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ArticleSupercriticalCO2ExtractionofExtractedOilfromPistacialentiscusL.
:MathematicalModeling,EconomicEvaluationandScale-UpAbdelkarimAydi1,*,AndréWüstZibetti2,AbdulaalZ.
Al-Khazaal3,AboulbabaELADEB1,3,ManefADBERRABA1andDanielleBARTH41LaboratoryMaterials,MoleculesandApplications,PreparatoryInstituteforScienticandTechnicalStudies,2070Marsa,Tunisia;eladebboulbaba@gmail.
com(A.
E.
);manef.
abderrabba@ipest.
RNU.
tn(M.
A.
)2LaboratoriodeControledeProcessos,DepartmentsofChemicalEngineeringandFoodEngineering,UniversidadeFederaldeSantaCatarina(UFSC),P.
O.
Box476,Florianópolis88010-970,Brazil;azibetti@gmail.
com3DepartmentofChemicalandMaterialsEngineering,FacultyofEngineering,NorthernBorderUniversity,ArarP.
O.
Box1321,SaudiArabia;abdulaal.
alkhazaal@gmail.
com4LaboratoireRéactionsetGéniedesProcédés,UniversitédeLorraine,CNRS,LRGPF-5400Nancy,France;danielle.
barth@univ-lorraine.
fr*Correspondence:aydiabdelkarim@gmail.
com;Tel.
:+49-152-377-50478Received:3December2019;Accepted:20December2019;Published:3January2020Abstract:Inthisstudy,theextractedoilofPistacialentiscusL.
theTunisregionwasextractedusingsupercriticalcarbondioxide(SC-CO2)extractioncontainingdierentmajorcomponentsintheoilsuchasα-pinene(32%)andterpinene-4-ol(13%).
Theinvestigationoftheeectofdierentvariablesontheextractionyieldwith5%levelofcondenceintervalshowedthattheCO2pressurewasthemainsignicantvariabletoinuencetheoilyield.
Inordertobetterunderstandthephenomena,threeparameterswereconsideredtoadjustallparametersofbrokenandintactcell(BIC)model:grindingeciency(G),theinternalmasstransferparameter(kSa0),andtheexternalmasstransferparameter(kfa0),whichwereestimatedbyexperimentalextractioncurvestocalculatethediusioncoecient.
Fromaneconomicpointofview,wefoundoutthatthehighcostofproductionoftheextractedoilwasduetothelowmassofextractedoilobtainedfromthistypeofplant.
Keywords:supercriticalcarbondioxide(SC-CO2)extraction;PistacialentiscusL.
;responsesurfacemethodology;diusioncoecient;masstransferparameter;economicstudy1.
IntroductionPlantspecieswithmedicinalpropertiesarebecomingcruciallyessentialinresearchduetotheirutilitiesinmanyareassuchastraditionalmedicine,food,cosmeticsandpharmaceuticals[1].
InTunisia,aspeciesofplantcalledPistacialentiscusL.
,commonlyknownas"Dharw"intheMaghreband"Elustaka"intheMiddleEast,hasmedicinalpropertiesinitsoilextract.
Theextractedoilhasnumerousmedicianalproperties,forinstanceanti-atherogenic[2],anti-inammatory[3–5],anti-oxidant[6–10],antimicrobial[9,11–13],hypotensive[14,15],anticancer[5,16],anti-arthritis[17],woundtreatment,andanti-asthmaticandanthelminticactivities[18–20].
Theessentialoilcanbeextractedfromspecicplantsbyseveralextractiontechniques:hydro-distillation[21],Soxhletextraction[22]andsupercriticalcarbondioxide(SC-CO2)extraction[23–25].
Themajorobjectiveoftheextractionprocessistoprovideamoreconcentratedformofthedesiredmaterial.
Althoughthecostnevercompromisesthequality,itcanbeadecisivefactorinchoosinganadequateprocess.
However,theextractioneectivenessandthesafetyprocessmustbepriorities.
Molecules2020,25,199;doi:10.
3390/molecules25010199www.
mdpi.
com/journal/moleculesMolecules2020,25,1992of19Infact,asthelimitsofsolventresiduesareincreasinglysubjectedtoreview,thesupercriticalsolventusedtoextracttheoilinsupercriticaluidextraction(SFE)canreplacetoxicsolvents.
Toobtainthedesiredproductwhichmeetstheneedsofconsumers,thiscanbeakeyelementindeningtheextractquality.
ModelingofSC-CO2extractionfromnaturalmatterisaveryimportanttoolanditrepresentsachallengeintheresearcheld.
Manymodelshavebeendevelopedandarecurrentlyusedinsupercriticaluidextraction[26–30].
ThemostwidelyusedmodelwasdevelopedbySovová[28,29].
Thismodelisknownasthebrokenandintactcell(BIC)model.
Itassumesdiusiveandconvectivetransportphenomenaduringtheextractionthatoccursinthreeperiods.
Also,hedevelopedananalyticalsolutiontoestimatetheextractionparametersbycomparingtheresultsoftheextractioncurvescalculatedbythemodelwiththeexperimentaldata.
Stástovaetal.
[30]simpliedthemodeldevelopedbySovová[29]todescribethebuckthornextractioncurvestoevaluategrindingeciency,masstransfercoecients,andowasymmetry.
Tothebestofourknowledge,thebulkofthepriorresearchinvolvingtheextractionofessentialoilsofPistacialentiscusarefocusedonhydro-distillationextraction.
FewstudieshavereportedthesupercriticalextractionprocessfortheplantofPistacialentiscus(PL).
Congiuetal.
[31]isolatedtheessentialoilfromtheleavesandtheberriesofPistacialentiscuscollectedintheregionofSardinia(CostaReyandCapoterra)usingasupercriticalCO2extractiontechniquecoupledwiththefractionalseparationtechnique(SFE).
Thus,theauthorsseparatedtheessentialoilfromcuticularwaxes.
Theobtainedyieldsoftheextractedoilfromtheleavesandtheberrieswere0.
45%and0.
20%,respectively,withthepresenceofmajorcompoundssuchasβ-caryophyllene,germacrene,β-myrcene,andα-pinene.
Itiswell-knownthatthequantityoftheextractyieldfromsupercriticalCO2extractionisaectedbyseveraloperatingparameterssuchastheCO2pressure,CO2massowrate,timeofextraction,andaverageparticlesize.
Inordertooptimizetheextractyieldoftheoilproducedfromtheleaves,anecientwaymightbetosystematicallycreatemodelsaroundthekeyingredientlevelsoftheproductviasometypeofresponsesurfaceexperimentaldesign[32].
