The contact between the drilling bit and formation is known to excite severe torsional and axial vibrations in the drillstring. A dynamic model of the drillstring including both drillpipe and drillcollars is formulated. The equation of motion of the rotating drillstring is derived using Lagrangean approach together with the finite element method. The model accounts for the gyroscopic effect, the torsional/bending inertia coupling, the axial/bending geometric nonlinear coupling, and the stiffening effect due to the gravitational force field. Reduced order modal form of the dynamic equations is obtained using complex modal transformation. The developed model is integrated into a computational scheme to calculate time-response of the drillstring due to torsional excitations.

1.
Bailey
J. J.
, and
Finnie
I.
, “
An Analytical Study of Drillstring Vibration
,”
J. Eng. For Ind. ASME Tans.
Vol.
82
(
2
),
1960
,
122
128
.
2.
Finnie
I.
, and
Bailey
J. J.
, “
An Experimental Study of Drillstring Vibration
,”
J. Eng. For Ind. ASME Tans.
Vol.
82
(
2
),
1960
,
129
135
.
3.
Dareing, D.W., and Livesay, B.J., “Longitudinal and Angular Drillstring Vibrations with Damping,” J. Eng. Ind. November 1968, p. 671–679.
4.
Kreisle, L.F., and Vance, J.M., “Mathematical Analysis of the Effect of Shock Sub on the Longitudinal Vibrations of an Oilwell Drillstring,” J. SPE, December 1970, p. 349–356.
5.
Eronini, I.G., Somerton, W.H., and Auslander, D.M., “A Dynamic Model for Rotary Rock Drilling,” J. Energy Resources Technology, June 1982, p. 108–120.
6.
Ashley, D. K. and Tomlinson, J. C., “Extending BHA Life with Multi Vibration Measurements,” SPE 67696 presented at SPE/IADC drilling conference, Amsterdam, 2001.
7.
Sananlkone, P., Kamoshima, O., and White, D. B., “A Field Method for Controlling Drillstring Torsional Vibrations,” SPE 23891 presented at SPE Drilling Conference, New Orleans, 1992.
8.
Van den Steen, “Suppression Stick-Slip Induced Drillstring Oscillations: A Hyperstability Approach,” Ph.D. Thesis, University of Twnte, The Netherlands 1997.
9.
Leine
R. I.
,
Van Campen
D. H.
,
de Kraker
A.
, and
van den Steen
L.
, “
Stick-Slip Vibrations Induced by Alternate Friction Models
,”
Nonlinear Dynamics
, vol.
16
, pp.
41
54
,
1998
.
10.
Halsey, G. w., Kyllingstad, A., Aarrestad, T. V. and Lysne, D., “Drillstring Torsional Vibrations: Comparison between Theory and Experiment on a Full-Scale Research Drilling Rig,” SPE 15564, SPE Annual Technical Conference and Exhibition, New Orleans, Oct, 5–8. 1986
11.
Kyllingstad, A., Halsey, G.W., “A study of slip/stick Motion of the Bit,” SPE 16659, 62nd Annual Technical Conference of the SPE, Dallas, Texas, Sept. 27–30, 1987
12.
Challamel, N., Sellami, E., Chenevez, E., and Gossuin, L., “A Stick-slip Analysis Based on Rock/Bit interaction: Theoretical and Experimental Contribution,” SPE 59230 presented at IADC/SPE Drilling Conference, Orleans, Louisiana, 2000
13.
Dawson, R., Lin, Y. Q., and Spanos, P. D., “Drillstring Stick-Slip Oscillations,” Spring Conference of the Society for Experimental Mechanics, Houston, Texas, 1987
14.
Lin
Y. Q.
, and
Wang
Y. H.
Stick-Slip Vibration of the Drill strings
Journal of Engineering for Industry, Trans. ASME
, Series B,
113
, pp.
38
43
,
1991
15.
Brett, J.F., “The Genesis of Bit-Induced Torsional Drill String Vibrations” SPE 21943, SPE/IADC Drilling Conference, Amsterdam, March 11–14, 1991
16.
Jansen
J. D.
and
van den Steen
L.
, “
Active Damping of Self-Excited Torsional Vibration in Oil Well Drillstrings
.”
Journal of Sound and Vibration
,
179
pp.
647
668
,
1995
17.
Tucker
R. W.
and
Wang
C.
, “
On The Effective Control of Torsional Vibrations in Drilling Systems
,”
Journal of Sound and Vibration
, vol.
224
, pp.
101
122
,
1999
18.
Richard, T., Detournay, E., Fear, M., Miller, B., Clayton, R., and Matthews, O., “Influence of Bit-Rock Interaction on Stick-Slip Vibrations of PDC bits,” SPE 77616 presented at SPE Annular Technical Conference and Exhibition, San Antonio, Texas, 2002
19.
Leseultre, A., Lamine, E., and Jonsson, A., “An Instrumented Bit: A necessary step to the intelligent BHA,” SPE 39341, IADC/SPE Drilling Conference, Dallas, Texas, 1998
20.
