# Study of Radial Vibration Impact on Friction and Torque of Rotary Drill String

Authors: Zifeng Li; Chaoyue Zhang; Wenming Ren; Jianwei Ma
Journal: Shock and Vibration
 (2020)

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## Abstract

During extended-reach well drilling, the torque of a rotary drill string is too large in the horizontal section, which results in the failure of the drill string. The effect of radial vibration on the friction and torque of the rotary drill string is unclear. In this work, first, the principle of the impact of radial vibration on the friction and torque of the rotary drill string in the horizontal section is analysed. Then, joints with an elliptical outer edge of the section are designed, which can generate low-amplitude vibration as the drill string rotates owing to the interaction with the wellbore wall. The radial vibration characteristics can be tuned by changing the major to minor radius ratio of the ellipse. A self-developed experimental device was designed to test the performance of tools with reduced friction and torque. The drill string torque with different penetration rates, rotation speeds, and ratios of the major radius to minor radius of the ellipse were systematically studied. The experimental results show that the average and the maximum amplitudes of the torque fluctuation first decrease to the lowest value and then increase with the increase of the ratio. When the ratio reaches 1.065, the average and the maximum amplitudes of the torque fluctuation evidently reduce; therefore, a joint with a ratio of 1.065 can effectively reduce frictional torque. The average torque reduces when the penetration rate and rotation speed decrease. At rotation speeds of 45 and 60 r/min, the maximum amplitude of torque fluctuation increases first and then decreases with an increase in penetration rate, and it reaches a maximum value at a penetration rate of 22.5 m/h. The fundamental frequency of torque fluctuation is almost linearly related to rotation speed, which is irrelevant to the penetration rate and the ratio of major to minor radius of the ellipse.


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## Body

## 1. Introduction

Extended-reach wells have been widely applied in the exploration of unconventional oil and gas reservoirs. During the drilling process in the horizontal section, the drill string lies on the bottom of the borehole wall by its gravity, and the friction caused by interaction between the drill string and the borehole wall is large because of the long horizontal section in extended-reach wells. It is difficult for the drill string to transmit torque, and the large torque results in the failure of the drill string. Therefore, good control of the friction and torque is critical to the success of the drilling operation [1, 2]. Engineering practice shows that there are three effective measures to reduce the friction and torque of the drill string: (1) improving wellbore environments [3], (2) using mechanical tools [4–10], and (3) optimizing engineering parameters such as bottom hole assemblies, drilling fluid performance, and conducting short trips, by monitoring or predicting the friction coefficient at different depths [11–14]. The most efficient method is using mechanical tools.Many studies have focused on the vibration to reduce the friction and torque of the drill string; however, most of them focused on the axial vibration [7, 8, 15–22], and only a few studies about the impact of radial vibration on the friction and torque of rotary drill string have been reported. Ouyang et al. [9] developed a turbine-type two-way vibration drag reduction tool that applied eccentric ring rotation to cause radial vibration and water hammer effects to enable axial vibration. This tool can control the exciting force by changing the eccentricity mass. Li [10] developed a radial vibration torsion reduction tool powered by drilling fluid. The field experiment showed that the tool can improve the transfer of drilling weight on the bit. Zhang et al. [23] analysed the impact of amplitude and frequency of the exciting force on the friction coefficient of plane friction pairs between the steel and rock plate by experiments. Ren [24] reported that the drill pipe friction reduction joints with an elliptical outer edge of the section can generate low-amplitude vibration as the drill string rotates. However, the effect of radial vibration on the friction and torque of the rotary drill string is not clear.In this work, the principle of the radial vibration impact on the friction and torque of the rotary drill string is analysed. At the same time, the instantaneous torques of the rotary drilling are measured with different experimental conditions, including the ratio of major radius to minor radius of the joint elliptical section (Ra/b), penetration rate, and rotation speed, which have major impacts on the radial vibration characteristics. The experimental results support the theoretical analysis, providing guidance to study the friction and torque reduction of the rotary drill string by radial vibration.


