Suppressing Axial-Torsional Coupled Vibrations in Drillstrings

Abstract

In drilling operation, a wide variety of oscillations causing failures often arise.
Torsional vibrations (stick-slip) are originated by the cutting device (bit) motion, these
vibrations in turn excite axial oscillations causing a phenomenon known as bit-bouncing. This
paper addresses two important challenges: the modeling of the coupled axial and torsional
dynamics in a vertical oilwell drilling system and the design of an effective controller to reduce
undesirable behaviors. Through the D'Alembert transformation, the distributed parameter
model of the drillstring is reduced to a neutral-type time-delay equation which effectively
describes the oscillatory behavior of the system. The Lyapunov theory allows to develop an
efficient strategy for the control synthesis guaranteeing the elimination of the stick-slip and
bit-bounce. This approach leads the "practical" stabilization of the closed loop system. All
results can be easily generalized to any time-delay system subject to bounded disturbances.
The effectiveness of the strategy is validated through simulations.