Modeling solutal convection in porous media: from pore to Darcy scale

We model the transport process of convective carbon dioxide dissolution in porous media on both pore and Darcy scales. Numerical simulations of the Navier-Stokes equations are performed in a two-dimensional granular packing with constant porosity. We vary the driving force by changing the grain/pore size and the density difference to explore the effect of mechanical dispersion on the convective pattern and flux. We upscale the problem and then perform the Darcy-scale simulations with Fickian mechanical dispersion. The Darcy model reproduces both the trend in the convective pattern and quantitative fluxes of the pore-scale results, via adjusting the longitudinal dispersivity and the anisotropy of mechanical dispersion. Our simulations show the flux recovers a linear scaling with reduced coefficient as dispersion becomes dominant, consistent with the recent laboratory experiments. sHowever, sub-linear flux scaling arises either in a transitional regime where diffusion and dispersion are comparable or if grains become too coarse. In this case, the pore-scale simulations show that convective up- and downwellings arise in individual pores. This leads to additional mixing not accounted for in Fickian dispersion model on the Darcy scale. The buoyancy-driven pore-scale mixing observed here therefore has different characteristics from mixing processes in pressure-driven flows and requires a new approach to upscale them to the Darcy scale.