Convective dissolution in porous media

Motivated by the geological storage of buoyant carbon dioxide (CO$_2$) we investigate dissolution of CO$_2$ into brine which increases security of storage over time. The rate of CO$_2$ dissolution is determined by convection in the brine driven by the increase of brine density with CO$_2$ saturation. We present a new analogue fluid system that reproduces the nonlinear density behaviour of CO$_2$ and brine. We show that the convective flux is proportional to the Rayleigh number to the $4/5$ power through a combination of laboratory experiments and high-resolution numerical simulations, in contrast with a classical linear relationship. This relationship allows us to extrapolate from the laboratory scale to geophysical scales. A scaling argument that incorporates the effect of the large-scale flow on mixing at the CO$_2$-brine interface confirms this nonlinear relationship for the convective flux and provides a physical picture of high Rayleigh number convection in a porous medium. The resultant model makes quantitative predictions of the CO$_2$ dissolution rates in natural and anthropogenic CO$_2$ accumulations. For example, at the Sleipner field we estimate a dissolution rate of roughly 10\% of the annual injected mass suggesting that storage security is significantly enhanced.