Continuous Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 616

and liquid volume can be maintained exactly constant. Consequently, a value of D slightly
less than D opt(DX) may be a good compromise between stability and biomass productivity.
Furthermore, when k d ¼

0, Eqn (12.22) is reduced to

s

K S
K S þ S 0

!

D opt ð DX Þ ¼ m max 1 (12.24)

It should also be apparent that D opt(DX) for biomass formation will not necessarily be
optimal for product formation. Example 12-1 illustrates the use of these equations to charac-
terize the performances of chemostats.
Example 12-1. A new strain of yeast is being considered for biomass production. Tab l e
E12-1.1 shows data obtained from a chemostat with a sterile feed. The substrate feed concen-
tration was 800 mg/L and an excess of oxygen was used at a pH of 5.5 and T 35 C. Deter- ¼

m net ¼ m max S

mine m max , K S ,YF X/S , k d , and m S , assuming

K S þ S k d .

TABLE E12-1.1

Dilution rate,
h L 1

Carbon substrate
concentration, mg/L

Cell concentration,
mg/L

0.05 9.6 301

0.1 16.7 366

0.2 33.5 407

0.3 59.4 408

0.4 101 404

0.5 169 371

0.6 298 299

0.7 702 59

m max , K S ,YF X/S , k d , and m S are all
kinetic parameters needing to be determined from the experimental data set. Mass balance
of the biomass inside the chemostat leads to:

Solution. This is a case of parametric estimation as

d

d

t ¼ DðX 0 XÞþðm G k d ÞX

(E12-1.1)

where D is dilution rate and D ¼ Q/V . Since the feed medium is sterile, X 0 ¼ 0, and the system

is at steady state ( d X/ d t ¼ 0), then Eqn (E12-1.1) gives rise to

X ¼ 0 (E12-1.2)

or

D ¼ m net ¼ m G k d (E12-1.3)