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Advances in Environmental Biology, 7(13) November 2013, Pages: 4356-4360
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Advances in Environmental Biology
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Management of Saltwater Intrusion in an Island by Ant Colony Algorithm
1
Mehdi Nezhad Naderi, 2Masoud Reza Hessami Kermani, 3Gholam-Abbas Barani
1
Department of Civil Engineering, Shahid Bahonar University, P.O. BOX 76169133, Kerman, Iran
Asisstant Professor, Department of Civil Engineering, Shahid Bahonar University, P.O. BOX 76169133, Kerman, Iran.
3
Professor, Department of Civil Engineering, Shahid Bahonar University, P.O. BOX 76169133, Kerman, Iran.
2
ARTICLE INFO
Article history:
Received 11 September 2013
Received in revised form 21 November
2013
Accepted 25 November 2013
Available online 29 December 2013
Keywords:
Saltwater Intrusion, Saltwater
Upconing, Wells Operation,
Optimization, Ant Colony Algorithm,
Water Management In An Island.
ABSTRACT
Pumping water from a well in the aquifer is caused the displacement of interface
between saltwater and freshwater below the well. This reaction is known to upconing.
Maximum height of upconing is located below the well, where the maximum reduction
of water level has occurred. Aim of this research is the maximization of net profit from
the exploitation of wells with minimum arrival of saline water to the wells. Because of
the huge, rupture and local minimum in search space, we have used from Ant colony
algorithm for finding optimal solutions. The application of model was developed for
consisting of seven wells a hypothetical this study is in an island. As result the optimal
amount of pumping and position of each of the wells were obtained. The maximum net
profit and upconing are affected by exploitation rate of wells and distance of each well
to sea. The results show that Ant colony algorithm can effectively and efficiently be
used to obtain nearly global solutions to this groundwater management problem. The
optimum solution is not solved for values of less than 10 𝒎𝒎/day for hydraulic
conductivity and problems will have high local solutions.
© 2013 AENSI Publisher All rights reserved.
To Cite This Article: Mehdi Nezhad Naderi, Masoud Reza Hessami Kermani, Gholam-Abbas Barani., Management of Saltwater Intrusion
in an Island by Ant Colony Algorithm. Adv. Environ. Biol., 7(13), 4356-4360, 2013
INTRODUCTION
In many coastal areas, high rates of urbanization and increased agriculture have arises the demand for
groundwater [1]. Several wells have been drilled to supply increasing water demand.The increase in water
withdrawals from the wells have caused unacceptable drawdowns and deterioration of the quality of water
pumped by some of the wells. A set of well-established withdrawal and management policies is necessary to
achieve more efficient management and operation of these aquifers. Groundwater management is posed as the
maximization of the net benefit obtained from water use subject to constraints of no intrusion of saltwater below
the wells, and pumping capacity limits restrictions. Initial efforts to support and improve the development and
operation of groundwater systemsby simulation and optimization techniques were made in the early 1970s.
These studies were conducted to maintain aquifer levels and prevent the saltwater intrusion so that undesirable
economic consequences and legal violations are prevented.Artificial intelligence approaches have predicted well
physical behavior of scour phenomena around hydraulic structures [17, 18]. In this paper, we deal the
development and application of an operational groundwater management model for a coastal aquifer system. For
simplicity and feasibility demonstration purposes the single-potential formulation of [13] isadopted for solving
boundary value problems. An Ant colony Algorithm [6,10] is used for optimization purposes.
MATERIALS AND METHODS
In this section, the governing equations of the salinity intrusion in the freshwater lens with an analytical
solution are used under appropriate simplifying assumptions. Let's first assume the correctness condition
Dupuit- Forchheimer which can result in a two-dimensional flow was assumed. Another assumption is that
flow is steady, and the third assumption is the correctness condition Ghyben- Herzberg for the position of the
boundary between saltwater and freshwater[16]. Theform of rising boundary level between two fluids issimilar
to cone. And it is known to upconing. Maximum height of upconing is located below the well. Under steady
flow of freshwater into horizontal wells, saltwater moves in the vertical direction, and the specific exact
interface between the two fluids, height of upconing in the below well axis (z) by using of the Ghyben Herzberg [16] equation wrote as follows[16, 18].
