The first order irreversible gas phase reaction
Normal Pentane Iso-pentane
is to be carried out in a packed bed reactor. Currently 1,000 kg of reforming catalyst are packed in a 4 cm diameter pipe. The catalyst particles are 0.5 cm in diameter and the bulk density of the packed catalyst is 1,000 kg/m3. Currently 14.1% conversion is realized. The entering pressure is 20 atm and the pressure at the exit of the reactor is 9.0 atmospheres. It is believes that this reaction is internal diffusion limited. For internal diffusion limitations, the rate of reaction varies inversely with the catalyst particle size. Consequently, one of the engineers suggests that the catalyst be ground up into a smaller size. She also notes that the smallest size to which the catalyst may be ground is 0.01 cm. and that there are 3 other pipe sizes available into which the catalyst could be packed. These non-corrosive heat-resistant pipes, which can be cut to any length, are 2 cm, 3 cm, and 6 cm in diameter.
then
[3rd Ed. P4-21]