Abstract
We study the temporal evolution of solute dispersion in three-dimensional porous rocks of different heterogeneity and pore structure. To this end, we perform direct numerical simulations of pore-scale flow and transport in a sand-like medium, which exhibits mild heterogeneity, and a Berea sandstone, which is characterized by strong heterogeneity as measured by the variance of the logarithm of the flow velocity. Solute dispersion is quantified by effective and ensemble dispersion coefficients. The former is a measure for the typical width of the plume, the latter for the deformation, that is, the spread of the mixing front. Both dispersion coefficients evolve from the molecular diffusion coefficients toward a common finite asymptotic value. Their evolution is governed by the interplay between diffusion, pore-scale velocity fluctuations and the medium structure, which determine the characteristic diffusion and advection time scales. Dispersion in the sand-like medium evolves on the transverse diffusion time across a characteristic streamtube diameter, which is the mechanism by which pore-scale flow variability is sampled by the solute. Dispersion in the Berea sandstone in contrast is governed by both the diffusion time across a typical streamtube, and the diffusion time along a pore conduit. These insights shed light on the evolution of mixing fronts in porous rocks, with implications for the understanding and modeling of transport phenomena of microbes and reactive solutes in porous media.