Ind. Eng. Chem. Res. 2009, 48, 2965–2971
2965
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 of EnVironmental 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 with wastewater treatment. This study developed a mathematical optimization model to synthesize existing distributed and terminal WTPs into an economical total wastewater treatment network system (TWTNS) from the perspective of life cycle cost (LCC). The objective function was formulated from the principal cost contributors in the construction, operations and maintenance, and disposal stages. The mass balances were formulated on the basis of the superstructure model, and the constraints were formulated to reflect real situations. A case study compared the LCC-minimized TWTNS (LNS) generated with this model to a conventional wastewater treatment system (CWTS) operated in a plant and to the TWTNS (FNS) generated by minimizing a total flowrate of wastewater treated in distributed WTPs. The LCC of the LNS was 12% less than that of the CWTS and was 27% less than that of the FNS, which validated the effectiveness of the model. This model can be used to practically retrofit existing WTPs. 1. Introduction Wastewater treatment strategies have been developed to meet the discharge restrictions of environmental regulations and to reduce economic costs. Distributed wastewater treatment plants (WTPs) have been networked as a strategy to reduce initial capital investment and operating costs.1 The synthesis of the network system has focused on minimizing the flowrate of wastewater treated in distributed WTPs and on maximizing the flowrate of wastewater bypassing distributed WTPs, with the quality of the final effluent complying with discharge permits. This is because of the assumption that total capital investment and operating costs would be proportional to the flowrate of wastewater treated in distributed WTPs.2-5 Heuristically graphical approaches have been proposed as an extension of water pinch technology to optimally design distributed wastewater treatment network systems.1,6 These graphical methods use a concentration-composite curve to obtain a minimum wastewater flowrate to be treated, and then heuristic design methodology generates and merges the independent wastewater treatment subnetworks used to remove each contaminant in wastewater streams. Mathematical optimization models have been applied to synthesize WTPs. Galan and Grossmann studied a search procedure used to yield a global or near global optimum solution on the basis of the successive solution of a relaxed linear model and an original nonconvex nonlinear problem.2 Huang et al. proposed a mathematical model to determine the optimal water use and treatment network with the lowest freshwater consumption rate and minimum wastewater treatment capacity.3 Hernandez-Suarez et al. developed a superstructure decomposition and parametric optimization approach to obtain a globally optimal network system.5 Lim et al. showed that wastewater treatment network synthesis decreased environmental performance even though the synthesis increased economic performance.7 However, these studies minimized the flowrate of * To whom all correspondence should be addressed. Tel.: +82-54279-2275. Fax: +82-54-279-2699. E-mail:
[email protected]. † University of California, Davis. ‡ Pohang University of Science and Technology.
wastewater treated in distributed WTPs as an objective function because of the assumption mentioned earlier. Opportunity for the synthesis of WTPs has increased in industrial plants, because wastewater generation rates have been decreased by the increasing efforts to reduce freshwater consumption rates: water reuse, recycling, and recirculation. Many WTPs have been treating lower wastewater flowrates than their design capacities and have superfluous treatment capacities. Therefore, the efficient operation of the WTPs has been required to effectively manage resources and costs: the synthesis of the WTPs is a good way to practically retrofit existing distributed and terminal WTPs. Life cycle cost (LCC) optimization is required to take into account tradeoffs among the costs incurred throughout life cycle stages such as construction, operations and maintenance (OM), and disposal. Life cycle costing has been employed to evaluate all the costs associated with products, systems, and processes because costs in one stage can be changed into other costs in other stages.8,9 Therefore, tradeoffs among all costs should be optimized to minimize the LCC which is the sum of all costs in all stages. A mathematical optimization model for LCC minimization should include principal cost contributors to the LCC in the formulation of an objective function to simplify the model because all the costs incurred throughout the life cycle cannot easily be formulated for practical applications. This study developed a mathematical optimization model to retrofit existing distributed and terminal WTPs into an economical total wastewater treatment network system (TWTNS) from the perspective of an LCC. The objective function was formulated with principal cost contributors to minimize the LCC. The mass balances were formulated on the basis of the superstructure model, and the constraints were formulated to reflect real situations. A case study was performed to validate the mathematical optimization model by demonstrating the economic performance of an LCC-minimized TWTNS (LNS). The LNS was compared to a conventional wastewater treatment system (CWTS) operated in a plant and to the TWTNS (FNS) optimized by minimizing a total flowrate of wastewater treated in distributed WTPs. The costs of the principal contributors in
10.1021/ie8010897 CCC: $40.75 2009 American Chemical Society Published on Web 01/27/2009
2966 Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009
Figure 1. Generalized superstructure model used to generate a TWTNS (WW wastewater, TP distributed WTP, TTP terminal WTP).
