Method for predicting fluid temperature field of middle-deep layer sleeve type buried pipe containing horizontal well

Abstract

The invention relates to a method for predicting a fluid temperature field of a middle-deep layer sleeve type buried pipe containing a horizontal well, and the method comprises the following steps: constructing a heat transfer model of the middle-deep layer sleeve type buried pipe containing the horizontal well, and dividing the model into a vertical section and a horizontal section; and carrying out iterative solution on the heat transfer model. Compared with the prior art, the method has the advantages that the calculation amount is reduced, the temperature field is accurately predicted, and the like.

Description

Technical Field

[0001] The invention relates to the technical field of ground source heat pumps, and in particular to a method for predicting the temperature field of a fluid in a medium-deep casing-type buried pipe containing a horizontal well. Background Art

[0002] The medium-deep casing buried pipe with horizontal wells can make full use of the significant enhancement effect of groundwater seepage on heat transfer performance due to its unique design, making its heat transfer performance far better than ordinary medium-deep casing vertical buried pipes. This advantage gives it a wide range of application prospects in ground source heat pump systems. In order to give full play to its performance advantages and ensure the stable operation of the system, predicting the temperature field of the buried pipe fluid has become a crucial research content. This is not only the basis for thermal response testing, but also the prerequisite for optimizing the design of buried pipes. At present, the prediction of the fluid temperature field of the medium-deep casing buried pipe with horizontal wells mainly relies on numerical models. These models can accurately simulate the heat transfer process of the fluid in the pipeline through refined modeling and calculation, providing a reliable theoretical basis for the design and operation of the system.

[0003] In July 2022, Gu Feng, Li Youwu, Tang Dazhen, Gao Ying, Zhang Yue, Yan Peng and Ye Hao published an article titled "Heatextraction performance of horizontal-well deep borehole heat exchanger and comprehensive comparison with the vertical well" in Volume 211, Article 118426 of Applied Thermal Engineering. The article proposed a medium-deep casing-type buried pipe with a horizontal well, established a three-dimensional heat and mass transfer numerical model, analyzed the temperature distribution of the fluid and rock, and compared it with the medium-deep casing-type vertical buried pipe. The results show that the temperature rise of the fluid in the horizontal section is 2.67 times that of the vertical section; when the groundwater seepage velocity exceeds a certain critical value, it has a significant promoting effect on convective heat exchange; flow rate and horizontal well length are important factors affecting the heat extraction performance of the system. Compared with the medium-deep casing-type vertical buried pipe, the increase in flow rate and horizontal well length significantly improves the efficiency and economy of the system to a certain extent. However, the calculation process of the numerical model in the above-mentioned literature is very complicated and the amount of calculation is large, so the existing buried pipe fluid temperature field prediction method is difficult to be widely used in actual engineering. Summary of the invention

[0004] The purpose of the present invention is to simplify the modeling of the casing-type buried pipe heat transfer model, discretize the differential equations, form a set of integral equations at different nodes and times, and efficiently solve them through an iterative method, thereby reducing the amount of calculation and realizing accurate prediction of the temperature field, and providing a method for predicting the fluid temperature field of a medium-deep casing-type buried pipe containing a horizontal well.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well, the method comprising the following steps:

[0007] A heat transfer model of a medium-deep casing buried pipe with a horizontal well is constructed. The model is divided into a vertical section and a horizontal section, and the models are independently constructed. For the vertical section, a transient heat transfer equation of the inner pipe fluid and the outer pipe fluid of the vertical section is established, and the vertical section boundary conditions and the vertical section initial conditions are set; for the horizontal section, a steady-state heat transfer equation of the inner pipe fluid and the outer pipe fluid of the horizontal section is established, and the horizontal section boundary conditions and the horizontal section initial conditions are set;

[0008] Solve the heat transfer model and divide the vertical section into M sections along the axial direction. The lengths of the first and M sections are both Δz / 2, and the length of the middle section is Δz. Then the axial coordinate z of the mth node is m =Δz×(m-1)+Δz / 2;

[0009] The horizontal segment is divided into K segments along the axial direction, where the lengths of the first and Kth segments are both Δx / 2, and the length of the middle segment is Δx. Then the axial coordinate x of the kth node is k =Δx×(k-1)+Δx / 2;

[0010] Set the time step Δt and the total simulation time to t tol , then the number of time segments is N = t tol / Δt, and t n =nΔt;

[0011] At a certain time t n , where 1≤n≤N, the equations of the heat transfer model are discretized, and the discretized equations are solved by the iterative method to obtain t n The temperature of each fluid element in the vertical and horizontal segments at the moment is calculated to obtain the temperature prediction result.

