Instabilities in homogeneous nonisothermal reactors: Comparison of deterministic and Monte Carlo simulations

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Abstract
A homogeneous nonisothermal continuous stirred tank reactor is modeled using the Monte Carlo method. The results are compared with deterministic bifurcation theory and time integration of the continuum unsteady state equations. Multiple solutions are determined for certain conditions and metastability is observed near ignition and extinction points. It is found that the amplitude of fluctuations increases near turning and Hopf bifurcation points. For finite size systems a supercritical Hopf bifurcation appears as a smooth transition from stationary solutions to oscillations, and near Hopf bifurcation point oscillations are more chaotic. Near a subcritical Hopf bifurcation, the stationary branch exhibits small amplitude oscillations of the same period as the oscillatory attractor, and metastability of both the stationary and the oscillatory attractors is observed. In the presence of isolas, metastability can cause a phase transition from the extinguished branch to the isola branch followed up by oscillations and subsequent extinction of the oscillations as the oscillatory attractor becomes metastable at high residence times.