CORRELATIONS Simultaneous Correlation of Liquid-Liquid, Liquid-Solid, and Liquid-Liquid-Solid Equilibrium Data for Water + Organic Solvent + Salt Ternary Systems: Hydrated Solid Phase Formation Antonio Marcilla,* Juan Antonio Reyes-Labarta, Marı ´a del Mar Olaya, and Marı ´a Dolores Serrano Departamento de Ingenierı ´a Quı ´mica, UniVersidad de Alicante, Apdo. 99, Alicante 03080, Spain The condensed phase equilibrium behavior of water + organic solvent + salt systems, when different hydrates are formed in the solid phase, increases the number of equilibrium zones, substantially complicating the simultaneous correlation of the equilibrium data in all the existing regions. In this paper, a procedure to perform the correlation of this type of system is presented in great detail, using, as an example, the water + 1-butanol + LiCl ternary system, where the salt appears in two forms: anhydrous and monohydrated (LiCl‚ H 2 O). To this end, the non-random two-liquid (NRTL) model for the excess Gibbs energy (G E ) has been implemented, because the assumption of an electrolytic character for the solution in the liquid phase, despite being potentially more correct physically, does not give more flexibility to the G E function, as was discussed in a previous work. The common tangent plane criterion is used as an equilibrium condition to determine the equilibrium compositions in all the regions. The results obtained show the limitations of the NRTL equation to model this type of system, as a consequence of its lack of flexibility, in terms of the topological concepts that are related to the Gibbs energy of mixing (G M ) function and the tangent plane criterion. 1. Introduction The industrial applications in which the salting-out effect is used on liquid-liquid equilibria (LLE) are many: extractive fermentation, 1-4 extractive crystallization, 5,6 solvent dehydra- tion, 7 etc. The addition of a salt to a solvent mixture modifies the interaction among the various solvent and solute molecules, resulting in a phase equilibrium modification that is usually favorable to the desired separation. For example, for an aqueous-organic solvent mixture, the addition of an electrolyte generally causes an enrichment of the organic phase with the solute component, improving the extraction conditions. Con- sequently, LLE for water + organic solvent + salt ternary systems are of interest for many unit operations. Molecular-interaction-based models for phase equilibria, such as non-random two-liquid (NRTL) or UNIQUAC, and their modified forms (to account for the presence of electrolytes), are generally used for data correlation of solvent mixture + salt systems where solid phases are present. The ability of a given model to represent all the equilibrium regions using a unique set of parameters is a necessary condition for the model to be considered to be thermodynamically consistent. In addition, this condition is very advantageous for design calculations. Despite this situation, many papers that involve equilibrium data far from critical conditions, where solid and liquid phases are both present, only consider LLE when trying to fit experimental data with a model. 8-12 Sometimes, when the solid phase is included in the phase equilibria regression, the liquid-liquid (LL) and solid-liquid (SL) data sets are fitted separately, adducing the difficulty of classical models to describe different types of equilibria with a single set of parameters. 13 When simultaneous correlation of all the phase equilibrium regions of systems that involve solids under moderate temperature and pressure conditions has been con- ducted, poor results or inconsistencies that are due to the be- havior of the models have frequently been found. For example, Iliuta et al. 14 and Thomsen et al. 15 have used the extended UNIQUAC model for electrolyte solutions to predict the solid- liquid-liquid-vapor (SLLV) equilibrium behavior of many systems, but poor results are obtained for some of them. Salts such as NH 4 NO 3 , Na 2 CO 3 , and K 2 CO 3 cause a liquid-phase split when added to a homogeneous solvent mixture (such as, for example, aqueous ethanol). However, the electrolyte-UNI- QUAC model does not reproduce the LLE region in aqueous ethanol solutions that contain NH 4 NO 3 or Na 2 CO 3 , and produces a three-liquid-phase region (LLLE) in the water-rich part that actually does not exist in the system that contains K 2 CO 3 . 15 Moreover, no article has been found that includes a liquid- liquid-solid equilibrium (LLSE) data correlation in which the solid phase corresponds to different hydrates of a salt. In a previous paper, 16 we presented a procedure to simulta- neously correlate the equilibrium data of all the equilibrium regions for a ternary system: water + organic solvent + inorganic salt. Afterward, some correlations were improved and the results that were obtained using the molecular NRTL model 17 and the electrolyte-NRTL model 18-20 were compared. 21 No improvement was found in the regression results by assuming dissociation of the salt into ions: the restrictions imposed on the equation for the activity coefficient, taking the electrolyte into account, resulted in a loss of flexibility of the model that still kept the same number of variables. The K-value method, which imposes equality of chemical potentials as equilibrium condition, 15 is frequently used to formulate phase equilibrium conditions. Nevertheless, it has been proven 22 that, because of the high nonlinearity of the Gibbs energy models, this method is slowly convergent and can result * To whom correspondence should be addressed. Tel.: (34) 965 903789. Fax (34) 965 903826. E-mail address: antonio.marcilla@ua.es. 2100 Ind. Eng. Chem. Res. 2008, 47, 2100-2108 10.1021/ie071290w CCC: $40.75 © 2008 American Chemical Society Published on Web 02/27/2008