Economic and environmental strategies for process design

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_{: DOI: 10. 1016/j.compchemeng.2011.09.016}

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_{Ouattara, Adama and Pibouleau, Luc and}

Azzaro-Pantel, Catherine and Domenech, Serge and Baudet, Philippe and Yao

Kouassi, Benjamin Economic and environmental strategies for process

design. (2012) Computers & Chemical Engineering, vol. 36 . pp. 174-188.

ISSN 0098-1354

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Economic

and

environmental

strategies

for

process

design

Adama

Ouattara

a

_{, Luc}

_Pibouleau

a

_{, Catherine}

_{Azzaro-Pantel}

a,∗

_,

Serge

Domenech

a

_,

_Philippe

_Baudet

b

_,

_Benjamin

_Yao

c

a_{LGC-CNRS-INPT,}_Université_de_Toulouse,_4,_Allée_Emile_Monso,_BP_84234,_F-31432_Toulouse_1,_France b_ProSim,_Stratège_Bâtiment_A,_BP_27210,_F-31672_Labège_Cedex,_France

c_Institut_National_{Polytechnique}_{Houphouët-Boigny,}_Département_de_génie_chimique_et_{agro-alimentaire,}_BP₁₀₉₃_{Yamoussoukro,}_Cote_d’Ivoire

Keywords: Multiobjectiveoptimization Geneticalgorithm Eco-efficiency Economiccriterion Environmentalimpact

a

b

s

t

r

a

c

t

Thispaperfirstaddressesthedefinitionofvariousobjectivesinvolvedineco-efficientprocesses,

tak-ingsimultaneouslyintoaccountecologicalandeconomicconsiderations.Theenvironmentalaspectat

thepreliminarydesignphaseofchemicalprocessesisquantifiedbyusingasetofmetricsorindicators

followingtheguidelinesofsustainabilityconceptsproposedbyIChemE(2001).Theresulting

multiob-jectiveproblemissolvedbyageneticalgorithmfollowinganimprovedvariantoftheso-calledNSGA

IIalgorithm.AkeypointforevaluatingenvironmentalburdensistheuseofthepackageARIANETM_,_a

decisionsupporttooldedicatedtothemanagementofplantsutilities(steam,electricity,hotwater,etc.)

andpollutants(CO2,SO2,NO,etc.),implementedherebothtocomputetheprimaryenergy

require-mentsof theprocessandtoquantify itspollutant emissions.Thewell-knownbenchmark process

forhydrodealkylation(HDA)oftoluenetoproducebenzene,revisitedhereinamultiobjective

opti-mizationway,isusedtoillustratetheapproachforfindingeco-friendlyandcost-effectivedesigns.

Preliminarybiobjectivestudiesarecarriedoutforeliminatingredundantenvironmentalobjectives.

Thetrade-offbetweeneconomicandenvironmentalobjectivesisillustratedthroughParetocurves.In

ordertoaiddecisionmakingamongthevariousalternativesthatcanbegeneratedafterthisstep,a

syntheticevaluationmethod,basedontheso-calledTechniqueforOrderPreferencebySimilarityto

IdealSolution(TOPSIS)(Opricovic&Tzeng,2004),hasbeenfirstused.Anothersimpleprocedurenamed

FUCAhasalsobeenimplementedandshownitsefficiencyvs.TOPSIS.Twoscenariosarestudied;in

theformer,thegoalistofindthebesttrade-offbetweeneconomicandecologicalaspectswhilethe

lattercaseaimsatdefiningthebestcompromisebetweeneconomicandmorestrictenvironmental

impacts.

1. Introduction

In traditional chemical process design, attention has been focusedprimarilyupontheeconomicviability.Yet,chemicalplants can no longer be designed on the unique basis of technico-economicconcernsandtheotherdimensionsofsustainability– environmentaland social–leadingtotheso-called“Triple Bot-tomline”,mustbepartandparcelofthedesignphase.Thisstudy aimsatthedevelopmentofadesignframeworkforeco-efficient processes,following theguidelinesoftheenvironmentally con-sciousdesign(ECD)methodologyproposedbyAllenandShonnard (2002).

∗ Correspondingauthor.

E-mailaddresses:luc.pibouleau@ensiacet.fr(L.Pibouleau),

Catherine.AzzaroPantel@ensiacet.fr(C.Azzaro-Pantel),

Philippe.Baudet@ProSim.net(P.Baudet),beyao@yahoo.fr(B.Yao).

Amajordifficultytotackletheproblemisthattherearemany independentbutoftencompetingobjectivesthathavetobe consid-eredsimultaneously.Lotsofongoingresearchesaimatdeveloping asetofmetricsor indicatorsasproposedbyIChemE(2001).In thededicated literature,the amountof metricsmay vary from 10(AIChE,1998)to134(CSD,1996)todrawaquantitative pro-file of sustainability.The implementation ofa process-oriented sustainability metrics hasbeencarried out in parallelwith the developmentof adesign framework foreco-efficient processes, followingtheguidelinesoftheenvironmentallyconsciousdesign (ECD)methodologyproposedbyAllenandShonnard(2002).For thispurpose,severalindexesofenvironmentalimpactincluding ozone depletion,GlobalWarming Potential,humanandaquatic toxicity,photochemicaloxidation aswellasacidrainpotentials have tobetaken intoaccount. Such problems leadto multiple and mostoftenconflictinggoalsand must besolvedby means ofefficientmultiobjectiveoptimizationtools.Manyrecentworks usedthecombinationofmultiobjectiveoptimizationandlifecycle assessment approach for theeco-design of chemical processes.

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Nomenclature

AP AtmosphericAcidificationPotential(eqtSO2/y)

Di distillateflowrateincolumnofdistillationi(kg/h)

EP EutrophicationPotential(eqtPO43−/y)

EBi ithenvironmentalburden

Fi alimentationflowrate(kg/h)

FUCA Frenchacronymfor“FaireUnChoixAdéquat” GWP GlobalWarmingPotential(eqtCO2/y)

HDA benzene production fromtoluene hydrodealkyla-tion

Hi,Ho enthalpiesofinputandoutputsteams(kJ/kg)

HP highpressure(Bar)

HTP HumanToxicityPotential(tC6H6/y)

hDi enthalpyofdistillateflowrateindevicei(kJ/kg)

hFi enthalpyofalimentationflowrateindevicei(kJ/kg)

hwi enthalpyofwasteflowrateindevicei(kJ/kg)

1Hstmi enthalpyofvapourizationofwaterinuniti(kJ/kg)

1Hstri enthalpy of vapourization of chemical stream i

(kJ/kg)

LP lowpressure(Bar)

MCDM multiple-criteriadecisionmaking MILP mixedintegerlinearprogramming MINLP mixedintegernonlinearprogramming

MP mediumpressure(Bar)

NLP nonlinearprogramming

˙mFO consumedflowrateoffueloil(t/h)

˙mstmi steamflowratedemandfordevicei(t/h)

˙m consumedflowrateofnaturalgasfuel(NM3_/h)

NSGA non-sortedgeneticalgorithm

PCOP PhotoChemicalOxidationorsmogformation Poten-tial(eqtC2H4/y)

PEI potentialenvironmentalimpact Qbi heatsuppliedtoreboileri(kJ/h)

Qci heatextractedfromtheuniti(kJ/h)

R refluxratio

ratio fuelratio(%)

SBX simulatedbinarycrossover

TOPSIS TechniqueforOrderPreferencebySimilaritytoIdeal Solution

WAR WasteReductionAlgorithm

Wi wasteflowrate(kg/h)

furnaceorboileryield(%)

correlationcoefficient

Thisapproachisincreasinglybeingusedintheliterature(Azapagic &Clift,1999;Berhane,Gonzalo,Laureano,&Dieter,2009,2010; Gonzalo,2011).

Thisworkaimsatdevelopingadesignframework incorporat-ingenvironmentalissuesduringthepreliminarystagesofaprocess design.Theenvironmentcomponentisidentifiedasseveraldesign objectivefunctionsatthelevelofaprocessflowsheetsynthesis. First,a briefliterature surveydedicated toeco-friendlyprocess designviamodellingandoptimizationformulationisproposedin thispaper.Then,themethodologicalframeworkadoptedinthis workforeco-efficientchemicalprocessdesignisdeveloped.Inthis study,optimizationisperformedbya geneticalgorithm imple-mentedintheMultigenlibrary(Gomezetal.,2010)thatturnedout tobeparticularlywell-suitedformultiobjectiveprocess optimiza-tion.Thewell-known benchmarkprocessfor hydrodealkylation (HDA)of toluene toproduce benzene (Douglas,1988)is revis-itedinamultiobjectivemodeandillustratestheusefulnessofthe approach infinding environmentallyfriendly and cost-effective designs. A key point of the methodology is to capture in the

modellingapproachbothprocessandutilityproductionunits,since theenvironmentalimpactofachemicalprocessisnotonly embed-dedintheproductsinvolvedintheprocessbutisalsorelatedtothe energyconsumption,theeffectofflowrecycle,percentconversion andsoon.Thetrade-offbetweenthesevenconsideredobjectives (production,annualcostandfiveenvironmentalimpacts)begins byabiobjectiveeconomicoptimization(production,annualcost). Then, for a given production, the annual cost is deducedfrom theParetocurve.Biobjective optimizations areimplementedto establishmultilinearrelationsbetweensomeobjectivesinorder toreducethemultiobjectiveproblemsizetothreeantagonist cri-teria.Twocasesarefinallystudied.Intheformercasestudy,under afixedproductionlevel,theaimistofindtheoperatingconditions forgloballyimprovingtheenvironmentalimpacts.Inthelatter sce-nario,theobjectiveis tosatisfyenvironmentalrequirementsas thosethat might bedefinedby anEnvironmentalProtection in ordertohaveaGWP(GlobalWarningPotential)valuelessthan agiventhreshold;theotherenvironmentalimpactsarerequired tobeinferiortothevaluesobtainedinthefirstscenario.

