Water distribution networks (WDNs) could present problems of pathogen intrusion that affect the health of consumers. One solution to diminish this risk is to add more disinfectant to the water at the drinking water treatment plant (DWTP). However, this increases the cost of water treatment and may also cause the formation of trihalomethanes. Mexico has the largest bottled water market in the world. Also, most houses are built with individual storage containers due to intermittent service, which generates a greater residence time of the water before use. This paper shows an alternative to guarantee minimum disinfection along WDNs and diminish the use of disinfectant at the DWTP considering the conditions of water consumption and use in Mexico. We propose a model based on Genetic Algorithms to obtain scenarios where free chlorine is maintained at the minimum permissible concentration throughout the day. In addition, Water Managers could optimize the use of disinfectant by implementing booster chlorination stations (BCSs). The results show that chlorine use could be reduced by 38%, therefore guaranteeing the chlorine concentration limits along the WDN.

INTRODUCTION

In recent years, a large number of water distribution networks (WDNs) have reached their planned life span (Lei & Sægrov 1998; Francisque et al. 2014). Pipes, tanks, and accessories have suffered damage due to abnormal operation. WDNs are vulnerable to pathogen intrusion, according to the type of operation and maintenance (Le-Chevallier et al. 2003; Mora et al. 2012). Specifically, microorganisms that affect consumers' health in the short term. The preservation of microbiological water quality is one of the most complex technological issues for water managers (WMs) due to the use of disinfectants, water characteristics, and network conditions. Therefore, numerical quality models are necessary tools for operating and maintaining water quality.

Optimal microbiological water quality is achieved when the disinfection process treats the water in the drinking water treatment plant (DWTP). The World Health Organization recommends a minimum residual concentration of 0.5 mg/L of free chlorine over 30 minutes of contact time at a maximum pH of 8.0 for terminal chlorination (WHO 2011). Disinfectants are mainly used to ensure the inactivation of microorganisms (Geldreich 1996) that could be present in the water from supply sources, and grow throughout the network (Figure 1), therefore a sufficient amount of free chlorine is required along the network to maintain most of the microorganisms inactive. The objective is to prevent gastrointestinal disease due to drinking contaminated water; therefore the minimum concentration of free chlorine should be 0.2 mg/L at the point of delivery to ensure the chlorine residual throughout the distribution network (WHO 2011). However, the addition of chlorine may result in disinfection by-products (DBPs). The DBPs are a consequence of the added chlorine reacting with organic and/or inorganic substances in the bulk water (Sadiq & Rodriguez 2004). In the case of the chlorine, among the DBPs formed are trihalomethanes (THMs). Diverse species of THMs have been linked to carcinogenic effects on human health (Chowdhury et al. 2009). The free chlorine concentration must be maintained throughout the WDN at a level between 0.2 to 0.5 mg/L at the points of delivery (WHO 2011) and not exceed the value of 5 mg/L. In the case of Mexico, the range of free chlorine must be between 0.20 and 1.50 mg/L according to the Official Mexican Standard (Norma Oficial Mexicana-127-SSA1-1994, or NOM-127), established by the Ministry of Health.
Figure 1

Microorganisms in pipes (based on Knobelsdorf & Mujeriego 1997).

Figure 1

Microorganisms in pipes (based on Knobelsdorf & Mujeriego 1997).

In Mexico, there are 2,457 municipalities and one Federal District, each one with separate WMs. The Mexican Institute of Water Technology (IMTA, in Spanish) implemented a system of management indicators of the WMs (IMTA 2014). The indicators are registered annually, and there are records from 2002 to 2013. There are two indicators related to intermittent water supply.

The first one is whether the consumer's tap has a continuous water supply. During the eleven years of implementation, 90 WMs (mean annual) provided information about this indicator. For almost half (47%) of WMs in Mexico, 98% of consumers have a continuous supply. However, 8% of WMs reported that less than 10% of consumers have a continuous water supply.

