Mixing, Multiple Solutions, and Forced Unsteady-State Operation

Three important (complicating) possibilities were not considered in the treatment of reactors presented in earlier chapters: (1) the residence time of the reactant molecules need not always be fully defined in terms of plug flow or fully mixed flow; (2) the equations describing certain situations can have more than one solution, leading to multiple steady states; and (3) there could be periods of unsteady-state operation with detrimental effects on performance, that is, transients could develop in a reactor. Actually, reactors can operate under conditions where there is an arbitrary distribution of residence times, leading to different degrees of mixing with consequent effects on reactor performance. Also, multiple solutions do exist for equations describing certain situations, and they can have an important bearing on the choice of operating conditions. And, finally, unsteady-state operation is a known feature of the start-up and shutdown periods of continuous reactor operation; it can also be introduced by intentional cycling of reactants. We briefly review these three important aspects of reactors in this chapter. However, because the subjects are highly mathematical, the treatment will be restricted to simple formulations and qualitative discussions that can act as guidelines in predicting reactor performance. All aspects of mixing in chemical reactors are based on the theory of residence time distribution first enunciated by Danckwerts (1953). Therefore, we begin our discussion of mixing with a brief description of this theory. When a steady stream of fluid flows through a vessel, different elements of the fluid spend different amounts of time within it. This distribution of residence times is denoted by a curve which represents, at any given time, the amount of fluid with ages between t and t + dt flowing out in the exit stream.