Instabilities in homogeneous nonisothermal reactors: Comparison of deterministic and Monte Carlo simulations

Abstract

Articles you may be interested inDosimetric accuracy of a deterministic radiation transport based 192Ir brachytherapy treatment planning system. Part III. Comparison to Monte Carlo simulation in voxelized anatomical computational models Med. Phys. 40, 011712 (2013); 10.1118/1.4770275 Dosimetric comparison of Acuros XB deterministic radiation transport method with Monte Carlo and model-based convolution methods in heterogeneous media Med. Phys. 38, 2651 (2011); 10.1118/1.3582690 Direct simulation Monte Carlo computation of reactor-feature scale flows J. Vac. Sci. Technol. A 15, 559 (1997); 10.1116/1.580683 Monte Carlo simulations and kinetic theory of homogeneous and heterogeneous adsorption with lateral interactionsA homogeneous nonisothermal continuous stirred tank reactor is modeled using the Monte Carlo method. The results are compared with deterministic bifurcation theory and time integration of the continuum unsteady state equations. Multiple solutions are determined for certain conditions and metastability is observed near ignition and extinction points. It is found that the amplitude of fluctuations increases near turning and Hopf bifurcation points. For finite size systems a supercritical Hopf bifurcation appears as a smooth transition from stationary solutions to oscillations, and near Hopf bifurcation point oscillations are more chaotic. Near a subcritical Hopf bifurcation, the stationary branch exhibits small amplitude oscillations of the same period as the oscillatory attractor, and metastability of both the stationary and the oscillatory attractors is observed. In the presence of isolas, metastability can cause a phase transition from the extinguished branch to the isola branch followed up by oscillations and subsequent extinction of the oscillations as the oscillatory attractor becomes metastable at high residence times.

A Simple Monte Carlo Method for Modeling Arborescent Polymer Production in Continuous Stirred Tank Reactor

“…To our knowledge, only a few research groups have developed Gillespie MC models for dynamic operation of CSTRs . These research groups focused on reactions involving small molecules or biosystems rather than polymers.…”

“…These research groups focused on reactions involving small molecules or biosystems rather than polymers. Vlachos developed a Gillespie MC model to study CSTR operation with exothermic reactions that lead to steady‐state multiplicity and complex nonlinear dynamics . They used random numbers to study the role of thermal fluctuations and finite‐size effects on ignition and extinction behavior.…”