The second indicator is hours of service per day, based on information from 60 WMs (mean annual) with intermittent service. The mean time of service per day is 10.6 hours. However, 45% of the WMs had an average daily service between 12 and 23.5 hours. In addition 12% had an average daily service between 4 and 1.5 hours.

The intermittent operation of water services does not guarantee disinfection throughout the networks. Therefore, the WMs increase the amount of chlorine used in the DWTP to maintain disinfection limits within those stipulated by the NOM-127, with the risk of producing THMs. Therefore, most people in Mexico have turned to consuming bottled water (Greene 2014). In fact, the Mexican bottled water industry is the largest in the world (Jaffee & Newman 2013).

Another important consequence related to the intermittent operation of WDNs is that the majority of houses have an individual storage container (Omisca 2011). In most cases, new-builds include an individual storage container despite the continuous water supply. In fact, the majority of houses have at least one container, which has consequences for the lifetime of free chlorine, and, therefore, drinking water quality.

Taking the conditions of consumption and use of water in Mexico into account, this paper proposes maintaining the minimum and more uniform chlorine concentration by optimizing the amount of chlorine used and thereby guaranteeing the reduction of problems of THMs generation and gastrointestinal disease incidence.

CHLORINATION IN WDN

The main disinfectants used in WDNs include free chlorine, chloramines, ozone, chlorine dioxide and ultraviolet light (Propato & Uber 2004). Free chlorine is one of the most effective agents to inactivate bacteria and other pathogens due to its residual effect of disinfection along the WDN (Geldreich 1996). In Mexico, free chlorine is the most widely used disinfectant (CONAGUA 2013). However, when chlorine gets in contact with water it reacts in different processes and the chlorine concentration tends to decrease.

Decay mechanism of chlorine and BCSs

Chlorine concentration decreases as a function of the characteristics of microorganisms, such as their state and their mixture with dissolved matter, besides other factors such as temperature and pH (Geldreich 1996). The chlorine decay curve describes its evolution (Figure 2). When chlorine comes into contact with water, it generates a reaction with reducing compounds; these substances can be dissolved or suspended. The compounds that react with chlorine are hydrogen sulfide, manganese, iron, and nitrites (AEAAS 1984). The additional chlorine begins to react with organic matter, producing organic chlorine compounds. Organic chlorine does not have the ability to disinfect and generates a characteristic odor and flavor. The chlorine continues to react with reducing substances, organic matter, and ammonia. Finally, the additional chlorine will remain as available or free chlorine, which is a very active disinfectant. After this point, all the nitrogen compounds have been destroyed. Therefore, any further addition of chlorine causes an increase in the level of free chlorine in the water (AEAAS 1984).
Figure 2

Chlorine decay curve (AEAAS 1984).

Figure 2

Chlorine decay curve (AEAAS 1984).

According to Castro & Neves (2003), loss of free chlorine concentration throughout a WDN is due to several separate mechanisms. Table 1 shows the diverse types of reactions and some related reaction coefficients (Phillip 2003; Al-Jasser 2007). These values depend on multiple variables, and they could vary according to the local conditions of each study. Ozdemir & Erkan (2005) related the decay of chlorine to the lifetime of water in the network, the quality of the treated water and the age of the pipes, the effectiveness of disinfection and microorganism resistance, the concentration of disinfectant, and the contact time.

Table 1

Range of chlorine reaction coefficients (diverse authors)

 Reaction coefficients
Type of reactionMinimum valuesMaximum values
Bulk water reaction 0.09–0.12 d−1 1.38–1.52 d−1 
Pipe wall reaction 0.03–0.04 m/d 1.34–1.52 m/d 
 Reaction coefficients
Type of reactionMinimum valuesMaximum values
Bulk water reaction 0.09–0.12 d−1 1.38–1.52 d−1 
Pipe wall reaction 0.03–0.04 m/d 1.34–1.52 m/d 

Alcocer & Velitchko (2004) mentioned that the lowest concentrations could occur in zones with low velocity and in storage tanks, but not necessarily in the farthest zones from the DWTP. Therefore, chlorine decays once introduced into the WDN, and there is a risk that the network could be unprotected in certain zones with the corresponding risk to consumers' health. Booster chlorination stations (BCSs) are a means of reducing this risk.

