(204g) Modelling the Solubility of Naphthalene and Phenanthrene in Binary and Ternary Systems Containing Carbon Dioxide

Experimental solid solubility data are necessary to develop new supercritical fluid processes. Solubility data for different solids in supercritical fluids are important in the petroleum, food and pharmaceutical industries. Because of the limited amount of experimental data for solid + supercritical fluid systems [1], it is important to have an experimental method to determine reliable properties, as well as models for correlation and prediction.

In this work, we present the results of correlation of solubility data of the binary system carbon dioxide + naphthalene and the ternary system carbon dioxide + naphthalene + phenanthrene. These solubility data were measured using an apparatus based on dynamic methods in order to test the newly developed apparatus in our laboratory; the solubilities of a solid in a binary system and in a ternary system were measured based on the dynamic analytic method. The developed equipment and the experimental methodology used were suitable for determining solubilities of solid in carbon dioxide over a wide range of pressure.

We used two approaches for modelling our obtained solubility data: density-based empirical models and a cubic equation of state. The first approach does not need properties of the solutes, while the latter approach does. Modelling by an equation of state requires critical and physical properties of the solutes and the solvent, as well as the selection of a proper mixing rule. For the binary system, the models tested in this work were the empirical models presented by Chrastil [2], Kumar and Johnston (K-J) [3], Bartle [4], Mendez-Santiago and Teja (M-S-T) [5], and the modification of Chrastil model by Garlapati and Madras [6]. These models relate the solubility of a solute to the temperature and density of the supercritical solvent. For the ternary system, we used the same models for the binary systems and also the modifications of Chrastil [7] and Mendez-Santiago and Teja [8] models.

The equation of state and the mixing rules used for both the binary and the ternary systems were the Peng-Robinson [9] equation of state and the van der Waals mixing rules, with 1 or 2 parameters. The average absolute relative deviation (AARD) was used to evaluate the results of the correlation.

For naphthalene in the binary and ternary systems, we had ranges of values for the AARD % of (3.14-18.48) with the use of empirical models. Using the Peng-Robinson equation of state, we had minimal AARD % values of 2.55. The addition of the co-volume parameter (lij) to the van der Waals mixing rule improved the correlation in all cases. This means that there might be complex interactions in the solid-supercritical fluid equilibrium. The energy parameters (kij) show little dependence with temperature for all cases.

The AARD % values had a range of (5.34-15.03), using empirical models for phenanthrene in the ternary system. The modelling of the ternary system with an equation of state gave values of AARD % up to 27 for naphthalene and 48 % for phenanthrene. This modelling was performed using optimised kij parameters for the two solutes with the solvent (naphthalene + carbon dioxide and phenanthrene + carbon dioxide), while the parameter for the interactions between naphthalene and phenanthrene was considered an adjustable parameter [10]. It is necessary to perform the modelling with another approach in order to obtain lower values of AARD.

We concluded that the use of empirical models is good for the modelling of solubility of solids in supercritical solvents, because they need the density of the solvent and give good results in correlation. However, the use of an equation of state improves the correlation when using a proper mixing rule for binary systems. In the case of ternary systems, it is necessary to use a different approach than the conventional one. Nevertheless, an equation of state cannot be a model that is required to give accurate results, because it is not designed to model solid compounds.

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