Economic Evaluation of a Water Network System through the Net

Sep 19, 2006 - However, the previous economic evaluations of water network systems did ... of a water network system using the net present value (NPV)...
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Ind. Eng. Chem. Res. 2006, 45, 7710-7718

Economic Evaluation of a Water Network System through the Net Present Value Method Based on Cost and Benefit Estimations Seong-Rin Lim, Donghee Park, Dae Sung Lee, 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 employed to conserve water resources and reduce freshwater costs for the sake of sustainable development. However, the previous economic evaluations of water network systems did not comprehensively include all of the tradeoffs incurred in water network synthesis. The objective of this work was to evaluate the economic feasibility of a water network system using the net present value (NPV) method and estimate the principal cost and benefit contributors to its NPV. The procedure used for the economic evaluation consisted of water network synthesis, water system design, the estimation of the incremental costs and benefits, and the application of the NPV method. A total of 10 water-using operations in the steel and iron industry suffering from the shortage of water were used to evaluate the profitability of a water network system. The water network system was optimized by minimizing the freshwater consumption rates through nonlinear mathematical programming. This water network system was specifically designed, and its incremental costs and benefits were estimated on the basis of the conventional water system. The principal cost contributor to the NPV was the piping cost in the construction stage, while the principal benefit contributor to the NPV was industrial water used in the operations and maintenance stage. The results of the NPV method including all of the tradeoffs showed that the water network system was more economical than the conventional water system, with reduced industrial water consumption and wastewater generation rates. This work was expected to activate the implementation of water network systems by demonstrating the high profitability and contribute to the simple generation of a NPV-maximized water network system by estimating the principal cost and benefit contributors to the NPV used for the streamlined objective function of mathematical formulation. 1. Introduction Much effort has been made in almost all industries to reduce costs and increase benefits in order to enhance competitiveness and profitability. The retrofitting of processes and the application of new technologies are the general methods used in industrial plants to effectively reduce the costs of capital investment and operating and maintenance (O&M). Because water is a very important natural resource for washing, cleaning, and cooling, and being a product in itself, a variety of water technologies have been developed to enhance the profitability of the water supply, water treatment, and wastewater treatment. Since they were first used for water network optimization in a petroleum refinery plant in 1980, water network synthesis technologies have been widely studied and applied to reduce freshwater consumption and wastewater generation rates.1-12 However, no overall economic evaluation has been performed to demonstrate the high profitability of water network systems, with respect to the tradeoffs of all of the costs and benefits resulting from water network synthesis. Most previous works have focused on solving the various types of mathematical formulations employed in water network synthesis, such as nonlinear programming (NLP) and mixedinteger nonlinear programming (MINLP).1-6 Because the nonconvexities derived from bilinear variables in the mass balances of contaminants make it difficult to obtain global optima, methodologies have been developed to obtain optimal solutions much closer to the global optima. A genetic algorithm was developed to avoid the unacceptable local optima associated with MINLP in wastewater minimization.7 * To whom all correspondence should be addressed. Tel.: +82-54279-2275. Fax: +82-54-279-2699. E-mail: [email protected].

Pinch analysis technologies5,13-17 have been studied to graphically analyze the process limiting data of water-using operations and heuristically produce a water network system. These graphical targeting methods suggest the minimum freshwater consumption rate of a water system and identify the key water-using operation which represents a bottleneck and should be retrofitted in order to further reduce freshwater consumption. However, these methods did not take the economic aspects of the design into consideration, even though the use of mathematical programming approaches helped to produce an economically friendly network configuration, with the objective function of formulations manipulated. The economic evaluation of profitability through the analysis of costs and benefits is essential to the selection of alternatives, because higher profitability is the most powerful driving force affecting the final decision-making process in all businesses and industries, when it comes to choosing among alternatives. All of the costs and benefits incurred by the various alternatives should be comprehensively examined and estimated by considering their time value of money and service life, to clearly evaluate their profitability. In the case of a water network system, more accurate economic evaluations are required to support its higher profitability, because water network synthesis is a complicated process which incurs many tradeoffs between the costs and benefits derived from the variations in the initial capital investment and O&M costs. To date, no detailed economic evaluations inclusive of all of the tradeoffs among the various cost contributors have been made, with the consequence that the higher profitability of water network systems has not been verified. The objective of this work was to evaluate the economic feasibility of a water network system through the net present value (NPV) method, to

