Extremes of conversion in continuous-flow reactors

The strong bounding theorem of micromixing has been proved using Bellman's principle of optimality. If the reaction rate depends on the concentration of a single component and is either a concave-upward or concave-downward function of that concentration, the conversion will attain extreme value...

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Bibliographic Details
Published in:Chemical engineering science 2004-07, Vol.59 (14), p.2831-2839
Main Authors: Buffham, B.A., Nauman, E.B.
Format: Article
Language:English
Subjects:
Applied sciences
Bounding theorem
Chemical engineering
Chemical reactors
Exact sciences and technology
Micromixing
Mixing
Reaction engineering
Reactors
Residence time
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Summary:The strong bounding theorem of micromixing has been proved using Bellman's principle of optimality. If the reaction rate depends on the concentration of a single component and is either a concave-upward or concave-downward function of that concentration, the conversion will attain extreme values when the reactor is completely segregated or is in a state of maximum mixedness. The extreme is a maximum when the reaction is concave-down (e.g. order less than one) and the reactor is maximally mixed and a minimum when the reactor is completely segregated. Conversely, the extreme is a minimum when the reaction is concave-up (e.g. order greater than one) and the reactor is maximally mixed and a maximum when the reactor is completely segregated. The new proof eliminates the need for the restrictive assumption that molecules can mix only when they have the same residual life. This assumption is untrue for many reactor models that approximate real physical behaviour.
ISSN:0009-2509
1873-4405
DOI:10.1016/j.ces.2004.03.018