PROCESS DESIGN AND CONTROL

Synthesis of an Economically Friendly Water Network System by Maximizing NetPresent Value

Seong-Rin Lim, Donghee Park, and Jong Moon Park*

AdVanced EnVironmental Biotechnology Research Center, Department of Chemical Engineering, School ofEnVironmental Science and Engineering, Pohang UniVersity of Science and Technology, San 31, Hyoja-dong,Pohang 790-784, South Korea

Water network synthesis has been used to conserve water resources and reduce freshwater costs. However,a mathematical optimization model to maximize the profitability of a water network system has not beendeveloped. The objective of this work was to develop the model to synthesize an economically friendly waternetwork system by maximizing its net present value (NPV). The mathematical optimization model includesprincipal contributors to incremental costs and benefits resulting from water network synthesis. Tradeoffsbetween the incremental costs and benefits derived from water reuse are optimized to maximize the NPV. Ina case study, an NPV-maximized water network system was more profitable than the total freshwater flow-rate-minimized and total freshwater cost-minimized water network systems. The model can be used topractically implement water network systems and can be applied to other process integration technologies togenerate economically friendly heat and hydrogen network systems.

1. Introduction

Much effort has been made to reduce costs and increasebenefits, to enhance the competitiveness and profitability ofindustries. Because water is an important resource for washing,cleaning, and cooling, and is a product in itself, many technolo-gies associated with water have been developed to reduce costsincurred from water supply, water treatment, and wastewatertreatment. Water network synthesis has also been used to reducecosts resulting from freshwater consumption and wastewatertreatment. A water network system is synthesized by optimizingall water sources (e.g., freshwater, wastewater, etc.) and sinks(e.g., water-using operations) to maximize water reuse: waste-water from water-using operations can be reused for otheroperations if the properties of the wastewater meet the opera-tional conditions.

Many water network synthesis technologies have beendeveloped and practiced in industrial plants. The first waternetwork optimization to reduce the rates of freshwater consump-tion and wastewater generation was used in a petroleum refineryplant in 1980.1

Most previous studies for water network synthesis havefocused on solving mathematical formulations, such as nonlinearprogramming (NLP) and mixed-integer nonlinear programming(MINLP), to find global optima.1-6 Genetic algorithm was alsodeveloped to solve MINLP used for wastewater minimizationand to avoid obtaining local optima.7 These approaches arenecessary because of nonconvexities resulting from bilinearvariables in mass balances on contaminants.

Objective functions in previous works have been formulatedintuitively without a clear basis for the selection of contributorsto economic costs and benefits. As a result, various types of

objective functions have been used. Simple formulas forinvestment and operating costs have been used to represent atotal annual cost.1 Most studies have minimized a singlecontributor, such as a total freshwater flow rate, the number ofinterconnections, or fixed costs.5,7-10 For an objective function,studies have used the sum of operating costs for freshwater andcapital costs for pipes and wastewater treatment, or the sum ofa few capital and operating costs,6,12 or the sum of the costs offreshwater supply, water and wastewater treatment, pipes, andsewers.11 One study that used multiobjective optimization,simultaneously minimizing the total annualized cost and envi-ronmental impacts, did not include piping costs.13 However,these intuitive formulations of the objective functions cannotalways generate economically friendly water network systems,even though global optima are obtained. This is because allprincipal contributors to economic costs and benefits are notincluded in the objective functions.

Pinch analysis technologies have been studied to graphicallyanalyze the process limiting data of water-using operations andheuristically generate water network systems.5,13-17 Thesegraphical targeting methods suggest the minimum freshwaterconsumption rate of a water system and identify any bottlenecksthat affect freshwater consumption. Procedure and heuristicswere proposed to extract correct limiting water data for pinchanalysis.27 However, these methods do not take the economicaspect of their designs into consideration.

In the present study, principal contributors to incrementalcosts and benefits were used to formulate a mathematicaloptimization model. The incremental cost or benefit in waternetwork synthesis is the difference between the costs of a waternetwork system and of a conventional water system that hasno interconnection for water reuse. According to a comprehen-sive economic evaluation of a water network system, theprincipal contributors to incremental costs are piping, mainte-

* To whom all correspondence should be addressed. Tel.:+82-54-279-2275. Fax:+82-54-279-2699. E-mail: jmpark@postech.ac.kr.

