Hope College Department of Physics and Engineering Research Experiences for Undergraduates Summer 2003 Project Summary

Project Title: Evaluation of Series Coefficients for the Peng-Robinson Equation.
Student Name: David Schaich
Student’s home institution: Amherst College
Research Advisor(s): Dr. Michael Misovich
Source of Support: NSF-REU
 

In chemical process design and many other fields, engineers require general methods for predicting the physical properties of various substances. Equations of state - functional relationships among the variables pressure, volume and temperature - are powerful tools for generating such predictions. Cubic equations of state such as the Peng-Robinson equation are particularly useful. While maintaining a relative simplicity, cubic equations of state are still capable of describing substances in both liquid and vapor phases. As a result, they can be used to predict vapor-liquid equilibrium properties such as vapor pressure, heat of vaporization, enthalpy departure and various other results.

It is possible to expand cubic equations of state as analytic power series in density and temperature around the critical point. The expansion for vapor pressure makes use of dimensionless deviation variables for density and temperature and involves mixed partial derivatives of reduced pressure with respect to the deviation variables. Requiring thermodynamic consistency produces a relationship among the partial derivatives that can be used to simplify the series. Additional simplification comes from replacing the density deviation terms with a power series in temperature deviation. After this simplification, the vapor pressure can be expressed as a series in temperature deviation, whose coefficients (Aj) are functions of known partial derivatives of pressure and unknown coefficients (Bi) of the density deviation series.

The goal of my research was to determine the coefficients for the vapor pressure series corresponding to the Peng-Robinson equation, considering only pure substances (i.e., not mixtures). To accomplish this it was necessary to calculate the coefficients of the density deviation series as well. Using programs written with the Maple mathematical software package I was able to calculate series coefficients for density up through the 12th order in temperature (B24) and for vapor pressure up through the 13th order in temperature (A13). These results have been successfully tested and checked for errors; they are available online at: http://www.amherst.edu/~daschaich/reu2003/results.htm.

Slide show of David Schaich's work (Requires Microsoft PowerPoint or a PowerPoint viewer.)