Stochastic Drill-String Dynamics Via Cosserat Rod Models

Abstract

The study of drill-string dynamics is a complex matter. With lengths surpassing 1000 m, due to their slenderness, geometrical aspects of oil-wells and contact forces, drill-strings usually exhibit a highly non-linear response. Operative conditions are very sensitive to changes in working parameters, namely rotary speed and hook load, among others. Moreover, many unwanted phenomena may occur when conditions for stable operation are not met, such as stick-slip oscillations. On top of that, there are several intrinsic uncertainties, e.g. modelling of soil, which may lead to unwanted operation regimes that negatively affect performance, i.e. degraded rate-of-penetration (ROP). In this work, a stochastic approach to drill-string dynamics is presented via a Cosserat rod model. The model is implemented in a finite element environment. Nonlinearities of the drill-string problem occur due to geometrical factors such as finite displacements and rotations, as well as to contact and friction at the borehole wall and bit. In particular, a friction model presented by (R. Tucker and C. Wang, Meccanica, 38(1):143-159(2003)) is used. The drill is set in motion via a PI-Controller driving the motor at the top drive. First, the deterministic model is implemented using the weak formulation mathematical interface from COMSOL Multiphysics, a finite element environment. Then, uncertainties are considered within soil characteristics. The random response is analysed by examining the trajectories of the drill-string axis.