Modeling imbibition in porous media using a two-dimensional network model

A two-dimensional network model of two-phase flow in a heterogeneous porous media consisting of two regions is implemented: a region of low-permeability with thin capillaries, surrounded by a region of high-permeability with thick capillaries. The case of capillary equilibrium being established as a result of countercurrent imbibition of a region is studied. Initially, the regions of high-permeability and low-permeability are saturated with wetting and non-wetting incompressible fluids, respectively. Numerical calculations based on this network model examining the dependence of saturation of wetting fluid with respect to time in the regions and the dependence of capillary pressure on the current saturation were performed. A qualitative agreement with known experimental and theoretical results has been obtained, which will further allow the model to be used to verify homogenized models of capillary nonequilibrium.