STOCHASTIC ANALYSIS OF MACRODISPERSION IN SEMI-CONFINED AQUIFERS

In this study, the macroscopic dispersion resulting from one- and two-dimensional flows through a semi-confined aquifer with spatially variable hydraulic conductivity K which is represented by a stationary (statistically homogeneous) random process is analyzed using spectral representation technique. Stochastic fluctuation equations of the steady flow and solute transport are solved to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of the leakage factor and input covariances describing the hydraulic conductivity in a semi-confined aquifer bounded by a leaky layer above and an impervious stratum below. The macrodispersivity tensor is studied using a few convenient forms of the log hydraulic conductivity process. The coupled effects on the macrodispersion of solute transport of both the leakage factor and the spatial variability in the hydraulic conductivity of the main aquifer are investigated in a wide parameter range. The sensitivity of the resulting macrodispersivity to the input covariances is discussed along with the influence of the leakage factor for both one- and two-dimensional flows. The influence of the leakage factor on the concentration fluctuation is of second order, and its influence on the head and the specific discharge (convective) fields is of first order. The results indicate that the longitudinal macrodispersivities are increased due to the presence of leakage, while the transverse mascrodispersivities are reduced due to the leakage.