An independent control simulation method for middle-deep ground heat exchanger array

Abstract

The application discloses an independent control simulation method for a middle-deep buried pipe heat exchanger array, first constructs a three-dimensional rock-soil temperature field containing all heat exchanger buried areas, and embeds the plane Cartesian coordinates, design buried depth and drilling radius of each heat exchanger, and characterizes the heat exchanger as a heat exchange interface along the depth distribution; subsequently, defines geometric and physical parameters, rock-soil layering characteristics and initial ground temperature conditions, and discretizes the temperature field by using a three-dimensional space variable step rectangular grid; based on a coaxial casing one-dimensional transient energy equation and a rock-soil three-dimensional transient heat conduction equation, a fluid-rock two-way coupling model is established through an equivalent thermal resistance on the heat exchange interface; finally, a multi-column unrelated hourly heat load sequence file is read in, each heat exchanger is independently driven in each time step, and iterative solution is obtained, and a shared temperature field is synchronously updated. The application realizes high-fidelity simulation of the independent operation strategy, and overcomes the limitations of traditional methods in heat interference prediction and differentiated control.

Description

Technical Field

[0001] This application relates to the field of numerical simulation technology for geothermal energy development, specifically to an independent control simulation method for medium-deep buried pipe heat exchanger arrays. Background Technology

[0002] Deep-bore-hole heat exchangers (DBHEs) have become an important technology for clean heating in cold northern regions due to their advantages in heat extraction depth, energy efficiency, and heat extraction stability. In practical engineering, a single DBHE is insufficient to meet the regional heating load demand, typically requiring the deployment of a well array consisting of multiple wells, operating in conjunction with a heat pump system. However, as the scale of the well array expands, the problem of inter-well thermal interference becomes increasingly prominent—adjacent wells cool each other during long-term heat extraction, leading to a continuous decrease in soil and rock temperature and a decline in system performance.

[0003] To optimize well cluster layout and operation strategies, the engineering community widely relies on numerical simulation methods to predict long-term thermal responses. Currently, the mainstream methods can be divided into two categories: The first type is the analytical model based on the principle of linear superposition, which achieves array simulation by superimposing the thermal responses of single wells in the spatial dimension. The advantage of this type of model is its fast computation speed, making it suitable for preliminary design. However, its fundamental drawback lies in its assumption that the system possesses linear and time-invariant characteristics, making it difficult to support refined control decisions.

[0004] The second category consists of refined three-dimensional numerical models based on the finite element method or finite volume method. These models can theoretically and accurately describe the transient heat transfer process between fluid, well casing, backfill, and soil, and support arbitrary geometry and boundary conditions. However, in practical applications, the modeling complexity is extremely high and the computational efficiency is low.

[0005] Furthermore, other technical challenges exist during the simulation process. For instance, while traditional radial mesh refinement is suitable for single-well simulations, it's difficult to ensure precise alignment of all wells with mesh nodes in multi-well rectangular or irregular arrangements, introducing geometric discretization errors and weakening simulation reliability. Crucially, existing commercial or open-source tools lack native support for independent control logic. Independent control refers to the ability of each well to dynamically adjust flow rate, inlet water temperature, or start / stop status based on its location, historical temperature drop, and current load demand under a unified thermal field constraint. This strategy has been proven by field operation data to effectively mitigate thermal interference and extend system lifespan. However, existing simulation methods either force all wells to run synchronously or forcibly stitch together single-well results through external scripts, failing to achieve truly differentiated control simulations while maintaining physical consistency. Summary of the Invention

[0006] This application provides an independent control simulation method for medium-deep buried pipe heat exchanger arrays, which solves the problem of independent control of well groups throughout the entire process from model establishment to simulation operation.

[0007] The technical solution of this application is as follows: An independent control simulation method for medium-deep buried pipe heat exchanger arrays includes the following steps: S1. Construct a three-dimensional temperature field in MATLAB to characterize the underground soil and rock medium. The spatial range of the three-dimensional temperature field includes the burial area of ​​all medium-deep buried pipe heat exchangers. S2. Embed the planar Cartesian coordinates, design burial depth, and drilling radius of each medium-deep buried pipe heat exchanger in the space of the three-dimensional temperature field, characterize the outer surface of each medium-deep buried pipe heat exchanger as a cylindrical heat exchange interface distributed along its burial depth, and use it as the inner boundary condition of the three-dimensional temperature field. S3. Define and read in the geometric parameters, physical property parameters, soil and rock media stratification parameters, initial geothermal gradient and atmospheric temperature of all medium and deep buried pipe heat exchangers; S4. Discretize the three-dimensional temperature field based on a three-dimensional spatial variable step-size rectangular grid; S5. Based on the one-dimensional transient energy equation of the coaxial casing and the three-dimensional transient heat conduction equation of the soil and rock, the heat exchangers of each medium-deep buried pipe are coupled with the three-dimensional temperature field through the equivalent thermal resistance of the drilling edge to establish a fluid-soil two-way heat exchange model. S6. Read in the hourly heat load table containing multiple columns of time series data, where each column in the hourly heat load table corresponds to the target heat load of a medium-deep buried pipe heat exchanger. S7. Set the total step size of the simulation cycle. Within each time step that advances hourly, based on the physical characteristic that the thermal disturbance distance within the time step is much smaller than the well spacing, sequentially traverse all medium-deep buried pipe heat exchangers that need to participate in the calculation within the current time step: solve the fluid-soil two-way heat exchange model of each well in turn, and immediately update the local soil temperature of its affected area after solving each well before solving the next well. After all wells within the current time step have been traversed, the updated global three-dimensional soil temperature field is shared uniformly, thereby realizing the real transmission of inter-well thermal interference and global energy conservation. S8. After each time step, update the three-dimensional temperature field and output the time, the inlet and outlet water temperatures of each medium-deep buried pipe heat exchanger, the soil and rock temperature distribution of the three-dimensional temperature field during the simulation period, and the heat output.

