Analysis of Oil Well Drilling Dynamics from Non-Smooth Models

Abstract

Drill-string vibration is one of the most undesirable problems that occur during the oil-well drilling operation. The control of this vibration is essential because they may cause low performace of the drilling, damage and failure of the drill-string and well problems. In this work, we present a coupled non-smooth two-degree of freedom system to model drilling vibrations, developing a parametric analysis of the drill-string vibrations. Special attention is dedicated to the bit/formation interaction, which is considered as the main external force. Moreover, we investigate the transitions between different phases of motion and the non-smooth dynamics associated with the stick-slip and bit-bounce. We adopt smooth functions that presents advantages in terms of mathematical description and numerical analysis. The undertaken numerical simulations show that the developed mathematical model is capable of predicting a full range of dynamic responses including the non-smooth behavior including stick-slip and bit-bounce responses. Experimental data is used as a reference for numerical simulations.