A method and software simulation device for solving heat transfer problems in a deeply buried single tube with arbitrary tube type.

Abstract

This invention discloses a method and software simulation device for solving heat transfer in a deeply buried single pipe of arbitrary pipe type. The method includes: digitally defining the geometric path; discretizing and dividing the geometric path into micro-elements; constructing a layered soil database; constructing a multi-layer thermal resistance series network and obtaining the total thermal resistance; deriving the outlet temperature of the entire pipe along the pipe path based on the heat transfer and heat balance of the micro-elements; independently performing micro-element heat balance related calculations based on a preset time to obtain the outlet temperature at each moment, recording the temperature distribution of the micro-element segments, and plotting the temperature curve along the pipe; and calculating the total heat transfer between the pipe and the soil. This invention, through parameterized control point sequences and discretization technology, can accurately describe pipes of U-shaped, trapezoidal, √-shaped, and even arbitrarily custom shapes, breaking through the limitation of traditional methods that are only applicable to simple pipe types. It can accurately reflect the impact of operating time on the soil-side heat transfer capacity and is suitable for the analysis of long-term operating conditions.

Description

Technical Field

[0001] This invention relates to the field of thermal analysis technology for deeply buried pipelines, and in particular to a method and software simulation equipment for solving heat transfer problems under arbitrary pipe types in a deeply buried single pipe. Background Technology

[0002] In fields such as deep geothermal energy extraction, oil and gas transportation, and utilization of underground energy structures, the heat exchange process between buried pipelines and the surrounding soil and rock media is a core issue in system design and operation optimization. Accurately calculating the temperature changes, total heat exchange, and thermal resistance distribution along the pipeline circulation medium is of great significance for evaluating system energy efficiency, determining the optimal pipeline burial path, and predicting long-term operational performance.

[0003] In existing technologies, the following methods are commonly used to solve the heat transfer problem for deeply buried pipelines: 1. Simplified geometric model method: This method simplifies the pipeline route to a single straight segment or a simple U-bend, ignoring the complex spatial routes that pipelines may have in actual engineering (such as trapezoids with unequal heights, zigzags, custom curves, etc.). This simplification leads to inaccurate responses to changes in formation temperature and thermophysical properties at different depths along the pipeline, resulting in significant deviations between the calculated results and the actual situation.

[0004] 2. Linear or Cylindrical Heat Source Model: This type of method treats the pipeline as an infinitely long linear or cylindrical heat source and solves the problem based on analytical solutions from classical heat transfer. Its core assumption is that the formation is a homogeneous, infinitely large medium, and the heat source intensity is constant or varies as a simple function over time. However, this type of model struggles to handle the non-uniformity of thermal properties along the pipeline (such as formation thermal conductivity, specific heat capacity, and density), and cannot accurately reflect the dynamic changes in heat transfer conditions when the pipeline changes depth or direction.

[0005] 3. Overall heat transfer coefficient method based on logarithmic mean temperature difference: In simplified engineering calculations, an overall method is often used, which multiplies the logarithmic mean temperature difference between the inlet and outlet by the overall heat transfer coefficient. This method treats the entire pipeline as a single heat exchanger, losing detailed information about the temperature distribution along the pipe and failing to analyze the impact of local thermal resistance variations on system performance.

[0006] 4. Numerical simulation methods (such as the finite element method): Although they can handle complex geometric and non-uniform physical property problems, their models are complex to build, consume a lot of computational resources, and take a long time to solve. They are not suitable for engineering scenarios that require rapid evaluation, parameter optimization, or real-time monitoring.

[0007] Therefore, existing technologies lack a solution method for heat transfer in deeply buried pipelines that can balance geometric universality (adapting to arbitrary spatial pipe types), computational efficiency (fast solution), and physical process precision (reflecting dynamic changes in thermal resistance and temperature along the pipeline). Summary of the Invention

[0008] This invention provides a method and software simulation device for solving heat transfer problems in a deeply buried single tube with arbitrary tube type, in order to solve the technical problems in the prior art.

[0009] To solve the above-mentioned technical problems, this invention provides a method for solving heat transfer problems under arbitrary tube types in a deeply buried single tube, including: S10, digitally defines the geometric path; S20, Discretize and divide the geometric path into infinitesimal elements; S30, construct a layered soil database; S40, construct a multi-layer thermal resistance series network and obtain the total thermal resistance; S50, along the pipeline path, based on the heat transfer and heat balance of the micro-segments, the outlet temperature of the entire pipeline is derived sequentially. S60, independently performs micro-element thermal balance related calculations based on a preset time to obtain the temperature distribution of the micro-element segment at each moment of the outlet temperature record, and plots the temperature curve along the path; S70, calculate the total heat exchange between the pipe and the soil.

