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PROCESS DESIGN AND CONTROL Synthesis of an Economically Friendly Water Network System by Maximizing Net Present Value Seong-Rin Lim, Donghee Park, and Jong Moon Park* 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
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 been developed. The objective of this work was to develop the model to synthesize an economically friendly water network system by maximizing its net present value (NPV). The mathematical optimization model includes principal contributors to incremental costs and benefits resulting from water network synthesis. Tradeoffs between the incremental costs and benefits derived from water reuse are optimized to maximize the NPV. In a case study, an NPV-maximized water network system was more profitable than the total freshwater flowrate-minimized and total freshwater cost-minimized water network systems. The model can be used to practically implement water network systems and can be applied to other process integration technologies to generate economically friendly heat and hydrogen network systems. 1. Introduction Much effort has been made to reduce costs and increase benefits, to enhance the competitiveness and profitability of industries. Because water is an important resource for washing, cleaning, and cooling, and is a product in itself, many technologies associated with water have been developed to reduce costs incurred from water supply, water treatment, and wastewater treatment. Water network synthesis has also been used to reduce costs resulting from freshwater consumption and wastewater treatment. A water network system is synthesized by optimizing all water sources (e.g., freshwater, wastewater, etc.) and sinks (e.g., water-using operations) to maximize water reuse: wastewater from water-using operations can be reused for other operations if the properties of the wastewater meet the operational conditions. Many water network synthesis technologies have been developed and practiced in industrial plants. The first water network optimization to reduce the rates of freshwater consumption and wastewater generation was used in a petroleum refinery plant in 1980.1 Most previous studies for water network synthesis have focused on solving mathematical formulations, such as nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP), to find global optima.1-6 Genetic algorithm was also developed to solve MINLP used for wastewater minimization and to avoid obtaining local optima.7 These approaches are necessary because of nonconvexities resulting from bilinear variables in mass balances on contaminants. Objective functions in previous works have been formulated intuitively without a clear basis for the selection of contributors to economic costs and benefits. As a result, various types of * To whom all correspondence should be addressed. Tel.: +82-54279-2275. Fax: +82-54-279-2699. E-mail:
[email protected].
objective functions have been used. Simple formulas for investment and operating costs have been used to represent a total annual cost.1 Most studies have minimized a single contributor, such as a total freshwater flow rate, the number of interconnections, or fixed costs.5,7-10 For an objective function, studies have used the sum of operating costs for freshwater and capital costs for pipes and wastewater treatment, or the sum of a few capital and operating costs,6,12 or the sum of the costs of freshwater supply, water and wastewater treatment, pipes, and sewers.11 One study that used multiobjective optimization, simultaneously minimizing the total annualized cost and environmental impacts, did not include piping costs.13 However, these intuitive formulations of the objective functions cannot always generate economically friendly water network systems, even though global optima are obtained. This is because all principal contributors to economic costs and benefits are not included in the objective functions. Pinch analysis technologies have been studied to graphically analyze the process limiting data of water-using operations and heuristically generate water network systems.5,13-17 These graphical targeting methods suggest the minimum freshwater consumption rate of a water system and identify any bottlenecks that affect freshwater consumption. Procedure and heuristics were proposed to extract correct limiting water data for pinch analysis.27 However, these methods do not take the economic aspect of their designs into consideration. In the present study, principal contributors to incremental costs and benefits were used to formulate a mathematical optimization model. The incremental cost or benefit in water network synthesis is the difference between the costs of a water network system and of a conventional water system that has no interconnection for water reuse. According to a comprehensive economic evaluation of a water network system, the principal contributors to incremental costs are piping, mainte-
10.1021/ie061353v CCC: $37.00 © 2007 American Chemical Society Published on Web 09/07/2007
