Vertical drilling thermal response calculation method based on novel discrete algorithm

Abstract

The invention discloses a vertical borehole thermal response calculation method based on a novel discrete algorithm. The vertical borehole thermal response calculation method comprises the following steps: 1, establishing an integral relational expression between the soil temperature of any position and the heat exchange capacity of all boreholes distributed along the depth; 2, expressing the soil temperature as the sum of the historical cumulative effect and the contribution of the current time period; 3, establishing a direct analysis relation between the thermal response function and the borehole wall temperature; 4, converting the thermal response function into a discretization form which can be solved through a linear system; and 5, introducing a regularization term for the thermal response function in the discretization form, and solving the problem of numerical instability caused by high-precision discretization. According to the method, the calculation speed and efficiency of the thermal response function can be remarkably improved, so that more accurate data support is provided for scheduling and optimization of the ground source heat pump system, and the operation efficiency of the system is improved.

Description

Technical Field

[0001] This invention belongs to the field of geothermal energy utilization technology, specifically a method for calculating the thermal response of vertical boreholes that can maintain high accuracy while possessing good numerical stability and computational efficiency. Background Technology

[0002] In recent years, with the widespread application of ground source heat pump systems in building energy conservation and renewable energy utilization, accurate assessment of their underground heat exchange performance has become crucial for optimal system design and efficient operation. Thermal response function ( g The thermal conductivity function (TDC) serves as a dimensionless temperature rise response of a borehole group under unit heat flux and is a core foundation for underground heat transfer analysis, long-term performance prediction, and system simulation. Its computational accuracy and efficiency directly affect the design rationality and operational economy of buried pipe heat exchangers.

[0003] Currently, widely used methods for calculating thermal response functions are mainly based on integral equation models, and often employ stacked finite line source models for spatial discretization. These methods divide the borehole along its depth into several segments, assuming a uniform heat flow distribution within each segment, and approximate the solution by integrating and superimposing the thermal response factors between segments. However, these methods still have several significant limitations in practice: First, the step function form of the heat flow approximation cannot accurately depict the actual continuously changing heat flow distribution along the borehole depth, especially in areas with large gradients at the borehole ends, which easily introduces errors; second, the discrete segmentation scheme lacks theoretical guidance, relying on empirical segmentation strategies, making it difficult to achieve an effective balance between computational cost and model accuracy; third, the calculation of the inter-segment response factors involves multiple integrations, and the numerical solution is significantly time-consuming, limiting its practical application efficiency in multi-bore, long-term simulations.

[0004] Furthermore, under complex geological conditions, non-uniform thermal properties, and dynamic operating conditions, traditional discretization methods often suffer from high model rigidity and insufficient adaptability, making it difficult to balance computational stability with response speed and accuracy. Especially in scenarios with high computational efficiency requirements, such as integrated system optimization and real-time control, existing methods frequently face issues of accuracy loss or excessive computational burden. Summary of the Invention

[0005] This invention aims to address the shortcomings of existing technologies by proposing a novel discrete algorithm-based method for calculating the thermal response of vertical boreholes. The goal is to construct a high-precision, high-efficiency, and numerically stable discretized solution framework to more accurately characterize the heat flow distribution along the borehole and its time-varying thermal response. This significantly improves the calculation accuracy and efficiency of the thermal response function and provides more reliable core algorithm support for the refined design, simulation, and optimization of ground source heat pump systems under multi-bore configuration and long-term dynamic operation in collaborative scheduling.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: The present invention provides a method for calculating the thermal response of vertical boreholes based on a novel discrete algorithm, characterized by the following steps: Step 1: Establish the integral relationship between soil temperature at any location and the heat exchange rate along the depth distribution of all boreholes; Step 2: Based on the integral relationship, the unit heat exchange of the borehole is discretized over time, and the soil temperature is expressed as the sum of the historical cumulative effect and the contribution of the current period. Step 3: Set the average heat exchange constraint and the boundary condition of uniform borehole wall temperature, and establish... Time-dependent thermal response function With borehole wall temperature Relationships; Step 4: Approximate the continuous spatial integral in the borehole wall temperature expression as a weighted sum at a finite number of integration points, and generate a borehole segmentation scheme based on the integration points, thereby approximating the thermal response function. Transform into Discretization equations; Step 5, through A regularization term is introduced into the discretized equation to establish a discretized thermal response function with the regularization term, so as to realize the calculation of the thermal response of vertical drilling.

