A method for determining the friction coefficient between drill rod and borehole wall during drilling rod lifting process.

Abstract

This invention relates to a method for determining the friction coefficient between the drill rod and the borehole wall during the drilling rod lifting process, belonging to the field of geological exploration technology. Addressing the problems of traditional rock mechanics parameter testing being detached from the in-situ environment and the difficulty in accurately quantifying the friction coefficient between the drill rod and the borehole wall, this invention relies on a digital drilling system to collect drilling parameters in real time. By simplifying the mechanical environment during the rod lifting process and establishing a segmented mathematical model of energy conservation and force balance, it achieves in-situ, dynamic, and high-precision acquisition of the drill rod-borehole wall friction coefficient corresponding to different borehole depths. This invention eliminates the need for indoor sample processing, can acquire friction parameters in-situ that closely match actual geological conditions, has a high data acquisition frequency and small error, and can provide accurate basic parameters for drilling-while-drilling lithology identification, rock mass quality evaluation, and intelligent drilling control. It is suitable for geological exploration projects in deep strata and complex geological environments.

Description

Technical Field

[0001] This invention relates to a method for determining the friction coefficient between the drill rod and the borehole wall during the drilling rod lifting process, belonging to the field of geological exploration technology. Background Technology

[0002] Currently, rock physical and mechanical parameters and rock mass quality classification are mainly achieved through laboratory tests and core drilling. Laboratory tests primarily obtain rock mass mechanical parameters through uniaxial or triaxial compression tests. However, the rock samples obtained from these laboratory tests are removed from the actual geological environment of the field. Uniaxial or triaxial tests require the core samples to be made into standard specimens, which places high demands on the rock samples retrieved from the field. Furthermore, the sample processing process inevitably causes damage to the rock. Therefore, the rock mass mechanical parameters obtained from laboratory tests cannot reflect the true characteristics of the rock mass in the field.

[0003] Drilling rig operating parameters are correlated with rock mechanics parameters and rock mass structural characteristics. Quantitatively characterizing these parameters is crucial for achieving rock mass quality classification research. Although numerous transformation mechanisms and theoretical systems have been proposed, the complex and variable geological conditions make it difficult to determine the friction coefficient between the drill rod and the borehole wall during operation. Summary of the Invention

[0004] To address the problems of traditional rock mechanics parameter testing being detached from the in-situ environment and the difficulty in accurately quantifying the friction coefficient between the drill rod and the borehole wall, this invention proposes a method for determining the friction coefficient between the drill rod and the borehole wall during the drilling rod lifting process. Based on an existing intelligent digital drilling system (which can monitor drilling pressure, oil pressure, pump pressure, rotational speed, and displacement parameters during the drilling process, with a data acquisition interval of 0.001 seconds, the high-frequency acquisition can reduce errors during the drilling process), drilling rig parameters (drill pressure, displacement, lifting speed) are collected during the drilling operation. By simplifying the mechanical environment of the rod lifting process, a segmented energy conservation and force balance mathematical model is established to achieve in-situ, dynamic, and high-precision acquisition of the drill rod-hole wall friction coefficient corresponding to different borehole depths.

[0005] A method for determining the friction coefficient between the drill rod and the borehole wall during the drilling rod lifting process, the specific steps of which are as follows: (1) Determine the weight M of the drill bit based on the selected drill bit and drill rod. 钻头 and the weight of a single drill pipe M 钻杆 ; (2) Connect the drill bit, drill rod and drilling machine, start the drilling machine to drill, and record the time node for adding the drill rod and the total displacement of the drill rod through the digital drilling system during the drilling process; (3) During the drilling and rod lifting stage, real-time data are collected on drilling pressure, displacement, and rod lifting speed, based on the single mechanical environment of overcoming only the weight of the drill string and axial friction during the rod lifting stage (see...). Figure 1Establish the energy conservation equation; divide the lifting process into several intervals, with the time in each interval being... A segmented energy conservation equation and a segmented force balance model were established, and the friction coefficient between the drill rod and the borehole wall in the corresponding depth section was calculated segment by segment.

