Select Thermodynamic Models for Process Simulation - A Practical Guide to a Three Steps Methodology

6/1/2015 SelectthermodynamicmodelsforprocesssimulationAPracticalGuidetoaThreeStepsMethodology

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SelectthermodynamicmodelsforprocesssimulationAPracticalGuidetoaThreeStepsMethodology

Casestudy1:Crystallizationoftracecomponentsinnaturalgasliquefactionprocess(LIQUEFINTM)

Thecontinuousexpansionofliquefiednaturalgas(LNG)tradefornowmorethanthreedecadeshasbeenachievedthankstothepermanentsearchforcostreduction,mainlyusingthesizeeffect.Topursuethisexpansionatthesamesustainedrateofupto10%percentperyear,someoperatorsarenowseriouslyconsideringtrainswithcapacitiesof6,7oreven8Mt/a.Inordertoreachsuchcapacities,withalwayshigherefficiencyandwithoutaddingcomplexityintheprocess,itisnecessaryto

departfromthetraditionalscheme.IFPandAxenshavedevelopedtheLIQUEFINTMprocesswiththeaimofproducinganLNGcheaperthanwithanyotherprocess,atgoodconditionsofreliabilityandsafety,andfriendliertoenvironment.

Due to the increaseof theworldnaturalgasconsumption, thedistancebetweenproductionandconsumptionsites isever increasing.Pipeline transportation isnoteconomicalfortheselongdistancesandonly liquidphasetransportationisfeasible.Asaconsequence,manyhighcapacitygasliquefactionplantsarepresently inproject.

Innaturalgasliquefactionprocesses,thegasfeediscooledtoverylowtemperatures(113Kor160C).Thepresenceoftracesofheavyhydrocarbonscomponentsin the liquefiednaturalgas(LNG)maythereforeresult incrystallization,andthereforepluggingthe installation.Thepresentwork investigates thevapourliquidsolidequilibriumandproposesawaytopredicttherisksofcrystallization.

Inafirstsection,theprocesswillbedescribedtoexplainthedifferentstepsinvolvedintheliquefactionofnaturalgas.Theoperatingconditionswillbespecifiedinthecrucialpointsoftheprocessandaspecificemphasiswillbegivenontheriskofcrystallizationofheavyelementspresentinverylowproportions.

Inasecondsection,thethreebasicquestionstobeaskedtogiveacorrectanswertoathermodynamicproblemwillbeanalyzed:

Whatarethepropertiesgivenandtobecalculatedtoobtainthesolution?

Whatarethecomponentspresentinthemixture?

Whatarethephasespresentinthedifferentpartoftheprocess?

Inathirdpart,inthelightofthepreviousanswers,athermodynamicmodelwillbedeveloped.Here,acubicEoScoupledwithaHuronVidalmixingrulewillbeused.Thechoiceofadequateexperimentaldatawillbediscussedaswellasthewaytoregressthem.

ThemodelwillbeappliedatthedifferentzonesoftheLIQUEFINTMprocessestablishedaspotentiallyriskyoperatingconditionsandsomerecommendationswillbegivenforhowtooperatetheprocessandhowtoenhancethemodel.

1Processdescription

AllprocessesforLNGproductionsarebasedoncompression/expansionandheatexchangers.Someseparationvesselsand/ordistillationcolumnsarepresentintheprocess to satisfy commercial purities of products. An interesting comparison of different processes can be found inMartinetal. (2002 [1]) or in Mokhatab and

Economides(2006[2,3]).ThecasestudypresentedhereisbasedontheLIQUEFINTMprocesssoldbyAxens.

TheLIQUEFINTMprocessoperatesaccordingtothebasicflowschemepresentedinfigure61.Attheexitoftheprecooling,thegasisscrubbedfromitsheavyendthe top is further refrigerated in the precooling section and the condensate is used as scrubbing fluid. The vapour then enters the cryogenic section. The liquid(bottom)ofthescrubberisintroducedtoademethanizertoremovetheheavycomponentsthatmayrepresentariskofcrystallization.Theheadofthedemethanizerisintroducedinthecryogenicexchanger,reachingatemperatureof113K.



Figure61:LIQUEFINTMgeneralscheme.

Thepresenceoftracesofheavycompounds(mainlyaromaticsandcyclohexane)inthenaturalgas,associatedtotheverylowtemperatureofthecryogenicprocess,createadistinctriskofplugginginthelinesandtheheatexchangersasaresultofcrystallization.Thisisthereasonoftherequestedthermodynamicstudy.

