Optimal Well Locations using Genetic Algorithm for Tushki Project, Western Desert, Egypt

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International Journal of Engineering Research Science IJOER ISSN: 2395-6992 Vol-3 Issue-7 July- 2017
Page | 1
Optimal Well Locations using Genetic Algorithm for Tushki
Project Western Desert Egypt
S. Khalaf
1
M.I. Gad
2
1
Irrigation and Hydraulics Dept. Faculty of Engineering Mansoura University Egypt.
2
Prof. Dr. Hydrology Division Desert Research Center Cairo Egypt
Abstract — The well location problem is challenging due to the non-linear discrete and often multi-modal objective
function. The optimal distribution of productive well locations mitigates the groundwater productivity problem that threats
the national projects in arid countries like Egypt. In this paper a trial to mitigate this problem in Tushki National Project
south western desert Egypt is supposed via delineating the optimal well locations and optimal pumping rates. The
methodology of combination between simulation and optimization techniques is applied. The simulation outputs of
groundwater flow system by Visual MODFLOW model is linked by the constructed Fortran Code for Optimal well Location
using Genetic Algorithm OLGA Code for obtaining the optimum management of groundwater resources in this project.
Two management cases are considered by running the model domain with adopted steady and transit calibrated parameters.
The first management case deals with the present well locations and predicts the optimal value of the objective function
maximum pumping rate. In the second case the optimal new well locations resulted from the OLGA Code is predicted from
flexible well location with the moving well option. Also the prediction of the future changes in both head and flow are
studied in steady and transient states.
Keywords — Groundwater Optimization Genetic Algorithm Tushki project.
I. INTRODUCTION
Selecting optimal well sites is a valuable problem to solve maximizing groundwater recovery increases oil reserves and
minimizing costs improves profitability. One of the best methods of selecting optimal sites is the combined use of simulation
and optimization S/O models. While simulation models basically provide solutions of the governing equations of
groundwater flow optimization models identify an optimal management and planning strategy from a set of feasible
alternative strategies. The genetic algorithm GA is widely used to modify the parameters of groundwater flow models Yan
et al. 2003 Yao et al. 2003 and to solve the management models of groundwater resources Mckinney and Lin 1994 Liu
et al. 2002 Zhu et al. 2003. Rana et al 2008 conducted a study on a spatio-temporal optimization of agricultural
drainage using groundwater model and GA. Guan et al. 2008 proposed an improved genetic algorithm IGA to solve
optimization problems with equality and inequality constraints. Hamid et al. 2009 presented a paper focusing on the S/O for
conjunctive use of surface water and groundwater on a basin-wide scale the Najafabad plain in west-central Iran. Gad et al.
2011 and Moharram et al. 2012 used an optimization model based on the combination of MODFLOW simulation with
GA to maximize the total pumping rate from the Nubian sandstone aquifer in El-Dakhla and El-Farafra depressions Egypt.
Saafan et al. 2011 applied multi-objective genetic algorithm MOGA Code in El-Farafra depression Egypt to study the
maximum pumping rate and minimum operation cost. Gad and Khalaf 2013 used MOGA model to develop the maximum
pumping rate and minimum operation cost in the Miocene aquifer of Wadi El-Farigh West Delta Egypt.
In the other side there are limited studies for the determination of optimal operating strategy including unknown well
locations and pumping rates for groundwater systems to the best of our knowledge Wang and Ahlfeld 1994 Karahan and
Ayvaz 2005 and Ayvaz and Karahan 2008. Saffi and Cheddadi 2007 developed an algebraic expression which gave the
matrix of transient influence coefficients for one-dimensional semi-confined aquifer model and solved the governing
equation by using a mixed compartment model. Tung and Chou 2004 integrated pattern classification and tabu search to
optimize the average zonal groundwater pumping for an aquifer. As a general the research conducted in this field dealt with
the identification of locations and released histories of unknown groundwater pollution sources Mahar and Datta 2000
2001 Aral et al. 2001 Ruperti 2002 Singh et al. 2004 Sun et al. 2006 pumping well optimization for optimum
remediation design Wang and Ahlfeld 1994 Huang and Mayer 1997 Guan and Aral 1999 Zheng and Wang 1999
Mantoglou and Kourakos 2007 Chang et al. 2007 and optimum well locations and pumping rates in the coastal sides
Park and Aral 2004 Ferreira da Silva and Haie 2007. Meira et al. 2016 proposed technique for decision-making process
in optimal well location including a step of risk analysis associated with the uncertainties present in the variables of the