[0006] During the drilling process, the feed pressure does work when the drill bit advances towards the bottom of the hole, the torque does work when the drill bit rotates, and the friction between the drill bit and the rock at the bottom of the hole does work. The friction work includes the circumferential friction work when the drill bit rotates and axial friction work when the drill bit advances forward. During the lifting process after drilling, it is only necessary to overcome the weight of the drill rod and drill bit and the axial friction between the drill rod and the hole wall. Its mechanical field environment is relatively simple. Therefore, the energy conservation equation for step (3) is: ; In the formula, This refers to the energy consumed by the drilling rig during the entire lifting process. This refers to the kinetic energy generated during the entire lifting process of the drill bit and drill rod. The work done by friction during the entire lifting process The work done by the weight of the drill bit and drill rod during the entire lifting process.

[0007] Due to the complex characteristics of the geological structure, the friction between the drill rod and the borehole wall varies throughout the drilling and hoisting process, and the friction coefficient is not a constant value. Therefore, the key to determining the friction coefficient between the drill rod and the borehole wall is to match the friction coefficient with the displacement inside the borehole at a certain time.

[0008] Furthermore, the piecewise energy conservation equation in step (3) is as follows: ; The lifting force is provided by the hydraulic cylinder and is related to the hydraulic pressure. ; ; Therefore, ; In the formula, To improve the energy consumed by the drilling rig during a certain period of the process, Here, A represents the oil pressure monitored at a certain time, and A is the effective pressure-bearing area of ​​the cylinder piston. The displacement over a certain time period. The kinetic energy of the drill bit and drill pipe over a certain time period. The number of drill pipes within a certain time period. , These refer to the mass of the drill bit and the mass of a single drill rod, respectively. The speed over a certain period of time.

[0009] Furthermore, the method for establishing the segmented force equilibrium model in step (3) is as follows: The work done by friction differs from the work done by kinetic energy and gravity. Kinetic energy and gravity work involve velocity and displacement over a specific time period, but friction involves energy loss in areas other than the displacement portion. Figure 2 As shown, assume that there are multiple regions u1 to u2 with different friction coefficients throughout the drilling process. x The contact area between the outer wall of the drill rod and the hole wall is rectangular. During the drilling and rod lifting stage, the drill rod offset simplifies the contact area between the drill rod and the hole wall to half of the outer wall of the drill rod, that is, the area of ​​friction force is half of the outer wall of the drill rod. During the drill string lifting stage, within the drilling depth H region, frictional work is performed between the entire drill string and the borehole wall: ; In the formula, Work done by friction Friction; Since the lifting speed per unit time is basically constant during the lifting process, meaning the drill pipe and drill bit are in a state of force equilibrium during lifting, and the hydraulic pressure is only used to overcome friction and gravity, the force analysis during the lifting process is as follows: Figure 1 The force equilibrium model per unit time is: ; in, ; ; In the formula, is the lateral normal force on the drill pipe, perpendicular to the contact surface with the borehole wall. Its magnitude is determined by factors such as borehole axis deviation, drill pipe self-weight bending, and local borehole diameter reduction, and is expressed in kN; H is the drilling depth throughout the process, expressed in meters.

[0010] Furthermore, step (3) involves calculating the friction coefficient between the drill rod and the borehole wall in segments corresponding to the borehole depth. The specific method is as follows: According to the piecewise energy conservation equation, the energy conservation equation for the lifting process is as follows: ; because , ; The drilling depth H and remaining depth L change with time t as follows: , This is the average speed over that time period; therefore, ; ; ; When the drill pipe is lifted Time When the formula changes, it becomes: ; Then, the section of road coefficient of friction for: ; In the formula, The coefficient of friction per unit contact area is the frictional force generated per unit contact area under a unit normal force, with units of 1. ; For the drilling process The displacement during this time period is expressed in meters (m). and t and The oil pressure data is monitored in real time, in MPa; A is the effective pressure-bearing area of ​​the cylinder piston, in square meters. and t and The velocity at any given moment, expressed in m / s; , The values ​​represent the mass of the drill bit and a single drill pipe, respectively, in tons (t); n represents the number of drill pipes included in this time period; g is the acceleration due to gravity, taken as 9.8 m / s² in this formula. 2 R represents the outer radius of the drill bit and drill rod, in meters; N represents the lateral normal force per unit length of the drill rod caused by hole inclination, bending, and diameter reduction, in kN / m; the direction of the lateral normal force is perpendicular to the contact surface, and its magnitude is determined by factors such as borehole axis deviation, drill rod self-weight bending, and local diameter reduction of the borehole wall.

