Comparing the group-contribution SAFT-γ Mie equation of state with SAFT-VR Mie

Hurter, Ruan Martin (2019-12)

Thesis (MEng)--Stellenbosch University, 2019.

Thesis

ENGLISH ABSTRACT: Group-contribution methods (GCMs) allow engineers to reduce time and other resources spent on conducting experiments for parameterisation of thermodynamic models, because GCMs grant users the ability to build new model fluids using previously parameterised functional groups (FGs). GCMs have widely been applied to semi-empirical cubic equations of state (EoS), activity coefficient models, and simpler variants of statistical associating fluid theory (SAFT) EoS, yet these models remain limited in regard to the types of systems and properties they can describe. The rigorous SAFT-VR Mie EoS has a variable-range Mie-potential reference fluid and a complex dispersion term that enable it to accurately model second-derivative dependent properties, and properties in the near-critical region, but its model parameters are specific to components. The latter trait poses a problem when no pure-component data are available. A group-contribution (GC) variant of SAFT-VR Mie, SAFT-γ Mie, was recently developed in an attempt to combine the convenience of a GC model with the holistic predictions of SAFT-VR Mie. However, this model is relatively new and prior to this investigation, effects of the GC approach in the SAFT-VR Mie framework had not been evaluated in detail. The purpose of this project was to investigate whether assumptions made by the GC approach benefit or deteriorate different applications of this complex SAFT formulation. A general comparison between SAFT-γ Mie and SAFT-VR Mie was done to identify characteristics posing a unique challenge to SAFT-γ Mie by modelling components of increasing complexity: nonpolar, non-associating n-alkanes and 1-alkenes; polar, non-self-associating n-alkyl acetates; and polar, self-associating 1-alcohols. It was found that SAFT-γ Mie is able tomodel alkanes, alkenes, and acetates accurately, but it failed to produce equally accurate results for 1-alcohols, suggesting that the modelling of small polar molecules poses a problem for SAFT-γ Mie. This notion cannot be verified without doing a comparison involving a larger sample of polar, non-self-associating components. Ketones and esters were modelled to evaluate the performance of SAFT-γ Mie for polar components. This part of the study also provided the opportunity to evaluate the performance of the pseudo-association approach used to account for dipolar interactions, as well as the consistency in modelling accuracy between linear isomers. SAFT-VR Mie with the Gross & Vrabec (GV) polar term was used as a benchmark. SAFT-γ Mie cannot distinguish between structural isomers using exactly the same functional groups; therefore, new groups were defined for 2-ketones, 3-ketones, and n-alkyl propanoates. Results mirrored the 1-alcohol results, indicating that the modelling of smaller, more polar molecules poses a challenge for SAFT-γ Mie likely due to the disregarding of proximity effects — a change in functional group characteristics based on its environment, i.e. its surrounding groups or atoms. One likely solution to the problem is to introduce second-order group contributions to act as adjustments to first-order contributions, but this empirical adjustment would reduce the model’s fundamental predictive capability. Besides proximity effects, SAFT-γ Mie also disregards structural considerations such as steric hindrance and the order of intramolecular bond formation; this is also expected to have an impact on SAFT-γ Mie’s performance. It was found that these structural considerations are vital for accurate modelling of branched alkanes, and that significant differences can be observed in properties of branched alkane isomers. While SAFT-VR Mie models all of the considered branched alkanes accurately, SAFT-γ Mie does not. It was found that the homosegmented approach followed in SAFT-γ Mie’s chain term prevents the model from making any distinctions based on a molecule’s layout. A new heterosegmented chain term was proposed: Bonding contributions would be calculated between segments of unique groups instead of between approximated molecular-average segments. Different methods for weighing the contributions of intra- and intergroup bonds were discussed. Although preliminary results suggest that a heterosegmented chain term would allow the model to distinguish between isomers, further investigation is required to evaluate the consequences of the proposed changes.

