CN104389589A - Method and system for determining wellbore temperature field distribution based on hollow rod - Google Patents

Abstract

The present invention provides a method and system for determining the temperature field distribution of a wellbore based on a hollow rod. The method includes: acquiring data related to the hollow rod and the wellbore; step length; according to the step size, the wellbore and the hollow rod are divided into multiple wellbore sections and hollow rod sections; The temperature of the fluid in the rod section; the temperature of the fluid in the plurality of hollow rod sections and the temperature of the liquid in the plurality of wellbore sections constitute the wellbore temperature field distribution. The distribution of the wellbore temperature field is determined, which provides a data basis for the subsequent selection of a reasonable wellhead mixing displacement and temperature to meet the existing heavy oil, extra heavy oil and super heavy oil production.

Description

Method and system for determining wellbore temperature field distribution based on hollow rod

technical field

The present invention relates to the technical field of oil and gas field exploration, in particular to the lifting technology of heavy oil, extra heavy oil and super heavy oil, specifically a method and system for determining the temperature field distribution of a wellbore based on a hollow rod.

Background technique

During the exploitation of oil reservoirs with low formation pressure, poor permeability, high freezing point of crude oil, high wax content, and high viscosity, oil wells are seriously waxed, which may easily cause pump leakage or difficulty in starting after stopping the pump, and even cause pump stuck accidents. Detrimental effects on oil well production.

In order to solve the pump stuck phenomenon caused by heavy oil and wax deposition in the pump barrel, the oil recovery process of hollow sucker rod mixed with hot water or thin oil or chemical agents is widely used in the prior art. The process flow is: use the existing hot water mixing pipeline on the surface of the pumping well to connect the hollow rod, the mixed hot water flows vertically through the inner hole of the hollow rod to the water nozzle at the bottom, and then sprays into the hollow plunger to mix with crude oil. The mixture enters the hollow rod and tubing annulus and will be lifted to the surface. The process has the advantages of low comprehensive cost, convenient maintenance and high heat utilization efficiency.

In actual use, one of the keys to the oil recovery technology of hollow sucker rod mixed with hot water or thin oil or chemical agent is to determine the wellhead mixing displacement and temperature of hot water or thin oil or chemical agent. These two parameters are mainly affected by the change of crude oil viscosity with temperature. Therefore, in order to determine the reasonable wellhead mixing displacement and temperature, it is necessary to study the distribution of the temperature field of crude oil in the wellbore.

Therefore, how to determine the distribution of the temperature field of crude oil in the wellbore, and then select a reasonable wellhead mixing displacement and temperature to meet the existing heavy oil, extra heavy oil and super heavy oil production is an urgent technology in this field. problem.

Contents of the invention

In order to solve the problem that the hollow rod electric heating technology in the prior art cannot determine the wellbore temperature field, and it is difficult to choose a reasonable wellhead to mix displacement and temperature, which cannot meet the existing heavy oil, extra heavy oil and super heavy oil production. The present invention provides a method and system for determining the temperature field distribution of the wellbore based on the hollow rod. It is an accurate solution for determining the temperature field distribution of the wellbore based on the hollow rod. By obtaining data related to the hollow rod and the wellbore, According to the set step length, the wellbore and hollow rod are divided into multiple wellbore sections and hollow rod sections, and the temperature of the liquid in each wellbore section and the temperature of the fluid in the hollow rod section are determined in turn, so that the temperature field distribution of the wellbore is obtained, as Subsequent selection of reasonable wellhead mixing displacement and temperature to meet the existing heavy oil, extra heavy oil and super heavy oil production provides a data basis.

One of the objectives of the present invention is to provide a method for determining the temperature field distribution of a wellbore based on a hollow rod, including: obtaining data related to the hollow rod and the wellbore; Determine the step length; divide the well bore and hollow rod into multiple well bore sections and hollow rod sections according to the step length; determine the temperature of the liquid in the multiple well bore sections, the multiple The temperature of the fluid in the hollow rod section; the temperature of the fluid in the plurality of hollow rod sections and the temperature of the liquid in the plurality of wellbore sections constitute the wellbore temperature field distribution.

One of the objects of the present invention is to provide a system for determining the temperature field distribution of the wellbore based on the hollow rod, including: a data acquisition device for obtaining data related to the hollow rod and the wellbore; a step setting device for The step size is set according to the height of the moving liquid level in the wellbore and the depth of the wellbore; the segmentation device is used to divide the wellbore and the hollow rod into a plurality of wellbore sections and hollow rod sections according to the step length The temperature determination device is used to determine the temperature of the liquid in the plurality of wellbore sections and the temperature of the fluid in the plurality of hollow rod sections respectively according to the data; the temperature field distribution determination device is used for the plurality of hollow rods The temperature of the fluid in the section and the temperature of the fluid in the plurality of wellbore sections constitute the wellbore temperature field distribution.

The beneficial effect of the present invention is that it provides a method and system for determining the temperature field distribution of the wellbore based on the hollow rod, which is an accurate solution for determining the temperature field distribution of the wellbore based on the hollow rod. By obtaining the data related to the hollow rod and the wellbore According to the set step length, the wellbore and hollow rod are divided into multiple wellbore sections and hollow rod sections, and the temperature of the liquid in each wellbore section and the temperature of the fluid in the hollow rod section are determined in turn, so that the temperature field distribution of the wellbore is obtained , which provides a data basis for the follow-up selection of reasonable wellhead mixing displacement and temperature to meet the existing heavy oil, extra heavy oil and super heavy oil production, thereby improving the production efficiency of heavy oil, extra heavy oil and super heavy oil efficiency.

In order to make the above and other objects, features and advantages of the present invention more comprehensible, preferred embodiments will be described in detail below together with the accompanying drawings.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is a flow chart of a method for determining the temperature field distribution of a wellbore based on a hollow rod provided by an embodiment of the present invention;

Fig. 2 is the specific flowchart of step S104 in Fig. 1;

Fig. 3 is the specific flowchart of step S201 in Fig. 2;

FIG. 4 is a specific flowchart of step S304 in FIG. 3;

FIG. 5 is a specific flowchart of step S305 in FIG. 3;

FIG. 6 is a specific flowchart of Embodiment 1 of step S202 in FIG. 2;

FIG. 7 is a specific flow chart of the second embodiment of step S202 in FIG. 2;

Fig. 8 is a structural block diagram of a system for determining wellbore temperature field distribution based on a hollow rod provided by an embodiment of the present invention;

Fig. 9 is a specific structural block diagram of the temperature determination device 104 in a system for determining the temperature field distribution of a wellbore based on a hollow rod provided by an embodiment of the present invention;

Fig. 10 is a specific structural block diagram of the thermal resistance determination module 201 in a system for determining the temperature field distribution of a wellbore based on a hollow rod provided by an embodiment of the present invention;

Fig. 11 is a specific structural block diagram of the first thermal resistance determination unit 304 in a system for determining the temperature field distribution of a wellbore based on a hollow rod provided by an embodiment of the present invention;

Fig. 12 is a specific structural block diagram of the second thermal resistance determination unit 305 in a system for determining the temperature field distribution of a wellbore based on a hollow rod provided by an embodiment of the present invention;

Fig. 13 is a specific structural block diagram of Embodiment 1 of the thermal resistance coefficient determining module 202 in a system for determining wellbore temperature field distribution based on a hollow rod provided by an embodiment of the present invention;

Fig. 14 is a specific structural block diagram of Embodiment 2 of the thermal resistance coefficient determination module 202 in a system for determining the temperature field distribution of a wellbore based on a hollow rod provided by an embodiment of the present invention;

Fig. 15 is a schematic structural diagram of the hollow rod electric heating process for pumping wells in the prior art.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Aiming at the exploitation of heavy oil, extra heavy oil and super heavy oil, the present invention proposes a calculation method for calculating wellbore temperature field distribution by mixing a hollow rod with hot water or thin oil or chemicals, and forms a set of interpretation tools. Through the step-by-step calculation and analysis of the temperature field of the wellbore after adding hot water, the viscosity of crude oil in each section can be calculated, and the rod fluid friction force and pipe fluid friction load can be further calculated, and finally the pumping unit can be calculated by the upstroke of the rod string. Suspended point load. The wellhead mixing displacement and temperature of hot water can be adjusted to achieve the purpose of optimizing the efficiency of the lifting system.

Basic assumptions of the present invention include:

(1) Neglect the heat transfer in the longitudinal direction of the sucker rod, wellbore and formation rock;

(2) The pressure and temperature of the wellhead produced fluid remain unchanged;

(3) The annular space formed by the tubing and casing is filled with low-pressure air;

(4) Taking the center line of the sucker rod as the axis of symmetry, the sucker rod, wellbore and formation rock are isotropic;

(5) The thermophysical parameters in the model system have nothing to do with temperature, that is, they are considered to have constant physical properties;

(6) The original formation temperature is linearly distributed;

(7) Hot water is injected from the center of the hollow rod.

Fig. 1 is a specific flow chart of a method for determining wellbore temperature field distribution based on a hollow rod proposed by the present invention. As can be seen from Fig. 1, the described method includes:

S101: Obtain data related to the hollow rod and the wellbore.

