Analysis of the anomalous scale-dependent behavior of dispersivity using straightforward analytical equations: Flow variance vs. dispersion Page: 16 of 34
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phenomenon have been developed. For example, Domenico and Robbins 
demonstrate that using an (n-1)-dimensional model to model an n-dimensional
physical system will introduce a dispersivity scale effect. Davis [19861
demonstrates that the scale effect is a mathematical result of representing
aquifer properties as mean values. The emerging consensus carries the concept
of aquifer properties further; for example Smith and Schwartz  conclude
that macroscopic dispersion results from large-scale spatial variations in
hydraulic conductivity and that the use of large dispersivity values and
uniform flow fields is an inappropriate description of transport of solutes
in subsurface geological systems.
As discussed in Konikow and Mercer , numerous investigators have
provided insights to place on firmer ground the largely intuitive concept of
spatial heterogeneity impacting apparent dispersivity. Gelhar and others
have developed robust numerical methods that describe dispersion in a randomly
varying porous medium using the Fourier transform [Gelhar et al., 1979;
Matheron and de Marsily, 1980; Gelhar and Axeness, 1983; Dieulin et al.,
1981]. Statistical and Green's functions [Dagan, 1984; Jury, 1982; Jury
et al., 1986], Monte Carlo methods [Schwartz, 1977; Smith and Schwartz, 19801,
and random walk methods [Dagan, 19821 have also been applied to porous media.
Results from describing fractured rock flow systems as networks suggest that
fractured media do not behave as an equivalent continuum [Long et al., 1982;
Robinson, 1983; Schwartz et al., 1983; Endo et al., 1984; Long and
Witherspoon, 1985; Rasmussen et al., 1985; Andersson and Dverstorp, 19871.
Some investigators have viewed subsurface media as a system of separate
channels, tubes, or strata in which flow proceeds independently at different
speeds [Neretricks, 1984; Molz, 19861. A large number of the techniques
described above, along with the model described herein, are predicated
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Looney, B. B. & Scott, M. T. Analysis of the anomalous scale-dependent behavior of dispersivity using straightforward analytical equations: Flow variance vs. dispersion, report, Spring 1988; Aiken, South Carolina. (https://digital.library.unt.edu/ark:/67531/metadc684121/m1/16/: accessed May 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.