2Thermodynamicanalysisoftheprocess

Accordingtothephilosophyproposedinthisbook(seechapter1),theanalysisiscentredonthreemainquestions:properties,componentsandphases.

2.1Properties

Themainriskintheprocess,fromathermodynamicpointofview,istheriskofplugging,i.e.toobserveasolidtocrystallizeinthelinesorintheexchangers.Fromathermodynamicpointofview,thephenomenonunderconsiderationisafluidsolidequilibrium.Yet,thiscrystallizationisnotwantedand,therefore,thetruechangeinphasecompositionwhenlargeamountsofsolidsareformed(socalledflashcalculation,asintroducedinchapter2,section2.3.1.3)isnotneeded.Instead,theonsetof crystallization, or the phase split boundary is the true quantity that is required here. The problem of phase boundary calculation has been discussed insection2.3.2.4.ofchapter2:themostgeneralapproachistoinvestigatethetangentplanecriterionusinganalgorithmasproposedbyMichelsen[4].Yet,aslongastheprecipitatingphasecanbeconsideredasapurecomponent (which is thecase in thiswork), it issufficient tocompare the fugacity (Gibbsenergy)of thatcomponent in theprecipitatingphase (solid)with the fugacityof this component in the fluidphase.Whenever the fugacity in theprecipitatingphase is lower, thencrystallizationwilloccur.Thealgorithmissummarizedinfigure62.

Figure62:Phaseborderevaluationbetweenliquidandsolid.

Itisconcludedthatinthisanalysis,aspecialattentionwillbegiventothefugacitycalculationofthecomponentsthatmaypotentiallycrystallize.

2.2Components

A typical feed for the process can be seen in table 61. All the components present in a natural gas are well known and belong to the type called "databasecomponents"inchapter3,section1.2.1.Subsequently,thecrystallizationtemperatureofallcomponentscanbefoundindatabases.Thesearediscussedinsection1.1.1.6ofchapter3,andintable62ofthatsection.

Table61:Typicalcompositionofanaturalgaswithahighbenzenecontent.

Feed

Component Composition(molar%)

N2 4.91

CH4 86.06

C2 5.45

C3 1.97

iC4 0.36

nC4 0.57

iC5 0.21

nC5 0.09

nC6 0.12

nC7 0.07



nC8 0.04

nC9 0.01

CO2 0.01

Benzene 0.05

Cyclohexane 0.05

nCxstandsfornalkanewithxatomsofcarbon

Table62:Purecomponentscrystallizationdata(DIPPR,2008[12]).

TriplepointTemperature(K) TriplepointPressure(Pa) Enthalpyoffusion(J/kmol) Volumeoffusion(m3/kmol)

Cyclohexane 279.7 5.36E+03 2.74E+06 8.30E03

Benzene 278.7 4.76E+03 9.87E+06 1.04E02

nC9 219.7 4.31E01 1.55E+07 2.17E02

nC8 216.4 2.11E+00 2.07E+07 1.97E02

nC7 182.6 1.83E01 1.41E+07 1.39E02

nC6 177.8 9.02E01 1.31E+07 1.26E02

Thecrystallization temperatureofanumberofpurecomponents, fromcyclohexane tonC6 is lower than theprocess temperature (near160K).Nevertheless, thepresenceofothercomponentsinthemixtureactsasasolventandlowerstheriskofcrystallization.Thefugacitycalculationwillgivethedefinitiveanswer.

Inthiswork,focuswillbecentredonbenzene.Compositionmayvarywiththegasinexploitation,butforriskanalysis,itisgoodtotakeacompositionthatisrichinbenzeneandotherheavycomponents.Someheaviercomponents likedecanesorxylenesoralkylcyclohexanescanbepresentbut insolowquantitiesthatthecrystallizationrisksareneglected.CarbondioxidemayalsobeanissueasdiscussedbyEggemanandChafin(2005[5]).

Asseenintable61,theconcentrationofbenzeneinthefeedisverylow.Asaresult,thebehaviour(activity)ofthiscomponentisverydifferentfromthatofthepurecomponent (asdiscussed inchapter3,section4.1. In fact, it shouldbealmostconsideredasan infinitelydilutedcomponent,andsection5.2.3discussedhow intheseconditions,veryspecificdatashouldbeused(evenmixturedatashouldbeconsideredwithcaution).Theavailabilityofthedatawillhoweverleadtoconsiderseveraltypesofinformationinthenextsection.

