Lateral vibration and vibration control methods for ultra-deep well drill strings based on Cosserat geometrically exact beam theory

In ultra-deep well operations, severe lateral vibration of drill string is a major factor in tool failure and decreased drilling efficiency. To investigate the vibration mechanisms and identify effective mitigation approaches, a dynamic model for lateral vibration in ultra-deep well drill strings was established using Cosserat geometrically exact beam theory. The model systematically examined the effects of rotational speed, WOB, and stabilizer position and size on the vibration behavior. Key findings were validated against downhole measurement data from ultra-deep wells. Additionally, two control strategies leveraging modal competition and transverse wave disturbance were proposed. Results indicate that the bottom hole assembly (BHA) is particularly prone to intense lateral vibrations, with its vibrational modes governed by rotational speed and WOB. When the WOB is below the critical buckling load, increasing either the rotational speed or WOB promotes backward whirling of the BHA, thereby intensifying the vibration severity and bending stress. Conversely, when the WOB exceeds the critical buckling load, the system transitions into a buckling–whirling competition mode, resulting in a significant reduction in the vibration intensity and bending stress. This trend was reasonably verified through field data. Artificially inducing this low-risk modal competition by adjusting the WOB and rotational speed can effectively reduce the probability of drill string failure. The motion of stabilizers shifts from forward whirling to backward whirling as the diameter decreases, which considerably alters the vibration-propagation patterns. The vibration-damping effects of both full-gauge and under-gauge stabilizers initially increase and then decrease as their installation position moves upward. Under-gauge stabilizers exhibit less consistent behavior under non-severe vibration conditions; nevertheless, they can suppress severe whirling by interfering with adjacent drill string vibrations through low-frequency transverse waves. They also demonstrate lower sensitivity to the installation position and enhance drill string safety through stress dispersion. Considering comprehensive vibration suppression, drill string integrity, and engineering applicability, installing under-gauge stabilizers can be a viable BHA optimization measure with significant practical value. This study provides a theoretical basis for vibration control in ultra-deep well drill strings, and the proposed strategy offers valuable insights for improving drilling efficiency and ensuring operational safety.