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A holistic approach for design of Cost-Optimal Water Networks Sehnaz Sujak a, b, Zainatul Bahiyah Handani c, Sharifah Raﬁdah Wan Alwi a, b, *, Zainuddin Abdul Manan a, b, Haslenda Hashim a, b, Lim Jeng Shiun a, b a

Process Systems Engineering Centre (PROSPECT), Research Institute for Sustainable Environment, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia b Faculty of Chemical and Energy Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia c Faculty of Chemical and Natural Resources Engineering, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Kuantan, Pahang, Malaysia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 March 2016 Received in revised form 22 June 2016 Accepted 28 June 2016 Available online xxx

This work presents a holistic approach for design of Cost-Optimal Water Networks (CWN) that considers the economics while exploring all water minimisation options in line with the water management hierarchy (WMH). Two stages are involved in analysing the model i.e., the freshwater saving mode (FWSmode) and the economic mode (E-mode). The ﬁrst stage applied the mixed integer linear program (MILP) formulation that yielded some initial values for the second stage. In the second stage, the model was formulated as a mixed integer nonlinear program (MINLP) that was used to optimise an existing water systems design. The novelty of the model lies in the simultaneous considerations of all levels of water management hierarchy (i.e. elimination, reduction, reuse, outsourcing and regeneration) and cost constraints in selecting the best water minimisation schemes that resulted in the maximum net annual savings at a desired payback period. The model is applicable for systems involving multiple contaminants, and is capable of predicting which water demand should be eliminated or reduced; how much external source is needed; which wastewater source should be reused/recycled, regenerated or discharged; and ﬁnally specify the minimum water network conﬁguration for maximising the net annual savings at a desired payback period. The model has been successfully applied on case studies involving a building (Sultan Ismail Mosque, UTM) and an industrial process plant (a chlor-alkali plant). © 2016 Elsevier Ltd. All rights reserved.

Keywords: Holistic water minimisation Mathematical modeling Optimal water network Water management hierarchy Multiple contaminants

1. Introduction Rapid economic development and population growth have contributed to rising water consumption globally. Wang et al. (2015) reported that China, which is the world's largest water consumer, consumes about 24.03% from total water demand in China, resulting in an estimated 23.75 billion t of wastewater discharge in 2010. Varbanov (2014) relates the increasing demand of water supply and energy causes the scarcity of both resources. Widespread awareness and concern over the security and sustainability of water supply have driven industries to explore various cost-effective strategies for efﬁcient water usage beyond the end-of-pipe treatment of wastewater. Freshwater demand in industry and the

* Corresponding author. Process Systems Engineering Centre (PROSPECT), Research Institute for Sustainable Environment, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia. E-mail address: [email protected] (S.R. Wan Alwi).

efﬂuent generated can be reduced via the adoption of water minimisation techniques, leading to reduced cost associated to water procurement and efﬂuent treatment. Extensive research effort has been focused on minimising freshwater and the cost associated in designing optimal water networks. Insight-based graphical methodology as well as mathematical modeling have been utilised in the design of optimal water networks to achieve the minimum total cost. Foo (2009) reviewed the conceptual approaches for water network synthesis, with the main aim to minimise freshwater cost while meeting the environmental discharge limit. The network synthesis between waterusing and water-regeneration operation are optimised using certain objectives and satisfy constraints especially on water ﬂow rates and impurity load balances. The challenges highlighted in the study include the lack of water network synthesis development for retroﬁt cases as well as the issue of establishing water network capital costs target for ﬁxed ﬂowrate problem (water ﬂowrate minimisation). Another water system design which incorporate water-using and treatment system also reviewed by Jezowski

http://dx.doi.org/10.1016/j.jclepro.2016.06.182 0959-6526/© 2016 Elsevier Ltd. All rights reserved.

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(2010). Methodologies for water system targeting and design based on mathematical programming as well as on the conceptual approach for network synthesis have been performed with the typical goal of minimising the total annual cost. Klemes (2012) employed the fundamental understanding of water and wastewater minimisation by reviewing both typical Pinch Analysis (conceptual approach) and mathematical programming techniques. The study indicates that the water network economic criteria such as the freshwater cost, piping and pumping should be optimised together to develop a realistic water network. A better water network design for more complex problem can be solved using mathematical programming techniques. A recent work on water minimisation is the development of optimal water network by Ying and Jintao (2016). The authors developed the regeneration water network structure and provide a step by step guide in developing regeneration-reuse and regeneration-recycling as an insight for the next design of waterusing network using mathematical modeling technique. The work provides the minimum freshwater ﬂowrate as well as the minimum recycle water ﬂowrate. Several other researches on water network synthesis that are associated with total cost minimisation have been developed. An example is the model developed by Alva-Argaez et al. (1998) who used the total cost as an objective function for the optimal design of industrial water system. Alva-Argaez (1999) then formulated the water system design problem as a Mixed Integer Non-Linear Programming (MINLP) model which was then decomposed into Mixed Integer Linear Programming (MILP) and Non-Linear Programming (NLP) for solving the mathematical formulation. The authors targeted the minimum total annual investment as well as the minimum operating cost for the water-using network that considers water reuse. An optimum solution consolidating all the functional constraints was the main purpose of their model. However, their model was not applicable for retroﬁt scenarios as there was no details in their development of water network system even though the water reuse, regeneration-reuse and regeneration recycling were considered. A complex trade-off which included capital and operating cost was considered in the work by Gunaratnam et al. (2005) in solving total water system problem. The work is able to simultaneously design water-using system and efﬂuent treatment considering control and safety, geographical layout as well as minimum or maximum allowable ﬂowrates. In their work of optimisation of industrial water network, Faria et al. (2009) used mathematical modeling technique to focus on freshwater minimisation as their primary objective and further looked into the operating cost optimisation as their secondary objective. Using an NLP to describe the model, all possible forms of water and wastewater minimisation technique such as reuse with and without regeneration, as well as water recycling, were considered for the network. The initial analysis of this study successfully presented the minimum water consumption within the process although it does not result in the lowest operating cost for the network. The study requires augmenting procedures such as the network operability, risk analysis and layout analysis to improve the developed model and improve the water network cost by formulating more equations that are speciﬁc to regeneration. Handani et al. (2010) has modelled the Minimum Water Network and considered all water minimisation options in WMH that resulted in reduction of freshwater usage using a mathematical programming technique. However, the work has not included economic analysis in the development of the model. A mathematical modeling technique was used by Lim et al. (2007) to maximise water network system proﬁtability using NLP model. They applied the incremental cost of piping, maintenance

