Geostatistical characterization of groundwater flow parameters in a simulated aquifer

An analog method is used to simulate a discrete transmissivity field free of the artifacts inherent in conventional multivariate Gaussian statistical generation methods. The simulated field provides a realistic model of a formation exhibiting the spatial continuity of extreme transmissivities which gives rise to barriers and preferential channels for flow. The heterogeneous transmissivity field and the corresponding steady-state head and discharge fields are characterized in a geostatistical framework and observed spatial statistics are compared with theoretical results from the stochastic hydrogeology literature. The simulated transmissivity field exhibits a bimodal distribution and strong directional anisotropy with nested scales of heterogeneity. Despite these significant departures from standard models, the observed head covariance and head-log-transmissivity cross-covariance agree well with theory. The spatial covariance of specific discharge is highly anisotropic reflecting preferential channeling in the mean direction of flow and the conservation of flux along streamlines. The effective transmissivity of the field is predicted more accurately by the spatial geometric average than by theoretical models despite the flow channeling and the anisotropy of heterogeneity. Tracer spreading, modeled by particle tracking, is non-Fickian at displacements of up to 13.4 times the log-transmissivity integral range because transport behavior is dominated by convection along a small number of preferential channels. The observed scale dependence of apparent longitudinal dispersivity is predicted generally well by theory. Results of this study suggest that ensemble theoretical models based on perturbation approaches can provide reasonable estimates of general flow and transport properties of single field realizations under moderate conditions of heterogeneity.