Rock-soil temperature field rapid solving method suitable for ground source heat pump system

Abstract

The invention discloses a rock-soil temperature field rapid solving method suitable for a ground source heat pump system, and the method comprises the steps: firstly building a three-dimensional unsteady-state heat transfer model in consideration of a buried pipe coaxial structure, a porous arrangement form and the characteristics of a multilayer heterogeneous soil body in the ground source heat pump system; then simulating a thermal response process by using the model, constructing a multi-domain coupled thermal conduction augmentation matrix, performing POD on the matrix, extracting a dominant mode function of a temperature field, and constructing a low-dimensional POD-based mode space; and finally, constructing a POD-Galerkin low-order model, simulating a buried pipe group soil temperature field, performing inversion of a heat source function, and outputting stratum thermophysical parameters. According to the method, the calculation efficiency and the simulation precision of the porous coupling and long-period unsteady state heat transfer process are remarkably improved, the problem that traditional finite element and finite difference methods are high in time consumption in porous strong coupling modeling is solved, and rapid prediction of the soil temperature and robust recognition of the heat source function under a complex stratum and a heat exchange structure can be achieved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of ground source heat pump, and particularly relates to a rock-soil temperature field fast solving method suitable for a ground source heat pump system. BACKGROUND

[0002] As a form of efficient renewable energy utilization, the ground source heat pump technology is increasingly widely applied in the field of building heating and refrigeration. Among them, the coaxial buried pipe gradually becomes a key heat exchange component in the ground source heat pump system due to the compact structure, low drilling cost and high heat exchange efficiency. However, the heat exchange capacity of the single-hole buried pipe is limited, and it is difficult to meet the overall heat load demand of large buildings or complex projects, and the multi-hole arrangement (i.e. multiple coaxial buried pipes are installed side by side) becomes the mainstream development trend. However, with the increase of the number of holes, the thermal interference effect between the holes is significantly enhanced, and the geothermal response characteristics become more complex. The traditional numerical modeling method (such as finite element and finite difference) has large calculation amount and slow convergence when dealing with multi-hole coupling and non-steady-state heat transfer process, and it is difficult to meet the demand for rapid evaluation and operation prediction of multiple schemes in engineering application. In addition, the buried pipe also faces problems such as uncertainty of soil thermal parameters and frequent changes of boundary conditions during operation. How to establish an efficient model that takes into account simulation accuracy, solving speed and parameter identification is a key technical problem in the current field. SUMMARY

[0003] In view of the problems in the above background art, the application provides a rock-soil temperature field fast solving method suitable for a ground source heat pump system, which can significantly improve the solving efficiency under the premise of ensuring the calculation accuracy, and takes into account the geothermal parameter inversion capability, and is suitable for multi-hole heat exchange process simulation under multi-layer heterogeneous strata and complex boundary conditions.

[0004] In order to achieve the above purpose, the application adopts the following technical scheme: A rock-soil temperature field fast solving method suitable for a ground source heat pump system, comprising the following steps: S1, considering the coaxial structure of the buried pipe in the ground source heat pump system, the multi-hole arrangement form and the multi-layer heterogeneous soil body characteristics, a three-dimensional non-steady-state heat transfer model is constructed, and initial and boundary value conditions containing fluid temperature, boundary heat flux and stratum thermal property parameters are set; ; In the formula, a is the thermal diffusivity of the rock-soil, θ is the rock-soil temperature distribution function about time t and spatial position ( r,z ), r and r boundary is the radial length and radial boundary value of the buried pipe, r b is the borehole radius,z and z boundary respectively as the buried pipe depth and the vertical boundary value of the buried pipe, H as the borehole depth, λ s as the average thermal conductivity of rock and soil, T f1 as the temperature of the outer pipe fluid, T b as the pipe wall temperature, R 1 as the thermal resistance between the outer pipe fluid and the borehole wall; S2, simulating the thermal response process of the ground source heat pump system by using the three-dimensional unsteady heat transfer model, obtaining thermal response data, and constructing a multi-domain coupled heat conduction augmented matrix; S3, performing an intrinsic orthogonal decomposition (POD) on the heat conduction augmented matrix, extracting dominant modal functions of the temperature field, and retaining the first several dominant modal functions through energy contribution rate screening, and constructing a low-dimensional POD basis modal space; S4, projecting the heat transfer control equation of the three-dimensional unsteady heat transfer model to the low-dimensional POD basis modal space by using the Galerkin projection method, and constructing a POD-Galerkin low-order model; S5, rapidly simulating the soil temperature field of the buried pipe group under different boundary conditions and structural parameters by using the POD-Galerkin low-order model, and inverting the heat source function based on observation data, and outputting the formation thermal physical parameters.

