Method for predicting heat exchange efficiency of coaxial heat exchange well in oil exploitation

Abstract

The application relates to a coaxial heat exchange well heat exchange efficiency prediction method in oil exploitation, which comprises the following steps: a coaxial heat exchange well coupling heat transfer physical model is established; according to the engineering structure and the geological conditions of a target block, a standardized heat transfer model directly used for mathematical solution is established; according to the temperature control equation in the oil pipe and the annular space, the wellbore temperature field partial differential equation is calculated by using Laplace transformation, the fluid temperature at a position of the wellbore is calculated, and the wellhead outlet temperature is obtained; the analytical solution of the formation temperature changing with the radial distance and the time in the target block is obtained, the range of the formation temperature drop in the radial direction after the coaxial heat exchange well runs for a predetermined time is evaluated; and the coaxial heat exchange well heat exchange efficiency is calculated and predicted according to the obtained wellhead outlet temperature and the known well inlet temperature. The application can solve the problems of long solution time in numerical simulation and inaccurate calculation results in the analytical solution based on the steady-state assumption, improve the oil production efficiency and reduce the energy consumption.

Description

Methods for predicting the heat transfer efficiency of coaxial heat exchange wells in oil extraction Technical Field

[0001] This invention relates to the field of oil extraction technology, specifically to a method for predicting the heat exchange efficiency of coaxial heat exchange wells in oil extraction. Background Technology

[0002] In the field of oil extraction, coaxial heat exchange well structures are used in downhole heat exchange scenarios, such as for wellbore heating in high-pour-point or heavy oil reservoirs, improving crude oil fluidity, or for waste heat recovery and utilization, thereby improving oil production efficiency and reducing energy consumption.

[0003] The working principle of a coaxial heat exchange well is based on heat conduction between the rock and the wellbore medium, with the heat exchange medium extracting heat through convective heat transfer within the wellbore. Calculations of the heat extraction efficiency of coaxial heat exchange wells include numerical and analytical methods. In numerical methods, some scholars have used a three-dimensional implicit finite difference method in a rectangular coordinate system to numerically simulate the heat transfer process of coaxial heat exchange wells. While this method yields relatively accurate results, the model is highly dependent on geometry, and the solution time is long and the operation is complex, making it impractical for large-scale, multi-parameter simulations and difficult to meet the needs of real-time optimization and on-site control in oil production engineering applications. Other scholars have used decoupling methods to calculate the wellbore temperature field of complex coaxial heat exchange well types. Although this method can improve solution efficiency, it treats the wellbore heat transfer problem as a pure heat conduction problem, ignoring the heat flow coupling effect caused by fluid flow, leading to inaccurate results. Especially for oil production processes involving fluid injection or extraction, the temperature prediction deviation may affect the design effectiveness of the thermal recovery scheme.

[0004] Regarding analytical methods, while they effectively avoid the unavoidable problems of operational complexity, strong dependence on geometric meshes, and long solution times inherent in numerical methods, most scholars have adopted a steady-state assumption when solving the heat transfer partial differential equations, leading to significant errors in the initial temperature calculations for coaxial heat transfer wells. Especially for problems with complex boundary conditions, the traditional method of separation of variables struggles to obtain analytical solutions to the heat transfer equations for coaxial heat transfer wells, limiting its application in dynamically changing oil production conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the heat exchange efficiency of coaxial heat exchange wells in oil extraction. This method is used to solve the problems of long solution time, strong dependence on field data, and inaccurate calculation results of analytical solutions based on steady-state assumptions in existing technologies that use numerical simulation to calculate the heat extraction efficiency of coaxial heat exchange wells.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows: This method for predicting the heat exchange efficiency of coaxial heat exchange wells in oil extraction includes the following steps:

[0007] Step 1: Establish a physical model of coupled heat transfer in a coaxial heat exchange well. Based on the engineering structure and geological conditions of the target block, establish a standardized heat transfer model that can be directly used for mathematical solutions.

