rocess streams for heat integration

Elvis Ahmetovic a,b,*, Zdravko Kriverzitetsd Chem

Improved and novel designs aregiven for heat-integrated waternetworks.

cold streams. This extendedmodel was formulated as a non-convexmixed-integer non-linear programmingxamples with single-process streams forrted in the literature.. All rights reserved.

Over the last fteen years, the synthesis of heat-integratedwater networks (HIWNs) or water-allocation and heat-exchange

rch area, and willcontinue to be so in the future. The main reasons are the needs ofthe chemical process industries for economic and sustainabledesign solutions that provide an efcient usage of raw materials,water, and energy whilst satisfying strict environmental regula-tions on the discharge of efuents into the environment. The readeris referred to Ref. [1] for more detail about the design and inte-gration of chemical processes, sustainability in the process industry[2], sustainable design through process integration [3]. Conse-quently, the challenge for the Process Systems Engineering (PSE)

* Corresponding author. Present address: Faculty of Technology, University ofTuzla, Univerzitetska 8, 75000 Tuzla, Bosnia and Herzegovina. Tel.: 387 35320756; fax: 387 35 320741.

E-mail addresses: elvis.ahmetovic@untz.ba (E. Ahmetovic), zdravko.kravanja@

Contents lists available at

Applied Therma

journal homepage: www.elsev

Applied Thermal Engineering 62 (2014) 302e317uni-mb.si (Z. Kravanja).integrationSuperstructureMINLP model

(MINLP) problem. The objective was to minimize the total annual network cost. Two eand multiple contaminants are used in order to demonstrate that involving process-toheat integration, novel and improved solutions can be obtained compared to those repo

2013 Elsevier Ltd

1. Introduction networks (WAHENs) has been an active reseaHeat-integrated water networksProcess-to-process streams for heat process stream. The second allows for the cooling and splitting of hot streams, and heating and splitting ofKeywords:Simultaneous optimization1359-4311/$ e see front matter 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.applthermaleng.2013.06.01integrated water networks. In this study, we presented two strategies for heat integration of process-to-process streams. The rst one includes the placement of heat exchangers on each hot and cold process-to-a r t i c l e i n f o

Article history:Received 1 March 2013Accepted 7 June 2013Available online 19 June 2013a b s t r a c t

This paper presents an extension of our recent work, in which we addressed the simultaneous synthesis ofheat-integrated water networks. The novelty and goal of this work is the development of an extended su-perstructure and simultaneous optimization model of heat-integrated water networks now involvingprocess-to-process streams, and other streams within the overall network, for heat integration. Those heat-integration opportunities have not yet been fully taken into account in most existing models of heat-aUniversity of Tuzla, Faculty of Technology, UnbUniversity of Maribor, Faculty of Chemistry an

h i g h l i g h t s

An extension is presented of the su-perstructure and optimization model.

Two strategies are proposed for theheat integration of process-to-process streams.

New constraints are proposed forfurther simplifying the HEN model.avanja b

ka 8, 75000 Tuzla, Bosnia and Herzegovinaical Engineering, Smetanova ulica 17, 2000 Maribor, Slovenia

g r a p h i c a l a b s t r a c tinvolving process-to-p

Simultaneous optimization of heat-integrated water networksAll rights reserved.0SciVerse ScienceDirect

l Engineering

ier .com/locate/apthermeng

hermcommunity concerns the development of integrated solutionmethods and new tools for the synthesis and design of sustainablechemical processes. The contribution [4] described the past, pre-sent and future of PSE. In order to achieve sustainable solutions, thescope of the synthesis needs to be extended to cover the wholechemical or biochemical supply-chain [5]. A review of major con-tributions in process synthesis and supply-chain management wasgiven in Refs. [6e8] highlighting that mathematical programmingtechniques offer a general framework for including environmentalconcerns regarding these problems.

In sustainable chemical processes HIWN should be designed tobe water and energy-efcient. Excellent contributions have beenmade towards the synthesis of water and energy networks. The lastreview of 264 contributions relating to water network (WN) designmethods was given in Ref. [9]. In addition, a brief reviews have alsobeen given by about 20 contributions regarding the synthesis ofHIWNs. Over the last two years, an increasing number of studiescan be identied concerning this eld, where systematic methodshave been used based on pinch analysis [10] or mathematicalprogramming [11]. A brief overview of the recent works relatingindustrial water recycle and reuse was given in Ref. [12] as well asseveral case studies were used in order to demonstrate the signif-icance of thementioned systematic methods for reducing thewaterand energy consumption in the process industries.

In our recent paper [13] we presented a detailed literature re-view of the important contributions related to the synthesis ofHIWNs based on pinch analysis and mathematical programming. Itis important to mention some of the studies based on pinch anal-ysis that have considered simultaneous energy and water mini-mization [14], direct and indirect heat transfer in water networks[15], simultaneous water and heat integration with no waterreuse [16], and maximum reuse of water [17], heat-integratedsystem design [18], synthesis of heat-integrated resource conser-vation networks [19], interactions between water and energy sys-tems [20] or the effect of non-isothermal mixing on waternetworks energy performances [21]. We also present a detailedreview of those contributions based on mathematical program-ming and superstructure optimization, as well as a review on thelatest developments in this area. Finally, we have highlighted thatthe synthesis of HIWNs has received considerable attention in theliterature over the last decade and it could also be one of the maindirections for future research in order to produce water andenergy-efcient and sustainable solutions. The synthesis problemhas been solved using sequential or simultaneous solution strate-gies. It is worth pointing out that only simultaneous strategy basedon superstructure optimization allows for appropriate trade-offsbetween freshwater (FW), utilities, and capital costs. A relativelysmall number of papers have addressed the simultaneous synthesisof HIWNs by using the mathematical programming approach. Asimultaneous optimization model [22] was proposed for a com-bined WN and modied HEN superstructure for the case of mixingand splitting streams within HEN. The state-space superstructurewas modied for simultaneously synthesizing of WN and HEN [23].In addition, the simultaneous design approach [24] was developedand applied to combined WN and HEN, and can be used for large-scale multiple contaminant problems. A systematic methodologyfor designing wastewater and heat-exchange networks was givenin Ref. [25], and the optimization of water and heat-exchangenetworks was performed simultaneously. In addition, holisticmathematical programming [26] was used for the synthesis ofHIWNs as well as stochastic optimization techniques [27] beingapplied for designing heat exchanger and water networks. Also, thereader is referred to the paper [13], in which a novel superstructureand optimization model for the simultaneous synthesis of process

E. Ahmetovic, Z. Kravanja / Applied Twater and heat-exchanger networks were proposed. Thesimultaneous synthesis of the process and its heat-exchangernetwork (HEN) was studied in Refs. [28,29], heat and water inte-gration for a process owsheet in Ref. [30]. Simultaneous water andenergy optimization was recently performed for an existing pulpand paper mill [31,32] as well as sugar process production [33] andsignicant reduction in energy and water consumption was ach-ieved. Also simultaneous process synthesis, heat and power inte-gration of a thermochemical process were addressed in Ref. [34],and later extended for water integration [35] in order to minimizefreshwater consumption and wastewater discharge. The HIWNconsists of WN, HEN, and their interconnections. In addition, thereare also important interconnections within WN and HEN. Only asimultaneous strategy can fully explore all the interactions withinan overall network. In order to achieve efcient HIWNs, andexplore trade-offs between FW, utilities, and capital costs, allpossible interconnections and opportunities for heat integration(HI) within the network should be taken into account. However,this increases the complexity of the simultaneous synthesis prob-lem and can result in expensive computational time for obtainingthe global optimum. It is worth pointing out that for obtaining goodlocal solutions for non-convex MINLP problems of HIWNs still re-mains a challenge. The non-convexities appear in concave terms,and the mass and heat balances (bilinear terms). In order to makethis problem easier to solve, the non-convexities can be approxi-mated using piecewise linear under-and over-estimators [36]. Inaddition, an efcient solution strategy or a good initialization closeto global optimum is necessary.

