On the aquitard–aquifer interface flow and the drawdown sensitivity with a partially penetrating pumping well in an anisotropic leaky confined aquifer Qinggao Feng a , Hongbin Zhan b,⇑ a Department of Geotechnical Engineering, Tongji University, Shanghai 200092, PR China b Department of Geology and Geophysics, Texas A&M University, College Station, TX 77843-3115, USA article info Article history: Received 3 September 2014 Received in revised form 19 November 2014 Accepted 21 November 2014 Available online 1 December 2014 This manuscript was handled by Corrado Corradini, Editor-in-Chief, with the assistance of Christophe Darnault, Associate Editor Keywords: Leaky confined aquifer Leakage rate Leakage volume Partially penetrating well Wellbore storage Anisotropy summary A mathematical model for describing groundwater flow to a partially penetrating pumping well of a finite diameter in an anisotropic leaky confined aquifer is developed. The model accounts for the jointed effects of aquitard storage, aquifer anisotropy, and wellbore storage by treating the aquitard leakage as a bound- ary condition at the aquitard–aquifer interface rather than a volumetric source/sink term in the govern- ing equation, which has never developed before. A new semi-analytical solution for the model is obtained by the Laplace transform in conjunction with separation of variables. Specific attention was paid on the flow across the aquitard–aquifer interface, which is of concern if aquitard and aquifer have different pore water chemistry. Moreover, Laplace-domain and steady-state solutions are obtained to calculate the rate and volume of (total) leakage through the aquitard–aquifer interface due to pump in a partially penetrat- ing well, which is also useful for engineers to manager water resources. The sensitivity analyses for the drawdown illustrate that the drawdown is most sensitive to the well partial penetration. It is apparently sensitive to the aquifer anisotropic ratio over the entire time of pumping. It is moderately sensitive to the aquitard/aquifer specific storage ratio at the intermediate times only. It is moderately sensitive to the aquitard/aquifer vertical hydraulic conductivity ratio and the aquitard/aquifer thickness ratio with the identical influence at late times. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction The classical theory for groundwater flow to a partially pene- trating well with a constant rate test in a leaky confined aquifer was first proposed by Hantush (1957) and later by others such as Hantush (1964), Halepaska (1972), Hunt (2005) and Perina and Lee (2006). Hantush (1957) assumed that the leakage from the aquitard was treated as a volumetric source/sink term contained in the governing flow equation which was later called ‘‘the Han- tush approximation’’ (Zhan and Bian, 2006). This approximation was utilized in many studies including Hantush (1960, 1964), Lai and Su (1974), Zhan and Park (2003), Zhan and Bian (2006), Hunt and Scott (2007) and Yang and Yeh (2009). In reality, the aquitard leakage does not happen over the entire aquifer volume; rather, it only occurs at the aquitard–aquifer interface, thus should be trea- ted as an interface problem, not a volumetric source/sink term. Hantush (1967) realized the drawbacks of using the volumetric source/sink approximation and solved the equation governing flow toward a partially penetrating well in a leaky confined aquifer by regarding the leakage term as a boundary condition. However, Hantush (1967) neglected both the aquitard storage and the aqui- fer anisotropy, apparently for the sake of mathematical simplicity. Halepaska (1972) obtained the drawdown distribution for flow to a partially penetrating well of an infinitesimal radius in a thick, homogeneous, isotropic leaky confined aquifer, and neglected the aquitard storage as well. Hunt (2005) made some closed-form ana- lytical solutions available for describing drawdown distribution in a leaky confined aquifer with a relatively thin aquitard. In the anal- ysis of Hunt (2005), the well was treated as the superposition of many point sources and the aquitard compressibility was excluded. Hence, the solution obtained by Hunt (2005) cannot be used to analyze the effect of aquitard storage and wellbore storage. Sun and Zhan (2006) analyzed the flow to a horizontal well in a leaky confined aquifer by treating the aquitard leakage as occurred at the aquitard–aquifer interface, and they found that the Hantush approximation could result in non-negligible errors, especially at http://dx.doi.org/10.1016/j.jhydrol.2014.11.058 0022-1694/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. Tel.: +1 979 574 4819. E-mail address: zhan@geos.tamu.edu (H. Zhan). Journal of Hydrology 521 (2015) 74–83 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol