Geoscience Reference
In-Depth Information
Soil surface
Recharge
R
Canal
Porosity
φ
Velocity
v
x
Flux
q
out
Height
H
Impermeable layer
x
=
x
x
=
L/2
Figure 5.15
Schematization with symbols of stationary low to parallel canals. The
groundwater divide occurs at
z
= 0.
x
=
0
Rx
H
v
x
=
φ
(5.31)
where
R
is the groundwater recharge (m d
-1
),
φ
is the porosity (-) and
H
is the aqui-
fer thickness (m). By integration we may derive the residence time
T
res
(d), the time
needed to low from
x
=
x
to the canal at
x
=
L
/2:
d
x
φ
H
R
d
x
x
φ
H
R
φ
H
R
L
x
L
/
2
L
/
2
=
[ ]
=
xL
=
/
2
∫
∫
T
=
=
ln
x
ln
(5.32)
res
v
2
xx
=
xx
=
xx
=
x
Thus the entrance place
x
for residence time
t
equals:
−
Rt
H
½e
φ
x
=
L
(5.33)
We may draw streamlines similar to
Figure 5.16
. The igure represents the situa-
tion at time
t
, where solutes in the denoted area have reached the canals. As we deal
with a streamline pattern at steady-state conditions, we may write for the water luxes
and deined lengths (
Figure 5.16
):
q
q
R
R
out
1
=
3
⇒=
1
3
(5.34)
out
2
4
2
4
where
q
out
is the water lux density at
x
=
L
/ 2. Suppose initially no solute were pre-
sent in the groundwater and from
t
= 0 onwards the concentration in the recharge
water amounts to
C
in
(kg m
-3
). Compared to the convective processes in such a
groundwater system, we may neglect the diffusive and dispersive transport (Duffy
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