Stochastic Analysis of Macrodispersion in a Semi-Confined Aquifer


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Abstract

In this paper, 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 the 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 some convenient forms of the log hydraulic conductivity process. 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. It is found that the longitudinal macrodispersivities are increased due to the presence of leakage, while the transverse macrodispersivities are reduced due to leakage.

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