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International Journal of Engineering Research Science IJOER ISSN: 2395-6992 Vol-3 Issue-7 July- 2017
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problem. The proposed technique was applied to two benchmark cases and the results evaluated by experts in the field
indicated that the obtained solutions were richer than those identified by previously adopted manual approaches.
Due to the few of scientific researches related to optimal well locations especially in our national governmental and invest
mental agricultural projects a trial was carried out in this paper to through a light on the optimal location for new fourteen
production wells in Tushki project required for irrigation of 25 thousand acres which will drill under the strategy of
reclamation of 1.5 million acres project.
II. DESCRIPTION OF CASE STUDY
2.1 Site description
Tushki area is a part of the Western Desert of Egypt between latitudes 22° 14 24.75" and 22° 50 6.10" N and longitudes
31° 0 44.06"and 31° 50 4.05E with total area of 2268 km
2
. Tushki project one of the national governmental and invest
mental agricultural projects aims to reclaim 540000 acres using both surface water from El-Sheikh Zaid artificial canal 1.5
km
3
/year and groundwater extracted from about 316 productive wells for cultivating 36000 acres. Moreover the agricultural
development in the north and south of Abu-Simbel area which depends only on the groundwater resource will extract 22.5
million m
3
/year from the present 75 productive wells Figure 1. This operation policy is expected to have its side effect on
groundwater regime of Nubia Sandstone Aquifer in Abu-Simbel Area NSAASA due to the absence of optimal well
locations which will be the fulcrum of this research.
2.2 Geomorphological and geological settings
Referring to the geomorphological studies prepared by El-Shazly et al. 1980 CONOCO 1987 and Aggour et al.
2012 five geomorphologic units are distinguished in the study area. Nasser lake the Nile valley Wadi Kurkur pediplain
Tushki depression and West Dungul plain. Wadi Kurkur pediplain represents most parts of the area. The pediplain surface is
covered mainly by nearly horizontal beds of Nubia sandstone with outcrops of igneous and metamorphic rocks as well as
several volcanic exposures. Tushki depression area is an elongated featureless smooth plain bounded by the topographic
contour line of 200m above sea level and is generally representing a topographic depression with an average absolute
elevation of less than 200m. It is bounded from the north and east by limestone plateau and from the south and the west by
sandy pediplain and peneplain respectively.
FIGURE1. LOCATION MAP OF ABU SIMBEL AREA SHOWING THE LOCATION OF 75 PRODUCTIVE WELLS AND
9 OBSERVATION WELLS
Geologically the main geological units in Tushki area are the Precambrian Basement rocks and sedimentary succession. The
basement rocks constitute some of the conspicuous ridges and high peaks in the area such as G. Umm Shaghir 318 m asl.
The lithostratigraphic sedimentary succession is dominated by Cretaceous Oligocene and Quaternary sediments Figure 2.
The Lower Cretaceous rocks are differentiated into the Abu Simbel Lake Nasser and Sabaya formations. The Abu Simbel
Formation covers vast parts south of Khour Tushki with thickness ranges from 30m to 87.45m Aggour et al. 2012. The
Lake Nasser Formation is underlain by the Abu Simbel Formation and overlain by the Sabaya Formation. In addition the
Upper Cretaceous rocks are represented by Kiseiba Formation with 150m thick. The Oligocene basalt rocks are widespread
near the head of Khour Tushki. Moreover the Quaternary deposits are represented by sand accumulations and Alluvial
sediments. As a general various structural elements are present among which are the uplift of the basement Nakhlai-Aswan
uplift trending NE-SW with 300 km long E-W faults north of Khour Tushki and NW-SE faults south of Khour Tushki
0 2 4
km
MEDITERRANEAN SEA
RED SEA
SINAI
Cairo
Assiut
Qena
Aswan
Lake
Nasser
Siwa
Qattara
Depression
El-
Bahariya
El-
Farafra
El-
Dakhla
El-
Kharga
W E S T E R N
D E S E R T
E A S T E R N D E S E R T
Gilf
Kebir
Plateau
25 00 30 00 35 00
22
00
26
00
30
00
0 100 200 km
Alexandria
Scale
Study area.
East
El Oweinat
o o o
o
o
o
Observation well