[0008] Furthermore, in S1, the medium-deep buried pipe heat exchanger is laid out in a rectangular pattern.

[0009] Furthermore, in S3, the medium-deep buried pipe heat exchanger adopts a coaxial sleeve. The geometric parameters of the coaxial sleeve include depth and pipe diameter, and the physical properties include thermal conductivity and specific heat capacity.

[0010] Furthermore, in S4, the surrounding grid is refined based on the planar Cartesian coordinates of the medium-deep buried pipe heat exchanger so that all wells are located at grid nodes.

[0011] Furthermore, in S5, the heat transfer energy control equation for the coaxial sleeve is first established: ; ; in: ; ; ; ; In the formula, , These represent the circulating fluid temperatures of the inner and outer tubes, respectively. Indicates the borehole wall temperature; M Indicates fluid mass flow rate; This represents the heat capacity per unit mass of the circulating fluid; C 1 represents the linear heat capacity of the outer pipe and the backfill material. C 2 indicates the heat capacity of the internal pipeline; d 1i , d 1o These represent the inner diameter and outer diameter of the outer tube, respectively. d 2i , d 2o These represent the inner diameter and outer diameter of the inner tube, respectively. , , and These represent the densities of the circulating fluid, the inner and outer pipes of the coaxial sleeve, and the backfill material, respectively. c 1. c 2 and These represent the mass heat capacities of the inner and outer tubes of the coaxial sleeve and the backfill material, respectively. R 1 and R 12 These represent the thermal resistance between the outer tube and the soil / rock, and the thermal resistance between the inner and outer tubes, respectively. and These represent the thermal conductivity of the outer tube, inner tube, and backfill material of the coaxial sleeve, respectively. Represents the depth coordinates; Indicates the drilling radius; Indicates the diameter of the well; t Represents a time variable; and The convective heat transfer coefficient between the outer and inner tubes of the coaxial sleeve is defined and calculated by the following equation: ; In the formula, Indicates the thermal conductivity of the heat transfer medium; D Indicates the hydraulic diameter; Nusel numbers: ; in, Darcy's coefficient of friction is represented. Representing the Reynolds number Represents Prandtl numbers; Establish the Robin and Dirichlet boundary conditions for the top and bottom ends of the coaxial sleeve: ; In the formula, H Indicates drilling depth; This indicates the amount of heat collected.

[0012] Furthermore, in S5, the boundary conditions for the soil and rock medium are established simultaneously with the establishment of the heat transfer energy control equation for the coaxial sleeve: ; In the formula, , r Indicates radial distance. x and y They represent x shaft and y Axis direction coordinates; Indicates the thermal conductivity of soil and rock; Indicates the temperature of the rock and soil; Indicates the radial distance from the far boundary of the soil / rock boundary; Indicates the depth of the bottom boundary of the soil and rock; Indicates the initial temperature; as well as, Establish the energy control equations within the soil and rock medium: ; In the formula, This represents the thermal diffusivity of the formation.

[0013] Furthermore, the deep underground pipe heat exchanger is coupled to the three-dimensional temperature field at the upper part of the well, the well installation area, and the rock area below the well, respectively: Radial range Define the upper part of the wellbore; Upper part of the well: : ; Drilling installation area: : ; : ; Rock area below the well: : ; In the above formula, It represents a dimensionless parameter for axial thermal conduction, describing the thermal conductivity effect of backfill material along the depth direction; This represents a dimensionless parameter for radial thermal conductivity in soil and rock, reflecting the radial heat flow from the soil and rock to the well wall nodes. This represents a dimensionless parameter indicating the heat flow on the fluid side, characterizing the thermal resistance through which the fluid passes within the pipe. R 1. The effect of heat flow transferred to the well wall on temperature change; Indicates the time step; express z Spatial step size in direction; Indicates the radial spatial step size; Size depends ; i Indicates the radial node index; l Indicates rock and soil strata; p Indicates the index of the current time step; p +1 indicates the index of the next time step; Indicates the air temperature at the surface of the soil and rock; Indicates the thermal conductivity of the wellbore; Indicates the density of the borehole casing; Indicates the mass heat capacity of the wellbore; Indicates the density of soil and rock; Indicates the mass heat capacity of soil and rock; j Indicates the depth node index; nj This represents the index of the node at the lowest depth.

