Abstract
Abstract. The drawdown solution has been widely used to analyze pumping test data for the determination of aquifer parameters when coupled with an optimization scheme. The solution can also be used to predict the drawdown due to pumping and design the dewatering system. The drawdown solution for flow toward a finite-radius well with a skin zone in a confined aquifer of infinite extent in radial direction had been developed before. To our best knowledge, the drawdown solution in confined aquifers of finite extent with a skin zone so far has never before been presented in the groundwater literature. This article presents a mathematical model for describing the drawdown distribution due to a constant-flux pumping from a finite-radius well with a skin zone in confined aquifers of finite extent. The analytical solution of the model is developed by applying the methods of Laplace transforms, Bromwich contour integral, and residue theorem. This solution can be used to investigate the effects of finite boundary and conductivity ratio on the drawdown distribution. In addition, the inverse relationship between Laplace- and time-domain variables is used to develop the large time solution which can reduce to the Thiem solution if there is no skin zone.
Highlights
The famous Theis solution (1935) was first introduced in the groundwater literature to describe the transient drawdown distribution induced by a constant pumping at a well of infinitesimal well radius in a homogeneous and isotropic confined aquifer of infinite extent
The curves gradually deviate from one another after τ > 100, indicating that the solution of finite aquifers is no longer suitable to approximate the solution of infinite aquifer at large times because of the effect of the finite outer boundary on the drawdown distribution
A mathematical model has been developed to describe the drawdown distribution for a pumping test performed in a two-zone confined aquifer of finite extent
Summary
The famous Theis solution (1935) was first introduced in the groundwater literature to describe the transient drawdown distribution induced by a constant pumping at a well of infinitesimal well radius in a homogeneous and isotropic confined aquifer of infinite extent. Yeh et al (2003) presented an analytical drawdown solution for the pumping test in an infinite confined aquifer by taking into account the effects of the well storage and the finite-thickness skin They mentioned that the effect of skin zone is negligible in short and large periods of pumping time. Perina and Lee (2006) developed a general well function in Laplace domain for constant pumping in a confined, leaky, or unconfined aquifer of infinite extent with a partially penetration well, finitethickness skin They adopted an approach such as a finite difference method to discretize the well screen for handling non-uniform wellbore flux problems. This new time-domain solution can be applied to: (1) predict the spatial and/or temporal drawdown distributions in both the skin and formation zones with known aquifer parameters such as the outer radius of the skin zone as well as the transmissivity and storage coefficient for each of the skin and aquifer zones, (2) determine the aquifer parameters if coupled with an optimization algorithm in the pumping test data analyses, (3) verify numerical codes in the prediction of the drawdown distribution in two-zone aquifer systems, and (4) perform the sensitivity analysis and assess the impacts of parameter uncertainty on the predicted drawdown
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