The geologic architecture in sedimentary reservoirs affects the behavior of density-driven flow and the dispersion of CO2-rich brine. The spatial organization and connectivity of facies types play an important role. Low-permeability facies may suppress fingering and reduce vertical spreading, but may also increase transverse mixing. This is more pronounced when geologic structures create preferential flow pathways through connected facies types. We perform high-resolution simulations of three-dimensional (3D) heterogeneous formations whose connectivity cannot be represented in two-dimensional models consistent with percolation theory. This work focuses on the importance of 3D facies-based heterogeneity and connectivity on advection-diffusion transport of dissolved CO2. Because the dissolution of CO2 and the subsequent density increase of brine are the driving force for gravitational instabilities, we model the phase behavior with the accurate cubic-plus-association equation-of-state, which accounts for the self-association of polar water molecules and the cross-association between CO2 and water. Our results elucidate how the spatial organization of facies affects the dynamics of CO2 convective mixing. Scaling relations for the evolution of a global dispersion-width provide insights that can be universally applied. The results suggest that the long-term evolution and scaling of dispersion are surprisingly similar for homogeneous and (binary and multiscale) heterogeneous porous media.