[0011] The drill pipe moves at a basically constant speed during the lifting process, that is... , The coefficient of friction between the drill rod and the borehole wall in the corresponding depth section is: ; If there is a reduction in drill pipe between the two sections, the coefficient of friction is: ; In the formula, The coefficient of friction per unit contact area is dimensionless. and t and The oil pressure data is monitored in real time, in MPa; A is the effective pressure-bearing area of ​​the cylinder piston, in MPa. R is the outer radius of the drill bit and drill rod, in meters; N is the lateral normal force per unit length of the drill rod caused by hole inclination, bending, and diameter reduction, in kN / m; the direction of the lateral normal force is perpendicular to the contact surface, and its magnitude is determined by factors such as borehole axis deviation, drill rod self-weight bending, and local diameter reduction of the borehole wall. The magnitude of the lateral normal force is affected by the field environment, and its value is not uniformly distributed.

[0012] The beneficial effects of this invention are: (1) Based on the existing intelligent digital drilling system, the present invention collects drilling rig parameters (drilling pressure, displacement, lifting speed) during drilling operations. By simplifying the mechanical environment of the rod lifting process, a segmented energy conservation and force balance mathematical model is established to achieve in-situ, dynamic, and high-precision acquisition of the drill rod-hole wall friction coefficient corresponding to different hole depth sections. (2) This invention does not require indoor sample processing and can obtain friction parameters that conform to actual geological conditions in situ. It has a high data acquisition frequency and small error, and can provide accurate basic parameters for drilling lithology identification, rock mass quality evaluation and drilling intelligent control. It is suitable for geological exploration projects in deep strata and complex geological environments. Attached Figure Description

[0013] Figure 1 This is a force analysis diagram for the lifting stage; Figure 2 This is a diagram showing the frictional force during the lifting stage; Figure 3 This is a diagram of the mechanical environment during the lifting stage of Example 1; Figure 4 The hole depth-time curve is shown. Figure 5 This is the original scatter plot of oil pressure in Example 1 within the time interval of 981~1867s. Detailed Implementation

[0014] The present invention will be further described in detail below with reference to specific embodiments, but the scope of protection of the present invention is not limited to the content described. Invention Overview A method for determining the friction coefficient between the drill rod and the borehole wall during the drilling rod lifting process, the specific steps of which are as follows: (1) Determine the weight M of the drill bit based on the selected drill bit and drill rod. 钻头 and the weight of a single drill pipe M 钻杆 ; (2) Connect the drill bit, drill rod and drilling machine, start the drilling machine to drill, and record the time node for adding the drill rod and the total displacement of the drill rod through the digital drilling system during the drilling process; (3) During the drilling and rod lifting stage, real-time data are collected on drilling pressure, displacement, and rod lifting speed, based on the single mechanical environment of overcoming only the weight of the drill string and axial friction during the rod lifting stage (see...). Figure 1Establish the energy conservation equation; divide the lifting process into several intervals, with the time in each interval being... A piecewise energy conservation equation and a piecewise force balance model are established, and the friction coefficient between the drill rod and the borehole wall is calculated piecewise for the corresponding borehole depth sections. Specifically, during the drilling process, the feed pressure does work when the drill bit advances towards the bottom of the hole, the torque does work when the drill bit rotates, and the friction work between the drill bit and the bottom rock is also done. The friction work includes the circumferential friction work when the drill bit rotates and the axial friction work when the drill bit advances forward. During the lifting process after drilling, it is only necessary to overcome the weight of the drill rod and drill bit and the axial friction between the drill rod and the borehole wall. Its mechanical field environment is relatively simple, so the energy conservation equation is: ; In the formula, This refers to the energy consumed by the drilling rig during the entire lifting process. This refers to the kinetic energy generated during the entire lifting process of the drill bit and drill rod. The drill bit and drill rod do work due to gravity throughout the entire lifting process.

[0016] Due to the complex characteristics of the geological structure, the friction between the drill rod and the borehole wall varies throughout the drilling and hoisting process, and the friction coefficient is not a constant value. Therefore, the key to determining the friction coefficient between the drill rod and the borehole wall is to match the friction coefficient with the displacement inside the borehole at a certain time.