[0008] Step 2: Based on the temperature control equations of the tubing and annulus, perform Laplace transformation on the partial differential equations of the wellbore temperature field to calculate the wellbore temperature of the coaxial heat exchange well in the target block, so as to quickly simulate the actual working conditions, draw the temperature profile along the well depth, calculate the fluid temperature at a certain location in the wellbore, and obtain the wellhead outlet temperature.

[0009] Step 3: Apply Duhamel's theorem to solve the coupled formation heat conduction equation to obtain the analytical solution of the formation temperature variation of the target block with radial distance and time. Use this analytical solution to evaluate the range of radial temperature drop in the formation after the coaxial heat exchange well has been in operation for a predetermined time, optimize the well spacing design, and predict the formation temperature recovery.

[0010] Step 4: Calculate and predict the heat transfer efficiency of the coaxial heat exchange well. Based on the obtained wellhead outlet temperature and the known well inlet temperature, calculate the heat transfer efficiency. Optimize and adjust the operating parameters under the current conditions based on the heat transfer efficiency to achieve maximum heat extraction or economic optimization. The heat transfer efficiency is calculated as follows:

[0011] ;

[0012] In the formula: ρ is the specific heat capacity of the working fluid; m is the mass flow rate; This refers to the wellhead outlet temperature. The known well inlet temperature is given.

[0013] Step one of the above scheme specifically involves: constructing a model based on the actual wellbore structure, geological data, and proposed operating parameters of the target block, while adhering to simplification principles.

[0014] ① Ignore axial heat conduction of the working fluid and associate the temperature field with radial heat transfer and convection;

[0015] ②The formation heat transfer is treated as a two-dimensional radial unsteady-state conduction centered on the wellbore;

[0016] ③ The working fluid temperature field inside the wellbore is simplified into a one-dimensional unsteady-state process, and a parameterized, linear coaxial heat exchange well coupled heat transfer physical model is constructed.

[0017] Step two in the above scheme is specifically as follows:

[0018] 2.1 Based on the temperature control equations of the working fluid in the tubing and the annulus, and considering the fluid flow during the circulation of the working fluid, the wellbore temperature field is solved using the Laplace transform.

[0019] Oil pipe working fluid temperature control equation: ;

[0020] Annular working fluid temperature control equation: ;

[0021] In the formula: The temperature of the circulating working fluid in the annulus; t represents the temperature of the circulating working fluid in the tubing; t represents time. Mass flow rate; ρ is the specific heat capacity of the fluid; z is the axial distance; The temperature difference between the top and bottom of the unit cell; The circulating working fluid velocity; This refers to the cross-sectional area of ​​the fluid inside the tubing and the annulus. The geothermal gradient; The well inclination angle; It refers to the surface temperature; , The relaxation distance function simplified using the Lagrange relaxation algorithm; The thermal storage coefficient is dimensionless.

[0022] 2.2. Perform Laplace transform on the partial differential equation of the wellbore temperature field to determine the calculation formula for the fluid temperature inside the tubing and annulus of the coaxial heat exchange well in the target block, and calculate the wellbore temperature of the coaxial heat exchange well in the target block:

[0023] Inside the oil pipe:

[0024] ;

[0025] Within the annulus:

[0026] ;

[0027] In the formula: e is the base of the natural logarithm, which has a value of 2.71828; Let be a step function, representing the time delay effect;

[0028] 2.3. Determine the thermal storage coefficient based on the actual operating conditions of the circulating working fluid in the target block. The value;

[0029] 2.4. Conduct a rapid simulation of actual working conditions, draw a temperature profile along the well depth, collect the parameters of each formula in 2.2, calculate the fluid temperature at a certain location in the wellbore, and obtain the wellhead outlet temperature.

[0030] Step three in the above scheme specifically refers to:

[0031] Establish the two-dimensional unsteady heat conduction equation in cylindrical coordinates:

[0032] ;

[0033] In the formula: Formation density; Specific heat capacity of the formation; ρ is the thermal conductivity of the formation; r is the radial heat transfer distance;

[0034] The analytical solution for formation temperature obtained using Duhamel's theorem is:

[0035] ;

[0036] In the formula: α is the thermal diffusivity, and its value is , It is a 0th-order Bessel equation; It is a first-order Bessel equation; This is the m-th positive root of the Bessel equation.