## 2. Theoretical Analysis

During drilling, the torque on the drill string is caused by the viscous force of the drilling fluid and the sliding friction between the drill string and wellbore [14]:(1)Mt=Mht+Mnt,where Mt is the torque on the drill string, Mht is the frictional torque, and Mnt is the torque generated by the viscous force of the drilling fluid.Therefore, through reducing the frictional torqueMht, the torque on the drill string Mt can be effectively reduced:(2)Mht=R0Fft,where R0 is the external radius of the drill string and Fft is the tangential component of sliding friction between the drill string and wellbore:(3)Fft=ftFNt,where FNt is the contact force between the drill string and wellbore and ft is the tangential component of the sliding coefficient.Because of the interaction between the joint with an elliptical outer edge of section and wellbore wall, it generates low-amplitude forced radial vibration as the drill string rotates, and the vibration frequency is associated with the rotation speed of the drill string. The contact force between the drill string and wellboreFNt is an instantaneous force, which changes over time, and is related to the radial vibration characteristics. When the drill string leaves the wellbore wall, FNt=0. At the same time, Fft changes with FNt, thereby further influencing Mht. Therefore, Mht can be influenced by the radial vibration. Because it is difficult to measure FNt, the torque is measured by a self-developed experimental device, which is designed to test the performance of tools with reducing friction and torque. From the analysis of the experimental results, the effect of the radial vibration on the frictional torque of the rotary drill string is researched in detail.


## 3. Experimental Device, Method, and Conditions

### 3.1. Experimental Device

Figure1 shows the experimental device to test the performance of tools with reducing friction and torque [25]. The device is mainly composed of the base, inner rod rotation part, outer cylinder vertical motion part, control and data acquisition system, and other elements. This device can simulate the motion of the rotary drill string with joints in the wellbore, and the penetration rate and rotation speed can be controlled.Figure 1
(a) Photograph of the experimental device used to test the performance of tools. (b) Schematic of the experimental device: (1) base, (2) main motor, (3) coupling A, (4) torque sensor, (5) coupling B, (6) bearing A and its support, (7) resilient coupling A, (8) inner rod (drill string), (9) outer cylinder (wellbore), (10) test tool, (11) support of outer cylinder, (12) resilient coupling B, (13) bearing B, (14) feed motor, (15) sliding table, (16) connection plate, (17) lifting table, (18) fluid container, and (19) computer.
(a)(b)The inner rod rotation part is composed of the main motor, couplings, the inner rod (drill string), and the test tool. The inner rod with the test tool can rotate in the outer cylinder driven by the main motor. The outer cylinder vertical motion part is composed of the outer cylinder (wellbore) and its support, lifting table, feed motor, and sliding table. The outer cylinder goes through linear translational motion on the sliding table driven by the feed motor. In addition, the height of the outer cylinder can be changed by adjusting the lifting table to meet the requirements of different test tools and prevent the motor from having a locked rotor. The main motor and the feed motor are controlled by a computer, the main motor adjusts the rotation speed, and the feed motor adjusts the penetration rate. The torque sensor measures the real-time torque and transfers the data to the computer.Figure2 shows the structure of the drill pipe friction reduction joint; Ra/b of the joint elliptical section is a key parameter to control the radial vibration, and the section parameters of different joint models are given in Table 1. The drill pipe friction reduction joints are named the 1617 joint, 1618 joint, and 1619 joint according to the value of the minor radius and major radius.Figure 2
Schematic of the drill pipe friction reduction joint.Table 1
Section parameters of different joints models.
Tool modelSection parametersMajor radiusa (×10−3m)Minor radiusb (×10−3m)Ratio of major radius to minor radius of the joint elliptical sectionRa/bCommon joint16161Drill pipe1617 joint17161.0625Friction1618 joint18161.125Reduction joints1619 joint19161.1875


### 3.2. Experimental Method

(1)
The test tool is assembled with other elements of the inner-rod rotation part, which should be away from the outer cylinder. At the same time, the slider should stay at one end of the sliding table.(2)
The bottom of the outer cylinder is covered with sand evenly.(3)
The rotation speed of the inner rod is adjusted by the main motor.(4)
The height of the outer cylinder is adjusted and fixed by the lifting table to make the test tool contact the outer cylinder.(5)
The horizontal velocity (i.e., penetration rate) of the outer cylinder is adjusted, and data collection is carried out.(6)
After the experiment, the power supply is turned off, and the outer cylinder is lowered and cleaned.Afterwards, the measurement results are subjected to fast Fourier transform (FFT), and the time domain signal is converted into a frequency domain signal; thereby, the amplitude spectrum of torque is obtained. Finally, the changing laws of the torque are analysed.


