Dispersion in Flow through Porous Media

Abstract

ABSTRACT Dispersion is a consequence of flow. It results from the different paths and speeds and the consequent range of transit times available to tracer particles convected across a permeable medium. The kinematic mechanism stems from the connectivity structure of porespace; the dynamic mechanism, from the effect of pore shape and size on flow. Molecular diffusion can modify both. In many circumstances these mechanisms lead to distributions of macroscopic average solute or tracer concentration that are diffusive, i.e. that can be modeled by the convective diffusion equation, dispersion coefficients taking the role of diffusivity. For cases of diffusive mixing locally at pore junctions and no appreciable diffusion between, a simple network approximation is appropriate. Square and simple cubic networks of variable pore segments, with average flow in one of the pore directions, are useful idealizations. Dispersion in one– and two–phase flow through these networks is studied here by the Monte Carlo strategy of replicated computer experiments. This strategy combined, with considerable computational savings, with the percolation theory of fluid distributions in two-phase flow. Network topology and pore geometry and thus the two basic mechanisms are precisely controlled. The results show that dispersion is diffusive in the cases simulated. Longitudinal (mean flow direction) dispersivity is an order of magnitude greater than dispersivity in transverse directions. In two-phase flow, longitudinal dispersivity in a given phase rises greatly as the saturation of that phase approaches residual, i.e. its percolation threshold; transverse dispersivity also increases, but more slowly. As the threshold is neared, the backbone of the subnetwork occupied by the phase becomes increasingly tortuous, with local mazes spotted along it that are highly effective dispersers. All of the findings accord qualitatively with most available data, except that dispersivities in reality are not constant but increase slowly with macroscopic average flow rate, which may stem from molecular diffusion that is lost from the network approximation used.