  Natural convection in porous media is a fundamental process for the long-term
storage of CO2 in deep saline aquifers. Typically, details of mass transfer in
porous media are inferred from the numerical solution of the volume-averaged
Darcy-Oberbeck-Boussinesq (DOB) equations, even though these equations do not
account for the microscopic properties of a porous medium. According to the DOB
equations, natural convection in a porous medium is uniquely determined by the
Rayleigh number. However, in contrast with experiments, DOB simulations yield a
linear scaling of the Sherwood number with the Rayleigh number (Ra) for high
values of Ra (Ra>>1,300). Here, we perform Direct Numerical Simulations (DNS),
fully resolving the flow field within the pores. We show that the boundary
layer thickness is determined by the pore size instead of the Rayleigh number,
as previously assumed. The mega- and proto- plume sizes increase with the pore
size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at
high porosity, and for the same Rayleigh number, higher Sherwood numbers are
predicted by DNS at lower porosities. It can be concluded that the scaling of
the Sherwood number depends on the porosity and the pore-scale parameters,
which is consistent with experimental studies.
