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Optimal design and operation of booster chlorination stations layout in water distribution systems Ziv Ohar, Avi Ostfeld* Faculty of Civil and Environmental Engineering, Technion e Israel Institute of Technology, Haifa 32000, Israel

article info

abstract

Article history:

This study describes a new methodology for the disinfection booster design, placement,

Received 26 November 2013

and operation problem in water distribution systems. Disinfectant residuals, which are in

Received in revised form

most cases chlorine residuals, are assumed to be sufficient to prevent growth of pathogenic

26 March 2014

bacteria, yet low enough to avoid taste and odor problems. Commonly, large quantities of

Accepted 27 March 2014

disinfectants are released at the sources outlets for preserving minimum residual disin-

Available online 12 April 2014

fectant concentrations throughout the network. Such an approach can cause taste and odor problems near the disinfectant injection locations, but more important hazardous

Keywords:

excessive disinfectant by-product formations (DBPs) at the far network ends, of which

Water distribution systems

some may be carcinogenic. To cope with these deficiencies booster chlorination stations

Booster chlorination stations

were suggested to be placed at the distribution system itself and not just at the sources,

Disinfection by-products

motivating considerable research in recent years on placement, design, and operation of

Trihalomethanes

booster chlorination stations in water distribution systems. The model formulated and

EPANET-MSX

solved herein is aimed at setting the required chlorination dose of the boosters for deliv-

Genetic algorithms

ering water at acceptable residual chlorine and TTHM concentrations for minimizing the overall cost of booster placement, construction, and operation under extended period hydraulic simulation conditions through utilizing a multi-species approach. The developed methodology links a genetic algorithm with EPANET-MSX, and is demonstrated through base runs and sensitivity analyses on a network example application. Two approaches are suggested for dealing with water quality initial conditions and species periodicity: (1) repetitive cyclical simulation (RCS), and (2) cyclical constrained species (CCS). RCS was found to be more robust but with longer computational time. ª 2014 Elsevier Ltd. All rights reserved.

1.

Introduction

Disinfection has been routinely carried out since the early 1900s as a major mean for preventing water born diseases. Disinfectants, in addition to removing pathogens from drinking water, can prevent biological re-growth if a

* Corresponding author. Tel.: þ972 4 8292782; fax: þ972 4 8228898. E-mail address: [email protected] (A. Ostfeld). http://dx.doi.org/10.1016/j.watres.2014.03.070 0043-1354/ª 2014 Elsevier Ltd. All rights reserved.

minimum disinfectant residual is maintained throughout the water distribution system (WDS). Chlorine and their compounds are the most popular disinfectants for water. This is due to the chlorine low cost and necessity to preserve a residual level. On the other hand high level of chlorine can cause complaints and be poisonous, thus the chlorine residual is kept within proper bounds.

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Table 1 e Summary of trihalomethanes (TTHMs) predictive models. Source

Output

Units

Predictive model

Amy et al. (1987)

TTHM

mmol/l

Adin et al. (1991)

TTHM

mg/l

0.0031(UV TOC)0.44(D)0.409(t)0.265(T)1.06(pH-2.6)0.715(Brþ1)0.036 2 3 ð1=ððK1 þ K3 ÞðK2 þ 0:19ÞÞÞ   5 where ðK1 ÞðK2 ÞðTOCÞ4 ðð1=ðK1 þ K3 ÞÞexpðK1 þ K3 ÞðtcÞ Þ þð1=ðK1 þ K3  K2  0:19ÞÞ  ðð1=ðK2  0:19ÞÞexpðK2 0:19ÞðtcÞ Þ K1 ¼ 4:38  108 ðDÞ; K2 ¼ 11:36  107 ðDÞ; K3 ¼ 7:14  1013 ðDÞ2

Watson (1993)

CHCl3 BDCM BDCM DBCM DBCM CHBr3

mg/l

TTHM

mg/l

Clark (1998)

0:0064ðTOCÞ0:329 ðUVÞ0:874 ðBr þ 0:01Þ0:404 ðpHÞ1:161 ðDÞ0:561 ðtÞ0:269 ðTÞ1:018 0:0098ðBrÞ0:181 ðpHÞ2:55 ðDÞ0:497 ðtÞ0:256 ðTÞ0:519 ðfor D=Br < 75Þ 1:325ðTOCÞ0:725 ðBrÞ0:794 ðDÞ0:632 ðtÞ0:204 ðTÞ1:441 ðfor D=Br > 75Þ 14:998ðTOCÞ1:665 ðBrÞ1:241 ðDÞ0:729 ðtÞ0:261 ðTÞ0:989 ðfor D=Br < 50Þ 0:028ðUVÞ1:175 ðTOCÞ1:078 ðBrÞ1:573 ðpHÞ1:956 ðDÞ1:072 ðtÞ0:2 ðTÞ0:596 ðfor D=Br > 50Þ 6:533ðTOCÞ2:031 ðBrÞ1:388 ðpHÞ1:603 ðDÞ1:057 ðtÞ0:136  Cl ð1  KÞ 0 where A Cl0  1  Keut u ¼ Mð1  KÞ A ¼ 4:44Cl00:44 TOC0:63 pH0:29 T0:14 K ¼ 1:38Cl0:48 TOC0:18 pH0:96 T0:28 0

