Intelligent control system of drilling fluid ground cooling equipment

Abstract

The invention belongs to the technical field of drilling engineering, particularly relates to an intelligent control system for drilling fluid ground cooling equipment, and aims to solve the problems that in the prior art, the well temperature change trend cannot be accurately predicted, the intelligent immediate adjustment function is not achieved, the labor cost is high, the equipment energy consumption is high, and the refrigeration effect is poor. The system comprises a drilling fluid conveying mechanism used for conveying drilling fluid into a drilling tool, and a measuring mechanism is arranged in the drilling tool and used for measuring temperature data of the drilling fluid at a well mouth and a well bottom; the drilling fluid output mechanism is arranged on the well mouth, is connected with the well mouth in a sealing manner, and is used for draining the drilling fluid which flows through the underground and then returns out; the cooling mechanism is arranged in the drilling fluid output mechanism and used for cooling the drilling fluid in the drilling fluid output mechanism. According to the method, the optimal power of the drilling fluid ground cooling equipment can be automatically calculated, the model is continuously self-corrected, the calculation accuracy is improved, and the labor cost can be remarkably reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of drilling engineering, and specifically relates to an intelligent control system for a surface cooling device of drilling fluid. Background Art

[0002] With the continuous increase in the exploration and development efforts of deep and unconventional oil and gas, the high-temperature problem faced by drilling operations has become increasingly prominent. In addition, during the development of new energy sources such as hot dry rock, the downhole temperature generally exceeds 180°C, and it also faces the high-temperature problem. Problems such as high failure rates of tools and instruments caused by high downhole temperatures, accelerated aging speed of drilling fluid, and unstable performance have severely restricted drilling efficiency and economy. The surface cooling device of drilling fluid is the core equipment for significantly reducing the temperature of high-temperature drilling fluid. By reducing the inlet temperature of the drilling fluid, the circulating temperature of the bottom-hole drilling fluid is further decreased.

[0003] The surface cooling devices of drilling fluid commonly used on-site still have the problem of low automation. The equipment cannot analyze the actual drilling data in real time, nor can it predict the trend of well temperature changes. It does not have an intelligent immediate adjustment function and only relies on experience for on-site manual adjustment by generally no less than 3 equipment configuration personnel, resulting in high labor costs, high equipment energy consumption, and poor refrigeration effect.

[0004] Based on this, the present invention proposes an intelligent control system for a surface cooling device of drilling fluid. Summary of the Invention

[0005] In order to solve the above problems in the prior art, that is, the prior art cannot accurately predict the trend of well temperature changes, does not have an intelligent immediate adjustment function, has high labor costs, high equipment energy consumption, and poor refrigeration effect, the present invention provides an intelligent control system for a surface cooling device of drilling fluid. The system includes a drilling fluid conveying mechanism, a measuring mechanism, a drilling fluid output mechanism, and a cooling mechanism;

[0006] The drilling fluid conveying mechanism is used to convey the drilling fluid into the drill string, and a measuring mechanism is arranged in the drill string. The measuring mechanism is used to measure the temperature data of the drilling fluid at the wellhead and the bottom hole;

[0007] The drilling fluid output mechanism is arranged on the wellhead and is hermetically connected to the wellhead. The drilling fluid output mechanism is used to divert the drilling fluid that returns after flowing through the downhole;

[0008] The cooling mechanism is arranged in the drilling fluid output mechanism. The cooling mechanism is used to cool the drilling fluid in the drilling fluid output mechanism.

[0009] In some preferred embodiments, the drilling fluid conveying mechanism includes a hose, an inlet tank, a drilling pump, and an inlet pipeline;

[0010] The inlet tank is fixed to the ground above the wellhead. The inlet tank is connected to the input end of the drilling pump. The output end of the drilling pump is hermetically fixed and communicated with one end of the inlet pipeline. The other end of the inlet pipeline is hermetically fixed and communicated with one end of the hose. The other end of the hose is hermetically fixed and communicated with the drill string.

[0011] In some preferred embodiments, the drill string includes a drill string above the wellhead, drill pipes, and a bottom hole assembly that are sequentially hermetically fixed and communicated. The drill string above the wellhead is hermetically connected and communicated with the other end of the hose. The bottom hole assembly is fixed to the drill bit.