2. Literaturereviewrelatedtoeco-friendlyprocessdesign In recent years, eco-design, which consists in taking into account environmental assessment at the preliminary stage of processdesign,hasbeenrecognizedasanefficient environmen-tallyfriendlyalternativetotraditionalprocessdesign.Currently, there is nostandardized methodology and almost no practical experienceinintegratingsustainablecriteriaintoprocessdesign (Azapagic,Millington,&Collett,2006).Generally,inthis kindof problem,theobjectiveistosimultaneouslymaximizeprofitwhile minimizingenvironmentalimpacts.Twoapproachesaregenerally consideredinchemicalsystemmodelling,thefirstoneisbasedon mathematicalprogrammingmethodsincludingeither determinis-ticalgorithmssuchasMINLP,NLP,MILPformulationsorstochastic optimizationtechniquestosolvethiskindofproblems.Some inter-estingreferencesinclude:SuryaandAlex(2002),Jia,Zhang,Wang, andHan(2006),TveitandFogelholm(2006),andVasiliosandShang (2008).Thesecondtechniquetomodelchemicalprocessesisthe useofsimulators.Flowsheetingprogrampackages,likeCHEMCAD, AspenPlus,HYSYS,PRO/II,and ProSimPlus,arecommonlyused inchemicalengineeringforprocessdesign.Theycanbeusedin anouter optimizationloop to optimizedifferent criteria.Some significantworks canbefoundinStanislav(2003),Lim,Dennis,

Murthy,andRangaiah(2005),Othman,Repke,Wozny,andHuang

(2010),andIskandarandRajagopalan(2011).Carvalho,Gani,and Matos(2008)developedagenericandsystematicmethodologyfor identifyingthefeasibleretrofitdesignalternativesofanychemical process.Thissystematicmethodologyhasbeenimplementedinto anEXCEL-basedsoftwarecalledSustain-pro.

More generally, sustainabledevelopment takesinto account theconceptoflifecycleassessment(LCA),whichisamethodfor analysingand assessing the environment impact of a material, productorservicethroughouttheentirelifecycle.Awholelifecycle includesallprocessesfromthecradletothegrave,i.e.rawmaterial, extraction,processing,transportation,manufacturing,distribution, use,reuse,maintenance,recyclingandwastetreatment.Björkand

Rasmuson(2002)developanewapproachtodesign

environmen-talimpactascumulativeformationofecopoints.Theyshowthat LCAisavaluabletool forenvironmentaloptimizationofenergy systems.Theapplicationofthewholelifecycleassessmentmay beconsideredas verytediousdue tothelackof informationat somestageofitsdevelopment.Tocircumventthisdifficulties,aset ofmetricsorindicatorsfollowingtheguidelinesofsustainability conceptshavebeendeveloped,IChemE(2001),AIChE(1998),CSD (1996)andsoon.Theseindicatorsusetheconceptofenvironmental

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burdensdefinedasaquantitativemeasureofthepotential contri-butionofsubstancesreleased,toaparticularenvironmental poten-tialimpact.Itmustbeyethighlightedthattheyareoftenlimitedto acradle-to-gateorgate-to-gatestudy.Theenvironmentalburdens areusedtoevaluatetheenvironmentalimpacts insome strate-giesliketheWasteReductionAlgorithm(WAR)(Chen&Li,2008; Douglas&Heriberto,1999;Heriberto,Jane,&Subir,1999;Teresa, Raymond,Douglas,&Carlos,2003),theIChemEsustainability met-rics(DinizdaCosta&Pagan,2006;Labuschagne,Brent,&vanErck, 2005)theSustainableProcessIndex(SPI)(Ku-Pineda&Tan,2006; Narodoslawsky&Krotscheck,2004;Sandholzer&Narodoslawsky, 2007).Foragivenprocess,thepotentialenvironmentalimpacts arecalculatedfromstreammassflowrates,streamcomposition andemissionsfromutilitysystemsandarelativepotential envi-ronmentalscore(index)foreachchemicalcompoundisdeduced. TheSustainableProcessIndex(SPI)isanecologicalevaluation sys-temindex specially developed for the requirementsof process engineering.NarodoslawskyandKrotscheck(2004)usedthis envi-ronmentalevaluationmethodologytostudythesustainabilityof energyproduction systems. TheWARalgorithm is a methodol-ogyfordeterminingthepotentialenvironmentalimpact(PEI)of achemicalprocess.ThePEIbalanceisaquantitativeindicatorof theenvironmentalfriendlinessorunfriendlinessofa manufactur-ingprocess.TheWARalgorithmwasfirstintroducedbyHilalyand Sikdar(1994).Theyintroducedtheconceptofapollutionbalance whichwastheprecursortothePEIbalance.Douglas,Richard,and Heriberto(2000)usedtheWARalgorithmtoevaluatethe environ-mentimpactofanallylchlorideproductionfacility.Asystematic approachforsustainableassessmentofchemicalandenergy pro-ductionprocesswhichincorporatesexergyanalysistoquantifythe efficiencyofaprocessandanenhancedinherentsafetyindexto quantifythesocietalimpactofaprocess,hasbeenproposedbyLi, Zanwar,Jayswal,Lou,andHuang(2011).AccordingtoChenandLi (2008),thismethodgenerallydividedtheimpactcategoriesinto twogeneralareaswithfourcategories. Thefirstgeneralareais theglobalatmosphericlevelinvolvingGlobalWarmingPotential (GWP),Ozone DepletionPotential (ODP),Acidificationand acid-rainPotential(AP),PhotoChemicalOxidationorsmogformation Potential(PCOP).Thesecondgeneralareaisrelatedtothelocal toxi-cologicalimpactlevelandisassociatedwithHumanToxicity Poten-tialbyIngestion(HTPI),HumanToxicityPotentialbyeither inhala-tionordermalExposure(HTPE),AquaticToxicityPotential(ATP) andTerrestrialToxicityPotential(TTP).LiketheWARalgorithm,the methodologydevelopedbyIChemE(2001),alsousestheconceptof potencyfactorsfordifferenttypesofpollutants.Thetotal environ-mentalburdenrelatedtoanenvironmentalimpactcategoryis cal-culatedbysummingtheproductofdifferentpotencyfactorsof pol-lutantwiththemassflowrateofpollutantswhichcontributetothis environmentalburden.VasiliosandShang(2008)usedtheIChemE (2001)methodtocalculatetheenvironmentalimpactsofutility productionsystems.Thistechniqueisalsoadoptedinthisstudy fortheenvironmentalevaluation,sincethesecriteriahavebeen identifiedasrepresentativeoftheprocessindustries.Atthefinal stageoftheoptimizationstep,itmaybenecessarytohelpdecision makersindeterminingtrade-offsolutions,severaldecision anal-ysismethodscanbeimplemented.Pirdashti,Ghadi,Mohammadi, andShojatalab(2009)andZhouandPoh(2006)classifydecision analysismethodsintothreemaingroups:singleobjectivedecision making(SODM)methods,Multi-CriteriaDecisionMaking(MCDM) methods,anddecisionsupportsystems(DSS).Theiranalysis high-lightsthatMCDMmethodsthatarestructuralapproachtoanalyse problemswithseveralcriteriaandalternativesarethemostwidely usedstrategies.Theyhelpdecisionmakerstomakeconsistent deci-sionsbytakingalltheimportantobjectiveandsubjectivefactors intoaccount.AcomparisoncanbefoundinGoughandWard(1996). Amongtheavailabletechniques,theso-calledTechniqueforOrder

PreferencebySimilaritytoIdealSolution(TOPSIS)whichbelongsto MCDMgroupisusedforidentifyingthesetofoptimalparameters innumerousinvestigations.Li,Zhang,Zhang,andSuzuki(2009), Jiaetal.(2006),Ren,Zhang,Wang,andSun(2007)usedTOPSISas multicriteriadecisionmethodtotrade-offsolutions.

3. Eco-efficientchemicalprocessdesign 3.1. Generalframework

Thedesignofeco-efficientchemicalprocessesproposedinthis study(seeFig.1)integratesamathematicalmodelforthe consid-eredprocess,coupledwithanimpactassessment model,which is embedded in an outer multiobjective optimization loop. For processmodelling,commercialdesignandflowsheetingpackages couldbeclassicallyused.Theproposedframeworkisan alterna-tivedesignmethodologyforwasteminimizationtotheso-called WARalgorithm(Cabezas,Bare,&Mallick,1999;Young,Scharp,& Cabezas,2000),whichhasbeenextensivelyusedintheliterature. Letusrecallthatthismethodisbasedonapotential environmen-talimpact(PEI)balanceforchemicalprocesses.ThePEIisarelative measureofthepotentialforachemicaltohaveanadverseeffect onhumanhealthandtheenvironment(e.g.aquaticecotoxicolgy, globalwarming,etc.).TheresultofthePEIbalanceisanimpact (pol-lution)indexthatprovidesaquantitativemeasurefortheimpact ofthewastegeneratedintheprocess.

