Directionalsolventextraction(DSE)isanemergingmembrane-freeliquid-liquidextractionprocesstodesalinatewaterusinglow-gradeheat.SeveraluniquefeaturesmakeDSEapotentiallydisruptivedesalinationtechnology:1)itisthermallydrivenandutilizeslow-gradeheat;2)itdoesnotrequiretheuseofmembranes;3)thereareopportunitiestointensify,modularizeandcustomizetheprocess;4)thereisavastsolventmoleculardesignspace.Thisworkestab-lishesatechnoeconomicmodelingframeworktosimultaneousoptimizeandheatintegratetheDSEprocess.Weperformrapidbottom-upscreeningtopredicttheenergyintensitylevelizedcostofwater(LCOW)oforganicacidandionicliquiddirectionalsolvents(DS)inanoptimizedDSEprocess.Likewise,weper-formtop-downanalysistosetcontinuoussolventpropertytargetsnecessarytorealizeaLCOWoflessthan$0.5/m3.LCOWismostsensitivetothesolubilityoftheDSinwaterandthermoresponsiveability(a.k.a.yield)ofthesolvent,i.e.,thechangeinthesolubilityofwaterintheDSwithtemperature.Despitetheirlowercost,organicacidshaveasmallthermoresponsiveabilityandLCOWofatleast$1.3/m3.Incontrast,wesetmodestquantitativethermophysicalpropertytargetsforionicliquidDStoachievebelow$0.5/m3LCOW.∗CorrespondingauthorEmailaddress:adowling@nd.edu(AlexanderW.Dowling)PreprintsubmittedtoDesalinationOctober14,2020 GraphicalabstractKeywords:thermaldesalination,liquid-liquidextraction,technoeconomicoptimization,levelizedcostofwater,heatintegrations,ionicliquids1.Highlights•Directionalsolventextraction(DSE)isapotentiallytransformativelow-gradeheatrenewabledesalinationtechnology•CreatedatechnoeconomicoptimizationframeworkforDSEwithembed-dedheatintegrationandidentiﬁedthemostimportantsolventthermo-5physicalproperties•Determinedfattyaciddirectionalsolventsareunabletomeet$0.50/m3levelizedcostofwater(LCOW)goalduetoinadequatesolventthermo-physicalproperties•Setquantitativesolventthermophysicalpropertytargetsforionicliquid10directionalsolventstoachievelessthan$0.50/m3LCOWgoal2 2.IntroductionWaterconsumptioniscriticaltomodernsociety;theaverageAmericanfam-ilyusesapproximation1140litersofmunicipalwaterperday[1],and130millionAmericansfaceseverewaterscarcityatleastpartoftheyear[2].Globally,3.815billionpeoplecurrentlyexperiencewaterscarcity[3],anditisestimatedthat66%oftheworld’spopulationcouldbelivingunderwater-stressedconditionsby2025[4].Althoughthecostsofwaterobtainedfromdesalinationhavefalleninthelastdecade,theyarehigherthanobtainingfreshwaterfromrivers,ground-water,orwaterrecycling.In2015,lessthanonepercentofthewaterconsumed20globallywasproducedbydesalination[5].TheexpansionofoilandgasextractionintheUShascreatednewwaterandenvironmentalchallenges[1].In2012,3.57billionm3ofproducedwaterwasextractedintheUS.IntheDelawareBasin,upto4barrelsofwaterareproducedperbarrelofoil[6];toputthisnumberinperspective,around0.5025litersofproducedwatermaybegeneratedtosupplyenergyforonehourinanaverageAmericanhousehold.Thesalinityofproducedwateristypically35,000ppmto300,000ppm,whichmaybeuptoeighttimeshigherthanseawatersalinity(35,000ppm)[7].Unfortunately,currentdesalinationtechnologiesareunpracticaltotreatsuchhighsalinitybrines[8].Largewatervolumes(about3020,000m3onaverageperwell)fromoilandgasproductionalsoremainchal-lenging,evenafterwatersupplychainoptimization.[9,10].Thereisapressingneedandopportunityfornewtechnologiestotreatproducedwater.Thereisnoone-size-ﬁts-alltechnologyforwatertreatment.Instead,thereisagrowingemphasisonﬁt-for-purposetreatmentindecentralizednetworks[12].35Inthisparadigm,wateristreatedtoonlythespeciﬁcationsneededforspeciﬁcenduses.Table1highlightsdiﬀerentwaterqualitylevels(salinity),appropri-ateenduses,andcandidatedesalinationtechnologies.Whileevaporativeandreverseosmosisdesalinationtechnologiesarecommonlydeployed,theyremainenergy-intensiveandunabletotreathighsalinitywatersources.Inthecontext40ofﬁt-for-purposewater,thereisagreatneedfornewtechnologiestotreata3 WaterclassiﬁcationSalinity(weight%)Salinity(ppm)UseMSFMEDRODSEFreshwater0-0.10%0-1,000ppmHumanconsumption,livestockandirrigation✓✓✓✓Slightlysalinewater0.10-0.16%1,000-1,600ppmLivestock,mayrequirespecialtreatmentforirrigation✓✓✓✓0.16-0.30%1,600-3,000ppmPoultryandpigs✓✓✓✓Moderatelysalinewater0.30-1.00%3,000-10,000ppmSuitableforcattleorsheepandforﬂushingtoilets✓✓✓✓Verysalinewater1.00-3.50%10,000-35,000ppmIndustrialusage(2%),thermoelectricpowerplants(95%)andmining(3%)✗✗✓(partially)✓Brinywater>3.50%>35,000ppm✗✗✗✓Table1:Naturalandmanmadesourcesofwaterrangefromfreshwater(0-0.10%salinity)tobrinywater(>3.50%salinity)[1].Salinityrequirementsvarywidelydependingonenduse.Forexample,lowsalinitywaterisusedforhumanandlivestockconsumption.Buthighsalinitywaterwithmorethan35,000ppmissuitableforindustrialusesincludingpowerplantcoolingandmining.Whilewell-establishedtechnologiesincludingMulti-stageFlash(MSF),Multi-eﬀectDesalination(MED)andReverseOsmosis(RO)havegreatlyadvanceddesalinationindustry[11],thereremainsaneedforsustainableandenergyeﬃcientprocesstotreathighsalinitywater.DirectionalSolventExtraction(DSE)hasbeenproventobeabletotreathighsalinitybrineswhileutilizinglow-gradeheat.widerangeofwaterqualitylevelsindistributednetworkswhileusingrenewableenergy.Directionalsolventextraction(DSE)usesathermoresponsivesolventtofa-cilitatetreatmentoverawidesalinityrange[13].DSEdoesnotrequiremem-45branes,whichoftenfoulathighsalinities,andcanutilizelow-gradeheat,in-cludingwasteorrenewable(solar)sources.PriorworkinDSEincludeschar-acterizationofmolecularphenomena,bench-scaledemonstrations,andlimitedprocessanalysis[14,15,13,16,17,18].Thispaperpresentsatechno-economicoptimizationframeworkwithtwonewcapabilities:ﬁrst,weperformsimulta-50neousprocessoptimizationandheatintegrationtorapidlyscreendirectionalsolventcandidatesinseconds.Second,weperformasensitivityanalysistoidentifythenecessarysolventpropertiestoenablecost-eﬀectiveDSEprocessesforaspeciﬁcapplication.Weemphasizetheseadvancesinprocess-scalemod-elscanrapidlyaccelerateDSEdevelopmentbyreducingtheneedforexpensive55experimentsandguiding(computational)moleculardesign.Toourknowledge,thisistheﬁrstapplicationofequation-orientedprocessoptimizationtofacilitatebottom-upandtop-downanalysisoftheDSEprocess.Theremainderofthispaperisorganizedasfollows.Section2reviewslitera-tureondesalinationandDSE,withanemphasisonthescopeforoptimization.604 