Continuous Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 624

effluent, Q is nutrient flow rate, V is culture volume, X 0 and X are cell concentrations in feed
and recycle streams, and X e is cell concentration in effluent from the cell separator.
At steady state and if d

ðVXÞ
d

¼ 0

and X 0 ¼

0 (that is, sterile feed), then Eqn (12.31) becomes

t

m net ¼ð1 þ R RC R ÞD ¼½1 þ Rð1 C R ÞD (12.32)

Since C R > D. That is, a chemostat can be operated at dilution

rates higher than the specific growth rate when cell recycle is used .
A material balance for growth-limiting substrate around the fermentor yields

1 and R (1

< m net <

C R ) 0, then

QS 0 þ RQS ð1 þ RÞQS V m G X

d ðSVÞ

d YF X = S ¼

(12.33)

t

At steady state, d

ð VS Þ

¼ 0 and

d t

X ¼ D

m G YF X = S ðS 0 SÞ

(12.34)

Substitution of growth rate into Eqn (12.34) yields

S 0 S
1 þ Rð1 C R Þþk d =D

X ¼ YF X = S (12.35)

Therefore, the steady-state cell concentration in a chemostat is increased by a factor of
1

by cell recycle. The substrate concentration in the effluent is deter-

1 þ R ð 1 C R Þþ k d =D

mined from Eqn (12.35) and the Monod Eqn (6.30) and is

K S ½ð1 þ R RC R ÞD þ k d
m max ½ð1 þ R RC R ÞD þ k d

S ¼ (12.36)

Then Eqn (12.35) becomes

YF X = S
1 þ Rð1 C R Þþk d =D

ð1 þ R RC R ÞD þ k d
m max ð1 þ R RC R ÞD k d

X ¼ S 0 K S (12.37)

Effluent cell concentrations in a chemostat with and without cell recycle are compared in
Fig. 12.10 . Cell concentrations and thus productivities are higher with cell recycle, resulting
in higher rates of substrate consumption. A finite death rate reduced the cell concentration
and thus the biomass productivity. This is more pronounced when the dilution rate is very
low. For example when dilution rate is zero, a finite death rate renders the biomass concen-
tration to be zero, whereas no cell death leads to the maximum biomass concentration achiev-
able. Cell washout limit dilution rate is increased due to the recycle. The washout is shown as
sharply decreased in cell biomass concentration with dilution rate.
Systems with cell recycle are used extensively in waste treatment and are finding
increasing use in ethanol production.
Example 12-2. In a chemostat with cell recycle, as shown in Fig. 12.2 , the feed flow rate and
culture volumes are Q ¼ 1 mL/min and V ¼ 1000 mL, respectively. The system is operated