Gang et al. (2002)

TTHM

M ¼ eð2:460:19TOC0:14pH0:07Tþ0:01T pHÞ aDf1  fekR t  ð1  fÞekS ¼ g

TTHM ¼ total trihalomethanes; CHCl3 ¼ chloroform; BDCM ¼ bromodichloromethane; DBCM ¼ dibromochloromethane; CHBr3 ¼ bromoform; UV ¼ UV absorbance at 254 nm (cm1); TOC ¼ total organic carbon (mg/l); T ¼ water temperature ( C); D ¼ chlorine dose (mg/l); f ¼ fraction of the chlorine demand attributed to rapid reactions; Cl0 ¼ initial residual chlorine (mg/l); a ¼ TTHM yield coefficient; kR and kS ¼ the first order rate constants for rapid and slow reactions, respectively; Br ¼ bromide ion (mg/l); and t ¼ reaction time (hr).

Disinfection by-products (DBPs) were first reported by Rook (1974) leading the US EPA in 1979 to establish a maximum contaminant level (MCL) regulation for total trihalomethanes (TTHMs), as trihalomethanes are suspected to be carcinogenic (Sadiq and Rodriguez, 2004). The common practice of sustaining a residual disinfectant level throughout a water distribution system is to inject large quantities of disinfectant at the outlet of the sources water treatment plants (WTPs). Such doses enable sufficient residuals at far- end locations of the network, but will likely result in extremely high disinfectant levels at consumers’ taps with short residence times near the WTPs, and excessive DBPs formations at the water network far ends (Amy et al., 1987; Clark, 1998; Boccelli et al., 2003). A possible way to cope with these deficiencies is to place booster chlorination stations throughout the network. Such boosters design and operation at key network locations will improve the uniformity of the disinfectant residuals spread, and lower DBPs formations. Another benefit from using booster chlorination can come in a contamination event. Detection by sensors and treatment by activating intensified chlorine injection in adjacent boosters can provide enhanced water quality control during contamination event (Parks et al., 2009). The objective of this study, based on Ohar (2011) and Ohar and Ostfeld (2009, 2010), is to develop a design tool which can address both chlorine and trihalomethanes regulations and can aid in deciding on were and how to inject chlorine to the WDS. An objective function is formulated considering both boosters’ operational and construction costs, and the species concentrations as constraints. The optimization model is solved through a genetic algorithm linked with EPANET multi-

species extension (MSX) (Shang et al., 2008) model. An example application demonstrates the model performances through base runs and sensitivity analyses.

2.

Literature review

The literature review herein is partitioned into three parts: (1) trihalomethanes formation models, (2) booster chlorination optimization, and (3) comparison of this study to previous work.

2.1.

Trihalomethanes formation models

Since the detection of chloroform in disinfected water by Rook (1974), more than 500 disinfection by-products (DBPs) have been identified (Clark et al., 1996). The formation of trihalomethanes has been shown to be a function of the total organic carbon content (TOC), chlorination dose, pH, temperature, bromide ion concentration, reaction time, and UV-254 absorbance (Amy et al., 1987). In addition THM levels and chlorine consumption in drinking water, originating in temperate environments, are significantly affected by seasonal variations (Singer et al., 1995). Research showed that higher THM concentrations will be observed at increased levels of the above mentioned parameters. This can enlighten, as reaction time is one of the above parameters, the generally higher THM concentrations observed in the extremities of a water distribution system, compared to the finished water at the treatment plants (Amy et al., 1987; Clark, 1998; Boccelli et al., 2003). Proper understanding, characterization, and prediction of water quality behavior in drinking water distribution systems

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Table 2 e Literature review map and comparison of booster chlorination placement models. Paper number

1

2

3

4

5

6

7

8A

8B

Water quality model

FOK

FOK

FOK

FOK

FOK

NFOK

FOK

MS

MS

Decision variables

e þ ITH þ e MCM LP

þ þ ITH þ e MCM MILP

e þ St þ e ** LLS

e þ ITH þ e MCM GA

e BCI þ BCD þ EC GA

þ þ ITH þ þ BCI þ BCD GA

þ þ CC þ þ BCI þ BCD GA

Booster location Booster operation Disinfectant periodicity Chlorine constraints TTHM constraints Objective function Optimization solution method