[0005] Further, in step S1, since the initial temperature distribution of the soil is generally based on the temperature change state when there is no disturbance, that is, it is suitable for the steady-state heat transfer equation, therefore, in the three-dimensional unsteady heat transfer model, if the rock and soil is a homogeneous medium, the temperature distribution expression at the initial moment is: ; If the rock and soil is a non-homogeneous medium, in the rock and soil layer of multiple horizontal layers, the temperature change expression at the initial moment is: ; Wherein, T 0 is the initial moment temperature, T sur is the ground surface temperature distribution, q s is the terrestrial heat flow density; T l represents the initial moment temperature of the first l layer of the formation, h s is the convective heat transfer coefficient of air and ground surface, m is the total number of layers, λ s,l andλ s,m respectively represent the first l layer and m the thermal conductivity of the ground of the first z l , z l-1 and z m-1 respectively represent the first l layer, the first l -1 layer and the first m -1 layer.

[0006] Further, in step S3, when the heat conduction augmented matrix is subjected to POD, the POD dimension reduction method can be directly expressed by a linear combination of eigenfunctions and their amplitudes, so the ground temperature distribution in a single borehole is represented by the following reconstruction formula, only the first M modal functions are retained: ; wherein, θ i ( t,r,z ) is the ground temperature distribution function of the first i borehole with respect to time t and spatial position ( r,z ), M is the order of the modal function, c k i ( t ) is a time-dependent coefficient, representing the weight of the first i modal of the first k borehole at time t ; φ k i ( r,z ) is the first k modal function, n is the number of boreholes. As can be seen from the above reconstruction formula, the numerical solution problem of the temperature field can be converted into the problem of solving the amplitude and the eigenfunction, and the solution of the eigenfunction can be obtained by the singular value decomposition method.

[0007] Further, in step S4, when the heat transfer control equation of the three-dimensional unsteady heat transfer model is projected to the low-dimensional POD modal space, since it is a multi-borehole heat exchanger, the final projection of the ground temperature response is represented as: ; wherein, T ( t,x,y,z ) represents the final projection of the ground temperature response, x ,y These represent the horizontal and vertical coordinates of the borehole within the horizontal plane.

[0008] Furthermore, in step S5, the inversion process of the heat source function is trained using a BP neural network model, with the input being the predicted temperature response characteristics and the output being the formation thermal property parameters.

[0009] Furthermore, the network structure of the BP neural network model includes: Input layer: Selects the temperature response vector at a specific spatiotemporal point as the input predicted temperature response feature; Hidden layers: consisting of 1 to 2 layers, employing a fully connected structure, with ReLU activation function; Output layer: Outputs formation thermal properties, including target parameters such as thermal conductivity, thermal diffusivity, and specific heat capacity; The training data was constructed by combining simulation data from the POD-Galerkin low-order model with comparative data from the full-order finite element model. Loss function: ; in, , These are the target sample points. j The predicted and actual values ​​are compared, and the weights are optimized using gradient descent and backpropagation. N This represents the total number of samples (i.e., the total number of data points used in training).

