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Assessment of the capabilities of two polar sPC-SAFT terms through application to measured ketone-alkane phase equilibria data

Cripwell, Jamie Theo (2014-04)

Thesis (MEng)--Stellenbosch University, 2014.


ENGLISH ABSTRACT: Thermodynamic models have been investigated extensively since Johannes van der Waals first devised a mathematical relation capable of predicting both vapour and liquid phases for a mixture at equilibrium. With the advent of modern computing power, these equations of state have gone from their humble empirical beginnings to the comprehensive and fundamentally derived models we have today. One such physically sound model is the Statistical Associating Fluid Theory (SAFT) family of equations, derived from the molecular perturbation theories of the 1980’s. The relative youth of this thermodynamic framework has meant that much work has gone into modification and optimisation of the model recently. The variants of particular interest to this work are the simplified perturbed chain SAFT equations with the Jog & Chapman (sPC-SAFTJC) and Gross & Vrabec (sPC-SAFTGV) polar terms. Each of the polar terms supports one adjustable polar parameter that relates to the quantity of polar segments in the reference fluid but not necessarily its position in the carbon chain. The strength of polar interactions is known to decrease as the functional group moves away from the terminal methyl group and the effects of steric hindrance increase. Thus, in question here is whether the models can account for the change in polar interactions associated with the changing position of the polar group, by only adjusting the values of the existing pure component parameters; that is, in lieu of a position specific parameter. The carbonyl group in ketone molecules is one such polar group, and it is this homologous series that is the focus of this study. The decrease in polar interactions as the carbonyl group in a ketone molecule shifts centrally is apparent from the lower boiling points of the isomers where the polar group is central as compared to those where the functional group is nearer the terminal methyl group. The effect of this functional group shift on binary phase behaviour has not previously been assessed for any system however, as the lack of experimental data attests. Thus, experiments had to be conducted to generate phase equilibrium data for systems comprising each structural isomer of a mid-length ketone with a common second component with no functionality. This limitation was imposed to isolate the cause of experimentally observed phenomena to the shifting polar group alone. The generated data could then be appropriately modelled using the polar sPC-SAFT variants and the capabilities of each model, as outlined above, assessed. To this end, isobaric binary vapour-liquid equilibrium data were measured for 2-, 3- & 4-heptanone with three separate normal alkanes of similar length (n-octane, n-nonane & n-decane) at 40kPa. The apparatus used was a dynamic Gillespie VLE still with temperature and pressure accuracies of 0.03°C and 1.6mbar respectively. Equipment verification was achieved through the reproduction of experimental data for the ethanol/1-butanol system at 1.013bar. The vapour and liquid samples for all nine systems were analysed by gas chromatography with a maximum compositional error of ±0.022 mole fraction. All reported data were found to be thermodynamically consistent using both the L/W and McDermott-Ellis consistency tests. When paired with a common n-alkane, all three structural heptanone isomers displayed similar qualitative trends in phase behaviour. Minimum boiling azeotropes were measured in all nine systems; in the high alkane region for n-octane systems (~98 mole%), the equal concentration region for n-nonane systems (34 mole% to 53 mole%) and in the very dilute n-alkane region for n-decane systems (~3 mole%). The n-nonane systems in particular highlighted the effect of shifting functional group, with completely separate phase envelopes away from the pure alkane composition space evident in a particularly small temperature range. Modelling was performed using in-house developed software, with pure component parameters generated for each system using five different regression procedures. The first was traditional fitting of the segment diameter (σ), segment number (m), segment energy (є/k) and the respective polar parameter (xp, np) to DIPPR correlations of pure component saturated vapour pressure, liquid density and the heat of vaporisation. The latter four procedures included the fixing of the polar parameter according to functional group correlations and the three instances of including the binary VLE data set for each of the three alkanes considered in this work. When applied to the nine binary ketone-alkane systems measured in this work, excellent predictions of the experimental data were in evidence in most cases and only small binary interaction parameters were necessary to correlate the data where pure predictions were poor. The performance of the parameter sets based on the fixing of the polar parameter and the inclusion of VLE data were consistent and of a high quality for both models, with near identical parameters generated in all four cases for each of the nine systems. The parameter sets generated in this fashion were shown to be applicable not only to the systems measured in this work, but also successfully predicted the independently measured experimental data of the n-hexane/4-heptanone system. It was thus concluded that either of these regression alternatives are viable for the generation of accurate component parameters, and the choice of VLE data set included is trivial. The pure predictions of the sPC-SAFTGV model were generally better than its sPC-SAFTJC counterpart, particularly in the case of the traditionally regressed parameter sets. sPC-SAFTGV displayed constant qualitative agreement with the experimental data for each of the heptanone isomers with a given n-alkane. The quality of the predictions of sPC-SAFTJC, however, worsened significantly as the polar interactions diminished from 2- to 4-heptanone, with no predictions even possible for the least polar isomer. This was attributed to the different perturbation theories used in the development of these terms, but a more detailed study would be necessary to confirm this. This work thus shows an apparent inability of the sPC-SAFTJC equation of state to account for the decreasing polar interactions associated with the carbonyl group in a ketone molecule shifting centrally, while sPC-SAFTGV produces qualitatively good fits for all three isomers. These flaws can be overcome through the incorporation of VLE data in the regression procedure if such data is available, or otherwise through the use of group specific correlations for fixing the polar parameter value.