The BCSs (Figure 3) are installed at critical locations (Parks & VanBriesen 2009). Specifically, where the free chlorine concentration is below the minimum permissible level (Islam et al. 2013). Using BCSs, WMs can guarantee disinfection with the minimum concentration and a more uniform disinfectant along the WDN (Boccelli et al. 1998).
Figure 3

Typical BCS (based on PAHO 2004).

Figure 3

Typical BCS (based on PAHO 2004).

To reduce the risk of microorganisms along the WDN, we propose the installation of BCSs in strategic locations to maintain the minimum permissible chlorine concentration. Besides reducing risk, the genetic algorithm (GA) model proposes an optimal use of chlorine considering: (a) avoiding higher concentrations, (b) maintaining the range from 0.20 to 0.50 mg/L of free chlorine in all the WDN, as proposed by WHO (2011), (c) saving disinfectant by optimizing the use of chlorine, and (d) two specific conditions in Mexico: the use of individual storage containers and the fact that many people do not drink tap water.

OPTIMAL BCS MODEL

The GA model achieves the optimal number and locations of BCSs, considering the minimum installation of BCSs and reducing the use of chlorine during the operation of the WDN. Every node of the network is analyzed for the last 24 hours of consumption of 72 hours of simulation, in order to ensure a simulation of stability. The model will establish the optimal scenario for the efficient use of disinfectant.

Genetic algorithms

GAs are adaptive methods that can be used to solve specialized problems of search and optimization (Beasley et al. 1993). The basic algorithm is comprised of the following steps:

  1. Randomly generate an initial population.

  2. Calculate the fitness of each individual.

  3. Selection (sample) on the basis of individual aptitude.

  4. Apply genetic operators (crossover and mutation) to generate the next population.

  5. Cycle over many generations until some condition is satisfied.

GAs use a direct analogy with natural selection (Holland 1992). GAs are applied to populations of individuals. Each individual represents a feasible solution to a given problem. Each individual obtains a score depending on the fitness of the solution. The greater the fitness of an individual, the more likely it will be selected to reproduce, crossing its genetic material with another individual selected in the same way. This crossover will produce new individuals, which share some of the characteristics of their parents. The lower the fitness of an individual the less likely they are to be selected for reproduction and, therefore, its genetic material is not passed down to successive generations and then disappears from the gene pool.

Using this method we found a new population of possible solutions. This population replaces the previous one, and the properties of this new generation must contain a higher proportion of good features in comparison with the previous population. If the GA has been well designed, the population will converge towards the optimal solution for the problem (Figure 4).
Figure 4

Flowchart of GA methodology.

Figure 4

Flowchart of GA methodology.

In the model, optimization increases with the number of generations. The larger the number of nodes, the greater the number of individuals needed to maintain diversity in order to conduct tests for greater fitness (Jiménez 2004). Using GAs significantly reduces the number of simulations required to find a better option in terms of limited use of chlorine.

Optimal locations of BCSs by GAs

The objective is to find the minimum number of BCSs necessary to maintain the concentration of free chlorine, reduce the use of the disinfectant, and maintain water quality within the NOM-127 standard, while considering the conditions of water consumption and use in Mexico. Moreover, human health must be guaranteed meaning that the level of disinfection will never be under 0.20 mg/L and the concentration near to the DWTP must maintain the concentration of free chlorine close to the value of 0.50 mg/L as proposed by WHO (2011).

The model considers that every node of the WDN represents a BCS by providing a value of additional supply concentration of chlorine. These concentration values are the variables for the GA, and they are represented in binary code (Table 2). Each four digit binary code sequence represents a value of the chlorine dose provided by the BCS.

