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United States Department of Agriculture

Agricultural Research Service

Title: The advective-dispersive equation with spatial fractional derivatives as a model for tracer transport in structured soil)

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

Submitted to: Vadose Zone Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/13/2008
Publication Date: 1/5/2009
Publication URL:
Citation: San Jose Martinez, F., Pachepsky, Y.A., Rawls, W.J. 2009. The advective-dispersive equation with spatial fractional derivatives as a model for tracer transport in structured soil. Vadose Zone Journal. 8:242-249.

Interpretive Summary: The accuracy of modeling contaminant transport in soils is critical in addressing many environmental issues, and in particular, groundwater and produce quality. Evidence has accumulated that the commonly used convective dispersive transport model does not simulate transport adequately in some cases. We have previously proposed the fractional convective dispersive model as a more general, physically based model of contaminant transport in structured porous media such as soils. The objective of this work was to evaluate this model using a collection of literature data on chemical transport in soil columns. We found that in 50% of cases the fractional convective dispersive model was more accurate than the traditional convective dispersive model, and in the rest of the cases the fractional model automatically reduced to the traditional convective dispersive model. These finding are important for researchers and practitioners dealing with the contaminant transport in soils in that the fractional convective dispersive transport model can give more accurate predictions of contaminant transport in soils.

Technical Abstract: The classical model to describe solute transport in soil is based on the advective-dispersive equation where Fick’s law is used to explain dispersion. From the microscopic point of view this is equivalent to consider that the motion of the particles of solute may be simulated by the Brownian motion. Since the beginning of the introduction of these types of models discrepancies between experimental and predicted data have been reported. During the last decade of the twenty century a new model to describe the motion of the solute particles was proposed: the Lévy flights. This allows describing non-Fickian dispersion through fractional derivatives: the fractional advective-dispersive equations. This model includes, as a particular case, the classical advective-dispersive equation, as the Brownian motion is a particular case of Lévy flights. The goal of this work was to evaluate and to compare these fractional models with theirs classical counterpart with published data of solute transport in soil columns. We observed that fractional models apresent a broad framework that includes the classical advective dispersive equation adequately simulate the experimental dataset on tracer migration through soil columns examined in this work.

Last Modified: 8/24/2016
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