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United States Department of Agriculture

Agricultural Research Service


item San Jose Martinez, Fernando
item Pachepsky, Yakov

Submitted to: American Geophysical Union
Publication Type: Abstract Only
Publication Acceptance Date: 9/18/2006
Publication Date: 12/11/2006
Citation: San Jose Martinez, F., Pachepsky, Y.A. 2006. Fractional solute transport equation evaluated with the miscible displacement experimental data. American Geophysical Union, December 11-15, 2006, San Francisco, CA. 0800h:H21C-1387.

Interpretive Summary:

Technical Abstract: A new solute transport model has been recently developed assuming that the movements of solute particles in hierarchically-structured porous media belongs to the family of Lévy motions rather than to the Brownian motion. The one-dimensional fractional advective-dispersive transport equation, or FADE, has been derived that had used fractional derivatives to describe the solute dispersion caused by Lévy motions. Compared with the common advective-dispersive equation (ADE), the FADE includes an additional parameter ' which serves as the order of fractional derivatives in this equation. The ADE is the specific case of FADE when '=2. Our objective was to test the FADE applicability to soils. We have assembled a database that presented a random sample from published experiments on conservative tracer transport in soil columns and field soils, and evaluated the FADE as a transport model in comparison with ADE. Overall, the FADE, as a general model that included the ADE as a specific case, accurately simulated experimental tracer breakthrough in soil columns. When ratios of effluent concentrations and input concentration were used to express the breakthrough curves (BTC), 31 out of 53 BTCs were fitted with the RMSE less than 0.019, and the largest RSME was 0.072. Of 53 experimental BTCs considered, 28 were better fitted with ' smaller than 2, i.e. with the FADE, and 25 BTCs were best fitted with ' = 2, i.e. with the classical ADE. Trends of the increase in values of ' with the increase in saturation and in flow velocity have been observed for the same soils. Because FADE is better suited to simulate long tails of breakthrough curves compared with the ADE, the fractional advective-dispersive equation as a generalization of classical advective-dispersive equation may be a useful addition to the contaminant hydrology toolbox.

Last Modified: 05/22/2017
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