Continuous Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 615

cell biomass concentration decreases monotonously with dilution although more sharply
near washout to zero when no endogenous needs required for cell growth ( Fig. 12.7 b). The
decrease is more pronounced when the saturation coefficient is increased at lower dilution
rates. However, the cell biomass concentration increases with increasing dilution rate, rea-
ches a maximum before decreases sharply to zero at washout (near D

k d )
when the endogenous needs are not exactly zero ( Fig. 12.7 b). Increasing cell death rate
and/or endogenous needs decreases the biomass productivity and washout limit dilution
rate for a given feed ( Fig. 12.7 c). An increase in the saturation coefficient ( K S )also
decreases the washout limit of dilution rate as well as the cell biomass productivity.
One can also observe that there is a maximum cell productivity that varies with growth
parameters.
Cytostat and turbidostat are designed to control the cell density (or biomass concentra-
tion) in the reactor. As one can observe from Fig. 12.7 b, the cell biomass concentration
depends on the dilution rate weakly, especially between 0.4

¼ m max m emax

m max . Therefore,
controlling cell density by adjusting the flow rate (or dilution rate) is not effective in
medium dilution rates. Normally, the cell density control by varying flow rate is operated
at high throughput, 0.8

m max < D < 0.8

m max < D < 0.95 m max , and when the productivity is near maximum

( Fig. 12.7 c).
The dilution rate that maximizes productivity is found by differentiating DP or DX with
respect to D and setting the derivative equal to zero. The optimal value of D, D opt , will
depend on whether endogenous metabolism and/or product formation is considered. Eqn
(12.19) gives

DX ¼ D 2 YF X = S
D þ k d

D þ k d
m max D k d

S 0 K S (12.20)

By setting

d ðDXÞ

d

¼ DðD þ 2k d Þ

ðD þ k d Þ 2 S 0 YF X = S K S YF X = S Dð2m max D 2k d Þ

0 ¼ (12.21)

D

ðm max D k d Þ 2

we obtain the optimum dilution rate, D in Eqn (12.21) ,or

S 0 ðm max D opt ðDXÞ k d Þ 2 ðD opt ð DX Þ þ 2k d Þ¼K S ðD opt ð DX Þ þ k d Þ 2 ð2m max D opt ð DX Þ 2k d Þ
(12.22)

k d ) 2 and Eqn (12.22) is

Since k d is usually small, D opt(DX) (D opt(DX) þ 2 k d ) (D opt(DX) þ

z

approximated by

s

K S
K S þ S 0

!

D opt ð DX Þ z ðm max k d Þ 1 (12.23)

Since S 0 is usually much greater than K S ,D opt(DX) will approach D ¼ m max k d or the washout

point. Stable chemostat operation with D

z m max

k d is very difficult, unless the flow rate