Onset of convection in a porous medium in the presence of chemical reaction

Abstract

Using scaling, we show that the stability of a buoyant boundary layer in a porous medium in the presence of a first-order chemical reaction is fully determined by the nondimensional number Da/Ra(2)=k(r)aDϕμ(2)/(kΔρ(0)g)(2), where Da=k(r)aL(Z)(2)/k(r)aL(Z)(2)(Dϕ) is the Damköhler number and Ra=kΔρ(0)gL(Z)/kΔρ(0)gL(Z)(μDϕ) is the solutal Rayleigh number. The time for onset of convection is shown to increase with rising Da/Ra(2). Above a critical Da/DaRa(2)≈2×10(-3) Ra(2)≈2×10(-3), no convection occurs as reaction stabilizes the diffusive layer at a finite thickness. This thickness decreases with increasing Da/Ra(2), becoming zero at Da/Ra(2)≈O(1). As applied to CO(2) geostorage, our results suggest distinct regimes for CO(2) transport in saline aquifers.