Robust Rotational Stability Analysis of a Vertical Drill-String

Bernardo Fonseca Nogueira¹; Thiago Gamboa Ritto¹; André Maciel Falcão¹

¹ UFRJ - Universidade Federal do Rio de Janeiro

doi:10.20906/CPS/COB-2015-0522

Resumo

We are interested in predicting rotational instability regions in the operation of a vertical drill-string, where stick-slip is likely to occur. The stick-slip is a severe type of self-excited vibration, which affects mainly polycrystalline diamond compact bits, characterized by large fluctuations in the angular velocity of the bit. Drill-string vibrations is one of the major causes for a decrease in drilling performance. We have modelled the drill-string as a shaft with piecewise constant cross section using Saint-Venant torsion theory with a non-linear boundary condition. Then, we converted the partial differential equation of movement to the discrete domain using the finite elements method. Finally, we represented the dynamical system in the state space and analysed its stability. We will introduce a new definition of stability suitable to predict the likelihood of stick-slip occurrence. Given the difficulty in characterizing some parameters of the model, uncertainties are present, and, to improve the predictability of the analysis, they will be taken into account.

Palavras-chave: Stability; Drill-String; Vibration