[0010] Optionally, step S10 includes: S101, based on the ordered control point sequence P=[(x0,y0), (x1,y1),…,(x n ,y n [ ], determine the geometric shape of the pipeline in space, where x represents the horizontal coordinate in meters and y represents the vertical burial depth in meters; S102, Set a parameterized shape template, which includes a U-shaped path, a right-angled trapezoidal path, a √-shaped path, and a custom path.

[0011] Optionally, step S20 includes: S201, based on any two adjacent control points (x i , y i ) and (x i+1 , y i+1 ), calculate the length L of the line segment. i The calculation formula is as follows: ; S202, divide each line segment into N equal parts. i The length of the infinitesimal segment is obtained based on the following formula. : In the formula: Indicates the length of the infinitesimal segment; S203, the midpoint depth of each micro-segment is obtained based on the following formula: In the formula: denoted by , where is the midpoint depth of the infinitesimal segment, and j represents the segment number.

[0012] Optionally, step S40 includes: S401 defines the geometric radius and material parameters; S402, the thermal resistance R of the pipe wall is obtained based on the following formula. p : in, r out , r in These are the outer and inner radii of the pipe, respectively, in meters (m). l p The value represents the thermal conductivity of the pipe, expressed in W / (mK). S403, the thermal resistance R of the insulation layer is obtained based on the following formula. ins : in, l ins The thermal conductivity of the insulation material; r cem Where the cementing radius is; r out The outer radius of the buried pipe; r in The inner radius of the buried pipe; S404, the transient thermal resistance R of the soil is obtained based on the following formula. s (t): In the formula: F 0 The Fourier number represents the timescale of thermal diffusion. l s The thermal conductivity of the soil; t Runtime; E 1(z) is an exponential integral function; S405, the total thermal resistance is obtained based on the following formula: In the formula: This indicates the total thermal resistance.

[0013] Optionally, step S50 includes: S501, preset length is dThe infinitesimal segment of l has a working fluid mass flow rate of l. m (kg / s), specific heat capacity is c w (J / (kg·K)); S502, assuming the working fluid temperature within the micro-element segment is approximately... T w The original temperature of the surrounding soil was T s (y), to obtain the heat transfer power from the working fluid to the soil; S503, acquires temperature change; S504, obtain the inlet temperature of the micro-element segment. T in, seg to outlet temperature T out, seg The relationship.

[0014] Optionally, the heat transfer power from the working fluid to the soil is obtained based on the following formula: in, δQ For heat exchange between the pipe and the soil; T s ( y ) as depth y Soil temperature under changing conditions T w The temperature of the fluid inside the pipe; R total Total thermal resistance; δl is the length of the infinitesimal segment.

[0015] Optionally, the temperature change is obtained based on the following formula: in, δQ For heat exchange between the pipe and the soil; T s ( y ) as depth y Soil temperature under changing conditions; T w The temperature of the fluid inside the pipe; R total Total thermal resistance; δl Δ is the length of the infinitesimal segment; T w This refers to the change in fluid temperature. m For mass flow rate; c w This is the specific heat capacity of water.

[0016] Optionally, the inlet temperature T of the micro-element segment in, seg To the outlet temperature T out, segThe relationship is: in, T out,seg The outlet temperature of the micro-element segment; T in,seg The inlet temperature of the micro-element segment; T s ( y ) as depth y Soil temperature under changing conditions; m For mass flow rate; c w This is the specific heat capacity of water; R total This is the total thermal resistance.

[0017] Optionally, the total heat exchange between the pipe and the soil, Q total Obtained based on the following formula: in, Q total Σ represents the total heat exchange between the pipe and the soil; Σ represents the summation over all infinitesimal elements. δQ For heat exchange between the pipe and the soil; T s ( y ) as depth y Soil temperature under changing conditions; T w The temperature of the fluid inside the pipe; R total This is the total thermal resistance.

[0018] To address the aforementioned technical problems, this invention also provides a software simulation device for solving heat transfer problems in a deeply buried single pipe of arbitrary pipe type, characterized by comprising: The human-computer interaction interface module is used to provide tabbed navigation using a graphical interface, including a geometric design page, a parameter and soil page, and a thermodynamic results page; The geometry path generation module is used to dynamically calculate the sequence of control points based on the shape type selected by the user in the interface and the geometric parameters input, and draw the pipe direction on the canvas in real time. The mesh discretization module is used to divide the polyline segments generated by the geometric path into micro segments according to a specified step size or equal fraction, extract the center depth and length of each micro segment, and create an index.