Responsesurfacemethodology(RSM)isacollectionofmathematicalandstatisticaltechniquesthatmakeafulldescriptionoftheeectofindependentvariablesneartheoptimumconditions[21,33,34].
SeveralclassesoftreatmentstructurescanbeusedasRSMexperiments[35].
Themainobjectiveofourstudyistousetheresponsesurfacemethodology(RSM)tostudytheeectofthreeoperatingconditions(pressure,averageparticlesize,andCO2owrate)andtheirinteractionontheextractyield.
WealsoaimtostudytheinuenceofoperatingparametersonmasstransferbyevaluatingaprocessapplyingtheBICmodelproposedbySovová[29]in1994whichwassimpliedlaterbyStástovaetal.
[30]ontheessentialoilextractioncurvesthatareacquiredfromPistacialentiscusleavesgrowinginthenorthernpartsofTunisia.
Intheend,weobtainedaneconomicevaluationinthescale-upprocessfortheCO2extractoftheseplantleaves.
2.
MaterialsandMethods2.
1.
MaterialsThePistacialentiscus(PL)plantleaveswereobtainedfromalocalmarketinTunis(Tunisia).
Theleaveswereair-driedunderacontrolledtemperatureof37Cfor48h,thenstoredinvacuum-sealedplasticbagsunderrefrigerationpriortoextraction.
Immediatelypriortosupercriticaluidextraction,onlytheleavesofthesampleswereused,andtheywereroundedinablendertogetparticlepowderwithdiameters220mand650m.
Thechemicalsusedwereabsoluteethanol(CarloErba,ValdeReuil,France),ultrapurewaterandcarbondioxide(MesserGroup,Nancy,France,99.
95%).
2.
2.
TheProcedureofSupercriticalFluidExtractionThemainpurposeofusingsupercriticaluidextraction(SFE)wastoobtaintheextractedoils.
TheSFEapparatusisshowninFigure1.
Molecules2020,25,1993of19Figure1.
Fluidextractionandfractionationunitschematicdrawing.
E:Extractor;S1,S2,S3:Separators[34].
Theextractwascollectedasafunctionoftimeduringtheprocessthroughvalveslocatedatthebaseoftheseparators.
Thesampleswereweighedafter30minofcollectiontoavoidmeasuringCO2remaininginthebottle.
Thetemperatureofextractionwasmaintainedconstantinalltheexperiments(40C)topreventtheheatdegradationofthermolabilecomponentsintheextractedoil.
Table1showstheexperimentalconditionsoftheSFEunitwherePisCO2pressure,QCO2isCO2owrate,dPistheaverageparticlesizeoftheleave,ρCO2isCO2density,andCO2isCO2velocity.
ObservingTable1,wenotedthattheconditionsofextractionusedduringtheseexperimentsshowthattheCO2owwasmanuallycontrolled,andtheestimatedvarianceoftheexperimentsisbetween2.
5%to5%oftheaverageow.
Table1.
Conditionsofsupercriticaluidextraction.
ExperimentsP[bar]dP[m]QCO2[kgh1]*ρCO2[kgm3]CO2·105[kgms1]12206500.
604857.
208.
1822202200.
602857.
208.
183806501.
202277.
902.
234806501.
209277.
902.
235802200.
602277.
902.
236806500.
603277.
902.
2371406501.
204763.
276.
5181802200.
913819.
517.
4591802200.
904819.
517.
45101806500.
908819.
517.
45*Deviation±0.
03kgh1ofCO2.
Referringtoapreviouspublication[29]andinordertoensurethesolubilityofmajorcompounds[36–39],thecollectionofextractedoilsandwaxeswasconductedusingseparators.
Therstseparatorwasmaintainedatalowtemperature(5C)withthesameextractionpressureastheexperimenttoprecipitatewaxeswhilethesecondseparatorwasmaintainedat30Cand40barforoilextractcollection.
ThebulkdensityofmilledPistacialeaveswasabout291kgm3,andthevoidfractionofthebedwasequalto0.
53.
Glassbeadswereplacedonthebottomoftheextractor,thepowderofPistacialeaves(23±0.
05g)wasplacedabovethemandanotherlayerofglassbeadwasputonthetop.
Inaddition,twolters(frits<15m)wereusedinboththeinletandtheoutletoftheextractingvessel.
2.
3.
AnalysisGasChromatography-FlameIonizationDetector/MassSpectrometry(GC-FID/MS)GC-FIDanalysiswascarriedoutwithaShimadzuGC2010Plus(Nancy,France),equippedwithanHP-5capillarycolumn(Shimadzu,Nancy,France,withdimension:30m*0.
25mm,lmthicknessMolecules2020,25,1994of190.
25m).
Theinjectorandthedetectorweresetat250and300C.
Thetemperaturecolumnwasprogrammedat50Cfor1minthengraduallyincreasedto270Cat3C/min.
Next,itwasheldfor5minthenincreasedto300Cat20C/minandsubsequentlyheldfor5min.
Thesplitratiowas5:1whereasthesplitowwasequalto10mL/min.
Nitrogenwasusedasacarriergaswithaconstantpressureof100kPa.
TheGCwasalsoequippedwithanAuto-Injector(Shimadzu,Nancy,France,AOC-20i)andtheinjectedvolumewasequalto1L.
ForGC-FID-MSanalysis,aShimadzuGCMS-GC2010-QP2010PlusequippedwithaDB5-MScapillarycolumn(Shimadzu,Nancy,France,withdimension:30m*0.
25mm,lmthickness0.
25m)wasexploited.
Theinjectorandthedetectorweresetat250C.
Theoventemperaturewasprogrammedat50Cfor1min,graduallyincreasedto250Cat5C/min.
Itwasheldfor10minthenincreasedlaterto270Cat5C/minthenheldfor5min.
Afterthat,itwasincreasedto280Cat5C/minandheldfor10moreminutes.
Althoughthesplitratiowas10:1,thesplitowwasequalto10mL/min.
Inthisprocess,heliumwasusedasacarriergaswithaconstantspeedof1.
69mL/min.
TheGCwasalsoequippedwithanAuto-Injector(Shimadzu,Nancy,France,AOC-5000)andtheinjectedvolumewasequalto1L.
Massunitsweremonitoredfrom35to400m/zat70eV.
ThemassspectraofthecomponentswereidentiedusingdatafromtheNISTLibrary(NIST08s).
2.
4.
ResponseSurfaceMethodology(RSM)ResponsesurfacemethodologywasusedtostudytheinfluenceofsupercriticaloperatingextractionparameterssuchasCO2pressure(P),CO2flowrate(QCO2),andaverageparticlesizeoftheleaf(dP),ontheextractoilyield.
Thesethreeresponsevariableswerecodedasx1,x2,andx3,respectively.
