Traditional mathematical models of multiphase flow in porous media use a straightforward extension of Darcy's equation. The key element of these models is the appropriate formulation of the relative permeability functions. It is well known that for one-dimensional flow of three immiscible incompressible fluids, when capillarity is neglected, most relative permeability models used today give rise to regions in the saturation space with elliptic behavior (the so-called elliptic regions). We believe that this behavior is not physical, but rather the result of an incomplete mathematical model. In this paper we identify necessary conditions that must be satisfied by the relative permeability functions, so that the system of equations describing three-phase flow is strictly hyperbolic everywhere in the saturation triangle. These conditions seem to be in good agreement with pore-scale physics and experimental data.
|Original language||English (US)|
|Number of pages||28|
|Journal||Transport in Porous Media|
|State||Published - Nov 2004|
Bibliographical noteFunding Information:
We are grateful to Dr Dmitriy Silin for numerous insightful suggestions and his careful review of the manuscript. We also thank Prof Martin Blunt for his comments and the vigorous discussion on elliptic regions, and for providing an electronic version of Oak’s relative permeability data. This work was supported by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under the Department of Energy Contract No. DE-AC03-76SF00098. Funding provided by Barrié de la Maza, Jane Lewis, and Repsol-YPF fellowships, awarded to the first author, is also gratefully acknowledged.
- Conservation laws
- Elliptic regions
- Hyperbolic system
- Oak experiments
- Relative permeability
- Three-phase flow
ASJC Scopus subject areas
- Chemical Engineering(all)