Iterative schemes for solving coupled, non-linear flow and transport in porous media

Abstract

In this thesis we compare different iterative approaches for solving the non-linear, coupled multiphase flow and reactive transport in porous media. Especially, we consider two-phase flow and one a-half phase flow (modeled by Richards equation) coupled with an one component transport equation. Implicit and explicit iterative schemes will be compared in terms of efficiency, robustness and accuracy. The best approach seems to be a fully implicit scheme, which is a slightly modified variant of the classical splitting iterative scheme for coupled equations. We concentrate on three linearization methods: L-scheme, Modified Picard and Newton. We implement them in Matlab and tested on both an academic example, built from a manufactured analytical solution and on a realistic problem, the Salinity Problem. In the first part of the thesis we will also briefly study the generic two-phase flow plus transport equation in porous media, presenting some of the most common solving algorithms such as the IMPES method and its Fully Implicit reformulation.