Instability of Gas–Liquid Interface in Porous Media Flow Governed by Forchheimer’s Law

The generalized nonlinear Forchheimer law and the normal mode method are used to analyze the spectral (linear) stability of the solution for the displacement of a liquid layer by a gas in a porous medium. Dispersion relations describing the growth of liquid–gas interface perturbations are obtained. These relations determine the linear stage of the evolution of the perturbations depending on the perturbation wavelength, parameters of boundary conditions, and the assumptions about the law of gas motion. It is shown that the anomalous dependence of the perturbation growth rate on the perturbation wavelength cannot be eliminated by replacing Darcy’s law with the generalized nonlinear Forchheimer law. The growth rate of the perturbation amplitude in the linear stage increases indefinitely with decreasing wavelength.