During studies on the simultaneous synthesis of HIWNs, the HIbetween process-to-process and other streams within the networkhave not as yet been taken into account [22]. However, indirectheating and cooling of process-to-process streams in processesmaybe required [37]. As a result, those networks that require the heatingor cooling of process-to-process streams can be excluded from thefeasible space, thus resulting in suboptimal solutions. In order tocircumvent this problem, process-to-process streams should betreatedashot and cold streams. Consequently, a heat exchanger (HE)should be placed on a process-to-process stream allowing for indi-rect heat transfer between other cold or hot streams within thenetwork. In addition, process-to-process streams can be heated upwith hot streams or cooled down with cold streams within thenetwork and after being split, directed towards the process units, aswill be shown later in thepaper. In thisway, additional opportunitiesfor HI are enabled within the network, thus resulting in the pro-duction of energy-efcient designs with lower total annual costs(TAC). This paper proposes an extension to the superstructure andmodel [13] recently developed, for taking into account the HI be-tween process-to-process streams and other streams within thenetwork. This paper is organized as follows. Firstly, the problemstatement is given, followed by the development details of theextended superstructure and model. Then, the model is applied tocase studies involving single andmultiple contaminants. Finally, themain conclusions are highlighted.

2. Problem formulation

Given is a set SW of freshwater sources s SW, a set PU ofprocess units p PU that require water of a certain quality andtemperature. A set HP of hot process streams i HP to be cooledand a set CP of cold process streams j CP to be heated can bedetermined on the basis of a total number (N) of process unitsPU, as shown later. It is necessary to consider the HI betweenprocess-to-process streams and other streams within the net-work, and determine the interconnections, owrates, contaminantconcentrations, and the temperatures of each stream within the

al Engineering 62 (2014) 302e317 303network. The standard assumptions for the synthesis problem of

utilities, now involving process-to-process streams for HI.

process units is provided in order to show that process-to-processstreams were not taken into account for HI, followed by an expla-nation of the proposed superstructure extension for involvingthose streams for HI.

TheWN superstructure consists of process units (PUs), and theirinterconnections. In order to minimize FW consumption andwastewater (WW) generation, the re-usage and recycling of wateris enabled within the network. The HEN superstructure consists ofHEs, and presents a stage-wise representation [28]. It allows fordifferent possibilities of matching any pair of hot and cold streams.The overall network superstructure includes opportunities fordirect (isothermal/non-isothermal mixing) and indirect heat re-covery (see Fig. A1 in the Appendix).

In order to present the combined superstructure (Fig. 1), andinterconnections within theWN and HEN superstructures a four PUnetwork is shown in Fig. 2. This network consists of units involvingPUs (PU1 has the minimum and PU4 the maximum temperature)and HEs, and their interconnections. The FW stream is heated up ina series of HEs within the superstructure. After each HE, the FW canbe split and sent to each PU. In addition, the FW of the initialtemperature can be split and directed towards each PU directly. TheFig. 1. Combined superstructure of WN and HEN [13].

E. Ahmetovic, Z. Kravanja / Applied Thermal Engineering 62 (2014) 302e3173043. Development of an extended superstructure involvingprocess-to-process streams for heat integration

The main goal of this section is to show the development ofextended superstructure involving process-to-process streams forHI. First, we have presented a combined superstructure of WN andHEN (Fig. 1) and their interconnecting streams, which can be hot,cold, or bypass streams, in order to obtain a broader view of theHIWNs are made, as given [13] in the literature. The freshwatersources s SW, the number of process units p PU and contami-nants c CC are specied, the water streams have constant heatcapacities and heat-transfer coefcients, the heat exchangers arecounter-current, the network operates continuously, with one hotutility (HU) and one cold utility (CU) being available. The main goalis to simultaneously synthesize the HIWN with the minimum totalannual cost and the optimal consumption of the freshwater andbasic concept [13]. Then a more detailed HIWN consisting of four

Fig. 2. The superstructure of HIWN consists of four process units (preheated FW streams, bypass FW streams, and WW streams aremixed at the front of the PUs. The temperatures of these streamsare usually different so the mixers act as direct HEs. Consequently,the mixed stream can have different temperatures. Its temperaturecan be the same as the temperature of PU (stream is bypass), higher(stream is hot) or lower (stream is cold) than the temperature of PU.If the stream is hot or cold, it is sent to the HEN for HI. However, wecannot know in advancewhether the outlet stream of the mixer is ahot or cold stream. In order to circumvent this problem, a newconvex-hull formulation for identifying the streams roles in theHEN, was proposed in our recent paper [13]. For different water andheat-recovery networks, different type of stream can be identiedand the proposed convex-hull formulation can be successfullyapplied. Also, this formulation can be used in the synthesis of boththreshold (e.g. the temperature of freshwater is less than thetemperature of wastewater and hot utility is required) as well aspinched (e.g. the temperature of freshwater is greater than thetemperature of wastewater and both hot and cold utilities arerequired) HIWN problems. The temperature of the outlet stream ofthe mixer, and the owrate through PU are treated as optimizationvariables. The inlet stream of PU must satisfy its contaminant andprocess-to-process streams are not taken into account for HI).

temperature constraints. A mass load of contaminant is transferredin PU from a contaminant rich process stream to a contaminantlean water stream. Consequently, the concentration of the processstream decreases, while the concentration of the water stream in-creases. The outlet stream of the PU can be a hot, cold or bypassstream. Similarly, as explained for the outlet stream of the mixer,the temperature and owrate of this stream are optimization var-iables. The outlet stream of the PU can be split, reused within thesame (local recycle) or another PU, in order to minimize FW con-sumption. Also, part of the WW stream from the splitter PU can besent for cooling within a series of WW coolers, or as a bypassdirected towards the mixer of the WW streams. Finally, the WWstream discharged into the environment must satisfy the dischargetemperature. Note in Fig. 2 that there are heaters, and coolerswithin the overall network, and external hot and cold utilities arerequired. However, in the case of heat recovery between hot andcold streams within the network, recovery heat exchangers aredenoted by dashed lines connecting various heaters and coolerswithin the network (e.g. see Figs. 8e12).

3.1. Additional opportunities for heat integration within a combinednetwork

This section presents and discusses additional opportunities forHI within the HIWNs, compared to the superstructure (Fig. 2), forthose cases when the process-to-process streams are taken intoaccount for HI. In order to illustrate these possibilities, threeisothermal process units (PU1ePU3) with different operating

temperatures are used (Fig. 3). The rst one (PU1) has the minimumoperating temperature (40 C), the second one (PU2) the interme-diate operating temperature (50 C), and the third one (PU3) themaximum operating temperature (75 C).