TherangeandlevelsofindependentfactorswerechosenbasedupontheresultsofpreliminarytestsandaregatheredinTable2.
Theindividualandinteractiveeffectsoftheseparametersonthedependentvariablewerestudied.
Equation(1)representsthelinearmodelwithinteractionsforthethreeoperatingconditions,YD=a0+a1x1+a2x2+a3x3+a12x1x2+a13x1x3+a23x2x3(1)whereYDrepresentsadependentvariable(theyieldofextractoil),a0isaconstant,a1,a2,anda3areindividuallinearcoecient,a12,a13,anda23aretheinteractivelinearcoecient,andx1,x2,andx3arethecodedvaluesofindependentfactors(pressure,CO2owrate,andaverageparticlesizerespectively).
Table2.
Conditionsofsupercriticaluidextraction.
VariableSymbolFactorLevel11Pressure(bar)x180220CO2owrate(kg/h)x20.
61.
2Averageparticlesize(m)x3220650Nemrod-wsoftwarepackagewasusedfortheregressionanalysisoftheexperimentaldataobtained[33].
FitqualityofthemathematicalmodelequationwasexpressedbythedeterminationcoecientR2,anditsstatisticalsignicancewascheckedbyanF-test.
Thesignicanceoftheregressioncoecientwastestedbyat-test.
Signicancelevelwasgivenas***p<0.
001,**p<0.
01,*p<0.
05.
Dierenceswithp-valuesuperiorto0.
05werenotconsideredsignicant.
Forourexperimentaldesignvalidation,optimumconditionswerexedbasedonthedataobtainedfromtheexperimentaldesign.
2.
5.
ModelingoftheSupercriticalExtractionProcessStastováetetal.
[30]madeseveralsimplicationsonSovová'smodel[29]byintroducingtwoparameters:thegrindingeciency(G)andthedimensionlesstime(ψ),Molecules2020,25,1995of19ψ=tQysNx0(2)wheretistheextractiontime,Qrepresentsthesolventmassowrate,ysistheoilsolubilityinthesolvent,Nistheinitialmassofthesolid,andx0istheinitialoilconcentrationinthesolid.
Themassofextractedoil(E)canbecalculatedbythefollowingEquation(3)–(7):EN.
x0=ψ[1exp(Z)]forψhk=1Yln1+expYψGZ1G(5)ThedimensionlessquantitiesZandYareproportionaltothemasstransfercoecientsaccordingtotherstandsecondextractionperiod,Z=Nkfa0ρfQ(1ε)ρs(6)Y=Nksa0x0Q(1ε)ys(7)wherekfandksaretheexternalandtheinternalmasstransfercoecientsrespectively,a0istheparticlespecicinterfacialarea,ρfstandsforthesolventdensity,ρsrepresentsthesoliddensity,andεisthebedvoidvolume.
ThemodelwasimplementedinMATLABTM.
Threeadjustableparameterswereconsidered:thegrindingeciency(G),theinternalmasstransferparameter(ksa0),andtheexternalmasstransferparameter(kfa0).
Equilibriumtype"A"modelwasconsideredaccordingtoSovová[28].
Sincetheexternalmasstransferparameter(kfa0)hadnosensitivity[40,41],Fiorietal.
[39]suggestedanapproachtodeterminethisparameterreferringtotheliteraturecorrelations—Sherwood(Sh),Reynolds(Re)andSchmidt(Sc)numbersofexperimentalruns.
CO2physicalpropertieswereevaluatedaccordingtoNISTdatabase[42]andtheoilextractpropertieswereassumedtoberelatedtothemajorcompoundfoundinGC-FID/MSanalysis,α-pinene[43,44].
Binarydiusioncoecient(DAB)betweentheCO2andthemajorcompoundwasobtainedbycorrelations.
Inthecaseofthesupercriticaluidextraction,Sherwoodnumber(Equation(8))isafunctionofonlyReynoldsandSchmidtwhennaturalconvectionisnotsignicant[45–47],Sh=c0Rec1Scc2(8)where,c0,c1andc2aretheadjustableparameters.
Accordingtothemost-proposedcorrelationsintheliterature[45–47],c0shouldbehigherthan1,c1isconstrainedbetween0.
5and0.
8,andc2=1/3.
Catchpoleetal.
[48]andLitoetal.
[49]usedtheapproachtoestimateonlytwoadjustableparameters(G,andksa0)directlyusingtheexperimentalkineticcurve,andtheycalculatedtheotherparameter(kfa0)usingtheSherwoodcorrelationbecausetheyconsideredthatitwasnotsignicant.
However,inourapproach,weestimatednotonlythesetwoparameters(Gandksa0),butalsotheexternalmasstransferparameter(kfa0)usingtheexperimentalcurveformoreaccuracy.
Molecules2020,25,1996of19Therelevanceofthemodelttingtotheexperimentaldatawasassessedconsideringtwostatisticalcriteria,namelythecoecientofdeterminationR2detrminedusingEquation(9)andtherootmeanssquareerror(RMSE)givenbyEquation(10),R2=1niy(i)expy(i)model2niy(i)expyexp2(9)RMSE=niy(i)expy(i)model2n(10)wherenrepresentsthenumberofavailableexperimentaldata,andyexpandymodelaretheexperimentalextractionyieldandtheextractionyieldpredictedbythemodel,respectively.
2.
6.
CostEstimationofProcessesandScale-UpThemanufacturingcostofthesupercriticalextractwasestimatedthroughmethodologyproposedelsewhere[50,51].
Concerningmaterialcost,electricityandlabor,theywerecollectedfromregionalinformationinTunis(Tunisia2016).
ThefixedinvestmentcostwasobtainedfromtheliteratureproposedbyTurtonetal.
[52]toevaluatethecostofmanufacturingaccordingtoEquation(11)includingdepreciation(10%ofFCI).
COM=0.
340FCI+2.
73COL+1.
23(CUT+CWT+CRM)(11)whereCOMisthecostofmanufacturingofsupercriticalextractofPistacia,FCIcorrespondstothexedcostofinvestment,COLrepresentsthecostofoperationallabor,CUTisthecostofutilities,CWTthecostofwastetreatment,andCRMisthecostofrawmaterial.
AccordingtoCarvalho[53],Equation(12)canbeusedinordertodeterminethesolventowraterequiredtomaintainthesamekineticbehaviorindierentSFEunits(scale-up)foragivenfeedmassandbadgeometry.
Researchers[54–57]declaredthattheextractiontimehasaninuenceonanextraction'sCOMandtheextractionrateincreasesbyincreasingthesolventowrate.
