Optimization of the Water Network with Single and Double Outlet

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Optimization of the water network with single and double outlet treatment units Kaili Zhang, Yuehong Zhao, Hongbin Cao, and Hao Wen Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b04263 • Publication Date (Web): 17 Feb 2017 Downloaded from http://pubs.acs.org on February 18, 2017

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Industrial & Engineering Chemistry Research

Optimization of the water network with single and double outlet treatment units Kaili Zhang*,†,‡,§, Yuehong Zhao†,‡,§, Hongbin Cao†,‡,Hao Wen†,‡ †

Beijing Engineering Research Centre of Process Pollution Control, Beijing 100190, China

‡

State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering,

Chinese Academy of Sciences, Beijing 100190, China §

University of Chinese Academy of Sciences, Beijing 100049, China

KEYWORDS: Water reuse/recycle; Double outlet treatment unit model; Superstructure; Optimization; Pretreatment

ACS Paragon Plus Environment

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ABSTRACT: Optimization of water networks can always reduce freshwater consumption and wastewater discharge via finding the potential opportunity of direct/indirect water reuse/recycling. In most cases, some treatment units (i.e., filtration, ion exchange) that are known to have two outlet streams and both the outlet streams are commonly reused in industry, however, were often modeled as single outlet units in previous works, and the published double outlet models cannot describe those units very well. Thus, in this paper, a new double outlet model was proposed. And such model was used to construct the water network superstructure, in which both the outlet streams of such double outlet treatment unit can be connected with process units, other treatment units or the discharge, aiming to find all the potentials of reusing the outlets of such treatment unit. In particular, a multiple, staged system consisting of such double outlet units that is widely adopted in industry was incorporated in the network, and the superstructure of that system was specially developed. And the discussion of double outlet units performing as pretreatment or distributed treatment units was also carried out. All those investigations were demonstrated through a case study of a practical water network in a power plant, and the results show that the proposed approach is applicable and effective.

1. INTRODUCTION Water is essential in process industry, significant amounts of water are consumed every year and the water demand keeps increasing. At the same time, the shortage of freshwater and ever more stringent environmental regulations on wastewater discharge, indeed, have led to much effort to reduce water consumption and effluent to the environment.1 Water network synthesis is a promising strategy that could minimize the water usage and waste generation, which has gained much attention in both industrial and academic research. Two main approaches have been intensively investigated for water network synthesis problem: insight-


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based graphical techniques and mathematical programming-based optimization methods. The former was developed by Wang and Smith,2 which typically involves water pinch analysis that uses limiting composite diagram to target flowrate followed by detailed design. The method is simple for single contaminant and small scale problem, and gained much attention since their seminal work.3-5 Programming-based method first given by Takama6 et al is another important tool which employs a superstructure containing all feasible interconnections of water network elements. The big advantage of this method is that it allows considering multiple contaminants, various topological constraints and cost functions and thus optimizes the target and network simultaneously.7-11 Water-using process unit and water treatment unit are the main elements in a water network formulation.6, 12 The reuse/recycle of process streams is termed as direct reuse/recycle, while the reuse/recycle of streams after treatment units is termed as indirect reuse/recycle. Previous works have indicated that incorporating indirect reuse/recycle can further reduce freshwater consumption than direct reuse/recycle only.13-14 However, most previous works suppose that each treatment unit has a single outlet stream for simplification, which is not comprehensive when considering its application to industry, because many treatment units generate more than one outlet stream. For example, reverse osmosis (RO) and ultrafiltration (UF) generate permeate and reject streams simultaneously, filtration units produce purified water and backwash wastewater alternately, ion exchange units also generate deionized water and regeneration wastewater alternately. The two outlet streams of each unit mentioned above are characterized in terms of the concentration that one outlet stream is of higher purity than inlet stream, the other is of lower purity than inlet stream. And all the outlet streams are available for reuse/recycle in a water network. In this regard, the conventional single


