Mathematical model types Segregated

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we will develop assume that the residence time distribution function may be attributed to one or the other of these flow situations. The first class of nonideal flow conditions leads to the segregated flow model of reactor performance. This model may be used... 

Since these two types of processes have drastically different effects on the conversion levels achieved in chemical reactions, they provide the basis for the development of mathematical models that can be used to provide approximate limits within which one can expect actual isothermal reactors to perform. In the development of these models we will define a segregated system as one in which the first effect is entirely responsible for the spread in residence times. When the distribution of residence times is established by the second effect, we will refer to the system as mixed. In practice one encounters various combinations of these two limiting effects. 

Statistics and probability theory provided the analyst with the theoretical framework that predicts the uncertainties in estimating proj rties of populations when only a part of the population is available for investigation. Unfortunately this theory is not well suited for analytical sampling. Mathematical samples have no mass, do not segregate or detoriate, are cheap and are derived from populations with nicely modelled composition, e.g. a Gaussian distribution of independent items. In practice the analyst does not know the type of distribution of the composition, he has usually to do with correlations within the object and the sample or the number of samples must be small, as a sample or sampling is expensive. 

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