Estimation method of heat extraction capacity of coaxial shell-and-tube heat exchanger in deep geothermal well

Abstract

The present invention belongs to the field of geothermal energy mining technology, and specifically discloses a method for estimating the heat extraction capacity of a coaxial sleeve heat exchanger in a deep geothermal well. It is used to solve the problem that the existing method has a large amount of calculation and does not take into account the complex geological conditions in the deep layer and the economic efficiency of the selection of thermal insulation inner tube materials. The present invention constructs a transient heat exchange model of a coaxial sleeve heat exchanger, comprehensively considering the heterogeneity of the formation under complex deep geological conditions, and the influence of seepage on the heat extraction capacity of the geothermal well and the heat transfer of the formation under the distribution of various permeabilities and porosities in the underground seepage layer, and considering the non-uniformity of the geothermal gradient and the economic efficiency of the selection of thermal insulation inner tube materials at different depths, the heat exchange process between the inner tube fluid, the thermal insulation inner tube, the outer tube fluid, the external casing, the cementing cement, and the rock formation is theoretically and modeled based on the finite element method. The present invention improves the calculation efficiency while ensuring the calculation accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of geothermal energy exploitation, and in particular relates to a method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger in a deep geothermal well. Background Art

[0002] The use of coaxial shell-and-tube heat exchangers to extract geothermal energy has the advantages of compact structure, small footprint, high heat exchange efficiency, "taking heat without taking water", and the ability to solve problems such as pipe scaling, corrosion, and groundwater recharge. It meets the application scenarios of projects that do not have hydrothermal extraction and recharge conditions or cannot arrange large-scale shallow buried pipe groups. However, due to the high cost of drilling geothermal wells, it is difficult to conduct experimental research, and numerical simulation has become the main research method.

[0003] However, the existing numerical simulation research on coaxial shell-and-tube heat exchangers is mainly based on the assumption that the stratum is a single structure, and a homogeneous heat transfer model is established. The entire stratum is assumed to have the same thermal conductivity, density and heat capacity. Only heat conduction processes exist in the stratum, and the underground porous seepage heat transfer process is ignored. The actual depth of geothermal wells is as high as several thousand meters. The stratum is a composite stratum, which covers various types such as clay, gravel, coarse sandstone, mudstone, siltstone and granite. Different types of strata have different thermophysical parameters and geothermal gradients. There is groundwater seepage in the stratum around the geothermal well, and the permeability and porosity of the same seepage layer are different at different locations. In the initial section of the geothermal well, the required thermal insulation performance of the inner pipe is required to be high; as the depth of the geothermal well increases, the temperature difference of the fluid in the inner and outer pipes of the geothermal well gradually decreases, and the required thermal insulation performance of the inner pipe is required to be reduced. The cost of the pipe is directly related to the thermal insulation performance, and the pipe with high thermal insulation performance is more expensive. Therefore, the segmented setting of the thermal insulation inner pipe can improve the economic efficiency of geothermal mining.

[0004] In addition, the traditional three-dimensional geothermal well model has a complex modeling process, a large number of grids, and a long calculation time, which makes it difficult to meet the urgent needs of actual geothermal engineering.

[0005] In summary, in the existing numerical simulation of coaxial shell-and-tube heat exchangers, there are problems of large amount of calculation, and the problem of not taking into account the deep and complex geological conditions and the economic efficiency of the material selection of the insulation inner tube. Summary of the invention

[0006] The purpose of the present invention is to provide a method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger in a deep geothermal well, which effectively solves the problem that the existing method has a large amount of calculation and does not take into account the complex geological conditions in the deep layer and the economic efficiency of the material selection of the thermal insulation inner tube.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for estimating the heat extraction capacity of a coaxial shell and tube heat exchanger in a deep geothermal well, constructing a transient heat exchange model of a coaxial shell and tube heat exchanger, wherein a one-dimensional model is constructed for the geothermal well part, and a three-dimensional model is constructed for the formation part, comprehensively considering the heterogeneity of complex deep geological formations and the distribution of various permeabilities and porosities in the underground seepage layer, the influence of seepage on the heat extraction capacity of the geothermal well and the heat transfer of the formation, and considering the non-uniformity of the geothermal gradient and the economic efficiency of the selection of the insulation inner pipe at different depths, based on the finite element method, the heat exchange process between the inner pipe fluid, the insulation inner pipe, the outer pipe fluid, the external casing, the cementing cement, and the rock and soil is modeled and analyzed, including the initial condition and boundary condition setting part and the mathematical calculation part of the heat exchange process. The model can be used to quickly estimate the heat extraction capacity of the coaxial shell and tube heat exchanger in the deep geothermal well and the temperature change of the formation.

[0008] Furthermore, the initial condition and boundary condition setting part includes: setting of initial formation temperature, setting of initial cement temperature, setting of initial temperature of fluid in geothermal well, setting of fluid inlet temperature in geothermal well, and setting of surface, bottom and side temperature of formation.

