Well hydraulics theory and data analysis of the constant head test in an unconfined aquifer with the skin effect

Abstract

In a constant‐head test (CHT), groundwater is withdrawn from a well that has a fixed drawdown. Accordingly, the CHT is particularly useful in aquifers of low transmissivity because the constant‐head well would not be dewatered owing to overpumping. The problem of interest pertains to a CHT in a homogeneous and anisotropic unconfined aquifer, where water released by the water table decline is assumed to be instantaneous and the skin effect surrounding the constant‐head well is represented by a skin factor. A two‐dimensional transient well hydraulics model is developed, and its Laplace domain solutions of aquifer drawdown and the constant‐head well discharge are determined. It is found that the three distinct segments typically noted in the time drawdown history of a constant‐rate test (CRT) are also characteristic of the temporal drawdown variation of the CHT. However, the early time and late time asymptotes conform to the radial flow solution of a CHT in confined aquifers as given by Hantush [1964]. Under the late time radial flow conditions the asymptotic solution is in terms of an apparent storage coefficient equal to the sum of the storage coefficient and the specific yield, and a specific mass balance relation exists among the constant‐head well discharge, the discharge due to aquifer storage, and the discharge resulted from the water table decline. While aquifer drawdown and the constant‐head well discharge are under the influence of well skin, their ratios are free from it. A curve matching method using this ratio is developed to determine the horizontal and the vertical hydraulic conductivities, the storage coefficient, and the specific yield. When the prescribed constant drawdown is not negligibly small in comparison to the initial saturated thickness, aquifer drawdown in late times may be large, and thus a drawdown correction is needed for data analysis. It is found that the Jacob correction for large drawdown of a CRT can also be used for the late drawdown correction in a CHT.