each system were estimated and compared to examine the effects of the objective function minimizing the LCC on the configuration of a TWTNS. 2. Mathematical Optimization Model 2.1. Superstructure Model. The FNS and LNS were generated by using the generalized superstructure model shown in Figure 1. This model includes all possible interconnections: from the wastewater sources to the inlets of the distributed and terminal WTPs and from the outlets of the distributed WTPs to their inlets and to the inlets of the terminal WTPs. Wastewater in all the streams is transferred by pumps, with the exception of the wastewater in the streams from the outlets of the distributed WTPs to the inlets of the terminal WTPs, which is transferred by gravity. It is assumed that the mixers combined all possible streams into one stream and that the splitters divided a given stream into all possible streams. 2.2. Mathematical Formulation. The mathematical optimization model for an economical TWTNS is a mixed integer nonlinear programming (MINLP) model because bilinear variables are included in the mass balances of contaminants and because binary variables are required to express whether the streams exist or the WTPs are operated. All symbols are explained in the Nomenclature. 2.2.1. Objective Function. An LCC was the objective function of the mathematical optimization model used to synthesize the most economical TWTNS. The LCC is the sum of discounted cash flows in the stages of construction, OM, and disposal. When interest and escalation rates are included to take into account the time value of money, the objective function is as follows: t
minimize LCC ) costcon +
∑ t)1
costOMt(1 + e)t (1 + i)t
+
stage; and pipe decommissioning, construction expenses, and the contractor’s overhead and profits in the disposal stage.7 Equipment for pumping is excluded from the formulation because it is a minor cost contributor and because pump and motor costs are arbitrarily related to the flowrate and discharge pressure of the pump. All the principal cost contributors, with the exception of the electricity and labor, are assumed to be performed by contractors, as is normal in the field of engineering and construction; therefore, contractors’ overhead and profits are included in this model. The construction cost consists of a total direct pipe material cost, a total direct labor cost for piping works, construction expenses, and a contractor’s overhead and profits. The total direct pipe material and labor costs are estimated by using the unit costs which are linearly regressed with the cross-sectional area of the pipe. Construction expenses are proportional to the sum of the total direct material and labor costs for piping.10 The contractor’s overhead in the construction stage is proportional to the sum of the total direct material and labor costs for piping, as well as the construction expenses.10 The contractor’s profits in the construction stage are proportional to the sum of the total direct labor cost for piping, construction expenses, and the contractor’s overhead.10 Equations used to estimate the construction cost are as follows: costcon ) TDPpiping + TDLpiping + EXPpiping + OHpiping + PROpiping (2) TDPpiping )
(1) Cost contributors to the LCC were screened to simplify the formulation because all contributors cannot easily be formulated for the model. Principal cost contributors are piping, construction expenses, and the contractor’s overhead and profits in the construction stage; electricity for pumping and for wastewater treatment, labor, and maintenance and repairs (MR) in the OM
∑
DPww,tp +
∑ ∑
∑
DPww,ttp +
ww∈WW ttp∈TTP
DPtp,tp +
tp∈TP tp∈TP
∑ ∑
DPtp,ttp (3)
tp∈TP ttp∈TTP
DPi,j ) (adpAi,j + bdp)li,jBi,j
costdist(1 + e)t (1 + i)t
∑ ∑
ww∈WW tp∈TP
TDLpiping )
∑ ∑
DLww,tp +
ww∈WW tp∈TP
∑ ∑
∑
(4)
∑
DLww,ttp +
ww∈WW ttp∈TTP
DLtp,tp +
tp∈TP tp∈TP
∑ ∑
DLi,j ) (adlAi,j + bdl)li,jBi,j Ai,j )
DLtp,ttp (5)
tp∈TP ttp∈TTP
Fi,j Vi,j
(6) (7)
Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 2967
Vi,j ) aopFi,j + bop
(8)
EXPpiping ) R(TDPpiping + TDLpiping)
(9)
OHpiping ) β(TDPpiping + TDLpiping + EXPpiping)
(10)
PROpiping ) γ(TDLpiping + EXPpiping + OHpiping)
(11)
