Page 430 - Modelling in Transport Phenomena A Conceptual Approach

410 CHAPTER 9. STEADY MICROSCOPIC BALANCES WTH GEN.

Since the volumetric flow rate is not constant, Le., E = 1, it is necessary to express
in terms of d. The use of Q. (9.5146) gives

Therefore, the total molar flow rate, n, is

h=hAo+i (12)

Substitution of Eq. (12) into Eq. (9.5-151) gives the volumetric flow rate QS

P

where e, is the volumetric flow rate at the inlet of the reactor.
Substitution of Eqs. (9) and (13) into Eq. (8) gives

di
-=- khAo [I - (i/hA,)]
dV eo (l+k/fi~,)
The fractional conversion expression for a plug flow reactor is similar to Eq. (5),
so

Substitution of Eq. (9) into Eq. (15) yields
b
X=--

The use of Eq. (16) in Eq. (14) and rearrangement gives

= 2.42 (F)

Substitution of the nume~cal values into Eq. (1 7) gives

(2.42) (0.05)
V= = 0.11 rn3
1.1