Lateral Buckling of Pipe With Connectors in Curved Wellbores
- Robert F. Mitchell (Landmark Graphics)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- March 2003
- Document Type
- Journal Paper
- 22 - 32
- 2003. Society of Petroleum Engineers
- 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 1.6.1 Drilling Operation Management, 1.6 Drilling Operations, 1.10 Drilling Equipment
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Connectors should clearly have an effect on pipe loading. For nonbuckled pipe, Lubinski analyzed the effect of connectors on pipe in tension in a curved borehole and Paslay and Cernocky extended this analysis to pipe in compression. Recently, helically buckled and laterally buckled pipes with connectors have been analyzed. In these papers, analytic solutions of the beam-column equations were developed in 3D, and critical loads were determined for buckling initiation. Conditions for positive contact forces were determined and compared to previous buckling criteria, such as Dawson-Paslay.
In this paper, the wellbore curvature effects studied by Lubinski, Paslay, and Cernocky are included in the buckling effects. The modifications necessary to analyze lateral buckling are made for a curved wellbore. The resulting model gives a buckling criterion similar to He and Kyllingstad's results for pipe without connectors. The buckling model is integrated with the Paslay-Cernocky analysis to resolve some of the odd bending-stress results developed by their model. Pipe deflections, contact loads, and bending stresses are determined with explicit formulas. Sag between connectors is calculated so that pipe contact with the wellbore between connectors can be determined. Conditions for positive contact forces are determined and compared to previous buckling criteria, such as Paslay-Dawson and He-Kyllingstad.
Applications include the analysis of bottomhole assemblies (BHAs), drillpipe, casing, and tubing. The solutions are simple formulas that are suitable for hand calculations.
Connectors should have an effect on the buckling of pipe. For instance, because the connector's outer diameter (OD) may be as much as 50% greater than the pipe body, the connector's wellbore radial clearance 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 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 used beam-column equations to analyze the effect of connectors on pipe bending stresses for a pipe in tension in a 2D constant-curvature wellbore,1 and Paslay and Cernocky completed this analysis by analyzing the pipe in compression.2 Pipe was found to be suspended between connectors, in point, or in wrap contact with the wellbore, depending on the pipe tension. Bending stresses were significantly magnified by the connector standoff.
The first step in the analysis of 3D buckling in pipes with connectors was taken by Mitchell.3 In this problem, a helical geometry was chosen similar to Lubinski's buckling analysis for pipe without connectors.4,5 The beam-column equations considered in the plane-buckling analysis1,2 were used, but there were now deflections out of the plane. A solution for helical buckling was developed that corresponded to Lubinski's solution for low axial compression but produced pipe sag and bending-stress magnification (BSM) for higher axial loads. Calculation results included connector contact forces, BSM, maximum dogleg angle, and pipe sag.
The next step, 3D buckling of a horizontal well with lateral loads on the pipe, was also taken by Mitchell.6 Lateral pipe buckling was analyzed, with critical loads for initiating buckling determined. Equilibrium lateral deflections were determined, along with pipe sag between connectors, bending stress, and contact loads. Conditions for positive contact forces were determined and compared to buckling criteria, such as Dawson-Paslay.7
This paper takes the third logical step in the investigation of the effect of connectors on pipe buckling - the introduction of wellbore curvature. As stated previously, the equilibrium of nonbuckled pipe in a curved wellbore has been studied by Lubinski and Paslay.1,2 Only Paslay's paper considered pipe in compression, but in this case, he cautioned that the results were contingent on no buckling taking place. This paper explicitly considers the possibility of lateral pipe buckling in a horizontal wellbore with curvature. Lateral pipe buckling is analyzed, with critical loads determined for buckling initiation. Equilibrium lateral deflections are determined, along with pipe sag between connectors, bending stress, and contact loads. Conditions for positive contact forces are determined and compared to buckling criteria for curved wellbores, such as He-Kyllingstad.8
Buckling is usually concerned with stability. In this sense, stability means that for axial forces greater than the "critical" or buckling force, there is no stable equilibrium load, and the column fails catastrophically.
In a horizontal wellbore, the situation is different. The first difference is that the pipe weight stabilizes it at the bottom of a horizontal wellbore. Dawson and Paslay7 analyzed this problem and determined that for buckling to occur, the axial force must exceed the Paslay force, Fp , where Fp is given by
where we=the buoyant pipe weight per foot, and rc =the pipe radial clearance. When the wellbore is curved, the Paslay force is modified to give
which is the He-Kyllingstad8 version of the Paslay force, with ?=the wellbore curvature, in which the positive sign is used if the wellbore curves upward and the negative sign if it curves downward. The axial force pushes the pipe into the wellbore if it curves upward and away from the bottom of the wellbore if the curvature is downward.
The second difference is that the wellbore constrains the pipe after it buckles and allows it to find a new equilibrium position. The first post-buckling equilibrium solution discovered was a helix4 in which the contact forces developed between the pipe and the wellbore balanced the destabilizing axial force. Subsequent studies have determined lateral buckling solutions in which pipe weight, in addition to contact forces, balances the axial force.5
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