Different scenarios in a controlled tubular reactor with a countercurrent coolant.

*(English)*Zbl 0801.35140Summary: A system of three partial differential equations, representing the dynamics of a tubular reactor with axial diffusion refrigerated by means of a countercurrent fluid, is studied. The PDE system is reduced to an ODE one applying the usual finite differences scheme. The use of a semi- implicit Runge-Kutta method, that has proved itself the most reliable integrator for highly oscillating systems, requires a careful analysis of the numerical integration procedure in order to save computational time. Simulation results show the possibility of chaotic behaviour in a specific parameters range. The variable temperature coolant system does not alter the features of the simplified model with a constant coolant temperature. However, beside the usual period doubling cascade, a mechanism of chaotic transition through type III intermittency and a hysteresis phenomenon are observed. After a preliminary characterization of the chaotic regime by means of the known methods, the paper focuses on the analysis of the new types of scenario.

##### MSC:

35Q80 | Applications of PDE in areas other than physics (MSC2000) |

34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |

65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |

92E20 | Classical flows, reactions, etc. in chemistry |

##### Keywords:

dynamics of a tubular reactor; Runge-Kutta method; chaotic behaviour; hysteresis phenomenon##### Software:

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\textit{L. Pellegrini} et al., Chaos Solitons Fractals 3, No. 5, 537--549 (1993; Zbl 0801.35140)

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##### References:

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