Analytical Model and Analysis of Solute Transport by Unsteady Unsaturated Gravitational Infiltration

Penetration of reactive solute into a soil during a cycle of water infiltration and redistribution is investigated by deriving analytical closed form solutions for fluid flux, moisture content and contaminant concentration. The solution is developed for gravitational flow and advective transport and is applied to two scenarios of solute applications encountered in the applications: a finite pulse of solute dissolved in irrigation water and an instantaneous pulse broadcasted onto the soil surface. Through comparison to simulations of Richards' flow, capillary suction is shown to have contrasting effects on the upper and lower boundaries of the fluid pulse, speeding penetration of the wetting front and reducing the rate of drying. This leads to agreement between the analytical and numerical solutions for typical field and experimental conditions. The analytical solution is further incorporated into a stochastic column model of flow and transport to compute mean solute concentration in a heterogeneous field. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying stage. The mean concentration profiles match those of the Monte-Carlo simulations for capillary length scales typical of sandy soils. The efficient column model is ideal for testing multiple scenarios. Its use is illustrated in determining transport parameters by the data from an experiment in a heterogeneous field. Parameter sensitivity is analyzed and confidence intervals are estimated for effective field reactive parameters (partition coefficient K_d and effective first order degradation rate λ ) of some common herbicides (Atrazine, Bromacil, and Terbuthylazine) The results are compared to literature reported values. The field data for this work was presented in the Fall 2000 AGU meeting, the stochastic analysis is reported in [S. C. Lessoff, P. Indelman and G. Dagan, Heat and Mass Transfer in the Natural Environment Raats, P., D. Smiles and A. Warrick Editors, in press] and the analytical model is reported in [Lessoff, S. C. and Indelman P. Analytical model of solute transport by unsteady unsaturated gravitational infiltration, J. Contam. Hydro., submitted]