Method for constructing two-phase flow heat transfer model of multi-stage gravity heat pipe and model construction system

Abstract

The present application relates to geothermal energy development technical field, specifically to a kind of multistage gravity heat pipe two-phase flow heat transfer model construction method and model construction system, method includes obtaining heat pipe evaporation section, adiabatic section, condensing section standardization basic parameter, establish flow pattern along the way conversion criterion and determine each position flow pattern, according to matching obtain heat transfer coefficient and flow coefficient, construct each section heat transfer submodel and flow submodel, obtain total heat transfer coefficient and resistance loss, all submodels are coupled in order according to space series and get first coupling model, establish formation heat conduction model and with first coupling model coupling and get second coupling model, simultaneous solution is obtained state prediction value, obtain the measured value of middle-deep layer geothermal simulation state, according to the error correction first and second coupling model, obtain two-phase flow heat transfer model.The present application breaks the pipe section fragmentation and formation fixed boundary limitation, realizes multistage coupling and flow pattern self-adapting prediction, greatly improves the prediction accuracy of deep well complex working condition.

Description

Technical Field

[0001] This invention relates to the field of geothermal energy development technology, and in particular to a method and system for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe. Background Technology

[0002] Medium-deep geothermal energy (typically referring to geothermal resources at depths of 2000-5000 meters) possesses significant advantages such as vast reserves, continuous and stable operation, and immunity to climate change, making it a crucial tool for constructing a clean, low-carbon, safe, and efficient energy system. Multi-stage ultra-long gravity heat pipes (hereinafter referred to as "multi-stage gravity heat pipes") have become one of the core technologies for enhanced downhole heat transfer in medium-deep geothermal energy due to their core characteristics, including no need for external power transmission, efficient heat transfer through working fluid phase change, and adaptability to complex high-temperature and high-pressure conditions in deep wells. These heat pipes are typically divided along the well depth into an evaporation section (downhole high-temperature section), an adiabatic section (intermediate wellbore section), and a condensation section (surface low-temperature section), and can be designed with multi-stage series or parallel configurations according to engineering needs. The overall heat transfer performance and operational stability of the heat pipe are essentially determined by the gas-liquid two-phase flow characteristics of the working fluid inside the pipe and the evaporation and condensation phase change heat transfer processes. Therefore, constructing a two-phase flow heat transfer model that can accurately describe this multi-physics coupling process is a key theoretical tool to guide the optimized design of heat pipe structures, selection of working fluids, pipe segment gradation, and system operation control. It has important practical engineering significance for promoting the efficient development and utilization of medium-deep geothermal resources.

[0003] Currently, the research and application of existing multi-stage gravity heat pipe two-phase flow heat transfer models still face many bottlenecks, making it difficult to meet the engineering needs of complex working conditions in medium-deep geothermal wells. For example: (1) Existing models are mostly constructed based on the steady-state heat transfer assumption of a single pipe section (such as a single evaporation section or a single condensation section), failing to fully consider the inter-segment coupling effect between the evaporation section, adiabatic section and condensation section under multi-stage configuration, ignoring the dynamic influence of the working fluid flow state and heat transfer characteristics of the upstream pipe section on the downstream pipe section, resulting in the model being unable to accurately depict the gas-liquid two-phase flow and heat transfer law of the entire heat pipe process; (2) The model oversimplifies the treatment of gas-liquid two-phase flow patterns, failing to combine the high temperature and high pressure environment of medium-deep geothermal wells, define the conversion interval of typical flow patterns such as bubble flow, plug flow, bullet flow and annular flow along the pipe, and also failing to establish targeted flow pattern conversion criteria, instead mechanically applying the heat transfer and resistance calculation method of a single flow pattern to the entire pipe section, resulting in a significant increase in prediction deviation; (3) Existing models simply set the formation temperature as a fixed edge. (3) The model does not establish a two-way coupling relationship between the thermal properties of the formation and the heat transfer process inside the heat pipe. It cannot reflect the influence of the dynamic change of the formation heat flux density on the phase state of the working fluid and the heat transfer efficiency inside the pipe, nor can it reflect the reaction of the heat pipe heat exchange on the formation temperature field. It is seriously out of touch with the real physical process. (4) The model parameter selection and solution method rely on experience. It does not quantitatively consider key factors such as the heat loss along the pipe and the gradient change of the working fluid filling rate of the ultra-long pipe section. It also lacks a systematic model verification and iterative optimization mechanism, resulting in poor engineering practicality of the model. (5) Existing models generally analyze the two core heat transfer processes of nucleation boiling in the evaporation section and film condensation in the condensation section separately. They fail to realize the heat transfer coupling calculation between the two and ignore the mass conservation relationship that should be satisfied between the steam production in the evaporation section and the condensate volume in the condensation section. This further aggravates the deviation between the model prediction results and the actual working conditions. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe, in order to solve the problem that existing multi-stage gravity heat pipe models are difficult to accurately predict the full-process two-phase flow heat transfer law under complex working conditions in deep wells due to pipe segmentation, single flow pattern, lack of formation coupling, and separation of heat transfer process.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: This invention discloses a method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe, comprising: Based on the evaporation section, insulation section and condensation section of the multi-stage gravity heat pipe, the standardized basic parameters of each pipe section are obtained respectively. Based on the basic parameters of each pipe section, a conversion criterion for multiple flow pattern categories of gas-liquid two-phase flow along the multi-stage gravity heat pipe is established, and the flow pattern category of two-phase flow at each pipe section location is determined. Based on the flow pattern category of the two-phase flow along the pipe section, the heat transfer coefficients of the evaporation section and the condensation section, as well as the flow coefficient of the adiabatic section, are matched and obtained, and heat transfer sub-models and flow sub-models along the pipe section and the adiabatic section are constructed. The total heat transfer coefficient from the evaporation section to the condensation section is obtained based on the heat transfer sub-model and the basic parameters of the corresponding pipe section, and the resistance loss along the adiabatic section is obtained based on the flow sub-model and the basic parameters of the corresponding pipe section. Based on the overall heat transfer coefficient and the resistance loss, all the heat transfer sub-models and the flow sub-models are coupled in series in the spatial direction of each pipe segment to obtain the first coupled model. A formation heat conduction model is established, and a second coupled model is obtained by coupling the formation heat conduction model and the first coupled model. The first coupled model and the second coupled model are solved simultaneously to obtain the predicted state values ​​of the two-phase flow along the multi-stage gravity heat pipe. The measured state values ​​of two-phase flow along the path under the simulated working conditions of medium-deep geothermal energy are obtained, and the first coupling model and the second coupling model are corrected according to the comparison error between the measured state values ​​and the predicted state values ​​to obtain the two-phase flow heat transfer model.

[0006] Optionally, the establishment of multiple flow pattern categories for the gas-liquid two-phase flow as a transition criterion along the multi-stage gravity heat pipe, and the determination of the flow pattern category of the two-phase flow at each pipe section location, includes: The gas-liquid two-phase flow patterns of the multi-stage gravity heat pipe are classified into different flow pattern categories; Based on the temperature and pressure range of the medium-deep geothermal well, the distribution range of different flow patterns along the entire length of the multi-stage gravity heat pipe is defined; Based on the basic parameters of each pipe section, obtain the pipe section inner diameter, hydraulic diameter, two-phase mixing velocity, gas phase velocity and liquid phase density for each distribution range; Based on the obtained inner diameter of the pipe section, the hydraulic diameter, the two-phase mixing velocity, the gas phase velocity, and the liquid phase density, the Reynolds number, Froude number, and Weber number for the corresponding distribution range are obtained. Based on the correspondence between the flow pattern category and the Reynolds number, the Froude number and the Weber number within the same distribution interval, the transformation discrimination criterion is established; The Reynolds number, Froude number, and Weber number are obtained at each pipe section along the friction point, and the flow pattern category of the two-phase flow at the corresponding pipe section along the friction point is determined by the transformation discrimination criterion.

[0007] Optionally, the step of matching and obtaining the heat transfer coefficients of the evaporation section and the condensation section, and the flow coefficient of the adiabatic section, based on the flow pattern category of the two-phase flow along each pipe section, and constructing heat transfer sub-models along the pipe sections of the evaporation section and the condensation section, and flow sub-models along the pipe sections of the adiabatic section, includes: Based on the flow pattern category of the two-phase flow along the evaporation section, the corresponding heat transfer coefficient correlation is matched, and the first convective heat transfer coefficient is obtained through the matched heat transfer coefficient correlation. Based on the first convective heat transfer coefficient, a first heat transfer sub-model for nucleate boiling heat transfer is constructed using the working fluid filling rate and wall superheat. Based on the flow pattern category of the two-phase flow along the condensation section, the corresponding heat transfer coefficient correlation is matched, and the second convective heat transfer coefficient is obtained through the matched heat transfer coefficient correlation. Based on the second convective heat transfer coefficient, a second heat transfer sub-model for film condensation heat transfer is constructed by considering the variation of condensate film thickness along the path. Based on the flow pattern category of the two-phase flow along the adiabatic section, the corresponding drag coefficient correlation is matched, and the drag coefficient along the flow and the local drag coefficient are obtained through the matched drag coefficient correlation. Based on the friction coefficient and the local resistance coefficient, a two-phase flow sub-model is constructed using the phase-separated flow model as a framework.

