Gas phase polyethylene reactors - A global study of stability behaviour

A global study of the occurrence of steady state multiplicity and limit cyc les in gas phase polyethylene reactors is carried out using elementary conc epts of singularity theory and continuation techniques, for both open loop and closed loop operations. The well-mixed model of the unit consisting of the reactor, the heat exchanger and the ethylene partial-pressure controlle r, is reduced analytically to one single algebraic equation. The singularit y theory is efficiently used for the classification, in multidimensional pa rameter space, of the different static and dynamic behaviour exhibited by t he unit. This includes regions of unique and stable behaviour, regions of h ysteresis, regions of limit cycles as well as regions of bistability result ing from interactions between hysteresis and limit cycles. A useful and pra ctical picture of the effect of the different kinetic and operating paramet ers of the unit is constructed. The tools developed for a single site type are also extended to study the dynamics induced by multiple catalytic site types. The dynamics of the process under a conventional temperature PI cont roller are also studied. It is shown that while the integral action elimina tes the steady state multiplicity, it introduces instability for some range s of catalyst feed rates. The stability analysis allows the construction of practical diagrams showing the effect of model parameters on the closed lo op stability behaviour of the process.