Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model

International audienceThis work proposes a strategy for the robust optimization of the nonlinear dynamics of a drill-string, which is a structure that rotates and digs into the rock to search for oil. The nonparametric probabilistic approach is employed to model the uncertainties of the structure as well as the uncertainties of the bit-rock interaction model. This paper is particularly concerned with the robust optimization of the rate of penetration of the column, i.e., we aim to maximize the mathematical expectation of the mean rate of penetration, respecting the integrity of the system. The variables of the optimization problem are the rotational speed at the top and the initial reaction force at the bit; they are considered deterministic. The goal is to find the set of variables that maximizes the expected mean rate of penetration, respecting, vibration limits, stress limit and fatigue limit of the dynamical system

Modeling uncertainties for local nonlinearities: application to the drill-string dynamics

International audienceA probabilistic model is proposed to model uncertainties for local nonlinearities. The model is applied to a slender structure that turns and drills into rocks in search of oil, called drill-string, in which the local nonlinearity is the bit-rock interaction. The Maximum Entropy Principle is used to construct a probabilistic model for the nonlinear operator related to the bit-rock interaction model. A numerical model is developed using the Timoshenko beam theory and it is discretized by means of the Finite Element Method. The nonlinear dynamics analyzed considers a imposed rotation at the top, weight-on-hook, a fluid-structure interaction (that takes into account the drilling fluid that flows downwards the column and upwards the annulus), impact and rubbing between the column and the borehole, and finite strains (what couples axial, torsional and lateral vibrations). The development presented corresponds to a new approach to take into account model uncertainties in local nonlinearities using a probabilistic approach