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E-W and NE-SW folds the Ring forms and the structural lineation. The fault systems play an important role in recharging
the NSAASA from Lake Nasser especially the NW-SE. They act as conduits and help in transmitting the groundwater within
the NSAASA supporting the hydraulic connection between the aquifer units Aggour et al. 2012.
2.3 Hydrogeological aspects
The NSAASA is mainly composed of three successive water-bearing units namely the Gilf Abu Simbel and Lake Nasser.
The middle unit is an aquiclude that extends under the lake and the lower unit overlying the granitic basement is a confined
aquifer of fluvial sandstones Figure 3. The groundwater of NSAASA exists under unconfined to semi-confined conditions.
The NSAASA maximum thickness reaches 400 m and decreases towards north and NW. The transmissivity of the NSAASA
ranges between 389 and 1322 m
2
/day Table 2 and increases from SW to NE. The constructed equipotential contour maps
Figure 4 show that the local recharge of the NSAASA depends upon the leakage from the Lake Nasser due west direction.
The estimated groundwater flow rate based on these contour maps Figure 4 reaches 0.054 m/day near Nasser Lake and
decreases to 0.044 m/day towards northwestern parts.
FIGURE 3: NSAASA POTENTIALITY MAP AND SW-NE CROSS-SECTION SHOWING AQUIFER THICKNESS
FIGURE 2: GEOLOGICAL MAP OF THE STUDY AREA AFTER
CONCO 1987

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III. MATERIALS AND METHODS
3.1 Field trip and data collection
The materials used in this paper are collected through carrying out four field trips in Abu Simbel area during the period
2010-12. The basic hydraulic parameters of NSAASA are estimated based on carrying out one step test and 13 long duration
pumping tests Tables 1 and 2. The different hydrologic data are obtained during the field trips. These materials also
include collection of archival data well drilling reports WRRI 2002 registration of discharge distribution of wells
proposed operating systems for both groundwater supply and reclaimed area beside recording depth to water for
groundwater level changes.
TABLE 1
RESULTS OF STEP DRAWDOWN TEST ANALYSIS IN NSAASA
Step No Step time Duration hour Well discharge Q m
3
/day Total DD s m s/ Q day/m
2
I 1.5 1080 8.32 0.008666667
II 1.5 1200 11.8 0.009833333
III 1.5 1368 13.38 0.009291667
IV 1.5 1488 15.82 0.01063172
TABLE 2
RESULTS OF LONG DURATION PUMPING TESTS ANALYSIS IN NSAASA
Well
No
Pumping rate
m
3
/h
Depth to water
m
Total DD
m
Screen
m
Hydraulic parameters
K regional
m/day
K local
m/day
T
m
2
/day
W27 105 79.4 5.67 80.5 6.88 12.45 1003
W30 120 76.79 7.89 80.5 4.9 9.09 732
W38 173 60.88 11.81 80.5 4.94 10.07 812
W40 120 62.59 10.01 80.5 9.21 16.42 1322
W43 112 71.26 - 80.5 - - 878
W45 160 55.6 16.28 80.5 5.19 10.41 839
W50 172 30.64 17.53 74.75 2.19 5.64 422
W55 123 58.6 24.87 57.5 - 9.28 534
W 57 110 63.15 20.84 57.5 - 8.06 464
W 60 100 74.07 13.17 135 - 7.11 389
W75 107 72.7 14.5 57.5 - 10.01 576
W80 110 68.8 11.25 57.5 - - 912
W85 130 58.2 - 57.5 - - 340
31 30
31 30
31 45
31 45
22 30
22 30
23 00
23 00
22 45
22 45
0 5 10 km
Lake Nasser
m a.s.l 110 120 130 140 150 160 170
FIGURE 4: THE GROUNDWATER EQUIPOTENTIAL MAPS OF NSAASA DURING 2008 LEFT MAP
AFTER EL-SABRI ET. AL. 2010 AND DURING 2010 RIGHT MAP-AFTER AGGOUR ET. AL. 2012