[0008] Optionally, obtaining the total heat transfer coefficient from the evaporation section to the condensation section based on the heat transfer sub-model and the basic parameters of the corresponding pipe section includes: Based on the basic parameters of the evaporation section and the condensation section, the heat exchange area of ​​the evaporation section, the heat exchange area of ​​the condensation section, the contact heat exchange area between the multi-stage gravity heat pipe and the ground, and the total heat exchange area of ​​the multi-stage gravity heat pipe are obtained respectively. Based on the obtained heat transfer areas, and combined with the first convective heat transfer coefficient and the second convective heat transfer coefficient, the total heat transfer coefficient is calculated. The functional expression for calculating the total heat transfer coefficient is as follows:

[0009] In the formula, Indicates the overall heat transfer coefficient. This represents the total heat exchange area of ​​the multi-stage gravity heat pipe. Indicates the first convective heat transfer coefficient. This indicates the heat transfer area of ​​the evaporation section. This indicates the thermal conductivity of the wall material of a multi-stage gravity heat pipe. This represents the average heat transfer area of ​​the wall surface of a multi-stage gravity heat pipe. This indicates the wall thickness of a multi-stage gravity heat pipe. This represents the second convective heat transfer coefficient. This indicates the heat transfer area of ​​the condenser section. Indicates the third convective heat transfer coefficient. This indicates the contact heat exchange area between the multi-stage gravity heat pipe and the ground.

[0010] Optionally, obtaining the friction loss along the adiabatic section based on the flow sub-model and the basic parameters of the corresponding pipe segment includes: Based on the basic parameters of the insulation section, the effective length of the insulation section, the hydraulic diameter of the multi-stage gravity heat pipe, the gas-liquid two-phase mixing density, and the gas-liquid two-phase mixing velocity are obtained respectively. Based on the effective length, the hydraulic diameter, the gas-liquid two-phase mixing density, and the gas-liquid two-phase mixing velocity, combined with the friction coefficient and the local resistance coefficient, the resistance loss is calculated. The functional expression for calculating the resistance loss is as follows:

[0011] In the formula, Indicates resistance loss. Indicates the friction coefficient. Indicates the effective length. Indicates the hydraulic diameter. This represents the density of a gas-liquid mixture. Indicates the flow rate of the gas-liquid two-phase mixture. Represents the local drag coefficient. This represents the sum of the local resistance coefficients at various locations along the insulation section.

[0012] Optionally, the first coupled model, which couples all the heat transfer sub-models and the flow sub-models in series order of each pipe segment in the spatial direction according to the overall heat transfer coefficient and the drag loss, includes: Based on the spatial distribution of each pipe section, the spatial series sequence of the evaporation section, the insulation section, and the condensation section is determined; The heat transfer of the two-phase flow from the evaporation section to the condensation section is determined based on the overall heat transfer coefficient, and the heat transfer between each pipe section is constrained by the principle of heat conservation. The superposition loss of the two-phase flow along the insulation section is determined based on the resistance loss, and the working fluid flow between each pipe section is continuously constrained by the mass flow rate. Based on the spatial series sequence, the working fluid outlet phase and temperature of the upstream pipe section are used as the inlet boundary conditions of the downstream pipe section. All the heat transfer sub-models and the flow sub-models are coupled to obtain the first coupled model.

[0013] Optionally, establishing the formation heat conduction model includes: Acquire a dataset of temperature data that varies with time at different distances along the radial direction of the multi-stage gravity heat pipe; Based on the radial thermal conductivity of the formation along the multi-stage gravity heat pipes, a one-dimensional unsteady-state heat conduction equation is constructed with formation temperature as the dependent variable and time and radial distance as the independent variables. The functional expression of the one-dimensional unsteady-state heat conduction equation is as follows:

[0014] In the formula, Indicates formation temperature. Indicates time, Indicates the thermal diffusivity of the formation. This indicates the radial distance of the strata along the multi-stage gravity heat pipe; Substitute the temperature dataset into the one-dimensional unsteady heat conduction equation, and use the least squares method to invert the one-dimensional unsteady heat conduction equation to obtain the formation thermal conductivity, volumetric specific heat capacity and formation thermal diffusivity, respectively. Based on the formation thermal conductivity, the volumetric specific heat capacity, and the formation thermal diffusivity, the formation thermal conduction model is constructed using the one-dimensional unsteady-state heat conduction equation as the governing equation.

[0015] Optionally, the step of obtaining the measured state values ​​along the two-phase flow path under medium-deep geothermal simulation conditions, and correcting the first coupling model and the second coupling model based on the comparison error between the measured state values ​​and the predicted state values, includes: Based on the multi-stage gravity heat pipe simulation experiment consistent with the medium-deep geothermal conditions, the measured values ​​of heat transfer coefficient, flow resistance and phase transition position were obtained. Based on the predicted heat transfer coefficient values ​​obtained from the solution results of the first coupled model and the second coupled model, the first relative error between the measured heat transfer coefficient value and the predicted heat transfer coefficient value is calculated. The functional expression for calculating the first relative error is as follows:

[0016] In the formula, Indicates the first relative error. This represents the predicted value of the heat transfer coefficient. This represents the measured value of the heat transfer coefficient; Based on the predicted flow resistance values ​​obtained from the solution results of the first coupled model and the second coupled model, a second relative error between the measured flow resistance value and the predicted flow resistance value is calculated. The functional expression for calculating the second relative error is as follows:

[0017] In the formula, This indicates the second relative error. This represents the predicted value of flow resistance. This represents the measured value of flow resistance; Based on the predicted phase transition position obtained from the solution results of the first coupling model and the second coupling model, a third relative error between the measured phase transition position and the predicted phase transition position is calculated. The functional expression for calculating the third relative error is as follows:

[0018] In the formula, Indicates the third relative error. This represents the predicted value of the phase transition position. Indicates the measured value of the state transition position; If any one of the first relative error, the second relative error, and the third relative error does not meet the preset application conditions for medium-deep geothermal engineering, the convective heat transfer coefficient in each of the heat transfer sub-models is corrected, and the boundary conditions of the second coupling model are also corrected.

[0019] This invention also discloses a model building system applied to the above-mentioned method for building a two-phase flow heat transfer model of a multi-stage gravity heat pipe, the model building system comprising: The parameter acquisition module is used to acquire the standardized basic parameters of each pipe segment based on the evaporation section, adiabatic section and condensation section that are disassembled sequentially along the multi-stage gravity heat pipe. The flow pattern classification module is used to establish a conversion criteria for multiple flow pattern classifications of gas-liquid two-phase flow along the multi-stage gravity heat pipe based on the basic parameters of each pipe section, and to determine the flow pattern classification of the two-phase flow at each pipe section location. The heat transfer-flow model construction module is used to match and construct heat transfer sub-models for the evaporation section and the condensation section along the pipe according to the flow pattern category of the two-phase flow at each pipe section, and to match and construct flow sub-models for the adiabatic section along the pipe. The heat transfer-resistance loss calculation module is used to obtain the total heat transfer coefficient from the evaporation section to the condensation section based on the heat transfer sub-model and the basic parameters of the corresponding pipe section, and to obtain the resistance loss along the adiabatic section based on the flow sub-model and the basic parameters of the corresponding pipe section. The heat pipe heat transfer-flow coupling module is used to couple all the heat transfer sub-models and the flow sub-models in series order of each pipe segment in the spatial direction according to the total heat transfer coefficient and the resistance loss, so as to obtain the first coupling model. The formation-heat pipe bidirectional coupling module is used to establish a formation heat conduction model, couple the formation heat conduction model with the first coupling model to obtain a second coupling model, and solve the first coupling model and the second coupling model simultaneously to obtain the state prediction value of the two-phase flow along the multi-stage gravity heat pipe; The two-phase flow heat transfer model establishment module is used to obtain the measured state values ​​of the two-phase flow along the path under the simulation conditions of medium-deep geothermal layers, and to correct the first coupling model and the second coupling model based on the comparison error between the measured state values ​​and the predicted state values, so as to obtain the two-phase flow heat transfer model.

[0020] The present invention also discloses a storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe.

[0021] Compared with the prior art, the beneficial effects of the multi-stage gravity heat pipe two-phase flow heat transfer model construction method and model construction system provided by the embodiments of the present invention are as follows: The heat transfer and flow coefficients are obtained by matching the flow pattern at each point along the pipe, ensuring that the heat transfer and flow sub-models at each point use calculation methods corresponding to the actual flow pattern at that location. This avoids prediction bias caused by mechanically applying a single flow pattern method to the entire pipe section. By coupling all heat transfer and flow sub-models in a spatially connected series, the outlet state of the upstream pipe section drives the inlet conditions of the downstream pipe section, and the steam production in the evaporation section and the condensate production in the condensation section satisfy mass conservation, eliminating the fragmentation of the heat transfer process and overcoming the limitations of the steady-state assumption of a single pipe section. By coupling the formation heat conduction model with the first coupled model, the heat transfer of the heat pipe and the formation temperature field interact, overcoming the limitation of the fixed boundary condition of formation temperature. The error between the measured and predicted values ​​is used to correct the first and second coupled models, improving the engineering applicability of the model. Attached Figure Description

[0022] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 A schematic diagram illustrating the steps of constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe provided in an embodiment of the present invention. Detailed Implementation

[0023] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0024] This invention discloses a method for constructing a two-phase flow heat transfer model for multi-stage gravity heat pipes, such as... Figure 1 As shown, it includes: S1. Based on the evaporation section, insulation section and condensation section that are disassembled along the multi-stage gravity heat pipe, obtain the standardized basic parameters of each pipe section. S2. Based on the basic parameters of each pipe section, establish the conversion criteria for multiple flow pattern categories of gas-liquid two-phase flow along the multi-stage gravity heat pipe, and determine the flow pattern category of two-phase flow at each pipe section location. S3. Based on the flow pattern of the two-phase flow at each pipe section along the friction point, match and obtain the heat transfer coefficient of the evaporation section and the condensation section, as well as the flow coefficient of the adiabatic section, and construct the heat transfer sub-model at the friction point of the evaporation section and the condensation section, and the flow sub-model at the friction point of the adiabatic section. S4. Obtain the total heat transfer coefficient from the evaporation section to the condensation section based on the heat transfer sub-model and the basic parameters of the corresponding pipe section, and obtain the resistance loss along the insulation section based on the flow sub-model and the basic parameters of the corresponding pipe section. S5. Based on the overall heat transfer coefficient and resistance loss, couple all heat transfer sub-models and flow sub-models in series in the spatial direction of each pipe segment to obtain the first coupled model. S6. Establish a formation heat conduction model, couple the formation heat conduction model and the first coupled model to obtain the second coupled model, and solve the first coupled model and the second coupled model simultaneously to obtain the predicted state value of the two-phase flow along the multi-stage gravity heat pipe. S7. Obtain the measured state values ​​of the two-phase flow along the path under the simulated working conditions of medium-deep geothermal heat, and correct the first coupling model and the second coupling model based on the comparison error between the measured state values ​​and the predicted state values ​​to obtain the two-phase flow heat transfer model.

