(574f) A Wertheim Activity Coefficient Model for Associating Mixtures

Accurate, robust thermodynamic models are essential for the design of separation equipment. Models must represent highly non-ideal solutions often encountered in industrial applications. With global interest in biofuels on the rise, these types of solutions are now more ubiquitous than ever and hence there is a demand for more accurate models to handle solutions containing polar components. Traditional models, such as NRTL[1], do not capture hydrogen bonding (or association) explicitly but instead use large dispersion parameters to empirically mimic its effects. Methods that do explicitly account for the association often do so through chemical theory or Wertheim’s theory[2–5]. In our previous work[6], we relate the constants in these two methods and develop a new generalized expression for self-associating systems.

Wertheim’s theory has been incorporated into a number of models as a means of calculating non-ideality due to association. Equations of state (EOS) have traditionally been the approach of choice and models such as SAFT[3], CPA[8] and ESD[9] have been used to represent a range of industrially important systems. However, the accuracy of an EOS hinges on its ability to simultaneously fit both vapor pressure and excess Gibbs energy data. In contrast, activity coefficient model parameters are fitted only to excess Gibbs and are therefore more favored by industry.

In the present work, an activity coefficient model combining NRTL and Wertheim’s theory is used to model two classes of systems. Class 1 systems, such as alcohols in alkanes, are those in which one component self-associates and the others are “inert” or inactive in hydrogen bonding. In contrast, class 2 systems involve components that only cross-associate and do not have any hydrogen bonding in their pure states. The proposed model is used to fit binary and ternary liquid-liquid equilibria data and the parameters are evaluated using infrared spectroscopy data.

[1] H. Renon, J.M. Prausnitz, On the thermodynamics of alcohol-hydrocarbon solutions, Chem. Eng. Sci. 22 (1967) 299–307. doi:10.1016/0009-2509(67)80116-7.

[2] M.S. Wertheim, Fluids with highly directional attractive forces.1. Statistical thermodynamics, J. Stat. Phys. 35 (1984) 19–34. doi:10.1007/bf01017362.

[3] M.S. Wertheim, Fluids with highly directional attractive forces. 2. Thermodynamic perturbation-theory and integral-equations, J. Stat. Phys. 35 (1984) 35–47. doi:10.1007/bf01017363.

[4] M.S. Wertheim, Fluids with highly directional attractive forces. 3. Multiple attraction sites, J. Stat. Phys. 42 (1986) 459–476. doi:10.1007/bf01127721.

[5] M.S. Wertheim, Fluids with highly directional attractive forces. 4. Equilibrium polymerization, J. Stat. Phys. 42 (1986) 477–492. doi:10.1007/bf01127722.

[6] A.M. Bala, C.T. Lira, Relation of Wertheim Association Constants to Concentration-based Equilibrium Constants for Mixtures with Chain-forming Components, Fluid Ph Equilib. 430 (2016) 47–56. doi:10.1016/j.fluid.2016.09.015.

[7] W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, New reference equation of state for associating liquids, Ind. Eng. Chem. Res. 29 (1990) 1709–1721. doi:10.1021/ie00104a021.

[8] G.M. Kontogeorgis, E.C. Voutsas, I.V. Yakoumis, D.P. Tassios, An Equation of State for Associating Fluids, Ind. Eng. Chem. Res. 35 (1996) 4310–4318. doi:10.1021/ie9600203.

[9] J.R. Elliott, S.J. Suresh, M.D. Donohue, A simple equation of state for nonspherical and associating molecules, Ind. Eng. Chem. Res. 29 (1990) 1476–1485. doi:10.1021/ie00103a057.