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XX Y Y ZZ s
h h h h
K K K W S
x x y y Z Z t
The methodological approach used in this paper is based on the mathematical modeling techniques which combines between
simulation and optimization model. A computer programming with FORTRAN language has been originally established to
apply the principles of the genetic algorithm for studying the optimal location of the groundwater productive wells as a
principal tool for groundwater resources management. The Optimal well Location applying Genetic Algorithm OLGA
Code links MODFLOW with genetic algorithm technique to establish a simulation optimization groundwater model.
3.2 Simulation technique
Groundwater flow simulation is carried out applying MODFLOW software. It describes groundwater flow of constant
density under non-equilibrium conditions in three-dimensional heterogeneous and anisotropic medium according to the
following equation Bear 1979:
1
in which
K
xx
K
yy
and K
zz
are values of hydraulic conductivity L
T
-l
along the x y and z coordinate axes h is the potentiometric
head L W is the volumetric flux per unit volume and represents sources and/or sinks of water T
-l
S
s
is the specific
storage of the porous material L
-1
and t is time T.
3.2.1 Conceptual Model
The conceptual model of the NSAASA is based on the geology of the study area which is comprised of Nubian sandstone
sediments. The hydrogeologic system is concerned two hydraulically connected through fault planes layers. The top
hydrostratigraphic unit Gilf Formation is considered to be a sandy unconfined aquifer zone up to 95 meters maximum thick.
The second confined aquifer zone of fluvial sandstones is separated from the sandy unconfined aquifer zone by aquiclude
and had maximum thickness of 79 meters. The scattered new communities around the asphaltic road in the N-S direction of
the Abu Simbel area are primarily planned for agriculture.
3.2.2 Model domain
The model domain of NSAASA is selected to cover 3315 km
2
51x65 Km-Figure 3. It is discretized using 130 rows × 102
columns rectangular cells. This discrimination produces 13260 cells in the model layer. The width of the cells along rows in
x-direction is 500m and along columns in y-direction is 500 m. The grid geometry is shown in Figure 5.
3.2.3 Boundary conditions
The hydraulic conditions at the boundaries of the model domain are specified Figure 5. Based on the groundwater flow
pattern of the NSAASA Figure 4 and the field measurements of the groundwater head in the present productive wells
Table 2 the initial and boundary conditions of the local model is defined. The lower boundary water body of Lake Nasser
is considered a time-constant head at level of 175 m asl DRC 2012. The equipotential contour line of 130m asl
characterizing to the upper boundary Figure 5 is far enough from the well fields to be genral head boundary condition. The
left and right boundaries are assumed to be no flow boundaries due to the regional flow direction from SE to the NW.
The impermeable Basement rock is assumed to be the bottom boundary of the model domain with no flow and maximum
depth 236.45m Table 3 and Figure 6. The hydraulic heads and hydraulic conductance are assigned to boundary cells. These
heads vary during the simulation process according to different stresses applied on the modeled area.
3.2.4 Aquifer properties
The aquifer material properties of the NSAASA include the transmissivity the storage coefficient and the hydraulic
conductivity. The transmissivity ranges from 389 and 1322 m
2
/day Table 2 and the storage coefficient from 1.2x10
-4
to
5x10
-4
El-Sabri et. Al. 2010. Vertical heterogeneity is assumed adequate to allow treatment as multi layered aquifer. The
vertical hydraulic conductivity estimated from the aquifer thickness Figure 6-left and aquifer transmissivity values is
varied from 5.64 to 16.42 m/day. Furthermore the availability of a relatively complete database of 75 groundwater drilled
wells and 9 observation wells in the NSAASA help in constructing the present model. In addition the initial piezometric
heads are computed from the absolute ground elevation values of the model domain extracted from the Digital Elevation
Model DEM of the study area Figure 6-right.

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TABLE 3
UPPER SURFACE OF BASEMENT ROCK AMSL IN ABU SIMBEL AREA
Well name
Ground elevation
m
Basement level
m
Well name
Ground elev.
m
Basement level
m
Akaria well 185.07 -34 O.B No11 85 -236.45
Well No 4 193.57 -176
O.B No 3
225 +107
Well No 5 204.72 -176
O.B No 3
225 0.0
Well No 13 194.05 +10
O.B No 6"
201 -129
Well No 21 195 -4
O.B No 7
165 -86
KADCO No 1 230 -2
O.B No 8
215 -9
KADCO No 2 233 +8
O.B No 10"
165 +75
KADCO No 3 233 +15
O.B No 18
190 -42
El Masria well 164 +92
O.B No 18"
190 -116
Akaria well 2 198.06 -124
O.B No 19
193 0.0
O.B No 4
193.05 -168
O.B No 20
165 +51
O.B No 10
186.07 -45
O.B No 25
183 -41
FIGURE 5. FLOW MODEL DOMAIN GRID AND THE BOUNDARY CONDITIONS OF THE NSAASA
MODEL

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FIGURE 6: AQUIFER THICKNESS CONTOUR MAP LEFT MAP AND GROUND ELEVATION EXTRACTED FROM
DEM RIGHT MAP
3.2.5 Model calibration
Calibration involves modification of the parameters and forcing functions in the model in such a way as to assure that the
model reproduced observed-head values Hill 1998 2000. The calibration process typically involves calibrating to steady-
state and unsteady state conditions. The performed steady state calibration permits the adjustment of the hydraulic
conductivity where NSAASA storage changes are not significant. The relation between the calculated and observed heads is
checked from the calculated-observed head curve and the variance appears as 45.966 Figure 8. This large value indicates
great difference between the heads calculated by the model and actual measured heads. After many times of changing the k
values the variance between the observed and calculated heads is minimized to 3.61 and the calculated head values is very
closely related to the field-measured head values Figure 7. Based on the calibrated model the estimated hydraulic
conductivity values are ranging from 4.33 to 7.60 m/day. These values are generally more slightly than the values calculated
from the field data. The difference may relate to the benchmarks uncertainty and grid refinement.
FIGURE 7: THE CALCULATED AND OBSERVED HEADS OF THE MODEL DOMAIN OF NSAASA FOR STEADY
STATE
Transient state specific yield values are modified on a trial and errors basis until a good match between the observed heads
in the years 2002 and 2012 sited in Kim and Sultan 2002 and Aggour et. Al. 2012 and the calculated heads are achieved.
The range of the resulted specific yield after the final calibration of the transient state is found to be varying from 0.14 to
0.34 Fig. 8. It can be seen that in general there is a good agreement between the observed and simulated head values.