[0025] By implementing the above-described embodiment of the multi-stage gravity heat pipe two-phase flow heat transfer model construction method, the evaporation section, adiabatic section, and condensation section of the multi-stage gravity heat pipe are disassembled sequentially along the pipe, and the standardized basic parameters of each section are obtained. For example, geometric parameters include the inner diameter, outer diameter, wall thickness, and effective heat transfer length of each section; working fluid parameters include the critical temperature, critical pressure, filling rate, saturated vapor pressure, liquid density, and gas density of the working fluid; and operating condition parameters include the formation ambient temperature, formation ambient pressure, initial charging temperature of the heat pipe working fluid, and thermal conductivity of the heat pipe wall material. These parameters are converted into dimensionless values ​​after eigenvalue normalization and used as the basic input for all subsequent calculations.

[0026] First, the gas-liquid two-phase flow patterns along the multi-stage gravity heat pipe are clearly classified into four categories: bubbly flow, plug flow, slug flow, and annular flow. Then, a conversion criterion for the gas-liquid two-phase flow patterns along the multi-stage gravity heat pipe is established. This conversion criterion allows for accurate determination of the flow pattern category at each location during subsequent matching calculations along the pipe.

[0027] Based on the flow pattern at each pipe section, corresponding heat transfer coefficients and flow coefficients are matched, and heat transfer sub-models and flow sub-models are constructed. This ensures that the calculation of heat transfer coefficients and flow coefficients at each pipe section uses methods corresponding to the actual flow pattern at that location. For example, the nucleus boiling heat transfer sub-model in the evaporation section considers the influence of the working fluid filling rate and wall superheat on boiling heat transfer; the film condensation heat transfer sub-model in the condensation section considers the influence of the change in condensate film thickness along the pipe on condensation heat transfer; and the flow sub-model in the adiabatic section uses a phase-separated flow model to calculate the flow resistance along the pipe. Thus, appropriate heat transfer coefficient calculation methods are used in each flow pattern interval of the evaporation and condensation sections, and appropriate flow coefficient calculation methods are used in each flow pattern interval of the adiabatic section. This fundamentally avoids the calculation deviation introduced by mechanically applying a single method to the entire pipe section.

[0028] All heat transfer and flow sub-models are coupled in series in the spatial direction, so that the outlet state of the upstream pipe segment serves as the inlet boundary condition of the downstream pipe segment. The mass flow rate between each pipe segment is continuous and the pressure loss is superimposed at each stage. The steam production in the evaporation section and the condensate production in the condensation section satisfy the mass conservation relationship. This eliminates the prediction bias caused by the analysis of nucleus boiling in the evaporation section and film condensation in the condensation section. It overcomes the limitation that the steady-state assumption of a single pipe segment cannot reflect the dynamic influence of the flow state and heat transfer characteristics of the upstream pipe segment on the downstream pipe segment. It also solves the problem that the model cannot accurately depict the whole process law due to the lack of coupling effect between pipe segments and the separation of heat transfer process.

[0029] A second coupled model is established, in which the heat exchange of each segment of the heat pipe is used as the boundary condition input of the formation heat conduction model. At the same time, the formation temperature field distribution results are fed back to the heat transfer calculation of each segment of the heat pipe. This enables the formation thermal properties and the heat transfer process inside the heat pipe to form a collaborative solution with each other as inputs. It can reflect the influence of the dynamic change of formation heat flux density on the phase state of the working fluid and heat transfer efficiency inside the pipe, and at the same time reflect the reaction of heat pipe heat exchange on the formation temperature field. This solves the problem of serious disconnect between the fixed boundary condition of formation temperature and the real physical process.

[0030] The measured values ​​of the state under the simulated working conditions of medium-deep geothermal energy are obtained and compared with the predicted values. The relative error of the predicted heat transfer coefficient, the relative error of the predicted flow resistance, and the prediction deviation of the phase transition position are calculated. If any error does not meet the requirements, the empirical coefficients of nucleation boiling and film condensation are corrected, and the formation-heat pipe coupling boundary conditions are corrected. Through multiple rounds of iteration, the prediction results are made to continuously approximate the real physical process, solving the problem of poor model engineering practicality caused by the lack of systematic verification and iterative optimization mechanism.

[0031] Furthermore, a conversion criterion for multiple flow pattern categories of gas-liquid two-phase flow along the multi-stage gravity heat pipe is established, and the flow pattern category of the two-phase flow at each pipe section location is determined, including: The gas-liquid two-phase flow patterns of multi-stage gravity heat pipes are classified into different flow pattern categories; Based on the temperature and pressure range of medium-deep geothermal wells, the distribution range of different flow patterns along the entire multi-stage gravity heat pipe is defined. Based on the basic parameters of each pipe section, obtain the inner diameter, hydraulic diameter, two-phase mixing velocity, gas phase velocity, and liquid phase density of each distribution range. Based on the obtained pipe section inner diameter, hydraulic diameter, two-phase mixing velocity, gas phase velocity, and liquid phase density, the Reynolds number, Froude number, and Weber number for the corresponding distribution range are obtained. Based on the correspondence between flow pattern categories and Reynolds number, Froude number and Weber number within the same distribution interval, a transformation discrimination criterion is established; Obtain the Reynolds number, Froude number, and Weber number at each pipe section along the friction point, and determine the flow pattern category of the two-phase flow at the corresponding pipe section along the friction point using the transformation discrimination criterion.

[0032] By implementing the above-described method for constructing a two-phase flow heat transfer model for multi-stage gravity heat pipes, the gas-liquid two-phase flow patterns of the multi-stage gravity heat pipes are first clearly classified into different flow pattern categories, rather than being treated as a general category. For example, they are classified into four categories: bubbly flow, plug flow, slug flow, and annular flow, establishing a classification basis for accurate identification at each location along the pipe. Based on this, the distribution range of different flow pattern categories along the entire multi-stage gravity heat pipe is defined according to the temperature and pressure range of medium-deep geothermal wells. This ensures that the definition of flow pattern ranges is not based on general experience under normal temperature and pressure or conventional operating conditions, but is specifically defined for the unique high-temperature and high-pressure environment of medium-deep geothermal wells, solving the problem of excessive deviation of conventional flow pattern diagrams or general discrimination criteria under extreme conditions in deep wells.

[0033] To transform the aforementioned distribution ranges into quantifiable numerical criteria, the pipe segment inner diameter, hydraulic diameter, two-phase mixing velocity, gas phase velocity, and liquid phase density for each distribution range are further obtained based on the basic parameters of each pipe segment. Among these parameters, the hydraulic diameter is directly determined by the pipe segment inner diameter under circular pipe conditions. The two-phase mixing velocity reflects the average velocity level of the gas-liquid co-flow, while the gas phase velocity separately characterizes the actual velocity of the gas phase passing through the pipe cross-section. The liquid phase density directly affects the momentum exchange intensity between the gas and liquid phases. Based on these flow parameters, the Reynolds number, Froude number, and Weber number for the corresponding distribution ranges are then obtained.

[0034] For example, the Reynolds number, calculated based on the two-phase mixing velocity and hydraulic diameter, characterizes the ratio of inertial force to viscous force, reflecting the driving effect of turbulence intensity on the breakup of the gas-liquid interface. The Froude number, calculated based on the two-phase mixing velocity and pipe section inner diameter, characterizes the ratio of inertial force to gravity, reflecting the regulating effect of buoyancy on bubble polymerization and liquid film distribution along the pipe wall. The Weber number, calculated based on gas phase velocity, liquid phase density, and pipe section inner diameter, characterizes the ratio of inertial force to surface tension, reflecting the restrictive effect of interfacial stability on droplet entrainment and liquid film rupture.

[0035] The reason for using three dimensionless numbers simultaneously instead of a single criterion is that flow pattern transformation in the high-temperature and high-pressure environment of deep wells is controlled by multiple physical mechanisms. A single dimensionless number cannot distinguish the flow pattern boundaries under different dominant mechanisms. However, combining the three dimensionless numbers can cover the coupled effects of multiple factors such as inertial force, viscous force, gravity, and surface tension, thereby accurately defining the critical points of transformation between various flow patterns within a wide parameter range in deep wells. By establishing a correspondence between flow pattern categories within the same distribution interval and specific numerical combinations of Reynolds number, Froude number, and Weber number, a transformation discrimination criterion is formed, which elevates flow pattern discrimination from an empirical dependence to a quantitatively calculable numerical mapping relationship.