þ þ CC þ e MCM LP þ GA

þ þ ITH þ e * MOGA

þ þ CWB þ

*Trade-off between (1) number of booster station and total disinfectant dose; and (2) total disinfectant dose and level of constraints satisfaction. **Minimization of the sum of squared deviations of residual chlorine from a desired target. Legend and paper notation: FOK ¼ first order kinetics; NFOK ¼ non first order kinetics; MS ¼ multi-species; ITH ¼ infinite time horizon; CC ¼ cyclical constraint; St ¼ stationary of disinfectant residuals; CWB ¼ concentration within bounds; MCM ¼ minimum chlorine mass; LP ¼ linear programming; MILP ¼ mixed integer linear programming; GA ¼ genetic algorithm; MOGA ¼ multi-objective genetic algorithm; LLS ¼ linear least squares; BCI ¼ booster chlorination operational injection cost; BCD ¼ booster chlorination design cost; EC ¼ electrical cost; 1. Boccelli et al. (1998); 2. Tryby et al. (2002); 3. Lansey et al. (2007); 4. Prasad et al. (2004); 5. Propato and Uber (2004); 6. Munavalli and Mohan Kumar (2003); 7. Ostfeld and Salomons (2006); 8A, 8B. This study.

is not only critical for regulatory compliance, but also for human health and wellbeing, and determination of appropriate regulatory requirements. This need led into extensive research in the last two decades, which focused mainly on linking the affect of the above parameters with the concentration of trihalomethanes. The majority of published studies on trihalomethanes formations are empirically and laboratory based, thus they do not take into consideration the affect of the pipes’ wall on the reaction mechanism (Table 1). A more extensive summary of past trihalomethanes models can be found in Sadiq and Rodriguez (2004). Clark (1998) and Clark and Sivaganesan (1998) presented a model for bulk chlorine decay and total trihalomethanes (TTHM) formation based on second reaction kinetics. The model assumes that the reaction rate is proportional to the first power of the product of the reaction components concentrations. One component is the hypochlorous acid, and the second represents the constituents in the water that cause the chlorine consumption. Among the products of this reaction is the TTHM, which is characterized in the model as a function of the chlorine demand. The results of Clark (1998) and Clark and Sivaganesan (1998) showed that the formation of TTHMs is a direct result of the chlorine consumption. In a supplementary work, Clark et al. (2001) extended the second order model for predicting the formation of each of the TTHM components and of haloacetic acids as a function of bromide ion concentration, pH, chlorine concentration and time. The models presented in Table 1 are unable to describe THM formation after rechlorination. Boccelli et al. (2003) extended Clark (1998) to provide an analytical solution capable of describing the chlorine decay and TTHM formation under single and multiple rechlorination scenarios. This model is employed in this study and is further described in the model development section.

2.2.

Booster chlorination optimization

The first to suggest the minimization of total disinfectant mass applied by booster chlorination was Boccelli et al. (1998).

They used the hydraulic solution of a water distribution system, chlorine decay kinetics of first order, and an assumption of linear superposition of water quality constituents (Shamir and Howard, 1991), all for solving the minimal required disinfectant dose at predefined booster locations. Their results indicated that booster disinfection can reduce the required disinfectant mass compared to conventional disinfection at the sources. It was also shown in their study that the efficiency of booster chlorination is significantly affected by the boosters’ locations. Tryby et al. (2002) extended Boccelli et al. (1998) through assigning a binary decision variable for each potential location. Since the problem is expressed in terms of both binary location variables and continuous injection rates, a mixed integer linear programming (MILP) model was formulated. To assure cyclical conditions, Lansey et al. (2007) added to the MILP model cyclical constraints on the chlorine concentrations in all response locations (nodes and tanks). Prasad et al. (2004) solved a multi-objective GA (MOGA) model with minimizing the total disinfectant dose versus maximizing the volume of water supplied with residual chlorine bounds. Munavalli and Mohan Kumar (2003) used a binary genetic algorithm formulation to determine the chlorine injection rates at defined booster locations, aimed at minimizing chlorine residual levels at the consumer nodes with respect to required levels. The operation of boosters, with known locations, was also approached by Propato and Uber (2004), which formulated a linear least-squares (LLS) optimization model to minimize the sum of the squared deviations of residual concentrations from a desired target. Ostfeld and Salomons (2006) linked a water quality simulation model with a GA for simultaneously optimizing the scheduling of pumping units and optimal design and operation of booster chlorination stations. Boccelli et al. (1998), Tryby et al. (2002), and Lansey et al. (2007) used minimization of the total chlorine mass injected as the objective function, where Ostfeld and Salomons (2006) utilized a combination of operational and construction costs for the model objective. Parts of the modeling formulation of Ostfeld and Salomons (2006) is adopted herein.

212

2.3.

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Comparison of this study to previous work

All of the cited above studies addressed the booster disinfection problem while solely accounting for chlorine decay models. Disinfection by-products (DBPs) were not taken into consideration. In this study, both the residual chlorine disinfection and DBPs are simultaneously considered through utilizing a multispecies approach. This is accomplished through approximating the chemistry of both chlorine decay and TTHM formation. The modeling of TTHM kinetics in the water distribution system enabled the inclusion of TTHM regulations as additional constraints. Two approaches are suggested herein for dealing with water quality species periodicity: (1) repetitive cyclical simulation (RCS) and (2) cyclical constrained species (CCS). Table 2 maps the major characteristics of previous booster chlorination placement models, and highlights the contributions of this work.

3.

