A complementarity-based vapor-liquid equilibrium formulation for equation-oriented simulation and optimization

Vapor-liquid equilibrium (VLE) is a cornerstone of computer-aided process engineering (CAPE). Embedded within process system models, VLE calculations are inherently procedural with non-smooth behavior that frequently requires discrete decisions. Traditionally, these features resist the incorporation of VLE within efficient, large-scale equation-oriented (EO) process simulation and optimization strategies. On the other hand, recent reformulation of VLE models through the incorporation of complementarity constraints has broadened its scope to deal seamlessly with phase transitions and even supercritical excursions in process simulation and optimization. In this study, we extend these VLE complementarity models to EO frameworks where procedural thermodynamic property libraries are still required. Here we develop an efficient, non-intrusive, and intuitive "square-flash " equation system that has been implemented within the IDAES Integrated Platform (IDAES-IP). The effectiveness of this modular approach is demonstrated on case studies for non-ideal flash calculations and distillation optimization, with disappearing phases and supercritical transitions.