70
Chapter 3
Both rc and
ra
appear to be well approximated by linear functions in
D.
By regression the following linear
relationships are determined
rc= 116
D -
20.4 mmoles CO î(gD W h) '
(6)
ra
= -29.1
D+
15.3
mmoles 0 3 (gD W h)'1
(7)
The decrease of the specific rate of oxygen consumption with increasing
D
is due to repression of the
respiratory system at the increasing glucose concentrations (see Example 7.3 for further discussion).
For
D
= 0.3 h 1
one obtains
- q , =
(28-0.1)*0.3/30 = 0.279
C -m o le (L -h )_1
7 1*09?
q =
-0.3 = 0.07785
C -m o le (L -h )“'
25.17
qp
=
• 0.3 = 0.0548
C - mole (L *
h) ~l
qc =
14.40-7.1 *10~3 - 0 .1 0 2 2 m o le(L • h)"1
-
qa
= 6.57 • 7.1 ■
10 3 = 0.0466 mole (L • h)_1
From these data the yield coefficients are calculated. The following table shows results for Z3 = 0.3 h 1
and also for
D
= 0.4 h'1
(all in mole or C-mole per C-mole glucose)
/>(h-')
r*
YK
Y
sPl
T„
0.3
0.279
0.196
0.366
0.167
0.159
0.355
0.4
0.175
0.394
0.312
0.044
0.119
0.513
A carbon balance shows that some carbon is missing in the products for both D = 0.3 and 0.4 h 1. The
yield coefficient of the missing carbon is shown in the column
Ysp{
of the table. A degree of reduction
balance yields:
D
sc 0.3 h'1
:
-4 + 4 0.167 + 0.279*4.20 + 0.196-6 + 0.159 ^ = 0
=>
KP
l
=6.19
and similarly at
D
= 0.4 h 1:
<f\ =
6.09. Thus, for both cases the degree of reduction for
P\
is close to 6.
There is good reason to believe that P, is ethanol. The final column of the table shows
Yse=Ysp
+
Ytp^
.
For the low dilution rate almost half the produced ethanol has been stripped off; for the highest dilution
rate only 23%. A loss of carbon of this magnitude is of course unacceptable.
Bijerk and Hall (1977) mention in their analysis of the von Meyenburg data that “ 12-13 wt % is missing
from the carbon balance”. In the analysis given here 16% is missing at
D =
0.3 h'1
and 12 % at 0.4 h'1
-
both calculated on a C-mole basis. Taking the averages 12.5 wt % and 14% respectively a tentative