[0019] The soil database management module provides a file upload interface; The transient thermal resistance calculation module is used to calculate the thermal diffusivity α for each micro-segment and each time point, based on the soil thermal properties at the corresponding depth of that micro-segment and the current running time t. s Fourier numberF 0 And by calling the high-precision approximation algorithm of the exponential integral function E1, we obtain... R s ( t ); The heat exchange solution module is used to execute the core calculation process; The results visualization module is used to dynamically draw four types of charts based on the Chart.js library.

[0020] One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages: This application uses parametric control point sequences and discretization techniques to accurately describe pipes of U-shape, trapezoid, √-shape, and even arbitrary custom shapes, breaking through the limitation of traditional methods that are only applicable to simple pipe types.

[0021] This application adopts an unsteady thermal resistance expression based on an exponential integral function, which avoids the simplification assumptions in the "line heat source" model and can accurately reflect the impact of operating time on the soil-side heat exchange capacity, making it particularly suitable for the analysis of long-term operating conditions.

[0022] The entire calculation process in this application is based entirely on a series network of infinitesimal thermal equilibrium and thermal resistance, without using traditional simplified concepts such as "logarithmic mean temperature difference" or "line heat source model". The physical meaning is clear and the mathematical derivation is rigorous.

[0023] This application provides a complete workflow from geometric modeling, layered soil import, calculation to result visualization, enabling engineers to complete thermal simulation of complex deep-buried pipelines without programming, thus greatly improving design efficiency. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating the method for solving heat transfer problems under arbitrary pipe types in a deeply buried single pipe, as provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the arbitrary tubular geometric path provided in the embodiments of the present invention; Figure 3 This is a comparison curve between the calculation results of the present invention and the field experiment or numerical results provided in the embodiments of the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] In the relevant descriptions of this embodiment, the terms "including," "containing," and "possessing" are all open terms and are generally understood to include but not be limited to; the term "at least one" is generally understood to mean one or more, where "multiple" refers to two or more; the term "at least one of the following" or similar expressions refer to any combination of these items, including any combination of single or multiple items, for example, "at least one of a, b, or c", or "at least one of a, b, and c", which can all mean: a, b, c, ab (i.e., a and b), ac, bc, or abc, where a, b, and c can be single or multiple; the symbol "A / B" is used to describe the selection relationship of associated objects, generally indicating an "or" relationship.

[0027] In the following description of the embodiments, the terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms "a" and "the" as used in the embodiments of this application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise.

[0028] Those skilled in the art should understand that, in the following description of the embodiments of this application, the sequence of numbers does not imply the order of execution. Some or all steps may be executed in parallel or sequentially. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0029] Those skilled in the art will understand that the numerical ranges in the embodiments of this application should be understood to specifically disclose each intermediate value between the upper and lower limits of the range. Any stated value or intermediate value within a stated range, as well as any other stated value or each smaller range between intermediate values ​​within a range, are also included within this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0030] Unless otherwise stated, the technical / scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. While this application describes only preferred methods and materials, any methods and materials similar or equivalent to those described herein may be used in the implementation or testing of this application. All references to this specification are incorporated by way of citation to disclose and describe the methods and / or materials associated with those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

[0031] This invention provides a method for solving heat transfer problems in a deeply buried single-pipe system with arbitrary pipe types. (Refer to...) Figure 1 The method may include the following steps: S10, digitally defines the geometric path.

[0032] In an exemplary embodiment, step S10 may include: S101, based on the ordered control point sequence P=[(x0,y0), (x1,y1),…,(x n ,y n The geometric shape of the pipeline in space is determined, where x represents the horizontal coordinate in meters and y represents the vertical burial depth in meters. The coordinate axes are centered on the ground and downward is positive. S102, Set a parameterized shape template, which includes a U-shaped path, a right-angled trapezoidal path, a √-shaped path, and a custom path.

[0033] Specifically, the system has pre-set a variety of typical shape templates. Users only need to input a few key geometric parameters to automatically generate a sequence of control points. Typical shapes include: U-shaped path: Given a span S1 and a maximum depth H, generate points (0, 0), (0, H), (S1, H), and (S1, 0).

[0034] Isosceles trapezoidal path: Given span S1 and left depth h L and the right depth h R Generate points (0, 0) and (0, h). L (S1, h) R ), (S1, 0).

[0035] Right trapezoid path: Generate a list of points based on the side of the right angle of the trapezoid.

[0036] √-shaped path: Given a horizontal span S1 and two alternating depths H1 and H2, generate a multi-point polyline.

