Numerical and experimental studies of stick–slip oscillations in drill-strings
Nonlinear Dyn
Numerical and experimental studies of stick-slip oscillations in drill-strings
Yang Liu 0 1
Joseph Páez Chávez Rulston De Sa 0 1
Scott Walker 0 1
0 J. Páez Chávez Department of Mathematics, Center for Dynamics, TU Dresden , 01062 Dresden , Germany
1 J. Páez Chávez Faculty of Natural Sciences and Mathematics, Center for Applied Dynamical Systems and Computational Methods (CADSCOM), Escuela Superior Politécnica del Litoral , P.O. Box 09-01-5863, Guayaquil , Ecuador
The cyclic nature of the stick-slip phenomenon may cause catastrophic failures in drillstrings or at the very least could lead to the wear of expensive equipment. Therefore, it is important to study the drilling parameters which can lead to stickslip, in order to develop appropriate control methods for suppression. This paper studies the stick-slip oscillations encountered in drill-strings from both numerical and experimental points of view. The numerical part is carried out based on path-following methods for nonsmooth dynamical systems, with a special focus on the multistability in drill-strings. Our analysis shows that, under a certain parameter window, the multistability can be used to steer the response of the drill-strings from a sticking equilibrium or stick-slip oscillation to an equilibrium with constant drill-bit rotation. In addition, a small-scale downhole drilling rig was implemented to conduct a parametric study of the stick-slip phenomenon. The parametric study involves the use of two flexible shafts with varying mechanical properties to observe the effects that would have on stick-slip during operation. Our experimental results demonstrate that varying some of the mechanical properties of the drill-string could in fact control the nature of stick-slip oscillations.
Drill-string; Stick-slip; Multistability; Non-smooth dynamical system; Numerical continuation
1 Introduction
A drill-string is mainly comprised of a series of
drillpipes followed by a section known as the bottom-hole
assembly (BHA), which consists of several moderately
thicker drill collars that work in compression to
supply the required weight on bit (WOB), and terminates
with a drill-bit. Figure 1 presents a schematic view of
a typical downhole drilling rig used in industry which
includes the derrick, hoisting system, rotary table,
drillstrings, drill-bit, and two drive systems to control the
axial and rotational motions of the drill-strings. The
Drawworks
first drive system employs an electrical motor coupled
with a mechanical transmission box to provide torque
to the rotary table at the surface. The rotary table is a
large disk which functions as a kinetic energy storage
unit used to sustain the desired rotational speed [
1
]. The
rotary motion supplied by the rotary table is then
transmitted through drill-strings to the drill-bit. Although
the primary function of the drill-strings is to convey
this rotary motion, they also provide the required axial
force, namely the WOB, in order to facilitate the
downhole drilling process. This axial force is normally
controlled by the second drive system which incorporates
the drill line and is powered by the drawworks.
In practice, drill-strings are required to be driven
at the desired constant speed maintaining the fastest
rate of penetration into the rock formation. From a
control system point of view, the drill-string structure
is underactuated as it has one control input actuating
on the rotary table from the surface and
multi-degreeof-freedom downhole parts comprising the drill-pipes,
drill collars, and drill-bit to be controlled. In the past
few years, a number of mathematical models have
been introduced to study the torsional Behaviour of
the drill-strings during drilling operation; see [
4
] for a
detailed review of the recent development. For
example, Richard et al. [
5
] studied a simplified model to
explore the root cause of stick–slip vibrations in drilling
systems with drag bits, and Germay et al. [
6
]
introduced a state-dependent delay at the bit–rock interface.
A reduced-order model allowing for radial, bending,
and torsion motions of a flexible drill-string and stick–
slip interactions between the drill-string and the outer
shell was developed by Liao et al. [
7
]. Later on, Liu
et al. [
8
] studied an eight degrees-of-freedom discrete
model taking into account axial, torsional, and lateral
dynamics of both the drill-pipes and the BHA.
Nandakumar and Wiercigroch [
9
] considered a fully
coupled two degrees-of-freedom model which assumed
a state-dependent time delay and a viscous damping
for both the axial and torsional motions. In order to
study various phenomena, such as stick–slip
oscillations, whirling, drill-bit bounce, and helical buckling of
the drill-strings, Kapitaniak et al. [
2
] carried out a
comprehensive investigation of a drill-string system
including a low-dimensional model of the drilling assembly
based on a torsional pendulum and a detailed
highdimensi (...truncated)