[0012] In some preferred embodiments, the measuring mechanism includes a downhole measuring element and a wellhead measuring element;

[0013] The downhole measuring element is fixed inside the bottom hole assembly of the drill string. The downhole measuring element is used to measure the temperature data of the drilling fluid inside the bottom hole assembly.

[0014] The wellhead measuring element is fixed inside the drill string above the wellhead. The wellhead measuring element is used to measure the drilling displacement, drilling weight on bit, drill string rotation speed, wellhead displacement, and wellhead temperature data.

[0015] In some preferred embodiments, the drilling fluid output mechanism includes an elevated tank, an outlet pipeline, and an outlet tank;

[0016] The elevated tank is fixed and communicated with the wellhead. The elevated tank is used to drain the drilling fluid returning from the wellbore annulus. The elevated tank is fixed and communicated with one end of the outlet pipeline. The other end of the outlet pipeline is disposed inside the outlet tank. The outlet tank is fixed to the ground above the wellhead.

[0017] In some preferred embodiments, the cooling mechanism includes a ground cooling device for drilling fluid, calculation software, and a control panel;

[0018] The ground cooling device for drilling fluid pumps high-temperature drilling fluid from the outlet tank. The ground cooling device for drilling fluid performs heat exchange through air cooling, heat exchanger water cooling, or / and spraying to remove the heat in the high-temperature drilling fluid;

[0019] The calculation software is used to predict the temperature at different well depths and send the best power obtained from the analysis to the control panel in the form of an instruction according to the set downhole circulation temperature range. The control panel adjusts the power of the ground cooling device for drilling fluid in real time.

[0020] In some preferred embodiments, the drilling parameter data includes well type, formation physical properties, drilling fluid physical properties, drill string movement state, normal drilling conditions, and complex drilling conditions information.

[0021] In some preferred embodiments, the drilling parameter data further includes the data measured by the measuring mechanism.

[0022] In some preferred embodiments, the wellhead temperature data includes the temperatures of the elevated tank 7 and the inlet tank 11.

[0023] In some preferred embodiments,

[0024] The calculation software further optimizes the drilling construction parameters within the set range of drilling construction parameter changes based on the downhole heat transfer calculation model and the initial conditions and boundary conditions set in the circulation process, so that the downhole temperature reaches the preset value;

[0025] The downhole heat transfer calculation model includes:

[0026] Fluid heat transfer model inside the drill string:

[0027]

[0028] Heat transfer model inside the drill string wall:

[0029]

[0030] Fluid heat transfer model in the annulus:

[0031]

[0032] Heat transfer model inside the wellbore wall:

[0033]

[0034] Heat transfer model in the formation:

[0035]

[0036] Where: T is the temperature; Q is the internal heat source, Q fe is the frictional heat energy per unit length, Q re is the frictional rotational heat energy per unit length; q is the drilling fluid flow rate; h is the convective heat transfer coefficient; r and Z are the radial coordinate and the axial coordinate respectively; ρ is the density; C is the specific heat; k is the thermal conductivity. Subscripts: m represents the drilling fluid, p represents the drill string, pi represents the inner wall of the drill tool, po represents the outer wall of the drill tool, w represents the drill tool wall, a represents the annulus, c represents the casing, ci represents the inner wall of the casing, co represents the outer wall of the casing, f represents the formation;

[0037] The initial conditions are: the initial temperatures of the fluid - wellbore - formation are all the original formation temperatures, and the temperature gradients of each component are all equal to the original formation temperature gradient; the temperature inside the drill pipe at the wellhead is equal to the injection fluid temperature;

[0038] The boundary conditions are as follows: at the bottom of the well, the temperatures of the drilling fluid inside the drill pipe, the temperature of the drill pipe wall, and the temperature of the annulus fluid are all equal; the formation at a certain distance outside the wellbore is not disturbed and is the original formation temperature.

