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270 Bioreactors

FIGURE 32 Variation of the steady sate biomass concentration and the productivity with dilution rate in a well-mixed
continuous flow bioreactor.

washout of cells from the bioreactor. In practice, the dilu- In Eq. (10), S o is the initial concentration of the substrate
tion rate must remain quite a bit less than the value needed in the reactor and S is the concentration at time t.
for optimal productivity (Fig. 32), or cells may be washed For Michaelis-Menten kinetics in a well-mixed batch
out because of an inadvertent slight increase in the dilution bioreactor, the conversion of the substrate at any time t is
rate. If viable biomass from the outflow of a continuous governed by the relationship:
flow well-mixed bioreactor is recycled to the reactor, as
k r Et
in Fig. 23b, then the reactor may be operated at a dilu- = S o C s − K m ln(1 − C s ) , (11)
tion rate greater than the maximum specific growth rate. V L
Such a bioreactor provides a greater biomass productivity where E is the total amount of enzyme in a bioreactor of
compared to one that does not recycle the biomass and volume V L . When the reaction is carried out in a contin-
the biomass concentration in the reactor outflow stream is uous flow well-mixed bioreactor, the expression for the
also greater. conversion is as follows:
k r E K m C s
3. Enzyme Kinetics = S o C s + , (12)
F 1 − C s
Instead of viable cells, a bioreactor may use nonviable where F is the volume flow rate of the feed. Similarly, in
cells and isolated enzymes as the biocatalyst. The reaction
a packed bed bioreactor, the expression for the conversion
in such a bioreactor may obey Michaelis-Menten kinetics
is the following:
but other kinetic patterns are also observed. For a reaction
that obeys Michaelis-Menten kinetics, the rate of reaction k r E
= S o C s + K m ln(1 − C s ) . (13)
(i.e., the rate of consumption of the substrate, −dS/dt) F
depends on the concentrations of the substrate S and the
Because F is the volume processed in time t in a contin-
enzyme e, as follows:
uous flow bioreactor and V L is the corresponding volume
in a batch reactor, a comparison of Eqs. (11) and (13)
dS k r eS
− = , (9) shows that batch and plug flow (i.e., packed bed) bioreac-
dt K m + S
tors containing the same amount of enzyme will achieve
where k r is the rate constant and K m is known as the equal conversions in a given time. This is a general conclu-
Michaelis-Menten constant. The dynamics of a bioreactor sion, irrespective of the reaction kinetics. A continuos flow
are often analyzed in terms of the conversion C s of the packed bed enzyme bioreactor may be advantageous rel-
substrate, where C s is the fraction of the original substrate ative to batch reactor, as the unproductive time for batch
transformed to a product, i.e., preparation could be eliminated in the continuous flow
unit. However, the batch reactor may have other important
S o − S advantages such as the ease of pH control in a well-mixed
C s = . (10)
S o device.