The decomposition of cyclohexane to benzene and hydrogen is mass transfer-limited at high temperatures. The reaction is carried out in a 5-cm-ID pipe 20 m in length packed with cylindrical pellets 0.5 cm in diameter and 0.5 cm in length. The pellets are coated with the catalyst only on the outside. The bed porosity is 40%. The entering volumetric flow rate is 60 dm³/min.

a. Calculate the number of pipes necessary to achieve 99.9% conversion of cyclohexane from an entering gas stream of 5% cyclohexane and 95% H₂ at 2 atm and 500°C.
b. Plot conversion as a function of pipe length.
c. How much would your answer change if the pellet diameter and length were each cut in half?
d. How would your answer to part (a) change if the feed were pure cyclohexane?
e. What do you believe is the point of this problem? Is the focus really green CRE? How so?