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

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/Ra²=kᵣaDφμ²/(kΔρ₀g)², where Da=kᵣaLZ²/kᵣaLZ²(Dφ) is the Damk\"ohler number and Ra=kΔρ₀gLZ/kΔρ₀gLZ(μDφ) is the solutal Rayleigh number. The time for onset of convection is shown to increase with rising Da/Ra². Above a critical $Da/Da{Ra}²{≈}2×{}{10}^{{-}3} {Ra}²{≈}2×{}{10}^{{-}3}$, 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.