Recently,severalsystematicmethodologieshavebecome avail-ableforthedetailedcharacterizationoftheenvironmentalimpacts of chemicals,products, and processes, which include LifeCycle Assessment.The ideais tousetheirpotentialtodevelop a Life CycleAnalysismethoddedicatedtoprocess development.Since ourapproachfocusesondecreasingtheenvironmentalimpactsof themanufacturingstageandutilitysystems,onlya“cradle-to-gate” analysisisperformed.

Akeypointofthemethodologyimplementedhereistheuse of ARIANETM ₍_{http://www.prosim.net/en/energy/ARIANE.html}_,

2005) a decision supporttool dedicated tothemanagement of plants that produce energy under the form of utilities (steam, electricity, hot water, etc.) included in the PlessalaTM _module

developedbyProSimS.A.(2005).ARIANETM_is_used_here_both_to

computetheprimaryenergyrequirementsoftheprocessandto quantifythepollutantemissionsduetoenergyproduction. 3.2. Multiobjectiveoptimization

Like many real world examples,the problemunder consid-erationinvolvesseveralcompetingmeasuresofperformance,or objectives(Collette&Siarry,2002).Usingtheformulationof mul-tiobjectiveconstrainedproblemsofFonsecaandFleming(1998), ageneralmultiobjectiveproblemismadeupasetofncriteriafk,

k=1,...,n,tobeminimizedormaximized.Eachfkmaybe

nonlin-ear,butalsodiscontinuouswithrespecttosomecomponentsofthe generaldecisionvariablexinanm-dimensionaluniverseU.

f(x)=(f1(x),...,fn(x)) (1)

Thiskindofproblemhasnotauniquesolutioningeneral,but presentsasetofnon-dominatedsolutionsnamedPareto-optimal setorPareto-optimalfront.ThePareto-dominationconceptlieson twobasicrules:intheuniverseUagivenvectoru=(u1,...,un)

dominatesanothervector

v

=(

v

₁,...,

v

_n),ifandonlyif,

∀

i∈{1,...,n}: ui≤

v

_i∧

∃

i∈{1,...,n}: u_i<

v

_i (2)

Foraconcretemathematicalproblem,Eq.(2)givesthe follow-ingdefinitionoftheParetofront:forasetofncriteria,asolution f(x),relatedtoadecisionvariablevectorx=(x1,...,xm),dominates

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Fig.1.Generaloptimizationandmodellingframework.

anothersolutionf(y),relatedtoy=(y1,...,ym)whenthefollowing

conditionischecked(foraminimizationproblem),

∀

i∈{1,...,n}: fi(x)≤fi(y)∧

∃

i∈{1,...,n}: fi(x)<fi(y) (3)

Onagiven setof solutions,itis possibletodistinguish non-dominatedsets.ThelastdefinitionconcernstheParetooptimality: asolutionxu∈UiscalledPareto-optimalifandonlyifthereisno

xv∈Uforwhich

v

=f(xv)=(

v

1,...,

v

_n)dominatesu=f(x_u)=(u₁,..., un).These Pareto-optimal non-dominated individuals represent

thesolutionsofthemultiobjectiveproblem.

Facedtothediversity ofmathematicalproblems,itis recog-nized thatthere is not a unique and generalalgorithm ableto solvealltheproblems perfectly.Actually,methodefficiency for aparticularexampleishardlypredictable,andtheonlycertainty wehave is expressedbytheNo Free Lunchtheory(Wolpert & Macready,1997):there isnomethodthatoutdoesalltheother onesforanyconsideredproblem.Thisfeaturegeneratesacommon lackofexplanationconcerningtheuseofamethodforthesolution ofaparticularexample,andusually,norelevantjustificationfor itschoiceisgivenapriori.Apossiblesolutionwastodevelop sev-eralalgorithms,distinguishingthembytheirstructureandbytheir typeofvariables(continuous,integer,binary)andcollecttheminto adatabase:Multigen(Gomezetal.,2010)liesonthis principle, andcurrently,sixdifferentalgorithmsareavailable.Theaimwas totreatmultiobjectiveconstrained-optimizationproblems involv-ingvarioustypesofvariables(boolean,integer,real)andsomeof theseproblemscanbestructuraloptimizationones.Multigenhas beenimplementedinVBAandinterfacedwithMicrosoftExcel®

. ThealgorithmsmusthandleconstraintsaswellasPareto domi-nationprinciples.Inthatway,proceduresbasedonindependent objectivestocarryouttheselection(likeVEGA,Schaffer,1985)are notadaptedtotheconsideredproblems.Proceduresbasedofthe nichenotion(NPGA–Horn,Nafpliotis,&Goldberg,1994;MOGA –Fonseca&Fleming,1993)cannotguarantee acorrect conver-genceoftheParetofront,duetothelowdiversityofthegenerated populations.MethodslikeSPEA(Zitzler&Thiele,1999)andNSGA

II(Deb,Pratap, Agarwal, & Meyarivan,2002) favournot domi-natedisolatedindividuals.InSPEA,theprobabilityofselectionis afunction oftheindividualisolation, whichis quitedifficultto implement.InNSGA,individualsfromthemostcrowdedzonesare eliminatedaccordingtoacrowdingsorting.Takingintoaccountall thepreviousitems,NSGAIIwaschosenasthebasisof develop-mentoftheMultigenlibrary.InthispaperthepackageNSGAIIb, whichdiffersfromtheinitialNSGAIIbythecrossoveroperator,has beenretained.Notethat,NSGAIIbimplementsthesamealgorithm thanNSGAII,withcorrectionsoncrossoveroperatortoavoidthe creationofclonesinherentofSBXoriginalversion.Whenthe gen-eratedrandomnumberusedtoperformthecrossoverisgreater thanagivencrossoverprobability,thecrossovermayproducetwo childrenidenticaltotheparents:SBXcrossovercodedinNSGAIIb includesaforcedmutationofchildrenwhenthiseventoccurs.The objectiveistoavoidunnecessarycalculationsforclonesofexisting solutions:allsolutionsgeneratedbythereproductionprocedure arestatisticallydifferent.TheNSGAIIbalgorithmwasimplemented totreatvariablesofdifferentnature,eithercontinuous,orinteger. Sinceouranalysisisrestrictedtotreatcontinuousvariables,the waytohandleintegervariablesisnotdetailedinthispaper.The interestedreaderwillfinmoreinformationin(Gomezetal.,2010). Constrainedmultiobjectiveoptimizationisthemostcommon, kindofprobleminengineeringapplications.Ingeneral,threekinds ofconstraintsareconsidered:simpleinequality(≤),strict inequal-ity(<),andequality(=):

g(x)≤c1 r(x)<c2 h(x)=c3











⇔











constr1(x)=c1−g(x)≥0 constr2(x)=c2−r(x)>0 constr3(x)=c3−h(x)=0 (6)

where(g,r,h)arereal-valuedfunctionsofadecisionvariablex=(x1,

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c3)areconstantvalues.Inthemoregeneralcase,theseconstraints arewrittenasvectorsofthetype:

coEnstr1(x)=((c1−g(x))1,...,(c1−g(x))n1) =(constr1(x)1,...,constr1(x)n1)≥0 coEnstr2(x)=((c2−r(x))1,...,(c2−r(x))n2) =(constr2(x)1,...,constr2(x)n2)>0 coEnstr3(x)=(−|(c3−h(x))|1,... ,−|(c3−h(x))|n3) =(constr3(x)1,...,constr3(x)n3)=0 (7)

where n1, n2, and n3 arerespectively, the number or inequal-ity, strict inequality and equality constraints. This formulation impliesthateachconstrivaluewillbenegativeifandonlyifthis

constraint is violated. The conversionof Eq. (6), that is a clas-sical representationof constraintsset,toEq. (7) representation constitutesthefirststepofaunifiedformulationof constrained-optimization problems. In practice, due to round-off error on real numbers, the equality constraint constr3 was modified as

follows: coEnstr3(x)′=(−|(c3−h(x))|1+ε1,...,−|(c3−h(x))|n3+εn3) =(coEnstr3(x))+ Eε =0 E ε=(ε1,...,εn3),

∀

i∈{1,...,n3}, εi∈R (8) E

εiscalleda“precisionvector”oftheequalityvector,andtakes lowvalues(lessthan10−6_for_example)._This_{approximation}_is_not

necessarywhenequalityconstraintinvolvesonlyintegerorbinary variables.

