THE CLOSURE PROBLEM FOR 2-PHASE FLOW IN HOMOGENEOUS POROUS-MEDIA

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 tenser fields. In this paper we show how the original closure problem is transformed to one containing Stokes'-like equations that can be solved to determine the two permeability tensors and the two viscous drag tensors. The permeability tensors, K-beta and K-gamma 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-beta gamma and K-gamma beta, are found to be constrained by K-beta gamma . K-gamma beta = 0(I).