A method and platform for solving heat exchange of deep-buried casing with arbitrary structure and angle

Abstract

The application provides a deep-buried casing heat exchange solving method and platform of any structure and angle, linearly characterizes any wellbore trajectory of a deep-buried casing heat exchanger in sections, establishes a bidirectional linear interpolation mapping relationship between a measured depth of the wellbore and a true vertical depth, and further constructs a wellbore trajectory model; determines a formation thermal resistance based on an exponential integral function, and further determines a total thermal resistance from an outer pipe to the formation; determines a thermal resistance and a convective heat exchange coefficient of an inner pipe to a ring cavity; uniformly disperses the total measured depth of the wellbore along the wellbore trajectory into N micro-segments, initializes the ring cavity temperature by adopting an outer pipe adiabatic assumption, reversely solves the inner pipe temperature, and introduces an equivalent ambient temperature to perform coupling correction iteration of the outer pipe-inner pipe, and determines a target inner pipe temperature; based on the target inner pipe temperature, determines an outlet fluid temperature of the wellbore, a total heat exchange amount, a unit length heat exchange amount and an average thermal resistance; by the above technical scheme, unified analytical modeling and solving of various wellbore configurations can be realized.

Description

Technical Field

[0001] This application relates to the field of geothermal energy development and utilization technology, and in particular to a method and platform for solving heat exchange problems in deeply buried casings with arbitrary structures and angles. Background Technology

[0002] Geothermal energy, with its large reserves, high stability, and high energy density, is a key renewable energy source. Compared to shallow ground source heat pump systems, which are typically buried at depths of less than 200 meters, medium-deep geothermal systems (2000-3000 meters) have a higher geothermal gradient and more stable heat output, effectively avoiding the cold and heat accumulation problems common in shallow geothermal systems. Coaxial deep-buried heat exchangers (C-DGHE), as the core infrastructure for the utilization of medium-deep geothermal energy, are particularly suitable for distributed heating needs in densely populated urban areas due to their advantages such as not extracting groundwater, minimal disturbance to the geological environment, and small footprint per well.

[0003] Currently, thermal modeling of coaxial deep-buried casing heat exchangers is mainly divided into three categories: numerical models, semi-analytical models, and fully analytical models. While numerical modeling methods (such as the finite element method and the finite volume method) can accurately capture the two-dimensional or three-dimensional distribution of wellbore-formation coupled heat transfer, their transient calculations typically take hours or even days, making it difficult to meet the needs of multi-condition optimization and rapid design iteration. Although semi-analytical and fully analytical models are significantly faster than numerical methods, most existing analytical models are based on simplified assumptions about vertical wellbore trajectories, resulting in severely insufficient adaptability to complex geometric configurations such as directional wells, horizontal wells, or wells of arbitrary shapes. Furthermore, these analytical models require extremely high levels of professional programming skills and mathematical background from users, and the lack of fast, user-friendly engineering calculation platforms based on mature analytical methods seriously hinders their widespread application in practical engineering.

[0004] It is evident that the current common finite element numerical solution framework of "one-dimensional wellbore + three-dimensional formation" coupling has the following problems: (1) It cannot perform unified analytical modeling and efficient solution for deep-buried casing heat exchangers with arbitrary wellbore trajectories (vertical, inclined, L-shaped and arbitrary free trajectories); (2) The existing analytical model has not established a two-way mapping relationship between the measured depth of the wellbore trajectory and the actual vertical depth; (3) It lacks an engineering calculation platform that can encapsulate complex analytical models into real-time interactive, real-time visualized, and data-secure and controllable platforms; (4) The numerical method takes too long to calculate, and the analytical method lacks versatility. Neither of them can meet the needs of rapid optimization design in engineering. Summary of the Invention

[0005] This application provides a solution method and platform for deep-buried casing heat exchangers with arbitrary structures and angles, which solves the problem in the prior art that it is impossible to perform unified analytical modeling and efficient solution for deep-buried casing heat exchangers with arbitrary well trajectories. It realizes analytical modeling and solution for various well configurations and breaks through the limitation that traditional models are only applicable to vertical wells.