[0039] Advantages of the present invention:

[0040] After a target temperature range at the bottom of the well is given, the present invention can automatically calculate the optimal power of the ground cooling equipment for the drilling fluid, continuously self-correct the model, and improve the calculation accuracy, which can significantly reduce labor costs, save energy, and improve drilling efficiency. Description of the drawings

[0041] By reading the detailed description of the non-restrictive embodiments with reference to the following drawings, other features, objects, and advantages of the present application will become more apparent:

[0042] Figure 1 It is an overall connection schematic diagram of an intelligent control system for a ground cooling equipment of drilling fluid according to the present invention. Detailed implementation manners

[0043] The present application will be further described in detail below with reference to the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the related invention and are not intended to limit the invention. Additionally, it should be noted that for the sake of description, only parts related to the relevant invention are shown in the drawings.

[0044] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The present application will be described in detail below with reference to the drawings and embodiments.

[0045] As Figure 1 shown, the present invention provides an intelligent control system for a ground cooling equipment of drilling fluid, which includes a drilling fluid conveying mechanism, a measuring mechanism, a drilling fluid output mechanism, and a cooling mechanism;

[0046] The drilling fluid conveying mechanism is used to convey the drilling fluid into the drill string, and a measuring mechanism is arranged in the drill string, and the measuring mechanism is used to measure the temperature data of the drilling fluid at the wellhead and the bottom of the well;

[0047] The drilling fluid output mechanism is arranged on the wellhead and is hermetically connected to the wellhead, and the drilling fluid output mechanism is used to recover the drilling fluid that returns after flowing through the wellbore;

[0048] The cooling mechanism is arranged in the drilling fluid output mechanism, and the cooling mechanism is used to cool the drilling fluid in the drilling fluid output mechanism.

[0049] Preferably, the drilling fluid conveying mechanism includes a hose 1, an inlet tank 11, a drilling pump 12, and an inlet pipeline 13;

[0050] The inlet tank 11 is fixed to the surface above the wellhead. The inlet tank 11 is connected to the input end of the drilling pump 12. The output end of the drilling pump 12 is hermetically fixed and communicated with one end of the inlet pipeline 13. The other end of the inlet pipeline 13 is hermetically fixed and communicated with one end of the hose 1. The other end of the hose 1 is hermetically fixed and communicated with the drill string.

[0051] Preferably, the drill string includes a drill string 2 above the wellhead, drill pipes 3, and a bottom hole assembly 4 that are hermetically fixed and communicated in sequence. The drill string 2 above the wellhead is hermetically connected and communicated with the other end of the hose 1. The bottom hole assembly 4 is fixed to the drill bit 5.

[0052] Preferably, the measuring mechanism includes a downhole measuring element 21 and a wellhead measuring element 22;

[0053] The downhole measuring element 21 is fixed in the bottom hole assembly 4 of the drill string. The downhole measuring element 21 is used to measure the temperature data of the drilling fluid in the bottom hole assembly 4.

[0054] The wellhead measuring element 22 is fixed in the drill string 2 above the wellhead of the drill string. The wellhead measuring element 22 is used to measure the drilling displacement, drilling weight on bit, drill string rotation speed, wellhead displacement, and wellhead temperature data.

[0055] Among them, the downhole measuring element 21 not only includes the function of measuring downhole parameters, but also can send hydraulic pulses or electromagnetic signals; the wellhead measuring element 22 not only includes the function of measuring wellhead (surface) parameters, but also includes converting the hydraulic pulses or electromagnetic signals sent by the downhole measuring element 21 or the bottom hole assembly 4 of the drill string into digital or / and image signals.

[0056] Preferably, the drilling fluid output mechanism includes an elevated tank 7, an outlet pipeline 8, and an outlet tank 9;

[0057] The elevated tank 7 is fixed and communicated with the wellhead. The elevated tank 7 is used to drain the drilling fluid returned from the wellbore annulus 6. The elevated tank 7 is hermetically fixed and communicated with one end of the outlet pipeline 8. The other end of the outlet pipeline 8 is disposed in the outlet tank 9. The outlet tank 9 is fixed to the surface above the wellhead.

[0058] Preferably, the cooling mechanism includes a drilling fluid surface cooling device 10, a calculation software 23, and a control panel 24;

[0059] The drilling fluid surface cooling device 10 pumps high-temperature drilling fluid from the outlet tank 9. The drilling fluid surface cooling device 10 performs heat exchange through air cooling, heat exchanger water cooling, or / and spraying to remove the heat in the high-temperature drilling fluid;

[0060] The calculation software 23 is used to predict the temperature at different well depths, and according to the set downhole circulation temperature range, send the best power obtained from the analysis to the control panel 24 in the form of an instruction, and the control panel 24 adjusts the power of the drilling fluid surface cooling device 10 in real time.