Only a few streams (Fig. 3) within the network are consideredfor the sake of simplicity and clear representation of the additionalopportunities for HI. Fig. 3a and b presents those interconnectionsstreams directed from the process unit PU1 with the lowest (40 C)temperature, towards the process units (PU2 and PU3) with thehigher (50 C and 75 C) temperatures. Consequently, these streamscan be treated as cold streams. In addition, Fig. 3c and d shows thoseprocess-to-process streams directed from PU3 with the highest(75 C) temperature to PU2 and PU1with the lower (50 C and 40 C)temperatures, so they can be treated as hot streams. Fig. 3a and cpresents those cases when process-to-process cold and hot streamsare discounted for an indirect heat transfer within the network, andare directly introduced together with other streams into the mixerof the process units PU2 and PU3. In this case, the other streamsintroduced into the mixer of PU must have sufciently high tem-

E. Ahmetovic, Z. Kravanja / Applied Thermal Engineering 62 (2014) 302e317 305Fig. 3. Placing an HE on process-to-process streams for HI.peratures, so that after mixing with process-to-process streams theoperating temperature of the PUs is achieved (the case when thetemperature of the mixed stream is the same as the operatingtemperature of PU). In order to produce more possibilities for HIand consequently obtain better energy performances within thenetwork, an HE unit can be placed on each of these cold and hotprocess-to-process streams, as shown in Fig. 3b and d. In this way,for example, the target temperatures of all the PUs can be achievedafter heat exchanging within the HEs of Fig. 3b and d.

In addition to the presented cases of Fig. 3b and d, process-to-process cold and hot streams can be split after heat exchange (seeFig. 4a and b) and sent to PUs with higher and lower temperatures.Note that the temperatures of the streams after heat exchange are75 C (Fig. 4a) and 40 C (Fig. 4b), and they are the same as thetemperatures of PU3 andPU1.However, in order to achieve the targetoperating temperature (50 C) of PU2, a part of the cold stream(40 C) from PU1 (bypass) is mixed with a part of the hot stream(75 C) after heat exchange (Fig. 4a). In Fig. 4b, the operating tem-perature of PU2 is achieved bymixing a hot stream (75 C) from PU3(bypass) and a part of a cold stream (40 C). However, in some casessuch as in Fig. 5, it could happen that the temperature of the streamafter heat exchange is lower than the temperature of PU3 (75) orhigher than the temperatureof PU1 (40 C). Consequently, additionalheating or cooling could be required. In order to capture these al-ternatives, the network in Fig. 4 can be extended as shown in Fig. 5.Fig. 4. The options of indirect heat transfer and the splitting of process-to-processstreams.

Figs. 3 and 5 present the basic ideas for extending the combinedHIWN superstructure of Figs. 1 and 2 by involving process-to-

3.2. Extensions of the combined heat-integrated water network

Fig. 5. Placing an HE on process-to-process streams for HI and the splitting of streams.

E. Ahmetovic, Z. Kravanja / Applied Therm306superstructure

On the basis of the concept for process-to-process HI as pre-sented in the previous section, Figs. 6 and 7 show extensions to theparts of the superstructure given in Fig. 2. However, for the sake ofsimplicity only parts of the superstructure representing its exten-sion are shown in Figs. 6 and7 (see the right hand side of thegures).Note that bypass streams, as well as the preheating and splitting ofprocess streams for HI. It should be mentioned that there aremany other possibilities for HI, especially for those cases when theoutlet streams of the intermediate PUs, e.g. PU2, are taken intoaccount for HI. In this case a part of the stream can be hot (directedto PU1) or cold (directed to PU3). It is worth pointing out that wheninvolving process-to-process streams for HI, the splitting andmixing of streams produces additional degrees of freedom forobtaining energy-efcient WNs with reduced TAC.Fig. 6. A part of the extended superstructure involving process-to-process streams for HI.FW, the cooling and mixing of WW, and local recycles, are not pre-sented in these gures, in order to keep the network simple.

It is worth pointing out that in both cases of superstructureextensions (Figs. 6 and 7) there are more degrees of freedom for HI,and improved network solutions can be obtained, as shown later.However, the challenge is to develop and solve a general non-convex MINLP model of the extended superstructures (variableset of process units, multiple contaminants, variable set of hot andcold streams for HEN, unknown temperatures of mixed and splitstreams for HI, variable owrates through process units, process-to-process streams for HI, etc.) that produce global optimum oreven good local solutions close to the global optimum.

4. Formulation of the extended model

Corresponding mathematical models have been developed onthe basis of the extended superstructures given in Figs. 6 and 7. Thebasic model for the simultaneous synthesis of HIWNs as recentlydeveloped in Ref. [13] has now been extended by consideringprocess-to-process streams for HI. A short description of the modelwithout involving process-to-process streams for HI is given in theAppendix to this paper. This model has been formulated as non-convex MINLPs. The objective is to minimize the TAC consistingof FW and utility costs, and the capital cost of the HEs. The modelinvolves mass and heat balances, contaminant mass balances,convex-hull formulation for identifying a streams role in HEN,connecting equations between WN and HEN, and logical con-straints. Binary variables and tight constraints have been intro-duced within a WN convex-hull formulation.

This section only presents the extended and modied equationsof the basic mathematical model, for the superstructure (Fig. 6)involving process-to-process streams for HI. The extended modelincludes newly-proposed equations for a set of hot and a set of coldstreams for HEN, modied equations for mass and heat balancesregarding mixer process units and the mass balances of splitterprocess units, new connecting equations between WN and HEN forhot and cold process-to-process streams, and logical constraints inorder to further reduce the complexity of the model.

4.1. A set of hot streams (HP) and a set of cold streams (CP) for HEN

The classical HEN model has given a set of hot process streams(HP) to be cooled, and a set of cold process streams (CP) to beheated. However, in the combined WN and HEN model, the set ofhot (HP) and cold (CP) streams is exible, and depends on thenumber of PUs (N). In addition, certain streams, for example,after the mixing points or after the process units in WN can behot, cold, or bypass streams, and thus unknown. Consequently,new generic equations (1) and (2) for determining a set of hotstreams (HP) to be cooled and a set of cold streams (CP) to beheated within HEN are proposed as follows, where N representsthe total number of PUs.

HP 3$N N$N Q0:5$NS$N 1 N P0:5$NR$2$Q0:5$NS(1)

CP 3$N N$N Q0:5$NS$N 1 N P0:5$NR$2$Q0:5$NS(2)

Note that QxS and PxR represent ceil and oor functions used inGAMS. The function QxS returns the smallest integer number greaterthan or equal to x, and PxR returns the greatest integer number lessthan or equal to x. These functions have to be used in the combined

al Engineering 62 (2014) 302e317WN and HEN model in order to determine in advance a set of hot

p0 < p

tcinj TSPUoutp ; c pPU; jCP; CSPUj;p;p0 (11)

hermX

p0PUFHPp0;p$THPUoutp0 c pPU (5)streams (HP) and a set of cold streams (CP) for HEN on the basis of atotal number of PUs (N) within the network.

4.2. Mixer process units

Fig. 6 presents an extended superstructure involving process-to-process streams for HI. Note that an HE unit is placed on each of thehot (FHPp0 ,p, p0 > p) and cold (FCPp,p0, p0 < p) process-to-processstreams, thus increasing the possibilities for HI within thenetwork. In this case, the outlet temperatures of the hot THPUoutp0 and cold TCPUoutp0 process-to-process streams are unknown.Consequently, the balance equations of the mixer process units,given in the Appendix, have to be modied in order to include hotand cold process-to-process streams. The mass balance for themixer process units is given by Eq. (3), the mass balance for eachcontaminant c by Eq. (4), and the heat balance by Eq. (5).

