Stochastic analysis of adsorbing solute transport in three-dimensional, heterogeneous, unsaturated soils

We analyze adsorbing solute transport in heterogeneous three-dimensional unsaturated soils using a first-order perturbation method. Both the unsaturated hydraulic conductivity and water content are treated as statistically anisotropic and stationary random space functions. The water flow is assumed to be steady state. Solute adsorption is described by a linear equilibrium isotherm with a spatially variable random adsorption coefficient. The macrodispersivity depends on the statistical properties of hydraulic and chemical parameters and on the distance traveled by the solute plume. The longitudinal macrodispersivity increases with the solute travel distance and approaches an asymptotic value at long travel distances. The transverse macrodispersivity increases with travel distance for short distances and then drops to zero. The effect of water content variability on macrodispersivity can be neglected only for a soil near saturation. Compared with effects of hydraulic gradient and suction head variabilities, the effects of soil conductivity parameters on macrodispersivity are dominant at high water content or long travel distance. Heterogeneous adsorption has a larger impact on longitudinal macrodispersivity than on the transverse one. Macrodispersivity increases as mean water content decreases and as mean retardation factor increases. The correlation between the adsorption coefficient and saturated hydraulic conductivity plays an important role in the determination df macrodispersivity.