STOCHASTIC ANALYSIS OF SPECIFIC DISCHARGE IN A LEAKY AQUIFER

The solute transport and movement at the field scale are determined by pore-scale dispersivity and by the velocity (specific discharge) field. The specific discharge field is itself controlled by inherent properties of the aquifer (e.g., the hydraulic conductivity). In this study, covariance functions of specific discharge for both one-dimensional and two-dimensional flows in a semiconfined aquifer were derived with mean flow parallel to the formation bedding. Spectral theory was used to analyze a unidirectional mean flow field of infinite extent which is perturbed by one- and two- dimensional statistically homogeneous hydraulic conductivity field. The procedure for the characterization of the specific discharge field in heterogeneous, statistically isotropic formations subject to leakage from the leaky layer has been developed. Relatively simple closed-form analytical expressions requiring only numerical integration for two-dimensional flows were obtained for the longitudinal and transverse components of specific discharge covariance. The spatial, statistical structure of the specific discharge field was investigated in terms of the leakage factor and spatial structure of hydraulic conductivity field. Our results indicate that the leakage factor has a significant effect on the components of the specific discharge covariances in formations with leaky layer.