and repair, pipe decommissioning and freshwater consumption into a conventional water network to rearrange the network into a cost-effective water network system. Another work based on proﬁtability for water network systems was developed by Faria and Bagajewicz (2009). They performed mathematical optimisation for grassroots and retroﬁt cases involving single and multiple contaminants and considered the regeneration process. The net present value and return of investment were maximised. Even though cost constraints have been successfully considered in developing a proﬁtable water network by other researchers, Poplewski et al. (2010) however, faced some issues in estimating the piping investment from a general linear formulation for the industrial practice. The developed basic model was found to eliminate one of the attractive networks which had minimised the cost or freshwater, due to some structural issues. Kim (2012) later included freshwater cost, treatment cost as well as piping cost in the development of their total water system design. The work highlighted an improved water network which included water reuse within the operation. A graphical method and mathematical optimisation techniques were used for the system-wide analysis in which the relevant economic trade-offs such as freshwater cost, treatment cost, wastewater discharge and piping cost were considered. Novak et al. (2014) discussed the inﬂuence of piping cost in their investment. Their work included the pipeline connections between water-using operations and treatment units. However, the solution obtained was not economically efﬁcient when freshwater cost is minimised. A water conservation network retroﬁt study was done by SoteloPichardo et al. (2011), favouring schemes such as water reuse, recycle and regeneration using mathematical programming method. The problem was modelled using MINLP that considers minimisation of total annual cost as their objective function. The formulation includes freshwater cost, existing treatment unit expansion and treatment unit addition. The results revealed the option of upgrading the existing treatment units rather than installing new treatment units, leading to the minimum total annual cost. Based on the retroﬁtted network, the freshwater consumption was greatly reduced when water sources were reused and recycled within the network. The model can be modiﬁed to suit different objectives functions, the proper piping and pumping costs can be easily determined and other constraints such as safety and operability can be considered. Ahmetovi c et al. (2014) in their work considered the total annual cost minimisation in their design of heat-integrated water-using and wastewater treatment network (HWTN). The network problem considered complex trade-offs involving the capital and operating costs as well as other practical constraints such as freshwater usage, hot and cold utilities consumption and wastewater treatment units. The network was then formulated as a non-convex mixed integer non-linear programming. The approach is capable of providing a simultaneous solution strategy such as the appropriate trade-offs between freshwater and utilities consumption as well as investment for heat exchangers and wastewater treatment units. Bozkurt et al. (2015) in their preliminary design of municipal wastewater treatment plants, presented a MINLP model which described the optimisation based on mathematical programming to identify optimal process technologies for retroﬁt design of wastewater treatment plants. The model attempted to minimise the total annual cost which was deﬁned as the summation of operational (OPEX) and capital cost expenses (CAPEX). Ouyang et al. (2015) developed a hierarchy framework to select the foremost technology for wastewater treatment system where the prime target was to obtain the maximum proﬁts. It involved the consideration of capital cost, maintenance cost and other indices. A further attention on the contradictory result between the

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environmental and economic criteria need to be taken into account is highlighted. In a decision guide by Spiller et al. (2015) for ﬂexible water and wastewater network designs, they reviewed the ﬂexible design alternatives which included robust design, phase design, modular design, modular platform design and design of manufacturing. In general, all the designs featured the element of robustness and oversizing. They took the example of pipes in a water system that are often designed with redundant capacity to procure future extension and resulted in increased development cost. Chaturvedi et al. (2016) analysed the optimum schedule that leads to reduction in a batch water allocation network's (WAN) operating cost. Their proposed model is demonstrated using a batch plant that includes water minimisation aspect. A minimum operating cost was obtained for multiple water resources where the authors discovered that the same schedule could lead to single water source minimum operating cost. In such a case, scheduling is vital in resource conservation for batch processes. The aforementioned review shows that numerous works have been done to achieve cost-effective minimum water utilisation networks. Although the total cost has typically been assigned as the objective function, however, most works were largely limited to water reuse and regeneration. The economic evaluation with consideration of process changes became more attractive as it could provide opportunities for further cost-effective water and wastewater reductions during the design of optimal water utilisation networks. As proposed by Wan Alwi and Manan (2008) in their work, the water management steps could be prioritised to obtain cost-effective pre-design water network. This work is an extension of the method developed by Wan Alwi et al. (2008) who proposed a cost-effective minimum water network (CEMWN) design for grassroots and retroﬁt cases involving single contaminant problems. The authors suggested a hierarchical procedure where each level of water management hierarchy (WMH) was explored to obtain the minimum water targets. The method considered elimination, reduction, reuse/ outsourcing and regeneration in reducing freshwater usage. The authors also introduced a cost screening technique known as the Systematic Hierarchical Approach for Resilient Process Screening Approach (SHARPS) to attain cost effective minimum water networks for urban and industrial sectors. The SHARPS technique provides clear quantitative insights to screen various water management options. By applying this methodology in accordance with the water management hierarchy, it is possible to identify which schemes should be partially applied or eliminated to satisfy a desired payback period, thereby allowing the designer to estimate maximum potential annual savings prior to design. Some processes can be replaced if the total payback period does not agree with the desired payback period set by a plant owner. This work extends the concept of cost effective minimum water network using mathematical modeling, thereby allowing designers to solve multiple contaminants problem of increased dimensionality, involving more complex industrial water networks while simultaneously considering aspects of economy. The core of the holistic approach is the ability of the method to simultaneously consider all water minimisation options to reduce fresh water usage through elimination, reduction, reuse/outsourcing and regeneration. This work presents a holistic approach for design of Cost-Optimal Water Networks (CWN). CWN also able to generate minimum water targets and design an optimal water network simultaneously. Water integration in industry is an effective process integration strategy that provides important long-term contribution towards solving the current global climate change issues (Varbanov, 2014). This paper extends the MILP model developed by Handani et al. (2010) by considering the economics factor in the water network design while exploring all water minimisation options which are in

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line with the water management hierarchy (WMH). It consists of two stages which include the freshwater savings mode (FWS-Mode) and economic mode (E-Mode). The FWS-Mode was solved to provide the initial values for the MINLP problem in the second stage. The development of E-Mode in the second stage aims to maximise the net annual savings of the water network while achieving the minimum possible fresh water and wastewater targets and satisfying the desired payback period for retroﬁt design. 2. Problem statement The problem addressed in this paper can be stated as follows: Given a water network system that includes a set of water sources, i2I with known ﬂowrates (Si) and concentration (Csi,k) of contaminant k2K that could be reused/recycle; Within the same network there are a set of water demand j, j2J with known ﬁxed ﬂowrates (Dj) and allowable inlet concentration (Cdj,k) of contaminant k2K; By considering the elimination and reduction at Dj, adjusted water demand ﬂowrate, Bj is obtained. The task of the model is to determine the best water minimisation scheme that considers all water minimisation options using mathematical programming approach to achieve maximum net annual savings for an economical optimal and holistic water network which would correspond to a desired payback period for a retroﬁt design. The key variables to be determined from this model include the following:

Freshwater ﬂowrate to water demand, Fwj; Water ﬂowrate from source i to regeneration unit r, Fi,r; Water ﬂowrate from regeneration unit r to demand j, Fr,j; The outsource ﬂowrate to water demand, Fosos,j; Flowrate of reduction option re for demand j, Daj,re; Capital investment for external water sources unit, CostU; Capital investment for regeneration unit, CRegU; Cost of elimination unit e for demand j, CostUEj,e; Cost of reduction unit re for demand j, CostURej,re; and Net annual savings, NAS.