[0007] The present invention provides a method for calculating the thermal response of vertical boreholes based on a novel discrete algorithm, wherein step 1 includes: Step 1.1: Establish using equations (1)-(2) Distance from the heat source at any time Soil temperature changes : (1) (2) In equations (1)-(2), This represents the instantaneous heat released by the heat source at the origin. express The distance between the current point and the heat source is Green's function of soil temperature at that location Indicates soil density, This indicates the specific heat capacity of the soil. Indicates the thermal diffusivity of the soil. Indicated by An exponential function with base 0; Step 1.2: Use equations (3)-(5) to establish... Time's up Time period Below the distance from the heat source point Soil cumulative temperature response caused by location : (3) (4) (5) In equations (3)-(5), Indicates the thermal conductivity of the soil. Represents the complementary error function. Represents the integral variable; Step 1.3: Establish using equation (6) The time coordinate position is soil temperature : (6) In equation (6), Indicates surface temperature. Indicates the number of boreholes. , They represent the first The depth and length of the root borehole, Indicates the first Root borehole at soil depth Heat exchange rate per unit time Indicates the first The coordinates of the root borehole. This indicates the distance between the target point and the heat source point.

[0008] Furthermore, step 2 includes: Step 2.1, use equation (7) to process the first... Root borehole at soil depth Heat exchange rate per unit time Discretize along time: (7) In equation (7), Indicates time The number of discretizations, Indicates the first Root borehole at soil depth The first time discrete points Heat exchange rate at time; Step 2.2: Substitute equation (7) into equation (6), and then use equation (8) to obtain the first... time discrete points Time coordinate position is soil temperature : (8) Step 2.3, using equations (9)-(11) to... Decompose to obtain the first time discrete points Time coordinate position is Historical cumulative temperature changes in soil And in the time discrete points and the time discrete points The time period between Inner soil temperature changes sum: (9) (10) (11).

[0009] Furthermore, step 3 includes: Step 3.1: Use equation (12) to establish the thermal response function with respect to the first... time discrete points Average heat exchange rate per unit length of borehole Boundary conditions: (12) Step 3.2: Establish uniform borehole wall temperature boundary conditions using equation (13): (13) In equation (13), Indicates the first time discrete points The borehole wall temperature at that time; Step 3.3, using equation (14) to obtain Time-dependent thermal response function With borehole wall temperature Relationship: (14).

[0010] Furthermore, step 4 includes the following steps: Step 4.1: Using equations (15)-(17), approximate equations (9)-(11) as a weighted sum at a finite number of heat source integration points: (15) (16) (17) In equations (15)-(17), This represents the number of heat source integration points used for discretizing the heat source integration along the depth direction for each borehole. Indicates the first Root drilling in the first Calculate the depth coordinates of the integration point for each heat source. Indicates the relationship with the first Root drilling in the first Depth coordinates of the integration point of each heat source Corresponding weighting coefficients; Step 4.2: Using equations (18)-(19), divide the borehole along the depth direction into sections corresponding to the number of integration points. Equal number of segments: (18) (19) In equations (18)-(19), , They represent the first The first root borehole The upper and lower depth boundaries of the segment, Indicates the first The first root borehole Calculate the depth coordinates of the integration point for each heat source. Indicates the first The first root borehole Calculate the depth coordinates of the integration point for each heat source; Step 4.3: Use formula (20) to measure the borehole wall temperature. This is approximately a weighted sum of the borehole wall temperatures at the integration point of the temperature within each segment: (20) In equation (20), This represents the number of temperature integration points used to approximate the integral of the borehole wall temperature. Indicates the first Root drilling in the first Determine the depth coordinates of the accumulation point based on the temperature of the segment. Indicates the relationship with the first Root drilling in the first Determine the depth coordinates of the temperature of the segment. The corresponding weights Indicates the first The coordinates of the root borehole; Step 4.4: Substitute equations (15)-(16) into equation (20), and then use equation (21) to obtain the first... time discrete points borehole wall temperature Discretized equations: (twenty one).

