A New Model of High-Frequency Torsional Oscillations (HFTO) of Drillstring in 3-D Wells
Authors: Tikhonov Vadim S , Bukashkina Olga S 
Published: May 2016

Abstract
Drillstring with polycrystalline diamond cutter (PDC) bit can cause severe torsional oscillations accompanying by periodic slowing down of the bit rotation up to its sticking and its subsequent violent speeding-up. These oscillations increase wear of bit, accelerated accumulation of fatigue and early failure of bit and drillstring. They are called stick-slip oscillations and are well-known for a long time.
In recent years downhole measurements revealed high-frequency torsional oscillations (HFTO) up to hundreds of hertz with sufficiently great amplitude. The majority of investigations are limited to the study of frequency characteristics of the separated BHA but not the all system: «drillstring – BHA – downhole motor - bit – rock". This paper presents a new model of HFTO for the drillstring in 3-D well. The axial stiffness of drillstring and BHA is taken into account with the axial motion equations coupled with the torsional equations. The total model of the system includes a positive displacement motor (PDM) which is used at present to perform a bulk of drilling operations. The rock cutting process is based on the model, which provides for effect of the bottomhole pressure and local pore pressure. The new model includes bit "bouncing" when it loses contact with the bottomhole. The equations are solved by time integration. By results of the analysis of transient processes the harmonic analysis of processes is carried out. Our objective is to improve understanding of HFTO nature for different drilling techniques: rotary drilling, sliding and combination drilling. Results of the study will help drillers to select and change drilling parameters more efficiently to reduce torsional oscillations.

1. INTRODUCTION
Drillstring with PDC bit can cause severe torsional oscillations accompanying by periodic slowing down of the bit rotation up to its sticking and its subsequent violent speeding-up. These oscillations increase wear of bit, accelerated accumulation of fatigue and early failure of bit and drillstring. They are called stick-slip oscillations and are well-known for a long time. These oscillations are nonlinear and self-induced and their frequency is determined by inertia and stiffness characteristics of BHA and a long drillstring and doesn't exceed some Hz.
The main modes of BHA oscillations are axial, torsional and lateral oscillations. As a result of interaction these modes may produce mixed oscillations: torsional-axial, including stick-slip [15], torsional-lateral [1], including whirling [11], and more complex torsional-lateral-axial oscillations [19].
Conventional stick-slip oscillations are characterized with nearly periodic sticking when the bit stops for some tenths of a second or a few seconds and subsequent speeding-up when its angular velocity rapidly increases by two and more times. Another effect, bouncing, is defined by loss of bit contact with the bottomhole and may even result in short-term reverse rotation of the BHA. These oscillations are propagated along the entire drillstring and their frequency is comparable with the natural frequencies of the "drillstring-BHA" torsional oscillations, being equal to units and tens of hertz [15, 17].
Whirling of the drillstring is a planetary motion of the drillstring axes around the hole axis and occurs at rather high rotary speed [9].