[0014] Furthermore, in the fluid-soil two-way heat exchange model, the fluid-side model is discretized using a fully implicit finite difference scheme: For fluid in the outer tube: z = 0: ; 0< z < H : ; z = H : ; For fluid in the inner tube: z = 0: ; 0< z < H : ; z = H : ; In the formula, N 1, N 2, N 3 represents the combined parameters: , , ; in, This indicates the mass heat capacity of the coaxial sleeve; In the fluid-soil two-way heat exchange model, the soil side model is discretized using an alternating direction implicit scheme: ; ; ; In the formula, N x , N y , N z Indicates combined parameters, , , ; express y The spatial step size in the direction, where k represents the node index in the y-direction.

[0015] Furthermore, in the simulation cycle of step S7, a working period label is established to simulate intermittent operation. When the value of the working period label is 0, the fluid mass flow rate and heat load of the medium-deep buried pipe heat exchanger are forced to zero, the fluid stops circulating, and natural heat exchange occurs with the surrounding rock and soil. The temperature gradually approaches the temperature of the rock and soil medium at the corresponding depth.

[0016] Beneficial effects Due to the adoption of the above technical solution, the beneficial effects of this application are as follows: 1. This application reads in multiple unrelated hourly heat load sequence files and, under the constraint of a unified and shared three-dimensional soil and rock temperature field, independently solves the fluid-soil heat exchange process of each medium-deep buried pipe heat exchanger. This method supports arbitrary independent control logic under the premise of physical consistency. Compared with the energy non-conservation defects caused by the forced synchronous operation of traditional analytical models or the need for external scripts to splice single-well results in commercial software, this application provides a reliable numerical simulation method that can alleviate thermal interference.

[0017] 2. This application employs a three-dimensional spatial variable-step rectangular mesh based on a Cartesian coordinate system at the technical level, and performs local refinement in the Cartesian coordinate plane of the soil and rock region near the wellbore wall to ensure that all DBHE well locations are precisely aligned with the mesh nodes. This method retains the efficiency of rectangular meshes in large-scale parallel computing while avoiding simulation distortion caused by geometric discretization errors in irregular well group layouts using traditional radially refined meshes. Simultaneously, by discretizing the soil and rock equations using an alternating direction implicit scheme and the fluid equations using a fully implicit finite-difference scheme, the computational resource consumption is significantly reduced while ensuring the stability of long-period transient simulations.

[0018] 3. At the structural level, this application, based on the one-dimensional transient energy equation of the coaxial casing and the three-dimensional transient heat conduction equation of the soil and rock, dynamically couples the fluid model and the soil and rock model through an equivalent thermal resistance network at the well edge (comprehensively considering the pipe material, backfill material, and convective heat transfer). This mechanism can not only accurately reflect the real-time impact of changes in circulation flow rate and inlet water temperature on heat extraction power, but also realistically reproduce the non-uniform decay of the soil and rock temperature field caused by long-term heat extraction, providing a high-confidence basis for system life assessment, capacity expansion design, and energy efficiency degradation early warning. Attached Figure Description

[0019] The accompanying drawings, which are provided to further illustrate this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application.

[0020] Figure 1 A flowchart of an independent control simulation method for a medium-deep buried pipe heat exchanger array provided in this application; Figure 2 A schematic diagram of mesh division for an embodiment of this application is provided; Figure 3 This is a schematic diagram of the thermal resistance of the coaxial sleeve in an embodiment of this application; Figure 4 This is a comparison chart of the model verification of the embodiments of this application; Figure 5 This diagram shows a comparison between the simulated values ​​of this model and the measured values ​​of the project, along with a relative error graph. Figure 6 This is a drilling arrangement diagram of an embodiment of this application; Figure 7 Design hourly heat load diagrams for embodiments of this application; Figure 8 The water temperature diagrams at the outlets of wells 1 and 4 are shown for 20 years of operation of the system according to the embodiments of this application. Figure 9 This is a graph showing the temperature field changes at 2900m during 20 years of operation of the system according to an embodiment of this application. Detailed Implementation