[0009] Among them, the initial temperature of the formation is determined by the initial geothermal gradient, and the initial temperature of the cementing cement and the fluid in the geothermal well both adopt the initial temperature of the formation at the same depth.

[0010] The formation surface temperature adopts a constant temperature boundary condition, and the atmospheric temperature is taken as the first type of boundary condition; the formation bottom temperature has a constant heat flux density, which is used as the second type of boundary condition; the formation side temperature adopts a constant temperature boundary condition, and the initial formation temperature is taken as the first type of boundary condition; the fluid inlet temperature in the geothermal well adopts a constant injection temperature as the first type of boundary condition.

[0011] Furthermore, for deep coaxial shell-and-tube heat exchangers under complex deep geological conditions, the depth of geothermal wells can reach several thousand meters. The bottom of the formation forms a geothermal gradient due to the existence of geothermal heat flow, and the formation is divided into Each part has different thermal conductivity and geothermal gradient. According to the geothermal gradient, the initial temperature distribution of the formation is: , , where represents the surface temperature, in °C; Represents the temperature distribution of the first layer along the depth direction, in °C; Represents the temperature rise gradient of the first layer, in °C / m; Represents the thickness of the first layer of rock and soil, in m; Representative The temperature distribution of the stratum along the depth direction, in °C; Representative The temperature distribution of the stratum along the depth direction, in °C; Representative The temperature rise gradient of the stratum, in °C / m; Representative The thickness of the rock and soil layer, in m.

[0012] Furthermore, a method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger for a deep geothermal well includes the following steps: (1) When the coaxial shell-and-tube heat exchanger is working, cold fluid is injected downward into the geothermal well along the annulus area formed between the outer shell and the insulating inner tube, and there are two forms of heat exchange: one is heat conduction and heat convection of the fluid along the axial direction of the geothermal well, and the other is heat transfer by convection between the outer tube wall and the formation and by convection between the inner tube wall and the inner tube fluid along the radial direction of the geothermal well.

[0013] When the working fluid flows to the bottom of the geothermal well, the flow direction is reversed, and the hot fluid flows upward along the inner tube. There are also two forms of heat exchange: one is heat conduction and heat convection along the axial direction of the geothermal well, and the other is convection heat exchange between the inner tube wall and the outer tube fluid along the radial direction of the geothermal well.

[0014] By incorporating the convective heat transfer between the fluid and the wall into the mathematical equation of axial heat transfer as a source term and simplifying it to the heat transfer between one-dimensional line elements, the number of grids when discretizing the geothermal well area is greatly reduced, thus speeding up the calculation.

[0015] A three-dimensional model is constructed for the formation part, and heat transfer is divided into two forms according to whether there is a seepage layer: when there is no seepage, the heat transfer form is pure heat conduction; when there is seepage, the heat transfer form is the simultaneous action of heat conduction and heat convection. After clarifying the above flow and heat transfer processes, a mathematical expression for the energy change of each control body is proposed.

[0016] (2) By incorporating the convective heat transfer between the fluid and the wall into the mathematical equation of axial heat transfer as a source term, it is simplified to the heat transfer between one-dimensional line elements. The energy balance equation of the fluid axial direction is: , where is the fluid density in kg / m 3 ; is the cross-sectional area of ​​the inner tube, in m 2 ; is the constant pressure specific heat capacity of the fluid, in kJ / (kg·℃); is the average flow velocity along the well axis, in m / s; is the Hamiltonian operator, is temperature, unit is ℃; For time, is the thermal conductivity of the pipe, unit: W / (m·℃); is the friction factor (related to the Reynolds number, pipe wall roughness, and pipe shape and size); is the inner diameter of the pipe, in m; It is the heat transfer of fluid through the tube wall, in J / (m·s).

[0017] The radial convection heat transfer equation of the fluid is: , where is the surface heat transfer coefficient, unit is W / (m 2 ℃); is the control body temperature outside the pipe wall, in °C; is the fluid temperature in the geothermal well, unit: °C.

[0018] For fluids transferring heat through the inner tube wall: , where is the inner diameter of the inner tube, in m; is the outer diameter of the inner tube, in m; is the surface heat transfer coefficient of the inner tube fluid, unit W / (m 2 ℃); is the surface heat transfer coefficient of the outer tube fluid, unit W / (m 2 ℃); is the thermal conductivity of the inner tube, unit is W / (m·℃).

[0019] (3) There are two forms of heat transfer in the formation. When there is seepage, the heat transfer form is heat conduction and heat convection acting simultaneously. Darcy's law is used to describe the fluid flow in the saturated seepage layer: , where is the porosity of rock and soil, For time, is the Hamiltonian operator, is the density of the fluid, in kg / m 3 ; is the Darcy speed in m / s.

