Buckling of Tubing Inside Casing

Abstract

Summary Oil wells typically have multiple concentric casing strings. For a set of two concentric strings, if the inner pipe has a compressive axial force, it will typically buckle within the outer string. The buckling of pipe can be important in the analysis of a well-completion design because the buckled pipe can develop bending stresses that may be significant. Most analyses of this problem assume that the outer casing is rigid. In reality, this external casing is also elastic and would displace owing to the loads generated by contact with the inner pipe. Further, if both strings have compressive axial forces, both strings will buckle, and the resulting buckled configuration must fit together so that contact forces between the two strings are positive and the pipes do not each occupy the same space. If the two strings have an external, cylindrical rigid wellbore, then any contact forces with this wellbore must also be positive, and the buckled pipe system must lie within this wellbore. The only known solution to the multiple concentric pipe-buckling problem is that of Christman (1976), who proposed a composite pipe based on the summed properties of the individual pipes. This analysis does not conform to the requirements posed in the preceding paragraph. This paper presents the various ways that two concentric pipes can interact when one or both pipes are in compression and would then have a tendency to buckle. The contact forces between the pipes and with the external wellbore are explicitly calculated, and contact or noncontact conditions are determined. All results are analytical so that they can easily be used in spreadsheets or hand calculations. Several examples of calculations are presented to illustrate how these results might be used.