Temporal Evolution of Solute Dispersion in Three‐Dimensional Porous Rocks

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 pack, 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. The impact of medium structure and pore‐scale mass transfer mechanisms is probed by effective and ensemble dispersion coefficients. The former is a measure for the typical width of a plume, while the latter for the deformation, that is, the spread of a mixing front. Both dispersion coefficients evolve from the molecular diffusion coefficients toward a common finite asymptotic value. Their behavior is governed by the interplay between diffusion, pore‐scale velocity fluctuations and medium structure, which determine the characteristic mass transfer time scales. We find distinctly different dispersion behaviors in the two media, which can be traced back to how particles sample pore‐scale velocity variability and how this depends on the medium structure. These are key elements for the upscaling of transport, mixing and reaction from the pore to the continuum scale.