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
wt.% polymer grade lactic
acid) will not match the cost of raw materials, labor and energy.
The feed is sterile, and in a conventional stirred tank, continuous reactor the effluent product
concentration is
p„.
The reactor volume is 10 m3.
In an ultrafilter cell recirculation system the separation factor D is chosen to 0.9, and vy
and
v2
are 1.5
previous page 386 Bioreaction Engineering Principles, Second Edition  read online next page 388 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off