2.3Phases

Initially, thefeedisfoundasavapour,directlyproducedfromgasfield.Theobjectiveof theprocess istocondensethisvapourtofacilitatetransportation.Thus,aliquid isobtainedasa resultof theprocess.Due to thevery low temperatureof thecryogenicplant, somesolidmayappearasananomalousbehaviour.For thisreason,studyisconcernedwiththreephases:vapourliquidsolidequilibrium.

In chapter 4, fluidsolid equilibria of mixtures containing organic compounds was discussed in section 2.2.3.1. Pressuretemperature phase diagrams ofmulticomponentmixturesmaybecomecomplexifsolidphasesareconsidered(Tiffinetal.1979[6]).Luksetal.(1981[7],1984[8])hasclassifiedthegasliquidsolidphase diagrams into four types.Only the first type is of interest here, as it is the one encountered for themethane + benzene system. Its pressuretemperatureprojection issketched in figure63.For the light component, thevapourpressure line, thesolidus lineand thesublimation lineareeasily recognized.For the lightcomponent, only the vapour pressure line is drawn. The locus of critical points is visible as a doted line that connects the critical point of each of the purecomponents.Inthisdiagram,thislineiscutbytwodashedlinesthatrepresentthreephasevapourliquidsolidequilibria(VLSE).

Themeaningofthesecurvesisbestunderstoodwheninvestigatingacutatconstantpressure.Anintermediatepressure(lineP1onfigure63),thatishigherthanthethree phase points of either components, but lower than the critical point of both components (i.e., for themethane + benzenemixture, that yields that type ofdiagram,between4.7kPaand4.6MPa)isanalyzed.Intheseconditions,thediagramsketchedonfigure64)isfound.

Figure63:PTvapourliquidsolidsketchforamethane+benzenemixture.



(61)

(62)

At high temperature, the mixture is always in the vapour phase. In a mixture rich in benzene (dotted line), the vapourliquid equilibrium (VLE) region is firstencountereduponcooling(dewpointinfigure64).Aliquidphaseappears,thatisricherinbenzenethanthevapourphase.Iftheinitialmixturewassufficientlyrichinbenzene(doteddashedline),themixturemaybecomeentirelyliquid(reachitsbubblepoint)beforeformingasolid(pointA).Inthiswork,itisassumedthattheheavycomponentalwayscrystallizesasapurecomponent.Thismaynotalwaysbetrue,butitrepresentsthehighestriskofcrystallizingatagiventemperature.Coolingonthemixture,a threephase line is reachedbefore themixturecanbecomeentirely liquid.Thishigh temperaturevapourliquidsolid threephaseequilibrium line (HTVLSE)formsthelimitbelowwhichtheliquidcrystallizesentirely:onlyavapourandasolidphasecoexistbelowthisline.Atstill lowertemperature,asecondthreephase line is encountered, where the vapour condenses to form a liquid. The solid phase remains. This is the low temperature vapourliquidsolid three phaseequilibriumline(LTVLSE).

Now,considerthecaseofamixturewiththecompositionshownasadashedline,stillricherinmethane(whichisthecaseinnaturalgasliquefactionprocesses).Inthiscase,decreasingthetemperaturewillresultincrystallizingdirectlyfromthevapourphase(noHTVLSEisencountered).Sofar,whenthetemperatureisfurtherlowered,thevapourwillcondenseinaliquidphase,thathasahighercapacityofdissolvingthemeltand,asaresult,belowtheLTVLSEthreephaseline,nocrystalisleft,butonlyaliquidandavapourphase:thisisthefarleftendoftheregularvapourliquidbiphasicequilibriumregion.Thevapourkeepscondensinguponfurthercoolinguntilthebubbletemperature,andeventually,atstilllowertemperature,benzenecrystals(SLE)willappearagain.

Figure64:Txyvapourliquidsolidsketchforamethane+benzenemixture.

3ProblemSolvingProcedure

3.1Evaluationofthemostappropriatemodel

Modelsforthecalculationofphaseequilibriumarebasedonthefugacities:phaseequilibriumisobservedwhenthefugacitiesofeachcomponentineachphaseareequal.Afugacitymodelisneededforeachphaseunderconsideration(seefigure62).

