On the upstream mobility scheme for two-phase flow in porous media

TL;DR

This paper compares the upstream mobility flux and Godunov flux in modeling two-phase flow in porous media, highlighting limitations of the upstream mobility flux when rock type changes.

Contribution

It introduces a detailed comparison of numerical fluxes for two-phase flow and demonstrates cases where the upstream mobility flux fails to produce correct results.

Findings

Upstream mobility flux can give incorrect solutions when rock type changes.

The study highlights the importance of choosing appropriate fluxes in numerical simulations.

Godunov flux provides more accurate results in certain scenarios.

Abstract

When neglecting capillarity, two-phase incompressible flow in porous media is modelled as a scalar nonlinear hyperbolic conservation law. A change in the rock type results in a change of the flux function. Discretizing in one-dimensional with a finite volume method, we investigate two numerical fluxes, an extension of the Godunov flux and the upstream mobility flux, the latter being widely used in hydrogeology and petroleum engineering. Then, in the case of a changing rock type, one can give examples when the upstream mobility flux does not give the right answer.