### 3.3. Experimental Conditions

The outer cylinder of the experimental device was a grooved acrylic tube, with an inner diameter of 55 mm and a wall thickness of 2 mm. The torque sensor was a strain-gauge-type torque sensor, with a rated load of 0–10 N.m and a total error of ±0.5% F.S. The sliding table was an automatic delicate sliding table, with a stroke of 1000 mm and a repositioning precision of 0.02∼0.03 mm.


## 3.1. Experimental Device

Figure1 shows the experimental device to test the performance of tools with reducing friction and torque [25]. The device is mainly composed of the base, inner rod rotation part, outer cylinder vertical motion part, control and data acquisition system, and other elements. This device can simulate the motion of the rotary drill string with joints in the wellbore, and the penetration rate and rotation speed can be controlled.Figure 1
(a) Photograph of the experimental device used to test the performance of tools. (b) Schematic of the experimental device: (1) base, (2) main motor, (3) coupling A, (4) torque sensor, (5) coupling B, (6) bearing A and its support, (7) resilient coupling A, (8) inner rod (drill string), (9) outer cylinder (wellbore), (10) test tool, (11) support of outer cylinder, (12) resilient coupling B, (13) bearing B, (14) feed motor, (15) sliding table, (16) connection plate, (17) lifting table, (18) fluid container, and (19) computer.
(a)(b)The inner rod rotation part is composed of the main motor, couplings, the inner rod (drill string), and the test tool. The inner rod with the test tool can rotate in the outer cylinder driven by the main motor. The outer cylinder vertical motion part is composed of the outer cylinder (wellbore) and its support, lifting table, feed motor, and sliding table. The outer cylinder goes through linear translational motion on the sliding table driven by the feed motor. In addition, the height of the outer cylinder can be changed by adjusting the lifting table to meet the requirements of different test tools and prevent the motor from having a locked rotor. The main motor and the feed motor are controlled by a computer, the main motor adjusts the rotation speed, and the feed motor adjusts the penetration rate. The torque sensor measures the real-time torque and transfers the data to the computer.Figure2 shows the structure of the drill pipe friction reduction joint; Ra/b of the joint elliptical section is a key parameter to control the radial vibration, and the section parameters of different joint models are given in Table 1. The drill pipe friction reduction joints are named the 1617 joint, 1618 joint, and 1619 joint according to the value of the minor radius and major radius.Figure 2
Schematic of the drill pipe friction reduction joint.Table 1
Section parameters of different joints models.
Tool modelSection parametersMajor radiusa (×10−3m)Minor radiusb (×10−3m)Ratio of major radius to minor radius of the joint elliptical sectionRa/bCommon joint16161Drill pipe1617 joint17161.0625Friction1618 joint18161.125Reduction joints1619 joint19161.1875


## 3.2. Experimental Method

(1)
The test tool is assembled with other elements of the inner-rod rotation part, which should be away from the outer cylinder. At the same time, the slider should stay at one end of the sliding table.(2)
The bottom of the outer cylinder is covered with sand evenly.(3)
The rotation speed of the inner rod is adjusted by the main motor.(4)
The height of the outer cylinder is adjusted and fixed by the lifting table to make the test tool contact the outer cylinder.(5)
The horizontal velocity (i.e., penetration rate) of the outer cylinder is adjusted, and data collection is carried out.(6)
After the experiment, the power supply is turned off, and the outer cylinder is lowered and cleaned.Afterwards, the measurement results are subjected to fast Fourier transform (FFT), and the time domain signal is converted into a frequency domain signal; thereby, the amplitude spectrum of torque is obtained. Finally, the changing laws of the torque are analysed.


## 3.3. Experimental Conditions

The outer cylinder of the experimental device was a grooved acrylic tube, with an inner diameter of 55 mm and a wall thickness of 2 mm. The torque sensor was a strain-gauge-type torque sensor, with a rated load of 0–10 N.m and a total error of ±0.5% F.S. The sliding table was an automatic delicate sliding table, with a stroke of 1000 mm and a repositioning precision of 0.02∼0.03 mm.


