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Drill string torsional and longitudinal oscillation can significantly reduce axial drag in horizontal drilling. An improved theoretical model for the analysis of the frictional force was proposed based on microscopic contact deformation theory and a bristle model. The established model, an improved dynamic friction model established for drill strings in a wellbore, was used to determine the relationship of friction force changes and the drill string torsional vibration. The model results were in good agreement with the experimental data, verifying the accuracy of the established model. The analysis of the influence of drilling mud properties indicated that there is an approximately linear relationship between the axial friction force and dynamic shear and viscosity. The influence of drill string torsional oscillation on the axial friction force is discussed. The results indicated that the drill string transverse velocity is a prerequisite for reducing axial friction. In addition, low amplitude of torsional vibration speed can significantly reduce axial friction. Then, increasing the amplitude of transverse vibration speed, the effect of axial reduction is not significant. In addition, by involving general field drilling parameters, this model can accurately describe the friction behavior and quantitatively predict the frictional resistance in horizontal drilling.

Directional drilling is a widely used method in the drilling engineering for oil and gas industry. The sliding drilling mode is a critical process that drilling string maintains only axial sliding movement to keep tool face of downhole assembly (BHA) from rotating (the orientation of tool face of BHA can control the direction of wellbore). Excessive axial drag has become a serious problem, especially in extended-reach horizontal wells with a motor/MWD system. Some techniques are available to reduce drill string drag. Rotary steering systems (RSSs) are configured so that the entire drill rotates continuously with steering capabilities. High costs hinder the promotion of RSS technology. Technology called “torque rocking” or pipe torsional oscillation systems [

Schematic diagram of “torque rocking”.

Friction performance is very complex [

Experimental investigations [

In this work, we presented a dynamic model on the dynamics of the motion of sliding and rotary drill strings for perfectly elastic contact in a viscous fluid environment. Unlike Tsai and Tseng [

The axial friction force (or called drag) in axial direction is a focus problem in drilling engineering. Low axial friction can be benefit for drilling. During rotary drilling or “torque rocking,” the motion of the drill string is a result of superposition of two motions. The first of these is drill string’s tangential rotary motion, whereas the second one is sliding motion in the wellbore’s axial direction.

On the macroscopic level, the apparent area of wellbore surfaces observed by the naked eye is “rough” [

Considering the real contact between the drill string and the borehole rock, we made the same assumption for the contact surface. This implies that the drill string surface is a slightly rough surface and the wellbore is a severe rough surface composed of a large number of elastic bristles, which is an abstraction of asperities. Due to the roughness and hardness difference between the drill string and wellbore rock by surface contact, the general elastic bristle in the dynamic friction model should be the bristles on the wellbore, which, unlike these models, was assumed on the motion body plane contact. The simplified model is shown in Figure

Modeling of contact’s elastic deformation.

To analyze the real working conditions of a drill string in a downhole, the following assumptions are made:

Based on the above assumptions, the drill string actual working conditions can be simplified into the interaction model as shown in Figure

Distribution of forces acting on the sliding and torsional oscillation of the drill string.

It assumed in the LuGre model that the rate

In the model for further analysis, the deformation in the contact zone formed by the contact of general bristles sliding and the rotary drill string was modeled by a generalized elastic-damping artificial element

Changes in a general bristles deformation at consecutive phases of sliding and torsional oscillation of the drill string.

An elastic-damping deformation

The position of

In the first phase, during the previous

At a consecutive time interval

At the same time, elastic deformation of the bristle projection vector moved along the path of

The velocity

Knowing the magnitude of elastic deflection

The angle between the elastic deformation

In the second phase, during the following

Velocity

Angle

Knowing the magnitude and direction of elastic deformation

The torque caused by bristle deformation was determined by the following expression:

The average magnitude force

The average magnitude torque

Therefore, the average friction drag due to bristle deformation and viscose fluid can be noted, respectively:

The average friction torque caused by bristle deformation and viscose fluid can be determined from the following relationship, respectively:

Based on the aforementioned calculation model, the solving procedure step of novel dynamic friction model was presented in Figure

Present model solution flow chart.

To assess the validity of the established model, experimental data and parameter mentioned in paper [^{2}, an area of ^{2}, a coefficient of contact rigidity in tangential direction of

The experiment presented in the paper was investigated in terms of the influence of tangential contact vibration on the friction force. The aforementioned model was adopted to calculate the change in the friction force with the dimensionless velocity and to compare it with the experimental results (Figure

Comparison between the numerical simulation and experimental results.

The model described in the paper by Gutowski and Leus [

According to the experimental results, the established model can accurately predict the friction from tangential vibration coupled with the sliding motion. Therefore, this model can also describe drill string torsional vibration with sliding in a downhole from a theoretical perspective. Drill pipes in a horizontal wellbore were adopted to analyze axial friction reduction mechanism caused by drill pipe torsional oscillation using general field drilling parameters.

