Phase equilibria of medium- and long-chain fatty acids in supercritical CO₂: Experimental data and thermodynamic modeling

Reliable phase equilibrium data are essential for the design and optimization of supercritical carbon dioxide (CO₂)–based separation and fractionation processes involving fatty acids. In this study, liquid–supercritical phase equilibria of three binary systems—caprylic acid (C8)–CO₂, capric acid (C10)–CO₂, and myristic acid (C14)–CO₂—were experimentally determined using a static analytical method. Measurements were carried out at temperatures of 333.15, 343.15, and 353.15 K over a pressure range of 14–30 MPa. The experimental data reveal a systematic decrease in fatty acid solubility in the supercritical phase with increasing carbon chain length, accompanied by increasingly asymmetric and nonideal phase behavior. The measured equilibrium data were correlated using the Peng–Robinson equation of state with four mixing rules: van der Waals quadratic, Panagiotopoulos–Reid, Stryjek–Vera, and Mathias–Klotz–Prausnitz. Comparative evaluation demonstrates that symmetric mixing rules provide only limited accuracy for highly asymmetric CO₂–fatty acid systems, particularly for long-chain fatty acids, whereas asymmetric mixing rules significantly improve the quality and robustness of the correlations. Among the tested formulations, the Stryjek–Vera and Mathias–Klotz–Prausnitz mixing rules exhibit superior performance across the investigated temperature and pressure ranges. The consistent experimental dataset and systematic modeling analysis presented in this work provide a reliable thermodynamic basis for the design of supercritical CO₂ processes involving medium- and long-chain free fatty acids.