Nonlinear integrated dynamic analysis of drill strings under stick-slip vibration

Stick-slip torsional vibration raising from bit-formation contact is a catastrophic dynamic phenomenon occurring in deep-water oil and gas drilling systems. The torsional vibrations can result in premature fatigue failure of drilling equipment and reduce drilling efficiency. Thus, studying the dynamics of the system is a vital key to identify the roots of the vibration and establish appropriate mitigation and remediation methods. In this paper, an efficient approach for finite element (FE) modeling of stick-slip vibrations of the full drill strings was proposed. The model was developed based on a rate-dependent formulation of bit-rock interaction, in which the cutting process was integrated through the frictional contact. The nonlinear effects of the large rotations and the geometrically nonlinear axial-torsional coupling were taken into account. The effect of energy dissipation due to the presence of drill mud along the drill pipes and drill collars was incorporated through Rayleigh viscous damping. Modal analysis was conducted to determine the natural frequencies and the mode shapes of the drill string. Furthermore, a five degree-of-freedom lumped parameter model was developed. The performance of the developed models was verified through comparisons with example stick-slip results from a field test. The study showed that the self-excited torsional vibrations may also occur at fundamental frequencies lower than the first natural torsional frequency of the drill string, depending on operational parameters. The conducted research work resulted in a robust and practical integrated FE model to simulate the entire drill string system dynamics under torsional vibrations.