Modeling Vapor–Liquid Eguilibria: Cubic Equations of State and Their Mixing Rules
Satyro, Marco A
Modeling Vapor-Liquid Equilibria: Cubic Equations of State and Their Mixing Rules
Hasan Orbey and Stanley I. Sandler Cambridge University Press, New York, 207 pp., $80,1998
Thermodynamics is a strange and wonderful discipline. Although based on rigorous mathematics, the problems it solves require a considerable degree of ingenuity and creativity, in which individuals and their styles come through. In 1992, I was lucky enough to be in a scientific meeting where Jean Vidal and Stan Sandler debated about the virtues of their mixing rules with openness and passion. Watching these two engineers arguing their points in an honest scientific debate was a wonderful experience, and it was with pleasure then that I undertook the task of reviewing Orbey and Sandler’s new monograph on equations of state and their mixing rules.
This book is written for the practicing engineer, and was motivated by a need perceived by the authors to show the potential of combining a cubic equation of state and Gibbs excess (activity coefficient) models. This work compares the performance of several different approaches for the combination of Gibbs excess models and cubic equations of state, including important considerations for process calculations, such as temperature extrapolation, performance in the low-concentration ranges and use of group contribution methods like UNIFAC in conjunction with cubic equations of state.
The use of cubic equations of state is not new for process engineers, especially those in the natural gas and petroleum refining industries. Nevertheless, the convenience of having a flexible model for the representation of strong liquidphase using an equation of state is not always recognized by users of activity coefficient models. For example, an equation of state with good mixing rules can provide vapor/liquid equilibrium information, but also volumetric and calorimetric properties, as well as natural handling of supercritical conditions. These characteristics are more and more important as synthesis and separation processes are modeled together for economic reasons, and a uniform model for high and low pressure conditions is of evident value.
After a brief Introduction, Chapter 2 presents a short, but adequate, review of phase equilibrium thermodynamics. Casual readers may be advised on not taking the authors’ view on regular solution theory too strictly, since it is more useful than they suggest. Chapter 3 presents an adequate discussion of quadratic mixing rules for cubic equations of state. A few examples to show the applicability of simple mixing rules are presented, as well as some of the empirical modifications, and some of their mathematical inconsistencies, such as the Michelsen-Kistenmacher syndrome.
Chapter 4 is the core of Orbey and Sandler’s monograph. In it, the Huron-Vidal and Wong-Sandler methods for Gibbs excess matching at infinite pressure are presented, as well as Michelsen’s approach for zero pressure matching and Boukouvalas’ hybrid method. Each method is illustrated with examples using several nonideal mixtures. Of note is Orbey and Sandler’s modification to the Wong-Sandler mixing rule, which can be used to emulate quadratic mixing rules for almost ideal mixtures (an obvious advantage for refinery or petrochemical applications). Surprisingly, the work of Heidemann and Kokal is not mentioned. Chapter 5 provides examples on how to use the Gibbs excess mixing rules using group contribution methods, specifically UNIFAC. A brief mention on the use of Gibbs excess mixing rules for modeling mixtures of condensable components with super critical gases is presented, but, unfortunately, a revision of Soave’s more recent group contribution method is missing.
The book concludes with some thoughts on the use of Gibbs excess mixing rules, including important problems such as high-dilution and polymer/solvent systems. The discussion on the implication of using Gibbs excess mixing rules for representation of derived thermodynamic properties is rather incomplete, and does not mention the fact that some of the Gibbs excess mixing rules change the shape of the Gibbs excess function when compared against the original Gibbs excess function, which, in turn, may have important consequences for process design. The interested reader can find a good part of the missing material in the works of Heidemann, Satyro and Trebble, and Coutsikos. The exact vintage of the UNIFAC method used in the calculations is not identified in the text, and it would be a welcomed addition to the work. It also would be useful if Appendix B could be rewritten using a general shape for cubic equations of state instead of casting most of the equations in the Peng-Robinson format.
The appendices provide useful computer programs for the calculation of vapor/liquid equilibrium and have several tutorials to guide the reader to their proper use, providing a convenient background for the development of other programs.
Marco A. Satyro
M. A. Satyro is president of SEA++ Inc., Calgary, AL, Canada.
Copyright American Institute of Chemical Engineers Aug 2000
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