Hope College Department of Physics and Engineering Research Experiences for Undergraduates Summer 2004 Project Summary

Project Title: Phase equilibrium predicted by the Soave-Redlich-Kwong equation at low temperatures
Student Name: Kimberly Wadelton
Student's home institution: Sweet Briar College
Research Advisor(s): Dr. Michael Misovich
Source of Support: NSF-REU

The objective of this study was to develop vapor-liquid equilibrium relationships for vapor pressure and liquid density predicted by the Soave-Redlich-Kwong cubic equation of state (SRK) in the low temperature limit. This extended previous work which determined similar relationships in the high temperature limit near the vapor-liquid critical point. A secondary objective was to describe phase equilibrium from zero to the critical temperature.

Dimensionless reduced variables were defined to simplify calculations. In a novel approach, reduced density was defined by dividing the actual density by liquid density in the zero temperature limit; reduced temperature and pressure were defined in the standard way by dividing by the value of the variable at the critical point.

Vapor pressures and phase densities were calculated numerically using an iterative regula falsi procedure to determine the pressure at which liquid and vapor fugacities were equal. The method gave accurate and efficient calculations for reduced temperatures from approximately 0.0002 to approximately 0.9999.

By manipulating these numerical data for reduced pressure and reduced temperature, functional relationships were suggested. Most of these were verified analytically by equating liquid and vapor fugacities in the zero temperature limit, although the process was involved due to the presence of several indeterminate forms in the equations. As part of this process, a useful form of the SRK equation was developed in the reduced variable set described above. Finally, results of the predictive equations for reduced pressure were compared to the numerical results and found to differ at worst within order of magnitude over the entire temperature range from zero to the critical point.

Further investigation of the relationships among vapor pressure, density, and temperature in the low temperature limit is suggested, along with modeling of the difference between the predictive equations and the actual SRK results.