Equation-Oriented Approach for Handling the Perturbed-Chain SAFT Equation of State in Simulation and Optimization of Polymerization Processes

The perturbed-chain SAFT (PC-SAFT) equation of state (EOS) is a very popular and promising model for fluids. Resolution of the PC-SAFT EOS is generally conducted by subroutine-based calculations that involve logical conditions. This approach can lead to nonsmoothness and convergence issues when used with gradient-based solvers in an equation-oriented (EO) framework. In this paper, we propose a novel EO approach for the PC-SAFT EOS embedded in large flowsheet optimization. First, the mathematical structure of the PC-SAFT EOS is analyzed through a digraph. It reveals that for polymerization systems, resolution of the PC-SAFT EOS is coupled not only by phase equilibrium but also by the polymerization kinetics. This feature strongly motivates implementation of both EOS resolution and process optimization in a complete EO framework. A novel EO approach is proposed for selecting the appropriate root of the PC-SAFT EOS by incorporating thermal stability criteria to eliminate the undesirable roots. Numerical examples in simulation and optimization of flash drums are presented to demonstrate that the proposed EO formulation can always select the appropriate root. Finally, the EO formulation is applied for simulation and optimization of an industrial polymerization process. The results show advantages of the proposed EO method compared to traditional sequential modular-based simulation software in terms of computational robustness and efficiency.