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

H Alhumade,J Azaiez

doi:10.1155/2015/920692

Abstract

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.

Highlights

Instability at the interface between flowing solutions in porous media can be triggered as a result of viscosities and/or densities mismatch between the fluids
In 1992, Rogerson and Meiburg carried out a linear stability analysis to investigate the interface of a nonreactive system with densities and viscosities mismatch in porous media where both normal and tangential velocities can be present [7]
The numerical code was validated by comparing the time evolution and the related finger structures for the case where the chemical reaction is complete (α = 0) with those presented by Hejazi and Azaiez [24] for the nonreversible case

Summary

Introduction

Instability at the interface between flowing solutions in porous media can be triggered as a result of viscosities and/or densities mismatch between the fluids. This instability develops in the form of intruding fingers and is referred to as viscous fingering or Saffman-Taylor instability in the case of viscosities mismatch or as density fingering or RayleighTaylor instability in the case of densities mismatch between the fluids [1,2,3,4,5]. An analytical expression for the growth of instability in a nonreactive system with variation in viscosities and densities was derived by Bacri et al [6]. In 1992, Rogerson and Meiburg carried out a linear stability analysis to investigate the interface of a nonreactive system with densities and viscosities mismatch in porous media where both normal and tangential velocities can be present [7]. The authors found that a stable viscous interface between the fluids can break the symmetry of the buoyancy-driven instability by acting as a barrier against the upward growth of instability

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