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STABILITY AND WIDTH OF REACTION FRONTS IN 3-D POROUS MEDIA

Volume 15, Issue 12, 2012, pp. 1093-1103
DOI: 10.1615/JPorMedia.v15.i12.20
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ABSTRACT

Transport of reactive fluids in porous media may form reaction fronts−narrow zones where the reaction takes place. We derive approximate solutions for the change in concentration and porosity across the front zone. These solutions are used to derive a condition for reaction fronts to be narrow. Reaction fronts tend to be unstable, and they often show a fingered growth into the porous medium. A criterion for the stability of sharp reaction fronts in a 3-D homogeneous porous medium is derived using linear stability analysis. The criterion gives that a perturbation of a flat reaction front of any wavelength becomes unstable if the permeability behind the front increases. The front instability grows faster for short wavelengths than for long wavelengths. Similarly, the perturbations of the front will die out if the permeability behind the front decreases, and short-wavelength perturbations will die out faster than long-wavelength perturbations. Front stability and the stability criterion are demonstrated with numerical examples where the fronts are narrow but not sharp.

CITED BY
  1. Nield Donald A., Bejan Adrian, Geophysical Aspects, in Convection in Porous Media, 2017. Crossref

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