Embed Size (px)
Citation preview
lable at ScienceDirect
Journal of Cleaner Production 71 (2014) 128e138
Contents lists avai
Journal of Cleaner Production
journal homepage: www.elsevier .com/locate/ jc lepro
Heat integrated resource conservation networks without mixing priorto heat exchanger networks
Yin Ling Tan a,*, Denny K.S. Ng b, Dominic C.Y. Foo b, Mahmoud M. El-Halwagi c,d,Yudi Samyudia a
aChemical Engineering Department, Curtin University, Sarawak Campus, CDT 250, 98009 Miri, Sarawak, MalaysiabDepartment of Chemical and Environmental Engineering/Centre Excellence for Green Technologies, The University of Nottingham, Malaysia Campus, BrogaRoad, 43500 Semenyih, Selangor, MalaysiacChemical Engineering Department, Texas A&M University, College Station, TX 77843, United StatesdKing Abdul-Aziz University, Jeddah, Saudi Arabia
a r t i c l e i n f o
Article history:Received 7 August 2013Received in revised form7 January 2014Accepted 7 January 2014Available online 18 January 2014
Keywords:Process integrationTargetingProperty integrationHeat integrationResource conservationOptimisation
* Corresponding author. Tel.: þ60 85 443833; fax:E-mail addresses: [email protected] (Y.L. Tan)
my (D.K.S. Ng), [email protected] (Dedu (M.M. El-Halwagi), [email protected]
0959-6526/$ e see front matter � 2014 Elsevier Ltd.http://dx.doi.org/10.1016/j.jclepro.2014.01.014
a b s t r a c t
This paper presents a generic approach for the synthesis of heat integrated resource conservation net-works (HIRCNs) of the fixed flow rate problem, where process sources linked directly to process sinkswithout any prior mixing. The mixed integer non-linear program (MINLP) formulation complemented byfloating pinch concept was developed to determine the optimum fresh material resources as well as hotand cold energy utilities. The proposed approach is applicable for both concentration- and property-based direct reuse/recycle system with variable operating parameters (i.e. flow rates, temperaturesand properties). Three literature case studies are solved to illustrate the proposed approach.
� 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Huge amount of energy and fresh resources (i.e. water, chem-icals, solvents) are consumed by process industries to achieve thedesired product throughput and quality. The current drive towardsustainability and business competitiveness has driven the processindustries to effectively use these resources. Thus, resource con-servation activities have become the centre of attention ascompared to conventional end-of-pipe waste treatment system.
With enormous developments in the past three decades, Pro-cess Integration techniques have been widely accepted as effectivetools for resource conservation and waste reduction for the pro-cess industry. El-Halwagi (2006) defines Process Integration as aholistic approach to process design, retrofitting and operationwhich emphasises the unity of the process. Available tools of
þ60 85 443837., [email protected]. Foo), el-halwagi@tamu.(Y. Samyudia).
All rights reserved.
Process Integration techniques for resource conservation andwaste reduction can be generally categorised as Heat, Mass andProperty Integration. Several important reviews can be found inliterature, e.g. Furman and Sahinidis (2002) for Heat ExchangeNetwork (HEN), Dunn and El-Halwagi (2003) for Mass ExchangeNetwork, and Foo (2009) for Material Resource Conservation Net-works (RCNs).
In the past decades, active developments were seen for RCNs,which includes Water, Hydrogen and Property Integration. In allcases, the main objective is to reduce both fresh resource con-sumption and waste generation. Review on RCNs synthesis can befound in textbooks, including both in-plant and inter plant materialrecovery systems (El-Halwagi, 2006; Foo, 2012).
It should be noted that most of the RCNs works do not considertemperature effect in the process streams. There are many caseswhere both mass and heat recovery are equally important. Forinstance, when dry air is used to remove volatile organic com-pounds fromwastewater stream in a stripper, the air stream needsto possess specific temperature and properties before entering thestripper. Therefore, simultaneous consideration of mass, propertyand heat recovery should be addressed.
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138 129
In the past decades, extensive work was reported for simulta-neous energy and water minimisation. These techniques can alsobe classified as insight-based and mathematical optimisation ap-proaches. The former are developed based on sequential approach;while the latter considered both sequential and simultaneous ap-proaches. As reported in the literature, various insight-basedtechniques were developed but they are limited to single prop-erty RCN problems. These techniques include two dimensional griddiagram and separate systems with (Savulescu et al., 2005b) andwithout water reuse (Savulescu et al., 2005a), water energy balancediagram (Leewongtanawit and Kim, 2009), source-demand energycomposite curves (Savulescu et al., 2002), heat surplus diagram(Manan et al., 2009), superimposed mass and energy curves (WanAlwi et al., 2011), stream merging principles (Feng et al., 2008),graphical thermodynamic rules (Sorin and Savulescu, 2004), ther-modynamic principles for threshold problem (Polley et al., 2010),energy recovery algorithm (Sahu and Bandyopadhyay, 2010),modified problem table algorithm (Bandyopadhyay and Saha, 2010)and temperature versus concentration diagram (Martínez-Patiñoet al., 2011).
On the other hand, mathematical optimisation techniques havebeen established to overcome limitation associated with insight-based techniques. Sequential linear programming models havebeen developed to first determine the minimum fresh water con-sumption followed by minimum energy requirement. DetailedHeat Integrated Water Network (HIWN) is then identified viaMINLP models. Bagajewicz et al. (2002) initiated the sequentialapproach for the synthesis of Heat Integrated Water Networks(HIWNs). The fresh water and energy targets are firstly achievedusing an LP formulation based on the necessary conditions ofoptimality. In the second stage, an MINLP heat transhipment modelis generated. These models incorporate non-isothermal mixing aswell as forbidden and compulsory flow connections and heattransfer matches (Bagajewicz et al., 2002).
