Nonlinear rotordynamics of a drillstring in curved wells: Models and numerical techniques

The drilling operations for oil or geothermic extraction use a slender structure introduced inside the drill well, hanging from a derrick and driven by a rotary table at the surface. The drilling structure consists in a series of drill-pipes and some heavy pipes at the well bottom. The drilling process involves nonlinear dynamic phenomena such as bit-bounce, stick-slip due to the well-drillstring multi-contacts and the pulsating mud flow. The drillstring vibrations may yield, the rate of penetration decrease, the premature wears and damages of drilling equipment. Many numerical models have been proposed to study the dynamics of drillstring to improve the reliability of drilling operations. However, the numerical models of drilling structures representing several kilometers length require a huge amount of computer memory storage and yield a too long computational time. The reduction technique proposed by Craig-Bampton (CB) has been developed for modelling the nonlinear dynamics of rotating machines to save the computational time but still limited in the context of rotordynamics. The paper focuses on the implementation of the CB method in the case of long drillstring assembly modelled by beam finite elements. The pre-loaded states of the drillstring due to the well curvature, well-structure contacts and fluid-structure interactions are determined and taken into account in the dynamic computation. The drillstring transient dynamics is simulated and the orbital motion of several nodes are analyzed. The result convergence and the reduction of computational time obtained by the CB method are investigated and discussed.