6936 Ind. Eng. Chem. Res.2007,46, 6936-6943

10.1021/ie061353v CCC: $37.00 © 2007 American Chemical SocietyPublished on Web 09/07/2007

nance and repairs (M&R), and pipe decommissioning, whereasthe principal contributor to incremental benefits is the decreasein freshwater consumption.18 This information was used tosimply synthesize an economically friendly water networksystem; a simplified mathematical optimization model isbeneficial to practical applications in industries, because allcontributors to economic costs and benefits cannot easily beformulated in a mathematical optimization model.

The net present value (NPV) was used as the objectivefunction of the mathematical optimization model proposed inthis study. The NPV is an economic feasibility indicator thatsupports a decision maker to determine whether to build a waternetwork system. In other words, the NPV shows how muchbenefit can be obtained when a conventional water system isreplaced with a water network system. The amount of benefitsis a stronger driving force to motivate a decision maker to buildthe system than the amount of costs. The NPV takes intoconsideration the time value of cash flows derived from theconstruction, operations and maintenance (O&M), and disposalof a water network system. The NPV is obtained by summingdiscounted cash flows and an initial capital investment cost,after a series of future cash flows is discounted. The mosteconomically friendly water network system can be synthesizedby maximizing the NPV. Incremental costs and benefits of thewater network system were calculated using the costs of theconventional water system as a baseline, and then they wereused to calculate the NPV.18 This approach was necessarybecause a water system that is used as a utility for productionsystems and processes cannot directly yield profits from its ownoperation.

In this study, we develop a mathematical optimization modelto synthesize an economically friendly water network systemby maximizing its NPV. An objective function was formulatedto calculate the NPV to be maximized in the model. Costs forpiping, M&R, pipe decommissioning, and freshwater consump-tion were formulated to calculate incremental costs and benefitsrequired for the NPV evaluation. Mass balances and constraintswere formulated to represent a generalized superstructure modelused for water network synthesis. A case study was performedto demonstrate the high profitability of a water network systemgenerated from the model and examine the effects of the modelon the configuration of a water network system. An NPV-maximized water network system was compared to a totalfreshwater flow-rate-minimized system and a total freshwatercost-minimized water system. The costs of principal contributorsin each water network system were estimated. The NPV of thewater network systems was evaluated to show their overallprofitability.

2. Mathematical Optimization Model

2.1. Superstructure Model. A generalized superstructuremodel18 is used to describe the true conditions of a water systemin industrial plants. The superstructure model includes allpossible interconnections between water sources and sinks, suchas those from the outlet of an operation to the inlet of the others,as well as between freshwater sources and water-using opera-tions, to fully utilize opportunities for water reuse and ultimatelyreduce the total freshwater consumption rate. However, to avoidexcessive costs derived from pumping with a high flow rate,local recycling from the outlet to the inlet within an operationis not allowed. This is because the small gap between theconcentrations of inlet and outlet in the local recycling requiresa high flow rate in the recycled line, to transfer the contaminantload of the operation into water.18 Furthermore, a loss of

freshwater is avoided by prohibiting direct connections betweenfreshwater sources and local wastewater treatment plants. Weassume that a mixer combines many streams into a single streamand that a splitter divides one stream into all possible streamsflowing to water sinks.

2.2. Mathematical Formulation. The mathematical formula-tion required to generate an economically friendly water networksystem is composed of an objective function (including an NPVequation and formulas used for cost estimations), as well asmass balances and constraints required to represent the super-structure model. All symbols are explained in the Nomenclaturesection at the end of this paper.

2.2.1. Objective Function. The NPV is maximized tosynthesize an economically friendly water network system basedon discounted incremental benefits (IBs). When depreciationcosts and a total income-tax rate are included, the objectivefunction is given as follows:

The incremental benefits are calculated by subtracting the costsof the water network system from those of the conventionalwater system. If the cost of a water network system is greaterthan that of a conventional water system, the incremental benefitis negative, which means an incremental cost. The costs of thewater system consist of total piping, O&M, and pipe decom-missioning costs.

Depreciation cost (DCt) is estimated by a straight-line methodover the service life,19 as shown in eq 4.

A salvage value is assumed to be zero.

Principal contributors to incremental costs and benefits areused to formulate the objective function, because all contributorscannot easily be formulated in the function. The principalcontributors are the piping cost in the construction stage, thetotal freshwater and M&R costs in the O&M stage, and thepipe decommissioning cost in the disposal stage.18 All principalcontributors, with the exception of the freshwater consumption,are assumed to be performed by contractors, as is normal inthe field of engineering and construction. Therefore, a contrac-tor’s overhead and profit are included in the mathematicaloptimization model.