[0037] Custom path: Users directly input coordinate strings, such as "0,0; 0,1700; 650,2781; 650,0", and the system generates control points after parsing.

[0038] Figure 2 This is a schematic diagram of an arbitrary tubular geometric path provided in an embodiment of the present invention. Figure 2 The figure shows typical shapes such as U-shape, trapezoid, √ shape, and arbitrary path. The horizontal axis represents the horizontal distance (m), the vertical axis represents the burial depth (m), the dots on the curves represent control points, and the numbers on the line segments represent the lengths of each segment.

[0039] S20, the geometric path is discretized and divided into infinitesimal elements.

[0040] In an exemplary embodiment, step S20 may include: S201, based on any two adjacent control points (x i , yi ) and (x i+1 , y i+1 ), calculate the length L of the line segment. i The calculation formula is as follows: ; S202, divide each line segment into N equal parts. i The length of the infinitesimal segment (or divided according to a fixed step size Δl) is obtained based on the following formula. : In the formula: Indicates the length of the infinitesimal segment; S203, the midpoint depth of each micro-segment is obtained based on the following formula: In the formula: denoted by , where is the midpoint depth of the infinitesimal segment, and j represents the segment number.

[0041] In this embodiment, the midpoint depth of the micro-element will be used for subsequent queries of soil temperature and physical property parameters.

[0042] S30, Construct a layered soil database.

[0043] Specifically, soil thermal properties change significantly with depth. This embodiment adopts a layered model, which obtains soil layer data (starting depth, ending depth, thermal conductivity, density, specific heat) by loading an Excel or CSV file. During calculation, the model finds the layer at the current depth and extracts the corresponding physical property parameters for thermal resistance calculation.

[0044] Furthermore, each soil layer contains the following field: starting depth d start Termination depth d end Thermal conductivity λ s (W / (m K)), density ρ s (kg / m³), specific heat capacity c s (J / (kg K)). The above fields can be imported by the user via Excel or CSV files, or the system's built-in sample data can be loaded. For any depth y, the system automatically retrieves the corresponding soil layer and obtains the corresponding λ. s (y), ρ s (y) and c s (y).

[0045] S40, construct a multi-layer thermal resistance series network.

[0046] Specifically, the construction steps of the multi-layer thermal resistance series network are as follows: define the geometric radius and material parameters of mo → calculate the thermal resistance of each layer of the cylindrical wall separately → connect the layers in series according to the actual flow channel sequence (pipe wall → cement ring → insulation layer → soil) to calculate the total thermal resistance. This network is used to calculate the heat transfer intensity per unit length of pipe and to solve the water temperature distribution inside the pipe by coupling the energy balance equation.

[0047] Furthermore, in an exemplary embodiment, step S40 may include: S401 defines the geometric radius and material parameters; S402, the thermal resistance R of the pipe wall is obtained based on the following formula. p : in, r out , r in These are the outer and inner radii of the pipe, respectively, in meters (m). l p The value represents the thermal conductivity of the pipe, expressed in W / (mK). S403, the thermal resistance R of the insulation layer is obtained based on the following formula. ins : in, l ins The thermal conductivity of the insulation material; r cem Where the cementing radius is; r out The outer radius of the buried pipe; r in The inner radius of the buried pipe; S404, the transient thermal resistance of the soil is obtained based on the following formula. R s ( t ): In the formula: F 0 The Fourier number represents the timescale of thermal diffusion. l s The thermal conductivity of the soil; t Runtime; E 1(z) is an exponential integral function; S405, the total thermal resistance is obtained based on the following formula: In the formula: This indicates the total thermal resistance.

[0048] S50, along the pipeline path, based on the heat transfer and heat balance of the micro-segments, the outlet temperature of the entire pipeline is derived sequentially.

[0049] In an exemplary embodiment, step S50 may include: S501, a micro-element segment with a preset length of δl, a working fluid mass flow rate of m (kg / s), and a specific heat capacity of... c w (J / (kg·K)); S502, assuming the working fluid temperature within the micro-element segment is approximately T. w The original temperature of the surrounding soil was T s (y) (varying with depth) is used to obtain the heat transfer power from the working medium to the soil; S503, acquires temperature change; S504, obtain the inlet temperature T of the micro-element segment. in, seg To the outlet temperature T out, seg The relationship.

[0050] Specifically, consider a small element of length δl, with a working fluid mass flow rate of m (kg / s) and a specific heat capacity of... c w (J / (kg·K)), then the heat transfer power from the working medium to the soil is: in, δQ For heat exchange between the pipe and the soil; T s ( y ) as depth y Soil temperature under changing conditions; T w The temperature of the fluid inside the pipe; R total Total thermal resistance; δl is the length of the infinitesimal segment.

