Time-to-Ignition in a Tubular Reactor Operated Adiabatically

Even a simple exothermic reaction can show multiple stationary states in flow through a tubular reactor. Discontinuous jumps of ignition and extinction can occur in response to continuous changes in such typical control parameters as flow-rates or inlet-temperatures (expressed by Damköhler or Péclet numbers, Da or Pe). Under marginally supercritical conditions, runaway develops expo­nentially but the time-constant becomes very large as criticality is approached. We show that the dependence can be written: tign = M/[(Da/Dacr) - 1]½. The validity of this form and the predicted size of the coefficient M are checked by numerical computation for the case of a single, exothermic reaction proceeding under adiabatic conditions. Similar expressions describe the decay of small perturbations to stationary states under marginally subcritical circumstances. At the point of criticality, these exponential growths or decays are replaced by hyperbolic forms.