The total piping cost consists of the total direct pipe materialcost, the total direct labor cost for piping works, constructionexpenses, and the contractor’s overhead and profit. Unit directmaterial and labor costs for the piping are assumed to beproportional to the cross-sectional area, which is calculated bydividing the flow rate by an optimal velocity through the pipe.11

Max{NPV ) ∑t)1

t [IB t(1 - TR) + DCtTR](1 + e)t

(1 + i)t+ IB0}

(1)

IBt ) Costtcws - Costt

wns (2)

Costtcwsor Costt

wns ) Costtpiping + Costt

O&M + Costtdecom

(3)

DCt )IB0

t(4)

Ind. Eng. Chem. Res., Vol. 46, No. 21, 20076937

Equations used to estimate the total piping cost are given asfollows:

Construction expenses are proportional to the sum of the totaldirect material and labor costs for piping. A contractor’soverhead in the construction stage is proportional to the sumof the total direct material and labor costs for piping, as well asthe construction expenses. A contractor’s profits in the construc-tion stage are proportional to the sum of the total direct laborcost for piping, construction expenses, and the contractor’soverhead. Equations used to estimate construction expenses, andthe contractor’s overhead and profit are given as follows:

The principal contributors in the O&M stage are the totalfreshwater and M&R costs. The total freshwater cost iscalculated from the freshwater consumption rate and its unitcost. The M&R cost is proportional to the total piping cost.19

Equations used to estimate the costs in the O&M stage are givenas follows:

where

and

The total pipe decommissioning cost consists of a pipedecommissioning cost, construction expenses, and the contrac-tor’s overhead and profit. The pipe decommissioning cost isproportional to the direct labor cost for piping in the constructionstage. The construction expenses in the disposal stage areproportional to the pipe decommissioning cost. The contractor’s

overheads in the disposal stage are proportional to the sum ofthe pipe decommissioning cost and construction expenses. Thecontractor’s profits in the disposal stage are proportional to thesum of the pipe decommissioning cost, construction expenses,and contractor’s overhead. Equations used to estimate the costsin the disposal stage are given as follows:

where

2.2.2. Mass Balances and Constraints.The formulation ofmass balances and constraints is based on the superstructuremodel previously described. Equations used for the massbalances and constraints are described as follows:

For the overall mass balance of the entire water networksystem:

For the mass balances of the mixers:

For the mass balances of the operations:

For the mass balances of the splitters:

For the constraints on the flow rates and concentrations ofthe operations:

For the constraints on the prevention of local recycling:

where the value of opout is the same as that of opin.

3. Case Study

A case study was performed to demonstrate the higherprofitability of a water network system generated from the

Costtpiping ) TDPpiping + TDLpiping +

EXPpiping + OHpiping + PROpiping (5)

TDPpiping ) ∑w∈W

∑opin∈OP

DPw,opin+ ∑

opin∈OP∑

opout∈OP

DPopout,opin+

∑opout∈OP

DPopout,ww (6)

DPw,opin, DPopout,opin

, DPopout,ww ) (adpParea+ bdp)l (7)

TDLpiping ) ∑w∈W

∑opin∈OP

DLw,opin+ ∑

opin∈OP∑

opout∈OP

DLopout,opin+

∑opout∈OP

DLopout,ww (8)

DLw,opin, DLopout,opin

, DLopout,ww ) (adpParea+ bdp)l (9)

Parea)Fw,opin

V, Parea)

Fopout,opin

V, Parea)

Fopout,ww

V(10)

V ) aopFw,opin+ bop, V ) aopFopout,opin

+ bop (11)

EXPpiping ) R(TDPpiping + TDLpiping) (12)

OHpiping ) â(TDPpiping + TDLpiping + EXPpiping) (13)

PROpiping ) γ(TDLpiping + EXPpiping + OHpiping) (14)

CosttO&M ) FWC + MRC (15)

FWC ) ∑w∈W

∑opin∈OP

Fw,opinUCw (16)

MRC ) δ × Costpiping (17)

Costtdecom) TDLdecom+ EXPdecom+

OHdecom+ PROdecom (18)

TDLdecom) ε × TDLpiping (19)

EXPdecom) R × TDLdecom (20)

OHdecom) â(TDLdecom+ EXPdecom) (21)

PROdecom) γ(TDLdecom+ EXPdecom+ OHdecom) (22)

∑w∈W

∑opin∈OP

Fw,opin- ∑

ww∈WW

Fopout,ww - ∑op∈OP

FL,op ) 0 (23)

∑w∈W

Fw,opin+ ∑

opout∈OP

Fopout,opin- Fopin

) 0 (24)

