Numerically stable determination of mixture critical points and loci with PC-SAFT Equation of State

Abstract

Compositional simulations are important for understanding, analyzing, and optimizing multiphase flows, especially in the petrochemical industry. These simulations are dependent on an accurate Equation of State (EOS) to model the relationships between phases under changing conditions. While cubic EOS (CEOS) models are widely used in the industry due to their simplicity and efficiency, the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) EOS offers a more physically accurate representation of molecular interactions. Despite the potential of PC-SAFT EOS, the application to predict mixture critical points remains underexplored. These challenges primarily arise from computational complexities and spurious stationary points that have long limited the practical use of PC-SAFT EOS for mixture criticality.

This study performs a systematic evaluation of two critical point computational methods using PC-SAFT EOS. The critical point calculation methods are applied to compute mixture critical temperatures and pressures, vapor–liquid equilibrium phase envelopes, and to trace full critical loci. Furthermore, the evaluation covers many distinct multicomponent mixtures ranging from two to eleven components. By directly comparing our results against experimental data and the results yielded by CEOS, we provide an evaluation of the performance of PC-SAFT EOS in predicting the critical points of pure compounds and mixtures.

For pure compounds in the tested mixtures, the results show that Global Optimization (GO) method demonstrates slightly better performance than the Newton–Raphson (NR) method for critical temperature ($T_c$) predictions with Average Absolute Relative Deviations (AARD%) of 1.538%, while both show nearly identical performance for critical pressure ($P_c$) predictions. For mixtures, PC-SAFT-based NR demonstrates superior performance in predicting critical points with AARD% of 1.687% for $T_c$ predictions and 4.623% for $P_c$ predictions. In contrast, GO demonstrates higher deviations, particularly for some heavier mixtures. When calculating critical loci of mixtures, both methods produce root mean square error values with typical errors below 10 K for $T_c$ predictions and 0.5 MPa for $P_c$ predictions.