Fed-Batch Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 672

(a) (b)

10 90

10 1

XV/(YF X/S S F V 0 ) 10 80

10 70

XV/(YF X/S S F V 0 )

10 60

10 0

10 50

10 40

SV/(S F V 0 )

10 30

10 -1

SV/(S F V 0 ) 10 20

10 10

10 -1

10 -2

0 200 400 600 800 1000

0 2 4 6 8 10 12 14 16

t

t

(c) (d)

1

1

X / (YF X/S S F )

X/(YF X/S S F )

0.1

0.1

S/S F

S / S F

0.01 0.01

0 2 4 6 8 10 12 14 16 1 10 100 1000

t t

FIGURE 13.6 Biomass production and substrate accumulation in the reactor at short times for exponential feed
rate of Q ¼ 0.1 m max V 0 exp(0.2 m max t ). The initial conditions are S 0 ¼ S F and X 0 ¼ 0.0105 YF X/S S F . The Monod satu-

ration constant K S ¼ 0.05 S F .

can consume. Fig. 13.5 a shows that the biomass production increases sharply initially, while
maintains increasing at a low rate at long time. This is similar to the constant feed rate case
shown in Fig. 13.4 a. The amount of the substrate in the reactor, on the other hand, decreases
sharply at start ( Fig. 13.5 c) and then increases with time. This is different from the constant
feed rate case shown in Fig. 13.4 a and c. The increasing trend remains at long time as shown
in Fig. 13.5 a.
Fig. 13.5 b and d shows the variation of substrate and biomass concentrations with time.
One can observe that the biomass concentration increases sharply initially to over 2 YF X/
S S F ( Fig. 13.5 d) and then decreases to the “steady” value ~YF X/S S F ( Fig. 13.5 b). The substrate
concentration, on the other hand, decreases sharply at start from S 0 ¼

S F to below 0.002 S F and

then recovers slowly to a steady value of S 0.0125 S F .

Fig. 13.6 shows the variations of the reactor contents as functions of time for the same feed
and growth conditions as shown in Fig. 13.5 . However, the initial biomass concentration is
lowered from 1.05 YF X/S S F to 0.0105 YF X/S S F . One can observe that the trends are similar
to those in Fig. 13.6 . The only differences are that the biomass concentration increases sharply
at start, and it take longer to reach “steady values” of biomass and substrate concentrations.

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