Fractional advective-dispersive equation as a model of solute transport in porous media

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. © 2007 Springer.