[0021] Based on the background technology described, as shown in the appendix Figure 1 As shown, this application provides an independent control simulation method for medium-deep buried pipe heat exchanger arrays, including the following steps: S1. A three-dimensional temperature field characterizing underground soil and rock media is constructed in MATLAB. The spatial extent of the three-dimensional temperature field includes the burial area of ​​all medium-deep buried pipe heat exchangers (DBHEs). In this application, a three-dimensional temperature field computational domain is constructed to characterize the thermal response characteristics of underground soil and rock media. The spatial extent of the three-dimensional temperature field must completely cover the burial area of ​​all medium-deep buried pipe heat exchangers (DBHEs). In specific implementation, a cuboid computational domain can be defined in a rectangular coordinate system by writing a numerical simulation program. In this embodiment, the computational domain is implemented using the MATLAB software environment. The temperature variables at the three-dimensional spatial grid points are initialized using arrays or structures, with initial values ​​set according to the local geothermal gradient. It should be noted that the technical solution of this application does not depend on a specific programming language or commercial software platform, and can also be implemented in Python, C++, Fortran, or other environments with scientific computing capabilities through equivalent program code. Its core lies in constructing a three-dimensional soil and rock temperature field model with clear physical boundaries and initial conditions.

[0022] S2. Embed the Cartesian coordinates, design burial depth, and drilling radius of each medium-deep buried pipe heat exchanger into the three-dimensional temperature field. Characterize each medium-deep buried pipe heat exchanger as a cylindrical heat exchange interface distributed along its burial depth, and use this as the inner boundary condition of the three-dimensional temperature field. Specifically, read in the design data of each DBHE, including its wellhead Cartesian coordinates, design burial depth, and drilling radius. Subsequently, in the three-dimensional rectangular mesh system, the first... i The DBHE is characterized as a cylindrical heat exchange interface distributed along the depth direction: the projection of this interface onto the horizontal plane is (… x i , y i Centered on, with radius ) r b,i A circular region; in the vertical direction, from the ground surface ( z =0) Extend to design depth z= H iIn this application, a structured rectangular mesh in a Cartesian coordinate system is used. To accurately characterize the cylindrical interface, it is necessary to ensure that ( x i , y i Local mesh refinement is performed near the drilling radius, ensuring that at least one mesh node is located at or adjacent to the drilling radius. r b,i The corresponding annular region is thus clearly identified as the physical interface where heat exchange occurs between the fluid and the soil / rock. This heat exchange interface does not participate as a physical entity in solving the soil / rock thermal conductivity equation; instead, it is defined as the inner boundary condition of the three-dimensional temperature field. That is, during the numerical solution process, the heat flow at this interface is provided by the fluid-side heat transfer model and coupled as a source / sink term to the energy balance equations of adjacent soil / rock grid nodes, achieving bidirectional energy interaction between the fluid and soil / rock systems.

[0023] S3. Define and import the geometric parameters, physical property parameters, soil and rock media stratification parameters, initial geothermal gradient, and atmospheric temperature of all medium-deep buried pipe heat exchangers; as shown in the appendix. Figure 2 and attached Figure 3 As shown, in S3, the medium-deep buried pipe heat exchanger uses a coaxial sleeve. The geometric parameters of the coaxial sleeve include depth and pipe diameter. The pipe diameter includes the outer and inner diameters of the inner and outer pipes. The physical properties include thermal conductivity and specific heat capacity, including the physical properties of the inner and outer pipes and the backfill material. In addition, it is still necessary to define the circulating water flow rate, underground thermal diffusivity, geothermal warming rate, underground thermal conductivity, and surface convective heat transfer coefficient.

[0024] S4. The three-dimensional temperature field is discretized based on a three-dimensional spatial variable-step rectangular grid. In S4, the surrounding grid of the medium-deep buried pipe heat exchanger is refined based on the planar Cartesian coordinates to ensure that all wells are located at grid nodes. In a specific embodiment, a certain area near the wells is designated as the critical region, and a fine grid is set in the critical region. In areas farther away from the wells, the grid size gradually increases. This approach ensures that all wellbores are accurately aligned with the grid nodes, achieving consistency between the simulated layout and the actual engineering, while also balancing computational accuracy and efficiency.

