Lateral vibrations of drill-strings used in oil well operations are considered. A finite elements based discretization procedure leads to a nonlinear dynamic system which is used to represent the drill-string inertia and stiffness characteristics, as well as the elasticity of the wall of the well. Due to the erratic pattern and the uncertainty of the forces at the drill-bit, a stochastic dynamics approach is adopted in investigating the problem. The method of statistical linearization is used, and expressions for determining an equivalent linear system to model the drill-string dynamics are derived. Further, a Monte Carlo simulation of the system dynamics is conducted by means of an Auto Regressive Moving Average (ARMA) digital filter, and by integrating the equations of motion using the Newmark scheme. Numerical results pertaining to data obtained by measurement while drilling (MWD) tools are presented. It is hoped that this study will enhance the interest in using stochastic dynamics techniques in drilling system analysis and design, as they can capture quite appropriately the inherent uncertainty of the bit forces and, potentially, of other sources.
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October 2002
Technical Papers
Nonlinear Stochastic Drill-String Vibrations
P. D. Spanos, Fellow ASME, L. B. Ryon Professor of Engineering,,
P. D. Spanos, Fellow ASME, L. B. Ryon Professor of Engineering,
Rice University, Department of Mechanical Engineering and Material Science, George R. Brown School of Engineering, 6100 Main Street, Houston, TX 77005-1892
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A. M. Chevallier, Engineering Consultant,,
A. M. Chevallier, Engineering Consultant,
Accenture Company, 49B NorthCote Road, London, SW111NJ, U.K.
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N. P. Politis, Graduate Student,
N. P. Politis, Graduate Student,
Rice University, Department of Civil Engineering, George R. Brown School of Engineering, 6100 Main Street, Houston, TX 77005-1892
Search for other works by this author on:
P. D. Spanos, Fellow ASME, L. B. Ryon Professor of Engineering,
Rice University, Department of Mechanical Engineering and Material Science, George R. Brown School of Engineering, 6100 Main Street, Houston, TX 77005-1892
A. M. Chevallier, Engineering Consultant,
Accenture Company, 49B NorthCote Road, London, SW111NJ, U.K.
N. P. Politis, Graduate Student,
Rice University, Department of Civil Engineering, George R. Brown School of Engineering, 6100 Main Street, Houston, TX 77005-1892
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 2001; revised June 2002. Associate Editor: G. T. Flowers.
J. Vib. Acoust. Oct 2002, 124(4): 512-518 (7 pages)
Published Online: September 20, 2002
Article history
Received:
October 1, 2001
Revised:
June 1, 2002
Online:
September 20, 2002
Citation
Spanos, P. D., Chevallier, A. M., and Politis, N. P. (September 20, 2002). "Nonlinear Stochastic Drill-String Vibrations ." ASME. J. Vib. Acoust. October 2002; 124(4): 512–518. https://doi.org/10.1115/1.1502669
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