FPUinp Xp0PU

FSSMp0;p XsSW

FIPs;p X

p0PUpsp0;Rp 0

FPp0;p

X

p0PURp 1

FPp0;p X

p0PUp0 < p

FCPp0;p

X

p0PUp0 > p

FHPp0;p c pPU (3)

FPUinp $xPUinp;c

Xp0PU

FSSMp0;p$xSSoutp0;c XsSW

FIP$xWins;c

X

p0PUpsp0;Rp 0

FPp0;p$xSPUoutp0;c

X

p0PURp 1

FPp0;p$xSPUoutp0;c

X

p0PUp0 < p

FCPp0;p$xSPUoutp0;c

X

p0PUp0 > p

FHPp0;p$xSPUoutp0;c c pPU; c cCC

(4)

FPUinp $Tmixp

Xp0PU

FSSMp0;p$TSSoutp0 XsSW

FIP$TIPs;p

X

p0PUpsp0;Rp 0

FPp0;p$TSPUoutp0

X

p0PURp 1

FPp0;p$TSPUoutp0

X

p0PUFCPp0;p$TCPUoutp0

E. Ahmetovic, Z. Kravanja / Applied Tp0 > ptcoutj TCPUoutp ; c pPU; jCP; CSPUj;p;p0 (12)Some streams, for example, after the mixing points or after the

process units in WN, can be introduced in HEN as hot or coldstreams. Consequently, matches between these hot i HP and coldj CP streams within stages k ST are infeasible in HEN at eachmixing of PU or after PU, and logical constraints, Eqs. (13) and (14)were used to x those infeasible matches leading to a simpliedHEN.

zi;j;k 0; iHP; jCP; kST ; i p; j p; i j (13)

zi;j;k 0; iHP; jCP; kST; i pjPUj; j pjPUj; i j (14)An external heat load is required for threshold HIWN problems

(temperature of the FW is lower than the temperature of the dis-charged water). The hot utility (HU) target can be calculated inadvance for minimum water consumption and temperature dif-4.3. Splitter process units

The mass balance for the splitter process unit, given in theAppendix, is extended in order to include the owrates of the hotand cold process-to-process streams, as given by Eq. (6).

FPUoutp Xp0PU

FSMMp;p0 FPOp X

p0PUpsp0;Rp 0

FPp;p0

X

p0PURp 1

FPp;p0 X

p0PUp < p0

FCPp;p0

X

p0PUp > p0

FHPp;p0 c pPU (6)

4.4. Connecting equations for HEN regarding process-to-processstreams

Process-to-process streams can be hot and cold. The heat-capacity owrates of these hot and cold streams (fhi, fcj) and theirinlet (thini, tcinj) and outlet (thouti, tcoutj) temperatures have to bedened by Eqs. (7)e(12) in order to simultaneously solve thecombined WN and HEN model by minimizing the TAC of thenetwork. Note that a certain number of streamsmust be assigned toeach hot and cold process-to-process streamwithin the network inorder to be recognized by the HEN model. This requires imple-mentation of loop-statements in GAMS for Eqs. (7)e(12) usingthose ag parameters for hot HSPUi;p0 ;p and cold CSPUj;p;p0 process-to-process streams from SPU to MPU.

fhi FHPp0;p$Cp; c pPU; p0 > p; iHP; HSPUi;p0;p (7)

thini TSPUoutp0 ; c p0PU; iHP; HSPUi;p0;p (8)

thouti THPUoutp0 ; c p0PU; iHP; HSPUi;p0;p (9)

fcj FCPp;p0$Cp; c pPU; p0 > p; jCP; CSPUj;p;p0 (10)

al Engineering 62 (2014) 302e317 307ference between an FW cold stream and a discharged WW hot

(HRAT), as all temperature driving forces are now considered asoptimization variables.

5. Examples

This section presents an application of the extended super-structure and the corresponding model in order to solve those

the area cost coefcient, and the cost exponent for HEs were

E. Ahmetovic, Z. Kravanja / Applied Thermal Engineering 62 (2014) 302e317308stream. In these cases, the inlet stream of PU with maximumtemperature (i.e. PU4 in Fig. 6) can only be a cold stream or bypass,and the outlet stream of PU a hot stream or bypass. Note thatadditional constraints can be formulated by Eqs. (15)e(20) in orderto further simplify the HEN model.

yhpp 0; pPU; p jPUj (15)

zi;j;k 0; iHP; j CP; kST; i jPUj (16)

zcui 0 iHP; i jPUj (17)

Fig. 7. A part of the extended superstructure involving process-to-process streams forHI and the splitting of streams.ycpsp 0; pPU; p jPUj (18)

zi;j;k 0; iHP; j CP; kST; j 2$jPUj (19)

zhuj 0; jHP; j 2$jPUj (20)The extended and modied basic model from the Appendix

together with the equations in this section present a simulta-neous synthesis model of HIWNs involving process-to-processstreams for HI. The presented model includes all possible heat-integration opportunities, as well as both freshwater and waste-water splitting and mixing, within the overall network. It enablesthe obtaining of an appropriate trade-off between utility con-sumption, water usage, and investment. The heat integrationapplied is performed simultaneously and the model does not relyon the assumption of a xed heat-recovery approach temperature

Table 1Problem data for Example 1.

Processunit

Contaminantmass load (g/s)

Maximum inletconcentration (ppm)

Maximum outlet Limiting water Temperature ( C)

1 5 502 30 503 50 800concentration (ppm) owrate (kg/s)

100 100 100800 40 75assumed to be 8000 $, 1200 $/m2, and 0.6; the overall heat-transfercoefcient 0.5 kW/(m2$C) (individual heat-transfer coefcients forwater streams and utilities were assumed to be 1 kW/(m2$C)); theworking hours of the network per year 8000 h; the inlet and outlettemperatures of the cooling water 10 C and 20 C; the tempera-tures of FWandWW, 20 C and 30 C, and the specic heat capacityof water 4.2 kJ/(kg$C).

This problem was solved by several authors using different so-lution strategies (sequential and simultaneous). First, Bagajewiczet al. [37] presented the water target (77.273 kg/s) for this problem,while the design of HIWN is not reported. Later, Dong et al. [23]solved the problem of HIWN. The objective was to minimize TAC.In addition, discussion about the obtained designs for this example,using different solution strategies (sequential and simultaneous),and their comparisons was given by Ahmetovic and Kravanja [40].Dong et al. [23] presented a network design consisting of two HEsand two heaters (TAC: 2,631,805.4 $/y; the capital investment:305,913.3 $/y; the FW consumption: 87.2 kg/s; HU consumption:3671.4 kW). Note that the FW and HU consumptions increased

examples of different complexities including single and multiplecontaminants, and process-to-process streams for HI. The problemwas implemented in GAMS [38]. The MINLP model of WN was rstsolved using BARON in order to provide a good initial point, andthen the MINLP of combined WN-HEN was solved using SBB. It isworth pointing out that providing a good initial point for solvingthe overall HIWN is very important for obtaining optimal solutions.The objective of WN was to minimize FW consumption, and com-bined WN-HEN for minimizing TAC. The overall problem wassolved on a PC machine (2.67 GHz, 8 GB RAM) within a reasonablecomputation time. First, we compared our results with those re-ported in the literature for the case when process-to-processstreams were not taken into account for HI. In addition, if thenetwork design involved the splitting of streams in HEN, an NLPsub-optimization was nally performed for the xed structure, asgiven in Refs. [39], allowing for non-isothermal mixing after thematches. The improved solutions and novel networks were ob-tained thus enabling process-to-process streams for HI with FWand WW streams, as shown later.

