Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 807

Substituting Eqn (E16-3.6) into Eqn (E16-3.4) , we obtain

R
ln 1 f A
f A

E =

DH R
r

T 0 ¼ C A0 f A (E16-3.7)

m cat k 0
Q

C P

Eqn (E16-3.7) is the mathematical description of the ignition e extinction curve (for conver-
sion versus the feed temperature). We now find the parameters:
C A0 ¼ r A0

u A
M A r 0 ¼

0:3
210 g

cm 3 ¼ 1:21410 3 mol cm 3

M A ¼ mol 0:85 g

= =

=

2:010 5 J DH R

r

= mol

cm 3 1:21410 3 mol

cm 3 C A0 ¼ = ¼ 163:26 K

C P

1:75 J =ð g $ K Þ0:85 g =

1:310 11 cm 3 m cat k 0

Q ¼

=ð h $ g-cat Þ20 g-cat

¼ 8:66610 10

0:5 cm 3 = min 60 min = h

Substituting these know parameters into Eqn (E16-3.7) , we obtain

16; 300
25:1853þ ln 1 f A
f A

T 0 ¼ 163:26 f A (E16-3.8)

which has a unit of Kelvin.
Eqn (E16-3.8) is plotted in Fig. E16-3.1 (by varying f A between 0 and 1, we computed
values of T 0 , and then graphing the data out to yield Fig. E16-3.1 ). One can observe that there
are multiple values of conversion f A for some given values of feed temperature T 0 (between
554.10 and 581.12 K).

1.0

0.8

0.6

0.4

0.2

0.0

500 520 540 560 580 600 620 640

T 0 , K

FIGURE E16-3.1 Variation of conversion with feed temperature.