[0037] Beneficial effects:

[0038] 1. Based on Laplace transform and Duhamel's theorem, this invention solves the heat transfer equation under the assumption of unsteady state and calculates the analytical expression of the temperature field in the wellbore of coaxial heat exchange wells. This can solve the problems of long solution time and strong dependence on field data in numerical simulation, as well as the inaccurate calculation results of analytical solutions based on steady-state assumptions. It provides a new method for accurate and rapid prediction of heat extraction efficiency in coaxial heat exchange wells, thereby improving oil production efficiency and reducing energy consumption.

[0039] 2. This invention can also be applied to wellbore thermal management, heavy oil thermal recovery design, and downhole heat exchange efficiency evaluation in oil production engineering, providing an efficient and reliable theoretical tool for thermal energy regulation in the oil production process, which helps to optimize oil production technology and improve oil and gas recovery rate.

[0040] 3. This invention uses Laplace transform to solve problems under unsteady-state assumptions, and Duhamel's theorem to solve complex non-homogeneous heat transfer differential equations. This can improve the calculation accuracy of outlet temperature and heat extraction efficiency of coaxial heat exchange wells at different times, while significantly reducing the solution time, improving the design effect of crude oil thermal recovery schemes, and increasing oil and gas recovery rate. It has broad application value. Attached Figure Description

[0041] Figure 1 shows the physical model of the wellbore temperature field during the circulation process of the circulating working fluid and a schematic diagram of the micro-element of the circulation process.

[0042] Figure 2 compares the results of the coupled analytical solution calculation of a coaxial heat exchange well at a joint station in the Songliao Basin of Jilin Province with the results of the Hasan method and numerical simulation.

[0043] Figure 3 shows the calculation results of the coupled analytical solution of the formation temperature influence range of a coaxial heat exchange well at a joint station in the Songliao Basin of Jilin Province. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings:

[0045] This method for predicting the heat exchange efficiency of coaxial heat exchange wells in oil extraction includes the following steps:

[0046] Step 1: Based on the heat transfer mechanism of the coaxial well and combined with the heat transfer process of the micro-element in the circulation process (see Figure 1), establish a coupled heat transfer physical model of the coaxial heat transfer well. According to the engineering structure and geological conditions of the target block, establish a standardized heat transfer model that can be directly used for mathematical solution.

[0047] As shown in Figure 1, the basic structure of a coaxial heat exchange well includes tubing, casing, cement sheath, and the thermal reservoir. The circulation path of the heat exchange medium is: injection into the annulus between the tubing and casing, and then extraction from the tubing. The heat transfer path is: formation—cement sheath—casing—fluid in the annulus—tubing—fluid in the tubing. The model established in this invention simulates the radial heat transfer process within a micro-element of length Δz. Temperature change characterizes heat transfer, starting from the initial formation temperature Te at a distance, reaching the cement sheath. Within the cement sheath with a width of rh-rco, the temperature decreases to Th, then to the casing with a thickness of rco-rci, where the temperature decreases to Tc. Next, the fluid in the annulus with a thickness of rci-rto decreases to Tan, then through the tubing with a thickness of rto-rti, where the temperature decreases to Tt, and finally, the temperature in the tubing decreases to Tf.

[0048] Based on the actual wellbore structure, geological data, and proposed operating parameters of the target block, a model was constructed under the principle of simplification:

[0049] ① Ignore axial heat conduction of the working fluid and associate the temperature field with radial heat transfer and convection;

[0050] ②The formation heat transfer is treated as a two-dimensional radial unsteady-state conduction centered on the wellbore;

[0051] ③ The working fluid temperature field inside the wellbore is simplified into a one-dimensional unsteady-state process, and a parameterized, linear coaxial heat exchange well coupled heat transfer physical model is constructed.

[0052] Step 2: Based on the temperature control equations of the tubing and annulus, perform Laplace transformation on the partial differential equations of the wellbore temperature field to calculate the wellbore temperature of the coaxial heat exchange well in the target block, so as to quickly simulate the actual working conditions, draw the temperature profile along the well depth, calculate the fluid temperature at a certain location in the wellbore, and obtain the wellhead outlet temperature.