Table 2

Binary code for the chlorine concentration at the BCS

Chlorine concentration (mg/L)Binary valueChlorine concentration (mg/L)Binary value
0.25 0000 0.70 1000 
0.00 0001 0.00 1001 
0.40 0010 0.80 1010 
0.00 0011 0.00 1011 
0.50 0100 1.00 1100 
0.00 0101 0.00 1101 
0.60 0110 1.20 1110 
0.00 0111 1.50 1111 
Chlorine concentration (mg/L)Binary valueChlorine concentration (mg/L)Binary value
0.25 0000 0.70 1000 
0.00 0001 0.00 1001 
0.40 0010 0.80 1010 
0.00 0011 0.00 1011 
0.50 0100 1.00 1100 
0.00 0101 0.00 1101 
0.60 0110 1.20 1110 
0.00 0111 1.50 1111 

The set of all these substrings represents the entire network, and it is called a chromosome. The length of the chromosome, Equation (1), is equal to the number of bits needed for each node, multiplied by the number of network nodes. In Figure 5 there is an example of an individual for a network composed of six nodes and the number of bits is four. Therefore the length of the chromosome is 24. 
formula
1
where Lc, length of the chromosome; nn, number of WDN nodes; nb, number of bits.
Figure 5

An example of individual code.

Figure 5

An example of individual code.

The evolutionary processes considered in this GA model are roulette wheel selection, 2-point crossover, and mutation. The simulation time depends on three factors: (a) the number of variables for each individual, (b) the evolutionary process, and (c) the number of generations to evaluate.

Fitness function

The fitness function (FF) is proposed to determine the effectiveness of the solutions generated by the model. A higher value of the FF represents a better solution for an individual for the use of BCSs. Three main conditions for obtaining an optimal solution are: (a) maintain the free chlorine concentration in the range established by the NOM-127 at all network nodes, (b) minimize the number of BCSs, as this implies a low investment cost, and (c) maintain an adequate concentration of chlorine in order to obtain the values of free chlorine proposed along the entire network during the last 24 hours of simulation. According to these conditions, the FF is presented in Equation (2). The FF can be described as a mathematical fraction composed of two factors, a growing component (numerator) and a penalizing component (denominator). The first one uses a similar version of the standard deviation, which basically assigns a higher value to those concentrations at all nodes approaching the minimum value (Cmin=0.2 mg/L). The penalizing component, however, decreases the value of FF depending on the number of BCSs proposed and when concentration results are outside of the range determined by Cmin=0.20 mg/L to Cmax=1.50 mg/L corresponding to the limits of the NOM-127. Therefore, the individuals who maintain a better control of chlorine use and propose the fewest number of BCSs will prevail in the elapse of evolutionary processes of GAs. 
formula
2
where , minimum chlorine concentration; , maximum chlorine concentration; , mean chlorine concentration for the node i; , BCS installation cost (approx. $6,000 USD for the cost of the equipment and the station build); , penalization cost due to the concentration out of NOM-127 range; , concentration of chlorine out of NOM-127 range for the node i; n, number of nodes in the network.

The main structure of the GA models for optimal BCSs was a program designed by the authors. The routine that solves the hydraulic and quality WDN is derived from the EPANET software. The steps of the GA: selection, crossover, and mutation are taken from the toolbox designed by Chipperfield & Fleming (1995) for MATLAB. The criteria to establish the number of iterations is the value of the FF. If the FF maintains a constant value for almost 25 generations, it is considered the optimal scenario.

APPLICATION OF THE MODEL ON A WDN

The model network used in the simulations is an example network from the EPANET (Rossman 2000). Net3, shown in Figure 6, was selected considering the complexity of its structure and operation and contains the following components:
  • two reservoirs

  • three tanks

  • two pumps

  • 117 pipes

  • 92 nodes (five nodes with its ID for the discussion)

  • one general demand pattern and a further four at certain nodes.

