Internal-Age Distribution Function, I t

The interaal-age distribution function I(t) is not as important as E(t) and F(t) in the characterization of chemical reactors. However, it is quite important in medicine, where tracer response techniques are used for a variety of purposes such as measuring blood flow rates and characterizing the behavior of internal organs. The interaal-age distribution function is discussed here primarily for the purpose of completeness. 

T/ j / fraction of fluid in vessel that has been in thel vessel for a time between r and r = dt J 

Notice the distinction between I(t) on one hand and F(t) and E(t) on the other. The distribution function I(t) is based on the fluid in the vessel. By contrast, both F(t) and E(t) are based on the fluid in the stream leaving the vessel. 

To relate/(/) to E(t) andF(t), consider a vessel with a constant-density fluid flowing through it at steady state. The vessel volume is Vand the volumetric flow rate through the vessel is u. Let s do a balance on the molecules of fluid that have been in the vessel for a time between 0 and t  

Equation (10-11) is a general result. It is valid for any closed vessel. Finally, combining Eqns. (10-6) and (10-10), 

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The exit age distribution function E(t) is obtained from outside the vessel while the internal age distribution function I(t) is obtained from inside the vessel. I(t) can be represented in terms of the RTD or the F-curve as... 

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