3. Assumptions and limitations i. All contaminants concentrations for each demand and sources are ﬁxed to their maximum values; ii. The ﬂowrates of all water source and water sinks are ﬁxed; iii. No contaminant limits have been considered for the efﬂuent discharge; iv. The water system is assumed to be operating continuously; v. No temperature effects are considered; vi. The economic evaluations are based on current price of freshwater, piping, pump and electricity.

4. Methodology This section presents the methodology for the development of cost-optimal water network (CWN) design that consists of four main steps. The ﬁrst step in the development of CWN involves derivation of water ﬂowrate limitation and contaminant data from case studies. The superstructure framework which consists a number of feasible conﬁgurations of water networks are presented in the second step. The mathematical formulation for the development of cost-optimal water network comprises of freshwater

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savings mode (FWS-mode) and economic mode (E-mode) are performed in the third step. The network was then coded into a commercial mathematical optimisation software package GAMS. In the fourth step, sensitivity analysis for the developed network is carried out. 4.1. Limiting data collection and extraction The data required in minimum water targeting includes the limiting ﬂowrate proﬁle from available for water sources and water demands, as well as contaminants data speciﬁcations. The limiting ﬂowrate data can be obtained from the plant historical records and real-time online monitoring available from the plant's distributed control system (DCS). In the case that the ﬂowrate and contaminant data are not available from the plant online monitoring system, manual measurements were performed. This is typically the case especially for smaller streams or non-process streams. 4.2. Superstructure representation The superstructure representation for the CWN development which considers water-using system has been suggested by Handani et al. (2010). Fig. 1 illustrates the superstructure which considers the WMH options in obtaining the adjusted demand ﬂowrate, Bj. Fig. 2 illustrates the general superstructure that incorporates the outsourcing and regeneration options. The main features of the superstructures representation are as follows: (i) Each freshwater stream, FWj, outsourced resources, OS, reused/recycled water, or regenerated water from regeneration unit, RU, can be supplied to water demand, Bj, that has been adjusted to consider options for elimination, Daj,e and reduction, Daj,re. or Daj,o denoted as the original water demand; (ii) The generated wastewater at each water source, Ai, may be released directly for end-of-pipe treatment, WWi; (iii) The generated wastewater at each water source, Ai, may also be partially treated at regeneration unit, RU, or reused at same or other processes. (iv) This superstructure permits all possible network conﬁgurations to achieve the minimum water utilisation that considers the water management hierarchy.

4.3. Mathematical formulation

further reduce the freshwater consumption and wastewater generation after implementation of maximum water recovery (MWR) strategies, process changes are then applied to the water sources and demands ﬂowrates and concentrations which ultimately lead to MWN benchmark. All possible techniques in the WMH can be used to obtain minimum water targets. It is important to note that the application of process changes shall result in new water target at this stage. The MILP solution obtained in the ﬁrst stage will be used and loaded as initial points to solve MINLP problem in the second stage. The detailed development of MWR and MWN targets strategies can be found in Handani et al. (2011) and Handani et al. (2010). 4.3.2. Stage 2: economic mode (E-mode) The objective of this stage is to obtain the maximum net annual savings while the network achieved the minimum possible freshwater and wastewater targets for the water network system at a desired payback period set by the user. The net annual savings is measured as the difference between the base-case water operating cost, from the water operating cost after employing all possible water minimisation schemes. The objective function includes the operating cost savings in fresh water demand, wastewater generation, chemicals used by water system and electricity required for pumping activities. The optimisation in this stage utilised the water networks obtained during the ﬁrst stage as initial points. Objective Function. The objective function is to maximise the net annual savings (NAS), which is expressed as:

P

3 FWjinitial FWj CostFW 7 6 j 7 6 P P initial 7 6 Fi;r þ Fi;r CostChemReg 7 6 7 6 7 6 P i r 6þ initial WWi WWi CostElec*POPump 7 7 6 7 6 i 7 6 P 7 6 initial þ WWi WWi CostWW 7 6 7 6 i 7 6 P initial 7 6 þ FW CostElec*POPump FW 7*AOT j j Max NAS ¼ 6 7 6 j 7 6 P P 6 þ initial Fi;j Fi;j CostElec*POPump 7 7 6 7 6 7 6 Pi j 7 6 initial Fosos;j Fosos;j CostElec*POPump 7 6þ 7 6 j 7 6 P P initial 7 6 7 6 þ F CostElec*POPump F i;r i;r 7 6 r i 7 6 P P initial 5 4 þ Fr;j Fr;j CostElec*POPump 2

r

4.3.1. Stage 1: freshwater savings mode (FWS-Mode) The objective of Freshwater Savings Mode (FWS-mode) is to minimise freshwater target and wastewater generation. As to

j

(1) Freshwater savings and wastewater generation are presented in the ﬁrst part of the equation. FWj and WWi presented the ﬂowrate of

Elimination, e=E

Dj

Reduction, re = RE

Bj

Original, o=1 Fig. 1. Water network superstructure considering the source elimination and reduction options in obtaining the adjusted demand ﬂowrate, Bj.

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Ai,i=1

Ai,

Ai,i=I

WWi,i=1

WWi

WWi,i=I

Demand Balance FWj, j=1 Bj, j=1 FWj OS

Bj, FWj, j=J Bj, j=J

RU Regeneration Balance Source Balance Fig. 2. Water network superstructure that incorporates outsourcing and regeneration for maximum water recovery.

freshwater and wastewater while the cost of freshwater and wastewater are represented by CostFwj and CostWWi expression. The chemical savings, termed as CostChemReg is used for the regeneration system chemicals cost. The pumping cost is included in the next term where CostElec is deﬁned as the electrical cost while POPump is represented as the power of pump used in the pumping system. All operating costs are proportional to the total ﬂow of freshwater, FWj, wastewater, WWi, external water sources, Fosos,j, wastewater to regeneration unit, Fi,r and regenerated water from regeneration unit, Fr,j. Maximisation of the objective function is subject to constraints given by Equations (2)e(23).