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outlet model cannot describe those treatment units well. Thus, conceptually a double outlet model is required. Tan et al15 proposed a partitioning model for some regenerators presented in Table 1, optimizing a water network with one such regenerator, and the results indicated reduction in freshwater consumption and cost. Tan et al16 then used graphical approach to minimum flowrate of a water network, incorporating one such regenerator that was used as pretreatment. Khor et al17 proposed a linear model mainly for RO and UF, treating the permeater and rejecter as units instead of streams, and optimized the network with membrane and non-membrane regenerators. Other works18-21 also addressed such problem using similar idea. However, most previous works haven’t considered following aspects: (1)Filtration units generate purified water and backwash wastewater alternately; and ion exchange units generate purified water and regeneration wastewater alternately. The wastewater of those treatment units are usually reused in industry, thus, filtration and ion exchange should be modeled each with two outlets. For example, such wastewater is very common in steel industry, where in circulating cooling systems side-filtration units produce a lot of backwash wastewater that is commonly reused in other units; and in desalination systems ion exchange units produce much regeneration wastewater that is also usually reused. However, previous models cannot describe ion exchange units well, because there are water and contaminant load gains obtained during the operation of the units, and such characteristic was not reported before. Hence, a new double outlet model is required to describe those double outlet units. (2)Most previous works have considered only one double outlet unit in a water network, generally membrane-based units, without considering a multiple, staged treatment system of double outlet treatment units that is common and practical in industry. So in this work, that kind


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system is incorporated in the total network, followed by the superstructure specially constructed for that system. (3)Many double outlet treatment units are used either as pretreatment or distributed treatment in industry.16 For example, desalination system (i.e., UF, RO) can use freshwater to produce desalted water required by process units, and can also use wastewater to produce high quality water that can also be used by those process units. Both the two types are common in industry, but they were rarely mentioned before. Thus, the analysis and comparison of the two types are meaningful. Therefore, in this paper, a new double outlet model was proposed covering all double outlet units mentioned above. And the model was used to construct a generalized superstructure, in which multiple freshwater sources, process units, single outlet treatment units, and double outlet treatment units are connected according to the general principles of superstructure construction, in particular, freshwater is allowed to be used in treatment units. The optimization of such network is formulated as an MINLP problem that minimizes the total annual cost. And to illustrate the applicability and effectiveness of the proposed mathematical optimization model, a case study of a power plant was presented, in which the superstructure of the multiple, staged system and the analysis of the treatment units used as pretreatment units or distributed treatment units were also carried out. This paper is organized as follows. Section 2 presents problem statement, followed by a proposed double outlet treatment model in section 3. In section 4, we present the superstructure definition and its corresponding mathematical model for the water network consisting of the double outlet treatment units. And a case study is presented to validate the proposed approach in section 5. Finally, the conclusions are made in section 6.


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2. PROBLEM STATEMENT The problem addressed in this paper is presented as follows: Given is a set of freshwater sources S = {s 1, 2,...S } with known concentrations cs, j of contaminant j ∈ J that are supplied to process units or to treatment units for pretreatment. Given is a set of process units P = { p 1, 2,...P} with fixed water flowrate requirements Fpin , evaporation losses F pv _ loss , other losses F po _ loss and mass loads Lp, j . The outlet stream of each process unit is available for reuse, recycle, or discharged to the environmentwhile the inlet stream can receive the water from freshwater sources, process units and treatment units. And the in,max water to it should satisfy the water demand Fpin and upper limits on inlet concentrations cp, j .

Given a set of single outlet treatment units T = {t 1, 2,...T } with fixed removal ratios of the loss contaminant Rt , j and water loss Ft , which treat water from process units, other treatment

units or freshwater sources for pretreatment, and produce a stream of purified water as product for reuse, recycle, or discharge. Given is a set of double outlet treatment units DT = {dt 1, 2,... DT } , which can treat water from process units, other treatment units or freshwater sources for pretreatment. Such treatment unit produces both lower purity stream and higher purity stream that can be potentially reused, recycled or discharged. For each double outlet treatment unit, the recovery ratio of higher purity stream α dt and removal ratio of the contaminants Rdt , j are assumed to be fixed, while the are assumed to be in flowrate of regenerants Fdtregenerants and mass load of regenerants Lregenerants dt , j proportion to the flowrate and mass load of lower purity stream, respectively. All these data can be specified based on expert experiences or data from industry.