[0010] Compared with the shortcomings and deficiencies of existing technologies, the present invention has the following beneficial effects: 1. This invention constructs a low-order model of the soil temperature field in a porous heat exchange system based on the POD-Galerkin order reduction algorithm, which significantly improves the computational efficiency and simulation accuracy of porous coupling and long-term unsteady heat transfer processes, and solves the problem of high time consumption in the traditional finite element and finite difference methods in porous strong coupling modeling. 2. The rapid solution method for soil and rock temperature fields in this invention significantly compresses the dimensionality of the POD-Galerkin low-order model, thereby reducing the computational cost of high-dimensional numerical models. It can significantly improve the efficiency of temperature field simulation and heat load identification while ensuring computational accuracy. It maintains high prediction accuracy even under multi-layered heterogeneous strata and unsteady conditions. It is applicable to different layouts, boundary conditions, and soil structures. It is particularly suitable for real-time simulation and operational status assessment of medium-deep buried pipe heat exchange systems and has good promotional value in engineering practice. 3. This invention optimizes and inverts the heat source function based on observation data. The inversion process combines a feedforward neural network structure. During the training process, the error backpropagation algorithm is used to continuously adjust the network weights to minimize the error between the predicted parameter output and the actual target, thereby achieving the goal of efficiently predicting soil and rock temperature. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the porous coaxial buried pipe heat exchange system provided in an embodiment of the present invention; Figure 2 This is a flowchart of a method for rapidly solving the soil and rock temperature field applicable to ground source heat pump systems, provided by an embodiment of the present invention. Figure 3 This is a graph showing the nominal heat loss attenuation of the system under different hole spacings, provided in an embodiment of the present invention. Figure 4 This refers to the identification error of the inversion algorithm provided in this embodiment of the invention under different noise intensities. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0013] For multi-hole buried pipe structures, this invention proposes a rapid solution method for the geothermal temperature field of ground source heat pump systems, applicable to geothermal heat transfer modeling and parameter identification in multi-layered heterogeneous soils and complex boundary conditions. In ground source heat pump systems, a 7×7 arrangement of buried pipe groups with coaxial internal structures in each well (e.g., ...) is used. Figure 1 As shown in the figure, the single-hole drilling depth is 2000 meters. The geological environment of the borehole is complex, containing heterogeneous strata such as clay layers, sand layers, and gravel interlayers, with significant spatial differences in thermal conductivity distribution, making it representative. During the system design phase, the building load changes and operating cycles were known, and the boundary heat flux and operating conditions were clearly defined.

[0014] The flowchart of the rapid solution method for the soil and rock temperature field of a ground source heat pump system proposed in this invention is as follows: Figure 2 As shown below, a detailed explanation will follow.

[0015] 1. Construct a three-dimensional unsteady heat transfer model Considering the coaxial structure of the buried pipes, the porous arrangement, and the characteristics of multi-layered heterogeneous soil in the ground source heat pump system, the following three-dimensional unsteady heat transfer model is constructed, and initial and boundary conditions including fluid temperature, boundary heat flux, and stratum thermal property parameters are set. ; In the formula, a The thermal diffusivity of the rock and soil θ It's about time. t and spatial location ( r,z The temperature distribution function of soil and rock. r and rboundary These represent the radial length and radial boundary value of the buried pipe, respectively. r b Where is the borehole radius, z and z boundary These represent the burial depth and the vertical boundary value of the buried pipe, respectively. H The drilling depth λ s The average thermal conductivity of the soil and rock is... T f1 The temperature of the fluid in the outer pipe. T b For pipe wall temperature, R 1 represents the thermal resistance between the fluid in the outer tube and the borehole wall.

[0016] The initial temperature distribution of soil is generally based on the undisturbed temperature change state, i.e., it conforms to the steady-state heat transfer equation. If the soil and rock are homogeneous media, then the expression for the initial temperature distribution is: ; If the soil and rock are non-homogeneous media, the initial temperature change expression in multiple horizontal soil and rock layers is: ; in, T 0 represents the initial temperature. T sur For surface temperature distribution, q s This refers to the Earth's heat flux density. T l Indicates the first l The initial temperature of each stratum. h s The convective heat transfer coefficient between air and the Earth's surface. m The total number of strata. λ s,l and λ s,m They represent the first l Layers and m The thermal conductivity of the soil and rock layer, z l , z l-1 and z m-1 The first l Layer, First l -1st floor and the m The coordinates of the bottom of the -1 layer.