X

Daj;e þ

X

e

sj;re Dj þ

re

X

X X Daj;e yd Xj;e ; Daj;re yd Xj;re ; Daj;o yd Xj;o

e

re

o

(2) X e

Daj;e þ

X

Daj;re þ

re

X

D j ¼ Bj

cj2J

(3)

o

Where Daj,o is equal to demand j, Dj. 4.3.2.1.2. Option for reduction constraint. A reduction to a certain percentage, sj,re for demand ﬂowrate Daj,re is obtained in the case where reduction option is choose.

Daj;re ¼ sj;re Dj

j2J

cre2RE

(4)

A linear constraints can be obtain when Daj,re in equation (4) is replace in equation (3). The equation is rewritten as below:

Dj ¼ Bj

cj2J

(3')

o

4.3.2.1.3. Water demand balance. The total ﬂowrate of freshwater streams, FWj, outsourced resources, Fosos,j, reused/recycled water, Fi,j, and regenerated water from regeneration unit, Fr,j, is equal to the adjusted water demand ﬂowrate, Bj, where the water balance for each demand can be expressed (5):

FWj þ

X

Fi;j þ

X

Fosos;j þ

X

os

i

4.3.2.1. Constraints 4.3.2.1.1. Adjusted demand constraint. The selection of elimination, Daj,e, reduction option, Daj,re as well as original ﬂowrate of water demand, Dj, resulted in adjusted demand ﬂowrate, Bj. A parameter, yd with a very large value is calculated with the selection of elimination and reduction levels which are denoted by the binary variables, Xj,e and Xj,re to determine each of the elimination, reduction and original demand ﬂowrate.

X

Fr;j ¼ Bj

cj2J

(5)

r

4.3.2.1.4. Water source balance. The water balance for source i can be expressed by equation (6) where water source, Ai, may be discharged straight as efﬂuent, WWi, reuse/recycle to demand Fi,j, or sent to regeneration unit, Fi,r.

WWi þ

X

Fi;j þ

X

Fi;r ¼ Ai

ci2I

(6)

r

j

4.3.2.1.5. Contaminant load at water demand. There are few sources that contribute to contaminant mass load at adjusted demand j, Bj Cdmax . The sources includes the freshwater, FWjCwk, j;k reused/recycle water, Fi;j Csmax , other resources, Fosos,jCosos,k or/and i;k regenerated water, Fr,jCror,k . All contaminant load must be less or equal to contaminant load for demand j. The centralized wastewater treatment concept is used for the regeneration units where the performance is measured by the contaminant removal ration, RRr,k.

FWj Cwk þ

X

i Bj Cdmax j;k

Fi;j Csmax i;k þ

X os

cj2J ck2K

Fosos;j þ

X

Fr;j Cror;k

r

(7)

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S. Sujak et al. / Journal of Cleaner Production xxx (2016) 1e14

FWj Cwk þ

X

Fi;j Csmax i;k þ

X

i

Fosos;j Cosos;k þ

os

X

Fr;j 1RRr;k Crir;k

r

Bj Cdmax j;k cj2J ck2K

4.3.2.1.13. Regeneration unit capital investment constraint. The total wastewater ﬂowrate entering the regeneration unit devoted by Fi,r is part of the capital investment for regeneration unit which includes pipes and pumps cost are presented in Eq. (16).

(8) 4.3.2.1.6. Regeneration unit balance. The demand for regeneration water, Fr,j determines the amount of wastewater to be regenerated in the regeneration unit, Fi,r. Equation (9) shows the total outlet ﬂowrate for regeneration unit equal to total inlet ﬂowrate.

X

X

Fi;r ¼

i

Fr;j

cr2R

(9)

j

4.3.2.1.7. External water source constraint. Equation (10) represents the external water source ﬂowrate to demand, Fosos,j, where it must be less than or equal to the maximum design limit, Fosmax os

X

Fosos;j

Fosmax os

cos2OS

4.3.2.1.8. Water minimisation schemes selection. The binary variables, Xj,e, Xj,re and Xj,o are introduced in this selection of water minimisation schemes where only one schemes can be chosen at a time. The binary variables represent the elimination, reduction and original operation for water minimisation schemes.

Xj;e þ

e

X

Xj;re þ

re

X

Xj;o ¼ 1

cj2J

o

cj2J ci2I

ci2I

(12)

(13)

4.3.2.1.11. Non-negativity constraints. Variables such as freshwater supply, wastewater generation, water ﬂowrate for reuse/ recycle, water source adjusted ﬂowrate, water demand adjusted ﬂowrate as well as water reduction ﬂowrate has positive values which is non-zero value.

FWj ; WWi ; Fi;j ; Fj;r ; Ai ; Bj ; Daj;re 0

(14)

4.3.2.1.12. External water sources unit capital investment constraint. The maximum ﬂowrate of external water sources, Fosmax is part of the capital investment for outsourcing unit funcos tion which includes pipes and pumps cost are presented in Eq. (15)

X A b CostOsUos Fosmax P þ CostPipe Fos os os os

þ CostPump

i

Fi;r FRegA

!b P þ CostPipe

r

(16) The sixth-tenth factor, b is used for calculating the reuse unit, regeneration unit and for external water sources equipment cost estimation. 4.3.2.1.14. Reuse system capital investment constraint. There are only cost of pipes and pumps are considered for the water reused and recycled capital investment.

CReuse ¼ CostPipe þ CostPump

(17)

4.3.2.1.15. Elimination unit total capital investment constraint. The elimination unit total capital investment (CElimU) is given in Eq. (19).

XX j

CostUEj;e εj yd X1j;e

(15)

(18)

e

XX j

CostUEj;e εj

(19)

e

The above equations represent the capital cost avoidance due to elimination of freshwater unit, where CostUEj,e is cost of freshwater elimination unit e for demand j; εj is number of equipment for demand j; X1j,e is binary variable that indicates the selection of eth elimination option for jth demand, multiply with a large number, yd. 4.3.2.1.16. Reduction unit total capital investment constraint. The freshwater reduction unit total capital investment (CRedU) is given in Eq. (21).

XX j

CostUREj;re εj yd X2j;re

(20)

e

CRedU ¼

XX j

COstU ¼

XX

þ CostPump

(11)

4.3.2.1.10. Non-mass-transfer based constraint. Should the stream exist for Non-mass transfer based operations, the water source adjusted ﬂowrate, Ai, is equal to the ﬂowrate of water source, Si, prior to the WMH options implementation.

Ai ¼ Si

CostRegUrA

r

CElimU ¼

4.3.2.1.9. Mass-transfer based constraint. In the case for masstransfer based operation, the water demand adjusted ﬂowrate, Bj, is equal to water source adjusted ﬂowrate, Ai.

