Comparing the Fractional and the Classical Solute Transport Equations with Data on Solute Breakthrough in Soil Columns

摘要

Solute transport in soils and sediments is commonly simulated with the parabolic advective-dispersive equation, or ADE. In the last decades, it has been reported that this model cannot take account of several important features of solute movement through soil. Recently, a new model base on the assumption that the movement of solute particles belongs to the family of Levy motions has been put forward. A one-dimensional solute transport equation was derived for Levy motions using fractional derivatives to describe the dispersion. Our objective was to test applicability of this fractional ADE, or FADE, to soils. We have assembled a database on published solute transport experiments in soil columns and field soils and evaluated the FADE as the transport model in comparison with ADE. An unified framework is considered in order to discuss the changes different conditions of the solute transport produces upon the parameter of differentiation α. The fractional advective-dispersive equation as a generalization of classical advective-dispersive equation is a promising enhancement in the hydrologist toolbox.