Theyalsoreportedthatoilyieldintheextractioncanbepositivelyinuencedbythesolventowrateincreasesasthefollowingequation:Q2CO2Q1CO2=F2F12HB1HB2dB1dB2(12)TheextractorgeometrydataandtheinstalledsupercriticalextractioncostwereobtainedfromNúezanddelValle[58–60].
Infact,aplantwithtwoextractionvessels,eachonehavinginternalvolumevaryingbetween0.
2,0.
4,0.
6and1.
0m3,wasevaluated.
Forinstance,foraplantwithvesselsof1.
0m3,theaspectratiowasH/d=8(with0.
542m*4.
334mofinnerdiameterandheightrespectively).
Thewallthicknesswithstands390bar.
Thexedcostofinvestment(FCI)ofeachSFEunitwasdeterminedinUSDbasedonthevaluesofRocha-Uribeetal.
[59].
AllthevaluesarereportedinTable3andarecalculatedusingtheChemicalEngineeringPlantCostIndex(CPECI)valuefor2014(CPECI2014=580)[61].
AccordingtoExperiment(2),therelationsoflaboratory-scaleH/dis3.
6,withtheowratefrom3.
36*105kg/s,thebedapparentdensityρ=296kg/m3,withtheoperationalconditionsof220barand40Cfortheextractionprocessweretakenintoconsideration.
Figure2showsthecycleofsolvent(pureCO2)duringthesupercriticalextractionprocessinanoperatingunit.
Thestepsareconsideredasbeingprimarilysolventcollectioninreservoir(64barand25C),followedbyacoolingprocess(10C),pumpingandpressurizationoftheextractionvessel(220barand35C),followedbytemperatureincrease(40C)untilobtainingthedesiredextractionconditionandfinally,afterthisprocess,reducingthepressure(60barand60C)forsoluteprecipitationforreuse.
Molecules2020,25,1997of19Table3.
Estimatedcostofeachsupercriticaluidextraction(SFE)unit,includingallequipment(ChemicalEngineeringPlantCostIndex,CPECI,2014=580).
ExtractorVessel(liters)H(m)d(m)H/dFixedCost(FCI)(US$)1002.
010.
2528.
0$853,9752002.
540.
3178.
0$1,378,5504003.
190.
3998.
0$2,225,4006003.
660.
4578.
0$2,944,90010004.
340.
5428.
0$4,191,250Figure2.
Entropy(s)diagramofCO2cycleduringsupercriticaluidextraction.
Circlednumber1representssaturatedliquidat25Cand64bar;2ispumpinlet(10Cand64bar);3ispumpexit(35Cand220bar);4isextractionvessels(40Cand220bar);5isseparationvessel(60Cand60bar).
Inthiscase,itisassumedthatduringtheprocessofdecompression,thesoluteisseparated,andthepuresolventisreturnedtothesystem.
Basedonthendingsofthisandthemutualvaluesfoundinotherresearchpapers,itisidentiedthatextractionyields(massextract/Pistaciaload)wereestimatedtoreach0.
3%,0.
5%,0.
7%,1.
0%and1.
5%.
Thecostof8000hperyearoperationalwork,withcontinuous24hperday,8hdailyshifts(2workers/shift)wasconsidered.
Thecostoflaborwasoperationallyconsideredtobe6.
60USD/h(1475.
60USD/monthtaxincluded).
TheutilitycostwasestimatedrelyingonenergyconsumptioninvolvedinthesolventcycleCO2,coldwater,andelectricity[51,58].
ThespecicenergiesofCO2forcooling,heating,andpumpinginthesolventcyclewereequalto261.
29kJ/kg,219.
2kJ/kgand55.
0196kJ/kg,respectively.
ThesecalculationswerebasedupontheworkofRock-Uribeetal.
[59].
Theelectricitycostwasequalto217.
10USD/MWh(pricechargedinTunis,Tunisia,taxincluded).
Concerningrawmaterialcosts,theconsideredvalueswere:1.
35USD/kgofdriedandmilledPistacialeaves,0.
15USD/kgofCO2and0.
97USD/kgofethanolforcleaningpurposes[60].
Itwasconsideredthat2%ofCO2masswaslostduringtheextractioncycleforalltheSFEprocessscaleevaluatedinthiswork.
ThecostofwastetreatmentwasnotconsideredbecauseCO2wasfullyrecycledandPistacialeafcanbeusedinsoilenrichmentorenergygeneration.
3.
ResultsandDiscussionTable4showstheexperimentalyieldresultsandoperatingconditionsofsupercriticalextractionforthetenexperiments.
TheexperimentaloilextractyieldwascalculatedusingthefollowingEquation(13):Molecules2020,25,1998of19Yield(wt%)=MassofleafextractMassofrawmaterial*100(13)Table4.
Theyieldofsupercriticalextraction,withthreedierentvariables(P,dpandQCO2).
Experimentx1P[bar]x2dP.
[m]x3QCO2[kgh1]Yield[%]12206500.
6040.
23422202200.
6020.
2853806501.
2020.
0934806501.
2090.
1195802200.
6020.
1236806500.
6030.
11771406501.
2040.
22181802200.
9130.
22091802200.
9040.
229101806500.
9080.
174Theyieldobservedforthetestedconditionsvariedbetween0.
093%and0.
285%.
WefoundthatExperiment(2)withthehighestpressure,lowestowrate,andthelowestaverageparticlediametergavethegreatesttestedincomeextractionconditions.
Thereplicationsperformedat80bars(0.
10%±0.
0184%),whichwereExperiment(3)and(4),demonstratedhighervariabilitythanthoseperformedat180bar(0.
022%±0.
0057%)(Experiments(8)and(9));therefore,theyhavecoecientsofvariationequalto17.
3%and2.
5%respectively.
Bycomparingallresults,weobservethatthepresentworkprovideddierentyieldsthatwereinsomecasesinferiortothosereportedbyotherauthors[31,60].
Infact,Bampoulietal.
[62]obtainedanoutcomefromtheleavesofPistacialentiscus(PL)var.
chia(fromChios,Greece)varyingbetween1.
6%and5%w/w.
Theconditionswererangingfrom100to250barand45Cwithaowrateof1.
5to3.
0kgCO2/h.
Also,Congiuetal.
[31]acquiredyieldsbetween0.
25%and0.
45%fortheleavesofPistacialentiscus(PL)comingfromtheregionsofCostaReyandCapoterra(Sardinia,Italy)providing90barand50Cwithaowrateof0.
9kgCO2/h.
Thevariationoftheobtainedyieldsmustbeduetotheareasofcultivationprocessing,treatmentofrawmaterialsandexperimentalconditionsintheextractionprocess.
AppendixAshowsthecharacterizationsoftheessentialoilobtainedfromtheleavesandcarriedoutusingGC-MS-FID.