[0020] For single-phase flow, considering the gravity effect, the Darcy velocity is expressed as: , where is the permeability, unit is mD; is the dynamic viscosity, unit is N·s / m 2 ; is the water pressure, unit is Pa; is the acceleration due to gravity, in m / s 2 ; is the water level, in m.

[0021] The energy conservation equation for saturated soil is: , where is the constant pressure specific heat capacity of the fluid, in kJ / (kg·℃); is the heat source, unit is kJ / (m 3 ·s); and are the effective volume heat capacity and effective thermal conductivity of rock and soil respectively.

[0022] , where is the density of rock and soil, in kg / m 3 ; It is the specific heat capacity of rock and soil at constant pressure, with the unit of kJ / (kg·℃).

[0023] , where is the thermal conductivity of rock and soil, unit: W / (m·℃); It is the thermal conductivity of the fluid, with the unit of W / (m·℃).

[0024] (4) The thermal conductivity of the heat-insulating inner tube in step (2) is set in sections. The heat-insulating inner tube is divided into sections according to the different heat-insulating properties required at different depths. There are pipe sections, and materials with different thermal conductivity are selected for each pipe section.

[0025] Generally, the thermal conductivity of the insulation inner pipe is proportional to the depth of the geothermal well, and inversely proportional to the cost of the insulation material, that is, the deeper the geothermal well, the greater the thermal conductivity of the required pipe and the lower the cost.

[0026] (5) For the porosity and permeability of the seepage layer rock and soil in step (3), a horizontal non-uniform distribution is adopted to divide the seepage layer horizontally into The permeability and porosity of rock and soil in different regions are different. Generally, the permeability increases with the increase of porosity.

[0027] (6) For the control equations and control volume settings in steps (2) to (5), which involve the one-dimensional transient heat transfer process of the geothermal well part and the three-dimensional transient heat transfer process of the formation part, the finite element method is used to discretize the above calculation area and control equations and perform numerical simulation.

[0028] (7) After completing the model meshing, taking the geothermal well as an example, based on the energy conservation equation, its heat conduction differential equation is discretized to obtain the discrete equation matrix expression of each node of the finite element method. By using algebraic matrix inversion, the real-time temperature distribution of the fluid in the geothermal well can be quickly obtained.

[0029] Furthermore, the axial and radial transient heat transfer processes of the coaxial shell-and-tube heat exchanger and its surrounding formations were modeled and analyzed, and the following assumptions were adopted: at the initial moment, the geothermal well is filled with fluid, and the temperature is the same as the initial temperature of the rock and soil at the same depth; the flow rate and temperature of the fluid in the geothermal well are uniform and consistent on the same cross-section; the fluid in the geothermal well will not undergo phase change within the design temperature and pressure range; the rock and soil properties of the formation are not affected by temperature, pressure and groundwater flow, that is, the fracturing, deposition and dissolution processes caused by temperature and pressure changes are not considered.

[0030] Furthermore, after the establishment of the transient heat transfer model of the coaxial shell and tube heat exchanger is completed, when the transient heat transfer model of the coaxial shell and tube heat exchanger is used, the parameters that need to be set in the formation part include the thermal conductivity and geothermal gradient of each formation, the permeability and porosity of each area of ​​the underground seepage layer, and the horizontal seepage velocity; the parameters that need to be set in the geothermal well part include the fluid injection temperature, the injection volume flow rate, the thermal conductivity of the insulation inner pipe material of each pipe section, and the operating time of the coaxial shell and tube heat exchanger. The model can be used to calculate the outlet water temperature, heat extraction, and real-time temperature changes of the geothermal well, providing a scientific, accurate and efficient method for engineering exploitation of high-grade geothermal energy under complex deep geological conditions.

[0031] Compared with the prior art, the beneficial technical effects of the present invention are as follows: the present invention focuses on the coaxial shell-and-tube heat exchanger of deep geothermal wells, analyzes the basic theory of heat exchange process under the condition of considering complex geological conditions and the economic efficiency of material selection of thermal insulation inner tubes, and based on a pseudo three-dimensional wellbore model, incorporates the convective heat exchange process between the fluid and the wall in the geothermal well into the mathematical equation of fluid axial heat transfer, and uses one-dimensional line elements to construct the inner and outer tubes of the geothermal well, reducing the need for three-dimensional discretization of the geothermal well part, thereby significantly reducing the grid size; and in order to comprehensively consider the complex geological structure in the deep strata and the influence of groundwater seepage on the heat exchange performance of the geothermal well, a three-dimensional model is constructed for the stratum part. Thus, while ensuring the calculation accuracy, the number of grids is greatly reduced and the calculation speed is accelerated. The transient heat exchange model of the coaxial shell-and-tube heat exchanger constructed by the present invention can calculate the outlet water temperature, heat extraction and real-time temperature changes of the stratum of the geothermal well, providing a scientific, accurate and efficient method for engineering exploitation of high-grade geothermal energy under complex deep geological conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the formation stratification and inner tube segmentation of a coaxial shell-and-tube heat exchanger in a deep geothermal well, wherein the hollow arrows indicate the flow direction of the fluid.