[0011] Furthermore, step 5 includes the following steps: Step 5.1: Use equation (22) to introduce a regularization term into equation (20): (twenty two) In equation (20), Indicates the first time discrete points The first time after regularization modification The borehole wall temperature of the root borehole Represents the regularization parameter. Indicates the first time discrete points Time The first root borehole Heat exchange rate of the section; Step 5.2: Use equation (23) to establish the discretized thermal response function with the regularization term introduced: (twenty three) In equation (21), This indicates that all heat sources are within the time period. The thermal influence coefficient matrix on borehole wall temperature It is the identity matrix. It is a column vector whose elements are all 1s. Indicates the first time discrete points The heat exchange matrix of all boreholes and their integral points at time. This indicates that all heat sources are at the th time discrete points and the time discrete points The time period between The heat source released internally to the first time discrete points The cumulative thermal effect matrix generated at that time, This represents the weight coefficient matrix for the borehole segments.

[0012] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program that supports the processor in executing the vertical drilling thermal response calculation method, and the processor is configured to execute the program stored in the memory.

[0013] The present invention discloses a computer-readable storage medium storing a computer program, characterized in that the computer program is executed by a processor to perform the vertical drilling thermal response calculation method.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention, based on the Nyström method and higher-order Gauss-Legend quadrature rules, discretizes the continuous heat flux distribution in the original integral equation into a weighted sum at a finite number of quadrature points, avoiding the spatial distribution error caused by the step function approximation in traditional stacked finite line source models. This method automatically generates optimal discrete points and weights through high-precision numerical integration, without relying on empirical piecewise strategies, thus achieving better approximation accuracy for any given number of discrete points and significantly improving the calculation accuracy of the thermal response function.

[0015] 2. This invention transforms complex inter-segment response integrals into a series of efficient analytical point-to-point response calculations. Furthermore, a pre-computation storage mechanism significantly reduces the computational complexity of numerical integration in the core iteration process. This discretization framework generates a theoretically guaranteed well-state linear system, with stable and efficient computation, making it particularly suitable for large-scale simulation scenarios involving multiple boreholes and long time series. In practical engineering design, this method provides reliable and efficient core algorithm support for refined modeling, rapid scheme comparison, and long-term energy efficiency prediction of ground source heat pump systems, effectively improving the scientific rigor and economic efficiency of the design. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0017] In this embodiment, to meet the important technical needs of refined design, dynamic simulation, and operational optimization of ground source heat pump systems, a novel vertical borehole thermal response calculation method based on a new discretization algorithm is proposed. This method, based on the Nyström method and the Gauss-Legend quadrature rule, is a numerical solution that ensures both computational accuracy and efficiency, effectively addressing the shortcomings of traditional methods in discretization strategies, computational stability, and applicability to large-scale simulations. This method not only avoids errors caused by empirical piecewise division and step function approximation but also adapts to different borehole configurations and complex operating conditions through an automated discretization framework, providing a reliable theoretical and numerical foundation for efficient and high-precision calculation of the thermal response function. Specifically, as... Figure 1 As shown, the method includes the following steps: Step 1: Establish the integral relationship between soil temperature at any location and the heat exchange rate along the depth distribution of all boreholes; Step 1.1: An instantaneous point heat source extracts energy at the origin. The temperature change caused by the heat source at any point depends on the elapsed time. and distance to the heat source This temperature change is caused by With Green's function The product representation. Using equations (1)-(2) to establish... Distance between the instantaneous heat source and the moment Soil temperature changes : (1) (2) In equations (1)-(2), This represents the heat released by a point heat source at the origin at an instant. express The distance between the current point and the heat source is Green's function of soil temperature at that location Indicates soil density, This indicates the specific heat capacity of the soil. Indicates the thermal diffusivity of the soil. Indicated by An exponential function with base 0.

