Chaotic dynamics in homogeneous tubular reactors with recycle

Effect of delay time on the generation of chaos in continuous systems. One-dimensional model. Two-dimensional model – tubular chemical reactor with recycle

“…, Θ H =−0.0268. Finally, it should be mentioned that in the case of a homogeneous reactor (Le=1, [1] and [4]) without dispersion ( ), the complete dynamic model , , and (condition (9) does not hold here) constitutes the logistic model and the quality of its solutions does not depend on the delay time τ d . In this case τ d affects solely the value of period of oscillations.…”

“…It may be shown, however, that even small values of these delays may lead to qualitative changes in the nature of process dynamics [2]. One of the classical and instructive, in this respect, systems is a chemical reactor [1], [4] and [5]. In traditional computations it is assumed that the times transport through recirculation loop are equal to zero.…”

Fractal structure of iterative time profiles of a tubular chemical reactor with recycle

“…1 [1] and [3], generated for the following values of the parameters: Da = 0.15, n = 1.5, γ = 15, β = 2, δ = 3. Crossing of the lines SN, FB or HB of this set leads to the change in the multiplication factor (saddlenode bifurcation), generation of jump oscillations (flip bifurcation) or generation of quasiperiodic oscillations (Hopf bifurcation), respectively.…”

“…The dynamics of a reactor was discussed, for example, in [1], [2], [3], [4] and [5], where it was demonstrated that the variables may be constant in the steady state or may oscillate in the form of rectangular time wave. The oscillations may be more or less complex, depending on the periodicity of the time series of the above-mentioned variables of a given state.…”

“…Thus, the time rate required for the system to reach the steady state is limited and depends on the values of the reactor parameters as well as on the values of temperature and concentration of the fluid flux at the initial moment. The reactor subjected to the theoretical analysis with external recycle [1], [3] and [5]. The time required for the reactor to reach the steady state was illustrated by means of various types of two and three-dimensional iterative time profiles [6].…”