∑w∈W

Fw,opinCc,w + ∑

opout∈OP

Fopout,opinCc,opout

-

FopinCc,opin

) 0 (25)

Fopin- FL,op - Fopout

) 0 (26)

FopinCc,opin

+ Mc,op - FopoutCc,opout

) 0 (27)

Fopout- ∑

opin∈OP

Fopout,opin- Fopout,ww ) 0 (28)

Fopin

min e Fopine Fopin

max (29)

Cc,opine Cc,opin

max (30)

Cc,opoute Cc,opout

max (31)

Fopout,opin) 0 (32)

6938 Ind. Eng. Chem. Res., Vol. 46, No. 21, 2007

aforementioned mathematical optimization model and to esti-mate the effects of the model on the configuration of a waternetwork system. Three types of water network systems weresynthesized on the basis of each objective function: NPVmaximization, total freshwater flow-rate minimization, and totalfreshwater cost minimization. The NPV-maximized waternetwork system (NWNS) was compared to the total freshwaterflow-rate-minimized water network system (FWNS) and totalfreshwater cost-minimized water network system (CWNS). Thecosts of the principal contributors in each water network systemwere estimated and compared. Each NPV of the water networksystems was evaluated to compare their overall profitability.

3.1. Methods.Five water-using operations in an iron and steelplant were selected as the water sources and sinks in this casestudy. The convention water system (CWS), which wascomposed of the water-using operations, is illustrated in Figure1. Their limiting process data for the water network synthesesare presented in Table 1. The distance matrix for the intercon-nections between the water sources and sinks, such as thefreshwater sources, water-using operations, and local wastewatertreatment plants, is shown in Table 2. The concentrations ofthe industrial and deionized water used as the freshwater sourcesare presented in Table 3.

3.1.1. Water Network Synthesis.The three water networksystems were generated by their own objective functions, subjectto mass balances and constraints. The objective functions usedto synthesize the FWNS and CWNS are described as follows:

For the objective function to minimize the total freshwaterflow rate:

For the objective function to minimize the total freshwatercost:

The FWNS was generated using eqs 23-33, and the CWNSwas synthesized based on eqs 23-32 and eq 34. The NWNSwas generated with eqs 1-32.

All parameters used in the objective functions were set beforeobtaining optimal solutions. The interest rate was set at 5.7%,with respect to the yields of treasury bonds (5-year bonds) overthe last 10 years in South Korea,20 and the escalation rate wasassumed to be the 3.0% that was targeted by the Bank of Korea

Figure 1. Conventional water system. Legend: FW, freshwater; OP, water-using operation; and TP, local wastewater treatment plant.

Table 1. Limiting Process Data for Water Network Synthesis

contaminantC c,opin

max

(mg/L)C c,opout

max

(mg/L)Mop

(kg/h)FL,op

(m3/h)F opin

min

(m3/h)F opin

max

(m3/h)

Operation OP1CODcr 30 500 3.3

49.7 50 90SS 5 100 0.5Cl- 120 2300 16.4

Operation OP2CODcr 20 250 2.3

36.6 40 90SS 3 50 0.4Cl- 20 300 3.0

Operation OP3CODcr 10 160 1.5

8.8 10 60SS 2 25 0.2Cl- 1 5 0.0

Operation OP4CODcr 30 250 3.4

3.1 10 60SS 1 50 0.6Cl- 80 750 11.5

Operation OP5CODcr 30 300 4.5

0.8 10 40SS 5 15 0.1Cl- 3 40 0.4

Table 2. Distance Matrixa

Distance (m)

FW1 FW2 OP1 OP2 OP3 OP4 OP5

OP1 2060 1010OP2 2090 410 280OP3 4600 4660 4470 4330OP4 2710 2490 2280 2440 1900OP5 2850 2580 2300 2580 1840 140TP1 520 300 4740 2820 2930TP2 4580 4440 280 2030 1980TP3 2410 2580 2060 300 350TP4 2360 2530 2110 350 300

a FW ) fresh water; OP) water-using operation; and TP) localwastewater treatment plant.

Table 3. Concentrations of Freshwater Sources

Concentration,Cc,w (mg/L)

freshwater source CODcr SS Cl-

FW1 industrial water 0 0 15FW2 deionized water 0 0 0

Table 4. Characteristics of the Conventional Water System and theThree Water Network Systemsa

Value

characteristic CWS FWNS CWNS NWNS

utility consumption rate (m3/h)industrial water 123.8 52.3 117.9 118.1deionized water 39.0 96.2 30.8 30.8total 162.8 148.5 148.7 148.9

wastewater generation rate (m3/h) 64.8 49.6 49.6 49.8pipe length (m) 15 800 35 440 38 470 34 720

a CWS ) conventional water system; FWNS) total freshwater flow-rate-minimized water network system; CWNS) total freshwater cost-minimized water network system; and NWNS) NPV-maximized waternetwork system.

