Activity coefficient models for

Activity coefficient models offer an alternative approach to equations of state for the calculation of fugacities in liquid solutions (Prausnitz ct al. 1986 Tas-sios, 1993). These models are also mechanistic and contain adjustable parameters to enhance their correlational ability. The parameters are estimated by matching the thermodynamic model to available equilibrium data. In this chapter, vve consider the estimation of parameters in activity coefficient models for electrolyte and non-electrolyte solutions. 

Chen, C.-C., Song, Y., 2005, Extension of NonRandom Two Liquid Segment Activity Coefficient Model for Electrolytes, Ind. Eng. Chem. Res, In Print -expected Oct / Nov. 

Two New Activity Coefficient Models for the Vapor-Liquid Equilibrium of Electrolyte Systems... 

Kontogeorgis, G.M., Fredenslund, A., Tassios, D.P. Simple activity coefficient model for the prediction of solvent activities in polymer solutions. Ind. Eng. Chem. Res., 1993,32 362-372. 

First, we need a predictive activity coefficient model for electrolyte systems. The electrolyte NRTL model is correlative, and it requires extensive experimental data sets from which NRTL binary interaction parameters can be identified. The OLI electrolyte model, with its extensive parameter database, has been serving as a pseudo-predictive model. However, use of the OLI electrolyte model is limited to dilute aqueous electrolytes, its parameter database is not open to the public, and its electrolyte speciation is not supported by experiments. 

Conversely, given the composition of the coexisting liquid phases, Eq. (7.7) can also be used to fit an activity coefficient model. For example, using the two-suffix Margules model for a binary mixture. 

The chemical potential gradient may be expressed in terms of mole fraction and activity coefficient gradients as shown in Section 2.2. Activity coefficient models for electrolyte systems are discussed by, for example, Newman (1991) and Zemaitis et al. (1986). 

Taylor, R. and Kooijman, H. A., Composition Derivatives of Activity Coefficient Models (For the Estimation of Thermodynamic Factors in Diffusion), Chem. Eng. Commun., 102, 87-106 (1991). 

This mixing rule has been successful in several ways. First, when combined with any cubic EOS that gives the correct vapor pressure and an appropriate activity coefficient model for the term, it has been shown to lead to very good correlations of vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria, indeed generally comparable to those obtained when the same activity coefficient models are used directly in the y-

mixing rule extends the range of application of equations of state to mixtures that previously could be correlated only with activity coefficient models. 

Kontogeorgis, G. M., Fredenslund, A., Economou, I. G., and Tassios, D. P., 1994a. Equations of state and activity coefficient models for vapor-liquid equilibria of polymer solutions. AIChEJ., 40 1711-1727. 

It may be difficult to formulate a rigorous mathematical expression of FV, fully consistent with the above physical picture. Bondi stated, every author defines the free-volume as what he wants it to mean. This may very well be true. Thus, various expressions have been proposed for the FV. Some of them are employed in the development of activity coefficient models for polymer solutions. 

Equations of state offer a number of advantages over activity coefficient models for example, they can be applied to both low and high pressures, for properties other than phase equilibria, and the density is not required as an input parameter. However, often they are more difficult to develop for complex fluids and mixtures than are activity coefficient models. Very many equations of state have been proposed for polymers Section 16.7 discusses the reason. Recent reviews have been presented. " " We will not attempt to cover all the various approaches, but essentially discuss in detail only two of them, which seem promising for polymer solutions and blends the cubic equations of state and the SAFT (Statistical Associating Fluid Theory) method. 

Simple cubic equations of state can correlate both VLE and LLE for polymer solutions and blends with a single interaction parameters. They can be combined with an activity coefficient model for predictive calculations using the so-called EoS/G mixing rules. Applications of cubic equations of state to high pressures are so far limited to those shown for the Sako et al. cubic equation of state. 

Polyzou, E.N. et ah. Assessment of activity coefficient models for predicting solid-liquid equilibria of asymmetric binary alkane systems, Ind Eng. Chem. Res., 38, 316-323, 1999. 

Voutsas, E.C., Kalospiros, N.S., and Tassios, D.P., A combinatorial activity coefficient model for symmetric and asymmetric mixtures, Eluid Phase Equilibria, 109, 1, 1995. 

However, before we proceed with the discussion, it is useful to consider the range of validity of the activity coefficient (y -activity coefficient (or excess Gibbs energy) models can be used for liquid mixtures of all species. This description generally does not include density, and therefore will not give a good description of an expanded liquid, which occurs near the vapor-liquid critical point of a mixture. Also, when two different models are used—for example, an activity coefficient model for the liquid phase and an equation-of-state model for the... 

Thus, from the ebulliometric experiment, one obtains the infinite-dilution activity coefficient directly. Now repeating the experiment by starting with pure component 2 and adding an infinitesimal amount of component 1, y x —> 0) = can be obtained. These two data points can then be used to determine the parameters in a two-constant activity coefficient model. For example, from the van Laar model of Eqs. 

The thermodynamic factor is evaluated for liquid mixtures from activity coefficient models. For a regular solution, for example,... 

The property packages available in HYSYS allow you to predict properties of mixtures ranging from well defined light hydrocarbon systems to complex oil mixtures and highly nonideal (non-electrolyte) chemical systems. HYSYS provides enhanced equations of state (PR and PRSV) for rigorous treatment of hydrocarbon systems semiempirical and vapor pressure models for the heavier hydrocarbon systems steam correlations for accmate steam property predictions and activity coefficient models for chemical systems. All of these equations have their own inherent limitations and you are encouraged to become more familiar with the application of each equation. 

R. M. CoNEORTi, T.A. Barbari, P. Vi-MALCHAND, and M.D. Donohue, A Lattice-Based Activity Coefficient Model for Gas Sorption in Glassy Polymers. Macromolecules, 1991, 24, 3388-3394. 

For the development of activity coefficient models for electrolyte solutions, the theory of Debye and Huckel is usually the starting point. It can be regarded as an exact equation to describe the behavior of an electrolyte system at infinite dilution. 

This chapter traces the history of activity coefficient models for aqueous solutions of single strong electrolytes. Of great importance is the Debye-Huckel equation, which has been the cornerstone of more recent models. In addition to Debye-Huckel, the following, more recent methods are outlined ... 

C2. Chen, C-C, H.I. Britt. J.F. Boston and L.B, Evans. "Twp New Activity Coefficient Models for the Vapor-Liquid Equilibrium of Electrolyte... 

---