In a specific embodiment, the data related to the hollow rod and the wellbore include the thermal conductivity of the formation, the average heat dissipation coefficient of the formation, the production time of the oil well, the radius of the wellbore, the radius of the outer wall of the casing, the thermal conductivity of the cement sheath, the thermal conductivity of the casing, the internal Wall radius, casing outer wall radius, annular radiation heat transfer coefficient, annular space natural convection heat transfer coefficient, tubing outer wall radius, tubing thermal conductivity, tubing inner wall radius, crude oil thermal conductivity, liquid moisture content, water thermal conductivity, hollow rod Radius of outer wall, relative density of crude oil, radius of inner wall of hollow rod, thermal conductivity of hollow rod.

S102: Set the step size according to the height of the fluid level in the wellbore and the depth of the wellbore. Fig. 15 is a schematic diagram of the technological structure of the hollow rod of the pumping well in the prior art. It can be seen from Fig. 15 that 1 is the formation, 2 is the cement sheath, 3 is the casing, 4 is the fluid surface, 5 is the heating cable, 6 is the tubing, 7 is the fluid in the well, and 8 is the oil layer.

S103: Divide the shaft and the hollow rod into multiple shaft sections and hollow rod sections according to the step size. In a specific implementation, assuming that the total depth of the wellbore is 1000 meters, as shown in Figure 15, the height of the dynamic fluid surface is 300 meters, and the set step size is 100 meters, then in this embodiment, the wellbore can be divided into There are 10 wellbore sections, which are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700- 800 meters, 800-900 meters, 900-1000 meters. In this embodiment, the hollow rod can be divided into 10 hollow rod sections in total, which are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, and 500 meters from the bottom of the well to the wellhead. -600 meters, 600-700 meters, 700-800 meters, 800-900 meters, 900-1000 meters.

S104: Determine the temperature of the fluid in the plurality of wellbore sections and the temperature of the fluid in the plurality of hollow rod sections respectively according to the data. FIG. 2 is a specific flowchart of step S104.

S105: The temperature of the fluid in the plurality of hollow rod sections and the temperature of the liquid in the plurality of wellbore sections constitute a wellbore temperature field distribution.

Fig. 2 is the specific flowchart of step S104, as can be seen from Fig. 2, step S104 specifically comprises:

S201: Determine the thermal resistance of each wellbore section and hollow rod section in sequence. FIG. 3 is a specific flowchart of step S201.

S202: Determine the thermal resistance coefficient of each wellbore section and hollow rod section according to the thermal resistance.

S203: Determine the integral constant according to the wellhead temperature and the bottom hole temperature.

S204: Determine the temperature of the liquid in each wellbore section and the temperature of the fluid in each hollow rod section according to the integral constant and the thermal resistance coefficient.

As can be seen from FIG. 3, step S201 specifically includes:

S301: sequentially determine whether each of the wellbore section and the hollow rod section is between the dynamic fluid level and the wellhead corresponding to the wellbore;

S302: When the judgment is yes, set multiple wellbore sections and hollow rod sections between the dynamic fluid surface and the wellhead corresponding to the wellbore as the first type of section;

S303: Otherwise, set multiple wellbore sections and hollow rod sections between the dynamic fluid surface and the well bottom corresponding to the wellbore as the second type of section;

In a specific implementation, assuming that the total depth of the wellbore is 1000 meters, as shown in Figure 15, the height of the dynamic fluid surface is 300 meters, and the set step size is 100 meters, then in this embodiment, the wellbore can be divided into There are 10 wellbore sections, which are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700- 800 meters, 800-900 meters, 900-1000 meters. In this embodiment, the hollow rod can be divided into 10 hollow rod sections in total, which are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, and 500 meters from the bottom of the well to the wellhead. -600 meters, 600-700 meters, 700-800 meters, 800-900 meters, 900-1000 meters.

According to step S301 to step S303, it can be known that the hollow pole sections 0-100 meters, 100-200 meters, and 200-300 meters are the second type of sections, and the hollow pole sections are 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700-800 meters, 800-900 meters, and 900-1000 meters are the first category. Wellbore sections of 0-100 meters, 100-200 meters, and 200-300 meters are the second type of sections; wellbore sections of 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700-800 meters 800-900 meters and 900-1000 meters are the first category.

S304: Determine the thermal resistance of the first type of segment according to the data;

S305: Determine the thermal resistance of the second type segment according to the data.

Fig. 4 is the specific flow chart of step S304, as can be seen from Fig. 4, this step specifically comprises:

S401: Determine the thermal resistance of the formation according to the thermal conductivity of the formation, the average heat dissipation coefficient of the formation, the production time of the oil well, and the radius of the wellbore. In a specific embodiment, the thermal resistance of the formation is represented by _R1 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}$

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; a</span>}}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; 29</span>}$

Among them, K _e is the thermal conductivity of the formation, a is the average heat dissipation coefficient of the formation, t is the production time of the oil well, and r _h is the radius of the wellbore.

S402: Determine the thermal resistance of the cement sheath according to the outer wall radius of the casing, the thermal conductivity of the cement sheath, and the wellbore radius. In a specific embodiment, the thermal resistance of the cement sheath is represented by _R2 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; cem</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; co</span>}}}$

Among them, r _co is the radius of the outer wall of the casing, K _cem is the thermal conductivity of the cement sheath, and r _h is the radius of the wellbore.

S403: Determine the thermal resistance of the casing wall according to the thermal conductivity of the casing, the radius of the inner wall of the casing, and the radius of the outer wall of the casing. In a specific embodiment, the heat conduction resistance of the formation is represented by R ₃ , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; cas</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; co</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}}$

Among them, K _cas is the thermal conductivity of the casing, r _ci is the radius of the inner wall of the casing, and r _co is the radius of the outer wall of the casing.

S404: Determine the heat convection thermal resistance between the air in the oil jacket annulus and the casing according to the annulus radiation heat transfer coefficient, the annulus natural convection heat transfer coefficient, and the inner wall radius of the casing. In a specific embodiment, The thermal resistance of the thermal convection liquid between the liquid and the bushing is represented by R ₄ , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}}$

Among them, h _r is the radiation heat transfer coefficient of the annular space, h _c is the natural convective heat transfer coefficient of the annular space, and r _ci is the inner wall radius of the casing.

The annular radiation heat transfer coefficient h _r is calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;F</span>}}_{\mathrm{<span\; class="notranslate">\; tci</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}^{<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}^{<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273.15</span>}$

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273.15</span>}$

$\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; tci</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, δ is the Stefan-Boltzmann constant, 2.189×10 ^-8 W/(m ² ·K); F _tci is the effective coefficient of radiation from the outer wall surface of oil pipe or adiabatic pipe to the inner surface of casing; ε _o is the blackness of the outer wall of adiabatic pipe; _εci is the blackness of the inner wall of the casing. is the absolute temperature of the outer wall of the tubing. T _to is the temperature of the outer wall of the tubing, T _ci is the temperature of the inner wall of the casing, is the absolute temperature of the inner wall of the casing.

The natural convection heat transfer coefficient h _c in the annular space is calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.049</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 0.55</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 0.074</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; ha</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}}}$

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; g</span>}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}_{\mathrm{<span\; class="notranslate">\; an</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}<span\; class="notranslate">\; )</span>}{{{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}_{\mathrm{<span\; class="notranslate">\; an</span>}}}$

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; an</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; an</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; ha</span>}}}$

Among them, Gr is the Grashof number, Pr is the Prandtl number, K _ha is the thermal conductivity of the annular fluid, W/(m K); g is the acceleration of gravity, m/s ² ; ρ _an is the average temperature of the annular fluid at T density at _an , kg/m ³ ; U _an is the viscosity of the annular fluid at the average temperature T _an , mPa·s; C _an is the heat capacity of the annular fluid at the average temperature T _an , J(m ³ · K). T _an is the average temperature of the oil jacket annulus.

S405: Determine the thermal resistance between the inner and outer walls of the oil pipe according to the radius of the outer wall of the oil pipe, the thermal conductivity of the oil pipe, and the radius of the inner wall of the oil pipe. In a specific embodiment, the heat conduction resistance between the inner and outer walls of the oil pipe is represented by _R5 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; tub</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ti</span>}}}$

Among them, K _tub is the thermal conductivity of the tubing, r _ti is the radius of the inner wall of the tubing, and r _to is the radius of the outer wall of the tubing.

S406: Determine the heat convection liquid thermal resistance between the liquid and the oil pipe according to the thermal conductivity of crude oil, the water content of the liquid, the thermal conductivity of water, the radius of the outer wall of the hollow rod, and the radius of the inner wall of the oil pipe. The heat convection thermal resistance between the inner walls is represented by _R6 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ti</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}$

Among them, λ ₀ is the thermal conductivity of crude oil, f _w is the water content of liquid, λ _w is the thermal conductivity of water, r _o is the radius of the outer wall of the hollow rod, and r _ti is the radius of the inner wall of the tubing.

S407: Determine the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod according to the relative density of crude oil, the radius of the inner wall of the hollow rod, and the thermal conductivity K _Rod of the hollow rod. In a specific embodiment, the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod is represented by _R , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; Rod</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$

Among them, _ri is the relative density of crude oil, r _o is the radius of the outer wall of the hollow rod, and K _Rod is the thermal conductivity of the hollow rod.