5.1. Example 1

Table 1 shows the problem data taken from Ref. [37]. Thisexample involves three process units and a single contaminant. Thecost and operating parameters are taken from Ref. [23] and they aregiven as follows. The freshwater cost (FWC) is assumed to be0.375 $/t; the cooling utility cost 189 $/(kW$y); the heating utility(low pressure steam, 120 C) cost 377 $/(kW$y); the xed charge,1100 166.7 100

g th

hermFig. 8. Solution of the network involvin

E. Ahmetovic, Z. Kravanja / Applied Tcompared to the FW (87.2 vs. 77.273 kg/s) and HU (3245.5 kW)targets. The reported network design (Fig. 8) by Ahmetovic andKravanja [40] consists of three HEs and two heaters (TAC:2,455,048.1 $/y; capital investment: 396,966.3 $/y; FWC:834,545.5 $/y; HUC: 1,223,536.4 $/y; FW consumption: 77.273 kg/s;HU consumption: 3245.5 kW). Note that this design has about 7%smaller TAC compared to the results given by Dong et al. [23].

5.1.1. Non-isothermal mixing after matchesIn the case where the network involves split streams, an NLP

sub-optimization can be performed for the xed structure andvariable ows and temperatures, in order to determine the optimalowrates and area distribution for the HEs, as suggested by Yee andGrossmann [39]. This removes the simplifying assumption forisothermal mixing by optimizing the outlet temperatures for thoseexchangers with split streams. This strategy was also used byEscobar and Grossmann [41] when solving corresponding modelswhen the HEN structure involves split streams. As the networkinvolves a split of the outlet stream PU3 (hot stream in HEN, Fig. 8),we now used the proposed strategy by Yee and Grossmann [39] andobtained the solution presented in Fig. 9 (TAC: 2,447,761.7 $/y;capital investment: 389,679.9 $/y; FWC: 834,545.5 $/y; HUC:

Fig. 9. Solution of an NLP sub-optimie splitting of the stream for Example 1.

al Engineering 62 (2014) 302e317 3091,223,536.4 $/y; FW consumption: 77.273 kg/s; HU consumption:3245.5 kW). Note that the capital investment of the design in Fig. 9was reduced about by 1.8% and the TAC by about 0.3%, compared tothe network in Fig. 8.

5.1.2. Extended superstructure and extended modelWe solved the MINLP problem for the case when process-to-

process streams are involved for HI, and the resulted network ispresented in Fig. 10 (TAC of 2,422,531.7 $/y, capital investment of364,449.9 $/y, FWC of 834,545.5 $/y, HU cost of 1,223,536.4 $/y, FWconsumption of 77.273 kg/s, and HU consumption of 3245.5 kW).The obtained network design exhibited the minimum FW con-sumption (77.273 kg/s), the minimum hot (3245.5 kW) and cold(0 kW) utilities consumption, and an about 8% reduction of TAC(2,422,531.7 $/y vs. 2,631,805.4 $/y) compared to the result givenby Dong et al. [23], or about a 1.3% reduction compared to theresult reported by Ahmetovic and Kravanja [40] (2,422,531.7 $/y vs.2,455,048.1 $/y). This network consists of two HEs and two heaters.Note that this network (Fig. 10) does not involve stream splits inthe HEN, and has fewer HEs compared to the design presented inFigs. 8 and 9. Consequently, the HE area was increased for thematch between the FW stream and the outlet stream of the

zation for the network in Fig. 8.

e 1

E. Ahmetovic, Z. Kravanja / Applied Thermal Engineering 62 (2014) 302e317310Fig. 10. Optimal design of HIWN for Examplprocess unit (PU3). The process-to-process streams are integrated(hot stream from PU1 to PU2 and cold stream from PU2 to PU3). Thetotal amount of heat recovery is 2112.9 kW, and the HE area isabout 530 m2.

In addition, a heater is placed on the process-to-process coldstream from PU2 to PU3. This example clearly shows that byallowing for additional process-to-process HI, an improved solutionwould be obtained compared to the reported results (Table 2).

5.2. Example 2

Table 3 shows the problem data taken from Bogataj and Bag-ajewicz [22]. This example is more complex than the previous one.It involves four process units (PU1ePU4) andmultiple contaminants(A, B, C).

Table 2Summarized results for Example 1.

Case 1 Cas

Freshwaterconsumption (kg/s)

87.2 77.

Hot utilityconsumption (kW)

3671.4 324

Annualizedinvestment ($/a)

305,913.3 396

Total annualcost ($/a)

2,631,805.4 2,4

Case 1. Results from Ref. [23]; Case 2. Process-to-process streams were not taken into accostreams were not taken into account for HI; Case 4. Process-to-process streams are take

Table 3Problem data for Example 2.

Processunit

Contaminant mass load (g/s) Maximum inlet concentration (p

A B C A B

1 2 1 3 0 152 5 0 15 50 1003 30 4 0 100 1004 4 22 17 400 380involving process-to-process streams for HI.The cost and operating parameters are the same as given inExample 1. Consequently, the results by Bogataj and Bagajewicz[22] were recalculated using these cost and operating parameters,in order to compare the results in this paper with their results.

This example was studied by Bogataj and Bagajewicz [22] andAhmetovic and Kravanja [13] using simultaneous optimizationapproaches for the synthesis of HIWNs. The reported network de-signs consist of the same number of HEs (three HEs and one heater)with approximately the same FW and HU consumptions. However,the TAC of the network (see Fig. 11) in Ahmetovic and Kravanja [13](897,625.7 $/y) is lower than in Bogataj and Bagajewicz [22](907,065.7 $/y) mainly due to the lower investment cost (IC) forHEs. It is worth pointing out that the inlet and outlet streams of PU1and PU4 play an important role in HI, and there is a split of the inletstream to PU4 (Fig. 11).

e 2 Case 3 Case 4

273 77.273 77.273

5.5 3245.5 3245.5

,966.3 389,679.8 364,449.9

55,048.1 2,447,761.7 2,422,531.7

unt for HI [40]; Case 3. Non-isothermal mixing after matches and process-to-processn into account for HI.

pm) Maximum outlet concentration (ppm) Temperature(C)

C A B C

0 100 100 100 4030 100 200 250 100

100 800 750 600 75250 800 800 800 50

5.2.1. Non-isothermal mixing after matches 5.2.2. Extended superstructure and extended model

Fig. 11. Solution of the network for Example 2 involving splits of the stream in HEN [13].

E. Ahmetovic, Z. Kravanja / Applied Thermal Engineering 62 (2014) 302e317 311As explained in Example 1, the proposed strategy by Yee andGrossmann [39] was used to perform sub-optimization for the xedstructure shown in Fig. 11. However, the obtained solution was thesame, probably because the temperature of the mixed stream at theinlet of PU4 is xed (50 C), and there are less degrees of freedomfor the solutions improvement.Fig. 12. Optimal design of HIWN for Example 2 iFinally, in order to explore further improvement of thenetwork design for this example, the proposed strategy was usedfor allowing process-to-process streams for HI. The obtainednetwork is presented in Fig. 12. It consists of the same number ofHEs (three HEs and one heater) and operates with the sameminimum FW (26.535 kg/s) consumption, HU (1114.5 kW), andnvolving process-to-process streams for HI.

PU2/ PU4 (3458.5 kW) play an important role in heat recovery

extension of the superstructure and model was presented on thebasis of these alternatives. The proposed model includes allpossible heat-integration opportunities within the overallnetwork. The heat integration applied was performed simulta-neously and the model does not rely on the assumption of a xedheat-recovery approach temperature (HRAT), as all the temper-ature driving forces were now considered as optimization vari-ables. In addition, the strategy [39] was used to further improvesolution in the case of the design involving split streams in theHEN. Two literature examples involving single and multiplecontaminants were solved in order to demonstrate the efciencyof the extended superstructure and extended model. The ob-tained results were compared with those reported in the litera-ture. It is worth pointing out that the proposed model canproduce very good solutions or even better than those reported(e.g. Example 1: about an 8% reduction of TAC compared to [23]and 1.3% compared to [40]; Example 2: 1.9% reduction of TAC

Acknowledgements

Appendix

Table 4Summarized results for Example 2.

