Stochastic analysis of flow in three-dimensional, heterogeneous, anisotropic aquifers: Synthetic simulations and case study

This dissertation investigates the behavior of the mean equivalent hydraulic conductivity in three-dimensional, anisotropic, strongly heterogeneous aquifers and the statistical properties of the flow parameters of a strongly heterogeneous, layered aquifer system. The mean equivalent hydraulic conductivity normal and parallel to stratification (K₁, and K₂, respectively) is studied through Monte Carlo simulations. For flow normal to stratification the value of K₁ is not unique; it ranges from an arithmetic to a geometric, and finally, to a harmonic mean behavior depending on field dimensions, and medium anisotropy. However, even for large anisotropy ratios, harmonic mean behavior appears to be a good approximation only for aquifer thickness L₁ that is large enough to allow stratified flow to occur, while for small aquifer thickness the limiting behavior, appears to be, instead, that of two-dimensional flow, i.e., water flows primarily parallel to the planes of stratification. When the aquifer thickness is very small compared to the horizontal dimensions (and with relative similar integral scales in the three directions) a behavior resembling arithmetic mean conditions is exhibited, i.e., water flow takes place through heterogeneous, vertical, soil volumes. The geostatistical expressions of Desbarats (1992a) for upscaling hydraulic conductivity values were utilized and closed form empirical relations were developed for the main components of the upscaled hydraulic conductivity tensor.; The second part of this dissertation is concerned with the statistical properties of the flow parameters of a multi-layered system in the central Savannah River Site, near Aiken, SC. A procedure is demonstrated for the upscaling of the statistical properties of point values to the grid resolution, for both unconditional and conditional simulations of the K-field. Through the use of Monte Carlo simulations the geostatistical characteristics of the mean flux and head fields are investigated and the effects of boundaries on the variability of the mean flux field are discussed. Analytical expressions for the head covariance of three-dimensional anisotropic media are generally supported by our numerical results. Conditioning simulations to point hydraulic conductivity measurements appears to have only a minimal effect on the variability of head and flux.