[0012] Furthermore, the transient heat transfer equations of the inner tube fluid and the outer tube fluid in the vertical section are:

[0013]

[0014] Among them, r ii ——Inner radius of the inner tube; (ρc)f ——Volume specific heat capacity of the inner tube fluid and the outer tube fluid; r io ——Outer radius of the inner tube; (ρc) ip ——Volume specific heat capacity of the inner tube; T i1 (z,t)——temperature of the fluid in the vertical section of the buried pipe; z——axial coordinate of the vertical section of the buried pipe; t——time; V(t)——volume flow rate of the fluid in the inner pipe and the fluid in the outer pipe; T a1 (z,t)——temperature of the fluid outside the vertical section of the underground pipe; L1——length of the vertical section of the underground pipe; r eo ——Outer radius of the outer tube; r ei ——Inner radius of the outer tube; (ρc) ep ——Volume specific heat capacity of the outer tube; R ia ——Thermal resistance between the inner tube fluid and the outer tube fluid; q1(z,t)——Thermal flow between the outer tube fluid and the backfill soil in the vertical section of the buried pipe.

[0015] Furthermore, the thermal resistance between the inner tube fluid and the outer tube fluid is:

[0016]

[0017] Among them, h i ——Convection heat transfer coefficient of the fluid in the inner tube;

[0018] λ ip ——Thermal conductivity of the inner tube;

[0019] h a ——Convective heat transfer coefficient of the fluid in the outer tube.

[0020] Furthermore, the heat flow between the outer pipe fluid of the vertical section of the buried pipe and the backfill soil is:

[0021]

[0022] Among them, R ae ——Thermal resistance between the outer tube fluid and the outer wall of the outer tube; T eo (z,t)——The temperature of the outer wall of the vertical section of the buried pipe.

[0023] Furthermore, the vertical segment boundary conditions and vertical segment initial conditions are:

[0024]

[0025] Among them, T in (t) —— inlet fluid temperature;

[0026] T sur ——rock and soil surface temperature; a——geothermal gradient; T i2(x, t) – the temperature of the fluid in the horizontal section of the buried pipe; L1 – the length of the vertical section of the buried pipe.

[0027] Furthermore, the steady-state heat transfer equations of the inner tube fluid and the outer tube fluid in the horizontal section are:

[0028]

[0029] Where, x is the axial coordinate of the horizontal section of the buried pipe; T a2 (x, t)——temperature of the fluid outside the horizontal section of the buried pipe; L2——length of the horizontal section of the buried pipe; q2(x, t)——heat flow between the fluid outside the horizontal section of the buried pipe and the backfill soil; R ia ——Thermal resistance between the inner tube fluid and the outer tube fluid; (ρc) f ——Volume specific heat capacity of the inner tube fluid and the outer tube fluid; T i2 (x, t) – the temperature of the fluid in the horizontal section of the buried pipe; V(t) – the volume flow rate of the fluid in the inner pipe and the fluid in the outer pipe.

[0030] Furthermore, the heat flow between the outer pipe fluid and the backfill soil in the horizontal section of the buried pipe is:

[0031]

[0032] Among them, R ab ——Thermal resistance between the outer pipe fluid and the outer wall of the buried pipe in the horizontal section; T b (x, t) is the temperature of the outer wall of the horizontal section of the buried pipe, which is calculated using the moving line heat source model based on the principle of heat flux superposition.

[0033] Furthermore, the temperature of the outer wall surface of the outer tube of the horizontal section of the buried pipe is:

[0034]

[0035] Where G2(t) is the G function of the moving line heat source model of the horizontal section of the buried pipe; T0(z) is the initial temperature of the rock and soil; L1 is the length of the vertical section of the buried pipe; t n ——The time corresponding to the nth moment; t j ——The time corresponding to the j-th moment.

[0036] Furthermore, the horizontal segment boundary conditions and the horizontal segment initial conditions are:

[0037]

[0038] Among them, T a2 (x, t)——temperature of the fluid outside the horizontal section of the buried pipe; L2——length of the horizontal section of the buried pipe; T i2(x, t)——the temperature of the fluid in the horizontal section of the buried pipe; T0(z)——the initial temperature of the rock and soil; T a1 (z,t)——The temperature of the fluid outside the vertical section of the buried pipe.