Case 1 Case 2 Case 3 Case 4

Freshwaterconsumption(kg/s)

26.5353 26.5351 26.5351 26.5351

Hot utilityconsumption(kW)

1115.7 1114.5 1114.5 1114.5

Annualizedinvestment($/a)

199,861 190,890 190,890 183,036

Total annualcost ($/a)

907,066 897,626 897,626 889,772

Case 1. Recalculated results from Ref. [22]; Case 2. Process-to-process streams werenot taken into account for HI [13]; Case 3. Non-isothermal mixing after matches andprocess-to-process streams were not taken into account for HI; Case 4. Process-to-process streams are taken into account for HI.

E. Ahmetovic, Z. Kravanja / Applied Thermal Engineering 62 (2014) 302e317312(Fig. 12).An improvement in TAC was obtained compared to the re-

ported results (889,772 $/y vs. 907,065.7 $/y or 1.9% compared toBogataj and Bagajewicz [22]; and 889,772 $/y vs. 897,625.7 $/y or0.9% compared to Ahmetovic and Kravanja [13] due to the lowerIC for HEs (8.4% compared to Bogataj and Bagajewicz [22], and4.1% compared to Ahmetovic and Kravanja [13]). It is worthpointing out that the total HE area of the improved design isreduced by about 12.7% compared to reported results. Fig. 12shows the best solution obtained so far and is based on theproposed strategy for HI of process-to-process streams and otherstreams within the overall network. Table 4 shows summarizedresults for Example 2.

6. Conclusions

This paper addressed the simultaneous synthesis of HIWNsinvolving process-to-process streams for HI within the overallnetwork. In order to improve network designs, two alternativeswere proposed for HI of the interconnection streams. Ancold utility (CU) (0 kW) consumption as the network given inFig. 11. However, the design does not involve stream splits withinthe HEN. In addition, allowing for HI of the process-to-processstreams and other streams within the network, the placementof HEs is completely different. It is worth mentioning thatprocess-to-process streams PU1 / PU3 (991.6 kW) andFig. A1. The HIWN where process-to-process stThis section presents the superstructure (Fig. A.1) and corre-sponding MINLP model, Eqs. (A.1)e(A.99), for the simultaneoussynthesis of HIWNs, as recently developed by Ahmetovic andKravanja [13], where process-to-process streams were not takeninto account for HI. This superstructure and model were used asthe bases for the extension presented in this paper, and whenconsidering the process-to-process streams for HI.The nancial support is gratefully acknowledged from theJoint EU-SEE Project (Scholarship scheme for academic exchangebetween the EU and Western Balkan countries), theSlovenian Research Agency (Programme No. P2-0032), and theFederal Ministry of Education and Science of Bosnia andHerzegovina.compared to [22] and 0.9% compared to [13]; 8.4% reduction of ICfor HEs compared to [22] and 4.1% compared to [13]; total heat-exchanger area was reduced more than 12%). In addition, novelalternative designs were obtained for the studied examples usingprocess-to-process streams for HI. Future work could be directedtowards an extension of the proposed superstructure and modelby incorporating wastewater treatment operations in order toallow wastewater recycling and reuse.reams were not taken into account for HI.

hermA. 1. Mathematical model of water network superstructure

Initial splitters of freshwater

FWs FWouts XpPU

FIPs;p c sSW (A.1)

FWouts FSSinp c sSW; c pPU; p 1 (A.2)

TFWs TSSinp c sSW; c pPU; p 1 (A.3)

TFWs TIPs;p c sSW; cpPU (A.4)

Freshwater splitters

FSSinp FSSoutp Xp0

FSSMp;p0 cp; p0PU; psjPUj (A.5)

FSSinp Xp

FSSMp;p0 c p; p0PU; p jPUj (A.6)

FSSoutp FSSinp1 c pPU; psjPUj (A.7)

xWins;c xSSoutp0;c c sSW; cp0PU; c cCC (A.8)

TSSoutp TSSinp1 c pPU; psjPUj (A.9)

TSSinp TSSoutp c pPU (A.10)

Mixer process units

FPUinp Xp0PU

FSSMp0;p XsSW

FIPs;p X

p0PUpsp0;Rp 0

FPp0;p

Xp0PURp 1

FPp0;p c pPU (A.11)

FPUinp $xPUinp;c

Xp0PU

FSSMp0;p$xSSoutp0;c XsSW

FIP$xWins;c

X

p0PUpsp0;Rp 0

FPp0;p$xSPUoutp0;c

Xp0PURp 1

FPp0;p$xSPUoutp0;c c pPU; c cCC

E. Ahmetovic, Z. Kravanja / Applied T(A.12)FMMoutp1$TMMoutp1

p0PUFSMMp0;p$TSPUoutp0FPUinp $Tmixp

Xp0PU

FSSMp0;p$TSSoutp0 XsSW

FIP$TIPs;p

X

p0PUpsp0;Rp 0

FPp0;p$TSPUoutp0

Xp0PURp 1

FPp0;p$TSPUoutp0 c pPU (A.13)

Process units

FPUinp FPUoutp c pPU (A.14)

FPUinp $xPUinp;c LPUp;c FPUoutp $xPUoutp;c c pPU; c cCC

(A.15)

xPUoutp;c xSPUinp;c c pPU; c cCC (A.16)

Splitter process units

FPUoutp Xp0PU

FSMMp;p0 FPOp X

p0PUpsp0;Rp 0

FPp;p0

Xp0PURp 1

FPp;p0 c pPU (A.17)

xSPUoutp;c xSPUinp;c c pPU; c cCC (A.18)

Wastewater mixers

FMMinp Xp0PU

FSMMp0;p FMMoutp c pPU; psjPUj (A.19)

Xp0PU

FSMMp0;p FMMoutp c pPU; p jPUj (A.20)

FMMinp FMMoutp1 c pPU; psjPUj (A.21)

FMMoutp1$xMMoutp1;c

Xp0PU

FSMMp0;p$xSPUoutp0;c

FMMoutp $xMMoutp;c c pPU; psjPUj (A.22)

Xp0PU

FSMMp0;p$xSPUoutp0;c FMMoutp $xMMoutp;c cpPU; p jPUj

(A.23)

X

al Engineering 62 (2014) 302e317 313 FMMoutp $TMMinp c pPU; psjPUj (A.24)

Hot and cold utility load

hermXp0PU

FSMMp0;p$TSPUoutp0 FMMoutp $TMMinp c pPU; p jPUj

(A.25)

TMMoutp TMMinp c pPU (A.26)

Final mixer

FMMoutp Xp0PU

FPOp0 Fout (A.27)

FMMoutp $xMMoutp;c

Xp0PU

FPOp0$xSPUoutp0;c Fout$xoutc ;

p 1; c cCC(A.28)

FMMoutp $TMMoutp

Xp0PU

FPOp0$TSPUoutp

Fout$Tout ; c pPU; p 1 (A.29)

Total mass balance and contaminant mass balance for the network

XsSW

FWs Fout (A.30)

XsSW

FWs$xWins;c XpPU

LPUp;c Fout$xoutc ; c cCC (A.31)

A.2. Convex-hull formulation for the identication of streams forHEN

Streams from mixer to process unit

yhpp ycpp 1; pPU (A.32)

