Submitted to: American Society of Mechanical Engineers
Publication Type: Proceedings
Publication Acceptance Date: May 16, 2005
Publication Date: September 24, 2005
Citation: San Jose, F., Pachepsky, Y.A., Rawls, W.J. 2005. Solute transport simulated with the fractional advective-dispersive equation. In: Proceedings of the American Society of Mechanical Engineers Second Symposium on Fractional Derivatives and their Applications, September 24-28, 2005, Long Beach, California. Paper No. DETC 2005-84340.
Interpretive Summary: Understanding solute transport in soils is a key to managing the fate of agricultural chemicals in environment, crop productivity, and agricultural sustainability. Models of solute transport package the knowledge that has been accumulated and quantified. Existing models fail to describe several important features of solute transport in soils, in particular the enhanced spreading of solutes in soils as the solute transport progresses. Some developments in simulating scale dependencies have led to theory of fractional dispersion. This theory assumes that the solute particles can stay trapped for a long time and then travel a large distance with a relatively large speed. This assumption is well applicable to field sols in which large stagnant zones border with small pathways of preferential flow. The theory leads to the fractional convective-dispersive equation that we have applied in this work to data from two field studies. The fractional convective-dispersive equation simulated solute transport in field soil better than the classical convective-dispersive equation and is a promising enhancement in the hydrologists toolbox.
Solute transport in soils and sediments is commonly simulated with the parabolic advective-dispersive equation, or ADE. Although the solute dispersivity in this equation is regarded as a constant, it has been found to increase with the distance from the solute source. This can be explained assuming the movement of solute particles belongs to the family of Lévy motions. A one-dimensional solute transport equation was derived for Lévy motions using fractional derivatives to describe the dispersion. Our objective was to test applicability of this fractional ADE, or FADE, to soils. The FADE has two parameters ' the fractional dispersion coefficient and the order of fractional differentiation ', 0<''2. Scale effects are reflected by the value of ', and the fractional dispersion coefficient is independent on scale. The ADE is a special case of the FADE. Analytical solutions of the FADE and the ADE were successfully fitted to the data from field experiments on chloride transport in sandy loam and clay loam soils. The FADE simulated scale effects on solute transport better than ADE. Attempts to fit ADE to the FADE solutions resulted in the increase of the dispersivity with the distance.