FromEqs.(7)and (8),theconstraintsatisfaction impliesthe maximization ofviolated constraintsin vectorsconstr1,constr2,

andconstr3.AccordingtoFonsecaandFleming(1998),the

satisfac-tionofanumberofviolatedinequalityconstraintsis,fromEq.(7), amultiobjectivemaximizationproblem.Fromatheoreticalpoint ofview,a constrainedmultiobjective optimizationproblemcan beformulatedasatwo-stepoptimizationproblem.Thefirststep impliesthecomparisonofconstraintsatisfactiondegreesbetween twosolutions,usingthePareto’sdominationdefinitionofEq.(3), butamoresimplesolutionconsistsincomparingthesumof val-uesofviolated constraintsonly,asin NSGAIIalgorithmofDeb etal.(2002),whichimplies therearenopriorityrulesbetween constraints.

3.3. Multiple-criteriadecisionmaking(MCDM) 3.3.1. Introduction

MCDMapproachesaremajorpartsofdecisiontheoryand anal-ysis.MCDMareanalyticmethodstoevaluatetheadvantagesand disadvantagesofalternativesbasedonmultiple-criteria.The objec-tiveistohelpdecision-makerstolearnabouttheproblemsthey face,andtoidentifyapreferredcourseofactionforagiven prob-lem.Huang,Poh,andAng(1995)mentionedthatdecisionanalysis (DA)wasfirstappliedtostudyproblemsinoilandgasexploration inthe1960sanditsapplicationwassubsequentlyextendedfrom industrytothepublicsector.Tillnow,MCDMmethodshavebeen widelyusedinmany researchfields.Differentapproaches have beenproposed by many researchers, includingsingle objective decision-making(SODM)methods,MCDMmethods,anddecision support systems (DSS). Literature shows that among MCDM methods,DAstrategiesarethemostcommonlyused(Zhou&Poh, 2006).TheselectionofasingleParetopointfromthePareto fron-tiermaybedifficultasthenumberofobjectivesincreases.Some intuitivemethodssuchastheso-called“knee-method”couldbe efficientforabinarycase.Thisiswhyothermethodsarenecessary

to tackle the multicriteria nature of the results generated by theGA.

3.3.2. Findingknees

Branke,Deb,Dierolf,andOsswald(2004),andTaboadaandCoit (2006)suggestpickingthekneesintheParetofront,thatistosay, solutionswhere asmallimprovement inoneobjectivefunction wouldleadtoalargedeteriorationinatleastoneotherobjective. 3.3.3. TOPSIS

Inpractice,theTechniqueforOrderingPreferencebySimilarity toIdealSolutions(TOPSISmethod)and othermultipleattribute decision making(OMADM)methods arethemostpopular(Ren et al., 2007; Yoon & Hwang, 1995). In this work, the TOPSIS methodologywasusedasdecisionmakingtool.Afterthe gener-ationofthePareto-optimalset,theTOPSISmethodisusedtoaid decision–makerintrade-offingthewholealternatives.Thebasic principleofTOPSISisthatthechosenalternativeshouldhavethe shortestdistancefromtheidealsolutionandthefarthestdistance fromthenegative-idealsolution(Opricovic&Tzeng,2004; Ren etal.,2007;Saaty,1980).

StepsusedinTOPSISasdescribedbyRenetal.(2007)arebriefly describedinwhatfollows:

Step1:Alltheoriginalcriteriareceivetendencytreatment.That consistintransformingthecostcriteriaintobenefitcriteria,which isshownindetailasfollows:

(i)Thereciprocalratiomethod(X′

ij=1/Xij)referstotheabsolute

criteria;

(ii)Thedifferencemethod(X′

ij=1−Xij),referstotherelative

cri-teria.

Aftertendencytreatment,constructamatrix X′_[X′

ij]_n×m, i=1,2,...,n; j=1,2,...,m. (9)

Step2:CalculatethenormalizeddecisionmatrixAasfollows: A=[aij]n×m aij= X′i j max(X′i j)

(j=1,2...,m.) foracriteriontobemaximized (10a) aij=1− X′i j max(X′i j)

(j=1,2...,m.)foracriteriontobeminimized (10b)

Step3:Determinethepositiveidealandnegativeidealsolution fromthematrixA

A+₌_(a+ i1,a + i2,...,a + im), a + ij =_1≤i≤nmax(aij), j=1,2,...,m (11) A−=(a−_i1,a−_i2,...,a−_im), a−_ij = min 1≤i≤n(aij), j=1,2,...,m (12)

Step 4: Calculate the separation measures, using the n-dimensionalEuclideandistance.Theseparationofeachalternative fromthepositiveidealsolutionisgivenas

D+_i =

v

u

t

m

X

j=1 Wj(a+ij−aij) 2 (13)

(7)

Similarly, theseparation from the negativeideal solution is givenas D−_i =

v

u

t

m

X

j=1 Wj(a−ij −aij) 2 (14)

Step5:Foreachalternative,calculatetheratioRias

Ri=

D−_i

D−_i +D+_i , i=1,2,...,n (15)

Step6:Rankalternativesinincreasingorderaccordingtothe ratiovalueofRiinstep5

3.3.4. FUCA

FUCAistheFrenchacronymforFaireUnChoixAdéquat(Make AnAdequateChoice).Thissimplemethodisbasedonindividual rankingsofobjectives;foragivencriterion,rankoneisassignedto itsbestvalueandrankn(nbeingthenumberofpointsofthePareto front)totheworstone.Then,foreachpointofthefront,aweighted summation(theweightsrepresentingthepreferences)ofranksis performed,andthechoiceiscarriedoutaccordingtothelowest valuesof thesum. Ina recent paper(Moralez-Mendoza, Perez-Escobedo,Aguilar-Lasserre,Azzaro-Pantel,&Pibouleau,2011)the FUCAmethodwascomparedwithclassicalMCDMproceduresona tricriteriaproblemrelatedtotheportfoliomanagementina phar-maceuticalindustry.ForeachsolutionfoundbyELECTRE(Teixeiro deAlmeida,deMiranda,&CabralSeixasCosta,2004),PROMETHEE (Zhaoxa&Min,2010)andTOPSIS,theFUCArankingisalsoreported. AverygoodagreementbetweenthethreeclassicalMCDM meth-odsandFUCAcanbeobserved,showingtheefficiencyoftheFUCA procedure,whichalwaysfindsthebestsolutionselectedbyoneof theothers.

3.4. Utilityproductionmodelling

ARIANETM _software _tool _has _been _developed _by _ProSim

Company(French chemical engineeringSoftware Company) for designing assistance and optimal operation of power plants. ARIANETM _makes_it_possible_to_optimize_and_model _any_energy

combinedproduction plant (steam, hotwater, electricity, com-pressedair,cooling),whateveritssizeandcomplexity.ARIANETM

isadecisionsupporttooldedicatedtothemanagementofplants thatproduceenergyundertheformofutilities(steam, electric-ity,hotwater,etc.).ARIANETM_,_written_in_VBA,_presents_a_standard

libraryofunitoperationsinvolvedinpowerplants:boilers (mono-fuel,bi-fuel,electrical),turboalternators (backpressureturbines, sidestreamturbines,condensating turbines),switchable or per-mutableturbines(inparallelwithelectricmotors),fuelturbines andthermalengines (withorwithoutrecoveryheatexchanger, withorwithoutpostcombustionboiler),valves,heatexchangers anddeaerators.Alltheseunitoperationscanbedescribed,from thesimplest(minimalistmodelling, withdefaultvalues) tothe mostcomplex(veryfinemodellingofthecharacteristicsand tech-nicalconstraints);thecomplexityofphysicalmodelsrequiringin manycasestousenonlinearequations.Theinherentmodel com-plexityanditsassociatedequationsaretotallytransparentforthe user.Intheframeworkofeco-designmodelling,theproblemlies inintegratingenvironmentalaspectsinsideARIANEsoftware,so thatemissionscanbetakenintoaccountintheglobalenergy bal-ance.Estimationmethods,toevaluatetheemissionsofallinvolved powerplantsequipmentitemshavethentobecompatiblewith existingroutinesthatnotrequirenumerousand complexinput data.InARIANE,classicalpollutantsasnitrogenoxides,carbonand sulphuroxides,andalsosolidparticleslikedusts,arewellknown. Theemissionsmodellingprocessstartsfromthecalculationof pollutantamountsinthesmokesofeachequipmentitem,global

emissionflowrateisfinallythesumofallflowrates,forallsite smokeemitters.Anotherproblemliesthenintheaccurate mod-ellingofthecombustionphenomenainallequipmentitemsofa powerplant.Wegivebelowsomeoftheequationsofunits oper-ationsimplemented in ARIANETM _and _used_at _the _{eco-efficient}

modellingstage.

4. ApplicationtoHDA(hydrodealkylationoftoluene) process

4.1. OverviewoftheHDAprocess

The traditional method of manufacturingbenzene fromthe distillationoflightoilsproducedduringthemanufacturingofcoke hasbeenovertaken bya number ofprocesses:The sourcesare now:catalyticreforming,hydrodealkylationoftoluene(HDA)and toluenedisproportionation.Theglobalworldbenzeneproduction capacitywillrisefromestimated41.8Mt/yin2009to55.8Mt/y in 2015: http://marketpublishers.com/lists/5873/news.html,

http://mcgroup.co.uk/researches/B/028500/Benzene.html. In

2005, the French production capacity was estimated at one Mt/yearonsevenindustrialsites,i.e.meanof143,000t/yearper site(www.ineris.fr/rsde/fiches/fichebenzene2005.pdf).

