0
Research Papers

Drill String Bit Whirl Simulation With the Use of Frictional and Nonholonomic Models

[+] Author and Article Information
V. I. Gulyayev

Department of Mathematics,
National Transport University,
Suvorov Street, 1,
Kiev 01010, Ukraine
e-mail: valery@gulyayev.com.ua

L. V. Shevchuk

Department of Mathematics,
National Transport University,
Suvorov Street, 1,
Kiev 01010, Ukraine

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 29, 2014; final manuscript received October 6, 2015; published online December 8, 2015. Assoc. Editor: Carole Mei.

J. Vib. Acoust 138(1), 011021 (Dec 08, 2015) (9 pages) Paper No: VIB-14-1362; doi: 10.1115/1.4031985 History: Received September 29, 2014; Revised October 06, 2015

The problem about computer simulation of whirl vibrations of a drill bit is considered. The dynamic process is assumed to be in an incipient stage when the bit rolls on the borehole bottom without reaching the well wall. Mathematic models of the bit moving based on assumptions of frictional (rolling with sliding) and kinematic (pure rolling) contact between the bit and borehole bottom surfaces are elaborated. The influence of the drill string (DS) bending flexibility and the bit shape on the whirl process is discussed. The most typical whirl phenomena are grounded due to computer simulation.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Topics: Whirls , Vibration
Your Session has timed out. Please sign back in to continue.

References

Aldred, W. , Plumb, D. , Bradford, I. , Cook, J. , Gholkar, V. , Cousins, L. , Minton, R. , Fuller, J. , Goraya, S. , and Tucker, D. , 1999, “ Managing Drilling Risk,” Oilfield Rev., 11(2), pp. 2–19.
Gulyayev, V. I. , Gaidaichuk, V. V. , Solovjov, I. V. , and Gorbunovich, I. , V . , 2009, “ The Buckling of Elongated Rotating Drill Strings,” J. Pet. Sci. Eng., 67(3–4), pp. 140–148. [CrossRef]
Gulyayev, V. I. , Andrusenko, E. N. , and Shlyun, N. V. , 2014, “ Theoretical Modelling of Post-Buckling Contact Interaction of a Drill String With Inclined Bore-Hole Surface,” Struct. Eng. Mech., 49(4), pp. 427–448. [CrossRef]
Liu, X. , Vlajic, N. , Long, X. , Meng, G. , and Balachandran, B. , 2014, “ State-Dependent Delay Influenced Drill-String Oscillations and Stability Analysis,” ASME J. Vib. Acoust., 136(5), p. 051008. [CrossRef]
Liu, Y. , Ji, Y. , and Dick, A. J. , 2015, “ Numerical Investigation of Lateral and Axial Wave Propagation in Drill-Strings for Stability Monitoring,” ASME J. Vib. Acoust., 137(4), p. 041014. [CrossRef]
Gulyayev, V. I. , Hudoliy, S. N. , and Glushakova, O. V. , 2011, “ Simulation of Torsion Relaxation Auto-Oscillations of Drill String Bit With Viscous and Coulombic Friction Moment Models,” J. Multibody Dyn., 225(1), pp. 139–152.
Gulyayev, V. I. , and Glushakova, O. V. , 2011, “ Large-Scale and Small-Scale Self-Excited Torsional Vibrations of Homogeneous and Sectional Drill Strings,” Interact. Multiscale Mech., 4(4), pp. 291–311. [CrossRef]
Vlajic, N. , Liao, C.-M. , Karki, H. , and Balachandran, B. , 2013, “ Draft: Stick-Slip Motions of a Rotor–Stator System,” ASME J. Vib. Acoust., 136(2), p. 021005. [CrossRef]
Warren, T. M. , Brett, J. F. , and Sinor, L. A. , 1990, “ Development of a Whirl—Resistant Bit,” SPE Drill. Eng., 5(4), pp. 267–275. [CrossRef]
Mongkolcheep, K. , Ruimi, A. , and Palazzolo, A. , 2015, “ Modal Reduction Technique for Predicting the Onset of Chaotic Behavior Due to Lateral Vibrations in Drillstrings,” ASME J. Vib. Acoust., 137(2), p. 021003. [CrossRef]
Gulyayev, V. I. , and Shevchuk, L. V. , 2013, “ Nonholonomic Dynamics of Drill String Bit Whirling in a Deep Bore-Hole,” J. Multibody Dyn., 227(3), pp. 234–244.
Stroud, D. , Pagett, J. , and Minett-Smith, D. , 2011, “ Real-Time Whirl Detector Improves RSS Reliability, Drilling Efficiency,” Hart Explor. Prod. Mag., 84(8), pp. 42–43.
Melakhessou, H. , Berlioz, A. , and Ferraris, G. , 2003, “ A Nonlinear Well-Drillstring Interaction Model,” ASME J. Vib. Acoust., 125(1), pp. 46–52. [CrossRef]
Spanos, P. D. , Chevallier, A. M. , and Politis, N. P. , 2002, “ Nonlinear Stochastic Drill-String Vibrations,” ASME J. Vib. Acoust., 124(4), pp. 512–518. [CrossRef]
Gulyayev, V. I. , and Borshch, O. I. , 2011, “ Free Vibrations of Drill Strings in Hyper Deep Vertical Bore-Wells,” J. Pet. Sci. Eng., 78(3–4), pp. 759–764. [CrossRef]
Batzer, S. A. , Gouskov, A. M. , and Voronov, S. A. , 2001, “ Modeling Vibratory Drilling Dynamics,” ASME J. Vib. Acoust., 123(4), pp. 435–443. [CrossRef]
Christoforou, A. P. , and Yigit, A. S. , 1997, “ Dynamic Modeling of Rotating Drillstrings With Borehole Interactions,” J. Sound Vib., 206(2), pp. 243–260. [CrossRef]
Leine, R. I. , Van Campen, D. H. , and Keultjes, W. J. G. , 2002, “ Stick-Slip Whirl Interaction in Drillstring Dynamics,” ASME J. Vib. Acoust., 124(2), pp. 209–220. [CrossRef]
Samuel, R. , 2010, “ Friction Factors: What are They for Torque, Drag, Vibration, Bottom Hole Assembly and Transient Surge/Swab Analyses?,” J. Pet. Sci. Eng., 73(3–4), pp. 258–266. [CrossRef]
Neimark, Ju. I. , and Fufaev, N. A. , 1972, Dynamics of Nonholonomic Systems (Translation of Mathematical Monographs), American Mathematical Society, Providence, RI, p. 519.
Borisov, A. V. , Mamaev, I. S. , and Kilin, A. A. , 2005, Selected Problems of Nonholonomic Mechanics, Moscow Institute of Computer Investigations, Moscow, p. 290 (in Russian).
Markeev, A. D. , 1992, Dynamics of a Body Touching a Rigid Surface, Nauka, Moscow, p. 336 (in Russian).
Rauth, E. J. , 1877, An Elementary Treatise on the Dynamics of a System of Rigid Bodies, Macmillan and Co., London, p. 564.
Walker, G. T. , 1895, “ On a Curious Dynamical Property of Celts,” Proc. Cambridge Philos. Soc., 8(5), pp. 305–306.
Walker, J ., 1979, “ The Mysterious ‘Rattleback’: A Stone That Spins in One Direction and Then Reverses,” Sci. Am., 241(4), pp. 144–149. [CrossRef]
Lindberg, R. E. , and Longman, R. W. , 1983, “ On the Dynamic Behavior of the Wobblestone,” Acta Mech., 49(1–2), pp. 81–94. [CrossRef]
Pascal, M ., 1983, “ Asymptotic Solution of the Equations of Motion for a Celtic Stone,” J. Appl. Math. Mech., 47(2), pp. 269–276. [CrossRef]
Kovalyshen, Y ., 2013, “ A Simple Model of Bit Whirl for Deep Drilling Applications,” J. Sound Vib., 332(24), pp. 6321–6334. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Frictional (a) and nonholonomic (b) models of a body movement on uneven surface

