Introducing sources of axial vibration into an oilwell drillstring has the potential to improve the drilling efficiency. Vibration generator tools, such as drillstring agitators, are under development or in current use to excite the bottom-hole assembly (BHA) axially in order to increase power and weight at the bit, improve the rate of penetration (ROP), reduce drillstring-wellbore friction, and accelerate the cutting removal process. Enhanced drilling under the effect of intentional imposed vibration is called “vibration-assisted rotary drilling” or VARD. While potentially enhancing the drilling process, VARD tools can also excite many unwanted vibration modes of the drillstring. These unwanted vibrations can cause fatigue damage and failure of BHA components such as “measurement while drilling” (MWD) tools, bit and mud motors, and consequently, inefficient drilling. This motivates a study of the complex dynamic behavior of an axially excited drillstring. Transverse vibration is the most destructive type of drillstring vibration, and the coupling between transverse and axial vibration of a drillstring subjected to an applied VARD force is of great interest to the experts in the field. In this study, the coupled axial-transverse vibration behavior of the entire drillstring under the effect of a VARD tool is investigated. A dynamic finite element method (FEM) model of the vertical drillstring assuming a multispan BHA is generated and validated with a coupled nonlinear axial-transverse elastodynamic mathematical model. The effects of mud damping, driving torque, multispan contact and spatially varying axial load are included. Geometry, axial stiffening and Hertzian contact forces are sources of nonlinearity in the model. A mesh sensitivity analysis is conducted to reduce computational time. The accuracy of the retained modes in the analytical equations is verified by extracting the total effective mass derived by the FEM model. There is agreement between the FEM and analytical models for coupled-transverse and axial vibration velocities, displacements, resonance frequencies and contact locations and behavior. While the analytical model has fast running time and symbolic solution, the FEM model enables easy reconfiguration of the drillstring for different boundary conditions, inclusion of additional elements such as shock subs, and changing the number and locations of stabilizers.

References

References
1.
Barton
,
S.
,
Baez
,
F.
, and
Alali
,
A.
,
2011
, “
Drilling Performance Improvements in Gas Shale Plays Using a Novel Drilling Agitator Device
,”
SPE
North American Unconventional Gas Conference and Exhibition
,
The Woodlands, TX
, Paper No. 144416. 10.2118/144416-MS
2.
Babatunde
,
Y.
,
Butt
,
S. D.
,
Molgaard
,
J.
, and
Arvani
,
F.
,
2011
, “
Investigation of the Effects of Vibration Frequency on Rotary Drilling Penetration Rate Using Diamond Drag Bit
,”
45th U.S. Rock Mechanics/Geomechanics Symposium (ARMA)
,
San Francisco, CA
, Paper No. 11-527.
3.
Spanos
,
P. D.
,
Chevallier
,
A. M.
, and
Politis
,
N. P.
,
2002
, “
Nonlinear Stochastic Drill-String Vibrations
,”
ASME J. Vib. Acoust.
,
124
(4)
, pp.
512
518
.10.1115/1.1502669
4.
Ghasemloonia
,
A.
,
Rideout
,
D. G.
, and
Butt
,
S. D.
,
2012
, “
Coupled Transverse Vibration Modeling of Drillstrings Subjected to Torque and Spatially Varying Axial Load
,”
IMechE Part C: J. Mech. Eng.
(in press). 10.1177/0954406212455126
5.
Ghasemloonia
,
A.
,
Rideout
,
D. G.
, and
Butt
,
S. D.
,
2012
, “
Analysis of Multi-Mode Nonlinear Coupled Axial-Transverse Drillstring Vibration in Vibration Assisted Rotary Drilling
,”
International J. Mech Eng. Science (IMechE)
(unpublished).
6.
Dykstra
,
M. W.
,
Chen
,
D. C. K.
,
Warren
,
T. M.
, and
Zannoni
,
S. A.
,
1994
, “
Experimental Evaluations of Drill Bit and Drill String Dynamics
,” 69th
SPE
Annual Technical Conference and Exhibition
,
New Orleans, LA
, Paper No. 28323. 10.2118/28323-MS
7.
Walker
,
B. H.
, and
Friedman
,
M. B.
,
1977
, “
Three-Dimensional Force and Deflection Analysis of a Variable Cross Section Drill String
,”
ASME J. Pressure Vessel Technol
,
99
(
2
), pp.
367
373
.10.1115/1.3454543
8.
Bailey
,
J. J.
, and
Finnie
,
I.
,
1960
, “
An Analytical Study of Drill-String Vibration
,”
ASME J. Eng. Industry
,
82
(
2
), pp.
122
127
.10.1115/1.3663017
9.
Trindade
,
M. A.
,
Wolter
,
C.
, and
Sampaio
,
R.
,
2005
, “
Karhunen-Loeve Decomposition of Coupled Axial/Bending Vibrations of Beams Subject to Impacts
,”
J. Sound Vib.
,
279
, pp.
1015
1036
.10.1016/j.jsv.2003.11.057
10.
