Fed-Batch Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 674

biomass reaches a maximum and then decreases to a lesser “steady value” of 0.652308 YF X/
S S F than that with negligible death rate of 0.9875 YF X/S S F substrate show. The concentration
of the substrate reaches a minimum and recovers ~0.0214286 S F as compared with the steady
value of 0.0125 S F for negligible cell death.
The condition of inequality

S F Q m G XV

(13.11)

YF X = S

can have a significant impact on fed-batch growth with a specific death rate. Fig. 13.9 shows
the variations of the reactor contents as functions of time for the same initial and constant
feed conditions as shown in Fig. 13.4 . However, a specific death rate of k d ¼

m max is
applied to the same Monod growth. One can observe that at long times ( Fig. 13.9 a), the
cell accumulation in the reactor is nearly unchanged, whereas the substrate accumulation
kept increasing slightly. The concentration of the substrate in the reactor, on the other
hand, remains nearly unchanged, while cell concentration kept decreasing ( Fig. 13.9 b).
Fig. 13.9 c and d shows the reactor content variations at short times. One can observe
that while the cell mass accumulation increases with time, the substrate accumulation

0.01

FIGURE 13.9 Biomass production and substrate accumulation in the reactor for constant feed rate of
Q

¼ m max V 0 . The initial conditions are S 0 ¼ S F and X 0 ¼ 1.05 YF X/S S F . The Monod saturation constant K S ¼ 0.05 S F .

Specific death rate k d ¼ 0.01 m max .