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United States Department of Agriculture

Agricultural Research Service

Title: Simulating Scale-Dependent Solute Transport in Soils with the Fractional Advective-Dispersive Equation

Authors
item Pachepsky, Yakov - DUKE UNIVERSITY
item Benson, David - DESERT RESEARCH INSTITUTE
item Rawls, Walter

Submitted to: Soil Science Society of America Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: January 24, 2000
Publication Date: July 1, 2000

Interpretive Summary: The anomalous transport of solutes can be an important phenomenon to consider in estimations of the fate of agricultural chemicals. As the dispersivity grows with depth, the spread of the solute concentrations can be larger than that estimated from data within a soil profile. There may be a potential for chemicals to travel into and within the vadose zone faster than expected from their movement in upper parts of the soil profiles. The anomalous transport of solutes in soils was satisfactorily simulated with the fractional advective dispersive model. The advantage of the fractional advective dispersive model to describe solute transport in soils is the separation of scale effects from the transport coefficients.

Technical Abstract: The advective-dispersive equation (ADE) is the first solute transport model widely and successfully used for soils. Results of ADE applications show that this model may not satisfactorily describe several important features of solute transport in soils. First, the dispersivity tends to increase as the length of a soil column or the soil depth increases. Second, breakthrough curves of non-reactive solutes may have shapes different from those predicted with the ADE so that the solute remains in the soil longer or leaves the soil faster than the ADE suggests. These problems can be addressed with a physical model assuming that the increments in the random movement of solute particles is not Gaussian and belongs to the family of so called Levy distributions. The objective of this paper was to test applicability of the ADE and fractional advective dispersive equation (FADE) to solute transport in soils and to compare results of the applications. The FADE can be solved using finite differences and also ha an analytical solution. This solution, together with the solution of the classical ADE, was fitted to the data from experiments on chloride transport in sand and in structured clay soil. The FADE model simulated tails on the breakthrough curves and column length effects better than or similar to the ADE model. The advantage of using FADE to describe solute transport in soils is the separation of the scale effect from the values of the transport coefficients. The scale effects are reflected by the exponent of the fractional derivative, and the transports coefficients need to be found at only one scale.

Last Modified: 7/30/2014
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