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The contaminant concentrations of effluent discharged to the environment should satisfy the max

discharge limit cout , j . The aim of this work is to determine optimal configuration and operation parameters of the water network, i.e., the piping connections, flowrates, contaminants concentration in the water stream, and the freshwater consumption, wastewater discharge with the aim of the minimum total annual cost of the network (total of cost of freshwater, investment and operating cost of treatment unit, cost of piping and pumping) for a water network incorporated with the double outlet treatment unit model. 3. DOUBLE OUTLET TREATMENT MODEL In terms of double outlet treatment units, previous works mainly focused on membrane-based units, i.e., reverse osmosis, ultrafiltration, few efforts have been put on filtration and ion exchange. And some features of filtration and ion exchange make them different from the units mentioned before: (1) the wastewater of filtration and ion exchange are generated periodically, different from the reject streams that membrane-based units continuously generate; (2) for ion exchange, the regeneration of resin introduces a concentrated solution of replacement ions, thus leading to water and load gains in regeneration wastewater; yet previous mentioned double outlet units15 in Table 1 were assumed to have no such gains. Considering the first feature, in fact, the periodically generated water is collected in a buffer tank before sent for use. Therefore, the wastewater is available for continuous use, which is consistent with common assumptions. The second feature indicates that earlier models are not appropriate for ion exchange. Thus, a new double outlet model was developed, aiming to describe the double outlet treatment units listed in Table 2. Note that ultrafiltration generally requires backwashing periodically to wash out the concentrate, which is different from other


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membrane-based processes mentioned earlier, thus ultrafiltration is classified as filtration unit in this paper. The schematic diagram of the model is illustrated in Figure 1. A feed stream enters the double outlet unit, then two outlet streams leave the unit available for use. One outlet stream is the purified stream, the other is of lower purity that contains pollutants originally from the inlet stream. For ion exchange, an external stream of regenerants is added to the stream of lower purity. The water flow and contaminant balances for double outlet treatment unit are given by eq 1 and eq 2.

Fdtin + Fdtregenerants = FdtH + FdtL dt ∈ DT

(1)

Fdtincdtin, j + Lregenerants = FdtH cdtH, j + FdtL cdtL , j dt ∈ DT , j ∈ J dt , j

(2)

in H Where Fdt is the inlet stream flowrate, Fdt and FdtL are the flowrates of outlet streams of

higher purity and lower purity, respectively. cdtin, j denotes the inlet contaminant concentration, cdtH, j denotes the contaminant concentration of higher purity outlet stream, cdtL , j denotes the

contaminant concentration of lower purity outlet stream. Besides, it’s worth noting that the flowrate and mass load of regenerants are apparently related to the corresponding values in the inlet water and performance parameters of the treatment unit. In this work, for simplification, Fdtregenerants and Lregenerants are supposed to be in proportion with the dt , j flowrate and contaminant load of the inlet stream, respectively, and the coefficients are obtained from expert experiences or industrial data. The expressions are given by eq 3 and eq 4.

Fdtregenerants = kdt Fdtin

dt ∈ DT

Lregenerants = ldt , j Fdtincdtin, j dt , j

(3)

dt ∈ DT , j ∈ J

(4)


8

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Where kdt and ldt , j are the corresponding coefficients. The flowrate of higher purity outlet stream can be calculated by eq 5.

FdtH = αdt Fdtin

dt ∈ DT

(5)

Another notice is that the removal ratio defined in previous works was calculated by eq 6,22 which is not applicable indeed, because in industry the removal ratio is typically defined as eq 7.23

Rdt , j =

Fdtincdtin, j − FdtH cdtH, j

Rdt , j = 1 −

dt ∈ DT , j ∈ J

Fdtincdtin, j cdtH, j cdtin, j

(6)

dt ∈ DT , j ∈ J

(7)

So the concentration expression for the outlet stream of high purity is given by eq 8.

cdtH, j = (1 − Rdt , j )cdtin, j

dt ∈ DT , j ∈ J

(8)

Stream of higher purity FdtH = α Fdtin

Feed stream

cdtH , j = (1 − Rdt , j )cdtin , j

Fdtin

DT

cdtin , j

Stream of regenerants Fdtregenerants

Stream of lower purity

cdtregenerants ,j

FdtL cdtL , j

Figure 1. Schematic diagram of the double outlet treatment unit model.


