Construction of three-phase data to model multiphase flow in porous media: Comparing an optimization approach to the finite element approach

Multiphase flow modelling is a major issue in the assessment of groundwater pollution. Three-phase flows are commonly governed by mathematical models that associate a pressure equation with two saturation equations. These equations involve a number of secondary variables that reflect the fluid behaviour in a porous medium. To improve the computational efficiency of multiphase flow simulators, several simplified reformulations of three-phase flow equations have been proposed. However, they require the construction of new secondary variables adapted to the reformulated flow equations. In this article, two different approaches are compared to quantify these variables. A numerical example is given for a typical fine sand.