Figure 6

Network model net3.

Figure 6

Network model net3.

The hydraulic model was simulated with the equation of Hazen–Williams using the English system of units. The pipes have diameters from 0.2 to 2.5 metres with roughness coefficients from 110 to 199. The total length of the network is 65,748 metres. The total base demand on the network is 0.192 m3/s.

The water quality model was used to analyze the free chlorine over an extended period of time (72 hours) with a quality time interval of 5 minutes. The analysis is going to focus on the last 24 hours when the hydraulic and quality variables have reached equilibrium. Both model reactions, bulk and wall, used in the simulation are first order. The scenarios proposed address the range of the chlorine reaction coefficients (CRCs) obtained from the literature (Table 1). The proposed scenarios are: scenario A with the minimum CRC, scenario B with values around 15% of maximum, and scenario C with values between 20 to 25% of maximum (Table 3), which are the three scenarios with the initial chlorine concentrations for the sources. Only 25% of the maximum values were applied because simulations made with more CRC generate doses of chlorine above the NOM-127 standards in a huge part of the network during the simulations.

Table 3

Scenarios proposed for optimizing use of chlorine

 Source chlorine concentrations
Reaction coefficients
ScenarioRiver (mg/L)Lake (mg/L)kb (L/d)kw (m/d)
1.50 1.50 0.120 0.04 
1.69 1.62 0.233 0.21 
1.79 1.68 0.350 0.32 
 Source chlorine concentrations
Reaction coefficients
ScenarioRiver (mg/L)Lake (mg/L)kb (L/d)kw (m/d)
1.50 1.50 0.120 0.04 
1.69 1.62 0.233 0.21 
1.79 1.68 0.350 0.32 

The initial chlorine concentration was selected in every scenario according to the limits of NOM-127. The main comments from the simulation of these scenarios are: the consumer nodes near to the sources have a concentration of 1.5 mg/L for 13 hours in B and C, and 15 hours in A. However, the critical nodes have concentrations below 0.20 mg/L for 10 hours in all three scenarios.

RESULTS AND DISCUSSION

The application of the GA model to the three scenarios was simulated with 1,200 to 2,500 individuals and stopped after no change in fitness was found for a minimum of 25 generations (Figure 7). The best FF of the three scenarios was obtained from 50 to 100 generations.
Figure 7

Evolution of GA model.

Figure 7

Evolution of GA model.

The results obtained with the optimized scenarios A, B, and C consider an initial concentration between 0.50 and 0.59 mg/L from both sources of water. With this optimized initial condition, the model obtained the result of specific locations of BCSs with the doses shown in Table 4.

Table 4

Initial vs. optimized scenarios

 Chlorine doses
Location of BCSs
 
ScenarioRiver (mg/L)Lake (mg/L)Node number dose (mg/L)Total chlorine used (mg/L)
1.50 1.50 – 3.00 
A (optimized) 0.50 0.50 Node 20 Node 241 Tank 2 1.87 
0.32 0.30 0.25 
1.69 1.62 – 3.31 
B (optimized) 0.56 0.53 Node 127 Node 211 Tank 1 Tank 2 2.95 
0.56 0.60 0.25 0.45 
1.79 1.68 – 3.47 
C (optimized) 0.59 0.55 N20 N40 N50 N131 N145 N211 3.40 
0.50 0.21 0.40 0.25 0.30 0.60 
 Chlorine doses
Location of BCSs
 
ScenarioRiver (mg/L)Lake (mg/L)Node number dose (mg/L)Total chlorine used (mg/L)
1.50 1.50 – 3.00 
A (optimized) 0.50 0.50 Node 20 Node 241 Tank 2 1.87 
0.32 0.30 0.25 
1.69 1.62 – 3.31 
B (optimized) 0.56 0.53 Node 127 Node 211 Tank 1 Tank 2 2.95 
0.56 0.60 0.25 0.45 
1.79 1.68 – 3.47 
C (optimized) 0.59 0.55 N20 N40 N50 N131 N145 N211 3.40 
0.50 0.21 0.40 0.25 0.30 0.60 

