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.

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

: piezometric head

: 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.