Understanding cubic equations of state: A search for the hidden clues of their success

• Published in: AIChE journal Vol. 61; no. 9; pp. 2824 - 2831
• Main Authors: Wilczek-Vera, Grazyna, Vera, Juan H.
• Format: Journal Article
• Language: English
• Published: New York Blackwell Publishing Ltd 01.09.2015; American Institute of Chemical Engineers
• Subjects: Algorithms; Chemical engineering; Chemical engineers; Compressibility; Cubic equations; Density; design; design (process simulation); Exploration; Liquids; Mathematical analysis; phase equilibrium; Temperature dependence; Temperature effects; Thermodynamics; thermodynamics/classical
• ISSN: 0001-1541; 1547-5905
• DOI: 10.1002/aic.14741

This work investigates the hidden details that are responsible for the practical success of cubic equations of state (EOS) in phase equilibrium calculations. A detailed consideration of the van der Waals method for evaluating the pure compound EOS parameters sheds new light on the reasons why the elimination of the actual critical volume as parameter was also adopted in the Redlich–Kwong and the Peng–Robinson (PR) frameworks. It is shown that an interesting relationship for the critical compressibility factor arising from the Martin–Hou method opens a new door for future exploration of different frameworks. A consideration of the key steps of Soave's reasoning for determining the temperature dependence of the attractive parameter explains the larger success of the Stryjek–Vera modification of PR EOS over the PR EOSs. A reference to the extension of cubic EOS to calculate liquid densities and enthalpies and a ready to use algorithm for the evaluation of the roots of a cubic equation are included for instructional purposes. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2824–2831, 2015