Geoscience Reference
In-Depth Information
A new optimization model is proposed in this study. The model can
identify optimal rates and locations not only for freshwater pumping wells,
but also for freshwater injection and saltwater pumping wells. The model
can be applied to heterogeneous aquifers of finite size and irregular shape.
Positive and negative impacts on groundwater environments are also con-
sidered. The optimization model proposed herein is an addition to the lit-
erature in that removes a significant portion of the limitations of previous
models and extends the applicability.
2. Optimization Model
2.1.
Objective function
The optimization process may become simpler by combining objective func-
tions into a single function. The constraints also need to be combined into
the objective function so that an unconstrained optimization technique,
such as the genetic algorithm, can be used. The final form of the objective
function in coastal aquifers becomes
N
opt
N
p
N
s
Q
s
Q
f
+
Q
s
−
maximize
Φ =
α
Q
f
−
ω
1
ω
2
Q
s
,
(1)
i
=1
i
=1
i
=1
where
Q
f
and
Q
s
are the freshwater and saltwater pumping rates in the
well
i
,
N
opt
is the number of targeted optimal wells,
N
p
is the total num-
ber of wells including both optimal wells and existing wells in a domain,
N
s
is the number of optimal wells designed to withdraw saltwater,
ω
1
and
ω
2
are the weighting factors. The first term can be considered a benefit,
the second term is a penalty function that reduces the value of the objec-
tive function when saltwater is pumped from the wells designed to pump
freshwater only, and the third term is the cost incurred from pumping salt-
water to control the saltwater wedge. The number of wells is assumed to
be determined
apriori
.
α
is a groundwater protection index representing
the adverse impacts caused by pumping on the groundwater environment
(Fig. 1). The groundwater protection index is defined as below:
α
=1
−
(
D
+
I
+
A
)
×
ω
3
,
(2)
where,
ω
3
is a weighting factor,
D
is the weighted normalized average draw-
down (=
V
D
/A
T
H
),
I
is the weighted normalized average increase in saltwa-
ter thickness (=
V
S
/A
T
H
),
A
is the weighted normalized saltwater volume
(=
A
I
/A
T
),
A
T
is the domain area,
V
D
isthevolumeofdrawdown,
H
is
