Effects of Drill String Length on Stick–Slip Oscillation of the Oilwell Drill String

It has been demonstrated by numerous field data that the stick–slip phenomenon tends to appear in deep wells. However, the explanation for this phenomenon has scarcely been studied. Based on a torsional pendulum model, the relationship between stick–slip oscillation and drill string (DS) length is studied in this work. Firstly, the drill bit (DB) dynamics are obtained by solving the kinetic motion of the DB. Secondly, case studies with different DS lengths are conducted by referring to the actual drilling parameters. Thirdly, results and discussions related to the case studies are carried out, including obtaining the DB dynamics, DB dynamics for different DS lengths, determination of the critical length, and plausible interpretation for the occurrence of stick–slip oscillation. Results show that two types of oscillation are obtained, e.g., oscillations with or without stick–slip phenomenon. In the cases of stick–slip, the state trajectories possess stable limit cycles. In the cases of no stick–slip, the state trajectories possess a spiral that denotes the DB motion tends to a stable phase (uniform motion).