Jansen
,
J. D.
,
1991
, “
Nonlinear Rotor Dynamics as Applied to Oil Well Drillstring Vibrations
,”
J. Sound Vib.
,
147
(
1
), pp.
115
135
.10.1016/0022-460X(91)90687-F
11.
Elsayed
,
M. A.
,
Wells
,
R. L.
,
Dareing
,
D. W.
, and
Nagirimadugu
,
K.
,
1994
, “
Effect of Process Damping on Longitudinal Vibrations in Drillstrings
,”
ASME J Energy Resour. Technol.
,
116
(2)
, pp.
129
135
.10.1115/1.2906017
12.
Berlioz
,
A.
,
Der Hagopian
,
J.
,
Dufour
,
R.
, and
Draoui
,
E.
,
1996
, “
Dynamic Behavior of a Drill-String: Experimental Investigation of Lateral Instabilities
,”
ASME J. Vib. Acoust.
,
118
(3)
, pp.
292
298
.10.1115/1.2888180
13.
Aminfar
,
O.
, and
Khajepour
,
A.
,
2008
, “
Torsional Vibration Analysis of Drillstrings in Blasthole Drilling
,”
ASME
International Mechanical Engineering Congress (IMECE)
,
Boston, MA
.10.1115/IMECE2008-67418
14.
Yigit
,
A. S.
, and
Christoforou
,
A. P.
,
1996
, “
Coupled Axial and Transverse Vibrations of Oilwell Drillstrings
,”
J. Sound Vib.
,
195
(
4
), pp.
617
627
.10.1006/jsvi.1996.0450
15.
Sampaio
,
R.
,
Piovan
,
M. T.
, and
Lozano
,
G. V.
,
2007
, “
Coupled Axial Torsional Vibrations of Drillstring by Means of Nonlinear Model
,”
J. Mech. Res. Commun.
,
34
, pp.
497
502
.10.1016/j.mechrescom.2007.03.005
16.
Yigit
,
A. S.
, and
Christoforou
,
A. P.
,
1998
, “
Coupled Torsional and Bending Vibrations of Drillstrings Subject to Impact With Friction
,”
J. Sound Vib.
,
215
(
1
), pp.
167
181
.10.1006/jsvi.1998.1617
17.
Christoforou
,
A. P.
, and
Yigit
,
A. S.
,
1997
, “
Dynamic Modeling of Rotating Drillstrings With Borehole Interactions
,”
J. Sound Vib.
,
206
(
2
), pp.
243
260
.10.1006/jsvi.1997.1091
18.
Elsayed
,
M. A.
, and
Washington
,
L. F.
,
2001
, “
Drillstring Stability Based on Variable Material Specific Force and Using a Sharp Three-Insert Polycrystalline Diamond Compact (PDC) Coring Bit
,”
ASME J. Energy Resour. Technol.
,
123
(2)
, pp.
138
143
.10.1115/1.1367857
19.
Spanos
,
P. D.
,
Sengupta
,
A. K.
,
Cunningham
,
R. A.
, and
Palsay
,
P. R.
,
1995
, “
Modeling of Roller Cone Bit Lift-Off Dynamics in Rotary Drilling
,”
ASME J. Energy Resour. Technol.
,
117
(3)
, pp.
197
207
.10.1115/1.2835341
20.
Millheim
,
K.
,
Jordan
,
S.
, and
Ritter
,
C. J.
,
1978
, “
Bottom-Hole Assembly Analysis Using the Finite-Element Method
,”
J. Pet. Technol.
,
30
(
2
), pp.
265
274
.10.2118/6057-PA
21.
Baird
,
J. A.
,
Caskey
,
B. C.
,
Wormley
,
D. N.
, and
Stone
,
C. M.
,
1985
, “
GEODYN2: A Bottomhole Assembly/Geological Formation Dynamic Interaction Computer Program
,”
SPE
Annual Technical Conference and Exhibition
,
Las Vegas, NV
, Paper No. 14328. 10.2118/14328-MS
22.
Apostal
,
M. C.
,
Haduch
,
G. A.
, and
Williams
,
J. B.
,
1990
, “
A Study to Determine the Effect of Damping on Finite-Element-Based, Forced-Frequency-Response Models for Bottomhole Assembly Vibration Analysis
,”
SPE
Annual Technical Conference and Exhibition
,
New Orleans, LA
.10.2118/20458-MS
23.
Burgess
,
T. M.
,
McDaniel
,
G. L.
, and
Das
,
P. K.
,
1987
, “
Improving BHA Tool Reliability With Drillstring Vibration Models: Field Experience and Limitations
,”
SPE
/IADC
Drilling Conference
,
New Orleans, LA
, Paper No. 16109. 10.2118/16109-MS
24.
Axisa
,
F.
, and
Antunes
,
J.
,
1992
, “
Flexural Vibration of Rotors Immersed in Dense Fluids: Part I- Theory
,”
J. Fluids Struct.
,
6
(
1
), pp.
3
21
.10.1016/0889-9746(92)90052-5
25.
Spanos
,
P. D.
,
Payne
,
M. L.
, and
Secora
,
C. K.
,
1997
, “
Bottom-Hole Assembly Modeling and Dynamic Response Determination
,”
ASME J. Energy Resour. Technol.