Corresponding Author: Mehdi Nezhad Naderi, Department of Civil Engineering, Shahid Bahonar University, P.O. BOX
76169133, Kerman, Iran,
E-mail:[email protected]
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Mehdi Nezhad Naderi et al, 2013
Advances in Environmental Biology, 7(13) November 2013, Pages: 4356-4360
ρf
z=
ρs −ρf
Sw
z=
2π(ρs −ρf ) d K x
(1)
WhereSw isdrawdown of groundwater level in well, ρf is density of freshwaterand ρs is density of saltwater.
[7] determined by below exact equation the height of upconing of the saltwater below well axis:
Q ρf
(2)
Where z is final elevation or balanced height of saltwater upconing below the well, K x is aquiferhydraulic
conductivity and d is depth of interface of between saltwater and freshwater from below the well before start of
pumping(sea Figure 1 and 2).Fieldand laboratorymeasurementshave shown thatequation (2)for values
ofz/dfrom0.3to0.5is true; so ifthebottom limit0.3isthe criterion, the pumping rate is the maximum allowed
without a wedge of saltwater into the wells to be as follows[21].
Fig. 1: Fresh water lenses on a small oceanic is land with pumping wells, zone1 is recharge zone, zone 2 is
underground water, zone 3 is boundary of freshwater and saltwater in steady state (yellow line), zone 4
is boundary of freshwater and saltwater in unsteady state (red line).
Fig. 2: A circular island with a central well in the center of the aquifer and rainfall, zone1 is underground water
surface with rainfall and no pumping, zone2 is underground water surface with no rainfall and pumping,
zone3 is underground water surface with rainfall and pumping.
Q max = 0.6πd2 K x
ρs −ρf
ρf
(3)
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Advances in Environmental Biology, 7(13) November 2013, Pages: 4356-4360
Last assumed ignoring the thickness of the transitional boundary between salt and fresh water. As a result of
this boundary is considered to be one page. Relation to the boundaries of salt water and fresh water depends on
the size of the island, aquifer hydraulic conductivity and recharge rates as follows[21]:
𝑧𝑧 = [
𝑤𝑤
0.05125 𝑘𝑘
1
(𝑅𝑅2 − 𝑟𝑟 2 )]2
(4)
Where z is the depth of the interface below sea level at radius r, R the radius of the circular-shaped island,
w is effective recharge rate as result of rainfall and k is aquifer hydraulic conductivity.
Fig. 3: Seawater intrusion by upconing to wells from the unconfined aquifer of an island and the correspondent
optimal solution for their net benefit.
Figure (3) a well has been drilled completely to the bottom impervious layer of the aquifer in the island.
The island form is almost a circle that R is the radius of it. The rain is fall with w rate on the island and
recharges the aquifer. Wells drilled in the middle of the island and the water is pumped at a rate of Q w instable
condition. Extraction of underground water level equation during pumping is as follows:
H 2 − h2 =
Qw
πK
R
ln −
r
w
2K
(R2 − r 2 )
(5)
Nowadays, Ant colony algorithm is recognized as powerful direct search algorithms and offers suitable
alternative to conventional optimization technique. The fundamental theory in an Ant ColonyOptimization
(ACO) algorithm is the simulation ofthe autocatalytic, positive feedback process exhibited by a colonyof ants
[5]. The ant colony system (ACS)is an ACO algorithm based upon the original work of [14, 11].A summary of
the ACS algorithm, asdeveloped by [12].defined in the structure of a TSP is presented.
The ranked ant system (𝐴𝐴𝐴𝐴𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ) developed by [3] is a modification to the ACS. In the 𝐴𝐴𝐴𝐴𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 , the tours
createdby the ants are ranked according to how well they solve theproblem. This update rule was found to
significantly improve the quality of the results obtained by the AS [13].
