Preview of Residence Time Theory

Example 8.1 derived a specific example of a powerful result of residence time theory. The residence time associated with a streamline st — LjV. The outlet concentration for this streamline is flbatch(t)- This is a general result applicable to arbitrary kinetics. Example 8.1 treated the case of a first-order reaction where flbatch(t) = flin exp(—kt). Assuming no diffusion, the mixing-cup average for the general case is 

Equation 8.15 can be used for any reaction, even a complex reaction where abatch(t) must be determined by the simultaneous solution of many ODEs. The restrictions on Equation 8.15 are isothermal, laminar flow in a circular tube with a parabolic velocity profile and negligible diffusion. 

The condition of negligible diffusion means that the reactor is completely segregated. A further generalization of Equation 8.11 applies to any completely segregated 

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