Section3describestheoptimizationframeworkandmathematicalmodels.Sec-tion4studiestheimpactofheatsourcetemperatureandsolventpropertiesontheoptimizedprocess’sminimumspeciﬁcenergy.Section5presentsquantita-tivesolventpropertygoalstoachieve$0.50/m3LCOWtargetfortwoclassesofmolecules:carboxylicacidsandionicliquids.Finally,Section6summarizes65conclusions,limitations,andfuturework.3.Literaturereview3.1.DesalinatontechnologiesModerndesalinationtechnologies,includingevaporativeandreverseosmo-sissystems,areenergy-intensiveandnotsuitabletotreathighsalinitywater.70Evaporativesystemssuchasmulti-stageﬂash(MSF)andmulti-eﬀectdistillation(MED)utilizethermalenergy(typically90◦Cand55◦C,respectively)toevapo-rateandcondensatewater[7].Thesesystemsrequirehighlycorrosion-resistantandcostlymaterials[19]andareheat-intensive(26.29-83.06kWh/m3);theyrequirethreeorfourtimesthetheoreticalminimumenergyofseparation[8,7].75Incontrast,membrane-basedtechnologiessuchasreverseosmosis(RO)useme-chanicalworktoovercometheosmoticpressureacrossamembrane.Membrane-basedtechnologiesusesigniﬁcantelectricityinputs,needfrequentmembranere-placement,andhavelimitedeﬀectivenesswhentreatingconcentratedbrines[8].Newtechnologies,includingelectrodialysisandforwardosmosis,showpromise80toreduceenergyconsumptionandlowercosts.Forexample,osmoticallyas-sistedreverseosmosis(OARO)andmechanicalvaporcompression(MVC)aresuitabletotreathighsalinitybrines(140,000ppmand150,000ppmrespec-tively)[20,21,22].Nevertheless,MVCenergyconsumptionishigh(single-eﬀectMVC2342kWh/m3,double-eﬀectMVC20kWh/m3)[22].OARO,RO,85andothermembrane-basedtechnologiesareoftensusceptibletomembranefoul-ingathighsaltconcentrations[23].Whilehybriddesalinationsystemspairedwithrenewableenergysourcesarewell-studied[24,25,26],thereislimitedworkoftechnologiessuitableforhighsalinitybrines.5 Table2:Comparisonofenergetics,costs,andlimitationsofcommondesalinationtechnologies[7,23].TechnologyMulti-StageFlash(MSF)Multi-EﬀectDistillation(MED)ReverseOsmosis(RO)Speciﬁcenergy26.29-83.06kWh/m326.29-76.26kWh/m33.05-8.33kWh/m3Thermalinputtemperature90◦C55-70◦CambientGlobaldeployment8%27%60%Cost0.27-1.49$/m30.80-1.50$/m30.45-1.62$/m3ThermalenergyinputHighHighLowElectricenergyinputLowLowHighEquipmentsizeLargeLargeSmallMembranereplacementorfoulingNoNoYes3.2.DirectionalSolventExtraction90Directionalsolventextractioncanovercomelimitationsofthermalandmembrane-basedsystemsbyeﬃcientlyseparatinghighsalinityfeedswithlow-gradewasteheat(40-80◦C).DSEexploitsthermoresponsivesolventsthatextractwaterfromsaltymixturesatelevatedtemperaturesandreleasewater(phasesepa-rate)whencooled.DirectionalSolvents(DS)haveseveralfeatures:(1)water95candissolveinthesolvent,andthesolubilityincreaseswithtemperature;(2)thesolventisvirtuallyinsolubleinwater;(3)thesolventdoesnotdissolvesalts.TheDSEprocess,whichisexplainedinFigure1,isbasedonliquid-liquidextrac-tion;thesolubilityofwaterinthedirectionalsolventastemperatureincreases(thermoresponsiveness),whichenablessimpleregeneration.Thesefeaturesgive100DSEseveraldistinctadvantagescomparedtoexistingtechnologies:(1)DSEismembrane-freeandthusisnotrestrictedbymembranefoulingconcernsforhighsalinitywater;(2)DSEoperatesintheliquidstate,whichreducesthesizeandcomplexityoftheequipment;(3)DSEcanbepairedwithalow-temperaturerenewableheatsource(e.g.,low-costthermalsolar).105Amines[27]andalcohols[28]wereexploredoverﬁftyyearsagoastheﬁrstdirectionalsolventsfordesalination.Thesesolventscanonlytreatlowsalinitywater(5000ppm)andhaveahighsolubilityinwater,leadingtohighsolventlosses[29].Inthe1990s,ThePuraqCompanyproposedaliquidpolymers-based[30,31]directionalsolvent,whichwascommerciallyunsuccessfulduetoelevated110solventproductioncosts[32],althoughrecentworkbyThanaplanetal.[33]6 reexaminestheenergeticsofthePuraqCompany’sprocess.Recently,Luoandco-workersproposedfattyacids,includingdecanoicacid(CH3(CH2)8COOH)andoctanoicacid(CH3(CH2)6COOH)asdirectionalsolvents.ThehighlypolarC−−0andO−Hgroupsinthefattyacidsfacilitatetheformationofhydrogen115bondswithwatermolecules,whichenablescarboxylicacidstodissolvewater.However,thechainendishydrophilic,whichhelpsensurethesolubilityoftheacidsinwaterisnegligible(30-150ppm)[15].Inrecentwork,Guoetal.[34]proposedtheuseofionicliquids,whichhaveagreaterthermoresponsivnessabilitycomparedtofattyacids.Inthiswork,wewillassessthetechnoeconomic120potentialoffattyacidandionicliquiddirectionalsolventsinthecontextofanoptimizedDSEprocess. 