Min{Fwt ) ∑

w∈W∑

opin∈OP

Fw,opin} (33)

Min{Costwt ) ∑

w∈ W∑

opin∈OP

Fw,opinUCw} (34)

Ind. Eng. Chem. Res., Vol. 46, No. 21, 20076939

for the period between 2004 and 2006.21 A total income-taxrate of 27.5% was applied, according to the tax law in SouthKorea.22 The service life was assumed to be 15 years, based onthe lifetime of the pipes. Parameters used to estimate the directmaterial and labor costs for piping in eqs 7 and 9 are

These parameters were obtained from the correlation betweenthe cost and the cross-sectional area of the pipes. Databases ofprice and cost information were used for the direct material andlabor costs for piping.23,24The optimal velocity in the pumpingflow was obtained from its correlation with a flow rate and wasset not to exceed a maximum head loss (2.0 kgf/cm2) forpumping flow. The parameters used to determine the optimalvelocity in eq 11 are

Figure 2. Comparison of the water network systems: (a) total freshwater flow-rate-minimized water network system (FWNS); (b) total freshwater cost-minimized water network system (CWNS); and (c) NPV-maximized water network system (NWNS). Legend: FW, freshwater; OP, water-using operation;and TP, local wastewater treatment plant.

Figure 3. Comparison of the costs of the principal contributors in each water network system. The costs were not discounted to present values. Legend:CWS, conventional water system; FWNS, total freshwater flow-rate-minimized water network system; CWNS, total freshwater cost-minimized water networksystem; and NWNS, NPV-maximized water network system.

adp ) 714.15, bdp ) 2.9053, adl ) 2106.3, bdl ) 16.326

6940 Ind. Eng. Chem. Res., Vol. 46, No. 21, 2007

These parameters were also obtained from correlations betweenhead losses through the pipe and the length and diameter of thepipe. However, the optimal velocity in gravity flow, suchas for the effluents from the water-using operations to thelocal wastewater treatment plants, was set at 0.5 m/s, be-cause (i) a maximum head loss basis for the gravity flowwas set at 0.2 kgf/cm2 and (ii) a lower velocity results inthe deposition of particles in the pipe.25 The distances be-tween water sources and sinks were used as pipe lengths.The parameters used to determine the construction expenses,as well as the contractor’s overhead and profit in eqs 12-14and 20-22, are23

The unit costs of industrial and deionized water were assumedto be $0.60 U.S. and $0.85 U.S. per cubic meter, respectively.The parameter used to calculate the M&R cost in eq 17 is19

The parameter used to calculate the pipe decommissioning costin eq 19 is24

The three water network systems were generated from theoptimal solutions to each mathematical optimization model.GAMS/MINOS26 was used as an NLP solver to find the optimalsolutions to the models. The configuration of each water networksystem was embodied by its optimal solution. Wastewaterstreams were connected to local wastewater treatment plants,taking into account real circumstances in the plant. The localwastewater treatment plants were considered to estimate costsassociated with pipelines between water-using operations andlocal wastewater treatment plants.

3.1.2. Cost Estimation of Principal Contributors and NPVEvaluation. The costs of the principal contributors in each waternetwork system were estimated using eqs 5-22, which wereused in the objective function to generate the NWNS. The costsof each principal contributor in the three water network systemswere compared to each other, to estimate the effects of theobjective function used for the NWNS on the principalcontributors. However, the costs of freshwater consumption,

M&R, and pipe decommissioning were not discounted to presentvalues, although the costs of the freshwater consumption andM&R recur annually and the pipe decommissioning cost isincurred at the end of the service life. This was because thetime values of the costs were taken into account in the NPVevaluation.

The NPV of each water network system was evaluated toestimate their profitability in a comprehensive manner. TheCWS (Figure 1) was used as a baseline, to estimate theincremental benefits. Equation 1 was used to calculate the NPV.(See Lim et al.18 for more details.)

