Nonisothermal Stirred-Tank Reactor with Irreversible Exothermic Reaction A → B: 2. Nonlinear Phenomena

Abstract

In this chapter, the non-linear dynamics of a nonisothermal CSTR where a simple first order reaction takes place is considered. From the mathematical model of the reactor without any control system, and by using dimensionless variables, it has been corroborated that an external periodic disturbance, either inlet stream temperature and coolant flow rate, can lead to chaotic dynamics. The chaotic behavior is analyzed from the sensitivity to initial conditions, the Lyapunov exponents and the power spectrum of reactant concentration. Another interesting case is the one researched from the self-oscillating regime, showing that a periodic variation of coolant flow rate can also produce chaotic behavior. Finally, steady-state, self-oscillating and chaotic behavior with two PI controllers have been investigated. From different parameters of the PI controllers, it has been verified that a new self-oscillating regime can appear. In this case, the saturation in a control valve gives a Shilnikov type homoclinic orbit, which implies chaotic dynamics. The existence of a new set of strange attractors with PI control has been analyzed from the initial conditions sensitivity. An Appendix to show a computationally simple form to implement the calculation of Lyapunov exponents is also presented.