[0018] Step 1.2, Green's function From time arrive The integral is denoted as Using equations (3)-(5), establish from Time's up Time period Below the distance from the heat source point Soil cumulative temperature response caused by location : (3) (4) (5) In equations (3)-(5), Indicates the thermal conductivity of the soil. Represents the complementary error function. This represents the integral variable.

[0019] Step 1.3, a combination of A borehole field consisting of vertical boreholes, the coordinates of each borehole being... ,in The burial depth and length of each borehole are respectively and All drilled holes at point The resulting total temperature change can be obtained by summing the contributions of each borehole. Each borehole is considered as a line composed of many heat source points, and the heat extraction per unit length and wall temperature of each borehole vary with underground depth and time. Therefore, the heat extraction per unit length and wall temperature are bivariate functions of depth and time. Using equation (6), we establish... The time coordinate position is soil temperature : (6) In equation (6), Indicates surface temperature. Indicates the number of boreholes. , They represent the first The depth and length of the root borehole, Indicates the first Root borehole at soil depth Heat exchange rate per unit time Indicates the first The coordinates of the root borehole. This indicates the distance between the target point and the heat source point.

[0020] Step 2: Based on the integral relationship, the unit heat exchange of the borehole is discretized over time, and the soil temperature is expressed as the sum of the historical cumulative effect and the contribution of the current period. Step 2.1, set the time Evenly divided into Segment, the first segment within each segment Root borehole at soil depth Heat exchange rate per unit time at the location Keeping it unchanged, use equation (7) to apply the first... Root borehole at soil depth Heat exchange rate per unit time Discretize along time: (7) In equation (7), Indicates time The number of discretizations, Indicates the first Root borehole at soil depth The first time discrete points The amount of heat exchanged at that time.

[0021] Step 2.2: Substitute equation (7) into equation (6), and then use equation (8) to obtain the first... time discrete points Time coordinate position is soil temperature : (8) Step 2.3, using equations (9)-(11) to... Decompose to obtain the first time discrete points Time coordinate position is Historical cumulative temperature changes in soil And in the time discrete points and the time discrete points The time period between Inner soil temperature changes The summation, this decomposition naturally forms a recursive solution structure in time, transforming the complex full-history convolution problem into an incremental problem that focuses only on the unknowns in the current time step, avoiding repeated integration calculations of the entire history at each time step: (9) (10) (11).

[0022] Step 3: Set the average heat exchange constraint and the boundary condition of uniform borehole wall temperature, and establish... Time-dependent thermal response function With borehole wall temperature Relationships; Step 3.1: Use equation (12) to establish the thermal response function with respect to the first... time discrete points Average heat exchange rate per unit length of borehole The boundary conditions. This formula defines the standard operating conditions upon which the thermal response function is calculated, and its physical meaning is: [The following is a partial translation of the original text, which is incomplete and requires further context.] Normalizing the average heat flux intensity per unit length of the entire borehole field makes the thermal response function a dimensionless characteristic function that only reflects the geometric layout of the borehole field and the thermal properties of the soil. This is the standard premise of the thermal response function theory.

