On the formation of limit cycle of the friction-induced stick-slip vibration in oilwell drillstring

Abstract

In this paper, the stick-slip vibration in oilwell drillstring is studied. The drilling system is modelled as a lumped-parameter torsional pendulum and the interaction between the drill bit and the rock is treated as Coulomb friction. Equation of motion of the drill bit is established and the dynamic responses of the drill bit are obtained. A drilling system with the drillstring length 3000 m is analysed, in which the system parameters are selected by reference to the actual drilling situation. After the slip vibrations in the initial stage, final state of the drill bit is a stable stick-slip vibration of which the limit cycle is a closed loop. In order to find the stability of the limit cycle corresponds to the periodically stick-slip vibration, different initial conditions for the drill bit are studied. Results show that the drill bit will lead to a periodic motion and the phase trajectories ultimately converge to the same limit cycle corresponds to stable stick-slip vibration.

Keywords

Stick-slip vibration / Friction / Drillstring / Drill bit / Limit cycle

Acknowledgements

This research is Supported by the Natural Science Fund for Outstanding Youth Science Fund (Grant No. 51222406), New Century Excellent Talents in University of China (NCET-12-1061), Scientific Research Innovation Team Project of Sichuan Colleges and Universities (12TD007), Youth Scientific Research Onnovation Team Project of Sichuan Province (2014TD0025), the key projects of academic and technical leaders cultivate Fund in Sichuan Province, China(2011-441-zxh), and Sichuan Science and Technology Innovation Talent Project (20132057).

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