3.1.1Fluidphasefugacity

As themixture contains only hydrocarbons (see chapter 4, section 2.2), a wide choice ofmodels is available for calculating these fugacities: activity coefficientmodelsaregenerallynotrecommendedforgases(not impossible,butmorecomplextouse).Amongtheequationsofstate, thecubicequationsarethemostwellknown,andwillbeusedhere.Acubic,PengRobinson[9]equationofstateisselectedhereforcalculatingtheliquidandvapourfugacities(chapter3,section4.3.4).

Theparameterizationrequiresspecialcarefortworeasons:

1. Theequationisusedatverylowtemperature,inaregionwhereveryfewdataexistformodelvalidationand

2. Thecomponentofinterestisverydilutedinamajoritycomponentthatismethane.Asaresult,specialattentionneedstobegiventothemixingrule.

3.1.1.1Selectionofthe(T)function

Thefirststep inparameterizingacubicequationofstate is tomakesure that thepurecomponentvapourpressuresarecorrectlymodelledusing theselected(T)function. The usual model is that of Soave, which is very acceptable for alkanes, but considering that the benzene properties will be extrapolated at very lowtemperatures,itwaspreferredtousetheTwuequation[10](seesection4.3.4.2,chapter3):

3.1.1.2Selectionofthemixingrule

Inordertobeabletoreachtheinfinitedilutionpropertiesofbenzene,itisimportanttohaveapowerfulmixingrule.Inthiswork,itwaschosentousethemixingruleofHuronVidal(1979[11]):



(63)

(64)

(65)

with,forthePengRobinsonequation:

TheexcessGibbsenergyinequation(62)isexpressedusingamodifiedNRTL:

3.1.2Solidphasefugacity

Asolidphaseappearsif,foranyofthecomponents,thesolidfugacityislowerthanthefugacityoftheequilibriumphase.ThissolidfugacityfS0, iscalculatedusingthegeneralthermodynamicrelationships(seechapter3,section4.4.1).:

ThisequationexpressesthechangeinGibbsenergybetweentheliquidandthesolidphase,atthesystempressureandtemperature.Onthelefthandside,fL0is thefluidphasefugacityofthepurecomponentatthesystemtemperatureandpressure.Itiscalculatedusingthefluidstateequationofstate.On the right hand side, the two first terms express the deviation due to the temperature difference between the fusion temperature and the system temperature.

Usually,onlythefirstterm,thatisproportionaltothefusionenthalpy(Hif)isused.However,verylargetemperaturedeviations(morethan100K)areconsidered,it

is important to includethesecondtermthat takes intoaccount that this fusionenthalpyvarieswith temperature.Theproportionality factor isherecpif , the fusionheatcapacitydifferencebetweensolidand liquid.Finally, thethird termofequation(65) isrequiredwhenthesystempressurediffers fromthatatwhichthefusionpropertiesareprovided (which isusuallyatmosphericpressure).This last term isproportional to thevolumeof fusion,i .Bothenthalpyof fusionandvolumeoffusionareavailableindatabases(table62).

3.2Datarequiredanddataavailable

Inorder to construct amodel it is essential tohaveexperimental data, either for regressingparameters, or for validating the results.As it hasbeenshown in theprevious point the selected equation(s) require(s) parameters. These parameters may be physical properties, available in data bases, or will be regressed fromexperimentaldata.

3.2.1Purecomponentdata

3.2.1.1Characteristicparameters

Thechosenmodel(PengRobinson)requirestheuseof thecriticalparametersforeverypurecomponentof themixture.Thankstothefact thatallcomponentsaredatabasecomponents,theycanreadilybefoundintheDIPPRdatabase.

Thesolidfugacitymodelequation(65),inadditionrequiresfourmorepurecomponentproperties:Tif,Hif,cpifandi.ThetwofirstareavailabletoointheDIPPR

database, butcpif will have to be determined. As a first approximation, the last parameter will be neglected (this Poyntingtype correction affects the pressuredependenceofthesolidfugacity,whichisgenerallysmall).

3.2.1.2Temperaturedependentdata

Inordertoparameterisethe(T)function(61),vapourpressuredataareneeded.Again,theDIPPRdatabaseprovidesanaccuratecorrelationofvapourpressureforallcomponentsofinterestinthiswork.

Finally,consideringthe lowtemperatures,andthefact thata fluidsolidequilibriumisconsidered,purecomponentsublimationpressureswillbeuseful (seesection1.1.2.3ofchapter3).ThisinformationisavailabletoointheDIPPRdatabase.

