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.
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