10.1021/ie060565p CCC: $33.50 © 2006 American Chemical Society Published on Web 09/19/2006

Ind. Eng. Chem. Res., Vol. 45, No. 22, 2006 7711 Table 1. Limiting Process Data for Water Network Synthesis operation

contaminant

max C c,opin (mg/L)

max C c,opout (mg/L)

Mop (kg/h)

FL,op (m3/h)

F min opin (m3/h)

F max opin (m3/h)

OP 1

CODcr SS ClCODcr SS ClCODcr SS ClCODcr SS ClCODcr SS ClCODcr SS ClCODcr SS ClCODcr SS ClCODcr SS ClCODcr SS Cl-

50 20 90 30 5 120 30 2 50 20 3 20 20 4 20 23 5 10 30 20 1 10 2 1 30 1 80 30 5 3

600 200 1100 500 100 2300 500 50 750 250 50 300 300 60 300 400 80 200 250 100 10 160 25 5 250 50 750 300 15 40

6.5 2.0 12.9 3.3 0.5 16.4 3.5 0.3 6.2 2.3 0.4 3.0 2.8 0.5 2.8 3.2 0.6 1.5 3.8 2.0 0.1 1.5 0.2 0.0 3.4 0.6 11.5 4.5 0.1 0.4

70.7

80

150

49.7

50

90

38.8

40

90

36.6

40

90

25.3

30

80

8.3

10

70

24.3

40

200

8.8

10

60

3.1

10

60

0.8

10

40

OP 2 OP 3 OP 4 OP 5 OP 6 OP 7 OP 8 OP 9 OP 10

Table 2. Distance Matrix between Water Sources and Sinks (FW, freshwater; OP, water-using operation; TP, local wastewater treatment plant; unit, meter)

OP1 OP2 OP3 OP4 OP5 OP6 OP7 OP8 OP9 OP10 TP1 TP2 TP3 TP4 TP5

FW1

FW2

2250 2060 4960 2090 920 980 4550 4600 2710 2850

280 1010 4930 410 1010 1140 4580 4660 2490 2580

OP1

OP2

OP3

OP4

OP5

OP6

OP7

OP8

OP9

OP10

1010 4980 460 1030 1200 4660 4710 2550 2600 460 4770 4820 2680 2630

4980 280 140 220 4390 4470 2280 2300 520 4500 4580 2410 2360

4140 4120 4060 380 410 2440 2550 4880 460 410 2200 2250

650 710 4280 4330 2440 2580 300 4390 4440 2580 2530

170 3900 4010 1790 1820 520 4010 4120 1930 1880

3850 3960 1740 1760 570 3960 4060 1870 1820

220 1930 1870 4660 300 330 2090 2140

1900 1840 4740 330 280 2060 2110

140 2820 2060 2030 300 350

2930 2120 1980 350 300

demonstrate its profitability, and estimate the principal cost and benefit contributors to the NPV required for the streamlined objective function to simply generate a NPV-maximized water network system. The procedure used for this economic evaluation consisted of water network synthesis, water system design, the estimation of incremental costs and benefits, and the application of the NPV method. A total of 10 water-using operations in the steel and iron industry suffering from the shortage of water were used to evaluate the profitability of a water network system. The water network system was synthesized on the basis of the optimal solution derived from mathematical programming, and detailed designs were completed for the water network and conventional water systems. The incremental costs and benefits of the water network system were estimated on the basis of the conventional water system. The principal cost and benefit contributors to the NPV were estimated. Finally, the NPV and NPV-related financial indicators including all of the tradeoffs incurred in the water network

synthesis were evaluated in order to confirm the high profitability of the water network system. 2. Methods Water-using operations in the steel and iron industry suffering from the shortage of water were selected as the water sources and sinks in this work. Operational data and field information were gathered through a site survey in order to examine potential opportunities for water reuse. Most of the water-using operations in the plant were ranked according to the rates of water consumption and wastewater generation. A total of 10 waterusing operations were finally selected on the basis of their water quality and regional proximity, with those operations making considerable use of freshwater being prioritized. These were used for steelmaking, continuous casting, cold forming, and electroplating processes. The limiting process data for the water network synthesis are presented in Table 1. The distance matrix for the interconnections between the water sources and sinks,

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Figure 1. Generalized superstructure of a water network system.