[0033] Figure 2 It is a schematic diagram of the one-dimensional geothermal well and three-dimensional stratum grid division at the wellhead of the present invention.

[0034] Explanation of the reference numerals: external casing-1; thermal insulation inner pipe-2; composite formation-3; cementing cement-4; one-dimensional inner pipe-5; one-dimensional outer pipe-6; three-dimensional annular formation-7; underground seepage layer-8. DETAILED DESCRIPTION

[0035] Example 1: A method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger in a deep geothermal well, constructing a transient heat transfer model of a coaxial shell-and-tube heat exchanger, wherein Figure 1 As shown, the entire calculation area consists of two fluid domains and four solid domains. During operation, the cold fluid is injected into the geothermal well from the annular area formed between the outer casing 1 and the insulation inner tube 2, and heat is exchanged with the surrounding composite formation 3. When the fluid flows to the bottom of the geothermal well, the flow direction is reversed, and the hot fluid flows out of the ground from the middle circular inner tube. In order to consider the heterogeneity of the thermophysical parameters of complex deep geological formations and the heterogeneity of geothermal gradients, the composite formation 3 is divided into n layers from top to bottom. In order to consider the economic efficiency of the material selection of the insulation inner tube 2 at different depths, the insulation inner tube 2 is divided into L pipe sections from top to bottom. Among them, in order to consider the influence of seepage on the heat extraction capacity of the geothermal well and the heat transfer of the formation under the condition that there are multiple different permeabilities and porosities in the underground seepage layer 8, the underground seepage layer 8 is divided into m regions in the horizontal area, each region has different porosity and permeability. Based on the finite element method, the heat transfer process between the inner tube fluid, the insulation inner tube 2, the outer tube fluid, the outer casing 1, the cementing cement 4, and the rock and soil is modeled and analyzed. Figure 2 As shown, the one-dimensional inner tube 5 and one-dimensional outer tube 6 of the geothermal well are constructed respectively. When calculating the inner tube, the temperature of the outer tube is projected onto the inner tube as the external temperature of the inner tube. When calculating the formation, the temperature of the one-dimensional outer tube 6 is projected onto the three-dimensional annular formation 7 as the calculated temperature of the formation. It also includes the initial condition and boundary condition setting part and the heat exchange process mathematical calculation part. The model can be used to quickly estimate the heat extraction capacity of the coaxial shell-and-tube heat exchanger in the deep geothermal well and the temperature change of the formation.

[0036] The initial condition and boundary condition setting part includes: the setting of the initial temperature of the formation, the setting of the initial temperature of the cementing cement 4, the setting of the initial temperature of the fluid in the geothermal well, the setting of the inlet temperature of the fluid in the geothermal well, and the setting of the surface, bottom and side temperatures of the formation.

[0037] The initial temperature of the formation is determined by the initial geothermal gradient, and the initial temperatures of the cementing cement 4 and the fluid in the geothermal well are both based on the initial temperature of the formation at the same depth.

[0038] The formation surface temperature adopts a constant temperature boundary condition, and the atmospheric temperature is taken as the first type of boundary condition; the formation bottom temperature has a constant heat flux density, which is used as the second type of boundary condition; the formation side temperature adopts a constant temperature boundary condition, and the initial formation temperature is taken as the first type of boundary condition; the fluid inlet temperature in the geothermal well adopts a constant injection temperature as the first type of boundary condition.

[0039] For deep coaxial tube heat exchangers under complex deep geological conditions, the depth of geothermal wells can reach thousands of meters. The bottom of the formation forms a geothermal gradient due to the existence of geothermal heat flow, and the formation is divided into Each part has different thermal conductivity and geothermal gradient. According to the geothermal gradient, the initial temperature distribution of the formation is: , , , , where represents the surface temperature, in °C; Represents the temperature distribution of the first layer along the depth direction, in °C; Represents the temperature rise gradient of the first layer, in °C / m; Represents the thickness of the first layer of rock and soil, in m; Represents the temperature distribution of the second layer along the depth direction, in °C; Represents the temperature rise gradient of the second layer, in °C / m; Represents the thickness of the second layer of rock and soil, in m; represents the temperature distribution of the third stratum along the depth direction, in °C; Represents the temperature rise gradient of the third stratum, in °C / m; represents the thickness of the third layer of rock and soil, in m; Representative The temperature distribution of the stratum along the depth direction, in °C; Representative The temperature distribution of the stratum along the depth direction, in °C; Representative The temperature rise gradient of the stratum, in °C / m; Representative The thickness of the rock and soil layer, in m.