Feng et al. (2009) analysed the interconnections between thedesign of a water allocation network and the design of a heatexchanger network. The authors discovered that reducing thenumber of temperature local fluctuations along the sub-streams inwater networks improves the energy performance of the system. Asa result, mathematical model with this considerationwas proposedto synthesise a HIWN.
However, the above-mentioned works are primarily applicableto fixed load problems. To overcome this limitation, George et al.(2011) established a sequential approach for the fixed flowrateproblems which is applicable for both single and multiple con-taminants problems with the incorporation of isothermal and non-isothermal mixing of streams. In this approach, a linear program-ming model is formulated to identify the fresh water target. As forHEN model, a linear transshipment model is formulated forisothermal mixing problemwhile a nonlinear programming modelwith a discountinuous derivative (DNLP) is formulated for non-isothermal mixing cases.
On the other hand, Liao et al. (2011) presented an approach forHIWNs that allow splitting of hot and cold streams. Based on Liaoet al. (2011), an MILP model that treats the direct and indirectheat transfer separately is developed to identify the promisingmatches between hot and cold streams. Next, anMINLPmodel withconsideration of the splitting and non-isothermal mixing featuresinside the HEN is initiated to achieve the desired HIWN.
Recently, Sahu and Bandyopadhyay (2012) extended theconcept of modified problem table algorithm (Sahu andBandyopadhyay, 2010) to formulate HIWNs as linear program-ming model. The authors formulated three LP models for targetingthe fresh water and energy consumptions for isothermal and non-isothermal mixing situations. The proposed formulation avoids the
sub-optimality issues of MINLP and DNLP formulations for the caseof non-isothermal mixing as found in the previous work (Georgeet al., 2011). However, iteration of different pinch points isneeded to identify the minimum energy requirement (Sahu andBandyopadhyay, 2012).
On the other hand, the total cost of HIWNs can be minimised viasimultaneous techniques. Leewongtanawit and Kim (2008) initi-ated mathematical models for synthesis of HIWNs with multiplecontaminants. The authors formulate the overall problem as anMINLP optimisation problem. Decomposition approach is intro-duced to decompose the overall MINLP problem into MILP and NLPsub-problems which are solved in sequence using an iterativeprocess. The method has also considered an economic trade-offbetween water network and HEN, non-isothermal and generationof separate systems. Furthermore, Bogataj and Bagajewicz (2008)developed another MINLP model for HIWNs synthesis. The estab-lishedMINLPmodel includes the NLP formulation of water networksuperstructure and the MINLP formulation of heat exchangenetwork superstructure for non-isothermal stream mixing.
Note that the models presented by Leewongtanawit and Kim(2008) and Bogataj and Bagajewicz (2008) utilised heuristics toreduce the number of hot and cold streams in the HEN, which hadreduced the size of the model. However, the limitation of theseapproaches is that, the potential promising HIWNs may beexcluded based on the heuristics. As a result, Dong et al. (2008)modify the state-space superstructure to formulate an MINLPmodel which covers a broader network structures. However, themodel is very large in size and it is computational extensive whenthe problem scale increases. Thus, Dong et al. (2008) established anintegrated optimisation strategy to improve the solution qualityand efficiency. The potential global optimum may be identified byapplying an interaction method proposed.
Ataei and Yoo (2010) proposed a sequential approach for mul-tiple contaminant systems with the consideration of flowratechanges and heat loss in the HIWNs. Firstly, an NLP model isestablished to identify the feasible non-isothermal mixing pointsthat provide the overall network with minimum fresh water andenergy consumptions. Next, HEN is simplified through a newgeneration of separate system in HEN (Ataei and Yoo, 2010).
Ahmetovi�c and Kravanja (2013) presented a HIWN superstruc-ture with direct heat exchange by the mixing of streams and indi-rect heat exchange in heat exchangers. The model is formulated asnon-convexMINLP and the objective is tominimise the total annualcosts. Furthermore, the authors developed a set of new constraintsto identify the interconnecting hot and cold streams betweenwaternetwork and HEN. Later, this model was extended to includeprocess-to-process streams and other streams within the overallnetwork for heat integration (Ahmetovi�c and Kravanja, 2014). Twostrategies were proposed for heat integration of process-to-processstreams. This extended model was also a non-convex MINLP whilethe objective is to minimise the total annual cost of the network.
Recently, some work on simultaneous Property and EnergyIntegration has been observed. The first work on simultaneousProperty and Energy Integration was presented by Kheireddineet al. (2011). The authors took into consideration of the thermalconstraints in mass and property-based RCN. A nonlinear pro-gramming (NLP) model was presented to minimise the total cost ofRCN, while satisfying a set of process and environmental con-straints. In addition, the model also accounts for heat of mixing andthe interdependency of properties. Nevertheless, the proposedmodel does not allow temperature adjustment through heaters andcoolers.
Thus, Rojas-Torres et al. (2013) established a systematicapproach for the synthesis of property-based RCN with propertyinterceptors where heaters and coolers are modelled as thermal
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138130
interceptors. Furthermore, the developed model incorporates thedependence of properties on temperature, thermal effects as wellas a new set of property operators which is used to track keyenvironmental properties such as odor, toxicity. However, theproposed model only involves heaters and coolers without heatintegration. In many problems, energy recovery need to be maxi-mised before external heating and cooling utilities are used.