Tmixp Thot;ini Tcold;inj TPUinp $

1 ycpp yhpp

;

pPU; iHP; jCP; i p; j p(A.33)

Thot;ini TPUin;maxp $yhpp ; pPU; iHP; i p (A.34)

Thot;ini TPUinp $yhpp ; pPU; iHP; i p (A.35)

Tcold;inj TPUinp $ycpp ; pPU; jCP; j p (A.36)

Tcold;inj TFWmins $ycpp ; pPU; jCP; j p (A.37)

Streams from process unit to splitter

yhpsp ycpsp 1; pPU (A.38)

TSPUoutp Thot;outi Tcold;outj TPUoutp $

1 ycpsp yhpsp

;

E. Ahmetovic, Z. Kravanja / Applied T314pPU; iHP; jCP; i p jPUj; j p jPUj(A.39)qi;j;k U$zi;j;k 0; iHP; jCP; kST (A.56)thi;NOK1 thouti

$fhi qcui; iHP (A.54)

tcoutj tci;1

$fcj qhuj; jCP (A.55)

Logic constraintsThot;outi TPUoutp $yhpsp ; pPU; iHP; i p jPUj (A.40)

Thot;outi TFWmins $yhpsp ; pPU; iHP; i p jPUj (A.41)

Tcold;outj TPUout;maxp $ycpsp ; pPU; jCP; j p jPUj

(A.42)

Tcold;outj TPUoutp $ycpsp ; pPU; jCP; j p jPUj (A.43)

A.3. Mathematical model of a heat-exchanger networksuperstructure

Overall heat balance for each stream

thini thouti$fhi XkST

XjCP

qi;j;k qcui; iHP (A.44)

tcoutj tcinj

$fcj

XkST

XiHP

qi;j;k qhuj; jCP (A.45)

Heat balance at each stream

thi;k thi;k1

$fhi

XjCP

qi;j;k; iHP; kST (A.46)

tcj;k tcj1

$fcj

XiHP

qi;j;k; jCP; kST (A.47)

Assignment of superstructure inlet temperatures

thini thi;1; iHP (A.48)

tcinj tcj;NOK1; jCP (A.49)

Feasibilities of temperatures

thi;k thi;k1; iHP; kST (A.50)

tcj;k tcj;k1; jCP; kST (A.51)

thouti thi;NOK1; iHP; kST (A.52)

tcoutj tcj;1; jCP; kST (A.53)

al Engineering 62 (2014) 302e317qcui U$zcui 0; iHP (A.57)

Connecting equations for HEN for streams from process unit to

hermtcoutj Tj TPUp $ 1 yp ; c pPU; jHP;splitter

fhi FPUoutp $Cp; c pPU; iHP; i p jPUj (A.70)

thini TPUoutp ; c pPU; iHP; i p jPUj (A.71)

thouti Thot;outi TPUoutp $1 yhpsp

; c pPU; iHP;

i p jPUj(A.72)

fcj FPUoutp $Cp; c pPU; jCP; j p jPUj (A.73)

tcinj TPUoutp ; c pPU; jCP; j p jPUj (A.74)

cold;out out cpsj p jPUjqhuj U$zhuj 0; jHP (A.58)

Logic constraints for temperature differences

Dti;j;k thi;k tcj;k G$1 zi;j;k

; iHP; jCP; kST

(A.59)

Dti;j;k1 thi;k1 tcj;k1 G$1 zi;j;k

; iHP; jCP; kST

(A.60)

Dti;CU thi;NOK1 TOUTCU G$1 zcui; iHP (A.61)

Dtj;HU TOUTHU tcj;1 G$1 zhuj

; jCP (A.62)

Dti;j;k;Dti;CU ;Dtj;HU EMAT ; iHP; jCP; kST (A.63)

A. 4. Connecting equations between WN and HEN

Connecting equations for HEN for streams from mixer to processunit

fhi FPUinp $Cp; c pPU; iHP; i p (A.64)

thini Thot;ini TPUinp $1 yhpp

; c pPU; iHP; i p

(A.65)

thouti TPUinp ; c pPU; iHP; i p (A.66)

fcj FPUinp $Cp; c pPU; jCP; j p (A.67)

tcinj Tcold;inj TPUinp $1 ycpp

; c pPU; jCP; j p

(A.68)

tcoutj TPUinp ; c pPU; jCP; j p (A.69)

E. Ahmetovic, Z. Kravanja / Applied T(A.75)Connecting equations for HEN for freshwater streams betweenfreshwater splitters

fcj FSSinp $Cp; c pPU; jCP; j p 2$jPUj (A.76)

tcinj TSSinp ; c pPU; jCP; j p 2$jPUj (A.77)

tcoutj TSSoutp ; c pPU; jCP; j p 2$jPUj (A.78)

Connecting equations for HEN for wastewater streams betweenwastewater mixers

fhi FMMoutp $Cp; c pPU; iHP; i p 2$jPUj (A.79)

thini TMMinp ; c pPU; iHP; i p 2$jPUj (A.80)

thouti TMMoutp ; c pPU; iHP; i p 2$jPUj (A.81)

Logical constraints for connecting streams in WN in HEN

zi;j;k yhpp ; pPU; iHP; j CP; kST ; i p (A.82)

zi;j;k ycpp ; pPU; iHP; j CP; kST; j p (A.83)

zcui yhpp ; pPU; iHP; i p (A.84)

zhuj ycpp ; pPU; jCP; j p (A.85)

zi;j;k yhpsp ; pPU; iHP; j CP; kST ; i p jPUj(A.86)

zi;j;k ycpsp ; pPU; iHP; j CP; kST ; j p jPUj(A.87)

zcui yhpsp ; pPU; iHP; i p jPUj (A.88)

zhuj ycpsp ; pPU; jCP; j p jPUj (A.89)

A. 5. Objective function

Objective function of the proposed model

TAC H$XsSW

FWs$CFWs XiHP

CCU$qcui XjCP

CHU$qhuj XiHP

XjCP

XkST

CFi;j$zi;j;k XiHP

CFi;CU$zcui XjCP

CFj;HU$zhuj

XiHP

XjCP

XkST

Ci;j$ABi;ji;j;k

XiHP

Ci;CU$ABi;CUi;CU

XjCP

Cj;HU$ABj;HUj;HU

al Engineering 62 (2014) 302e317 315(A.90)

herm(A.94)

LMTDi;CU

Dti;CU$TOUTiTINCU$

Dti;CU TOUTiTINCU

2

1=3;

iHP

(A.95)

LMTDj;HU

Dtj;HU$

TINHU TOUTj

$

Dtj;HU

TINHU TOUTj

2

1=3;

jCP

(A.96)

1Ui;j

1hi 1hj; iHP; jCP (A.97)

1Ui; CU

1hi 1hCU

; iHP (A.98)

1Uj;HU

1hj 1hHU

; jCP (A.99)

References

[1] R. Smith, Chemical Process Design and Integration, John Wiley & Sons Ltd.,Chichester, England, 2005.

[2] J. Klemes, F. Friedler, I. Bulatov, P. Varbanov, Sustainability in the Process In-dustry: Integration and Optimization, McGraw-Hill, New York, USA, 2010.

[3] M.M. El-Halwagi, Sustainable Design through Process Integration, Funda-mentals and Applications to Industrial Pollution Prevention, Resource Con-servation, and Protability Enhancement, Butterworth-Heinemann, Oxford,England, 2012.

[4] P. Glavic, Thirty years of international symposia on process systems engi-neering, Current Opinion in Chemical Engineering 1 (2012) 421e429.

