Multi-criteria optimization for parameterization of SAFT-type equations of state for water

Finding appropriate parameter sets for a given equation of state (EoS) to describe different properties of a certain substance is an optimization problem with conflicting objectives. Such problem is commonly addressed by single-criteria optimization in which the different objectives are lumped into a single goal function. We show how multi-criteria optimization (MCO) can be beneficially used for parameterizing equations of state. The Pareto set, which comprises a set of optimal solutions of the MCO problem, is determined. As an example, the perturbed-chain statistical associating fluid theory (PC-SAFT) EoS is used and applied to the description of the thermodynamic properties of water, focusing on saturated liquid density and vapor pressure. Different options to describe the molecular nature of water by the PC-SAFT EoS are studied and for all variants, the Pareto sets are determined, enabling a comprehensive assessment. When compared to literature models, Pareto optimization yields improved models.