In the original publication on helical buckling by Lubinski et al. (1962),
it was assumed that no torsion can be developed in buckled tubular string
(Lubinski–Woods problem) if there is no casing-to-tubing friction and tubing
remains in an elastic range of bending.
Recent theoretical work by Mitchell (2004) presented the large-displacement
analysis of a helically buckled slender beam and predicted that shear force and
twisting moment are induced in helically buckled pipe without externally
In short, there is an induced left-hand torsion in tubing buckled into a
right-hand helix that is surprisingly large and, in some cases, may approach or
exceed the makeup-torque values for connections.
For study of this phenomenon, an experimental facility was set up at the
University of Tulsa, depicting a straight horizontal wellbore with the inner
steel tubing having a 0.50-in. (12.7-mm) outside diameter (OD) and the outer
acrylic tube having a 1.90-in. (48.3-mm) inside diameter (ID), representing
drillstring and wellbore, respectively.
For a precise measurement of pure torsion in the tubing, strain gauges were
employed, arranged into the full-torsion bridge configuration.
The experiments were performed with the "bottom end" of the steel
tubing held stationary and with axial-buckling force applied from the "top
The end conditions for the tubing were represented by clamped and pinned
It was observed that torsional equilibrium in the tubing is disturbed as
soon as buckling force is applied, with further increase in torsion as the
shape of the tubing transforms from sinusoidal to helical.
Upon the tubing reaching full helical shape, the internal torsion continues
to increase with the increase of axial-buckling force in the manner predicted
The results of this study are important for practical design and analysis of
drillstrings and completion tubing.
© 2009. Society of Petroleum Engineers
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- Original manuscript received:
10 November 2004
- Meeting paper published:
23 February 2005
- Revised manuscript received:
13 November 2008
- Manuscript approved:
23 November 2008
- Published online:
1 June 2009
- Version of record:
1 June 2009