| Summary: | 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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