State multiplicity in CSTR–separator–recycle polymerisation systems

Abstract

This article continues earlier work (Comput. Chem. Eng. 24 (2000) 209) concerning the design and control of isothermal reactor–separator–recycle systems. The multiplicity behaviour of six reaction systems of increasing complexity, from one-reactant, first-order reaction to chain-growth polymerisation, is investigated. Below a critical value of the plant Damkohler number, Da< Da cr, the only steady state involves infinite flow rates. Feasible steady states become possible if the critical value is exceeded, Da> Da cr. For one-reaction systems, one stable steady state is born at a transcritical bifurcation. For consecutive-reaction systems, including polymerisation, a fold bifurcation can lead to two feasible steady states. Moreover, the transcritical bifurcation is destroyed when two reactants are involved. If the gel-effect is included, a maximum of four steady states are possible. When multiple steady states exist, the achievable conversion is constrained by the instability of the low-conversion branch. This has practical importance for polymerisation systems when the radicals’ quasi-steady state assumption is not valid or the gel effect is significant.