# SPE Drilling & Completion Volume 22, Number 2, June 2007, pp. 112-118

SPE-99099-PA

### The Effect of Friction on Initial Buckling of Tubing and Flowlines

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DOI  10.2118/99099-PA http://dx.doi.org/10.2118/99099-PA

### Citation

• Mitchell, R.F. 2007. The Effect of Friction on Initial Buckling of Tubing and Flowlines. SPE Drill & Compl22 (2): 112-118. SPE-99099-PA.

### Discipline Categories

• 1.2.2 Drillstring Design
• 1.2.3 Torque/Drag Modeling, BHA Performance Prediction
• 1.2.5 Materials Selection (Casing, Fluids, Cement)

### 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.

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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