Single-CSTR RTD

In an ideal CSTR the concentration of any substance in the effluent stream is identical to the concentration throughout the reactor. Consequently, it is possible to obtain the RTD from conceptual considerations in a fairly straightforward manner. A material balance on an inert tracer that has been injected as a pulse at time t = 0 into a CSTR yields for f 0 

Distributions of Residence Times for Chemical Reactors Chap. 13 

Because the reactor is periectly mixed, C in this equation is the concentration of the traeer either in the effluent or within the reactor. Separating the variables and integrating with C = Q at / = 0 yields 

This relationship gives the concentration of tracer in the effluent at any time t. 

To find E(t) for an ideal CSTR, we first recall Equation (13-7) and then substitute for C(t) using Equation (13-39). That is, 

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