[0036] After obtaining the Reynolds number, Froude number, and Weber number at each pipe section location, the flow pattern of the two-phase flow at the corresponding pipe section location is determined by the transformation criterion. This enables automatic flow pattern identification based on local actual flow parameters at each location throughout the entire process, providing accurate spatial distribution input for matching the corresponding heat transfer coefficient and flow coefficient at each pipe section location. This fundamentally avoids the systematic calculation bias introduced by mechanically applying a single flow pattern method to the entire pipe section.

[0037] Furthermore, based on the flow pattern category of the two-phase flow at each pipe section's friction point, the heat transfer coefficients of the evaporation and condensation sections, as well as the flow coefficient of the adiabatic section, are obtained. Then, heat transfer sub-models for the evaporation and condensation sections and flow sub-models for the adiabatic section's friction point are constructed, including: Based on the flow pattern of the two-phase flow along the evaporation section, the corresponding heat transfer coefficient correlation is matched, and the first convective heat transfer coefficient is obtained through the matched heat transfer coefficient correlation. Based on the first convective heat transfer coefficient, a first heat transfer sub-model for nucleate boiling heat transfer is constructed using the working fluid filling rate and wall superheat. Based on the flow pattern of the two-phase flow along the condensation section, the corresponding heat transfer coefficient correlation is matched, and the second convective heat transfer coefficient is obtained through the matched heat transfer coefficient correlation. Based on the second convective heat transfer coefficient, a second heat transfer sub-model for film condensation heat transfer is constructed by considering the variation of condensate film thickness along the path. Based on the flow pattern of the two-phase flow along the adiabatic section, the corresponding drag coefficient correlation is matched, and the drag coefficient along the flow path and the local drag coefficient are obtained through the matched drag coefficient correlation. Based on the friction coefficient and local resistance coefficient, a two-phase flow sub-model is constructed using the phase-separated flow model as a framework.

[0038] By implementing the above-described embodiment of the multi-stage gravity heat pipe two-phase flow heat transfer model construction method, the corresponding heat transfer coefficient correlation is matched according to the flow pattern category of the two-phase flow along the evaporation section, and the first convective heat transfer coefficient is obtained. The principle is that the geometric morphology and turbulent structure of the gas-liquid interface differ fundamentally under different flow patterns: nucleation boiling of discrete bubbles in bubbly flow and evaporation heat transfer of continuous liquid film in annular flow have different dominant heat transfer mechanisms. Therefore, it is necessary to use the heat transfer coefficient correlation corresponding to each flow pattern interval to obtain the accurate first convective heat transfer coefficient at each location along the flow path. Based on this, a first heat transfer sub-model for nucleation boiling heat transfer is constructed using the working fluid filling rate and wall superheat. For example, the working fluid filling rate affects the number of activated cavities on the wall and the frequency of bubble detachment; the wall superheat determines the driving temperature difference for nucleation boiling and the bubble nucleation rate. Both of these factors jointly determine the actual output of the nucleation boiling heat transfer intensity in the evaporation section, enabling the first heat transfer sub-model to automatically match the corresponding correlation to calculate the local heat transfer coefficient at each location based on the changes in the flow pattern along the flow path.

[0039] The heat transfer coefficient correlation is matched to the flow pattern of the two-phase flow along the condensation section to obtain the second convective heat transfer coefficient. This is because the thermal resistance of continuous liquid film flowing along the wall in annular flow has different thermal resistance and heat transfer path than that of forced convection condensation when liquid plugs alternately pass through in plug flow or slug flow. Therefore, the heat transfer coefficient correlation corresponding to each flow pattern interval must be used to obtain the accurate second convective heat transfer coefficient at each position along the flow path. Based on this, a second heat transfer sub-model of film condensation heat transfer is constructed based on the change of condensate film thickness along the flow path. For example, when the condensate film is thinner at the inlet of the condensation section, the thermal resistance is smaller and the heat transfer coefficient is higher. As condensation progresses, the liquid film gradually thickens along the flow path, increasing the thermal resistance and decreasing the heat transfer coefficient. Incorporating the condensate film thickness as a variable along the flow path into the sub-model can reflect the actual physical process of the heat transfer coefficient at each position in the condensation section decreasing as the liquid film grows.

[0040] Based on the flow pattern classification of the two-phase flow along the adiabatic section, the corresponding drag coefficient correlation is matched to obtain the friction drag coefficient and local drag coefficient. This is because in bubbly flow, when bubbles are dispersed in the liquid phase, the wall shear is dominated by continuous turbulence in the liquid phase; in annular flow, when high-speed gas nuclei carry liquid films along the wall, the interfacial shear force between the gas and liquid phases is dominant; and in slug flow, the alternating passage of atmospheric slugs and liquid slugs generates additional liquid slug impact and acceleration drag. The drag composition and dissipation mechanism under different flow patterns are completely different, and it is necessary to match the drag coefficient correlation corresponding to each flow pattern to obtain the accurate drag coefficient at each location. On this basis, a two-phase flow sub-model is constructed using a phase-separated flow model as a framework. For example, the gas phase and liquid phase are treated as independent flow phases, and momentum equations are established separately and coupled through interphase interaction terms. This can simultaneously capture the influence of velocity slip and interphase momentum exchange on drag loss, so that the drag calculation method corresponding to the actual local flow pattern is used at each location of the adiabatic section to obtain the accurate friction drag distribution.

[0041] Furthermore, based on the heat transfer sub-model and the basic parameters of the corresponding pipe section, the total heat transfer coefficient from the evaporation section to the condensation section is obtained, including: Based on the basic parameters of the evaporation section and the condensation section, the heat transfer area of ​​the evaporation section, the heat transfer area of ​​the condensation section, the contact heat transfer area between the multi-stage gravity heat pipe and the stratum, and the total heat transfer area of ​​the multi-stage gravity heat pipe are obtained respectively. Based on the obtained heat transfer areas, and combined with the first and second convective heat transfer coefficients, the overall heat transfer coefficient is calculated. The functional expression for calculating the overall heat transfer coefficient is as follows:

[0042] In the formula, Indicates the overall heat transfer coefficient. This represents the total heat exchange area of ​​the multi-stage gravity heat pipe. Indicates the first convective heat transfer coefficient. This indicates the heat transfer area of ​​the evaporation section. This indicates the thermal conductivity of the wall material of a multi-stage gravity heat pipe. This represents the average heat transfer area of ​​the wall surface of a multi-stage gravity heat pipe. This indicates the wall thickness of a multi-stage gravity heat pipe. This represents the second convective heat transfer coefficient. This indicates the heat transfer area of ​​the condenser section. Indicates the third convective heat transfer coefficient. This indicates the contact heat exchange area between the multi-stage gravity heat pipe and the ground.

[0043] By implementing the above-described embodiment of the multi-stage gravity heat pipe two-phase flow heat transfer model construction method, the heat transfer area of ​​the evaporation section is determined by the inner diameter of the evaporation section and the effective heat transfer length; the heat transfer area of ​​the condensation section is determined by the inner diameter of the condensation section and the effective heat transfer length; the contact heat transfer area between the multi-stage gravity heat pipe and the stratum is determined by the outer wall area of ​​the heat pipe; and the total heat transfer area of ​​the multi-stage gravity heat pipe covers all heat transfer areas of the inner and outer walls of the heat pipe, so that all the area parameters required for the calculation of the total heat transfer coefficient are derived from the basic parameters of each pipe section.

[0044] Based on this, and using the obtained heat transfer areas, combined with the first and second convective heat transfer coefficients, the total heat transfer coefficient is calculated using a functional expression. The principle is that the total thermal resistance is composed of four series-superimposed terms: the convective heat transfer resistance of the working fluid inside the evaporation section, the thermal conductivity resistance of the heat pipe wall, the convective heat transfer resistance of the working fluid inside the condensation section, and the convective heat transfer resistance between the heat pipe outer wall and the ground. Specifically, the first convective heat transfer coefficient corresponds to the nucleus boiling heat transfer resistance of the working fluid inside the evaporation section; the second convective heat transfer coefficient corresponds to the film condensation heat transfer resistance of the working fluid inside the condensation section; the thermal conductivity of the wall material, wall thickness, and average heat transfer area together constitute the wall thermal conductivity resistance; and the third convective heat transfer coefficient corresponds to the convective heat transfer resistance between the heat pipe outer wall and the ground. The total heat transfer coefficient is obtained by taking the reciprocal of the series-superimposed terms.

[0045] By incorporating the two core heat transfer processes—evaporation and condensation—into a single overall heat transfer coefficient function expression for unified solution, the nucleus boiling heat transfer resistance of the working fluid inside the evaporation section, the film condensation heat transfer resistance of the working fluid inside the condensation section, the thermal conductivity resistance of the heat pipe wall, and the convective heat transfer resistance between the heat pipe outer wall and the formation are synchronously correlated at the calculation level. All the heat carried by the steam produced in the evaporation section must be transferred to the condensation section through the path controlled by this overall heat transfer coefficient. This fundamentally eliminates the contradiction that the mass conservation relationship between the steam production in the evaporation section and the condensate volume in the condensation section cannot be satisfied when the two heat transfer processes are analyzed separately. Simultaneously, this function uniformly incorporates the geometric parameters of each pipe section in the form of heat transfer area, the working fluid parameters in the form of convective heat transfer coefficient, and the operating parameters in the form of thermal conductivity and wall thickness into the calculation, allowing the structural characteristics and operating conditions of the multi-stage gravity heat pipe to be directly reflected in the overall heat transfer coefficient value.

[0046] The first and second convective heat transfer coefficients obtained based on the flow pattern categories matched at each location along the pipeline already include the heat transfer correlation effects corresponding to each flow pattern interval. Therefore, the total heat transfer coefficient is automatically adapted to the flow pattern changes in each pipe section throughout the entire process, so that the total heat transfer coefficient adopts the heat transfer calculation method corresponding to the local flow pattern in the entire pipe section.