Table 3. Capacities and Concentrations of Freshwater Sources Cc,w (mg/L) freshwater FW 1 FW 2

industrial water deionized water

3 F max w (m /h)

CODcr

SS

Cl-

600 250

0 0

0 0

15 0

such as the freshwater sources, water-using operations, and local wastewater treatment plants, was used for the cost estimations of the pipes and piping works, as shown in Table 2. Water was used for direct and indirect cooling, wet scrubbers, scale breaking, flume flushing, cleaning, washing, and rinsing.18 The capacities and concentrations of the industrial and deionized waters of the freshwater sources are presented in Table 3. 2.1. Water Network Synthesis. Superstructure Model. The superstructure model was generalized to reflect real situations of a water system in industrial plants, as illustrated in Figure 1. This model included all possible interconnections between water sources and sinks, such as those from the outlet of one operation to the inlet of the others, as well as between freshwater sources and water-using operations, to maximize the opportunity for water reuse and ultimately reduce the consumption of freshwater. However, local recycling from the outlet to the inlet within an operation was not allowed, so as to prevent the excessive costs derived from pumping with a high flowrate. This was because the small gap between the concentrations of the inlet and outlet in the local recycling requires the high flowrate in the recycled line, to transfer the contaminant load of the operation into water. For example, assume that the contaminant load of an operation is 1.2 kg/h. When freshwater is used without local recycling, the concentrations of the inlet and outlet of the operation are zero and 100 mg/L, respectively, and the freshwater flowrate required is 12 m3/h. If local recycling is allowed in the superstructure model, it is possible to obtain the following system: the concentrations of the inlet and outlet of the operation are 80 and 100 mg/L, with the wastewater in the effluent of the operation recycled with a flowrate of 48 m3/h, even though freshwater is supplied with the same flowrate of 12 m3/h.5 It should be noted that the local recycling is useless if the operational conditions do not require a high flowrate. Direct connections between freshwater sources and local wastewater treatment plants were also prohibited so as not to incur any loss of freshwater. It was assumed that the mixers combined the many streams into a single stream and that the

splitters divided a stream into all possible streams flowing to the water sinks. Mathematical Formulation. To optimize a water network system, the objective function of mathematical formulation was targeted to the minimization of the total freshwater flowrate in the water system, because the steel and iron plant suffered from the shortage of water; the reduction of freshwater consumption rather than cost reduction was the first priority in the water management of the plant. The entire mathematical formulation of the superstructure model is as follows: For the objective function

minimize F tw )

∑ ∑

Fw,opin

(1)

w∈W opin∈OP

Subject to the following: For the overall mass balance of the entire water network system

∑ ∑

Fw,opin -

w∈W opin∈OP

∑

Fopout,ww -

ww∈WW

∑ FL,op ) 0

(2)

op∈OP

For the mass balances of the mixers

∑ Fw,opin + opout∈OP ∑ Fopout,opin - Fopin ) 0

(3)

w∈W

∑ Fw,opinCc,w + opout∈OP ∑ Fopout,opinCc,opout - FopinCc,opin ) 0

w∈W

(4)

For the mass balances of the operations

Fopin - FL,op - Fopout ) 0

(5)

FopinCc,opin + Mc,op - FopoutCc,opout ) 0

(6)

For the mass balances of the splitters

Fopout -

∑

Fopout,opin - Fopout,ww ) 0

(7)

opin∈OP

For the constraints on the flowrates and concentrations of the operations max F min opin e Fopin e F opin

(8)