[0006] To achieve the above objectives, the technical solution of this application embodiment is as follows: In a first aspect, embodiments of this application provide a method for solving the heat transfer problem of deeply buried sleeves with arbitrary structures and angles, the method comprising: The arbitrary well trajectory of the deep-buried casing heat exchanger is segmented linearly represented, and a two-way linear interpolation mapping relationship between the measured depth and the actual vertical depth of the well is established, thereby constructing a well trajectory model; The formation thermal resistance is determined based on the exponential integral function. The formation thermal resistance is then connected in series with the cement sheath thermal resistance, the outer pipe wall thermal conductivity thermal resistance, and the outer pipe inner wall convection thermal resistance to determine the total thermal resistance from the outer pipe to the formation. The thermal resistance from the inner tube to the annular cavity was determined, and the convective heat transfer coefficient was dynamically determined using the Dittus-Boelter correlation. The total measured depth of the wellbore is uniformly discretized along the wellbore trajectory. N For each micro-element segment, the annular cavity temperature is initialized using the outer tube adiabatic assumption, the inner tube temperature is solved in reverse, and the equivalent ambient temperature is introduced to perform coupling correction iteration of the outer tube and inner tube to determine the target inner tube temperature. Based on the target inner tube temperature, the wellbore outlet fluid temperature, total heat transfer, heat transfer per unit length, and average thermal resistance are determined.

[0007] In one possible implementation, the segmented linear characterization of the arbitrary wellbore trajectory of the deep-buried casing heat exchanger includes: The arbitrary well trajectory is defined by multiple control points, and adjacent control points are connected by straight line segments to achieve a piecewise linear representation of the well trajectory.

[0008] In one possible implementation, the well trajectory can be vertical, L-shaped, inclined, or an arbitrary coordinate trajectory; the inclination angle of the inclined trajectory is the angle between the well and the vertical direction; the L-shaped well consists of a vertical segment and a horizontal segment; the arbitrary coordinate trajectory defines an arbitrary free path by directly inputting the coordinates of the control points.

[0009] In one possible implementation, the formation thermal resistance is expressed as: ;in, For formation thermal resistance, It is an exponential integral function of the first kind. Where is the borehole radius, The thermal diffusivity of the formation is . To accumulate running time, The thermal conductivity of the formation; The total thermal resistance is expressed as: ;in, For total thermal resistance, For formation thermal resistance, For the thermal resistance of the cement ring, The thermal resistance of the outer tube wall is the thermal resistance. The convection thermal resistance of the inner wall of the outer tube.

[0010] In one possible implementation, the thermal resistance from the inner tube to the annular cavity is determined based on the segmented configuration of the insulation layer; With the insulation layer completely covering the surface, the thermal resistance from the inner tube to the annular cavity is expressed as: ;in, This is the thermal resistance from the inner tube to the annular cavity. and These are the inner radius and outer radius of the inner tube, respectively. and These are the convective heat transfer coefficients at the inner and outer walls of the inner tube, respectively. The thermal conductivity of the insulation material; With the insulation layer partially covering the surface, the thermal resistance of the composite wall is determined segment by segment based on the insulation layer thickness and the inner radius of the inner tube. The thermal resistance of the composite wall is expressed as follows: Among them, represents the thermal resistance of the composite wall surface. The thermal conductivity of the inner tube substrate is given. This refers to the thickness of the insulation layer.

[0011] In one possible implementation, the process of introducing an equivalent ambient temperature to perform an iterative correction of the outer tube-inner tube coupling, and determining the target inner tube temperature, includes: The convergence criterion for the maximum change in the temperature field is iterated at fixed points until global convergence is achieved. The inner tube temperature output after global convergence is taken as the target inner tube temperature.

[0012] In one possible implementation, the outlet fluid temperature is expressed as: ;in, The outlet fluid temperature. This refers to the temperature of the inner tube. The total heat exchange is expressed as: ;in, For total heat exchange, For fluid mass, Specific heat capacity of the fluid The outlet fluid temperature is... Inlet fluid temperature; The heat exchange per unit length is expressed as: ;in, For heat exchange per unit length, For total heat exchange, This represents the total measured depth. The average thermal resistance is the average thermal resistance from the outer tube to the formation and the average thermal resistance from the inner tube to the annular cavity.