Table73:Dataforpurecomponents

Dataneeded Dataavailable

Criticaltemperature Inallcommondatabaseandprocesssimulators

Criticalpressure Inallcommondatabaseandprocesssimulators

Acentricfactor Inallcommondatabaseandprocesssimulators

TwuconstantsSomepublishedinoriginalpublication.Availableinmostsimulatorsorfittedfromvapourpressure

Fusiontemperature Inmostcommondatabaseandprocesssimulators

Fusionenthalpy Inmostcommondatabaseandprocesssimulators

Heatcapacityoffusion Unavailable

3.2.2Mixturedata



3.2.2.1Fluidsolidequilibriumdata

Sincethisworkdealswithcrystallizationoftracecomponentsfromagasmixture,itisessentialtofinddataofthesamekindthatcanvalidatetheapproach.Afteracarefulliteraturesearch,followingtypesofdatacouldbeidentified(seetable64):

Table64:Availablefluidsolidequilibriumdataforthemethane+benzeneequilibrium

Reference Pointsnumber Temperaturerange(K) Datatype

Kuebler,G.P.McKinley,C.{Kuebler,19742391/id} 39 99200 lowtemperatureSLE

Neumann,A.etal.[13] 12 104185 lowtemperatureSLE

Luks,K.D.Hottovy,J.D.Kohn,J.P.[7] 23 165278 2SLVElines

Rijkers,M.P.W.Malais,M.Peters,C.J.DeSwaanArons,J.[14] 100 262298 lowandhightemperatureSLE+VSE+HTVLSEline

Neumannetal. (1972 [13]) havemeasuredbenzeneandcyclohexanecrystallizationoutofmethane.As it canbeseenon figure65, the riskof crystallizationofbenzeneisgreaterthanforcyclohexane,becauseatthesametemperature,alowercompositionofbenzenecanleadtosolidprecipitation.Yet,thetemperatureandconcentrationsdonotfitwiththoseoftheprocess.

The data of Neumannetal. don't provide pressure information. This is a clear drawback in using them. Nevertheless, it can be considered that pressure has anegligibleeffectonphaseequilibriumofcondensedphases,asitisthecasehere.

Figure65:CrystallizationofCyclohexaneandbenzeneinmethane(dataofNeumannetal.1972[13]).

IthasbeenobservedthattheconditionsthatmaybeofinteresttoLNGprocessesarethosewherevapoursolidequilibrium(VSE)isencountered.Unfortunately,veryfewsuchdatahavebeenfound.OnlyRijkersetal.(1992[14])publishessuchdata,butforveryhighbenzeneconcentrations(10%benzene).

Theother informationfoundin literature isgivenbyLuksetal. [7].Theyprovidethreephasevapourliquidsoliddata.Twobranchesareobservedonfigure66,onecorresponding to the high temperature branch (HTVLSE) and the other corresponding to the low temperature branch (LTVLSE), information compatible with thedescriptionoffigure63.

Figure66:PressureTemperatureprojectionofthemethane+benzenethreephaselines,accordingtothedataofLuksetal.(1981)



(66)

(67)

(68)

(69)

Theyprovideasa functionof temperatureandpressure, thecompositionof the liquidphase.Thegraphof figure66clearly showshow the two threephase lineschangewithpressure.Thelowerthreephaselineendsatthemethanecriticalpoint.Asamatteroffact,fromthatpointonward,itbecomesimpossibletomakethedifferencebetweentheliquidandthevapourphase.Thehightemperaturethreephaselinecontinuesuntilmuchhigherpressuresbecausethecriticalpointslocusofthemethane+benzenemixturereacheshighpressures.

3.2.2.2Vapourliquidequilibriumdata

In order to determine parameters for the HuronVidal mixing rule, vapourliquid equilibria are generally used. Most often, bubble pressures are regressed, andsometimesvapourcomposition,asdiscussedinchapter3,section3.

Methane (majority component) and benzene (crystallizing component) are the key components and will be focused on. Vapourliquid equilibrium data for thesemixturesexist,butat temperatures thatarewellabove theprocess temperature.The lowest temperaturedata thatwere foundoriginate fromRijkersetal. {Rijkers,19921537/id},andcovereightdifferentisotherms,between270and330K.

3.3Parametersfitting

Inordertousethemodeldefinedabove,followingparametersneedtobedetermined:

Twu'sparametersfor(T)functiontousewiththePREoS.

