# SPE Journal Volume 14, Number 4, December 2009, pp. 782-796

SPE-111511-PA

### Effects of Boundary Conditions and Friction on Static Buckling of Pipe in a Horizontal Well

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DOI  10.2118/111511-PA http://dx.doi.org/10.2118/111511-PA

### Citation

• Gao, G. and Miska, S. 2009. Effects of Boundary Conditions and Friction on Static Buckling of Pipe in a Horizontal Well. SPE J.  14 (4): 782-796. SPE-111511-PA. doi: 10.2118/111511-PA.

### Discipline Categories

• 1 Drilling and Completions
• 5 Production and Operations
• 2 Health, Safety, Security, Environment and Social Responsibility
• 4 Projects, Facilities and Construction

### Keywords

• drilling pipe, tubing, horizontal well, stability, friction

### Summary

A comprehensive buckling model, a group of fourth-order nonlinear ordinary differential equations, was derived by applying the principle of virtual work. Lateral friction force is included in this model. The equations were normalized to make the solutions independent of the wellbore size, type of pipe, and mud. The critical sinusoidal buckling load of tubing with different boundary conditions typically seen in drilling and well-completion applications was analyzed on the basis of the analytical solution of the linearized buckling equation. The results show that the effect of the boundary conditions can be neglected when the dimensionless length of tubing is greater than 5π. The authors further investigated the effects of friction on sinusoidal buckling by applying the principle of virtual work. The critical conditions for initiating sinusoidal buckling were determined by a group of three nonlinear equations. A perturbation solution of these nonlinear equations was obtained. It was found that the critical loads for sinusoidal buckling will increase by 30 to 70% for friction coefficients between 0.1 and 0.3. The authors also conducted an experimental study. The experimental results, including both data obtained by the authors and results published by other researchers, support the proposed model.

### Introduction

Various pipes, including drill pipe, casing, tubing, coiled tubing, and sucker rods, are widely used in drilling, well completions, formation stimulation, water injection, and the pumping of wells. During drilling, completion, production, or stimulation operations, the drilling pipe or tubing may be subjected to some degree of axial compression or the pressure inside the pipe may exceed the external pressure. In both cases, the pipe may lose its stability and buckle into a sinusoidal or helical shape. Consequently, stability and post-buckling analysis of pipe in various kinds of wellbores attracts intense interest from the petroleum industry.

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### History

• Original manuscript received: 16 December 2007
• Meeting paper published: 4 March 2008
• Revised manuscript received: 25 November 2008
• Manuscript approved: 27 November 2008
• Published online: 20 August 2009
• Version of record: 22 December 2009