The principal cost contributors in the OM stage are the costs of electricity for pumping and for wastewater treatment, labor, and MR. The electricity cost for pumping is estimated from the power which is calculated with the flowrate and pressure for pumping. The pressure is the sum of the head loss through the pipes and the additional head required to take into account the elevations of WTPs. The head loss is calculated by using the Darcy-Weisbach equation.12 The electricity cost for wastewater treatment is required to operate equipment such as agitators, flocculators, and sludge scrapers in distributed and terminal WTPs. The labor cost includes operators’ wages, as well as their expenses and overheads. The MR cost is assumed to be proportional to the construction cost for piping.13 Equations used to estimate the OM cost are as follows:
ECpt )
(
costOMt ) ECpt + ECwtt + LCt + MRCt
∑ ∑
Pww,tp +
ww∈WW tp∈TP
∑
∑
( )
li,j π g Ai,j
HLi,j ) f
0.5 Vi,j
)
Ptp,tp · UCe · top (13)
tp∈TP tp∈TP 2
4
Bi,j
FFi,jg(HLi,j + Ha) 1 Pi,j ) ηpumpηmotor 1000
ECwtt )
(∑
PtpBtp +
tp∈TP
LC ) t
∑
)
PttpBttp · UCe · top
ttp∈TTP
∑ UC
l,tpBtp +
tp∈TP
∑
UCl,ttpBttp
∑
∑
∑
Ftp*,tp -Ftp ) 0
(24)
tp*∈TP
∑
Fww,tpCc,ww +
ww∈WW
in Ftp*,tpCout c,tp* -FtpCc,tp ) 0 (25)
tp*∈TP
For the mass balances of the distributed WTPs, out Cin c,tp(1 - Rc,tp) - Cc,tp ) 0
(26)
For the mass balances of the distributed WTP outlet splitters,
∑
Ftp -
∑
Ftp,tp* -
tp*∈TP
Ftp,ttp ) 0
(27)
ttp∈TTP
For the mass balances of the terminal WTP inlet mixers,
∑F
tp,ttp +
tp∈TP
∑F
∑
Fww,ttp -Fttp ) 0
(28)
ww∈WW
out tp,ttpCc,tp +
tp∈TP
∑
Fww,ttpCc,ww -FttpCin c,ttp ) 0
(29)
ww∈WW
out Cin c,ttp(1 - Rc,ttp) - Cc,ttp ) 0
(30)
For the constraints of flowrates and loads on the distributed and terminal WTPs,
(14) (15) (16)
Ftp - Fmax tp Btp e 0
(31)
Ftp g 0
(32)
max FtpCin c,tp - Ltp e 0
(33)
Fttp - Fmax ttp Bttp e 0
(34)
Fttp g 0
(35)
(17)
max FttpCin c,ttp - Lttp e 0
(36)
(18)
Fi,j - Fmax i,j Bi,j e 0
(37)
Fi,j - Fmin i,j Bi,j g 0
(38)
ttp∈TTP
MRC ) δ · costcon
Fww,tp +
ww∈WW
For the mass balances of the terminal WTPs,
Pww,ttp +
ww∈WW ttp∈TTP
∑ ∑
(12)
reflect the real situations of WTPs. The mass balances and constraints are as follows: For the mass balances of the distributed WTP inlet mixers,
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 labor cost for piping in the construction stage.11 The construction expenses in the disposal stage are proportional to the pipe decommissioning cost. The contractor’s overheads in the disposal stage are proportional to the sum of the pipe decommissioning cost and construction expenses. The contractor’s profits in the disposal stage are proportional to the sum of the pipe decommissioning cost, construction expenses, and the contractor’s overhead. Equations used to estimate the costs in the disposal stage are as follows: costdist ) TDLdecom + EXPdecom + OHdecom + PROdecom (19) TDLdecom ) ε · TDLpiping
(20)
EXPdecom ) R · TDLdecom
(21)
OHdecom ) β(TDLdecom + EXPdecom)
(22)
PROdecom ) γ(TDLdecom + EXPdecom + OHdecom)
(23)
2.2.2. Mass Balances and Constraints. The mass balances in this model are formulated on the basis of the superstructure model described above, and the constraints are formulated to
For the constraint of concentrations on the discharge quality of the terminal WTP required to consistently meet the discharge limits of environmental regulations, out,max e0 Cout c,ttp - Cc,ttp
(39)
3. Case Study A case study was performed to demonstrate that the mathematical optimization model presented in this study is suitable for the generation of an economical TWTNS and to estimate the effects of the model on the configuration and costs of the TWTNS. Two types of TWTNSs were synthesized independently using their objective functions: minimization of the total flowrate of wastewater treated in distributed WTPs and minimization of the LCC. The flowrate-minimized TWTNS (FNS) and the LCC-minimized TWTNS (LNS) were compared to the conventional wastewater treatment system (CWTS) which was operated in an iron and steel plant. The costs of the principal cost contributors in each system were estimated and compared. 3.1. Methods. Wastewater sources and existing distributed and terminal WTPs in an iron and steel plant were used to generate the FNS and LNS. Characteristics of the five wastewater sources are described in Table 1, and those of the five