WeobservedthatthemajorcompoundsfortheextractionofPistacialentiscusintheTunisregionareα-pinene(32%),followedbyterpinene-4-ol(13%),1-8-cineole(6%),α-terpineol(4%),β-caryophyllene(4%)andborneol(4%),assummarizedinTable5.
Furthermore,asexpected,thesecompositionsarenotsignicantlyinuencedbychangingtheoperatingconditionsduetotheconstantextractiontemperature.
Table5.
AreasofcompoundsfoundintheoilsobtainedbySFEfromleaves.
CompoundsRIExp.
1Exp.
2Exp.
3Exp.
4Exp.
5Exp.
6Exp.
7Exp.
8Exp.
9Exp.
10α-pinene93933.
3030.
0034.
2130.
1033.
2132.
1034.
3131.
1032.
4132.
1Terpinene-4-ol117813.
0413.
2413.
0813.
6813.
0212.
0112.
7712.
0613.
1212.
161-8-cineole10335.
106.
106.
026.
625.
856.
425.
666.
115.
067.
11α-terpineol11894.
614.
014.
584.
884.
124.
214.
064.
674.
684.
55β-caryophyllene14344.
024.
924.
224.
824.
884.
034.
124.
434.
014.
93Borneol11653.
923.
124.
624.
024.
224.
124.
454.
164.
854.
66Others36.
0138.
6131.
2735.
8834.
7037.
1134.
6337.
4735.
8734.
493.
1.
StudytheEectofOperatingConditionsontheYieldUsingRSMResponsesurfacemethodology(RSM)wasusedtostudytheindividualandtheinteractiveinuenceofoperatingextractionparametersontheextractyieldtondtheoptimaloperatingconditions.
Table6showstheexperimentaldesignyieldforthetenexperiments.
Molecules2020,25,1999of19Table6.
Designyield(YD)forsupercriticalextractionofPistacialentiscus.
Experimentx1x2x3YD(%)11.
00001.
00000.
99340.
2321.
00001.
00001.
00000.
2831.
00001.
00000.
97690.
0941.
00001.
00001.
00000.
1251.
00001.
00001.
00000.
1261.
00001.
00000.
99670.
1270.
14291.
00000.
98350.
2280.
42861.
00000.
02470.
2290.
42861.
00000.
00490.
23100.
42861.
00000.
00820.
17Weusedtheanalysisofvariance(ANOVA)toevaluatethestatisticalsignicanceofthelinearmodelrepresentedinEquation(1).
Themodelcandescribethevariationoftheresultsbecauseitissignicantat<5%.
We,also,veriedthemodeleciencyandtheadaptabilitytotheexperimentaldatabyestimatingthecoecientofactualandpredicteddetermination(R2andpredictedR2respectively)calculatedbytheanalysisofvariance.
Wefoundoutthattheactualdeterminationcoecientindicatesthatthettedmodelexplains91.
2%ofthevariabilityintheextractionyield.
ThepredictedR2was0.
998(agoodagreement)indicatingthatourexperimentaldesigncanbeusedformodelingtheresponsevariablesemployed,asshowninFigure3.
Figure3.
Experimentaldesignyield(YD)versusexperimentalyield(Y).
Table7gathersthestatisticalresultsoftheconstantparametersinEquation(1):thelinearinterceptconstant(a0),theindividuallineareectsofthethreeindependentvariables(a1,a2,anda3),andtheirinteractivelineareects(a12,a13,anda23).
Therefore,thelinearregressionequationusedtoevaluatetheexperimentalyieldbecomes(YD),YD=0.
183+0.
084x1(14)ThisequationindicatesthatthemainfactorthatsignicantlyinuencestheyieldwastheCO2pressurewhenthecondenceof5%wasconsidered.
Theequationidentiesthebestconditionsthroughvariationofchosenparameterstomaximizetheextractioneciency,whichispresentedinExperiment(2).
Forabetterunderstandingofthestatisticalresults,Figure4representsthe2Dresponsesurfaceoftheexperimentalyieldsbythefunctionofpressure,averageparticlesizeandtheowrateofCO2.
AscanbeobservedinFigure4,thehighestyieldwasobtainedaroundthemaximumpointofpressure(P=220bar)whentheowrateofCO2andaverageparticlesizewerearoundminimumpoints.
Molecules2020,25,19910of19Table7.
Coecientofalinearregressionequation(Equation(1)).
CoecientCoecientValueTestExperimentp-ValuealongwithCondence%a00.
18312.
43***a10.
0843.
71*a20.
0000.
0199.
1%a30.
0020.
1092.
2%a120.
0130.
8048.
5%a130.
0170.
7153.
3%a230.
0190.
8645.
3%*p<0.
05;***p<0.
001.
Figure4.
Surfaceplotsoftheexperimentaldesignyieldasafunctionof(a)CO2pressureandaverageparticlesize(b)CO2pressureandCO2owrate.
3.
2.
AnalysisandValidationofExperimentalDesignThestatisticalanalysisforthenalselectedmodelshowsthattheeectoftheCO2pressureistheonlyvariablethathasasignicanteectontheyield,comparedtotheothervariablesthathavenoeects.
Forthisreason,weanalyzedtheselectioneectoftheidenticationandvalidationpointsusedforourexperimentaldesign.
Theexistenceofacorrelationbetweentheparametersincreasesthesizeofthecondenceintervals[63],thereforeweneedtocontrolthevalueofthecorrelationcoecients2to2.
Inourinvestigation,wehaveusedtheD-optimalitycriterion[64]toseparatetheexperimentsusedforbothparametricidenticationandvalidationmodel.
ThismethodconsistsofchoosingasetofparametricidenticationpointstoobtainthehighestdeterminantoftheFischermatrixinformation[65].
Toinvestigatetheinuenceofselectiononthecondenceintervalsofeachparameter,westudiedthecorrelationsbetweentheparametersusingthefollowingmatrixcorrelationcoecientssummarizedinTable8.
Table8.
Matrixcorrelationcoecients.
Parametersa1a2a3a12a13a23a11.
00000.
30390.
32910.
26080.
36230.
2981a20.
30391.
00000.
39090.
04550.
23350.
2095a30.
32910.
39091.
00000.
37480.
37710.
4994a120.
26080.
04550.
37481.
00000.
25650.
2247a130.
36230.
23350.
37710.
25651.
00000.
2563a230.
29810.
20950.
49940.
22470.
25631.
0000Molecules2020,25,19911of19Figure5,whichrepresentsthefrequencyofthecorrelationcoecient,mimics87%ofthecorrelationbetweentheparameterspairsareintherangeof0.
2to0.
4.