TheHydrodealkylation(Douglas,1988)processforproducing benzene,aclassicalbenchmarkinchemicalprocesssynthesis stud-ies,isusedinthispaper(HDAprocess).Thisprocessinvolvestwo reactions:theconversionoftoluenetobenzene(Eq.(16))andthe equilibriumbetweenbenzeneanddiphenyl(Eq.(17)).

Toluene+H2→Benzene+CH4 (16)

2Benzene↔ Diphenyl+H2 (17)

Douglas(1988) has firstextensively studied this process by usingahierarchicaldesign/synthesisapproach.Thehydrogenfeed streamhasapurityof95%andinvolves5%ofmethane;thisstream ismixedwithafreshinletstreamoftoluene,recycledtoluene,and recycledhydrogen.Thefeedmixtureisheatedinafurnacebefore beingfed toan adiabatic reactor.The reactoreffluent contains unreactedhydrogenandtoluene,benzene(thedesiredproduct), biphenyl,andmethane;itisquenchedandsubsequentlycooled inahigh-pressureflashseparatortocondensethearomaticsfrom thenon-condensablehydrogenandmethane.Thevapoursteam fromthehigh-pressureflashunitcontainshydrogenandmethane thatisrecycled.Theliquidstreamcontainstracesofhydrogenand methanethatareseparatedfromthearomaticsinalow-pressure flashdrum.Theliquidstreamfromthelow-pressureflashdrum consistingofbenzene,biphenyl andtolueneisseparatedintwo distillationcolumns.Thefirstcolumnseparatestheproduct, ben-zene,frombiphenylandtoluene,whilethesecondoneseparates thebiphenyl from toluene, which isrecycled backat the reac-torentrance.Energyissavedbyusingtheoutletstreamleaving thereactorasitstemperatureis intherangeof 620◦_C,_to

pre-heatthefeedstreamcomingfromthemixer,viaaheatexchanger (Fehe)someenergyintegrationisachieved(Cao,Rossiter,Edwards, Knechtel,&Owens,1998)(seeFig.2).

Asabovementioned,ARIANETM_is_used_here_both_to_compute

theprimaryenergyrequirementsoftheprocessandtoquantify thepollutantemissions related toenergy production. Atypical steamgeneratingfacilityisconsidered:steamisproducedfrom aconventionalmono-fuelfiredboiler(40barand400◦_C)_and_let

downto lowerpressure levels (respectively,10bar,336◦_C _and

5bar,268◦_C)_through_turbines_which_produce_electricity_used_in

theplant.ARIANETM_is_also_used_to_model_the_fired_heater

(fur-nace)oftheprocessasabi-fuelfiredheater(mixofnaturalgasand fuel).

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Fig.2.HDAplantwithisutilityproductionunit.

TomodeltheHDAprocess,commercialdesignandflowsheeting packagescouldbeusedinordertocomputetheobjectivefunctions. However,ratherthanusingsuchpackages,theequationsproposed byDouglas(1988)havebeendirectlyimplementedandsolvedby theExcel®

solver.Biphenylhasbeenconsideredasapollutant,and theenvironmentalimpactcontributionsforthecomponentsinthe HDAprocesshavebeentakenfromSikdarandEl-Halwagi(2001).

4.2. InteractionbetweenHDAprocessandutilityproduction system

FromthestudiesofDouglas(1988)andTurton,Bailie,Whiting, &Shaeiwitz(1997,2009),sevenvariableswereselectedforHDA processbecauseoftheirinfluenceontheeconomicand environ-mentaloptimizationcriteria.Thesevariablesareinitiallyusedto computetheoverallmaterialbalanceofthemainchemical com-poundsandaswellastheassociatedthermodynamicproperties (enthalpy,density,heatcapacity, etc.)atvariousprocessnodes, withuseofSimulis® _{Thermodynamics}_as_a_calculation_server_of

thermodynamicproperties.Theyservefinallytocomputethesize ofallequipmentitemsinvolvedintheprocessforcarryingoutthe requiredunitoperations.Fig.3showstheinteractionbetweenthe variablesof theHDA processandtheutilityproductionsystem. HDAprocessoperationneedsthermalandelectricalutilities.The thermaldemandisformulatedintermsoffuelflowratetomeet theneedofheatingthemixtureinthefurnaceaswellasofsteam tomeettheheatingdemandsfortheexchangers,reboilerandother itemsoftheprocess.Eqs.(18)–(20)describethedemandofsteamin thecaseofareboiler.Theserequirementsobtainedfromtheenergy balancesoftheHDAsimulatoraretransmittedviaPlessalaTM_as

variablestotheunitoperationsinvolved,whicharemodelledby useofArianeTM_(boiler,_furnace)._Then,_fuel_oil_flow_rate_of,_the

nat-uralgasflowrateandsteamflowratebecomesecondaryvariables forArianeTM_._The_use_of_ArianeTM_provides_typical_results_related_to

thethermalpowerplanti.e.thepowerproducedbytheturbineand theflowratesofallthepollutantsresultingfromfuelcombustion.

˙mstmi=

Qbi

1Hstmi

(9)

Fig.3.Interactionbetweenvariablesandsimulationtools.

with Qbi=DihDi+WihWi−FihFi+Qci (19)

and Qci=Di(R+1)1Hstri (20)

4.2.1. Furnacemodelling

Thefurnaceismodelledasabi-fuelboilerfedwithbothnatural gasandfueloil.Theirflowratesarelinkedbytheso-calledenergetic ratioandthefurnaceenergeticdemandasfollows:

Consumednaturalgasflowrateinthefurnace:QNG

˙m = QFurnace ·LHVNG·ratio

(21) Consumedfueloilflowrateinthefurnace:QFO

˙m = QFurnace ·LHVFO·(1−ratio)

(22) Energeticratio:

ratio= Energyprovidedbynaturalgas

Totalenergyofnaturalgasandfueloil (23)

Thefuelsconsideredarenaturalgas(fuel1)andfueloil(fuel2). Caseofamono-fuelboiler:

Theboilerisusedtoproducesuperheatedvapour,forthe oper-ationoftheturbineandhotwaterfortheotherunits

˙m= QBoiler ·LHVNG

. (24)

4.2.2. Sidestreamturbinemodelling

Aboilerisusedtoproductsteamathighlevelofpressureand temperature,and thenthis steamis expended througha back-pressureandcondensingturbinetogeneratepower.Theturbineis modelledwiththefollowingequations,implementedinARIANETM_:

Si(Ti,Pi)=So(To∗,Po) (25)

Turbinemaximumwork

Wmax=Hi(Ti,Pi)−Ho(To∗,Po) (26)

Turbineisentropicyield = Weff

Wmax

(27)

5. Optimizationproblemformulation 5.1. Economicobjectives

AsmentionedbyCutlerandPerry(1983),amajorobjectiveof anyindustrial processis profitmaximization. In thisstudy,the benzeneproduction(ProdB)tobemaximizedandtheannualcost (Annualcost)havebeenchosenaseconomicfunctions.Thebenzene productionisadirectoutputoftheHDAprocess,whiletheannual costiscomputedaccordingtorelations(28)–(31).

Annual cost=0.1FCI+CRM+CUT (28)

FCI:Fixedcapitalinvestment($) 0.1FCI:depreciationcost($/y) CRM:costofrawmaterials($/y)

CUT:costofutilities($/y)

FCI=

X

i

(Purchase costi+Installedcosti) (29)

CRM=

X

i

(10)

Table1

Capitalcostestimationformainitems(M&S:Marshall&SwiftEquipmentsCostIndex=1,468.6(2009))fromChemicalEngineeringJanuary2010.

Equipmentinvestmentcost($) Nonlinearform Columncost

D:columndiameter(m) Purchasecost=9.201

!

M&S 280

(101.9D1.066_H0.802_F c) H:columnheight(m)

Fc:materialpressure Installedcost=9.202

!

M&S₂₈₀

D1.066H0.802(2.18+Fc)+20.69

!

M&S 280

4.7D1.55_HF′ c F′

c:material,trayspace,traytype

Exchangercost Purchasecost=

!

M&S 280

(474.7A0.65_F c) A:heatexchangerarea(m2₎ _Installed_cost₌

!

M&S

280

(474.7A0.65_)(2.29₊_F c) Furnacecost Purchasecost=

!

M&S

280

(5.52×103_)Q0.85_F c Q:furnaceabsorbed(293kW) Installedcost=

!

M&S

280

(5.52×103_)Q0.85_(1.27₊_F c)

Table2

Capitalcostfortheutilitysystem.

Equipmentsinvestmentcost(1000$) Nonlinearform Fielderectedboiler 8.09F0.82_f

p1

F:steamflowrate(kg/s);P:pressure(bar) With,fp1=0.6939+0.01241P−3.7984Exp(−3P2) Steamturbine Wst:power(MW) 25.79Wst0.41 Deaerator F:BFWflowrate(kg/s) 0.41F0.62 Condenser Q:heatdissipated(MW) 4.76Q0.68 CUT=

X

i ˙mUTiPUTi (31)

˙mRMi:massflowrateofrawmateriali(kg/h)

PRMi:unitpriceofrawmateriali($/kg)

˙mUTi:flowrateofutilityi(kg/h,stdm3/h,m3/horkW)

PUTi:unitpriceofrawmateriali($/kg,$/stdm3,$/m3or$/kWh)

Forthemainequipmentitems,thepurchaseandinstalledcosts werecomputed fromtheclassical Guthrie’scorrelations (1969) (seeTable1).Fortheutilitysystem,capitalcostestimationwas performedbyusingexpressionsdevelopedinBruno,Fernandez, Castells,andGrossmann(1998)(seeTable2).Finally,thecostsof rawmaterialsandutilitiesfromTurtonetal.(2009)aredisplayed inTable3.Forconvenience,theAnnualcostwillbeexpressedin M$/yinwhatfollows.