S408: Determine the heat convection thermal resistance between the thermal fluid and the interior of the hollow rod according to the thermal conductivity of the water. In a specific embodiment, the heat convection thermal resistance between the thermal fluid and the hollow rod is represented by _R8 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}$

Among them, _λw is the thermal conductivity of water.

Fig. 5 is the specific flow chart of step S305, as can be seen from Fig. 5, this step specifically comprises:

S501: Determine the thermal resistance of the formation according to the thermal conductivity of the formation, the average heat dissipation coefficient of the formation, the production time of the oil well, and the radius of the wellbore. In a specific implementation, the thermal resistance of the formation is represented by _R1 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}$

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; a</span>}}\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; 29</span>}$

Among them, K _e is the thermal conductivity of the formation, a is the average heat dissipation coefficient of the formation, t is the production time of the oil well, and r _h is the radius of the wellbore.

S502: Determine the thermal resistance of the cement sheath according to the outer wall radius of the casing, the thermal conductivity of the cement sheath, and the wellbore radius. In a specific embodiment, the thermal resistance of the cement sheath is represented by _R2 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; cem</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; co</span>}}}$

Among them, r _co is the radius of the outer wall of the casing, K _cem is the thermal conductivity of the cement sheath, and r _h is the radius of the wellbore.

S503: Determine the thermal resistance of the casing wall according to the thermal conductivity of the casing, the radius of the inner wall of the casing, and the radius of the outer wall of the casing. In a specific embodiment, the heat conduction resistance of the formation is represented by R ₃ , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; cas</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; co</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}}$

Among them, K _cas is the thermal conductivity of the casing, r _ci is the radius of the inner wall of the casing, and r _co is the radius of the outer wall of the casing.

S504: Determine the heat convection liquid thermal resistance between the liquid and the casing according to the thermal conductivity of crude oil, the thermal conductivity of water, the water content of the liquid, the outer wall radius of the oil pipe, and the inner wall radius of the casing. The thermal resistance of the thermal convection liquid between the bushings is denoted by _R′4 , which is determined by the following formula:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ci</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}}$

Wherein, λ _o =0.01172(1-0.00054T)/γ _o

λ _w ＝3.51153-0.04436(T+273.15)+2.41233×10 ^-4 ×(T+273.15) ² -6.051×10 ^-7 ×(T+273.15) ³ +7.22766×10 ^-10 (T+273.15) ⁴ - 3.3716×10 ^-13 (T+273.15) ⁵

R′ ₄ is the thermal resistance of the convective liquid between the liquid and the casing, λ _o is the thermal conductivity of crude oil, γ _o is the relative density of crude oil, λ _w is the thermal conductivity of water, f _w is the water content of the liquid, r _to is the radius of the outer wall of the tubing , T is the temperature value of the annular fluid between the liquid and the casing.

S505: Determine the thermal resistance between the inner and outer walls of the oil pipe according to the radius of the outer wall of the oil pipe, the thermal conductivity of the oil pipe, and the radius of the inner wall of the oil pipe. In a specific embodiment, the heat conduction resistance between the inner and outer walls of the oil pipe is represented by _R5 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; tub</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; to</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ti</span>}}}$

Among them, K _tub is the thermal conductivity of the tubing, r _ti is the radius of the inner wall of the tubing, and r _to is the radius of the outer wall of the tubing.

S506: Determine the heat convection liquid thermal resistance between the liquid and the oil pipe according to the thermal conductivity of crude oil, the water content of the liquid, the thermal conductivity of water, the radius of the outer wall of the hollow rod, and the radius of the inner wall of the oil pipe. The thermal resistance between the heat convection liquid is represented by _R6 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ti</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}$

Among them, λ ₀ is the thermal conductivity of crude oil, f _w is the water content of liquid, λ _w is the thermal conductivity of water, r _o is the radius of the outer wall of the hollow rod, and r _ti is the radius of the inner wall of the tubing.

S507: Determine the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod according to the relative density of crude oil, the radius of the inner wall of the hollow rod, and K _Rod . In a specific embodiment, the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod is represented by _R , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; Rod</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$

Among them, _ri is the relative density of crude oil, r _o is the radius of the outer wall of the hollow rod, and K _Rod is.

S508: Determine the heat convection thermal resistance between the thermal fluid and the interior of the hollow rod according to the thermal conductivity of the water. In a specific embodiment, the heat convection thermal resistance between the thermal fluid and the hollow rod is represented by _R8 , then:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}$

Among them, _λw is the thermal conductivity of water.

Fig. 6 is a specific flow chart of the first embodiment of step S202 in Fig. 2. In this embodiment, when the wellbore section and the hollow rod section are the first type of section, step S202 includes:

S601: Determine the first thermal resistance according to the thermal convection liquid thermal resistance between the liquid and the oil pipe, the thermal convective liquid thermal resistance between the inner and outer walls of the hollow rod, and the thermal convective thermal resistance between the thermal fluid and the hollow rod coefficient, in a specific embodiment, the first thermal resistance coefficient is represented by K ₁₁ , then:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}}$

Among them, _R6 represents the heat convection liquid thermal resistance between the liquid and the oil pipe, _R7 represents the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod, and _R8 represents the heat convection thermal resistance between the thermal fluid and the interior of the hollow rod use.

S602: According to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the thermal convection thermal resistance between the air in the oil casing annulus and the casing, the thermal resistance between the inner and outer walls of the tubing, The heat convection liquid thermal resistance between the liquid and the oil pipe determines the second thermal resistance coefficient. In a specific embodiment, the second thermal resistance coefficient is represented by _K12 , then:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}}$

Among them, _R1 is the thermal resistance of the formation, _R2 is the thermal resistance of the cement sheath, _R3 is the thermal resistance of the casing wall, _R4 is the heat convection thermal resistance between the air in the oil jacket annulus and the casing, R ₅ is the thermal resistance between the inner and outer walls of the oil pipe, and _R6 is the thermal resistance of the heat convection liquid between the liquid and the oil pipe.

S603: Determine the third thermal resistance coefficient according to the thermal resistance between the inner and outer walls of the oil pipe, and the heat convection liquid thermal resistance between the liquid and the oil pipe. In a specific embodiment, the third thermal resistance coefficient is represented by _K13 , but:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}}$

Among them, _R5 is the thermal resistance between the inner and outer walls of the oil pipe, and _R6 is the heat convection liquid thermal resistance between the liquid and the oil pipe.

S604: Determine the fourth thermal resistance coefficient according to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, and the thermal convection thermal resistance between the air in the annulus of the oil jacket and the casing. In the implementation manner, the fourth thermal resistance coefficient is represented by K ₁₄ , then:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}$

Among them, _R1 is the thermal resistance of the formation, _R2 is the thermal resistance of the cement sheath, _R3 is the thermal resistance of the casing wall, and _R4 is the heat convection thermal resistance between the air in the oil jacket annulus and the casing.

Fig. 7 is a specific flowchart of the second embodiment of step S202 in Fig. 2. In this embodiment, when the wellbore section and the hollow rod section are the second type of section, step S202 includes:

S701: Determine the first thermal resistance according to the thermal convection liquid thermal resistance between the liquid and the oil pipe, the thermal convective liquid thermal resistance between the inner and outer walls of the hollow rod, and the thermal convective thermal resistance between the thermal fluid and the inside of the hollow rod coefficient, in a specific embodiment, the first thermal resistance coefficient is represented by K ₁₁ , then:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}}$

Among them, _R6 represents the heat convection liquid thermal resistance between the liquid and the oil pipe, _R7 represents the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod, and _R8 represents the heat convection thermal resistance between the thermal fluid and the interior of the hollow rod use.

S702: According to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the heat convection liquid thermal resistance between the liquid and the casing, the thermal resistance between the inner and outer walls of the tubing, and the The heat convection liquid thermal resistance between determines the second thermal resistance coefficient, in a specific embodiment, the second thermal resistance coefficient is represented by K ₁₂ , then:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}}$

Among them, R ₁ is the thermal resistance of the formation, R ₂ is the thermal resistance of the cement sheath, R ₃ is the thermal resistance of the casing wall, R′ ₄ is the thermal resistance of the thermal convection liquid between the liquid and the casing, and R ₅ is the thermal resistance of the oil The thermal resistance between the inner and outer walls of the tube, _R6 is the thermal resistance of the heat convection liquid between the liquid and the oil tube.

S703: Determine the third thermal resistance coefficient according to the thermal resistance between the inner and outer walls of the oil pipe and the heat convection liquid thermal resistance between the liquid and the oil pipe. In a specific embodiment, the third thermal resistance coefficient is represented by _K13 , but:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}}$

Among them, _R5 is the thermal resistance between the inner and outer walls of the oil pipe, and _R6 is the heat convection liquid thermal resistance between the liquid and the oil pipe.

S704: Determine the fourth thermal resistance coefficient according to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, and the thermal resistance of the thermal convection liquid between the liquid and the casing. In a specific embodiment, The fourth thermal resistance coefficient is represented by K ₁₄ , then:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}$

Among them, _R1 is the thermal resistance of the formation, _R2 is the thermal resistance of the cement sheath, _R3 is the thermal resistance of the casing wall, and _R′4 is the thermal resistance of the thermal convection liquid between the liquid and the casing.

As can be seen from FIG. 2, step S104 also includes:

S203: Determine the integral constant according to the wellhead temperature and the bottom hole temperature. In a specific embodiment, the integral constants are C ₁ , C ₂ , C ₃ , and C ₄ , which can be calculated by the following formula combined with characteristic values (ie known wellhead temperature and bottom hole temperature).

