An experimental and numerical study on drillstring stick-slip oscillations in ultra-deep wells

Severe drillstring stick–slip oscillations can substantially reduce drilling efficiency and accelerate bit wear in ultra-deep wells. In this study, full-scale downhole measurements are first obtained during drilling of an ultra-deep vertical well using a 333.4-mm PDC bit. The measured tri-axial accelerations reveal severe low-frequency stick–slip oscillations, with a period of approximately 10.0 s, consisting of about 3.0 s of stick phase and 7.0 s of slip phase, and a maximum estimated downhole angular velocity of approximately 350 rev/min at a surface rotary speed of 120 rev/min. A nonlinear finite-element model considering coupled axial and torsional motions, axial–torsional geometric nonlinearity, drilling-fluid damping, and a non-regularized velocity-weakening bit-rock interaction law is then developed. The resulting nonlinear equations of motion are solved numerically using the Newmark time-integration method. The key bit-rock interaction parameters are calibrated against the field measurements by reproducing the maximum downhole angular velocity and the characteristic stick–slip period and phase durations. The calibrated model reproduces the measured maximum angular velocity of approximately 350 rev/min and the 10.0-s stick–slip period. Parametric analyses further show that increasing WOB intensifies stick–slip oscillations, with the stick–slip severity index increasing from approximately 0.52–1.46 as WOB increases from 60 to 160 kN at 120 rev/min, whereas increasing surface rotary speed reduces the severity index from approximately 1.75–0.78 as rotary speed increases from 60 to 160 rev/min at a WOB of 120 kN. The results provide a physics-based framework for understanding stick–slip behavior and evaluating drilling-parameter effects in ultra-deep wells.