To overcome this limitation, Tan et al. (2013) presented a meth-odology for Heat Integrated Resource Conservation Network(HIRCN) synthesis, covering both concentration- and property-based direct reuse/recycle systems. The proposed method is able tohandle HIRCN problems with variable operating range of processparameters, such as stream flowrates, temperatures and properties.For uncertain temperature, the authors adopted the floating pinchconcept (Duran and Grossmann, 1986) to identify hot and cold util-ities. However, the main drawback of the previous work is that, theproposed superstructure is too complex and required discretisationapproach (Phamet al., 2009) to solve theMINLPproblem,whichmaylead to global or near global optimal results. Furthermore, when thediscretisation approach is used for complex problems (e.g. withmultiple property operators), the MILP model becomes computa-tional intensive. Hence, it is desired to develop a simple and yetgenericmodel for the synthesis of a cost effective concentration- andproperty-based HIRCN. This is the subject of this paper.
In this paper, a simple superstructure is presented for HIRCNof the fixed flow rate problem. The problem is formulated asMINLP model, which satisfies a set of process and environmentalconstraints. It makes use of the floating pinch concept (Tan et al.(2014) in solving cases with varying process parameters. Threeliterature case studies are used to illustrate the proposedmethod.
2. Problem statement
The problem definition of a HIRCN is given as follows:Given NSOURCES number of process sources that can be
considered for reuse/recycle in the process sinks, or be dischargedas waste. Given also NSINKS number of process sinks which areunits that can accept process sources. Each process source i, hasfixed flow rate (Wi), property operator p (ji,p) and temperature (Ti).Each sink j, has an acceptable range of flowrate (Gj), property (jj,p)and temperature (Tj), given as in Eqs. (1)e(3).
Gminj � Gj � Gmax
j j˛NSINKS (1)
jminj;p � jj;p � jmax
j;p j˛NSINKS p˛NPROP (2)
Tminj � Tj � Tmax
j j˛NSINKS (3)
where Gminj ;Gmax
j ;jminj;p ;jmax
j;p ; Tminj ; Tmax
j are the respective lowerand upper bounds of the admissible flow rate, property operator pand temperature for sink j. NFRESH number of external fresh re-sources may be purchased to supplement the requirement of thesinks. Each fresh resource r has property operator p (jr,p) andtemperature (Tr); and its flow rate is to be determined as part of thesolution model. Fresh resources and process sources may undergoexternal heating and cooling in order to meet the desired tem-perature range of the sinks and waste.
A general linearisedmixing rule for property integration is givenas follows (Shelley and El-Halwagi, 2000):
jðpÞ ¼Xm
xmjm;p (4)
where jm,p and jðpÞ are the operators for property p of stream mand mixture property p respectively; while xm is the fractionaldistribution of stream m of the total mixture flowrate. Eq. (4) isneeded to identify all possible mixing patterns for each property.
Each source is split and supplied to all sinks or discharge aswaste. These streams are intended for the HEN and their flowratesis to be determined simultaneously within the HIRCN. Note thatthese streams can take the form as a set of NHOT hot streams or a setof NCOLD cold streams. In this work, hot stream is defined as astream with supply temperature (Ts
h) higher than target tempera-ture (T t
h); while cold stream has supply temperature (Tsc ) lower thantarget temperature (T t
c). Therefore, based on the target temperatureof sink j, source i can be considered as either hot or cold stream.However, if source i temperature falls within the target tempera-ture range of sink j, source i can be split into hot and cold streams.For instance, for a sink with acceptable temperature range of 300e400 K, a source with temperature of 350 K may be split into hot(Tsh ¼ 350 K and Tth ¼ 300 Ke349 K) and cold streams (Ts
c ¼ 350 Kand Ttc ¼ 351 Ke400 K). In other words, the temperatures beforeHEN and after HEN are set or bounded based on the source i andsink j temperatures respectively. This simplification enables one tocategorise the HEN streams as hot or/and cold streams and extractthe respective temperatures directly from the given source and sinktemperature limiting data. More importantly, it has significantlyreduced the number of temperature variables and also the searchspace of this formulation.
Besides, external hot (Qh) and cold (Qc) utilities are available tofurther heat/cold the process streams to meet the process sinksrequirement, after maximising energy recovery between hot andcold streams. It is assumed that no mass transfer occur in the heatexchangers. Therefore, the compositions and flowrates of processstreams remain unchanged after the HEN. Fig. 1 shows the source-HEN-sink superstructure of the problem. The objective of this workis to synthesise a HIRCN of minimum cost, whichmay take the formof minimum operating or total annualised costs. Literature casestudies are solved to illustrate the proposed model.
3. Model formulation
The following sub-sections present the models for both con-centration- and property-based RCNs, as well as the HEN section ofthe HIRCN (see source-HEN-sink superstructure in Fig. 1).
3.1. Concentration- and property-based RCN
The mass and energy balances for various sources and sinks canbe defined as follows:
Splitting of fresh source r:
Fr ¼X
j˛NSINKSfr;j r˛NFRESH (5)
where fr,j is the flow rate of fresh source r to sink j.Splitting of process source i:
Wi ¼X
j˛NSINKSwi;j þ Bi;waste i˛NSOURCES (6)
wherewi,j and Bi,waste are the flow rates of source i recovered to sinkj and discharged as waste.
Mass balances at the mixing point before sink j:
Gj ¼X
i˛NSOURCESwi;j þ
Xr˛NFRESH
fr;j j˛NSINKS (7)
where Gj is the total flow rate of sink j.
j=NSINKSi=1
j=1Fresh 1 Process Sinks
Wastei=NSOURCES
. . .
Fr
Gj
M
M
M
wi,j
. . .
Wi
. . .
r =NFRESH
wi,waste
Process Sources i
fr,j
Heat Exchanger Network (HEN)
Fig. 1. Sourceesink representation for a HIRCN.