5.2. Environmentalobjectives

The environmental impacts are quantified by the so-called environmental burdens listed by IChemE. From the classifica-tionproposedbyAzapagic,Emsley,andHamerton(2003),eight

Table3

CostofrawmaterialsandutilitiesusedinHDAprocess.

Rawmaterials Cost($/kg)

Toluene 0.648

Hydrogen 1

Utilities Cost($/commonunit)

Fueloil(n◦₂₎ _$549/m3

Naturalgas $0.42/stdm3

Electricity $0.06/kWh

SteamfromBoiler

Highpressure $29.97/1000kg

Mediumpressure $28.31/1000kg

Lowpressure $27.70/1000kg

Coolingtowerwater(30–40◦_C) _$14.8/1000_m3

categoriesofimpactscanbeidentified,andenvironmentalburden EBiiscomputedas: EBi= n

X

j=1 ec_ijBj (32)

whereec_ijistheestimatedclassificationofthejthparticipantinthe ithburdenandBjistheemissionofthejthgreenhousegas.Fora

givenapplication,thechoiceofparticularimpactscanbededuced from the flowsheet analysis, and they are quantified through massandenergybalances.Amongtheenvironmentalimpacts pro-posedbyAzapagicetal.(2003),fiverepresentativeitemsforthe consideredchemicalprocesshavebeenretainedforcomposingthe EnvironmentalBurdens(EBi).EachconsideredEnvironmental

Bur-dencanbebrieflydescribedasfollows(seethestudyofAzapagic etal.(2003)formoreinformation).

- GlobalWarmingPotential(GWPintCO2equivalent/y)whichis

ameasureofhowagivenmassofgreenhousegasisestimated tocontributetotheglobalwarming.Itisarelativescale,which comparesthemassofaconsideredgastothesamemassofcarbon dioxide.ItisequaltothesumofeightemissionsBjofgreenhouse

gasesmultipliedbytheirrespectiveGWPfactorsecj_GWP.

-AcidificationPotential(APintSO2equivalent/y)isbasedonthe

contributionsofSO2andNOxtothepotentialaciddeposition,that

isontheirpotentialtoforH+_protons._The_five_AP_factors_ecj APare

expressedrelativelytotheAPofSO2.

-Photochemical Ozone Creation Potential (POCP in

tC2H4equivalent/y) (or PCOP) very often defined as

sum-mer smog, is theresult of reactionsthat take place between nitrogenoxides NOx andVOCs exposed toUVradiations.The

POCPisrelatedtoethyleneasreferencesubstance,thatistosay thatthePOCPfactorsecj_APfortheeightconcernedproductsare expressedrelativelytothePOCPofC2H4.

- HumanToxicityPotential(HTPintC6H6-equivalent/y)expresses

thepotentialharmofchemicalsreleasedintotheenvironment. HTPincludesbothinherenttoxicityandgenericsource-to-dose relationships for pollutant emissions. It uses a margin-to-exposureratiotoevaluatethepotentialforhealthimpactfrom

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exposuretoharmfulagents,bothcarcinogensandnon carcino-gens.It iscalculated byaddinghumantoxic releasestothree differentmedia,i.e.air,waterandsoil.Thetoxicologicalfactors arecalculatedusingtheacceptabledailyintakeorthetolerable dailyintakeofthetoxicsubstances.Thehumantoxicological fac-tors(26fromAzapagicetal.,2003)arestillatdevelopmentstage, sothat HTPcanonly betaken asanindicationandnot asan absolutemeasureofthetoxicitypotential.

-EutrophicationPotential(EPintPO43−equivalent/y)isdefinedas

thepotentialofnutrientstocauseover-fertilisationofwaterand soilwhichinturncanresultinincreasedgrowthofbiomass.

Itmustbeemphasizedatthislevelthattheapproachpresented heredoesnotaccountfortheentirelifecycleoftheprocesssince theenvironmentalburdensareassociatedwiththeemissions gen-eratedbytheprocessbothfromthematerialcomponentsandfrom theenergyvectors. Forinstance,theoutcomeof benzeneisnot consideredhereasitisviewedasthedesiredproductforthe pro-cess.Wearethusawarethattheapproachdevelopedheredoesnot embedthewholelifecycleoftheproduct.Moreover,the extrac-tionresourceassociatedwithrawmaterialssuchastolueneisnot included.Briefly,onlytheprocesscontributionisconsideredinthis study.

Ofcourse,alifecycleassessmentmethodologycouldbe attrac-tive to be more general and the abovementioned drawbacks could be partially overcome by using standard environmental databasesavailablein theliterature (e.g.EcoInvent forinstance http://www.ecoinvent.ch/)implementedinlifecycleassessment softwaretools.Thisissuewillconstituteaperspectiveofthiswork. 5.3. Multiobjectiveproblemformulation

Using the previous economic and environmental objective functionsdefinedabove,thefollowing multiobjective nonlinear optimizationproblemisformulatedasfollows:determinedecision variables(processoperatingconditions)inorderto:

Max(ProdB) (33)

Min(Annualcost) (34)

Min(EBi), i=1, 5 (35)

s.t.

Massandenergybalances(Excel®_and_ARIANETM₎

Boundsondecisionvariables

ProdBrepresentsthebenzeneproductionatthetopofcolumn 2(inkmol/h).

Theadditionalfollowingconstraintshavebeenconsideredinthe Multigeninterface,thenumericalvaluesvaluehavebeendeduced fromtheanalysisofDouglas(1988)andTurtonetal.(1997). -Thepurityofthebenzeneproductisatleast99.97% - Thehydrogenfeedmusthaveapurityof95% -Thereactoroutlettemperatureislessthan704.50◦_C

-Thequencheroutlettemperatureislessthan621.16◦_C

-TheconversionrateCisboundedas:0.5≤C≤0.9

-The hydrogen flow rate purged FPH (kmol/h) is bounded as:

30≤FPH≤300

-Allpollutants,CO2,NOx,CO,SO2,dustsflowrate(kg/h)musttake

onlypositivevalues. 5.4. GAparameters

Thetwoclassesofoptimizationproblemspresentedbelowhave beensolvedbyusingthecodeNSGAIIboftheMultigentoolbox, withthefollowing operatingparameters: populationsize=200,

Fig.4. Benzeneproductionvs.Annualcost.

numberofgenerations=200, Crossoverrate=0.75 andMutation rate=0.2.

Douglas(1988)thenTurtonetal.(1997)defineboundsonthe HDAvariablesasreportedinTable4.Theinitialpopulationwas randomlygeneratedbetweenthesebounds,anda particularset ofvariableshasbeenextractedfromtheinitialpopulation(column InitialvalueofTable4)forfurthercomparisonpurposes(seeTable5 line“Initial”).

6. Case1:economicfollowedbyecologicalstudy 6.1. Solutionstrategy

Fortheprobleminvolvingalltheobjectives,theParetofrontisa cloudofpointslocatedinahypercubeofℜ7.Toreducethis hyper-cubedimensioninordertointerpretasgoodaspossiblethegenetic algorithmresults,a twostepssolutionstrategyisimplemented. Inthefirststep,thebiobjectiveproblem((33)and(34))issolved toobtainanefficienttrade-off(ProdB*,Annualcost*)betweenthe maximalbenzene productionand theminimalinvestmentcost. Thenthebenzeneproduction,beingfixedatavalueProdB*obtained fromtheParetocurve,theproblem((33)–(35))issolvedforthe investmentcostlyinginalowrange[Annualcost*,Annualcost*+˛], withavalueof˛equalto15%forinstance.Adegradationofthe annualcostisalsoallowed,thusimprovingtheenvironmental per-formancesoftheprocessofbenzeneproduction.

6.2. Economicstudy:biobjectiveoptimization(ProdB,Annual cost)

TheParetofrontcorrespondingtotheoptimizationofthepair (ProdB,Annualcost)isdisplayedinFig.4.Thecurveiscomposedof twoportionsofstraightlines.Thekneelocatedonthecurvegives thebesttrade-off(Brankeetal.,2004),thatistosay(205.04M$, 299.96kmol/h).Withoutenvironmentalconsiderations,this solu-tion would be adopted for plant design. In the following, the benzeneproductionwillbelowerboundedat300kmol/handthe annualcostwillvaryintherange[205.04M$,299.96M$]inorder tocompetewithadditionalenvironmentalobjectives.Thevalues ofallconsideredobjectivesforthefirstpoint(204.5,299.9)noted “First”oftheflatlineofFig.4and theinitialpointdescribedin Table4areusedforcomparingobjectivesinTable5.