2968 Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 Table 1. Wastewater Stream Data Used to Synthesize Distributed and Terminal WTPs (WW wastewater, CODcr chemical oxygen demand by dichomate, SS suspended solid, F- fluoride ion) flowrate (m3/h) WW1
7.0
WW2
20.9
WW3
10.5
WW4
187.5
WW5
179.2
contaminant
concentration (mg/L)
CODcr SS FCODcr SS FCODcr SS FCODcr SS FCODcr SS F-
48 10 115 54 24 10 62 10 89 74 7 10 32 15 2
Table 2. Operational and Design Data of Distributed and Terminal WTPs (TP distributed WTP, TTP terminal WTP) max max Ftp , Fttp (m3/h)
power (kW)
TP1
10
0.4
TP2
30
0.8
TP3
12
0.4
TP4
210
3.3
TP5
205
3.3
TTP
470
7.4
contaminant
removal ratio (%)
max max Ltp , Lttp (kg/h)
CODcr SS FCODcr SS FCODcr SS FCODcr SS FCODcr SS FCODcr SS F-
72 90 95 63 88 10 75 88 92 85 86 12 80 82 17 50 93 20
0.5 0.3 1.0 1.4 1.6 0.3 0.8 0.5 1.3 17.5 10.7 2.2 7.3 6.2 0.5 8.3 18.2 3.1
Table 3. Distance Matrix (TP distributed WTP, TTP terminal WTP, unit meter)
TP2 TP3 TP4 TP5 TTP
TP1
TP2
TP3
TP4
TP5
1840 680 4440 2280 3600
2300 5150 3390 1900
4170 1870 4060
2300 7310
5010
distributed and one terminal WTPs are shown in Table 2. The distributed WTPs were used to treat the wastewater sources oneto-one. The terminal WTP was used to polish the effluents of the distributed WTPs, in order to consistently meet discharge limits. All the WTPs consisted of physical and chemical treatment processes, such as coagulation, flocculation, and sedimentation. A distance matrix for interconnections between the WTPs is shown in Table 3; the locations of the wastewater sources were assumed to be the same as those of the distributed WTPs because wastewater storage tanks were within the distributed WTPs. The required discharge quality of the terminal WTP is set at 20 mg/L for CODcr, 5 mg/L for SS, and 8 mg/L for F- to consistently meet the discharge limits of environmental regulations. 3.1.1. Total Wastewater Treatment Network Synthesis. The FNS and LNS were independently generated using their own objective functions subjected to the mass balances and constraints. For the objective function used for the FNS,
minimize Ftpt )
∑F
(40)
tp
tp∈TP
The FNS was generated with eqs 24-40, and the LNS with eqs 1-39. All parameters were set to optimize the mathematical model for the LNS, as shown in Table 4. The FNS and LNS were generated from the optimal solutions to each model, which were found by using GAMS:14 CPLEX for linear programming, MINOS for nonlinear programming, and DICOP for MINLP. The optimal solutions were employed as the configuration of each system. It should be mentioned that even local solutions are useful for industrial applications if the solutions can meet the goal of the synthesis. This is because global optima cannot easily be obtained because of the nonconvexities derived from bilinear variables in the mass balances of contaminants. 3.1.2. Cost Estimation. The costs required for the CWTS, FNS, and LNS were estimated using eqs 1-23. The costs of the FNS and LNS were compared to those of the CWTS which had been revised with the same assumptions and equations applied to the FNS and LNS. 3.2. Results and Discussion. The FNS and LNS were embodied from the optimal solutions to their models, as shown in Figure 2. Characteristics of the FNS, LNS, and CWTS are summarized in Table 5. The TWTNS synthesis required more pipes and pumps to network between the wastewater sources and the distributed and terminal WTPs. The power requirements for pumping in the FNS and LNS were greater than that in the CWTS because of their complicated networks. The FNS needed higher power consumption than the LNS because in the FNS wastewater was transferred by pump from WW 5 to TTP, while in the LNS wastewater was by gravity from TP 5 to TTP and because the pipe length of pumping streams in the LNS was less than that in the FNS. The FNS required less power consumption for wastewater treatment than the LNS, because the power requirement in the closed TP 5 of the FNS was greater than the sum of those of the closed TPs 1 and 2 of the LNS. The FNS and LNS treated less wastewater through distributed