AFRIKAANSE OPSOMMING: Sedert Johannes van der Waals die eerste wiskundige verhouding ontwikkel het wat beide die damp- en vloeibare fases van 'n mengsel by ewewig kon voorspel, is die veld van termodinamiese modellering al deeglik ondersoek. Na die koms van die moderne rekenaars het hierdie vergelykings van hul nederige empiriese wortels gegroei tot die omvattende, fundamentele modelle wat ons vandag het. Een so 'n fundamenteel gebaseerde familie van vergelykings is die ‘Statistical Associating Fluid Theory’ (SAFT) modelle, wat afgelei is vanaf molekulêre versteuringsteorieë, ontwikkel in die 1980s. Hierdie relatiewe jong modelle het in die afgelope ruk aansienlike aanpassing en optimering ondervind. Modelvariante van besondere belang tot hierdie werk, is die vereenvoudigde versteurde ketting of ‘simplified perturbed chain’ SAFT vergelykings, met Jog & Chapman (sPC- SAFTJC) en Gross & Vrabec (sPC- SAFTGV) polêre terme. In die sPC-SAFT toestandsvergelyking word elkeen van die polêre terme ondersteun deur een polêre veranderlike. Hierdie veranderlike is afhanklik van die aantal polêre segmente in die verwysingsvloeistof, maar nie noodwendig hul posisie in die koolstofketting nie. Daarteen is dit bekend dat die polêre interaksies tussen molekules swakker word soos die polêre groep wegbeweeg van die terminale metielgroep, en steriese hindernis ʼn groter rol begin speel. Dus is die vraag of die model die verandering in die polêre interaksie, as gevolg van veranderende posisie van die polêre groep, kan voorspel deur in plek van ʼn posisie afhanklike parameter, slegs ʼn aanpassing van die polêre waardes van die suiwer komponente te maak. Die karbonielgroep in ketoon molekules is een so 'n polêre groep, en ʼn homoloë reeks ketone word in hierdie studie ondersoek. Die afname in die polêre interaksie soos wat die karbonielgroep in 'n ketoon molekule weg skuif vanaf die terminale metiel groep is sigbaar deur die afname in kookpunt van die verskillende isomere. Hierdie effek van die funksionele groepsposisie op binêre fasegedrag is nog nie voorheen vir enige stelsels geëvalueer nie en geen eksperimentele data is vrylik beskikbaar nie. Om hierdie tekortkoming in die literatuur aan te spreek, is eksperimentele fase ewewig data gemeet. ʼn Reeks stelsels is ondersoek wat elk bestaan uit ʼn struktuurisomeer van ʼn mid-lengte ketoon en ʼn tweede komponent met geen funksionele bydrae. Eksperimente is so opgestel om die effek van die skuiwende polêre groep op die fasegedrag te isoleer en kwalitatief te ondersoek. Die gegenereerde data is dan gemodelleer met behulp van die polêre sPC- SAFT variante, soos hierbo gespesifiseer, en die vermoëns van elke model is beoordeel. Isobariese binêre fase ewewig data is by 40kPa gemeet vir damp-vloeistof stelsels bestaande uit 2, 3 & 4 heptanoon, gemeng met drie verskillende normaal alkane van vergelykbare kettinglengte (n-oktaan, n-nonaan & n-dekaan). Die apparaat wat gebruik was is 'n dinamiese Gillespie VLE eenheid met temperatuur- en drukakkuraatheid van 0,03°C en 1.6mbar, onderskeidelik. Die akkuraatheid van die toerusting is bevestig deur eksperimentele data vir ʼn etanol/1-butanol stelsel by 1.013bar te reproduseer. Die damp en vloeibare monsters vir al nege stelsels is ontleed deur gaschromatografie met 'n maksimum komposisionele fout van ± 0,022 (molfraksie). Alle data is as termodinamies konsekwent gevind deur van beide die L/W en McDermott-Ellis konsekwentheidstoetse gebruik te maak. Mengsels van die drie strukturele isomere van heptanoon met ʼn gemene n-alkaan het tydens