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

You‐Kuan ‐K Zhang, Shlomo P Neuman

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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 σY 2 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 σY 2. 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.

Original languageEnglish (US)
Pages (from-to)903-913
Number of pages11
JournalWater Resources Research
Volume26
Issue number5
DOIs
Publication statusPublished - 1990
Externally publishedYes

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ASJC Scopus subject areas

  • Water Science and Technology

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