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

Project Title: Series Solutions for Soave-Redlich-Kwong
Student Name: Kurt Blohm
Student's home institution: Hope College
Research Advisor(s): Dr. Misovich
Source of Support: Hope College

The purpose of this project is to improve the methods of predicting vapor pressure from temperature by a Taylor series expansion of the Soave-Redlich-Kwong cubic equation of state. Cubic equations of state, like the SRK equation, enable engineers to accurately approximate the vapor pressure of pure substances, which is very important in many process calculations.

Previous work on series expansions of the Peng-Robinson and Soave-Redlich-Kwong equations of state have shown that the accuracy of the equations depends directly on the number of terms in the Taylor series. To improve the simplicity of vapor pressure calculations, it is desirable to find a result using fewer terms without losing the accuracy of the total series.

Using algebraic relationships, the thirteen original pressure series coefficients, labeled A i , were related to a new series of coefficients, labeled A i ', which could be expanded around different temperatures. The goal of this method was to minimize the error from the original series from being far from the critical point while using fewer terms. The new series was truncated to various numbers of terms between zero and ten and expanded around various reduced temperatures to examine the accuracy. Initially there was a considerable amount of error in the new series from moving up the temperature scale and away from the expansion point. The error of the series associated with moving away from the expansion point was reduced by a correctional term that was set equal to the absolute error at the critical point.

The method was effective in reducing the number of terms for many situations. For most acentric factors, the new series truncated to five terms was as comparable in accuracy at all temperatures to the original thirteen term series and also covered a much wider temperature range than the original series having the same number of terms.