Residence time distribution positive reaction order

Now that a combination of the tabulated data and exponential tail allows a complete description of the residence time distribution, we are in a position to evaluate the moments of this RTD, i.e. the moments of the system being tested [see Appendix 1, eqn. (A.5)] The RTD data are used directly in Example 4 (p. 244) to predict the conversion which this reactor would achieve under specific conditions when a first-order reaction is occurring. Alternatively, in Sect. 5.5, the system moments are used to evaluate parameters in a flexible flow-mixing transfer function which is then used to describe the system under test. This model is shown to give the same prediction of reactor conversion for the specified conditions chosen. 

Whereas a conventional fixed-bed reactor with flow of gas closely approaches an ideal plug-flow reactor in the sense that the residence-time distribution of the gas is very narrow, this may no longer be the case in very shallow beds, as in the LFR. For reactions with a positive order, extra catalyst is therefore required to achieve the same conversion as in an ideal plug-flow reactor. 

Fig. 19. Choice of residence time distribution for isothermal reactions of positive, zero, and negative order.

---