7 Figure1:Illustrationofthebasicdirectionalsolventextraction(DSE)process.Seawater(stream1)isheatedtothemaximumallowabletemperature(80◦Cisshown)intheprocessandmixedwiththedirectionalsolvent(stream8).Themixedemulsionofwateranddirectionalsolvent(stream9)settlesinthewarmsettlingtank.Waterdissolvesinthedirectionalsolvent,andconcentratedbrine(stream4)isextractedfromthemixturebygravity.Thedirectionalsolventanddissolvedwater(stream3)arethencooleddown.Freshwaterisexpelledfromthemixtureanddecanted(stream6).Decanoicacidisreheatedandrecycled(stream8).Asmallamountofdirectionalsolventdissolvesinthefreshwaterandislost(stream6).Thusasmalldirectionalsolventmake-upfeedisaddedtothesystem(stream12)toensuresteady-stateoperation.3.2.1.Eﬀectivelyutilizelow-gradeheatandno/limitedmembranecostsLuoandco-workers[14,15,13,16,17,18]recentlydemonstratedoctanoicanddecanoicacidcaneﬃcientlydesalinatewater.Speciﬁcally,theyexperimen-125tallyobservedthesolubilityofwaterindecanoicacidchangesfrom3.8wt%at34◦Cto5.9%at80◦C,withnegligiblesolubilityoffattyacidinwater[16].ThisthermoresponsivecharacteristicofthedirectionalsolventenablesthermalregenerationandisessentialtotheDSEprocess.Luoandco-workersthendemonstratedtheDSEconceptinacontinuousbench-scaleprocess,success-130fullyextracting2.5gallonsoffreshwaterperdayfroma700ppmto1100ppmsalinityfeed(0.07-0.11wt%)utilizingoctanoicacid[16].Basedontheseexperi-8 ments,theyestimatedatotalenergyconsumptionof184kWh/m3fordecanoicacidand101kWh/m3foroctanoicacid,assumingheatintegrationwith90%heatexchangereﬃciency[16].1353.2.2.DemonstratedperformanceforhighersalinitiesBajpayeeetal.[14]demonstratedtheeﬀectivenessofoctanoicacidtotreatsaltybrinesfrom3,667ppmto58,333ppmTDS(totaldissolvedsolids).Like-wise,theysuccessfullytreatedsaturatedbrinesshowwaterextractionwithDSEofbrinewith290,000ppm(NaCl)[14].TheseresultsarepromisingforDSEto140treatproducedwaterwithhighTDSfromoilandgasextraction(upto460,000ppm).3.2.3.Scopeformolecular-to-systemsoptimizationTherearevastunexploredopportunitiestooptimizeDSEacrossmolecularandprocessscales.Existingfattysolventsrequire≈90m3ofrecycleper1m3145offreshwater,whichmakestheprocessesremainenergy-intensive.Alotaibietal.[16]performedheatintegrationforasingle-stagecontinuousprocessforDSEutilizingoctanoicanddecanoicacidsusingﬂowratesobtainedfrombench-scaleexperiments[16].Theiranalysisusedthetransshipmentheatintegrationmodel,whichassumesﬁxedﬂowratesandtemperatures[35].Whileinsightful,thisanal-150ysistechniqueoftenoverlooksopportunitiestoreduceenergyintensitythatareonlyrealizablebysimultaneouslyoptimizingprocessconditions(ﬂowrates,tem-peratures,compositions)andperformingheatintegration[36].Inthiswork,weshowthebeneﬁtsofmoreextensiveprocessoptimization.Atthemolecu-larscale,Guoetal.[34]recentlymeasuredthethermophysicalpropertiesofa155handfulofionicliquidsascandidatedirectionalsolvents.However,therearewelloverabillioncandidatesolventstoconsider.Inthiswork,weuserigorousprocessmodelingandoptimizationtosetquantitativesolventthermophysicalpropertytargetsasameanstonarrowthevastmoleculardesignspace.9 4.Methods:technoeconomicoptimizationframework160Asaﬁrststeptorealizemolecular-to-systemoptimizationoftheDSEplat-form,weproposeacomputationalframeworkforbottom-uprapidscreeningofcandidatesolventandtop-downidentiﬁcationofcontinuoussolventproperties.Inthissection,wefullydeﬁnethemathematicalmodelsandcomputationalimplementation.1654.1.ProblemstatementGiveninletwatersalinity(e.g.,35,000ppmNaCl),waterrejectionratio(e.g.,50%waterrejectionrate),physicalpropertiesofthedirectionalsolvent,andamaximumtemperatureoftheheatinput,manipulatethetemperatureandmaterialﬂowsintheDSEprocess(streamsinFigure1)tominimizethe170speciﬁcenergyoftheproblem.Weformulatethisasanonlinearoptimizationproblem(M1):minSpeciﬁcThermalEnergys.t.UnitOperationModelsTable3EmbeddedHeatIntegrationEq.(4)-(10)PhysicalBounds50%WaterRejectionRateInletWaterSpeciﬁcation(Seawater)Weusevariationsoftheoptimizationproblem(M1)forbothbottom-upscreeningandtop-downanalysis.Weadoptanequation-oriented(EO)ap-proach,whereinalloftheprocessspeciﬁcsandgoverningengineeringphenom-175ena(e.g.,thermodynamics,equipmentperformance,energycosts,etc.)areexpressedasmathematicalequationsthataresimultaneouslyconvergedduringoptimization.Thisapproachisextremelyﬂexible.Itnaturallyaccommodatesvariableboundsandfacilitatesembeddedheatintegrationduringtheoptimiza-tionprocedure.(M1)isanonconvexoptimizationproblemwith77linearequal-180ityconstraints,26nonlinearequalityconstraints,6linearinequalityconstraints,10 6nonlinearequalityconstraints,30quadraticequalityconstraints,and136vari-ables.UsingtheJulia[37]andJuMP[38]computationalenvironment,wecaneﬃcientlysolve(M1)usingIPOPTsolver[39]andHSL(MA27)[40]inapproxi-mately0.2secondsafterthoughtfulinitialization.Theremainderofthissection185describesallofthemathematicalequationsandinputdatausedin(M1).4.2.UnitOperationModelsTheDSEprocessisacollectionoftanks,heatexchangers,splitters,andmixers,asshowninFigure1,connectedbythirteenstreamscontainedinsetS.VariablesﬂowrateFandtemperatureTareindexedbysetS.Themole190fractionvariableisindexedbythesetofstreams(S)andthesetofcomponents(C)whichincludesthedirectionalsolvent,water,andsalt.Massandenergybalancesandliquid-liquidequilibriaequations,whichasshowninTable3,areusedtorelatethesevariablesforinletandoutletstreams.Weassumetheentireprocessoperatesatasteady-stateandtherearenochemicalreactions.195 11 Table3:Eachunitoperationismodeledasacollectionofequationsthatrelatetheinletandoutletstreams.ThefollowingvariablesareindexedoverthesetofstreamsS:themolarﬂowF(kmol/s),thetemperatureT(K),andtheheatcapacityCp(J/mol-K).ThemolarfractionsxareindexedoverbothSandthecomponentsCwhichincludethesolvent,water,andsalt.ThesetsI⊂SandO⊂Saretheinletandoutletstreamsofeachunitoperation.Forsimplicity,theindexinoroutisusedifthereisonlyoneinletoroutlet,respectively.Thesettlingtankoutletshaveindiceso1ando2fortheaqueousandsolventphases,respectively,suchthat{o1,o2}=O.Weassumesalthasaﬁxedsolubilityofκs(molefraction)inthesolventphaseandthedirectionalsolventhasaﬁxedsolubilityofκd(molefraction)intheaqueousphase.EquationTanksIsothermalmixerSinglephaseheatexchangerOverallmassbalanceFin=󰁓j∈OFj󰁓i∈IFi=FoutFin=FoutOverallcomponentbalanceFinxin,c=󰁓j∈OFjxj,c∀c∈C󰁓i∈IFixi,c=Foutxout,c∀c∈Cxin,c=xout,c∀c∈CChemicalequilibriumWater:xo1,w=A+BTo1Salt:xo1,s=κsDirectionalSolvent:xo2,d=κdSummationequation󰁓c∈C(xo1,c−xo2,c)=0EnergyBalanceTin=To1=To2Ti=Tout∀i∈IQ=CpFin(Tout−Tin)4.2.1.Liquid-liquidphaseseparationTheDSEprocessreliesontemperaturevaryingsolubilityofwaterinthedirectionalsolvent.Unfortunately,temperature-dependentternaryphasedataforwater,solvent,andsaltarenotavailableintheliterature.Forpreliminaryprocessanalysis,weassumethesolubilityofwaterinthesolventislinearly200dependentontemperatureshowninEq.