Measurement and simulation of nonlinear drillstring stick-slip and whirling vibrations

When drilling ultra-deep wells with polycrystalline diamond compact (PDC) bits, the drillstring suffered from severe vibrations that were responsible for the premature failure of drillstring components and the inefficient drilling process. In this paper, a field experiment was conducted in an ultra-deep well to measure the downhole tri-axial accelerations of the drillstring. The analyses of the acceleration data in the time and frequency domains show that the drillstring is subjected mainly to violent stick–slip and whirling vibrations. Comparisons between two adjacent sets of tri-axial acceleration data suggest that the occurrence of stick–slip oscillations intensifies the downhole drillstring whirling vibrations. To numerically study the measured stick–slip and whirling vibrations, a fully coupled finite element model for the axial, torsional and lateral vibrations of the drillstring is developed. The bit–rock interaction, which is responsible for the stick–slip oscillations, is modeled by a non-regularized dry friction law, the key parameters of which are fitted by the experimental results. Hertzian contact theory is used to model the nonlinear contacts between the drillstring and the wellbore wall. The downhole angular velocity fluctuations that are due to the stick–slip oscillations are also considered, and they lead to the coupling between the stick–slip and the whirling vibrations. The satisfactory agreement between the numerical and experimental results supports the fidelity of the proposed finite element model. The experimentally observed intensifying effects of the stick–slip oscillations on the whirling vibrations are verified via comparisons between simulation results with and without consideration of the coupling effects. On this basis, parametric studies are conducted to analyze the influence of the drilling parameters on the stick–slip oscillations and the whirling behaviors.