[0013] Secondly, embodiments of this application provide a solution platform for deep-buried casing heat exchange with arbitrary structure and angle. The platform includes: a geometric modeling module, a thermal property input module, a formation layer import module, a solution engine module, and a visualization and data export module. The solution engine module is connected to the geometric modeling module, the thermal property input module, the formation layer import module, and the visualization and data export module, respectively. The geometric modeling module is used to provide real-time interactive drawing of global topology map and local structural schematic diagram, and automatically annotate the geometric parameters of each segment in the well trajectory; The thermal property input module includes a pipe size and material property submodule, a fluid parameter submodule, and an operating parameter submodule, which are used to obtain thermal property parameters and solve the convective heat transfer coefficient through a solver. The formation layer import module is used to transmit formation layer data files and obtain formation thermal property parameters of each micro-element segment of the wellbore based on linear interpolation of the actual vertical depth. The solution engine module is used to execute the deep buried casing heat transfer solution method with arbitrary structure and angle described in the first aspect based on the obtained geometric parameters, the convective heat transfer coefficient and the formation thermal property parameters. The visualization and data export module is used to generate and output interactive charts based on the output results of the solution engine module.

[0014] In one possible implementation, the partial structural diagram in the geometric modeling module indicates the direction of working fluid flow; fluid is injected downwards into the annular cavity and extracted upwards from the inner tube, forming a countercurrent heat exchange configuration.

[0015] In one possible implementation, the platform is based on browser-side JavaScript technology, integrating the Chart.js and SheetJS libraries. All calculations are completed in the user's local browser, without the need to install software or deploy a backend server, and it is compatible across operating systems and browsers.

[0016] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: (1) Strong versatility: An analytical solution method is proposed to handle various well configurations such as vertical, inclined, L-shaped and arbitrary free trajectory. A precise two-way mapping between the measured depth and the actual vertical depth is established through piecewise linear representation, breaking the limitation that the traditional model is only applicable to vertical wells. (2) High computational efficiency: The thermal resistance and temperature field are solved by a fully analytical method. The solution speed is more than three orders of magnitude faster than the traditional finite element method. The 200 segments of the 72-hour working condition can be discretized in just a few seconds in a normal browser environment. (3) High engineering precision: After on-site testing in a certain location, the absolute relative error was less than 5% and the average error was less than 3% after 12 hours; (4) Good convergence of coupling iteration: By introducing the concept of equivalent ambient temperature, the two-pipe thermal coupling problem is transformed into an equivalent single-pipe heat dissipation problem. The convergence criterion is clear, the number of iterations is small, and it has global convergence. (5) High degree of platformization: It can be packaged into a browser-side visual interactive platform, requiring no programming experience, no software installation, no backend server, and supports all mainstream operating systems and browsers, ensuring data security; (6) Strong adaptability to layered foundations: Supports importing actual geological survey data and automatically matches local thermal property parameters based on vertical depth interpolation, truly reflecting the characteristics of strata layering; (7) High economic guidance value: It can quickly and quantitatively assess the impact of key parameters such as tilt angle, vertical depth, and horizontal section length on heat exchange performance, providing a scientific basis for engineering optimization design. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating a method for solving heat exchange problems in deeply buried sleeves with arbitrary structures and angles, provided in an embodiment of this application; Figure 2 A schematic diagram of a coaxial buried tube heat exchanger provided in this application embodiment; Figure 3 A schematic diagram illustrating a piecewise linear characterization method for different wellbore trajectories provided in this application embodiment; Figure 4 A radial thermal resistance network diagram provided for an embodiment of this application; Figure 5A block diagram of a deep-buried sleeve heat exchange solution platform with arbitrary structure and angle provided in the embodiments of this application; Figure 6 A schematic diagram of a time-varying outlet temperature provided in an embodiment of this application; Figure 7 A schematic diagram of a time-varying heat exchange curve provided in an embodiment of this application; Figure 8 This is a schematic diagram illustrating the influence of tilt angle on heat transfer performance, provided as an embodiment of this application. Figure 9 This is a schematic diagram showing a comprehensive comparison of the heat exchange performance of different well types, provided as an embodiment of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0020] In the description of the embodiments of this application, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the embodiments of this application and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. The terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Furthermore, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; a mechanical connection or an electrical connection; a direct connection or an indirect connection through an intermediate medium; or a connection within two components. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of this application according to the specific circumstances.

[0021] Figure 1 This is a flowchart illustrating a method for solving heat transfer problems in deeply buried sleeves with arbitrary structures and angles, as provided in an embodiment of this application. Figure 1 As shown, the method may include the following steps.

[0022] S101. Perform piecewise linear characterization on arbitrary wellbore trajectories of deeply buried casing heat exchangers, establish a bidirectional linear interpolation mapping relationship between the measured depth of the wellbore and the actual vertical depth, and then construct a wellbore trajectory model.

