Gibbs free energy models

Solubility of solids in supercritical fluids using equations of state - excess Gibbs free energy models. 

Equations (4.1.4 or 4.1.5) use one degree of freedom in establishing a relation between the EOS parameters a and b and the mixture composition with activity coefficient or exeess Gibbs free-energy models. Coupled with another independent piece of information that connects a or b (or both) to composition, one can solve for the EOS parameters a and b in terms of the mole fractions. There are several alternative ways of implementing such a procedure, and they are reviewed here and in the following sections. 

The correlation of data for the methane and pentane binary system is shown in Figure 4.2.1. In this case the van Laar excess Gibbs free-energy model has been used in the HVO model the two model parameters were fitted to VLE data on the 277 K isotherm, and the vapor-liquid equilibria at higher temperatures were predicted with the same temperature-independent parameters. The results are very good in this case and similar to those obtained with the IPVDW and 2PVDW models. 

It should be noted that even when using activity coefficient models directly, temperature dependent parameters are needed. There is no excess Gibbs free energy model... 

Apostolou, D, A., Kalospiros, N. S and Tassios, D. P., 1995. Prediction of gas solubilities using the LCVM equation of state/excess Gibbs free energy model. Ind. Eng. Chem. Res., 34 948-957. 

Mollerup, J. M., 1986. A note on the derivation of mixing rales from excess Gibbs free energy models. Fluid Phase Eq., 25 323-326. 

The next step is to fit parameters in the Gibbs free energy models to the experimental data. I have done this assuming small errors in all the variables (T, P, x and y) and using the maximum likelihood method. The results of the different models are given below ... 

The study of dilute fluid solutions has been essential to the foundation of solvation thermodynamics and the development of macroscopic modeling for the description of observed behavior and the correlation of experimental data. Typical studies of dilute solutions have dealt with the determination of limiting values for the solute activity coefficients and the corresponding slope of their composition dependence at infinite dilution (Jonah 1983, 1986), where these quantities played a crucial role in constraining the parameterization of excess Gibbs free-energy models (Van Ness and Abbott 1982 Lupis 1983 Wallas 1985 Chialvo 1990a). 

For calculation of the equilibrium compositions of the liquid phase either the equilibrium constants of the dissociation and polycondensation reactions have to be known or they can be computed by methods which use the approach of minimizing Gibbs free energy [200-202]. In addition, ab initio modeling techniques such as density functional theory (DFT) in combination with reactive molecular dynamic (MD) simulations could be used. Once the liquid phase system is modeled, there are in principle two options to describe the vapor-liquid equilibrium. Either equations of state (EOS) or excess Gibbs free energy models (g -models) may be used to describe the thermodynamics of the liquid... 

Martins RJ, Cardoso MJED, Barcia OE (2000) Excess Gibbs free energy model for calculating the viscosity of binary liquid mixtures. Ind Eng Chem Res 39 849-854... 

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