(1).WeﬁtAandBviaregressionanalysisusingexperimentaldataforthemixturedecanoicacid,water,andsaltfromBajpayeeetal.[14]andOliveiraetal.[41]forthemixturedecanoicacidandwater.Figure2showsthissimplemodelﬁtsthedatawell.FittedparametersarereportedinTable4.Weassumethedirectionsolventhasaﬁxedsolubility205intheaqueousphase,denotedκd.ValuesaregiveninTable5.Likewise,weassumesalthasaﬁxedsolubilityofκs=65ppm(0.0199mol/mol)inthesolvent12 phase.xw=A+BT(1) Figure2:Weperformlinearregressiononsolubilitytocalculatethetemperatureswing(ther-moresponsiveness)ofthesolubilityofwaterinthecarboxylicacid(solventphase)usingtwosetsofexperimentaldata.Bajpayeeetal.[14]providesdataforternarymixturesC8andC10fattyacids,water,andsalt.Oliveiraetal.[41]providesdataforbinarymixturesofC6toC10fattyacidsandwater. 13 Table4:Coeﬃcientsfortheequationxw=A+BTforsolubilitycorrelationforcarboxylicacidsand[emim][Tf2N][34].Bajpayeeetal.[14]NumberofcarbonsA(mol/mol)B(mol/molK)8-0.83040.003210-0.40910.0022Oliveiraetal.[41]NumberofcarbonsA(mol/mol)B(mol/molK)6-0.57310.00397-0.76180.00318-0.73670.00319-0.57430.002310-0.81870.0036IonicliquidA(mol/mol)B(mol/molK)[emim][Tf2N]-1.34170.0063Table5:Solubilityofcarboxylicacidsandionicliquidinwater[42,34].AcidNcSolventsolubilityinwater(mol/mol)Solubilityinwater[ppm]Hexanoic61.678E-310,820Heptanoic73.348E-42,419Octanoic88.495E-5680Nonanoic93.416E-5300Decanoic101.339E-5128IonicLiquidSolventsolubilityinwater(mol/mol)Solubilityinwater[ppm][emim][Tf2N]5.985E-63004.2.2.Single-phaseheatexchangerTheheatdutyintheheatexchangerisQ=CpFin(Tout−Tin),whereCpistheheatcapacity,Finistheﬂowrate,andTout−Tinisthetemperaturediﬀerence.WecalculateCpifortheorganicsolventiwiththecapacitygroup14 contributionmethod[43]:Cpi=󰁛k∈GNk(Ak+Bkt)t=T/1000(2)Eq.(2)capturestheinﬂuenceofNktimesoffunctionalgroupkappearsintheorganiccomponenti.ForwaterweusecoeﬃcientsgiveninTable7[43]:Cpi=A+Bt+Ct2+Dt3+E/t2,t=T/1000(3)andfortheionicliquid,weusecoeﬃcientsgiveninTable7andEqs.(4)[44].210Cpi=A+BT(4)WethencalculatetheCpofeachstream(mixtures)usingthethecomponentheatcapacitiesCpiandthemolefractionsxi:Cp=󰁛i∈CCpixi(5)TheheatcapacityofNaClisconsideredconstantwithavalueof15.058J/mol-K[43].CoeﬃcientsforEqs.(2)-(4)aregiveninTables6and7.Table6:Heatcapacityparametersforgroupcontributionmethod[43].FunctionalgroupABJ/molKJ/mol-K2CH314.5504540.60CH219.53932.21COOH-49.7595421.114.3.EmbeddedHeatIntegration215WeembedtheDuran-Grossmanheatintegrationequations[45]directlyintotheprocessoptimizationproblem.Thisallowsustosimultaneouslyoptimizethe15 Table7:HeatcapacityparametersforEq.(3)[43]andEq.(4)[44].Cpi=A+Bt+Ct2+Dt3+E/t2,t=T/1000(J/mol-K).ComponentABCDE(J/mol-K)(J/mol-K*kK)(J/mol-K*kK2)(J/mol-K*kK3)(JkK2/molK)H2O-203.60601583.29-3196.432474.4553.855326[emim][Tf2N]430.390.315000processoperatingconditions(ﬂowrates,compositions,temperatures)whilemin-imizingthethermalenergyinputperunitoffreshwaterproduct.Incontrast,Alotaibietal.[16]onlyperformheatintegrationforaﬁxedprocessoperat-220ingconditions.Weemphasizeourapproachissuperiorbecauseitoptimizesmoredegreesoffreedom.Theoptimizermanipulatesﬂowrates,compositions,andtemperaturestobalancecomplexinterdependenciesbetweentemperature-dependentphaseequilibriaandthepinchpointwhichlimitsheatintegration.Forcompleteness,wenowsummarizetheheatintegrationmodel.225Eachsingle-phaseheatexchangerhalfisdesignatedasahotstream(requirescooling)oracoldstream(requiresheating),denotedwithsetsSHandSC,respectively.WethenconsidertheinletofeachheatexchangerasapinchcandidatetemperatureTpandaddtheminimumdrivingforce∆Tmintothecoldstreamtemperatures:Tp=󰀻󰀿󰀽Tinp∀p∈SHTinp+∆Tmin∀p∈SC(6)WeusethesetP=SC∪SHtodenoteallpinchcandidatetemperatures.Foreachpinchcandidatep∈P,wecalculatetheheatcontentabovepinchtemperatureTp:QApH=󰁛i∈SHFCpi[m˜ax(Tini−Tp)−m˜ax(Touti−Tp)],∀p∈P(7)Similarly,wecalculatetheheatcontentbelowpinchtemperatureTp:QApC=󰁛i∈SCFCpi[m˜ax(Toutj−Tp+∆Tmin)−m˜ax(Tini−Tp∆Tmin)],∀p∈P(8)16 TheminimumhotutilitydutyQSmustbelargerthanthediﬀerencebetweentheheatcontentsbelowandaboveeachpinchcandidate.QS󰁿󰁾󰁽󰂀heatingutility≥QApC󰁿󰁾󰁽󰂀heatcontentabovepinchcandidate−QApH󰁿󰁾󰁽󰂀heatcontentbelowpinchcandidate∀p∈P(9)Finally,weuseanenergybalancetocalculatetheminimumcoldutilitydutyQW:QW󰁿󰁾󰁽󰂀coolingutility=QS󰁿󰁾󰁽󰂀heatingutility+󰁛j∈SCQinj󰁿󰁾󰁽󰂀internalheating−󰁛i∈SHQouti󰁿󰁾󰁽󰂀internalcooling(10)Toensureoptimizationproblemisdiﬀerentiable,weuseasmoothedapprox-imationforthemaxoperator:m˜ax(x)=12󰀃󰁳x2+󰂃2󰀄≈max(x,0),󰂃2=10−6(11)Thismodeliseﬀectivebecausethecombinatorialsearchforthepinchcan-didateiscastasinequalityconstraintEq.(9),whichiseﬃcientlyhandledinequationorientedprocessoptimization.4.4.CostmodelAftersolving(M1),weestimateequipmentandoperatingcostsandthen230calculatethepriceperunitoffreshwaterproduction.Theheatintegrationmodeldescribedaboveonlycomputestheminimumhotandcoldutilitieswhensolving(M1).Asapost-processingstep,weperformsequentialoptimizationtodesigntheheatexchangernetwork.Weﬁrstsolveamixedintegerlinearprogramtopredictmatchestominimizethenumberofheatexchangers.Wethensolveanonlinearprogramtocalculatetheheatexchangerareas.