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nance and repairs (M&R), and pipe decommissioning, whereas the principal contributor to incremental benefits is the decrease in freshwater consumption.18 This information was used to simply synthesize an economically friendly water network system; a simplified mathematical optimization model is beneficial to practical applications in industries, because all contributors to economic costs and benefits cannot easily be formulated in a mathematical optimization model. The net present value (NPV) was used as the objective function of the mathematical optimization model proposed in this study. The NPV is an economic feasibility indicator that supports a decision maker to determine whether to build a water network system. In other words, the NPV shows how much benefit can be obtained when a conventional water system is replaced with a water network system. The amount of benefits is a stronger driving force to motivate a decision maker to build the system than the amount of costs. The NPV takes into consideration the time value of cash flows derived from the construction, operations and maintenance (O&M), and disposal of a water network system. The NPV is obtained by summing discounted cash flows and an initial capital investment cost, after a series of future cash flows is discounted. The most economically friendly water network system can be synthesized by maximizing the NPV. Incremental costs and benefits of the water network system were calculated using the costs of the conventional water system as a baseline, and then they were used to calculate the NPV.18 This approach was necessary because a water system that is used as a utility for production systems and processes cannot directly yield profits from its own operation. In this study, we develop a mathematical optimization model to synthesize an economically friendly water network system by maximizing its NPV. An objective function was formulated to calculate the NPV to be maximized in the model. Costs for piping, M&R, pipe decommissioning, and freshwater consumption were formulated to calculate incremental costs and benefits required for the NPV evaluation. Mass balances and constraints were formulated to represent a generalized superstructure model used for water network synthesis. A case study was performed to demonstrate the high profitability of a water network system generated from the model and examine the effects of the model on the configuration of a water network system. An NPVmaximized water network system was compared to a total freshwater flow-rate-minimized system and a total freshwater cost-minimized water system. The costs of principal contributors in each water network system were estimated. The NPV of the water network systems was evaluated to show their overall profitability. 2. Mathematical Optimization Model 2.1. Superstructure Model. A generalized superstructure model18 is used to describe the true conditions of a water system in industrial plants. The superstructure model includes all possible interconnections between water sources and sinks, such as those from the outlet of an operation to the inlet of the others, as well as between freshwater sources and water-using operations, to fully utilize opportunities for water reuse and ultimately reduce the total freshwater consumption rate. However, to avoid excessive costs derived from pumping with a high flow rate, local recycling from the outlet to the inlet within an operation is not allowed. This is because the small gap between the concentrations of inlet and outlet in the local recycling requires a high flow rate in the recycled line, to transfer the contaminant load of the operation into water.18 Furthermore, a loss of
freshwater is avoided by prohibiting direct connections between freshwater sources and local wastewater treatment plants. We assume that a mixer combines many streams into a single stream and that a splitter divides one stream into all possible streams flowing to water sinks. 2.2. Mathematical Formulation. The mathematical formulation required to generate an economically friendly water network system is composed of an objective function (including an NPV equation and formulas used for cost estimations), as well as mass balances and constraints required to represent the superstructure model. All symbols are explained in the Nomenclature section at the end of this paper. 2.2.1. Objective Function. The NPV is maximized to synthesize an economically friendly water network system based on discounted incremental benefits (IBs). When depreciation costs and a total income-tax rate are included, the objective function is given as follows:
{
Max NPV )
t
∑ t)1
[IBt(1 - TR) + DCtTR](1 + e)t (1 + i)t
}
+ IB0
(1)
The incremental benefits are calculated by subtracting the costs of the water network system from those of the conventional water system. If the cost of a water network system is greater than that of a conventional water system, the incremental benefit is negative, which means an incremental cost. The costs of the water system consist of total piping, O&M, and pipe decommissioning costs.
- Costwns IBt ) Costcws t t or Costwns ) Costpiping + CostO&M + Costdecom Costcws t t t t t
(2) (3)
Depreciation cost (DCt) is estimated by a straight-line method over the service life,19 as shown in eq 4.
