Sliding-mode control of a multi-DOF oilwell drillstring with stick-slip oscillations

A dynamical sliding-mode control is used to avoid different bit sticking problems present in a conventional vertical oilwell drillstring. The control goal of driving the rotary velocities of drillstring components to a constant positive value is achieved by means of this control. A discontinuous lumped- parameter torsional model of four degrees of freedom is considered. This model allows to describe drill pipes and drill collars behavior. The closed-loop system has two discontinuity surfaces. One of them gives rise to self-excited bit stick-slip oscillations and bit sticking phenomena. The other surface is introduced to accomplish the control goal despite variations in the weight on the bit (key to the dynamics) and other system parameters.

I. Introduction

Oilwell drillstrings are mechanisms that play a key role in the petroleum extraction industry. Failures in drillstrings can be significant in the total cost of the perforation process. These devices are complex dynamical systems with many unknown and varying parameters due to the fact that drillstring characteristics change as the drilling operation makes progress. The drillstring interaction with the borehole gives rise to a wide variety of non-desired oscillations. These oscillations are a major cause of drillstring component failures [1]–[3]. Permanent stuck bit and stick-slip at the bit are two phenomena particularly harmful. The first happens when the bit is unable to rotate, and the second causes the top-rotary system to move with a constant rotary speed, whereas the bit rotary speed varies between zero and up to six times the rotary speed at the surface.