Macrodispersion of sorbing solutes in heterogeneous porous formations with spatially periodic retardation factor and velocity field

Abstract

Expressions for the macroscopic velocity vector and dispersion tensor for sorbing solute transport in heterogeneous porous formations whose hydrogeologic properties are repeated at intervals were derived via Taylor‐Aris‐Brenner moment analysis. An idealized three‐dimensional porous formation of infinite domain with spatially periodic retardation factor, velocity field, and microdispersion coefficients in all three directions was considered. Sorption was assumed to be governed by a linear equilibrium isotherm under local chemical equilibrium conditions. The analytical expressions presented are based on a perturbation method where all of the spatially periodic parameters employed were assumed to have “small” fluctuations. It was shown that the effective velocity vector is given by the volume‐averaged interstitial velocity vector divided by the volume‐averaged retardation factor, and the effective dispersion dyadic (second‐order tensor) is given by the volume‐averaged microdispersion dyadic divided by the volume‐averaged dimensionless retardation factor plus a dyadic expressing the increase in solute spreading caused by the spatial variability of the parameters.