DCt )
IB0 t
(4)
A salvage value is assumed to be zero. Principal contributors to incremental costs and benefits are used to formulate the objective function, because all contributors cannot easily be formulated in the function. The principal contributors are the piping cost in the construction stage, the total freshwater and M&R costs in the O&M stage, and the pipe decommissioning cost in the disposal stage.18 All principal contributors, with the exception of the freshwater consumption, are assumed to be performed by contractors, as is normal in the field of engineering and construction. Therefore, a contractor’s overhead and profit are included in the mathematical optimization model. The total piping cost consists of the total direct pipe material cost, the total direct labor cost for piping works, construction expenses, and the contractor’s overhead and profit. Unit direct material and labor costs for the piping are assumed to be proportional to the cross-sectional area, which is calculated by dividing the flow rate by an optimal velocity through the pipe.11
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Equations used to estimate the total piping cost are given as follows:
Costpiping ) TDPpiping + TDLpiping + t EXPpiping + OHpiping + PROpiping (5)
∑ ∑
TDPpiping )
w∈W opin∈OP
DPw,opin +
∑ ∑
opin∈OP opout∈OP
∑
opout∈OP
DPopout,opin + DPopout,ww (6)
∑ ∑
w∈W opin∈OP
DLw,opin +
∑ ∑
opin∈OP opout∈OP
Costdecom ) TDLdecom + EXPdecom + t OHdecom + PROdecom (18) where
DPw,opin, DPopout,opin, DPopout,ww ) (adpParea + bdp)l TDLpiping )
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 contractor’s overhead. Equations used to estimate the costs in the disposal stage are given as follows:
(7)
TDLdecom ) × TDLpiping
(19)
DLopout,opin +
EXPdecom ) R × TDLdecom
(20)
OHdecom ) β(TDLdecom + EXPdecom)
(21)
∑ DLop op ∈OP
out,ww
(8)
PROdecom ) γ(TDLdecom + EXPdecom + OHdecom) (22)
out
DLw,opin, DLopout,opin, DLopout,ww ) (adpParea + bdp)l Parea )
Fw,opin Fopout,opin Fopout,ww , Parea ) , Parea ) V V V
V ) aopFw,opin + bop, V ) aopFopout,opin + bop
(9)
(10) (11)
Construction expenses are proportional to the sum of the total direct material and labor costs for piping. A 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. A 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. Equations used to estimate construction expenses, and the contractor’s overhead and profit are given as follows:
EXPpiping ) R(TDPpiping + TDLpiping)
2.2.2. Mass Balances and Constraints. The formulation of mass balances and constraints is based on the superstructure model previously described. Equations used for the mass balances and constraints are described as follows: For the overall mass balance of the entire water network system:
∑ ∑
w∈W opin∈OP
Fw,opin -
∑
ww∈WW
Fopout,ww -
∑
FL,op ) 0
(23)
op∈OP
For the mass balances of the mixers:
∑ Fw,op
w∈W
∑ Fw,op
w∈W
in
Cc,w +
∑
+ in
opout∈OP
∑
opout∈OP
Fopout,opin - Fopin ) 0
(24)
Fopout,opin Cc,opout Fopin Cc,opin ) 0 (25)
(12)
For the mass balances of the operations:
OHpiping ) β(TDPpiping + TDLpiping + EXPpiping) (13)
Fopin - FL,op - Fopout ) 0
(26)
PROpiping ) γ(TDLpiping + EXPpiping + OHpiping) (14)
FopinCc,opin + Mc,op - FopoutCc,opout ) 0
(27)
The principal contributors in the O&M stage are the total freshwater and M&R costs. The total freshwater cost is calculated from the freshwater consumption rate and its unit cost. The M&R cost is proportional to the total piping cost.19 Equations used to estimate the costs in the O&M stage are given as follows:
) FWC + MRC CostO&M t
For the mass balances of the splitters:
Fopout -
∑ ∑
w∈W opin∈OP
Fw,opin UCw
Fopout,opin - Fopout,ww ) 0
(28)
For the constraints on the flow rates and concentrations of the operations:
(15)
where
FWC )
∑
opin∈OP
max Fmin opin e Fopin e Fopin
(29)
max Cc,opin e Cc,op in
(30)
max Cc,opout e Cc,op out
(31)
(16)
and
For the constraints on the prevention of local recycling:
MRC ) δ × Costpiping
(17)