ThisindicatestheuseoftheDetmaxFedrovalgorithm[66]thathasnoeectonthecorrelationbetweentheparameters.
Therefore,theusedsupportsofalinearmodelwithinteraction,andsubsequentlytheexperimentaldesign,areapplicableatleastinthisstudy.
Figure5.
Percentageofcorrelationcoecientsbetweenparamaters.
3.
3.
EectofOperatingConditionsontheMassTransferAllexperimentaldatawereusedtodeterminethemodelparameters(G,andksa0,andkfa0)(seeAppendixB).
Table9showsthatthetwoadjustedparameters(grindingefficiency(G)andinternalmasstransferparameter(ksa0),whichisestimatedbytheexperimentalkineticcurves,havenosignificantchangebetweenthetwoapproaches.
Asexpected[3,13,31],thevalueofgrindingefficiency(G)increasesbydecreasingtheaverageparticlesize.
Thisparameterisnotonlyrelatedtotheparticlesize,butalsototheshapeofitsdistribution(normal,bimodal).
Asaresult,itinfluencesthecurveshapeduetothesolventflowasymmetryeffect.
Table9.
Theadjustedparameters(Gandksa0)betweentwoapproaches.
Exp.
P[bar]dP[m]QCO2[kg.
h1]Gksa0.
105(s1)1stApp.
2ndApp.
1stApp.
2ndApp.
LitoCatchpoleAYDIA.
LitoCatchpoleAYDIA.
12206500.
6040.
360.
360.
377.
487.
487.
3522202200.
6020.
610.
610.
617.
017.
017.
013806501.
2020.
390.
390.
400.
1820.
1820.
1824806501.
2090.
360.
360.
370.
1070.
1070.
1075802200.
6020.
520.
520.
529.
289.
289.
306806500.
6030.
440.
440.
457.
587.
587.
5871406501.
2040.
350.
350.
377.
837.
847.
7181802200.
9130.
620.
620.
662.
752.
752.
3191802200.
9040.
540.
540.
592.
322.
321.
91101806500.
9080.
230.
230.
230.
1080.
1080.
108Intherstapproach,weappliedthecorrelationsproposedbyLito,Catchpole,andKingusingonlythebinarydiusioncoecient(CO2-α-pinene)toestimatetheexternalmasstransferparameter(kfa0).
Ontheotherhand,theadjustedparameterswerenotonlygrindingeciency(G)andtheinternalmasstransferparameter(ksa0)butalsotheexternalmasstransferparameter,whichwasestimatedbyexperimentalextractioncurvesinthesecondapproach.
Molecules2020,25,19912of19Table10showstheparameters(kfa0,andDAB)forbothapproaches.
Theadjustedparameter(kfa0)estimatedbytheexperimentalkineticcurvesinthesecondapproachisdierentthanthecorrelatedparameterproposedbyLitoandCatchpoleintherstapproach.
ThisparameteraectsthevaluesofthediusioncoecientasshowninTable10.
Table10.
Parameters(kfa0,andDAB)betweentwoapproaches.
Exp.
P[bar]dP[m]QCO2[kg.
h1]kfa0.
103(s1)DAB.
109(m2s1)1stApp.
2ndApp.
1stApp.
2ndApp.
LitoCatchpoleAYDIA.
LitoCatchpoleAYDIA.
12206500.
6041.
411.
460.
7368.
639.
062.
9722202200.
6026.
566.
771.
728.
639.
061.
063806501.
2020.
1140.
1188.
7038.
040.
20.
734806501.
2090.
1140.
1198.
9538.
040.
20.
765802200.
6020.
3550.
3693.
4238.
040.
21.
046806500.
6037.
637.
934.
0338.
040.
213.
371406501.
2042.
672.
771.
2610.
711.
33.
1581802200.
9139.
199.
510.
7739.
49.
96.
6191802200.
9049.
149.
460.
9299.
49.
98.
79101806500.
9081.
972.
042.
649.
49.
913.
4Inthesecondapproach,theparametervaluesoftheSherwoodnumberwereexperimentallyobtainedfromtheextractioncurvesandkfvalues.
Theparametercorrelationsuggestedinthesecondapproachwasdeterminedfromc0andc1settings,resultingintheequationasshowninTable11.
Sh=0.
0349Re0.
58Sc1/3(15)Theadjustedparametersarewithintherangereportedby[19]andtheirapplicabilityforReynoldsandSchmidtvaluesareintheranges2≤Re≤60and2≤Sc≤12.
Table11.
Numberandthecoecientofdeterminationr2betweentwoapproaches.
Exp.
P[bar]dP[m]QCO2[kg.
h1]Shr21stApp.
2ndApp.
1stApp.
2ndApp.
LitoCatchpoleAYDIA.
LitoCatchpoleAYDIA.
12206500.
6040.
240.
240.
9698.
47898.
47798.
47222202200.
6020.
130.
134.
1699.
35299.
35299.
3553806501.
2020.
450.
440.
0699.
71699.
71699.
7184806501.
2090.
450.
440.
0599.
63299.
63299.
6265802200.
6020.
160.
161.
2499.
29799.
29799.
3576806500.
6030.
300.
300.
1398.
30298.
30198.
32271406501.
2040.
370.
370.
4098.
54898.
54198.
66381802200.
9130.
170.
165.
8498.
26898.
26899.
13791802200.
9040.
170.
165.
1198.
42198.
42199.
019101806500.
9080.
310.
310.
2999.
38199.
38199.
381Thevaluesofthemasstransfercoecients(kfa0)rangedfrom1.
4*102to3.
7*101fortheestimationperformedwiththecorrelationsofLitoandCatchpole.
ConcerningtheadjustmentmadewiththethreeparametersG,kfa0andksa0(thevalueofkfa0is0.
020),itrangedfrom7.
3*103s1to8.
9*102s1.
Thesevaluesarelowerthanthoseobtainedbyadjustmentwiththecorrelations.
Theparametersksa0wereinallcasesbetween1.
9*105s1and1.
8*104s1.
3.
4.
CostEstimationofProcessesandScale-UpThegreatestimpactonthecostofmanufacturingextractedoilproductionofP.
lentiscusinTunisiaisrepresentedbytherawmaterialcost(RMC),followedbythexedcostofinvestmentandtheutilitycost,asindicatedinFigure6.
Molecules2020,25,19913of19Figure6.
EachcostcategoryinthemanufacturingcostofPistacialentiscussupercriticalextract.
Table12showsthemanufacturingcostsofthesupercriticalextractofPistacialentiscusintheUS.
Wenotethatforthesameyield,thelowestcostswerethoseobtainedatthehighestproductionvolume,aswasexpected.
Table12.
ManufacturingcostofasupercriticalextractofPistacialentiscusleaves,inabatchof60min(220barand40C).
