Life Cycle Cost Minimization of a Total Wastewater Treatment Network System

Seong-Rin Lim,† Haewoo Lee,‡ and Jong Moon Park*,‡

Department of Chemical Engineering and Materials Science, UniVersity of California, DaVis, California 95616,and 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

Distributed wastewater treatment plants (WTPs) have been synthesized to reduce costs associated withwastewater treatment. This study developed a mathematical optimization model to synthesize existing distributedand terminal WTPs into an economical total wastewater treatment network system (TWTNS) from theperspective of life cycle cost (LCC). The objective function was formulated from the principal cost contributorsin the construction, operations and maintenance, and disposal stages. The mass balances were formulated onthe basis of the superstructure model, and the constraints were formulated to reflect real situations. A casestudy compared the LCC-minimized TWTNS (LNS) generated with this model to a conventional wastewatertreatment system (CWTS) operated in a plant and to the TWTNS (FNS) generated by minimizing a totalflowrate of wastewater treated in distributed WTPs. The LCC of the LNS was 12% less than that of theCWTS and was 27% less than that of the FNS, which validated the effectiveness of the model. This modelcan be used to practically retrofit existing WTPs.

1. Introduction

Wastewater treatment strategies have been developed to meetthe discharge restrictions of environmental regulations and toreduce economic costs. Distributed wastewater treatment plants(WTPs) have been networked as a strategy to reduce initialcapital investment and operating costs.1 The synthesis of thenetwork system has focused on minimizing the flowrate ofwastewater treated in distributed WTPs and on maximizing theflowrate of wastewater bypassing distributed WTPs, with thequality of the final effluent complying with discharge permits.This is because of the assumption that total capital investmentand operating costs would be proportional to the flowrate ofwastewater treated in distributed WTPs.2-5

Heuristically graphical approaches have been proposed as anextension of water pinch technology to optimally designdistributed wastewater treatment network systems.1,6 Thesegraphical methods use a concentration-composite curve to obtaina minimum wastewater flowrate to be treated, and then heuristicdesign methodology generates and merges the independentwastewater treatment subnetworks used to remove each con-taminant in wastewater streams.

Mathematical optimization models have been applied tosynthesize WTPs. Galan and Grossmann studied a searchprocedure used to yield a global or near global optimum solutionon the basis of the successive solution of a relaxed linear modeland an original nonconvex nonlinear problem.2 Huang et al.proposed a mathematical model to determine the optimal wateruse and treatment network with the lowest freshwater consump-tion rate and minimum wastewater treatment capacity.3 Her-nandez-Suarez et al. developed a superstructure decompositionand parametric optimization approach to obtain a globallyoptimal network system.5 Lim et al. showed that wastewatertreatment network synthesis decreased environmental perfor-mance even though the synthesis increased economic perfor-mance.7 However, these studies minimized the flowrate of

wastewater treated in distributed WTPs as an objective functionbecause of the assumption mentioned earlier.

Opportunity for the synthesis of WTPs has increased inindustrial plants, because wastewater generation rates have beendecreased by the increasing efforts to reduce freshwaterconsumption rates: water reuse, recycling, and recirculation.Many WTPs have been treating lower wastewater flowrates thantheir design capacities and have superfluous treatment capacities.Therefore, the efficient operation of the WTPs has been requiredto effectively manage resources and costs: the synthesis of theWTPs is a good way to practically retrofit existing distributedand terminal WTPs.

Life cycle cost (LCC) optimization is required to take intoaccount tradeoffs among the costs incurred throughout life cyclestages such as construction, operations and maintenance (OM),and disposal. Life cycle costing has been employed to evaluateall the costs associated with products, systems, and processesbecause costs in one stage can be changed into other costs inother stages.8,9 Therefore, tradeoffs among all costs should beoptimized to minimize the LCC which is the sum of all costsin all stages. A mathematical optimization model for LCCminimization should include principal cost contributors to theLCC in the formulation of an objective function to simplifythe model because all the costs incurred throughout the life cyclecannot easily be formulated for practical applications.