$\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ml</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\sqrt{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{{\mathrm{<span\; class="notranslate">\; ww</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}}$

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\sqrt{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{{\mathrm{<span\; class="notranslate">\; ww</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}}$

$\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; w</span>}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; w</span>}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ml</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}\frac{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}$

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\sqrt{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; ww</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}}$

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\sqrt{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; ww</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}}$

S204: Determine the temperature of the liquid in each wellbore section and the temperature of the fluid in each hollow rod section according to the integral constant and the thermal resistance coefficient. The present invention adopts the following energy balance equation in calculating the temperature field: enthalpy flowing into the unit body per unit time - enthalpy flowing out of the unit body per unit time + potential energy change = energy change in the unit body per unit time. From this, it can be deduced that the temperature of the liquid in the wellbore section is calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ml</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}\frac{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}$

The temperature of the fluid in the hollow rod section is calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ml</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; W</span>}\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}<span\; class="notranslate">\; )</span>$

Among them, _θ1 is the temperature of the liquid in the wellbore section, _θ2 is the temperature of the fluid in the hollow rod section, and t is the temperature of hot water or thin oil or chemical agent (the temperature of hot water or thin oil or chemical agent is mixed The temperature at the wellhead is close to the wellhead temperature, and the temperature at the bottom of the well is close to the temperature at the bottom of the well when the temperature of hot water or thin oil or chemical agent is mixed), K ₁₁ is the first thermal resistance coefficient, that is, the total heat transfer coefficient between the fluid inside and outside the hollow rod , W/m·℃; K ₁₂ is the second thermal resistance coefficient, that is, the total heat transfer coefficient between the hollow rod and tubing annular fluid and the surrounding formation, W/m·℃; K ₁₃ is the third thermal resistance coefficient, that is, the tubing The total heat transfer coefficient between internal and external fluids, W/m·℃; K ₁₄ is the fourth thermal resistance coefficient, that is, the total heat transfer coefficient between the fluid in the oil casing annulus and the bottom layer, m is the geothermal gradient, l is the temperature along the well depth direction length, g is the acceleration of gravity, q is the intensity of the heat source, and t _s is the temperature of the surface constant temperature layer. W is the water equivalent of oil-gas mixture, We is the water equivalent mixed with hot water or thin oil or chemical agent, W/℃; M _f is the mass flow rate of crude oil, C _f is the specific heat of crude oil, M _g is the mass flow rate of water, C _g is the specific heat of water, and W can be calculated as follows: W=M _f C _f +M _g C _g .

Fig. 8 is a structural block diagram of a system for determining wellbore temperature field distribution based on hollow rods provided by an embodiment of the present invention. It can be seen from Fig. 8 that the system includes:

The data acquisition device 101 is used for acquiring data related to the hollow rod and the wellbore.

In a specific embodiment, the data related to the hollow rod and the wellbore include the thermal conductivity of the formation, the average heat dissipation coefficient of the formation, the production time of the oil well, the radius of the wellbore, the radius of the outer wall of the casing, the thermal conductivity of the cement sheath, the thermal conductivity of the casing, the internal Wall radius, casing outer wall radius, annular radiation heat transfer coefficient, annular space natural convection heat transfer coefficient, tubing outer wall radius, tubing thermal conductivity, tubing inner wall radius, crude oil thermal conductivity, liquid moisture content, water thermal conductivity, hollow rod Radius of outer wall, relative density of crude oil, radius of inner wall of hollow rod, thermal conductivity of hollow rod.

The step length setting device 102 is used to set the step length according to the height of the fluid level in the wellbore and the depth of the wellbore. Fig. 15 is a schematic diagram of the technological structure of the hollow rod of the pumping well in the prior art. It can be seen from Fig. 15 that 1 is the formation, 2 is the cement sheath, 3 is the casing, 4 is the fluid surface, 5 is the heating cable, 6 is the tubing, 7 is the fluid in the well, and 8 is the oil layer.

The sectioning device 103 is used for dividing the wellbore and the hollow rod into a plurality of wellbore sections and hollow rod sections according to the step length. In a specific implementation, assuming that the total depth of the wellbore is 1000 meters, as shown in Figure 15, the height of the dynamic liquid surface is 300 meters, and the set step length is 100 meters, then in this embodiment, the wellbore can be divided into There are 10 wellbore sections, which are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700- 800 meters, 800-900 meters, 900-1000 meters. In this embodiment, the hollow rod can be divided into 10 hollow rod sections in total, from the bottom of the well to the wellhead, they are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, 500 meters -600 meters, 600-700 meters, 700-800 meters, 800-900 meters, 900-1000 meters.

The temperature determination device 104 is used to respectively determine the temperature of the liquid in the plurality of wellbore sections and the temperature of the fluid in the plurality of hollow rod sections according to the data. FIG. 2 is a specific flowchart of step S104.

The temperature field distribution determination device 105 is used for the temperature of the fluid in the multiple hollow rod sections and the temperature of the liquid in the multiple wellbore sections to form the wellbore temperature field distribution.

Fig. 9 is a specific structural block diagram of the temperature determining device 104 in a system for determining wellbore temperature field distribution based on a hollow rod provided by an embodiment of the present invention. It can be seen from Fig. 9 that the temperature determining device 104 specifically includes:

The thermal resistance determination module 201 is used to sequentially determine the thermal resistance of each wellbore section and hollow rod section. FIG. 10 is a specific diagram of the thermal resistance determination module used in 201 .

The thermal resistivity determination module 202 is configured to determine the thermal resistivity of each wellbore section and hollow rod section according to the thermal resistance.

The integral constant determination module 203 is used to determine the integral constant according to the wellhead temperature and the bottom hole temperature.

The temperature determination module 204 is configured to determine the temperature of the liquid in each wellbore section and the temperature of the fluid in each hollow rod section according to the integral constant and the thermal resistance coefficient.

As can be seen from FIG. 10, the thermal resistance determination module 201 specifically includes:

A judging unit 301, configured to sequentially judge whether each of the wellbore section and the hollow rod section is between the dynamic fluid level and the wellhead corresponding to the wellbore;

The first-type section setting unit 302 is used to set a plurality of wellbore sections and hollow rod sections between the dynamic fluid surface and the wellhead corresponding to the wellbore as the first when the judgment module judges yes. class segment;

The second-type segment setting unit 303 is used to set the plurality of wellbore segments and hollow rod segments between the dynamic fluid level and the well bottom corresponding to the wellbore as the second-type segment when the judgment module judges No ;

In a specific implementation, assuming that the total depth of the wellbore is 1000 meters, as shown in Figure 15, the height of the dynamic fluid surface is 300 meters, and the set step size is 100 meters, then in this embodiment, the wellbore can be divided into There are 10 wellbore sections, which are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700- 800 meters, 800-900 meters, 900-1000 meters. In this embodiment, the hollow rod can be divided into 10 hollow rod sections in total, which are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, and 500 meters from the bottom of the well to the wellhead. -600 meters, 600-700 meters, 700-800 meters, 800-900 meters, 900-1000 meters.

According to the judging unit 301 to the second type segment setting unit 03, it can be seen that the hollow rod segments 0-100 meters, 100-200 meters, and 200-300 meters are the second type segments, and the hollow rod segments are 300-400 meters, 400-500 meters , 500-600 meters, 600-700 meters, 700-800 meters, 800-900 meters, and 900-1000 meters are the first category. Wellbore sections of 0-100 meters, 100-200 meters, and 200-300 meters are the second type of sections; wellbore sections of 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700-800 meters 800-900 meters and 900-1000 meters are the first category.

A first thermal resistance determination unit 304, configured to determine the thermal resistance of the first type of segment according to the data;

The second thermal resistance determination unit 305 is configured to determine the thermal resistance of the second type of segment according to the data.

Fig. 11 is a specific structural block diagram of the first thermal resistance determination unit 304 in a system for determining wellbore temperature field distribution based on a hollow rod provided by an embodiment of the present invention. It can be seen from Fig. 11 that the first thermal resistance determination unit specifically includes:

The first thermal resistance determination unit 401 is used to determine the thermal resistance of the formation according to the thermal conductivity of the formation, the average heat dissipation coefficient of the formation, the production time of the oil well, and the radius of the wellbore. In a specific embodiment, the thermal resistance of the formation is represented by _R1 .

The second thermal resistance determination unit 402 is used to determine the thermal resistance of the cement sheath according to the outer wall radius of the casing, the thermal conductivity of the cement sheath, and the wellbore radius. In a specific embodiment, the thermal resistance of the cement sheath is represented by _R2 .

The third thermal resistance determination unit 403 is used to determine the thermal resistance of the casing wall according to the thermal conductivity of the casing, the radius of the inner wall of the casing, and the radius of the outer wall of the casing. In a specific embodiment, _R3 express.

The fourth thermal resistance determination unit 404 is used to determine the heat convection thermal resistance between the air in the oil jacket annulus and the casing according to the annular space radiation heat transfer coefficient, the annular space natural convection heat transfer coefficient, and the casing inner wall radius , in a specific embodiment, the thermal resistance of the heat convection liquid between the liquid and the casing is represented by R ₄ .