[0017] 2. Construct a multi-domain coupled heat conduction augmentation matrix Using the established three-dimensional unsteady heat transfer model, the thermal response process under the representative operating conditions of the ground source heat pump system is simulated based on the high-precision full-order numerical solution method, the thermal response data is obtained, and the heat conduction augmented matrix of multi-domain coupling is constructed: = ; The first 800 columns of the heat conduction augmented matrix T store sample data with a heat extraction time of 1 year, the middle 800 columns store sample data with a heat extraction time of 3 years, and the last 800 columns store sample data with a heat extraction time of 5 years.

[0018] 3, Construct a low-dimensional POD base modal space The heat conduction augmented matrix T is subjected to intrinsic orthogonal decomposition (POD) by the "snapshot" method, the sample data is subjected to dimension reduction processing, and the dominant modal function of the temperature field is extracted. The POD projection method is used to construct a low-order model of the ground heat exchanger group. In order to realize model simplification and dimension reduction, the dominant modal function with a cumulative energy contribution rate of not less than 99.99% is selected. The number of modes retained is: 6, 7, 5, 7, 8, and 8 for single pipe and pipe group under 1 year, 3 years and 5 years of heat extraction conditions, respectively, which are used to represent the temperature field distribution under different time scales and structural configurations, can accurately capture the main evolution characteristics of the temperature field, and realize efficient and rapid dimension reduction calculation; and then a low-dimensional POD base modal space is constructed, and a low-order approximate model of the temperature field is established.

[0019] The POD dimension reduction method can be directly expressed by a linear combination of characteristic functions and their amplitudes. The temperature distribution of the single-hole ground heat exchanger is represented by the following reconstruction formula, and only the first M modal functions are retained: ; Among them, θ i ( t,r,z ) is the temperature distribution function of the first i ground heat exchanger with respect to time t and spatial position r,z , M is the order of the modal function, c k i ( t ) is a time-dependent coefficient, which represents the weight of the first i modal of the first k ground heat exchanger at time t ; φ k i ( r,z ) is the first k modal function, nThe number of boreholes for the ground heat exchanger is determined. As can be seen from the above reconstruction formula, the problem of solving the numerical solution of the temperature field can be transformed into the problem of solving the amplitude and the characteristic function, and the solution of the characteristic function can be obtained by the singular value decomposition method.

[0020] 4. Constructing a POD-Galerkin low-order model The heat transfer control equation of the three-dimensional unsteady heat transfer model is projected into the low-dimensional POD basis modal space by the Galerkin projection method to construct a POD-Galerkin low-order model. The key of the POD projection method is to project the original partial differential equation into a low-dimensional subspace composed of main modes, and this process involves solving an eigenvalue problem to find the main modes that best represent the system dynamics.

[0021] When the porous ground heat exchanger is in heat transfer, the final projection of the ground temperature response is represented as: ; wherein, T ( t,x,y,z ) represents the final projection of the ground temperature response, x 、 y and and are the horizontal and vertical coordinate positions of the borehole in the horizontal plane, respectively.

[0022] 5. Solution and inversion Under different groups of perturbed boundary conditions (such as different running interval strategies, variable load conditions, etc.) and structural parameters, the POD-Galerkin low-order model is used to carry out rapid prediction simulation of the soil temperature field of the ground heat exchanger group, and the inversion of the heat source function is carried out based on the observation data to output the thermal physical parameters of the stratum.

