Residence Time Distributions for Ideal Reactors

The RTD function E(0) or E(0), obtained from the tracer experiment conducted on the reaction vessel, can be used to characterise the non-ideality as the fluid mixing pattern in the vessel has a strong influence on the distribution of residence time. Given the RTD for a reaction vessel, we would first like to know if the mixing patterns in the reaction vessel match well with the mixing patterns assumed for ideal reactors (ideal CSTR or ideal PER). This can be done by comparing the RTD function (F-curve or E-curve) for the given reactors with the RTD functions for the ideal CSTR or ideal PER. For this, we should know the RTD functions for ideal reactors. As the ideal CSTR and ideal PER are theoretical reactors, the RTD function equations for these reactors are derived theoretically. 

Assume that the CSTR is subjected to a step test by continuous injection of tracer at the inlet, starting from a reference time 0 = 0. Inlet tracer concentration is Q(9) = Cfl. For all 0 0. At any time 0 0, the outlet concentration of the tracer is C(0). As the CSTR is ideal, mixing in the vessel is uniform and the concentration of the tracer in the vessel is the same everywhere and is equal to the outlet concentration C(0). 

Taking an unsteady-state tracer balance around the reactor. 

Rate of flow tracerl fRate of flow tracer fRate of accmnulationl 

Dividing all the terms in the above equation by q and defining the mean residence time Q = V/q, we get 

---