[0023] For example, the structure of this deeply buried jacket heat exchanger can be as follows: Figure 2 As shown, (a) is the global wellbore structure, and (b) is the radially layered structure of the cross section.

[0024] S102. Determine the formation thermal resistance based on the exponential integral function, and then connect the formation thermal resistance in series with the cement ring thermal resistance, the outer pipe wall thermal conductivity thermal resistance, and the outer pipe inner wall convection thermal resistance to determine the total thermal resistance from the outer pipe to the formation.

[0025] S103. Determine the thermal resistance from the inner tube to the annular cavity, and use the Dittus-Boelter correlation to dynamically determine the convective heat transfer coefficient.

[0026] S104. Distribute the total measured depth of the wellbore uniformly along the wellbore trajectory. N For each infinitesimal segment, the annular cavity temperature is initialized using the outer tube adiabatic assumption, the inner tube temperature is solved in reverse, and an equivalent ambient temperature is introduced for coupling correction iteration of the outer tube and inner tube to determine the target inner tube temperature.

[0027] S105. Based on the target inner tube temperature, determine the wellbore outlet fluid temperature, total heat transfer, heat transfer per unit length, and average thermal resistance.

[0028] Based on the above technical solutions, an analytical solution method for handling various well configurations is proposed. By establishing a precise two-way mapping between the measured depth and the actual vertical depth through piecewise linear characterization, the traditional model is limited to vertical wells. Furthermore, a fully analytical method is used to solve for thermal resistance and temperature field, and the solution speed is more than three orders of magnitude faster than the traditional finite element method.

[0029] In one possible implementation, S101 may include: defining the arbitrary well trajectory with multiple control points, and connecting adjacent control points with straight line segments to achieve a piecewise linear representation of the well trajectory.

[0030] For example, the piecewise linear representation and depth mapping of the wellbore trajectory described above may include the following steps.

[0031] Define arbitrary wellbore trajectory as N s There are control points, where the coordinates of the control points are... , Indicates horizontal displacement (unit: m). Indicates vertical depth (unit: m, downward is positive). Adjacent control points are connected by straight line segments. i Segment (by control point) P i To the control point P i+1 The geometric parameters of ) are calculated using the following formulas: , , ;in, For the first i The measurement depth increment of the segment (unit: m).

[0032] Measuring depth S Defined as the arc length parameter along the wellbore trajectory: The total measured depth is the sum of all segments, i.e. For any given measurement depth S First, determine the segment index in which it is located. i (satisfy Then, linear interpolation is used to obtain the true vertical depth at that point. : Horizontal displacement The same linear interpolation method is used to determine the trajectory. Based on the above piecewise linear representation framework, four wellbore trajectory modes are implemented through encoding: vertical, L-shaped, inclined, and arbitrary coordinate trajectory.

[0033] In one possible implementation, the well trajectory can be vertical, L-shaped, inclined, or an arbitrary coordinate trajectory; the inclination angle of the inclined trajectory is the angle between the well and the vertical direction; the L-shaped trajectory consists of a vertical segment and a horizontal segment; the arbitrary coordinate trajectory defines an arbitrary free path by directly inputting the coordinates of control points. For example, the well trajectory type can refer to... Figure 3 As shown, the tilt angle is 30°.

[0034] In one possible implementation, the formation thermal resistance is expressed as: ;in, For formation thermal resistance, It is an exponential integral function of the first kind. Where is the borehole radius, The thermal diffusivity of the formation is . To accumulate running time, The thermal conductivity of the formation is given by: The total thermal resistance is expressed as: ;in, For total thermal resistance, For formation thermal resistance, For the thermal resistance of the cement ring, The thermal resistance of the outer tube wall is the thermal resistance. The convection thermal resistance of the inner wall of the outer tube.

[0035] In some embodiments, the radial heat transfer path of the coaxial buried tube heat exchanger involves multiple stages in series, from the outside to the inside: ground heat conduction, cement ring heat conduction, outer tube wall heat conduction, outer tube inner wall convection heat transfer, annular fluid and outer tube inner wall convection heat transfer, inner tube wall (including insulation layer) heat conduction, and inner tube inner wall convection heat transfer. Among these, the thermal resistance of ground heat conduction is the only transient term that changes with time, while the other terms are steady-state thermal resistances.

