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Nonlinear Behavior of Reactor-Separator and Reactor-Distillation Networks : Influence of the Energy Balance Formulation

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons86527

Zeyer,  K. P.
Process Synthesis and Process Dynamics, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons86359

Kienle,  A.
Process Synthesis and Process Dynamics, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;
Otto-von-Guericke-Universität Magdeburg, External Organizations;

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Citation

Zeyer, K. P., Kulkarni, A., Kienle, A., Mantravadi, V., & Pushpavanam, S. (2007). Nonlinear Behavior of Reactor-Separator and Reactor-Distillation Networks: Influence of the Energy Balance Formulation. In V. Plesu, & P. S. Agachi (Eds.), 17th European Symposium on Computer Aided Process Engineering (pp. 425-430).


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-98A0-D
Abstract
Modeling of evaporative separators with mass and energy balances, only, often leads to di erential algebraic systems (DAE) with di erential index 2. To overcome the problems which are associated with the numerical solution of index 2 DAEs either a formal index reduction can be applied or the model can be reformulated by modifying the underlying assumptions. Typical modi cations leading to index 1 problems are either the assumption of a quasistatic energy balance or the inclusion of some simple uid dynamics. In the present paper the dynamic behavior predicted by these di erent model formulations are analyzed and compared with each other. First, focus is on an isolated single stage ash process with given heat input. The well-known adiabatic ash is included as a special case. It is shown that the dynamic behavior of the di erent model formulations for a stand alone ash are rather close. In particular, in all cases a stable steady state is predicted. Second, a simple reactor-separator system with recycle is considered. The reactor is a CSTR, whereas the separator is again a constantly heated ash. In a previous paper we have shown, that the recycle in such a system can induce instability and multiplicity of steady states [1]. In the present paper it is shown, that although the stand alone ash is rather insensitive to the speci c model formulation, the dynamics of the coupled system can under certain conditions to be speci ed in this paper depend on the speci c model formulation applied. In particular, a new type of bifurcation is found where the eigenvalues have a pole with a change of sign. The analysis is based on a model with negligible transportation delay of the recycle. Furthermore, these investigations are extended to reactor-distillation column models. In such models complex bifurcation structures consisting of periodic, complex-periodic, and even deterministic chaotic oscillations have been characterized. These bifurcation structures show interesting analogies to scenarios found in isothermal autocatalytic oscillators, like the Belousov-Zhabotinsky reaction [2] or the peroxidase-oxidase reaction [3]. It is illustrated that the observed bifurcation scenario critically depends on the formulation of the energy balance equation of the distillation column. © 2007 Elsevier B.V. All rights reserved. [accessed 2013 December 4th]