eksperimente soortgelyke kwalitatiewe tendense in fasegedrag getoon. Gedurende eksperimente is die lae kookpunt asiotrope gemeet vir al nege stelsels. Die asiotrope verskyn in die hoë alkaan konsentrasies (~98 mol%) vir n-oktaan stelsels, medium konsentrasies (34 mol% tot 53 mol%) vir n-nonaan stelsels en baie verdunde konsentrasies (~ 3 mol%) vir n-dekaan stelsels. Die n-nonaan stelsels beeld veral die effek van die verskuiwing van die funksionele groep uit, met diskrete fasegrense wat duidelik apart staan van die suiwer alkaan ruimte, binne ʼn klein temperatuurverskil. Modellering van die stelsels is uitgevoer met behulp van sagteware wat in-huis ontwikkel is. Suiwer komponent data is gegenereer vir elke stelsel deur van vyf verskillende regressie prosedures gebruik te maak. Die eerste is die tradisionele passing van die segment deursnee (σ), segment nommer (m), segment energie (є/k) en die onderskeie polêre parameters (xp, np) op DIPPR korrelasies van die suiwer komponent versadigde dampdruk, vloeistof digtheid en die hitte van verdamping. Die oorblywende vier prosedures sluit in die bepaling van die polêre parameter deur funksionelegroep korrelasies, en drie gevalle waar die binêre VLE data vir elk van die drie alkane ingesluit is. Deur hierdie prosedures op die modellering van die nege binêre ketoon/alkaan stelsels toe te pas, is uitstekende passings van die eksperimentele data verkry met slegs baie klein binêre interaksie parameters nodig waar voorspellings minder akkuraat was. Die prestasie van die parameter stelle, gebaseer op die bepaling van die polêre parameter en die insluiting van VLE data, is konsekwent en van 'n hoë gehalte vir albei modelle, met 'n byna identiese parameters gegenereer in al vier gevalle vir elk van die nege stelsels. Die parameter stelle wat op hierdie metode gegenereer is, is nie net toepaslik gevind op eksperimentele data gemeet in hierdie werk nie, maar ook op onafhanklike data vir die n-heksaan/4-heptanoon stelsel. Daar is tot die gevolgtrekking gekom dat beide van die regressie alternatiewe lewensvatbaar is vir die generasie van akkurate suiwer komponent parameters, en dat die insluiting van die VLE data triviaal is. Die suiwer sPC - SAFTGV voorspelling was oor die algemeen beter as die suiwer sPC- SAFTJC model met die voorspelling van data, veral in die geval van passings gedoen met parameters verkry vanaf tradisionele regressie metodes. sPC- SAFTGV het ʼn voortdurende, kwalitatiewe ooreenkoms met eksperimentele data getoon vir elk van die nege stelsels. Daarteen het voorspellings deur sPC- SAFTJC beduidend verswak soos die polêre interaksies afgeneem het vanaf 2- na 4- heptanoon, met geen akkurate voorspelling moontlik vir die minste polêre isomeer nie. Die verskynsel kan toegeskryf word aan die verskil in versteuringsteorieë wat gebruik word in die ontwikkeling van die onderskeie toestandsvergelykings, maar ʼn meer in-diepte ondersoek is nodig om hierdie teorie te bevestig. Hierdie werk toon dus 'n skynbare onvermoë van die sPC - SAFTJC toestandsvergelyking om die verandering in polêre interaksie, as gevolg van die veranderende posisie van die polêre groep, vir die karbonielgroep in ʼn ketoon te voorspel, terwyl die sPC-SAFTGV toestandsvergelyking goeie kwalitatiewe passings vir al drie isomere bied. Hierdie tekortkominge kan oorkom word deur VLE data, indien beskikbaar, in die regressie prosedure in te sluit, of deur die gebruik van groep spesifieke korrelasies vir die aanpassing van die polêre parameter.

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