Pore-scale modeling of transverse dispersion in porous media

Abstract

A physically based description is provided for the transverse dispersion coefficient in porous media as a function of Péclet number, Pe. We represent the porous medium as lattices of bonds with square cross section whose radius distribution is the same as computed for Berea sandstone and describe flow (Stokes equation) and diffusion (random walk method) at the pore scale (∼μm) to compute the transverse dispersion coefficient at a larger scale (∼cm to ∼m). We show that the transverse dispersion coefficient DT∼ Pe for all Pe ≫ 1. A comprehensive comparative study of transverse dispersion with experiment indicates that the model can successfully predict the trends for the asymptotic macroscopic dispersion coefficient over a broad range of Péclet numbers, 0 < Pe < 105. We discuss the relation between transverse and longitudinal dispersion coefficient and show that unless one studies solute transport in the advection dominated regime, it is not appropriate to take DTto be 1 order of magnitude less than DL. Copyright 2007 by the American Geophysical Union.