Relative Permeabilities for Strictly Hyperbolic Models of Three-Phase Flow in Porous Media |
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Authors: | Juanes Ruben Patzek Tadeusz W |
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Institution: | (1) Institute of Mechanics, Moscow State Lomonosov University, Michurinsky pr. 1, 119192 Moscow, Russia;(2) Instituto Nacional de Matem?tica Pura e Aplicada – IMPA, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro, RJ, Brazil |
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Abstract: | Traditional mathematical models of multiphase flow in porous media use a straightforward extension of Darcys 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. |
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Keywords: | three-phase flow relative permeability hyperbolic system conservation laws elliptic regions Oak experiments |
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