Environmental Engineering Reference
In-Depth Information
and the hydraulic gradient can be problematic
and costly (
Section 2.3.5
).
K
s
is highly variable in
space, so the method is limited by the ability to
determine representative values of
K
s
.
(a)
4
3
6.3.2 Hantush (
1956
)
Leakage through aquitards is an important
source of recharge for regionally extensive,
deep, confined aquifers. Leakage does not con-
form to the definition of recharge given in
Chapter 1
; instead, leakage is referred to as
interaquifer flow. Estimates of interaquifer
flow usually rely on knowledge of ground-
water levels. As pumping lowers water levels
in the confined aquifer, water is drawn out of
the confining units or adjoining aquifers, in
accordance with Darcy's law. For steady flow of
water through confining beds, Hantush (
1956
)
expressed Darcy's law as:
2
(b)
0.2
0.1
0
(c)
0.010
0.005
0
1/1/2001
1/1/2002
Date
1/1/2003
R Q A
=
/
=
( '/
km
')
∆
(6.16)
c
c
where
Q
c
is the volumetric rate of leakage
through the confining bed;
A
c
is the area over
which leakage is occurring;
( k'/m'
) is the leakage
coefficient or leakance, where
k'
is the vertical
hydraulic conductivity and
m'
is the thickness
of the confining bed; and Δ
H
is the difference
in total head between the aquifer and the top
of the confining bed. The method requires
measurements of water levels (head) in the
aquifer and at the top or above the confining
bed as well as measurements or estimates of
k'
. Hydraulic conductivity can be measured in
the laboratory if core samples of the confining
bed are available (
Section 2.3.5
). Piezometers
in the confining bed can also be used to con-
duct single-borehole slug tests for estimating
k'
(Neuzil,
1986
). Alternatively,
( k'/m'
) can be
determined through analysis of a constant-rate
pumping test on the confined aquifer or from
drawdown vs. distance or drawdown vs. time
data in a manner similar to that described for
type-curve matching (Walton,
1970
; Neuman
and Witherspoon,
1972
).
Figure 6.10
Data from observation well tapping the
Tomago sand beds: (a) water-table elevation; (b) apparent
specific yield; and (c) estimated recharge rate (Crosbie
et al
.,
2005
).
6.3 Methods based on the Darcy
equation
6.3.1 Theis (
1937
)
Theis (
1937
) used Darcy's equation to estimate
flow through a cross section of the Southern High
Plains aquifer in New Mexico. A simple water
budget was constructed assuming steady condi-
tions and no water extraction. The calculated
flow rate through the cross section was divided
by the contributing upgradient area to give an
estimate of recharge. The approach requires
estimates of saturated hydraulic conductivity
(
K
s
), hydraulic gradient, cross sectional area, and
the area up gradient from the cross section over
which recharge occurs. Using a range of values
of
K
s
determined from laboratory and aquifer
tests and water levels from a network of obser-
vation wells, Theis (
1937
) estimated the annual
recharge rate to be 3 to 7 mm. The method is
easy to apply if information on
K
s
and water lev-
els is available. However, determination of
K
s
6.3.3 Flow nets
Estimates of groundwater recharge can also
be obtained by graphical analysis of flow nets
for both confined and unconfined aquifers.