The objective is to obtain an optimal pumping policy by maximizing the net benefit, subject to constraints
of no intrusion of saltwater front to the wells, and pumping capacity limits restrictions. The solution of the
model determines the optimal sustainable spatial distribution of the pumping for beneficial uses from a specified
set of potential locations in the two dimensional space, while the saltwater intrusion will not contaminated wells.
The pumping costs are assumed to be directly proportional to the product of the pumping rate and the total lift at
each well [22]. The mathematical expression of the objective function of this model can be written as [11].
Z = Maximize Net Benefit = ∑ni=1(BP Q w (i) − Cp Q w (i) (Li − hi )
(6)
with respect to𝑄𝑄𝑤𝑤 (𝑖𝑖) and other design variables where Z is the objective function, subject to the constraints : The
management aspects are satisfied:
i) Toe location constraints:
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Advances in Environmental Biology, 7(13) November 2013, Pages: 4356-4360
0 < 𝑑𝑑𝑤𝑤 (𝑖𝑖) < 𝑑𝑑0 + [
𝑤𝑤
0.05125 𝐾𝐾
1
(𝑅𝑅2 − rw (i) 2 )]2 −
𝑄𝑄𝑤𝑤 (𝑖𝑖) 𝜌𝜌 𝑓𝑓
2𝜋𝜋(𝜌𝜌 𝑠𝑠 −𝜌𝜌 𝑓𝑓 )𝑑𝑑 𝑤𝑤 (𝑖𝑖) 𝐾𝐾𝑥𝑥
ii) The pratical pumping capacity limits should not be exceeded:
𝑄𝑄𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 ≤ 𝑄𝑄𝑤𝑤 (𝑖𝑖) ≤ 𝑄𝑄𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 i=1,m(8)
iii)The locations of wells limits:
(7)
0.30 < rw (i) < 𝑅𝑅,dw (i) > d0 + H − hw (i) i=1…n(9)hw(i) = (H 2 − �
Q w (i)
πK
R
ln −
r
w
2K
�R2 − rw (i) 2 ��)^0.5
In the aboveQ w (i) is the discharge rate of well i, rw (i) is the distance of well i from thecenter of island, Qmin
i
and Qmax
are respectivelythe minimum and maximum discharge of a well constrained by equipment capacity, hi
i
is thehydraulic head at well point i,Li is initial lift at well i, BP is the benefit per unit supply of water at well point
i, Cp is the cost of pumping a unit volume per unit head at well point i; m is the number of wells.The design
variables are the pumping rate Q w(i) and locations of wells rw (i) , dw (i) ). For example for 7 existing wells the
design variables are(Q w (i) , i = 1 to 7), (rw (i) , i = 1 to 7) and (dw (i) , i = 1 to 7).dw (i) is height of below every
wells from ground surface and d0 is height of ground surface of island to sea level of island sides and H is
depth of seawater in island sides to bedrock and h is ground water level in the well to the below well.
The proposed optimization model, is applied to a specific hypothetical unconfined coastal aquifer in an
island. The management model solutions is useful for establishing the potential applicability of the proposed
model. However, the evaluations of these solutions are no doubt limited in scope, because: 1) the study area is
hypothetical, and 2) uncertainties in parameter estimates, boundary conditions, and imposed stresses are not
incorporated for this problem, the numerical solution is required two search processes. In the first step, the
governing equation (1-5) with a given pumping pattern is solved to give the solution in height of upconing.
