The closure problem for two-phase flow in homogeneous porous media

Abstract

In a previous study of two-phase flow in homogeneous porous media, the closure problem was presented in terms of a pair of boundary value problems involving four integro-differential equations for second-order tensor fields. In this paper we show how the original closure problem is transformed to one containing Stoke's-like equations that can be solved to determine the two permeability tensors and the two viscous drag tensors. The permeability tensors, K β and K γ, are symmetric, exhibit a clear dependence on the volume fractions of the two phases, and may depend on the ratio of viscosities. On the basis of order of magnitude analysis, the coupling, or viscous drag tensors, K βγ and K γβ, are found to be constrained by K βγ K γβ = O(1).