The fifth thermal resistance determination unit 405 is used to determine the thermal resistance between the inner and outer walls of the oil pipe according to the radius of the outer wall of the oil pipe, the thermal conductivity of the oil pipe, and the radius of the inner wall of the oil pipe. In a specific embodiment, the thermal resistance of heat conduction between the inner and outer walls of the oil pipe Represented by _R5 .

The sixth thermal resistance determining unit 406 is used to determine the heat convection liquid thermal resistance between the liquid and the oil pipe according to the thermal conductivity of crude oil, the water content of the liquid, the thermal conductivity of water, the radius of the outer wall of the hollow rod, and the radius of the inner wall of the oil pipe. In the embodiment, the heat convection thermal resistance between the gas and the inner wall of the oil pipe is represented by R ₆ .

The seventh thermal resistance determination unit 407 is configured to determine the thermal resistance of the heat convection liquid between the inner and outer walls of the hollow rod according to the relative density of crude oil, the radius of the inner wall of the hollow rod, and the thermal conductivity of the hollow rod. In a specific embodiment, the heat convective liquid thermal resistance between the inner and outer walls of the hollow rod is denoted by R ₇ .

The eighth thermal resistance determination unit 408 is configured to determine the thermal convection thermal resistance between the thermal fluid and the interior of the hollow rod according to the thermal conductivity of the water. In a specific embodiment, the heat convection thermal resistance between the thermal fluid and the interior of the hollow rod is represented by R ₈ .

Fig. 12 is a specific structural block diagram of the second thermal resistance determination unit 305 in a system for determining wellbore temperature field distribution based on a hollow rod provided by an embodiment of the present invention. It can be seen from Fig. 12 that the second thermal resistance determination unit specifically includes:

The first thermal resistance determination unit 501 is used to determine the thermal resistance of the formation according to the thermal conductivity of the formation, the average heat dissipation coefficient of the formation, the production time of the oil well, and the radius of the wellbore. In a specific embodiment, the thermal resistance of the formation is represented by _R1 .

The second thermal resistance determination unit 502 is used to determine the thermal resistance of the cement sheath according to the outer wall radius of the casing, the thermal conductivity of the cement sheath, and the radius of the wellbore. In a specific embodiment, the thermal resistance of the cement sheath is represented by _R2 .

The second thermal resistance determination unit 503 is used to determine the thermal resistance of the casing wall according to the thermal conductivity of the casing, the radius of the inner wall of the casing, and the radius of the outer wall of the casing. In a specific embodiment, _R3 express.

The fourth thermal resistance determination unit 504 is used to determine the heat convection liquid thermal resistance between the liquid and the casing according to the thermal conductivity of crude oil, the thermal conductivity of water, the water content of the liquid, the radius of the outer wall of the tubing, and the radius of the inner wall of the casing. In a specific embodiment, the heat convection liquid thermal resistance between the liquid and the casing is represented by _R′4 .

The fifth thermal resistance determination unit 505 is used to determine the thermal resistance between the inner and outer walls of the oil pipe according to the radius of the outer wall of the oil pipe, the thermal conductivity of the oil pipe, and the radius of the inner wall of the oil pipe. In a specific embodiment, the thermal resistance of heat conduction between the inner and outer walls of the oil pipe Represented by _R5 .

The sixth thermal resistance determination unit 506 is used to determine the heat convection liquid thermal resistance between the liquid and the oil pipe according to the thermal conductivity of crude oil, the water content of the liquid, the thermal conductivity of water, the radius of the outer wall of the hollow rod, and the radius of the inner wall of the oil pipe. In the embodiment, the thermal resistance of the heat convection liquid between the liquid and the oil pipe is represented by R ₆ .

The seventh thermal resistance determination unit 507 is configured to determine the thermal resistance of the heat convection liquid between the inner and outer walls of the hollow rod according to the relative density of crude oil, the radius of the inner wall of the hollow rod, and the thermal conductivity of the hollow rod. In a specific embodiment, the heat convective liquid thermal resistance between the inner and outer walls of the hollow rod is denoted by R ₇ .

The eighth thermal resistance determining unit 508 is configured to determine the thermal convection thermal resistance between the thermal fluid and the interior of the hollow rod according to the thermal conductivity of the water. In a specific embodiment, the heat convection thermal resistance between the thermal fluid and the interior of the hollow rod is represented by R ₈ .

Fig. 13 is a specific structural block diagram of Embodiment 1 of the thermal resistance coefficient determination module 202 in a system for determining the temperature field distribution of a wellbore based on a hollow rod provided by an embodiment of the present invention. In this embodiment, when the wellbore section 1. When the hollow rod segment is the first type segment, the thermal resistance coefficient determination module 202 includes:

The first thermal resistance coefficient determining unit 601 is used to determine the thermal resistance of the heat convection liquid between the liquid and the oil pipe, the thermal resistance of the heat convection liquid between the inner and outer walls of the hollow rod, and the thermal resistance between the thermal fluid and the interior of the hollow rod. The heat convection thermal resistance determines the first thermal resistance coefficient, and in a specific embodiment, the first thermal resistance coefficient is represented by K ₁₁ .

The second thermal resistance coefficient determining unit 602 is used for determining the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the thermal convection thermal resistance between the air in the oil jacket annulus and the casing, The thermal resistance between the inner and outer walls of the oil pipe and the heat convection liquid thermal resistance between the liquid and the oil pipe determine the second thermal resistance coefficient. In a specific embodiment, the second thermal resistance coefficient is represented by _K12 .

The third thermal resistance coefficient determination unit 603 is used to determine the third thermal resistance coefficient according to the thermal resistance between the inner and outer walls of the oil pipe and the heat convection liquid thermal resistance between the liquid and the oil pipe. In a specific embodiment, the first The three thermal resistivity coefficients are represented by K ₁₃ .

The fourth thermal resistance coefficient determining unit 604 is used to determine the thermal resistance according to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, and the thermal convection thermal resistance between the air in the oil jacket annulus and the casing The fourth thermal resistance coefficient, in a specific embodiment, the fourth thermal resistance coefficient is represented by K ₁₄ .

Fig. 14 is a specific structural block diagram of Embodiment 2 of the thermal resistance coefficient determination module 202 in a system for determining the temperature field distribution of a wellbore based on a hollow rod provided by an embodiment of the present invention. In this embodiment, when the wellbore section 1. When the hollow rod segment is the second type segment, the thermal resistance coefficient determination module 202 includes:

The thermal resistance coefficient first determining unit 701 is used for determining the thermal resistance of the heat convection liquid between the liquid and the oil pipe, the thermal resistance of the heat convection liquid between the inner and outer walls of the hollow rod, and the thermal resistance between the thermal fluid and the interior of the hollow rod. The heat convection thermal resistance determines the first thermal resistance coefficient, and in a specific embodiment, the first thermal resistance coefficient is represented by K ₁₁ .

The thermal resistance coefficient second determination unit 702 is used to determine the thermal resistance according to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the thermal resistance of the thermal convection between the liquid and the casing, and the relationship between the inner and outer walls of the tubing. The thermal resistance between the liquid and the heat convection liquid between the liquid and the oil pipe determines the second thermal resistance coefficient. In a specific embodiment, the second thermal resistance coefficient is represented by _K12 .

The third thermal resistance coefficient determination unit 703 is used to determine the third thermal resistance coefficient according to the thermal resistance between the inner and outer walls of the oil pipe and the heat convection liquid thermal resistance between the liquid and the oil pipe. In a specific embodiment, the first The three thermal resistivity coefficients are represented by K ₁₃ .

The fourth determination unit 704 of thermal resistance coefficient is used to determine the fourth thermal resistance according to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, and the thermal resistance of the thermal convection liquid between the liquid and the casing coefficient, in a specific embodiment, the fourth thermal resistance coefficient is represented by K ₁₄ .

As can be seen from FIG. 9, the temperature determination device 104 also includes:

The integral constant determination module 203 is used to determine the integral constant according to the wellhead temperature and the bottom hole temperature. In a specific embodiment, the integral constants are C ₁ , C ₂ , C ₃ , and C ₄ , which can be calculated by combining the characteristic values (that is, the known wellhead temperature and bottomhole temperature) through formulas.

