Stochastic analysis of the relationships between saturated hydraulic conductivity variance and solute dispersion in heterogeneous soils
Azimi-Zonooz, Ali, and Clark C.K. Liu
The effect of three-dimensional heterogeneity of saturated hydraulic conductivity on the vertical transport of solutes in soils is examined by means of controlled numerical experiments. Saturated hydraulic conductivity, an important transport parameter that controls the dispersion of pollutants in heterogeneous soils, is assumed to be composed of a homogeneous mean value and a perturbation caused by the vertical variability of soil properties, producing a stochastic process in the mean flow direction. The spatial heterogeneity of porous soils is characterized by the variance and correlation scale of the saturated hydraulic conductivity in the transport domain. Numerical experiments are carried out to evaluate the extent of contaminant dispersion in Hawaiian Oxic soils when uncertainty exists as a result of the spatial heterogeneity of saturated hydraulic conductivity. Statistical analysis of the saturated hydraulic conductivity measurements on undisturbed soil cores from two locations in Hawaiian Oxic soils indicated two different soils with the same mean and different variances. The partial differential equations describing three-dimensional transient flow and solute transport in soils with a random conductivity field were solved to evaluate the effect of these two variance levels on the transport of a contaminant plume originating from the surface. The significance of the variance on the spatial and temporal distribution of tracer concentrations is demonstrated using solute breakthrough curves at various depths in the soil profile. The longitudinal macrodispersivity resulting from tracer spreading in the heterogeneous soils with a finite local dispersivity is also analyzed. The analysis shows a similar solute dispersion behavior for the two variances. However, there is an overall reduction in the dispersion of solutes resulting from a uniform velocity field with the same mean. Macrodispersivity values in heterogeneous soils are proportional to the variance at smaller travel distances but converge to the same value at larger travel distances.