[0017] Furthermore, the piecewise energy conservation equation is as follows: ; The lifting force is provided by the hydraulic cylinder and is related to the hydraulic pressure. ; ; Therefore, ; In the formula, To improve the energy consumed by the drilling rig during a certain period of the process, Here, A represents the oil pressure monitored over a certain period of time, and A is the effective pressure-bearing area of ​​the cylinder piston. Displacement over a certain period of time The kinetic energy of the drill bit and drill pipe over a certain time period. The number of drill pipes within a certain time period. , These refer to the mass of the drill bit and the mass of a single drill rod, respectively. The speed over a certain period of time.

[0018] The method for establishing the segmented force equilibrium model is as follows: The work done by friction differs from the work done by kinetic energy and gravity. Kinetic energy and gravity work involve velocity and displacement over a specific time period, but friction involves energy loss in areas other than the displacement portion. Figure 2 As shown, assume that there are multiple regions u1 to u2 with different friction coefficients throughout the drilling process. x The contact area between the outer wall of the drill rod and the hole wall is rectangular. During the drilling and rod lifting stage, the drill rod offset simplifies the contact area between the drill rod and the hole wall to half of the outer wall of the drill rod, that is, the area of ​​friction force is half of the outer wall of the drill rod. During the drill string lifting stage, within the drilling depth H region, frictional work is performed between the entire drill string and the borehole wall: ; In the formula, Work done by friction Friction; Since the lifting speed per unit time is basically constant during the lifting process, meaning the drill pipe and drill bit are in a state of force equilibrium during lifting, and the hydraulic pressure is only used to overcome friction and gravity, the force analysis during the lifting process is as follows: Figure 1 The force equilibrium model per unit time is: ; in, ; ; In the formula, N represents the lateral normal force on the drill pipe, perpendicular to the contact surface with the borehole wall. Its magnitude is determined by factors such as borehole axis deviation, drill pipe self-weight bending, and local borehole diameter reduction. The magnitude of the lateral normal force is affected by the field environment, and its value is not uniformly distributed. Here, N is the lateral force generated per unit length, in kN / m; H is the drilling depth throughout the process, in meters.

[0019] The method for calculating the friction coefficient between the drill pipe and the borehole wall in segments corresponding to the borehole depth is as follows: According to the piecewise energy conservation equation, the energy conservation equation for the lifting process is as follows: ; because , ; The drilling depth H and remaining depth L change with time t as follows: , This is the average speed over that time period; therefore, ; ; ; When the drill pipe is lifted Time When the formula changes, it becomes: ; Then, the section of road coefficient of friction for: ; In the formula, The coefficient of friction per unit contact area is dimensionless. For the drilling process The displacement during this time period is expressed in meters (m). and t and The oil pressure data is monitored in real time, in MPa; A is the effective pressure-bearing area of ​​the cylinder piston, in MPa. ; and t and The velocity at any given moment, expressed in m / s; , The values ​​represent the mass of the drill bit and a single drill pipe, respectively, in tons (t); n represents the number of drill pipes included in this time period; g is the acceleration due to gravity, taken as 9.8 m / s² in this formula. 2 R represents the outer radius of the drill bit and drill rod, in meters; N represents the lateral normal force per unit length of the drill rod caused by hole inclination, bending, and diameter reduction, in kN / m; the direction of the lateral normal force is perpendicular to the contact surface, and its magnitude is determined by factors such as borehole axis deviation, drill rod self-weight bending, and local diameter reduction of the borehole wall.

[0020] The drill pipe moves at a basically constant speed during the lifting process, that is... , The coefficient of friction between the drill rod and the borehole wall in the corresponding depth section is: ; If there is a reduction in drill pipe between the two sections, the coefficient of friction is: ; In the formula, The coefficient of friction per unit contact area is dimensionless. and t and The oil pressure data is monitored in real time, in MPa; A is the effective pressure-bearing area of ​​the cylinder piston, in MPa. R is the outer radius of the drill bit and drill rod, in meters; N is the lateral normal force per unit length of the drill rod caused by hole inclination, bending, and diameter reduction, in kN / m. The direction of the lateral normal force is perpendicular to the contact surface, and its magnitude is determined by factors such as borehole axis deviation, drill rod self-weight bending, and local diameter reduction of the borehole wall.

[0021] Example 1: Field test was conducted on the Yunnan-Guizhou Plateau in China. This area is mainly composed of backfill layer and argillaceous limestone. The backfill layer is composed of backfill soil and gravel. The drilling time was short, the borehole wall was intact and there was no narrowing, and the data collection was complete.

