Source Flow in Heterogeneous Aquifers with Application to Hydraulic Tomography

Enhanced spreading of contaminants by groundwater (macrodispersion) is governed by advection by the velocity field, whose spatial variability is caused by the heterogeneity of the hydraulic conductivity K. Characterization of K distribution in space is a major topic of research. While considerable knowledge has been accumulated for natural gradient flows, hydraulic tomography methods have been forwarded only recently. A typical setup consists of short segments of a well through which water is pumped (injected) and the head H response is measured by pressure transducers along observation piezometers at different distances and elevations. Attempts in the past were done mainly to derive K from measured H by numerical inversion of the flow equation accordingly to a global optimality condition. The present study considers stochastic hydraulic tomography by which measured H are employed in order to identify the statistical parameters of the log-conductivity Y= ln K field (mean, variance, integral scales). As a first step we investigate and present the solution of the steady flow equations relating H statistical moments to those of the K field for the strongly nonuniform source flow, which approximates the main constitutive element of the tomographic setup. This is achieved by numerical simulations for values of the Y variance up to 4 and the derivation of type curves which helps in the identification of K statistics. Application to identification of logconductivity moments for a hydraulic tomography setup is illustrated by a synthetic example.