Analysis of the anomalous scale-dependent behavior of dispersivity using straightforward analytical equations: Flow variance vs. dispersion Page: 5 of 34
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INTRODUCTION AND SUMMARY
Development of mathematical models that accurately describe the transport
of solutes in saturated and unsaturated porous media is an integral part in
the assessment of the location and management of new and existing waste
disposal facilities, as well as an important element in our fundamental
understanding of geochemistry and diagenesis in the subsurface. A large
number of computational algorithms are available to describe the behavior of
solutes in subsurface flow systems. These range from direct solutions of
governing equations based on assumed initial and boundary conditions to
numerical finite element and finite difference methods. Despite the apparent
diversity of methods, the various algorithms almost exclusively rely on the
same governing equation--the advection and dispersion equation. Critical
evaluation of this equation is important, affecting most of the available
models. From a practical standpoint, any deficiencies identified should be
put into perspective (i.e., how significant are differences between the model
predictions and field measurements). Also, alternate methods, or the general
path toward these methods, should be identified.
Recent data on laboratory- and field-scale dispersivity measurements
[Silliman and Simpson, 1987; Gelhar et al., 1985; Moltz et al., 19861
document a phenomenon that is not consistent with the advection and dispersion
approach; measured dispersivity values are a function of the measurement scale
rather than a constant value. A variety of explanations have been developed
for this phenomenon [Gelhar et al., 1985; Molz et al., 1986; Dagan, 1987;
Greenkorn and Cala, 1986; Russo and Bresler, 1982; Konikow and Mercer, 1988;
and Domenico and Robbins, 19841. A consensus among the various investigators
is emerging, however. Many geohydrologists and modelers attribute the effect
to the heterogeneity found in the subsurface flow systems and the stochastic
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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/m1/5/: accessed May 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.