This study developed a mathematical optimization model toretrofit existing distributed and terminal WTPs into an economi-cal total wastewater treatment network system (TWTNS) fromthe perspective of an LCC. The objective function wasformulated with principal cost contributors to minimize the LCC.The mass balances were formulated on the basis of thesuperstructure model, and the constraints were formulated toreflect real situations. A case study was performed to validatethe mathematical optimization model by demonstrating theeconomic performance of an LCC-minimized TWTNS (LNS).The LNS was compared to a conventional wastewater treatmentsystem (CWTS) operated in a plant and to the TWTNS (FNS)optimized by minimizing a total flowrate of wastewater treatedin distributed WTPs. The costs of the principal contributors in

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

† University of California, Davis.‡ Pohang University of Science and Technology.

Ind. Eng. Chem. Res. 2009, 48, 2965–2971 2965

10.1021/ie8010897 CCC: $40.75 2009 American Chemical SocietyPublished on Web 01/27/2009

each system were estimated and compared to examine the effectsof the objective function minimizing the LCC on the configu-ration of a TWTNS.

2. Mathematical Optimization Model

2.1. Superstructure Model. The FNS and LNS were gener-ated by using the generalized superstructure model shown inFigure 1. This model includes all possible interconnections: fromthe wastewater sources to the inlets of the distributed andterminal WTPs and from the outlets of the distributed WTPs totheir inlets and to the inlets of the terminal WTPs. Wastewaterin all the streams is transferred by pumps, with the exceptionof the wastewater in the streams from the outlets of thedistributed WTPs to the inlets of the terminal WTPs, which istransferred by gravity. It is assumed that the mixers combinedall possible streams into one stream and that the splitters divideda given stream into all possible streams.

2.2. Mathematical Formulation. The mathematical opti-mization model for an economical TWTNS is a mixed integernonlinear programming (MINLP) model because bilinear vari-ables are included in the mass balances of contaminants andbecause binary variables are required to express whether thestreams exist or the WTPs are operated. All symbols areexplained in the Nomenclature.

2.2.1. Objective Function. An LCC was the objectivefunction of the mathematical optimization model used tosynthesize the most economical TWTNS. The LCC is the sumof discounted cash flows in the stages of construction, OM, anddisposal. When interest and escalation rates are included to takeinto account the time value of money, the objective function isas follows:

minimize LCC) costcon +∑t)1

t costOMt(1+ e)t

(1+ i)t+

costdist(1+ e)t

(1+ i)t

(1)

Cost contributors to the LCC were screened to simplify theformulation because all contributors cannot easily be formulatedfor the model. Principal cost contributors are piping, constructionexpenses, and the contractor’s overhead and profits in theconstruction stage; electricity for pumping and for wastewatertreatment, labor, and maintenance and repairs (MR) in the OM

stage; and pipe decommissioning, construction expenses, andthe contractor’s overhead and profits in the disposal stage.7

Equipment for pumping is excluded from the formulationbecause it is a minor cost contributor and because pump andmotor costs are arbitrarily related to the flowrate and dischargepressure of the pump. All the principal cost contributors, withthe exception of the electricity and labor, are assumed to beperformed by contractors, as is normal in the field of engineeringand construction; therefore, contractors’ overhead and profitsare included in this model.

The construction cost consists of a total direct pipe materialcost, a total direct labor cost for piping works, constructionexpenses, and a contractor’s overhead and profits. The totaldirect pipe material and labor costs are estimated by using theunit costs which are linearly regressed with the cross-sectionalarea of the pipe. Construction expenses are proportional to thesum of the total direct material and labor costs for piping.10

The contractor’s overhead in the construction stage is propor-tional to the sum of the total direct material and labor costs forpiping, as well as the construction expenses.10 The contractor’sprofits in the construction stage are proportional to the sum ofthe total direct labor cost for piping, construction expenses, andthe contractor’s overhead.10 Equations used to estimate theconstruction cost are as follows:

costcon )TDPpiping +TDLpiping +EXPpiping +OHpiping +PROpiping (2)

TDPpiping ) ∑ww∈ WW

∑tp∈ TP

DPww,tp + ∑ww∈ WW

∑ttp∈ TTP

DPww,ttp +

∑tp∈ TP

∑tp∈ TP

DPtp,tp+ ∑tp∈ TP

∑ttp∈ TTP

DPtp,ttp (3)

DPi,j ) (adpAi,j + bdp)li,jBi,j (4)

TDLpiping ) ∑ww∈ WW

∑tp∈ TP

DLww,tp + ∑ww∈ WW

∑ttp∈ TTP

DLww,ttp +

∑tp∈ TP

∑tp∈ TP

DLtp,tp+ ∑tp∈ TP

∑ttp∈ TTP

DLtp,ttp (5)

DLi,j ) (adlAi,j + bdl)li,jBi,j (6)

Ai,j )Fi,j

Vi,j(7)

Figure 1. Generalized superstructure model used to generate a TWTNS (WW wastewater, TP distributed WTP, TTP terminal WTP).