[0025] S5. Based on the one-dimensional transient energy equation of the coaxial casing and the three-dimensional transient heat conduction equation of the soil and rock, the heat exchangers of each medium-deep buried pipe are coupled to the three-dimensional temperature field through the equivalent thermal resistance at the well edge to establish a fluid-soil two-way heat exchange model; specifically, the heat transfer energy control equation of the coaxial casing is first established: ; ; in: ; ; ; ; In the formula, , These represent the circulating fluid temperatures of the inner and outer tubes, respectively. Indicates the borehole wall temperature; M Indicates fluid mass flow rate; This represents the heat capacity per unit mass of the circulating fluid; C 1 represents the linear heat capacity of the outer pipe and the backfill material. C 2 indicates the heat capacity of the internal pipeline; d 1i , d 1o These represent the inner diameter and outer diameter of the outer tube, respectively. d 2i , d 2o These represent the inner diameter and outer diameter of the inner tube, respectively. , , and These represent the densities of the circulating fluid, the inner and outer pipes of the coaxial sleeve, and the backfill material, respectively. c 1. c 2 and These represent the mass heat capacities of the inner and outer tubes of the coaxial sleeve and the backfill material, respectively. R 1 and R 12 These represent the thermal resistance between the outer tube and the soil / rock, and the thermal resistance between the inner and outer tubes, respectively. and These represent the thermal conductivity of the outer tube, inner tube, and backfill material of the coaxial sleeve, respectively. Represents the depth coordinates; Indicates the drilling radius; Indicates the diameter of the well; t Represents a time variable; and The convective heat transfer coefficient between the outer and inner tubes of the coaxial sleeve is defined and calculated by the following equation: ; In the formula, Indicates the thermal conductivity of the heat transfer medium; D Indicates the hydraulic diameter; Nusel numbers: ; in, Darcy's coefficient of friction is represented. Representing the Reynolds number Represents Prandtl numbers; Establish the Robin and Dirichlet boundary conditions for the top and bottom ends of the coaxial sleeve: ; In the formula, H Indicates drilling depth; This indicates the amount of heat collected.

[0026] The boundary conditions for the soil and rock medium are established simultaneously with the establishment of the heat transfer energy control equations for the coaxial sleeve: ; In the formula, , r Indicates radial distance. x and y They represent x shaft and y Axis direction coordinates; Indicates the thermal conductivity of soil and rock; Indicates the temperature of the rock and soil; Indicates the radial distance from the far boundary of the soil / rock boundary; Indicates the depth of the bottom boundary of the soil and rock; Indicates the initial temperature; as well as, Establish the energy control equations within the soil and rock medium: ; In the formula, This represents the thermal diffusivity of the formation.

[0027] Drill wall ( r = r b ( ) is the coupling point between the fluid and the soil / rock model. By coupling the boundary condition equations, the fluid temperature at the same depth ( T f1 ), wellbore temperature ( T b ) and adjacent soil and rock node temperatures ( T s By linking them together, synchronous calculation of heat exchange can be achieved.

[0028] The deep underground pipe heat exchanger is coupled to the three-dimensional temperature field in the upper part of the well, the well installation area, and the rock area below the well, respectively: Radial range Define the upper part of the wellbore; Upper part of the well: : ; Drilling installation area: : ; : ; Rock area below the well: : ; In the above formula, It represents a dimensionless parameter for axial thermal conduction, describing the thermal conductivity effect of backfill material along the depth direction; This represents a dimensionless parameter for radial thermal conductivity in soil and rock, reflecting the radial heat flow from the soil and rock to the well wall nodes. This represents a dimensionless parameter indicating the heat flow on the fluid side, characterizing the thermal resistance through which the fluid passes within the pipe. R 1. The effect of heat flow transferred to the well wall on temperature change; Indicates the time step; express z Spatial step size in direction; Indicates the radial spatial step size; i Indicates the radial node index; l Indicates rock and soil strata; p Indicates the index of the current time step; p +1 indicates the index of the next time step; Indicates the air temperature at the surface of the soil and rock; Indicates the thermal conductivity of the wellbore; Indicates the density of the borehole casing; Indicates the mass heat capacity of the wellbore; Indicates the density of soil and rock; Indicates the mass heat capacity of soil and rock; j Indicates the depth node index; nj This represents the index of the node at the lowest depth.

[0029] In the fluid-soil two-way heat exchange model, the fluid-side model is discretized using a fully implicit finite difference scheme: For fluid in the outer tube: z = 0: ; 0< z < H : ; z = H : ; For fluid in the inner tube: z = 0: ; 0< z < H : ; z = H : ; In the formula, N 1, N 2, N 3 represents the combined parameters: , , ; in, This indicates the mass heat capacity of the coaxial sleeve; In the fluid-soil two-way heat exchange model, the soil side model is discretized using an alternating direction implicit scheme: ; ; ; In the formula, N x , N y , N z Indicates combined parameters, , , ; express y Spatial step size in the direction.

