An alternative strategy to EoS parameter optimization to avoid using unstable phase-equilibrium points

Parameter fitting of thermodynamic models is fundamental to process design and optimization in the chemical industry. Phase-equilibrium calculations rely on equations of state (EoS), whose predictive capability is strongly conditioned by the parameters used. Conventional fitting procedures typically target saturation properties using standard saturation-point or flash calculations. For complex models or multicomponent mixtures, however, these approaches may yield parameter sets for which equilibrium calculations converge to thermodynamically unstable stationary solutions rather than to the stable equilibrium corresponding to a global minimum of the Gibbs free energy. In other cases, the fitted model may predict phase boundaries in close proximity to the experimental conditions, but still without a solution for a typical  specification, e.g. T-x. This happens, for example, when the experimental point falls inside a predicted L-L separation region.

We present an alternative methodology for parameter fitting of complex systems, with emphasis on Huron–Vidal–type mixing rules for cubic equations of state and multicomponent mixtures. The proposed approach is based on calculating complete phase envelopes instead of isolated saturation points. Although envelope calculations are more computationally demanding, they provide improved numerical robustness and avoid the inclusion of unstable equilibrium solutions during optimization. Moreover, the method defines objective functions based on the distance from experimental points to the closest state on the predicted phase envelope, avoiding ill-posed specifications inherent to pointwise fitting.

While this study focuses on cubic EoS mixing rules, the methodology is general and can be extended to other thermodynamic models. The results show that envelope-based fitting yields more reliable phase-equilibrium predictions and reduces the need for ad hoc stability analysis, supporting more robust parameterization strategies.