Thesis (PhD)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: In this study an equation of state has been developed for the specific purpose of representing
systems of simple non-polar spherical and chain-like components and their mixtures for
practical applications. To be applied in engineering calculations, the model has to be accurate,
be able to represent mixtures with large size asymmetry without the use large binary
interaction parameters, and be mathematically simple enough to ensure rapid computations.
The model is developed through a sequential evaluation of the statistical mechanical theory of
particles and the various approaches available to extend it to real fluid systems.
The equation of state developed in this work models the real fluid systems as interacting with a
highly simplified two step potential model. The repulsive interactions are represented by a
newly developed simplified form of the hard sphere equation of state, capable of representing
the known hard sphere virial coefficients and phase behaviour to a high degree of accuracy.
This equation has a realistic closest packed limiting density in between the idealised hard
sphere fluid random and crystal structure limits. The attractive interactions between the
particles are incorporated into the model through a perturbation expansion represented in the
form of a double summation perturbation approximation. The perturbation matrix was
optimised to have the lowest order in density necessary to still be able to accurately represent
real fluid properties. In a novel approach to obtain simple mixing rules that result in the
theoretically correct second virial coefficient composition dependence, the perturbation matrix
is constrained in such a manner that only the first perturbation term has a term that is first
order in density. From a detailed evaluation of the various methods available to represent
chain-like non-spherical systems it was finally concluded that the Perturbed Hard Chain
Theory provided an ideal compromise between model simplicity and accuracy, and this
method is used to extend the equation to chain-like systems. Finally the model is extended to
fluid mixtures by uniquely developed mixing rules resulting in the correct mixture composition
dependence both at low and high system densities.
The newly developed equation of state is shown to be capable of representing the pure
component systems to a comparable degree of accuracy as the generally applied equations of
state for non-spherical systems found in the literature. The proposed equation is furthermore
also shown equal or improve on the predictive ability of these models in the representation offluid mixtures consisting out of similar chainlike or size and energetic asymmetric
components.
Finally, the computational time required to model the behaviour of large multi-component
fluid mixtures using the new equation of state is significantly shorter that that of the other
semi-empirical equations of state currently available in the literature. / AFRIKAANSE OPSOMMING: Hierdie werkstuk behels die ontwikkeling van ‘n toestandsvergelyking wat spesifiek gerig is
op toepassings in alledaagse, praktiese ingenieurstipe berekeninge en daartoe instaat is om
sisteme bestaande uit nie-polêre spferiese- en ketting-tipe komponente en hulle mengsels teKettingteorie (PHCT) die mees geskikde metode is vir hierdie doel en is op die vergelyking
toegepas.
As ‘n laaste stap in die toestandsvergelykingontwikkelling is daar mengreëls ontwikkel vir die
vergelyking wat die korrekte samestellingsafhanklikheid toon vir beide die lae en hoë
digtheidskondisies.
Die model wat in hierdie studie ontwikkel is, is met verskeie ander bekende
toestandsvergelykings, wat daartoe instaat is om nie-spferiese sisteme te modelleer, vergelyk
en daar is gevind dat die nuwe model daartoe instaat is om suiwer sisteme net so goed as die
bestaande vergelykings te modelleer. Verder is daar ook gevind dat die nuwe vergelyking die
modellering van verskeie mensels van kettingtipe komponente en komponente van
uiteenlopende groottes of interaksie energieë kan ewenaar of verbeter.
Laastens is daar ook gevind dat die tyd nodig vir die modellering van die termodinamiese
gedrag van mengsels van ‘n groot hoeveelheid komponente aansienlik korter is vir die nuwe
model as die ander bekende semi-empiriese vergelykings.
kan beskyf. Om aan hierdie vereistes te voldoen moet die toestandsvergelyking die relevante
sisteme akkuraat kan modelleer, slegs klein interaksie parameters benodig om mengsels van
komponente met groot verskille in molekulêre groottes akkuraat voor te stel en steeds
wiskundig eenvoudig genoeg wees om vinnige berekeninge te verseker.
Die vergelyking is ontwikkel deur ‘n sistematiese evaluering van die statisitiese meganiese
teorie van partikels en die verskillende metodes om hierdie teorië op werklike sisteme toe te
pas.
Die toestandsvergelyking beskryf die intermolekulêre interaksie tussen die verskillende
komponente met ‘n hoogs vereenvoudigde twee-stap interaksie potensiaal model. Die
afstotende kragte tussen die komponente word in ag geneem deur ‘n nuwe vergelyking wat
ontwikkel is om die gedrag van ‘n ideale harde spfeer sisteem te modelleer. Hierdie
hardespfeermodel is daartoe instaat om die viriale koeffisiënte en die fase gedrag van
teoretiese harde spfeer sisteme akkuraat te modelleer, en het ‘n maksimum digtheidslimiet wat
tussen teoretiese waardes van ‘n perfek geordende en nie-geordende harde spheer sisteem lê.
Die aantrekkinskragte tussen die partikels word beskou as ‘n perturbasie van die harde-spheer
vergelyking. ‘n Term bestaande uit ‘n dubbelle sommasiefunksie word gebruik om hierdie
perturbasie uitbreiding voor te stel. Die sommasie term is geoptimiseer sodat die finale
toestandsvergelyking die laagste digtheidsgraad het wat steeds tot ‘n akkurate voorstelling van
die termodinamiese gedrag van werklike sisteme lei. Die sommasiefunksie is so gespesifiseer
dat die eerste term van die perturbasie uitbreiding slegs ‘n eerste graadse orde in digtheid het in
‘n unieke benadering om te verseker dat die mengreëls van die toestandsvergelyking die
teoreties korrekte samestellingafhanklikheid van die mengselvirialekoeffisiente tot gevolg het.
‘n Deeglike ondersoek van die verskillende metodes om die toepassing van die
toestandsvergelyking uit te brei tot die moddellering van nie-spheriese ketting-tipe molekules
is gedoen en daar is uiteindelik tot die gevolgtrekking gekom dat die Geperturbeerde Harde
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/16043 |
| Date | 12 1900 |
| Creators | Du Rand, Marlie |
| Contributors | Nieuwoudt, I., University of Stellenbosch. Faculty of Engineering. Dept. of Process Engineering. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | xxvi, 361 leaves : ill. |
| Rights | University of Stellenbosch |
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