6.3. Studyofenvironmentalburdensviabiobjectiveoptimizations Thebenzeneproductionbeingfixedat299.96kmol/handthe Annualcostlyingintherange[205.04M$,299.96M$],the crite-ria are optimized by pairs for identifying redundantobjectives expressedintermsofmultilinearfunctionsofthethreeremaining ones(Annualcost,EPandAP).Thesedependentimpacts(GWP,HTP andPOCP)willberemovedfromthemultiobjectiveoptimization problem,wheresomedegradationsoftheAnnualcostareallowed

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Table4

DecisionvariablesfortheHDAprocess.

Decisionvariables Lowerbound Initialvalue Upperbound

Conversionrate(%) 0.5 0.75 0.9

Hydrogenpurgeflowrate(kmol/h) 31 198 308

Flashpressure(bar) 30 34 34

Stabilizerpressure(bar) 4 10 10

Column1pressure(bar) 2 2 4

Column2pressure(bar) 1 1 2

Ratio(bi-fuelfurnace)(%) 0.1 0.85 0.9

Table5

Valuesofobjectives.

Objective ProdBt/y AnnualcostM$/y EPtPO43−/y APtC2H4/y GWPtCO2/y HTPtC6H6/y POCPtC2H4/y Initial 305.00 277.42 9759.06 11,190.34 1,884,528.48 18,699.58 2472.32 First 299.96 205.04 13,831.12 4829.26 1,410,428.13 26,537.88 1944.11 Gainvs.initial(%) −1.62 26.00 −29.44 56.85 25.16 −41.91 21.36 1410500 1411000 1411500 1412000 1412500 1413000 1413500 205,34 205,32 205,3 205,28 205,26 205,24 205,22 205,2 205,18 205,16

Annual cost (M$/y)

GWP (t CO

2

/ y)

Fig.5.GWPvs.Annualcost.

0 5000 10000 15000 20000 25000 30000 235 230 225 220 215 210 205 200

HTP (t C

6

H6

/ y)

Fig.6.HTPvs.Annualcost.

forgloballyimprovingalltheenvironmentalimpacts(includingthe redundantones).

(GWP,Annualcost):Nondominatedpointsappearonlyinlow rangesforthetwoobjectives(seeFig.5),suggestingastrong rela-tionbetweenthem(seesection5.4).(HTP,Annualcost_):ThePareto frontisdisplayedinFig.6,wherethetwoobjectiveshaveopposite effects.(EP,Annualcost_):_The_results_are_shown_in_Fig.₇_._The_curves displayedinFigs.6and7exhibitverysimilartrends,duetoastrong linkbetweenthem(seeSection5.4).(AP,Annualcost):ThePareto

0 2000 4000 6000 8000 10000 12000 14000 235 230 225 220 215 210 205 200

EP (t PO

4

3-/y)

BT2 BT1

Fig.7.EPvs.Annualcost.

4300 4400 4500 4600 4700 4800 4900 235 230 225 220 215 210 205 200

AP (t SO

4

/y)

BT1

BT2

Fig.8. APvs.Annualcost.

1910 1915 1920 1925 1930 1935 1940 1945 1950 222 220 218 216 214 212 210 208 206 204

PCOP (t C

2

H4

/y)

Fig.9. POCPvs.Annualcost.

frontisdisplayedinFig.8.(POCP,Annualcost):theresultsreported inFig.9showthatnondominatedpointsappearonlyinalowrange forthePOCPobjective,suggestingastrongrelationbetweenthese twofunctions.(AP,EP):concerningthepair(AP,EP),the biobjec-tiveoptimizationgivesthefrontdisplayedinFig.10,whereitcan bepointedoutthatthetwoimpactsexhibitantagonistbehaviours.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 16000 14000 12000 10000 8000 6000 4000 2000 0 EP (t PO43-/y) AP (t SO 2 /y) BT1 BT2 Fig.10. APvs.EP.

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Table6

Resultsofthemultilinearregressions–Case1.

Objective AnnualcostM$/y EPtPO43−/y APtC2H4/y y-Intercept Coeff.corr. Errormax(%)

GWPtCO2/y 5445.29 −0.64 43.95 90,529.67 0.9988 0.51 HTPtC6H6/y −6.29×10−5 1.92 −3.70×10−5 9.25×10−3 1.000 10−6 POCPtC2H4/y 0.44 4.07×10−3 8.67×10−2 1377.95 0.9999 0.03 4000 5000 6000 7000 8000 0 5000 10000 15000 205 210 215 220 225 230 AP (t SO2 / y) EP (t PO4 (3-) / y) Annual cost (M$ / y) TT1 TT2 TF1 TF2

Fig.11. Triobjectiveoptimization(Annualcost,EP,AP)– Case1.

6.4. Redundantobjectives

Fromtheprevioussection,environmentalimpactsGWP,HTP andPOCPwerefoundtobelinkedwithotherobjectivesAnnual cost, EP and AP. From 200 randomly generated values for the independentvariables(definedinTable4),theobjectivesAnnual cost,EP,AP,GWP,HTPandPOCPwerecomputedandmultilinear regressionswereperformed ontheExcel platform.The experi-mentwascarriedoutseveraltimesandgivesthefollowingresults ofTable6.

Inallcases, thecoefficientofcorrelationis verygood. From thecoefficientsofmultilinearequations,itcanbeobservedthat GWPandPOCParemainlyincreasingfunctionsoftheAnnualcost, whileHTPdependsprincipallyonEP.SoimpactsGWP,POCPand HTPbeingexplicitfunctionsoftermsAnnualcost,EPandAP,they canbesuppressedfromthefollowingmultiobjectiveoptimization phase.

6.5. Triobjectiveoptimization

Fromthepreviousbiobjectivestudy,onlythreeindependent objectivesareremaining: Annualcost,EPand AP.Theyarenow simultaneouslyoptimized,andtheresultsaredisplayedinFig.11. TheflatportionofthecloudofpointsnearAnnualcost≈205M$/y, EP≈10,000tPO43−andAP≈5000tSO2/ysuggeststhatgood

solu-tionsmayexistinthiszoneforthethreeobjectives.

Table7

ResultsofTOPSISanalysisforbiobjectiveoptimizations.

Pair AnnualcostM$/y EPtPO43−/y APtSO2/y (EP,Cost)1 226.42 3590.12 (EP,Cost)2 226.64 3574.40 (AP,Cost)1 210.13 4499.36 (AP,Cost)2 210.18 4498.29 (AP,EP)1 5918.37 4763.31 (AP,EP)2 5886.94 4819.97 6.6. Selectingsolutions 6.6.1. Biobjectiveoptimizations

Fromthethreeindependentobjectives,Annualcost,EPandAP, aTOPSISanalysisiscarriedouttwiceforthethreepossiblepairs inordertodetectineachcasethetwobestpointscalledBT1and BT2(BTsignifyBiobjectiveTopsis)inFigs.7,8and10.Theresults areindicatedinTable7.NotethattheFUCAprocedurecannotbe implementedonbiobjectiveproblems,insofarastheParetofront beingperdefinitionasetofnondominatedpoints,thesumofranks isconstantandequaltothenumberofpointsinthefrontplusone (thebestpointforoneobjectivebeingtheworstonefortheother). 6.6.2. Triobjectiveoptimization

ATOPSISandaFUGAanalysisarecarriedouttwiceontheglobal setofobjectives(Annualcost,EP,AP,GWP,HTPandPOCP).Inthese studieseventhedependantobjectivesGWP,HTPandPOCP, com-putedbyusingTable6fromthethreeindependentones,haveto beconsidered,becausetheycan influencethedecisionmaking. However,theresults areonly displayedfor thethree indepen-dentcriteriain Fig.11.Let uspointoutthat therankingswere performedwithoutanypreferencefactor.Thetwobestsolutions obtainedfromTOPSIS(respectivelyFUCA)arecalledTT1andTT2 (respectivelyTF1andTF2)onthe3Dcurve.

Table8exhibitstheresultsobtainedbothforthethree inde-pendentobjectivesandforthethreedependentonesinthelast columns.Foreachobjectivethegainin%iscomputedvs.solution called“first”inTable5.Thevaluesofthecorrespondingvariables aregiveninTable9.Obviously,thesolutionsobtainedwhen pro-jecting3-Dsolutionsinthecorresponding2-Dspacesgloballyover estimatethesolutionsobtainedinthepure2-Doptimizations.As apartialconclusion,preliminary2-Doptimizationscannotbeused forestimatingthesolutionsofthe3-Dproblem.TheTOPSISand FUCArankingsprovideyetsurprisinglywithscatteredvalues.The FUCAproceduregivesresultsthataremuch moreinagreement

Table8

ResultsofTOPSISandFUCAanalysisforthetriobjectiveoptimization.

Case AnnualcostM$/y EPtPO43−/y APtSO2/y GWPtCO2/y HTPtC6H6/y POCPtC2H4/y

TT1 227.34 4404.41 6221.15 1,599,077.01 8439.0316 2038.64 Gain −10.88 67.08 −28.82 −13.36 68.20 −4.86 TT2 222.28 4735.06 6043.41 1,563,468.01 9072.59 2022.27 Gain −8.41 64.61 −25.14 −10.85 65.81 −4.02 TF1 206.99 9770.38 4930.16 1,428,118.43 18,720.83 1939.25 Gain −0.95 26.98 −2.09 −1.25 29.46 0.25 TF2 209.03 10,109.41 4782.53 1,432,472.39 19,370.44 1928.70 Gain −1.95 24.45 0.97 −1.56 27.01 0.79

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Table9

Valuesofthedecisionvariablesforthetriobjectiveoptimization.