Ind. Eng. Chem. Res., Vol. 45, No. 22, 2006 7713 max Cc,opin e C c,opin max Cc,opout e C c,opout

(9) (10)

For the constraints on the maximum flowrates of the freshwater sources

Fw,opin - F max ∑ w e0 opin∈OP

(11)

For the constraints on the prevention of local recycling

Fopout,opin ) 0

(12)

where the value of opout is the same as that of opin. Mathematical formulation on the prevention of chemical precipitation and scaling problems, as well as the water temperature at the inlet and outlet of the operations, was not included in this model. Because the contaminant loads from the operations did not generate high concentrations of calcium, magnesium, sulfate, and carbonate, chemical precipitation and scaling problems were not expected in this work. Therefore, chemical oxygen demand by dichromate (CODcr), suspended solids (SS), and Cl- were used as good indicators of water quality in this water network synthesis, because they represent the concentrations of organic contaminants, particles, and ions. The water temperatures at the inlet and outlet of the operations needed to be reflected in the mathematical optimization model required for the utilization of water reuse in the direct and indirect cooling processes. However, mathematical formulation on the water temperatures was not included for the sake of simplicity of this model, because cooling towers, coolers, and chillers could be used to lower water temperatures at the inlet of the operations. A water network system was produced from the optimal solution of the mathematical formulation above. GAMS/ MINOS19 as an NLP solver was used to find the reasonable solutions of the mathematical programming model. It should

be mentioned that even local solutions were very useful for industrial applications if they achieved a significant reduction in freshwater consumption. This was because global optima cannot easily be obtained, because of the nonconvexities derived from the bilinear variables in the mass balances of the contaminants. The optimal solution of the mathematical programming model was used to directly embody a water network system. However, the original water network system resulting from the optimal solution was simplified by eliminating inefficient interconnections with a low flowrate, to exclude the minor contributors to water reuse and easily perform the cost evaluations. The wastewater streams were connected to local wastewater treatment plants, reflecting the real circumstances in the plant. The local wastewater treatment plants were considered to estimate costs related to the pipelines between the operations and local wastewater treatment plants, as well as pump pits. 2.2. Water System Design. The water network and conventional water systems were designed in detail for the estimation of their costs and benefits. All constituents in the two water systems were specifically designed for practical implementations. To make impartial comparisons between the two water systems, the conventional water system was revised using the same design criteria as those applied to the water network system. Pipe Design. The pipe diameter and head loss were simultaneously calculated with the flowrate and pipe length. The maximum head loss criteria were applied to determine the nominal pipe diameter. The Darcy-Weisbach equation20 was used to calculate the head loss. The maximum head loss basis was set at 2.0 and 0.2 kgf/cm2 for pumping and gravity flow, respectively. Carbon steel was selected for the pipe material. The Korean Standard, KS D3507, was used to determine specific data, such as the nominal diameter, wall thickness, and weight. The minimum nominal pipe diameter was set at 1 in. for the sake of simplicity of design. The distances between the water sources and sinks were used as the pipe lengths of the interconnections.

Figure 2. Original water network system generated from the optimal solution of mathematical programming (FW, freshwater; OP, water-using operation; TP, local wastewater treatment plant).

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Figure 3. Conventional water system (FW, freshwater; OP, water-using operation; TP, local wastewater treatment plant).