AFRIKAANSE OPSOMMING: Met behulp van groepsbydraemetodes (GCM’s) spaar ingenieurs tyd en ander hulpbronne wat op eksperimente vir die parameterisering van termodinamiese modelle bestee sou word, want GCM’s laat die gebruiker toe om nuwe vloeiers met voorheen geparameteriseerde funksionele groepe (FG’s) te bou. Die toepassing van GCM’s in semi-empiriese kubiese toestandsvergelykings (EoS), aktiwiteitskoëffisiëntmodelle en eenvoudiger weergawes van statistical associating fluid theory (SAFT) EoS is algemeen, tog bly hierdie modelle beperk ten opsigte van die tipes sisteme en eienskappe wat beskryf kan word. Die breedvoerige SAFT-VR Mie EoS maak gebruik van ’n reëlbare rekwydte Mie-potensiaal verwysingsvloeier en komplekse dispersie term wat dit in staat stel om eienskappe wat afhanklik is van tweede-orde afgeleides, asook eienskappe naby aan die kritiese gebied, meer akkuraat te voorspel. Die modelparameters is egter eie aan chemiese komponente, wat problematies is indien suiwerkomponentdata nie beskikbaar is nie. ’n Groepsbydrae (GC) weergawe van SAFT-VR Mie, SAFT-γ Mie, is onlangs ontwikkel om die gerieflikheid van ’n GC model met die holistiese modellering van SAFT-VR Mie te kombineer. SAFT-γ Mie is egter nuut, en geen vorige ondersoeke het die uitwerkings van die GC benadering in die SAFT-VR Mie raamwerk deeglik bestudeer nie. Die doel van hierdie projek was om te ondersoek of aannames wat deur die GC benadering gemaak word, verskeie toepassings van hierdie komplekse SAFT formulering bevoordeel of verswak. ’n Algemene vergelyking is tussen SAFT-γ Mie en SAFT-VR Mie getref om te bepaal watter molekulêre eienskappe uitdagings vir SAFT-γ Mie stel. Die vergelyking bestaan uit voorspellings vir komponente met toenemende kompleksiteit: niepolêre, nie-assosiërende n-alkane en 1-alkene; polêre, nie-self-assosiërende n-alkielasetate; en polêre, self-assosiërende 1-alkohole. Daar is bevind dat SAFT-γ Mie alkane, alkene, en asetate akkuraat kan modelleer, maar dat dit nie ewe akkurate resultate vir 1-alkohole lewer nie, wat moontlik aandui dat die modellering van klein polêre molekule uitdagend vir SAFT-γ Mie is. Hierdie voorstel kan egter nie bevestig word sonder om ’n vergelyking te tref met ’n groter steekproef van polêre, nie-self-assosiërende komponente nie. Ketone en esters is gemodelleer om SAFT-γ Mie se mate van akkuraatheid vir polêre komponente te evalueer. Hierdie deel van die studie het ook die geleentheid gebied om die akkuraatheid van pseudo-assosiasie, ’n benadering wat gebruik word om dipolêre interaksies in ag te neem, sowel as die konsekwentheid van modellering tussen lineêre isomere te evalueer. SAFT-VR Mie met die Gross & Vrabec (GV) polêre term is as maatstaf gebruik. SAFT-γ Mie kan nie onderskei tussen strukturele isomere wat presies dieselfde FG’s gebruik nie, daarom is nuwe groepe vir 2-ketone, 3-ketone, en n-alkielpropanoate gedefinieer. Resultate weerspieël die resultate van 1-alkohole, wat aandui dat die modellering van kleiner, meer polêre molekule moontlik ’n uitdaging vir SAFT-γ Mie is omdat nabyheidseffekte nie in ag geneem word nie. Nabyheidseffekte verwys na ’n verandering in die eienskappe van ’n FG as gevolg van interaksies met omliggende groepe. ’n Moontlike oplossing vir die probleem is om tweede-orde groepsbydraes by te voeg om die eerste-orde groepsbydraes aan te pas, maar hierdie empiriese aanpassing sal die model se fundamentele voorspellingsvermoë verminder. SAFT-γ Mie ignoreer ook strukturele oorwegings soos steriese verhindering en die orde van intramolekulêre verbindings; dit sal na verwagting ook ’n uitwerking op SAFT-γ Mie se voorspellingsvermoë hê. Daar is bevind dat die bogenoemde strukturele oorwegings noodsaaklik is om vertakte alkane akkuraat te modelleer, en dat beduidende verskille tussen die eienskappe van vertakte alkaan-isomere waargeneem kan word. SAFT-VR Mie kan al die vertakte alkane akkuraat modelleer, maar SAFT-γ Mie kan nie. Die homogesegmenteerde benadering wat in SAFT-γ Mie se kettingterm gevolg word, verhoed dat die model onderskeidings op grond van molekulêre uitleg maak. ’n Nuwe heterogesegmenteerde kettingterm is voorgestel: Die bydraes van intramolekulêre verbindings word sodoende tussen unieke groepe, in plaas van beraamde gemiddelde molekulêre segmente, bereken. Verskillende metodes om die bydraes van intra- en intergroepverbindings te weeg, is bespreek. Alhoewel voorlopige resultate dui dat ’n heterogesegmenteerde kettingterm die model sal toelaat om tussen isomere te onderskei, is verdere ondersoek nodig om die uitwerkings van die voorgestelde veranderinge te evalueer.

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