Model development

Rechlorination of previously chlorinated water does not occur exclusively at the booster chlorination stations. Rechlorination scenarios can take place at any of the system nodes while mixing water with different chlorine residuals. The chlorine demand e TTHM formation model must account for the concentrations discontinuities that are associated with those rechlorination events. The model utilized in this study follows Boccelli et al. (2003), which is an extension of Clark (1998). Boccelli et al. (2003) provides a description of the chlorine decay and TTHM formation kinetics under single, and multiple rechlorination scenarios. Clark (1998) simplified the TTHM formation through a second order model which accounts for both disinfectant (A) and a fictitious reactant (B): aA þ bB/pP

(1)

where: a, b and p are stoichiometric reaction coefficients. The reaction rate is assumed to be of first order with respect to A and B, and of second order overall: dCA dCB dCP ¼ kA CA CB ; ¼ kB CA CB ; ¼ kP CA CB dt dt dt

(2)

where: C and k are the concentration and decay rate coefficients for the reaction’s components, respectively. The decay rate coefficients fulfill the equality of: kA =a ¼ kB =b ¼ kP =p

(3)

Using the equality of (3), the analytical solution of (2) (Clark, 1998) is: CA ðtÞ ¼

 CA;0  aCB;0 b   1  ðaCB;0 bCA;0 Þexp½  ðbCA;0 aCB;0  1ÞkA CB;0 t

(4)

where: CA,0 and CB,0 are the disinfectant and the fictive reaction components at t ¼ 0. For computing CA(t), the a/b ratio and the kA parameter need to be calibrated using experimental

data. Since the fictive component is unknown, CB,0 must be incorporated in the estimation process by defining new parameters to the model. Boccelli et al. (2003) rearranged (4) into: CA ðtÞ ¼

CA;0  a   1  ða CA;0 Þexp½  ðCA;0 a  1Þbt

(5)

aC

where: a ¼ bB;0 and b ¼ kA CB;0 The parameter a (M/L3) describes the “stoichiometric” chlorine concentration required for complete chlorine decay (i.e., the required concentration for the fictive reaction to complete), where b (1/T) is a pseudo first order decay rate coefficient. In this form a and b, need to be determined for a given water source and represent the effect of the various variables as specified in the literature review. These parameters enable the usage of the model over a range of initial chlorine values since they are independent of CA,0 and exclude the need to evaluate CB,0. At rechlorination, model updating is required. This is accomplished by: (1) resetting t, to t* ¼ t  tb, where tb is the time of rechlorination, (2) defining the new initial chlorine dose CA;0 , and (3) updating the parameters, a and b to account for the changes caused by the new segment initial concentration of the reactive component, in consistency with the kinetic model assumption: b CB;0 ¼ CB;0  xðtb Þ a

(6)

aCB;0 ¼ a  xðtb Þ b

(7)

  xðtb Þ b ¼ kA CB;0 ¼ b 1  a

(8)

a ¼

where: x(tb) ¼ CA,0  CA(tb) is the chlorine demand of the previous dose at time of rechlorination. As such, after rechlorination CA ðtÞ will be calculated as a function of   CA ðtÞ ¼ f CA;0 ; t ; a ; b

(9)

The TTHM formation, as solution (2) implies, is a linear function of the chlorine demand: TTHMðtÞ ¼ TxðtÞ þ M0

(10)

where: x(t) is the chlorine demand at time t, T ¼ p/a is a parameter relating the TTHM formation to the chlorine demand (mg/mg), and M0 is the TTHM concentration at t ¼ 0. Eq. (10) can be applied for multiple rechlorination scenarios through relating to x, the demand at the observed segment, and to M0, the TTHM concentration at the beginning of the segment. The given values for a and b represent water that was chlorinated for the first time, and since the water needs to be reassessed after each rechlorination scenario, as implies from Eqs. (7) and (8), their initial values along the network need to be defined. As water distribution systems are complex, it will be very difficult to calculate these initial values since the exact water quality “history” distribution is unknown. In a large scale network, these initial water quality values may defer significantly and affect the reliability of the

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proposed model. This problem is tackled in this study by adopting one of two approaches: repetitive cyclical simulation (RCS) or cyclical constrained species (CCS). Both methods are utilized for creating water quality periodicity; thus eliminating the influence of initial water quality conditions. The RCS method, as will be demonstrated below in the example application, yields better solutions but with a substantial price of computational intensity.

3.1.

Repetitive cyclical simulation (RCS)

Given the assumption that a water distribution system operates under a closed periodic hydraulic cycle, and through using periodic injection rates, it is assumed that regardless of the initial concentrations of the species, they will eventually converge into the same periodic water quality cycle and a monitoring window can be defined. However, the number of cycle repetitions needed to attain that periodicity differ as a function of the system initial conditions. The top of Fig. 1 shows a schematic description of water quality periodicity in a storage tank, starting from an arbitrary zero value and reaching stable periodicity after several cycles, and the selected monitoring window.

3.2.

minimum number of simulation cycles to eliminate the affect of initial concentrations distribution along the network pipes. The bottom of Fig. 1 shows a schematic description of the attained water quality periodicity at a node using this approach, starting from a selected initial condition and converging into repetitive cycle after small number of cycles.