Equipment Design. The specifications of the pumps and electric motors were determined in relation to the flowrate and water head requirements. The flowrate was obtained from field data or the optimal solution of the mathematical programming model for the water network synthesis. The discharge pressure of a pump was determined by summing both the head losses through the pipes and the water pressure required for the waterusing operation. In the case of a pump having a manifold connected to more than one operation, the maximum head loss among those of the various pipelines was selected to determine its specifications. The water pressures required at the end of the pipe were assumed to be 2.5 and 1.0 kgf/cm2 for waterusing operations and local wastewater treatment plants, respectively. Pump Pit Design. Pump pits were required for the storage of wastewater prior to its being pumped to the local wastewater treatment plants. The hydraulic retention times of the pump pits were all set at 30 min, to prevent the short circuit of the electric motors derived from their frequent startup. 2.3. The Estimation of Incremental Cost and Benefit. All of the costs of the two water systems were classified and estimated over the duration of the service life on the basis of their detailed designs before calculating the incremental costs and benefits. The conventional costs used for the traditional management accounting were estimated in this work, because of their tangibility, even though the environmental accounting, which includes potentially hidden costs, contingent costs, image/ relationship costs, and external costs, has recently been highlighted.21,22 To utilize the NPV methods for the evaluation of profitability, the incremental costs and benefits of the water network system were estimated, with the costs of the conventional water system used as a baseline. In other words, the incremental benefits, such as the reduction in costs compared with the baseline, were regarded as profits in the economic evaluation, because a water system employed as a utility for the main production systems could not directly yield profits through its own operations.23 This method was generally applied to decision-making processes for the selection of the best option among alternative investments. The cost estimations were first performed for four categories: engineering and supervision, construction, O&M, and disposal. All of the categories, with the exception of O&M, were assumed to be performed by contractors, which was normal in the field of engineering and construction. Therefore, the contractor’s overheads and profits were estimated for the sake of the accuracy of the cost analysis. The engineering and

supervision cost was composed of the costs of the basic and detailed designs, as well as supervision activities. The construction cost was specifically divided into the costs of pipes, piping works, equipment, installation, pump pit works, and construction expenses, as well as the contractor’s overheads and profits. The O&M cost included the utilities consumption costs for industrial and deionized water and electricity, as well as maintenance and repairs cost. The disposal cost consisted of decommissioning, recycling, landfill, and construction expenses, as well as the contractor’s overheads and profits. Detailed cost estimations were performed using a database consisting of price and cost information.24,25 The O&M cost recurred over the service life of the two water systems, while the other costs, such as engineering and supervision, construction, and disposal, were incurred at the starting and finishing points of the service life. The incremental costs and benefits of the water network system were consecutively generated from the results of the preceding cost estimations. The costs of the conventional water system were used as a baseline to calculate the incremental costs and benefits. The incremental costs were obtained by subtracting the costs of the conventional water system from those of the water network system in the categories of engineering and supervision, construction, and disposal. Most of the incremental costs were derived from the complicated interconnections required for networking. The incremental benefits were calculated by subtracting the costs of the water network system from those of the conventional water system in the O&M category and were derived from the reduction in the consumption of utilities resulting from the reuse of water. 2.4. The Application of the Net Present Value Method. The NPV method was used to economically evaluate and verify the profitability of a water network system using its incremental costs and benefits.23 The NPV method was based on the time value of money in relation to cash flows. The NPV was obtained by summing the discounted amounts and the initial investment after a series of future cash flows was discounted. The more positive the NPV, the more profitable the investment. When total income taxes are included in the economic evaluation,23 the equation for the NPV can be expressed as follows: t

NPV )

∑ t)1

[(IBt - ICt)(1 - TR) + DCtTR](1 + e)t (1 + i)t

- IC0 (13)

This NPV method was useful to support the final decisionmaking process for alternative investments, because all of the tradeoffs between costs and benefits were comprehensively combined and expressed as a single value, regardless of the time points at which they were incurred. The NPV method was modified to calculate the payout period23 and the internal rate of return (IRR),23 both of which were applied to the economic evaluation of alternative investments. The payout period was regarded as the duration required for the incremental benefits to allow for the full recovery of the initial incremental costs, with the NPV set to zero in eq 13. The IRR was obtained by calculating the interest rate which caused the NPV to be equal to zero in eq 13. The payout period and IRR related to the NPV method were also used as profitability indicators for the comparison of different alternatives. All of the factors in the above NPV equation should be determined in order to accurately evaluate the profitability. The service life was set to 15 years with respect to the lifetime of the pipes and mechanical equipment. To discount future costs and benefits, the interest rate was set to 5.7%, by taking into

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Figure 4. Simplified water network system, modified by eliminating those interconnections with a low flowrate of less than 4 m3/h (FW, freshwater; OP, water-using operation; TP, local wastewater treatment plant).