[0053] 2.1 Based on the temperature control equations of the working fluid in the tubing and the annulus, and considering the fluid flow during the circulation of the working fluid, the wellbore temperature field is solved using the Laplace transform.

[0054] Oil pipe working fluid temperature control equation:

[0055] Annular working fluid temperature control equation:

[0056] In the formula: The temperature of the circulating working fluid in the annulus is ℃; The temperature of the circulating working fluid in the tubing is °C; t is time, seconds. Mass flow rate, kg / s; Specific heat capacity of the fluid z is the axial distance, in meters. The temperature difference between the top and bottom of the unit cell is expressed in °C. The velocity of the circulating working fluid is m / s; The cross-sectional area of ​​the fluid inside the tubing and the annulus is given in m. 2 ; The geothermal gradient is expressed in °C / m. The inclination angle is °; The surface temperature is expressed in °C. , The relaxation distance function is simplified using the Lagrange relaxation algorithm, with units of 1 / m. The thermal storage coefficient is dimensionless.

[0057] 2.2. Perform Laplace transform on the partial differential equation of the wellbore temperature field to determine the calculation formula for the fluid temperature inside the tubing and annulus of the coaxial heat exchange well in the target block, and calculate the wellbore temperature of the coaxial heat exchange well in the target block:

[0058] Inside the oil pipe:

[0059]

[0060] Within the annulus:

[0061]

[0062] In the formula: e is the base of the natural logarithm, which has a value of 2.71828; Let be a step function, representing the time delay effect.

[0063] 2.3. Determine the thermal storage coefficient based on the actual operating conditions of the circulating working fluid in the target block. The value;

[0064] 2.4. Conduct a rapid simulation of actual working conditions, draw a temperature profile along the well depth, collect the parameters of each formula in 2.2, calculate the fluid temperature at a certain location in the wellbore, and obtain the wellhead outlet temperature.

[0065] Step 3: Apply Duhamel's theorem to solve the coupled formation heat conduction equation to obtain the analytical solution of the formation temperature variation of the target block with radial distance and time. Use this analytical solution to evaluate the range of radial temperature drop in the formation after the coaxial heat exchange well has been in operation for a predetermined time, optimize the well spacing design, and predict the formation temperature recovery.

[0066] Establish a two-dimensional unsteady heat conduction equation in cylindrical coordinates.

[0067]

[0068] In the formula: The density of the formation is kg / m³. 3 ; For the specific heat capacity of the formation, ; The thermal conductivity of the formation, ; r is the radial heat transfer distance, in meters.

[0069] The analytical solution for formation temperature obtained using Duhamel's theorem is:

[0070]

[0071] In the formula: α is the thermal diffusivity, and its value is , It is a 0th-order Bessel equation; It is a first-order Bessel equation; This is the m-th positive root of the Bessel equation.

[0072] Step 4: Calculate and predict the heat transfer efficiency of the coaxial heat exchange well. Based on the obtained wellhead outlet temperature and the known well inlet temperature, calculate the heat transfer efficiency. Optimize and adjust the operating parameters under the current conditions based on the heat transfer efficiency to achieve maximum heat extraction or economic optimization. The heat transfer efficiency is calculated as follows:

[0073]

[0074] In the formula: ρ is the specific heat capacity of the working fluid; m is the mass flow rate; This refers to the wellhead outlet temperature. The known well inlet temperature is given.

[0075] Example:

[0076] A well at a joint station in the Songliao Basin of Jilin Province is used for geothermal resource development and utilization. It employs a coaxial heat exchanger well with a depth of 1319.2m, a geothermal gradient of 3℃ / 100m, and is a vertical well. Currently, it is necessary to calculate the heat exchange efficiency of this well over 30 years. This invention is used to predict the outlet temperature and heat exchange efficiency of this coaxial heat exchanger well during its 30-year operation. The steps are as follows:

[0077] Step 1: Establish a physical model of coupled heat transfer in a coaxial heat exchange well. Based on the engineering structure and geological conditions of the target block, establish a standardized heat transfer model that can be directly used for mathematical solutions.

