Nonlinear Dynamic Modeling and Analysis of Drill Strings Under Stick–Slip Vibrations in Rotary Drilling Systems

This paper presents a comprehensive study of torsional stick–slip vibrations in rotary drilling systems through a comparison between two lumped parameter models with differing complexity: a simple two-degree-of-freedom (2-DOF) model and a complex high-degree-of-freedom (high-DOF) model. The two models are developed under identical boundary conditions and consider an identical nonlinear friction torque dynamic involving the Stribeck effect and dry friction phenomena. The high-DOF model is calculated with the Finite Element Method (FEM) to enable accurate simulation of the dynamic behavior of the drill string and accurate representation of wave propagation, energy build-up, and torque response. Field data obtained from an Algerian oil well with Measurement While Drilling (MWD) equipment are used to guide modeling and determine simulations. According to the findings, the FEM-based high-DOF model demonstrates better performance in simulating basic stick–slip dynamics, such as drill bit velocity oscillation, nonlinear friction torque formation, and transient bit-to-surface contacts. On the other hand, the 2-DOF model is not able to represent these effects accurately and can lead to inappropriate control actions and mitigation of vibration severity. This study highlights the importance of robust model fidelity in building reliable real-time rotary drilling control systems. From the performance difference measurement between low-resolution and high-resolution models, the findings offer valuable insights to optimize drilling efficiency further, minimize non-productive time (NPT), and improve the rate of penetration (ROP). This contribution points to the need for using high-fidelity models, such as FEM-based models, in facilitating smart and adaptive well control strategies in modern petroleum drilling engineering.