[0039] Furthermore, the discretized equation is:

[0040]

[0041]

[0042] Among them, A 1、 B 1、 D1 and B2 are both intermediate variables:

[0043]

[0044] Among them, C(m,n) and F(k,n) are intermediate variables:

[0045]

[0046]

[0047] Among them, T i1 ——Temperature of the fluid in the vertical section of the buried pipe; m ——The axial coordinate of the mth node; t n =nΔt, Δt——time step, V(t)——volume flow rate of inner tube fluid and outer tube fluid; (ρc) f ——Volume specific heat capacity of the inner tube fluid and the outer tube fluid; Δz——The length of the middle section of the vertical section; R ia ——Thermal resistance between the fluid in the inner pipe and the fluid in the outer pipe of the vertical section of the buried pipe; T i2 (x,t)——the temperature of the fluid in the horizontal section of the buried pipe; T a1 (z,t)——temperature of the fluid outside the vertical section of the buried pipe; R ae ——Thermal resistance between the outer pipe fluid and the outer wall of the vertical section of the buried pipe; G1(t)——G function of the composite medium column heat source model of the vertical section of the buried pipe; G2(t)——G function of the moving line heat source model of the horizontal section of the buried pipe; T0(z)——The initial temperature of the rock and soil; T a2 (x,t)——the temperature of the fluid outside the horizontal section of the buried pipe; r ii ——Inner radius of inner tube; r io ——Outer radius of the inner tube; (ρc) ep ——Volume specific heat capacity of the outer tube; (ρc) ip ——Volume specific heat capacity of the inner tube; r eo ——Outer radius of the outer tube; r ei——Inner radius of the outer tube, Δx——length of the middle section of the horizontal section.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] The present invention uses a moving line heat source model to accurately simulate the effect of groundwater seepage on the non-steady-state heat transfer of rock and soil in the horizontal section, and constructs a comprehensive and detailed heat transfer model of a casing-type buried pipe containing a horizontal well. Based on this heat transfer model, the method further divides the inner pipe fluid and the outer pipe fluid of the vertical section and the horizontal section into multiple nodes along the axial direction, discretizes the differential equations, and establishes a system of integral equations for the inner and outer pipe fluids at different nodes and times. Finally, an efficient iterative method is used for calculation to achieve accurate prediction of the fluid temperature field. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a cross-sectional schematic diagram of a medium-deep casing buried pipe;

[0051] Figure 2 It is a top view schematic diagram of a medium-deep casing buried pipe;

[0052] Figure 3 It is a schematic diagram of a medium-deep casing buried pipe containing a horizontal well;

[0053] Figure 4 A comparison diagram of the outlet fluid temperature predicted by the present invention and the experimental results;

[0054] Figure 5 This is a comparison chart of the outlet fluid temperature predicted by the present invention and the prediction result of the three-dimensional numerical model. Figure 5 (a) is a comparison chart of fluid temperature at different flow rates under 1-day conditions. Figure 5 (b) is a comparison of the fluid temperature at different flow rates at the outlet under 10-day conditions. Figure 5 (c) is a comparison diagram of fluid temperature at different flow rates at the outlet under 120-day conditions;

[0055] The following are marked in the figure:

[0056] 1. Inner tube fluid; 2. Inner tube; 3. Outer tube fluid; 4. Outer tube; 5. Backfill soil; 6. Rock and soil. DETAILED DESCRIPTION

[0057] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0058] The present invention provides a test method for predicting the temperature field of casing-type underground pipe fluid in medium and deep layers with horizontal wells, which belongs to the core research field of ground source heat pump technology. The method first divides the model into a vertical section and a horizontal section, and performs modeling and integration respectively. In the vertical section, the transient heat transfer equations of the inner and outer pipe fluids are constructed, and the radial one-dimensional heat transfer process in the backfill soil and rock is analyzed by the composite medium column heat source model. In the horizontal section, the steady-state heat transfer equations of the inner and outer pipe fluids are established, and the moving line heat source model is used to explore the non-steady-state heat transfer mechanism of rock and soil under groundwater seepage conditions. The method also sets precise boundaries and initial conditions, and integrates the analysis into a casing-type underground pipe heat transfer model with horizontal wells. Subsequently, based on this model, the inner and outer pipe fluids of the vertical and horizontal sections are divided into multiple nodes along the axial direction, and the differential equations are discretized to form a set of polynomial equations at different nodes and times, and the equations are efficiently solved by the iterative method, thereby achieving accurate prediction of the temperature field. First, the method finely divides the model into vertical and horizontal sections, and independently models them respectively, and finally couples the two parts of the model. In the vertical section, the method uses the composite medium column heat source model to construct the transient heat transfer equations of the inner and outer pipe fluids, and then deeply analyzes the one-dimensional temperature field in the backfill soil and rock. Subsequently, in the horizontal section, the method also creates the steady-state heat transfer equations of the inner and outer pipe fluids, and innovatively applies the moving line heat source model to accurately simulate the influence of groundwater seepage on the unsteady heat transfer of the horizontal section rock. At the same time, to ensure the accuracy and completeness of the model, the method also carefully sets the boundary conditions and initial conditions, and finally integrates these elements to construct a comprehensive and detailed heat transfer model of the casing buried pipe with horizontal wells. Based on this heat transfer model, the method further divides the inner and outer pipe fluids of the vertical and horizontal sections into multiple nodes along the axial direction, discretizes the equations, and establishes the integral equation system of the inner and outer pipe fluids at different nodes and times. Finally, an efficient iterative method is used for calculation to achieve accurate prediction of the fluid temperature field. This method not only improves the accuracy of prediction, but also provides strong technical support for the optimization and application of ground source heat pump technology.

