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Analytical Model for Computing Residence Times Near a Pumping Well
Author(s) -
Simpson Matthew J.,
Clement T. Prabhakar,
Yeomans Francis E.
Publication year - 2003
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.2003.tb02604.x
Subject(s) - residence time (fluid dynamics) , expression (computer science) , aquifer , flow (mathematics) , function (biology) , simple (philosophy) , series (stratigraphy) , mechanics , mathematics , residence time distribution , steady state (chemistry) , mathematical optimization , physics , computer science , engineering , geology , geotechnical engineering , chemistry , groundwater , paleontology , philosophy , epistemology , evolutionary biology , biology , programming language
An analytical solution for calculating the residence time of fluid flowing toward a pumping well in an unconfined aquifer has been developed. The analytical solution was derived based on a radial, steady‐state, Dupuit‐Forchheimer flow model. The resulting integral expression involved computing the imaginary error function, for which a simple series expansion is proposed. The validity of the analytical expression is demonstrated by testing its results against numerical results for an example problem. The analytical solution compared favorably with the numerical approximation.