BinaryinteractionparameterstousewiththeHuronVidalmixingrule.

Heatcapacityoffusiontouseinthesolidfugacitycalculation.

3.3.1Purecomponentparameters

Thevery firststep isalways toverify thepurecomponentparametersof theequationofstate.Useofvalidatedcriticalparameters,and regressionof theL,M,Nparametersofequation(61)foreachcomponentofthemixtureisaprerequisiteforthefurtheranalysis.Inthiswork,noemphasiswillbegiventothisfirststep.

3.3.2Binaryinteractioncoefficients

ThechoiceoftheHuronVidalmixingrule,that isbasedonthemodifiedNRTLequation(64)results inthreeinteractionparametersatanygiventemperature:ji,ijandji.Inaddition,theseparametersareafunctionoftemperature:

ThestrengthoftheHuronVidalmixingruleisthat,whennodataisavailable,anadequatechoiceoftheinteractionparametersisequivalenttoasimplecubicmixingrulewithij:takingij=0,itispossibletofind:

Ontheotherhand,whensufficientdataexist,itispossibletoregressthemallinordertoimprovetheaccuracyofthecalculations.Inthiswork,focuswillbecentredonthemethane+benzenebinarymixture.

Thebinary interactionparameters (BIP)aregenerally fittedonvapourliquidequilibria. In thecaseof themethane+benzenemixture, thesedataareabundant,butexist only at temperatures that are well above the process temperatures. The parameters available in the simulator that was used so far, were fitted on hightemperaturedata.Inthiswork,focuswillbeondataofRijkersetal.astheygoto250K,thelowestofallisothermsknownforthatmixture.Forcomparison,afirstsetofBIPhasbeenobtainedwithdatathatdonotincludetheRijkersetal.dataset.

The deviation table 65 clearly shows that the first parameters were adapted to the high temperature conditions, but provide large deviations for the lowertemperatures.Thesecondsetwasadjustedonalldatausingfollowingobjectivefunction:

Rijkersetal.providenodataonthevapourcomposition,sothatthiscouldnotbeincludedintheregression.

Table65:Deviationtableforbinaryinteractionparametersets

Datasource(K)parameters

ij=0Firstset Secondset

270 15.05% 39.36% 46.0%

280 8.91% 32.20% 39.0%

290 6.40% 26.03% 33.0%

300 6.94% 21.28% 27.0%

310 8.53% 17.13% 23.0%

320 11.00% 14.11% 19.0%

330 11.18% 10.86% 16.0%



(610)

(611)

340 12.30% 7.41% 15.0%

3.3.3Heatcapacityoffusion

Theparametersofthesolidfugacityfunction,equation(65),areallknownquantities(HifJ/molandifm3/mol)excepttheheatcapacityoffusionCpif.Asafirstapproximation,itispossibletoassumeitisnegligible.

Inordertovalidatethisapproach,thefirststepistoevaluatethepurecomponentfluidsolidequilibriumline,i.e.thesublimationline.Doingso,andassumingthatthevapourfugacityequalsthepartialpressure:

where istherighthandsideofequation(65)withoutthePoyintingcorrectionterm(pressureislowandthistermisverysmall).

Figure67:Evaluationofthecorrectionterm(equation(610))asafunctionoftemperatureforbenzenecrystallization.

Figure67showstheresultofthiscalculation.Obviously,atthetriplepoint,allfugacitiesareequal(thisissobyconstructionofequation(65),butitisclearthatatlowtemperature,thebenzenesublimationpressuredeviatesfromthesimplifiedmodel.Correctiontermcannotbeneglected.Itcanbeconcludedthatthesolidheat

capacityuponfreezing,Cpif,willneedtobefitted.Consideringtheexpressionsused,thecorrectiontermhasbeenchosenintheobjectivefunction:

Indeed,itisrathereasytocalculatetheexperimentalvalueofln(fi/fL0)byobservingthatwhencrystallizationoccurs,fi=fS0,wherefiisthefugacityofcomponentiinthestablephase(calculatedusingtheequationofstateattheexperimentaltemperature,pressureandcomposition),whileiscalculatedusingthesameequationofstate,forpurebenzeneatintheliquidphaseatthesametemperatureandpressure.

