Higher-Order Effects on Flow and Transport in Randomly Heterogeneous Porous Media

Abstract

Advective solute transport in nonuniform geologic media is generally nonlocal and non-Fickian [Neuman, 1993; Cushman and Ginn, 1993]. In statistically homogeneous log conductivity fields under uniform mean flow, the transport is expected to become asymptotically local and Fickian at late time. During the earlier preasymptotic regime, macrodispersivity (a measure of the rate at which a plume spreads) is expected to vary with solute residence time. A first-order (linear in the natural log hydraulic conductivity variance, σ²) analysis of this variation has been performed by Dagan [1984, 1987, 1988]. He found that, when local dispersion is neglected, the longitudinal macrodispersivity increases monotonically from zero toward a constant asymptote. However, the transverse macrodispersivity first increases from zero to a peak value, then decreases monotonically toward zero. The first-order asymptotic analyses by Winter [1982], Gelhar and Axness [1983] and Winter et al. [1984] also yield zero transverse macrodispersivity when local dispersion is disregarded.