Mathematical Problems in Engineering
Volume 2005 (2005), Issue 6, Pages 641-661

Characterization of the speed of a two-phase interface in a porous medium

Adil Abbassi and Gawtum Namah

Laboratoire Mathématiques de Besançon, UMR 6623 CNRS, Université de Franche-Comté, 16 route de Gray, Besançon Cedex 25030, France

Received 8 November 2004; Revised 15 February 2005

Copyright © 2005 Adil Abbassi and Gawtum Namah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A typical situation of oil reservoir simulation is considered in a porous medium where the resident oil is displaced by water injection. An explicit expression of the speed of the oil-water interface is given in a pseudo-2D case via the resolution of an auxiliary Riemann problem. The explicit 2D solution is then corroborated with numerical simulations by solving the transport equation with a generalized scheme of Harten type.