3.2. Results and Discussion.The FWNS, CWNS, andNWNS were generated from the optimal solutions to eachmathematical optimization model (see Figure 2). The charac-teristics of the three water network systems and CWS aresummarized in Table 4. When the FWNS, CWNS, and NWNSwere compared to the CWS, their total freshwater consumptionrates were reduced by 8.8%, 8.7%, and 8.5%, respectively, andthe consumptions of industrial water were decreased by 57.8%,4.8%, and 4.6%, respectively. However, the consumption ofdeionized water in the FWNS increased by 146.7%, but thosein the CWNS and NWNS both decreased by 21.0%. The totalfreshwater consumption rate in the FWNS was the lowest,because its objective function drove the high consumption ofdeionized water, rather than that of industrial water. Totalwastewater generation flow rates in the FWNS, CWNS, andNWNS were also reduced by 23.5%, 23.5%, and 23.1%,respectively. This reduction in flow rate for freshwater con-sumption and wastewater generation allowed a decrease in thepipe diameter and reduced the costs of the piping, M&R, andpipe decommissioning. Note that the total pipe length of theNWNS was the shortest, because its objective function wasformulated to simultaneously minimize the costs of the piping,freshwater consumption, M&R, and pipe decommissioning. Asa result, the tradeoffs between the reduction of freshwaterconsumption rate and increase in the other principal contributorswere different in each water network system, because of theirdiffering objective functions.

Costs of the principal contributors in each water networksystem were estimated, as shown in Figure 3. This figure showsthe results of the tradeoffs mentioned in Table 4. When theFWNS, CWNS, and NWNS were compared to the CWS, theirtotal piping costs increased by 80.0%, 91.9%, and 76.5%,respectively. The total piping cost of the NWNS was less than

Figure 4. Variations of each NPV over the service life. Legend: FWNS, total freshwater flow-rate-minimized water network system; CWNS, total freshwatercost-minimized water network system; and NWNS, NPV-maximized water network system.

aop ) 0.0297, bop ) 0.6173

R ) 0.2,â ) 0.05,γ ) 0.1

δ ) 0.3

ε ) 0.4

Ind. Eng. Chem. Res., Vol. 46, No. 21, 20076941

those of the FWNS and CWNS, because the objective functionused for the NWNS simultaneously optimized all principalcontributors; however, the other water network systems did notoptimize pipe-related costs. The annual freshwater costs of theCWNS and NWNS were reduced by 9.8% and 9.7%, respec-tively. The objective function used for the CWNS minimizedthe total freshwater cost. However, the total freshwater cost inthe FWNS was even 5.4% greater than that of the CWS, becausethe objective function used for the FWNS increased the flowrate of deionized water with higher water quality but higherunit cost, to minimize the total freshwater flow rate. The trendof the M&R and total pipe decommissioning costs in eachwater network system was similar to that of the total pipingcost, because their costs were calculated from the total pipingcost.

The variations of each NPV over the service life of the threewater network systems are shown in Figure 4. The NPV of theFWNS, CWNS, and NWNS were $-1190000 U.S., $-33000U.S., and $101000 U.S., respectively, which showed that theNWNS was the most profitable. Note that the reductions in thecosts of the piping, M&R, and pipe decommissioning in theNWNS outweighed the increase in the total freshwater cost,when the NWNS was compared to the CWNS. This occurredbecause the objective function used for the NWNS controlledthe tradeoffs among the principal contributors, to maximize thesum of all incremental costs and benefits from the increase anddecrease in the costs of the principal contributors. The increasein the costs of all the principal contributors in the FWNS didnot incur incremental benefits; the NPV of the FWNS wasconsistently decreased over its service life. The NPV of theCWNS changed to a negative value at the end of its servicelife, although the total piping cost in the construction stage wasrecovered in the 13th year, as a result of the incremental benefitsfrom the reduction of the total freshwater cost. This was becausethe pipe decommissioning cost incurred in the disposal stageoutweighed the positive NPV, In other words, the total costsincurred from the interconnections used for water reuse exceededthe reduction of the total freshwater cost during the service lifeof the system.

In the NWNS, the total piping cost was recovered in the 11thyear, as a result of incremental benefits from the reduction ofthe total freshwater cost, so the NPV of the NWNS was positiveat the end of its service life. The payback period of the NWNSwas shorter than that of the CWNS, because the total pipingand M&R costs of the NWNS were less than those of theCWNS. Therefore, the mathematical optimization model thatwas developed to generate an economically friendly waternetwork system was in accordance with the results of this casestudy. In addition, the case study demonstrated the characteristicsof the model.

