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Approximation for Steady Interface Beneath a Well Pumping Fresh Water Overlying Salt Water
Author(s) -
Haubold Reiner G.
Publication year - 1975
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.1745-6584.1975.tb03083.x
Subject(s) - position (finance) , interface (matter) , computation , mechanics , salt water , aquifer , geometry , groundwater , materials science , mathematics , geology , physics , geotechnical engineering , algorithm , finance , bubble , maximum bubble pressure method , economics
A mathematical expression was developed which would approximate the steady position and shape of a sharp, upconed interface between fresh and salt water in an aquifer when the fresh water only is being pumped from a well. The computation of the interface shape was based on an empirically derived modification of Muskat's approximation for the height of the cone beneath a well. Differing depths of well penetrations and their effect on the upconed interface were investigated with the approximation. The computed interfaces were compared with corresponding interfaces determined experimentally in a Hele‐Shaw model. Close agreements could be achieved for interfaces which penetrated as much as 50% of the distance between the bottom of the well and the initial interface position. Changing the length of the producing interval of the well while keeping its pumping rate constant did not have a significant influence on the shape or position of the upconed interface. Even though the shape and position of the upconed interface could be approximated, a refinement of the analytical methods used in deriving the approximation for the interface may be necessary before it can be applied reliably.