[0030] S6. Read in the hourly heat load table containing multiple columns of time series data, where each column in the hourly heat load table corresponds to the target heat load of a medium-deep buried pipe heat exchanger. S7. Set the total step size of the simulation cycle. Within each time step that advances hourly, traverse all wells according to the order of the deep buried pipe heat exchangers in the heat load table, iteratively solve the fluid-soil bidirectional heat exchange model, and simultaneously update the three-dimensional temperature field. This step adopts the core control mechanism shown in Figure 1: within a single time step, each well is solved independently. After the fluid temperature field and wellbore heat flow calculation for each well is completed, the global soil temperature field of the corresponding location and affected area of ​​that well is immediately updated before proceeding to the solution process for the next well, rather than completing the solution for all wells first and then updating the temperature field uniformly. This mechanism ensures that the heat extraction / release behavior of the preceding wells will change the soil thermal environment of the subsequent wells in real time, thereby achieving completely independent operation control of each well under the premise of physical consistency. During the simulation cycle, a working period label can be established to simulate intermittent operation. When the working period label value is 0, the fluid mass flow rate and heat load of the medium-deep buried pipe heat exchanger are forcibly reduced to zero, the fluid stops circulating, and natural heat exchange occurs with the surrounding soil and rock, with the temperature gradually approaching the temperature of the soil and rock medium at the corresponding depth. The working label is set in the main program loop, and the maximum time loop checks whether the running time is within the working period. If not, the flow rate is reduced to zero and the system shuts down.

[0031] S8. After each time step, update the three-dimensional temperature field and output the inlet and outlet water temperatures of each medium-deep buried pipe heat exchanger and the temperature distribution of the three-dimensional temperature field within the simulation period.

[0032] The above technical solution can output key performance indicators such as inlet and outlet water temperature, heat extraction, and system average COP for each well in real time. It can also periodically output the distribution of the entire soil and rock temperature field at different depths and locations for analyzing the spatiotemporal evolution of thermal disturbances.

[0033] Application Example: This application example relies on a medium-deep geothermal heat pump project for centralized heating in a certain area of ​​Shenyang. This project is a typical demonstration project of medium-deep geothermal heating in cold northern regions. The core system uses a rectangular array of 14 coaxial medium-deep buried pipe heat exchangers (DBHE), with a design depth of 2900m for each well and a uniform well spacing of 40m. (See attached diagram.) Figure 6 As shown, the drilling layout is a regular rectangle. The system serves a surrounding area of ​​approximately 100,000 m³. 2 The heating demand of public buildings in winter, with the heating season from November to March of the following year, is simulated using the simulation method of this application for a 20-year long-term dynamic operation simulation of the well group, to verify the feasibility of the independent control strategy and the evolution law of thermal interference of the well group.

[0034] This simulation strictly adopted actual engineering parameters: 1) Drilling parameters: single well depth 2900m, coaxial casing outer pipe diameter 177.8mm, inner pipe diameter 110mm, backfill material thermal conductivity 3.0W / (m·K); 2) Geotechnical parameters: formation thermal conductivity 2.5W / (m·K), geothermal gradient 0.0236℃ / m, initial geothermal temperature linearly distributed along depth; 3) Operating parameters: time step 3600s (1 hour), total simulation duration 20 years, hourly heat load during the heating season was input based on actual building energy consumption data, as shown in the attached figure. Figure 7 As shown; 4) Control strategy: adopt an independent control mode with load levels and well locations, and implement differentiated start and stop rules for central wells and peripheral wells.

[0035] Based on the hourly heat load fluctuation of the building, the heating load is divided into 7 levels, corresponding to different numbers of wells and operation strategies. The central well (No. 4) is given priority for intermittent shutdown, and the peripheral wells bear the basic load. The specific operation plan is shown in Table 1.

[0036] Table 1 Operation Plan A 20-year long-term simulation was completed using the independent control simulation method described in this application. The analysis focuses on the evolution of the water outlet temperature and the cold deposition characteristics of the soil and rock temperature field in the peripheral well (No. 1) and the central well (No. 4). The core results are as follows: Table 2. Changes in circulating water outlet temperature over 10 and 20 years of system operation. Table 3. Changes in soil and rock temperature after 10 and 20 years of system operation. like Figure 7 , Figure 8 , Figure 9 As shown in Tables 2 and 3: 1. Drilling outlet water temperature decay As shown in Table 2, under a well spacing of 40 m, the temperature drop at the outlet water of Well No. 1 after 10 and 20 years was 5.07℃ and 8.76℃, respectively; the corresponding temperature drops for Well No. 4 were 4.70℃ and 9.51℃, respectively. It is noteworthy that although Well No. 4 is a central well, under the independent control strategy, its temperature drop over the first 10 years was actually lower than that of the peripheral Well No. 1. This indicates that differentiated rotation operation can effectively slow down the thermal decay process of the central well. However, as the operating time extends to 20 years, the temperature drop of the central well gradually increases, eventually approaching that of the peripheral wells. This suggests that relying solely on a fixed rotation strategy is insufficient to completely offset the long-term cold accumulation effect, necessitating the introduction of dynamic temperature monitoring and adaptive control mechanisms to further improve the precision of independent control.

[0037] 2. Characteristics of cold deposition in the temperature field of soil and rock Table 3 shows the average temperature drop of the soil and rock at depths of 1500 m and 2900 m after 10 and 20 years. The temperature drop at 2900 m is significantly greater than that at 1500 m, with drops of 17.67℃ and 9.36℃ respectively after 20 years, indicating that deep soil and rock are the main areas of cold deposition. This result suggests that during engineering operations, it is crucial to monitor the changing trend of deep geothermal temperatures and dynamically adjust the operational weight of each well based on temperature evolution to prevent excessive depletion of deep geothermal reservoirs.