4.

The model formulated and solved herein is aimed at setting the required chlorination dose of the boosters for delivering water at acceptable residual chlorine and TTHM concentrations for minimizing the overall cost of booster placement, construction, and operation under extended period hydraulic simulation conditions. The objective function, constraints, and decision variables are described below.

4.1.

Objective function

The objective function includes two parts (Ostfeld and Salomons, 2006): the booster chlorination operational injection cost (BCI), and the booster chlorination capital cost (BCD):

Cyclical constrained species (CCS) BCI ¼ l

This method attempts to satisfy the cyclical water quality conditions through adding penalties to deviations from cyclical equality constraints. This process requires a

Model formulation

mb X nb¼1

(

k X

) Cli ðtnb ÞDtnb

(11)

i¼1

where: BCI ¼ booster chlorination operational injection cost ($); nb ¼ subscript of the time periods set:1,., mb; mb ¼ number of time periods into which the booster chlorination injection operational time horizon is partitioned; k ¼ number of design boosters (), indexed i; tnb ¼ time period nb (); Cli(tnb) ¼ i-th booster chlorination injection mass rate at time period tnb (mg min1); Dtnb ¼ length of time period nb (min); and l ¼ unit chlorine injection cost ($ mg1). 2 BCD ¼ DRVðAI; BLDÞ4

3 k u  X max s Clj þ gVj 5

(12)

j¼1

where: BCD ¼ booster chlorination capital cost ($); DRV ¼ daily return value coefficient (day1) [AI¼ annual interest (%), BLD ¼ booster chlorination life duration (years)]; k ¼ set of ¼ designed booster chlorination stations, indexed j; CLmax j maximum j-th booster chlorination injection rate (mg min1); Vi ¼ total j-th booster chlorination injection amount (mg); and s [$ (mg min1)u ], u (), g ($ mg1) ¼ empirical booster chlorination capital cost coefficients.

4.2.

Constraints

Constraints are on the residual chlorine concentrations, the threshold TTHM concentrations, the cyclical constrained species (CCS), and the maximum number of designed boosters.

4.2.1. Fig. 1 e Schematics of the repetitive cyclical simulation (RCS) and the cyclical constrained species (CCS) methods.

Residual chlorine concentration

The Residual chlorine concentration at the consumers’ nodes should be kept, according to regulations, between lower and upper bounds:

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Fig. 2 e Solution scheme.

min

Cl

i;j

max

 Cl  Cl

i ¼ 1; :::; mb; j ¼ 1; :::; ncn

(13)

where: Cli,j ¼ residual chlorine concentration at consumer node j at time duration i (mg l1); Clmin and Clmax ¼ minimum and maximum residual chlorine requirements, respectively (mg l1); and ncn ¼ number of consumer nodes (nodes with non-zero demand).

4.2.2.

Maximum TTHM concentration

The TTHM concentration at the consumers’ nodes should be below the defined regulation: TTHMi;j  TTHMmax

i ¼ 1; :::; mb; j ¼ 1; :::; ncn

(14)

i,j

where: TTHM ¼ TTHM concentration at consumer node j at time duration i (mg l1); and TTHMmax ¼ TTHM maximum concentration level (mg l1).

4.2.3.

Cyclical constrained species (CCS)

In case the CCS method is utilized, the following constraints are added: 0;j

0;j

Cl

¼ Cl

mb;j

 ε ; TTHM0;j ¼ TTHMmb;j  ε ;

mb;j

dCl dCl ¼ dt dt

ε j

k  Kmax

(16)

where: Kmax ¼ maximum number of possible designed boosters.

4.3.

Decision variables

The model decision variables differ for the RCS and the CCS methods. For the RCS: (1) the locations of the designed booster chlorination stations (i.e., Kmax integer variables), and (2) the boosters injection mass rates for each of the time periods (i.e., Kmax  mb real variables). For the CCS: (1) the initial concentrations of all species throughout the water distribution system (3  nnodes variables, see Section 5.2 below), (2) the locations of the designed booster chlorination stations (i.e., Kmax integer variables), and (3) the boosters injection mass rates for each of the time periods (i.e., Kmax  mb real variables).

4.4.

Overall optimization model

The overall optimization model objective is to minimize the BCI plus BCD plus constraint penalty as follow:

¼ 1; :::; nnodes

0 (15)

where: nnodes ¼ total number of nodes; and ε ¼ small number to allow flexibility in meeting equality constraints. In case the RCS is used, the constraints in (15) are assumed to be fulfilled.

Minimize @l

(

mb X

k X

nb¼1

) Cli ðtnb ÞDtnb

2 þ DRVðAI; BLDÞ4

i¼1

1 3 k u  X max s Clj þ gVj 5 þ PENA 

(17)

j¼1

4.2.4.