2966 Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009

Vi,j ) aopFi,j + bop (8)

EXPpiping )R(TDPpiping +TDLpiping) (9)

OHpiping ) �(TDPpiping +TDLpiping +EXPpiping) (10)

PROpiping ) γ(TDLpiping +EXPpiping +OHpiping) (11)

The principal cost contributors in the OM stage are the costs ofelectricity for pumping and for wastewater treatment, labor, andMR. The electricity cost for pumping is estimated from thepower which is calculated with the flowrate and pressure forpumping. The pressure is the sum of the head loss through thepipes and the additional head required to take into accountthe elevations of WTPs. The head loss is calculated by usingthe Darcy-Weisbach equation.12 The electricity cost forwastewater treatment is required to operate equipment such asagitators, flocculators, and sludge scrapers in distributed andterminal WTPs. The labor cost includes operators’ wages, aswell as their expenses and overheads. The MR cost is assumedto be proportional to the construction cost for piping.13 Equationsused to estimate the OM cost are as follows:

costOMt )ECp

t +ECwtt +LCt +MRCt (12)

ECpt ) ( ∑

ww∈ WW∑

tp∈ TP

Pww,tp + ∑ww∈ WW

∑ttp∈ TTP

Pww,ttp +

∑tp∈ TP

∑tp∈ TP

Ptp,tp) ·UCe · top (13)

HLi,j ) fli,j

g ( πAi,j

)0.5Vi,j2

4Bi,j (14)

Pi,j )FFi,jg(HLi,j +Ha)

ηpumpηmotor

11000

(15)

ECwtt ) ( ∑

tp∈ TP

PtpBtp+ ∑ttp∈ TTP

PttpBttp) ·UCe · top (16)

LCt ) ∑tp∈ TP

UCl,tpBtp+ ∑ttp∈ TTP

UCl,ttpBttp (17)

MRC) δ · costcon (18)

The disposal cost consists of a pipe decommissioning cost,construction expenses, and a contractor’s overhead and profits.The pipe decommissioning cost is proportional to the direct laborcost for piping in the construction stage.11 The constructionexpenses in the disposal stage are proportional to the pipedecommissioning cost. The contractor’s overheads in thedisposal stage are proportional to the sum of the pipe decom-missioning cost and construction expenses. The contractor’sprofits in the disposal stage are proportional to the sum of thepipe decommissioning cost, construction expenses, and thecontractor’s overhead. Equations used to estimate the costs inthe disposal stage are as follows:

costdist )TDLdecom +EXPdecom +OHdecom + PROdecom

(19)

TDLdecom ) ε ·TDLpiping (20)

EXPdecom )R ·TDLdecom (21)

OHdecom ) �(TDLdecom +EXPdecom) (22)

PROdecom ) γ(TDLdecom +EXPdecom +OHdecom) (23)

2.2.2. Mass Balances and Constraints. The mass balancesin this model are formulated on the basis of the superstructuremodel described above, and the constraints are formulated to

reflect the real situations of WTPs. The mass balances andconstraints are as follows:

For the mass balances of the distributed WTP inlet mixers,

∑ww∈ WW

Fww,tp + ∑tp*∈ TP

Ftp*,tp-Ftp ) 0 (24)

∑ww∈ WW

Fww,tpCc,ww + ∑tp*∈ TP

Ftp*,tpCc,tp*out -FtpCc,tp

in ) 0 (25)

For the mass balances of the distributed WTPs,

Cc,tpin (1-Rc,tp)-Cc,tp

out ) 0 (26)

For the mass balances of the distributed WTP outlet splitters,

Ftp - ∑tp*∈ TP

Ftp,tp* - ∑ttp∈ TTP

Ftp,ttp ) 0 (27)