Decisionvariables TT1 TT2 TF1 TF2

Conversionrateoftoluene 0.59 0.60 0.70 0.75

Hydrogenpurgeflowrate(kmol/h) 300 300 300 300

Flashpressure(bar) 33.98 33.98 33.98 33.88

Stabilizerpressure(bar) 9.99 9.71 10 9.97

Column1pressure(bar) 3 3 3 3

Column2pressure(bar) 1.68 1.21 1.31 1.02

Ratio(bi-fuelfurnace) 0.29 0.32 0.24 0.34

witha simplegraphicalanalysis:besides,theglobalgaininthe setofobjectivesishigherthanthevaluecomputedbytheTOPSIS analysis.AcloserexaminationofTF1andTF2finallyleadstoselect thesolutionTF2,becauseitgivesonlyonenegativegainin envi-ronmentalimpacts.Inthefollowingstudiedcase,onlytheFUCA rankingwillbeused.

7. Case2:simultaneouseconomicandecologicalstudies 7.1. Context

Let us consider now that according to the EPA’s more stringent regulations, the GWP must be below a threshold of 1,400,000tCO2/y, which may have some effects on production

level.Besides,incentivemeasuresforenvironmentprotectionlead toimprovesimultaneouslytheotherenvironmentalobjectivesEP, AP,HTPandPOCP(ascomparedwiththepreviouscase).

Afterrandomlygeneratingseveralthousandsofvaluesfor inde-pendentvariables,it appearsthatvalues ofGWPslightly lower than1,400,000tCO2/yarelocatedinabenzeneproductionrange

of[250,280]kmol/h.Sothemultiobjectiveoptimizationisnow car-riedoutinthisrangeofproduction.Thesamestrategyasinthe previouscaseconsistingindecouplingobjectivesindependentand independentsetsisimplementedagain.Inordertoavoid extrapo-lationmodelproblemsthatmayoccur,multilinearregressionsare performedagainfordependentobjectives.Finally,atriobjective optimizationiscarriedoutforidentifyingthebestsolutionunder thesenewenvironmentalconstraints.

7.2. Multilinearregressions

For200valuesofindependentvariables withina production range[250,280]kmol/hrandomlygenerated,thevaluesoftheother objectivesarecomputedandtheresultsofmultilinearregressions aredisplayedinTable10.

0 0.5 1 1.5 2 2.5 _{x 10} 3 4 2000 4000 ₆₀₀₀ 8000 10000₁₂₀₀₀ 14000 250 255 260 265 270 275 280 AP (t SO2/y) EP (t PO4 (3-)/y) ProdB (kmol /h) TF3 TF4 TF5

Fig.12. Triobjectiveoptimization(ProdB,EP,AP)–Case2.

7.3. Triobjectiveoptimization

Atriobjectiveoptimizationiscarriedoutonthethree indepen-dentobjectives(ProdB,EPandAP),theotherdependantobjectives GWP,HTP,POCPandAnnualcost,beingcomputedbyusingTable10 fromthethreeindependentones.TheParetocurveobtainedfrom thetricriteriaoptimizationof(ProdB,EP,AP)isdisplayedinFig.12, wherethepointscalledTF3,TF4andTF5correspondrespectively tothebestsolutionfoundbyperforminganon weighted(resp. weighted)sumofranksofthesevenobjectives.

7.4. Selectingsolutions

AFUCArankingisfirstcarriedoutwiththesameweightfor alltheobjectives.ThebestsolutionnotedTF3isidentifiedamong thefivefirstones.However,inthissituation,benzeneproduction isimprovedonlyby14%.Thegoalofanyindustrialprocessbeing firstlyprofitmaximization,asecondFUCArankingisperformed withdifferentweightsonobjectives:0.4forbenzeneproduction

Table10

Resultsofthemultilinearregressions–scenario2.

Objective ProdBkmol/h EPtPO43−/y APtC2H4/y y-Intercept Coeff.corr. Errormax(%)

GWPtCO2/y 4901.44 −11.61 23.36 10,945.95 0.9397 3.75

HTPtC6H6/y −2.14×10−5 1.92 −3.68×10−5 1.66×10−4 1.000 6×10−6 POCPtC2H4/y 5.08 2.04×10−3 7.950×10−2 5.46 0.9942 0.69

COSTM$/y 0.6959 0 0 −5.03502 0.9997 2.10

Table11

ResultsofFUCAanalysisforthetriobjectiveoptimization.

Case BenzeneProd(kmol/y) AnnualcostM$/y EPtPO43−/y APtSO2/y GWPtCO2/y HTPtC6H6/y POCPtC2H4/y

TF3 253.50 171.30 7901.62 3737.16 1,249,024.11 15,104.58 1599.81 Gain −16.34 19.08 21.84 21.86 12.81 22.02 17.05 TF4 276.73 188.21 7149.41 4446.35 1,388,198.24 13,666.63 1772.36 Gain −9.49 18.04 29.28 7.03 3.09 29.45 8.11 TF5 259.88 175.95 8982.89 3799.92 1,269,260.85 17,171.37 1639.400 Gain −14.23 15.82 11.15 21.86 11.39 11.35 15.00

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Table12

Valuesofthedecisionvariablesforthetriobjectiveoptimization–Case2.

Decisionvariables TF3 TF4 TF5

Conversionrateoftoluene 0.74 0.71 0.76 Hydrogenpurgeflowrate(kmol/h) 299.30 299.92 299.92 Flashpressure(bar) 29.27 28.73 32.57 Stabilizerpressure(bar) 8.60 6.02 7.00 Column1pressure(bar) 2.13 2.03 2.21 Column2pressure(bar) 1.02 1.33 1.74 Ratio(bi-fuelfurnace) 0.16 0.24 0.17

and0.1forthesixcriteria.Asinthepreviouscase,thebestsolution notedTF4isidentifiedamongthefivefirstones.Finally,a compro-misesolutionTF5generatedwiththerespectiveweightsof0.35for thebenzeneproduction,0.15fortheGWPand0.1foralltheothers isalsodetermined.

Table11exhibitstheresultsobtainedbothforthethree inde-pendentobjectivesand forthe threedependentones. Foreach objectivethegainin%iscomputedvs.solutionTF2ofTable8.The valuesofthecorrespondingvariablesaregiveninTable12. 8. Conclusions

Thispaperhaspresented a methodologyfor eco-design and optimizationofachemicalprocesstakingintoaccountthe contri-butionofutilitygeneration,viatheindustrialsoftwareARIANETM_.

The well-known benchmark HDA process first developed by Douglas(1988)illustratestheapproach,whichistotallydifferent withthetraditionalend-of-pipetreatmentmethods.Theprocess wasdesignedunderclassicalengineeringobjectiveslikebenzene production and total annual cost, by also considering classical environmentalburdensastheGlobalWarmingPotential,the Acid-ificationPotential,thePhotochemicalOzoneCreationPotential,the HumanToxicityPotentialandtheEutrophicationPotential.A vari-antoftheclassicalmultiobjectivegeneticalgorithmNSGAIIwas usedforsolvingthevariousmultiobjectivesproblems.

Inapreliminarystudy,agoodvalueofthebenzeneproduction wasidentifiedonalimitedrangeofcosts,thenapossible degra-dationoftheannualcostinthisrange,andthusofthebenzene productionwereallowedtoimprovetheenvironmental perfor-mancesoftheprocess.InsteadofsearchingforaParetofrontonthe wholesetofobjectives,apreliminarystudyofobjectiveswas car-riedoutfordeterminingasub-setofdependentcriteriaexpressed asmultilinearfunctionsoftheremainingindependentones.Sothe multiobjectiveproblemwasreducedtoatricriteriaone.The val-uesofcorrespondingdependentobjectiveswerecomputedfrom theindependentones,andaTOPSISandFUCAanalyseswere per-formedonthewholesetofobjectives,FUCAgivingmuchbetter resultsthanTOPSIS.Analternativewouldbetoidentifyanideal pointontheParetofrontbydefiningametricdistancetoanutopia point(i.e.minimizingallobjectivesforinstance)asanobjective functionusingasingleobjectiveGA.

Asecondscenarioisbasedonanotherformulationforwhich a more stringent environmental regulation has tobe satisfied, expressedastheGWPcriteriontobelowerthanagiven thresh-old.Theobjectivealsohaspositivegainsoverallenvironmental objectivesEP,AP,HTPandPOCP.Multilinearregressionswere per-formedagain,toobtainanewtricriteriaproblem,solvedagainby meansofNSGAII.Bysimplytuningtheweightingfactorsusedin theFUCAranking,severalsolutionsofferingagoodtrade-offcanbe deducedforobjectives.Herethreesolutionscorresponding respec-tivelytohigh,mediumandlowrangesofbenzeneproductionare generated.Thismethodologycanbeappliedtoawidespectrumof chemicalprocessdesignproblemswithmultipleand environmen-talobjectivesandmakesexplicitthetrade-offsbetweenthem.

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