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138 131
Mass balance of waste:
Bwaste ¼X
i˛NSOURCESBi;waste (8)
where Bwaste is the flow rate of waste.Based on Eq. (4), property operator balance for property p at the
mixing point before sink j:
jj;pGj ¼X
i˛NSOURCES
hji;pwi;j
i
þX
r˛NFRESH
hjr;pfr;j
ij˛NSINKS p˛NPROP (9)
Property operator balance at the mixing point before waste:
jwaste;pBwaste ¼
Xi˛NSOURCES
hji;pBi;waste
ip˛NPROP (10)
where jwaste,p is the property operator p for waste.
BwasteCPwaste�Twaste � To� ¼
Xi˛NSOURCES
mHi;wasteCP
Hi;waste
�TH;outi;waste � To
�þ
Xi˛NSOURCES
mCi;wasteCP
Ci;waste
�TC;outi;waste � To
�(15)
Note that Eqs. (9) and (10) are used to determine the meanproperty value of each sink j andwaste, and should be carried out forall concerned properties for each process sink. As discussed previ-ously, the same stream sent from fresh resource r and source i to sinkj and waste can take the form as hot and cold streams, if its tem-perature falls in between the operating temperature range of thesink and waste. Therefore, Eqs. (11)e(13) are included in the model.
fr;j ¼ mHr;j þmC
r;j r˛NFRESH j˛NSINKS (11)
wi;j ¼ mHi;j þmC
i;j i˛NSOURCES j˛NSINKS (12)
Bi;waste ¼ mHi;waste þmC
i;waste i˛NSOURCES (13)
where mHr;j, m
Hi;j, m
Cr;j and mC
i;j are flowrate of hot and cold streamsfrom fresh resource r and source i to sink j; mH
i;waste and mCi;waste are
the flowrate of hot and cold streams from source i to waste.
Energy balances at the mixing point before the sink j:
GjCPj Tj � To� � ¼
Pr˛NFRESHm
Hr;jCP
Hr;j TH;outr;j � To� �
þP
r˛NFRESHmCr;jCP
Cr;j TC;outr;j � To� �
þP
i˛NSOURCESmHi;jCP
Hi;j TH;outi;j � To� �
þP
i˛NSOURCESmCi;jCP
Ci;j TC;outi;j � To� �
j˛NSINKS
(14)
where CPj, CPHr;j, CPHi;j, CP
Cr;j, and CPCi;j are heat capacities of sink j, hot
and cold streams from fresh resource r and source i to sink j; TH;outr;j ,
TH;outi;j , TC;outr;j and TC;outi;j are the target temperatures of hot and cold
streams from fresh resource r and source i to sink j, while To is thereference temperature.
Energy balance at the mixing point before waste:
where CPwaste, CPHi;waste and CPCi;waste are the heat capacities of waste,hot and cold streams from source i to waste; Twaste, TH;out
i;waste andTC;outi;waste is the temperature of waste, target temperatures of hot andcold streams from source i to waste.
3.2. Heat exchanger networks
The HEN floating pinchmethod established by Tan et al. (2014) isapplied in this work. This method is used because of the variableflow rates and temperatures in the problem formulation, whichcannot utilise the established heat integration models for fixedstreams conditions. The background concept of this method isbased on the shifted hot and cold composite curves. According toDuran and Grossmann (1986), the potential pinch candidates arethose corner points on the composite curves which corresponds tothe inlet temperatures of any hot and cold streams. Therefore,overall energy balance equation and energy balance equationabove or below pinch are developed for each of the postulated
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138132
pinch point candidates, which will then identify the true pinchpoint and also the minimum hot and cold utilities. Detail descrip-tion of HEN floating pinch method can be referred to Tan et al.(2014). The following section presents the HENmodel of the HIRCN.
The supply and target temperatures of the hot and cold streamsfrom fresh resource r and source i to sink j and waste are firstshifted based on minimum temperature of driving force, DTmin(subtract DTmin/2 for hot streams; add DTmin/2 for cold streams) asfollow,
Tsh ¼
26666666666666664
T inr;j�DTmin2
«
T inðNFRESHþiÞ;j�DTmin2
«
T inðNFRESHþNSOURCESþiÞ;waste�DTmin2
«
T inðNFRESHþNSOURCESþNSOURCESÞ;waste�DTmin2
37777777777777775
i˛NSOURCESj˛NSINKSr˛NFRESHh˛NHOT
(16)
T th ¼
26666666666666664
Toutr;j �DTmin2
«
ToutðNFRESHþiÞ;j�DTmin2
«
ToutðNFRESHþNSOURCESþiÞ;waste�DTmin2
«
ToutðNFRESHþNSOURCESþNSOURCESÞ;waste�DTmin2
37777777777777775
i˛NSOURCESj˛NSINKSr˛NFRESHh˛NHOT
(17)
Tsc ¼
26666666666666664
T inr;jþDTmin2
«
T inðNFRESHþiÞ;jþDTmin2
«
T inðNFRESHþNSOURCESþiÞ;wasteþDTmin2
«
T inðNFRESHþNSOURCESþNSOURCESÞ;wasteþDTmin2
37777777777777775
i˛NSOURCESj˛NSINKSr˛NFRESHc˛NCOLD
(18)
T tc ¼
26666666666666664
Toutr;j þDTmin2
«
ToutðNFRESHþiÞ;jþDTmin2
«
ToutðNFRESHþNSOURCESþiÞ;wasteþDTmin2
«
ToutðNFRESHþNSOURCESþNSOURCESÞ;wasteþDTmin2
37777777777777775
i˛NSOURCESj˛NSINKSr˛NFRESHc˛NCOLD
(19)
where Tsh and T th are shifted supply and target temperatures of the
hot stream, while Tsc and Ttc are shifted supply and target temper-
atures of the cold streams in HEN. Note that the size of NHOT and
NCOLD sets are j(r þ i) þ i respectively and each of the entriesrepresents a vector column.
