Continuous Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 653

12.4. The kinetics of microbial growth, substrate consumption, and mixed-growth-
associated product formation for a chemostat culture are given by the following
equations:

r X ¼ m max S

K S þ S X

YF X = S m max S

1

r S ¼

K S þ S X

r P ¼ ar X þ bX ¼ðam G þ bÞX

0.7 h 1 , K S ¼ The kinetic parameter values are m max ¼ 20 mg/L, YF X/S ¼ 0.5 g-cells/

0.02 h 1 , and S 0 ¼

1 g/L.
(a) Determine the optimal dilution rate maximizing the productivity of product
formation ( P D).
(b) Determine the optimal dilution rate maximizing the productivity of cell (biomass)
formation (D X ).
12.5. In a two-stage chemostat system, the volumes of the first and second reactors are
V 1 ¼

g-substrate, YF P/X ¼ 0.15 g-P/g-cells, a ¼ 0.1, b ¼

300 L, respectively. The first reactor is used for biomass
production and the second is for a secondary metabolite formation. The feed flow rate
to the first reactor is Q

500 L and V 2 ¼

¼ 100 L/h, and the glucose concentration in the feed is

S 0 ¼ 5.0 g/L. Use the following constants for the cells.

h 1 m max ¼ 0:3 ; K S ¼ 0:1 g = L ; YF X = S ¼ 0:4 g-cells = g-glucose

(a) Determine cell and glucose concentrations in the effluent of the first stage.
(b) Assume that growth is negligible in the second stage and the specific rate of
product formation is

0.6 g-P/g-S.
Determine the product and substrate concentrations in the effluent of the
second reactor.
12.6. Ethanol is to be used as a substrate for SCP production in a chemostat. The available
equipment can achieve an oxygen transfer rate of 10 g-O 2 /L of liquid per hour.
Assume the kinetics of cell growth on ethanol is of the Monod type, with

m P ¼ 0.02 g-P/(g-cell $ h) and YF P/S ¼

m m ¼ 0.5/h,

2 g-O 2 /g-EtOH. We wish to
operate the chemostat with an ethanol concentration in the feed of 22 g/L. We also
wish to maximize the biomass productivity and minimize the loss of unused ethanol
in the effluent. Determine the required dilution rate and whether sufficient oxygen can
be provided.
12.7. Figure P12.7 shows a special two-stage chemostat systemwhere the second chemostat
is simply drawing its feed from the first chemostat and returning the contents back
into the first chemostat. This is a convenient model to describe the nonideal chemostat
operations where a stagnant region presents in a chemostat. Derive at a relationship
for S and X as functions of the feed and operating conditions, based on Monod growth
equation with a finite cell death rate.

K S ¼ 30 mg/L, YF X/S ¼ 0.5 cells/g-ethanol, and YF O 2 = S ¼