[0040] The method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger in a deep geothermal well includes the following steps: (1) When the coaxial shell-and-tube heat exchanger is working, the cold fluid is injected downward into the geothermal well along the annulus area formed between the outer shell 1 and the insulating inner tube 2, and there are two forms of heat exchange: one is heat conduction and heat convection of the fluid along the axial direction of the geothermal well, and the other is heat convection between the outer tube wall and the formation and between the inner tube wall and the inner tube fluid along the radial direction of the geothermal well.

[0041] When the working fluid flows to the bottom of the geothermal well, the flow direction is reversed, and the hot fluid flows upward along the inner tube. There are also two forms of heat exchange: one is heat conduction and heat convection along the axial direction of the geothermal well, and the other is convection heat exchange between the inner tube wall and the outer tube fluid along the radial direction of the geothermal well.

[0042] By incorporating the convective heat transfer between the fluid and the wall into the mathematical equation of axial heat transfer as a source term and simplifying it to the heat transfer between one-dimensional line elements, the number of grids when discretizing the geothermal well area is greatly reduced, thus speeding up the calculation.

[0043] A three-dimensional model is constructed for the formation part. There are two forms of heat transfer: when there is no seepage, the heat transfer form is pure heat conduction; when there is seepage, the heat transfer form is the simultaneous action of heat conduction and heat convection. After clarifying the above flow and heat transfer processes, a mathematical expression for the energy change of each control body is proposed.

[0044] (2) By incorporating the convective heat transfer between the fluid and the wall into the mathematical equation of axial heat transfer as a source term, it is simplified to the heat transfer between one-dimensional line elements. The energy balance equation of the fluid axial direction is: , where is the fluid density in kg / m 3 ; is the cross-sectional area of ​​the inner tube, in m 2 ; is the constant pressure specific heat capacity of the fluid, in kJ / (kg·℃); is the average flow velocity along the well axis, in m / s; is the Hamiltonian operator, is temperature, unit is ℃; For time, is the thermal conductivity of the pipe, unit: W / (m·℃); is the friction factor (related to the Reynolds number, pipe wall roughness, and pipe shape and size); is the inner diameter of the pipe, in m; It is the heat transfer of fluid through the tube wall, in J / (m·s).

[0045] The radial convection heat transfer equation of the fluid is: , where is the surface heat transfer coefficient, unit is W / (m 2 ℃); is the control body temperature outside the pipe wall, in °C; is the fluid temperature in the geothermal well, unit: °C.

[0046] For fluids transferring heat through the inner tube wall: , where is the inner diameter of the inner tube, in m; is the outer diameter of the inner tube, in m; is the surface heat transfer coefficient of the inner tube fluid, unit W / (m 2 ℃); is the surface heat transfer coefficient of the outer tube fluid, unit W / (m 2 ℃); is the thermal conductivity of the inner tube, unit is W / (m·℃).

[0047] (3) There are two forms of heat transfer in the formation. When there is seepage, the heat transfer form is heat conduction and heat convection acting simultaneously. Darcy's law is used to describe the fluid flow in the saturated seepage layer: , where is the porosity of rock and soil, For time, is the Hamiltonian operator, is the density of the fluid, in kg / m 3 ; is the Darcy speed in m / s.

[0048] For single-phase flow, considering the gravity effect, the Darcy velocity is expressed as: , where is the permeability, unit is mD; is the dynamic viscosity, unit is N·s / m 2 ; is the water pressure, unit is Pa; is the acceleration due to gravity, in m / s 2 ; is the water level, in m.

[0049] The energy conservation equation for saturated soil is: , where is the constant pressure specific heat capacity of the fluid, in kJ / (kg·℃); is the heat source, unit is kJ / (m 3 ·s); and are the effective volume heat capacity and effective thermal conductivity of rock and soil respectively.

[0050] , where is the density of rock and soil, in kg / m 3 ; It is the specific heat capacity of rock and soil at constant pressure, with the unit of kJ / (kg·℃).

[0051] , where is the thermal conductivity of rock and soil, unit: W / (m·℃); It is the thermal conductivity of the fluid, with the unit of W / (m·℃).

[0052] (4) The thermal conductivity of the heat-insulating inner tube 2 in step (2) is set in sections. According to the different heat-insulating properties of the heat-insulating inner tube 2 required at different depths, the heat-insulating inner tube 2 is divided into There are pipe sections, and materials with different thermal conductivity are selected for each pipe section.

[0053] Generally, the thermal conductivity of the insulating inner tube 2 is proportional to the depth of the geothermal well, and inversely proportional to the cost of the insulating material, that is, the deeper the geothermal well, the greater the required thermal conductivity of the tube and the lower the cost.

[0054] (5) For the porosity and permeability of the seepage layer rock and soil in step (3), a horizontal non-uniform distribution is adopted to divide the seepage layer horizontally into The permeability and porosity of rock and soil in different regions are different. Generally, the permeability increases with the increase of porosity.

