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300 K.L. Katsifarakis If application of an approximate form of the method of images could substitute a numerical simulation of a flow field, it would greatly reduce the respective computational volume. Such an attempt, in the frame of an optimization process by means of genetic algorithms, has been made by Koutsourelakis et al (2006). The aquifer studied is shown in figure 2. The angle of intersection of the two constant head boundaries (representing a lake coast) is 120 o , while the coordinates x 0 , y 0 of the intersection point are 0 and 1500 respectively. The optimization problem is the following: Define the location of 5 wells and the distribution of a total flow rate Q T = 500 l/s among them, which minimize the sum of the following cost items: a) pumping cost C p and b) amortization C a of the construction of the pipe network, which connects the wells with a central water tank (with coordinates x T = 3000, y T = 1500), shown also in figure 2. C p and C a are expressed as: n ∑ C = A ⋅ Q ⋅ s (4) p p n ∑ i= 1 i= 1 i i C = A ⋅ L (5) a In eq. (4) n is the number of real wells, while Q i and s i are the flow rate and the hydraulic head drawdown at well i, respectively. Actually water should be pumped up to the tank, but only s i values enter the optimization procedure. Finally A p is a pumping cost coefficient, depending on duration of pumping, pump efficiency and electricity cost. In eq. (5) L i is the length of the pipe, which carries water away from well i and A ai is a cost parameter, depending on network construction cost, amortization period and interest rate. In order to calculate C a , the following tasks should be performed: a) construction of the shortest tree-type pipe network, which connects the wells to the central tank and b) calculation of the flow rate through each pipe i. In order to calculate C p , the flow simulation model should be solved, to find the values of s i , using as input the combination of well flow rates and coordinates, which is each chromosome represents. It is worth mentioning that the wells can be placed only inside the polygon defined by the broken line in figure 2, namely the smallest permissible distance between well and coast is 50 m. In theory the method of images does not apply in this case, although it leads to a finite number of imaginary wells, since it creates singular points inside the real flow field. In practice, it leads to areas with increased hydraulic head, which may distort the optimization process completely (when an imaginary injection well falls close to a real one). So, the case of one real well was studied first, in order to find an approximate solution, relaxing, as little as possible, observance of the boundary conditions. ai i
Flow Simulation and Optimal Management of <strong>Groundwater</strong> Resources… 301 Y (xi·sin30+yicos30-1500·cos30,xi·cos30-yi·sin30+2250) (3000,3000) (-xi,3000-yi) (-xi,yi) (0,1500) 120° (x,y) (3000,1500) (xi,yi) injection well pumping well (3000,0) X Figure 2. Semi-infinite aquifer with 2 straight-line boundaries (after Koutsourelakis et al, 2006). s b (50m) 0,5 s b (m) 0,0 -0,5 -1,0 -1,5 -2,0 -2,5 0 500 1000 1500 2000 2500 3000 Υ(m) Figure 3a. Hydraulic head drawdown on the boundary (s b )-Basic approximation (after Koutsourelakis et al, 2006).
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GROUNDWATER: MODELLING, MANAGEMENT
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Copyright © 2009 by Nova Science P
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vi Chapter 8 Chapter 9 Chapter 10 C
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viii Luka F. König and Jonas L. We
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x Luka F. König and Jonas L. Weiss
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xii Luka F. König and Jonas L. Wei
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xiv Luka F. König and Jonas L. Wei
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SHORT COMMUNICATION
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4 Goloka Behari Sahoo and Chittaran
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Table 2. Number of Samples in Train
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12 Goloka Behari Sahoo and Chittara
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14 Goloka Behari Sahoo and Chittara
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In: Groundwater: Modelling, Managem
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GIS-Based Aquifer Modeling and Plan
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80 Sabrina Saponaro, Sara Puricelli
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100 Sabrina Saponaro, Sara Puricell
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Groundwater Interactions with Surfa
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134 Marek Šváb and Lenka Wimmerov
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Fundamentals of Groundwater Modelli
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6.0. Model Calibration Fundamentals
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2. Subsurface Contaminants Contamin
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Contaminants in Groundwater and the
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6.2. In Groundwater Contaminants in
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Preliminary Studies for Designing a
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Simulation Study Preliminary Studie
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Water Budget Preliminary Studies fo
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Figure 1. Location of the study are
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Table 1. Continued EVENT BEGINNING
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Groundwater Management in the North
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232 Franco Cucchi, Giuliana Frances
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Table 1. Chemical and isotopical co
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Table 1. Continued Borehole ID Type
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Table 2. Univariate overview of the
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350 Nigel J. Cassidy Weiller, K. W.
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352 Nick Cartwright, Peter Nielsen,
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362 A. Akber, A. Mukhopadhyay, E. A
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392 Index Bangladesh, 188 banks, 11
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394 Index definition, 18, 20, 26, 1
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396 Index goals, 306 government, 19
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398 Index Miami, 349 migration, x,
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400 Index probability, 166, 295 pro
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402 Index specific heat, 90, 108 sp
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