Bj ¼ Ai

X

(10)

j

X

CRegU ¼

CostURej;re εj

(21)

re

The above equations represent the capital cost avoidance due to reduction of freshwater unit, where CostURej,re is cost of reduction unit e for demandj; εj is number of equipment for demandj; X2j,re is binary variable that indicates the selection of reth reduction options for jth demand multiply with a large number, yd. 4.3.2.1.17. Net capital investment constraints. The net capital investment includes the external water sources unit capital investment, regeneration unit capital investment, reuse water capital investment, elimination unit capital investment and reduction unit capital investment.

NCI ¼ COstU þ CRegU þ CReuse þ CElimU þ CRedU

(22)

4.3.2.1.18. Payback period constraints. The payback limit for investment is used as a guideline for the total payback period, where it must be set to equal or less than the payback period limit. The payback period limit is calculated using Eq. (23). g is the investment payback limit which is set by the plant owner. This constraint is

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applicable only if the obtained payback period exceeded the payback period set by the plant owner. Any cost increment leads to the determination of all possible cost required for the water network system.

PP ¼

Net Capital InvestmentðNCIÞ g Net Annual SavingðNASÞ

7

the initial points that are needed to solve the MINLP problem that will lead to the optimal solution during the second stage. The minimum freshwater and wastewater ﬂowrates were found to be 18.5 t/h and 0 t/h. The water distributions as well as water data for the Chlor-Alkali plant can be referred to Handani et al. (2010).

(23)

4.4. Sensitivity analysis Sensitivity analysis was performed to study the variation in model parameters by estimating the change in the optimal solution. Sensitivity analysis is a tool that may be used to study the behavior of a model and to ascertain how much the outputs of a given model depend on each or some of the input parameters. It is necessary to assess the sensitivity of the optimum ﬂow sheet to model parameters that may be subject to variation and uncertainty. In this work, the impact of fresh water price is discussed. A ﬂowchart in Fig. 3 shows the decision making process to obtain the CWN. 5. CWN application Analysis of the FWS-mode and E-mode of the cost-optimal water networks (CWN) were performed via two case studies involving a manufacturing plant and an urban building. Both FWSmode and E-mode were coded into GAMS. Handani et al. (2010) used GAMS/CPLEX solver to achieve optimal solutions for the FWS-mode (Stage 1) where the initial point obtained from Stage 1 was formulated as an MILP problem. In the E-mode (Stage 2), a general MINLP is used to reﬁne the solution obtained in Stage 1 using GAMS/BARON. The sensitivity analysis was carried out using different freshwater cost and this analysis determine how sensitive the ﬁnal solution is to uncertainty in the model parameter.

5.1.2. Economic mode (E-mode): stage 2 The maximum net annual savings for retroﬁt case was determined at this stage using the results from the ﬁrst stage. The economic data used for the operating cost calculation and capital cost for individual equipment are given in Tables 1 and 2 while Table 3 presents the optimal results and selection of WMH options for the Chlor-alkali plant. Initially, the model yielded the total payback period for retroﬁt design of 1.87 y with USD 105,383/y net annual savings. The minimum freshwater and wastewater ﬂowrates of this water system are 18.51 t/h and 0 t/h. This corresponded to 35.8% freshwater and 100% wastewater savings. In the case when the plant owner set the maximum payback period limit at 1.25 y (15 months), the net annual savings was reduced to USD 33,589/y with the minimum amount of freshwater consumption and wastewater generation increased to 25.42 t/h and 6.83 t/h. This gave reductions of 11.8% of freshwater and 27.6% wastewater for retroﬁt case. The optimiser chose to reduce ﬂowrates of D6 and D8 due to the payback period constraints since the reduction at both demands D6 and D8 affected the reduction in freshwater consumption that corresponded to the maximum net annual savings, without any need for capital investment. The optimiser also favoured to reduce D14 because it also gave reduction in freshwater usage and is cheaper in terms of capital investment as compared to elimination of freshwater usage at D10. In contrast, the total regenerated water ﬂowrate was signiﬁcantly deceased when payback period limit was set to 15 months. This is because, the regeneration unit is the most expensive equipment needed among all other process changes options. In this study, the impact of fresh water price based on baseline payback period limit is discussed. Due to the fact that the demand

5.1. Case study 1: chlor-alkali plant 5.1.1. Freshwater savings mode (FWS-mode): stage 1 The objective of Freshwater Savings Mode (FWS-mode) is to minimise freshwater target and minimum wastewater generation. In this mode, the economics were not considered. It is important to note that the application of process changes employed by considering the WMH options resulted in new minimum water targets. Solving the MILP model proposed by Handani et al. (2010) provide

Step 1 Perform water audit

Step 2

Step 3

Determine limiting water data potential for water reuse, elimination, reduction, outsourcing and regeneration options. Collect data for water and wastewater tariff and all the cost equations for each process changes.

Run the Stage 1 Model to determine minimum water network considering all water management hierarchy

Table 1 Economic data for Chlor-alkali plant operating cost. Types

Unit

Freshwater cost, CostFW Wastewater treatment cost, CostWW Electricity tariff (Type E2), CostElec Power of pump, POPump Annual Operating Time, AOT

USD 0.83 t/h USD 0.42 t/h USD 0.064/kW.h 0.4 kW 8304 h/y

Step 4 Run the Stage 2 Model by using the guess value from Stage 1 to determine the cost effective minimum water network system.

Step 5 Perform sensitivity analysis to assess the proposed water network sensitivity to price changes and disturbance

Step 6 Select the water network design with less technical and economic risk.

Fig. 3. Decision making ﬂowchart for CWN model.

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S. Sujak et al. / Journal of Cleaner Production xxx (2016) 1e14

Table 2 Capital Cost for individual equipment. Process

New equipment

No. of Cost formula (USD) unit

Unit

Ablution

Laminar ﬂow with installation. (aj,re ¼ 0.5)

7

25

Toilet ﬂushing

Option 1: Composting toilet with installations

8

1000

Option 2: Vacuum toilet with installation (aj,re ¼ 0.97)

8

800

Option 3: Dual ﬂush toilet with installations (aj,re ¼ 0.5)

8

300

1

Nil

1

Nil

USD/ Unit USD/ Unit USD/ Unit USD/ Unit USD/ System USD/ System

e

[50,000*(

HCl Scrubber Reduce freshwater consumption for scrubbing system. No investment involved (aj,re ¼ 0.07) Reduce freshwater consumption by replacing chemical treatment with new Cooling polymer chemical. No need capital investment (aj,re ¼ 0.07) water system Reuse Reuse system and pumps with installation

Regeneration pH adjustment tank, multimedia ﬁlter, carbon bed, EDI and UV treatment unit with 1 control, pumps and installation Rainwater Rainwater systems and pumps with installation e harvesting