The potential pinch candidate, Tp are taken as the inlet tem-peratures of the hot and cold streams,
Tp ¼8<: Tsh
Tsc
h˛NHOTc˛NCOLDp˛NPINCH
(20)
The total energy balance is to be used together with energybalance above or below the pinch point candidate to identify thetrue pinch point and to ensure thermodynamic feasibility. In thiswork, energy balance above the pinch point candidate is used.
To determine the energy balance above the pinch point candi-dates, stream locations parameterisation is needed. In this work,binary variables are used to parameterise the stream locations,given by the constraints in Eqs. (21)e(24).
bth;p ¼�1 if T th > Tp0 if T th � Tp
h˛NHOTp˛NPINCH (21)
bsh;p ¼�1 if Tsh > Tp0 if Tsh � Tp
h˛NHOTp˛NPINCH (22)
gtc;p ¼�1 if Ttc > Tp0 if Ttc � Tp
c˛NCOLDp˛NPINCH (23)
gsc;p ¼�1 if Tsc > Tp0 if Tsc � Tp
c˛NCOLDp˛NPINCH (24)
where bth;p,bsh;p,g
tc;p and gs
c;p are the binary integer. The energybalance above the pinch point candidate is expressed as:
Qh�X
c˛NCOLDmcCPc
ngsc;p
�Tp�Tsc
��gtc;p�Tp�T tc
�o
�X
h˛NHOTmhCPh
nbth;p
�Tp�T th
��bsh;p
�Tp�Tsh
�op˛NPINCH
(25)
where mh, mc, CPc, CPh, T th and Ttc are flow rate, heat capacities and
target temperatures for hot and cold streams in HEN. Readers mayrefer to Tan et al. (2014) for the details of the usefulness of Eq. (25).
The following equation shows the total energy balance.
Xh˛NHOT
mhCPh�Tsh�T th
�� Xc˛NCOLD
mcCPc�T ts�Tss
�þQh�Qc ¼ 0
(26)
Note that the total energy balance (Eq. (26)) together with en-ergy balance above the pinch point candidate (Eq. (25)) with therespective constraints (Eqs. (21)e(24)) are used to identify the truepinch point and the minimum hot and cold utilities of a givenproblem.
In order to ensure the connection between property-based RCNmodel and HEN model, Eqs. (27e33) are used to relate the flowrates and temperatures in these models.
Flow rate of hot and cold streams from fresh resource r andsource i to sink j are classified as follow,
Table 1Data for Case Study 1.
Flowrate (kg/s) Temperature (�C) Concentration (ppm)
SinkSK1 350 30 0SK2 677 187 40SK3 126 55 75SK4 202 98 100
SourceSR1 530 21 30SR2 68 43 150SR3 1130 130 300SR4 36 35 500
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138 133
mh ¼
2666666664
mHr;j«
mHðNFRESHþiÞ;j
«mH
ðNFRESHþNSOURCESþiÞ;waste«
mHðNFRESHþNSOURCESþNSOURCESÞ;waste
3777777775
i˛NSOURCESj˛NSINKSr˛NFRESHh˛NHOT
(27)
mc ¼
2666666664
mCr;j«
mCðNFRESHþiÞ;j
«mC
ðNFRESHþNSOURCESþiÞ;waste«
mCðNFRESHþNSOURCESþNSOURCESÞ;waste
3777777775
i˛NSOURCESj˛NSINKSr˛NFRESHc˛NCOLD
(28)
Supply temperature of hot and cold streams from fresh resourcer and source i to sink j are the same as that of fresh resource r andsource i.
TH;inr;j ¼ TC;inr;j ¼ Tr r˛NFRESH j˛NSINKS (29)
TH;ini;j ¼ TC;ini;j ¼ Ti i˛NSOURCES j˛NSINKS (30)
Target temperature of hot and cold streams from fresh resourcer and source i to sink j are based on the temperature of sink j.
TH;outr;j ¼ TC;outr;j ¼ Tj r˛NFRESH j˛NSINKS (31)
TH;outi;j ¼ TC;outi;j ¼ Tj i˛NSOURCES j˛NSINKS (32)
Supply and target temperature of hot and cold streams fromsource i to waste are the same as that of source i and waste.
TH;ini;waste ¼ TC;ini;waste ¼ Ti i˛NSOURCES (33)
TH;outi;waste ¼ TC;outi;waste ¼ Twaste i˛NSOURCES (34)
It is worth noting that the above model is simpler as comparedto that presented by earlier work Tan et al. (2013). This model onlyinvolves one splitting point (for sources) and one mixing point (forsinks). However, the model presented by Tan et al. (2013) consistsof two mixing points (i.e. one for HEN and the other for the sinks)and two splitting points (one for sources and the other for HEN)which is similar to a non-convex pooling problem formulation.Besides, in Tan et al. (2013), the supply and target temperatures forHEN are unknown variables as they depend on the flow rate ofsources being mixed. Hence, this leads to non-linearity with Eq.(25), which makes the model to be highly non-convex andcomputational intensive. As a result a solution strategy is needed.However, in this work, the proposedmodel avoids such situation, asthe supply and target temperatures are directly based on thetemperature of sources and sinks of known values.
4. Case studies
To illustrate the proposed model, three literature case studiesare solved. All cases are solved using Extended LINGO v11.0 withGlobal Solver. Solution strategy is not required in this proposedmodel as the solver is able to provide the global optimal solution. Inall case studies, the costs of hot and cold utilities (Costh and Costc)
are given as $80/kW.y and 20$/kW.y (Kim et al., 2009). In addition,total annual operating hour (k) is taken as 8000 h.