[0038] In summary, this application example fully verifies the high accuracy and engineering practicality of the independent control simulation method proposed in this invention under large-scale, long-cycle, and multi-well differentiated operating conditions. This method can be directly applied to the well cluster layout optimization, operation strategy formulation, and long-term performance prediction of medium-deep geothermal energy arrays, providing reliable core technical support for heating projects using medium-deep geothermal energy well clusters in cold northern regions, and has significant engineering promotion value.

[0039] Model validation: As attached Figure 4 As shown, compared with the Beier model: the root mean square error (RMSE) of a single well in the left-hand attached figure does not exceed 0.46℃; the RMSE of a 5-well array (well spacing 50m) does not exceed 0.53℃. Figure 5 Comparison with actual measured data from a project in Shenyang: the average relative error between the simulated and measured values ​​of the outlet water temperature is 1.81%, and the RMSE is 0.59℃. This fully demonstrates the high accuracy of this model at both the theoretical and practical engineering levels.

[0040] For any parts not mentioned in this application, existing technologies may be used or referenced.

[0041] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. An independent control simulation method for medium-deep buried pipe heat exchanger arrays, characterized in that, Includes the following steps: S1. Construct a three-dimensional temperature field in MATLAB to characterize the underground soil and rock medium. The spatial range of the three-dimensional temperature field includes the burial area of ​​all medium-deep buried pipe heat exchangers. S2. Embed the planar Cartesian coordinates, design burial depth, and drilling radius of each medium-deep buried pipe heat exchanger in the three-dimensional temperature field space, characterize the outer surface of each medium-deep buried pipe heat exchanger as a cylindrical heat exchange interface distributed along its burial depth, and use it as the inner boundary condition of the three-dimensional temperature field. S3. Define and read in the geometric parameters, physical property parameters, soil and rock media stratification parameters, initial geothermal gradient and atmospheric temperature of all medium and deep buried pipe heat exchangers; S4. Discretize the three-dimensional temperature field based on a three-dimensional spatial variable step-size rectangular grid; S5. Based on the one-dimensional transient energy equation of the coaxial casing and the three-dimensional transient heat conduction equation of the soil and rock, the heat exchangers of each medium-deep buried pipe are coupled with the three-dimensional temperature field through the equivalent thermal resistance of the drilling edge to establish a fluid-soil two-way heat exchange model. S6. Read in the hourly heat load table containing multiple columns of time series data, where each column in the hourly heat load table corresponds to the target heat load of a medium-deep buried pipe heat exchanger. S7. Set the total step size of the simulation cycle. In each time step that advances hour by hour, based on the physical characteristic that the thermal disturbance distance within the time step is much smaller than the well spacing, sequentially traverse all medium-deep buried pipe heat exchangers that need to participate in the calculation within the current time step: solve the fluid-soil bidirectional heat exchange model of each well in turn, update the local soil temperature of its affected area immediately after solving each well, and then solve the next well; after all wells within the current time step have been traversed, share the updated global three-dimensional soil temperature field in a unified manner to realize the real transmission of thermal interference between wells and the conservation of energy in the whole domain; S8. After each time step, update the three-dimensional temperature field and output the time, the inlet and outlet water temperatures of each medium-deep buried pipe heat exchanger, the soil and rock temperature distribution of the three-dimensional temperature field during the simulation period, and the heat output.

2. The independent control simulation method for medium-deep buried pipe heat exchanger arrays according to claim 1, characterized in that, In S1, the medium-deep buried pipe heat exchangers are laid out in a rectangular layout.

3. The independent control simulation method for medium-deep buried pipe heat exchanger arrays according to claim 2, characterized in that, In S3, the medium-deep buried pipe heat exchanger adopts a coaxial sleeve. The geometric parameters of the coaxial sleeve include depth and pipe diameter, and the physical properties include thermal conductivity and specific heat capacity.

4. The independent control simulation method for medium-deep buried pipe heat exchanger arrays according to claim 3, characterized in that, In S4, the surrounding grid is refined based on the planar Cartesian coordinates of the medium-deep buried pipe heat exchanger so that all wells are located at grid nodes.

