Page 191 - Elements of Chemical Reaction Engineering Ebook

162 isothermal Reactor Design Chap. 4

Solution
1. biffereatial mole balance:

(E4-6.1)

2. Rate law:
113 213 = (E4-6.2)
-rd, = kPA PB k(CART)113(CBRT)2/3
1/3 2l3
= kRTCA CB (E4:6.3)
The algorithm 3. Stoichiometry. Gas-phase, isothermal u = vo(l + &X)(P0/P):

(E4-6.4)

(E4-6.5)
We can evaluate the
combine step either
1) Analytically 4. Combining the rate law and concentrations:
2) Graphically
3) Numerically, or (E4-6.6)
4) Using software

(E4-6.7)

For stoichiometric feed, OB = i :

(E4-6.8)
= k(-) 1-x p
1+&X P,

where k’ = kPAo = 0.63kPA0.
5. Developing the design equation. For a packed-bed reactor, the relationship
between P and W when EX^ 1 is
-
Eq, (4-33) is valid -- (1-aW)’” (4-33)
oalyif E = 0 PO
or ex41
(Note that we will check this assumption in Example 4-7.) Combining Equa-
tions (E4-6.8) and (4-33) g’ ives us

(E4-6.9)

Combining Equations (E4-6.9) and (E4-6. l), we have