# Laboratory experiment: Residence Time Distribution (Cascade)

## Models of Ideal Reactors

Reactors are specified according to the following: discontinuously operated (batch reactor), continuously operated (flow reactor), and half-continuously operated (semi batch reactor). The ideal borderline cases of continuous reactors are represented by the ideally mixed continuously stirred tank reactor or the ideal plug flow reactor. Below are shown (a) the temporal and (b) the spatial dependence of the concentration of the reactant A ($c A,E$ und ($c A,A$) under steady state conditions for the ideal continuously stirred tank reactor, the ideal plug flow reactor as well as the ideal batch reactor:

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Fig.1

The figure shows a) the temporal and b) the spatial dependence of the concentration of the reactive component A for a continuously operated ideal stirred tank reactor. The continuously added reactants are mixed immediately with the contents of the reactor and products are constantly being removed. This borderline case is referred to as "homogenous, steady state" which means the composition of the reactor mixture and the reaction rate are identical at all times and at every spot for all components in the reactor.

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Fig.2

The figure shows a) the temporal and b) the spatial dependence of the concentration of the reactive component A for the ideal plug flow reactor. The residence time is the same for all parts and is equivalent to the mean residence time. The composition of the reactor mixture is constant through the cross section of the reactor (radial) and no mixing of the reactants occur in the flow direction (axial)(plug flow). At steady state the concentration is all times constant at every point of the flow reactor. In accordance to the reaction, a concentration gradient in flow direction (axial) appears. This borderline case is referred to as "non-homogenous, steady state".

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Fig.3

The figure shows a) the temporal and b) the spatial dependence of the concentration of the reactive component A for an ideally stirred batch reactor. It is also characterized by a fully mixed content. The reactants are brought into the reactor prior to reaction and the products are removed after of reaction-conclusion. The concentration of the reactants decrease a) in time and are b) spatially constant. In this case, all particles have the same mean residence time. This borderline case is referred to as "homogenous, non-steady state" (regarding the operation of the reactor).

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Fig.4

In practice, the use of countinuously stirred tank reactors in series (a cascade of continuously stirred tank reactors) is widespread. In this case a stair-shaped concentration profile of the reactants is achieved for the cascade of ideal stirred tank reactors (see figure). With an increasing number of tanks (n) the observed concentration change is similar to that of the plug flow reactor.

Whith an infinite number of tanks the dependance of the concentration of the cascade of stirred tank reactors is equivalent to the plug flow reactor. For a small number (n) of tanks the residence time for a large part of the molecules differs from the mean residence time (broad residence time distribution). A higher number of tanks causes an adjustment towards the mean residence time (narrow residence time distribution).

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