Bioreactor Design and Operation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 920

Batch operations are not controllable as all the substrate is added into the reactor at the
start. Fed-batch reactor is based on feeding of a growth-limiting nutrient substrate to
a culture. Cell growth and fermentation can be controlled by the feeding strategy. The fed-
batch strategy is typically used in bio-industrial processes to reach a high cell density in
the bioreactor. Mostly, the feed solution is highly concentrated to avoid dilution of the biore-
actor. In essence, fed-batch reactor is applied in such a fashion that a chemstat or CSTR is
simulated with a seemingly batch operation. The controlled addition of the nutrient directly
affects the growth rate of the culture and allows avoiding overflow metabolism (formation of
side metabolites, such as acetate for Escherichia coli, lactic acid in cell cultures, ethanol in
Saccharomyces cerevisiae), oxygen limitation (anaerobiosis).
Substrate limitation offers the possibility to control the reaction rates to avoid technological
limitations connected to the cooling of the reactor and oxygen transfer. Substrate limitation
also allows the metabolic control, to avoid osmotic effects, catabolite repression, and overflow
metabolism of side products. Therefore, there are different operation strategies for fed-batch:
1) constant feed rate or constant growth/fermentation rate; 2) exponential feed rate or
constant specific growth rate. The exponential growth with fed-batch operation can be at
any rate, up to the maximum rate in the exponential growth phase of a batch growth. This
is the case that closely resembles a chemostat operation. Usually, maximum growth rate is
not wanted for undesired by-product production which can be high at maximum growth.

18.3. AERATION, AGITATION, AND HEAT TRANS FER

For industrial-scale fermentors, oxygen supply and heat removal are key design limita-
tions. The severity of the oxygen requirement is a function of the organism. The oxygen
uptake ratio (OUR) can be written:

OUR ¼ Xm O 2 (18.1)

where m O 2 d specific uptake rate of oxygen and X is the biomass concentration. Typical values
of m O 2 are shown in Table 18.4 .
OUR represents the consumption rate of oxygen, which is the demand from the cells. OUR
is balanced by the OTR when pseudo steady state is reached. OTR is given by

¼ K L a ðC C L Þ (18.2)

where C d oxygen solubility, C L d actual dissolved oxygen (DO), and K L a is the volumetric
mass transfer coefficient.
The value of K L a can be estimated by:

OTR

0:4 0:5

0:5

(18.3)
where k d empirical constant, P 0 d power requirement, V d bioreactor volume, v S d superficial
gas velocity, and

K L a ¼ kðP 0 =VÞ ðv s Þ u

ud agitator rotation rate.
The value of P 0 can be estimated from other correlations, such as

! 0:45

u uD i

P

P 0 ¼ k 0 (18.4)

Q

0:56