(Spherical Reactor) Because it is readily available from coal, methanol has been investigated a an alternative raw material for producing valuable olefins such as ethane and propane. One of the first steps in the reforming process involves the dehydration of methanol.
2CH3OH CH2=CH2 + 2H2O
This gas-phase reaction is carried out over a zeolite catalyst and follows an elementary rate law. The catalyst is packed in a tubular PBR that is 2 m in diameter and 22 m in length. Pure methanol is fed at a molar flow rate of 950 mol/s, a pressure of 1500 kPa, a concentration of 0.4 mol/dm3, and 490 °C. The conversion and pressure at the exit are 0.5 and 375 kPa, respectively.Flow throughout the bed is known to be such that the turbulent contribution in the Ergun equation (i.e. G2) can be neglected. The tubular PBR is to be replaced with a spherical PBR containing an equal amount of identical catalyst. The spherical PBR measures 5.2 m, in diameter and has screens placed 2 dm from each end (i.e., L = L' = 24 dm)
[The data given in this problem are based on kinetics data given in H. Schoenfelder, J. Hinderer, J. Werther, F.J. Keil, Methanol to olefins - prediction of the performance of a circulating fluidized-bed reactor on the basis of kinetic experiments in a fixed-bed reactor. Chem. Eng. Sci. 49 5377 (1994).]
[3rd Ed. P4-24]