Leine
R. I.
,
Van Campen
D. H.
and
Keultjes
W. J.
Stick-slip Whirl Interaction in Drillstring Dynamics
,”
Journal of Sound and Acoustics
vol.
124
, pp.
209
220
,
2002
21.
Yigit
A. S.
and
Christoforou
A. P.
,
Coupled Axial and Transverse Vibrations of Oilwell Drillstrings
,
Journal of Sound and Vibration
, vol.
195
, no.
4
,
1996
, pp.
617
627
.
22.
Yigit
A. S.
and
Christoforou
A. P.
, “
Coupled Torsional and Bending Vibrations of Drillstrings Subject to Impact with Friction
,”
Journal of Sound and Vibration
,
1998
, Vol.
215
(
1
), p.
167
181
.
23.
Tucker
R. W.
, and
Wang
C.
, “
An Integrated Model for Drill-String Dynamics
,”
J. Sound and Vibration
,
224
(
1
),
1999
, p.
123
165
.
24.
Millheim, K., Jordan, S., and Ritter, C.J., “Bottom-Hole Assembly Analysis Using the Finite-Element Method,” SPE paper No. 6057, 1978, p. 265–274.
25.
Besaisow, A.A., and Payne, M.L., “A Study of Excitation Mechanisms and Resonances inducing BHA Vibrations,” The 61st Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, LA, October 5–8, 1986, SPE No. 15560
26.
Burgess, T.M., McDaniel, G.L. and Das, P.K., “Improving BHA Tool Reliability with Drillstring Vibration Models: field Experience and Limitations,” SPE/ADC Drilling Conference, New Orleans, LA, March 15–18, 1987, SPE No. 16109
27.
Mitchell, R.F., and Allen, M.B., “Case Studies of BHA Vibration Failure, The 62nd SPE Annual Technical Conference & Exhibition, Dallas, TX, September 27–30 1987, SPE No. 16675
28.
Costa, F.S., and Rebeiro, P.R., “Finite Element modeling of the mechanical behavior of unbalanced drillcollars,” Fifth Latin American & Caribbean Petroleum Engineering Conference & Exhibition, Rio de Janeiro, Brazil, August 30 - Sept. 3, 1997, SPE No. 39025.
29.
Apostal, M.C., Haduch, G.A., and Williams, J.B., “A Study To Determine the Effect of Damping on Finite-Element-Based, Forced-Frequency-Response Models for Bottomhole Assembly Vibration Analysis,” The 65th SPE Annual Technical Conference & Exhibition, New Orleans, LA, September 23–25, 1990, SPE No. 20458.
30.
Axisa, F., and Antunes, J., “Flexural Vibrations of Rotors Immersed in Dense Fluids: Part I - Theory,” Third Intl. Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-3, Honolulu, Hawaii, 2(2), 1990, p. 23–38.
31.
Dunayevsky, V.A., and Abbassian, F. and Judzis, A., “Dynamic Stability of Drillstring under Fluctuating Weight on Bit,” SPE Drilling & Completion, June1993, p. 84–92, SPE Paper No. 14329.
32.
Berlioz
A.
,
Der Hogopian
J.
,
Dufour
R.
, and
Draoui
E.
, “
Dynamic behavior of a drillstring: Experimental investigation of lateral instabilities
,”
Trans. of ASME, Journal of Vibration and Acoustics
, Vol.
118
,
1996
, p.
292
298
.
33.
Melakhessou
H.
,
Berlioz
A.
, and
Ferraris
G.
, “
A Nonlinear Well-Drillstring Interaction Model
,”
J. of Vibration and Acoustics
, Vol.
125
,
2003
, p.
46
52
.
34.
Schmalhorst, B., and Baumgart, A., “Combined Simulation of Whirl and Stick-Slip Phenomena using a Nonlinear Finite Element Model,” Drilling and production engineering Conference. pp. 53–60, 1997
35.
Tucker
R. W.
, and
Wang
C.
, “
An Integrated Model for Drill-String Dynamics
,”
J. Sound and Vibration
,
224
(
1
),
1999
, p.
123
165
.
36.
Khulief, Y.A. and Al-Naser, H., “Finite element dynamic analysis of drillstrings’, Finite Element in Analaysis & Design, 2005, (in Press).
37.
Gupta
K. K.
,
Eigenproblem solution of damped structural systems
,
Int. J. Numerical Methods Engrg.
,
8
,
1974
, p.
877
911
.
38.
Khulief
Y. A.
and
Mohiuddin
M. A.
, “
On the Dynamic Analysis of Rotors Using Modal Reduction
,”
Int. J. Finite Element in Analysis & Design
, Vol.
26
(
1
), p.
41
55
,
1997
.
39.
Khulief
Y. A.
and
Shabana
A. A.
, “
Impact Responses in Multibody Systems with Consistent and Lumped Masses
,”
J. Sound & Vibration
, Vol.
104
(
2
),
1986
, p.
187
207
.
This content is only available via PDF.
You do not currently have access to this content.