[0023] (12) Step 3.2: In a real system, the borehole wall temperature should vary along the depth and between different boreholes. Directly solving for its distribution is extremely difficult. Therefore, we can ensure that all boreholes and all depths have the same wall temperature at any given time. This gives a function about space. It has been simplified into a scalar quantity that is only related to time. The uniform borehole wall temperature boundary condition is established using equation (13): (13) In equation (13), Indicates the first time discrete points The borehole wall temperature at that time.

[0024] Step 3.3, using equation (14) to obtain Time-dependent thermal response function With borehole wall temperature Relationship: (14) Step 4: Approximate the continuous spatial integral in the borehole wall temperature expression as a weighted sum at a finite number of integration points, and generate a borehole segmentation scheme based on the integration points, thereby approximating the thermal response function. Transform into The discretized equations.

[0025] Step 4.1: Using equations (15)-(17), approximate equations (9)-(11) as a weighted sum at a finite number of heat source integration points. To transform the continuous integral equation into a computer-solvable discrete form, this step introduces the Nyström method and uses the Gauss-Legend quadrature rule to approximate the spatial integral. The core of this step is to transform the continuous integral along the borehole depth... Replace with a finite number of integration points Weighted sum This method achieves the highest algebraic accuracy with a given number of discrete points by selecting the optimal integration points and corresponding weights, thereby avoiding the spatial error of the traditional step function approximation and significantly improving the accuracy of the heat flow distribution approximation.

[0026] (15) (16) (17) In equations (15)-(17), This represents the number of heat source integration points used for discretizing the heat source integration along the depth direction for each borehole. Indicates the first Root drilling in the first Calculate the depth coordinates of the integration point for each heat source. Indicates the relationship with the first Root drilling in the first Depth coordinates of the integration point of each heat source The corresponding weighting coefficients.

[0027] Step 4.2: Using equations (16) and (17), divide the borehole along the depth direction into sections corresponding to the number of integration points. The number of segments is equal. To ensure the systematic nature of discretization and facilitate the application of boundary conditions, this step generates a drilling segmentation scheme based on the location of the quadrature points. The segment boundary is taken as the midpoint of adjacent quadrature points. This strategy ensures that each segment contains exactly one quadrature point, so that there is a one-to-one correspondence between discrete points and segments.

[0028] (18) (19) In equations (18)-(19), , They represent the first The first root borehole The upper and lower depth boundaries of the segment, Indicates the first The first root borehole Calculate the depth coordinates of the integration point for each heat source. Indicates the first The first root borehole Calculate the depth coordinates of the integration point for each heat source.

[0029] Step 4.3: Use formula (20) to measure the borehole wall temperature. This step approximates the calculation of the average temperature within each segment as a weighted sum of the temperatures at the temperature integration points within the segment. This transforms the originally continuous boundary conditions into a set of discrete algebraic equations, thereby enabling the embedding of physical constraints into the numerical solution framework.

[0030] (20) In equation (20), This represents the number of temperature integration points used to approximate the integral of the borehole wall temperature. Indicates the first Root drilling in the first Determine the depth coordinates of the accumulation point based on the temperature of the segment. Indicates the relationship with the first The first root borehole Determine the depth coordinates of the temperature of the segment. The corresponding weights Indicates the first The coordinates of the root borehole.

[0031] Step 4.4: Substitute equations (15)-(16) into equation (20), and then use equation (21) to obtain the first... time discrete points borehole wall temperature Discretized equations: (twenty one) Step 5: By introducing a regularization term, the numerical instability problem caused by high-precision discretization is solved, thereby ensuring the stability and reliability of the thermal response function calculation process. Step 5.1: Introduce a regularization term into equation (20) using equation (22). The fundamental reason is that after fine discretization, the linear system corresponding to the original first-kind integral equation exhibits severe ill-conditioning, causing the solution to be extremely sensitive to numerical errors and thus produce distortion. By constructing a regularized temperature field... A correction term proportional to the local heat exchange intensity is explicitly introduced into the original physical temperature field. Through this mathematical construction, the original problem is transformed into a second-kind integral equation with a unique stable solution, thus obtaining a reliable solution.