4. Conclusions

A mathematical optimization model was developed tosynthesize an economically friendly water network systemby maximizing its net present value (NPV). A case studywas performed to demonstrate the highest profitability ofthe water network system generated from the model and est-imate the characteristics of the model. The simplified modelused to generate an NPV-maximized water network systemcan be easily applied to practically implement water net-work systems in industrial plants, because many minor contribu-tors to the economic costs and benefits of water network sys-tems are excluded from the model. The model also providesimportant information for other process integration technologies,

such as heat and hydrogen network syntheses, because allequations for the principal contributors can be applied togenerate economically friendly heat and hydrogen networksystems.

Acknowledgment

This work was financially supported by the Korean Scienceand Engineering Foundation (R11-2003-006) through AdvancedEnvironmental Biotechnology Research Center at PohangUniversity of Science and Technology, by the Korean Ministryof Commerce, Industry, and Energy through the Korean NationalCleaner Production Center and by the Program for AdvancedEducation of Chemical Engineers (the second stage of BK21).

Nomenclature

Sets

C ) {c|c is a contaminant in the water}, c ) 1, 2, ...,Nc

W ) {w|w is freshwater available}, s ) 1, 2, ...,Nm

WW) {ww|ww is wastewater}, ww ) 1, 2, ...,Nn

OP ) {op|op is a water-using operation}, op ) 1, 2, ...,Nn

OP) {opin|opin is a water-using operation}, opin ) 1, 2, ...,Nn

OP) {opout|opout is a water-using operation}, opout ) 1, 2, ...,Nn

Variables

Cc,opin ) concentration at the inlet of a water-using operationCc,opout ) concentration at the outlet of a water-using operationCostt

cws ) costs of a conventional water systemCostt

wns ) costs of a water network systemCostt

piping ) total piping costCostt

O&M ) total O&M costCostt

decom) total pipe decommissioning costCostw

t ) total freshwater cost per hourDCt ) depreciation costDLw,opin ) direct labor cost for piping from freshwater source

to water-using operationDLopout,opin ) direct labor cost for piping from the outlet of water-

using operation to the inlet of anotherDLopout,ww ) direct labor cost for piping from water-using

operation to local wastewater treatment plantDPw,opin ) direct pipe material cost from freshwater source to

water-using operationDPopout,opin ) direct pipe material cost from the outlet of water-

using operation to the inlet of anotherDPopout,ww ) direct pipe material cost from water-using operation

to local wastewater treatment plantEXPdecom ) construction expenses for pipe decommissioningEXPpiping ) construction expenses for pipingFopin ) flow rate at the inlet of water-using operationFopout ) flow rate at the outlet of water-using operationFopout,opin ) flow rate from the outlet of water-using operation

to the inlet of anotherFopout,ww ) flow rate from water-using operation to local

wastewater treatment plantFw,opin ) flow rate from freshwater source to water-using

operationFWC ) total freshwater costIBt ) incremental benefitIB0 ) initial incremental costl ) pipe lengthMRC ) maintenance and repair costsOHdecom) contractor’s overhead for pipe decommissioningOHpiping ) contractor’s overhead for piping

6942 Ind. Eng. Chem. Res., Vol. 46, No. 21, 2007

Parea) cross-sectional area of a pipePROdecom) contractor’s profits for pipe decommissioningPROpiping ) contractor’s profits for pipingTDPpiping ) total direct pipe material costTDLdecom ) total direct labor cost for pipe decommissioningTDLpiping ) total direct labor cost for pipingV ) optimal velocity through pipeNPV ) net present value

Parameters

adl ) regression parameter for a direct labor cost for pipingadp ) regression parameter for a direct pipe material costaop ) regression parameter for an optimal velocityR ) coefficient for construction expensesbdl ) regression parameter for a direct labor cost for pipingbdp ) regression parameter for a direct pipe material costbop ) regression parameter for an optimal velocityâ ) coefficient for contractor’s overheadCc,opin

max ) maximum concentration at inlet of water-using op-eration

Cc,opout

max ) maximum concentration at outlet of water-usingoperation

Cc,w ) freshwater concentrationγ ) coefficient for a contractor’s profitsδ ) coefficient for M&R coste ) escalation rateε ) coefficient for total direct labor cost of pipe decommis-

sioningFL,op ) water loss rate in water-using operationFopin

min ) minimum flow rate at inlet of water-using operationFopin

max ) maximum flow rate at inlet of water-using operationFw

max ) maximum flow rate for freshwateri ) interest rateMc,op ) mass load of a contaminantt ) timeTR ) income-tax rateUCw ) unit cost of freshwater

Literature Cited

(1) Takama, N.; Kuriyama, T.; Shiroko, K.; Umeda, T. Optimal WaterAllocation in a Petroleum Refinery.Comput. Chem. Eng.1980, 4, 251-258.