[0022] A method for determining the friction coefficient between the drill rod and the borehole wall during the drilling rod lifting process, the specific steps of which are as follows: (1) Determine the weight M of the drill bit based on the selected drill bit and drill rod. 钻头 and the weight of a single drill pipe M 钻杆 The quality of the drill bit selected for this test is: , The outer radius R of the drill bit and drill rod is 0.0475m, and the effective pressure-bearing area A of the hydraulic cylinder piston is taken as 0.00785. ; (2) Connect the drill bit, drill rod and drilling machine, start the drilling machine to drill, and record the time node for adding the drill rod and the total displacement of the drill rod through the digital drilling system during the drilling process; (3) During the drilling and rod lifting stage, real-time data are collected on drilling pressure, displacement, and rod lifting speed, based on the single mechanical environment of overcoming only the weight of the drill string and axial friction during the rod lifting stage (see...). Figure 3 Establish the energy conservation equation; divide the lifting process into several intervals, with the time in each interval being... Establish piecewise energy conservation equations and piecewise force balance models, and calculate the friction coefficient between drill rod and borehole wall for corresponding borehole depth sections. The drilling operation reached a total depth of 5.5 meters. Data for the lifting phase, concentrated in the periods approximately 350-600, 981-1867, and 2300-2400, represents the process of lifting the drill pipe. The displacement during this process is not included in the borehole depth calculation. Therefore, if... Figure 4 The rotation speed-time graph shows a straight line. The most obvious feature of this process is that the rotation speed is 0. In this example, the lifting data from the 981 to 1867 segment is selected because, based on other monitoring data, the lifting time in other time segments is too short and there are slight fluctuations in rotation speed. This is because the process involves adding drill pipes, and the data is not very representative. Figure 5 This is a scatter plot of the original oil pressure distribution within the range of 981 to 1867; from Figure 5As can be seen, the raw oil pressure data exhibits certain high-frequency fluctuations. This is due to mechanical vibrations during drilling, mud pump pressure pulsations, and sensor noise, which are normal phenomena in field testing. Figure 5 As can be seen, between the two lifting processes, the number of drill pipes is reduced by one, the oil pressure difference is about 0.055MPa, and the corresponding lifting force is reduced by about 0.43kN. The weight of a single drill pipe in the hole is about 0.392kN. The relative error between the two is less than 10%, which verifies the basic rationality of the energy conservation and force balance model. The calculation process in this embodiment is as follows: It should be noted that during actual drilling, the lateral normal force N between the drill rod and the borehole wall is not a constant value. Its magnitude is affected by factors such as borehole inclination, drill rod bending due to its own weight, local diameter reduction, and borehole wall stability. In this embodiment, N is taken as 2kN. The first segment of data was selected and calculated. The calculation results are as follows: ; As can be seen from the pressure in the table, due to mechanical vibration during drilling, mud pump pressure pulsation, and sensor noise, some pressure differences are negative and do not decrease in a regular, monotonically decreasing manner. This is because the drilling displacement per second is too small, and the frictional force does not change much, thus having little impact on the oil pressure. Therefore, the calculation should be restarted from this point. Because the number of drill pipes decreases between the first and second data segments, the number of drill pipes, n, changes between the two segments. Therefore, the above formula needs to be improved by changing the original formula. ; Revised to: ; At this time, The expression is: ; Based on the known quantities above, the coefficient of friction between this section of the borehole wall and the drill pipe is 0.325965. In summary, within the range where the number of drill pipes remains constant, the friction coefficient is mainly concentrated between 0 and 0.50. When entering the unloading stage (after the 988th second), the physical meaning of the oil pressure difference changes due to the reduction in the number of drill pipes. Therefore, the formula needs to introduce a correction term for the change in the number of drill pipes. The friction coefficient calculated after correction is 0.325965.

[0023] The specific embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for determining the coefficient of friction between the drill rod and the borehole wall during the drilling rod lifting process, characterized in that, The specific steps are as follows: (1) Determine the weight M of the drill bit based on the selected drill bit and drill rod. 钻头 and the weight of a single drill pipe M 钻杆 ; (2) Connect the drill bit, drill rod and drilling machine, start the drilling machine to drill, and record the time node for adding the drill rod and the total displacement of the drill rod through the digital drilling system during the drilling process; (3) During the drilling and rod lifting stage, real-time data are collected on drilling pressure, displacement, and rod lifting speed. Based on the single mechanical environment of overcoming only the gravity of the drill string and axial friction during the rod lifting stage, an energy conservation equation is established. The rod lifting process is divided into several intervals, with each interval containing a time of... A segmented energy conservation equation and a segmented force balance model were established, and the friction coefficient between the drill rod and the borehole wall in the corresponding depth section was calculated segment by segment.

