#### Location

Cherry Auditorium, Kirk Hall

#### Start Date

2-23-2012 1:00 PM

#### Description

Classical engineering cubic equations of state (e.g., Soave-Redlich-Kwong and Peng-Robinson EOS) present difficulties when applied to systems at extreme conditions or which contain associating components. Conversely, molecularly-based equations of state (i.e., statistical associating fluid theory EOS and its many variants) are much more accurate when successfully applied to such systems; however, their application is computationally complex due to their large number of molar volume roots and nested iterations. An optimum solution to this dilemma is to develop a formalism for design of equations of state which retain the computationally attractive cubic in molar volume form while incorporating the rich molecular level behavior of the species involved.

This talk will investigate one such route to obtaining a molecularly-based cubic EOS. Molecules are considered (as in the SAFT approach) to be made of bonded segments (chains), which undergo repulsive, dispersive, and structure-dependent multi-polar and associative interactions with each other. A simple molecular theory is used for each contribution to the Helmholtz free energy, which remarkably results in an equation of state which is cubic in molar volume. The repulsive contribution to the compressibility factor is obtained from an exact fit of hard-sphere molecular simulation data. Moreover, this simple expression produces a self-consistent analytical form of the reference hard-sphere fluid radial distribution function (RDF), which is used with the square-well intermolecular potential to obtain analytical solutions to the perturbation integrals for dispersion and dipole-dipole interactions. Furthermore, Wertheim’s (first thermodynamic perturbation theory) TPT1 is applied to the reference fluid RDF to obtain an expression for the Helmholtz free energy of chain formation. A variation of scaled-particle theory, which accounts for the low density, energy and entropy environment and orientational dependence of hydrogen bonding, is proposed for association. Finally, some typical results for pure fluids are presented, and recommendations for future work are discussed.

A Molecularly Constructed Cubic Equation of State for Simple and Complex Fluids

Cherry Auditorium, Kirk Hall

Classical engineering cubic equations of state (e.g., Soave-Redlich-Kwong and Peng-Robinson EOS) present difficulties when applied to systems at extreme conditions or which contain associating components. Conversely, molecularly-based equations of state (i.e., statistical associating fluid theory EOS and its many variants) are much more accurate when successfully applied to such systems; however, their application is computationally complex due to their large number of molar volume roots and nested iterations. An optimum solution to this dilemma is to develop a formalism for design of equations of state which retain the computationally attractive cubic in molar volume form while incorporating the rich molecular level behavior of the species involved.

This talk will investigate one such route to obtaining a molecularly-based cubic EOS. Molecules are considered (as in the SAFT approach) to be made of bonded segments (chains), which undergo repulsive, dispersive, and structure-dependent multi-polar and associative interactions with each other. A simple molecular theory is used for each contribution to the Helmholtz free energy, which remarkably results in an equation of state which is cubic in molar volume. The repulsive contribution to the compressibility factor is obtained from an exact fit of hard-sphere molecular simulation data. Moreover, this simple expression produces a self-consistent analytical form of the reference hard-sphere fluid radial distribution function (RDF), which is used with the square-well intermolecular potential to obtain analytical solutions to the perturbation integrals for dispersion and dipole-dipole interactions. Furthermore, Wertheim’s (first thermodynamic perturbation theory) TPT1 is applied to the reference fluid RDF to obtain an expression for the Helmholtz free energy of chain formation. A variation of scaled-particle theory, which accounts for the low density, energy and entropy environment and orientational dependence of hydrogen bonding, is proposed for association. Finally, some typical results for pure fluids are presented, and recommendations for future work are discussed.

## Comments

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