[0036] For example, the above For a first-type exponential integral function, a piecewise approximation strategy is used in the numerical implementation. When the Fourier number... (Right now When using Euler constant, The series expansion approximation: ;in, Euler constant ( 0.5772156649), this series is in It converges rapidly. When (Right now When using the continuous fraction acceleration method (Modified Lentz algorithm), the convergence speed is fast and the numerical stability is good.

[0037] For example, in the case of layered foundation conditions, the thermal resistance of the stratum is determined independently based on the local thermal properties at that depth. The total thermal resistance from the outer pipe to the stratum consists of four components connected in series: the thermal resistance of the stratum, the thermal resistance of the cement sheath, the thermal resistance of the outer pipe wall (conductive), and the thermal resistance of the inner wall of the outer pipe (convective).

[0038] In one possible implementation, the thermal resistance from the inner tube to the annular cavity is determined based on the segmented configuration of the insulation layer; when the insulation layer is fully covered, the thermal resistance from the inner tube to the annular cavity is expressed as: ;in, This is the thermal resistance from the inner tube to the annular cavity. and These are the inner radius and outer radius of the inner tube, respectively. and These are the convective heat transfer coefficients at the inner and outer walls of the inner tube, respectively. Let be the thermal conductivity of the insulation material; when the insulation layer partially covers the surface, the thermal resistance of the composite wall is determined segment by segment based on the insulation layer thickness and the inner radius of the inner tube. This thermal resistance of the composite wall is expressed as: Among them, represents the thermal resistance of the composite wall surface. The thermal conductivity of the inner tube substrate is given. This refers to the thickness of the insulation layer.

[0039] For example, the thermal resistance from the inner tube to the annular cavity is also composed of series components, with particular consideration given to the segmented configuration of the insulation layer. Let the total wall thickness of the inner tube be... The insulation layer thickness is When the insulation layer is completely covered ( Thermal resistance is calculated using the following formula: When the insulation layer only partially covers the area, The thermal resistance of the composite wall is calculated segment by segment, using the boundary radius as the dividing line: The convective heat transfer coefficient was dynamically calculated using the Dittus-Boelter forced convection correlation: when hour, ;when hour, The hydraulic diameter of the annular cavity, Dh, is equal to the inner diameter of the outer pipe. Inner tube outer diameter, .

[0040] For example, the total thermal resistance from the outer tube to the bottom layer and the thermal resistance from the inner tube to the annular cavity are both composed of different series components, and their structural schematic diagram can be shown as follows: Figure 4 As shown.

[0041] In one possible implementation, S104 includes: performing fixed-point iteration on the convergence criterion for the maximum change in the temperature field until global convergence; and taking the inner tube temperature output after global convergence as the target inner tube temperature.

[0042] For example, the above process may include the following steps: Measuring the total depth. Uniformly discretized along the wellbore trajectory N Axial micro-segments (preferred) N = 200), distance from walking distance Δ S = H MD / N .by This indicates the temperature distribution of the fluid within the annular cavity (flowing downwards). This indicates the temperature distribution of the fluid inside the inner tube (flowing upwards). This indicates the original temperature distribution of the strata.

[0043] The initialization phase adopts the assumption of external tube insulation, only considering heat dissipation from the annular fluid to the formation: ;in, Mass flow rate (kg / s). Let be the specific heat capacity of the fluid (J / (kg·K)). Discretization yields an explicit forward recurrence relation: .

[0044] After obtaining the adiabatic assumption solution for the outer tube, perform the reverse calculation for the inner tube (note...). dS (Direction opposite to the flow direction inside the tube) Discretization from the bottom of the well ( j = NReverse recursion, For the first j Average temperature of fluid in the annular cavity: .

[0045] After obtaining the preliminary solution, a fixed-point iterative method is used for coupled solution. The modified energy equation for the outer tube simultaneously includes heat dissipation to the formation and heat transfer between the outer tube and the inner tube: Introducing equivalent ambient temperature This combines two parallel heat transfer paths into a single equivalent heat dissipation environment: .

[0046] Based on the equivalent ambient temperature, the coupled-corrected outer tube temperature distribution is obtained through an explicit recursive formula. ): The convergence criterion is... Because fixed-point iteration has good convergence characteristics, in actual calculations, the accuracy requirements can usually be met within 20 iterations.

