Title: Dynamical behaviour of miscibles fluids in porous media

Authors: A. Assala; N. Djedaidi; F.Z. Nouri

Addresses: Mathematical Modeling and Numerical Simulation Laboratory, Faculty of Sciences, Badji Mokhtar University, BP 12, Annaba, Algeria ' Mathematical Modeling and Numerical Simulation Laboratory, Faculty of Sciences, Badji Mokhtar University, BP 12, Annaba, Algeria ' Mathematical Modeling and Numerical Simulation Laboratory, Faculty of Sciences, Badji Mokhtar University, BP 12, Annaba, Algeria

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.

Keywords: finite elements; fluid dynamics; porous media; stability.

DOI: 10.1504/IJDSDE.2018.092664

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.3, pp.176 - 189

Received: 14 Dec 2016
Accepted: 26 May 2017
Published online: 27 Jun 2018 *

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