## 4. Experimental Results and Analysis

The instantaneous output torque of the motor changed periodically around a certain average value, which was caused by its mechanical structure and the output of the rotor rotary inertia. Therefore, the measured torque fluctuated periodically over time. Figure3 shows the torque-time curves with a rotation speed of 30 r/min and a penetration rate of 18 m/h. The torque fluctuation had a certain periodicity, and the torque fluctuation range was different when using different joints. At the same time, tuning Ra/b of the joint could change the radial vibration characteristics, further influencing the torque fluctuation range.Figure 3
Torque-time curves with a rotation speed of 30 r/min and a penetration rate of 18 m/h.The linear trend of torque-time could be obtained by the detrend function. Figure4 shows the linear trend of the torque-time curves when the rotation speed was 30 r/min and the penetration rate was 18 m/h. The torque was minimum when the main motor was idling (without installing an inner rod and test tool). Compared with the common joint, the torque-time curves with drill pipe friction reduction joints grew faster, which can be attributed to the sand accumulation. During the experiment, the bottom of the outer cylinder was covered with sand evenly to simulate the real wellbore condition. However, there was no circulation of the drilling fluid. Therefore, when the drill pipe friction reduction joint was moving in the outer cylinder horizontally, a small amount of sand grains gradually accumulated at the front end of the joint, and the formation of sand piles led to the increase of torque. Consequently, the drilling fluid should have a strong carrying capacity when using the drill pipe friction reduction joint.Figure 4
Linear trend of torque-time curves with a rotation speed of 30 r/min and a penetration rate of 18 m/h.


### 4.1. Effects ofRa/b on Torque

To study the effect ofRa/b on torque under different penetration rates and rotation speeds, the torques using joints with different Ra/b (1, 1.0625, 1.125, and 1.1875) are measured under penetration rates of 18 m/h, 22.5 m/h, and 27 m/h. The experiments were conducted by keeping penetration rate and rotation speed as constant, and the rotation speeds adopted are 30 r/min, 45 r/min, and 60 r/min.With rotation speeds of 30, 45, and 60 r/min and penetration rates of 18, 22.5, and 27 m/h, the relationship between theRa/b and the average torque was obtained, as shown in Figure 5. The average torque decreased first and then increased with the increase of Ra/b under the three different rotation speeds. The average torque dropped the most with the increase of Ra/b under a rotation speed of 30 r/min, as in Figure 5(a), and decreased the least under a rotation speed of 60 r/min, as in Figure 5(c). When Ra/b was 1.0625, the average torque reached its minimum, which was obviously lower than that of the common joint. After that, with the further increase of Ra/b, the average torque gradually increased. When Ra/b reached 1.1875, the average torque was even higher than that of the common joint.Figure 5
Curves of the average of torque changing withRa/b. (a) Rotation speed Vr = 30 r/min. (b) Rotation speed Vr = 45 r/min. (c) Rotation speed Vr = 60 r/min.
(a)(b)(c)The time domain signal was converted into a frequency domain signal through the FFT of the experimental results, and the amplitude spectrum of the torque was obtained. The amplitude spectra of torque with different joints and the main motor idling, when the rotation speed was 30 r/min and the penetration rate was 18 m/h, are displayed in Figure6. The frequency corresponding to the maximum amplitude of torque fluctuation was the fundamental frequency. The maximum amplitudes of the torque fluctuation were different when using different joints, while the fundamental frequency was the same and equal to the fundamental frequency when the main motor was idling. It can be concluded that the fundamental frequency of the torque fluctuation is irrelevant to Ra/b. Therefore, by tuning the Ra/b, the amplitudes of drill string radial vibration can be changed without affecting the frequency of the drill string radial vibration. A violent vibration of the drill string makes serious accidents, such as drill string failure and borehole diameter enlargement [26]; thus, it is necessary to minimise the vibration amplitude, that is, to reduce the maximum amplitude of the torque fluctuation.Figure 6
Amplitude spectrum of torque with a rotation speed of 30 r/min and a penetration rate of 18 m/h.Figure7 shows the curves of the maximum amplitude of the torque with different Ra/b. With the increase of Ra/b, the maximum amplitude of torque fluctuation decreased first and then increased. It can be clearly seen that the maximum amplitude of torque fluctuation was lower than that of the common joint when Ra/b reached 1.0625. With further increase of Ra/b, the change of maximum amplitude tended to be gentle. When Ra/b exceeded 1.125, the maximum amplitude increased rapidly.Figure 7
Curves of the maximum amplitude of the torque changing withRa/b. (a) Rotation speed Vr = 30 r/min. (b) Rotation speed Vr = 45 r/min. (c) Rotation speed Vr = 60 r/min.
(a)(b)(c)The results indicate that both the average and the maximum amplitude of torque fluctuation can be affected by changingRa/b and can be obviously reduced by using 1617 and 1618 joints. In consequence, the 1617 and 1618 joints can effectively reduce the frictional torque of the drill string under experiment condition. Among them, the 1617 joint (Ra/b = 1.0625) exhibits the best frictional torque reduction properties with the minimum average value of torque.


