in relation to the minimum surrounding rock temperature and the outlet temperature, specifically includes: Outlet temperature: when <48m 3 / h time: ; when ≥48m 3 / h time: ; Minimum temperature of surrounding rock: when <48m 3 / h time: ; when ≥48m 3 / h time: ; In the formula: Circulation flow rate, unit: m 3 / h; : Temperature at the outlet of the underground pipe, unit: °C; Minimum temperature of surrounding rock, unit: °C; : Logarithmic fitting coefficient of outlet temperature; Logarithmic fitting coefficients for surrounding rock temperature; The outlet temperature is a constant saturation value. : The minimum constant saturation value of the surrounding rock temperature.

8. The method for optimizing the design of medium-shallow coaxial buried pipe groups as described in claim 5, characterized in that, The data patterns extracted based on parameter sensitivity analysis in step S3 specifically include: During the pre-embedding stage, the range of the pipe burial depth H is limited to 2000 m ≤ H ≤ 3000 m; During the operation phase, the minimum inlet water temperature ≥4 ℃ is used as the target constraint and substituted into the prediction model to derive the maximum allowable limit heat extraction power P and the most economical pump flow boundary, outputting the optimal combination of operating parameters: The range of the circulating flow rate V is limited to 38 m³ / h ≤ V ≤ 48 m³ / h 3 / h; The range of heat extraction power P is limited to 250 kW ≤ P ≤ 325 kW.

9. The method for optimizing the design of medium-shallow coaxial buried pipe groups as described in claim 5, characterized in that, The hardware architecture of the shallow coaxial buried pipe group in the dynamic feedback adjustment mentioned in step S4 includes: Sensing unit: Install high-precision water temperature sensors on the outlet branch pipes of the medium-shallow underground pipe group; Execution unit: A variable frequency circulating water pump supporting stepless flow regulation is configured on the medium-shallow circulation pipeline; a variable frequency heat pump unit with variable load is configured on the heat source side of the system; Control unit: A PLC or microprocessor is used as the central controller. The controller stores a univariate regression prediction model of the buried pipe depth, heat extraction power and circulation flow rate with the minimum temperature of the surrounding rock and the outlet temperature, as well as the optimal range of each operating parameter.

10. The method for optimizing the design of medium-shallow coaxial buried pipe groups as described in claim 9, characterized in that, The control strategy for the shallow coaxial buried pipe group in step S4, which involves dynamic feedback adjustment, specifically includes: Step 1: Real-time monitoring and deviation analysis by the sensing unit. The central controller reads the actual outlet temperature Treal of the shallow buried pipe in real time and compares it with the safety red line threshold of 4 ℃ required by the regulations and the theoretical operating temperature Tpredict output by the prediction model to determine whether the system has a cold accumulation trend. Step 2: Level 1 Defense Against Circulating Traffic: When the sensing unit detects that Treal is continuously decreasing and approaching the minimum inlet water temperature, the controller determines that preliminary cold accumulation has occurred in the shallow layer. Based on the segmented saturation prediction model of the circulation flow rate V, the minimum surrounding rock temperature, and the outlet temperature, the controller first issues a frequency increase command to the variable frequency circulating water pump to gradually increase the circulation flow rate of the deep buried pipe. If the current flow rate V has not reached the saturation threshold of the interval range, the flow rate is continuously increased until it reaches the saturation threshold to alleviate the temperature drop by increasing convective heat transfer. If the current flow rate is already within the interval range, it is adjusted to the optimal value. Step 3: Secondary defense for heat extraction power: When the circulation flow rate V has reached the saturation threshold, if Treal still falls below the minimum inlet water temperature, it indicates that the system has entered a deep heat deficit state. The control unit triggers the power limiting strategy, which links the variable frequency heat pump unit of the execution unit to reduce the overall heat extraction power of the system step by step according to the set step size, until the shallow surrounding rock temperature sensor reports that the local ground temperature has rebounded, the outlet temperature has recovered to above 4 ℃, and the heat extraction power P is not lower than the lower limit of the range. Step 4: Continuous monitoring and homeostasis maintenance: Once the outlet temperature recovers to above the safe threshold and remains stable, the controller adjusts the flow rate and power to the optimal values ​​to maintain steady-state operation of the system, continuously monitors various parameters, and responds promptly to new temperature deviations.

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