Tubing forces and displacements have long been calculated for design
purposes. Formulations, such as Lubinski's buckling model (Lubinski et al.
1962), have the underlying assumption that the fluids are static. Adding the
effects of fluid dynamics to the pipe-force-equilibrium problem is not as
straightforward as one might think.
The key point is the loads generated by the fluid on the tubing. What
information can we obtain from a simple balance of momentum of the fluid in
bulk? For example, for flow inside a pipe, we can determine exactly the load
exerted on the pipe by the flowing fluid in terms of only the fluid density,
pressure, and momentum.
What might be the effect of fluid dynamics? Most papers have dealt with
static fluids, but how are these static effects modified for a flowing fluid?
Do we need to add a pressure gradient to the pipe buoyancy? How is fluid
friction included in the pipe loading? How does fluid momentum affect the pipe?
For curved pipes, we might expect a centrifugal force term. The answers to
these questions are often surprising, even counterintuitive.
In this paper, the general equations for the balance of fluid momentum are
combined with the equilibrium equation for the pipe. The effective force then
emerges as a natural combination of pipe-force and fluid-force terms. Pipe
displacement is usually formulated in terms of the actual axial force, but the
necessary modifications to this formulation are presented for the effective
© 2011. Society of Petroleum Engineers
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- Original manuscript received:
10 March 2011
- Meeting paper published:
2 March 2011
- Revised manuscript received:
14 June 2011
- Manuscript approved:
15 June 2011
- Published online:
12 August 2011
- Version of record:
15 September 2011