### 4.2. Effects of Penetration Rate on Torque

Based on the above analysis, the 1617 and 1618 joints with frictional torque reduction properties were selected to analyse the effect of penetration rate on the torque of the drill string. With the 1617 (theRa/b is 1.0625) and 1618 (the Ra/b is 1.125) joints, the torque with different penetration rates (Vp = 18, 22.5, 27, and 36 m/h) was measured under rotation speeds of 30, 45, and 60 r/min. The change rules of the average and the maximum amplitude of torque fluctuation with the penetration rate are shown in Figures 8 and 9.Figure 8
Variation of the average of torque changing with penetration rate.Figure 9
Variation of the maximum amplitude of torque fluctuation changing with penetration rate.As shown in Figure8, the average torque increased gradually with the increase of penetration rate. When using the 1617 joint, the effect of the penetration rate on the average torque was more obvious than that when using the 1618 joint.With the 1617 and 1618 joints, the variation laws of maximum amplitude of torque fluctuation with penetration rate are similar at the same rotation speed, as shown in Figure9. The variation of maximum amplitude with penetration rate is closely related to the rotation speed. When the rotation speed was 30 r/min, the maximum amplitude of torque fluctuation increased gradually with the increase of penetration rate. With the rotation speeds of 45 and 60 r/min, the maximum amplitude of torque fluctuation increased first and then decreased with the increase of penetration rate, and the maximum amplitude reached maximum value at a penetration rate of 22.5 m/h. Therefore, the penetration rate should be as far away as possible from 22.5 m/h in the drilling process.As shown in Figure10, the amplitude spectra of torque using the 1617 joint were obtained at penetration rates of 18, 22.5, and 27 m/h. The fundamental frequency of torque fluctuation was 0.4482 Hz at different penetration rates. The maximum amplitudes of the torque fluctuation were different for different penetration rates, but the fundamental frequency was the same. It can be concluded that the fundamental frequency of the torque fluctuation is irrelevant to the penetration rate of drill string. Therefore, through changing the penetration rate, the amplitudes of drill string radial vibration can be changed without affecting the frequency of drill string radial vibration.Figure 10
Amplitude spectrum of torque at different penetration rates with a rotation speed of 30 r/min and the 1617 joint.


### 4.3. Effects of Rotation Speed on Torque

With the 1617 (theRa/b is 1.0625) and 1618 (the Ra/b is 1.125) joints, the torque with different rotation speeds (Vr = 30, 45, 60, and 90 r/min) was measured under penetration rates of 18, 22.5, and 27 m/h. The change rules of the average and the maximum amplitude of torque fluctuation with rotation speed are shown in Figures 11 and 12.Figure 11
Variation of the average of torque changing with rotation speed.Figure 12
Variation of the maximum amplitude of torque fluctuation changing with rotation speed.With the increase of rotation speed, the average torque increased gradually, as shown in Figure11. The effect of the rotation speed on the average torque was more obvious when using the 1617 joint compared with the 1618 joint.As shown in Figure12, with the 1617 joint and the 1618 joint, the variation laws of the maximum amplitude of torque fluctuation with rotation speeds are similar at same rotation speed. For penetration rates of 18 and 22.5 m/h, there was a big difference between the maximum amplitude at rotation speeds of 30 and 45 r/min, while the difference between the maximum amplitude at the rotation speeds of 45 to 90 r/min was small. For the penetration rate of 27 m/h, the rotation speed had little effect on the maximum amplitude.Figure13 shows the fundamental frequency of torque fluctuation at rotation speeds of 30, 45, 60, 90, 120, and 180 r/min. The fundamental frequency increases almost proportionally with the increase of the rotation speed. This phenomenon is consistent with the above theoretical analysis.Figure 13
Variation of the fundamental frequency of torque under different rotation speeds.