[0051] This heat causes a change in the temperature of the working fluid, resulting in heat equilibrium: in, δQ For heat exchange between the pipe and the soil; m For mass flow rate; c w Δ is the specific heat capacity of water; T w This represents the change in fluid temperature.

[0052] If T w >T s If the working fluid releases heat, the temperature decreases; if T w <Ts The working fluid absorbs heat, and its temperature rises. From this, the temperature change can be calculated as follows: in, δQ For heat exchange between the pipe and the soil; T s ( y ) as depth y Soil temperature under changing conditions; T w The temperature of the fluid inside the pipe; R total Total thermal resistance; δl Δ is the length of the infinitesimal segment; T w This refers to the change in fluid temperature. m For mass flow rate; c w This is the specific heat capacity of water.

[0053] Therefore, from the inlet temperature T of the micro-element segment in, seg To the outlet temperature T out、seg The relationship is: in, T out,seg The outlet temperature of the micro-element segment; T in,seg The inlet temperature of the micro-element segment; T s ( y ) as depth y Soil temperature under changing conditions; m For mass flow rate; c w This is the specific heat capacity of water; R total This is the total thermal resistance.

[0054] An explicit first-order approximation is used here, and the accuracy is sufficient when δl is small enough.

[0055] Starting from the inlet along the pipeline path, the outlet temperature of each infinitesimal segment is calculated sequentially, and this temperature is used as the inlet temperature of the next infinitesimal segment. Finally, the outlet temperature T of the entire pipeline is obtained. out .

[0056] S60 independently performs micro-element thermal balance related calculations based on a preset time to obtain the temperature distribution of the micro-element segment at each moment of the outlet temperature record, and plots the temperature curve along the process.

[0057] Specifically, due to the soil thermal resistance R s(t) varies with time, therefore the outlet temperature differs at different operating times. In this embodiment, the full path integration in step S50 is performed independently once for each calculation time (e.g., every hour) to obtain the outlet temperature T at that time. out (t). At the same time, the temperature distribution of each micro-element segment is recorded to plot the temperature curve along the path.

[0058] S70, calculate the total heat exchange between the pipe and the soil.

[0059] Specifically, the total heat exchange between the pipe and the soil, Q total Obtained based on the following formula: in, Q total Σ represents the total heat exchange between the pipe and the soil; Σ represents the summation over all infinitesimal elements. δQ For heat exchange between the pipe and the soil; T s ( y ) as depth y Soil temperature under changing conditions; T w The temperature of the fluid inside the pipe; R total This is the total thermal resistance.

[0060] Total thermal resistance R total The thermal resistance can be expressed as average or integral. In this embodiment, the total thermal resistance value at each moment is provided in the result output for subsequent calculation and analysis of the total heat exchange. The value obtained by dividing the temperature difference by the thermal resistance is the subsequent heat exchange.

[0061] The following is a more specific example: heat exchange calculation of a geothermal well with a deeply buried U-shaped tube.

[0062] Step 1. Setting the Geometry Path The user selects "Standard U-Shape" in the human-computer interaction interface and inputs the parameters: span S1 = 650 m, maximum depth H = 2781 m. The geometric path generation module automatically calculates the control point sequence P: P=[(0,0), (0,2781), (650,2781), (650,0)] Total pipe length: L total =2781+650+2781=6212m; The interface draws a U-shaped curve in real time and marks the length at the midpoint of each line segment.

[0063] Step 2. Pipeline Structure and Property Input In the "Pipe Dimensions" tab, enter: Outer Diameter D out=177.8 mm, then r out =0.0889 m; wall thickness δ p = 9.19 mm, then r in = 0.07971m; Cement ring outer diameter D cem =241.3mm, then r cem =0.12065m; Thermal conductivity λ of the pipe p =14.48 W / (m·K), density ρ p =7912.58 kg / m 3 Specific heat capacity c p =485.62 J / (kg K); Thermal conductivity λ of cement ring c =1.34 W / (m K), density ρ c =2100 kg / m 3 Specific heat capacity c c = 1000J / (kg K); The insulation layer is only installed in the last 700m of the outlet section, and the material's thermal conductivity is 1000J / (kg K); l ins = 0.03119 W / (m K), density r ins =2299.29kg / m 3 Specific heat capacity c ins =133 J / (kg K).

[0064] Step 3. Operating conditions and soil stratification On the "Parameters & Soil" page, set the inlet water temperature T. in = 12 ℃; mass flow rate m = 6.53 kg / s; total calculation time t max = 2904 hours, or 121 days; Soil original temperature function: T s ( y = 20.524 +0.02703 y, where y is a variable representing the soil's original temperature function and the soil depth in meters; this step loads the preset stratified data through the "LoadSample" page (Load Sample Data).