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Table 1. Regenerators mentioned in the work by Tan.15 membrane-based processes( e.g. ultrafiltration, reverse osmosis, etc) Partitioning regenerators

flotation systems(e.g. dissolved air flotation, induced air flotation, etc) gravity settling systems(e.g. coagulation, flocculation, clarification, etc)

Table 2. Double outlet treatment units. Filtration units

membrane filtration (e.g., microfiltration, ultrafiltration, etc) depth filtration (e.g., conventional downflow filtration, deepbed downflow filtration, pulsed bed filtration, etc) surface filtration (e.g., cloth-media filtration, disc filtration, etc) ion exchange (e.g., cation exchange, anion exchange, mix-bed, etc)

Ion exchange units

membrane-based processes(e.g., electrodialysis, nanofiltration, reverse osmosis, etc) flotation systems(e.g., dissolved air flotation, induced air flotation, etc)

Mentioned in previous works

gravity settling clarification, etc)

systems(e.g.,

coagulation,

flocculation,

4. MATHEMATICAL MODEL The superstructure of the problem embedding all potential configurations of interest is shown in Figure 2, in which treatment units of T, DT were all included. The mathematical model for the superstructure includes balances of flows and contaminants of all processes and streams, limits on concentrations of entering streams, certain design and structural specifications and objective function. The detailed information of the model is presented in section S1 in the Supporting Information.


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Fp ', p

Fp , p ''

Fs , p

Fpin Ft , p

P

c inp, j FdtH, p

FdtL, p

Fp , dt

Fs , p FdtL, p

Fdtin

cdtin, j

Fs

Fp ,t

c out p, j

Fp , dt Fs ,dt

Fp ,o

Fpout

DT

FdtL,t

FdtL

FdtL,o

cdtL , j

FdtH,o

Ft ,dt

Fout

FdtH

cdtH, j

H dt , p

FdtH,t

F

FdtL,t Fs ,t

H dt ,t

F

Fp ,t

Ft ,o Ft

in

ctin, j

T

Ft

out

ctout ,j

Ft , p Ft ,dt

Figure 2. The superstructure of the network 5. CASE STUDY In this section, a case study of a power plant is used to illustrate the proposed approach. In the plant, water is mainly used for generating steam, cooling and flue gas desulfurization. The schematic diagram of the current water network is shown in Figure 3. As shown, freshwater is supplied to cooling system, and that system recycles a large percent of outlet water. Part of the blowdown water of cooling system is sent to desalination system to produce desalting water, meeting the water demand and concentration limit of boiler. And the other part is treated in


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industrial wastewater treatment system (IWT). Desulfurization system (DF) also consumes some freshwater, then the wastewater is treated in the desulfurization wastewater treatment system (DFWT). 108915 Fresh Water

Cooling System

1433

55

240

62

164

Multi-media Filtration

10

Industrial Wastewater Treatment System

230 Ultrafiltration

30

115 Discharge

10

200 Desulfurization System 30

66

Reverse Osmosis

Boiler

72

Desulfurization Wastewater Treatment System

Mix-bed

10

62

30 Discharge

Figure 3. Schematic diagram of the power plant in this case. Note that the desalination system consists of four staged treatment units, i.e., multi-media filtration, ultrafiltration, reverse osmosis, mix-bed. In this case, those four units are identified as double outlet treatment units. Since few works have investigated the multiple, staged subnetwork of double outlet treatment units, a superstructure of that system was developed and presented in


12

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Figure 4. As shown, in the staged system, the purified water of each unit can be sent to the following unit in the desalination system, or other units in the network; while the wastewater of each unit is restricted to be used outside the staged system, in order to avoid accumulation of pollutants. In addition, only the first unit can use water outside the system, the other units can only consume water from previous units, because the previous units generally perform as pretreatment for the following units. As the models in section 4 cannot well describe the structural features of this system, we added the models in section S2 in the Supporting Information to illustrate aforementioned connection restrictions.