[0032] (twenty two) In equation (22), Indicates the first time discrete points The first time after regularization modification The borehole wall temperature of the root borehole Represents the regularization parameter. Indicates the first time discrete points Time The first root borehole The heat exchange volume of the section.

[0033] Step 5.2: Use equation (23) to establish the discretized thermal response function with the introduction of a regularization term. The introduction of the regularization term ensures that the linear system can still be solved stably and accurately with high discretization accuracy, thus obtaining a reliable discretized thermal response function: (twenty three) In equation (21), This indicates that all heat sources are within the time period. The thermal influence coefficient matrix on borehole wall temperature It is the identity matrix. It is a column vector whose elements are all 1s. Indicates the first time discrete points The heat exchange matrix of all boreholes and their integral points at time. This indicates that all heat sources are at the th time discrete points and the time discrete points The time period between The heat source released internally to the first time discrete points The cumulative thermal effect matrix generated at that time, This represents the weight coefficient matrix for the borehole segments.

[0034] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0035] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A vertical drilling heat response calculation method based on a new discrete algorithm, characterized by, The method comprises the following steps: Step 1, establishing integral relationship between soil temperature at any position and heat exchange amount along depth distribution of all boreholes; Step 2, based on the integral relationship, discretizing unit heat exchange amount of boreholes along time, and expressing soil temperature as sum of historical cumulative effect and current time period contribution; Step 3, set the average heat exchange constraint of the borehole and the uniform borehole wall temperature boundary condition, establish the relationship between the time moment thermal response function and the borehole wall temperature . Step 4, approximating the continuous spatial integrals in the borehole wall temperature expression as weighted sums over a finite number of quadrature points, and generating a borehole segmentation scheme from the quadrature points, thereby transforming the thermal response function into a discretized equation ; Step 5, by introducing a regularization term in the discretization equation of The thermal response function after introducing the regularization term is established to realize the calculation of the vertical borehole thermal response.

