Practical equation of state for non-spherical and asymmetric systems

[摘要] ENGLISH ABSTRACT: In this study an equation of state has been developed for the specific purpose of representingsystems of simple non-polar spherical and chain-like components and their mixtures forpractical 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 binaryinteraction parameters, and be mathematically simple enough to ensure rapid computations.The model is developed through a sequential evaluation of the statistical mechanical theory ofparticles 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 ahighly simplified two step potential model. The repulsive interactions are represented by anewly developed simplified form of the hard sphere equation of state, capable of representingthe 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 hardsphere fluid random and crystal structure limits. The attractive interactions between theparticles are incorporated into the model through a perturbation expansion represented in theform of a double summation perturbation approximation. The perturbation matrix wasoptimised to have the lowest order in density necessary to still be able to accurately representreal fluid properties. In a novel approach to obtain simple mixing rules that result in thetheoretically correct second virial coefficient composition dependence, the perturbation matrixis constrained in such a manner that only the first perturbation term has a term that is firstorder in density. From a detailed evaluation of the various methods available to representchain-like non-spherical systems it was finally concluded that the Perturbed Hard ChainTheory provided an ideal compromise between model simplicity and accuracy, and thismethod is used to extend the equation to chain-like systems. Finally the model is extended tofluid mixtures by uniquely developed mixing rules resulting in the correct mixture compositiondependence both at low and high system densities.The newly developed equation of state is shown to be capable of representing the purecomponent systems to a comparable degree of accuracy as the generally applied equations ofstate for non-spherical systems found in the literature. The proposed equation is furthermorealso 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 asymmetriccomponents.Finally, the computational time required to model the behaviour of large multi-componentfluid mixtures using the new equation of state is significantly shorter that that of the othersemi-empirical equations of state currently available in the literature.

[发布机构] Stellenbosch University