An analysis of chemical reactor stability and control—VII : Two-phase chemical reacting systems with fast reactions

Abstract

Pertinent to the design of any chemical reactor is a knowledge of its transient characteristics, in particular the stability of a steady state both to small and large disturbances. The dynamic behaviour of the well agitated continuous reactor both with and without control devices has been extensively studied for homogeneous reacting media. It is the purpose of this work to consider the natural behaviour of reacting systems involving two fluid phases in the well agitated continuous reactor operating under constant conditions. To this end models of the physical rate processes of interfacial heat and mass transfer are constructed for perfectly mixed systems and analyzed for multiplicity and stability of steady state solutions. Some methods of non-linear mechanics are applied, and phase plots resulting from digital computer solutions of the non-linear transient equations are constructed for some chosen numerical examples. The study includes systems in which phases are in physical equilibrium, in which there are resistances to interfacial heat and mass transfer and in which components of a phase are in chemical equilibrium, the reaction rate being controlled by the transfer of mass. It is found that the number of possible steady state solutions to the non-isothermal equations depends on the rates of exchange of heat and material between the phases. Phase plots are shown for systems which have no stable state, but exhibit continued oscillations in temperature and concentration. Other examples are shown of systems which possess more than one steady state. In some cases a majority of these states are unstable. In this paper, which is a continuation of Va, Vb, and VI, the cases in which there are resistances to heat and mass transfer but with fast chemical reactions are investigated.