[0061] Among them, the control panel 24 is installed on the drilling fluid surface cooling device 10. The instruction of the control panel 24 comes from the calculation software 23 on the computer, and the control panel 24 can control the power change of the drilling fluid surface cooling device.

[0062] Preferably, the drilling parameter data includes well type, formation physical properties, drilling fluid physical properties, drill string movement state, normal drilling working conditions and complex drilling working conditions information.

[0063] Preferably, the drilling parameter data also includes the data measured by the measuring mechanism.

[0064] Preferably, the wellhead temperature data includes the temperatures of the elevated tank 7 and the inlet tank 11.

[0065] Preferably, after drilling a certain well section, the calculation software 23 analyzes the change of the bottom hole temperature actually measured by the downhole measuring element 21, and corrects the temperature prediction model at different well depths.

[0066] Through the correction of the prediction model at different well depths, the present invention can predict the temperature at different well depths more accurately, and then further optimize the best power of the drilling fluid surface cooling device.

[0067] Preferably, when the drilling fluid circulates in the wellbore, heat exchange occurs between the formation and the annular drilling fluid, and heat exchange occurs between the annular drilling fluid and the drilling fluid in the drill string. The entire circulation process of the drilling fluid in the well can be regarded as a heat exchanger with certain boundary conditions, and the heat exchange method is convective heat transfer and heat conduction; therefore, the calculation software 23 also optimizes the drilling construction parameters within the set range of drilling construction parameter changes based on the downhole heat transfer calculation model and the initial conditions and boundary conditions set in the circulation process, so that the downhole temperature reaches the preset value;

[0068] The downhole heat transfer calculation model includes:

[0069] Fluid heat transfer model in the drill string:

[0070]

[0071] Heat transfer model in the drill string wall:

[0072]

[0073] Fluid heat transfer model in the annulus:

[0074]

[0075] Heat transfer model in the wellbore wall:

[0076]

[0077] Heat transfer model in the formation:

[0078]

[0079] Where: T is the temperature, °C; Q is the internal heat source, Qfe is the frictional heat energy per unit length, Qre is the frictional rotational heat energy per unit length, W / m; q is the drilling fluid flow rate, L / s; h is the convective heat transfer coefficient, W / (m²·°C); r and Z are the radial coordinate and axial coordinate respectively, m; ρ is the density, kg / m³; C is the specific heat, J / (kg·°C); k is the thermal conductivity, W / (m·°C). Subscripts: m represents the drilling fluid, p represents the drill string, pi represents the inner wall of the drill tool, po represents the outer wall of the drill tool, w represents the drill tool wall, a represents the annulus, c represents the casing, ci represents the inner wall of the casing, co represents the outer wall of the casing, f represents the formation.

[0080] The initial conditions are: the initial temperatures of the fluid - wellbore - formation are all the original formation temperature, and the temperature gradients of each component are all equal to the original formation temperature gradient; the temperature inside the drill pipe 3 at the wellhead is equal to the injection fluid temperature;

[0081] The boundary conditions are: at the bottom of the well, the temperatures of the drilling fluid inside the drill pipe 3, the temperature of the drill pipe wall, and the temperature of the annulus fluid are all equal; the formation at a certain distance outside the wellbore is not disturbed and is the original formation temperature.

[0082] Among them, "the formation at a certain distance outside the wellbore is not disturbed" specifically means that the formation at a certain distance (≤2.8 m) outside the wellbore is not disturbed.

[0083] Among them, by optimizing the drilling construction parameters as the guiding parameters for on - site operators, on - site operators can make selective judgments according to these guiding parameters. For example, they can adjust the part of the guiding parameters that overlaps with the parameters actually used on site.

[0084] Among them, the drilling construction parameters described in this embodiment include the data measured by the wellhead measuring element 22 and the drilling parameter data mentioned in the present invention.