account the yields of treasury bonds (5 years) over the last 10 years in South Korea.26 The escalation rate was assumed to be 3.0% targeted by the Bank of Korea for the period between 2004 and 2006.27 And the sensitivity analysis of the NPV and NPV-related methods was performed to estimate the effect of the interest and escalation rates. Deprecation costs were estimated by the straight-line method over the service life.23 A total income-tax rate of 27.5% was applied to this economic evaluation, according to the tax law in South Korea.28 3. Results and Discussion Water Network Synthesis. The original water network system was generated from the optimal solution of the mathematical programming formulated for the water network superstructure model after the process-limiting and freshwater source data were applied to the formulation, as illustrated in Figure 2. When the original water network system was compared with the conventional water system shown in Figure 3, the total freshwater consumption rate was reduced by 11.1%, from 405.1 to 360.3 m3/h, with the water network system contributing to the conservation of water resources and the reduction of the operating cost. The saving of industrial water was greater than that of deionized water. The flowrate of industrial water decreased by 12.5%, from 297.5 to 260.3 m3/h, while that of deionized water was diminished by 7.1%, from 107.6 to 100.0 m3/h. This result was derived from the objective function of the mathematical programming, which was to minimize the sum of all of the freshwater flowrates, regardless of the water quality and unit cost of the freshwater sources. The total wastewater flowrate was also reduced by 47.7%, from 138.7 to 93.9 m3/h. Because decreasing the hydraulic loads engendered the stable equalization of contaminant loads and flowrate in the influents of the local wastewater treatment plants, because of high hydraulic retention times in the pump pits, the enhancement of removal efficiencies and the reduction of operating cost were

expected in the existing local wastewater treatment plants, even though the contaminant loads were not changed through the water network synthesis. In other words, because all of the local wastewater treatment plants were composed of physical and chemical treatment processes, such as coagulation, flocculation, and sedimentation, their chemical dosages and velocity gradients for mixing could be stably maintained without sudden variations, because of equalized concentrations and the flowrate in the influents of the local wastewater treatment plants. The initial capital investment cost could be reduced by constructing smaller wastewater treatment plants if the water network system were applied to a new plant. The simplified water network system was generated from the original one, with the interconnections having a low flowrate removed. This was because the economic efficiency of the original water network system and its applicability to real field situations might otherwise be decreased, because of the complexities derived from these inefficient interconnections, which might even maximize water reuse. The original water network system was modified, with those interconnections having a flowrate of less than 4.0 m3/h being eliminated. However, it should be mentioned that the total freshwater flowrates increased from 260.3 to 266.5 m3/h and 100.0 to 108.6 m3/h for the industrial and deionized waters, respectively, when the water network was so modified. The flowrate of deionized water in the simplified water network was higher than that in the conventional water system. Because more freshwater was required to compensate for the decrease in water reuse, the amount of wastewater increased, from 93.9 to 108.7 m3/h. The simplified water network system is illustrated in Figure 4, and this design was used for the estimation of the incremental costs and benefits. Water System Design. The detailed design performed as the preparatory step for the cost and benefit estimations showed that the tradeoffs between the initial capital investment and operating costs were essentially incurred through the water

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Table 4. Summary of the Design Results for the Conventional Water System and the Water Network System item pipe pump motor pump pit utility consumption

length weight weight weight volume industrial water deionized water electricity

unit

conventional water system

water network system

m kg kg kg m3 m3/h m3/h kW

32 010 669 902 874 845 70 297.5 107.6 99.6

44 400 756 592 935 857 97 266.5 108.6 110.4

Figure 7. Cost estimation of all the processes in the disposal stage.

Figure 5. Cost estimation of all the processes in the construction stage.

