Browsing by Author "Cripwell, Jamie Theo"

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    Assessment of the capabilities of two polar sPC-SAFT terms through application to measured ketone-alkane phase equilibria data
    (Stellenbosch : Stellenbosch University, 2014-04) Cripwell, Jamie Theo; Burger, A. J.; Schwarz, C. E.; Stellenbosch University. Faculty of Engineering. Dept. of Process Engineering.
    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.
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    Improvement of the thermodynamic description of polar molecules and their mixtures in the SAFT framework
    (Stellenbosch : Stellenbosch University, 2017-03) Cripwell, Jamie Theo; Burger, A. J.; Schwarz, C. E.; Stellenbosch University. Faculty of Engineering. Dept. of Process Engineering.
    ENGLISH SUMMARY: Chemical processes are designed around the manipulation of thermodynamic properties of chemical species and their mixtures. The ability to predict these properties accurately has driven the development of thermodynamic models from the humble beginnings of the van der Waals equation to the fundamental statistical mechanical theories we have today. Despite the successes of recent years resulting from improved fundamental understanding and availability of increased computational power, the accurate representation of certain chemical species and some thermodynamic properties remain elusive. This is particularly true of the holistic properties of polar components and their mixtures, which is the focus of the work presented here. Arguably the most successful product of the more fundamental approach to thermodynamic modelling is the Statistical Associating Fluid Theory (SAFT). This equation of state has allowed for the accurate representation of molecular geometries, molecular association and the accurate representation of polar interactions. The resulting model framework produces highly accurate predictions of mixture phase equilibria of many systems, which has been the focus of the model’s development. Exceptions still remain however, with one such systematic fault providing specific context for model improvement in this work. A central aim of this work was to establish whether there is deterioration in the predictive capacity of polar sPC-SAFT when applied to the phase equilibrium of different polar isomers. This follows from previous work, where such systematic deterioration was found for ketones, and is extended to ethers and esters here. A lack of previously measured data for isomers of these polar functional groups necessitated generation of such experimental data. Thus, new isobaric vapour-liquid equilibrium data were generated for two C6 ether isomers with n-heptane, and five C6 ester isomers with n-octane at 60 kPa. The experimental data showed that significant differences in mixture phase behaviour and resulting phase envelopes are present for each isomer considered, consistent with the experimental trend seen for ketones. Modelling of the experimental data using sPC-SAFT with the Jog & Chapman (JC) and Gross & Vrabec (GV) polar terms showed that similar trends to that witnessed for ketones previously are apparent for ethers and esters. Using pure component data alone, sPC-SAFTGV parameters were determined for all but one considered isomer, displaying a consistent level of accuracy in the prediction of mixture VLE. Significant parameter degeneracy was apparent for sPC-SAFTJC however, resulting in an inability to regress unique parameter sets for less polar isomers. The results constitute the first case of systematic superiority of the Gross & Vrabec polar term over that of Jog & Chapman. The modelling results served to clarify the relationship between isomer identity and predictability of the component properties. The predictive capacity of polar sPC-SAFT decreases as the behaviour of the isomer approaches that of an equivalent size/mass nonpolar component. In the case of ketones previously and esters here, this behaviour is linked to the shifting of the polar group centrally, while a more terminally located functional group produces this result in ethers. The incorporation of VLE data in the parameter regression, or fixing the value of the polar parameter, were shown to be excellent mitigation strategies for regressing accurate parameter sets. The systematic difficulties in modelling isomer phase behaviour raises questions over the overall predictive capacity of the sPC-SAFTJC and sPC-SAFTGV models. Combined with the previously demonstrated inability of these models to simultaneously model phase equilibria and derivative properties using a single parameter set lead to the decision to consider a new polar SAFT framework. To this end, the recently developed SAFT-VR Mie equation of state provided an ideal foundation, and the new SAFT-VR MieJC and SAFT-VR MieGV variants, using the same JC and GV polar terms, were proposed. An extensive regression exercise demonstrated the difficulty with which polar SAFT-VR Mie parameters are determined. This comes as a result of the more complex regression space, being a function of five regressed parameters (σ, m, ε/k, λr and xp/np). For SAFT-VR MieJC in particular, the problem of broad minima in the objective function was more widespread, resulting in an inability to generate parameter sets with nonzero polar contributions. This was true for all components when considering pure component data alone, but also for the ketone functional group when mixture data were considered. This finding supports similar conclusions drawn for sPC-SAFT and points to an inferiority of this variant. SAFT-VR MieGV proved a more robust model and, applied to the same phase behaviour of isomeric systems, demonstrated that the model performs at least as well as its sPC-SAFT counterpart when a unique parameter set was determined. As with polar sPC-SAFT before it, accurate parameter sets were shown to be determinable for SAFT-VR MieGV when VLE data were incorporated in the regression procedure. These optimum VLE parameter sets were demonstrated to produce highly accurate predictions, not only for the traditional application to mixture phase equilibria, but to derivative properties such as speed of sound in mixtures as well. This signifies a significant improvement over the polar sPC-SAFT framework, achieving the elusive simultaneous prediction of VLE and derivative properties using a single parameter set. Novel application to mixture excess properties further demonstrates that, while the new polar SAFT-VR Mie models yield similar predictions to their sPC-SAFT counterparts, room for improvement still exists. This is particularly true for representation of the temperature dependence of Ar in SAFT type models. The prediction results of the Correlation parameter sets represent the most significant contribution of this work - the reliance of generating an accurate parameter set on the availability of mixture VLE data is simply not an acceptable caveat in promoting a new predictive model. Here, the value of the polar parameter is fixed to physically meaningful values while the remaining parameters are regressed using pure component data alone. In particular, the pure component speed of sound is incorporated to produce a more well-balanced parameter set. Using these parameters improves the prediction of mixture speed of sound, while incurring only a small deterioration of the mixture VLE prediction. However, the ability to yield such accurate, holistic predictions for polar components by regression using pure component data alone is a characteristic of a truly predictive model.