[0085] Among them, the calculation software 23 is installed on a computer, and its working steps are as follows:

[0086] Step S1, analyze the design data, analyze 6 types of wellbore circulation temperature influencing factors including well type, formation physical properties, drilling fluid physical properties, drill string motion state, normal drilling conditions, and complex drilling conditions, and predict the temperature at different well depths;

[0087] Step S2: Set the downhole circulating temperature range. Based on the predicted well temperature, calculation software 23 combines the actual drill string assembly, drilling displacement, rate of penetration, drill string rotation speed, bottom hole temperature, and wellhead temperature data to determine the range of the drilling fluid inlet temperature when the downhole set target temperature is reached after circulating for a certain period of time, and then determines the optimal power of the equipment.

[0088] Step S3: Calculation software 23 sends the analyzed optimal power to control panel 24 in the form of an instruction. Control panel 24 adjusts the power of the drilling fluid surface cooling equipment 10 in real time to reduce the ground drilling fluid inlet temperature.

[0089] Step S4: After drilling a certain well section, the calculation software analyzes the change in the bottom hole temperature, corrects the temperature prediction model for different well depths, and predicts the temperature of the un-drilled well section more accurately.

[0090] In the process of drilling in the present invention, the drilling fluid is pressurized by a drilling pump 12 from an inlet tank 11, enters an inlet pipeline 13, further flows through a hose 1 on the ground and a drill string 2 above the wellhead, and then enters the interior of the downhole drill string. Then it flows through the interior of a drill pipe 3 and a bottom hole assembly 4, and jets out from a drill bit 5 into the annulus 6 between the drill string and the wellbore wall, and finally returns to the wellhead from an elevated trough 7 and enters an outlet tank 9. To reduce the temperature of the drilling fluid in the inlet tank 11, a drilling fluid surface cooling equipment 10 is connected after the outlet tank 9. It conducts heat exchange through air cooling, heat exchanger water cooling, or / and spraying to take away the heat in the high-temperature drilling fluid and reduce the temperature of the drilling fluid.

[0091] Terms such as "first", "second", etc. are used to distinguish similar objects, rather than to describe or represent a specific order or sequence.

[0092] The term "comprising" or any other similar term is intended to cover non-exclusive inclusion, such that a process, method, article, or equipment / device comprising a series of elements includes not only those elements but also other elements not expressly listed, or also elements inherent to these processes, methods, articles, or equipment / device.

[0093] So far, the technical solution of the present invention has been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. An intelligent control system for drilling fluid surface cooling equipment, It is characterized in that The system includes a drilling fluid delivery mechanism, a measuring mechanism, a drilling fluid output mechanism and a cooling mechanism; The drilling fluid delivery mechanism is used to deliver the drilling fluid to the drilling tool, and the drilling tool is provided with a measuring mechanism, and the measuring mechanism is used to measure the temperature data of the drilling fluid at the wellhead and the bottom of the well; The drilling fluid output mechanism is arranged on the wellhead and is sealed and connected to the wellhead, and the drilling fluid output mechanism is used to drain the drilling fluid that returns after flowing through the well; The cooling mechanism is arranged in the drilling fluid output mechanism, and is used for cooling the drilling fluid in the drilling fluid output mechanism.

2. According to claim 1, an intelligent control system for drilling fluid surface cooling equipment, It is characterized in that The drilling fluid delivery mechanism comprises a water hose (1), an inlet tank (11), a drilling pump (12) and an inlet pipeline (13); The inlet tank (11) is fixed to the surface of the well, the inlet tank (11) is connected to the input end of the drilling pump (12), the output end of the drilling pump (12) is sealed and fixed to and communicated with one end of the inlet pipeline (13), the other end of the inlet pipeline (13) is sealed and fixed to and communicated with one end of the water hose (1), and the other end of the water hose (1) is sealed and fixed to and communicated with the drilling tool.

3. According to claim 2, an intelligent control system for drilling fluid surface cooling equipment, It is characterized in that The drilling tool comprises an upper wellhead drilling tool (2), a drill rod (3) and a lower drilling tool assembly (4) which are sealed, fixed and connected in sequence; the upper wellhead drilling tool (2) is sealed and connected to the other end of the water hose (1); and the lower drilling tool assembly (4) is fixed to a drill bit (5).

