Applying a Low Temperature Limit of a Cubic Equation of State to Model Pure Component Phase Equilibrium

Caitlin A. Kowalsky1, Joshua L. Lanser1, Emily J. Walsh2, Kimberly Wadelton1, and Michael J. Misovich1. (1) Engineering, Hope College, 27 Graves Pl, Holland, MI 49422-9000, (2) SmartSignal Corporation, 901 Warrenville Road, Suite 300, Lisle, IL 60532

Equations of state may be used to calculate pure component vapor-liquid equilibrium properties such as vapor pressure, heat of vaporization, liquid density, and vapor density. The standard approach requires coupling the EOS with a phase equilibrium criterion such as free energy, chemical potential, or fugacity. The resulting equations are nonlinear and must be solved by numerical methods.

An alternative approach is applicable to cubic EOS such as the commonly used Soave-Redlich-Kwong and Peng-Robinson equations. Equilibrium properties may be explicitly expressed as power series in reduced temperature or related functions. These results are more convenient than numerical calculations, but the series diverge and become unbounded at low to moderate temperatures away from the critical point.

An alternative method was developed using a series expansion in a low temperature limit rather than the critical point limit. Although the limiting behavior itself was unphysical because it fell below the triple point of the substance, the expressions remained convergent over a very wide range of temperatures and they remained bounded over all temperatures from zero to the critical point. Dimensionless results for equilibrium properties such as vapor pressure and liquid density were determined as general expressions of the acentric factor of a substance. The deviations between these results and the exact equilibrium property predictions from the EOS were quantitatively characterized.