[0047] Furthermore, based on the flow sub-model and the basic parameters of the corresponding pipe section, the friction loss along the insulation section is obtained, including: Based on the basic parameters of the insulation section, the effective length of the insulation section, the hydraulic diameter of the multi-stage gravity heat pipe, the gas-liquid two-phase mixing density, and the gas-liquid two-phase mixing velocity are obtained respectively. Based on the effective length, hydraulic diameter, gas-liquid two-phase mixing density, and gas-liquid two-phase mixing velocity, combined with the friction coefficient and local resistance coefficient, the resistance loss is calculated. The functional expression for calculating the resistance loss is:

[0048] In the formula, Indicates resistance loss. Indicates the friction coefficient. Indicates the effective length. Indicates the hydraulic diameter. This represents the density of a gas-liquid mixture. Indicates the flow rate of the gas-liquid two-phase mixture. Represents the local drag coefficient. This represents the sum of the local resistance coefficients at various locations along the insulation section.

[0049] By implementing the above-described method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe, the effective length is derived from the actual heat transfer length of the adiabatic section along the axial direction; the hydraulic diameter is directly determined by the inner diameter of the adiabatic section under circular pipe conditions; the gas-liquid two-phase mixing density is obtained by weighting the gas-liquid phase densities according to the local gas content; and the gas-liquid two-phase mixing velocity reflects the average velocity of the gas and liquid phases flowing through the cross section. These parameters provide the basic inputs required for calculating resistance loss from four dimensions: geometric scale, flow cross section, working fluid properties, and motion state.

[0050] After obtaining the friction loss coefficient and local resistance coefficient, the effective length, hydraulic diameter, gas-liquid two-phase mixing density, and gas-liquid two-phase mixing velocity are substituted into the resistance loss function expression for calculation. The principle is that the total resistance loss of the adiabatic section consists of two parts: friction loss and local resistance loss. The friction loss term uses the ratio of the effective length to the hydraulic diameter to characterize the amplification effect of the pipe's length-to-diameter ratio on wall friction dissipation; the product of the gas-liquid two-phase mixing density and the square of the mixing velocity to characterize the magnitude of the inertial force per unit volume of fluid; and the friction loss coefficient to characterize the combined influence of wall roughness and flow state on the friction factor. The local resistance loss term uses the local resistance coefficient to characterize the additional energy dissipation caused by local disturbances such as pipe section connections, cross-sectional changes, or phase interface area accumulation, and the sum of the local resistance coefficients reflects the cumulative effect of multiple local disturbances throughout the section.

[0051] By calculating and summing the friction loss term and the local resistance loss term independently in the function expression, the energy losses caused by the two different physical mechanisms of continuous wall friction dissipation and local intermittent additional dissipation can be clearly distinguished and quantified separately in the same total resistance loss, avoiding the calculation distortion caused by treating the two different dissipation mechanisms uniformly. Furthermore, since the friction loss coefficient and local resistance coefficient have been matched according to the flow pattern at each friction location when constructing the adiabatic section flow sub-model (e.g., using the friction loss coefficient correlation formula and local resistance coefficient correlation formula corresponding to the flow pattern in different flow pattern intervals of the adiabatic section), after substituting the friction loss coefficient and local resistance coefficient at each location throughout the adiabatic section into the resistance loss function expression, the resistance calculation method corresponding to the actual local flow pattern is used at each location throughout the section. The friction loss coefficient is accumulated along the friction as the ratio of effective length to hydraulic diameter, and the local resistance coefficient is directly summed using the coefficients at each local location, ultimately obtaining a friction loss that reflects the actual flow pattern distribution characteristics of the adiabatic section.

[0052] Furthermore, based on the overall heat transfer coefficient and drag loss, all heat transfer sub-models and flow sub-models are coupled in series in the spatial direction for each pipe segment to obtain the first coupled model, which includes: Based on the spatial distribution of each pipe section, determine the spatial series sequence of the evaporation section, insulation section, and condensation section; The heat transfer of the two-phase flow from the evaporation section to the condensation section is determined based on the overall heat transfer coefficient, and the heat transfer between each pipe section is constrained by the principle of heat conservation. The superposition loss of two-phase flow along the adiabatic section is determined based on the resistance loss, and the working fluid flow between each pipe section is continuously constrained by the mass flow rate. Based on the spatial series sequence, the working fluid outlet phase state and temperature of the upstream pipe section are used as the inlet boundary conditions of the downstream pipe section. All heat transfer sub-models and flow sub-models are coupled to obtain the first coupled model.

[0053] By implementing the above-described embodiment of the multi-stage gravity heat pipe two-phase flow heat transfer model construction method, the sequence of the working fluid flowing through the evaporation section, the adiabatic section, and the condensation section is determined according to the series sequence of each pipe segment in the spatial direction, for example, according to the actual extension direction of the heat pipe from the bottom to the top of the well. This ensures that the subsequent coupling calculation has a clear spatial direction of advancement and avoids the inability of the front-stage outlet state to be correctly transmitted to the rear-stage inlet due to disordered pipe segment sequence.

[0054] Based on this, the heat transfer of the two-phase flow from the evaporation section to the condensation section is determined according to the overall heat transfer coefficient, and the heat transfer between each pipe section is constrained by the heat conservation principle. The principle is that the overall heat transfer coefficient has been matched with the corresponding correlation formula according to the flow pattern category at each position along the flow path. Therefore, the heat transfer calculation adopts the heat transfer calculation method corresponding to the actual flow pattern at the current position along the flow path in each pipe section of the entire process. The heat conservation constraint ensures that the heat released by the upstream pipe section is accurately transferred to the energy equation of the downstream pipe section in numerical terms, avoiding the cumulative error caused by the non-conservation of heat during the inter-stage transfer process.

[0055] Meanwhile, the superimposed losses of the two-phase flow along the adiabatic section are determined based on the resistance loss, and the working fluid flow between each pipe section is continuously constrained by the mass flow rate. For example, the mass flow rate between each pipe section remains continuous, and the resistance losses of each pipe section are superimposed step by step along the flow direction to form the total pressure drop of the entire pipe section. The continuous constraint of the mass flow rate ensures that the mass flow rate of the working fluid at the outlet of the upstream pipe section is strictly equal to the mass flow rate at the inlet of the downstream pipe section, avoiding non-physical phenomena such as arbitrary increases or decreases of the working fluid between stages due to non-conservation of mass.

[0056] Based on the spatial series sequence, the working fluid outlet phase state and temperature of the preceding tube section are used as the inlet boundary conditions of the subsequent tube section. For example, the gas mass flow rate at the outlet of the preceding evaporation section is used as the inlet condition of the adiabatic section, the outlet pressure of the adiabatic section is used as the inlet pressure of the condensation section, and the condensate flow rate of the preceding condensation section is returned to the evaporation section to satisfy the mass conservation of the working fluid in the total heat pipe. The principle is that in a multi-stage gravity heat pipe, the working fluid outlet phase state of the preceding tube section determines the gas-liquid two-phase ratio and temperature level at the inlet of the subsequent tube section, thus affecting the local heat transfer temperature difference and phase change driving potential of the subsequent tube section. By using this outlet state as the inlet boundary condition of the subsequent stage, the parameters of the entire process can be transferred step by step, so that the steam production of the evaporation section and the condensate flow rate of the condensation section automatically satisfy the mass conservation relationship in the global solution, eliminating the prediction deviation caused by the analysis of nucleus boiling in the evaporation section and film condensation in the condensation section, and overcoming the limitation that the steady-state assumption of a single tube section cannot reflect the dynamic influence of the flow state and heat transfer characteristics of the preceding tube section on the subsequent tube section.

[0057] Furthermore, a formation heat conduction model is established, including: Obtain a dataset of time-varying formation temperatures at different distances along the radial direction of a multi-stage gravity heat pipe; Based on the radial thermal conductivity characteristics of the formation along the multi-stage gravity heat pipe, a one-dimensional unsteady-state heat conduction equation is constructed with formation temperature as the dependent variable and time and radial distance as the independent variables. The functional expression of the one-dimensional unsteady-state heat conduction equation is as follows:

[0058] In the formula, Indicates formation temperature. Indicates time, Indicates the thermal diffusivity of the formation. This indicates the radial distance of the strata along the multi-stage gravity heat pipe; Substitute the temperature dataset into the one-dimensional unsteady-state heat conduction equation and use the least squares method to invert the one-dimensional unsteady-state heat conduction equation to obtain the formation thermal conductivity, volumetric specific heat capacity and formation thermal diffusivity, respectively. Based on the formation thermal conductivity, volumetric specific heat capacity, and formation thermal diffusivity, a formation thermal conduction model is constructed using a one-dimensional unsteady-state heat conduction equation as the governing equation.

[0059] By implementing the above-described method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe, a temperature dataset showing the change of formation temperature over time at different distances along the radial direction of the multi-stage gravity heat pipe is obtained. For example, temperature-time series data from multiple measuring points can be continuously collected by temperature sensors buried at different radial positions from the heat pipe, so that subsequent inversion calculations are supported by real field data rather than relying on empirical assumptions.

[0060] A one-dimensional unsteady-state heat conduction equation is constructed based on the radial thermal conductivity characteristics of the formation along a multi-stage gravity heat pipe. The principle is that heat transfer in the formation mainly manifests as a one-dimensional radial outward diffusion process, with axial heat transfer being negligible relative to radial transfer. Therefore, using the one-dimensional unsteady-state heat conduction equation as the governing equation captures the main physical characteristics of formation heat conduction while avoiding the excessive computational complexity associated with three-dimensional models. In the equation, the right-hand side uses the product of the thermal diffusivity and the second derivative of temperature with respect to radial distance to characterize the rate and intensity of radial heat diffusion, while the left-hand side uses the first partial derivative of temperature with respect to time to characterize the rate of temperature rise or fall over time. Together, they describe the dynamic evolution of the formation temperature field over time and space.