Static and kinetic friction coefficients are fundamental parameters for friction force simulation of drilling string. In the paper [

Wang et al. [

However, there are rare reports about friction damping coefficient between steel and rock obtained through experiment research. The parameter can be 0.316 N·s/mm [

Stribeck velocity is also less sensitive than

Basic simulation parameters were assumed to analyze the drill string axial friction performance affected by rotation and torsional vibration, as shown in Table

Simulation parameters [

Number | Parameter/unit | Value |
---|---|---|

1 | Coulomb friction coefficient | 0.21 |

2 | Static friction coefficient | 0.25 |

3 | Friction Stiffness coefficient/(N/mm) | 50 |

4 | Friction Damping coefficient/(N/(mm/s)) | 0.316 |

5 | Stribeck velocity/( |
190 |

6 | Length of drill pipe/m | 10 |

7 | Outer diameter of drill pipe/m | 0.127 |

8 | Inner diameter of drill pipe/m | 0.1086 |

9 | Wellbore diameter/m | 0.2156 |

10 | Dynamic shear/Pa | 15 |

11 | Viscosity/Pa⋅s | 0.03 |

12 | Density of drill pipe/(kg/m^{3}) |
7850 |

13 | Density of drill mud/(kg/m^{3}) |
2200 |

14 | Volume rate/(L/s) | 30 |

Tsai and Tseng [

Maidla et al. [

The effect of the amplitude of the Stribeck velocity is depicted in Figure

Influence of the Stribeck velocity on the change in friction.

The simulation result of friction ratio was extremely low using drilling field operation parameters. However, the axial friction ratio held steady with varied Stribeck velocity at the same vibration amplitude. It indicated that the axial friction ratio was low sensitive to the Stribeck velocity using the drilling operation parameter. The result of Yu et al. was also confirmed [

The damping coefficient

The numerical results are shown in Figure

Influence of the damp coefficient of general bristles on the change in friction.

Parametric studies were run to explore the relationship between dynamic shear and axial friction resistance for drill pipes, as shown in Figure

Influence of dynamic shear of drilling mud on the change in axial viscous force.

This section discussed influence of torsional vibration amplitude of average axial viscous force. The ROP was equal to 7 m/h. The range of torsional oscillation amplitude was between 10 rpm and 30 rpm, while there were common parameters in the drilling fluid. Average axial viscous force decreased with torsional oscillation amplitude increasing (Figure

Influence of frequency of torsional oscillation on the axial viscous force.

Axial viscous force was also affected by viscosity of drilling mud. As shown in Figure

Influence of viscosity of drilling mud on the change in axial viscous force.

To analyze viscous friction force reduction, axial viscous friction force and viscous friction torque were compared in time domain. As shown in Figure

Viscous force and torque of drilling pipes in time domain.

The effect of the frequency of torsional oscillation on the axial drag force was discussed in this section. According to the common frequency and amplitude range of torque rocking drilling, 0.1 Hz, 1 Hz, and 10 Hz were selected to analyze the friction reduction in the longitudinal direction. The drill string slide velocity was equal to 0.0025 m/s, corresponding to an ROP of 9 m/h. Other simulation parameters were listed in Table

As shown in Figure

In addition to studying the interesting drag reduction of torsional oscillation drilling, an analysis was run to explore the relationship between ROP and the longitudinal friction force, as shown in Figure

The ratio of the axial and Coulomb friction decreased as the torsional oscillation amplitude increased. The reduction rate was remarkable in the region that the amplitude was below 20 rpm, and the downward rate of curves decreased out of that region. The increasing ROP led to a larger axial friction component ratio. The higher axial velocity component of the drill string contributed to a longer length of the bristle projected in the axial direction according the established model (Figure

Influence of frequency of torsional oscillation on the axial friction due to bristle deformation.

Influence of amplitude of drill string torsional oscillation on the change in axial friction.

The curve for the transverse friction force and transverse vibration velocity formed a loop that described hysteresis friction. The relationship between the axial friction force and relatively motion velocity had hysteretic properties, as depicted in Figure

Influence of different amplitudes of torsional oscillation on transverse friction.

The relationship of axial direction friction and velocity was shown in Figure

Loop of the axial force of the drill string and relative motion velocity.

The trajectory of the bristle projection point was depicted in Figure

Trajectory of general bristle end point projection.

Shape of trajectory liked a symbol of infinite. However, the trajectory loops of different drag velocities were symmetric with respect to

The trajectory loop was flat and narrow when the drag velocity was low. However, the loop became wider and curved with increase of drag velocity. The up and down ends of loop were toward the back. It was because stiffness coefficient of bristle deformation was greater than value of Gutowski and Leus [

Projection position of bristle in

Trajectory of bristle projection and drilling pipe torsional oscillation in time domain.