Another search is conducted in the wells discharges space to find the optimal pumping rates. We examine an
unconfined aquifer with k =20m/day,q=4𝑚𝑚3 /day/m,r=0.3m, 𝜌𝜌𝑠𝑠 =1.025 g/𝑐𝑐𝑐𝑐3 , and 𝜌𝜌𝑓𝑓 =1 g/𝑐𝑐𝑐𝑐3 . Figure 4 gives
an aerial view of the coast and the locations of 7 pumping wells. The optimal well coordinates are shown in
column (2) and (3) in Table1. For each well we assume that there exist a lower bound 𝑄𝑄min and an upper bound
𝑄𝑄max for pumping rate. The upper bound is limited by equipment and operational conditions. A constant 𝑄𝑄max
=5000𝑚𝑚3 /day is initially chosen for all wells. We then check the critical pumping rates of each well assuming
that the well exists alone. Since there is no reason that a well can pump more than the critical rate (𝑄𝑄c ), the
smaller of 𝑄𝑄c and 5000 𝑚𝑚3 /day is used as the upper bound, which is listed in column (4) of Table 1. The value
of 𝑄𝑄min = 0𝑚𝑚3 /day is used for all wells. Position of wells are in area with dimension
of𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚 = 2000𝑚𝑚 𝑎𝑎𝑎𝑎𝑎𝑎 𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚 = 14𝑚𝑚 𝑎𝑎𝑎𝑎𝑎𝑎 𝑑𝑑0 = 4𝑚𝑚, 𝑎𝑎𝑎𝑎𝑎𝑎 𝐻𝐻 = 10,Li − hi = 5m.With a uniform benefit rate of
0.16 $ per 𝑚𝑚3 of water and a pumping cost of 0.0024 $ per 𝑚𝑚3 per m lift of water [8], the total optimum water
withdrawals are given in Figure 3.
Table 1: Optimal well coordinates and optimum water withdrawals.
Well ID
(𝑟𝑟𝑤𝑤(𝑖𝑖) )(𝑚𝑚)
1
0.3
2
33
3
0.3
4
33
5
0.3
6
66
7
0.3
𝑑𝑑𝑤𝑤(𝑖𝑖) (𝑚𝑚)
6.4
4
4
5.2
4.15
4.45
4
𝑄𝑄𝑤𝑤 (𝑖𝑖) (𝑚𝑚3 /day)
4850
4320
1040
4400
4800
3760
400
Result:
As results of pumping tests on 60operatedwellsin Amol- Babol aquifer between Babolrood and Haraz[13],
obtained Transfer coefficient = 40𝑚𝑚2 /day, hydraulic conductivity coefficient = 0.2𝑚𝑚/dayand hydraulic gradient
= 3.18× 10−3 thus
q=T.I= �40(
m3
m.day
day
)/86400(
s
) �×3.18×10−3 = 1.472×10−6 (m3 /s)/m=0.123𝑚𝑚3 /day/m. If we assume hydraulic
conductivity coefficient is limited between 0.1 𝑚𝑚/day to 100𝑚𝑚/day we obtained that for the multiple pumping
wells problem, the optimum solutionis not solved for values of less than 10 𝑚𝑚/daythusproblem has high local
solutions. For low amount of H we obtained that the positions of pumping wells (rw (i) )are located in out of
island. It means that discharge pumping from the well is provided from the seawater.
Conclusion:
Management model with economic objective function for sustainable use of islandaquifers is formulated
and solved. For the multiple pumping well problem, the analytical solution, e.g. Dagan and Bear Pumping Well
Solution, is most useful for engineers to conduct feasibility study and preliminary design. The optimization
technique has been applied to the saltwater problem in such a way to locate either the interface or the upconing
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Advances in Environmental Biology, 7(13) November 2013, Pages: 4356-4360
position of the saltwater that entered into aquifer. The coupling of the analytical solution upconing interface
approach with Ant colony system is a very promising tool for use in solving this economic objective
optimization problem. We have demonstrated the use of the Ant colony system to conduct the search. The
search space is huge, but we believe that we have obtained a near-optimal solution. The computational time
required for the solution of management model increases with the complexity of the problem. The optimum
solutionis not solved for values of less than 10 𝑚𝑚/day thus problem has high local solutions. Because of the full
of discharge pumping is provided from recharge of rainfall must be reduced discharge pumping or H must be
higher than default.
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