The concepts of residence time distribution and backmixing

In Chapter 3 two ideal types of continuous flow reactors were presented the plug flow reactor and the perfectly mixed reactor. In the first one all fluid elements have the same residence time. In the second one all fluid elements entering the reactor are mixed instantaneously. The consequence is that two volume elements entering the reactor at the same moment, may leave the reactor at different moments. In fact the residence times of different volume elements may vary between zero and infinite, though a large fraction has a residence time on the order of the mean residence time. In a well mixed reactor there is a large residence time distribution, in a plug flow reactor there is none. 

Real continuous reactors can be divided into two groups those that are tubular in shape and have a relatively narrow residence time distribution, and those that are comparatively well mixed and have a wide distribution of residence times. There are in fact only a few reactor types that do not resemble either of these two extremes. 

Obviously the residence time distribution has consequences for the conversion of a chemical reaction taking place in the fluid, since conversions generally increase with time. A distribution of residence times will generally reduce the conversion (except for reactions of zero order, or of a negative order). The residence time distribution is a physical characteristic of a continuous flow reactor, so that it can be determined by physical measurements. Consider a vessel and a fluid flow passing through it at a constant flow rate, from an entrance to an exit port. The flow conditions in the vessel are not known. By injecting a tracer component into 

In experiment a, the measured signal will be bell shaped in experiment b it will be S- shaped see figure 7.1. Let us first find the mass balance for experiment a. The amount of injected tracer and the volumetric fluid flow rate are, respectively, m and F  

The first residence time distribution (RTD)-function E(t) is defined as follows  

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