4.1. Case Study 1
Case Study 1 is an ammonia recovery case study taken fromWanAlwi et al. (2011). It involves a process plant that utilises ammoniaas themass separating agent in a sour gas absorption column and asa dust-cleaning agent. On the other hand, ammonia waste is pro-duced in the calcium chloride production section of the plant,which is currently sent to waste treatment system. Therefore, toreduce the waste generation, ammonia can be recovered into theprocess units which require ammonia. The limiting data for thiscase study is shown in Table 1. In addition, fresh ammonia may bepurchased externally and is available at 30 �C, with unit cost of$500/t and waste ammonia has to be discharged at 40 �C (Wan Alwiet al., 2011). In this case study, the major component in all stream isammonia; thus, heat capacities of all streams (CPn, CPi, CPr and CPj)are assumed to take a constant value of 2.19 kJ/kg K; and DTmin of35 �C is used (Wan Alwi et al., 2011).
The objective of this case study is to minimise annual operatingcost (AOC), which consists of operating costs for fresh resources, aswell as hot and cold utilities in the HIRCN. The optimisationobjective is given as follows:
minFr ;Qh;Qc
AOC ¼ k*
( XNFRESH
r¼1
CostrFr þ CosthQh þ CostcQc
)(35)
where Costr is the cost of fresh resources r.Eq. (35) is solved subject to the constraints in Eqs. (1)e(9) and
(11)e(34). The optimised HIRCN is shown in Fig. 2. As shown, theHIRCN consume a fresh ammonia flow rate (Fr) of 654.9 kg/s, andwith utility targets of Qh ¼ 132,927 kW and Qc ¼ 79,228 kW. Tofurther verify the results of Qh and Qc, the HEN for this case study issynthesised using the pinch design method (Linnhoff et al., 1982),and is presented in Fig. 3. Note that in this case study, the unit costof fresh ammonia is much higher than that of hot and cold utilities.As a result, fresh ammonia is minimised while allowing using moreutilities. It is worth mentioning that the results are identical withthe reported result in Sahu and Bandyopadhyay (2012), if a twostage LP model is solved such as that in Case Study 1.
4.2. Case Study 2
Case study 2 is a single property-based water network whichadapted from Sahu and Bandyopadhyay (2012). It consists of twoprocess sinks and two process sources, with limiting data given inTable 2. Toluene is assumed as the key contaminant in this casestudy. The available fresh resource is given as pure fresh water(0 ppm), with unit cost of $0.45/t and available at 20 �C. Besides,wastewater has to be discharged at temperature of 30 �C (Sahu and
Fig. 2. Optimal solution for Case Study 1.
Fig. 3. HEN for Case Study 1.
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138134
Bandyopadhyay, 2012). The minimum approach temperature forHEN (DTmin) is assumed as 10 �C for the case study.
In this case study, all the heat capacities of sink, source, freshresource as well as hot and cold streams (CPj, CPi, CPr and CPn) canbe determined via equation below:
CP ¼X
xkCPkk˛NCOMP (36)
where xk is the mole fraction of component k and CP for eachcomponent can be determined using Eq. (37). Note that the heatcapacity values are temperature-dependence.
CPk ¼ ak þ bkT þ ckT2 þ dkT
3 k˛NCOMP (37)
where a , b , c and d are parameters in temperature-dependent
k k k kexpression for heat capacity of each component. a, b, c and d parame-ters for toluene are given as 1.8083 J/(gmol K), 81.222 � 10�2 J/(gmol K2), �151.27 � 10�5 J/(gmol K3), and 1630 � 10�9 J/(gmol K4)while a, b, c and d parameters for water are 18.2964 J/(gmol K),47.212 � 10�2 J/(gmol K2), �133.88 � 10�5 J/(gmol K3), and1314.2 � 10�9 J/(gmol K4).
The objective of this case study is to minimise the AOC, whichconsists of operating costs for fresh water, as well as hot and cold
Table 2Data for Case Study 2.
Flowrate (kg/s) Temperature (�C) Concentration (ppm)
SinkSK1 100 100 50SK2 40 75 50SK3 166.67 100 800
SourceSR1 100 100 100SR2 40 75 800SR3 166.67 100 1100
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138 135
utilities in the HIRCN. Solving the optimisation objective in Eq. (35),subject to the constraints in Eqs. (1)e(9), (11)e(34), (36) and (37)yield the minimum AOC of $1,302,222. The optimal HIRCN isshown in Fig. 4. The fresh water flow rate (Fr) is determined as79.76 kg/h; while the hot (Qh) and cold utilities (Qc) for the HIRCNare determined as 3348.38 kW and 34.80 kW. To further verify theresults of Qh and Qc, the HEN for this case study is synthesised usingthe pinch design method (Linnhoff et al., 1982), and is presented inFig. 5. As shown, only one heater with a duty of 3348.38 kW isneeded. This shows the same result as the energy targets obtainedby the proposed model.
On the other hand, the same case study was solved by Tan et al.(2013) with constant heat capacities of 4.2 kJ/kg K and reported anAOC of $1,383,822 (Fr ¼ 77.27 kg/h, Qh ¼ 4473 kW andQc ¼ 1227 kW). It is worth mentioning that if this case study issolved using the proposed model in this work with the same con-stant heat capacities (solving Eq. (35) subject to constraints in Eqs.(1)e(9) and (11)e(34), higher fresh water flow rate (Fr ¼ 79.7 kg/h),but lower utility targets (Qh¼ 3347.5 kWand Qc¼ 0 kW). This leadsto a lower AOC of $1,300,764.
4.3. Case Study 3
Case Study 3 is adopted fromNápoles-Rivera et al. (2010), wheremultiple properties are considered, i.e. concentration, toxicity,THOD, pH, density, viscosity and temperature. The lower and upperbound constraints on concentration, toxicity, THOD, pH, density,viscosity and temperature ensure that the operational conditions of
Fig. 4. Optimal solution
the sinks are to be fulfilled. Table 3 shows the limiting data forprocess sinks and sources for this case study.
