First-order Exothermic Reaction Research Articles

CHAOS IN A PERIODICALLY PERTURBED CSTR

The occurrence of chaotic behavior is analyzed in a periodically perturbed dynamic nonisothermal CSTR with first-order exothermic chemical reaction A→B and an Arrhenius expression for the rate constant. When sinusoidal forcing functions for the cooling-fluid temperature and the volumetric feed rate are applied to the unperturbed part of the system, period-doubling behavior leading to a strange attractor is observed as the amplitude of the perturbation in the cooling-fluid temperature is increased. Chaos and period-doubling are also verified through Fourier spectra analysis, adherence to the Feigenbaum Theory, and analysis of the Poincare return map The basis for obtaining chaotic behavior in the reactor system is the Melnikov theory, which slates that chaos can be obtained in a periodically perturbed system if the phase plot of the unperturbed system closely corresponds to that of a homoclinic orbit (a phase trajectory which contains the stable and unstable separatrices of a saddle). From linear stability...

Dynamics of lumped chemically reacting systems near singular bifurcation points

The systematic method of locating and classifying complex dynamical regimes of lumped reactors involves analysis of dynamics near singular bifurcation points at multiple eigenvalues. Amplitude expansion in the proximity of a singular bifurcation combined with multiple time scaling are used to derive universal equations that, though valid quantitatively only in a narrow patch of the parametric space, give full qualitative information on dynamics of a system possessing the respective highest singularity. The principal general result is that an algebraic singularity of a certain order is required to obtain dynamics of a certain dimensionality. In the lowest order, this is cusp singularity for two-dimensional dynamics in the proximity of bifurcation at double zero eigenvalue, and swallowtail singularity for three-dimensional dynamics at triple zero eigenvalue. The basic equation of two-dimensional dynamics describes various transitions between stationary and periodic states as observed, for example, in a first-order exothermic reaction. The equation of three-dimensional dynamics generates more complex phenomena, in particular, chaotic regimes.

A Qualitative Study of the Steady-State Solutions for a Continuous Flow Stirred Tank Chemical Reactor

An approach to the bifurcation of steady-state equilibria using singularity theory is applied to the problem of multiple equilibria in a continuous flow stirred tank chemical reactor where the flow rate is the bifurcation parameter. Under the assumption of a single first-order exothermic chemical reaction, all the qualitatively different bifurcation diagrams which occur locally are found. They form the universal unfolding of the singular bifurcation problem $x^3 + \lambda ^2 = 0$.

Optimal location of measurements in tubular reactors

The optimal location of temperature measurements along the length of a non-adiabatic tubular reactor in which a first-order exothermic reaction is occu

Stability analysis of non-interacting control of continuous stirred tank reactor†

Abstract A continuous stirred tank reactor operating around a stable equilibrium point and having interaction may become unstable when made noii-intcractivo by tho addition of compensators. Procedures for selecting the settings of tho feedback controllers to obtain any desired degree of stability in the non-interacting system are worked out in this paper. A numerical example of a continuous stirred tank reactor with an irreversible, exothermic first-order reaction is taken and controller settings for its stable non-interacting operation worked out.