[0047] In one possible implementation, the outlet fluid temperature is expressed as: ;in, The outlet fluid temperature. The temperature of the inner tube is given; the total heat exchange is expressed as: ;in, For total heat exchange, For fluid mass, Specific heat capacity of the fluid The outlet fluid temperature is... Inlet fluid temperature; the heat transfer per unit length is expressed as: ;in, For heat exchange per unit length, For total heat exchange, The total measurement depth; the average thermal resistance is the average thermal resistance from the outer tube to the formation and the average thermal resistance from the inner tube to the annulus. For example, the outlet fluid temperature is the temperature of the inner tube at the surface wellhead (…). S = 0) fluid outlet temperature (unit: °C).

[0048] Figure 5 This is a block diagram of a deep-buried sleeve heat exchange solution platform with arbitrary structure and angle provided in an embodiment of this application. Figure 5 As shown, the platform 500 may include: a geometric modeling module 510, a thermal property input module 520, a formation layer import module 530, a solver engine module 540, and a visualization and data export module 550; the solver engine module 540 is connected to the geometric modeling module 510, the thermal property input module 520, the formation layer import module 530, and the visualization and data export module 550, respectively.

[0049] The geometric modeling module 510 provides real-time interactive drawing of global topology maps and local structural schematic diagrams, automatically annotating the geometric parameters of each segment in the well trajectory; the thermal property input module 520 includes pipe size and material property submodules, fluid parameter submodules, and operating parameter submodules, used to acquire thermal property parameters and solve for convective heat transfer coefficients through a solver; the formation layer import module 530 is used to transfer formation layer data files and obtain formation thermal property parameters of each micro-segment of the wellbore based on linear interpolation of the actual vertical depth; the solver engine module 540 is used to execute the aforementioned method for solving heat transfer in deeply buried casings with arbitrary structures and angles based on the acquired geometric parameters, convective heat transfer coefficients, and formation thermal property parameters; the visualization and data export module 550 is used to generate and output interactive charts based on the output results of the solver engine module.

[0050] In one possible implementation, the partial structural diagram in the geometric modeling module 510 indicates the direction of working fluid flow; fluid is injected downward in the annular cavity and extracted upward in the inner tube, forming a countercurrent heat exchange configuration.

[0051] In one possible implementation, the platform 500 is based on browser-side JavaScript technology, integrating the Chart.js and SheetJS libraries. All calculations are completed in the user's local browser, without the need to install software or deploy a backend server, and it is compatible across operating systems and browsers.

[0052] The workflow of the technical solution of this application will be described below with reference to the embodiments.

[0053] Example 1 (Vertical Deep-buried Shell Heat Exchanger).

[0054] A case study of a coaxial deep-buried heat exchanger project in a certain location was used for verification. The experimental well in this project was vertical, with a total depth of 2539 meters. The geometric structural parameters and thermophysical operating parameters of the coaxial deep-buried heat exchanger (C-DGHE) are shown in Table 1 and Table 2 below, respectively.

[0055] Table 1: Table 2: Reference Figure 6 and Figure 7In the experiment, the inlet water temperature was kept constant at 12 ℃, the mass flow rate was 4.88 kg / s, and the system operated continuously for 72 hours. Data on the changes in formation thermal conductivity, density, and specific heat capacity with depth were compiled into a layered Excel file and imported into the platform. The platform automatically performed 200-segment axial discretization, and at each time step, it executed the following steps: formation thermal resistance update → thermal resistance network assembly → outer pipe adiabatic initialization → inner pipe counter-current back calculation → coupled iterative solution. The simulation results were compared point-by-point with the field measured data: after 12 hours of operation, the absolute relative errors of the outlet water temperature and heat exchange were both steadily reduced to below 5%, and the average error was less than 3% over the entire 72-hour period, fully verifying the engineering reliability and practical accuracy of the method and platform provided in this application.

[0056] Example 2 (Inclined Deep Buried Shell Heat Exchanger).

[0057] Total measured depth = 2500 meters as constraint, take the inclination angle respectively = 0°、 = 15° = 30° and =45° four working conditions. Corresponding actual vertical depth The elevations are 2500 m, 2414.8 m, 2165.1 m, and 1767.8 m, respectively. The operating duration for each is 2904 hours (approximately 121 days), with a time step of 24 hours.