WTPs than the CWTS in order to more utilize the treatment capability of the terminal WTP. The LNS treated more wastewater through distributed WTPs than the FNS: the configuration of the FNS was more complex than that of the LNS to minimize the flowrate of the wastewater treated in the distributed WTPs. The LNS reduced more cost of electricity for pumping and labor than the FNS but needed more cost for the other cost factors. The CWTS needed higher costs than the FNS and LNS, with the exception of the electricity cost for pumping, which was derived from the simple configuration of the CWTS. Figure 3a shows the results of the cost estimation in the construction stage. Although the total pipe length in the FNS was greater than that in the LNS, the LNS required higher piping cost than Table 4. Parameters Used for the Case Study parameter
value
parameter
value
adl adp aop R bdl bdp bop β γ δ e ε
2106.3 714.15 0.0297 0.2 16.326 2.9053 0.6173 0.05 0.1 0.3 0.03 0.4
f Ha ηpump ηmotor i F t UCl,tp UCl,ttp UCe top Vtp,ttp
0.02 10 0.65 0.80 0.057 1000 15 96000 320000 0.065 8760 0.5
Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 2969
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 (CWTS Conventional Wastewater Treatment System, FNS Flowrate-Minimized TWTNS, LNS LCC-Minimized TWTNS)
pipe
pump distributed WTPs terminal WTP power consumption
Unit
CWTS
FNS
LNS
m
120
21890
16330
length (pumping stream) length (gravity stream) number number flowrate of treated wastewater flowrate of bypassing wastewater flowrate of treated wastewater pumping
m
21880
16870
16380
m3/h
6 5 405.1
13 4 261.7
9 3 353.5
m3/h
0
143.4
76.7
m3/h
405.1
405.1
405.1
kW
123.9
1061.7
193.2
wastewater treatment
kW
15.6
12.3
14.4
the FNS because the cost depended primarily on pipe diameter related to a wastewater flowrate. The piping cost was a principal contributor to the construction costs. Figure 3b shows the result of the cost estimation on an annual basis in the OM stage. The FNS and LNS needed higher electricity costs for pumping than the CWTS because of their complex networks, but required less electricity costs for wastewater treatment because of the closed distributed WTPs, which also induced the reduction of labor costs in the FNS and LNS. The costs of electricity for pumping and labor were principal contributors to the difference between the OM costs of the FNS and LNS. Figure 3c shows all the costs estimated in the disposal stage. Each cost of the FNS and LNS was greater than that of the CWTS, in line with the cost estimation results in the construction stage. The pipe decommissioning costs were principal contributors to the disposal costs. The LNS was the most economical from the life cycle perspective. Figure 4 shows the total costs in each life cycle
2970 Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009
tion model effectively optimized all the cost contributors to the LCC of a TWTNS. 4. Conclusions A mathematical optimization model was developed to synthesize an economical TWTNS from the perspective of life cycle thinking. A case study was performed to validate the model by demonstrating that the TWTNS generated from the model had the lowest LCC and by appraising the characteristics of the TWTNS. This model can be used to effectively retrofit existing WTPs which treat lower wastewater flowates than their design flowrates. Moreover, this model can easily be employed to practically implement TWTNSs in industrial plants, because minor cost contributors to the LCC of a TWTNS are excluded from the model. Acknowledgment This work was financially supported in part by the Korean Science and Engineering Foundation (R11-2003-006) through the Advanced Environmental Biotechnology Research Center at Pohang University of Science and Technology and in part by the program for advanced education of chemical engineers (2nd stage of BK21). Nomenclature
Figure 3. Comparison of the costs of the principal cost contributors in each system: (a) construction stage; (b) OM stage; (c) disposal stage. The costs were not discounted to present values, and the OM costs were estimated on an annual basis (CWS conventional wastewater treatment system, FNS flowrate-minimized TWTNS, LNS LCC-minimized TWTNS).
