Design of Fermentation Processes
363
*
= 5 . 0 1 g L " 1
( 5 )
and the fraction of cells recirculated depends on the effectiveness of the cell separator. Thus for
R =
2 one obtains
p =
1.36 and
a =
90.8%. The cell concentration in the recycle loop is
xR
= p x =
6.8
lg L'1, For a less efficient operation of the centrifuge,
R =
3, one obtains
p -
1.24,
cr = 93.1 %, and
xR
=
6.21 g L 1.
Example 9.5 Design of a recirculation system—with maintenance requirement
We shall add on to Example 9.4 to include the influence of maintenance on the solution of the optimal
productivity problem. Take
ms = mp
=0.1h’
1
andTjUE
= 7j£ue = 0.5, i.e., complete conversion of substrate
to either product or biomass. All other kinetic and operational parameters are as in Example 9.4. Formulas
for calculating
Xmac
and the corresponding S value are derived in Example 9.3.
=o.766o
(i)
Sma*,* = -a" +Vfl* +£J* =0.09785
(2)
Since
D
is given, the maximum productivity is obtained when
X
= -Tmax s i.e.,
(Px)mut=DXimsf Y ^ =
2-0.7660-4-0.5 = 3.06 g L -'h
-1
(3)
which is obtained for M
= 0.2813 h
'1
./= 0.1406, and* = 0.7660 ‘ 0.5'4/0.1406 = 10.90 g L
'1
. For
R
= 2,
the value of
p
is calculated from Eq. (9.43).
p=
1.43 and
xR
= 15.58 g L'1.
a
“ 95.3% of the cells are
recycled, and the recycle stream is much thicker than for the corresponding maintenance-free example.
Example 9.6 Design of an integrated lactic acid production unit.
4.5 wt. % lactose in a waste stream from a large cheese factory is to be converted to lactic acid in a
stirred tank continuous reactor. The feed stream is 15 m
3
h
"1
to which enzymatically hydrolyzed whey
protein is added as nitrogen source. A high yield of lactic acid on lactose is not a requirement
per se,
but
the product is going to be used as the monomer for production of polylactate, and to avoid prohibitory
down-stream costs it is necessary to convert almost all the sugar, and at the same time to work with a
high enough D value to avoid formation of byproducts (the “mixed acids” of Example 5.6). The choice
of a continuous process is obligatory. Otherwise the value of the product
(88