## 4.1. Effects ofRa/b on Torque

To study the effect ofRa/b on torque under different penetration rates and rotation speeds, the torques using joints with different Ra/b (1, 1.0625, 1.125, and 1.1875) are measured under penetration rates of 18 m/h, 22.5 m/h, and 27 m/h. The experiments were conducted by keeping penetration rate and rotation speed as constant, and the rotation speeds adopted are 30 r/min, 45 r/min, and 60 r/min.With rotation speeds of 30, 45, and 60 r/min and penetration rates of 18, 22.5, and 27 m/h, the relationship between theRa/b and the average torque was obtained, as shown in Figure 5. The average torque decreased first and then increased with the increase of Ra/b under the three different rotation speeds. The average torque dropped the most with the increase of Ra/b under a rotation speed of 30 r/min, as in Figure 5(a), and decreased the least under a rotation speed of 60 r/min, as in Figure 5(c). When Ra/b was 1.0625, the average torque reached its minimum, which was obviously lower than that of the common joint. After that, with the further increase of Ra/b, the average torque gradually increased. When Ra/b reached 1.1875, the average torque was even higher than that of the common joint.Figure 5
Curves of the average of torque changing withRa/b. (a) Rotation speed Vr = 30 r/min. (b) Rotation speed Vr = 45 r/min. (c) Rotation speed Vr = 60 r/min.
(a)(b)(c)The time domain signal was converted into a frequency domain signal through the FFT of the experimental results, and the amplitude spectrum of the torque was obtained. The amplitude spectra of torque with different joints and the main motor idling, when the rotation speed was 30 r/min and the penetration rate was 18 m/h, are displayed in Figure6. The frequency corresponding to the maximum amplitude of torque fluctuation was the fundamental frequency. The maximum amplitudes of the torque fluctuation were different when using different joints, while the fundamental frequency was the same and equal to the fundamental frequency when the main motor was idling. It can be concluded that the fundamental frequency of the torque fluctuation is irrelevant to Ra/b. Therefore, by tuning the Ra/b, the amplitudes of drill string radial vibration can be changed without affecting the frequency of the drill string radial vibration. A violent vibration of the drill string makes serious accidents, such as drill string failure and borehole diameter enlargement [26]; thus, it is necessary to minimise the vibration amplitude, that is, to reduce the maximum amplitude of the torque fluctuation.Figure 6
Amplitude spectrum of torque with a rotation speed of 30 r/min and a penetration rate of 18 m/h.Figure7 shows the curves of the maximum amplitude of the torque with different Ra/b. With the increase of Ra/b, the maximum amplitude of torque fluctuation decreased first and then increased. It can be clearly seen that the maximum amplitude of torque fluctuation was lower than that of the common joint when Ra/b reached 1.0625. With further increase of Ra/b, the change of maximum amplitude tended to be gentle. When Ra/b exceeded 1.125, the maximum amplitude increased rapidly.Figure 7
Curves of the maximum amplitude of the torque changing withRa/b. (a) Rotation speed Vr = 30 r/min. (b) Rotation speed Vr = 45 r/min. (c) Rotation speed Vr = 60 r/min.
(a)(b)(c)The results indicate that both the average and the maximum amplitude of torque fluctuation can be affected by changingRa/b and can be obviously reduced by using 1617 and 1618 joints. In consequence, the 1617 and 1618 joints can effectively reduce the frictional torque of the drill string under experiment condition. Among them, the 1617 joint (Ra/b = 1.0625) exhibits the best frictional torque reduction properties with the minimum average value of torque.


