Linearized Richards' equation approach to pumping test analysis in compressible aquifers

Abstract

There is increasing acceptance of the importance of slow drainage from the unsaturated zone (SDUZ) when interpreting drawdown-time curves derived from pumping tests. Previous analytical solutions have generally assumed instantaneous drainage from the unsaturated zone. Such models typically underestimate the specific yield. Some authors have sought to account for SDUZ by assuming that drainage from the unsaturated zone declines exponentially with time, giving rise to an empirical delay index. These models tend to overestimate drawdown at early times and underestimate it during late times. More recently, the superposition of an arbitrary number of exponential models with different delay indices has been advocated, giving rise to an overparameterized and complicated empirical function. Following the work of Kroszynski and Dagan (1975), we obtain a new drainage function based on a linearized Richards' equation assuming that moisture content and hydraulic conductivity are exponential functions of pressure head. Furthermore, the drainage function can be incorporated into existing analytical solutions (e.g., Moench, 1997) with minor adjustment. The resulting model requires an additional three parameters: a moisture retention exponent, a hydraulic conductivity exponent, and the initial unsaturated zone thickness. The new drainage function can also be used in an empirical fashion with only one parameter (the other two are lost by assuming an infinitely deep unsaturated zone and that the moisture retention and relative permeability exponents are equal). Its applicability is demonstrated using pumping test data sets from Borden and Cape Cod. The results show improved consistency with the experimental data in comparison with previous studies. Copyright 2006 by the American Geophysical Union.