[35,36].Finally,weuseGuthrie’sMethod[36]tocalculatetheequipmentcosts.WeusethepresentcostindexofDecember2018(613.6)andastraight-linedepreciation:ADE=(CotA−SV)ULA(12)17 Here,ADEistheAnnualDepreciationExpense,CotAisthecostoftheassets,SVisthesalvagevalueaftertheusefullifeoftheplant(20%ofthecostoftheassets),andULAistheestimatedusefullifeoftheplant.Weassumeacostofelectricityof0.05$/kWh(averagepriceofTexas,Oklahoma,Lousiana,235NewMexico,Georgia,andUtah)[46].Weassumea2psipressuredropevery100feet,andtheheighofthetanksiscalculatedforeveryprocesssolutionforpumpingelectricity.Weassumeacostofheatingutilitiesof2.778$/GJfromwasteheat,asimilarcosttosolidwaste,coal,ornuclearenergy[47].Weassumethesystemhasausefullifeof20yearsforcostcalculations,andweselected240stainlesssteelforthematerialoftheequipmentbecausetheplanthandlessalinebrinesandfreshwater.Thecostofdecanoicacidissetto12$/kg[48].5.Results:Bottom-upProcessOptimizationWenowsolvetheoptimizationproblem(M1)inseveralbottom-upcasestudiestopredictthebestpossibleperformanceofcandidatedirectionalsolvents245inafullyoptimizationprocess.WeﬁrstcompareouroptimizedreferencedesignwithAlotaibietal.[16].Then,weperformasensitivityanalysistoquantifytheimpactof∆Tmin(heatexchangersize)andthemaximumtemperature(heatsourcequality).Finally,wecomparecandidateorganicacidsolvents.5.1.ReferenceDesignforDecanoicAcidDirectionalSolvent250Wesetthetemperatureboundsbetween34◦Cand80◦C,specifya50%rejectratio,andset∆Tmin=6◦C1tomatchAltoabietal.[16].Resultsfromsolving(M1)areshowninTables8,9,10andFigure3.Fromtheresults,wedrawtheseobservations:ObservationA1.Aconsiderableportionofthedecanoicacid(128255ppm)issolubilizedintheoutletoffreshwaterandsaltybrine.Wecalculatethat,atsteady-state,theprocessrequires10−4kmol/sofmake-updirectional1Altoabietal.[16]reportaheatexchangereﬀectivenessof90%,whichweconvertto∆Tmin=6◦C.18 solvent.Weemphasizethismake-upwasnotconsideredbyAlotaibietal.[16],whobasedtheirprocessanalysisonpseudo-steady-stateexperimentaldata.ObservationA2.Ourapproachﬁndsthesamepinchpoint,50◦C,260asshowninAltoabietal.[16].ObservationA3.Solving(M1)predictsspeciﬁc(thermal)energyof191kWht/m3offreshwaterwithdecanoicacidasasolvent,whereasAlotaibietal.[16]180kWht/m3offreshwater.Wehighlighttwodiﬀerencesthatcanexplainour9%largerspeciﬁcenergy:ﬁrst,theadditionofafeed(make-up)265streamofdecanoicacid.Second,wecooldownthesolvent-wateremulsionstreamto34◦C(limitingtemperatureduetosolventcrystallization)incontrasttothe40◦CusedbyAlotaibietal.[16].ObservationA4.Solvingthecostanalysisfortreating1m3ofwaterresultsinacostof$3.31/m3offreshwater.Thecostishighcomparedto270moderntechnologies:between$0.27/m3and$1.62/m3offreshwater.SolventlosshasasigniﬁcantinﬂuenceonthecostofDSEdesalination. 19 Table8:Streamresultsforreferencedesignwithdecanoicacidassolventusing80◦Casmaximumallowabletemperature∆Tmin=6◦C.SeeFigure1forschematics.FlowratesarecomparabletoTable3inAlotaibietal.[16].StreamFlowTemperaturexdxwxskmol/s◦C%mol%mol%mol10.5250.0098.891.1120.5800.0098.891.1131.818063.1836.7810−440.258010−397.971.9951.813463.1836.7810−460.253410−499.780.2171.563473.3326.6610−481.568073.3326.6610−492.068055.5044.220.26100.252510−397.971.99110.252510−499.780.211210−4341000.000.001310−4801000.000.00 20 Table9:Heatexchangersizesandtemperaturesforthereferencedesign(decanoicacidassolvent,80◦Casmaximumallowabletemperature).Morethan90%oftheheatingandcoolingoccursinheatexchangersHX3andHX2,respectively.Thisisduetothelargeamountofdecanoicacidthatmustberecycledtoaachieveanoverall50%extractionratio.Forpracticalconsiderations,onemaychoosenottoaddHX6duetothelowheatdutyoftheheatexchangerandthesmallﬂowofsolvent.HeatexchangerStreamTemp(◦C)Q(kWh)InletOutletInletOutletHX1S1S225802.09HX2S3S58034-23.44HX3S7S8348023.00HX4S4S108025-1.045HX5S6S113425-0.17HX6S12S1334803.2E-3 Table10:Heatintegrationresultsforthereferencedesign.QAhistheheatexchangedabovethepinchtemperatureandQAcistheheatbelowthepinchtemperature.BothstreamsS3andS4areatthepinchtemperatureof50◦C.HeatexchangerExchangerInletTypeofStreamQAh(kWh)QAc(kWh)QAc-QAh(kWh)HX1S1Cold24.0324.310.28HX2S3Hot0.013.123.11*HX3S7Cold20.7723.883.10HX4S4Hot0.013.123.11*HX5S6Hot23.8824.170.28HX6S12Cold20.7723.883.10*Pinchtemperature21 Figure3:Compositecurvesforthereferencedesign,includingutilities.MostoftheheatexchangeisdoneinHX2andHX3,whichhavethelargesttemperaturediﬀerenceandthehighestﬂowrates.RecallHX1heatsinletseawatertothetemperatureofthewarmsettlingtank,HX2coolsthewater-decanoicacidemulsion,andHX3heatstherecycleddirectionalsolvent.HX4andHX5cooltheoutletconcentratedbrineandfreshwater,respectively.QSandQWaredeﬁnedastheminimumheatingandcoolingutilityduties,respectively.Table11:LCOWforthreediﬀerentdirectionalsolventswithoutconsiferingsolventrecovery.Costsofthermalenergy,pumpingelectricityandequipmentarelowerusingionicliquid.Howeverthecostofthesolventmake-upincreasesconsiderably.DirectionalsolventLCOWSolventcostElectricitycostThermalenergycostEquipmentcost$$%$%$%$%Decanoicacid3.301.0331.210.319.391.9258.180.041.21Octanoicacid4.132.4860.050.204.851.4234.380.030.73[emim][Tf2N]43.0342.6099.020.070.170.340.780.010.035.2.SensitivityAnalysis:MaximumTemperatureand∆TminNext,weconsideredthesensitivityofprocessdesignstoboththemaximumtemperatureand∆Tmin,whichcontrolstheheatexchangersizeandeﬀective-275ness.Wesolve(M1)withthreediﬀerentsetsofexperimentaldataastheLLEcorrelationinput:decanoicacid-waterdataformOliveiraetal.