P Fi,j/28.82)0.6]*150%

P P [281,900*( Fi,r/45.5)0.6]*120% þ[50,000*( Fi,r/ P 0.6 0.6 28.82) ]*150% þ[50,000*( Fr,j/28.82) ]*150% P [50,000* Fos/F0.6 a ]*150%

USD/ System USD/ System USD/ System

Table 3 Chlor-alkali plant comparison optimal results for the payback period limit. Before MWR

Without setting payback period limit

Set payback period limit at 15 months

Water elimination (t/h) Water reduction (t/h)

e e

e

Total reused/recycled water (t/h) Total external water sources (t/h) Total regenerated water (t/h) Total freshwater consumption (t/h) Total wastewater generation (t/h) Net annual savings (USD/y) Net capital investment (USD) Total payback period (y)

e e e 28.82 9.44 e 231,560 e

D10 ¼ 0 a6,1D6 ¼ 3.73 a8,1D8 ¼ 7.75 a14,1D14 ¼ 0.16 2.53 0.21 6.57 18.51 0 105,383 197,183 1.87

for water doubles every two decades, but the increase in water supply is much less, it was assumed that the cost increase would be the most reasonable scenario for fresh water. Table 4 presents the results of the case when freshwater price was assumed to be to increase by 10%, 20%, 40%, 80% and 100% from the baseline price of USD 0.83/t.

a6,1D6 ¼ 3.73 a8,1D8 ¼ 7.75 a14,1D14 ¼ 0.16

2.03 0.21 0.23 25.42 6.83 33,589 41,986 1.25

5.1.3. Effects of freshwater prices on the selection of water minimisation schemes Fig. 4 shows the effects of freshwater prices on percentage change in water ﬂowrate involving freshwater, regenerated water, reused/recycled water, outsourcing and wastewater generation. As the price of freshwater increases to 20% higher than the baseline, it

Table 4 Effects of increasing freshwater price on optimal design of water network.

Water elimination (t/h) Water reduction (t/h)

Total reused/recycled water (t/h) Total external water sources (t/h) Total regenerated water (t/h) Total freshwater consumption (t/h) Total wastewater generation (t/h) Net annual savings (USD/ y) Net capital investment (USD) Total payback period (y)

Set payback period limit at 15 months (baseline)

Freshwater price þ10%

Freshwater price þ20%

Freshwater price þ40%

Freshwater price þ60%

Freshwater price þ80%

Freshwater price þ100%

e

e

e

e

e

D10 ¼ 0

D10 ¼ 0

2.03

2.04

2.05

2.54

2.54

2.53

2.53

0.21

0.21

0.21

0.21

0.21

0.21

0.21

0.23

0.31

0.39

6.56

6.56

6.57

6.57

25.42

25.34

25.24

18.59

18.59

18.51

18.51

6.83

6.76

6.66

0

0

0

0

33,589

36,816

40,361

132,953

147,025

162,111

176,293

41,986

46,020

50,451

166,191

166,191

197,183

197,183

1.25

1.25

1.25

1.25

1.13

1.22

1.12

a6,1D6 ¼ 3.73 a8,1D8 ¼ 7.75 a14,1D14 ¼ 0.16

a6,1D6 ¼ 3.73 a6,1D6 ¼ 3.73 a6,1D6 ¼ 3.73 a6,1D6 ¼ 3.73 a6,1D6 ¼ 3.73 a6,1D6 ¼ 3.73 a8,1D8 ¼ 7.75 a8,1D8 ¼ 7.75 a8,1D8 ¼ 7.75 a8,1D8 ¼ 7.75 a8,1D8 ¼ 7.75 a8,1D8 ¼ 7.75 a14,1D14 ¼ 0.16 a14,1D14 ¼ 0.16 a14,1D14 ¼ 0.16 a14,1D14 ¼ 0.16 a14,1D14 ¼ 0.16 a14,1D14 ¼ 0.16

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9

Fig. 5. Effects of freshwater prices on the percentage change in net annual savings, net capital investment and total payback period. Fig. 4. Effects of freshwater prices on the percentage change in ﬂowrates.

is clearly shown that regenerated water ﬂowrate increases up to 69.1%. Outsourcing ﬂowrate remains unchanged, while for the other water ﬂowrate, there are slightly changes obtained. It is due to the possibility of the rainwater to be harvested has already reaches its maximum limit contributed to the reason of the remaining same ﬂowrate for outsourcing water. As freshwater price increases to 40% higher than baseline, the percentage change in regenerated water ﬂowrate drastically increases. This is due to the reduction of freshwater ﬂowrate by 26.7%. More wastewater is regenerated and being reused/recycled to fulﬁl the water demand ﬂowrate. The reused/recycled water ﬂowrate also increased by 24.9% and amount of wastewater reduces by 100%. As the freshwater price escalates to 80% higher than baseline, freshwater ﬂowrates decreases to 27.2% due to the elimination of water demand at D10 which was not selected previously due to its high investment. All the other water ﬂowrates remain the same. Beyond 80% increase of freshwater price, there are no more changes in all water ﬂowrate. This is due to the remaining water demand which requires purer contaminants concentration which can only be provided by freshwater. 5.1.4. Effects of freshwater prices on net annual savings, net capital investment and payback period The net annual savings as well as net capital investment and payback period may inﬂuence the escalation of freshwater price when different water minimisation schemes and freshwater consumption are selected. Fig. 5 shows that the net annual savings and net capital investment have the same percentage change as freshwater price which escalates up to 40% higher than baseline. The payback period is maintained at 15 months. However, as the price of freshwater increased more than 40% from the baseline, the net annual savings and net capital investment increased to almost 300%. These increments arise due to the reduction of freshwater requirement as well as more wastewater is generated. Although net capital investment maintained at the same value as freshwater price increased to 60% higher than baseline, the net annual savings increases due to the rise of freshwater price. Consequently, the net capital investment remains unchanged while a shorter payback period is expected as a result from the water minimisation schemes. A similar situation occurs when freshwater price increases to 80% and 100% higher than the baseline. Once the CWN targets have been established, the optimal water network design is developed. A simultaneous generation of optimal water network as well as minimum target for water network is one of the advantages