$\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ml</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\sqrt{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{{\mathrm{<span\; class="notranslate">\; ww</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}}$

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\sqrt{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{{\mathrm{<span\; class="notranslate">\; ww</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}}$

$\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; w</span>}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; w</span>}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ml</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}\frac{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}$

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\sqrt{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; ww</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}}$

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\sqrt{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; ww</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}}$

The temperature determination module 204 is configured to determine the temperature of the liquid in each wellbore section and the temperature of the fluid in each hollow rod section according to the integral constant and the thermal resistance coefficient. The present invention adopts the following energy balance equation in calculating the temperature field: enthalpy flowing into the unit body per unit time - enthalpy flowing out of the unit body per unit time + potential energy change = energy change in the unit body per unit time. From this, it can be deduced that the temperature of the liquid in the wellbore section is calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ml</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}\frac{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}$

The temperature of the fluid in the hollow rod section is calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ml</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; W</span>}\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}}<span\; class="notranslate">\; )</span>$

Among them, _θ1 is the temperature of the liquid in the wellbore section, _θ2 is the temperature of the fluid in the hollow rod section, and t is the temperature of hot water or thin oil or chemical agent (the temperature of hot water or thin oil or chemical agent is mixed The temperature at the wellhead is close to the wellhead temperature, and the temperature at the bottom of the well is close to the temperature at the bottom of the well when the temperature of hot water or thin oil or chemical agent is mixed), K ₁₁ is the first thermal resistance coefficient, that is, the total heat transfer coefficient between the fluid inside and outside the hollow rod , W/m·℃; K ₁₂ is the second thermal resistance coefficient, that is, the total heat transfer coefficient between the hollow rod and tubing annular fluid and the surrounding formation, W/m·℃; K ₁₃ is the third thermal resistance coefficient, that is, the tubing The total heat transfer coefficient between internal and external fluids, W/m·℃; K ₁₄ is the fourth thermal resistance coefficient, that is, the total heat transfer coefficient between the fluid in the oil casing annulus and the bottom layer, m is the geothermal gradient, l is the temperature along the well depth direction length, g is the acceleration of gravity, q is the intensity of the heat source, and t _s is the temperature of the surface constant temperature layer. W is the water equivalent of oil-gas mixture, We is the water equivalent mixed with hot water or thin oil or chemical agent, W/℃; M _f is the mass flow rate of crude oil, C _f is the specific heat of crude oil, M _g is the mass flow rate of water, C _g is the specific heat of water, and W can be calculated as follows: W=M _f C _f +M _g C _g .

The technical solutions of the present invention will be described in detail below in combination with specific implementation modes. In a specific implementation, assuming that the total depth of the wellbore and the length of the hollow rod are both 1000 meters, as shown in Figure 15, the height of the dynamic fluid surface is 300 meters, and the set step length is 100 meters, then this implementation In total, the wellbore can be divided into 10 wellbore sections, from the bottom to the wellhead are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, 500-600 meters, 600 meters -700 meters, 700-800 meters, 800-900 meters, 900-1000 meters. In total, the hollow rod can be divided into 10 hollow rod sections, which are 0-100 meters, 100-200 meters, 200-300 meters, 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700-800 meters, 800-900 meters, 900-1000 meters. According to steps S301 to S303, it can be seen that the wellbore sections 0-100 meters, 100-200 meters, and 200-300 meters are the second type of sections, and the wellbore sections are 300-400 meters, 400-500 meters, 500-600 meters, 600- 700 meters, 700-800 meters, 800-900 meters, and 900-1000 meters are the first category. Hollow pole sections 0-100 meters, 100-200 meters, 200-300 meters are the second type of sections, hollow pole sections 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700-800 meters meters, 800-900 meters, and 900-1000 meters are the first category. The following describes how to determine the liquid temperature in each wellbore section and the fluid temperature in the hollow rod section according to the data.

1. The second category

Wellbore section 0-100 meters, 100-200 meters, 200-300 meters, hollow rod section 0-100 meters, 100-200 meters, 200-300 meters are the second type of section, taking the wellbore section 0-100 meters as an example Be explained.

(1) Determine the thermal resistance of the formation in the wellbore section of 0-100 meters, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the heat convection liquid thermal resistance between the liquid and the casing, and the thermal resistance between the inner and outer walls of the tubing Resistance, heat convection liquid heat resistance between liquid and oil pipe, heat convection liquid heat resistance between inner and outer walls of hollow rod, heat convection heat resistance between thermal fluid and hollow rod.

(2) According to the thermal resistance, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the heat convection liquid thermal resistance between the liquid and the casing, the thermal resistance between the inner and outer walls of the tubing, and the thermal resistance between the liquid and the tubing Convection liquid thermal resistance, thermal convection liquid thermal resistance between the inner and outer walls of the hollow rod, thermal convection thermal resistance between the thermal fluid and the hollow rod determine the first thermal resistance coefficient, the second thermal resistance coefficient, and the third thermal resistance coefficient , The fourth thermal resistance coefficient.

(3) Determine the integral constants C ₁ , C ₂ , C ₃ , and C ₄ according to the wellhead temperature and bottom hole temperature.

(4), according to ${\mathrm{\&theta;}}_1=C_1(1+\frac{r_1{w}_e}{K_{11}})e^{r_{1}l}+C_2(1+\frac{r_2{w}_e}{K_{11}})e^{r_{2}l}+t_{\mathrm{the\; s}}+\mathrm{ml}+m\frac{w-w_e}{K_{12}}$ Calculate the temperature of the fluid in the wellbore section.

according to ${\mathrm{\&theta;}}_2=C_3{e}^{r_{3}l}+C_4{e}^{r_{4}l}+t_{\mathrm{the\; s}}+\mathrm{ml}+m(\frac{w_e}{K_{14}}-W\frac{K_{13}+K_{14}}{K_{13}{K}_{14}})$ Calculate the temperature of the fluid in the hollow rod segment.

2. The first type of wellbore section

The wellbore sections of 300-400 meters, 400-500 meters, 500-600 meters, 600-700 meters, 700-800 meters, 800-900 meters, and 900-1000 meters are the first category sections, and the hollow rod sections are 300-400 meters , 400-500 meters, 500-600 meters, 600-700 meters, 700-800 meters, 800-900 meters, and 900-1000 meters are the first category of sections. The following wellbore section of 300-400 meters is taken as an example for illustration.

(1) Determine the thermal resistance of the formation at 300-400 meters in the wellbore section, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the heat convection thermal resistance between the air in the oil casing annulus and the casing, and the inner and outer walls of the tubing The thermal resistance between the liquid, the heat convection liquid heat resistance between the liquid and the oil pipe, the heat convection liquid heat resistance between the inner and outer walls of the hollow rod, and the heat convection heat resistance between the thermal fluid and the hollow rod.

(2) According to the thermal resistance, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the thermal convection thermal resistance between the air in the oil jacket annulus and the casing, the thermal resistance between the inner and outer walls of the tubing, the liquid and the tubing The heat convection liquid thermal resistance between, the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod, and the heat convection thermal resistance between the thermal fluid and the hollow rod determine the first thermal resistance coefficient, the second thermal resistance coefficient, and the second thermal resistance coefficient. Three coefficients of thermal resistance, the fourth coefficient of thermal resistance.

(3) Determine the integral constants C ₁ , C ₂ , C ₃ , and C ₄ according to the wellhead temperature and bottom hole temperature.

(4), according to ${\mathrm{\&theta;}}_1=C_1(1+\frac{r_1{w}_e}{K_{11}})e^{r_{1}l}+C_2(1+\frac{r_2{w}_e}{K_{11}})e^{r_{2}l}+t_{\mathrm{the\; s}}+\mathrm{ml}+m\frac{w-w_e}{K_{12}}$ Calculate the temperature of the fluid in the wellbore section.

according to ${\mathrm{\&theta;}}_2=C_3{e}^{r_{3}l}+C_4{e}^{r_{4}l}+t_{\mathrm{the\; s}}+\mathrm{ml}+m(\frac{w_e}{K_{14}}-W\frac{K_{13}+K_{14}}{K_{13}{K}_{14}})$ Calculate the temperature of the fluid in the hollow rod segment.

This scheme does not need iterative calculation of the total thermal conductivity, and the calculation speed is faster, and the calculation step size can be set arbitrarily. The smaller the step size, the higher the calculation accuracy. This method has very good stability and convergence, and is more suitable for computer programming. As follows:

1. Data preparation, the data mainly includes: formation thermal conductivity, formation average heat dissipation coefficient, oil well production time, wellbore radius, casing outer wall radius, cement sheath thermal conductivity, casing thermal conductivity, casing inner wall radius, casing outer wall radius, Annular radiation heat transfer coefficient, annular natural convection heat transfer coefficient, oil pipe outer wall radius, oil pipe thermal conductivity, oil pipe inner wall radius, crude oil thermal conductivity, liquid moisture content, water thermal conductivity, hollow rod outer wall radius, crude oil relative density, hollow The radius of the inner wall of the rod, the thermal conductivity of the hollow rod.

2. Calculate the thermal resistance.

3. Calculate the thermal resistance coefficient K ₁₁ , K ₁₂ , K ₁₃ , K ₁₄ .

4. Calculated from the wellhead, l=0, k=1.

5. Calculate C1, C2, C3, and C4 from known conditions.

6. Calculate the temperature θ ₁ of the fluid in the wellbore and θ ₂ of the fluid in the hollow rod.

7. k=k+1, l=l+dl, return to step 3 to continue iterative calculation. If l>well depth, the iteration ends.

In summary, the present invention provides a method and system for determining the temperature field distribution of the wellbore based on the hollow rod, which is an accurate solution for determining the temperature field distribution of the wellbore based on the hollow rod. By obtaining data related to the hollow rod and the wellbore According to the set step length, the wellbore and hollow rod are divided into multiple wellbore sections and hollow rod sections, and the temperature of the liquid in each wellbore section and the temperature of the fluid in the hollow rod section are determined in turn, so that the temperature field distribution of the wellbore is obtained , which provides a data basis for the follow-up selection of reasonable wellhead mixing displacement and temperature to meet the existing heavy oil, extra heavy oil and super heavy oil production, thereby improving the production efficiency of heavy oil, extra heavy oil and super heavy oil efficiency.

