Control strategies for mitigating torsional and axial vibrations in rotary oilwell drilling systems.

This article focuses on modeling, analyzing, and controlling the coupled torsional and axial vibrations in rotary oil well drilling systems using a nonlinear dynamics framework. The study employs a coupled system of a damped wave partial differential equation (PDE) for torsional dynamics and an ordinary differential equation (ODE) for axial dynamics, linked through a nonlinear friction function representing the drill bit-rock interaction. It establishes the well-posedness of this PDE-ODE system and proposes feedback control laws based on Lyapunov methods to ensure system stability and suppress harmful stick-slip and bit-bounce vibrations. Numerical simulations using realistic drilling parameters demonstrate the effectiveness of the designed controllers in stabilizing the coupled vibrations, thereby improving drilling performance. The work aims to contribute practical control strategies for mitigating detrimental vibrations in drilling operations and suggests future research on integrating these methods with Managed Pressure Drilling systems.