Stick-slip Oscillations in Oillwell Drilstrings: Distributed Parameter and Neutral Type Retarded Model Approaches

The drill pipe model is described by the wave equation with mixed boundary conditions in which a sliding velocity is considered at the top end. The proposal of an energy function for the distributed model allows to find a control law that ensures the energy dissipation during the drilling operation. The distributed parameter model is reduced through the d'Alembert transformation to a difference equation model. Torsional drillstring vibrations, also known as “stick-slip” oscillations appearing in oilwell drillstrings are a source of failures which reduce penetration rates and increase drilling operation costs. Some experience-based control strategies are evaluated in order to reduce stick-slip oscillations. The use of the angular velocity at the drillstring upper part, the torque on the bit and the weight on the bit is shown to have a key effect in the reduction of drillstring torsional vibrations.