We quantify the destabilising effect of a first-order chemical reaction on the fingering instability of a diffusive boundary layer in a porous medium. Using scaling, we show that the dynamics of such a reactive boundary layer is fully determined by two dimensionless groups: Da/Ra, which measures the timescale for convection compared to those for reaction and diffusion; and β/β, which reflects the density change induced by the product relative to that of the diffusing solute. Linear stability and numerical results for β/β in the range 0-10 and Da/Ra in the range 0-0.01 are presented. It is shown that the chemical reaction increases the growth rate of a transverse perturbation and favours large wavenumbers compared to the inert system. Higher β/β and Da/Ra not only accelerate the onset of convection, but crucially also double the transport of the solute compared to the inert system. Application of our findings to the storage of carbon dioxide in carbonate saline aquifers reveals that chemical equilibrium curtails this increase of CO flux to 50%.

We investigate the effects of a dissolution reaction, A(aq) + B(s) → C(aq), on the gravitational instability and nonlinear dynamic behaviour of a diffusive boundary layer in a porous medium. Our linear stability and numerical results reveal that, unexpectedly, even when the density contribution of the soluble product C is smaller than that of the dissolved solute A, the chemical reaction can destabilize the layer and accelerate the onset of convection. However, for a very light product, the reaction stabilizes the layer. We show that these widely disparate characteristics of the reactive-diffusive layer are outcomes of the nonlinear competition between two reaction effects, the destabilizing sharpening of the solute concentration gradient and associated increase in the solute diffusive flux, and the stabilizing replacement of the solute by a less dense product near the interface.

Abstract:Reactive convection in a porous medium has received recent interest in the context of the geological storage of carbon dioxide in saline formations. We study theoretically and numerically the gravitational instability of a diffusive boundary layer in the presence of a first-order precipitation reaction. We compare the predictions from normal mode, linear stability analysis, and nonlinear numerical simulations, and discuss the relative deviations.