Summary
The introduction of friction into the analysis of buckling stability causes
problems. For sliding friction, the friction force is fully developed for small
lateral motion, while the destabilizing effect of the axial force is
proportional to the lateral motion. Because the sliding-friction force develops
so rapidly and destabilizing effects develop so slowly, buckling is essentially
impossible.
Yet we know that pipe buckles with friction. In conventional analysis, the
only possible way for buckling to occur is to have an initial nonzero lateral
displacement, so that the axial-force contribution can exceed the fully
mobilized friction force. This initial displacement cannot normally be
estimated accurately, so the force needed to buckle pipe with sliding friction
is essentially unknown.
A cylindrical pipe has another possible mode of lateral displacement.
Instead of sliding, the pipe can roll. In this case, the friction force
developed is static friction. Static friction may take on any value between
zero and the peak static-friction value, where the value of the static friction
usually is determined from a balance of known forces in the problem of
interest. Here, the magnitude of the static friction is determined from a
balance of torsional forces on the pipe. The key fact is that the friction
force develops gradually, so a critical buckling force can be determined in the
traditional sense.
The introduction of axial torque adds further complications to the buckling
analysis. This paper develops a comprehensive model for pipe undergoing axial
forces and torque and then develops the critical buckling loads for three cases
of interest. The first case corresponds to the pipe in the wellbore, as
investigated by Dawson and Paslay (1984). The second problem looks at a pipe
lying on a flat plane, for example a pipeline on the seabed. In both cases, a
critical buckling load is determined for pipe in which lateral motion is
constrained by friction. The third case involves a rotating pipe and determines
its critical buckling load. Several sample calculations are performed to
illustrate the importance of friction forces in ensuring the stability of
tubing and of seafloor flowlines.
Introduction
The prediction of buckling is important for drillstring design and for
well-completion analysis. The earliest buckling stability analysis was done by
Euler, as noted in Timoshenko and Gere (1961). In an analysis of helical
buckling for tubing design by Lubinski et al. (1962), the pipe was assumed to
be vertical and sufficiently long that the Euler buckling load could be
neglected.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
7 December 2005
- Revised manuscript received:
4 January 2007
- Manuscript approved:
16 January 2007
- Version of record:
20 June 2007
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