Nonideal Flow Pattern and Definition of RTD

Herein, only the steady-state flow without any reaction and without density changes (Vg = of a single fluid flow through an open vessel is considered. 

In order to design a flow reactor rationally, one needs to know how long the individual molecules stay in the vessel (the residence time). If for the ideal plug flow reactor all molecules come in and go out together (piston type flow pattern) meaning that the residence time is the same for the whole reacting mixture, in real reactors some elements of the fluid may have different pathways resulting in 

Madhvanand N. Kashid, Albert Renken and Lioubov Kiwi-Minsker. 

After an infinitely long observation time, the probability that all volume elements fed into the reactor at the time t = 0 have left is equal to one. 

The fraction of the fluid in the exit stream, which is younger than t, corresponds to 

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