[0023] To test the effectiveness of the POD-Galerkin low-order model, the results are compared and analyzed with those of the full-order model, and the results show that: under various perturbed working conditions, the temperature prediction error of the POD-Galerkin low-order model is less than 3%; the full-order model originally requiring 37 minutes of calculation can complete the same precision prediction in only 27 seconds after the reduction processing of the present application, and the efficiency is improved by more than 80 times.

[0024] In addition, the advantages of the POD-Galerkin low-order model are compared under different pipe spacings, and the results are shown in Figure 3 as Figure 3It can be seen that the heat extraction rate of the group system is higher at the initial stage, but it gradually decreases and tends to be stable with the increase of operation time. The smaller the well spacing, the more significant the thermal interference, resulting in faster attenuation of heat extraction. After 5 years, the heat extraction rate of the group with a spacing of 10 m is only about 60% of that of a single well. When the well spacing increases to more than 30 m, the curve tends to be close to the single well result, indicating that the inter-well thermal interference effect is weak at this time. Overall, increasing the well spacing helps to reduce the thermal interference effect and improve the long-term heat extraction stability.

[0025] The inversion process of the heat source function (POD-ROM inversion algorithm) uses a BP neural network model for training, with the predicted temperature response characteristics as input and the formation thermal property parameters as output. The network structure of the BP neural network model includes: Input layer: the temperature response vector of a specific spatiotemporal point (e.g., 10 depth points x 5 time points = 50-dimensional features) is selected as the input predicted temperature response characteristics; Hidden layer: contains 1-2 layers, uses a fully connected structure, and the activation function is ReLU; Output layer: outputs the formation thermal property parameters, including thermal conductivity, thermal diffusivity, specific heat capacity, and other target parameters; The training data is derived from the POD-Galerkin low-order model simulation data and the full-order finite element model comparison data to construct the training set; Loss function: ; Where, , are the predicted and actual values of the target sample points, j uses gradient descent and backpropagation to optimize the weights, N is the total number of samples (i.e., the number of data points participating in training).

[0026] Generalization ability: cross-validation is used to ensure that the model has good prediction effect on unknown temperature response samples.

[0027] The identification error of the inversion algorithm under different noise intensities is shown in Figure 4 . The heat source identification error changes non-monotonically with the noise intensity σ . When <0.05, the heat source identification error reaches a minimum value of about 0.02, indicating that the POD-Galerkin low-order model has good robustness under moderate noise levels. Subsequently, the heat source identification error fluctuates with the increase of noise intensity, but it remains in the range of 0.02-0.08, indicating that the POD-ROM inversion algorithm still has good stability and anti-interference ability under certain noise conditions.

[0028] The POD-Galerkin low-order model constructed by the application has a greatly compressed dimension, and the calculation speed is significantly improved compared with traditional methods; in multiple rounds of tests, the POD-Galerkin low-order model shows good numerical stability and generalization ability; can accurately identify the heat source characteristics of the ground source heat pump system, realize efficient and high-precision temperature field prediction and inversion, and significantly improve the calculation efficiency of long-term operation performance analysis of the system.

[0029] The above merely describes preferred embodiments of the application and is not intended to limit the application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A method for rapid solution of the soil and rock temperature field suitable for ground source heat pump systems, characterized in that, Includes the following steps: S1. Considering the coaxial structure of the buried pipe, the porous arrangement, and the characteristics of multi-layer heterogeneous soil in the ground source heat pump system, the following three-dimensional unsteady heat transfer model is constructed, and initial boundary conditions including fluid temperature, boundary heat flux, and stratum thermal property parameters are set. ； In the formula, a The thermal diffusivity of the rock and soil is... θ It's about time. t and spatial location ( r , z The temperature distribution function of soil and rock. r and r boundary These represent the radial length and radial boundary value of the buried pipe, respectively. r b Where is the borehole radius, z and z boundary These represent the burial depth and the vertical boundary value of the buried pipe, respectively. H The drilling depth λ s The average thermal conductivity of the soil and rock is... T f1 The temperature of the fluid in the outer pipe. T b For pipe wall temperature, R 1 represents the thermal resistance between the fluid in the outer tube and the borehole wall; S2. Use the three-dimensional unsteady heat transfer model to simulate the thermal response process of the ground source heat pump system, obtain thermal response data, and construct a multi-domain coupled heat conduction augmentation matrix. S3. Perform POD on the heat conduction augmented matrix, extract the dominant mode functions of the temperature field, select and retain the first few dominant mode functions by energy contribution rate, and construct a low-dimensional POD basis mode space. S4. The heat transfer control equations of the three-dimensional unsteady heat transfer model are projected onto the low-dimensional POD basis mode space using the Galerkin projection method to construct a POD-Galerkin low-order model. S5. The soil temperature field of the buried pipe group is quickly simulated using the POD-Galerkin low-order model under different boundary conditions and structural parameters. Based on the observation data, the heat source function is inverted, and the formation thermal property parameters are output.