[0065] Step 4. Calculation After clicking "Start Simulation", the heat transfer solution module will start: Initialization: Read all input parameters and discretize the pipeline into approximately 622 micro-segments with a step size Δl=10 m. Record the depth and length of each micro-segment.

[0066] Time loop: Perform the following operations for t = 1, 2, …, 2904 hours respectively: Initialize the working fluid temperature to T. w =T in .

[0067] For each micro-element, the soil layer is queried based on its depth to obtain λ. s , ρ s , c s Calculate the thermal diffusivity α s and Fourier number F 0 .

[0068] Call and calculate the exponential integral function E 1 .

[0069] Calculate the pipe wall thermal resistance R p = 0.000258 K·m / W; thermal resistance Rc of cement ring = 0.0452 K·m / W; thermal resistance R of insulation layer ins = 1.943 K·m / W; Total thermal resistance R total = R p + R c + R ins + R s (t).

[0070] Update the working fluid temperature according to the infinitesimal heat balance formula; accumulate the infinitesimal heat exchange and record the outlet temperature and temperature distribution along the process.

[0071] Step 5. Output Results After the calculation is complete, the results visualization module automatically switches to the "Thermal Results" page, displaying the results as shown below: Temperature distribution along the route: The horizontal axis is depth (m) and the vertical axis is water temperature (°C). It shows the curve of water temperature change with depth from inlet to outlet. It can be seen that the water temperature gradually increases in the downstream section and the temperature drop is slowed down in the upstream section due to the effect of the insulation layer.

[0072] The curve of outlet temperature change over time: the horizontal axis is time (hours) and the vertical axis is outlet water temperature (°C). The outlet temperature rises rapidly in the early stage and tends to stabilize in the later stage, reflecting the effect of increased soil thermal resistance.

[0073] The curve of total heat exchange over time shows that the heat exchange is relatively large in the initial stage, and gradually decreases over time and approaches a certain stable value.

[0074] The curve showing the change of total thermal resistance over time shows a monotonically increasing trend in total thermal resistance as the operating time increases, with soil thermal resistance contributing the most significantly.

[0075] Users can click the "Export Excel" button below any chart to save the corresponding data as an .xlsx file for later analysis or reporting.

[0076] Using the method provided in the above embodiments of the present invention, the outlet water temperature obtained at hour 2904 was approximately 31.78°C, and the heat exchange at that time was approximately 542 kW. Compared with the field experiment or numerical results, the heat exchange error after stable operation is within 5%. Verification results are as follows... Figure 3 As shown, Figure 3 The left side shows a comparison curve between the calculation results of this invention and the results of field experiments. Figure 3 The right side shows a comparison curve between the calculated results and the numerical results of this invention, proving that this invention has higher accuracy in long-period simulations. Furthermore, because it supports arbitrary pipe shapes, this method can still be directly applied when pipelines need to bypass underground obstacles and use non-U-shaped paths in actual engineering projects, without modifying the underlying algorithm.

[0077] In one or more embodiments of this application, the present application can accurately describe U-shaped, trapezoidal, √-shaped, or even arbitrarily custom-defined pipes by using parameterized control point sequences and discretization technology, breaking through the limitation of traditional methods that are only applicable to simple pipe types.

[0078] This application adopts an unsteady thermal resistance expression based on an exponential integral function, which avoids the simplification assumptions in the "line heat source" model and can accurately reflect the impact of operating time on the soil-side heat exchange capacity, making it particularly suitable for the analysis of long-term operating conditions.

[0079] The entire calculation process in this application is based entirely on a series network of infinitesimal thermal equilibrium and thermal resistance, without using traditional simplified concepts such as "logarithmic mean temperature difference" or "line heat source model". The physical meaning is clear and the mathematical derivation is rigorous.

[0080] This application provides a complete workflow from geometric modeling, layered soil import, calculation to result visualization, enabling engineers to complete thermal simulation of complex deep-buried pipelines without programming, thus greatly improving design efficiency.

[0081] Furthermore, this invention also provides a software simulation device for solving heat transfer problems under arbitrary pipe types in a deeply buried single pipe, characterized in that it includes: The human-computer interaction interface module is used to provide tabbed navigation using a graphical interface, including a geometric design page, a parameter and soil page, and a thermodynamic results page; The geometry path generation module is used to dynamically calculate the sequence of control points based on the shape type selected by the user in the interface and the geometric parameters input, and draw the pipe direction on the canvas in real time. The mesh discretization module is used to divide the polyline segments generated by the geometric path into micro segments according to a specified step size or equal fraction, extract the center depth and length of each micro segment, and create an index.