[0078] Step 2: Based on the temperature control equations of the tubing and annulus, perform Laplace transformation on the partial differential equations of the wellbore temperature field to calculate the wellbore temperature of the coaxial heat exchange well in the target block, so as to quickly simulate the actual working conditions, draw the temperature profile along the well depth, calculate the fluid temperature at a certain location in the wellbore, and obtain the wellhead outlet temperature.

[0079] 2.1 Based on the fluid flow conditions during the circulation of the working medium, the formula for calculating the fluid temperature inside the tubing and annulus is determined:

[0080] Inside the oil pipe:

[0081]

[0082] Within the annulus:

[0083]

[0084] 2.2 Determine the heat storage coefficient based on the actual operating conditions of the circulating working fluid. The value of is given. For annular injection with tubing return, the thermal storage coefficient is taken as 3.

[0085] 2.3. Obtain the parameters appearing in the formula, substitute them into the formula, and you can calculate the fluid temperature at a certain location over 30 consecutive years, thus obtaining the fluid temperature at the outlet. The parameter range used in the solution is shown in Table 1:

[0086]

[0087] Based on the parameters in Table 1, the outlet temperature of the circulating working fluid at the wellhead of the coaxial heat exchange well over 30 years was calculated, and the model results are shown in Figure 2. Figure 2 shows the outlet temperature results calculated by the coupled calculation method of the present invention, and compares them with the traditional Hasan method and numerical simulation method. It shows that the method of the present invention has the advantages of being fast, accurate, and able to reflect the heat transfer behavior in the initial transient stage while ensuring that the calculation results closely match the numerical simulation.

[0088] Based on the actual wellbore structure, geological data, and proposed operating parameters of the target block, a model was constructed under the principle of simplification:

[0089] ① Ignore axial heat conduction of the working fluid and associate the temperature field with radial heat transfer and convection;

[0090] ②The formation heat transfer is treated as a two-dimensional radial unsteady-state conduction centered on the wellbore;

[0091] ③ The working fluid temperature field inside the wellbore is simplified into a one-dimensional unsteady-state process, and a parameterized, linear coaxial heat exchange well coupled heat transfer physical model is constructed.

[0092] Step 3: Apply Duhamel's theorem to solve the coupled formation heat conduction equation to obtain an analytical solution for the formation temperature variation with radial distance and time in the target block. This analytical solution is used to evaluate the range of radial temperature drop in the formation after the coaxial heat exchange well has been in operation for a predetermined time, optimize the well spacing design, and predict the formation temperature recovery. Figure 3 shows the formation temperature influence range of a coaxial heat exchange well at a joint station in the Songliao Basin, Jilin Province, after 30 years of operation. The figure shows that the formation temperature change obtained by combining Duhamel's theorem is as follows: after 30 years, the formation temperature disturbance radius at a depth of 3000m reaches 117.04m. This result can provide a reference for the selection of well spacing during group well heat exchange, ensuring no thermal disturbance between wells.

[0093] Step 4: Calculate the heat transfer efficiency of the coaxial heat exchanger well based on the outlet and inlet temperatures. The calculation formula is as follows:

[0094]

[0095] In the formula: For heat exchange efficiency, W; is the specific heat capacity of the circulating working fluid (J / (kg·℃)); m is the mass flow rate of the circulating working fluid (kg / s). The temperature difference between the inlet and outlet is expressed in °C.

[0096] This invention provides accurate temperature prediction for oil production processes involving fluid injection or extraction, improving the design effectiveness of thermal recovery schemes, and is particularly suitable for applications in dynamically changing oil production conditions.

