A Stochastic Approach for a Cosserat Rod Drill-String Model with Stick-Slip Motion

Drill-strings employed in the oil extraction process present complex dynamics. Due to their slenderness (with length surpassing 1000 m), geometrical aspects of oil-wells, and contact forces, drill-strings exhibit a strong non-linear response. Many unwanted phenomena, like stick-slip oscillations, may occur under certain conditions. Moreover, there are several intrinsic uncertainties, e.g. in modelling the soil, which may lead to unwanted operation regimes and affect performance, i.e. degraded rate-of-penetration (ROP), and stick-slip. In this work, a stochastic approach to study drill-string dynamics is employed. The physical model is based on the Cosserat rod theory. Non-linearities of the drill-string problem may occur due to geometrical factors, such as finite displacements and rotations in deviated wells, as well as to contact and friction at the borehole wall and bit. In this particular paper, uncertainties are considered within the friction parameters. The random response is analysed through the trajectories of the drill-string axis and other quantities, such as the evolution of the angular velocities.