[0082] The soil database management module provides a file upload interface; The transient thermal resistance calculation module is used to calculate the thermal resistance for each micro-segment and each time point, based on the soil thermal properties at the corresponding depth of that micro-segment and the current running time. t Calculate the thermal diffusivity α s Fourier number F 0 and call the exponential integral function. E 1 A high-precision approximation algorithm was obtained. R s ( t ); The heat exchange solution module is used to execute the core calculation process; The results visualization module is used to dynamically draw four types of charts based on the Chart.js library.

[0083] The following is a further description of each module: Human-computer interaction interface module: Users can interact with the system through controls such as sliders, numeric input boxes, and file selectors.

[0084] Geometric path generation module: Supports multiple modes such as U-shape, isosceles trapezoid, right trapezoid (left / right), √ shape, and custom coordinates. The total length is automatically calculated and displayed.

[0085] Mesh Discretization Module: Divides the polyline segments generated by the geometric path into micro segments according to a specified step size (default 10 m) or equal fractions, extracts the center depth and length of each micro segment, and creates an index.

[0086] Soil Database Management Module: Provides a file upload interface, supporting the parsing of soil stratification data in .xlsx, .xls, and .csv formats. Files must include five columns: starting depth, ending depth, thermal conductivity, density, and specific heat capacity. The system includes built-in sample data, and the loaded stratification information can be previewed on the interface.

[0087] Transient thermal resistance calculation module: For each micro-segment and each time node, based on the soil thermal properties at the corresponding depth of that micro-segment ( l s , r s , c s Calculate the thermal diffusivity α using the current running time t. s Fourier number F0 and call the exponential integral function. E 1 A high-precision approximation algorithm was obtained. R s ( t This module ensures that all thermal resistances vary with time and space.

[0088] Heat transfer solution module: Executes the core calculation process. For each time step, it traverses all infinitesimal segments starting from the entry point and calls the transient thermal resistance calculation module to obtain the results. R total The working fluid temperature is updated according to the infinitesimal heat balance equation, and the heat exchange is accumulated to finally obtain the outlet temperature and friction temperature arrays. After the calculation is completed, the results are stored in a data structure for use by the visualization module.

[0089] Results visualization module: Dynamically draws four types of charts based on the Chart.js library: The system displays the following data: temperature distribution along the pipeline with depth (scatter plot); outlet temperature variation over time (line plot); total heat transfer variation over time (filled area plot); and total thermal resistance variation over time (line plot). It also provides an "Export to Excel" function to save the above data as a local file.

[0090] In the description of this application, it should be noted that the terms "first", "second", and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0091] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the software simulation device and unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0092] In the several embodiments provided in this application, it should be understood that the disclosed software simulation devices and methods can be implemented in other ways. The software simulation device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another, or some features may be ignored or not executed. Additionally, the shown or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces. Indirect couplings or communication connections between software simulation devices or units may be electrical, mechanical, or other forms.

[0093] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0094] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0095] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0096] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The protection scope of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the technical scope disclosed in this application. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be covered within the protection scope of this application. Therefore, the protection scope of this application should be determined by the protection scope of the claims.

[0097] Furthermore, although the operations of the method of this application are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

Claims

1. A method for solving heat transfer problems in a deeply buried single tube of arbitrary tube type, characterized in that, include: S10, digitally defines the geometric path; S20, Discretize and divide the geometric path into infinitesimal elements; S30, construct a layered soil database; S40, construct a multi-layer thermal resistance series network and obtain the total thermal resistance; S50, along the pipeline path, based on the heat transfer and heat balance of the micro-segments, the outlet temperature of the entire pipeline is derived sequentially. S60, independently performs micro-element thermal balance related calculations based on a preset time to obtain the temperature distribution of the micro-element segment at each moment of the outlet temperature record, and plots the temperature curve along the process. S70, calculate the total heat exchange between the pipe and the soil.

2. The method according to claim 1, characterized in that, Step S10 includes: S101, based on the ordered control point sequence P=[(x0,y0), (x1,y1),…,(x n ,y n [ ], determine the geometric shape of the pipeline in space, where x represents the horizontal coordinate in meters and y represents the vertical burial depth in meters; S102, Set a parameterized shape template, which includes a U-shaped path, a right-angled trapezoidal path, a √-shaped path, and a custom path.