,
119
(3)
, pp.
153
158
.10.1115/1.2794983
26.
Ritto
,
T. G.
,
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
, pp.
865
876
.10.1016/j.ijnonlinmec.2009.06.003
27.
Khulief
,
Y. A.
, and
Al-Naser
,
H.
,
2005
, “
Finite Element Dynamic Analysis of Drillstrings
,”
Finite Elem. Anal. Des.
,
41
, pp.
1270
1288
.10.1016/j.finel.2005.02.003
28.
Hsu
,
F.
, and
Wilhoit
,
J. C., Jr.
,
1965
, “
Lateral Vibration of Drill Pipe Including Wall Reaction
,”
Conference on Drilling and Rock Mechanics
,
Austin, TX
,
SPE
, Paper No. 1046. 10.2118/1046-MS
29.
Mitchell
,
R. F.
, and
Allen
,
M. B.
,
1987
, “
Case Studies of BHA Vibration Failure
,”
SPE
Annual Technical Conference and Exhibition
,
Dallas, TX
, Paper No. 16675. 10.2118/16675-MS
30.
Melakhessou
,
H.
,
Berlioz
,
A.
, and
Ferraris
,
G.
,
2003
, “
A Nonlinear Well-Drillstring Interaction Model
,”
ASME J. Vib. Acoust
,
125
(1)
, pp.
46
52
.10.1115/1.1523071
31.
Khulief
,
Y. A.
,
Al-Sulaiman
,
F. A.
, and
Bashmal
,
S.
,
2008
, “
Vibration Analysis of Drillstrings With String-Borehole Interaction
,”
IMechE Part C: J. Mech. Eng.
,
222
, pp.
2099
2110
.10.1243/09544062JMES968
32.
Khulief
,
Y. A.
, and
Al-Sulaiman
,
F. A.
,
2009
, “
Laboratory Investigation of Drillstring Vibrations
,”
IMechE Part C: J. Mech. Eng.
,
223
(
10
), pp.
2249
2262
.10.1243/09544062JMES1550
33.
Khulief
,
Y. A.
,
2000
, “
Spatial Formulation of Elastic Multibody Systems With Impulsive Constraints
,”
Multibody Syst. Dyn.
,
4
(
4
), pp.
383
406
.10.1023/A:1009801322539
34.
Wong
,
S. V.
,
Hamuda
,
A. M. S.
, and
Hasmi
,
M. S. J.
,
2001
, “
Kinematic Contact-Impact Algorithm With Friction
,”
Int. J. Crashworthiness
,
6
(
1
), pp.
65
82
.10.1533/cras.2001.0163
35.
2012
,
abaqus
Theory Manual (version 6.10),
Dassault Systèmes Simulia Corp.
,
Rhode Island
.
36.
Beck
,
A. T.
, and
da Silva
,
C. R. A.
, Jr.
,
2010
, “
Timoshenko Versus Euler Beam Theory: Pitfalls of a Deterministic Approach
,”
Struct. Safety
,
33
(
1
), pp.
19
25
.10.1016/j.strusafe.2010.04.006
37.
Mitchell
,
R. F.
, and
Miska
,
S. Z.
,
2011
,
Fundamentals of Drilling Engineering
,
SPE Textbook Series
,
Texas
, Chap. 10.
38.
Thomsen
,
J. J.
,
2003
,
Vibrations and Stability
,
2nd ed.
,
Springer
,
Berlin, Germany
, Chap. 3.
39.
Paidoussis
,
M. P.
,
Luu
,
T. P.
, and
Prabhakar
,
S.
,
2008
, “
Dynamics of a Long Tubular Cantilever Conveying Fluid Downwards, Which Then Flows Upwards Around the Cantilever as a Confined Annular Flow
,”
J. Fluids Struct.
,
24
, pp.
111
128
.10.1016/j.jfluidstructs.2007.07.004
40.
Zhang
,
Q.
, and
Miska
,
S.
,
2005
, “
Effects of Flow-Pipe Interaction on Drill Pipe Buckling and Dynamics
,”
ASME J. Pressure Vessel Technol.
,
127
(2)
, pp.
129
136
.10.1115/1.1858922
41.
Ritto
,
T. G.
,
Sampaio
,
R.
, and
Soize
,
C.
,
2009
, “
Drill-String Nonlinear Dynamics Accounting for Drilling Fluid
,”
30 deg CILAMCE-Iberian-Latin-American Congress on Computational Methods in Engineering
,
Armação dos Búzios, Rio de Janeiro
.
42.
Nour-Omid
,
B.
,
Parlett
,
B. N.
, and
Taylor
,
R. L.
,
1983
, “
Lanczos Versus Subspace Iteration for Solution of Eigenvalue Problems
,”
Int. J. Numer. Methods Eng.
,
19
(
6
), pp.
859
871
.10.1002/nme.1620190608
43.
Simitses
,
G.
, and
Hodges
,
D.
,
2005
,
Fundamentals of Structural Stability
,
Elsevier
,
Oxford, UK
, Chap. 8.
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