Evaluation and improvement of the sPC-SAFT equation of state for complex mixtures.

De Villiers, Adriaan Jacobus (Stellenbosch : Stellenbosch University, 2011-12)

Thesis

ENGLISH ABSTRACT: Efficient process design commonly relies on equation-of-state (EOS) models to provide reliable estimates of thermodynamic properties. The accuracy of EOS models, in turn, depends on the extent to which they account for intermolecular forces. The aim of this project was to improve the simplified Perturbed Chain - Statistical Associating Fluid Theory (sPC-SAFT), enabling it to account more accurately for complex molecular interactions. The more simple SAFT-based Cubic-Plus-Association (CPA) model was evaluated along similar lines for comparative purposes. A literature review showed that both sPC-SAFT and CPA have been widely applied in phase equilibria problems, but not extensively for the prediction of other thermodynamic properties. Consequently, an initial evaluation was performed on the ability of sPC-SAFT and CPA to predict first- and second-order thermodynamic properties. The properties of non-polar, polar and hydrogen bonding fluids were considered, showing that: a) sPC-SAFT and CPA generally predict first-order properties with the same accuracy, but sPC-SAFT provides improved predictions of second-order properties. Significant errors are, however, still observed with sPC-SAFT. b) A parameter regression study with sPC-SAFT, using model parameters obtained by including second-order properties in the regression function, results in poor predictions of the saturated vapour pressure and liquid density. c) Treating strong polar and dispersive forces together as Van der Waals forces results in many properties being poorly predicted by both sPC-SAFT and CPA. d) The major limitation of the association term in both CPA and sPC-SAFT is its inability to account for the influence of bond co-operativity, especially in alcohol/water mixtures. Based on these findings, the following improvements could be made: a) The development of a new association scheme for 1-alcohols, denoted the 2C association scheme. b) The extension of sPC-SAFT with the polar theories of Jog & Chapman (JC) and Gross & Vrabec (GV) to obtain sPC-SAFT-JC and sPC-SAFT-GV. c) The extension of CPA with modified versions of the aforementioned polar theories to obtain CPA-JC and CPA-GV. d) The development of a new ‘universal’ cross-association approach. The new 2C association scheme consists of one bipolar association site and one negative electron donor site and is a combination of the 1A and 2B/3B association schemes. Modelling 1-alcohols with the 2C scheme in sPC-SAFT results in improved VLE predictions of alcohol/water and alcohol/alcohol mixtures, but alcohol/alkane VLE is predicted less accurately compared to the 2B and 3B association schemes. sPC-SAFT-JC and sPC-SAFT-GV provide improved VLE predictions of mixtures with non-associating polar components compared to sPC-SAFT. VLE of polar/alkane and polar/polar systems can be represented accurately with no or only very small binary interaction parameters (BIPs). CPA-JC and CPA-GV also enable improved VLE predictions of the polar/alkane and polar/polar mixtures compared to CPA. sPC-SAFT-GV and sPC-SAFT-JC were also applied to several mixtures of associating components including alcohol/alkane, alcohol/alcohol and alcohol/water systems. New alcohol model parameters for both sPC-SAFT-GV and sPC-SAFT-JC based on the 2C, 2B and 3B association schemes were determined. The predictions of both sPC-SAFT-GV and sPC-SAFT-JC, based on any of the three association schemes, provide similar alcohol/alkane and alcohol/alcohol VLE representations, but the best phase equilibria predictions of water/alcohol systems are obtained when alcohols are modelled with the newly proposed 2C association scheme. The usefulness of a new ‘universal’ cross-association approach was demonstrated with both sPC-SAFT-GV and sPC-SAFT-JC. The philosophy behind the new approach is to set the association volume value of the solvating component equal to the cross-associating volume value of the 1-alcohol of the same molecular size and to determine an association energy value from binary VLE data. This approach aims to characterize the solvating behaviour of the cross-associating component. Preliminary results are demonstrated with systems containing acetone, propyl formate and ethyl acetate. Other thermodynamic properties, such as excess enthalpy and excess volume can be described with the new polar sPC-SAFT and CPA models. In the majority of cases, improvements are observed compared to the normal sPC-SAFT and CPA models, but BIPs are still required to obtain accurate correlations. However, these BIPs cannot be used in phase equilibria calculations and are generally property-specific. To summarise: Through the development of the 2C scheme, and the incorporation of polar terms into the sPC-SAFT model structure, notable improvement in the VLE predictions of polar (nonhydrogen bonding)/alkane, alcohol/alkane, alcohol/water and polar/alcohol systems could be obtained if compared to the original sPC-SAFT EOS. As such, the research pesented in this thesis encapsulates some significant novel contributions, viz.: a) A systematic evaluation of sPC-SAFT and CPA, providing better insight into their ability to predict thermodynamic properties. b) The development of the new 2C association scheme for 1-alcohols, as published in Ind. Eng. Chem. Res. 2011, 50, 8711–8725. c) The extension of sPC-SAFT with the polar theories of JC and GV, with application to non-associating components, as published in Fluid Phase Equilib. 2011, 305, 174–184. d) The extension of CPA with the JC and GV polar theories, as published in Fluid Phase Equilib. 2011, 312, 66–78. e) The application of sPC-SAFT-GV and sPC-SAFT-JC to associating components, including results with the new 2C association scheme. f) The development of the new ‘universal’ cross-association approach.