Freshwater/Wastewater

units outside the system

…

DT1

DT2

units outside the system

…

…

…

DTn

…

Figure 4. The superstructure of multiple, staged double outlet treatment system. (The dotted arrows denote the lower purity streams) Another notice is that the desalination system can either use freshwater or wastewater to produce desalted water required by boiler. And the cost of the two types are different. Hence, it’s


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necessary to compare two water networks incorporating the two different desalination types respectively, and determine the impact of using different feed water to the desalination system. So, in the following sections, we first optimize the network assuming only wastewater can be used by the desalination system. We refer to the structure as Scheme A, and compare the results with practical values. Then we optimize the network assuming the system as pretreatment system, which means in the network desalination system use freshwater to generate high quality water. We refer to the structure as Scheme B, and then we compare Scheme A and Scheme B with various freshwater prices for further analysis. 5.1. Optimization of the network of Scheme A In this case, one freshwater source, three process units (i.e., cooling system, boiler, DF), two single outlet treatment units (i.e., IWT, DFWT), and four double outlet units are included. Below are the assumptions about connection restrictions made in this case: (1) Except for cooling tower, the outlet water of other process units are restricted to be recycled; (2) Fresh water is restricted to be used in wastewater treatment units; (3) Wastewater from boiler can only be treated in IWT; (4) Wastewater from DF can only be treated in DFWT, and DFWT can only treat water from DF. Besides, total suspended solids (TSS) and Cl- are characterized as the key pollutants. For freshwater, the concentrations of Cl- and TSS are 15 and 5 ppm, respectively. And the environmental discharge limit for contaminant Cl- and TSS are 500 and 30 ppm, respectively. Data for process units, single outlet treatment units and double outlet treatment units are shown in Tables S1-S4 in the Supporting Information. Specially, the data extraction for limiting concentrations of typical processes are illustrated in section S3.2 in the Supporting Information.


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The freshwater cost is 2 RMB/m3. The operating cost coefficient and investment cost coefficient for piping are assumed to be 0.1 and 600 RMB/ m3, respectively. The exponent γ for piping is 0.6 and the fixed cost for each individual pipe is 40 RMB/pipe. The total time for operation in a year is assumed to be 8000 h. This problem was solved with BARON24 to obtain the global optimality, and the problem size and CPU time are illustrated in Table 3 using a PC (Intel® CoreTM2 Duo at 2.00 GHz with a 4.00 GB of RAM).

Table 3. Problem size and CPU time in this case study. Case study

Constraints

Continuous variables

Integer variables

CPU time (s)

Power plant

387

335

84

0.031

Note that recycling is allowed for cooling system, and the flowrate and concentration of that recycle stream were optimized simultaneously in this case. The optimal network is presented in Figure 5. As shown, less freshwater is needed, and less wastewater is discharged compared with the practical network. After optimization, the desulfurization system consumes large amounts of wastewater instead of freshwater, including the blowdown water of cooling system, the backwash wastewater of multi-media filtration and UF, in addition to the brine of RO. The wastewater of mix-bed is also reused in cooling system. Hence, all the wastewater of the desalination system is reused in process units without discharge, thus reducing the total freshwater consumption. Besides, in desalination system, only the finally produced water is used by boiler, no other purified water is used outside the desalination system, which results in reduction in water consumption of that system. Furthermore, no water from IWT is discharged, and the total treated water is reused in cooling system, thus, the freshwater


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consumption of the total network is further reduced. Therefore, in summary those optimization results show reduction in freshwater consumption and wastewater discharge, and also show that the proposed method is able to solve the practical problem of optimizing the water network in a power plant, particularly can provide all the potentials of reusing the outlets of double outlet treatment units, and then determine the optimal reuse.

108902 Fresh Water

Cooling System

1488

10 160 128

Multi-media Filtration

5

Industrial Wastewater Treatment System

123 10 30

Desulfurization System

Ultrafiltration 107 Boiler

35

Reverse Osmosis

30 Desulfurization Wastewater Treatment System

72

10

62

Mix-bed

30 Discharge

Figure 5. Optimal network of the power plant of Scheme A.


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Comparison of optimal cost with practical values is shown in Table 4. The optimal total annual cost is 3.59 × 107 RMB/year, about 10% reduction compared with practical cost. And as shown in the last column in the table, the cost reduction represents the difference of practical values and optimal values, and the results show that all items in the total annual cost illustrated in Table 4 have decreased, especially the freshwater cost and the desalination system cost that the cost reductions of the two items contribute to a great proportion of total cost reduction, which is mainly because the reductions of freshwater consumption and the feed water to desalination system.

