Nonlinear Model for Dynamic Behavior of Drill-String

This article is devoted to the study of the contact between the drill-string and the well during drilling operations. The study focuses on the Bottom-Hole-Assembly (BHA), which is submitted to compression. The work is motivated by the need to understand the complex behavior of such a system, in order to improve control their constructive and destructive potentials. The contact, which is supposed to be localized on the drill-collar or stabilizers, is prejudicial and involves a premature abrasive wear of the drill-string, reduction of the rate of penetration of the tool into the rock (ROP) and reduction of the mean time between failure (MTBF). The proposed mathematical model is expressed in terms of four independent degrees of freedom. They include the effects of bending and torsion; the whirling motion of the drill-string as well as the phenomena of friction between the drill-string and the well. The tangential effect is modeled by using Coulomb’s law of friction. The nonlinear equations of the movement are derived using Lagrange equations and are solved numerically to obtain the response. Specific attention is paid to the study of friction and a consistent contact model which is capable of taking into account the rolling of the drill-string, both with and without slip, is included in the model. This paper also presents a parametric study on the influence of the initial position of the string and the friction coefficient of the contact on the dynamic behavior of the structure. An experimental set-up, equipped with two optolineic devices, is used to validate the model.