Extremes of conversion in continuous-flow reactors

Abstract 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.