Total chlorine used in the optimized scenarios was reduced by 37.7%, 10.9% and 2.1% for the scenarios A, B, and C, respectively. In the optimized scenarios, the chlorine concentrations throughout the network are within the range recommended by WHO (2011). The limits in all simulations result in a better control of the use of chlorine, ensuring lower chlorine usage for water disinfection, whilst taking into consideration the operating conditions and water uses in Mexico.

In Figure 8, we show the free chlorine concentration of five nodes during the 72 hours of simulation. Graphs on the left are the initial scenarios and those on the right are the optimized scenarios. The nearest nodes of consumption to the sources are nodes 101 and 123, and the nodes which have the lowest values of free chlorine during the last 24 hours of the simulation are numbers 131, 219, and 243. In the initial scenarios, the nodes near to the sources have the maximum concentration according to the NOM-127 (1.5 mg/L), and for the same hours the critical nodes have values under the minimum concentration established by the NOM-127 (0.20 mg/L). In the optimized scenarios, the five nodes have values between 0.5 and 0.20 mg/L during the last 24 hours of simulation. Only in the optimized scenario C, does the node 243 have concentrations under 0.20 mg/L during 2 hours. However in the initial scenario C, two of the three critical nodes have concentrations under the same value.
Figure 8

Free chlorine in five nodes on the initial and optimized scenarios.

Figure 8

Free chlorine in five nodes on the initial and optimized scenarios.

With these results we may validate the GA model proposed for optimizing the use of chlorine, finding the optimal use of chlorine according to WHO (2011) and considering the range from the minimum to 25% of reaction coefficients described in the literature. For the minimum range of reaction coefficient values, we recommend investing in BCSs for maintaining the free chlorine at optimal values. In the first two scenarios, the use of chlorine could be reduced by 11 to 38%, the initial investment for the locations of the four and three BCSs, respectively (Figure 9).
Figure 9

Locations of the BCSs in the optimized scenarios.

Figure 9

Locations of the BCSs in the optimized scenarios.

In the case of the third scenario, when the reaction coefficients are in the range of 25% from those reported in the literature, from an economical point of view, the initial investment could be unprofitable because of the six BCSs proposed by the model (view locations in Figure 9) and the reduction of chlorine is only by 2%. However, from the health point of view, almost the same amount of chlorine is used in the third scenario but the optimization must focus on the better distribution of the free chlorine, maintaining the range proposed by WHO (2011) along the consumer nodes.

Maximum consumption is presented in hour 50 (when there was practically twice the base demand). The configuration of free chlorine for the three scenarios along the networks is shown in Figure 10. Scenarios A, B, and C are compared with the optimized results. On the left are the initial scenarios with a range of concentrations up to 1.80 mg/L. The maximum limit of the NOM-127 is reached at the consumer nodes near to the sources. Even so, in the south zone there are nodes with concentrations under the NOM-127 guidelines. On the right, the optimized scenarios have concentrations ranging up to 0.60 mg/L. We observe that the values below 0.20 mg/L disappear. To maintain the concentrations in the range proposed by WHO (2011), there is a BCS with a dose of 0.60 mg/L in the south zone in B and C. The free chlorine concentration is maintained between 0.20 and 0.60 mg/L.
Figure 10

Free chlorine concentration at hour 50 of the simulation.

Figure 10

Free chlorine concentration at hour 50 of the simulation.