Maximum number of designed boosters

The Maximum number of designed boosters is, as described is section 4.3, a decision variable of the designer. The optimization process can recommend on applying lower amount of booster stations, therefore:

Subject to the constraints listed in Section 4.2; where: PEN ¼ penalty function incurred on constraints violation: PEN ¼ 41

3 X mb X ncn X n¼1 i¼1

j¼1

  max 0; gn;i;j

(18)

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215

Fig. 3 e Example application layout (EPANET Example 3).

where: g1,i,j¼Cli,jClmax; g2,i,j¼ClminCli,j; g3,i,j¼TTHi,j max ; and 41 ¼ a penalty coefficient of 103. M TTHM

5.

Solution scheme

The solution scheme is described in Fig. 2. It is a genetic algorithm (GA) (Holland, 1975; Goldberg, 1989) based framework linking MATLABTR GA toolbox with the EPANET multi-species extension (Shang et al., 2008). Below is a brief description of the GA, the EPANET-MSX model, and the overall tailored solution methodology.

5.1.

Genetic algorithms

A GA is a heuristic search procedure based on the mechanisms of genetics and Darwin’s natural selection principles, combining an artificial survival of the fittest with genetic operators abstracted from nature (Holland, 1975; Goldberg, 1989). GAs differ from other search techniques in that they search among a population of elements and use probabilistic rather than deterministic transition rules. As a result, GAs search more globally (Wang, 1997; Haupt and Haupt, 1998). A typical genetic algorithm incorporates three main stages: (1) initial population generation: the GA generates a bundle of chromosomes (entitled a population), this chromosomes are strings, each string is a coded representation of the decision variables; (2) computation of the strings fitness: the GA evaluates each strings fitness (i.e., the value of the objective function

corresponding to each string); and (3) generation of a new population: the GA generates the next population by performing: selection, crossover, and mutation, where: selection involves the process of choosing chromosomes from the current population for reproduction according to their fitness values, crossover involves partial exchange of information between pairs of strings, and mutation involves a random change in one of the strings locations. Strings can have binary, integer, or real values. In this study, the following GA operations are used: Selection which is using weighted random pairing; where the better the fitness of a chromosome, the higher is its likelihood to be selected as a parent. Crossover herein employs the one point crossover method for integer variables, and a linear combination of the two parents, for real variables. Mutation is used through randomly altering one of the chromosome’s parameter values. Elitism defines the best chromosome in each generation, which is moved unchanged to the next. During the last decade, GAs became one of the more successful robust optimization techniques employed for water resources and environmental engineering management (Nicklow et al., 2010).

5.2.

Utilization of EPANET-MSX

EPANET-MSX (Shang et al., 2008) is a program for modeling complex reaction schemes between multiple chemical and biological species in water distribution systems, based on the hydraulic engine of EPANET.

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Table 3 e Summery of Net 3 example application results. Analysis

Analysis’s main characteristics

Selected boosters’ node ID

*Cost ($/day)

BCI ($/day)

BCD ($/day)

RCS e BR RCS e SA1 RCS e SA2

e BCI ¼ 0 TTHM average concentration as the cost function Multiple sources with different qualities e BCI ¼ 0 TTHM average concentration as the cost function

61,10,187 River,10,123,205,166 123,Lake,211,249

132 95 (147.2)

109.5 95 (120.1)

22.5 (32.6) (27.1)

(11.65) (11.02) 9.25

200 200 200

Lake,123,20,119,211

116.5

81.9

34.6

(4.33)

350

123,10,206,Lake,243 61,Lake,111,237,261 123,10,211,20,184

226.6 174 (204.3)

178.1 174 (173.9)

32.5 (31.7) (30.4)

(12.93) (19.5) 13.93

70 70 70

RCS e SA3 CCS e BR CCS e SA1 CCS e SA2

TTHM average concentration (mm/l)

Run time (min)

* Not including penalty for deviation from the cyclical condition. ** In brackets values not included in the cost function of the analysis.

EPANET-MSX is related to two significant physical processes within a water distribution system: (1) a mobile bulk water phase and (2) a fixed pipe surface phase. Bulk phase species are chemical or biological components that exist within the bulk water phase and are transported through the system by advection. Surface phase species, also known as wall species, are components that are attached or incorporated into the pipe wall. Material transport in EPANET-MSX is based on the advection equation, the assumption of complete and instantaneous mixing at junctions, and the utilization of Lagrangian timedriven method (TDM). Chemical reaction kinetics are implemented through a set of ordinary differential equations (ODEs) which can be integrated over time to simulate changes in species concentrations and are solved through numerical integration methods. Fast/equilibrium reactions are described by a set of algebraic equations and solved using an implementation of the Newton method. The EPANET-MSX water quality ODEs model implemented in this work is utilizing Eq. (2) and the parameters formulated in Boccelli et al. (2003): a¼

aCB;0 b CB;0 0 ¼ a b a

b ¼ kA CB;0 0kA ¼

b CB;0

(19)

(20)

b CB;0 b b ¼ kB ¼ kA ¼ a a CB;0 a

(21)

p b kP ¼ kA ¼ T a CB;0

(22)

The ODE system solved by EPANET-MSX during the water quality simulations is: dCA b dCB b dCP b ¼ ¼  CA CB ; ¼T CA CB ; CA CB CB;0 a CB;0 dt dt dt

5.3.