Equations that follow outline the mixing rules for toxicity (Tox),THOD, density (r) and viscosity (m) (Nápoles-Rivera et al., 2010),
Tox ¼P
ixiToxi (38)
THOD ¼P
ixiTHODi (39)
1r¼P
ixi1ri
(40)
log m ¼P
ixilog mi (41)
In addition, mixing rules of pH (Hortua et al., 2013) for differentpH range are also given as follow.
For acid mixing (0 � pH � 7):
10�pH ¼P
ixi10�pHi (42)
For base mixing (7 � pH � 14):
10pH�14 ¼P
ixi10pHi�14 (43)
For neutralisation between acid and base streams:
10�pH ¼P
Acidxacid10�pHacid �
PBasexbase10
�pHbase (44)
Unit cost for fresh resource is given as $0.0009/lb (Costr)(Nápoles-Rivera et al., 2010). In addition, all the heat capacities inthis case study (CPn, CPi, CPr and CPj) can be determined via Eqs. (36)and (45).
CPk ¼ ak þ bkT k˛NCOMP (45)
where ak and bk are parameters in linearised temperature-dependent expression for heat capacity of each component. Sincethis case study involves a binary system with phenol and water, aand b parameters for phenol are taken as 0.4685 J/(g K) and0.0044 J/(g K2) while a and b parameters for water are1.3724 J/(g K)and 0.0083 J/(g K2).
for Case Study 2.
Fig. 5. HEN for Case Study 2.
Table 3Data for Case Study 3.
Sink Flowrate (lb/h) Composition (ppm) Toxicity (%) THOD (mg O2/l) pH Density (lb/l) Viscosity (cP) Temperature (�F)
SK1 3000 0e0.013 0�2 0�75 5.9e8.0 1.8e2.8 0.871e1.202 157e203SK2 1900 0e0.011 0�2 0�75 5.7e7.9 1.7e2.5 0.782e1.430 113e135Waste e e e e e e e 93
Source Flowrate (lb/h) Composition (ppm) Toxicity (%) THOD (mg O2/l) pH Density (lb/l) Viscosity (cP) Temperature (�C)
SR1 2900 0.033 0.8 75 5.3 2.000 1.256 176SR2 2450 0.022 0.5 88 5.1 2.208 1.220 149Fresh e 0 0 0 7.0 2.204 1.002 77
Fig. 6. Optimal solution for Case Study 3.
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138136
Fig. 7. HEN for Case Study 3.
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138 137
Solving the optimisation objective in Eq. (35), subject to theconstraints in Eqs. (1)e(3), (5)e(34), (36) and (38)e(45) resultswith theminimum AOC of $253,917/y, with the optimal values of Fr,Qh and Qc determined as 3523.07 lb/h, 0 Btu/h and 43,679.75 Btu/h.The optimal HIRCN and the HEN design for this case study areshown in Figs. 6 and 7. As observed from the HEN design in Fig. 7,four coolers are needed for this HIRCN, with a total duty of43,679.75 Btu/h. This matches the targeted value as obtained viathe proposed model.
5. Conclusion
A new generic model for the synthesis of HIRCN is presented inthis work. An MINLP formulation has been developed to identifythe minimum cost of a HIRCN, which simultaneously optimised thefresh resources as well as the external hot and cold utilities.Furthermore, the methodology is able to solve for problems withvaried process parameters (e.g. flow rates, temperatures andproperties). Three case studies of single andmultiple properties areused to demonstrate the proposed methodology.
References
Ahmetovi�c, E., Kravanja, Z., 2013. Simultaneous synthesis of process water and heatexchanger networks. Energy 57, 236e250.
Ahmetovi�c, E., Kravanja, Z., 2014. Simultaneous optimization of heat-integratedwater networks involving process-to-process streams for heat integration.Appl. Therm. Eng. 62, 302e317.
Ataei, A., Yoo, C.K., 2010. Simultaneous Energy and water optimization in multiple-contaminant systems with flowrate changes consideration. Int. J. Environ. Res.4, 11e26.
Bagajewicz, M., Rodera, H., Savelski, M., 2002. Energy efficient water utilizationsystems in process plants. Comput. Chem. Eng. 26, 59e79.
Bandyopadhyay, S., Saha, G.C., 2010. Modified problem table algorithm for energytargeting. Ind. Eng. Chem. Res. 49, 11557e11563.
Bogataj, M., Bagajewicz, M.J., 2008. Synthesis of non-isothermal heat inte-grated water networks in chemical processes. Comput. Chem. Eng. 32,3130e3142.
Dong, H.-G., Lin, C.-Y., Chang, C.-T., 2008. Simultaneous optimization approach forintegrated water-allocation and heat-exchange networks. Chem. Eng. Sci. 63,3664e3678.
Dunn, R.F., El-Halwagi, M.M., 2003. Process integration technology review: back-ground and applications in the chemical process industry. J. Chem. Technol.Biotechnol. 78, 1011e1021.
Duran, M.A., Grossmann, I.E., 1986. Simultaneous optimization and heat integrationof chemical processes. AIChE J. 32, 123e138.
El-Halwagi, M.M., 2006. Process Integration. Academic Press, New York, USA.Feng, X., Li, Y., Shen, R., 2009. A new approach to design energy efficient water
allocation networks. Appl. Therm. Eng. 29, 2302e2307.Feng, X., Li, Y., Yu, X., 2008. Improving energy performance of water allocation
networks through appropriate stream merging. Chin. J. Chem. Eng. 16,480e484.
