Porous Media Group
MSc project

Iterative schemes for solving coupled, non-linear flow and transport in porous media, 2016

Davide Illiano

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Advisor: Florin Radu

Short description of the project:

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 a 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 them 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.

Link to thesis at Bora-UiB: https://bora.uib.no/bora-xmlui/handle/1956/15288