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United States Department of Agriculture

Agricultural Research Service

Title: Modeling Solute Transport in Soil Columns Using Advective-Dispersive Equation with Fractional Spatial Derivatives

item San Jose Martinez, Fernando
item Pachepsky, Yakov
item Rawls, Walter

Submitted to: Advances in Engineering Software
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 12/1/2008
Publication Date: 2/18/2009
Citation: San Jose Martinez, F., Pachepsky, Y.A., Rawls, W.J. 2009. Modeling Solute Transport in Soil Columns Using Advective-Dispersive Equation with Fractional Spatial Derivatives. Advances in Engineering Software. 41(1):4-8.

Interpretive Summary: Different parts of soil pore water move with different velocities. Pollutants in forms of molecules or cells molecules or cells are transported by water, and therefore the distribution of pore water velocities strongly affects the pollutant transport. The currently used pollutant transport models assume that both very large and the very small pore water velocities are relatively rare as compared with the average velocity. Our analysis of experimental data on solute transport in soils shows that this assumption is violated in many cases. The explanation of this is that the pollutant transport models been developed based on experiments with relatively homogeneous porous media, such as sands. Soils have a hierarchical arrangement of particles in aggregates of different sizes. This creates more opportunities for both very slow and very fast pollutant transport. This work examines the new, fractional derivative-based model that has been suggested as a generalization of exiting models for hierarchically structured porous media. The literature on pollutant transport in soil was used to assemble a database of test cases. In about a half of cases, the new model is superior to the old one. For the same soil, the new model was giving better results when physical conditions created bigger differences between velocities of different parts of pore space, e.g. when soil was unsaturated It is suggested to use fractional model as the new general model of solute transport in soils.

Technical Abstract: It has been reported that this model cannot take into account several important features of solute movement through soil. Recently, a new model has been suggested that results in a solute transport equation with fractional spatial derivatives, or FADE. We have assembled a database on published solute transport experiments in soil columns to test the new model. The FADE appears to be a useful generalization of the ADE. The order of the fractional differentiation reflects differences in physical conditions of the solute transport in soil.

Last Modified: 06/22/2017
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