[0061] By substituting the temperature dataset into the one-dimensional unsteady-state heat conduction equation and using the least squares method for inversion, the formation thermal conductivity, volumetric specific heat capacity, and formation thermal diffusivity are obtained. The principle is that the least squares method determines the optimal estimates of these three formation thermal property parameters by finding the parameter combination that minimizes the sum of squared residuals between the measured temperature values ​​and the calculated values ​​from the equation. Specifically, the formation thermal conductivity characterizes the formation's ability to conduct heat, the volumetric specific heat capacity characterizes the formation's ability to store heat, and the formation thermal diffusivity, determined by the ratio of thermal conductivity to volumetric specific heat capacity, characterizes the rate at which temperature disturbances propagate within the formation. These three parameters together constitute a complete system of thermal property parameters describing the formation's thermal response characteristics.

[0062] A formation heat conduction model is constructed using a one-dimensional unsteady-state heat conduction equation as the governing equation, based on the formation thermal conductivity, volumetric specific heat capacity, and formation thermal diffusivity. This model can calculate the dynamic changes in formation temperature over time at different radial distances based on the heat flux density boundary condition transmitted from the heat pipe wall to the formation. It can also feed back the calculated formation temperature at each location to the heat transfer calculations of each segment within the heat pipe. For example, the heat exchange of each heat pipe segment can be used as the third type of boundary condition input to the formation heat conduction model, and the calculated distribution of the formation temperature field can be fed back to the heat transfer temperature difference correction in the heat transfer calculations of each heat pipe segment. Through iterative calculation, a two-way coupling between formation thermal properties and the heat transfer process within the heat pipe is achieved. This allows the formation temperature to be dynamically adjusted with the heat transfer process, rather than being a fixed boundary condition. The heat exchange of the heat pipe is also corrected in real time based on the feedback from the formation temperature, overcoming the limitation that a fixed boundary condition of formation temperature cannot reflect the impact of dynamic changes in formation heat flux density on the phase state and heat transfer efficiency of the working fluid within the pipe.

[0063] Furthermore, the measured state values ​​along the two-phase flow path under the simulated conditions of medium-deep geothermal activity are obtained, and the first and second coupled models are corrected based on the comparison error between the measured and predicted state values, including: Based on the multi-stage gravity heat pipe simulation experiment consistent with the medium-deep geothermal conditions, the measured values ​​of heat transfer coefficient, flow resistance and phase transition position were obtained. Based on the predicted heat transfer coefficient values ​​obtained from the solutions of the first and second coupled models, the first relative error between the measured and predicted heat transfer coefficient values ​​is calculated. The functional expression for calculating the first relative error is as follows:

[0064] In the formula, Indicates the first relative error. This represents the predicted value of the heat transfer coefficient. This represents the measured value of the heat transfer coefficient; Based on the predicted flow resistance values ​​obtained from the solutions of the first and second coupled models, the second relative error between the measured and predicted flow resistance values ​​is calculated. The functional expression for calculating the second relative error is as follows:

[0065] In the formula, This indicates the second relative error. This represents the predicted value of flow resistance. This represents the measured value of flow resistance; Based on the predicted phase transition position obtained from the solutions of the first and second coupled models, the third relative error between the measured and predicted phase transition positions is calculated. The functional expression for calculating the third relative error is as follows:

[0066] In the formula, Indicates the third relative error. This represents the predicted value of the phase transition position. Indicates the measured value of the state transition position; If any one of the first relative error, the second relative error, and the third relative error fails to meet the pre-set application conditions for medium-deep geothermal engineering, the convective heat transfer coefficients in each heat transfer sub-model are corrected, and the boundary conditions of the second coupled model are also corrected.

[0067] By implementing the above-described embodiment of the multi-stage gravity heat pipe two-phase flow heat transfer model construction method, measured values ​​of heat transfer coefficient, flow resistance, and phase transition location are obtained based on a multi-stage gravity heat pipe simulation experiment consistent with medium-deep geothermal conditions. For example, measured data of heat transfer coefficient and flow resistance are obtained by measuring the inlet and outlet parameters of each pipe section using pressure sensors, temperature sensors, and flow meters in the simulation experimental platform. The specific spatial location of the gas-liquid two-phase flow pattern transition within the pipe is observed and recorded using a high-speed camera as measured data of the phase transition location. This ensures that subsequent error assessment has an experimental benchmark completely consistent with the model input conditions, rather than relying on empirical estimation.

[0068] The principle of substituting the predicted and measured values ​​of the heat transfer coefficient into the function expression of the first relative error is that the first relative error uses the measured value as the denominator to calculate the degree of deviation of the predicted value from the measured value. This eliminates the problem of incomparability of absolute errors under different orders of magnitude of heat transfer coefficients, making the relative error a dimensionless percentage index that can uniformly measure the accuracy of heat transfer prediction under different operating conditions and different pipe section locations.

[0069] Similarly, by substituting the predicted and measured values ​​of flow resistance into the function expression of the second relative error, the predicted deviation of flow resistance is also presented in the form of a dimensionless relative error, thus avoiding the large range of absolute pressure drop values ​​due to differences in pipe length and flow velocity, which makes it difficult to conduct a unified assessment.

[0070] Substituting the predicted and measured phase transition positions into the function expression of the third relative error, since the phase transition position itself has a clear spatial coordinate dimension and the range of change of the transition position under different operating conditions is relatively fixed, using absolute deviation rather than relative deviation can intuitively reflect the spatial distance between the predicted transition point and the actual transition point, thereby evaluating the impact of the accuracy of the flow pattern interval division on the applicability of subsequent heat transfer and resistance calculation methods.

[0071] When any of the first, second, or third relative errors fails to meet the pre-set application conditions for medium-deep geothermal engineering, the convective heat transfer coefficients in each heat transfer sub-model are corrected. For example, the least squares method is used to fit and correct the wall superheat coefficient in the nucleate boiling heat transfer sub-model and the condensate film thickness calculation coefficient in the film condensation heat transfer sub-model. Simultaneously, the boundary conditions for the formation-heat pipe bidirectional coupling are corrected, such as fine-tuning the values ​​of the formation-heat pipe contact heat transfer coefficient boundary conditions. After correction, an iterative optimization mechanism is established. The corrected model parameters are re-introduced, and error calculations are repeated based on new experimental or engineering measurement data until all prediction error indicators converge to within the allowable range for engineering applications. This ensures that the model prediction results continuously approximate the real physical process in actual engineering applications, solving the problem of poor model engineering practicality caused by the lack of systematic verification and iterative optimization mechanisms.

[0072] Preferably, when simultaneously solving the first and second coupled models, the first and second coupled models form a bidirectional coupling relationship through heat pipe heat exchange and the formation temperature field, with each model containing a series coupled structure of heat transfer sub-models and flow sub-models along the pipe section. This dual coupling characteristic makes it impossible to directly obtain a closed solution for the entire integrated model analytically. Therefore, a structured grid is used to spatially partition the computational domain of the heat pipe section and the computational domain of the formation. Based on spatial discretization, the finite volume method is used to spatially and temporally discretize the integrated model of the first and second coupled models. The characteristic of applying the conservation equation directly to each control volume using the finite volume method ensures that mass, momentum, and energy are naturally conserved at the discretization level. In the discretized algebraic equations, the pressure field and velocity field are coupled through the continuity equation. The SIMPLE algorithm is selected as the numerical solution algorithm for the model. Through iterative correction between the pressure field and velocity field, the continuity equation is gradually satisfied, achieving a stable solution to the pressure-velocity coupling problem in two-phase flow. The mass conservation residual is set to be less than... And the energy conservation residual is less than As a convergence condition, the mass and energy deviations within each control volume are compressed to a minimum level when the iteration terminates, ensuring that the final numerical solution satisfies both the fundamental physical constraints of mass conservation and energy conservation under the engineering accuracy requirements.

[0073] As described above, to verify the effectiveness of the two-phase flow heat transfer model constructed in this invention, R245fa, commonly used in medium-deep geothermal development, was selected as the working fluid, and a three-stage gravity heat pipe experimental device was designed: The evaporation section of the device has an inner diameter of 50 mm, a wall thickness of 3 mm, and an effective length of 2 m; the insulation section has an inner diameter of 50 mm, a wall thickness of 3 mm, and an effective length of 1.5 m; the condensation section has an inner diameter of 50 mm, a wall thickness of 3 mm, and an effective length of 2 m; the heat pipe wall material is 316 stainless steel; the thermal conductivity is 16.2 W / (m·K); and the working fluid filling rate is 35%.

[0074] The experimental platform simulates medium-deep geothermal conditions, with the formation environment temperature set at 150℃ and the formation environment pressure at 5MPa. Heat transfer from the formation to the evaporation section is simulated by electric heating, with a heating power range of 5-20kW. Pressure sensors, temperature sensors, and flow meters are used to measure the inlet and outlet pressures, temperatures, and working fluid flow rates of each pipe section. A high-speed camera is used to observe and record the gas-liquid two-phase flow pattern and phase transition position inside the pipe.