For the mass balances of the terminal WTP inlet mixers,

∑tp∈ TP

Ftp,ttp + ∑ww∈ WW

Fww,ttp-Fttp ) 0 (28)

∑tp∈ TP

Ftp,ttpCc,tpout + ∑

ww∈ WW

Fww,ttpCc,ww-FttpCc,ttpin ) 0 (29)

For the mass balances of the terminal WTPs,

Cc,ttpin (1-Rc,ttp)-Cc,ttp

out ) 0 (30)

For the constraints of flowrates and loads on the distributedand terminal WTPs,

Ftp -FtpmaxBtpe 0 (31)

Ftpg 0 (32)

FtpCc,tpin - Ltp

maxe 0 (33)

Fttp -FttpmaxBttpe 0 (34)

Fttpg 0 (35)

FttpCc,ttpin - Lttp

maxe 0 (36)

Fi,j -Fi,jmaxBi,je 0 (37)

Fi,j -Fi,jminBi,jg 0 (38)

For the constraint of concentrations on the discharge qualityof the terminal WTP required to consistently meet the dischargelimits of environmental regulations,

Cc,ttpout -Cc,ttp

out,maxe 0 (39)

3. Case Study

A case study was performed to demonstrate that the math-ematical optimization model presented in this study is suitablefor the generation of an economical TWTNS and to estimatethe effects of the model on the configuration and costs of theTWTNS. Two types of TWTNSs were synthesized indepen-dently using their objective functions: minimization of the totalflowrate of wastewater treated in distributed WTPs and mini-mization of the LCC. The flowrate-minimized TWTNS (FNS)and the LCC-minimized TWTNS (LNS) were compared to theconventional wastewater treatment system (CWTS) which wasoperated in an iron and steel plant. The costs of the principalcost contributors in each system were estimated and compared.

3.1. Methods. Wastewater sources and existing distributedand terminal WTPs in an iron and steel plant were used togenerate the FNS and LNS. Characteristics of the five waste-water sources are described in Table 1, and those of the five

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distributed and one terminal WTPs are shown in Table 2. Thedistributed WTPs were used to treat the wastewater sources one-to-one. The terminal WTP was used to polish the effluents ofthe distributed WTPs, in order to consistently meet dischargelimits. All the WTPs consisted of physical and chemicaltreatment processes, such as coagulation, flocculation, andsedimentation. A distance matrix for interconnections betweenthe WTPs is shown in Table 3; the locations of the wastewatersources were assumed to be the same as those of the distributedWTPs because wastewater storage tanks were within thedistributed WTPs. The required discharge quality of the terminalWTP is set at 20 mg/L for CODcr, 5 mg/L for SS, and 8 mg/Lfor F- to consistently meet the discharge limits of environmentalregulations.

3.1.1. Total Wastewater Treatment Network Synthesis.The FNS and LNS were independently generated using theirown objective functions subjected to the mass balances andconstraints. For the objective function used for the FNS,

minimize Ftpt ) ∑

tp∈ TP

Ftp (40)

The FNS was generated with eqs 24-40, and the LNS witheqs 1-39. All parameters were set to optimize the mathematicalmodel for the LNS, as shown in Table 4.

The FNS and LNS were generated from the optimal solutionsto each model, which were found by using GAMS:14 CPLEXfor linear programming, MINOS for nonlinear programming,and DICOP for MINLP. The optimal solutions were employedas the configuration of each system. It should be mentionedthat even local solutions are useful for industrial applications ifthe solutions can meet the goal of the synthesis. This is becauseglobal optima cannot easily be obtained because of the non-convexities derived from bilinear variables in the mass balancesof contaminants.

3.1.2. Cost Estimation. The costs required for the CWTS,FNS, and LNS were estimated using eqs 1-23. The costs ofthe FNS and LNS were compared to those of the CWTS whichhad been revised with the same assumptions and equationsapplied to the FNS and LNS.

