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Mathematical Problems in Engineering
Volume 2015, Article ID 920692, 13 pages
Research Article

Numerical Simulations of Gravity Driven Reversible Reactive Flows in Homogeneous Porous Media

1Department of Chemical Engineering, The University of Waterloo, Waterloo, ON, Canada N2L 3G1
2Department of Chemical and Petroleum Engineering, The University of Calgary, Calgary, AB, Canada T2N 1N4

Received 1 April 2015; Accepted 9 June 2015

Academic Editor: Junwu Wang

Copyright © 2015 H. Alhumade and J. Azaiez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The effect of reversibility on the instability of a miscible vertical reactive flow displacement is examined. A model, where densities and/or viscosities mismatches between the reactants and the chemical product trigger instability, is adopted. The problem is governed by the continuity equation, Darcy’s law, and the convection-diffusion-reaction equations. The problem is formulated and solved numerically using a combination of the highly accurate spectral methods based on Hartley’s transform and the finite-difference technique. Nonlinear simulations were carried out for a variety of parameters to analyse the effects of the reversibility of the chemical reaction on the development of the flow under different scenarios of the frontal instability. In general, faster attenuation in the development and growth of the instability is reported as the reversibility of the chemical reaction increases. However, it was observed that reversibility is capable of triggering instability for particular choices of the densities and viscosities mismatches. In addition, the effect of the reversibility in enhancing the instability was illustrated by presenting the total relative contact area between the reactants and the product.