CONTACT BOUNDARY INSTABILITY GAS-LIQUID IN POROUS MEDIUM DURING FILTRATION WITHIN THE FRAMEWORK OF FORCHHEIMER’S LAW

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Abstract

The spectral (linear) stability of the solution obtained when considering the problem of displacement of a liquid layer by a gas in a porous medium is studied using the generalized nonlinear Forchheimer filtration law by the method of normal modes . Dispersion relations describing the growth of perturbations of the liquid-gas surface were obtained. These relations determine the evolution of perturbations at the linear stage of their development depending on the wavelength of the perturbation, parameters of boundary conditions and assumptions about the law of gas motion. It is shown that the use of the generalized nonlinear Forchheimer filtration law instead of Darcy’s law does not eliminate the anomalous nature of the dependence of the perturbation growth rate on the perturbation wavelength. The growth rate of the perturbation amplitude at the linear stage grows unboundedly with decreasingwavelength.

About the authors

V. A. Shargatov

Mathematical Institute named after V.A. Steklov RAS, Russia (V.A. Steklov Mathematical Institute, Russian Academy of Sciences)

Email: shargatov@mail.ru
Moscow, Russia

P. I. Kozhurina

Mathematical Institute named after V.A. Steklov RAS, Russia (V.A. Steklov Mathematical Institute, Russian Academy of Sciences)

Email: polinakozhurina2020@gmail.com
Moscow, Russia

S. V. Gorkunov

Mathematical Institute named after V.A. Steklov RAS, Russia (V.A. Steklov Mathematical Institute, Russian Academy of Sciences)

Email: gorkunov.ser@mail.ru
Moscow, Russia

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