Dynamical behaviour of miscibles fluids in porous media
by A. Assala; N. Djedaidi; F.Z. Nouri
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 8, No. 3, 2018

Abstract: In this paper, we are interested in studying the dynamics of miscible fluids in porous media. The model describing this issue is a system of equations, coupling the standard Navier-Stokes equations with gravity g as external force and a convective diffusion equation for a dilute concentration in the carrier fluid. By assuming that the fluids are incompressible, we first derive a new system of equations, by taking into account additional terms, due to the concentration inhomogeneties and an interfacial tension between the fluids. Then we propose a numerical approach to solve our system in order to illustrate the effectiveness of the dynamics during the fluid miscibility process. At this stage, we start by showing a stability result for our numerical scheme and then present numerical results.

Online publication date: Wed, 06-Dec-2017

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