(23)

case CCS method is used are evaluated using EPANET-MSX. Each string receives a cost equal to the boosters chlorination cost if the solution string yields a feasible solution or is penalized otherwise. Genetic algorithm operations of selection, crossover and mutation are performed until stopping conditions are met, which are a maximum generations number or no objective function improvement at some consecutive generations. The entire computer code of the proposed methodology and metadata on the program structure are provided as supplementary material.

6.

Application

The model is demonstrated on EPANET (USEPA, 2013) Example 3. The water distribution system consists of two constant head sources, a Lake and a River; three elevated storage tanks, 120 pipes, 94 nodes (consumers and internal nodes) and two pumping stations (Fig. 3). The system is subject to a demand flow pattern of 24 h. The data for the pipes and consumers is similar to the data of Example 3 in EPANET, and thus is not repeated herein. A maximum of five boosters (i.e., Kmax ¼ 5) was considered and the injection intervals were considered to be 2 h each (i.e., a total of 12 possible injection rate variations for each booster station). Although the injected mass rate remains constant during the time interval, changes in flow rates might create varying outgoing chlorine concentrations. The minimum and maximum chlorine concentration levels at the consumer nodes were set to 0.2 and 4 mg l1, respectively; and the TTHM maximum concentration level was 0.08 mg l1, following the USEPA regulations (USEPA, 2009). The water quality and cost parameters were defined as: (1) water quality parameters: a ¼ 1.19 mg l1; b ¼ 1.09 d1; T ¼ 37.2 (mg/mg); the water quality at the sources was set to be free from chlorine residuals and of TTHM, and (2) cost parameters: cost of chlorine injection $2 kg1 Cl; s ¼ 2.21 (mg min1); u ¼ 0.13; and g ¼ 0 ($ mg1). A summary of the results is given in Table 3.

Overall solution scheme 6.1.

At each generation (see Fig. 2), a population of GA strings of decision variables: of designed booster locations (integer), chlorine injection rates (real) and concentrations initial levels in

RCS versus CCS comparison

To compare the closure behavior of the RCS to the CCS method, a norm of the errors was utilized, defined as the sum of the

w a t e r r e s e a r c h 5 8 ( 2 0 1 4 ) 2 0 9 e2 2 0

217

Fig. 4 e Typical behavior of relative concentrations for the cyclical constrained species (CCS) and for the repetitive cyclical simulation (RCS) in the example application.

relative concentrations between the beginning and end concentrations of all species in the monitoring window (Fig. 4). It can be seen from the RCS plot in Fig. 4 that similar peak behavior of all relative errors of all species was attained once a stable multi-species solution was reached. On the other hand, the CCS graph in Fig. 4 does not show this behavior, thus it can be concluded that the CCS has not reached chemical stability conditions. This is further demonstrated in Fig. 5, where the norm of the relative error for the CCS is plotted as a function of the simulation cycle, showing an increase in error norm values after 5e7 cycles, and a decrease in norm error with cycles increase. This implies that the relative error of the two approaches should be compared on a similar time scale; In the following example application the norm value for the CCS method base run after 4 simulation was 1.96 and after 28 simulation cycles improved and was found to be 0.15 (Fig. 5), about six times smaller than the RCS norm error of 0.92.

On the other hand (as will be shown further below), the RCS method attains a better overall cost solution compared to the CCS, while the CCS reaches a better cyclical closure, and requires about 33% of the computational time compared to the RCS.

6.2.

Repetitive cyclical simulation (RCS)

For creating a hydraulic cycle, the tanks initial heads were altered to match the tanks heads at the end of a hydraulic long run time horizon simulation; and for creating a cycle water quality pattern, 28 simulation period cycles were found to be sufficient in most of the cases. The genetic algorithm population contained 150 strings, and a maximum of 300 generations.

6.2.1.

Base run

Fig. 6 describes the results of a base run and two sensitivity analyses for the RCS method. For the base run, three booster stations were selected; the total cost was $132 d1 of which $109.5 d1 were associated to BCI, and $22.5 d1 to BCD. Run time, including the simulation trials for receiving a cyclic water quality pattern, was approximately200 min on a PC i7 2.4 GHz, 16 GB RAM machine.

6.2.2.

Sensitivity analysis 1

In this sensitivity analysis (SA) it is examined how the methodology resolves the problem when only BCI is used in the cost function. As a result, five boosters were selected at various parts of the system (Fig. 6). The total cost which was allocated only to the chlorine injection was $95.

6.2.3.

Fig. 5 e Typical behavior of the relative error norm of the cyclical constrained species (CCS) for the example application base run.

Sensitivity analysis 2

The described methodology can be used to evaluate the solution in order to minimize human health effects. In SA2 the cost function was replaced by Min. average TTHM concentration in the consumers nodes throughout the monitoring window. This run was resulted in the location of four boosters

218

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Fig. 6 e Example application results for the repetitive cyclical simulation (RCS) method.

with average TTHM concentration of 9.25 mm/l compared to 11.65 mm/l in the BR. The capital cost of this run was $147.2 d1, which is higher than the result of the BR demonstration that optimal booster configuration and exposure to TTHM are competitive objectives. One more aspect of this results is the BCI which was $120.1 d1, again higher than the BR and SA1 results indicating that direct correlation between chlorine mass and TTHM formation is not straight forward.