Claims

1. A method for predicting the heat transfer efficiency of coaxial heat exchange wells in oil extraction, characterized in that... The process includes the following steps: Step 1: Establish a coupled heat transfer physical model for the coaxial heat exchange well. Based on the engineering structure and geological conditions of the target block, establish a standardized heat transfer model directly applicable to mathematical solutions. Step 2: Based on the temperature control equations within the tubing and annulus, perform a Laplace transform on the partial differential equations of the wellbore temperature field to calculate the wellbore temperature of the coaxial heat exchange well in the target block for rapid simulation of actual operating conditions. Draw a temperature profile along the well depth, calculate the fluid temperature at a specific location in the wellbore, and obtain the wellhead outlet temperature. 2.1: Based on the temperature control equations for the working fluid within the tubing and annulus, and considering the fluid flow during the circulation of the working fluid, use a Laplace transform to solve for the wellbore temperature field. The temperature control equations for the working fluid within the tubing are: ; Circulatory working fluid temperature control equation: In the formula: The temperature of the circulating working fluid in the annulus; The temperature of the circulating working fluid in the oil pipe is t; time is t. For mass flow rate; denoted as ρ_f(z) = specific heat capacity of the fluid; z is the axial distance. The temperature difference between the top and bottom of the unit cell; The circulating working fluid velocity; This refers to the cross-sectional area of ​​the fluid inside the tubing and the annulus. The geothermal gradient; The well inclination angle; It refers to the surface temperature; 、 The relaxation distance function simplified using the Lagrange relaxation algorithm; The thermal storage coefficient is dimensionless. 2.

2. Perform Laplace transform on the partial differential equation of the wellbore temperature field to determine the calculation formula for the fluid temperature inside the tubing and annulus of the coaxial heat exchange well in the target block. Calculate the wellbore temperature of the coaxial heat exchange well in the target block: Tubing: ;In the empty space: In the formula: e is the base of the natural logarithm, which has a value of 2.71828; Let be a step function, representing the time delay effect; 2.

3. Determine the thermal storage coefficient based on the actual operating conditions of the circulating working fluid in the target block. The value; 2.

4. Conduct rapid simulation of actual operating conditions, plot the temperature profile along the well depth, collect the parameters of each formula in 2.2, and calculate the fluid temperature at a certain location in the wellbore to obtain the wellhead outlet temperature; Step 3. Apply Duhamel's theorem to solve the coupled formation heat conduction equation to obtain the analytical solution of the formation temperature of the target block as a function of radial distance and time. Use this analytical solution to evaluate the range of radial temperature drop in the formation after the coaxial heat exchange well has been running for a predetermined time, optimize the well spacing design, and predict the formation temperature recovery; Step 4. Calculate and predict the heat exchange efficiency of the coaxial heat exchange well. Based on the obtained wellhead outlet temperature and the known well inlet temperature, calculate the heat exchange efficiency. Optimize and adjust the operating parameters under the current operating conditions based on the heat exchange efficiency to achieve maximum heat extraction or economic optimization. The heat exchange efficiency is calculated as follows: In the formula: ρ is the specific heat capacity of the working fluid; m is the mass flow rate; This refers to the wellhead outlet temperature. The known well inlet temperature is given.

2. The method for predicting the heat exchange efficiency of coaxial heat exchange wells in oil extraction as described in claim 1, characterized in that: Step one specifically involves: based on the actual wellbore structure, geological data, and proposed operating parameters of the target block, and completing the model construction under the principle of simplification: ① Ignoring the axial heat conduction of the working fluid, and associating the temperature field with radial heat transfer and convection; ② Treating the formation heat transfer as a two-dimensional radial unsteady-state conduction centered on the wellbore; ③ Simplifying the working fluid temperature field inside the wellbore into a one-dimensional unsteady-state process, and constructing a parameterized, linear coaxial heat exchange well coupled heat transfer physical model.

3. The method for predicting the heat transfer efficiency of coaxial heat exchange wells in oil extraction according to claim 2, characterized in that: Step three specifically involves: establishing a two-dimensional unsteady heat conduction equation in cylindrical coordinates. In the formula: Formation density; Specific heat capacity of the formation; ρ is the thermal conductivity of the formation; r is the radial heat transfer distance; the analytical solution for the formation temperature obtained by Duhamel's theorem is: In the formula: α is the thermal diffusivity, and its value is... , It is a 0th-order Bessel equation; It is a first-order Bessel equation; This is the m-th positive root of the Bessel equation.

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