[0059] The method of the present invention comprises the following steps:

[0060] A heat transfer model of a medium-deep casing buried pipe with a horizontal well is constructed. The model is divided into a vertical section and a horizontal section, and the models are independently constructed. For the vertical section, a transient heat transfer equation of the inner pipe fluid and the outer pipe fluid of the vertical section is established, and the vertical section boundary conditions and the vertical section initial conditions are set; for the horizontal section, a steady-state heat transfer equation of the inner pipe fluid and the outer pipe fluid of the horizontal section is established, and the horizontal section boundary conditions and the horizontal section initial conditions are set;

[0061] Solve the heat transfer model and divide the vertical section into M sections along the axial direction. The lengths of the first and M sections are both Δz / 2, and the length of the middle section is Δz. Then the axial coordinate z of the mth node is m =Δz×(m-1)+Δz / 2;

[0062] The horizontal segment is divided into K segments along the axial direction, where the lengths of the first and Kth segments are both Δx / 2, and the length of the middle segment is Δx. Then the axial coordinate x of the kth node is k =Δx×(k-1)+Δx / 2;

[0063] Set the time step Δt and the total simulation time to t tol , then the number of time segments is N = t tol / Δt, and t n =nΔt;

[0064] At a certain time t n , where 1≤n≤N, the equations of the heat transfer model are discretized, and the discretized equations are solved by the iterative method to obtain t n The temperature of each fluid element in the vertical and horizontal segments at the moment is calculated to obtain the temperature prediction result.

[0065] First, the complex model is subdivided into two main parts: the vertical section and the horizontal section, and the models are refined separately. Finally, the two parts of the model are cleverly coupled to form a complete and accurate prediction model. This modular modeling strategy not only improves the flexibility and accuracy of modeling, but also greatly simplifies the complex fluid temperature field prediction process.

[0066] The transient heat transfer equations of the inner and outer pipe fluids in the vertical section of the buried pipe and their boundary conditions and initial conditions are clearly established. The establishment process is as follows:

[0067] In the vertical section of the medium-deep casing buried pipe containing horizontal wells, the transient heat transfer equations of the inner pipe fluid and the outer pipe fluid are:

[0068]

[0069] r ii - inner radius of the inner tube;

[0070] (ρc) f ——Volume specific heat capacity of the inner tube fluid and the outer tube fluid;

[0071] r io ——outer radius of the inner tube;

[0072] (ρc) ip ——Volume specific heat capacity of the inner tube;

[0073] T i1(z,t)——the temperature of the fluid in the vertical section of the buried pipe;

[0074] z——axial coordinate of the vertical section of the buried pipe;

[0075] t——time;

[0076] V(t)——Volume flow rate of inner tube fluid and outer tube fluid;

[0077] T a1 (z,t)——Temperature of the fluid outside the vertical section of the buried pipe;

[0078] L1——the length of the vertical section of the buried pipe;

[0079] r eo ——outer radius of the outer tube;

[0080] r ei - inner radius of the outer tube;

[0081] (ρc) ep ——Volume specific heat capacity of the outer tube;

[0082] R ia ——Thermal resistance between the inner pipe fluid and the outer pipe fluid in the vertical section of the buried pipe:

[0083]

[0084] h i ——Convection heat transfer coefficient of the inner tube fluid;

[0085] λ ip ——Thermal conductivity of the inner tube;

[0086] h a ——Convection heat transfer coefficient of the fluid in the outer tube;

[0087] q1(z,t)——The heat flow between the outer pipe fluid and the backfill soil in the vertical section of the buried pipe:

[0088]