Figure 8. Cost estimation for each stage over the service life. Future costs were not discounted to present values. Figure 6. Cost estimation of all the processes on an annual basis in the O&M stage.

network synthesis, as summarized in Table 4. The total length and weight of the pipes increased by 38.7 and 12.9%, respectively. The total weight of the pumps and motors increased by 7.0 and 1.4%, respectively, and the total volume of the pump pits increased by 38.6%, because four more pumps, motors, and pump pits were required for water networking. In the O&M, stage, the electricity requirement increased by 10.8%, from 99.6 to 110.4 kW. These results were because the increases in the quantities of the pipe, pump, motor, pump pit, and electricity consumption required for the water reuse outweighed the decreases in those resulting from the decrease in the industrial water consumption and wastewater generation. However, it should be noted that the overall profitability derived from these two different effects cannot be determined, because of the tradeoffs among the constituents of the water network system. The Estimation of the Incremental Cost and Benefit. All of the possible costs required for the conventional water and water network systems were estimated throughout the service life, to evaluate the incremental costs and benefits. None of the costs incurred in the O&M and disposal stages took into consideration the time value of money in this step, because those costs could be discounted in the NPV method. The costs in the O&M stage were estimated on an annual basis. All of the costs incurred in the construction, O&M, and disposal stages for the two water systems were first estimated on the basis of their detailed designs. Figure 5 shows the results of the cost estimations in the construction stage. The piping cost was dominant over the other costs and had significant effects on the construction expenses and the contractor’s

overheads and profits. The piping cost required for the water network system was higher, because of its complicated network, even though the nominal diameters of the pipes were smaller than those used in the conventional water system. Industrial and deionized waters were the principal components in the annual O&M cost, as shown in Figure 6. However, the cost of the electricity required for pumping was not significant when compared with the freshwater costs and was even smaller than the maintenance and repairs cost. The water network system was more economical from the point of view of O&M. Figure 7 shows all of the costs incurred in the disposal stage. The pipe decommissioning cost was dominant, and small revenue was obtained from the recycling of the steel and iron scraps resulting from the disposal of pipes and equipment. The totals of all of the costs incurred in each stage were calculated for the two water systems over the service life. Figure 8 shows that the O&M stage was the main cost producer in the conventional water and water network systems, occupying 88.2 and 85.9% of all of the costs that were not discounted to the present values, respectively. The proportion of the O&M cost in the water network system was smaller than that in the conventional water system, because the utilities consumptions were reduced through water reuse. The O&M cost decreased by 5.2% using the water network synthesis, while the costs of engineering and supervision, as well as construction, increased by 16.2%. It should be noted that more detailed evaluations were required to examine the ultimate result of the tradeoffs between the O&M costs and the other costs. The incremental costs and benefits for the water network system were calculated, to precisely evaluate its profitability using the NPV method and estimate principal cost and benefit contributors to the NPV. These costs were obtained from the

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Figure 9. Incremental costs and benefits. Future costs were not discounted to present values. Figure 11. Variations of the IRR over the service life. The sensitivity analysis was also performed to estimate the effect of the escalation rate on IRR (e: escalation rate).

of the sensitivity analysis also showed the consistently high IRRs of the water network system. On the basis of the results of the NPV and NPV-related methods, such as the payout period and IRR, the overall tradeoffs incurred through the water network synthesis were found to make the water network system more profitable than the conventional water system. 4. Conclusions Figure 10. Variations of the NPV over the service life. The sensitivity analysis was also performed to estimate the effect of the interest and escalation rates on NPV (i, interest rate; e, escalation rate).

