The Barlow Equation for Tubular Burst: A Muddled History

Abstract

Abstract The Barlow equation for tubular internal yield pressure is widely used in American Petroleum Institute (API) and International Organisation for Standardisation (ISO) standards, but its provenance and accuracy have never been established: indeed, until very recently, the original reference had been lost to the industry. This has led to doubt and confusion about its use. This paper presents the work done by ISO TC67 SC5 workgroup 2 to remedy this, and explains the background and technical basis for the upcoming revisions to ISO TR 10400. It is shown that Barlow's 1836 derivation violates the 3D constitutive law, and the result is therefore incorrect as originally purposed (a thick wall hoop stress). Moreover, hoop stress is a uniaxial (1D) check: the modern approach is 2D or 3D checking, based on a material failure condition such as the Von Mises yield criterion. However, the result also happens to represent the thin wall approximation to the VME failure pressure for plane stress (i.e., zero axial load), which gives an accurate measure of the yield pressure. Remarkably, this does not seem to have been recognised in previous work. The derivation is given, and the assumptions and limitations explained. Present design practice is over-conservative for thick wall pipe, and potentially unconservative for thin wall. This is not the fault of the Barlow equation per se: it is caused by the difference in physics between the design equation (VME yield) and the ultimate limit state (ULS) behaviour (ductile rupture). The industry should therefore consider revising OCTG burst ratings and accompanying design practice to achieve a more uniform safety level over the full D/t range of casing and tubing.