Figure 4. Comparison of the total costs of each life cycle stage and life cycle costs (LCCs). The costs were discounted to present values (CWS conventional wastewater treatment system, FNS flowrate-minimized TWTNS, LNS LCC-minimized TWTNS).
stage and the LCCs of the three systems, which were discounted to the present values. The OM costs were the most significant factor to the LCC. The OM cost of the LNS was less than that of the CWTS because the decrease of the costs of labor, electricity for wastewater treatment, and MR outweighed the increase of the electricity cost for pumping. However, the OM cost of the FNS was greater than that of the CWTS because the increase of the electricity cost for pumping outweighed the decrease of the costs of labor, electricity for wastewater treatment, and MR. Therefore, the LNS required the lowest LCC, which showed that the presented mathematical optimiza-
Sets C ) {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 Variables Ai,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 (-) in Cc,tp ) concentration at the inlet of a distributed WTP (mg/L) out Cc,tp ) concentration at the outlet of a distributed WTP (mg/L) in Cc,ttp ) concentration at the inlet of a terminal WTP (mg/L) out Cc,ttp ) concentration at the outlet of a terminal WTP (mg/L) costcon ) construction cost ($ U.S.) costOMt ) OM cost ($ U.S.) costdist ) 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)
Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 2971 Ftp,ttp ) flowrate from the inlet of a distributed WTP to the inlet of a terminal WTP (m3/h) Ftp,tp ) flowrate from the outlet of a distributed WTP to the inlet of a distributed WTP (m3/h) Ftp,ttp ) flowrate from the outlet of a distributed WTP to the inlet of 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) Ftpt ) 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 (WW to 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) Parameters adl ) 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 (-) β ) coefficient for contractor’s overhead (-) out,max Cc,ttp ) 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 decommissioning (-) f ) friction factor (-) max Ftp ) maximum flowrate at the inlet of a distributed WTP (m3/h) max Ftp,tp ) maximum flowrate from the outlet of a distributed WTP to the inlet of a distributed WTP (m3/h) max Ftp,ttp ) maximum flowrate from the outlet of a distributed WTP to the inlet of a terminal WTP (m3/h) max Fww,tp ) maximum flowrate from a wastewater source to the inlet of a distributed WTP (m3/h) max Fww,ttp ) maximum flowrate from a wastewater source to the inlet of a terminal WTP (m3/h) max Fttp ) maximum flowrate at the inlet of a terminal WTP (m3/h)
) minimum flowrate from the outlet of a distributed WTP to the inlet of a distributed WTP (m3/h) min Ftp,ttp ) minimum flowrate from the outlet of a distributed WTP to the inlet of a terminal WTP (m3/h) min Fww,tp ) minimum flowrate from a wastewater source to the inlet of a distributed WTP (m3/h) min Fww,ttp ) minimum flowrate from a wastewater source to the inlet of 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) max Ltp ) maximum contaminant load of a distributed WTP (kg/h) max Lttp ) 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) min Ftp,tp
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ReceiVed for reView July 16, 2008 ReVised manuscript receiVed December 17, 2008 Accepted December 23, 2008 IE8010897