3.2. Results and Discussion. The FNS and LNS wereembodied from the optimal solutions to their models, as shownin Figure 2. Characteristics of the FNS, LNS, and CWTS aresummarized in Table 5. The TWTNS synthesis required morepipes and pumps to network between the wastewater sourcesand the distributed and terminal WTPs. The power requirementsfor pumping in the FNS and LNS were greater than that in theCWTS because of their complicated networks. The FNS neededhigher power consumption than the LNS because in the FNSwastewater was transferred by pump from WW 5 to TTP, whilein the LNS wastewater was by gravity from TP 5 to TTP andbecause the pipe length of pumping streams in the LNS wasless than that in the FNS. The FNS required less powerconsumption for wastewater treatment than the LNS, becausethe power requirement in the closed TP 5 of the FNS was greaterthan the sum of those of the closed TPs 1 and 2 of the LNS.The FNS and LNS treated less wastewater through distributedWTPs than the CWTS in order to more utilize the treatmentcapability of the terminal WTP. The LNS treated morewastewater through distributed WTPs than the FNS: theconfiguration of the FNS was more complex than that of theLNS to minimize the flowrate of the wastewater treated in thedistributed WTPs.

The LNS reduced more cost of electricity for pumping andlabor than the FNS but needed more cost for the other costfactors. The CWTS needed higher costs than the FNS and LNS,with the exception of the electricity cost for pumping, whichwas derived from the simple configuration of the CWTS. Figure3a shows the results of the cost estimation in the constructionstage. Although the total pipe length in the FNS was greaterthan that in the LNS, the LNS required higher piping cost than

Table 1. Wastewater Stream Data Used to Synthesize Distributedand Terminal WTPs (WW wastewater, CODcr chemical oxygendemand by dichomate, SS suspended solid, F- fluoride ion)

flowrate (m3/h) contaminant concentration (mg/L)

WW1 7.0 CODcr 48SS 10F- 115

WW2 20.9 CODcr 54SS 24F- 10

WW3 10.5 CODcr 62SS 10F- 89

WW4 187.5 CODcr 74SS 7F- 10

WW5 179.2 CODcr 32SS 15F- 2

Table 2. Operational and Design Data of Distributed and TerminalWTPs (TP distributed WTP, TTP terminal WTP)

Ftpmax, Fttp

max

(m3/h)power(kW)

contaminantremovalratio (%)

Ltpmax, Lttp

max

(kg/h)

TP1 10 0.4 CODcr 72 0.5SS 90 0.3F- 95 1.0

TP2 30 0.8 CODcr 63 1.4SS 88 1.6F- 10 0.3

TP3 12 0.4 CODcr 75 0.8SS 88 0.5F- 92 1.3

TP4 210 3.3 CODcr 85 17.5SS 86 10.7F- 12 2.2

TP5 205 3.3 CODcr 80 7.3SS 82 6.2F- 17 0.5

TTP 470 7.4 CODcr 50 8.3SS 93 18.2F- 20 3.1

Table 3. Distance Matrix (TP distributed WTP, TTP terminalWTP, unit meter)

TP1 TP2 TP3 TP4 TP5

TP2 1840TP3 680 2300TP4 4440 5150 4170TP5 2280 3390 1870 2300TTP 3600 1900 4060 7310 5010

Table 4. Parameters Used for the Case Study

parameter value parameter value

adl 2106.3 f 0.02adp 714.15 Ha 10aop 0.0297 ηpump 0.65R 0.2 ηmotor 0.80bdl 16.326 i 0.057bdp 2.9053 F 1000bop 0.6173 t 15� 0.05 UCl,tp 96000γ 0.1 UCl,ttp 320000δ 0.3 UCe 0.065e 0.03 top 8760ε 0.4 Vtp,ttp 0.5

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the FNS because the cost depended primarily on pipe diameterrelated to a wastewater flowrate. The piping cost was a principalcontributor to the construction costs. Figure 3b shows the resultof the cost estimation on an annual basis in the OM stage. TheFNS and LNS needed higher electricity costs for pumping thanthe CWTS because of their complex networks, but required lesselectricity costs for wastewater treatment because of the closeddistributed WTPs, which also induced the reduction of laborcosts in the FNS and LNS. The costs of electricity for pumpingand labor were principal contributors to the difference betweenthe OM costs of the FNS and LNS. Figure 3c shows all thecosts estimated in the disposal stage. Each cost of the FNS andLNS was greater than that of the CWTS, in line with the costestimation results in the construction stage. The pipe decom-missioning costs were principal contributors to the disposalcosts.

