A quasi‐linear theory of non‐Fickian and Fickian subsurface dispersion: 2. Application to anisotropic media and the Borden site

Abstract

When the quasi‐linear theory developed in paper 1 is applied to anisotropic media it shows, in contrast to the isotropic case, that longitudinal and transverse dispersivities may become asymptotically proportional to σY when the log hydraulic conductivity variance σY2 is much smaller than 1. It further implies, among other phenomena, that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the long axis of a plume is generally offset toward the direction of the largest log hydraulic conductivity correlation scale; when μ is at 45° to the bedding in strongly stratified media, the longitudinal axis is nearly parallel to the bedding under non‐Fickian conditions. As Fickian conditions are approached, the plume rotates toward μ and stabilizes asymptotically at a relatively small angle of deflection depending on σY2. Application of the quasi‐linear theory to depth‐averaged concentration data from a tracer experiment at Borden, Ontario, yields a consistent and improved fit to a two‐dimensional model without any need for parameter adjustment. Three‐dimensional models are shown to be in fundamental conflict with observed behavior at Borden and in other stratified formations; we show that, in principle, this conflict is easy to resolve by accounting for local hydraulic anisotropy.