(337f) The Effect of the Choice of the Primitive Variables on the Numerical Efficiency of Highly Transient Flows

Pressurised pipelines are increasingly used for the transport of large quantities of highly flammable hydrocarbons and their rupture can give rise to catastrophic consequences. Indeed in recent years their have been many instances of pipeline rupture which have caused enormous damage to the environment.

The accurate prediction of outflow and its variation with time following pipeline rupture are therefore extremely important since this information will dictate all the major consequences associated with such types of failures including fire, explosion and environmental pollution.

The development of a transient two-phase fluid outflow model for pipeline rupture entails three main steps. The first involves the formulation of the conservation equations governing the flow incorporating heat transfer and frictional effects. The resulting quasi-linear partial differential equations are hyperbolic and cannot be solved analytically as they contain terms that are unknown or complex functions of their dependent and independent variables. The second step involves the transformation of these non-linear equations into a finite difference form. The final step requires their solution in conjunction with the relevant boundary conditions using a suitable numerical technique. Previous attempts include a finite difference method, a finite element method and the method of characteristics (MOC). As all of these techniques involve the numerical discretisation of the pipeline into a large number of elements, their solution for a typical pipeline often requires very long CPU time (e.g 15 days on a Pentium IV processor for a 300 km, 1 m dia pipeline transporting a condensable hydrocarbon mixture at 100 bar pressure). This is despite significant advances involving the use of nested grid systems (ref) and higher speed computer processing powers.

In this paper a more fundamental approach is described which for the first time demonstrates the significant effect of the choice of the primitive variables such as fluid enthalpy, density and entropy incorporated in different formulations of the conservation equations on the computational run time and accuracy. The model’s efficacy is demonstrated based on comparison with recorded data for the rupture of a real pipeline.