Existing plastic limit load equations for casing design include approximations that can result in overly conservative (and costly) well designs and ignore forces that may prove critical for assured integrity in complex operations. The use of effective tension in place of physical tension can simultaneously simplify casing design and eliminate existing approximations and wall thickness limitations.
Effective tension has not yet been widely adopted because a rigorous derivation based on axiomatic mechanics and calculus does not exist in the current body of literature. This paper presents a thorough derivation for effective tension in terms of working stresses, with tensile, radial, and tangential stresses all receiving proper treatment. Unlike Barlow’s equation, which is routinely used for casing selection, the analytical result presented here allows fully plastic limit loads to be established for tubulars of any wall thickness, without introducing any approximations.
Determining plastic limit loads is a crucial component of designing for well integrity, especially with complex operational loads where classical load equations are too conservative. The methods of transformation detailed in this paper facilitate the use of effective tension, which is often the more efficient primary tension load variable for pipe design, as opposed to physical tension. The rigorous model can also be used to derive strains as functions of loads, which is required for some design problems such as seal effectiveness. Additionally, the formulas can be used to dynamically simulate load changes and dimensional changes of pipe when it deforms, such as expandable casing, deformable ball seats, or when approaching rupture pressure.
The elimination of approximations in the equations presented in this paper is significant in today’s well design climate, where integrity is demanded yet excessive cost is not tolerated. The derivation provides a foundation upon which existing casing design can be improved by eliminating wall thickness limitations and dependencies on approximations. This foundation will allow new design techniques to be developed that were not previously achievable due to the inefficiencies inherent in the use of physical tension.