AFRIKAANSE OPSOMMING: Doeltreffende prosesontwerp steun grotendeels op toestandvergelykings (EOS) om goeie skattings van vloeistofeienskappe te voorspel. Die akkuraatheid van hierdie modelle word bepaal deur hoe goed hulle die invloed van molekulêre kragte kan naboots. Die doel van hierdie projek was dus om die ‘simplified Perturbed Chain-Statistical Associating Fluid Theory’ (sPC-SAFT) te verbeter, sodat dit komplekse molekulêre kragte beter kan beskryf. Die meer vereenvoudigte SAFT-gebaseerde ‘Cubic-Plus-Association’ (CPA) model was ook geëvalueer vir vergelykende doeleindes. 'n Literatuurstudie het getoon dat beide sPC-SAFT en CPA reeds wyd toegepas is in fase ewewig probleme, maar nie vir ander termodinamiese eienskappe nie. Gevolglik, is 'n aanvanklike ondersoek uitgevoer waarin die vermoë van sPC-SAFT en CPA om eerste- en tweede-orde termodinamiese eienskappe te voorspel, geëvalueer is. Die eienskappe van nie-polêre, polêre en waterstof-bindinde komponente is oorweeg en die hoof bevindinge uit hierdie ondersoek is: a) sPC-SAFT en CPA voorspel oor die algemeen eerste-orde eienskappe met dieselfde akkuraatheid, maar sPC-SAFT bied verbeterde voorspellings van tweede-orde eienskappe. Beduidende foute is egter steeds teenwoordig in die voorspellings van sPC-SAFT. b) 'n Model parameter regressie studie met sPC-SAFT het getoon dat deur tweede-orde eienskappe ook in die regressie-funksie in te sluit, swak skattings van die eienskappe wat nodig is vir 'n goeie fase-ewewig voorspellings, verkry word. c) Die gesamentlike behandeling van sterk polêre en dispersie kragte as Van der Waals kragte, lei tot swak voorspellings van baie eienskappe deur sPC-SAFT en CPA. d) Die hoof beperking van die assosiasie term wat gebruik word deur beide CPA en sPC-SAFT, is die term se onbekwaamheid om die invloed van verbinding-samewerkings te beskryf, veral in mengsels van alkohole met water. Hierdie bevindings het as basis gedien om die volgende verbeterings aan te bring: a) Die ontwikkeling van 'n nuwe assosiasie skema vir 1-alkohole: die 2C-assosiasie skema. b) Die uitbreiding van sPC-SAFT met die polêre teorieë van Jog & Chapman (JC) en Gross & Vrabec (GV) om sPC-SAFT-JC en sPC-SAFT-GV onderskeidelik te kry. c) Die uitbreiding van CPA met gewysigde weergawes van die polêre teorieë om CPA-JC en CPA-GV te kry. d) Die ontwikkeling van ʼn nuwe ‘universele’ kruis-assosiasie benadering. Die nuut-voorgestelde 2C assosiasie skema bestaan uit een bipolêre assosiasie sone en een negatiewe elektron skenker sone en is ʼn kombinasie van die 1A en 2B/3B assosiasie skemas. Die modellering van 1-alkohole met die 2C skema in sPC-SAFT lei tot 'n verbetering in damp-vloeistof ewewig (VLE) voorspellings van alkohol/water en alkohol/alkohol sisteme, maar vir alkohol/alkaan sisteme is minder akkurate voorspellings verkry in vergelyking met die 2B en 3B assosiasie skemas. sPC-SAFT-JC en sPC-SAFT-GV lewer beter VLE voorspellings van mengsels met nie-assosiërende polêre komponente in vergelyking met sPC-SAFT. Die VLE van polêre/alkaan