Submitted to: Springer Verlag
Publication Type: Book / chapter
Publication Acceptance Date: 8/18/2006
Publication Date: 5/6/2007
Citation: San Jose Martinez, F., Pachepsky, Y.A., Rawls, W.J. 2007. Fractional advective-dispersive equation as a model of solute transport in porous media. In: Sabatier, J., Agrawal, O.P., Teneiro, Machado, I.A. - editors. Advances in Fractional Calculus. Berlin, Germany. Springer Verlag. p. 199-219. 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 a field study. In this work, we have developed a novel procedure to equate the solute fluxes in soil and in water above the soil. The fractional convective-dispersive equation simulated solute transport in field soil better than the classical convective-dispersive equation.
Technical Abstract: Understanding and modeling transport of solutes in porous media is a critical issue in the environmental protection. The common model is the advective-dispersive equation (ADE) describing the superposition of the advective transport and the Brownian motion in water-filled pore space. Deviations from the advective-dispersive transport have been documented and attributed to the physical heterogeneity of natural porous media. It has been suggested that the solute transport can be modeled better assuming that the random movement of solute is the Lévy motion rather than the Brownian motion. The corresponding fractional advective-dispersive equation (FADE) was derived using fractional derivatives to describe the solute dispersion. We present and discuss an example of fitting the FADE numerical solutions to the data on chloride transport in columns of structured clay soil. The constant concentration boundary condition introduced a substantial mass balance error then the solute flux boundary condition was used. The FADE was a much better model compared to the ADE to simulate chloride transport in soil at low flow velocities.