[0055] (6) For the control equations and control volume settings in steps (2) to (5), which involve the one-dimensional transient heat transfer process of the geothermal well part and the three-dimensional transient heat transfer process of the formation part, the finite element method is used to discretize the above calculation area and control equations and perform numerical simulation.

[0056] (7) After completing the model meshing, taking the geothermal well as an example, based on the energy conservation equation, its heat conduction differential equation is discretized to obtain the discrete equation matrix expression of each node of the finite element method. By using algebraic matrix inversion, the real-time temperature distribution of the fluid in the geothermal well can be quickly obtained.

[0057] The transient heat transfer process of the coaxial shell-and-tube heat exchanger and its surrounding strata in the axial and radial directions was modeled and analyzed, and the following assumptions were adopted: at the initial moment, the geothermal well is filled with fluid, and the temperature is the same as the initial temperature of the rock and soil at the same depth; the flow rate and temperature of the fluid in the geothermal well are uniform and consistent on the same cross-section; the fluid in the geothermal well will not undergo phase change within the design temperature and pressure range; the rock and soil properties of the strata are not affected by temperature, pressure and groundwater flow, that is, the fracturing, deposition and dissolution processes caused by temperature and pressure changes are not considered.

[0058] After the establishment of the transient heat transfer model of the coaxial shell and tube heat exchanger is completed, when the transient heat transfer model of the coaxial shell and tube heat exchanger is used, the parameters that need to be set in the formation part include the thermal conductivity and geothermal gradient of each formation, the permeability and porosity of each area of ​​the underground seepage layer 8, and the horizontal seepage velocity; the parameters that need to be set in the geothermal well part include the fluid injection temperature, the injection volume flow rate, the thermal conductivity of the insulation inner tube 2 of each pipe section, and the operating time of the coaxial shell and tube heat exchanger. The model can be used to calculate the outlet water temperature, heat extraction and real-time temperature changes of the geothermal well, which provides a scientific, accurate and efficient method for engineering exploitation of high-grade geothermal energy under complex deep geological conditions.

[0059] In this embodiment, if Figure 1 In the coaxial shell-and-tube heat exchanger of the deep geothermal well shown in the figure, the composite formation 3 is layered in the vertical direction (the 1st to the nth layer); the seepage layer is divided into different regions in the horizontal direction (regions 1 to m), and there is horizontal seepage; the geothermal well partial insulation inner pipe 2 is divided into pipe sections 1 to L along the axial direction.

[0060] By adopting the deep complex geological conditions and the setting of the insulation inner tube 2 segmentation conditions of this embodiment, a coaxial sleeve heat exchanger in a depression area of ​​a certain place was numerically simulated using COMSOL finite element software to obtain the outlet water temperature of the geothermal well at different times. The relevant parameters of the deep geothermal well coaxial sleeve heat exchanger of this embodiment are shown in Table 1, the relevant parameters of the composite formation 3 stratification are shown in Table 2, the relevant parameters of the underground seepage layer 8 partition are shown in Table 3, and the relevant parameters of the insulation inner tube 2 segmentation are shown in Table 4.

[0061] Table 1 Related parameters of the coaxial shell-and-tube heat exchanger for deep geothermal wells in Example 1

[0062]

[0063] Table 2 Parameters related to the three layers of composite strata

[0064]

[0065] Table 3 Related parameters of 8 zones of underground vadose layer

[0066]

[0067] Table 4 Parameters of insulation inner pipe 2 sections

[0068]

[0069] It is known that the length of the coaxial shell-and-tube heat exchanger of the deep geothermal well in this embodiment is 2500 m. When dividing the grid, the geothermal well is divided into 250 sections along the axial direction, that is, each section is 5 m long.

[0070] The total simulation duration is 120 days (one heating cycle), and the maximum solution time step is set to 1 day.

[0071] At the initial moment, the initial temperatures of the fluids in the inner and outer tubes and the formation are all functions of depth, and the geothermal gradients are different in different formations: , , , , where Represents the temperature distribution of the fourth layer along the depth direction, Represents the thickness of the fourth layer of rock and soil.

[0072] Based on the initial moment The temperature field of the internal and external fluids is solved by an iterative method based on Gaussian elimination to calculate the discrete equations at the next moment. The temperature of the fluid in each section of the inner and outer tubes, and so on, until the last moment is calculated The temperature of the fluid in each section is calculated to complete the calculation of the fluid temperature field.