en polêre/polêre stelsels kan akkuraat beskryf word deur beide modelle wanneer geen of baie klein binêre interaksie parameters (BIPs) gebruik word. CPA-JC en CPA-GV lewer ook verbeterde VLE voorspellings van polêre/alkaan en polêre/polêre mengsels in vergelyking met CPA. sPC-SAFT-GV en sPC-SAFT-JC is ook toegepas op verskeie assosiërende mengsels, insluitend: alkohol/alkaan, alkohol/alkohol en alkohol/water stelsels. Nuwe alkohol parameters is vir beide sPC-SAFT-GV en sPC-SAFT-JC bepaal gebaseer op die 2C, 2B en 3B assosiasie skemas. Die voorspellings van sPCSAFT- GV en sPC-SAFT-JC, gebaseer op enigeen van die drie assosiasie skemas, lewer soortgelyke alkohol/alkaan en alkohol/alkohol VLE voorspellings, maar die beste fase-ewewig voorspellings vir water/alkohol sisteme is verkry wanneer alkohole gemodelleer word met die 2C assosiasie skema. Die nuwe ‘universele’ kruis-assosiasie benadering is gedemonstreer met beide sPC-SAFT-GV en sPC-SAFT-JC. Die filosofie agter die nuwe benadering is om die assosiasie volume waarde van die solverende komponent gelyk te stel aan die kruis-assosiasie volume waarde van die 1-alkohol met dieselfde molekulêre massa. Die assosiasie energie waarde word dan bepaal vanaf binêre VLE data. Hierdie benadering poog om die solverende gedrag van die kruis-assosiërende komponent meer akkuraat te karakteriseer. Voorlopige resultate met mengsels van asetoon, propiel formaat en etiel asetaat dui aan dat merkwaardige verbeterings in VLE voorspellings gekry word. Ander termodinamiese eienskappe, soos oortollige entalpie en oortollige volume, is ook ondersoek met die nuwe polêre sPC-SAFT en CPA-modelle. In meeste gevalle word verbeterde resultate gekry in vergelyking met die oorspronklike sPC-SAFT en CPA modelle, maar groot BIPs word steeds benodig om aanvaarbare korrelasies te kry. Hierdie BIPs kan egter nie gebruik word vir fase-ewewig voorspellings nie en is eienskap-spesifiek. Om op te som: deur die ontwikkeling van die 2C skema, en insluiting van die polêre terme in die sPC-SAFT model struktuur, is merkwaardige verbeterings in die VLE voorspellings van polêre/alkaan, alkohol/alkaan, alkohol/water en polêre/alkohol sisteme gekry in vergelyking met die oorspronklike sPC-SAFT EOS. Die navorsing voorgelê in hierdie tesis het dus gelei tot die volgende nuwe bydraes: a) Die sistematiese evaluering van die vermoë van sPC-SAFT en CPA om termodinamiese eienskappe te voorspel. b) Die ontwikkeling van die nuwe 2C assosiasie skema vir 1-alkohole soos gepubliseer in Ind. Eng. Chem. Res. 2011, 50, 8711–8725. c) Die uitbreiding van sPC-SAFT met die polêre teorieë van JC en GV soos gepubliseer in Fluid Phase Equilib. 2011, 305, 174–184. d) Die uitbreiding van CPA met die polêre teorieë van JC en GV soos gepubliseer in Fluid Phase Equilib. 2011, 312, 66–78. e) Die toepassing van hierdie nuwe modelle op assosiërende komponente, insluitend resultate met die nuwe 2C skema. f) Die ontwikkeling van ʼn nuwe kruis-assosiasie benadering.

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