Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects

In this article, a discrete model of a drill-string system is developed taking into account stick-slip and time-delay aspects, and this model is used to study the nonlinear motions of this system. The model has eight degrees-of-freedom and allows for axial, torsional, and lateral dynamics of both the drill pipes and the bottom-hole assembly. Nonlinearities that arise due to dry friction, loss of contact, and collisions are considered in the development. State variable dependent time delays associated with axial and lateral cutting actions of the drill bit are introduced in the model. Based on this original model, numerical studies are carried out for different drilling operations. The results show that the motions can be self-exited through stick-slip friction and time-delay effects. Parametric studies are carried out for different ranges of friction and simulations reveal that when the drill pipe undergoes relative sticking motion phases, the drill-bit motion is suppressed by absolute sticking. Furthermore, the sticking phases observed in this work are longer than those reported in previous studies and the whirling state of the drill pipe periodically alternates between the sticking and slipping phases. When the drive speed is used as a control parameter, it is observed that the system exhibits aperiodic dynamics. The system response stability is seen to be largely dependent upon the driving speed. The discretized model presented here along with the related studies on nonlinear motions of the system can serve as a basis for choosing operational parameters in practical drilling operations.

[1]  Henrik Schiøler,et al.  Proceedings of the 2006 IEEE International Conference on Control Applications , 2006 .

[2]  van Dh Dick Campen,et al.  Stick-Slip Vibrations Induced by Alternate Friction Models , 1998 .

[3]  Nathan van de Wouw,et al.  Nonlinear Drillstring Dynamics Analysis , 2009, SIAM J. Appl. Dyn. Syst..

[4]  J. F. Brett,et al.  Bit whirl: a new theory of PDC bit failure , 1990 .

[5]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .

[6]  Edwin Kreuzer,et al.  Active Damping of Spatio-Temporal Dynamics of Drill-Strings , 2005 .

[7]  Henk Nijmeijer,et al.  Analysis of Friction-Induced Limit Cycling in an Experimental Drill-String System , 2004 .

[8]  Henk Nijmeijer,et al.  A Semi-Analytical Study of Stick-Slip Oscillations in Drilling Systems , 2011 .

[9]  Ahmet S. Yigit,et al.  Stick-Slip and Bit-Bounce Interaction in Oil-Well Drillstrings , 2006 .

[10]  Balakumar Balachandran,et al.  Drill-String Dynamics: Reduced-Order Models and Experimental Studies , 2011 .

[11]  Emmanuel M Detournay,et al.  A phenomenological model for the drilling action of drag bits , 1992 .

[12]  Emmanuel M Detournay,et al.  A simplified model to explore the root cause of stick–slip vibrations in drilling systems with drag bits , 2007 .

[13]  T. M. Warren,et al.  Torsional resonance of drill collars with PDC bits in hard rock , 1998 .

[14]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[15]  Balakumar Balachandran,et al.  Dynamics of milling processes with variable time delays , 2006 .

[16]  Emmanuel M Detournay,et al.  Multiple mode analysis of the self-excited vibrations of rotary drilling systems , 2009 .

[17]  Balakumar Balachandran,et al.  Nonlinear dynamics of milling processes , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  R. Suarez,et al.  Practical approach to modelling and controlling stick-slip oscillations in oilwell drillstrings , 2004, Proceedings of the 2004 IEEE International Conference on Control Applications, 2004..

[19]  Processes in Mechanics,et al.  IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics : proceedings of the IUTAM symposium held in Rome, Italy, 8-13 June 2003 , 2005 .

[20]  van Dh Dick Campen,et al.  Stick-Slip Whirl Interaction in Drillstring Dynamics , 2002 .

[21]  Min Wan,et al.  Prediction of chatter stability for multiple-delay milling system under different cutting force models , 2011 .

[22]  Z. C. Feng,et al.  Rubbing phenomena in rotor–stator contact , 2002 .

[23]  Balakumar Balachandran,et al.  Parametric studies on drill-string motions , 2012 .

[24]  J. Tlusty,et al.  Basic Non-Linearity in Machining Chatter , 1981 .

[25]  J. F. Brett,et al.  Development of a whirl-resistant bit , 1990 .

[26]  Min Wan,et al.  A unified stability prediction method for milling process with multiple delays , 2010 .

[27]  James Ford Brett,et al.  SPE-019571-MS - Bit Whirl: A New Theory of PDC Bit Failure , 1989 .

[28]  Balakumar Balachandran,et al.  Stick-Slip and Whirl Motions of Drill Strings: Numerical and Experimental Studies , 2011 .

[29]  D. R. Pavone,et al.  Application of High Sampling Rate Downhole Measurements for Analysis and Cure of Stick-Slip in Drilling , 1994 .

[30]  Joseph Mathew,et al.  USING THE CORRELATION DIMENSION FOR VIBRATION FAULT DIAGNOSIS OF ROLLING ELEMENT BEARINGS—I. BASIC CONCEPTS , 1996 .

[31]  Emmanuel M Detournay,et al.  Self-excited stick–slip oscillations of drill bits , 2004 .

[32]  J. F. Brett.  The genesis of torsional drillstring vibrations , 1992 .