[41],decanoic22 acid-water-saltdatafromBajpayeeetal.[15],and[emim][Tf2N]-water-saltdatafromGuoetal.[34].Figure4showsspeciﬁcenergyatsixmaximumtemper-aturebetween40◦Cand90◦Candtendiﬀerent∆Tminbetween1◦Cand28010◦C.Figure5showsspeciﬁcenergyatﬁvemaximumtemperaturebetween35◦Cand75◦Candtendiﬀerent∆Tminbetween1◦Cand10◦C.Solving(M1)169timestogenerateFigures4and5tooklessthan1minute.Table12givesthestreaminformationforasingledesignfromthesensitivityanalysis(Tmax=50◦C,∆Tmin=6◦C).Fromtheseresults,weobserve:285ObservationB1.Weﬁndconsistenttrendswithbothsetsofsol-ubilitydata.Bajpayeeetal.data[15]showed2.6%moresolubilityofwaterinthesolventphase,whichleadsto2timeslowerenergy-intensiveprocessastheprocessneedsfewerextractionsperpass.ThediﬀerencebetweenthesolubilitiesisbecauseOliveiraetal.onlyconsideredbinarywater-acidmixtures.290ObservationB2.Asexpected,highermaximumtemperaturesen-ablehigherperpassextraction,whichallowsforalowerrecycleﬂowrate(1.81kmol/sforTmax=80◦Cversus4.91kmol/sforTmax=50◦C)andlowerenergyin-tensity(191.84kWht/m3forTmax=80◦Cverus551.90kWht/m3forTmax=50◦C).Thissuggeststhatmanipulatingthesolventchemistrytoincreasetheperpass295extractionatalowertemperaturewilldecreasetheenergyintensity.ObservationB3.Thespeciﬁcenergydiﬀerencebetweentempera-ture≤80◦Cand≤90◦Cisnegligible.Thisisbecauseincreasingthepassperextractionincreasesthefractionofwaterinthesolvent-wateremulsion,whichdecreasestheCpofthemixture.Astheamountofheatrequiredtoheatthe300mixturedecreasesatahighermaximumallowabletemperature,sodoesthespe-ciﬁcenergyoftheprocess.Thisresultemphasizeslittlebeneﬁtforheatsourcesgreaterthan80◦Cforoﬀ-the-shelforganicacidsolvents.ObservationB4.Heatexchangerswithatemperaturediﬀerenceoflessthan3◦Carelikelyrequiredtoachievelessthan50kWht/m3and4◦Cto305achievelessthan100kWht/m3utilizingdecanoicacidasasolvent.Theheatexchangerswouldneedtohaveaneﬀectivenessofapproximately96%orhighertoachievethe50kWht/m3goalutilizingdecanoicacid.23 ObservationB5.WeobservetheILthesolvent[emim][Tf2N]canachieve50kWht/m3usingmaximumallowabletemperatureof65◦Cand∆Tmin310of6◦C.Ouranalysisshowsthat,fromanenergeticsperspective,ILsareamorepromisingclassofdirectionalsolvents.Table12:Streamresultsforreferencedesignwithdecanoicacidassolventusing50◦Casmaximumallowabletemperature∆Tmin=6◦C.SeeFigure1forstreamnumbers.StreamFlowTemperaturexdxwxskmol/s◦C%mol%mol%mol10.5250.0098.891.1120.5500.0098.891.1135.165069.7930.180.0340.255010−398.411.5855.163469.7930.180.0360.253410−499.370.6274.913473.3326.6610−484.915073.3326.6610−495.165066.5633.330.10100.252510−398.411.58110.252510−499.370.631210−4341000.000.001310−4501000.000.00 24 (a)UsingdatafromOliveiraetal.[41] (b)UsingdatafromBajpayeeetal.[15]Figure4:Sensitivityofspeciﬁcenergytomaximumtemperature(heatsourcequality)and∆Tmin(heatexchangersize).Bajpayeeetal.[15]datashowed2.6%moresolubilityofwaterinthesolventphasefromOliveiraetal.[41].Thediﬀerencemaybeexplainedbytheinteractionofsaltinthemixture.Highermaximumtemperaturesenablehigherperpassextraction,whichallowsforalowerrecycleﬂowrateandlowerenergyintensity.Solventsthatenableshigherperpassextractionatalowertemperature,thedecreaseinenergyintensitywouldbehigher.Thespeciﬁcenergydiﬀerencebetweenallowing(M1)toreach80◦Cand90◦Cisnegligible.Heatexchangerswithatemperaturediﬀerenceoflessthan3◦Caretoachievelessthan50kWht/m3.25 Figure5:Eﬀectsofmaximumtemperatureallowedfortheprocessutilizing[emim][Tf2N]assolvent.Thespeciﬁcenergyoftheprocessisgreatlyreducedcomparedtocarboxylicacids. 26 5.3.SensitivityAnalysis:LengthoftheChainofCarboxylicAcidsWenowrapidlyscreenﬁvecarboxylicacidsasdirectionalsolvents.Wesolve(M1)usingacid-watermixturedataforOliveiraetal.[41].Wesettheamount315ofaciddissolvedintheaqueousphaseasthesolubilityofthefattyacidat20◦C,showninTable5.Theminimumtemperaturefortheprocessissetasthelargerofthemeltingtemperatureoftheacidor25◦Catambienttemperature.The120instancesof(M1)showninFigure6weresolvedinapproximately25secondstotal.Fromtheresults,weobserve:320ObservationC1.InFigure2,weseethereisnotaclearrelationshipbetweenthesolubilityofwaterinorganicacidandthelengthofthecarbonchain.However,weﬁndtheslopeB,i.e.,thethermoresponsivenessofsolubility,ismostinﬂuentialonspeciﬁcenergy.ObservationC2.Forsolventselection,thethreemostimportant325factorsarei)thechangeinwatersolubilityforaﬁxedtemperaturechange(ther-moresponsiveness);ii)themeltingtemperatureofthefattyacid,whichlimitstheminimumoperatingtemperature;andiii)thesolubilityofthedirectionalsolventinfreshwater.ObservationC3.SimilartoobservationB4,high-performanceheat330exchangersarerequiredtoachievelessthan50kWht/m3usingC6toC10fattyacidsObservationC4.Thecostoftheprocessincreaseswiththelengthofthecarboxylicacidchain.Thesolventsolubilityinwaterdecreasesasthecarbonchainincreases,diminishingtheamountofsolventlossandthesolvent335make-upcostintheprocess.ObservationC5.DSEprocessusingfattyacidsarenoteconomicallyviable,withabest-casescenarioof$1.29perm3offreshwaterfordecanoicacidwithheatexchangerswith∆Tminof1◦C. 27 (a)EﬀectsonspeciﬁcenergyusingdiﬀerentcarboxylicacidsastheDS. (b)EﬀectsonthecostoftheDSEprocessutilizingC6toC10fattyacids.Figure6:Thereisnotaclearinﬂuenceinthelengthofthechainofcarbons(Nc)intheenergyrequiredfortheseparationandthecostoftheprocess.DSEremainsenergyintensiveutilizinganyC6toC10carboxylicacidandsuﬀersfromsolventlost.Thecostoftheprocessincreaseswiththeincreaseofsolubilityofthesolventinwater.Thevaluesofthecostatutilizinga∆Tminfrom1◦Cto◦C10fordiﬀerentcarboxylicacidsare:forNc=6:$107.91-108.99perm3,forNc=7:$21.91-23.55perm3,forNc=8:$5.90-7.86perm3,forNc=9:$3.00-6.18perm3,forNc=10:$1.29-3.79perm3.seeTable5forspeciﬁcquantitiesofsolventloss.28 