2. The method for determining the friction coefficient between the drill rod and the borehole wall during the drilling and rod lifting process according to claim 1, characterized in that: The energy conservation equation for step (3) is: ； In the formula, This refers to the energy consumed by the drilling rig during the entire lifting process. This refers to the kinetic energy generated during the entire lifting process of the drill bit and drill rod. The work done by friction during the entire lifting process The work done by the weight of the drill bit and drill rod during the entire lifting process.

3. The method for determining the friction coefficient between the drill rod and the borehole wall during the drilling rod lifting process according to claim 2, characterized in that: The piecewise energy conservation equation for step (3) is: ； in, ; ； Therefore, ; In the formula, To improve the energy consumed by the drilling rig during a certain period of the process, Here, A represents the oil pressure monitored over a certain period of time, and A is the effective pressure-bearing area of ​​the cylinder piston. Displacement over a certain period of time The kinetic energy of the drill bit and drill pipe over a certain time period. The number of drill pipes within a certain time period. , These refer to the mass of the drill bit and the mass of a single drill pipe, respectively. The speed over a certain period of time.

4. The method for determining the friction coefficient between the drill rod and the borehole wall during the drilling rod lifting process according to claim 3, characterized in that: The method for establishing the segmented force equilibrium model in step (3) is as follows: Assume that there are multiple regions u1 to u2 with different friction coefficients throughout the drilling process. x The contact area between the outer wall of the drill rod and the hole wall is rectangular. During the drilling and rod lifting stage, the drill rod deflects, simplifying the contact area between the drill rod and the hole wall to half of the outer wall of the drill rod. That is, the area of ​​friction force is half of the outer wall of the drill rod. During the drill string lifting stage, within the drilling depth H region, frictional work is performed between the entire drill string and the borehole wall: ； In the formula, Work done by friction Friction; Since the lifting speed within a unit time is basically the same during the rod lifting process, meaning that the drill rod and drill bit are in a state of force equilibrium during the lifting process, and the hydraulic pressure is only used to overcome friction and gravity, the force equilibrium model per unit time is: ； in, ; ； In the formula, This is the lateral normal force of the drill pipe, with its direction perpendicular to the contact surface of the hole wall.

5. The method for determining the friction coefficient between the drill rod and the borehole wall during the drilling rod lifting process according to claim 4, characterized in that: Step (3) Calculate the friction coefficient between the drill rod and the hole wall in segments corresponding to the hole depth sections. The specific method is as follows: According to the piecewise energy conservation equation, the energy conservation equation for the lifting process is as follows: ； because , ; The drilling depth H and remaining depth L change with time t as follows: , This is the average speed over that time period; therefore, ; ； ； When the drill pipe is lifted Time When the formula changes, it becomes: ； Then, the section of road coefficient of friction for: ； In the formula, The coefficient of friction per unit contact area is dimensionless. For the drilling process The displacement during this time period is expressed in meters (m). and t and The oil pressure data is monitored in real time, in MPa; A is the effective pressure-bearing area of ​​the cylinder piston, in m². 2 ; and t and The velocity at any given moment, expressed in m / s; , The values ​​represent the mass of the drill bit and a single drill pipe, respectively, in tons (t); n represents the number of drill pipes included in the time period; g is the acceleration due to gravity, with a value of 9.8 m / s². 2 R represents the outer radius of the drill bit and drill rod, in meters; N represents the lateral normal force per unit length of the drill rod caused by hole inclination, bending, and diameter reduction, in kN / m. The drill pipe moves at a basically constant speed during the lifting process, that is... , The coefficient of friction between the drill rod and the borehole wall in the corresponding depth section is: ； If there is a reduction in drill pipe between the two sections, the coefficient of friction is: ； In the formula, The coefficient of friction per unit contact area is dimensionless. and t and The oil pressure data is monitored in real time, in MPa; A is the effective pressure-bearing area of ​​the cylinder piston, in MPa. R is the outer radius of the drill bit and drill pipe, in meters. N is the lateral normal force per unit length of the drill pipe caused by hole inclination, bending, and diameter reduction, and its unit is kN / m.

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