[0075] During the experiment, the geometric parameters, working fluid parameters, and operating condition parameters of the device were first standardized according to step one. The geometric parameters such as inner diameter and length were divided by the maximum characteristic length (5.5m), and the original values ​​of parameters such as working fluid filling rate were directly taken (already in the 0-1 range) to obtain dimensionless parameters. Following step two, by calculating the Reynolds number (range 5000-25000), Froude number (range 0.8-3.5), and Weber number (range 100-500) under different heating powers, and combining the flow pattern conversion criteria, it was determined that bubbly flow is mainly distributed in the 0-0.3m interval of the evaporation section inlet, plug flow is distributed in the 0.3-1.0m interval of the evaporation section, slug flow is distributed in the 1.0-1.8m interval of the evaporation section and the 0-0.5m interval of the adiabatic section inlet, and annular flow is distributed in the 1.8-2.0m interval of the evaporation section, the 0.5-1.5m interval of the adiabatic section, and the 0-1.0m interval of the condensation section inlet.

[0076] Based on the sub-models established in step three, in the nucleus boiling heat transfer sub-model of the evaporation section, the coupling coefficient between the wall superheat (5-15℃) and the filling rate is adjusted to make the calculated heat transfer coefficient consistent with the experimentally measured value (1200-2500W / ( Preliminary matching was performed; the friction loss in the adiabatic section was calculated using a split-phase flow model. When the mixing velocity was 1.2-3.0 m / s, the calculated friction loss was 800-3500 Pa, with a deviation from the measured value by the differential pressure sensor within 15%; the film condensation heat transfer sub-model in the condensation section considered the condensate film thickness gradually increasing from 0.2 mm at the inlet to 0.8 mm at the outlet, and the calculated condensation heat transfer coefficient was 800-1800 W / ( ·K).

[0077] Following step four, multi-stage pipe coupling calculations are performed. The gas mass flow rate (0.05-0.2 kg / s) at the outlet of the pre-evaporation section is used as the inlet condition of the adiabatic section, and the outlet pressure of the adiabatic section (4.8-4.9 MPa) is used as the inlet pressure of the condensation section. The amount of condensation flowing back from the condensation section to the evaporation section is kept in balance with the amount of evaporation in the evaporation section, thus achieving mass conservation.

[0078] In step five, based on experimentally measured temperature change data at different radial distances (0.5m, 1.0m, 1.5m) in the formation, with an initial temperature of 150℃, the temperature decreased to 145℃, 148℃, and 149℃ respectively after 100 hours of operation. The formation thermal diffusivity was calculated to be 1.2 × 10⁻⁶ using the one-dimensional unsteady-state heat conduction equation. / s, thermal conductivity is 2.5 W / (m·K), and volumetric specific heat capacity is 2.1 × J / ( The constructed formation heat conduction model (K) is fed back to the heat pipe heat transfer calculation, which reduces the calculated heat exchange value of the evaporation section by 8-12% compared with the case where formation coupling is not considered.

[0079] Step six involves dividing the computational domain using a structured mesh. The mesh size is 0.05m for phase transition regions (e.g., evaporation section 1.0-1.8m) and 0.2m for non-phase transition regions (e.g., condensation section 1.0-2.0m). After mesh independence verification, the calculated heat transfer coefficient deviation is 3.2% < 5% after mesh refinement. An explicit difference scheme and the SIMPLE algorithm are used for solving the problem. When the mass conservation residual is reduced to 8 × 10⁻⁷ and the energy conservation residual is reduced to 6 × 10⁻⁷, the solution is achieved. The model converges at that time.

[0080] Step 7: Calculate the heat transfer coefficient predicted by the model (1250-2400 W / ( By comparing the predicted heat transfer coefficient (·K), flow resistance (850-3300Pa), and phase transition location (e.g., the predicted value of the bubbly-to-slug transition point is 0.32m, and the measured value is 0.3m) with experimental data, the first relative error of the predicted heat transfer coefficient is calculated. The second relative error in flow resistance prediction is 3.5-8.2%. The third relative error in the prediction of phase transition position is 4.1-12.3%. It is 0.02-0.05m.

[0081] According to step eight, the wall superheat coefficient in the nucleate boiling heat transfer sub-model is corrected using the least squares method, with the correction factor adjusted from 1.0 to 1.08. The condensate film thickness calculation coefficient in the film condensation heat transfer sub-model is also corrected, with the correction factor adjusted from 0.95 to 1.03. Simultaneously, the boundary conditions for the formation-heat pipe contact heat transfer coefficient are fine-tuned, from 200 W / ( ·K) adjusted to 220W / ( After iterative optimization, the relative error of the heat transfer coefficient prediction was reduced to 2.1-5.8%, the relative error of the flow resistance prediction was reduced to 3.3-9.5%, and the deviation of the phase transition position prediction was reduced to 0.01-0.03m, which meets the requirements of model error for medium and deep geothermal engineering applications.

[0082] This invention also discloses a model building system applied to the above-mentioned method for building a two-phase flow heat transfer model of a multi-stage gravity heat pipe. The model building system includes: The parameter acquisition module is used to acquire the standardized basic parameters of each pipe segment based on the evaporation section, adiabatic section and condensation section that are disassembled sequentially along the multi-stage gravity heat pipe. The flow pattern classification module is used to establish the conversion criteria of multiple flow pattern categories of gas-liquid two-phase flow along the multi-stage gravity heat pipe based on the basic parameters of each pipe section, and to determine the flow pattern category of the two-phase flow at each pipe section location. The heat transfer-flow model building module is used to match and build heat transfer sub-models for the evaporation section and condensation section along the pipe according to the flow pattern of the two-phase flow at each pipe section, and to match and build flow sub-models for the adiabatic section along the pipe. The heat transfer-resistance loss calculation module is used to obtain the total heat transfer coefficient from the evaporation section to the condensation section based on the heat transfer sub-model and the basic parameters of the corresponding pipe section, and to obtain the resistance loss along the insulation section based on the flow sub-model and the basic parameters of the corresponding pipe section. The heat pipe heat transfer-flow coupling module is used to couple all heat transfer sub-models and flow sub-models in series order of each pipe segment in the spatial direction according to the total heat transfer coefficient and resistance loss, so as to obtain the first coupling model. The formation-heat pipe bidirectional coupling module is used to establish a formation heat conduction model, couple the formation heat conduction model and the first coupling model to obtain a second coupling model, and solve the first coupling model and the second coupling model simultaneously to obtain the state prediction value of the two-phase flow along the multi-stage gravity heat pipe; The two-phase flow heat transfer model establishment module is used to obtain the measured state values ​​of the two-phase flow along the path under the simulation conditions of medium-deep geothermal layers, and to correct the first coupling model and the second coupling model based on the comparison error between the measured state values ​​and the predicted state values, so as to obtain the two-phase flow heat transfer model.

[0083] The present invention also discloses a storage medium storing a computer program, which, when executed by a processor, implements the above-described method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe.

[0084] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0085] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0086] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0087] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of processing steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0088] It should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Those skilled in the art can modify the technical solutions described in the above embodiments, or make equivalent substitutions for some of the technical features; and all such modifications and substitutions should fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe, characterized in that: The method for constructing the two-phase flow heat transfer model of the multi-stage gravity heat pipe includes: Based on the evaporation section, insulation section and condensation section of the multi-stage gravity heat pipe, the standardized basic parameters of each pipe section are obtained respectively. Based on the basic parameters of each pipe section, a conversion criterion for multiple flow pattern categories of gas-liquid two-phase flow along the multi-stage gravity heat pipe is established, and the flow pattern category of two-phase flow at each pipe section location is determined. Based on the flow pattern category of the two-phase flow along the pipe section, the heat transfer coefficients of the evaporation section and the condensation section, as well as the flow coefficient of the adiabatic section, are matched and obtained, and heat transfer sub-models and flow sub-models along the pipe section and the adiabatic section are constructed. The total heat transfer coefficient from the evaporation section to the condensation section is obtained based on the heat transfer sub-model and the basic parameters of the corresponding pipe section, and the resistance loss along the adiabatic section is obtained based on the flow sub-model and the basic parameters of the corresponding pipe section. Based on the overall heat transfer coefficient and the resistance loss, all the heat transfer sub-models and the flow sub-models are coupled in series in the spatial direction of each pipe segment to obtain the first coupled model. A formation heat conduction model is established, and a second coupled model is obtained by coupling the formation heat conduction model and the first coupled model. The first coupled model and the second coupled model are solved simultaneously to obtain the predicted state values ​​of the two-phase flow along the multi-stage gravity heat pipe. The measured state values ​​of two-phase flow along the path under the simulated working conditions of medium-deep geothermal energy are obtained, and the first coupling model and the second coupling model are corrected according to the comparison error between the measured state values ​​and the predicted state values ​​to obtain the two-phase flow heat transfer model.

2. The method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe according to claim 1, characterized in that, The establishment of multiple flow pattern categories for gas-liquid two-phase flow as a transition criterion along the multi-stage gravity heat pipe, and the determination of the flow pattern category of the two-phase flow at each pipe section location, includes: The gas-liquid two-phase flow patterns of the multi-stage gravity heat pipe are classified into different flow pattern categories; Based on the temperature and pressure range of the medium-deep geothermal well, the distribution range of different flow patterns along the entire length of the multi-stage gravity heat pipe is defined; Based on the basic parameters of each pipe section, obtain the pipe section inner diameter, hydraulic diameter, two-phase mixing velocity, gas phase velocity and liquid phase density for each distribution range; Based on the obtained inner diameter of the pipe section, the hydraulic diameter, the two-phase mixing velocity, the gas phase velocity, and the liquid phase density, the Reynolds number, Froude number, and Weber number for the corresponding distribution range are obtained. Based on the correspondence between the flow pattern category and the Reynolds number, the Froude number and the Weber number within the same distribution interval, the transformation discrimination criterion is established; The Reynolds number, Froude number, and Weber number are obtained at each pipe section along the friction point, and the flow pattern category of the two-phase flow at the corresponding pipe section along the friction point is determined by the transformation discrimination criterion.

