Correlation and Prediction of Liquid–Liquid and Solid-Liquid Equilibrium for the Phenol (C6H5OH) + n-Hexane (C6H14) Binary System Using the NRTL and COSMO-Based Models

Abstract

This study investigates the thermodynamic phase behavior of the binary system phenol (C₆H₅OH) + n-hexane (C₆H₁₄), a mixture relevant to separation processes in refining and coal conversion. Liquid–liquid equilibrium (LLE) and solid–liquid equilibrium (SLE) data were measured at atmospheric pressure, providing an independent, internally consistent dataset that verifies and complements the available literature data. The system exhibits strong non-ideality, with a broad miscibility gap, an upper critical solution temperature (UCST) of 325.62 K, and a deep freezing-point depression in the SLE region. The data were correlated using the Non-Random Two-Liquid (NRTL) model, with a single set of temperature-dependent binary interaction parameters regressed simultaneously to both equilibria, giving a thermodynamically consistent representation of the complete phase diagram. The predictive capabilities of the COSMO-RS and COSMO-SAC (2010) models were evaluated using molecular σ-profiles generated via DFT calculations (M06-2X/6-311+G(2d,p)). While the correlated NRTL model best described the LLE region, the fully predictive COSMO-SAC model reproduced the SLE liquidus with an accuracy (RMSD = 0.0133) better than the correlated NRTL model (RMSD = 0.0347). These results suggest that while NRTL remains the standard for rigorous process simulation, COSMO-based approaches offer a reliable alternative for screening solubility in polar–nonpolar systems where experimental data are scarce.