2. The vertical drilling thermal response calculation method based on a new discrete algorithm of claim 1, wherein, The step 1 comprises: Step 1.1, establishing a relationship between the time and the heat source point the temperature change of the soil at the point the temperature change of the soil at the point : (1) (2) in formula (1) - formula (2), denotes the instantaneous heat released by the heat source point at the origin, denotes the time instant and the temperature of the soil at a distance of the heat source point, denotes the density of the soil, denotes the specific heat capacity of the soil, denotes the thermal diffusivity of the soil, denotes the exponential function with base ; Step 1.2, establishing from time to time the period below the site of the heat source caused soil cumulative temperature response : (3) (4) (5) in formulae (3) to (5), denotes the thermal conductivity of the soil, denotes the complementary error function, denotes the integral variable; Step 1.3, establishing the time coordinate position with formula (6) the soil temperature at the time coordinate position : (6) In formula (6), represents the ground temperature, represents the number of boreholes, , respectively represent the depth and length of the i-th borehole, respectively represent the depth and length of the i-th borehole, represents the heat exchange amount of the i-th borehole per unit time at the soil depth represents the heat exchange amount of the i-th borehole per unit time at the soil depth represents the heat exchange amount of the i-th borehole per unit time at the soil depth represents the heat exchange amount of the i-th borehole per unit time at the soil depth represents the heat exchange amount of the i-th borehole per unit time at the soil depth represents the heat exchange amount of the i-th borehole per unit time at the soil depth 3. The vertical borehole thermal response calculation method based on a new discrete algorithm of claim 2, wherein, The step 2 comprises: Step 2.1, drilling a hole in the soil with a drill of a diameter of 2 cm at a depth of 10 cm Discretization along time:​​ (7) In formula (7), denotes the discretization number of time , denotes the heat exchange amount at the th time discrete point of the th borehole at the soil depth , . Step 2.2, substituting formula (7) into formula (6) and using formula (8) to obtain the first time discrete point :​​​ (8) Step 2.3, using equations (9)-(11) to... Decompose to obtain the first time discrete points Time coordinate position is Historical cumulative temperature changes in soil And in the time discrete points and the time discrete points The time period between Inner soil temperature changes sum: (9) (10) (11)。 4. The vertical borehole thermal response calculation method based on a new discrete algorithm of claim 3, wherein, The step 3 comprises: Step 3.1, Establishing the heat response function with respect to the average heat exchange per unit length of borehole at the first time discrete point using equation (12) Boundary conditions:​​ (12) Step 3.2, establishing uniform borehole wall temperature boundary condition by using formula (13): (13) In formula (13), represents the temperature of the borehole wall at the time-discrete point in time. Step 3.3, utilizing formula (14) to obtain Time-dependent thermal response function Relationship with borehole wall temperature Relationship: (14)。 5. The vertical borehole thermal response calculation method based on a new discrete algorithm according to claim 4, characterized in that, The step 4 comprises the following steps: Step 4.1, approximating formula (9)-(11) to weighted sum on limited heat source quadrature points by using formula (15)-(17): (15) (16) (17) in formulas (15) to (17), denotes the number of heat source quadrature points used for discretizing the heat source integral along the depth direction for each borehole, denotes the depth coordinate of the th heat source quadrature point of the th borehole, denotes the weight coefficient corresponding to the depth coordinate of the th heat source quadrature point of the th borehole, denotes the weight coefficient corresponding to the depth coordinate of the Step 4.2, split the borehole into segments of equal length along the depth direction using formula (18) - (19) to determine the number of quadrature points segments of equal length: (18) (19) In equations (18)-(19), , They represent the first The first root borehole The upper and lower depth boundaries of the segment, Indicates the first The first root borehole Calculate the depth coordinates of the integration point for each heat source. Indicates the first The first root borehole Calculate the depth coordinates of the integration point for each heat source; Step 4.3, utilize the borehole wall temperature approximation as a weighted sum of the temperature at the quadrature points within each segment: Step 4.3, utilize the borehole wall temperature approximation as a weighted sum of the temperature at the quadrature points within each segment: (20) In equation (20), This represents the number of temperature integration points used to approximate the integral of the borehole wall temperature. Indicates the first Root drilling in the first Determine the depth coordinates of the accumulation point based on the temperature of the segment. Indicates the relationship with the first Root drilling in the first Determine the depth coordinates of the temperature of the segment. The corresponding weights Indicates the first The coordinates of the root borehole; Step 4.4, after introducing the formula (15) - formula (16) into the formula (20), the first time discrete point of the drilling wall temperature discrete equation: (21)。 6. The vertical borehole thermal response calculation method based on a new discrete algorithm according to claim 5, characterized in that, The step 5 comprises the following steps: Step 5.1, introducing regularization term to formula (20) by using formula (22): (22) In formula (20), denotes the time discrete point at which the wall temperature of the first borehole is corrected by regularization, denotes a regularization parameter, denotes the time discrete point at which the heat exchange quantity of the first section of the first borehole, denotes the Step 5.2, establishing discrete heat response function after introducing regularization term by using formula (23): (23) In formula (21), denotes the time period of all heat source points in the time interval The heat influence coefficient matrix of the borehole wall temperature, is the unit matrix, is a column vector with all elements being 1, denotes the heat exchange matrix of all boreholes and their quadrature points at the time discrete point , denotes the cumulative heat influence matrix of all heat source points between the time discrete point and the time discrete point to the time discrete point , , denotes the weight coefficient matrix of the borehole section.

7. An electronic device comprising a memory and a processor, characterized in that The memory is used for storing program supporting the processor to execute the vertical borehole heat response calculation method in any one of claims 1-6, and the processor is configured to execute the program stored in the memory.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to execute the vertical borehole heat response calculation method in any one of claims 1-6.

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