3. The method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe according to claim 1, characterized in that, The process involves matching and obtaining the heat transfer coefficients of the evaporation section and the condensation section, as well as the flow coefficient of the adiabatic section, based on the flow pattern category of the two-phase flow along each pipe section, and constructing heat transfer sub-models along the pipe sections of the evaporation section and the condensation section, and flow sub-models along the pipe sections of the adiabatic section, including: Based on the flow pattern category of the two-phase flow along the evaporation section, the corresponding heat transfer coefficient correlation is matched, and the first convective heat transfer coefficient is obtained through the matched heat transfer coefficient correlation. Based on the first convective heat transfer coefficient, a first heat transfer sub-model for nucleate boiling heat transfer is constructed using the working fluid filling rate and wall superheat. Based on the flow pattern category of the two-phase flow along the condensation section, the corresponding heat transfer coefficient correlation is matched, and the second convective heat transfer coefficient is obtained through the matched heat transfer coefficient correlation. Based on the second convective heat transfer coefficient, a second heat transfer sub-model for film condensation heat transfer is constructed by considering the variation of condensate film thickness along the path. Based on the flow pattern category of the two-phase flow along the adiabatic section, the corresponding drag coefficient correlation is matched, and the drag coefficient along the flow and the local drag coefficient are obtained through the matched drag coefficient correlation. Based on the friction coefficient and the local resistance coefficient, a two-phase flow sub-model is constructed using the phase-separated flow model as a framework.

4. The method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe according to claim 4, characterized in that, The process of obtaining the total heat transfer coefficient from the evaporation section to the condensation section based on the heat transfer sub-model and the basic parameters of the corresponding pipe section includes: Based on the basic parameters of the evaporation section and the condensation section, the heat exchange area of ​​the evaporation section, the heat exchange area of ​​the condensation section, the contact heat exchange area between the multi-stage gravity heat pipe and the ground, and the total heat exchange area of ​​the multi-stage gravity heat pipe are obtained respectively. Based on the obtained heat transfer areas, and combined with the first convective heat transfer coefficient and the second convective heat transfer coefficient, the total heat transfer coefficient is calculated. The functional expression for calculating the total heat transfer coefficient is as follows: In the formula, Indicates the overall heat transfer coefficient. This represents the total heat exchange area of ​​the multi-stage gravity heat pipe. Indicates the first convective heat transfer coefficient. This indicates the heat transfer area of ​​the evaporation section. This indicates the thermal conductivity of the wall material of a multi-stage gravity heat pipe. This represents the average heat transfer area of ​​the wall surface of a multi-stage gravity heat pipe. This indicates the wall thickness of a multi-stage gravity heat pipe. This represents the second convective heat transfer coefficient. This indicates the heat transfer area of ​​the condenser section. Indicates the third convective heat transfer coefficient. This indicates the contact heat exchange area between the multi-stage gravity heat pipe and the ground.

5. The method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe according to claim 3, characterized in that, The step of obtaining the friction loss along the insulation section based on the flow sub-model and the basic parameters of the corresponding pipe section includes: Based on the basic parameters of the insulation section, the effective length of the insulation section, the hydraulic diameter of the multi-stage gravity heat pipe, the gas-liquid two-phase mixing density, and the gas-liquid two-phase mixing velocity are obtained respectively. Based on the effective length, the hydraulic diameter, the gas-liquid two-phase mixing density, and the gas-liquid two-phase mixing velocity, combined with the friction coefficient and the local resistance coefficient, the resistance loss is calculated. The functional expression for calculating the resistance loss is as follows: In the formula, Indicates resistance loss. Indicates the friction coefficient. Indicates the effective length. Indicates the hydraulic diameter. This represents the density of a gas-liquid mixture. Indicates the flow rate of the gas-liquid two-phase mixture. Represents the local drag coefficient. This represents the sum of the local resistance coefficients at various locations along the insulation section.

6. The method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe according to claim 1, characterized in that, The first coupled model is obtained by coupling all the heat transfer sub-models and the flow sub-models in series in the spatial direction according to the total heat transfer coefficient and the resistance loss, resulting in a first coupled model, including: Based on the spatial distribution of each pipe section, the spatial series sequence of the evaporation section, the insulation section, and the condensation section is determined; The heat transfer of the two-phase flow from the evaporation section to the condensation section is determined based on the overall heat transfer coefficient, and the heat transfer between each pipe section is constrained by the principle of heat conservation. The superposition loss of the two-phase flow along the insulation section is determined based on the resistance loss, and the working fluid flow between each pipe section is continuously constrained by the mass flow rate. Based on the spatial series sequence, the working fluid outlet phase and temperature of the upstream pipe section are used as the inlet boundary conditions of the downstream pipe section. All the heat transfer sub-models and the flow sub-models are coupled to obtain the first coupled model.

7. The method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe according to claim 1, characterized in that, The establishment of the formation heat conduction model includes: Acquire a dataset of temperature data that varies with time at different distances along the radial direction of the multi-stage gravity heat pipe; Based on the radial thermal conductivity of the formation along the multi-stage gravity heat pipes, a one-dimensional unsteady-state heat conduction equation is constructed with formation temperature as the dependent variable and time and radial distance as the independent variables. The functional expression of the one-dimensional unsteady-state heat conduction equation is as follows: In the formula, Indicates formation temperature. Indicates time, Indicates the thermal diffusivity of the formation. This indicates the radial distance of the strata along the multi-stage gravity heat pipe; Substitute the temperature dataset into the one-dimensional unsteady heat conduction equation, and use the least squares method to invert the one-dimensional unsteady heat conduction equation to obtain the formation thermal conductivity, volumetric specific heat capacity and formation thermal diffusivity, respectively. Based on the formation thermal conductivity, the volumetric specific heat capacity, and the formation thermal diffusivity, the formation thermal conduction model is constructed using the one-dimensional unsteady-state heat conduction equation as the governing equation.

8. The method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe according to claim 1, characterized in that, The step of obtaining the measured state values ​​of the two-phase flow along the path under the simulated working conditions of medium-deep geothermal energy, and correcting the first coupling model and the second coupling model based on the comparison error between the measured state values ​​and the predicted state values, includes: Based on the multi-stage gravity heat pipe simulation experiment consistent with the medium-deep geothermal conditions, the measured values ​​of heat transfer coefficient, flow resistance and phase transition position were obtained. Based on the predicted heat transfer coefficient values ​​obtained from the solution results of the first coupled model and the second coupled model, the first relative error between the measured heat transfer coefficient value and the predicted heat transfer coefficient value is calculated. The functional expression for calculating the first relative error is as follows: In the formula, Indicates the first relative error. This represents the predicted value of the heat transfer coefficient. This represents the measured value of the heat transfer coefficient; Based on the predicted flow resistance values ​​obtained from the solution results of the first coupled model and the second coupled model, a second relative error between the measured flow resistance value and the predicted flow resistance value is calculated. The functional expression for calculating the second relative error is as follows: In the formula, This indicates the second relative error. This represents the predicted value of flow resistance. This represents the measured value of flow resistance; Based on the predicted phase transition position obtained from the solution results of the first coupling model and the second coupling model, a third relative error between the measured phase transition position and the predicted phase transition position is calculated. The functional expression for calculating the third relative error is as follows: In the formula, Indicates the third relative error. This represents the predicted value of the phase transition position. Indicates the measured value of the state transition position; If any one of the first relative error, the second relative error, and the third relative error does not meet the preset application conditions for medium-deep geothermal engineering, the convective heat transfer coefficient in each of the heat transfer sub-models is corrected, and the boundary conditions of the second coupling model are also corrected.

9. A model building system, applied to the method for building a two-phase flow heat transfer model of a multi-stage gravity heat pipe as described in any one of claims 1-8, characterized in that, The model building system includes: The parameter acquisition module is used to acquire the standardized basic parameters of each pipe segment based on the evaporation section, adiabatic section and condensation section that are disassembled sequentially along the multi-stage gravity heat pipe. The flow pattern classification module is used to establish a conversion criteria for multiple flow pattern classifications of gas-liquid two-phase flow along the multi-stage gravity heat pipe based on the basic parameters of each pipe section, and to determine the flow pattern classification of the two-phase flow at each pipe section location. The heat transfer-flow model construction module is used to match and construct heat transfer sub-models for the evaporation section and the condensation section along the pipe according to the flow pattern category of the two-phase flow at each pipe section, and to match and construct flow sub-models for the adiabatic section along the pipe. The heat transfer-resistance loss calculation module is used to obtain the total heat transfer coefficient from the evaporation section to the condensation section based on the heat transfer sub-model and the basic parameters of the corresponding pipe section, and to obtain the resistance loss along the adiabatic section based on the flow sub-model and the basic parameters of the corresponding pipe section. The heat pipe heat transfer-flow coupling module is used to couple all the heat transfer sub-models and the flow sub-models in series order of each pipe segment in the spatial direction according to the total heat transfer coefficient and the resistance loss, so as to obtain the first coupling model. The formation-heat pipe bidirectional coupling module is used to establish a formation heat conduction model, couple the formation heat conduction model with the first coupling model to obtain a second coupling model, and solve the first coupling model and the second coupling model simultaneously to obtain the state prediction value of the two-phase flow along the multi-stage gravity heat pipe; The two-phase flow heat transfer model establishment module is used to obtain the measured state values ​​of the two-phase flow along the path under the simulation conditions of medium-deep geothermal layers, and to correct the first coupling model and the second coupling model based on the comparison error between the measured state values ​​and the predicted state values, so as to obtain the two-phase flow heat transfer model.

10. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for constructing a two-phase flow heat transfer model for a multi-stage gravity heat pipe as described in any one of claims 1-8.

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