Research Papers

Modal Reduction Technique for Predicting the Onset of Chaotic Behavior due to Lateral Vibrations in Drillstrings

[+] Author and Article Information
Kathira Mongkolcheep

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77845
e-mail: k.mongkolcheep@gmail.com

Annie Ruimi

Department of Mechanical Engineering,
Texas A&M University at Qatar,
241 D Texas A&M Engineering Building,
Education City,
P.O. Box 23874,
Doha, Qatar
e-mail: annie.ruimi@qatar.tamu.edu

Alan Palazzolo

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77845
e-mail: a-palazzolo@tamu.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 1, 2013; final manuscript received September 29, 2014; published online November 14, 2014. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 137(2), 021003 (Apr 01, 2015) (11 pages) Paper No: VIB-13-1418; doi: 10.1115/1.4028882 History: Received December 01, 2013; Revised September 29, 2014; Online November 14, 2014

Drillstrings used for oil and gas exploration and extraction consist of a drillpipe (slender columns on the order of 3–5 km long), drill collars (DCs) (thick-walled large-diameter pipes), stabilizers (cylindrical elements with short sections and diameter near that of the borehole), and a rock-cutting tool that uses rotational energy to penetrate the soil. Several types of vibrations ensue from these motions and play a major role in added costs resulting from unforeseen events such as abandoning holes, replacing bits, and fishing severed bottom-hole assemblies (BHAs). It is thus of critical importance to understand, predict, and mitigate the severe vibrations experienced by drillstrings and BHA to optimize drilling time while lowering fuel consumption and related emissions of NOX and/or other pollutants. In this paper, we present a dynamical analysis of the behavior of drillstrings due to the violent lateral vibrations (LVs) DCs may experience as a result of rotating drillstrings. The behavior is represented by a system of two coupled nonlinear ordinary equations that are integrated numerically with a finite element analysis based on Timoshenko beam (TB) formulation combined to a modal condensation technique to reduce the computational time. Various nonlinear dynamical analysis tools, such as frequency spectrum, Poincaré maps, bifurcation diagrams, and Lyapunov exponents (LE), are used to characterizing the response. The DC section between two stabilizers is essentially modeled as a Jeffcott rotor with nonlinearity effects included. The model builds on two earlier models for the finite element formulation and the treatment of chaotic vibrations. Nonlinearity appears in the form of drillstring/borehole contact force, friction, and quadratic damping. The DC flexibility is included to allow investigation of bending modes. The analysis takes into account the length of time to steady state, number of subintervals, presence of rigid body modes, number of finite elements, and modal coordinates. Simulations results indicate that by varying operating conditions, a spectrum of behaviors from periodic to chaotic may be observed.

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Fig. 2

Contact forces on the stabilizer

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Fig. 1

Components of a drillstring

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Fig. 3

Mass eccentricity due to motion of DC or other imperfections

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Fig. 5

First five modes of the DC–stabilizer model

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Fig. 9

Bifurcation diagrams with varying load: (a) without friction and quadratic damping, (b) without friction but with quadratic damping, (c) with friction but without quadratic friction, and (d) with friction and quadratic damping

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Fig. 10

Bifurcation diagrams with varying coefficient of friction: (a) μb = 0.1, (b) μb = 0.2, and (c) μb = 0.3

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Fig. 6

Displacements of the DC–stabilizer with and without drillpipe at 40 rpm

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Fig. 7

Displacements of the DC–stabilizer with and without drillpipe at 55 rpm

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Fig. 8

Displacement of the DC with varying number of modes at a chaotic rpm

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Fig. 11

MLE versus drillstring rpm with: (a) μb = 0.1, (b) μb = 0.2, and (c) μb = 0.3

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Fig. 12

Bifurcation diagrams for varying DC length: (a) 15 m, (b) 20 m, (c) 23 m, and (d) 25 m

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Fig. 13

Bifurcation diagram for midspan transverse velocity with varying radial clearance at stabilizer: (a) 1.27 cm, (b) 2.54 cm, and (c) 5.08 cm

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Fig. 14

Poincaré map for DC midspan transverse velocity

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Fig. 15

MLE convergence with time for (a) a nonchaotic and (b) a chaotic response



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