Page 216 - Numerical methods for chemical engineering

202 4 Initial value problems

a × 1 −
A
B
s
2

1

2 1

−
× 1
1
A
B
cat v

c 2
2 1

Figure 4.15 (a) Molar flow rate and (b) catalyst site concentrations as functions of catalyst mass in a
packed bed reactor.

To evaluate these functions, we first have to compute some intermediate quantities from a
set of auxiliary equations

F tot = F A + F B + F C + F G0

F A F B F C
p A = P p B = P p C = P (4.232)
F tot F tot F tot

c B·S p C
ˆ r R = k s c A·S −
K s
For our system, we use the parameters

P 0 = 1 atm p A0 = 0.1 atm T 0 = T = 373 K
c tot = 10 −3 moles of sites per kilogram of catalyst
−5
3
ρ 0 = 2.9kg/m 3 µ = 2 × 10 Pa s υ 0 = 0.001 m /s
(4.233)
D p = 5mm φ = 0.64 A c = 0.0079 m 2 ρ s = 900 kg/m 3
K aA = 4.2 × 10 −5 Pa −1 K aB = 2.5 × 10 −5 Pa −1
5
k s = 30 s −1 K s = 9.12 × 10 Pa

PBR DAE sim.m simulates the packed bed reactor for a user-specified total mass of catalyst
in the reactor (example results are shown in Figure 4.15).