[0073] The present invention focuses on deep coaxial shell-and-tube heat exchangers, analyzes the basic theory of the heat exchange process under the conditions of complex geological conditions and the economical selection of the thermal insulation inner tube 2, and based on a pseudo three-dimensional wellbore model, incorporates the convective heat transfer process between the fluid and the wall in the geothermal well into the mathematical equation of the axial heat transfer of the fluid, and uses one-dimensional line elements to construct the inner and outer tubes of the geothermal well, reducing the need for three-dimensional discretization of the geothermal well part, thereby significantly reducing the grid size, and in order to comprehensively consider the complex geological structure in the deep strata and the influence of groundwater seepage on the heat exchange performance of the geothermal well, a three-dimensional model is constructed for the stratum part, which greatly reduces the number of grids and speeds up the calculation while ensuring the calculation accuracy.

[0074] After the deep coaxial shell and tube heat exchanger model is established, when using this model, the parameters that need to be set in the formation part include the thermal conductivity and geothermal gradient of different formations, the permeability and porosity of different areas of the underground seepage layer 8, and the horizontal seepage velocity; the parameters that need to be set in the geothermal well part include the fluid injection temperature, the injection volume flow rate, the thermal conductivity of the insulation inner pipe 2 of different pipe sections, and the operation time of the coaxial shell and tube heat exchanger. The model can be used to calculate the outlet water temperature, heat extraction and real-time temperature changes of the geothermal well, which provides a scientific, accurate and efficient method for engineering exploitation of high-grade geothermal energy under complex deep geological conditions.

[0075] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger in a deep geothermal well, characterized in that: Construct a transient heat transfer model of a coaxial shell-and-tube heat exchanger, in which a one-dimensional model is constructed for the geothermal well part and a three-dimensional model is constructed for the formation part. Comprehensive consideration is given to the heterogeneity of complex deep geological formations and the distribution of various permeabilities and porosities in the underground seepage layer, the effect of seepage on the heat extraction capacity of the geothermal well and the heat transfer of the formation. In addition, the non-uniformity of the geothermal gradient and the economic efficiency of the selection of the insulation inner tube at different depths are taken into account. Based on the finite element method, the heat transfer process between the inner tube fluid, the insulation inner tube, the outer tube fluid, the external casing, the cementing cement, and the rock and soil is modeled and analyzed, including the initial condition and boundary condition setting part and the mathematical calculation part of the heat transfer process. The model is used to estimate the heat extraction capacity of the coaxial shell-and-tube heat exchanger in the deep geothermal well and the temperature change of the formation. The initial condition and boundary condition setting part includes: the setting of the initial temperature of the formation, the setting of the initial temperature of the cementing cement, the setting of the initial temperature of the fluid in the geothermal well, the setting of the inlet temperature of the fluid in the geothermal well, and the setting of the surface, bottom and side temperatures of the formation; The initial temperature of the formation is determined by the initial geothermal gradient, and the initial temperatures of the cementing cement and the fluid in the geothermal well are both based on the initial temperature of the formation at the same depth; The formation surface temperature adopts constant temperature boundary conditions, taking the atmospheric temperature as the first type of boundary conditions; the formation bottom temperature has a constant heat flux density, which is the second type of boundary conditions; the formation side temperature adopts constant temperature boundary conditions, taking the initial formation temperature as the first type of boundary conditions; the fluid inlet temperature in the geothermal well adopts constant injection temperature as the first type of boundary conditions; The stratum is divided into n parts according to the geophysical properties. Each part has different thermal conductivity and geothermal gradient. According to the geothermal gradient, the initial temperature distribution of the stratum is: T g,1 =T g,s +D1·z1,T g,n =T g,n-1 +D n ·Z n , where T g,s represents the surface temperature, T g,1 represents the temperature distribution of the first layer of strata along the depth direction, D1 represents the temperature rise gradient of the first layer of strata, z1 represents the thickness of the first layer of rock and soil, T g,n represents the temperature distribution of the nth layer along the depth direction, T g,n-1 represents the temperature distribution of the n-1th layer along the depth direction, D n represents the temperature rise gradient of the nth layer, z n represents the thickness of the nth layer of rock and soil; The heat exchange process of the coaxial shell-and-tube heat exchanger in a deep geothermal well is as follows: when the coaxial shell-and-tube heat exchanger is working, the cold fluid is injected downward into the geothermal well along the annular area formed between the outer shell and the thermal insulation inner tube, and there are two forms of heat exchange: one is the heat conduction and heat convection of the fluid along the axial direction of the geothermal well, and the other is the convection heat exchange between the outer tube wall and the formation and the convection heat exchange between the inner tube wall and the inner tube fluid along the radial direction of the geothermal well; When the working fluid flows to the bottom of the geothermal well, the flow direction is reversed, and the hot fluid flows upward along the inner tube. There are two forms of heat exchange: one is heat conduction and heat convection along the axial direction of the geothermal well, and the other is convection heat exchange between the inner tube wall and the outer tube fluid along the radial direction of the geothermal well. There are two forms of heat transfer in the formation: when there is no seepage, the heat transfer form is pure heat conduction; when there is groundwater seepage, the heat transfer form is the simultaneous action of heat conduction and heat convection; The convective heat transfer between the fluid and the wall is equivalent to the source term and incorporated into the mathematical equation of axial heat transfer, which is simplified to the heat transfer between one-dimensional line elements. The energy balance equation of the fluid axial direction is: In the formula, is the Hamiltonian operator, ρ f is the fluid density, t is the time, A is the cross-sectional area of ​​the inner tube, C p,f is the constant pressure specific heat capacity of the fluid, u is the average flow velocity along the well axis, T is the temperature, k is the thermal conductivity of the pipe, and f D is the friction factor, d i is the inner diameter of the pipe, Q wall The heat transfer of the fluid through the tube wall; The radial convection heat transfer equation of the fluid is: Q wall =(hZ) eff (T ext -T f ), where (hZ) eff is the surface heat transfer coefficient, T ext is the temperature of the control body outside the tube wall, T f is the fluid temperature in the geothermal well; For fluids transferring heat through the inner tube wall: In the formula, r0 is the inner diameter of the inner tube, r1 is the outer diameter of the inner tube, and h int is the surface heat transfer coefficient of the fluid in the inner tube, h ext is the surface heat transfer coefficient of the fluid in the outer tube, k p is the thermal conductivity of the inner tube; There are two forms of heat transfer in the formation. When there is seepage, the heat transfer form is heat conduction and heat convection at the same time. Darcy's law is used to describe the fluid flow in the saturated seepage layer: In the formula, ε p is the porosity of rock and soil, t is the time, is the Hamiltonian operator, ρ f is the density of the fluid, u' is the Darcy velocity; For single-phase flow, considering the gravity effect, the Darcy velocity is expressed as: In the formula, κ' is the permeability, μ is the dynamic viscosity, P is the water pressure, g is the gravitational acceleration, and Z is the water level; The energy conservation equation for saturated soil is: In the formula, C p,f is the constant pressure specific heat capacity of the fluid, Q is the heat source, (ρC p ) eff and k eff are the effective volume heat capacity and effective thermal conductivity of rock and soil respectively; (ρC p ) eff =(1-ε p )ρ s C p,s +ε p ρ f C p,f , where ρ s is the density of rock and soil, C p,s is the constant pressure specific heat capacity of rock and soil; k eff =(1-ε p ) s +ε p k f , where k s is the thermal conductivity of rock and soil, k f is the thermal conductivity of the fluid.