Inadditiontothepurecomponentsublimationpressure,itispossibletoconsiderthemixtureLSEdatabyNeumannetal.,Itisessentialtoreproducecorrectlytheselatterdatasince the temperatureandconcentrationconditionsareclose to theprocessconditions.Figure68shows the logarithmof the fugacity ratio for the twotypesofsolidequilibriumdata. It isclearlyvisible that thetwocurvesarenotcolinear.Thereasonfor this ismostprobablydueto the imperfectionsof theHuronVidal mixing rule that is used. When sublimation data are used, no mixing rule is needed, as all data concern the pure component. On the opposite, the lowtemperatureLSEdataconcernverysmallbenzeneconcentrations inalmostpuremethane.Hence, in the lattercase, the infinitedilution fugacity isused,which isextrapolatedfromtheequationthathasbeenvalidatedonhightemperatureVLEdata.

Yet,inthepresentstudy,attentionhasbeenfocusedonthelowtemperatureandhighdilutionbehaviour.Doingsoforbenzene,ithasbeenfound,withafewtrialand

error,thevalueofCpif=200kJ/(kmol.K).



Figure68:Correctionterm(equation(65))asafunctionoftemperatureforbenzenecrystallization.Thediamondsrefertosublimationdatathetrianglestobenzenecrystallizationinmethane.

3.4Modelvalidation

Firstatall,itisimportanttocheckthevalidityofthesolidificationmodel.Evolutionofbothfugacities(thebenzenesolidfugacityandthebenzenefluidfugacityinthemixturecalculatedwithEoS)iscomparedasafunctionoftemperature.Whenfugacitiesarethesame,afluidsolidequilibriumisexpected.Itcanbeappreciatedinfigure69thatthismodelpredictscorrectlythethreecasesshowninfigure64(thedashedlineatlowbenzenecomposition).

Figure69:Correctionterm(equation(65))asafunctionoftemperatureforbenzenecrystallization.Thediamondsrefertosublimationdatathetrianglestobenzenecrystallizationinmethane.

Themodelthatisthusdevelopedhasbeenfirstvalidatedbyextrapolationofpressureandtemperatureconditions,usingthedataofRijkersetal.(1992)asshowninfigure610.Thisplotshowstwodistincttypesofbehaviour.Athighertemperatures,andhighconcentrationsofbenzene,LSElinesareseen.Thedatapointsandthemodel (line) agree within 5 K. The model overpredicts crystallization temperatures which is acceptable for a safe design. At lower temperature, a vapoursolidequilibriumlineisshown.Again,themodelqualitativelyagreeswiththedata.Thecrystallizationtemperatureincreaseswhilepressuredecreases.Atlowerpressures(processconditions), it isexpectedtooverpredict thecrystallization temperature,againasaferesult.Unfortunately,nodatacouldbefoundshowingcrystallizationfromthevapourphaseatbenzeneconcentrationsthatareclosertotheprocessconditions(lessthan1%).



Figure610:ModelvalidationonthebenzenecrystallizationdataoutofmethaneofRijkersetal.(1992).

4Applicationtoprocessanalysis

Asmentionedpreviously,fourdifferentpointshavebeenselectedforanalyzingtheriskofcrystallization.ThefeedtoLNGprocessisofcourseofmainimportanceduetothepresenceofthehighercontent inheavycomponents.Othercriticalflowsarethoseofthecryogenicsectionoftheexchangeratthelowertemperatureoftheprocess.Twodifferentflows,withsimilarcomposition,areanalysed:theheadofdemethanizerandtheLNGproductavailableatthetopofthevessel.Finally,thebottomofthescrubberhasverydifferentcompositionandisanalyzedtoo.Thecompositionofthedifferentcurrentsissummarizedintable66.

Table66:Typicalmolarcompositionofthepointsanalyzedinprocess

ComponentFeed

Composition(molar%)HeadofdemethanizerComposition(molar%)

N2 5 1.64

CH4 86 91.66

C2 5 5.71

C3 2 0.96

iC4 0.5 0.01

nC4 0.8

iC5 0.1

nC5 0.3

nC6 0.1

nC7 0.06

nC8 0.02

nC9 0.01

CO2 0.01 0.02

Benzene 0.05 10ppm

Cyclohexane 0.05

4.1Feedcrystallizationphasediagram

Using the feedcompositiongiven in table61, figure611shows thecrystallizationofbenzeneatdifferent temperaturepressureconditions.Thevapourliquid (VL)phaseenvelopeispredicted.Thereisaclearriskbelow90C,butpressurehasaneffectaswell:

When pressure is very low (atmospheric), solid appearsmuch earlier (i.e. at higher temperature). This can be explained rather easily by observing that in theseconditions,theliquidphaseisratherconcentratedinbenzene.

