Modelling and detection of slipping in distributed damping subs for drillstring torsional vibration mitigation

Torsional vibrations during drilling are detrimental to the equipment used and result in sub-optimal performance. A recently developed method to mitigate such vibrations involves the use of distributed damping subs fitted around the drillstring at various locations throughout non-vertical sections of the well. An eddy current brake, which may be actively controlled in practice, dampens the vibrations but the reactionary torque results in lateral motion of the subs which may cause slipping. To minimize slipping between the damping subs and the wellbore wall during operation, the controller needs to know if and when this happens in order to alter the control input accordingly. A control-oriented mathematical model is derived to describe the lateral and torsional motion of a sub within the wellbore, with the wellbore friction modelled as Coulomb friction with stiction. Next, a slip detection algorithm based on measurements from inertial measurement units placed within the damping sub is proposed. A simulation of the control-oriented damping sub model coupled to a low-order drillstring model featuring torsional vibrations is presented, where the reactionary damping torque causes the sub to slip along the wellbore wall. Simulated accelerometer signals and the resultant residual for detecting slippage are shown to demonstrate the methodology. The slip detection methodology is further verified on data from a high-fidelity simulator.