The LNS was the most economical from the life cycleperspective. Figure 4 shows the total costs in each life cycle

Figure 2. Comparison of wastewater treatment systems: (a) conventional wastewater treatment system (CWTS); (b) flowrate-minimized TWTNS (FNS); (c)LCC-minimized TWTNS (LNS) (WW wastewater, TP distributed WTP, TTP terminal WTP).

Table 5. Characteristics of the CWTS, FNS, and LNS (CWTSConventional Wastewater Treatment System, FNSFlowrate-Minimized TWTNS, LNS LCC-Minimized TWTNS)

Unit CWTS FNS LNS

pipe length (pumpingstream)

m 120 21890 16330

length (gravitystream)

m 21880 16870 16380

pump number 6 13 9number 5 4 3

distributedWTPs

flowrate of treatedwastewater

m3/h 405.1 261.7 353.5

flowrate of bypassingwastewater

m3/h 0 143.4 76.7

terminal WTP flowrate of treatedwastewater

m3/h 405.1 405.1 405.1

powerconsumption

pumping kW 123.9 1061.7 193.2

wastewater treatment kW 15.6 12.3 14.4

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stage and the LCCs of the three systems, which were discountedto the present values. The OM costs were the most significantfactor to the LCC. The OM cost of the LNS was less than thatof the CWTS because the decrease of the costs of labor,electricity for wastewater treatment, and MR outweighed theincrease of the electricity cost for pumping. However, the OMcost of the FNS was greater than that of the CWTS because theincrease of the electricity cost for pumping outweighed thedecrease of the costs of labor, electricity for wastewatertreatment, and MR. Therefore, the LNS required the lowestLCC, which showed that the presented mathematical optimiza-

tion model effectively optimized all the cost contributors to theLCC of a TWTNS.

4. Conclusions

A mathematical optimization model was developed to syn-thesize an economical TWTNS from the perspective of life cyclethinking. A case study was performed to validate the model bydemonstrating that the TWTNS generated from the model hadthe lowest LCC and by appraising the characteristics of theTWTNS. This model can be used to effectively retrofit existingWTPs which treat lower wastewater flowates than their designflowrates. Moreover, this model can easily be employed topractically implement TWTNSs in industrial plants, becauseminor cost contributors to the LCC of a TWTNS are excludedfrom the model.

Acknowledgment

This work was financially supported in part by the KoreanScience and Engineering Foundation (R11-2003-006) throughthe Advanced Environmental Biotechnology Research Centerat Pohang University of Science and Technology and in partby the program for advanced education of chemical engineers(2nd stage of BK21).

Nomenclature

SetsC ) {c|c is a contaminant in wastewater}, c ) 1, 2,..., Nc

WW ) {ww|ww is a wastewater source}, ww ) 1, 2,..., Nm

TP ) {tp|tp is a distributed WTP}, tp ) 1, 2,..., Nn

TTP ) {ttp|ttp is a terminal WTP}, ttp ) 1, 2,..., Nk

VariablesAi,j ) cross-sectional area of a pipe from a source i to a sink j

(WW to TP; WW to TTP; TP to TP; and TP to TTP) (m2)Btp ) binary variable for the existence of a distributed WTP (-)Btp,tp ) binary variable for the existence of a pipe from the outlet

of a distributed WTP to the inlet of a distributed WTP (-)Btp,ttp ) binary variable for the existence of a pipe from the outlet

of a distributed WTP to the inlet of a terminal WTP (-)Bttp ) binary variable for the existence of a terminal WTP (-)Bww,tp ) binary variable for the existence of a pipe from a

wastewater source to the inlet of a distributed WTP (-)Bww,ttp ) binary variable for the existence of a pipe from a

wastewater source to the inlet of a terminal WTP (-)Cc,tp

in ) concentration at the inlet of a distributed WTP (mg/L)Cc,tp

out ) concentration at the outlet of a distributed WTP (mg/L)Cc,ttp

in ) concentration at the inlet of a terminal WTP (mg/L)Cc,ttp

out ) concentration at the outlet of a terminal WTP (mg/L)costcon ) construction cost ($ U.S.)costOM

t ) OM cost ($ U.S.)costdis

t ) disposal cost ($ U.S.)DLi,j ) direct labor cost for piping from a source i to a sink j (WW

to TP; WW to TTP; TP to TP; and TP to TTP) ($ U.S.)DPi,j ) direct pipe material cost for piping from a source i to a

sink j (WW to TP; WW to TTP; TP to TP; and TP to TTP)($ U.S.)