6.Results:Top-DownSolventPropertyTargets340Basedonthebottom-upanalysisinSection5,weconcludethatknowncar-boxylicacidsarenotaneconomicalsolutionfordirectionalsolventextraction.Although[emim][Tf2N]is,fromanenergeticperspective,amorepromisingdi-rectionalsolvent,limiteddataforIL-water-saltmixturespreventsbottom-upscreeningofmorecandidateILsolvents.345Inthissection,wegeneralizetheoptimizationproblem(M1)toconsiderhy-potheticaldirectionalsolventmoleculeparameterizedbythreecontinuousprop-erties:solubilitiesintheaqueousandsolventphasesandcostofthesolvent.Thusweperturbfourparametersinthetechnoeconomicanalysis:A,B,solventcost,andκd.Wethenperformtop-downsensitivityanalysistoidentifyide-350alizeddirectionalsolventpropertytargetstoaddinmoleculardiscovery.Thesecontinuousareaprecursortodiscretemolecularoptimization[49].6.1.Top-DownAnalysis:CarboxylicAcidsWestartbyperformingasensitivityanalysisforhypotheticalcarboxylicacidsolventsoveragridforthreeproperties:1)thethermoresponsivenessofthesolubilityofthesolvent(B),2)theamountofwaterthatsolubilizesinthesolventatareferencetemperature(A),and3)theamountofsolventdissolvedinthefreshwaterattheoutletoftheDSEprocess(κd).EachcandidatesetofpropertiesisﬁrstcheckedtoensurethesolubilitycorrelationEq.(1)predictsavalidmolefractionbetween0and1attheprocesstemperaturebounds(TminandTmax):0≤A+BTmax,1≥A+BTmax,0≤A+BTmin,1≥A+BTmin(13)WefoundEq.(13)isextremelyeﬀectiveatpredictingif(M1)willbeinfeasible.ForeachsetofpropertiesthatsatisfyEq.(13),wesolve(M1)tocompute355ﬂowratesandtemperaturesthatminimizespeciﬁcenergy.Foreachsolutionof(M1),weestimateLCOWforafewsolventcosts.FromtheresultsshowninFigure7,weconclude:29 Figure7:ThecoloredcontoursshowLCOWcalculatedusing$12/kgcostofdecanoicacidasafunctionofthermoresponsivness(A,verticalaxis)andthesolubilityofwaterat40◦C(B,horizontalaxis).Bothaxesarescaledsuchthat1.0,whichismarkedwitha󰂏,correspondstodecanoicacid.(Top)Usingthecurrentsolubilityofthesolventinwater(κd=128ppm),a2-foldimprovementinbothpropertiesAandBresultinaLCOWabove$1/m3.(Bottom)Reducingthesolubilityofthesolventinwaterby10-fold(κd=12.8ppm)reducestheLCOWto$2.88/m3.Evenwiththisimprovement,AandBbothneedtoincreaseby1.5-foldtoreachthe$0.5/m3LCOWgoal.30 ObservationD1.Foradirectionalsolventsimilartoafattyacid,increasingthermoresponsiveability(B)anddecreasingsolubilityofthesolvent360inwater(κd)wouldcausethegreatestreductioninLCOW.Likewise,increasingsolubilityofwaterinthesolventatareferencetemperature(B)alsoreducestherecycleratiobydecreasingtheamountofsolventneededforwatertodissolve.WecalculateLCOWof$3.30/m3and$4.13/m3fordecanoicandoctanoicacids,respectively.EventhoughenergycontributiontoLCOWislowerfromoctanoic365acid($1.62/m3versus$2.20/m3),theoverallLCOWislargerbecausethehighersolubilityofthesolventκdislarger(128ppmfordecanoicacidversus300ppmforoctanoicacid),whichcauseslargersolventmake-upcosts($1.03/m3offreshwaterfordecanoicacidversus$2.48/m3offreshwaterforoctanoicacid).ObservationD2.Figure7givesquantitivetargetstoreduceLCOW370forafattyacid-likedirectionalsolvent.Forexample,doublingthethermore-sponsiveability(B)andreducingthesolubilityofthesolventinwaterby10-fold(κd=128ppmto12.8ppm)relativetodecanoicwouldgiveaLCOWlessthan$0.50/m3.ObservationD3.Therecycleratioisreducedasthethermorespon-375siveability(B)ofthesolventandthebasesolubilityofwaterinthesolvent(A)increase.Thisreducesthethermalandelectricenergyrequiredtoheat,pump,andcooltherecycleoftheDSE-wateremulsion.Reducingtherecycleratioalsodrasticallyshrinksthesizeoftheequipment.Forexample,increasingthethermoresponsivenessofthesolventbyafactorof2decreasestherecycleratio380byafactorof20,whichdecreasestheheatandelectricitycostsfrom$2.20perm3offreshwaterto$0.21perm3offreshwater,anddecreasesequipmentsizesby400%.6.2.Top-downAnalysis:IonicLiquidsNext,weperformasensitivityanalysisforhypotheticalILdirectionalsol-385vents.Comparedtocarboxylicacids,ILsarealessmaturechemicaltechnology.Weconsideracurrentbenchmarkpriceof$1,000/kgof[emim][Tf2N][50].How-ever,manyexpecteconomiesofscaletodramaticallyreducethecostofILsas31 themarketforthesesolventsgrows.Forexample,Shiﬂettetal.[51]showsapricereductionof92%for[C2MIM]+[Ace]−and90%for[C2MIM]+[BF4]−.For390thesensitivityanalysis,weconsiderthreeILcosts:$1,000/kg,$100/kg,and$10/kg.Duetothesecomparativelyhighcosts,solventlossisespeciallyim-portantforILscomparedtocarboxylicacids.Thus,itisdesirabletoconsidersolventrecoverysystems,suchasamembraneforpost-treatment.2Forsimplic-ity,weconsiderthecompleterecoveryofthesolventfromthefreshwaterfeed395product,whichcanberecoveredwithananoﬁltrationpolishingstep.ObservationE1.[emim][Tf2N]isapproximates2timesmorether-moresponsive(A)thandecanoicacid(0.0063mol/mol/◦Cvs.0.0022mol/mol/◦C).However,atthecurrentpriceoftheionicliquid,thesolventloss(κd)iscritical.Figure8predictsthataten-folddecreaseinκddecreaseLCOWtoonly12%of400theoriginalcost.Improvingthethermoresponsiveness(B)aloneisinsuﬃcientforILstobeLCOW-competitivewithcarboxylicacids.AssumingthecurrentpriceofIL,thesolventwouldstillrequirea100foldreductionofthesolventsolubility(xo1,d).ObservationE2.Assuminga90%costreduction,thethermore-405sponsivnesswouldneedtobeincreased1.5timesorthesolubilityofwater1.25times.However,thesolvent’ssolubilityinwaterwouldneedtobereducedbyaten-fold,asshowninFigure8.ObservationE4.Foracostof[emim][Tf2N]of$10/kg,thesolventsolubilityinwaterwouldhavetobe10timeslower,andthegoalof$0.50/m3of410freshwaterwouldbeachieved.However,itwouldstillbepossibletoreachthetargetgoalbyincreasing1.2thesolubilityofwaterinthesolventorincreasing1.5thethermoresponsiveness.2ILrecoveryfromthefreshwaterstreamisachievablewithoﬀ-the-shelfﬁltrationsystems.Post-treatmentforthebrinerejectismuchmorechallengingduetoconcernsofmembranefouling.Fullcostingofthefreshwaterpost-treatmentsystemisbeyondthescopeofthiswork.Instead,weneglectcapitalcostsandenergyusage.Assuch,thepropertytargetsareoptimisticbutinformative.32 ObservationE5.Forsolventwithacostashighas[emim][Tf2N],thethermoresponsivness(B)andthesolubilityofwaterinthesolvent(κd)are415themostimportantproperties.Withthecurrentsolventsolubilitydata,onewouldneedtoreducethesolventlossatleastten-foldforILstobeLCOW-competitive,evenwithasolventcostreductionof99%. 