[5] Z. Kravanja, Challenges in sustainable integrated process synthesis and thecapabilities of an MINLP process synthesizer MipSyn, Computers & ChemicalEngineering 34 (2010) 1831e1848.

[6] A.P. Barbosa-Pvoa, Progresses and challenges in process industry supplychains optimization, Current Opinion in Chemical Engineering 1 (2012)446e452.

[7] J.M. Lanez, L. Puigjaner, Prospective and perspective review in integratedsupply chain modelling for the chemical process industry, Current Opinion inChemical Engineering 1 (2012) 430e445.

[8] I.E. Grossmann, G. Guilln-Goslbez, Scope for the application of mathematicalThe areas (A), temperature differences (LMTD), and overall heat-transfer coefcients (U) of the exchangers, coolers, and heaters, aregiven as follows.

Ai;j;k qi;j;k

Ui;j$LMTDi;j;k; iHP; jCP; kST (A.91)

Ai;CU qi;CU

Ui;CU$LMTDi;CU; iHP (A.92)

Aj;HU qj;HU

Uj;HU$LMTDj;HU; jCP (A.93)

LMTDi;j;k Dti;j;k$Dti;j;k1

$

Dti;j;k Dti;j;k1

2

1=3;

iHP; jCP; kST

E. Ahmetovic, Z. Kravanja / Applied T316programming techniques in the synthesis and planning of sustainable pro-cesses, Computers & Chemical Engineering 34 (2010) 1365e1376.[9] J. Je _zowski, Review of water network design methods with literature anno-tations, Industrial & Engineering Chemistry Research 49 (2010) 4475e4516.

[10] D.C.Y. Foo, State-of-the-art review of pinch analysis techniques for waternetwork synthesis, Industrial & Engineering Chemistry Research 48 (2009)5125e5159.

[11] L.T. Biegler, I.E. Grossmann, A.W. Westerberg, Systematic Methods of Chem-ical Process Design, Prentice-Hall, New Jersey, 1997.

[12] J.J. Klemes, Industrial water recycle/reuse, Current Opinion in Chemical En-gineering 1 (2012) 238e245.

[13] E. Ahmetovic, Z. Kravanja, Simultaneous synthesis of process water and heatexchanger networks, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.02.061.

[14] L.E. Savulescu, R. Smith, Simultaneous energy and water minimisation, in:Presented at the 1998 AIChE Annual Meeting, Miami Beach, FL (1998).

[15] L.E. Savulescu, M. Sorin, R. Smith, Direct and indirect heat transfer in waternetwork systems, Applied Thermal Engineering 22 (2002) 981e988.

[16] L. Savulescu, J.-K. Kim, R. Smith, Studies on simultaneous energy and waterminimisationdpart I: systems with no water re-use, Chemical EngineeringScience 60 (2005) 3279e3290.

[17] L. Savulescu, J.-K. Kim, R. Smith, Studies on simultaneous energy and waterminimisationdpart II: systems with maximum re-use of water, ChemicalEngineering Science 60 (2005) 3291e3308.

[18] B. Leewongtanawit, J.K. Kim, Heat-Integrated System Design, University ofManchester, School of CEAS, 2005.

[19] Y.L. Tan, D.K.S. Ng, M.M. El-Halwagi, Y. Samyudia, D.C.Y. Foo, Synthesis ofheat-integrated resource conservation networks, in: A.K. Iftekhar,S. Rajagopalan (Eds.), Computer Aided Chemical Engineering, vol. 31, Elsevier,2012, pp. 985e989.

[20] J. Martnez-Patio, M. Picn-Nez, L.M. Serra, V. Verda, Systematic approachfor the synthesis of water and energy networks, Applied Thermal Engineering48 (2012) 458e464.

[21] L. Yiqing, M. Tingbi, L. Sucai, Y. Xigang, Studies on the effect of non-isothermalmixing on water-using networks energy performance, Computers & ChemicalEngineering 36 (2012) 140e148.

[22] M. Bogataj, M.J. Bagajewicz, Synthesis of non-isothermal heat integratedwater networks in chemical processes, Computers & Chemical Engineering 32(2008) 3130e3142.

[23] H.-G. Dong, C.-Y. Lin, C.-T. Chang, Simultaneous optimization approach forintegrated water-allocation and heat-exchange networks, Chemical Engi-neering Science 63 (2008) 3664e3678.

[24] B. Leewongtanawit, J.-K. Kim, Synthesis and optimisation of heat-integratedmultiple-contaminant water systems, Chemical Engineering & Processing:Process Intensication 47 (2008) 670e694.

[25] J. Kim, J. Kim, J. Kim, C. Yoo, I. Moon, A simultaneous optimization approachfor the design of wastewater and heat exchange networks based on costestimation, Journal of Cleaner Production 17 (2009) 162e171.

[26] W. Xiao, R.-j. Zhou, H.-G. Dong, N. Meng, C.-Y. Lin, V. Adi, Simultaneousoptimal integration of water utilization and heat exchange networks usingholistic mathematical programming, Korean Journal of Chemical Engineering26 (2009) 1161e1174.

[27] J. Je _zowski, R. Bochenek, G. Poplewski, On application of stochastic optimi-zation techniques to designing heat exchanger- and water networks, Chem-ical Engineering and Processing: Process Intensication 46 (2007) 1160e1174.

[28] T.F. Yee, I.E. Grossmann, Z. Kravanja, Simultaneous optimization models forheat integrationdIII. Process and heat exchanger network optimization,Computers & Chemical Engineering 14 (1990) 1185e1200.

[29] R. Drobez, Z.N. Pintaric, B. Pahor, Z. Kravanja, Simultaneous synthesis of abiogas process and heat exchanger network, Applied Thermal Engineering 43(2012) 91e100.

[30] L. Yang, I.E. Grossmann, Water targeting models for simultaneous owsheetoptimization, Industrial & Engineering Chemistry Research 52 (2013) 3209e3224.

[31] I.M.L. Chew, D.C.Y. Foo, H.L. Lam, J.C. Bonhivers, P. Stuart, L.E. Savulescu,A. Alva-Argaez, Simultaneous water and energy optimisation for a pulp andpaper mill, Chemical Engineering Transactions 25 (2011) 441e446.

[32] I.M.L. Chew, D.C.Y. Foo, J.-C. Bonhivers, P. Stuart, A. Alva-Argaez,L.E. Savulescu, A model-based approach for simultaneous water and energyreduction in a pulp and paper mill, Applied Thermal Engineering 51 (2013)393e400.

[33] C.M. Gonzalez, H. Verelst, S.E. Gonzalez, Simultaneous energy and waterminimization applied to sugar process production, Chemical EngineeringTransactions 25 (2011) 177e182.

[34] R.C. Baliban, J.A. Elia, C.A. Floudas, Optimization framework for the simulta-neous process synthesis, heat and power integration of a thermochemicalhybrid biomass, coal, and natural gas facility, Computers & Chemical Engi-neering 35 (2011) 1647e1690.

[35] R.C. Baliban, J.A. Elia, C.A. Floudas, Simultaneous process synthesis, heat, po-wer, and water integration of thermochemical hybrid biomass, coal, andnatural gas facilities, Computers & Chemical Engineering 37 (2012) 297e327.

[36] R. Karuppiah, I.E. Grossmann, Global optimization for the synthesis of inte-grated water systems in chemical processes, Computers & Chemical Engi-neering 30 (2006) 650e673.

al Engineering 62 (2014) 302e317[37] M. Bagajewicz, H. Rodera, M. Savelski, Energy efcient water utilization sys-tems in process plants, Computers & Chemical Engineering 26 (2002) 59e79.