The present invention is aimed at the exploitation of heavy oil, extra heavy oil and super heavy oil, and the viscosity is mainly affected by temperature. It proposes a method for calculating the temperature field distribution of the hollow rod mixed with hot water wellbore, and forms a set of interpretation tools. . Through the step-by-step calculation and analysis of the temperature field of the wellbore after adding hot water, the viscosity of crude oil in each section can be calculated, and the rod fluid friction force and pipe fluid friction load can be further calculated, and finally the pumping unit can be calculated by the upstroke of the rod string. Suspended point load. It can adjust the displacement and temperature of the wellhead mixing of hot water, which has achieved the purpose of optimizing the efficiency of the lifting system. It can not only be used for the calculation of the temperature field distribution of the hollow rod mixed with hot water, but also can be used for mixing thin oil and chemical agents. The iterative calculation of the total thermal conductivity has faster calculation speed, and the calculation step size can be set arbitrarily. When the step size is smaller, the calculation accuracy is higher. It has very good stability and convergence, and is more suitable for computer programming.

Aiming at the extraction of crude oil with high freezing point, high wax content and high viscosity, the present invention uses the basic principles of thermodynamics to establish a mathematical model describing the temperature field distribution of the hollow rod mixed with hot water wellbore, and uses numerical methods to solve the problem, so as to understand and master the method of mixing hot water During the process, the rod, wellbore and formation rock temperature distribution and change trend are used to guide the production practice to choose a reasonable wellhead mixing discharge rate and temperature.

The calculation method involved in the present invention has good calculation stability and high calculation accuracy, and the calculation method and the interpretation tool can well predict and adjust the hollow rod cable heating power and lifting process parameters.

Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be implemented through computer programs to instruct related hardware to complete, and the programs can be stored in general computer-readable storage media. During execution, it may include the processes of the embodiments of the above-mentioned methods. Wherein, the storage medium may be a magnetic disk, an optical disk, a read-only memory (Read-Only Memory, ROM) or a random access memory (Random Access Memory, RAM), etc.

Those skilled in the art can also understand that whether various functions listed in the embodiments of the present invention are implemented by hardware or software depends on specific applications and design requirements of the entire system. Those skilled in the art may use various methods to implement the described functions for each specific application, but such implementation should not be understood as exceeding the protection scope of the embodiments of the present invention.

In the present invention, specific examples have been applied to explain the principles and implementation methods of the present invention, and the descriptions of the above examples are only used to help understand the method of the present invention and its core idea; meanwhile, for those of ordinary skill in the art, according to this The idea of the invention will have changes in the specific implementation and scope of application. To sum up, the contents of this specification should not be construed as limiting the present invention.

Claims (16)