[0089] R ae ——The thermal resistance between the fluid in the outer pipe of the vertical section of the buried pipe and the outer wall of the outer pipe; T eo (z,t)——Temperature of the outer wall of the vertical section of the buried pipe:

[0090]

[0091] t n ——The time corresponding to the nth moment;

[0092] T0(z)——initial temperature of rock and soil;

[0093] t j ——The time corresponding to the jth moment;

[0094] G1(t)——G function of the composite medium column heat source model of the vertical section of the buried pipe; the boundary conditions and initial conditions of the vertical section of the buried pipe are:

[0095]

[0096] T in (t) —— inlet fluid temperature;

[0097] T sur - rock and soil surface temperature;

[0098] a——geothermal gradient;

[0099] T i2 (x,t)——The temperature of the fluid in the horizontal section of the buried pipe.

[0100] Turning the focus to the horizontal section of the buried pipe, the transient heat transfer equations of the inner pipe fluid and the outer pipe fluid and their boundary conditions and initial conditions are carefully established. The establishment process is as follows:

[0101] In the horizontal section of the medium-deep casing buried pipe containing horizontal wells, the steady-state heat transfer equations of the inner pipe fluid and the outer pipe fluid are:

[0102]

[0103] x——axial coordinate of the horizontal section of the buried pipe;

[0104] T a2 (x, t)——the temperature of the fluid outside the horizontal section of the buried pipe;

[0105] L2——the length of the horizontal section of the buried pipe;

[0106] q2(x,t)——The heat flow between the outer pipe fluid and the backfill soil in the horizontal section of the buried pipe:

[0107]

[0108] R ab ——Thermal resistance between the outer pipe fluid and the outer wall of the outer pipe in the horizontal section of the buried pipe;

[0109] T b (x, t) is the temperature of the outer wall of the horizontal section of the buried pipe, which is calculated using the moving line heat source model based on the principle of heat flow superposition:

[0110]

[0111] G2(t)——G function of the moving line heat source model of the horizontal section of the buried pipe;

[0112] In the horizontal section of the buried pipe, the boundary conditions and initial conditions are:

[0113]

[0114] The nodes and time steps in the discretization process of the vertical section and horizontal section of the buried pipe are divided as follows:

[0115] The vertical section of the buried pipe is divided into M sections along the axial direction, where the lengths of the first and Mth sections are both Δz / 2, and the length of the middle section is Δz. Then the axial coordinate z of the mth node is m =Δz×(m-1)+Δz / 2;

[0116] The horizontal section of the buried pipe is divided into K sections along the axial direction, where the lengths of the first and Kth sections are both Δx / 2, and the length of the middle section is Δx. Then the axial coordinate x of the kth node is k =Δx×(k-1)+Δx / 2;

[0117] Set the time step Δt and the total simulation time to t tol , then the number of time segments is N = t tol / Δt, and t n =nΔt.

[0118] The discretization and calculation process of the vertical section and horizontal section of the buried pipe are as follows:

[0119] At a certain time t n (1≤n≤N), the equation of the above heat transfer model is discretized as follows:

[0120]

[0121]

[0122] Among them, A 1、 B 1、 D1 and B2 are both intermediate variables:

[0123]

[0124] Among them, C(m,n) and F(k,n) are intermediate variables:

[0125]

[0126] By solving the above equations (12), (13), (14), (15) and (16) using an iterative method, we can obtain t n The temperature of each fluid element in the vertical and horizontal segments at the moment, that is, T i1 (z1,t n ), Ti1 (z2,t n )…T i1 (z M ,t n ), T a1 (z1,t n ), T a1 (z2,t n )…T a1 (z M ,t n ), T i2 (x1,t n ), T i2 (x2,t n )…T i2 (x K ,t n ), T a2 (x1,t n ), T a2 (x2,t n )…T a2 (x K ,t n ); therefore, the fluid temperature distribution at t1, t2, t3…t N The situation at the moment.

[0127] In the present invention, first, the method finely divides the model into vertical and horizontal sections, and independently models them respectively, and finally combines the two parts of the model. In the vertical section, the method constructs the transient heat transfer equation of the inner tube fluid and the outer tube fluid, and uses the composite medium column heat source model to deeply analyze the radial one-dimensional heat transfer mechanism in the backfill soil and rock. Subsequently, in the horizontal section, the method creates the steady-state heat transfer equation of the inner tube fluid and the outer tube fluid, and innovatively applies the moving line heat source model to accurately simulate the influence of groundwater seepage on the non-steady-state heat transfer of the horizontal section rock. At the same time, in order to ensure the accuracy and completeness of the model, the method also carefully sets the boundary conditions and initial conditions, and finally integrates these elements to construct a comprehensive and detailed casing-type buried pipe heat transfer model containing horizontal wells. Based on this heat transfer model, the method further finely divides the inner tube fluid and the outer tube fluid of the vertical section and the horizontal section into multiple nodes along the axial direction, discretizes the differential equation, and establishes a system of integral equations for the inner and outer tube fluids at different nodes and times. Finally, an efficient iterative method was used to calculate and accurately predict the fluid temperature field. This method not only improves the accuracy of the prediction, but also provides strong technical support for the optimization and application of ground-source heat pump technology.

