Application to RTDs

The concept of residence time distributions (RTDs) is central to classical chemical engineering. In this concept, the outlet response of a system to a known input disturbance (i.e. tracer concentration) is analyzed. Relations are derived for the outlet age distribution using material balances. In the following, we will demonstrate that identical relations are obtained via a completely different ronte using population balances. 

Let us consider the age of fluid particles in an arbitrary flow system (no generation). If we denote age by a, the growth rate of age is given by 

Let /be the number of fluid particles of age a. Equation (3.10) for this case becomes 

Insertion of these definitions into Equation (3.12) and using the mass balance, 

Equation (3.15) is ihe generalized relationship between the residence time distribution, E, and the internal age distribution, I, in the transient state for an arbitrary flow system. For an incompressible fluid (given a constant volume). 

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