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. The application of our findings to the storage of carbon dioxide in a siliciclastic aquifer shows that while the reactive-diffusive layer can become unstable within a timescale of 1 to 1.5 months after the injection of carbon dioxide, it can take almost 10 months for sufficiently vigorous convection to produce a considerable increase in the dissolution flux of carbon dioxide.
Highlights
Motivated by the processes occurring during the geological storage of carbon dioxide in saline aquifers, we theoretically investigated the gravitational instability of a diffusive boundary layer in a porous medium in the presence of a precipitating chemical reaction
We discuss the effect of a first-order precipitation reaction on the growth rate of perturbations considering the dominant mode of a self-similar diffusion operator
We discuss the effect of a first-order precipitation reaction on the growth rate of considering the dominant mode of a self-similar diffusion operator
Summary
Motivated by the processes occurring during the geological storage of carbon dioxide in saline aquifers, we theoretically investigated the gravitational instability of a diffusive boundary layer in a porous medium in the presence of a precipitating chemical reaction. We compare the results of a linear stability analysis using three different methods, namely the dominant mode of a self-similar diffusion operator [6], an initial-value-problem approach [7], and a quasi-steady state assumption (QSSA) method [8] for a reactive-diffusive boundary layer in a porous medium where the product of a first-order reaction precipitates out from the system (Figure 1). We present the governing equations and the scaling for a reactive-diffusive boundary layer in a porous medium, along with the linear stability equations, .
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