[0128] Compared with the prior art, the present invention has the following beneficial effects:

[0129] (1) The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well of the present invention comprehensively considers the transient heat transfer process of the vertical section and the steady-state heat transfer process of the horizontal section, and also considers the influence of groundwater seepage in the horizontal section. Therefore, the predicted fluid temperature field of the buried pipe has a certain accuracy and meets the requirements of engineering practice.

[0130] (2) The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well of the present invention is simple to model, requires only simple one-dimensional grid division, has a small amount of calculation, and is suitable for engineering practice applications.

[0131] The following is the actual experiment:

[0132] In this embodiment, an experimental study on a medium-deep casing buried pipe system was conducted, focusing on the variation of the fluid temperature field in the vertical pipe with time and depth. The experiment aims to verify the accuracy and reliability of the present invention through measured data and provide a reference for the engineering application of the medium-deep buried pipe system.

[0133] The vertical pipe profile and cross-sectional diagram of the experimental device are shown in Figure 1 and Figure 2 As shown in the figure, it is mainly composed of a vertical buried pipe structure. During the experiment, the system simulated the actual operating conditions in the geothermal environment, injected fluid into the vertical pipe, and monitored the temperature change of the outlet fluid over time. The experimental device parameters are shown in Table 1, including the geometric dimensions of the vertical pipe, the thermophysical parameters of the pipeline material, the buried depth of the pipeline, etc., to ensure that the experimental conditions are as close to actual applications as possible. Figure 1 Among them, 1. inner tube fluid; 2. inner tube; 3. outer tube fluid; 4. outer tube; 5. backfill soil; 6. rock and soil.

[0134] Table 1 Parameters of the medium-deep casing buried pipe in Example 1

[0135]

[0136]

[0137] In order to further verify the accuracy of the present invention, the experimental results and the prediction results of the present invention were compared and analyzed in detail. By comparing the outlet fluid temperature change curves at different times, it was found that the temperature change trend measured by the experiment was basically consistent with the simulation results of the present invention, especially in terms of the dynamic change of the fluid temperature, the two showed a high degree of consistency.

[0138] Comparative analysis shows that the model of the present invention can accurately reflect the heat transfer process in the vertical pipe, proving that the boundary conditions and initial conditions of the model are reasonably set, and verifying the accuracy and reliability of the present invention. Under the condition of no groundwater seepage velocity, the maximum temperature difference between the experimental data and the simulation results of the present invention is 0.55°C, and the minimum temperature difference is 0.12°C, showing that under the condition of no seepage, the prediction error of the model is very small, proving its excellent performance and high accuracy. Figure 4 As shown, the excellent performance of the present invention under different working conditions is further demonstrated.

[0139] By comparing the experimental results with those of the present invention, it can be concluded that the present invention can effectively predict the temperature field change in the vertical buried pipe system under the condition of no seepage, and has high accuracy in practical applications.

[0140] The profile and cross-section of the medium-deep casing buried pipe with horizontal wells are shown in Figure 3 and Figure 2 As shown, the present invention is used to predict the fluid temperature field at different times, and the prediction results are compared with the simulation results of the three-dimensional numerical model. Among them, the relevant parameters of the medium-deep casing buried pipe containing horizontal wells are shown in Table 2.

[0141] The total duration of the simulation is 120 days. Set the time step to Δt = 60 seconds, then the number of time segments N = t tol / Δt=172800, and t n =nΔt.

[0142] The inner tube fluid 1 is divided into 1251 segments along the vertical section axis, that is, M = 1251, the vertical section length of the buried pipe L1 = 2500m, Δz = 2, then the axial coordinate z of the mth node is m =2×(m-1)+1; the inner tube fluid 1 is divided into 251 sections along the horizontal section axis, that is, K=251, and the horizontal section length L2=500m, then the axial coordinate x of the kth node k =2×(k-1)+1; Similarly, the outer tube fluid 3 is divided into 1251 sections along the vertical section axially and 251 sections along the horizontal section axially.

