Page 517 - Elements of Chemical Reaction Engineering Ebook

Sec. 8.!5 Nonadiabatic Reactor Operation: Oxidation of Sulfur Dioxide Example 487
Substituting in Equation (E8-10.18), we get

dP
-- - -1.12X 10-s(l-0.55X)T (5500p+2288! (E8- 10.20)
dW P
We wish to obtain an order-of-magnitude estimate of the pressure drolp. To
obtain this estimate, we consider the reaction to be carried out isothennally
with E =: 0,

I
I dW=- -0.0432
P
dp
Back-of-the- Integrating with limits Po = 2 atm at W = 0 and P = P at W = 28.54 lb of cat-
enevelope alyst yields
calculation for AP
p2
-- - - -0.0432(0 - 28.54)
2
P = 1.239 atm
AP = 2- 1.24 = 0.76 atm
Because the gas-phase viscosity is a weakly varying function of temperature
we
(i.e., p, -- fi), shall consider viscosity to be independent of temperature:
dP
_.- - f3(T,P,X) (E8-10.21)
dW
9. Solution procedure. There are three coupled differential equations that must
be solved simultaneously:

Mole balance: -_ - fl(T p, X) (8-10.11)
dX
dW
The coupled
differential dT
equations to be Energy balance: -_ - f2 (K p, X) (8-10.17)
solved with an ODE dW
solver
Momentum balance: - - (8-10.21)
dP - f3(T,P,X)
dW
'IO. Numerical procedure. The rate equation is independent of conversion
between X = 0.0 and X = 0.05 and the rate of disappearance of SO, over this
range is equal to the rate of reaction at X = 0.05:

(E8-10.22)

a. Set X = 0.00, T = To, and P = Po.
b. Calculate k from Equation (E8-10.2).
c. Calculate Kp from Equation (E8-10.1).
d. If X<O.O5, calculate -ria, from Equation (E8-10.22). If X>O.O5, use
Equation (E8-10.10).
e. Calculate X, T, and P from a numerical solution to Equations (E8-10.10),
(E8-10.16) and (E8-10.20).