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Natural convection and the evolution of a reactive porous medium

Published online by Cambridge University Press:  17 February 2011

LINDSEY T. RITCHIE  and
DAVID PRITCHARD
LINDSEY T. RITCHIE*
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland, UK
DAVID PRITCHARD
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland, UK
*
†Email address for correspondence: lindsey.ritchie@strath.ac.uk
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Abstract

We describe a mathematical model of buoyancy-driven flow and solute transport in a saturated porous medium, the porosity and permeability of which evolve through precipitation and dissolution as a mineral is lost or gained from the pore fluid. Imposing a vertically varying equilibrium solubility creates a density gradient which can drive convective circulation. We characterise the onset of convection using linear stability analysis, and explore the further development of the coupled reaction–convection system numerically. At low Rayleigh numbers, the effect of the reaction–permeability feedback is shown to be destabilising through a novel reaction–diffusion mechanism; at higher Rayleigh numbers, the precipitation and dissolution have a stabilising effect. Over longer time scales, reaction–permeability feedback triggers secondary instabilities in quasi-steady convective circulation, leading to rapid reversals in the direction of circulation. Over very long time scales, characteristic patterns of porosity emerge, including horizontal layering as well as the development of vertical chimneys of enhanced porosity. We discuss the implications of these findings for more comprehensive models of reactive convection in porous media.

JFM classification

Convection: Convection in porous media Geophysical and Geological Flows: Geophysical and Geological Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 673 , 25 April 2011 , pp. 286 - 317
Copyright
Copyright © Cambridge University Press 2011

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