The minimum consumption is presented in hour 68 of the simulation (practically 64% of the base demand). The configuration of free chlorine is shown in Figure 11. On the left, the range of concentrations is up to 1.80 mg/L for the initial scenarios. The northeast zone has nodes with concentrations below 0.20 mg/L. In this zone, the nodes maintain that concentration for 10 hours. On the right, the optimized scenarios have a range of concentrations up to 0.60 mg/L. The northeast zone has nodes with concentrations below 0.20 mg/L. Only node 243 has concentrations around 0.15 mg/L for 2 hours of simulation in B and C. The concentrations are in the range of 0.20 to 0.50 mg/L at the consumer nodes and only the nodes proposed to have a BCS have values over 0.50 mg/L.
Figure 11

Free chlorine concentration at hour 68 of the simulation.

Figure 11

Free chlorine concentration at hour 68 of the simulation.

CONCLUSIONS

Maintaining chlorine concentrations within the standards for drinking water is a complex concern. It requires optimal infrastructure and optimal operation by WMs. The operating conditions of some WDNs in Mexico do not guarantee safe drinking water at the consumers' taps, and the consumers do not drink water from the WDN. Therefore, in this paper we propose a model to optimize the use of chlorine by installing BCSs and optimizing the use of disinfectant.

The validation of the GA in the net3 network with a diverse range of CRCs shows that the doses could decrease by up to 37.7% when compared to the minimum values of reaction coefficients described in the literature. We observed a decrease in chlorine optimization when the reaction coefficients increase.

The BCS proposal with a minimum dosage led the WMs to maintain concentrations in the range of 0.50 to 0.20 mg/L, avoiding the excessive use of chlorine. These concentrations are enough to eliminate microorganisms. The solution presents the lowest concentration of free chlorine in the network while at the same time providing safe water to consumers who have individual storage containers and, in general, do not drink water from the network.

The GA model with the FF proposed in this paper was validated in order to obtain scenarios with more stable concentrations of chlorine over the 24 hour analysis period. The model is robust enough to be used in a real network of any size. However, it requires the hydraulic and water quality calibration of the WDN model previous to its application. We propose optimized scenarios for WDNs within the specific context of Mexico. These results generate a better distribution of the disinfectant and minimize the doses required for operation according to the uses of the water.

ACKNOWLEDGEMENTS

The research was made with the financial support of the Universidad de Guanajuato (UG): 20113.2013 and 391/2014. The authors would like to thank the DAIP translation services (Servicios de Traducción del Departamento de Apoyo a la Investigación y al Posgrado, in Spanish) of the UG for the American English revision.

