Page 178 - Elements of Chemical Reaction Engineering 3rd Edition

150 Isothermal Reactor Design Chap. 4

The uses Determine the plug-flow reactor volume necessary to produce 300 million
pounds of ethylene a year from cracking a feed stream of pure ethane. The reac-
tion is irreversible and follows an elementary rate law. We want to achieve 80%
conversion of ethane, operating the reactor isothermally at 1100 K at a pressure of
6 atm.

Solution

CZH, C,Hq+H,

Let A = C2Hs, B = C,H,, and C = H2. In symbols,
A --+ B+C

The molar flow rate of ethylene exiting the reactor is
6 lb 1 year 1 day 1 h Ibmol
FB=30OX10 -X-X-X-
year 365 days 24h 3600s x' ?%%
lb mol
= 0.340 -
S
Next calculate the molar feed rate of ethane. To produce 0.34 lb mol/s of eth-
ylene when 80% conversion is achieved,

lb mol
0'34 - 0.425 -
FAO = 0.x - S

1. Plug-flow design equation:

Rearranging and integrating for the case of no pressure drop and isothermal
operation yields

(E4-4.1)

2. Ratelaw:'
-rA = kCA with k = 0.072 s-l at 1000 K (E4-4.2)

The activation energy is 82 kcaVg mol.
3. Stoichiometry. For isothermal operation and negligible pressure drop, the
concentration of ethane is calculated as follows:

'Ind. Eng. Chem. Process Des. Dev., 14, 218 (1975); Id. Eng. Chem., 59(5), 70
(1967).