AXIALLY SYMMETRIC 3D SATURATED-UNSATURATED FLOW TO A PARTIALLY PENETRATING WELL IN A COMPRESSIBLE UNCONFINED AQUIFER

A new analytical solution is presented for saturated-unsaturated flow to a well in a compressible unconfined aquifer. 3D axially symmetric flow in the unsaturated zone is described by a linearized version of Richards' equation in which conductivity and water content vary exponentially with incremental capillary pressure head relative to air entry. Unsaturated properties are characterized by an exponent κ or a dimensionless exponent κ_D=κb where b is initial saturated thickness. Unsaturated flow has significant impact on dimensionless time-drawdown when κ_D < 1 (the aquifer has large retention capacity and/or small initial saturated thickness) but less so at κ_D > 10 (small retention capacity and/or large saturated thickness). We demonstrate that the effect of pumping propagates vertically and horizontally through the unsaturated zone at a rate that generally increases with decreasing κ_D. We additionally fit our solution individually and simultaneously to time-drawdown data from 20 piezometers and observation wells, and simultaneously to data from three piezometers in each of two clusters, obtained during an aquifer test in a Glacial Outwash Deposit at Cape Cod, Massachusetts, by the US Geological Survey [Moench et al., 2001]. Optimum fits are obtained by minimizing the sum of squared differences between observed and computed drawdowns. The results of individual fits exhibit some variability due in part to estimation errors and in part to spatial variability of medium properties. Parameter estimates obtained by simultaneous fits to all or part of the data are well within the range of these variations. Our simultaneous fits to all 20 time-drawdown records, obtained using a single physically-based unsaturated zone parameter κ_D, are an improvement over those reported previously using 3 empirical parameters by Moench et al. [2001] and Moench [2004]. Our estimates of horizontal (0.20 ft/min) and vertical (0.16 ft/min) saturated hydraulic conductivity, and specific yield (0.22), are close to theirs; our estimate of specific storage (3x10^-5 ft^-1) is somewhat larger than theirs (1.3x10^-5 ft^-1); but our estimate of the constitutive exponent κ (0.07 ft^-1) is not comparable to their empirical parameters.