1. A method for determining wellbore temperature field distribution based on a hollow rod, characterized in that, the method comprises: Obtain data related to hollow rods and wellbore; Setting the step size according to the height of the moving liquid level in the wellbore and the depth of the wellbore; Dividing the shaft and the hollow rod into a plurality of shaft sections and hollow rod sections according to the step size; Determining the temperature of the liquid in the plurality of wellbore sections and the temperature of the fluid in the plurality of hollow rod sections respectively according to the data; The temperature of the fluid in the plurality of hollow rod sections and the temperature of the liquid in the plurality of wellbore sections constitute the wellbore temperature field distribution. 2. The method according to claim 1, characterized in that, said data include formation thermal conductivity, formation average heat dissipation coefficient, oil well production time, wellbore radius, casing outer wall radius, cement sheath thermal conductivity, casing thermal conductivity Coefficient, casing inner wall radius, casing outer wall radius, annular radiation heat transfer coefficient, annular space natural convection heat transfer coefficient, tubing outer wall radius, tubing thermal conductivity, tubing inner wall radius, crude oil thermal conductivity, liquid moisture content, water thermal conductivity coefficient, the radius of the outer wall of the hollow rod, the relative density of crude oil, the radius of the inner wall of the hollow rod, and the thermal conductivity of the hollow rod. 3. The method according to claim 2, wherein determining the temperature of the liquid in the plurality of wellbore sections and the temperature of the fluid in the plurality of hollow rod sections respectively according to the data includes: Determine the thermal resistance of each wellbore section and hollow rod section in turn; Determine the thermal resistance coefficient of each wellbore section and hollow rod section according to the thermal resistance; Determine the integral constant according to the wellhead temperature and bottom hole temperature; The temperature of the liquid in each wellbore section and the temperature of the fluid in each hollow rod section are determined according to the integral constant and the thermal resistance coefficient. 4. The method according to claim 3, wherein determining the thermal resistance of each shaft section and hollow rod section in turn comprises: Sequentially determine whether each of the wellbore section and the hollow rod section is between the dynamic fluid level and the wellhead corresponding to the wellbore; When it is judged to be yes, set multiple wellbore sections and hollow rod sections between the dynamic fluid surface and the wellhead corresponding to the wellbore as the first type of section; Otherwise, set multiple wellbore sections and hollow rod sections between the dynamic fluid surface and the well bottom corresponding to the wellbore as the second type of section; determining the thermal resistance of said first type segment according to said data; The thermal resistance of said second type of segment is determined from said data sheet. 5. The method according to claim 4, wherein determining the thermal resistance of the first type of segment according to the data includes: Determine the thermal resistance of the formation according to the thermal conductivity of the formation, the average heat dissipation coefficient of the formation, the production time of the oil well, and the radius of the wellbore; Determine the thermal resistance of the cement sheath according to the outer wall radius of the casing, the thermal conductivity of the cement sheath, and the wellbore radius; Determine the thermal resistance of the sleeve wall according to the thermal conductivity of the sleeve, the radius of the inner wall of the sleeve, and the radius of the outer wall of the sleeve; Determine the heat convection thermal resistance between the air in the oil jacket annulus and the casing according to the annulus radiation heat transfer coefficient, the annulus natural convection heat transfer coefficient, and the inner wall radius of the casing; Determine the thermal resistance between the inner and outer walls of the oil pipe according to the radius of the outer wall of the oil pipe, the thermal conductivity of the oil pipe, and the radius of the inner wall of the oil pipe; Determine the heat convection liquid thermal resistance between the liquid and the oil pipe according to the thermal conductivity of crude oil, the water content of the liquid, the heat conductivity of water, the radius of the outer wall of the hollow rod, and the radius of the inner wall of the oil pipe; Determine the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod according to the relative density of crude oil, the radius of the inner wall of the hollow rod, and the thermal conductivity of the hollow rod; The heat convection thermal resistance between the thermal fluid and the interior of the hollow rod is determined according to the thermal conductivity of the water. 6. The method according to claim 5, characterized in that, when the wellbore section and the hollow rod section are the first type section, the thermal resistance of each wellbore section and the hollow rod section is determined according to the thermal resistance Coefficients include: The first thermal resistance coefficient is determined according to the heat convection liquid thermal resistance between the liquid and the oil pipe, the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod, and the heat convection thermal resistance between the thermal fluid and the inside of the hollow rod; According to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the thermal convection thermal resistance between the air in the oil casing annulus and the casing, the thermal resistance between the inner and outer walls of the tubing, the liquid and The thermal resistance of the heat convection liquid between the oil pipes determines the second thermal resistance coefficient; Determine the third thermal resistance coefficient according to the thermal resistance between the inner and outer walls of the oil pipe and the heat convection liquid thermal resistance between the liquid and the oil pipe; The fourth thermal resistance coefficient is determined according to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, and the thermal convection thermal resistance between the air in the annulus of the oil jacket and the casing. 7. The method according to claim 4, wherein determining the thermal resistance of the second type of segment according to the data includes: Determine the thermal resistance of the formation according to the thermal conductivity of the formation, the average heat dissipation coefficient of the formation, the production time of the oil well, and the radius of the wellbore; Determine the thermal resistance of the cement sheath according to the outer wall radius of the casing, the thermal conductivity of the cement sheath, and the wellbore radius; Determine the thermal resistance of the sleeve wall according to the thermal conductivity of the sleeve, the radius of the inner wall of the sleeve, and the radius of the outer wall of the sleeve; Determine the heat convection liquid thermal resistance between the liquid and the casing according to the thermal conductivity of crude oil, the thermal conductivity of water, the water content of the liquid, the radius of the outer wall of the tubing, and the radius of the inner wall of the casing; Determine the thermal resistance between the inner and outer walls of the oil pipe according to the radius of the outer wall of the oil pipe, the thermal conductivity of the oil pipe, and the radius of the inner wall of the oil pipe; Determine the heat convection liquid thermal resistance between the liquid and the oil pipe according to the thermal conductivity of crude oil, the water content of the liquid, the heat conductivity of water, the radius of the outer wall of the hollow rod, and the radius of the inner wall of the oil pipe; Determine the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod according to the relative density of crude oil, the radius of the inner wall of the hollow rod, and the thermal conductivity of the hollow rod; The heat convection thermal resistance between the thermal fluid and the interior of the hollow rod is determined according to the thermal conductivity of the water. 8. The method according to claim 7, characterized in that, when the wellbore section and the hollow rod section are of the second type, the thermal resistance of each wellbore section and the hollow rod section is determined according to the thermal resistance Coefficients include: The first thermal resistance coefficient is determined according to the heat convection liquid thermal resistance between the liquid and the oil pipe, the heat convection liquid thermal resistance between the inner and outer walls of the hollow rod, and the heat convection thermal resistance between the thermal fluid and the inside of the hollow rod; According to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the thermal resistance of the thermal convection liquid between the liquid and the casing, the thermal resistance between the inner and outer walls of the tubing, and the thermal resistance between the liquid and the tubing The thermal convection liquid thermal resistance determines the second thermal resistance coefficient; Determine the third thermal resistance coefficient according to the thermal resistance between the inner and outer walls of the oil pipe and the heat convection liquid thermal resistance between the liquid and the oil pipe; The fourth thermal resistance coefficient is determined according to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, and the thermal resistance of the thermal convection liquid between the liquid and the casing. 9. A system for determining the temperature field distribution of a wellbore based on a hollow rod, characterized in that the system includes: The data acquisition device is used to acquire data related to the hollow rod and the wellbore; Step length setting device, used to set the step length according to the height of the fluid level in the wellbore and the depth of the wellbore; segmenting device, used to divide the wellbore and the hollow rod into multiple wellbore sections and hollow rod sections according to the step length; A temperature determination device, used to determine the temperature of the liquid in the plurality of wellbore sections and the temperature of the fluid in the plurality of hollow rod sections respectively according to the data; The temperature field distribution determination device is used for the temperature of the fluid in the plurality of hollow rod sections and the temperature of the liquid in the plurality of wellbore sections to form the wellbore temperature field distribution. 10. The system according to claim 9, characterized in that said data include formation thermal conductivity, formation average heat dissipation coefficient, oil well production time, wellbore radius, casing outer wall radius, cement sheath thermal conductivity, casing thermal conductivity Coefficient, casing inner wall radius, casing outer wall radius, annular radiation heat transfer coefficient, annular space natural convection heat transfer coefficient, tubing outer wall radius, tubing thermal conductivity, tubing inner wall radius, crude oil thermal conductivity, liquid moisture content, water thermal conductivity coefficient, the radius of the outer wall of the hollow rod, the relative density of crude oil, the radius of the inner wall of the hollow rod, and the thermal conductivity of the hollow rod. 11. The system according to claim 9, wherein said temperature determining means comprises: The thermal resistance determination module is used to sequentially determine the thermal resistance of each wellbore section and hollow rod section; A thermal resistivity determination module, configured to determine the thermal resistivity of each wellbore section and hollow rod section according to the thermal resistance; The integral constant determination module is used to determine the integral constant according to the wellhead temperature and the bottom hole temperature; The temperature determination module is used to determine the temperature of the liquid in each wellbore section and the temperature of the fluid in each hollow rod section according to the integral constant and the thermal resistance coefficient. 12. The system according to claim 11, wherein said thermal resistance determining module comprises: A judging unit, used to sequentially judge whether each of the wellbore section and the hollow rod section is between the dynamic fluid level and the wellhead corresponding to the wellbore; The first-type section setting unit is used to set a plurality of wellbore sections and hollow rod sections between the dynamic fluid level and the wellhead corresponding to the wellbore as the first type when the judging module judges yes part; The second-type section setting unit is used to set the plurality of wellbore sections and hollow rod sections between the dynamic fluid surface and the well bottom corresponding to the wellbore as the second-type section when the judging module judges No; a first thermal resistance determining unit, configured to determine the thermal resistance of the first type of segment according to the data; The second thermal resistance determining unit is configured to determine the thermal resistance of the second type of segment according to the data. 13. The system according to claim 12, wherein the first thermal resistance determining unit comprises: The first thermal resistance determining unit is used to determine the thermal resistance of the formation according to the formation thermal conductivity, the average heat dissipation coefficient of the formation, the production time of the oil well, and the radius of the wellbore; The second thermal resistance determining unit is used to determine the thermal resistance of the cement sheath according to the outer wall radius of the casing, the thermal conductivity of the cement sheath, and the wellbore radius; The third thermal resistance determination unit is used to determine the thermal resistance of the sleeve wall according to the thermal conductivity of the sleeve, the radius of the inner wall of the sleeve, and the radius of the outer wall of the sleeve; The fourth thermal resistance determination unit is used to determine the heat convection thermal resistance between the air in the oil jacket annulus and the casing according to the annular radiation heat transfer coefficient, the annular natural convection heat transfer coefficient, and the inner wall radius of the casing; The fifth thermal resistance determination unit is used to determine the thermal resistance between the inner and outer walls of the oil pipe according to the radius of the outer wall of the oil pipe, the thermal conductivity of the oil pipe, and the radius of the inner wall of the oil pipe; The sixth thermal resistance determination unit is used to determine the heat convection liquid thermal resistance between the liquid and the oil pipe according to the thermal conductivity of crude oil, the water content of the liquid, the thermal conductivity of water, the radius of the outer wall of the hollow rod, and the radius of the inner wall of the oil pipe; The seventh thermal resistance determination unit is used to determine the thermal resistance of the heat convection liquid between the inner and outer walls of the hollow rod according to the relative density of crude oil, the radius of the inner wall of the hollow rod, and the thermal conductivity of the hollow rod; The eighth thermal resistance determination unit is configured to determine the thermal resistance of heat convection between the thermal fluid and the interior of the hollow rod according to the thermal conductivity of the water. 14. The system according to claim 13, characterized in that, when the wellbore section and the hollow rod section are the first type of section, the thermal resistance coefficient determination module includes: The first thermal resistance coefficient determining unit is used to determine the thermal resistance of the thermal convection liquid between the liquid and the oil pipe, the thermal resistance of the thermal convection liquid between the inner and outer walls of the hollow rod, and the thermal resistance between the thermal fluid and the interior of the hollow rod. The convective thermal resistance determines the first thermal resistance coefficient; The second thermal resistance coefficient determination unit is used for determining the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the thermal convection thermal resistance between the air in the oil jacket annulus and the casing, and the thermal resistance of the oil casing. The thermal resistance between the inner and outer walls of the tube and the heat convection liquid thermal resistance between the liquid and the oil tube determine the second thermal resistance coefficient; The third thermal resistance coefficient determination unit is used to determine the third thermal resistance coefficient according to the thermal resistance between the inner and outer walls of the oil pipe and the heat convection liquid thermal resistance between the liquid and the oil pipe; The fourth thermal resistance coefficient determination unit is used to determine the first thermal resistance coefficient according to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, and the thermal convection thermal resistance between the air in the oil jacket annulus and the casing. Four thermal resistance coefficients. 15. The system according to claim 12, wherein the second thermal resistance determining unit comprises: The first thermal resistance determining unit is used to determine the thermal resistance of the formation according to the formation thermal conductivity, the average heat dissipation coefficient of the formation, the production time of the oil well, and the radius of the wellbore; The second thermal resistance determining unit is used to determine the thermal resistance of the cement sheath according to the outer wall radius of the casing, the thermal conductivity of the cement sheath, and the wellbore radius; The third thermal resistance determination unit is used to determine the thermal resistance of the sleeve wall according to the thermal conductivity of the sleeve, the radius of the inner wall of the sleeve, and the radius of the outer wall of the sleeve; The fourth thermal resistance determining unit is used to determine the heat convection liquid thermal resistance between the liquid and the casing according to the thermal conductivity of crude oil, the thermal conductivity of water, the water content of the liquid, the radius of the outer wall of the tubing, and the radius of the inner wall of the casing; The fifth thermal resistance determination unit is used to determine the thermal resistance between the inner and outer walls of the oil pipe according to the radius of the outer wall of the oil pipe, the thermal conductivity of the oil pipe, and the radius of the inner wall of the oil pipe; The sixth thermal resistance determination unit is used to determine the heat convection liquid thermal resistance between the liquid and the oil pipe according to the thermal conductivity of crude oil, the water content of the liquid, the thermal conductivity of water, the radius of the outer wall of the hollow rod, and the radius of the inner wall of the oil pipe; The seventh thermal resistance determination unit is used to determine the thermal resistance of the heat convection liquid between the inner and outer walls of the hollow rod according to the relative density of crude oil, the radius of the inner wall of the hollow rod, and the thermal conductivity of the hollow rod; The eighth thermal resistance determination unit is configured to determine the thermal resistance of heat convection between the thermal fluid and the interior of the hollow rod according to the thermal conductivity of the water. 16. The system according to claim 15, characterized in that, when the wellbore section and the hollow rod section are the second-type sections, the thermal resistance coefficient determination module includes: The first determination unit of the thermal resistance coefficient is used for the thermal resistance of the thermal convection liquid between the liquid and the oil pipe, the thermal resistance of the thermal convection liquid between the inner and outer walls of the hollow rod, and the thermal resistance between the thermal fluid and the interior of the hollow rod. The convective thermal resistance determines the first thermal resistance coefficient; The second determination unit of the thermal resistance coefficient is used for determining the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, the thermal resistance of the thermal convection liquid between the liquid and the casing, and the thermal resistance between the inner and outer walls of the tubing. The thermal resistance of the thermal resistance, the heat convection liquid thermal resistance between the liquid and the oil pipe determines the second thermal resistance coefficient; The third thermal resistance coefficient determination unit is used to determine the third thermal resistance coefficient according to the thermal resistance between the inner and outer walls of the oil pipe and the heat convection liquid thermal resistance between the liquid and the oil pipe; The fourth determining unit of the thermal resistance coefficient is used to determine the fourth thermal resistance coefficient according to the thermal resistance of the formation, the thermal resistance of the cement sheath, the thermal resistance of the casing wall, and the thermal resistance of the thermal convection liquid between the liquid and the casing .