Research Papers: Petroleum Engineering

An Analysis of Common Drill Stem Vibration Models

[+] Author and Article Information
Mohammed F. Al Dushaishi

School of Engineering,
Texas A&M International University,
Laredo, TX 78045
e-mail: aldushaishi@gmail.com

Runar Nygaard

School of Chemical Engineering,
Oklahoma State University,
Stillwater, OK 74078
e-mail: runar.nygaard@okstate.edu

Daniel S. Stutts

Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
Rolla, MO 65409
e-mail: stutts@mst.edu

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received December 6, 2016; final manuscript received August 14, 2017; published online September 12, 2017. Assoc. Editor: Arash Dahi Taleghani.

J. Energy Resour. Technol 140(1), 012905 (Sep 12, 2017) (12 pages) Paper No: JERT-16-1493; doi: 10.1115/1.4037682 History: Received December 06, 2016; Revised August 14, 2017

Excessive drill stem (DS) vibration while rotary drilling of oil and gas wells causes damages to drill bits and bottom hole assemblies (BHAs). In an attempt to mitigate DS vibrations, theoretical modeling of DS dynamics is used to predict severe vibration conditions. To construct the model, decisions have to be made on which beam theory to be used, how to implement forces acting on the DS, and the geometry of the DS. The objective of this paper is to emphasize the effect of these assumptions on DS vibration behavior under different, yet realistic, drilling conditions. The nonlinear equations of motion were obtained using Hamilton's principle and discretized using the finite element method. The finite element formulations were verified with uncoupled analytical models. A parametric study showed that increasing the weight on bit (WOB) and the drill pipe (DP) length clearly decreases the DS frequencies. However, extending the drill collar length does not reveal a clear trend in the resulting lateral vibration frequency behavior. At normal operating conditions with a low operating rotational speed, less than 80 RPM, the nonlinear Euler–Bernoulli and Timoshenko models give comparable results. At higher rotational speeds, the models deliver different outcomes. Considering only the BHA overestimates the DS critical operating speed; thus, the entire DS has to be considered to determine the critical RPM values to be avoided.

