(231t) At the Interface Between Academic Statistical Mechanics and Industrial Process Design: Some Practical Guidelines for Equation of State Development

The quest for a fundamental understanding of the microscopic behavior of matter has been ongoing since the time of J. D. van der Waals (1873). Central to this endeavor have been equations of state (EOS’s), the most significant of which are “empirical” cubic equations of state proposed during the last half of the twentieth century (Redlich and Kwong, 1949; Soave, 1972; Peng and Robinson, 1976). Molecular-based equations of state (the statistical associating fluid theory, SAFT, models) (Huang and Radosz, 1990; Chapman et. al., 1990; and reviewed in Mueller et. al., 2001) have emerged over the past twenty-five years. However, there is a clear disconnect between industrial and academic EOS users/audiences. Industrial users favor accuracy and ease of use, where as academic parties are concerned with theoretical correctness. EOS reviews (Martin, 1979; Abbott, 1979 Wei and Sadus, 2001; Mueller and Gubbins 2001; Valderrama, 2003) clearly show the “mathematical” development of empirical (mostly cubic) EOS’s and the “theoretical” development of molecular-based (SAFT-type) EOS’s. 

What is needed is a synthesis of the mathematical simplicity of the empirical cubic EOS’s with the theoretical eloquence and correctness of the molecular-based EOS’s. We present a systematic approach based on the decomposition of the Helmholtz free energy into a sum of contributions due to individual effects (repulsion, dispersion, chain formation and hydrogen bonding) for designing new EOS’s to meet the entire range of objectives. First, we show that developing new models should start with accurate description of pure fluid volumetric properties and include restrictions regarding the correct limiting ideal gas compressibility factor and segment hard sphere radial distribution function at contact value. We show that mathematically simple terms (leading to an overall cubic or quartic EOS) can be developed for these effects. Furthermore, we reformulate the “thermodynamic perturbation theory” (TPT) framework to permit simple EOS development from various forms of the radial distribution function at contact value (Lennard-Jones, Yukawa, square-well, etc.).  Moreover, we also present theoretical guidelines for developing EOS mixing and combining rules. Several practical examples from our our work are given in this talk to illustrate the above features.

REFERENCES

Abbott, M. M., Cubic Equations of State: An Interpretive Review, Advances in Chemistry, 182, Chapter 3, 47-70 (1979).

Chapman, W. G., K. E. Gubbins, G. Jackson and M. Radosz, New Reference Equation of State for Associating Liquids, Ind. Eng. Chem. Res. 29, 1709-1721 (1990).

Huang, S. H. and M. Radosz, Equation of State for Small, Large, Polydisperse and Associating Molecules, Ind. Eng. Chem. Res., 29, 2284-2294 (1990).

Martin, J. J., Cubic Equations of State – Which?, Ind. Eng. Chem. Fundam., 18, 81-97 (1979).

Mueller, E. A. and K. E. Gubbins, Molecular-Based Equations of State for Associating Fluids: A Review of SAFT and Related Approaches, Ind. Eng. Chem. Res., 40, 2193-2211 (2001).

Peng, D.-Y. and D. B. Robinson, A New Two-Constant Equation of State, Ind. Eng. Chem., 15, 59-64 (1976).

Redlich, O. and J. N. S. Kwong, On the Thermodynamics of Solutions. V. An Equation of State. Fugacities of Gaseous Solutions, Chem. Rev. 44, 233-244 (1949).

Soave, G. Equilibrium Constants from a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci., 27, 1197-1203 (1972).

Valderrama, J. O., The State of Cubic Equations of State, Ind. Eng. Che. Res., 42, 1603-1618 (2003).

van der Waals, J. D., Over de Continuiteit van den Gas- en Vloeistoftoestand (On the Continuity of the Gas and Liquid State). Ph.D. thesis, Leiden, The Netherlands, (1873).

Wei, Y. S. and R. J. Sadus, Equations of State for the Calculation of Fluid Phase Equilibria, AIChE J., 46, 169-196 (2000).