Improved forward and inverse analyses of saturated‐unsaturated flow toward a well in a compressible unconfined aquifer

Abstract

[1] We present an analytical solution for flow to a partially penetrating well in a compressible unconfined aquifer that allows inferring its saturated and unsaturated hydraulic properties from drawdowns recorded in the saturated and/or unsaturated zone. We improve upon a previous such solution due to Tartakovsky and Neuman (2007) by (1) adopting a more flexible representation of unsaturated zone constitutive properties and (2) allowing the unsaturated zone to have finite thickness. Both solutions account for horizontal as well as vertical flows throughout the system. We investigate the effects of unsaturated zone constitutive parameters and thickness on drawdowns in the saturated and unsaturated zones as functions of position and time; demonstrate the development of significant horizontal hydraulic gradients in the unsaturated zone in response to pumping; validate our solution against numerical simulations of drawdown in a synthetic aquifer having unsaturated properties described by the van Genuchten-Mualem constitutive model; use our solution to analyze drawdown data from a pumping test conducted by the U.S. Geological Survey at Cape Cod, Massachusetts; and compare our estimates of van Genuchten-Mualem parameters with laboratory values obtained for similar materials in the area.Citation: Mishra, P. K., and S. P. Neuman (2010), Improved forward and inverse analyses of saturated-unsaturated flow toward a well in a compressible unconfined aquifer, Water Resour. Res., 46, W07508,

Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system

“…Mishra et al [18] presented an analytical solution for flow toward a partially penetrating large diameter well in a leaky-unconfined aquifer. They considered the effect of finite thickness unsaturated zone following the same procedure as Mishra and Neuman [17].…”

“…6), (governing the flow in the underlying fractured aquifer ) and its related initial and boundary conditions (Eqs. [14][15][16][17] in the Laplace domain are…”

Joint interpretation of sequential pumping tests in unconfined aquifers

“…Traditional characterization approaches have adopted homogeneous conceptual models that assume aquifer homogeneity and have attempted to derive effective hydraulic parameters based on drawdowns from a single pumping test, for example, those by Theis [1935] and Cooper and Jacob [1946] for confined aquifers and those by Boulton [1963], Dagan [1967], Brutsaert [1970], Streltsova [1972aStreltsova [ , 1972b, Neuman [1972], Lakshminarayana and Rajagopalan [1978], Moench [1995], Mathias and Butler [2006], and Mishra and Neuman [2010] for unconfined aquifers. Recent numerical, sandbox, and field experiments by Wu et al [2005], Straface et al [2007], Xiang et al [2009], Wen et al [2010], Huang et al [2011], and Berg and Illman [2011b] however questioned the representativeness of the estimates from these conventional approaches.…”

Recent advances in modeling of well hydraulics

“…Their solution considered both the vertical and horizontal flows in the unsaturated zone. Mishra and Neuman [212] improved the solution of Tartakovsky and Neuman [33] by introducing four-parameter representation of the hydraulic conductivity and water content functions and allowing the unsaturated zone to have a finite thickness. Mishra and Neuman [213] further considered the case of a finite diameter pumping well with storage and explored the effects of wellbore storage and delayed piezometer response on drawdowns in the unsaturated-saturated flow system.…”