## 4.2. Effects of Penetration Rate on Torque

Based on the above analysis, the 1617 and 1618 joints with frictional torque reduction properties were selected to analyse the effect of penetration rate on the torque of the drill string. With the 1617 (theRa/b is 1.0625) and 1618 (the Ra/b is 1.125) joints, the torque with different penetration rates (Vp = 18, 22.5, 27, and 36 m/h) was measured under rotation speeds of 30, 45, and 60 r/min. The change rules of the average and the maximum amplitude of torque fluctuation with the penetration rate are shown in Figures 8 and 9.Figure 8
Variation of the average of torque changing with penetration rate.Figure 9
Variation of the maximum amplitude of torque fluctuation changing with penetration rate.As shown in Figure8, the average torque increased gradually with the increase of penetration rate. When using the 1617 joint, the effect of the penetration rate on the average torque was more obvious than that when using the 1618 joint.With the 1617 and 1618 joints, the variation laws of maximum amplitude of torque fluctuation with penetration rate are similar at the same rotation speed, as shown in Figure9. The variation of maximum amplitude with penetration rate is closely related to the rotation speed. When the rotation speed was 30 r/min, the maximum amplitude of torque fluctuation increased gradually with the increase of penetration rate. With the rotation speeds of 45 and 60 r/min, the maximum amplitude of torque fluctuation increased first and then decreased with the increase of penetration rate, and the maximum amplitude reached maximum value at a penetration rate of 22.5 m/h. Therefore, the penetration rate should be as far away as possible from 22.5 m/h in the drilling process.As shown in Figure10, the amplitude spectra of torque using the 1617 joint were obtained at penetration rates of 18, 22.5, and 27 m/h. The fundamental frequency of torque fluctuation was 0.4482 Hz at different penetration rates. The maximum amplitudes of the torque fluctuation were different for different penetration rates, but the fundamental frequency was the same. It can be concluded that the fundamental frequency of the torque fluctuation is irrelevant to the penetration rate of drill string. Therefore, through changing the penetration rate, the amplitudes of drill string radial vibration can be changed without affecting the frequency of drill string radial vibration.Figure 10
Amplitude spectrum of torque at different penetration rates with a rotation speed of 30 r/min and the 1617 joint.


## 4.3. Effects of Rotation Speed on Torque

With the 1617 (theRa/b is 1.0625) and 1618 (the Ra/b is 1.125) joints, the torque with different rotation speeds (Vr = 30, 45, 60, and 90 r/min) was measured under penetration rates of 18, 22.5, and 27 m/h. The change rules of the average and the maximum amplitude of torque fluctuation with rotation speed are shown in Figures 11 and 12.Figure 11
Variation of the average of torque changing with rotation speed.Figure 12
Variation of the maximum amplitude of torque fluctuation changing with rotation speed.With the increase of rotation speed, the average torque increased gradually, as shown in Figure11. The effect of the rotation speed on the average torque was more obvious when using the 1617 joint compared with the 1618 joint.As shown in Figure12, with the 1617 joint and the 1618 joint, the variation laws of the maximum amplitude of torque fluctuation with rotation speeds are similar at same rotation speed. For penetration rates of 18 and 22.5 m/h, there was a big difference between the maximum amplitude at rotation speeds of 30 and 45 r/min, while the difference between the maximum amplitude at the rotation speeds of 45 to 90 r/min was small. For the penetration rate of 27 m/h, the rotation speed had little effect on the maximum amplitude.Figure13 shows the fundamental frequency of torque fluctuation at rotation speeds of 30, 45, 60, 90, 120, and 180 r/min. The fundamental frequency increases almost proportionally with the increase of the rotation speed. This phenomenon is consistent with the above theoretical analysis.Figure 13
Variation of the fundamental frequency of torque under different rotation speeds.


## 5. Conclusions

(1)
Because of the interaction between the joint with an elliptical outer edge of section and the wellbore wall, low-amplitude forced radial vibration was generated as the drill string rotates, and the effect of the radial vibration on the frictional torque of the rotary drill string was researched in detail.(2)
The average torque and the maximum amplitude of torque fluctuation decreased first and then increased with the increase of the ratio of major radius to minor radius of the joint elliptical section. When the ratio was 1.0625, the joint exhibited the best frictional torque reduction properties with the minimum average value of torque.(3)
With the increase of rotation speed, the average torque increased gradually. For a penetration rate of 27 m/h, the rotation speed had a little effect on the maximum amplitude of torque fluctuation. At rotation speeds of 45 and 60 r/min, the difference between the maximum amplitudes was very small at the same penetration rate, and the maximum amplitude of torque fluctuation increased first and then decreased with the increase of penetration rate, and it reached its maximum value at a penetration rate of 22.5 m/h. Therefore, the penetration rate should be as far away as possible from 22.5 m/h in the drilling process.(4)
The fundamental frequency of torque fluctuation was almost linearly related to the rotation speed, which was irrelevant to the penetration rate and the ratio of the major radius to minor radius of the joint.(5)
During drilling, a small number of sand grain easily gradually accumulates at the front end of the drill pipe friction reduction joint, and the formation of sand piles leads to an increase of torque. Consequently, the drilling fluid should have a strong carrying capacity when using the drill pipe friction reduction joint.



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*Source: 8852530-2020-07-24.xml*