Stability analysis of a state dependent delayed, coupled two DOF model of drill-stringvibration

Nandakumar, Kutty Selva; Wiercigroch, Marian

doi:10.1016/j.jsv.2012.12.020

Cited by 111 publications

(62 citation statements)

References 33 publications

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“…Interestingly, the RGD model predicts a decrease of the resisting torque under an imposed angular velocity at the rig; thus the velocity weakening response of the bit is an outcome of the RGD model, rather than a starting hypothesis as in the classical approach. Models built on the same rate-independent bit/rock interface law, but that include additional degrees of freedom and viscous dissipation in the representation of the drillstring and/or consider alternate boundary conditions at the rig, have recently been studied [12][13][14][15]; they yield similar although richer responses than the basic RGD model. Also, comparable state-dependent delay models to analyze regenerative chatter in metal turning processes have been independently developed by Insperger et al [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…On the one hand, the RGD model is always unstable according to a recently published linear stability analysis [14]. Previous stability analyses [2,19] neglected the dynamics of the delay based on the assumption of a timescale separation between the axial and torsional dynamics, and concluded that the steady-state solution is unstable only if the prescribed angular velocity is below a critical velocity.…”

Section: Introductionmentioning

confidence: 99%

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Instability regimes and self-excited vibrations in deep drilling systems

Depouhon

Detournay

2014

Journal of Sound and Vibration

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This paper analyzes the stability of the discrete model proposed by Richard et al. [1,2] to study the self-excited axial and torsional vibrations of deep drilling systems. This model, which relies on a rate-independent bit/rock interaction law, reduces to a coupled system of state-dependent delay differential equations governing the axial and angular perturbations to the stationary motion of the bit. A linear stability analysis indicates that, although the steady-state motion of the bit is always unstable, the nature of the instability depends on the nominal angular velocity Ω 0 of the drillstring imposed at the rig. On the one hand, if Ω 0 is larger than a critical velocity Ω c , the angular dynamics is responsible for the instability. However, on the timescale of the resonance period of the drillstring viewed as a torsional pendulum, the system behaves like a marginally stable one, provided that exogenous perturbations are of limited magnitude. The instability then only appears on a much larger timescale, in the form of slowly growing oscillations that ultimately lead to an undesired drilling regime such as bit-bouncing or stick-slip vibrations. On the other hand, if Ω 0 is smaller than Ω c , the instability manifests itself on the timescale of the bit motion due to a dominating unstable axial dynamics; perturbations to the steady-state motion then rapidly degenerate into stick-slip limit cycles or bit-bouncing. For typical deep drilling field conditions, the critical angular velocity Ω c is virtually independent of the axial force acting on the bit and of the bit bluntness. It can be approximated by a power law monomial, a function of known parameters of the drilling system and of the intrinsic specific energy (a quantity characterizing the energy required to drill a particular rock). This approximation holds on account that the dissipation in the drilling structure is negligible with respect to that taking place through the bit/rock interaction, as is typically the case. These findings are further illustrated on an example of deep drilling and shown to match the trends observed in the field.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Instability regimes and self-excited vibrations in deep drilling systems

Depouhon

Detournay

2014

Journal of Sound and Vibration

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“…The result of the numerical continuation of the dynamical response of the drill-string model (8) with respect to the WOB W b , showing the average angular speed of the drill-bit [see (9)] on the vertical axis, is presented in Fig. 4.…”

Section: Numerical Investigation Of the Drill-string Modelmentioning

confidence: 99%

“…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 highdimensional model of the drilling rig using finite element modeling.…”

Section: Introductionmentioning

confidence: 99%

Numerical and experimental studies of stick–slip oscillations in drill-strings

Liu

Chávez

et al. 2017

Nonlinear Dyn

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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.

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“…Many models considers the drill-string as a lumped mass, representing the bottom hole assembly (BHA) inertia, and a torsional e-mail: ujfa@iris.no e-mail: roman.shor@ucalgary.ca spring, representing the drill-string stiffness [3,4], while more realistic, higher order, models have also been considered [5][6][7]. Stick-slip is then introduced as a self-excited vibration (see example in Fig.…”

Section: Introductionmentioning

confidence: 99%

Stick-slip and Torsional Friction Factors in Inclined Wellbores

Aarsnes

Shor

2018

MATEC Web Conf.

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Abstract. Stick slip is usually considered a phenomenon of bit-rock interaction, but is also often observed in the field with the bit off bottom. In this paper we present a distributed model of a drill string with an alongstring Coulomb stiction to investigate the effect of borehole inclination and borehole friction on the incidence of stick-slip. This model is validated with high frequency surface and downhole data and then used to estimate static and dynamic friction. A derivation of the torsional drill string model is shown and includes the along-string Coulomb stiction of the borehole acting on the string and the 'velocity weakening' between static and dynamic friction. The relative effects of these two frictions is investigated and the resulting drillstring behavior is presented. To isolate the effect of the along-string friction from the bit-rock interaction, field data from rotational start-ups after a connection (with bit off bottom) is considered. This high frequency surface and downhole data is then used to validate the surface and downhole behavior predicted by the model. The model is shown to have a good match with the surface and downhole behavior of two deviated wellbores for depths ranging from 1500 to 3000 meters. In particular, the model replicates the amplitude and period of the oscillations, in both the topside torque and the downhole RPM, as caused by the along-string stick slip. It is further shown that by using the surface behavior of the drill-string during rotational startup, an estimate of the static and dynamic friction factors along the wellbore can be obtained, even during stick-slip oscillations, if axial tension in the drillstring is considered. This presents a possible method to estimate friction factors in the field when off-bottom stick slip is encountered, and points in the direction of avoiding stick slip through the design of an appropriate torsional start-up procedure without the need of an explicit friction test.

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Stability analysis of a state dependent delayed, coupled two DOF model of drill-stringvibration

Cited by 111 publications

References 33 publications

Instability regimes and self-excited vibrations in deep drilling systems

Instability regimes and self-excited vibrations in deep drilling systems

Numerical and experimental studies of stick–slip oscillations in drill-strings

Stick-slip and Torsional Friction Factors in Inclined Wellbores

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