The total pipe decommissioning cost consists of a pipe decommissioning cost, construction expenses, and the contractor’s overhead and profit. The pipe decommissioning cost is proportional to the direct labor cost for piping in the construction stage. The construction expenses in the disposal stage are proportional to the pipe decommissioning cost. The contractor’s
Fopout,opin ) 0
(32)
where the value of opout is the same as that of opin. 3. Case Study A case study was performed to demonstrate the higher profitability of a water network system generated from the
Ind. Eng. Chem. Res., Vol. 46, No. 21, 2007 6939
Figure 1. Conventional water system. Legend: FW, freshwater; OP, water-using operation; and TP, local wastewater treatment plant. Table 2. Distance Matrixa
Table 1. Limiting Process Data for Water Network Synthesis contaminant
max C c,opin (mg/L)
max C c,opout (mg/L)
Mop (kg/h)
30 5 120
Operation OP1 500 3.3 100 0.5 2300 16.4
CODcr SS Cl-
20 3 20
Operation OP2 250 2.3 50 0.4 300 3.0
CODcr SS Cl-
10 2 1
Operation OP3 160 1.5 25 0.2 5 0.0
CODcr SS Cl-
30 1 80
Operation OP4 250 3.4 50 0.6 750 11.5
CODcr SS Cl-
30 5 3
Operation OP5 300 4.5 15 0.1 40 0.4
CODcr SS Cl-
FL,op (m3/h)
F min opin (m3/h)
F max opin (m3/h)
49.7
50
90
36.6
40
90
8.8
10
60
Distance (m) OP1 OP2 OP3 OP4 OP5 TP1 TP2 TP3 TP4
FW1
FW2
2060 2090 4600 2710 2850
1010 410 4660 2490 2580
OP1
OP2
OP3
OP4
OP5
280 4470 2280 2300 520 4580 2410 2360
4330 2440 2580 300 4440 2580 2530
1900 1840 4740 280 2060 2110
140 2820 2030 300 350
2930 1980 350 300
a FW ) fresh water; OP ) water-using operation; and TP ) local wastewater treatment plant.
Table 3. Concentrations of Freshwater Sources 3.1
10
Concentration, Cc,w (mg/L)
60
FW1 FW2 0.8
10
freshwater source
CODcr
SS
Cl-
industrial water deionized water
0 0
0 0
15 0
40
aforementioned mathematical optimization model and to estimate the effects of the model on the configuration of a water network system. Three types of water network systems were synthesized on the basis of each objective function: NPV maximization, total freshwater flow-rate minimization, and total freshwater cost minimization. The NPV-maximized water network system (NWNS) was compared to the total freshwater flow-rate-minimized water network system (FWNS) and total freshwater cost-minimized water network system (CWNS). The costs of the principal contributors in each water network system were estimated and compared. Each NPV of the water network systems was evaluated to compare their overall profitability. 3.1. Methods. Five water-using operations in an iron and steel plant were selected as the water sources and sinks in this case study. The convention water system (CWS), which was composed of the water-using operations, is illustrated in Figure 1. Their limiting process data for the water network syntheses are presented in Table 1. The distance matrix for the interconnections between the water sources and sinks, such as the freshwater sources, water-using operations, and local wastewater treatment plants, is shown in Table 2. The concentrations of the industrial and deionized water used as the freshwater sources are presented in Table 3. 3.1.1. Water Network Synthesis. The three water network systems were generated by their own objective functions, subject to mass balances and constraints. The objective functions used to synthesize the FWNS and CWNS are described as follows: For the objective function to minimize the total freshwater flow rate:
Table 4. Characteristics of the Conventional Water System and the Three Water Network Systemsa Value characteristic
CWS
FWNS
CWNS
NWNS
(m3/h)
utility consumption rate industrial water 123.8 52.3 117.9 118.1 deionized water 39.0 96.2 30.8 30.8 total 162.8 148.5 148.7 148.9 64.8 49.6 49.6 49.8 wastewater generation rate (m3/h) pipe length (m) 15 800 35 440 38 470 34 720 a CWS ) conventional water system; FWNS ) total freshwater flowrate-minimized water network system; CWNS ) total freshwater costminimized water network system; and NWNS ) NPV-maximized water network system.
