Environmental Engineering Reference
In-Depth Information
effective. A doublet consists of a pumping well and an
injection well operating as part of a pump-and-treat
system. Doublets form a circulation cell within the
aquifer and are frequently used as a means of injecting
and removing aquifer mitigation solutes, such as cosol-
vents, surfactants, or both (Kemblowki and Urroz, 1999).
Typically, the recharge well is positioned directly upgra-
dient from the discharge well, and the magnitudes of the
pumping and injection rates are the same. This arrange-
ment isolates a circulation cell within the groundwater
and is sometimes referred to as
hydrodynamic isolation
.
The upstream and downstream boundaries of the circu-
lation cell are defined by the points (−
x
s
, 0) and (
x
s
, 0),
respectively, where the
x
-axis is parallel to the direction
of the regional groundwater flow, and the origin of the
coordinate system is located at the midpoint between
the two wells. The stagnation points (−
x
s
, 0) and (
x
s
, 0)
are the roots of the equation
Solution
From the given data,
L
= 80 m,
W
= 25 m,
J
= 0.25% =
0.0025,
K
= 8 m/day,
H
= 30 m, and
Q
w
= 60 L/min =
86.4 m
3
/day. The regional flow specific discharge,
q
0
, is
given by the Darcy equation as
q KJ
0
=
=
8 0 0025
( .
)
=
0 02
. m/d
Requiring the upstream and downstream stagnation
points (−
x
s
, 0) and (
x
s
, 0) to coincide with the upstream
and downstream edges of the contaminant plume
requires that
2
x
s
=
80
m
which yields
x
s
= 40
m
q Hd
Q
1
2
x d
x d
/
x d
x d
/
=
Substituting given data into Equation (5.119) gives
0
+
−
0
(5.119)
2
2
π (
/
+
1
)
(
/
−
1
)
w
q Hd
Q
1
2
x d
x d
/
x d
x d
/
=
0
+
−
0
π (
/
+
1
)
2
(
/
−
1
)
2
where
q
0
is the specific discharge of the regional flow,
2
d
is the distance between the wells, and
Q
w
is the
pumping rate (= injection rate). The boundary of the
circulation cell is defined by
w
( .
0 02 30
86 4
)(
)
d
1
40
40
/
d
40
40
/
d
=
+
−
0
.
2
π
(
/
d
+
1
)
2
(
/
d
−
1
)
2
which can be written as
q Hy
Q
1
2
y d
x d
/
y d
x d
/
1
2
=
0
+
π
tan
−
1
−
tan
−
1
0 278
.
1
1
=
(5.121)
/
+
1
/
−
1
+
0 159
.
χ
−
0
w
χ
(
χ
+
1
)
2
(
χ
−
1
)
2
(5.120)
where
The circulation cell is symmetric with respect to
the
y
-axis, and the circulation cell is delineated by
first estimating the stagnation points, varying
x
between
zero and
x
s
, and using Equation (5.120) to solve
for
y
.
χ=
40
d
The only feasible solution of Equation (5.121) is
χ= 2 93
.
EXAMPLE 5.22
which gives
A well doublet is to be used as part of a pump-and-treat
system to remediate contaminated groundwater. The
contaminant plume is approximately 80 m long and
25 m wide. The regional hydraulic gradient is 0.25%, the
average hydraulic conductivity of the aquifer is 8 m/day,
and the saturated thickness of the aquifer is 30 m. If the
on-site treatment system is capable of treating the
pumped water at 60 L/min, what is the required spacing
of the wells so that the circulation cell within the aquifer
encompasses the entire plume?
d
= 13 . m
Therefore, for the upstream and downstream stagna-
tion points in the doublet to coincide with the upstream
and downstream edges of the contaminant plume, the
pumping and injection wells must be 2 × 13.7 = 27.4 m
apart and placed symmetrically within the contaminant
plume.
It is necessary to verify that the circulation cell
encompasses the entire width of the contaminant plume.
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