2. The method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger in a deep geothermal well according to claim 1, characterized in that: The thermal conductivity of the insulation inner pipe is set in sections. According to the different insulation performances of the insulation inner pipe required at different depths, the insulation inner pipe is divided into L sections, and materials with different thermal conductivity are selected for each section. The thermal conductivity of the insulating inner pipe is proportional to the depth of the geothermal well, and inversely proportional to the cost of the insulation material, that is, the deeper the geothermal well, the greater the thermal conductivity of the required pipe and the lower the cost.

3. The method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger in a deep geothermal well according to claim 2, characterized in that: For the porosity and permeability of the seepage layer rock and soil, a horizontal non-uniform distribution is adopted to divide the seepage layer into m regions horizontally. The permeability and porosity of the rock and soil in different regions are different, and the permeability increases with the increase of porosity.

4. The method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger in a deep geothermal well according to claim 3, characterized in that: The transient heat transfer process of the coaxial shell-and-tube heat exchanger and its surrounding strata in the axial and radial directions was modeled and analyzed, and the following assumptions were adopted: at the initial moment, the geothermal well is filled with fluid, and the temperature is the same as the initial temperature of the rock and soil at the same depth; the flow rate and temperature of the fluid in the geothermal well are uniform and consistent on the same cross-section; the fluid in the geothermal well will not undergo phase change within the design temperature and pressure range; the rock and soil properties of the strata are not affected by temperature, pressure and groundwater flow, that is, the fracturing, deposition and dissolution processes caused by temperature and pressure changes are not considered.

5. The method for estimating the heat extraction capacity of a coaxial shell-and-tube heat exchanger in a deep geothermal well according to claim 4, characterized in that: After the establishment of the transient heat transfer model of the coaxial shell and tube heat exchanger is completed, when using the transient heat transfer model of the coaxial shell and tube heat exchanger, the parameters that need to be set in the formation part include the thermal conductivity and geothermal gradient of each formation, the permeability and porosity of each area of ​​the underground seepage layer, and the horizontal seepage velocity; the parameters that need to be set in the geothermal well part include the fluid injection temperature, injection volume flow rate, thermal conductivity of the insulation inner pipe material of each pipe section, and the operation time of the coaxial shell and tube heat exchanger. The transient heat transfer model of the coaxial shell and tube heat exchanger is used to calculate the outlet water temperature, heat extraction, and real-time temperature changes of the formation of the geothermal well.

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