[0058] Reference Figure 8 It can be seen that as the tilt angle increases from 0° to 45°, the average heat transfer over 2904 hours gradually decreases from 376.13 kW to 215.14 kW, a total reduction of 42.8%. This corresponds to an average decrease of approximately 9.5% in heat transfer for every 10° increase in tilt angle. Although the decrease in heat transfer is significant, the tilted section still participates in effective heat transfer, and the fixed total measurement length compensates to some extent for the losses caused by the reduction in vertical depth. In practical engineering, it is recommended to control the tilt angle within the range of 15°-30°, at which point both the vertical depth loss and the reduction in heat transfer rate are within acceptable levels.

[0059] Example 3 (L-type deep buried tube heat exchanger).

[0060] Two complementary sub-conditions are set here: Sub-condition (A) Fixed total measurement depth = 2500 meters, vertical depth Take 500, 1000, 1500, and 2000 meters respectively, corresponding to the lengths of the horizontal sections. After 2904 hours of operation, when the vertical depth increased from 500m to 2000m, the average heat exchange increased significantly from 31.65 kW to 262.38 kW (+729%), with the growth showing a marginal decreasing trend.

[0061] Sub-condition (B) Fixed vertical depth = 2500 meters, length of horizontal section The measurements were taken at depths of 500, 1000, 1500, and 2000 meters, corresponding to a total measurement depth of 3000-4500 meters. When the horizontal section increased from 500m to 2000m, the total heat exchange increased from 504.61 kW to 960.15 kW (+90.3%), but the heat exchange per unit length tended to saturate. In practical engineering, it is recommended that the vertical section depth be no less than 1500m, and the horizontal section length be controlled within 1500m.

[0062] Example 4 (Arbitrary Trajectory Type Deep Buried Shell Heat Exchanger).

[0063] Reference Figure 9 Design a typical complex trajectory: 1000m vertical section → 500m inclined section (θ=10°) → 1000m horizontal section, with a total measurement depth. =2500m. Compared with a purely vertical well of the same depth, the average heat transfer of the vertical well after 2904 hours was 376.13kW, while that of any trajectory well decreased accordingly due to the reduction in effective vertical depth. This comparison confirms that, under the condition of the same total measurement length, the contribution of vertical depth to heat transfer performance is far greater than the surface area compensation added by the horizontal or inclined sections, and vertical depth is the primary factor determining heat extraction potential.

[0064] Based on the above four embodiments, the following conclusions can be drawn: First, pure vertical wells should be preferred to maximize the heat exchange capacity per unit drilling length; second, inclined wells should be limited to the range of 15°-30°; third, the vertical section depth of L-shaped wells should be no less than 1500m, and the horizontal section length should be ≤1500m; fourth, when the total drilling length is constrained, investment should be focused on increasing the vertical depth rather than extending the horizontal or inclined sections.

[0065] The various embodiments in this specification are described in a progressive manner. For the same or similar parts between the various embodiments, please refer to each other. Each embodiment focuses on describing the differences from other embodiments.

[0066] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.

Claims

1. A method for solving heat transfer problems in deeply buried sleeves with arbitrary structures and angles, characterized in that, The method includes: The arbitrary well trajectory of the deep-buried casing heat exchanger is segmented linearly represented, and a two-way linear interpolation mapping relationship between the measured depth and the actual vertical depth of the well is established, thereby constructing a well trajectory model; The formation thermal resistance is determined based on the exponential integral function. The formation thermal resistance is then connected in series with the cement sheath thermal resistance, the outer pipe wall thermal conductivity thermal resistance, and the outer pipe inner wall convection thermal resistance to determine the total thermal resistance from the outer pipe to the formation. The thermal resistance from the inner tube to the annular cavity was determined, and the convective heat transfer coefficient was dynamically determined using the Dittus-Boelter correlation. The total measured depth of the wellbore is uniformly discretized along the wellbore trajectory. N For each micro-element segment, the annular cavity temperature is initialized using the outer tube adiabatic assumption, the inner tube temperature is solved in reverse, and the equivalent ambient temperature is introduced to perform coupling correction iteration of the outer tube and inner tube to determine the target inner tube temperature. Based on the target inner tube temperature, the wellbore outlet fluid temperature, total heat transfer, heat transfer per unit length, and average thermal resistance are determined.

2. The method according to claim 1, characterized in that, The segmented linear characterization of arbitrary wellbore trajectories for deeply buried casing heat exchangers includes: The arbitrary well trajectory is defined by multiple control points, and adjacent control points are connected by straight line segments to achieve a piecewise linear representation of the well trajectory.