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1
w
N
jj
j
Z Q P
FIG. 8: THE CALCULATED AND OBSERVED HEADS OF THE MODEL DOMAIN OF NSAASA FOR UNSTEADY
STATE
3.3 Optimization Technique
Genetic Algorithms GA are adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and
genetic. The basic concept of GA is designed to simulate processes in natural system necessary for evolution. A solution for
a given problem is represented in the form of a string called “chromosome” consisting of a set of elements called “genes”
that hold a set of values for the optimization variables the decision variables. The fitness of each chromosome is determined
by evaluating it against an objective function. The chromosome represents a feasible solution for the problem under study.
The length of the chromosome equals the number of variables. A Gene value is real coding actual values. The concept of
GA is based on the initial selection of a relatively small population. Each individual in the population represents a possible
solution in the parameter space. The fitness of each individual is determined by the value of the objective function calculated
from a set of parameters. The natural evolutional processes of reproduction selection crossover and mutation are applied
using probability rules to evolve the new and better generations. The probabilistic rules allow some less fit individuals to
survive. The objective of this study is to maximize the benefit function Z with respect to pumping rate to obtain optimal
location of wells Q
j
as design variable where:
Max 2
in which: N
w
is the total number of pumping wells and P
j
is penalty.
Moreover the management objectives must be achieved within a set of constraints. The constraints may be decision
variables. The objective function is subjected to the following constrains:
3.3.1 Objective function constraints
3.3.1.1 Pumping constraint
The pumping rates at potential pumping wells in the water demand are constrained to values between some minimum Q
j
min
and maximum Q
j
max
permissible pumping rates as the following:
Q
j
min
≤ Q
j
≤ Q
j
max
j ……..N
w
3
In the GA simulation this constraint can be easily satisfied by restricting the population space of the design variables to be
within the proposed limits. Hence no special treatment is needed for this constraint.
3.3.1.2 Drawdown constraint
This constraint normally means to protect the ecosystem by avoiding excessive drawdown. In this work the drawdown
constraints were formulated to avoid mining and formulated as follows:-

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1
w
N
ji
j
rd
1
w
N
jD
j
QQ
all i
D D
at arbitrary point 1 Drawdown constraint r
w1
+ r
w2
+ r
w3
+ r
w4
+ r
w5
+………+ r
w68
at arbitrary point 2 Drawdown constraint r
w1
+ r
w2
+ r
w3
+ r
w4
+ r
w5
+………+ r
w68
at arbitrary point 3 Drawdown constraint r
w1
+ r
w2
+ r
w3
+ r
w4
+ r
w5
+………+ r
w68
at arbitrary point N
c
Drawdown constraint r
w1
+ r
w2
+ r
w3
+ r
w4
+ r
w5
+……..+ r
w68
Accordingly it postulates the relation
4
In which: r
w1
is drawdown at point 1 due to pumping well no 1 r
w2
is drawdown at point 1 due to pumping well no 2 r
w3
is
drawdown at point 1 due to pumping well no 3 N
c
no of control points rj is the drawdown at control point i caused by a
pumping rate from pumping well j value of rj in Table 4 to 6 di is the permissible drawdown at control point i equals to 30
m.
3.3.1.3 Water demand constraint
The NSAASA is considered as the sole source of water. This therefore means that the designed optimal pumping strategy
must supply at least the minimum water demand. It is formulated as follows:
5
In which Q
D
is water demand.
3.3.1.4 Distance between wells constraint
This constraint obeys the relation:
6
Where D
i
is actual distance between wells and D
all
is minimum distance between wells.
3.3.1.5 Location of wells
The locations of wells constraint is to be decided by the model itself within a user defined region of the model grid until the
optimal location is reached Figure 9.
FIG. 9: PLAN VIEW SHOWING FINITE DIFFERENCE GRID WITH SUB-DOMAIN FOR WELL LOCATIONS

