Predicting conversion from RTD data

We are now in the position of being able to predict the form of tracer response curves from systems for which we have theoretical descriptions. From these curves we can recover the system RTD the details of the processing method required to achieve this will depend on the forcing function in question and Sects. 3.2.1—3.2.5 have considered the most common of these. In addition, we have seen in Example 1 how raw experimental measurements can be processed to give E(f) or E(0) data in the absence of any theoretical model. In this section, we now see how to use theoretical or experimental RTD data to predict the conversion which will be expected when a reaction with known kinetics takes place under steady-state conditions in the system under consideration. 

Consider the system to possess a specific RTD, E(f), and that the reactor is fed with a homogeneous, perfectly mixed feed stream. If a first-order reaction takes place within this reactor the system will be described by linear equations. In this case, the reaction kinetics and the system residence time distribution totally define the conversion of reactant which would be achieved in that system. In other words, any reactor system possessing that particular RTD under consideration would give the same feed conversion 

Fraction of feed staying in the reactor for a time netween t and t + At 

for known kinetics and a specified residence time distribution, we can predict the fractional conversion of reactant which the system of Fig. 9 would achieve. Recall, however, that this performance is also expected from any other system with the same E(t) no matter what detailed mixing process gave rise to that RTD. Equation (34) therefore applies to all reactor systems when first-order reactions take place therein. In the following example, we apply this equation to the design of the ideal CSTR and PFR reactors discussed in Chap. 2. The predicted conversion is, of course, identical to that which would be derived from conventional mass balance equations. 

If a batch reactor is charged with reactant at initial concentration and a reaction 

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