Recent results in optimal reactor synthesis via attainable region theory

Abstract

In consideration of (isothermal) reactor designs involving only chemical reaction and mixing, Feinberg and Hildebrandt (1997, Chem. Engng Sci. 52, 1637–1665) showed that the set of all attainable composition vectors (the attainable region) has a certain universal character. In particular, manifolds of extreme points (protrusions) on the attainable region’s boundary are invariably made up of plug-flow reactor trajectories. These trajectories therefore form a system of PFR “highways” that provide access to the attainable region’s extreme points. They also showed that, in a certain sense, CFSTRs and differential sidestream reactors (DSRs) provide means to navigate along the attainable region’s boundary to a PFR trajectory of choice. Here we consider the special character of DSR trajectories that reside on the attainable region’s boundary. Ideas from geometric control theory indicate that critical DSRs of this kind must conform to a very special sidestream addition rate policy. Indeed, highly detailed equations that govern such a policy can be written in terms of the sidestream composition and the reaction kinetics.