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10
0
ff
f
3.4 Optimization Procedure of the Simulation-Optimization model
In groundwater management problems there are two sets of variables decision variables and state variables where the
decision variable is the pumping and injection rates of wells. Also other decision variables include well locations and the
on/off status of a well. By optimization techniques the decision variables can be managed to identify the best combination of
them. Moreover hydraulic head is the state variable. The simulation model updates the state variables and the optimization
model determines the optimal values for all decision variables. In this work MODFLOW FORTRAN code is used as the
simulation of groundwater flow which links with GA optimization OLGA Code. The flowchart for simulation-optimization
model is given in Fig. 10.
FIGURE 10: FLOWCHART FOR THE SIMULATION/OPTIMIZATION MODEL
It must refer that MODFLOW simulation without wells is used to generate the initial head but initial population is generated
from GA via random number for each well according to constraints and number of chromosome.
3.4.1 Checking the termination criterion
The optimization algorithm continues to be executed by iterating until the given termination criteria are satisfied Fig. 10.
Note that different termination criteria can be used to stop the computation. These may be: Stopping the computation after a
given number of iterations reaching a specific objective function value no improvement in the objective function value for a
specified number of passed iterations or after limited time. In this study the relative error definition is used to check the
convergence of iterations. Thus the convergence criterion is defined as
7
Where ε is a tolerance for the convergence of iterations if two consecutive objective values f1 f
o
satisfy the criterion.

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3.5 Testing scenarios
The testing scenarios include three proposed pumping rates and well locations policies. The first scenario estimates the
pumping rates from 75 productive wells with their present locations. The second scenario checks the present locations for
these 75 productive wells and the optimality of their pumping rates. The third one proposes water exploitation policy aimed
at increasing the present productive wells by 14 wells as a result of the increase in reclamation activities new 25 thousand
acres and delineates the optimal locations of these new wells and keeping the present locations of the other 75 present wells
besides estimating the optimal pumping rates for all.
IV. RESULTS AND DISCUSSIONS
The expected interference between cones of depression of the present productive wells due to their configurations around the
highway roads of the Abu Simbel area will affect the groundwater productivity of the NSAASA. Accordingly the need to
determine optimal well location strategy for the new drilled wells required for future expansion of the project 1.5 million
acres national project is essential.
In addition applying the constructed OLGA Code for solving the optimization problems related to the optimal pumping rates
and the optimal well locations the initial pumping rates are assigned to each well as more than 700 m
3
/day and less than
1000 m
3
/day and then the optimization procedure explained before is used. The GA parameters used in the optimization
problem are given in Table 4. The optimal well location and pumping rate are determined based on OLGA Code from one
feasible solution to the other according to the calculated residual errors values where they improve quickly in the early
iterations and change slowly in subsequent iterations till satisfying the constraints.
TABLE 4
THE GA SOLUTION PARAMETERS APPLYING OLGA CODE
Continuous GA Parameter Value
Population size 200
Mutation ratio 0.006
Type of crossover uniform crossover
Crossover probability 0.7
Tolerance for the convergence of iterations 0.01
On the other side the results of the three testing optimal policies applying OLGA Code show the future predictions in the
optimal pumping rates after 5 10 15 20 25 30 40 and 50 years. The first scenario investigates the proposed pumping rates
from the 75 productive wells penetrating the NSAASA under their current locations. The OLGA simulation results show that
the optimal pumping rates under the present conditions of water demand Q
D
of 60000 m
3
/day range from 57585 to 50144
m
3
/day with corresponding total drawdown ranges from 3.42 to 13.73 m during the simulation period of 50 years Table 5.
TABLE 5
OPTIMAL PUMPING RATE FOR FIRST SCENARIO
Year 5 10 15 20 25 30 40 50
N 75 75 75 75 75 75 75 75
r m 3.42 5.62 6.78 7.88 8.93 9.96 11.85 13.73
Q
min
/well 746.8 726.4 708.6 695.6 645.2 629.2 613.8 605.7
Q
max
/well 1000 1000 1000 1000 1000 1000 1000 1000
Q
opt
m
3
/day 57585 56033 54511 53021 52292 51568 50852 50144
N is number of operation wells r is maximum drawdown Q
min
/well is min optimal pumping rate for well Q
max
/well is max
optimal pumping rate for well and Q
opt
total optimal pumping rate for all wells.
Moreover by running the developed OLGA Code for time step of 5 years the predicted head distribution maps of the
NSAASA under the current pumping rates at years 2015 2025 2035 and 2060 are shown in Figure 11. It is noticed from
Figure 11 that the groundwater levels change from 164.5 masl to 161.3 masl in the center of the cone of depression. Few
productive wells in the southwestern part of the model domain show relatively slight drawdown amounts to 13 m at East El-
Emaratiah Company well field. This is mainly attributed to the effect of increasing the thickness of water bearing formation
towards the northwestern and western parts. In addition one large cone of depression will develop in the cultivated areas.