Table 4. Comparison of optimal results with practical values.

(×106 RMB/year)

Optimized by proposed Cost reduction method (×106 RMB/year) 6 (×10 RMB/year)

Freshwater cost

25.55

23.71

1.84

Cost of double outlet treatment units

3.74

2.86

0.88

Cost of single outlet treatment units

0.98

0.42

0.56

Cost of piping and pumping 9.43

8.91

0.52

Total annual cost

35.90

3.80

Practical network

39.70

5.2. Optimization of the network of Scheme B As mentioned before, in Scheme B the desalination system is used as pretreatment system. And since the cost of the desalination system using freshwater is lower than the type using wastewater, the cost coefficients are adjusted shown in Table S5 in the Supporting Information. Besides, in order to provide a further analysis of Scheme A and Scheme B, their optimization results are compared with different freshwater prices.


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In order to compare the optimal cost of the two schemes clearly, here we define ∆TAC as the difference of TACA and TACB ( ∆TAC=TACA − TACB ), where TAC denotes the total annual cost, and the footnotes of A and B represent the Scheme A and Scheme B respectively. The results are presented in Figure 6. We change the freshwater price from 0.1 RMB/t to 15 RMB/t, then ∆TAC changes from positive to negative. As shown, when the freshwater price is lower than about 10 RMB/t, TACA is larger than TACB , which means it’s better to place the double outlet system as pretreatment when the freshwater price is lower than a certain value, instead, when the freshwater price keeps increasing, it’s better for the desalination system to use wastewater. The reason for that is when the freshwater price is high, it’s better for the desalination system to use wastewater to produce high quality water, which can reduce the total freshwater consumption, thus the freshwater cost is lower and then the total annual cost maybe lower than the scheme using freshwater. Instead, when the freshwater price is low, in both two networks, compared with the treated water from treatment units, freshwater is preferred to be used in all units, and that the desalination system may be used to produce purified water only sent to boiler in both networks, hence, the cost of the desalination system using freshwater maybe lower than the other type, thus, in summary, it’s possible for the total cost of Scheme B to be lower than cost of Scheme A.


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1.6 1.4 1.2

6

∆ TAC (×10 RMB/year)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0

TACA> TACB

0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6

2

4

6

8

10

12

14

16

TACA< TACB 3

Freshwater price (RMB/m ) Figure 6. The difference of optimal total annual cost of Scheme A and Scheme B. 6. CONCLUSION In this paper, a new double outlet treatment unit model was developed for the treatment units having two outlet streams, including the units mentioned in previous works and filtration, ion exchange that were rarely investigated before. Then, a superstructure-based mathematical model for the optimization of a water network including several single and double outlet treatment units was proposed, assuming that both the outlet streams of the double outlet treatment unit can be connected with other units in the network and freshwater can be treated in treatment units for further decontamination. The proposed method was demonstrated using an example of an industrial power plant, in which a multiple, staged system of double outlet units was included, and the superstructure of that system was specially developed, besides, further investigation of


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the multiple, staged system performing as pretreatment or distributed treatment was also carried out. The results show that all wastewater of double outlet treatment units, including filtration and ion exchange, are reused to lower freshwater consumption and wastewater discharge. And the comparison of the two types of multiple, staged systems indicate that it’s better for the system to use wastewater other than freshwater to produce high quality water when the freshwater price is high. All results have shown applicability and effectiveness of the proposed method.

