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

Abstract eng:
A 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.

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