Bioreactor Design and Operation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 948

Exhaust gas

Mixer
Motor

Feed

Compartment 1

V 1

Compartment 2

V 2

Gas
Supply

Valve

Product

Pump

Separator

FIGURE 18.13 Schematic of compartment formation in a chemostat.

d S 1

d YF X = S m max S 1

1

t ¼ k LS aðS 2 S 1 Þþð1þa 1 ÞDðS 0 S 1 Þ K S þS 1 X 1

(18.61)

where a 1 is the volumetric ratio of the lower compartment to the top compartment, the volu-

metric mass transfer coefficients (k LX a and k LS a) are based on the top compartment and the
dilution rate (D) is based on the total reactor volume. In strongly mixed flow reactors
(high Reynolds number), the mass transfer coefficients are nearly the same for all species
(as molecular diffusion is negligible compared to flow-induced diffusion or dispersion),
either be (fine) solid particles (like microbes) or soluble molecules (like sugar substrates).
Mass balances in the lower compartment with Monod growth model lead to

m max S 2

K S þS 2 k d

d X 2

d t ¼ k LX a a 1 ðX 1 X 2 Þþ

X 2 (18.62)

d S 2

d t ¼ k LS a YF X = S m max S 2

1

a 1 ðS 1 S 2 Þ K S þS 2 X 2

(18.63)

For steady-state operations, none of the concentrations would be changing with time.
Therefore, Eqns (18.60) through (18.63) are reduced to a set of algebraic equations as usual
for the continuous cultures.