differences between the costs of the two water systems, as shown in Figure 9. The incremental costs were incurred in the engineering and supervision, construction, and disposal stages, whereas the incremental benefit occurred annually in the O&M stage. The total incremental cost was $827 000 U.S., and the incremental benefit per annum was $131 000 U.S. The principal cost contributor was the piping cost in the construction stage, as shown in Figures 5 and 9. The principal benefit contributor was the industrial water used in the O&M stages, according to Figures 6 and 9. These principal cost and benefit contributors to the NPV can be employed for the streamlined objective function of mathematical formulation to simply generate a NPVmaximized water network system, because all of the contributors estimated in this work are not generally included in the objective function. The Application of the Net Present Value Method. The NPV method was employed to accurately evaluate the profitability of the water network system, while comprehensively taking into account the interest rate, escalation rate, depreciation costs, income taxes, and service life. When the incremental costs and benefits were applied to eq 13, the NPV increased over the service life, as shown in Figure 10. When an interest rate of 5.7% and an escalation rate of 3.0% were applied, the NPV was $547 000 U.S. at the end of the service life, which clearly demonstrates that the water network system was more profitable than the conventional water system, after including all of the tradeoffs. The results of the sensitivity analysis (Figure 10) showed the consistent profitability of the water network system. Figure 10 also shows that the payout period was 6.8 years, indicating that the initial incremental costs for capital investments could easily be recovered from the incremental benefits and that the water network system was financially beneficial. When an escalation rate of 3.0% was applied, the IRR of the water network system was 16.8% through the service life, which also demonstrated its high profitability when the IRR was compared with an interest rate of 5.7%. The variations of the IRR over the service life are shown in Figure 11. The results

The profitability of the water network system was examined through the economic evaluation, which allowed for the comprehensive estimation of all of the tradeoffs derived from water network synthesis. All of the costs and benefits in the two water systems were identified and estimated over the service life. The NPV method demonstrated the higher profitability of the water network system on the basis of its incremental costs and benefits. The principal cost and benefit contributors to the NPV were also estimated, which can be employed for the streamlined objective function of mathematical formulation to simply generate a NPV-maximized water network system. This economic evaluation can be used to support the final decision-making processes for the implementation of water network systems. Even though much has been said about the many advantages associated with water network synthesis, such as the reduction of the freshwater consumption and wastewater generation, the conservation of natural resources, and the improvement of the efficiency of wastewater treatment, it is difficult to apply the concept of the water network system to industrial plants without being certain of its profitability. This is because the demonstration of the profitability of a water network system in a reliable economic evaluation is the strongest driving force for its implementation. The economic evaluation presented in this work is expected to contribute to the successful implementation of water network systems. Nomenclature C ) {c|c is a contaminant in the water}, c ) 1, 2, ..., Nc W ) {w|w is a freshwater available}, s ) 1, 2, ..., Nm WW ) {ww|ww is a 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 Cc,opin ) concentration at the inlet of a water-using operation max C c,opin ) maximum concentration at the inlet of a water-using operation Cc,opout ) concentration at the outlet of a water-using operation

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max C c,opout ) maximum concentration at the outlet of a waterusing operation Cc,w ) freshwater concentration DC ) depreciation cost FL,op ) water loss rate in a water-using operation Fopin ) flowrate at the inlet of a water-using operation F min opin ) minimum flowrate at the inlet of a water-using operation F max opin ) maximum flowrate at the inlet of a water-using operation Fopout ) flowrate at the outlet of a water-using operation Fopout,opin ) flowrate from the outlet to the inlet of a waterusing operation Fopout,ww ) flowrate from the outlet of a water-using operation to a wastewater ) maximum flowrate for a freshwater F max w Fwt ) total flowrate of freshwaters Fw,opin ) flowrate from a freshwater to a water-using operation Mc,op ) mass load of contaminant NPV ) net present value e ) escalation rate i ) interest rate IBt ) incremental benefit IC0 ) initial incremental cost ICt ) incremental cost t ) time TR ) income-tax rate

Acknowledgment This work was financially supported in part by the Korean Science and Engineering Foundation (R11-2003-006-01001-1) through the Advanced Environmental Biotechnology Research Center at Pohang University of Science and Technology and in part by the Korean Ministry of Commerce, Industry, and Energy through the Korean National Cleaner Production Center. This work was also supported by the program for advanced education of chemical engineers (second stage of BK21). 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) Doyle, S.; Smith, R. Targeting Water Reuse with Multiple Contaminants. Process Saf. EnViron. Prot. 1997, 75, 181-189. (5) Mann, J. G.; Liu, Y. A. Industrial Water Reuse and Wastewater Minimization; McGraw-Hill: New York, 1999.

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ReceiVed for reView May 5, 2006 ReVised manuscript receiVed July 14, 2006 Accepted July 20, 2006 IE060565P