ECpt ) electricity cost for pumping ($ U.S.)

ECwtt ) electricity cost for wastewater treatment ($ U.S.)

EXPdecom ) construction expenses for pipe decommissioning($ U.S.)

EXPpiping ) construction expenses for piping ($ U.S.)Fi,j ) flowrate from a source i to a sink j (WW to TP; WW to

TTP; TP to TP; and TP to TTP) (m3/h)Ftp ) flowrate at the inlet or outlet of a distributed WTP (m3/h)

Figure 3. Comparison of the costs of the principal cost contributors ineach system: (a) construction stage; (b) OM stage; (c) disposal stage.The costs were not discounted to present values, and the OM costs wereestimated on an annual basis (CWS conventional wastewater treatmentsystem, FNS flowrate-minimized TWTNS, LNS LCC-minimized TWT-NS).

Figure 4. Comparison of the total costs of each life cycle stage and lifecycle costs (LCCs). The costs were discounted to present values (CWSconventional wastewater treatment system, FNS flowrate-minimized TWT-NS, LNS LCC-minimized TWTNS).

2970 Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009

Ftp,ttp ) flowrate from the inlet of a distributed WTP to the inlet ofa terminal WTP (m3/h)

Ftp,tp ) flowrate from the outlet of a distributed WTP to the inletof a distributed WTP (m3/h)

Ftp,ttp ) flowrate from the outlet of a distributed WTP to the inletof a terminal WTP (m3/h)

Fttp ) flowrate at the inlet or outlet of a terminal WTP (m3/h)Fww,tp ) flowrate from a wastewater source to the inlet of a

distributed WTP (m3/h)Ftp

t ) total flowrate of wastewater treated in the distributed WTPs(m3/h)

HLi,j ) head loss though a pipe from a source i to a sink j (WWto TP; WW to TTP; and TP to TP) (m H2O)

LCC ) life cycle cost ($ U.S.)LCt ) labor cost ($ U.S.)MRCt ) MR cost ($ U.S.)OHdecom ) contractor’s overhead for pipe decommissioning ($ U.S.)OHpiping ) contractor’s overhead for piping ($ U.S.)Ptp ) power requirement for wastewater treatment in a distributed

WTP (kW)Ptp,tp ) power requirement for pumping wastewater from the outlet

of a distributed WTP to the inlet of a distributed WTP (kW)Pttp ) power requirement for wastewater treatment in a terminal

WTP (kW)Pww,tp ) power requirement for pumping wastewater from a

wastewater source to the inlet of a distributed WTP (kW)Pww,ttp ) power requirement for pumping wastewater from a

wastewater source to the inlet of a terminal WTP (kW)PROdecom ) contractor’s profits for pipe decommissioning ($ U.S.)PROpiping ) contractor’s profits for piping ($ U.S.)TDPpiping ) total direct pipe material cost ($ U.S.)TDLdecom ) total direct labor cost for pipe decommissioning

($ U.S.)TDLpiping ) total direct labor cost for piping ($ U.S.)Vi,j ) optimal velocity though a pipe from a source i to a sink j

(WW to TP; WW to TTP; and TP to TP) (m/s)Parametersadl ) regression parameter for a direct labor cost for piping (-)adp ) regression parameter for a direct pipe material cost (-)aop ) regression parameter for an optimal velocity (-)R ) coefficient for construction expenses (-)bdl ) regression parameter for a direct labor cost for piping (-)bdp ) regression parameter for a direct pipe material cost (-)bop ) regression parameter for an optimal velocity (-)� ) coefficient for contractor’s overhead (-)Cc,ttp

out,max ) maximum concentration at the outlet of a terminal WTP(mg/L)

Cc,ww ) concentration of a wastewater source (mg/L)γ ) coefficient for a contractor’s profits (-)δ ) coefficient for a MR cost (-)e ) escalation rate (-)ε ) coefficient for the total direct labor cost of pipe decommis-

sioning (-)f ) friction factor (-)Ftp

max ) maximum flowrate at the inlet of a distributed WTP (m3/h)Ftp,tp

max ) maximum flowrate from the outlet of a distributed WTP tothe inlet of a distributed WTP (m3/h)