Intheliquidregion,itisseenthatincreasingpressureresultsinahighersolubilityofthesolid.Thisisbecausethisliquidphaseremainssomewhatcompressibleasitisessentiallycomposedofmethane,andthereforethetemperatureisclosetothecriticaltemperature.Hence,athigherpressure,theliquidisdenserwhichmeansitisabettersolventforthebenzenecrystals.Notethatthephenomenonhadbeenoppositeiftheliquidhadbeenlesscompressible,asisthecasewithpurebenzene:thehigherthepressure,thelargerthetendencytoformasolidphase.



Figure611:Phasediagramofthefeed,givenintable61.LVmeansvapourliquidFmeansfluidphase.When'S'isincluded,benzeneiscrystallized.

4.2Demethanizerdiagram

A typical composition of the head of the demethanizer is shown in table 66. For this exercise, Benzene specification in the demethanizer and the LNG productoverheadhavebeenrelaxedto10ppminsteadofthegenerallyconsidered1ppm.

Thecorrespondingphasediagramsarepresentedinfigure66.

Figure612:Phasediagramoftheheadofthedemethanizerwith10ppmofbenzene(asshownintable66.

Thisfigure612againshowsthevapourliquidequilibriumzoneas'LV',andthesinglephaseregionas'F'.Threedifferentcrystallizationzonescanbeidentified:

Below115Kbenzenecrystallizesfromtheliquidphase.

Inthesamewayasinthefeed,benzenecrystallizationcanbeobservedatlowpressurewithinthevapourliquidzone.Inoppositionwithwhatisseeninfigure611,thefluidisveryrichinmethane,andasaresultthevapourzone,belowthevapourliquidequilibrium,isvisible.Inthiszone,wherethefluidissinglephasevapour,crystallizationalsooccurs,atratherhightemperatures(upto200K),eventhoughthebenzeneconcentrationisassmallas10ppmmolar.

ThislastcrystallizationzonecanbeexplainedwhenconsideringtheTxysketchof64.Itwasexplainedhow,atafixedpressure,afirstcrystallizationzonefromthevapourphasecouldbeobservedatmoderate temperature.When temperaturedecreases, thecrystalsdissolve in the liquid thatappears.Thecrystals reappearatmuchlowertemperature,outoftheliquidmethane.

Unfortunately,noexperimentaldataillustratingthisbehaviourcouldbefound.

5Conclusions

ThisworkwasexecutedinordertoevaluatetheriskofbenzenecrystallizationintheLIQUEFINTMgasliquefactionprocess.Theworkispresentedinthreestages:

Inordertounderstandthephysicalphenomenonofcrystallization,thephasediagramofthemethane+benzenebinarysystemisfirstinvestigatedindetail.Itisshownthattwoliquidsolidandonevapoursolidequilibriumzonesexist,inadditiontothewellknownvapourliquidequilibrium.

Inasecondstage,athermodynamicmodelisdeveloped,thatusesthePengRobinsonequationofstatewiththeHuronVidalMixingrule.Theparametersfor



thismodelhavebeendeterminedbasedonhightemperatureVLEdata.Itisobviousthatthemodelisusedattemperaturesthatarewellbelowthetemperatureofthedataused.Hence,carehasbeentakenthattheextrapolationtolowertemperaturesisasacceptableaspossible.Anadditionalparameter(fusionheatcapacity)isdeterminedusinglowtemperatureLSEdata.

Inafinalstage,themodelisusedtocalculatethephasediagramoftwotypicalcompositionsencounteredintheLIQUEFINTMprocess.Thefirstcompositionisrichinheavyendcomponents.Asaresult,aliquidphaseisalwayspresent.Thisliquidmaybeconcentratedinbenzene,whichincreasesthecrystallizationriskathighertemperaturesandlowpressures.Thesecondcompositionisverypuremethane.Asaresult,asinglevapourphasemayexistathightemperatureandlowpressure.Eventhoughthebenzeneconcentrationisverysmallinthiscontext(10ppmmolar),acrystallizationriskfromthevapourphaseexistswhichjustifythechoiceforalowerbenzenespecificationinthedemethanizeroverhead.ThisphenomenonisofimportanceforthedesignoftheLNGprocess,butnoexperimentaldatavalidatingthisbehaviourhasbeenfound.

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