Invariants for optimal operation of a reactor-separator-recycle process

Abstract

Globally optimal invariants for the one unconstrained degree of freedom in an A + B → C reactor-separator-recycle process are derived for four alternative reaction kinetic expressions from an analysis of the overall plant material balance. The derivation is performed for the simplified economic objective of minimizing recycle rate (Mode I) at given production and maximizing production (Mode II) with maximum recycle rate as the capacity bottleneck. For power law kinetics, holding the reactor A/B ratio constant is obtained as the invariant while a more complex non-linear expression is obtained for Langmuir-Hinshelwood kinetics. For the more practical economic objective of minimizing separation column boilup or maximum column boilup as the capacity bottleneck, the invariant as the controlled variable (CV) achieves near optimal operation with the loss being <0.1% over the envisaged operating space in all cases. The invariants are thus good self-optimizing CVs (SOCVs). The work provides a physical basis for using reactant ratio as an SOCV in plantwide control.