State multiplicity in CSTR-separator-recycle polymerisation systems

Anton A. Kiss, Costin S. Bildea, Alexandre C. Dimian, Piet D. Iedema

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


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 < Dacr, the only steady state involves infinite flow rates. Feasible steady states become possible if the critical value is exceeded, Da > Dacr. 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.

Original languageEnglish
Pages (from-to)535-546
Number of pages12
JournalChemical Engineering Science
Issue number4
Publication statusPublished - Feb 14 2002


  • Kinetics systems
  • Nonlinear dynamics
  • Polymerisation
  • Reaction engineering

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)
  • Industrial and Manufacturing Engineering

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