REFERENCES

REFERENCES
AEAAS
,
1984
Manual de la cloración, Asociación Española de Abastecimientos de Agua y Saneamiento
,
Editorial AEAAS
,
Madrid, Spain
, p.
32
.
Alcocer
Y. V. H.
Velitchko
T. G.
2004
Modelo de calidad del agua en redes de distribución
.
Ingeniería Hidráulica en México. IMTA
19
(
2
),
77
88
.
Beasley
D.
Martin
R. R.
Bull
D. R.
1993
An overview of genetic algorithms: part 1. fundamentals
.
University Computing
15
,
58
69
.
Boccelli
D. L.
Tryby
M. E.
Uber
J. G.
Rossman
L. A.
Zierolf
M. L.
Polycarpou
M. M.
1998
Optimal scheduling of booster disinfection in water distribution systems
.
Journal of Water Resources Planning and Management
124
(
2
),
99
111
.
Castro
P.
Neves
M.
2003
Chlorine decay in water distribution systems case study – Lousada network
.
Electronic Journal of Environmental, Agricultural and Food Chemistry
2
,
261
266
.
Chipperfield
A. J.
Fleming
P. J.
1995
The MATLAB Genetic Algorithm Toolbox
.
The Institution of Electrical Engineers Colloquium
,
London
,
UK
, pp.
10/1
10/4
.
Chowdhury
S.
Champagne
P.
McLellan
P. J.
2009
Models for predicting disinfection byproduct (DBP) formation in drinking waters: a chronological review
.
Science of the Total Environment
407
(
14
),
4189
4206
.
CONAGUA
2013
Estadísticas del Agua en México
.
Edn 2013
.
Secretaría de Medio Ambiente y Recursos Naturales
,
Mexico City, Mexico
, p.
176
.
Francisque
A.
Shahriar
A.
Islam
N.
Betrie
G.
Siddiqui
R. B.
Tesfamariam
S.
Sadiq
R.
2014
A decision support tool for water mains renewal for small to medium sized utilities: a risk index approach
.
Journal of Water Supply: Research and Technology – AQUA
63
(
4
),
281
302
.
Geldreich
E. E.
1996
Microbial Quality of Water Supply in Distribution Systems
.
CRC Press
, p.
504
.
Greene
J. C.
2014
The Bottled Water Industry in Mexico
.
Master Thesis
,
Public Policy Department. University of Texas, Austin
,
Texas, USA
.
Holland
J. H.
1992
Adaptation in Natural and Artificial Systems
. 2nd edn.
MIT Press
,
Cambridge, MA
.
IMTA
2014
Programa de Indicadores de Gestión de Organismos Operadores
.
http://www.pigoo.gob.mx/index.php (accessed 15 January 2015)
.
Islam
N.
Sadiq
R.
Rodriguez
M. J.
2013
Optimizing booster chlorination in water distribution networks: a water quality index approach
.
Environmental Monitoring and Assessment
185
(
10
),
8035
8050
.
Jiménez
M.
2004
Optimal Design of Water Distribution Network Using a Simple Genetic Algorithm (in Spanish)
.
Master Thesis
.
División de Estudios de Posgrado, UNAM
,
Mexico City, Mexico
.
Knobelsdorf
M. J.
Mujeriego
S. R.
1997
Crecimiento bacteriano en las redes de distribución de agua potable: una revisión bibliográfica
.
Ingeniería del agua
4
(
2
),
17
28
.
Le-Chevallier
M. W.
Gullick
R. W.
Karim
M. R.
Friedman
M.
Funk
J. E.
2003
The potential for health risks from intrusion of contaminants into the distribution systems from pressure transients
.
Journal of Water and Health
1
,
3
14
.
Lei
J.
Sægrov
S.
1998
Statistical approach for describing failures and lifetimes of water mains
.
Water Science and Technology
38
(
6
),
209
217
.
Mora
R. J.
López-Jiménez
P. A.
Ramos
H. M.
2012
Intrusion and leakage in drinking systems induced by pressure variation
.
Journal of Water Supply: Research and Technology – AQUA
61
(
7
),
387
402
.
Norma Oficial Mexicana 127-SSA1
1994
Salud ambiental, agua para uso y consumo humano. Límites permisibles de calidad y tratamientos a que debe someterse el agua para su potabilización
.
Diario Oficial de la Federación
,
México, DF,
p.
18
.
Omisca
E.
2011
Environmental Health in the Latin American and Caribbean Region: Use of Water Storage Containers, Water Quality, and Community Perception
.
PhD Thesis
.
University of South Florida
,
Tampa, Florida, USA
.
Ozdemir
O. N.
Erkan Ucaner
M.
2005
Success of booster chlorination for water supply networks with genetic algorithms
.
Journal of Hydraulic Research
43
(
3
),
267
275
.
PAHO
2004
Manual de tratamiento. Biblioteca virtual de Desarrollo Sostenible y Salud ambiental
. .
Parks
S. L. I.
VanBriesen
J. M.
2009
Booster disinfection for response to contamination in a drinking water distribution system
.
Journal of Water Resources Planning and Management
135
(
6
),
502
511
.
Phillip-Cooper
J.
2003
Development of a Chlorine Decay and Total Trihalomethane Formation Modeling Protocol Using Initial Distribution System Evaluation Data
.
Master Thesis
,
University of Akron
,
USA
.
Rossman
L. A.
2000
EPANET 2: User's Manual
.
WHO
2011
Guidelines for Drinking-Water Quality
. 4th edn.
World Health Organization
,
Geneva, Switzerland
.