The amplitude of trajectory was lower than amplitude of torsional vibration. It was because the connection point between bristle and drilling pipe was ruptured and rebuilt. Meanwhile, there was obvious hysteresis between trajectory of projection point and trajectory of torsional oscillation. In the area that trajectory of torsional vibration intersected with trajectory of projection point, there was obvious difference of trajectory with different drag velocity.

Figure

Friction force of bristle deformation and viscous fluid in time domain.

Figure

Friction torque of bristle deformation and viscous fluid in time domain.

Given the microscope, complex, and field-oriented nature of the current rotation and torsional oscillation drill string axial friction resistance, the goal of this paper was to present a simple dynamic friction model based on the discrete LuGre model for the analysis of tribological effects in horizontal well drilling. This model was established on the basis of the average deflection of the general bristle model and considers the viscosity effect of mud. It is superior for describing the tribological behavior between the drill string and the rock of the wellbore. A computational program was developed to solve the present model, which was utilized to predict instantaneous general bristle deformation and frictional resistance at the contact surface.

The established model was verified using experimental data without adopting a coefficient of vibration transfer. The computational results were consistent with the experimental results. The model can be applied to analyze the frictional resistance of the drill string and wellbore. The parameter sensitivity studies were used to evaluate the effect of the magnitude of the Stribeck velocity and general bristle deformation damp. The results indicated that Stribeck velocity and damp of bristle deformation were not sensitive to friction using the drilling operation parameter.

Drilling parameters of general field were adopted to analyze drill string axial and circumferential friction torque using the present model. The amplitude of dynamic shear and viscosity of drilling mud was positively correlated with the drill string axial friction resistance.

The drag of drilling pipe also decreased with increase of torsional vibration amplitude. There was an optimal frequency that minimizes axial friction in the range of drilling parameters of general field. The axial friction would increase with increase of ROP. There was the order of magnitudes that the value of axial friction caused by bristle deformation and viscous fluid. The torque caused by bristle deformation was greater than ones of viscous fluid in range of drilling parameters of general field.

We introduce this concept into drilling engineering to capture the reality of drill string torque and drag. We can combine the model of conventional drill string mechanics with the discrete LuGre model to forecast proper technology in drilling horizontal wells.

Average of friction torque of bristle deformation and viscous fluid, N

Average of friction torque of bristle deformation and viscous fluid, N

A unit vector of axial direction of drill string

Average of friction force of bristle deformation, N

Average of friction force of viscous fluid, N

Average of friction torque of bristle deformation, N

Average of friction torque of viscous fluid, N

Diameter of wellbore, mm

Dynamic friction force, N

Coulomb friction force, N

Axial direction component of dynamic friction force, N

Tangential direction component of dynamic friction force, N

Static friction force, N

Outer diameter of drill string, mm

Friction force of bristle deformation, N

Friction force of viscous fluid, N

Friction torque of bristle deformation, N

Friction torque of viscous fluid, N

Velocity of relative motion drill string, m/s

Virtual relative velocity of motion drill string in previous half of time step,

Virtual relative velocity of motion drill string in following half of time step,

Stribeck velocity,

Axial direction velocity component of motion drill string, m/s

Instantaneous tangential direction velocity component of motion drill string, m/s

Tangential stiffness of general bristles, N/

Damp coefficient of general bristles, N/(

Damp coefficient of mud viscous friction, N/(m/s)

The well-hole inner diameter, m

The length of drilling pipes, m

The outer radius of drilling pipes, m

The axial velocity of drilling pipes considering fluid, consist of

Angle between virtual elastic deformation vector of general bristle and axial direction, rad

Angle between elastic deformation vector of general bristle and axial direction, rad

Coefficient of drill string eccentric, dimensionless

Viscosity of drilling mud, Pa·s

Dynamic shear of drill string, MPa

The rotating angular velocity of drilling pipe, rad/s

End point of bristle projection

Number of time step in one second, dimensionless

Elastic deformation of general bristles,

Virtual elastic deformation of general bristles in the calculation time step,

Time step,

Axial direction relative displacement of motion drill string in one time step,

Axial direction relative displacement of motion drill string in one time step,

Amplitude of torsional oscillation, rpm

Macroscope velocity relative to drilling fluid, m/s.

The authors declare that they have no conflicts of interest.

This research was sponsored by the National Natural Science Foundation of China (Grant no. 51274171), the Sichuan Province Science & Technology Program (Grant no. 2015SZ0003), and the National Science and Technology Major Project of China (Grant no. 2016ZX05022-01).