[0143] By using an iterative method, combined with t n The discrete equations of the temperature field of the inner and outer tube fluids at all times before time t and their boundary conditions and initial conditions are solved. n The inner and outer pipe fluid temperatures of each vertical and horizontal section at the time, including T i1 (z1,t n )~T i1 (z M ,t n ), T a1 (z1,tn )~T a1 (z M ,t n ), T i2 (x1,t n )~T i2 (x K ,t n ), T a2 (x1,t n )~T a2 (x K ,t n ). Therefore, t1~t N Temperature distribution of vertical and horizontal tubes at all times.

[0144] Table 2 Parameters of the medium-deep casing buried pipe containing horizontal wells in Example 2

[0145]

[0146]

[0147] Under the same groundwater seepage velocity conditions, the fluid outlet temperatures calculated by the present invention under the three conditions of t=1d, t=10d and t=120d are compared with the simulation results of the three-dimensional numerical model. Figure 5 (a) Figure 5 (b) and Figure 5 (c). For t=1d, under different inlet flow rate conditions, the outlet fluid temperature calculated by the present invention is less consistent with the simulation value, but the maximum error of the present invention is less than 1.3°C; for t=10d, under different inlet flow rate conditions, the outlet fluid temperature calculated by the present invention is better consistent with the simulation value, and the maximum error is less than 0.7°C; for t=120d, under different inlet flow rate conditions, the maximum error of the present invention is less than 0.6°C. It can be seen that the error of the outlet fluid temperature calculated by the present invention is larger in the early stage and smaller in the later stage. Therefore, the present invention has a certain accuracy in predicting the fluid temperature field of medium-deep casing buried pipes containing horizontal wells.

[0148] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well, characterized in that: The method comprises the following steps: A heat transfer model of a medium-deep casing buried pipe with a horizontal well is constructed. The model is divided into a vertical section and a horizontal section, and the models are independently constructed. For the vertical section, a transient heat transfer equation of the inner pipe fluid and the outer pipe fluid of the vertical section is established, and the vertical section boundary conditions and the vertical section initial conditions are set; for the horizontal section, a steady-state heat transfer equation of the inner pipe fluid and the outer pipe fluid of the horizontal section is established, and the horizontal section boundary conditions and the horizontal section initial conditions are set; Solve the heat transfer model and divide the vertical section into M sections along the axial direction. The lengths of the first and M sections are both Δz / 2, and the length of the middle section is Δz. Then the axial coordinate z of the mth node is m =Δz×(m-1)+Δz / 2; The horizontal segment is divided into K segments along the axial direction, where the lengths of the first and Kth segments are both Δx / 2, and the length of the middle segment is Δx. Then the axial coordinate x of the kth node is k =Δx×(k-1)+Δx / 2; Set the time step Δt and the total simulation time to t tol , then the number of time segments is N = t tol / Δt, and t n =nΔt; At a certain time t n , where 1≤n≤N, the equations of the heat transfer model are discretized, and the discretized equations are solved by the iterative method to obtain t n The temperature of each fluid element in the vertical and horizontal segments at the moment is calculated to obtain the temperature prediction result.

2. The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well according to claim 1, characterized in that: The transient heat transfer equations of the inner tube fluid and the outer tube fluid in the vertical section are: Among them, r ii ——Inner radius of the inner tube; (ρc) f ——Volume specific heat capacity of the inner tube fluid and the outer tube fluid; r io ——Outer radius of the inner tube; (ρc) ip ——Volume specific heat capacity of the inner tube; T i1 (z,t)——temperature of the fluid in the vertical section of the buried pipe; z——axial coordinate of the vertical section of the buried pipe; t——time; V(t)——volume flow rate of the fluid in the inner pipe and the fluid in the outer pipe; T a1 (z,t)——temperature of the fluid outside the vertical section of the underground pipe; L1——length of the vertical section of the underground pipe; r eo ——Outer radius of the outer tube; r ei ——Inner radius of the outer tube; (ρc) ep ——Volume specific heat capacity of the outer tube; R ia ——Thermal resistance between the inner tube fluid and the outer tube fluid; q1(z,t)——Thermal flow between the outer tube fluid and the backfill soil in the vertical section of the buried pipe.

3. The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well according to claim 2, characterized in that: The thermal resistance between the inner tube fluid and the outer tube fluid is: Among them, h i ——Convection heat transfer coefficient of the inner tube fluid; λ ip ——Thermal conductivity of the inner tube; h a ——Convective heat transfer coefficient of the fluid in the outer tube.

