Research Papers

Numerical Study of Forward and Backward Whirling of Drill-String

[+] Author and Article Information
Marcin Kapitaniak

Centre for Applied Dynamics Research,
School of Engineering,
University of Aberdeen,
Aberdeen AB24 3UE, UK
e-mail: marcin.kapitaniak@abdn.ac.uk

Vahid Vaziri

Centre for Applied Dynamics Research,
School of Engineering,
University of Aberdeen,
Aberdeen AB24 3UE, UK
e-mail: vahid.vaziri@abdn.ac.uk

Joseph Páez Chávez

Center for Applied Dynamical Systems and
Computational Methods (CADSCOM),
Faculty of Natural Sciences and Mathematics,
Escuela Superior Politécnica del Litoral,
P.O. Box 09-01-5863,
Guayaquil EC0901, Ecuador;
Center for Dynamics,
Department of Mathematics,
TU Dresden,
Dresden D-01062, Germany
e-mail: jpaez@espol.edu.ec

Marian Wiercigroch

Centre for Applied Dynamics Research,
School of Engineering,
University of Aberdeen,
Aberdeen AB24 3UE, UK
e-mail: m.wiercigroch@abdn.ac.uk

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 23, 2016; final manuscript received July 10, 2017; published online September 7, 2017. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 12(6), 061009 (Sep 07, 2017) (7 pages) Paper No: CND-16-1576; doi: 10.1115/1.4037318 History: Received November 23, 2016; Revised July 10, 2017

This work presents a numerical investigation of the undesired lateral vibrations (whirling) occurring in drill-strings, which is one of the main sources of losses in drilling applications. The numerical studies are conducted using a nonsmooth lumped parameter model, which has been calibrated based on a realistic experimental drilling rig. The numerical investigations are focused on identifying different types of whirling responses, including periodic and chaotic behavior, which have been previously observed experimentally. As a result, the parameter space is divided into different regions showing dynamically relevant responses of the model, with special interest on the influence of the mass and angular velocity of the drill-string system. In particular, the study reveals the coexistence of various types of whirling motion for a given set of parameters and their sensitivity to initial conditions. The obtained theoretical predictions confirm previous experimental studies carried out by the authors, which provides a solid basis for a better understanding of whirling phenomena in drill-string applications.

Copyright © 2017 by ASME
Topics: Whirls , Drill strings
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Fig. 1

(a) A schematic of the 2DOF rotor system to describe a planar motion of the BHA using a disk of mass m rotating around its centroid (point O2) with velocity Ω, inside the borehole of clearance γ and (b) a velocity diagram

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Fig. 2

Conditions determining transitions between the operational modes of the system: N—noncontact, C—contact, and CS—contact-stick

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Fig. 3

A parameter space diagram showing the most probable whirling responses, for given mass M and angular speed Ω. The examples of the main whirling types are NPF (orange color, Ω = 3.0 rad/s, top left panel), CPF (red color, Ω = 4.5 rad/s, top right panel), CCF (black color, Ω = 5.5 rad/s, bottom left panel), and CPB (blue color, Ω = 10.5 rad/s, bottom right panel) (see color figure online).

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Fig. 4

Probabilities of observing different whirling responses as a function of Ω for different WOBs: (a) M = 209.98 kg, (b) M = 221.20 kg, (c) M = 232.41 kg, (d) M = 243.12 kg, (e) M = 253.82 kg, (f) M = 265.04 kg, and (g) M = 276.25 kg. The panels on the left present an overall trend where forward/backward responses are considered together as noncontact periodic (pink), contact periodic (green), and chaotic (black) whirls, whereas the panels on the right depict probabilities for each specific case (see color figure online).

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Fig. 5

Basins of attraction showing possible co-existing whirling solutions depending on the initial conditions (r0, θ0) and the angular velocity Ω: (a) Ω = 3.0 rad/s, (b) Ω = 4.5 rad/s, (c) Ω = 5.5 rad/s, and (d) Ω = 10.5 rad/s (see color figure online)



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