{
Min Ftw )
∑ ∑
w∈W opin∈OP
}
Fw,opin
(33)
For the objective function to minimize the total freshwater cost:
{
Min Costtw )
∑ ∑
w∈ W opin∈OP
Fw,opinUCw
}
(34)
The FWNS was generated using eqs 23-33, and the CWNS was synthesized based on eqs 23-32 and eq 34. The NWNS was generated with eqs 1-32. All parameters used in the objective functions were set before obtaining optimal solutions. The interest rate was set at 5.7%, with respect to the yields of treasury bonds (5-year bonds) over the last 10 years in South Korea,20 and the escalation rate was assumed to be the 3.0% that was targeted by the Bank of Korea
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Figure 2. Comparison of the water network systems: (a) total freshwater flow-rate-minimized water network system (FWNS); (b) total freshwater costminimized 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 network system; and NWNS, NPV-maximized water network system.
for the period between 2004 and 2006.21 A total income-tax rate of 27.5% was applied, according to the tax law in South Korea.22 The service life was assumed to be 15 years, based on the lifetime of the pipes. Parameters used to estimate the direct material and labor costs for piping in eqs 7 and 9 are
adp ) 714.15, bdp ) 2.9053, adl ) 2106.3, bdl ) 16.326
These parameters were obtained from the correlation between the cost and the cross-sectional area of the pipes. Databases of price and cost information were used for the direct material and labor costs for piping.23,24 The optimal velocity in the pumping flow was obtained from its correlation with a flow rate and was set not to exceed a maximum head loss (2.0 kgf/cm2) for pumping flow. The parameters used to determine the optimal velocity in eq 11 are
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Figure 4. Variations of each NPV over the service life. Legend: FWNS, total freshwater flow-rate-minimized water network system; CWNS, total freshwater cost-minimized water network system; and NWNS, NPV-maximized water network system.
aop ) 0.0297, bop ) 0.6173 These parameters were also obtained from correlations between head losses through the pipe and the length and diameter of the pipe. However, the optimal velocity in gravity flow, such as for the effluents from the water-using operations to the local wastewater treatment plants, was set at 0.5 m/s, because (i) a maximum head loss basis for the gravity flow was set at 0.2 kgf/cm2 and (ii) a lower velocity results in the deposition of particles in the pipe.25 The distances between 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 12-14 and 20-22, are23
R ) 0.2, β ) 0.05, γ ) 0.1 The unit costs of industrial and deionized water were assumed to 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
δ ) 0.3 The parameter used to calculate the pipe decommissioning cost in eq 19 is24
) 0.4 The three water network systems were generated from the optimal solutions to each mathematical optimization model. GAMS/MINOS26 was used as an NLP solver to find the optimal solutions to the models. The configuration of each water network system was embodied by its optimal solution. Wastewater streams were connected to local wastewater treatment plants, taking into account real circumstances in the plant. The local wastewater treatment plants were considered to estimate costs associated with pipelines between water-using operations and local wastewater treatment plants. 3.1.2. Cost Estimation of Principal Contributors and NPV Evaluation. The costs of the principal contributors in each water network system were estimated using eqs 5-22, which were used in the objective function to generate the NWNS. The costs of each principal contributor in the three water network systems were compared to each other, to estimate the effects of the objective function used for the NWNS on the principal contributors. However, the costs of freshwater consumption,
M&R, and pipe decommissioning were not discounted to present values, although the costs of the freshwater consumption and M&R recur annually and the pipe decommissioning cost is incurred at the end of the service life. This was because the time values of the costs were taken into account in the NPV evaluation. The NPV of each water network system was evaluated to estimate their profitability in a comprehensive manner. The CWS (Figure 1) was used as a baseline, to estimate the incremental 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, and NWNS were generated from the optimal solutions to each mathematical optimization model (see Figure 2). The characteristics of the three water network systems and CWS are summarized in Table 4. When the FWNS, CWNS, and NWNS were compared to