Solution of a robust optimization problem to maximize the rate of penetration of horizontal drillstrings using a nonlinear stochastic dynamic model

International audienceA drillstring is a long column under rotation, composed by a sequence of connected drill-pipes and auxiliary equipment, which is used to drill the soil in oil prospecting. During its operation, this column presents a three-dimensional dynamics, subjected to longitudinal, lateral, and torsional vibrations, besides the effects of friction, shock, and bit-rock interaction. Due to the relevance of this equipment in some engineering applications,this work aims to analyze the nonlinear dynamics of drillstrings in horizontal configuration. A computational model, which uses a nonlinear beam theory of Timoshenko type that takes into account the coupling between longitudinal, transverse, and torsional vibrations, is considered. This model also takes into account the effects of friction and shock, induced by the lateral impacts between the drillstring and borehole wall, as well as bit-rock interaction effects. The uncertainties of the bit-rock interaction model are taken into account using a parametric probabilisticapproach. Numerical simulations have shown that the mechanical system of interest has a very rich dynamics, which reproduces phenomena such as bit-bounce, stick-slip, and transverse impacts. Two optimizations problems (one deterministic and one robust), where the objective is to maximize the drillstring rate of penetration (ROP) into the soil, respecting its structural limits, are formulated and solved. In order to optimize the ROP, it is possible to vary the drillstring velocities of translation and rotation. The solutions of these optimization problems provided two different strategies to maximize the ROP