33 Figure8:ThecoloredcontoursshowLCOWcalculatedusing$1,000/kgcostof[emim][Tf2N]asafunctionofthermoresponsivness(A,verticalaxis)andthesolubilityofwaterat40◦C(B,horizontalaxis).Bothaxesarescaledsuchthat1.0,whichismarkedwitha󰂏,correspondsto[emim][Tf2N].ThreescenariosforthesolubilityofILinwaterκdareconsidered:(top)baseline,(middle)10-folddecrease,and(bottom)100-folddecrease.34 Figure9:ColoredcontoursshowLCOWcalculatedusing$100/kgof[emim][Tf2N].(Top)Assumingκd=130ppm,thesolventlossseverelyraisesLCOW.(Bottom)Assumingaten-folddecreaseinκd,onlya1.25-foldincreaseinAora1.5-foldincreaseinBisneededtoachieveaLCOWlessthan$0.50/m3.Newunpublisheddatasuggesttheselowsolubilityscenarioisreasonableforasaltybrine.(Bottom)A100-folddecreaseinκdalonegivesaLCOWof$0.49/m3underthislowILcostscenario.35 Figure10:SensitivyofLCOWwithacostof$10/kgof[emim][Tf2N].(Top)Withcurrentsolubility,thethermoresponsivnessorthesolubilityofwaterwouldneedtoimprovetoachievetherequiredLCOW.(Bottom)Witha10foldreductionofthesolubilityofthesolventinwaterwecanachieveaLCOWof$0.50/m3offreshwater.36 7.ConclusionsandFutureWorkDirectionalsolventextractionisamembrane-freedesalinationtechnology420thatcantreathighsalinitywaterresourcesusinglow-gradeheat.DSEcanbepairedwithothertechnologies,e.g.,renewablesolarthermalcollectors,tocreatehybridsustainablesystems.Inthiswork,wecreatedacomputationalframeworkthatfacilitatestheoptimizationoftheprocessandrapidsensitivityanalysis.Throughtheseanalyses,wefoundthathighermaximumtemperatures425enablehigherperpassextraction,whichallowsforalowerrecycleﬂowrateandlowerenergyintensity.Forsolventselection,wefoundthatthelengthofthecarbonchainhasnoapparentinﬂuenceandthatthemostcriticalfactorsarethechangeinwatersolubilityforalow-temperatureswing(40◦C-80◦C),themeltingtemperatureofthefattyacid,whichlimitstheminimumoperating430temperatureandthesolubilityofDSinfreshwater.Technoeconomicoptimiza-tionwasperformedforﬁvecandidatefattydirectionalsolventsranging,givingLCOWpredictionsbetween$1.3/m3and$109/m3.Sensitivityanalysisshowssigniﬁcantimprovementsinthreesolubilitypropertiesareneededforthehypo-theticalfattyacid-likeDStoachievelessthan$0.5/m3.Incontrast,ILsshow435muchgreaterpromiseasdirectionalsolvents.Usingnewlypublisheddatafrom[emim][Tf2N]andassumingamoderatesolventpriceof$100/kg,wepredictamodest$2.65/m3LCOW.SensitivityanalysisshowstherequiredcombinationofthermophysicalpropertiesnecessarytoachieveLCOWtobelow$0.5/m3.TheseresultsemphasizethepotentialofILdirectionalsolvents.440Asfuturework,weplantoexploreprocessintensiﬁcationopportunities(stageconﬁguration,nanoﬁltrationforsolventloss,electrocoalescer)andcon-sidermoredetailedequipmentmodels(nanoﬁltrationtorecoverysolvent,elec-trocoalescertoreplacesettlingtanks).Computer-aidedmoleculardesign(CAMD)approaches[52,53,54]oﬀerpromisetosystematicallysearchthebillionsofpos-445sibleionicliquids.Weultimatelyseecomputationalmolecularandprocessscalemodelinggreatlyacceleratedthesearchforeconomicallyviabledirectionalsol-vents.WealsoplantoexploretheopportunitiesandcostsofcouplingDSEwith37 inexpensivesolarheatingforsustainableanddistributeddesalination.Nomenclature450SetsandElementsCComponentsd∈CDirectionalsolvents∈CSaltw∈CWaterGFunctionalGroupsCH2∈GCH2functionalgroupCH3∈GCH3functionalgroupCOOH∈GCarboxylicacidfunctionalgroupH2O∈GWaterNFattyAcidDirectionalSolvents6∈NHexanoicacid7∈NHeptanoicacid8∈NOctanoicacid9∈NNonanoicacid10∈NDecanoicacidSStreamsinProcessSeeFigure1forstreamnumbersI⊂SInletstreams(foraspeciﬁcunitoperation)O⊂SOutletstreams(foraspeciﬁcunitoperation)P⊂SPinchcandidatesSC⊂PColdstreamsSH⊂PHotstreams 38 Indicesi∈CComponentk∈GFunctionalgroupin∈IEquipmentinletstreamNc∈NNumberofcarbonatomsinfattyacidDSo1∈OSolventphase(tankeﬄuent)o2∈OAqueous/saltyphase(tankeﬄuent)out∈OEquipmentoutletstreamVariablesASolubilityofthesolventinwateratareferencetemperatureBThermoresponsivenessofthesolubilityofthesolventCpHeatcapacity(J/mol-K)FMolarﬂow(kmol/s)Qheatdutyintheheatexchanger(kWh)QApCheatcontentbellowpinchtemperature(kWh)QApHheatcontentabovepinchtemperature(kWh)QSHeatfromhotutility(kWh)QWHeatfromcoldutility(kWh)TTemperature(K)TpPinchcandidatetemperature(K)xMolarfraction(mol/mol)ParametersκdFixedsolubilityofdirectionalsolventintheaqueousphase(tankeﬄuent)(mol/mol)κsFixedsolubilityofsaltinthesolventphase(tankeﬄuent)(mol/mol)∆TminHeatrecoveryapproachtemperature(K)TmaxMaximumallowabletemperatureoftheprocess(◦C)TminMinimumallowabletemperatureoftheprocess(◦C)NCNumberofcarbonatomsNkNumberoffunctionalgroups39 AbbreviationsADEAnnualDepreciationExpenseCotACostofAssetsDSDirectionalSolventDSEDirectionalSolventExtractionILIonicLiquidLCOWLevelizedCostofWaterMEDMulti-EﬀectDistillationMSFMulti-StageFlashMVCMechanicalVaporCompressionROReverseOsmosisOAROOsmoticallyAssistedReverseOsmosisSVSalvageValueTDSTotalDissolvedSolidsULAUsefulLifeosAssets455