the CWS, their total freshwater consumption rates were reduced by 8.8%, 8.7%, and 8.5%, respectively, and the consumptions of industrial water were decreased by 57.8%, 4.8%, and 4.6%, respectively. However, the consumption of deionized water in the FWNS increased by 146.7%, but those in the CWNS and NWNS both decreased by 21.0%. The total freshwater consumption rate in the FWNS was the lowest, because its objective function drove the high consumption of deionized water, rather than that of industrial water. Total wastewater generation flow rates in the FWNS, CWNS, and NWNS were also reduced by 23.5%, 23.5%, and 23.1%, respectively. This reduction in flow rate for freshwater consumption and wastewater generation allowed a decrease in the pipe diameter and reduced the costs of the piping, M&R, and pipe decommissioning. Note that the total pipe length of the NWNS was the shortest, because its objective function was formulated to simultaneously minimize the costs of the piping, freshwater consumption, M&R, and pipe decommissioning. As a result, the tradeoffs between the reduction of freshwater consumption rate and increase in the other principal contributors were different in each water network system, because of their differing objective functions. Costs of the principal contributors in each water network system were estimated, as shown in Figure 3. This figure shows the results of the tradeoffs mentioned in Table 4. When the FWNS, CWNS, and NWNS were compared to the CWS, their total piping costs increased by 80.0%, 91.9%, and 76.5%, respectively. The total piping cost of the NWNS was less than
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those of the FWNS and CWNS, because the objective function used for the NWNS simultaneously optimized all principal contributors; however, the other water network systems did not optimize pipe-related costs. The annual freshwater costs of the CWNS and NWNS were reduced by 9.8% and 9.7%, respectively. The objective function used for the CWNS minimized the total freshwater cost. However, the total freshwater cost in the FWNS was even 5.4% greater than that of the CWS, because the objective function used for the FWNS increased the flow rate of deionized water with higher water quality but higher unit cost, to minimize the total freshwater flow rate. The trend of the M&R and total pipe decommissioning costs in each water network system was similar to that of the total piping cost, because their costs were calculated from the total piping cost. The variations of each NPV over the service life of the three water network systems are shown in Figure 4. The NPV of the FWNS, CWNS, and NWNS were $ -1190000 U.S., $ -33000 U.S., and $101000 U.S., respectively, which showed that the NWNS was the most profitable. Note that the reductions in the costs of the piping, M&R, and pipe decommissioning in the NWNS outweighed the increase in the total freshwater cost, when the NWNS was compared to the CWNS. This occurred because the objective function used for the NWNS controlled the tradeoffs among the principal contributors, to maximize the sum of all incremental costs and benefits from the increase and decrease in the costs of the principal contributors. The increase in the costs of all the principal contributors in the FWNS did not incur incremental benefits; the NPV of the FWNS was consistently decreased over its service life. The NPV of the CWNS changed to a negative value at the end of its service life, although the total piping cost in the construction stage was recovered in the 13th year, as a result of the incremental benefits from the reduction of the total freshwater cost. This was because the pipe decommissioning cost incurred in the disposal stage outweighed the positive NPV, In other words, the total costs incurred from the interconnections used for water reuse exceeded the reduction of the total freshwater cost during the service life of the system. In the NWNS, the total piping cost was recovered in the 11th year, as a result of incremental benefits from the reduction of the total freshwater cost, so the NPV of the NWNS was positive at the end of its service life. The payback period of the NWNS was shorter than that of the CWNS, because the total piping and M&R costs of the NWNS were less than those of the CWNS. Therefore, the mathematical optimization model that was developed to generate an economically friendly water network system was in accordance with the results of this case study. In addition, the case study demonstrated the characteristics of the model. 4. Conclusions A mathematical optimization model was developed to synthesize an economically friendly water network system by maximizing its net present value (NPV). A case study was performed to demonstrate the highest profitability of the water network system generated from the model and estimate the characteristics of the model. The simplified model used to generate an NPV-maximized water network system can be easily applied to practically implement water network systems in industrial plants, because many minor contributors to the economic costs and benefits of water network systems are excluded from the model. The model also provides important information for other process integration technologies,
