Stick-Slip Model for PDC Bits Accounting for Coupled Torsional and Axial Oscillations

Abstract

Drilling with PDC bits can cause severe torsional and axial oscillations. These oscillations are accompanied by periodic sticking of the bit followed by accelerated rotation. The so-called “stick-slip” increases bit wear and fatigue and causes premature failure of BHA and drillstring components. It is well known that these torsional oscillations are nonlinear and self-induced. The present study investigates the coupling between axial and torsional oscillations. The cutting process is based on the Detournay model, which provides for the effect of the bottomhole pressure and the local pore pressure. The axial stiffness of the drillstring is taken into account with the axial motion equations coupled with the torsional equations, in contrast to previous models where axial equations were considered independently. Axial oscillations are allowed to occur even when the bit is in the stick phase. The new model also includes bit “bouncing” when it loses contact with the bottomhole. The equations are solved by time integration. By results of the analysis of transient processes the spectral density is determined. The objective of the paper is to improve understanding of stick-slip oscillation nature and assess the contribution of parameters that influence their intensity. The study includes the effect of the rotor rpm, intrinsic specific energy of rock, number of PDC blades, wear flat length of blades, etc. Results of the study will help drillers to select and change drilling parameters more efficiently to reduce severe stick-slip oscillations.