The Residence Time Distribution Functions and their Relationships

THE RESIDENCE TIME DISTRIBUTION FUNCTIONS AND THEIR RELATIONSHIPS  

Mae Mullin and Weber [1] introdueed the eoneept of the RTD in the analysis of ehemieal reaetors, and Danekwerts [2] developed this eoneept further in his elassieal paper, whieh has sinee formed the basis of various investigations involving flow systems in ehemieal and bioehemieal reaetors. Levenspiel [3], Levenspiel and Bisehoff [4], Himmelblau and Bisehoff [5], Wen and Fan [6], and Shinnar [7] have given extensive treatments of this subjeet. 

AGE DISTRIBUTION FUNCTIONS AND RESIDENCE TIME DISTRIBUTION FUNCTION E(t) 

Consider a system of constant volume V through which a stream of fluid is passing at a steady volumetric rate u. If t is the age of elements in the stream at a point or over a region in the system, then the element whose age is between t and t + dt is known as the t-element. The relative frequency of the appearance of t-elements at a point or over a region in the system is an age distribution at the point or over that region. 

This is defined as the fraction of material in the outlet stream that has been in the system for the period between t and t + dt, and is equal to E(t)dt, where E(t) is called the exit age distribution function of the fluid elements leaving the system. This is expressed as 

The age of an element of fluid is defined as the time elapsed since it entered the system. The fraction of fluid having ages between t and t + dt is (uc/m) dt, where u is the volumetric rate of flow of fluid through the system, m is the quantity of tracer injected, and c is the local concentration of tracer at time t after injection. Danckwerts [8] introduced the concept of a fluid element or point, meaning a small volume with respect to the reactor vessel size, but still large enough 

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