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This cone is in the central part of Abu Simbel-Tushki road and may attribute to the present extraction rates from the
reclaimed areas.
FIGURE 11: PREDICTED HEAD DISTRIBUTION MAP OF THE NSAASA FOR OPTIMAL PUMPING RATES
APPLYING 1ST SCENARIO a at 2015 b at 2025 c at 2035 and d at 2060
Otherwise the second scenario seems to be theoretical more than practical since it studies the optimal locations of already 75
present productive wells under the present constraint of water demand Q
D
of 120000 m
3
/day and predict their optimal
pumping rates. The GA parameters used in this optimization case are given in Table 6. The initial pumping rates are
assigned to each well as less than 1500 m
3
/day and the optimal pumping rates after 5 10 15 20 25 30 40 and 50 years are

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International Journal of Engineering Research Science IJOER ISSN: 2395-6992 Vol-3 Issue-7 July- 2017
Page | 13
predicted Table 6. It is noticed from Table 6 that the number of the total operating wells N is still constant 75 wells and
the maximum drawdown r ranges from 2.22 to 12.13 m while Q
min
/well begins with 1460.6 and ends by 1053.2 m
3
/day for
the simulation period. The total optimal pumping rate for all wells Q
opt
ranges between 102038 and 100773 m
3
/day Table
6.
TABLE 6
OPTIMAL PUMPING RATE FOR THE 2ND SCENARIO APPLYING OLGA CODE
Year 5 10 15 20 25 30 40 50
N 75 75 75 75 75 75 75 75
r m 2.22 4.32 5.43 6.63 7.73 8.64 10.53 12.13
Q
min
/well 1460.6 1369.5 1301.6 1286.4 1201.3 1183.2 1102.4 1053.2
Q
max
/well 1500 1500 1500 1500 1500 1500 1500 1500
Q
opt
m
3
/day
102038 101797 101561 101330 101103 100992 100882 100773
In the same side the results of the OLGA Code based on this scenario show that the predicted optimal location of the
productive wells differ more or less from the present location Figure 12. Although the proposed OLGA approach
successfully identified all the well locations and pumping rates of the present numerical study identification of all the well
locations and pumping rates may not be feasible for real-world applications since the number of pumping wells is usually
very high. Instead the proposed procedure may be applied to the suspected illegal pumping areas as noticed in the field trips.
As an extension of this study the performance of the proposed OLGA Code should be tested on a real field system in a
future study.
FIGURE 12: OPTIMAL LOCATION OF PRESENT WELLS 2ND SCENARIO
Otherwise the predicted head distribution maps of the NSAASA under the 2
nd
scenario Figure 13 show groundwater levels
change from 165.5 masl to 162.5 masl in the center of the cone of depression. It is noticed from Figure 13 that the normal
decline in the groundwater levels 3 m may attribute to the small thickness and low hydraulic conductivity of the NSAASA
in these localities. Moreover the cone of depression will appear in the cultivated areas during the simulation time with
diameter of 2.5 to 4 km approximately. While the southern and western cultivated parts of the model domain does not be

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Page | 14
affected with this scenario. This may attribute to the effect of the great aquifer thickness and the presence of thin clay layers
in the southern and western parts rather than the geologic structure impact. Accordingly this reflects the low potentiality of
the northern cultivated parts for positive response to this scenario.
FIGURE 13: PREDICTED HEAD DISTRIBUTION MAPS OF THE NSAASA FOR OPTIMAL WELL LOCATIONS
APPLYING 2ND SCENARIO A AT 2015 B AT 2025 C AT 2035 AND D AT 2060
The third scenario proposes water exploitation policy aimed at increasing the present productive wells by 14 wells as a result
of the increase in reclamation activities under the constraints of 500 m as minimum distance between wells and 900000
m
3
/day as water demand Q
D
and delineates the optimal locations of these new productive wells and keeping the present
locations of the other 75 present productive wells besides estimating the optimal pumping rates for all. The GA parameters

slide 15:

