Investigation of field scenarios using a 4n degrees of freedom transient torque and drag model

A coupled drill string dynamics model presents an opportunity to understand, replicate and potentially control the vibrations occurring along a drill string in a deep well. This paper describes a 4n degrees of freedom (4nDOF) model of the axial, torsional and lateral dynamics, consisting of coupled wave equations and lumped elements, which include modeling of the contact between the drill string and wellbore with a stiff string assumption. The model accounts for the bit-rock interaction, structural damping, and hydraulic forces acting on the lumped elements. The 4nDOF model is compared with three field scenarios from a drilling operation in the North Sea: a three-stage top drive start-up procedure, a drilling sequence starting from off-bottom conditions, and a backreaming operation at low rotational speed. The selected cases include instances of stick- slip and higher modes of torsional vibrations, which persist despite the use of a surface vibration mitigation system. High-frequency data recorded by a downhole measurement sub placed near the drill bit are used to verify the simulated downhole rotational speed and triaxial accelerations. The model is useful for analyzing torsional stick-slip events, which are replicated with a similar period and amplitude as in the downhole measurements. Furthermore, the model accurately reproduces the transition between first and second mode torsional oscillations upon the activation of a tuned top drive vibration mitigation system. The model can also be used to analyze lateral deformations and whirling of the drill string at various depths. The field case simulations show that the lateral dynamics can undergo significant changes at certain points in the drill string during torsional stick-slip and higher-mode torsional oscillations. The proposed model can be used to run simulations in close to real-time on a standard personal workstation, thus making it a valuable tool for devising and testing new drill string vibration mitigation solutions.