4. According to claim 3, an intelligent control system for drilling fluid surface cooling equipment, It is characterized in that The measuring mechanism comprises a downhole measuring element (21) and a wellhead measuring element (22); The downhole measuring element (21) is fixed in the lower drilling tool assembly (4) of the drilling tool, and the downhole measuring element (21) is used to measure the temperature data of the drilling fluid outside the lower drilling tool assembly (4); The wellhead measuring element (22) is fixed in the drilling tool (2) above the wellhead of the drilling tool, and the wellhead measuring element (22) is used to measure drilling displacement, drilling pressure, drilling tool rotation speed, wellhead displacement, and wellhead temperature data.

5. According to claim 4, an intelligent control system for drilling fluid surface cooling equipment, It is characterized in that The drilling fluid output mechanism comprises an elevated tank (7), an outlet pipeline (8) and an outlet tank (9); The elevated trough (7) is fixed to and communicated with the wellhead. The elevated trough (7) is used to drain the drilling fluid returned from the wellbore annulus (6). The elevated trough (7) is sealed and fixed to and communicated with one end of the outlet pipeline (8). The other end of the outlet pipeline (8) is arranged in an outlet tank (9), and the outlet tank (9) is fixed to the ground above the well.

6. The intelligent control system for the ground cooling equipment of drilling fluid according to claim 5, It is characterized in that The cooling mechanism includes a drilling fluid surface cooling device (10), a calculation software (23) and a control panel (24); The drilling fluid surface cooling device (10) pumps high-temperature drilling fluid from the outlet tank (9), and the drilling fluid surface cooling device (10) performs heat exchange through air cooling, heat exchanger water cooling or / and spraying to remove heat from the high-temperature drilling fluid; The calculation software (23) is used to predict the temperature at different well depths and send the optimal power obtained by analysis to the control panel (24) in the form of instructions according to the set downhole circulation temperature range. The control panel (24) adjusts the power of the drilling fluid surface cooling device (10) in real time.

7. The intelligent control system for the ground cooling equipment of drilling fluid according to claim 6, It is characterized in that The drilling parameter data includes well type, formation properties, drilling fluid properties, drill string movement status, normal drilling conditions and complex drilling conditions information.

8. The intelligent control system for the ground cooling equipment of drilling fluid according to claim 7, It is characterized in that The drilling parameter data also includes data measured by a measuring mechanism.

9. The intelligent control system for the ground cooling equipment of drilling fluid according to claim 8, It is characterized in that The wellhead temperature data includes the temperatures of the elevated tank 7 and the inlet tank 11 .

10. An intelligent control system for drilling fluid surface cooling equipment according to claim 9, It is characterized in that The calculation software (23) also optimizes the drilling construction parameters within a set range of drilling construction parameter variations based on the downhole heat transfer calculation model and the initial conditions and boundary conditions set in the cycle process, so that the downhole temperature reaches a preset value; The downhole heat transfer calculation model includes: Heat transfer model of fluid in drill string: Heat transfer model in drill string wall: Heat transfer model of fluid in annulus: Heat transfer model in the well wall: Heat transfer model in the formation: Where: T is temperature; Q is internal heat source, Q fe is the friction heat energy per unit length, Q re is the friction rotation heat energy per unit length; q is the drilling fluid flow rate; h is the convective heat transfer coefficient; r and Z are radial and axial coordinates respectively; ρ is density; C is specific heat; k is thermal conductivity. Subscripts: m represents drilling fluid, p represents drill string, pi represents the inner wall of drill tool, po represents the outer wall of drill tool, w represents the wall of drill tool, a represents annulus, c represents casing, ci represents the inner wall of casing, co represents the outer wall of casing, and f represents formation; The initial conditions are: the initial temperatures of the fluid-wellbore-formation are all the original geothermal temperatures, the temperature gradients of the various components are all equal to the original geothermal gradients; the temperature inside the wellhead drill pipe (3) is equal to the temperature of the injected fluid; The boundary conditions are: at the bottom of the well, the temperature of the drilling fluid in the drill pipe (3), the temperature of the drill pipe wall, and the temperature of the annular fluid are all equal; the strata at a certain distance from the wellbore are undisturbed and are at the original ground temperature.

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