Grahic Jump Location
Fig. 2

Structural (a) and calculation (b) schemes of drill bit whirling

Grahic Jump Location
Fig. 3

Schematic of forces and moments acting on separated bit in the inclination plane

Grahic Jump Location
Fig. 4

Top view of positions of points C and G and trace of the inclination plane σ

Grahic Jump Location
Fig. 5

Diagram of friction force change in the regimes of bit rolling and sliding

Grahic Jump Location
Fig. 6

The trajectories of the oblong bit center C moving in the fixed reference frame (a=0.1m, b=0.3m, T=−1×104N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=1.0; d−μ=10; e−μ=30; f− nonholonomic model

Grahic Jump Location
Fig. 7

The trajectories of the oblong bit center C moving in the fixed reference frame (a=0.1m, b=0.3m, T=−1×105N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=1.0; d−μ=10; e−μ=30; f− nonholonomic model

Grahic Jump Location
Fig. 8

The trajectories of the oblong bit center C moving in the fixed reference frame (a=0.3m, b=0.1m, T=−1×104N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=1.0; d−μ=10; e−μ=30; f− nonholonomic model

Grahic Jump Location
Fig. 9

The trajectories of the oblong bit center C moving in the fixed reference frame (a=0.3m, b=0.1m, T=−1×105N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=1.0; d−μ=10; e−μ=30; f− nonholonomic model

Grahic Jump Location
Fig. 10

Modes of bit vibrations in the fixed coordinate system (a=0.3m, b=0.1m, T=−1×105N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=30; d− nonholonomic model

Grahic Jump Location
Fig. 11

The trajectory of the oblong bit center C moving in the fixed reference frame (a=0.3m, b=0.1m, T=−1×104N, Mz=−1×104N m, ω=10rad/s, μ=1, 0≤t≤20s)

Grahic Jump Location
Fig. 12

Functions of angular velocities of the bit whirling (ωb) and the DS rotation (ω)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In