Ftp,ttpmax ) maximum flowrate from the outlet of a distributed WTPto the inlet of a terminal WTP (m3/h)

Fww,tpmax ) maximum flowrate from a wastewater source to the inletof a distributed WTP (m3/h)

Fww,ttpmax ) maximum flowrate from a wastewater source to the inletof a terminal WTP (m3/h)

Fttpmax ) maximum flowrate at the inlet of a terminal WTP (m3/h)

Ftp,tpmin ) minimum flowrate from the outlet of a distributed WTP tothe inlet of a distributed WTP (m3/h)

Ftp,ttpmin ) minimum flowrate from the outlet of a distributed WTP tothe inlet of a terminal WTP (m3/h)

Fww,tpmin ) minimum flowrate from a wastewater source to the inletof a distributed WTP (m3/h)

Fww,ttpmin ) minimum flowrate from a wastewater source to the inletof a terminal WTP (m3/h)

g ) acceleration of gravity (9.8 m/sec2)Ha ) additional head required to take into account the elevation of

WTPs (m H2O)i ) interest rate (-)ηmotor ) motor efficiency (-)ηpump ) pump efficiency (-)li,j ) pipe length from a source i to a sink j (WW to TP; WW to

TTP; TP to TP; and TP to TTP) (m)Ltp

max ) maximum contaminant load of a distributed WTP (kg/h)Lttp

max ) maximum contaminant load of a terminal WTP (kg/h)F ) density of wastewater (kg/m3)Rc,tp ) removal efficiency of a distributed WTP (-)Rc,ttp ) removal efficiency of a terminal WTP (-)t ) service lifetime (y)top ) annual operating time (h)UCe ) unit cost of electricity ($ U.S.)UCl,tp ) unit cost of the labor to operate a distributed WTP ($ U.S.)UCl,ttp ) unit cost of the labor to operate a terminal WTP ($ U.S.)Vtp,ttp ) optimal velocity in the gravity flow though a pipe from the

outlet of a distributed WTP to the inlet of a terminal WTP(m/s)

Literature Cited

(1) Wang, Y. P.; Smith, R. Design of distributed effluent treatmentsystems. Chem. Eng. Sci. 1994, 49, 3127–3145.

(2) Galan, B.; Grossmann, I. E. Optimal design of distributed wastewatertreatment networks. Ind. Eng. Chem. Res. 1998, 37, 4036–4048.

(3) 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.

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

(5) Hernandez-Suarez, R.; Castellanos-Fernandez, J.; Zamora, J. Super-structure decomposition and parametric optimization approach for thesynthesis of distributed wastewater treatment networks. Ind. Eng. Chem.Res. 2004, 43, 2175–2191.

(6) Kuo, W.-C.; Smith, R. Effluent treatment system design. Chem. Eng.Sci. 1997, 52, 4273–4290.

(7) Lim, S.-R.; Park, D.; Park, J. M. Environmental and economicfeasibility study of a total wastewater treatment network system. J. EnViron.Manage. 2008, 88, 564–575.

(8) Rebitzer, G.; Hunkeler, D. Life cycle costing in LCM: ambitions,opportunities, and limitations - discussing a framework. Int. J. Life CycleAssess 2003, 8, 253–256.

(9) Spitzley, D. V.; Grande, D. E.; Keoleian, G. A.; Kim, H. C. Lifecycle optimization of ownership costs and emissions reduction in US vehicleretirement decisions. Transport. Res. Part D 2005, 10, 161–175.

(10) The Price Information; Korea Price Information, Corp.: Seoul, SouthKorea, 2006; Vol. 422.

(11) The Cost Estimation; Korea Price Information, Corp.: Seoul, SouthKorea, 2006.

(12) McGhee, T. J. Water Supply and Sewerage; McGraw-Hill: NewYork, 1991.

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

(14) GAMS: A User Guide; GAMS Development Corporation: Wash-ington DC, 2005.

ReceiVed for reView July 16, 2008ReVised manuscript receiVed December 17, 2008

Accepted December 23, 2008

IE8010897

Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 2971