6.2.4.

Sensitivity analysis 3

Water quality model parameters at the sources can vary significantly. The blending of the water sources requires redefining of the water quality model to accurate reflect the constituent modifications. One simple approach to deal with blending of various sources is to assume that at any given time and location, the reaction constants are given by a weighted average sum of the original sources reaction constants and associated tracer concentrations. Those fractions can be deduced by introducing fictitious conservative constituent tracers at the sources. At each source, a tracer is introduced to the system at a constant concentration of 1.0 mg l1. Then, at any location in the network, the fraction of the water originating at that source would be the concentration of the tracer, and the reaction constant would be computed through a weighted summation of the tracer concentrations. In this example application, two sources (i.e., the River and the Lake) exist, thus the second tracer concentration is the complementary concentration of the first. Only one tracer thus needs to be introduced to the system of equations.

This idea was implemented in EPANET-MSX using reported parameters from Boccelli et al. (2003): a ¼ 1.19 mg l1; b ¼ 1.09 d1; T ¼ 37.2 (mg/mg); and M (mg/l) ¼ 0 for the Lake, and a ¼ 0.57 mg l1; b ¼ 0.36 d1; T ¼ 12.4 (mg/mg); and M (mg/l) ¼ 0 for the River. The tracer concentrations at the Lake and River were assumed to be zero and 1.0 mg l1, respectively. This sensitivity run resulted in three boosters with a total cost of $116.5 d1 compared to $144.5 d1 at the base run. This reduction in cost and number of boosters can be attributed to the River which supplies about 83% of the total system water demand, and its water quality parameters that are lower compared to the base run. The chlorine decay is thus lower, and consequently lower quantities of chlorine are required to satisfy the chlorine regulations.

6.3.

Cyclical constrained species (CCS)

Fig. 7 shows the results of a base run and two sensitivity analyses runs for the CCS method. The genetic algorithm population contained 200 strings, and a maximum of 300 generations. Run time was approximately 70 min on a PC i7 2.4 GHz, 16 GB RAM machine.

6.3.1.

Base run

The CCS base run capital cost was $226.6 d1 of which $178.1 d1 was the BCI, and $32.5 d1 was the BCD. In addition, a closure penalty cost of $142 d1 was incurred. The increase in cost compared to the RCS method is attributed to the additional cyclical constraints. In both the CCS and RCS methods, the concentration constraints were fully met.

w a t e r r e s e a r c h 5 8 ( 2 0 1 4 ) 2 0 9 e2 2 0

219

Fig. 7 e Example application results for the cyclical constrained species (CCS) method.

6.3.2.

Sensitivity analysis 1 and 2

In order to compare between the methods similar SAs’ to the RCS were performed. In SA1, five booster stations were selected with BCI of $174 d1, which is almost twice of the equivalent result of the RCS SA1 SA2 resulted in an average TTHM concentration of 13.93 mm/l higher than the RCS result. This result is also higher than the CCS BR result, and indicates that the solution had converged into a local minima.

7.

Conclusions

Since the detection of trihalomethanes, numerous studies were undertaken over the last three decades on trihalomethanes formations. In parallel, a major development in the field of water quality modeling in water distribution systems has evolved, leading to the ability to model multi-species chemical reaction kinetics. Several studies addressed the booster chlorination optimization problem, ranging from an LP formulation to utilizing genetic algorithm optimization. No study so far tackled the booster optimization problem while including disinfection byproducts regulations as constraints. This work formulated a model using GA optimization technique and EPANET-MSX. The EPANET-MSX was used to calculate a reaction that describes the chlorine decay-TTHM formation kinetics and their propagation in the network based on the hydraulic conditions. Kinetics of a specific trihalomethane or any other DBP are not treated in this research. This can be further elaborated in

future directions of this study. The purpose of this study was to develop a design tool which can aid in the design of booster chlorination stations while considering both chlorine and trihalomethanes regulations. It was shown that using the cyclical constrained approach, results would be found faster and with more accuracy regarding the cyclical closure, but would hold a more expensive solution in comparison to the repetitive cycles approach and might converge into less than optimal results due to the additional constraints and penalties. Therefore, the RCS approach is preferred unless the calculation duration is critical. TTHM formation is linked in a chemical reaction to the chlorine decay, however in WDS environment characterized by changing hydraulics and varying injections time series uncorrelated results can be found. The results also showed that the optimal booster configuration and exposure to TTHM are competitive objectives, and thus formulation of a multiobjective model for trading off the capital cost versus the TTHM consumer exposure can be the subject of future complementary research. Another direction for extending this study is to connect the boosters to a sensor system for triggering injections, which will imply modifications of the booster’s operation regime.

Acknowledgment This work was supported by the Technion Funds for Security research and by the Technion Grand Water Research Institute.

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Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.watres.2014.03.070.

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