such as heat and hydrogen network syntheses, because all equations for the principal contributors can be applied to generate economically friendly heat and hydrogen network systems. Acknowledgment This work was financially supported by the Korean Science and Engineering Foundation (R11-2003-006) through Advanced Environmental Biotechnology Research Center at Pohang University of Science and Technology, by the Korean Ministry of Commerce, Industry, and Energy through the Korean National Cleaner Production Center and by the Program for Advanced Education 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 operation Cc,opout ) concentration at the outlet of a water-using operation Costcws ) costs of a conventional water system t Costwns ) costs of a water network system t Costpiping ) total piping cost t ) total O&M cost CostO&M t Costdecom ) total pipe decommissioning cost t Costtw ) total freshwater cost per hour DCt ) depreciation cost DLw,opin ) direct labor cost for piping from freshwater source to water-using operation DLopout,opin ) direct labor cost for piping from the outlet of waterusing operation to the inlet of another DLopout,ww ) direct labor cost for piping from water-using operation to local wastewater treatment plant DPw,opin ) direct pipe material cost from freshwater source to water-using operation DPopout,opin ) direct pipe material cost from the outlet of waterusing operation to the inlet of another DPopout,ww ) direct pipe material cost from water-using operation to local wastewater treatment plant EXPdecom ) construction expenses for pipe decommissioning EXPpiping ) construction expenses for piping Fopin ) flow rate at the inlet of water-using operation Fopout ) flow rate at the outlet of water-using operation Fopout,opin ) flow rate from the outlet of water-using operation to the inlet of another Fopout,ww ) flow rate from water-using operation to local wastewater treatment plant Fw,opin ) flow rate from freshwater source to water-using operation FWC ) total freshwater cost IBt ) incremental benefit IB0 ) initial incremental cost l ) pipe length MRC ) maintenance and repair costs OHdecom ) contractor’s overhead for pipe decommissioning OHpiping ) contractor’s overhead for piping
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Parea ) cross-sectional area of a pipe PROdecom ) contractor’s profits for pipe decommissioning PROpiping ) contractor’s profits for piping TDPpiping ) total direct pipe material cost TDLdecom ) total direct labor cost for pipe decommissioning TDLpiping ) total direct labor cost for piping V ) optimal velocity through pipe NPV ) net present value 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 max Cc,op ) maximum concentration at inlet of water-using opin eration max Cc,op ) maximum concentration at outlet of water-using out operation Cc,w ) freshwater concentration γ ) coefficient for a contractor’s profits δ ) coefficient for M&R cost e ) escalation rate ) coefficient for total direct labor cost of pipe decommissioning FL,op ) water loss rate in water-using operation min ) minimum flow rate at inlet of water-using operation Fop in max ) maximum flow rate at inlet of water-using operation Fop in Fmax w ) maximum flow rate for freshwater i ) interest rate Mc,op ) mass load of a contaminant t ) time TR ) income-tax rate UCw ) unit cost of freshwater Literature Cited (1) Takama, N.; Kuriyama, T.; Shiroko, K.; Umeda, T. Optimal Water Allocation in a Petroleum Refinery. Comput. Chem. Eng. 1980, 4, 251258. (2) Bagajewicz, M. A Review of Recent Design Procedures for Water Networks in Refineries and Process Plants. Comput. Chem. Eng. 2000, 24, 2093-2113. (3) Quesada, I.; Grossmann, I. E. Global Optimization of Bilinear Process Networks with Multicomponent Flows. Comput. Chem. Eng. 1995, 19, 1219-1242. (4) Karuppiah, R.; Grossmann, I. E. Global optimization of the synthesis of integrated water systems in chemical processes. Comput. Chem. Eng. 2006, 30, 650-673.
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ReceiVed for reView October 21, 2006 ReVised manuscript receiVed June 8, 2007 Accepted June 11, 2007 IE061353V
