Hantush Well Function Revisited

Journal article (2010)
Department
Department Water Management (CEG) (TU Delft)
Copyright: © 2010 Veling, E.J.M.; Maas, C.
DOI: https://doi.org/doi:10.1016/j.jhydrol.2010.08.033
Time series analysis Hantush Well Function Generalized Incomplete Gamma Function Pumping test Leaky aquifer Closed-form representation
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Published Date

03-12-2010

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Source:

Journal of Hydrology, 393 (3-4), 2010 ; pre-print version

ISSN:

0022-1694

Faculty

Civil Engineering and Geosciences

Department

Department Water Management

Abstract

In this paper we comment on some recent numerical and analytical work to evaluate the Hantush Well Function. We correct an expression found in a Comment by Nadarajah (J. of Hydrology, vol. 338, p. 152-153 (2007)) to a paper by Prodanoff et al. (J. of Hydrology, vol. 318, p. 173-183 (2006)). We subsequently derived another analytic representation based on a generalized hypergeometric function in two variables and from the hydrological literature we cite an analytic representation by Hunt (J. of Hydrology, vol. 33, p. 179-183 (1977)). We have implemented both representations and compared the results. Using a convergence accelerator Hunt's representation of Hantush Well Function is efficient and accurate. While checking our implementations we found that Bear's table of the Hantush Well Function ("Hydraulics of Groundwater", 1979, Table 8-6) contains a number of typographical errors that are not present in the original table published by Hantush (Transactions, American Geophysical Union, vol. 36, p. 95-100 (1956)). Finally, we offer a very fast approximation with a maximum relative error of 0.0033 for the parameter range in the table given by Bear.