Methods Note/ Solutions for Non-Darcian Flow to an Extended Well in Fractured Rock by Zhang Wen 1,2 , Guanhua Huang 2,3 , and Hongbin Zhan 4,5 Abstract We have investigated non-Darcian ﬂow to a vertical fracture represented as an extended well using a linearization procedure and a ﬁnite difference method in this study. Approximate analytical solutions have been obtained with and without the consideration of fracture storage based on the linearization procedure. A numerical solution for such a non-Darcian ﬂow case has also been obtained with a ﬁnite difference method. We have compared the numerical solution with the approximate analytical solutions obtained by the linearization method and the Boltzmann transform. The results indicate that the linearized solution agrees generally well with the numerical solution at late times, and underestimates the dimensionless drawdown at early times, no matter if the fracture storage is considered or not. When the fracture storage is excluded, the Boltzmann transform solution overestimates the dimensionless drawdown during the entire pumping period. The dimensionless drawdowns in the fracture with fracture storage for different values of dimensionless non-Darcian hydraulic conductivity β approach the same asymptotic value at early times. A larger β value results in a smaller dimensionless drawdown in both the fracture and the aquifer when the fracture storage is included. The dimensionless drawdown is approximately proportional to the square root of the dimensionless time at late times. Introduction Fractured aquifers are important for providing ground water resources (Kohut et al. 1983). To maximize ground- water production in such aquifers, it is favorable to let the pumping wells intercept the main fractures or fracture zones (Sen 1987). If a pumping well intercepts a main 1 School of Environmental Studies, China University of Geo- sciences, Wuhan, Hubei 430074, China; wenzhangcau@gmail.com 2 Department of Irrigation and Drainage, College of Water Conservancy and Civil Engineering, China Agricultural University, Beijing 100083, China. 3 Corresponding author: Chinese-Israeli International Center for Research and Training in Agriculture, China Agricultural University, Beijing 100083, China; +86-10-62737144; fax: +86- 10-62737138; ghuang@cau.edu.cn 4 Department of Geology and Geophysics, Texas A & M University, College Station, TX 77843-3115; zhan@geo.tamu.edu 5 Faculty of Engineering, China University of Geosciences, Wuhan, Hubei 430 074, China. Received January 2010, accepted May 2010. Copyright  2010 The Author(s) Journal compilation  2010 National Ground Water Association. doi: 10.1111/j.1745-6584.2010.00728.x fracture in a fractured aquifer, ﬂow near the well will have quite different features from what has been seen in ﬂow near a well in a granular porous medium (Gringarten et al. 1974; Jenkins and Prentice 1982; Sen 1986, 1992; Snow 1969). For instance, Lewis and Burgy (1964) found that the relationship between the drawdown and the time in fractured rock aquifers could not be described by the clas- sical radial ﬂow model. Smith and Vaughan (1985) have also presented that non-radial ﬂow response was observed when pumping tests were performed in low-permeability media, including clayey glacial tills as well as consoli- dated rocks. A pumping well installed in a main fracture has some unique features, as shown in Figure 1. As the permeability of the main fracture itself is often several orders of magnitude greater than that of the surrounding medium, water ﬂows from the medium to the fracture nearly perpendicular to the fracture plane, and subse- quently goes to the well. Therefore, the entire fracture itself can be regarded as a planar well which is often named “extended well,” provided that the permeability of the fracture is sufﬁciently large. In this case, the ﬂow lines to the fracture might be approximately linear (Jenkins and 280 Vol. 49, No. 2 – GROUND WATER – March-April 2011 (pages 280 – 285) NGWA.org