Mathematical Problems in Engineering 
Volume 2005 (2005), Issue 6, Pages 641-661
doi:10.1155/MPE.2005.641

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

Abstract

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.