International Journal of Engineering Research Science IJOER ISSN: 2395-6992 Vol-3 Issue-7 July- 2017
Page | 15
used in this optimization case are given in Table 7. The OLGA Code runs for time step of 5 years. The predicted optimal
location of the new productive wells is checked Figure 14 and the predicted head distribution maps of the NSAASA for the
optimal pumping rates at years 2015 2025 2035 and 2060 are shown in Figure 15.
TABLE 7
OPTIMAL PUMPING RATE FOR THIRD SCENARIO
Year 5 10 15 20 25 30 40 50
N 89 89 89 89 89 89 89 89
r m 4.27 6.47 7.63 8.72 9.77 10.80 12.68 14.56
Q
min
/well 923.2 913.3 902.8 879.6 823.6 813.2 800 800
Q
max
/well 1500 1500 1500 1500 1500 1500 1500 1500
Q
opt
m
3
/day 87187 85635 84114 82623 81894 81171 80454 79747
FIG. 14: OPTIMAL LOCATION OF THE NEW PRODUCTIVE WELLS BLUE COLORED 3RD SCENARIO
It is noticed from Table 7 that the maximum drawdown r ranges from 4.27 to 14.56 m while Q
min
/well begins with 923.2
and ends by 800 m
3
/day in case of number of total operating wells N of 91 productive wells. Moreover Q
min
/well begins with
923.2 and ends by 800 m
3
/day during the simulation period. The total optimal pumping rate for all wells Q
opt
ranges
between 87187 and 79747 m
3
/day.
However it is noticed from the predicted head distribution maps Figure 15 that the groundwater level decreases from 163m
asl in the beginning of the simulation period the year 2015 to 158m asl in the end of the simulation period the year 2060.
The depression cones related to the first and the second scenarios are mitigated in the northern part of the model domain.
Moreover limits are placed on the total optimal pumping rates of the productive groundwater wells beside its optimal
locations in the reclaimed areas. Accordingly it is preferred to extend the future reclamation activities parallel to the western
side of the Khour Tushki area. Although the results of this scenario provide more or less good degree of confidence in the
optimal location of the new productive wells and optimal pumping rates the expected sharp decline in groundwater levels in
the concerned area assumes more applied studies. The Q
opt
in the 3
rd
scenario is actually lower than that in the 2
nd
scenario
because the second scenario studies the optimal locations for these 75 productive wells and their optimal pumping rates. The
third one proposes water exploitation policy aimed at increasing the present productive wells by 14 wells. The predicted
value of r based on the 3
rd
scenario is more or less similar to the results of the other two scenarios although the number of
the operating wells is increased by 19. This reflects the great importance to apply the optimal well location concept in any

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International Journal of Engineering Research Science IJOER ISSN: 2395-6992 Vol-3 Issue-7 July- 2017
Page | 16
new reclamation projects. As a result of the above discussion of the OLGA Code optimal well location and pumping rates
results it can be concluded that the groundwater withdrawal from the NSAASA under this optimization study could be safely
conducted.
FIGURE 15: PREDICTED HEAD DISTRIBUTION MAPS OF THE NSAASA FOR OPTIMAL WELL LOCATIONS
APPLYING 3RD SCENARIO a at 2015 b at 2025 c at 2035 and d at 2060
V. CONCLUSION AND RECOMMENDATION
This paper is devoted to propose an assisted methodology to identify representative models for optimal well locations. To do
so first a mathematical equations were developed to model the representativeness of a subset of constrains with respect to
the full set that characterizes the well location problem. Then an optimization tool was implemented to identify the
representative constrains of any problem considering not only the main output variables but also the probability distribution
of the attribute-levels of the problem. Accordingly OLGA Code was linked MODFLOW with genetic algorithm technique
to establish a simulation optimization groundwater model. This model was applied for NSAASA to develop the optimal
location of the groundwater productive wells with maximum pumping rate. Three scenarios were tested to choose the proper

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Page | 17
water exploitation policy. For the first scenario the predicted groundwater drawdown after simulation period of 50 years
ranged from 3.42 to 13.73 m while the corresponding optimal pumping rates ranged from 57585 to 50144 m
3
/day. Under the
second proposed scenario the predicted drawdown r and the corresponding total optimal pumping rate for all wells Q
opt
ranged from 2.22 to 12.13 m and between 102038 and 100773 m
3
/day respectively. Moreover the predicted value of r
based on the 3
rd
scenario was more or less similar to the results of the other two scenarios although the number of the
operating wells was increased by 19. Computational restrictions were common and likely the cause of the systemic lack of
algorithm benchmarking for well location optimization. Still some valuable insight can be gained from these results that
could guide further investigation.
Based on the results of the OLGA model it is highly recommended to choose the new productive well locations in staggered
system parallel to the western side of the Khour Tushki area. More applied studies are needed for verification the results of
this optimal well location model. Also this study should be extended to contain more test cases and more comprehensive
selection of algorithms including interpolation methods ad joint methods and hybrid methods.
ACKNOWLEDGEMENTS
The data of this work were presented from Desert Research Center Station in Abu Simbel through Development of South
Wadi Project Egypt Tushki project which carried out by the team work of DRC. Assistance from project team work and
Groundwater Sector Office is gratefully acknowledged. I’m indebted to them especially Prof Himida and Dr El-Sheikh for
their help in performing field works and providing the required data. I appreciate the insightful comments and suggestions of
the editor and anonymous reviewers which greatly improved this manuscript.
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