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

​
r
B
0.5
W(u)
Wu,
r
B
This Demonstration represents the response (in terms of the well function
W(·)
) 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
W(·)
has a single argument for the Theis (or nonleaky) case named
u
, whereas for the Hantush (or leaky) case, there are two arguments,
u
and
r
B
. Notice how the Hantush–Jacob solution deviates from the Theis curve as the ratio
r
B
increases.

Details

The governing equation for the pumped confined aquifer nonleaky case is
2
∂
h(r,t)
∂
2
r
+
1
r
∂h(r,t)
∂r
=
S
T
∂h(r,t)
∂t
with solution
h
o
-h(r,t)=s(r,t)=
Q
4πT
W(u)
,
where
W(u)=
∞
∫
u
-z
e
z
dz
and
u=
2
r
S
4Tt
.
The governing equation for the leaky case is
2
∂
s(r,t)
∂
2
r
+
1
r
∂s(r,t)
∂r
-
s(r,t)
2
B
=
S
T
∂s(r,t)
∂t
with solution
s(r,t)=
Q
4πT
Wu,
r
B
,
where
Wu,
r
B
=
∞
∫
u
-z-
2

r
B


1
4z

e
z
dz
,
B=
Tb'
K'
, and
u=
2
r
S
4Tt
,
with
h(r,t)
: piezometric head
r
: distance from the pumping well
t
: time since the pump was turned on
S
: storativity coefficient
T
: main aquifer transmissivity
h
o
: piezometric head at rest (before pumping)
s(r,t)
: drawdown
Q
: constant pumping rate
W(·)
: well function
b'
: thickness of the adjacent hydrogeologic unit
K
': 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.

Permanent Citation

Diego M. Oviedo Salcedo
​
​"Response of a Confined Aquifer to Pumping: Nonleaky and Leaky Cases"​
​http://demonstrations.wolfram.com/ResponseOfAConfinedAquiferToPumpingNonleakyAndLeakyCases/​
​Wolfram Demonstrations Project​
​Published: October 19, 2015