2. The method for rapid solution of soil and rock temperature field applicable to ground source heat pump systems as described in claim 1, characterized in that, In step S1, in the three-dimensional unsteady heat transfer model, if the soil and rock are homogeneous media, the initial temperature distribution expression is: ； If the soil and rock are non-homogeneous media, and there are multiple horizontal layers of soil and rock, the expression for the initial temperature change is: ； in, T 0 represents the initial temperature. T sur For surface temperature distribution, q s This refers to the Earth's heat flux density. T l Indicates the first l The initial temperature of each stratum. h s The convective heat transfer coefficient between air and the Earth's surface. m The total number of strata. λ s,l and λ s,m They represent the first l Layers and m The thermal conductivity of the soil and rock layer, z l , z l-1 and z m-1 The first l Layer, First l -1st floor and the m The coordinates of the bottom of the -1 layer.

3. The method for rapid solution of soil and rock temperature field applicable to ground source heat pump systems as described in claim 1, characterized in that, In step S3, when performing POD on the augmented heat conduction matrix, the soil and rock temperature distribution in the single-hole buried pipe is represented by the following reconstruction formula, retaining only the first part. M Term mode function: ； in, θ i ( t,r,z ) is the first i Regarding the time of drilling for underground pipes t and spatial location ( r,z The temperature distribution function of soil and rock. M Let be the order of the modal function. c k i ( t ) is a time-dependent coefficient, representing the first... i The first underground pipe drilling hole k Each mode in time t The weights; φ k i ( r,z ) is the first k One modal function, n This refers to the number of boreholes drilled for underground pipes.

4. The method for rapid solution of soil and rock temperature field applicable to ground source heat pump systems as described in claim 3, characterized in that, In step S4, when the heat transfer control equations of the three-dimensional unsteady heat transfer model are projected onto the low-dimensional POD fundamental mode space, the final projected expression of the soil and rock temperature response is as follows: ； in, T ( t,x,y,z ) represents the final projection of the soil temperature response. x , y These represent the horizontal and vertical coordinates of the borehole within the horizontal plane.

5. The method for rapid solution of soil and rock temperature field applicable to ground source heat pump systems as described in claim 1, characterized in that, In step S5, the inversion process of the heat source function is trained using a BP neural network model, with the input being the predicted temperature response characteristics and the output being the formation thermal property parameters.

6. The method for rapid solution of soil and rock temperature field applicable to ground source heat pump systems as described in claim 5, characterized in that, The network structure of the BP neural network model includes: Input layer: Selects the temperature response vector at a specific spatiotemporal point as the input predicted temperature response feature; Hidden layers: consisting of 1 to 2 layers, employing a fully connected structure, with ReLU activation function; Output layer: Outputs formation thermal properties, including target parameters such as thermal conductivity, thermal diffusivity, and specific heat capacity; The training data was constructed by combining simulation data from the POD-Galerkin low-order model with comparative data from the full-order finite element model. Loss function: ; in, , These are the target sample points. j The predicted and actual values ​​are compared, and the weights are optimized using gradient descent and backpropagation. N The total number of samples.

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