378
Chapter 9
9*00
/fcr/(l + /f)
-
af
In
(sf + Rs)/(l + R)
= (l + a r )ln |
\ -a A ln
“(* +
1
) /
-In
s f
L
*
RS
= In
R
R
+ 1
R
+ a f
In
Rs
1
+ RS
R
and the right-hand side of Eq. (9.80) is
x
- JC
,
1
/
(1
+
R)
/ v ~ -------- = - + ■
q
x(x\)
R
R(l + Rs/Sf)
(9.82)
(9.83)
For given values of
s, afi
and
sfi
one may determine
Ropi
by solution of Eq. (9.80) with Eqs. (9.82)
and (9.83) inserted.
Example 9.10. Recycle reactor design
Determine the optimal recycle ratio for a tubular reactor that reduces a feed stream substrate concentration
from 60 to 3 g m'3. The kinetics are given in Example 9.9. The optimal recycle ratio is determined by
solution of
jg + n (
1
f 20 + R
)
1 |
R + l
1/15
R
J+
15 °V
R
)
R
+
R
1
+ /f
/20
0
)
Any kind of reasonable iteration method gives the solution
R
= 2.50 in a few iterations. From Eq. (9.77),
with Eq. (9.82) inserted for the integral,
fit
r = (/f + l)
+ — In
15
f
Sy +
Rs
Rs
or
r = 0.75 -3.5
ln(1.4) + — ln(9)
= 1.26 h
This result is obviously better than what would have been obtained in a chemostat:
f ,
r _ D _
3 + 4
*
-3
V
3 J
(
2
)
(
3
)
= 1.75 h
(
4
)