# SPE Drilling & Completion Volume 21, Number 2, June 2006, pp. 108-115

SPE-87205-PA

### Helical Buckling of Pipe With Connectors and Torque

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DOI  10.2118/87205-PA http://dx.doi.org/10.2118/87205-PA

### Citation

• Mitchell, R.F. and Miska, S. 2006. Helical Buckling of Pipe With Connectors and Torque. SPE Drill & Compl21 (2): 108-115. SPE-87205-PA.

### Discipline Categories

• 1 Drilling and Completions
• 1.2.2 Drillstring Design
• 1.2.5 Materials Selection (Casing, Fluids, Cement)

### Summary

It has been generally recognized that connectors (tool joints and couplings) should have some effect on the buckling of pipe. For instance, the connector outside diameter may be as much as 50% greater than the pipe-body diameter. As a result, the radial clearance of the connector can be substantially smaller than the radial clearance of the pipe body.

The analysis of buckling has received extensive attention in the last 20 years. The effect of connectors on pipe stresses has received somewhat less attention. Lubinski (1977) used the beam-column equations to analyze the effect of connectors on pipe-bending stresses for a pipe in tension in a 2D constant-curvature wellbore. Bending stresses were significantly magnified by the connector standoff. Paslay and Cernocky (1991) completed this analysis by analyzing the pipe in compression. Mitchell (2000) extended these results to 3D helical buckling.

Torque adds a new dimension to the buckling problem. Without torque, buckling occurs only for positive effective axial force (compressive axial force plus pressure effects). A pipe with applied torque can buckle in tension (Greenhill 1883). The contact force between pipe and wellbore can be increased or decreased, depending on the direction of the applied torque. And, of course, pipe used in rotary drilling always has applied torque—so buckling analysis without torque is not complete.

This paper looks at 3D buckling of pipes with connectors with applied torque. The problem formulation is similar to Lubinski et al.’s (1962) buckling analysis: the wellbore is vertical and straight. The beam-column equations considered in the plane-buckling analysis are used, but now there are deflections out of the plane. A solution for helical buckling is developed that produces pipe sag, maximum dogleg angle, contact force, and bending-stress magnification as a function of pipe effective axial force and torque. An application problem is solved, and the relative effects of compressive axial force and torque on sag between connectors, contact loads, and maximum bending stress are examined.

Applications include the analysis of bottomhole assemblies, drillpipe, casing, and tubing. The final results are simple enough to be suitable for spreadsheet calculations.

### Introduction

There are a number of practical design problems that involve buckling and post-buckling analysis of tubulars in wellbores. Pipe stresses, contact forces, length change, and maximum acceptable doglegs are strongly influenced by buckling.

Clearly, connectors should have an effect on the buckling of pipe. For instance, because the connector outside diameter may be as much as 50% greater than that of the pipe body, the wellbore radial clearance of the connector can be substantially smaller than the radial clearance of the pipe body. Buckling criteria such as the Paslay- Dawson formula depend on the radial clearance. Which radial clearance should be used? Should it be the pipe-body clearance or the connector clearance? Further, there should be a measurable effect of connectors on pipe stresses for axially loaded pipe.

There is limited analysis available on nonbuckled pipe with connectors. Lubinski (1977) used the beam-column equations to analyze the effect of connectors on pipe-bending stresses for a pipe in tension in a 2D constant-curvature wellbore, and Paslay and Cernocky (1991) completed this analysis by analyzing the pipe in compression. Pipe was found to be either suspended between connectors, in point contact with the wellbore, or in wrap contact with the wellbore, depending on the pipe tension. Bending stresses were significantly magnified by the connector standoff.

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### History

• Original manuscript received: 2 June 2004
• Revised manuscript received: 10 November 2005
• Manuscript approved: 26 January 2006
• Version of record: 20 June 2006