Nonequilibrium Effects in Immiscible Two-Phase Flow

Two-dimensional, high-resolution, numerical solutions for the classical formulation and two widely accepted nonequilibrium models of multiphase flow through porous media are generated and compared. Flow equations for simultaneous flow of two immiscible phases through porous media are written in a vorticity stream-function form. In the resulting system of equations, the vorticity stream-function equation is solved using a spectral method and the transport equation is discretized in space using a central-upwind scheme. A semi-implicit time-stepper is used to solve the coupled system of equations. The solutions reveal that inclusion of dynamic capillary pressure sharpens the front and lengthens the viscous fingers. The inclusion of nonequilibrium effects in constitutive relations introduces diffusion and smears the otherwise highly resolved viscous fingers in the saturation front.