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An Analytical Solution for Stream Depletion by Cyclic Pumping of Wells Near Streams with Semipervious Beds
Author(s) -
Darama Yakup
Publication year - 2001
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.1745-6584.2001.tb00353.x
Subject(s) - clogging , dimensionless quantity , aquifer , penetration (warfare) , streams , hydrology (agriculture) , mechanics , geotechnical engineering , geology , groundwater , mathematics , computer network , physics , archaeology , operations research , computer science , history
A study was made of the rate of stream depletion produced by cyclic pumping of wells located in a semi‐infinite phreatic aquifer bounded by a partially penetrating stream with semipervious bed. Analytical solutions were developed by applying superposition principles to the solutions for a continuous pumping well near a stream whose bed is semipervious and partially penetrates the aquifer (i.e., Hantush's 1965 solution). A relationship developed by Spalding and Khaleel (1991) was incorporated into the solutions in order to include the effects of the effective pumping distance and stream‐bed clogging layer, which represent the degree of stream penetration and stream‐bed resistance, respectively. A dimensionless plot based on these equations has been developed for the dimensionless volume of stream depletion over a pumping cycle. Analysis of this figure showed that effective resistance of the semipermeable stream bed is the dominant parameter for the determination of equilibrium time. Also a dimensionless plot has been developed to determine the magnitudes of error in the maximum rate of stream depletion at the time at which a practical state of dynamic equilibrium is achieved, when partial penetration of the stream and stream‐bed clogging layer is neglected. Analysis of this figure also showed that neglecting the effects of both the partial penetration of the stream and the resistance of the semipermeable layer of the stream bed produces a substantial amount of error in the maximum stream depletion rates com‐ puted by the methods developed by Wallace et al. (1990) and Darama (1991).