Foo, D.C.Y., 2009. State-of-the-Art review of pinch analysis techniques for waternetwork synthesis. Ind. Eng. Chem. Res. 48, 5125e5159.
Foo, D.C.Y., 2012. Process Integration for Resource Conservation. CRC Press, BocaRaton, Florida, USA.
Furman, K.C., Sahinidis, N.V., 2002. A critical review and annotated bibliography forheat exchanger network synthesis in the 20th century. Ind. Eng. Chem. Res. 41,2335e2370.
George, J., Sahu, G.C., Bandyopadhyay, S., 2011. Heat integration in process waternetworks. Ind. Eng. Chem. Res. 50, 3695e3704.
Hortua, A.C., El-Halwagi, M.M., Ng, D.K.S., Foo, D.C.Y., 2013. Integrated approach forsimultaneous mass and property integration for resource conservation. ACSSustain. Chem. Eng. 1, 29e38.
Kheireddine, H., Dadmohammadi, Y., Deng, C., Feng, X.A., El-Halwagi, M., 2011.Optimization of direct recycle networks with the simultaneous consideration ofproperty,mass, and thermal effects. Ind. Eng. Chem. Res. 50, 3754e3762.
Kim, J., Kim, J., Kim, J., Yoo, C., Moon, I., 2009. A simultaneous optimization approachfor the design of wastewater and heat exchange networks based on cost esti-mation. J. Clean. Prod. 17, 162e171.
Leewongtanawit, B., Kim, J.-K., 2008. Synthesis and optimisation of heat-integratedmultiple-contaminant water systems. Chem. Eng. Process 47, 670e694.
Leewongtanawit, B., Kim, J.-K., 2009. Improving energy recovery for water mini-misation. Energy 34, 880e893.
Liao, Z., Rong, G., Wang, J., Yang, Y., 2011. Systematic optimization of heat-integratedwater allocation networks. Ind. Eng. Chem. Res. 50, 6713e6727.
Linnhoff, B., Townsend, D.W., Boland, D., Hewitt, G.F., Thomas, B.E.A., Guy, A.R.,Marshall, R.H., 1982. A User Guide on Process Integration for the Efficient Use ofEnergy. IChemE, Rugby, UK.
Manan, Z.A., Tea, S.Y., Wan Alwi, S.R., 2009. A new technique for simultaneous waterand energy minimisation in process plant. Chem. Eng. Res. Des. 87, 1509e1519.
Martínez-Patiño, J., Picón-Núñez, M., Serra, L.M., Verda, V., 2011. Design of waterand energy networks using temperatureeconcentration diagrams. Energy 36,3888e3896.
Nápoles-Rivera, F., Ponce-Ortega, J.M., El-Halwagi, M.M., Jimenez-Gutierrez, A.,2010. Global optimization of mass and property integration networks with in-plant property interceptors. Chem. Eng. Sci. 65, 4363e4377.
Pham, V., Laird, C., El-Halwagi, M., 2009. Convex Hull discretization approach to theglobal optimization of pooling problems. Ind. Eng. Chem. Res. 48, 1973e1979.
Polley, G.T., Picon-Nunez, M., Lopez-Maciel, J.D., 2010. Design of water and heatrecovery networks for the simultaneous minimisation of water and energyconsumption. Appl. Therm. Eng. 30, 2290e2299.
Rojas-Torres, M.G., Ponce-Ortega, J.M., Serna-González, M., Nápoles-Rivera, F., El-Halwagi, M.M., 2013. Synthesis of water networks involving temperature-basedproperty operators and thermal effects. Ind. Eng. Chem. Res. 52, 442e461.
Y.L. Tan et al. / Journal of Cleaner Production 71 (2014) 128e138138
Sahu, G.C., Bandyopadhyay, S., 2010. Energy conservation in water allocation net-works with negligible contaminant effects. Chem. Eng. Sci. 65, 4182e4193.
Sahu, G.C., Bandyopadhyay, S., 2012. Energy optimization in heat integrated waterallocation networks. Chem. Eng. Sci. 69, 352e364.
Savulescu, L., Kim, J.K., Smith, R., 2005a. Studies on simultaneous energy and waterminimisationePart I: Systemswithnowaterre-use. Chem.Eng.Sci. 60, 3279e3290.
Savulescu, L., Kim, J.K., Smith, R., 2005b. Studies on simultaneous energy and waterminimisation e Part II: Systems with maximum re-use of water. Chem. Eng. Sci.60, 3291e3308.
Savulescu, L.E., Sorin, M., Smith, R., 2002. Direct and indirect heat transfer in waternetwork systems. Appl. Therm. Eng. 22, 981e988.
Shelley, M.D., El-Halwagi, M.M., 2000. Component-less design of recovery andallocation systems: a functionality-based clustering approach. Comput. Chem.Eng. 24, 2081e2091.
Sorin, M., Savulescu, L., 2004. On minimization of the number of heat exchangers inwater networks. Heat. Transfer Eng. 25, 30e38.
Tan, Y.L., Ng, D.K.S., El-Halwagi, M.M., Foo, D.C.Y., Samyudia, Y., 2013. Synthesis ofheat integrated resource conservation networks with variable operating pa-rameters. Ind. Eng. Chem. Res. 52, 7196e7210.
Tan, Y.L., Ng, D.K.S., El-Halwagi, M.M., Foo, D.C.Y., Samyudia, Y., 2014. Floating pinchmethod for utility targeting in heat exchanger network (HEN). Chem. Eng. Res.Des. 92, 119e126.
Wan Alwi, S.R., Ismail, A., Manan, Z.A., Handani, Z.B., 2011. A new graphicalapproach for simultaneous mass and energy minimisation. Appl. Therm. Eng.31, 1021e1030.
