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# Response of a Confined Aquifer to Pumping: Nonleaky and Leaky Cases

This Demonstration represents the response (in terms of the well function ) of a confined aquifer subject to pumpage from a fully penetrating well. If there is no leakage from an adjacent hydrogeologic unit to the main aquifer, the response is the red curve, widely known as the Theis-type solution. When an adjacent aquifer is hydraulically connected to the main unit, the latter becomes a leaky confined aquifer, leading under this condition to the cyan curve, known as a Hantush–Jacob-type solution. The well function has a single argument for the Theis (or nonleaky) case named , whereas for the Hantush (or leaky) case, there are two arguments, and . Notice how the Hantush–Jacob solution deviates from the Theis curve as the ratio increases.

### DETAILS

The governing equation for the pumped confined aquifer nonleaky case is
with solution
,
where
and .
The governing equation for the leaky case is
with solution
,
where
, , and ,
with
: distance from the pumping well
: time since the pump was turned on
: storativity coefficient
: main aquifer transmissivity
: piezometric head at rest (before pumping)
: drawdown
: constant pumping rate
: well function
: thickness of the adjacent hydrogeologic unit
': hydraulic conductivity coefficient of the adjacent unit
References
[1] C. V. Theis, "The Relation between the Lowering of the Piezometric Surface and the Rate and Duration of Discharge of a Well Using Ground-Water Storage," Transactions of the American Geophysical Union, 16(2), 1935 pp. 519–524. onlinelibrary.wiley.com/doi/10.1029/TR016i002p00519/abstract.
[2] M. S. Hantush and C. E. Jacob, "Non-steady Radial Flow in an Infinite Leaky Aquifer," Transactions of the American Geophysical Union, 36(1), 1955 pp. 95–100. onlinelibrary.wiley.com/doi/10.1029/TR036i001p00095/abstract.
[3] F. W. Schwartz and H. Zhang, Fundamentals of Ground Water, New York: Wiley, 2003.

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