5. The independent control simulation method for a medium-deep buried pipe heat exchanger array according to claim 4, characterized in that, In S5, the heat transfer energy control equation for the coaxial sleeve is first established: ； ； in: ； ； ； ； In the formula, , These represent the circulating fluid temperatures of the inner and outer tubes, respectively. Indicates the borehole wall temperature; M Indicates fluid mass flow rate; This represents the heat capacity per unit mass of the circulating fluid; C 1 represents the linear heat capacity of the outer pipe and the backfill material. C 2 indicates the heat capacity of the internal pipeline; d 1i , d 1o These represent the inner diameter and outer diameter of the outer tube, respectively. d 2i , d 2o These represent the inner diameter and outer diameter of the inner tube, respectively. , , and These represent the densities of the circulating fluid, the inner and outer pipes of the coaxial sleeve, and the backfill material, respectively. c 1. c 2 and These represent the mass heat capacities of the inner and outer tubes of the coaxial sleeve and the backfill material, respectively. R 1 and R 12 These represent the thermal resistance between the outer tube and the soil / rock, and the thermal resistance between the inner and outer tubes, respectively. and These represent the thermal conductivity of the outer tube, inner tube, and backfill material of the coaxial sleeve, respectively. Represents the depth coordinates; Indicates the drilling radius; Indicates the diameter of the well; t Represents a time variable; and The convective heat transfer coefficient between the outer and inner tubes of the coaxial sleeve is defined and calculated by the following equation: ； In the formula, Indicates the thermal conductivity of the heat transfer medium; D Indicates the hydraulic diameter; Nusel numbers: ； in, Darcy's coefficient of friction is represented. Representing the Reynolds number Represents Prandtl numbers; Establish the Robin and Dirichlet boundary conditions for the top and bottom ends of the coaxial sleeve: ； In the formula, H Indicates drilling depth; This indicates the amount of heat collected.

6. The independent control simulation method for a medium-deep buried pipe heat exchanger array according to claim 5, characterized in that, In S5, the boundary conditions for the soil and rock media are established simultaneously with the establishment of the heat transfer energy control equations for the coaxial sleeve: ； In the formula, , r Indicates radial distance. x and y They represent x shaft and y Axis direction coordinates; Indicates the thermal conductivity of soil and rock; Indicates the temperature of the rock and soil; Indicates the radial distance from the far boundary of the soil / rock boundary; Indicates the depth of the bottom boundary of the soil and rock; Indicates the initial temperature; as well as, Establish the energy control equations within the soil and rock medium: ； In the formula, This represents the thermal diffusivity of the formation.

7. The independent control simulation method for a medium-deep buried pipe heat exchanger array according to claim 6, characterized in that, The deep underground pipe heat exchanger is coupled to the three-dimensional temperature field in the upper part of the well, the well installation area, and the rock area below the well, respectively: Radial range Define the upper part of the wellbore; Upper part of the well: ： ； Drilling installation area: ： ； ： ； Rock area below the well: ： ； In the above formula, It represents a dimensionless parameter for axial thermal conduction, describing the thermal conductivity effect of backfill material along the depth direction; This represents a dimensionless parameter for radial thermal conductivity in soil and rock, reflecting the radial heat flow from the soil and rock to the well wall nodes. This represents a dimensionless parameter indicating the heat flow on the fluid side, characterizing the thermal resistance through which the fluid passes within the pipe. R 1. The effect of heat flow transferred to the well wall on temperature change; Indicates the time step; express z Spatial step size in direction; Indicates the radial spatial step size; Size depends ; i Indicates the radial node index; l Indicates rock and soil strata; p Indicates the index of the current time step; p +1 indicates the index of the next time step; Indicates the air temperature at the surface of the soil and rock; Indicates the thermal conductivity of the wellbore; Indicates the density of the borehole casing; Indicates the mass heat capacity of the wellbore; Indicates the density of soil and rock; Indicates the mass heat capacity of soil and rock; j Indicates the depth node index; nj This represents the index of the node at the lowest depth.

8. The independent control simulation method for a medium-deep buried pipe heat exchanger array according to claim 7, characterized in that, In the fluid-soil two-way heat exchange model, the fluid-side model is discretized using a fully implicit finite difference scheme: For fluid in the outer tube: z = 0： ； 0< z < H ： ； z = H ： ； For fluid in the inner tube: z = 0： ； 0 < z < H ： ； z = H ： ； In the formula, N 1, N 2, N 3 represents the combined parameters: , , ; in, This indicates the mass heat capacity of the coaxial sleeve; In the fluid-soil two-way heat exchange model, the soil side model is discretized using an alternating direction implicit scheme: ； ； ； In the formula, N x , N y , N z Indicates combined parameters, , , ; express y The spatial step size in the direction, where k represents the node index in the y-direction.

9. The independent control simulation method for a medium-deep buried pipe heat exchanger array according to claim 8, characterized in that, In the simulation cycle of step S7, a working period label is established to simulate intermittent operation. When the value of the working period label is 0, the fluid mass flow rate and heat load of the medium-deep buried pipe heat exchanger are forced to zero, the fluid stops circulating, and natural heat exchange occurs with the surrounding rock and soil. The temperature gradually approaches the temperature of the rock and soil medium at the corresponding depth.

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