(The) bifurcation analysis of a simultanaeous first order reaction in CSTR

Abstract

The dynamic behavior of stirred tank reactor with first order exothermic simultaneous reaction system was analyzed by using the bifurcation theory. The static bifurcations (i.e. multiplicity) and dynamic features of the Hopf bifurcation points such as the stability and direction of periodic orbits were investigated. The response diagrams which dispalys the steady state solutions, the bifurcating periodic direction, and their stability versus the $Damk\ddot{o}hler$ number Da were represented. The region of multiplicity was represented as a function of system parameters. The phase trajectory in the domain of temperature and concentration was depicted by numerical calculation. Especially, as a result of phase trajectory analysis at static bifurcation, the two jump phenomena (ignition and extinction processes ) have been discovered. In this simultaneous system there are two turning points at most, and therefore, nine trajectories may be possible in connection with static and Hopf bifurcation, but seven phase trajectories were found in this paper. The jump phenomena was also found at the unstable Hopf bifurcation point, but not at stable Hopf bifurcation point and oscillation phenomena occurs at this point.