Modeling and Analysis of Axial and Torsional Vibrations of Drillstrings with Drag Bits
Authors: Kamel Jasem M. , Yigit Ahmet 
Published: March 2015

Abstract
Rotary oil-well drilling systems supplied with drag bits are used to drill deep boreholes for the exploration and the production of oil and natural gas. Drilling systems usually suffer from severe vibrations, which occur as axial, lateral and torsional oscillations. These vibrations mostly cause failures of drill-strings, abrasive wear of tubulars, damage of the bit, reduction of the rate of penetration (ROP), and incur high costs. Despite extensive research in this area, there is still a need to develop a consistent model that adequately captures all relevant phenomena such as nonlinear cutting and friction forces at the bit/formation interface, drive system characteristics and coupling between various models of vibrations. This study presents a physically consistent nonlinear lumped-parameter model for the coupled axial and torsional motions of a rotating drill string equipped with a drag bit. An innovative cutting and contact model is used to model rock/bit interaction. The dynamics of rotary and axial drive systems including hoisting system are also considered. The equations of motion are solved numerically to carry out parametric studies. The effects of various operational parameters are investigated for achieving a smooth and efficient drilling. The proposed model appears to capture stick-slip and bit-bounce as the simulation results qualitatively agree well with field observations and published theoretical results. The rotational and axial motions of the bit are obtained as a result of the overall dynamic behavior rather than prescribed functions or constants. The results show that with a proper choice of operational parameters it is possible to minimize the effects of stick-slip and bit-bounce and to increase the ROP. Therefore, it is anticipated that the results will help reduce the time spent in drilling process and costs incurred due to severe vibrations and consequent damage to equipment.

1. Introduction
A rotary drilling system supplied with a drag bit is used to drill deep boreholes for the production and the exploration of oil and natural gas. Bottom hole measurements [1–2] show that drag bits are subjected to different types of severe oscillations. Namely, lateral, axial and the torsional modes of vibration can be observed with large amplitudes [3–5] The main causes of these vibrations include contact and friction at the borehole/drillstring and bit/rock formation interfaces, eccentricity, imbalance, initial curvature in the drill collar sections, and various linear or nonlinear resonances. These severe vibrations often cause failures of drillstrings, abrasive wear of tubulars, damage of the bit, and reduction of the rate of penetration (ROP) and incur high costs [6–9]. The current paper concentrates on the axial and torsional modes of vibrations, bit bounce and stick-slip vibrations. Bit bouncing is related to strong axial vibrations in such a way that the bit loses contact with the rock formation at the bottom of the hole. Stick-slip vibrations are related to the torsional vibrations where bit passes through periodically two phases: sticking (the bit stops rotating) and slipping phases (the bit is released from sticking phase with angular velocity higher than nominal velocity). It has been documented that for about 50% of the on bottom drilling time the drill bit experiences stick slip vibrations [10].