(149b) A Molecular Thermodynamic Perturbed Hard-Sphere Chain Cubic Equation of State for Hydrocarbons

Chemical process design requires simple and reliable equations of state. Popular cubic equations of state (Redlich and Kwong, 1949; Soave, 1973; Peng and Robinson, 1976) are commonly used owing to their simple form and three well-defined molar volume roots. However, while these EOS’s are fairly successful for many simple pure fluids, application at extreme conditions, or to complex pure fluids or mixtures containing associating components is problematic. Specifically, both the repulsive and attractive term in these equations of state are sufficiently flawed such that poor estimates of liquid density (molar volume) and mixture phase equilibria are typically obtained.

Conversely, accurate molecularly-based equations of state, the statistical associating fluid theory (SAFT) equations (Huang and Radosz, 1990; Chapman et. al., 1990), which incorporate individual molecular effects (i.e., hard-sphere repulsion, London dispersion, covalent bond chain formation, multipolar forces and hydrogen bonding) have successfully emerged in the past two decades. While these EOS’s capture the major molecular level effects, there are mathematical difficulties including convergence problems and the existence of many molar volume roots (making it hard to identify the true liquid and vapor molar volume roots), which complicate process design.

Consequently, a research program has evolved to systematically study, characterize and incorporate the molecular level effects described above into a new accurate statistical-mechanically based EOS, which is cubic in molar volume. Specifically, molecular simulation data for hard-sphere compressibility factor is nearly exactly fit to a simple empirical function in packing fraction, which ensures an overall cubic in molar volume equation of state and obtains two universal parameters (applicable to all fluids and fluid mixtures). Furthermore, hard-sphere London dispersion attractive forces are described by an extremely simple polynomial refit of data generated for Chen and Kreglewski’s (1977) thirty-six term double sum in reciprocal absolute temperature and packing fraction.

Finally, chain formation (covalent bond formation) is described by a modified form of Wertheim’s (1984) thermodynamic first-order perturbation theory (TPT1) for segment covalent bonding, in which a diimer reference radial distribution function is employed to obtain more accurate results. Conventional forms of the hard-dimer radial distribution function (Chiew, 1991; Yethiraj and Hall, 1992; Ghonasgi and Chapman, 1994; Sadus, 1999) are refit to a novel empirical functional form which results in an equation of state which is overall cubic in molar volume.

The resulting molecular thermodynamically-based EOS is applied to predict the compressibility factor versus packing fraction isotherms, the vapor-liquid coexistence curves and the second-virial coefficient versus temperature for nonpolar and slightly polar chain, branched and cyclic alkanes and alkenes. The results are generally superior to results obtained from conventional cubic equations of state and about equivalent to the results obtained using the more complex non-cubic SAFT equations of state for the same fluids but with much less computational effort. Ongoing work involves developing mixing rules for multicomponent mixtures of simple nonpolar chain molecules; adding dipolar groups to the hydrocarbon chains (inclusion of hydrofluorocarbons), and ultimately introducing hydrogen-bonding species.

REFERENCES

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Chen, S. S. and A. Kreglewski, Applications of the Augment van der Waals Theory of Fluids: I. Pure Fluids, Berichte der Bunsengesellschaft fur Physikalische Chemie, 81, 1048-1052 (1977).

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