Steady-state solutions of a propagating borehole

Perneder, Luc; Detournay, Emmanuel

doi:10.1016/j.ijsolstr.2012.12.011

Cited by 20 publications

(18 citation statements)

References 33 publications

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“…These resistances, theoretically, do not depend on the rock formation (Perneder et al 2012). Number g (which can be interpreted as the inverse of the bit lateral steerability) is related mainly to the length, geometry, and cutting structure of the bit gauge (Dupriest and Sowers 2009); g is of order O ð10Þ (Menand et al 2002), whereas v is typically at least one order of magnitude smaller than g.…”

Section: Bit/rock Interaction and Kinematic Relationshipsmentioning

confidence: 99%

“…1a) (Detournay et al 2008;Perneder et al 2012). The bit/rock interaction for a planar borehole is assumed to follow a general linear form that finds its origin in the bilinear law for the single-cutter/ rock interaction (Fig.…”

Section: Bit/rock Interaction and Kinematic Relationshipsmentioning

confidence: 99%

“…According to Eq. 2, the axial penetration is proportional to the active weight, W a ¼ W À G 1 , where G 1 is the part of W mobilized at the cutter wear flats, a function of the rock strength and the state of wear of the bit (Perneder et al 2012). After defining the scaled active weight P as…”

Section: Bit/rock Interaction and Kinematic Relationshipsmentioning

confidence: 99%

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Influence of Rotary-Steerable-System Design on Borehole Spiraling

Marck

Detournay

2016

SPE Journal

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The paper investigates the influence of the design of push-the-bit rotary-steerable systems (RSSs) on the tendency to drill spiraled boreholes by analyzing the directional stability of the bit trajectory. In this model, differences in RSS designs are accounted for conceptually by assigning a lateral stiffness to the RSS pads. This simple device, which introduces a dependence of the force on the pads upon the deflection of the bottomhole assembly (BHA) relative to the borehole axis, enables exploration of the influence of the actuation mechanism, with the RSS behaving at the ends of the spectrum either as a soft or as a stiff node of the drilling structure.According to this analysis, low pad stiffness has little consequence on the general behavior of the system. However, as the pad stiffness increases, any perturbation in the borehole geometry sensed by the pads alters the drilling direction of the bit and triggers, under certain conditions, self-excited oscillations in the borehole geometry. By increasing the transverse rigidity of the BHA in the vicinity of the bit, stiff RSS pads thus enhance the propensity of a drilling structure to drill spiraled holes and generate, if the system is directionally unstable, borehole oscillations with pitch that corresponds to the distance between the bit and the pads. In contrast, a directionally unstable BHA equipped with RSS characterized by a low stiffness produces spiraled holes with a wavelength corresponding to the distance between the bit and the first stabilizer.

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Section: Bit/rock Interaction and Kinematic Relationshipsmentioning

confidence: 99%

Section: Bit/rock Interaction and Kinematic Relationshipsmentioning

confidence: 99%

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Influence of Rotary-Steerable-System Design on Borehole Spiraling

Marck

Detournay

2016

SPE Journal

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“…Theorem 3: Consider system (12) and observer (16). Suppose the conditions in Theorem 1 are satisfied for system (12) and that the observer error dynamics in (17) satisfies the conditions in Theorem 2. Then, (ξ, e) = (0, 0) is a locally asymptotically stable equilibrium point of the interconnected system (12), (17) for anyφ satisfying Assumptions 1 and 2.…”

Section: Output-feedback Controlmentioning

confidence: 99%

Observer-based output-feedback control to eliminate torsional drill-string vibrations

Vromen

Wouw

Doris³

et al. 2014

53rd IEEE Conference on Decision and Control

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“…The work described here has been extended to three-dimensional trajectories by analyzing the stability of the system of two coupled delay differential equations (DDE), one for its inclination and one for its azimuth, that govern the propagation of the borehole (Perneder 2013;Perneder and Detournay 2013b). Compared to the planar borehole-propagation model, new parameters are introduced to capture the out-of-plane coupling: the bit walk (the angle between the lateral force and the lateral penetration on the bit) and the bit flip (the angle between the moment and the angular penetration vectors).…”

Section: Introductionmentioning

confidence: 99%

Spiraled Boreholes: An Expression of 3D Directional Instability of Drilling Systems

Marck

Detournay

2015

SPE/IADC Drilling Conference and Exhibition

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The occurrence of borehole spiraling is predicted by analyzing the delay differential equations that govern the propagation of a borehole. These evolution equations for borehole inclination and azimuth are obtained by considering the following three model components: (i) a bit/rock interaction law that relates the force and moment acting on the bit to its penetration into the rock; (ii) kinematic relationships that describe the local borehole geometry from the bit penetration; and (iii) a beam model for the bottom-hole assembly (BHA) that can be used to express the force and moment at the bit from the external loads applied on the BHA and the geometrical constraints arising from the stabilizers conforming to the borehole geometry.The analytical nature of borehole propagation equations makes it possible to conduct a stability analysis in terms of a key dimensionless group that controls the directional stability of the drilling system. This group depends on the downhole weight on bit (WOB), on properties of the BHA, on the bluntness of the bit, and on parameters characterizing its response. The directional stability of a particular drilling system can be assessed by comparing the magnitude of this group with a critical value that depends only on the BHA configuration and on the bit walk. If this dimensionless group, which depends on the actual drilling conditions, is less than the bifurcation value, the system is deemed to be directionally unstable, and borehole spiraling is likely. Stability curves for an ideal BHA with two stabilizers are shown to depend on the bit walk. An application to a field example is discussed. Borehole simulations, based on solving the equations of propagation, also are presented to illustrate that, for unstable systems, the model reproduces spiraled boreholes with a pitch, comparable to what is observed in the field.

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Steady-state solutions of a propagating borehole

Cited by 20 publications

References 33 publications

Influence of Rotary-Steerable-System Design on Borehole Spiraling

Influence of Rotary-Steerable-System Design on Borehole Spiraling

Observer-based output-feedback control to eliminate torsional drill-string vibrations

Spiraled Boreholes: An Expression of 3D Directional Instability of Drilling Systems

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