Math. Model. Nat. Phenom.
Volume 16, 2021
Control of instabilities and patterns in extended systems
|Number of page(s)||22|
|Published online||28 June 2021|
Dynamics and control of loop reactors: a review
Department of Chemical Engineering, Technion - I.I.T.,
32 000, Israel.
* Corresponding author: firstname.lastname@example.org
Accepted: 10 June 2021
In the loop reactor (LR) the system is composed of several reactor units that are organized in a loop and the feeding takes place at one of several ports with switching of the feed port in a periodic way. In its simplest operation a pulse is formed and rotates around it, producing high temperatures which enable combustion of dilute streams. A limiting model with infinite number of units was derived. Rotating pulses, that are steady in a coordinate moving with the switch velocity, emerge in both asymptotic and discrete models when the ratio of switching to front propagation velocities is around unity. But this behavior exists over a narrow domain of this ratio. Simulations were conducted with generic first order Arrhenius kinetics. Experimental observations of simple frozen rotating pulses are reviewed. Outside the narrow frozen rotating patterns domain the system may exhibit multi- or quasi-periodic operation separated by domains of inactive reaction. The bifurcation set incorporates many ’finger’-like domains of complex frequency-locked solutions that allow to significantly extend the operation domain with higher feed temperature or concentration. Control is necessary to attain stable simple rotating frozen patterns within the narrow domains of active operation. Various control approaches that were suggested, or experimentally applied for this purpose, are reviewed. Actual implementation of combustion in LR will involve several reactants of different ignition temperatures and varying concentration. Design and control should be aimed at producing locked fronts and avoid extinction of the slower reaction.
Mathematics Subject Classification: 35A18 / 35B35 / 35B36 / 35B40 / 35K57 / 37G99 / 93C20
Key words: Moving pulses / network of chemical reactors / loop-reactor / distributed systems / control / control of distributed system / bifurcations
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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