Filtration of highly miscible liquids based on two-scale homogenization of the Navier–Stokes and Cahn–Hilliard equations

This paper presents the results of numerical analysis of the filtration equations for highly miscible liquids obtained by two-scale homogenization of the Navier–Stokes and Cahn–Hilliard equations for two-dimensional flows. It is shown that the permeability tensor is generally anisotropic. For one-dimensional flows, the miscibility dynamics is investigated, and it is shown that the displacement of one phase by injection of another phase can occur even in the absence of a pressure gradient in the sample.