Volume(m3)COM(US$/kg)ExpectedOilYield(%)0.
30.
50.
71.
01.
50.
1999.
63599.
78428.
41299.
89199.
930.
2942.
63565.
58403.
99282.
79188.
530.
4952.
04571.
22408.
02285.
61190.
410.
6945.
12567.
07405.
05283.
53189.
021.
0813.
95488.
37348.
83244.
18162.
79Concerningyieldvaluesobtainedonapilotscale(0.
30%),thecostofthemanufacturingprocessofthesupercriticalextractweasbetween999.
63USD/kgand813.
95USD/kg.
Thesevaluesareconsideredveryhighwhencomparedtothecostsofothervegetablerawmaterialssuchasrosemaryextractwhichisworth49.
71USD/kg[21],gingeroleoresinwhichcosts99.
80USD/kg[20],CurcumalongaL.
extractwhichisworth164.
4USD/kg[40]andhabaneropepperextractwithacostof540.
19USD/kg[33].
Ayieldincreaseintheextractionprocessreducesthecostofmanufacturing.
Thus,thehighcostofproductionisduetothelowyieldsgainedfromthiskindofplant.
PricesoftradedextractedoilsofPistacialentiscussoldin5mL,10mLor30mLvialsareabout5.
83USD/g(5830.
00USD/kg).
ThesevaluesareobtainedfromthelocalmarketinTunis,Tunisia.
4.
ConclusionsPistacialentiscusL.
plantfromtheTunisianregionisappeasedofmedicinalpropertiesinitsextractoilthatcanbeproducedusingsupercriticalcarbondioxide(SC-CO2)extraction.
Inthisstudy,weobservedthattheα-pinene(32%)wasthemajorcompoundoftheextractedoilofPistacialentiscusintheTunisregion.
Theexperiment(2)havingthehighestpressure,lowestowrate,andthelowestaverageparticlediametergavethegreatesttestedincomeextractionconditions.
WeinvestigatedtheinuenceofCO2pressure,averageparticlesize,andCO2owrateandtheirinteractionontheextractyieldusingtheresponsesurfacemethodology(RSM).
ItwasobservedthatthemainfactorthatsignicantlyinuencestheyieldwastheCO2pressureand,therefore,thebestconditionsthroughvariationofchosenparameterstomaximizetheextractioneciencywerepresentedinExperiment(2).
Westudiedtheinuenceofoperatingparametersonmasstransferbyevaluatingaprocessapplyingbrokenandintactcell(BIC)ontheessentialoilextractioncurvesthatareacquiredfromtheMolecules2020,25,19914of19leavesofPistacialentiscusL.
Thetwoadjustedparameters(grindingeciency(G)andinternalmasstransferparameter(ksa0)),whichwereestimatedbytheexperimentalkineticcurves,havenosignicantchangebetweenthetwoapproaches(LitoandCatchpoleapproach,andAYDIAapproach).
However,theexternalmasstransferparameter(kfa0)proposedbyAYDIAwasdierentfromthecorrelatedparameterintherstapproachthatsignicantlyinuencesthevaluesofthediusioncoecient.
Theeconomicevaluationinthescale-upprocesswasobtainedfortheSC-CO2extractionoftheseplantleaves.
Weindicatedthatthelowestcostswereobtainedatthehighestproductionvolumeforthesameyield.
Themanufacturingcostofoilproductionisreducedbyayieldincreaseintheextractionprocessbecauseofthelowyieldsobtainedfromthistypeofplant.
AuthorContributions:A.
A.
,A.
Z.
A.
-K.
andA.
W.
Z.
conceivedanddesignedtheexperiments;A.
A.
andA.
W.
Z.
simulatedtheexperimentaldatausingBICmodelandcalculatedthemanufacturingcost;A.
A.
andA.
E.
Analysedandcommentedthemodelingpart;A.
A.
andA.
W.
Z.
preparedandanalyzedtheGC-MSanalysis;M.
A.
andD.
B.
supervisedallthework;A.
A.
,A.
W.
Z.
andA.
Z.
A.
-K.
wrotethearticle.
Allauthorshavereadandagreedtothepublishedversionofthemanuscript.
Funding:Thisresearchreceivednoexternalfunding.
Acknowledgments:TheauthorsaregratefulforthenancialsupportreceivedfromIPESTandLRGP.
ConictsofInterest:Theauthorsdeclarenoconictofinterest.
AppendixATableA1.
PercentagesareasofcompoundsfoundintheoilsobtainedbySFEfromleavesineachexperiment.
CompoundsRIExp.
1Exp.
2Exp.
3Exp.
4Exp.
5Exp.
6Exp.
7Exp.
8Exp.
9Exp.
10Tricyclene9241.
050.
90.
480.
580.
481.
20.
750.
640.
460.
14α-pinene93933.
330.
034.
2130.
133.
2132.
134.
3131.
132.
4132.
1Z-3-hexenol8550.
120.
150.
320.
220.
230.
110.
86b0.
820.
640.
32E-2-hexenol8560.
090.
0100000.
0330.
080.
030.
01Hexanol8650.
250.
360.
310.
510.
410.
450.
630.
840.
650.
8E-2-hexenal8500.
190.
120.
280.
480.
580.
580.
650.
670.
910.
56α-thujene9280.
20.
210.
410.
210.
310.
240.
560.
580.
560.
88Camphor9541.
61.
81.
451.
051.
651.
151.
661.
532.
061.
43xxCamphene9540.
89*1.
21.
021.
421.
121.
221.
081.
020.
66Sabinene9750.
190.
220.
220.
320.
420.
220.
560.
130.
640.
23β-pinene9802.
042.
542.
172.
072.
372.
172.
812.
832.
252.
12Myrcene9910.
240.
260.
170.
270.
370.
170.
40.
240.
30.
14α-phellandrène10060.
240.
250.
30.
220.
320.
280.
240.
140.
180.
24-3-carene10110.
220.
1200000000p-cymene10261.
72.
73.
043.
542.
953.
842.
63.
012.
053.
11Limonene10301.
191.
892.
012.
412.
212.
512.
021.
552.
121.
951-8-cineole10335.
16.
16.
026.
625.
856.
425.
666.
115.
067.
11(E)-β-Ocimene10500.
520.
820.
820.
620.
920.
720.
780.
620.
440.
44γ-terpinene10530.
50.
660.
560.
360.
330.
560.
120.
120.
180.
44OxydedeCis-linalool10740.
941.
41.
791.
491.
091.
441.
721.
681.
021.
38OxydedeTranslinalool10880.
60.
80.
980.
580.
880.
580.
850.
660.
750.
76Terpinolene10920.
060.
