Consider a real tubular reactor in which dispersion is occurring.
a. For small deviations from plug flow, show that the conversion for a first-order reaction is given approximately as X=1−exp[−tk+(τk)2Per](P18-20.1)
b. Show that to achieve the same conversion, the relationship between the volume of a plug-flow reactor, VP, and volume of a real reactor, V, in which dispersion occurs is VPV=1−(τk)Per=1−kDeU2(P18-20.2)
c. For a Péclet number of 0.1 based on the PFR length, how much bigger than a PFR must the real reactor be to achieve the 99% conversion predicted by the PFR?
d. For an nth-order reaction, the ratio of exit concentration for reactors of the same length has been suggested as CACAplug = 1 + nPer(τkCA0n−1)lnCA0CAplug. What do you think of this suggestion?
e. What is the effect of dispersion on zero-order reactions?