A two-phase eleven-equation model for numerical simulations of aerated slug flow in horizontal and nearly horizontal pipelines

In this work, we propose a new model for the description of a one-dimensional two- phase flow. This model consists in a derivation of the hyperbolic, one-dimensional, five-equation, two-fluid model developed in previous work, which proved to be a good model to automatically capture the transition to slug flow regime adopting a flow description consistent with stratified conditions. The model presented here is built on eleven equations, namely four mass and four momentum conservation equations and three equations to describe the advection of the three interfaces. It is shown that this model owns the same hyperbolicity properties found for the five-equation system. The explicit form of the eigenstructure of the eleven-equation system allows to apply the high resolution extension of Godunov’s method with Roe linearization at cell interfaces.

This model can describe stratified and wavy flow in pipeline; nevertheless, to numerically simulate slug flow, a slug criterion is developed and implemented to describe the disappearance of the field composed by continuous gas and droplets in some regions of the pipeline. Particular care is paid to the description of bubble entrainment and deposition in the slug body.