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Heisig, G. , and Neubert, M. , 2000, “ Lateral Drillstring Vibrations Inextended-Reach Wells,” IADC/SPE Drilling Conference, New Orleans, LA, Feb. 23–25, SPE Paper No. SPE-59235-MS.
Cobern, M. E. , Perry, C. A. , Barbely, J. A. , Burgess, D. E. , and Wassell, M. E. , 2007, “ Drilling Tests of an Active Vibration Damper,” SPE/IADC Drilling Conference, Amsterdam, The Netherlands, Feb. 20–22, SPE Paper No. SPE-105400-MS.
Ahmadian, H. , Nazari, S. , and Jalali, H. , 2007, “ Drill String Vibration Modeling Including Coupling Effects,” Int. J. Ind. Eng. Prod. Res., 18(3–4), pp. 59–66. http://ijiepr.iust.ac.ir/article-1-30-en.pdf
Piovan, M. T. , and Sampaio, R. , 2006, “ Non Linear Model for Coupled Vibrations of Drill-Strings,” Mec. Comput., 25(19), pp. 1751–1765. http://www.cimec.org.ar/ojs/index.php/mc/article/view/570
Spanos, P. , Chevallier, A. , and Politis, N. P. , 2002, “ Nonlinear Stochastic Drill-String Vibrations,” ASME J. Vib. Acoust., 124(4), pp. 512–518. [CrossRef]
Yigit, A. , and Christoforou, A. , 1998, “ Coupled Torsional and Bending Vibrations of Drillstrings Subject to Impact With Friction,” J. Sound Vib., 215(1), pp. 167–181. [CrossRef]
Leine, R. , Van Campen, D. , and Keultjes, W. , 2002, “ Stick-Slip Whirl Interaction in Drillstring Dynamics,” ASME J. Vib. Acoust., 124(2), pp. 209–220. [CrossRef]
Navarro-López, E. M. , and Cortés, D. , 2007, “ Avoiding Harmful Oscillations in a Drillstring Through Dynamical Analysis,” J. Sound Vib., 307(1), pp. 152–171. [CrossRef]
Ghasemloonia, A. , Rideout, D. G. , and Butt, S. D. , 2013, “ Vibration Analysis of a Drillstring in Vibration-Assisted Rotary Drilling: Finite Element Modeling With Analytical Validation,” ASME J. Energy Resour. Technol., 135(3), p. 032902. [CrossRef]
Liao, C.-M. , Balachandran, B. , Karkoub, M. , and Abdel-Magid, Y. L. , 2011, “ Drill-String Dynamics: Reduced-Order Models and Experimental Studies,” ASME J. Vib. Acoust., 133(4), p. 041008. [CrossRef]
Richard, T. , Germay, C. , and Detournay, E. , 2007, “ A Simplified Model to Explore the Root Cause of Stick-Slip Vibrations in Drilling Systems With Drag Bits,” J. Sound Vib., 305(3), pp. 432–456. [CrossRef]
Ghasemloonia, A. , Rideout, D. G. , and Butt, S. D. , 2012, “ Coupled Transverse Vibration Modeling of Drillstrings Subjected to Torque and Spatially Varying Axial Load,” Proc. Inst. Mech. Eng. Part C, 227(5), pp. 946–960.
Payne, M. L. , 1992, “ Drilling Bottom-Hole Assembly Dynamics,” Ph.D. thesis, Rice University, Houston, TX. https://scholarship.rice.edu/handle/1911/19083
Chen, S. , and Géradin, M. , 1995, “ An Improved Transfer Matrix Technique as Applied to BHA Lateral Vibration Analysis,” J. Sound Vib., 185(1), pp. 93–106. [CrossRef]
Trindade, M. A. , Wolter, C. , and Sampaio, R. , 2005, “ Karhunen–Loève Decomposition of Coupled Axial/Bending Vibrations of Beams Subject to Impacts,” J. Sound Vib., 279(3), pp. 1015–1036. [CrossRef]
Ritto, T. , Soize, C. , and Sampaio, R. , 2009, “ Non-Linear Dynamics of a Drill-String With Uncertain Model of the bit–Rock Interaction,” Int. J. Non-Linear Mech., 44(8), pp. 865–876. [CrossRef]
Han, S. M. , Benaroya, H. , and Wei, T. , 1999, “ Dynamics of Transversely Vibrating Beams Using Four Engineering Theories,” J. Sound Vib., 225(5), pp. 935–988. [CrossRef]
Stutts, D. S. , 1995, “ Analytical Dynamics: Lagrange's Equation and Its Application—A Brief Introduction,” Missouri University of Science and Technology, Rolla, MO, accessed Aug. 28, 2017, http://web.mst.edu/~stutts/SupplementalNotes/EL10.pdf
Rao, S. S. , 2007, Vibration of Continuous Systems, Wiley, Hoboken, NJ.
Majkut, L. , 2009, “ Free and Forced Vibrations of Timoshenko Beams Described by Single Difference Equation,” J. Theor. Appl. Mech., 47(1), pp. 193–210. http://www.ptmts.org.pl/jtam/index.php/jtam/article/view/v47n1p193
Yigit, A. , and Christoforou, A. , 1996, “ Coupled Axial and Transverse Vibrations of Oilwell Drillstrings,” J. Sound Vib., 195(4), pp. 617–627. [CrossRef]
Dareing, D. W. , 1984, “ Drill Collar Length is a Major Factor in Vibration Control,” J. Pet. Technol., 36(04), pp. 637–644. [CrossRef]


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Fig. 1

Drilling assembly showing the DS (Lds) that consists of DPs (Ldp) and BHA, including drill collars (Ldc) and stabilizers, on the left and the modeling configuration on the right

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Fig. 2

Configuration of axis orientation (a) rotation around the x-axis, (b) rotation around the yx-axis, and (c) rotation around the zxy-axis

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Fig. 3

Free vibration frequencies obtained from finite element and analytical models (a) axial, (b) torsional, and (c) lateral

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Fig. 4

First and tenth lateral natural frequencies under varying axial load for Euler–Bernoulli (EBT) and Timoshenko (TBT) models

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Fig. 5

Effect of changing WOB, length of DS (Lds), length of drill collar (Ldc), and fluid density (MW) on the DS (a) lateral, (b) torsional, and (c) axial frequencies

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Fig. 6

Percentage difference of lateral frequency between the Euler–Bernoulli (EBT) and the Timoshenko (TBT) models under varying drilling conditions for (a) first mode results and (b) tenth mode results

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Fig. 7

Drill stem first axial, torsional, and lateral natural frequencies when considering only the BHA, the DS consisting of DP only, and the entire DS



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