3. The method according to claim 2, characterized in that, The well trajectory can be vertical, L-shaped, inclined, or any coordinate trajectory; the inclination angle of the inclined trajectory is the angle between the well and the vertical direction; the L-shaped well consists of a vertical segment and a horizontal segment; the arbitrary coordinate trajectory defines an arbitrary free path by directly inputting the coordinates of the control points.

4. The method according to claim 1, characterized in that, The formation thermal resistance is expressed as: ;in, For formation thermal resistance, It is an exponential integral function of the first kind. Where is the borehole radius, The thermal diffusivity of the formation is . To accumulate running time, The thermal conductivity of the formation; The total thermal resistance is expressed as: ;in, For total thermal resistance, For formation thermal resistance, For the thermal resistance of the cement ring, The thermal resistance of the outer tube wall is the thermal resistance. The convection thermal resistance of the inner wall of the outer tube.

5. The method according to claim 1, characterized in that, The thermal resistance from the inner tube to the annular cavity is determined based on the segmented configuration of the insulation layer; With the insulation layer completely covering the surface, the thermal resistance from the inner tube to the annular cavity is expressed as: ;in, This is the thermal resistance from the inner tube to the annular cavity. and These are the inner radius and outer radius of the inner tube, respectively. and These are the convective heat transfer coefficients at the inner and outer walls of the inner tube, respectively. The thermal conductivity of the insulation material; With the insulation layer partially covering the surface, the thermal resistance of the composite wall is determined segment by segment based on the insulation layer thickness and the inner radius of the inner tube. The thermal resistance of the composite wall is expressed as follows: Among them, represents the thermal resistance of the composite wall surface. The thermal conductivity of the inner tube substrate is given. This refers to the thickness of the insulation layer.

6. The method according to claim 1, characterized in that, The process involves introducing an equivalent ambient temperature to perform coupling correction iterations between the outer and inner tubes, determining the target inner tube temperature, including: The convergence criterion for the maximum change in the temperature field is iterated at fixed points until global convergence is achieved. The inner tube temperature output after global convergence is taken as the target inner tube temperature.

7. The method according to claim 1, characterized in that, The outlet fluid temperature is expressed as: ;in, The outlet fluid temperature. This refers to the temperature of the inner tube. The total heat exchange is expressed as: ;in, For total heat exchange, For fluid mass, Specific heat capacity of the fluid The outlet fluid temperature is... Inlet fluid temperature; The heat exchange per unit length is expressed as: ;in, For heat exchange per unit length, For total heat exchange, This represents the total measured depth. The average thermal resistance is the average thermal resistance from the outer tube to the formation and the average thermal resistance from the inner tube to the annular cavity.

8. A solution platform for deep-buried casing heat exchangers with arbitrary structure and angle, characterized in that, The platform includes: a geometric modeling module, a thermal property input module, a formation layer import module, a solution engine module, and a visualization and data export module; the solution engine module is connected to the geometric modeling module, the thermal property input module, the formation layer import module, and the visualization and data export module, respectively. The geometric modeling module is used to provide real-time interactive drawing of global topology map and local structural schematic diagram, and automatically annotate the geometric parameters of each segment in the well trajectory; The thermal property input module includes a pipe size and material property submodule, a fluid parameter submodule, and an operating parameter submodule, which are used to obtain thermal property parameters and solve the convective heat transfer coefficient through a solver. The formation layer import module is used to transmit formation layer data files and obtain formation thermal property parameters of each micro-element segment of the wellbore based on linear interpolation of the actual vertical depth. The solution engine module is used to execute a deep buried casing heat transfer solution method with arbitrary structure and angle according to any one of claims 1 to 7, based on the obtained geometric parameters, convective heat transfer coefficient and formation thermal property parameters. The visualization and data export module is used to generate and output interactive charts based on the output results of the solution engine module.

9. The platform according to claim 8, characterized in that, The partial structural diagram in the geometric modeling module indicates the direction of working fluid flow; fluid is injected downwards into the annular cavity and extracted upwards from the inner tube, forming a countercurrent heat exchange configuration.

10. The platform according to claim 8, characterized in that, The platform is implemented based on browser-side JavaScript technology, integrating Chart.js and SheetJS libraries. All calculations are completed in the user's local browser, without the need to install software or deploy a backend server, and it is compatible with both operating systems and browsers.

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