SPE Drilling & Completion
Volume 23, Number 4, December 2008, pp. 361-370

Summary

Almost unique in engineering analysis is the problem of tubing buckling in wellbores. In general, structures loaded above their critical load fail catastrophically. Yet, both tubing and drillstrings are commonly operated above the critical load. These tubing strings do not fail because the wellbore provides the necessary support for "post-buckling" equilibrium.

The two fundamental questions about tubing buckling are

• What is the critical load?
• What is the post-buckled configuration?

The critical load tells us if the tubing will buckle. Euler solved the problem for "short" columns, but these results rarely have application in a wellbore because the pipes in a wellbore are usually very long (Timoshenko and Gere 1961). The first stability criterion that considered the stabilizing effect of weight on long pipes in inclined wellbores was developed by Dawson and Paslay (1984).

The post-buckled configuration tells us about tubing movement, bending stresses, contact forces, and axial-load distributions. The original buckling analysis by Lubinski et al. (1962) proposed a helical configuration in a vertical wellbore and used the method of virtual work to determine a specific constant pitch for that helix as a function of the axial force and bending stiffness.

These two works set the following themes for further analysis of tubing buckling:

• What is the critical buckling load in curved, 3D wellbores?
• How does torque affect the critical buckling load?
• How do tapered strings affect the critical buckling load?
• What is the buckling configuration in inclined wellbores?
• How do the boundary conditions affect the configuration?
• How do tapered strings buckle?
• How does torque affect the buckling configuration?
• What effect does friction play in tubing buckling?

Many of these questions have been, at least, partly answered in the past three decades. This paper will examine the technical fundamentals of the tubing-buckling problem; summarize the most useful, new results from these papers, and discuss the remaining challenges in tubing-buckling analysis.

Introduction

Accurate buckling calculations are important for several reasons. Bending stresses because of tubing buckling may cause permanent deformations, called "corkscrewing," which is to be avoided. For a fixed packer, an inaccurate estimation of tubing movement may greatly underestimate the axial loads, resulting in a nonconservative design. For a free packer or a packerbore receptacle, exaggerated tubing motion will require excessive seal length. Further, because tubing incremental motion will control the friction-load direction, errors in overall tubing displacement will generate further errors in friction loads.

The first publication of the analysis of helical buckling (Lubinski et al. 1962) answered two basic questions about tubing buckling

1. How does fluid pressure influence buckling?
2. What is the pitch of helically buckled tubing?

Their solution was brilliant but seemingly simple and has strongly influenced the basic approach to buckling analysis in the petroleum industry. The unfortunate side effect has been that many fundamental questions cannot be answered with this approach (Mitchell 1988). For instance, how do boundary conditions at a packer affect the buckling solution? The solution by Lubinski et al. (1962) does not connect to a packer, so we must assume that their result applies far from the boundary conditions, and that boundary conditions do not matter. When we have a deviated well, there is the possibility of lateral buckling. When does helical buckling happen in this case, and what is the pitch of this helix?

The study of buckling in deviated wells produced the second theme of this review: At what axial load does tubing buckling begin in deviated wells? The first explicit calculation for deviated wells was published by Dawson and Paslay (1984).

Many papers have followed these two seminal papers (see Appendix C). This review will list only what the author considers to be the best current knowledge on tubing buckling and will list a few open questions that need further study.

© 2008. Society of Petroleum Engineers

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History

• Original manuscript received: 27 June 2006
• Meeting paper published: 24 September 2006
• Revised manuscript received: 15 April 2008
• Manuscript approved: 15 April 2008
• Version of record: 10 December 2008