160.
480.
680.
580.
740.
640.
920.
20.
82Linalool10982.
592.
892.
892.
292.
692.
192.
942.
062.
862.
26Borneol11653.
923.
124.
624.
024.
224.
124.
454.
164.
854.
66Terpinene-4-ol117813.
0413.
2413.
0813.
6813.
0212.
0112.
7712.
0613.
1212.
16α-terpineol11894.
614.
014.
584.
884.
124.
214.
064.
674.
684.
55Geraniol12550.
690.
890.
790.
990.
590.
590.
690.
40.
550.
65Acetatedebornyle12952.
822.
122.
022.
122.
012.
192.
782.
852.
082.
15Tridecane13000.
080.
080.
030.
050.
050.
060.
040.
060.
030.
05Linalyldeproprionate13251.
551.
551.
951.
851.
552.
011.
841.
271.
121.
2Acetated'αterpenyle13440.
730.
730.
630.
690.
770.
740.
880.
980.
180.
48α-cubebene13510.
040.
040.
260.
330.
460.
530.
770.
670.
470.
7Copaene13720.
770.
960.
860.
660.
850.
670.
660.
610.
440.
81B-elemene13910.
830.
780.
930.
91.
21.
11.
431.
311.
131.
41β-caryophyllene14344.
024.
924.
224.
824.
884.
034.
124.
434.
014.
93α-humulene14540.
640.
640.
290.
310.
250.
420.
430.
710.
120.
91Allo-aromandrene14740.
510.
110.
210.
310.
210.
610.
240.
510.
410.
15Deltamuurolene4760.
110.
410.
660.
650.
860.
780.
940.
310.
440.
39GermacreneD14800.
120.
310.
720.
770.
620.
840.
910.
550.
770.
65Nonadecanone19000.
040.
0800000.
020.
0400.
05*Notidentiedcompound.
Molecules2020,25,19915of19AppendixBTableA2.
OperatingconditionsestimatedTWOparametersfrombestttingandmodelingerrorsusedbyLito.
ExperimentP(bar)QCO2(kgh1)dP.
104(m)G(dimensionless)kfa0102(s1)ksa0105(s1)ys104(kgkg1)kf106(ms1)ks109(ms1)DAB109(m2s1)ShReScr2RMSE10212200.
6046.
50.
361.
417.
484.
13.
250.
1728.
630.
247.
3311.
0698.
4783.
7322200.
6022.
20.
616.
567.
015.
25.
125.
478.
630.
132.
4711.
0699.
3522.
413801.
2026.
50.
390.
1140.
1820.
90.
2630.
4200.
380.
4553.
532.
1199.
7161.
734801.
2096.
50.
360.
1140.
1070.
90.
2630.
2460.
380.
4553.
832.
1199.
6321.
965800.
6022.
20.
520.
3559.
282.
20.
2777.
240.
380.
169.
082.
1199.
2972.
626800.
6036.
50.
447.
637.
582.
60.
1760.
1750.
380.
3026.
842.
1198.
3023.
7771401.
2046.
50.
352.
677.
831.
56.
160.
1800.
1070.
3718.
377.
9898.
5483.
8581800.
9132.
20.
629.
192.
752.
47.
172.
159.
400.
174.
129.
6798.
2683.
3791800.
9042.
20.
549.
142.
322.
97.
131.
819.
400.
174.
089.
6798.
4213.
00101800.
9086.
50.
231.
970.
1081.
84.
532.
499.
400.
3112.
109.
6799.
3812.
73TableA3.
OperatingconditionsestimatedTWOparametersfrombestttingandmodelingerrorsusedbyCatchpole.
ExperimentP(bar)QCO2(kgh1)dP.
104(m)G(dimensionless)kfa0102(s1)ksa0105(s1)ys104(kgkg1)kf106(ms1)ks109(ms1)DAB109(m2s1)ShReScr2RMSE10212200.
6046.
50.
361.
467.
484.
13.
360.
1729.
060.
247.
3310.
5498.
4773.
7322200.
6022.
20.
616.
777.
015.
25.
295.
479.
060.
132.
4710.
5499.
3522.
413801.
2026.
50.
390.
1180.
1820.
90.
2730.
4200.
4020.
4453.
532.
0099.
7161.
734801.
2096.
50.
360.
1190.
1070.
90.
2740.
2470.
4020.
4453.
832.
0099.
6321.
965800.
6022.
20.
520.
3699.
282.
20.
2887.
240.
4020.
169.
082.
0099.
2972.
626800.
6036.
50.
447.
937.
582.
60.
1830.
1750.
4020.
3026.
842.
0098.
3013.
7771401.
2046.
50.
352.
777.
841.
56.
390.
1800.
1130.
3718.
377.
5598.
5413.
8581800.
9132.
20.
629.
512.
752.
47.
422.
159.
900.
164.
129.
1898.
2683.
3791800.
9042.
20.
549.
462.
322.
97.
381.
819.
900.
164.
089.
1898.
4213.
00101800.
9086.
50.
232.
040.
1081.
84.
692.
499.
900.
3112.
109.
1899.
3812.
73Molecules2020,25,19916of19TableA4.
OperatingconditionsestimatedTHREEparametersfrombestttingandmodelingerrorsusedbyAYDIA.
ExperimentP(bar)QCO2(kgh1)dP.
104(m)G(dimensionless)kfa0102(s1)ksa0105(s1)ys104(kgkg1)kf106(ms1)ks109(ms1)DAB109(m2s1)ShReScr2RMSE10212200.
6046.
50.
3773.
67.
354.
11.
700.
16999.
10.
117.
330.
9698.
4723.
7422200.
6022.
20.
611.
727.
015.
21.
345.
4722.
90.
092.
474.
1699.
3552.
403801.
2026.
50.
408.
700.
1820.
90.
2010.
41914400.
1453.
530.
0699.
7181.
734801.
2096.
50.
378.
950.
1070.
90.
2060.
24614700.
1353.
830.
0599.
6261.
985800.
6022.
20.
523.
429.
302.
22.
677.
2565.
000.
139.
081.
2499.
3572.
56800.
6036.
50.
454.
037.
582.
69.
290.
175597.
00.
1226.
840.
1398.
3223.
7571401.
2046.
50.
371.
267.
711.
52.
900.
178215.
00.
1418.
370.
4098.
6633.
6981800.
9132.
20.
6677.
32.
312.
46.
031.
8115.
600.
144.
125.
8499.
1372.
3891800.
9042.
20.
5992.
91.
912.
97.
251.
4917.
80.
144.
085.
1199.
0193.
26101800.
9086.
50.
232.
640.
1081.
86.
100.
25318.
00.
1012.
100.
2999.
3812.
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