Filtration of Highly Miscible Liquids Based on Two-Scale Homogenization of the Navier-Stokes and Cahn-Hilliard Equations
V. V. Shelukhin1, V. V. Krut'ko2, K. V. Trusov3
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
2Gazpromneft NTT, St. Petersburg, Russia
3Novosibirsk National Research State University, Novosibirsk, Russia
Keywords: Navier-Stokes equations, Cahn-Hilliard equations, filtration of miscible liquids, two-scale homogenization
Abstract
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.
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