(2) Bagajewicz, M. A Review of Recent Design Procedures for WaterNetworks in Refineries and Process Plants.Comput. Chem. Eng.2000, 24,2093-2113.

(3) Quesada, I.; Grossmann, I. E. Global Optimization of Bilinear ProcessNetworks with Multicomponent Flows.Comput. Chem. Eng.1995, 19,1219-1242.

(4) Karuppiah, R.; Grossmann, I. E. Global optimization of the synthesisof integrated water systems in chemical processes.Comput. Chem. Eng.2006, 30, 650-673.

(5) Mann, J. G.; Liu, Y. A.Industrial Water Reuse and WastewaterMinimization; McGraw-Hill: New York, 1999.

(6) Alva-Argaez, A.; Kokossis, A.; Smith, R. Wastewater Minimizationof Industrial Systems Using an Integrated Approach.Comput. Chem. Eng.1998, 22, S741-S744.

(7) Prackotpol, D.; Srinophakun, T. GAPinch: Genetic AlgorithmToolbox for Water Pinch Technology.Chem. Eng. Process.2004, 43, 203-217.

(8) Huang, C. H.; Chang, C. T.; Ling, H. C.; Chang, C. C. AMathematical Programming Model for Water Usage and Treatment NetworkDesign.Ind. Eng. Chem. Res.1999, 38, 2666-2679.

(9) Bagajewicz, M.; Savelski, M. On the Use of Linear Models for theDesign of Water Utilization Systems in Process Plants with a SingleContaminant.Trans. Inst. Chem. Eng., Part A2001, 79, 600-610.

(10) Yang, Y. H.; Huang, Y. L. Synthesis of an Optimal WastewaterReuse Netowork.Waste Manage.2000, 20, 311-319.

(11) Gunaratnam, M.; Alva-Argaez, A.; Kokossis, A.; Kim, J.-K.; Smith,R. Automated Design of Total Water Systems.Ind. Eng. Chem. Res.2005,44, 588-599.

(12) Thoming, J. Optimal Design of Zero-Water Discharge RinsingSystems.EnViron. Sci. Technol.2002, 36, 1107-1112.

(13) Wang, Y. P.; Smith, R. Wastewater Minimization.Chem. Eng. Sci.1994, 49, 981-1006.

(14) Wang, Y. P.; Smith, R. Wastewater Minimization with FlowrateConstraint.Trans. Inst. Chem. Eng., Part A1995, 73, 889-904.

(15) Kuo, W.-C.; Smith, R. Designing for the Interactions betweenWater-Use and Effluent Treatment.Trans. Inst. Chem. Eng., Part A1998,76, 287-301.

(16) Hallale, N. A New Graphical Targeting Method for WaterMinimization, AdV. EnViron. Res.2002, 6, 377-390.

(17) El-Halwagi, M. M.; Gabrien, F.; Harell, D. Rigorous GraphicalTargeting for Resource Conservation via Material Recycle/Reuse Networks.Ind. Eng. Chem. Res.2003, 42, 4319-4328.

(18) Lim, S. -R.; Park, D.; Lee, D. S.; Park, J. M. Economic Evaluationof a Water Network System through the Net Present Value Method Basedon Cost and Benefit Estimations.Ind. Eng. Chem. Res.2006, 45, 7710-7718.

(19) Peters, M. S.; Timmerhaus, K. D.Plant Design and Economicsfor Chemical Engineers; McGraw-Hill: New York, 1991.

(20) Korea National Statistical Office, http://www.nso.go.kr (accessedJanuary 2006).

(21) The Bank of Korea, http://www.bok.or.kr (accessed January 2006).(22) Korea National Tax Service, http://www.nts.go.kr (accessed January

2006).(23) The Price Information, Vol. 422; Korea Price Information Corp.:

Seoul, South Korea, 2006.(24) The Cost Estimation; Korea Price Information Corp.: Seoul, South

Korea, 2006.(25) Metcalf & Eddy, Inc.Wastewater Engineering; McGraw-Hill:

New York, 1991.(26) GAMS, A User Guide; GAMS Development Corporation: Wash-

ington, DC, 2005.(27) Foo, D. C. Y.; Manan, Z. A.; El-Halwagi, M. M. Correct

Identification of Limiting Water Data for Water Network Synthesis.CleanTechnol. EnViron. Policy 2006, 8, 96-104.

ReceiVed for reView October 21, 2006ReVised manuscript receiVed June 8, 2007

AcceptedJune 11, 2007

IE061353V

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