Effective dispersion in heterogeneous media under random transient flow conditions

Abstract

Under steady state flow conditions, solute dispersion in heterogeneous porous media is much smaller in the transverse than in the longitudinal direction. This holds particularly for effective dispersion of a plume originating from a point-like injection. The effective dispersion coefficient describes the actual dispersive mixing of solutes in the aquifer. The lack of dispersive transverse mixing may limit considerably natural attenuation of certain contaminants. Temporal fluctuations of the flow direction enhance horizontal transverse dispersion. This has been shown previously for uniform flow and for macrodispersion in stationary media. We present a linear stochastic theory for effective dispersion under quasi-steady state flow conditions with random temporal fluctuations of the mean flow direction. As for macrodispersion, effective transverse dispersion proves to be dominated by transient flow effects. We compare semianalytical results derived from linear theory to those from particle-tracking random-walk simulations for a three-dimensional test case. The parameters of the test case are similar to those obtained at the Borden site, where the mean transverse flow component fluctuated approximately by ±10°. Linear theory and particle simulations agree well.