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3.10 Nonsteady Radial Flow 81
flow to become stabilized in a portion of the cone of depression. The minimum duration of
pumping depends on the properties of the aquifer.
The observed drawdown s, if large compared to the initial depth of flow h , should
0
2
be reduced by a factor s 2h to account for the decreased thickness of flow due to de-
0
watering before Eq. 3.15 can be applied. For an observation well at a distance greater
than 0.2h , the minimum duration of pumping beyond which the approximation is valid
0
is given as:
t min 37.4h >K (U.S. Customary Units) (3.29a)
0
where t is time in days, h is the saturated aquifer thickness in ft, and K is hydraulic con-
0
2
ductivity in gpd/ft .
t min 5h >K (SI Units) (3.29b)
0
Where t min is time in days, h is saturated aquifer thickness in m, and K is hydraulic con-
0
2
3
ductivity in m /d/m .
3.10.5 Leaky Aquifers

The partial differential equation governing nonsteady radial flow toward a steadily dis-
charging well in a leaky confined aquifer is
2
0 s 1 0s s S 0s
+ - 2 = (3.30a)
2
0r r 0r B T 0t
where
T
B = (3.30b)
AK¿>b¿
and s is the drawdown at a distance r from the pumping well, T and S are the transmissiv-
ity and storage coefficient of the lower aquifer, respectively, and K and b are the vertical
permeability and thickness of the semipervious confining layer, respectively. The solution
in an abbreviated form is given as
s 114.6Q>T[W(u, r>B)] (3.31)
where
q 2
1 -y -r
W(u, r>B) = exp 2 dy
L u y 4B y
and
2
u 1.87 r S>Tt (3.32)
Here, W(u, r>B) is the well function of the leaky aquifer, Q is the constant discharge of the
well in gpm, T is transmissivity in gpd/ft, and t is the time in days.
In the earlier phases of the transient state, that is, at very small values of time, the
system acts like an ideal elastic artesian aquifer without leakage and the drawdown pat-
tern closely follows the Theis type curve. As time increases, the drawdown in the leaky
aquifer begins to deviate from the Theis curve. At large values of time, the solution ap-
proaches the steady-state condition. With time, the fraction of well discharge derived
from storage in the lower aquifer decreases and becomes negligible at large values of time
as steady state is approached.