Submitted to: International Workshop on Fractal Mathematics Describing Soil and Heterogeneous Systems
Publication Type: Abstract Only
Publication Acceptance Date: 5/3/2002
Publication Date: 6/28/2002
Citation: Pachepsky, Y.A. 2002. Scaling and fractional equations of water and contaminant transport in soils. International Workshop on Fractal Mathematics Describing Soil and Heterogeneous Systems, Barco de Avila, Spain, June 29-July 4, 2002. p.19. Interpretive Summary:
Technical Abstract: Simulations of water and solute transport in soil are ubiquitous, and the Richards' and CDE equation are main tools for that purpose. For experiments on water transport in soil horizontal columns, Richards' equation predicts that volumetric water contents should depend solely on the ratio (distance)/(time)q where q=0.5 and the dispersivity should be constant. Substantial experimental evidence shows that value of q is significantly less than 0.5 in some cases and that dispersivity exhibits a power-law increase with distance and/or time. The physical model of such transport is the transport of particles being randomly trapped and having a power law distribution of waiting periods or a power-law distribution of travel distances. The corresponding mathematical models are generalized Richards' equation and CDE in which the derivatives of water content on time and of solute concentration on distance are fractional ones with the order equal or less than one. We solved this equation numerically and fitted the solution to data on horizontal water transport and solute transport in soil columns. The generalized transport equations described all observations well with single diffusivity and dispersivity functions. Introducing fractional derivatives effectively incorporates scale in transport equations. Validity of the fractional transport equations indicates presence of memory effects in soil water and solute transport phenomena and may help to explain scale-dependence and variability in soil hydraulic properties encountered by researchers and practitioners using classical transport water and solute transport models.