MOMENTUM-TRANSFER ACROSS FLUID-FLUID INTERFACES IN POROUS-MEDIA - A NETWORK MODEL

Two-phase flow in porous media is described based on the extended form of Darcy's law, which ignores momentum transfer at fluid-fluid interf aces. Two forms of corrections to this simple description have been pr oposed in the literature: one on the relative permeability dependence on viscosity ratio; the other on the velocities assumed to be proporti onal to both phase pressure gradients and so introducing an additional saturation-dependent cross coefficient. In this article, to identify the correct form of transport equations, a simple cubic network model of 30 x 30 x 30 bonds is used. The cross section of the bonds is that of a four-cusp duct. The fluid interface in each duct is located by ca pillary equilibrium. The duct hydraulic conductances are then obtained as a function of viscosity ratio and phase volume fraction using a fi nite element calculation. These individual duct results are used in th e network calculations for which a percolation algorithm is applied to simulate nonwetting phase displacing wetting phase, a process also kn own as initial drainage. Flow calculations show that both the nonwetti ng-phase relative permeability and the cross coefficient are strong fu nctions of saturation and viscosity ratio. Also, the off-diagonal term s may contribute to a nonnegligible fraction of the flow. The proposed generalization of the Darcy equations is applicable to all problems i nvolving multiphase flow in porous media. The current practices for re lative permeability measurements and reservoir simulation may have to be reexamined in the context of the proposed transport equations.