4. The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well according to claim 3, characterized in that: The heat flow between the outer pipe fluid and the backfill soil in the vertical section of the buried pipe is: Among them, R ae ——Thermal resistance between the outer tube fluid and the outer wall of the outer tube; T eo (z,t)——The temperature of the outer wall of the vertical section of the buried pipe.

5. The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well according to claim 4, characterized in that: The vertical segment boundary conditions and vertical segment initial conditions are: Among them, T in (t) —— inlet fluid temperature; T sur ——rock and soil surface temperature; a——geothermal gradient; T i2 (x, t) – the temperature of the fluid in the horizontal section of the buried pipe; L1 – the length of the vertical section of the buried pipe.

6. The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well according to claim 1, characterized in that: The steady-state heat transfer equations of the inner tube fluid and the outer tube fluid in the horizontal section are: Where, x is the axial coordinate of the horizontal section of the buried pipe; T a2 (x, t)——temperature of the fluid outside the horizontal section of the buried pipe; L2——length of the horizontal section of the buried pipe; q2(x, t)——heat flow between the fluid outside the horizontal section of the buried pipe and the backfill soil; R ia ——Thermal resistance between the inner tube fluid and the outer tube fluid; (ρc) f ——Volume specific heat capacity of the inner tube fluid and the outer tube fluid; T i2 (x, t) – the temperature of the fluid in the horizontal section of the buried pipe; V(t) – the volume flow rate of the fluid in the inner pipe and the fluid in the outer pipe.

7. The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well according to claim 6, characterized in that: The heat flow between the outer pipe fluid and the backfill soil in the horizontal section of the buried pipe is: Among them, R ab ——Thermal resistance between the outer pipe fluid and the outer wall of the buried pipe in the horizontal section; T b (x, t) is the temperature of the outer wall of the horizontal section of the buried pipe, which is calculated using the moving line heat source model based on the principle of heat flux superposition.

8. The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well according to claim 7, characterized in that: The temperature of the outer wall of the horizontal section of the buried pipe is: Where G2(t) is the G function of the moving line heat source model of the horizontal section of the buried pipe; T0(z) is the initial temperature of the rock and soil; L1 is the length of the vertical section of the buried pipe; t n ——The time corresponding to the nth moment; t j ——The time corresponding to the j-th moment.

9. The method for predicting the fluid temperature field of a medium-deep casing buried pipe containing a horizontal well according to claim 8, characterized in that: The horizontal segment boundary conditions and the horizontal segment initial conditions are: Among them, T a2 (x, t)——temperature of the fluid outside the horizontal section of the buried pipe; L2——length of the horizontal section of the buried pipe; T i2 (x, t)——the temperature of the fluid in the horizontal section of the buried pipe; T0(z)——the initial temperature of the rock and soil; T a1 (z,t)——The temperature of the fluid outside the vertical section of the buried pipe.

10. The method for predicting fluid temperature field of medium-deep casing buried pipe containing horizontal wells according to claim 1, characterized in that: The discretized equation is: Among them, A 1、 B 1、 D1 and B2 are both intermediate variables: Among them, C(m,n) and F(k,n) are intermediate variables: Among them, T i1 ——Temperature of the fluid in the vertical section of the buried pipe; m ——The axial coordinate of the mth node; t n =nΔt, Δt——time step, V(t)——volume flow rate of inner tube fluid and outer tube fluid; (ρc) f ——Volume specific heat capacity of the inner tube fluid and the outer tube fluid; Δz——The length of the middle section of the vertical section; R ia ——Thermal resistance between the fluid in the inner pipe and the fluid in the outer pipe of the vertical section of the buried pipe; T i2 (x,t)——the temperature of the fluid in the horizontal section of the buried pipe; T a1 (z,t)——temperature of the fluid outside the vertical section of the buried pipe; R ae ——Thermal resistance between the outer pipe fluid and the outer wall of the vertical section of the buried pipe; G1(t)——G function of the composite medium column heat source model of the vertical section of the buried pipe; G2(t)——G function of the moving line heat source model of the horizontal section of the buried pipe; T0(z)——The initial temperature of the rock and soil; T a2 (x,t)——the temperature of the fluid outside the horizontal section of the buried pipe; r ii ——Inner radius of inner tube; r io ——Outer radius of the inner tube; (ρc) ep ——Volume specific heat capacity of the outer tube; (ρc) ip ——Volume specific heat capacity of the inner tube; r eo ——Outer radius of the outer tube; r ei ——Inner radius of the outer tube, Δx——length of the middle section of the horizontal section.

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