of this approach. Fig. 6 represents the optimal network for water system for the manufacturing plant for this case study. 5.2. Case study 2: Sultan Ismail Mosque (SIM) 5.2.1. Freshwater savings mode (FWS-mode): stage 1 The Sultan Ismail case study is taken from Handani et al. (2010) where in FWS-mode, minimum freshwater is targeted and lead to minimum wastewater generation. The MWN can be achieved through process changes to ﬂowrates and concentration of water sources and demands to scale down the MWR targets. Handani et al. (2010) solved the FWS-mode and obtained an optimal solution where the minimum freshwater is 0.03 t/d while and wastewater ﬂowrate target is 0.14 t/d. 5.2.2. Economic mode (E-mode): stage 2 The maximum net annual savings for retroﬁt case for SIM is determined at this stage using the results from the ﬁrst stage. Initially, 9.98 y of total payback period for retroﬁt design is obtained with 0.03 t/d of freshwater and 9.27 t/d of wastewater for the minimum water targets. Elimination of water demand decision by the optimiser at D8 (toilet ﬂushing) is for achieving the water systems maximum annual savings. The 12 L of toilet ﬂushing is changed to a composting toilet. The freshwater consumption at demand D1 can also be reduced by modifying the normal water taps to another alternative such as laminar taps. A maximum 5 y of payback period limit for retroﬁt scenario has been set by the building owner (Wan Alwi, 2007). The maximum net annual savings developed from the model was USD 5366/y while the minimum freshwater obtain is 1.37 t/d and wastewater ﬂowrate targets is 9.04 t/d. After the implementation of WMH, the minimum water networks resulted in 95.3% of freshwater and 64.7% of wastewater savings. Water ﬂowrate at D1 is opted for reduction by the optimisation solver due to the payback period constraints. It is also due to the lower capital investment at demand D1 as to compared demand D8 being reduced or eliminated. Rainwater harvesting was added as an external source for both scenarios. Water outsourcing through rainwater harvesting was employed to the maximum limit to take advantage of the high quality of rainwater as compared to quality of reuse and recycle water. The reused and recycled water as well as the total regenerated water shown a slight increment at 5 y payback period limit and resulted in the reduction of wastewater generation. The optimal solutions of SIM case study are summarised in Table 5.

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Fig. 6. Cost optimal water network design for the Chlor-Alkali Plant.

Table 5 SIM comparison optimal results for the payback period limit.

Water elimination (t/d) Water reduction (t/d) Total reused/recycled water (t/d) Total external water sources (t/d) Total regenerated water (t/d) Total freshwater consumption (t/d) Total wastewater generation (t/d) Net annual savings (USD/d) Net capital investment (USD) Total payback period (y)

Before MWR

Without setting payback period limit

Set payback period limit at 15 months

e e e e e 29.10 25.63 e 72,618 e

D8 ¼ 0 a1D1 ¼ 12.52 0.23 11.14 3.62 0.03 9.27 5646 56,341 9.98

e

Similar to the previous case study, the impact of fresh water price based on baseline payback period limit is discussed. Table 6 presents the results of the case when freshwater price was assumed to increase by 10%, 20%, 40%, 80% and 100% from the baseline price of USD 0.56/t. 5.2.3. Effects of freshwater prices on the selection of water minimisation schemes Fig. 7 shows the effects of freshwater prices on percentage change in water ﬂowrate involving freshwater, regenerated water, reuse/recycled water, outsourcing and wastewater generation. The positive sign for percentage change in water ﬂowrates represents the increments in water ﬂowrates while the negative sign indicates the reduction in water ﬂowrates. From the ﬁgure, it is clearly shown that the freshwater consumption decreases when freshwater price increases to 10% higher than the baseline. The outsourcing ﬂowrate remains the same, while reused/recycled decreases by 12.0% and wastewater ﬂowrates decreases by 14.8%. On the contrary, the regenerated water increases by 36.4% with the increments of

a1D1 ¼ 12.52 0.29 11.14 3.78 1.37 9.04 5366 26,830 5

freshwater price. As freshwater price escalates to 20% higher than baseline, all water ﬂowrates remain the same. However, as freshwater price increases from 20% to 80% higher than baseline, the regenerated and reused/recycled water ﬂowrate decrease while wastewater ﬂowrate continues to be increased due to the payback period constraints. There are also no more changes in freshwater ﬂowrate until freshwater price is doubled. This is due to remaining water demands which requires purer contaminants concentration which inly can be provided by freshwater. After 80% increase of freshwater price, freshwater and outsourcing ﬂowrates remains the same while there are slight changes in other ﬂowrates. The changes in regenerated water as well as reused and recycled water will correspond to the increment or reduction of wastewater generation. 5.2.4. Effects of freshwater prices on net annual savings, net capital investment and payback period In the case of most water minimisation schemes, water ﬂowrate shall determine the capital investment and inﬂuences the net

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Table 6 Effects of increasing freshwater price on optimal design of water network. Set payback period limit at 5 years (baseline) Water elimination (t/d) Water reduction (t/d) Total reused/recycled water (t/d) Total external water sources (t/d) Total regenerated water (t/d) Total freshwater consumption (t/d) Total wastewater generation (t/d) Net annual savings (USD/ y) Net capital investment (USD) Total payback period (y)

e

Freshwater price þ10% e

Freshwater price þ20% e

Freshwater price þ40% e

Freshwater price þ60% e

Freshwater price þ80%

Freshwater price þ100%

a1,1D1 ¼ 12.52

a1,1D1 ¼ 12.52

a1,1D1 ¼ 12.52

a1,1D1 ¼ 12.52 a 8,1D8 ¼ 0.79

a1,1D1 ¼ 12.52 a 8,1D8 ¼ 0.79

a1,1D1 ¼ 12.52 a 8,2D8 ¼ 0.05

D10 ¼ 0

D10 ¼ 0 a1,1D1 ¼ 12.52

0.29

0.26

0.26

0.24

0.24

0.23

0.22

11.14

11.14

11.14

11.14

11.14

11.14

11.14

3.78

5.16

5.16

4.39

4.39

3.67

3.62

1.37

0.03

0.03

0.03

0.03

0.03

0.03

9.04

7.70

7.70

8.49

8.49

9.22

9.27

5366

6184

6773

7998

9181

10,398

11,587

26,830

29,678

29,678

37,067

37,067

50,449

56,341

5

4.80

4.38

4.64

4.64

4.85

4.86

depends on both net annual savings as well as capital investment. The optimal water network design for SIM case study is presented in Fig. 9.

annual savings. The effects of freshwater prices on net annual savings, net capital investment and payback period is shown in Fig. 8. The net annual savings increment can be seen as the price of freshwater increases. As freshwater price increases to 10% higher than the baseline, the net annual savings and net capital investment also increase by 15.2% and 10.6%. The net annual savings still increases while the net capital investment maintains at the same value when the price of freshwater higher than baseline by 20%. Consequently, a shorter payback period can be achieved. It is due to the same selection and amount of water minimisation schemes that resulted in the unchanged value of the net capital investment. A similar scenario is observed when freshwater price increases up to 60% from 40% higher than baseline. As freshwater price increases to 80% and 100% higher than the baseline, the net annual savings and net capital investment also increases. A different selection of water minimisation at demand D8 resulted in the increment of freshwater price and the net capital investment. As freshwater price doubled, the optimiser favoured to eliminate water at demand, D10 which was not selected previously due to its high investment. The pattern of payback period is not stable since it

It is clearly shown from the case studies, different water minimisation options were obtained for both approaches. The results obtained from CWN are better than CEMWN in terms of the net annual savings and payback period. However, a higher freshwater target by CWN is expected due to multiple contaminants present in the water system. The comparison between CWN and CEMWN approach by Wan Alwi (2007) for SIM case study is shown in Table 7. It is proven that CWN has the advantages of handling multiple contaminants problem compared to CEMWN. The model is not only able to predict which water source should be eliminated, regenerated or reduced but is also capable to simultaneously determine the minimum water target that satisﬁes the maximum net annual savings.

