Transient diffusive boundary layers in heterogeneous porous media

The onset of convection of gravitationally unstable transient, diffusive boundary layers in saline aquifers has been extensively investigated due to its importance in carbon dioxide sequestration. However, due to theoretical complexities, the onset of convection in heterogeneous porous media with span-wise variation in permeability (varying crosswise to direction of gravity) has been relatively less explored. Unlike homogeneous porous media, we demonstrate that the onset of convection in such heterogeneous media is simultaneously triggered by a combination of several individual span-wise perturbation modes. Using a combination of linear stability analysis and numerical simulations, we obtain the dominant two dimensional global perturbation structures for different spatially varying permeability fields. We compare our results with previous literature for homogeneous porous media, and conclude whether the onset of convection in heterogeneous media is enhanced or delayed.