Supporting Information The Supporting Information is available free of charge via the Internet at http://pubs.acs.org/. Detailed information of the mathematical model; the models of connection restrictions on multiple staged system; Table S1, water-using data in the case study; Table S2, single outlet treatment unit data in the case study; Table S3, double outlet treatment unit data in the case study. Table S4, cost data of treatment units in the case study; illustration of data extraction for limiting concentration; Table S5, adjusted cost data of double outlet treatment units performing as pretreatment. AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected]

ORCID Kaili Zhang: 0000-0001-7619-3046

Notes


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The authors declare no competing financial interest. ACKNOWLEDGEMENTS We would be grateful for the financial support from the National Natural Science Foundation of China (Grant No. 2156112001) and Major Science and Technology Program for Water Pollution Control and Treatment of China (Grant No. 2015ZX07202-013). NOTES

Continuous variables

Fs , p

water flowrate of stream from freshwater source s to process unit p

Fs ,t water flowrate of stream from freshwater source s to single outlet treatment unit t

Fs,dt water flowrate of stream from freshwater source s to double outlet treatment unit dt

Fp , p ' water flowrate of stream from process unit p to process unit p’

Fp ,t water flowrate of stream from process unit p to single outlet treatment unit t

Fp,dt water flowrate of stream from process unit p to double outlet treatment unit dt

Fp,o water flowrate of stream from process unit p to discharge

Ft , p

water flowrate of stream from single outlet treatment unit t to process unit p

Ft ,t ' water flowrate of stream from single outlet treatment unit t to single outlet treatment unit t’


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Ft ,dt water flowrate of stream from single outlet treatment unit t to double outlet treatment unit dt

Ft ,o water flowrate of stream from single outlet treatment unit t to discharge

FdtH, p water flowrate of stream from higher purity double outlet treatment unit dt to process unit p

FdtH,t water flowrate of stream from higher purity outlet of double outlet treatment unit dt to

single outlet treatment unit t FdtH,dt ' water flowrate of stream from higher purity outlet of double outlet treatment unit dt to

double outlet treatment unit dt’ FdtH,o water flowrate of stream from higher purity outlet of double outlet treatment unit dt to

discharge FdtL, p water flowrate of stream from lower purity outlet of double outlet treatment unit dt to

process unit p FdtL,t water flowrate of stream from lower purity outlet of double outlet treatment unit dt to single

outlet treatment unit t FdtL,dt ' water flowrate of stream from lower purity outlet of double outlet treatment unit dt to

double outlet treatment unit dt’ FdtL,o water flowrate of stream from lower purity outlet of double outlet treatment unit dt to

discharge


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Fs water flowrate of freshwater source s

cinp, j concentration of inlet stream of the process unit p

cout p , j concentration of outlet stream of the process unit p

Ft in water flowrate of inlet stream of the single outlet treatment unit t

Ft out water flowrate of outlet stream of the single outlet treatment unit t

ctin, j concentration of inlet stream of the single outlet treatment unit t

ctout , j concentration of outlet stream of the single outlet treatment unit t

Fdtin water flowrate of inlet stream of the double outlet treatment unit dt

FdtL water flowrate of lower purity outlet stream of the double outlet treatment unit dt

FdtH water flowrate of higher purity outlet stream of the double outlet treatment unit dt

cdtin, j concentration of inlet stream of the double outlet treatment unit dt

cdtL , j concentration of lower purity outlet stream of the double outlet treatment unit dt

cdtH, j concentration of higher purity outlet stream of the double outlet treatment unit dt

Fout water flowrate of discharge

cout , j concentration of stream of discharge


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Superscripts

in inlet stream

out outlet stream max maximal L lower purity outlet stream H higher purity outlet stream REFERENCES (1)

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(23) an AECOM Company, M.; Eddy, I.; Asano, T.; Burton, F., Water Reuse. McGraw-Hill Publishing: 2007. (24) Sahinidis, N. V., BARON: A general purpose global optimization software package. Journal of Global Optimization 1996, 8 (2), 201-205.


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Figure 7. For Table of Contents Only


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Schematic diagram of the double outlet treatment unit model 73x46mm (600 x 600 DPI)



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The superstructure of the network 148x139mm (300 x 300 DPI)


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Schematic diagram of the power plant in this case 165x158mm (300 x 300 DPI)



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The superstructure of multiple, staged double outlet treatment system. (The dotted arrows denote the lower purity streams) 92x60mm (600 x 600 DPI)


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Optimal network of the power plant of Scheme A 171x193mm (300 x 300 DPI)



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The difference of optimal total annual cost of Scheme A and Scheme B 83x58mm (300 x 300 DPI)


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61x35mm (300 x 300 DPI)


Optimization of the Water Network with Single and Double Outlet

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