Thick-Wall Elastic Collapse for Casing Design

Elastic collapse is an important piece of the tubular collapse formulation in API TR 5C3 (2008) and ISO/TR 10400 (2007). Elastic collapse is significant because it is independent of the strength of the tubing, for example, K-55 and Q-125 have the same resistance to elastic collapse. Advanced collapse models, such as Klever and Tamano (2006), require a thick-wall collapse result as part of their formulation. What would the effect of a thick wall have on elastic collapse? There really is no way to tell from the classic formulation. The primary issue is whether the elastic collapse formula overpredicts or underpredicts collapse pressure. The developers of the API collapse equation thought the thin-wall equation overpredicted collapse pressure and put in terms to reduce the predictions. Other studies suggested the opposite effect. What is needed is a formulation that is based on an elastic solution for a thick-wall cylinder, but that can derive the classic solution for a thin wall. The elastic equations for a thick-walled cylinder exist, known as the Kirsch equations (Kirsch 1898). A new set of physically reasonable boundary conditions are proposed for the Kirsch equation, which was then used to determine the collapse resistance for a thick-wall pipe. This result also yielded the classic result in the limit because t/D is small. The thick-wall elastic collapse formula is then applied to the standard API TR 5C3 (2008) collapse formulation and to the Klever-Tamano formulation (Klever and Tamano 2006).