3. The method according to claim 1, characterized in that, Step S20 includes: S201, based on any two adjacent control points (x i , y i ) and (x i+1 , y i+1 ), calculate the length L of the line segment. i The calculation formula is as follows: ； S202, divide each line segment into N equal parts. i The length of the infinitesimal segment is obtained based on the following formula. : In the formula: Indicates the length of the infinitesimal segment; S203, the midpoint depth of each micro-segment is obtained based on the following formula: In the formula: denoted by , where is the midpoint depth of the infinitesimal segment, and j represents the segment number.

4. The method according to claim 1, characterized in that, Step S40 includes: S401 defines the geometric radius and material parameters; S402, the thermal resistance R of the pipe wall is obtained based on the following formula. p : in, r out , r in These are the outer and inner radii of the pipe, respectively, in meters (m). λ p The value represents the thermal conductivity of the pipe, expressed in W / (m K). S403, the thermal resistance R of the insulation layer is obtained based on the following formula. ins : in, λ ins The thermal conductivity of the insulation material; r cem Where is the cementing radius; r out The outer radius of the buried pipe; r in The inner radius of the buried pipe; S404, the transient thermal resistance R of the soil is obtained based on the following formula. s (t): In the formula: F 0 The Fourier number represents the timescale of thermal diffusion. λ s The thermal conductivity of the soil; t Runtime; E 1(z) is an exponential integral function; S405, the total thermal resistance is obtained based on the following formula: In the formula: This indicates the total thermal resistance.

5. The method according to claim 1, characterized in that, Step S50 includes: S501, preset length is δ The infinitesimal segment of l has a working fluid mass flow rate of l. m (kg / s), specific heat capacity is c w (J / (kg·K)); S502, assuming the working fluid temperature within the micro-element segment is approximately... T w The original temperature of the surrounding soil was T s (y), to obtain the heat transfer power from the working fluid to the soil; S503, acquires temperature change; S504, obtain the inlet temperature of the micro-element segment. T in, seg to outlet temperature T out, seg The relationship.

6. The method according to claim 5, characterized in that, The heat transfer power from the working medium to the soil is obtained based on the following formula: in, δQ For heat exchange between the pipe and the soil; T s ( y ) as depth y Soil temperature under changing conditions T w The temperature of the fluid inside the pipe; R total Total thermal resistance; δl is the length of the infinitesimal segment.

7. The method according to claim 5, characterized in that, The temperature change is obtained based on the following formula: in, δQ For heat exchange between the pipe and the soil; T s ( y ) as depth y Soil temperature under changing conditions; T w The temperature of the fluid inside the pipe; R total Total thermal resistance; δl Δ is the length of the infinitesimal segment; T w This refers to the change in fluid temperature. m For mass flow rate; c w This is the specific heat capacity of water.

8. The method according to claim 5, characterized in that, The inlet temperature T of the micro-element segment in, seg To the outlet temperature T out, seg The relationship is: in, T out,seg The outlet temperature of the micro-element segment; T in,seg The inlet temperature of the micro-element segment; T s ( y ) as depth y Soil temperature under changing conditions; m For mass flow rate; c w This is the specific heat capacity of water; R total This is the total thermal resistance.

9. The method according to claim 1, characterized in that, The total heat exchange between the pipeline and the soil is Q total Obtained based on the following formula: in, Q total Σ represents the total heat exchange between the pipe and the soil; Σ represents the summation over all infinitesimal elements. δQ For heat exchange between the pipe and the soil; T s ( y ) as depth y Soil temperature under changing conditions; T w The temperature of the fluid inside the pipe; R total This is the total thermal resistance.

10. A software simulation device for solving heat transfer problems under arbitrary pipe types in a deeply buried single pipe, characterized in that, include: The human-computer interaction interface module is used to provide tabbed navigation using a graphical interface, including a geometric design page, a parameter and soil page, and a thermodynamic results page; The geometry path generation module is used to dynamically calculate the sequence of control points based on the shape type selected by the user in the interface and the geometric parameters input, and draw the pipe direction on the canvas in real time. The mesh discretization module is used to divide the polyline segments generated by the geometric path into micro segments according to a specified step size or equal fraction, extract the center depth and length of each micro segment, and create an index; The soil database management module provides a file upload interface; The transient thermal resistance calculation module is used to calculate the thermal resistance for each micro-segment and each time point, based on the soil thermal properties at the corresponding depth of that micro-segment and the current running time. t Calculate the thermal diffusivity α s Fourier number F 0 and call the exponential integral function. E 1 A high-precision approximation algorithm was obtained. R s ( t ); The heat exchange solution module is used to execute the core calculation process; The results visualization module is used to dynamically draw four types of charts based on the Chart.js library.

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