Fig. 7. Effects of freshwater prices on percentage change in water ﬂowrates.

Fig. 8. Effects of freshwater prices on percentage changes in net annual savings, net capital investment and payback period.

5.3. Comparison of CWN and CEMWN

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Fig. 9. Optimal water network design for SIM case study.

Table 7 Comparison of CWN and CEMWN for Sultan Ismail Mosque case study.

Contaminant Approach Total freshwater consumption (t/d) Total wastewater generation (t/d) Total reused/recycled water (t/d) Total regenerated water (t/d) Total external water sources (t/d) Net annual savings (USD/y) Net capital investment (USD) Total payback period (y) Selection of elimination option Selection of reduction option

CWN

CEMWN

% Different

Multiple contaminants Mathematical Programming 1.37 9.04 0.29 3.78 11.14 5366 26,830 5 e D1

Single Contaminant Water Pinch Analysis (Graphical) 0.73 8.4 1.83 2.89 11.14 5343 26,757 5.01 e D1

46.7 7.00 84.2 23.5 0 0.42 0.27 0.19 e e

6. Conclusion A holistic two-stage approach for the design of Cost-Optimal Water Networks (CWN) has been developed. The proposed model allows designers and plant owners to simultaneously select the optimal network choices that can provide the best water minimisation scheme while achieving the maximum net annual savings within a speciﬁed payback period. The novelty of the approach lies in the development of a two-stage procedure that combines the use of MILP to generate initial values, followed by MINLP to ﬁnd the global optimal solutions for freshwater savings mode as well as the economic mode. The ﬁrst stage considers the best water minimisation scheme by taking into account all possible water saving options within the water management hierarchy. The economic mode at the second stage provides suitable water minimisation schemes to achieve the water system's maximum annual savings targets while meeting the payback period constraint set by a plant owner. The study has allowed the CWN to yield more accurate and practical results as compared to the use of heuristic and graphical approaches from previous studies. The performance of the new model is proven beneﬁcial for retroﬁt of real-life urban and industrial water networks. It is also proven that the CWN yields more realistic annual savings as well as the payback periods. From the sensitivity analysis, it was shown that as the freshwater price increased, a different scheme of water minimisation was selected.

Future water minimisation scenarios can be forecasted using the sensitivity analysis approach. Note that, this study has currently assumed isothermal water operations. Our future works will focus on the use of CWN for simultaneous minimisation of multiple resources such as heat and water. Acknowledgment The authors greatly appreciate the ﬁnancial support from Universiti Teknologi Malaysia via the Research University grant number Q.J130000.2409.03G13 (Industrial waste water minimisation along Sungai Johor basin), and the MyBrain15 scholarship provided by the Ministry of Higher Education of Malaysia. Nomenclature Adjusted ﬂowrate of water source i Adjusted demand j ﬂowrate Contaminant k concentration at demand outlet j Maximum concentration limit of contaminant k at demand j CElimU Freshwater elimination unit total capital investment CostElec Cost of electricity CostFW Cost of freshwater supplies A Cost of outsourcing unit os with given ﬂowrate A CostOsUos Ai Bj Cdj,k Cdmax j;k

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CostRegUrA Cost of regeneration unit r with given ﬂowrate A CostChemReg Cost of chemicals needed for regeneration Cosos,k Outsource concentration of contaminant k CostPipe Cost of piping CostPump Cost of pumping CostUEj,e Cost of elimination unit e for demand j CostURej,re Cost of reduction unit re for demand j CostU Total cost of outsourcing unit CostWW Cost of wastewater generation CRedU Freshwater reduction unit total capital investment CregU Total cost of regeneration unit Creuse Total cost of reuse unit Crir,k Inlet concentration of contaminant k to regeneration unit r Cror,k Outlet concentration of contaminant k to regeneration unit r Csi,k Contaminant k concentration at water source i Csmax Maximum concentration limit of contaminant k from i;k water source i Cwk Freshwater contaminant of contaminant k Daj,e Flowrate of elimination option e for demand j Daj,o Original ﬂowrate o at demand j Daj,re Reduction ﬂowrate re option for demand j Dj Demand j ﬂowrate Fi,j Water ﬂowrate from source i to demand j initial Fi;j Initial water ﬂowrate from source i to demand j Fi,r Water ﬂowrate from source i to regeneration unit r initial Fi;r Initial water ﬂowrate from source i to regeneration unit r Fosinitial Initial outsource ﬂowrate os to demand j os;j Fosos,j Outsource ﬂowrate os to demand j Fosmax Maximum ﬂowrate of outsource os os FosAos Flowrate of A for outsource os Fr,j Water ﬂowrate from regeneration unit r to demand j initial Fr;j Initial water ﬂowrate from regeneration unit r to demand j FRegA Flowrate of A for regeneration Fwj Freshwater supplied to demand j Fwinitial Initial freshwater ﬂowrate to demand j j Max Maximum Min Minimum OC Total water operating cost OCbase case Base case expenses savings OCnew New expenses on water P Percentage of equipment cost installation POPump Power of pump RRr,k Contaminant k removal ratio at regeneration unit r Si Flowrate of water source i TPP Total payback period WWi Unused portion of water source i (waste) WWiinitial Initial wastewater ﬂowrate from source i Xj,e Selection of eth elimination options for jth demand Xj,re Selection of reth reduction options for jth demand Xj,o Selection of original ﬂowrate o for jth demand X1j,e Binary variable of elimination e option for demand j X2j,re Binary variable of reduction re options for demand j Yd Large value parameter to calculate the selection of elimination, reduction & original demand ﬂowrate sj,re Water reduction percentage b Sixth-tenth rule εj Number of equipment j g Payback period limit Greek letter S Summation c All belongs to

Subscripts I Index j Index k Index r Index e Index re Index o Index os Index Units t t/d t/h y %

for for for for for for for for

13

water source water demand water contaminant regeneration unit elimination option water reduction option original water demand outsourcing

ton ton per day ton per hour Year percentage

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