A Smooth, Square Flash Formulation for Equation-Oriented Flowsheet Optimization

This work introduces a novel flash formulation to calculate vapor-liquid equilibria (VLE) based on a general cubic equation of state (cEOS). The approach leverages smooth max operators to implement complementarity conditions leading to a model with an equal number of variables and constraints (i.e., a square problem). The model correctly calculates equilibrium phase fractions and compositions over a broad range of temperatures and pressures by ensuring that the VLE calculation is only enforced below the critical pressure and between the bubble point and dew point temperatures. We demonstrate the robustness of the flash model by embedding it directly into optimization problems that require moving from initial temperatures and pressures across phase transition boundaries as well as between subcritical and supercritical regions. The flash model is implemented in the open source, Python-based, algebraic modeling language, Pyomo. The roots of the cEOS are calculated analytically using an external function call that returns exact 1st and 2nd derivatives and is embedded directly via the AMPL Solver Library. The model will be publicly available as part of the Institute for the Design of Advanced Energy Systems (IDAES) process systems engineering framework.