Fed-Batch Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 693

13.6. Cell growth with uncompetitive substrate inhibition is taking place in a chemostat. The
cell growth rate law for this system is

m max S
K S þ Sð1 þ S=K I Þ

m G ¼

1.5 h 1 , K S ¼ with m max ¼ 1 g/L, K I ¼ 50 g/L, S 0 ¼ 30 g/L, YF X/S ¼ 0.08 g-cells/g-S, and

0.5 g/L.
Initially, 0.5 g/L of bacteria was placed in the reactor containing the substrate (equal
to the feed) and the flow to the tank started. Plot the concentrations of bacteria and
substrate as functions of time.
13.7. In a fed-batch culture operating with the intermittent addition of glucose solution, the
initial culture volume is V 0 ¼

X 0 ¼

0.1 L and glucose-containing nutrient solution is added
exponentially with a flow rate of Q

0.1 exp(0.1 h 1

t ) L/h. Glucose concentration in
the feed solution and the initial concentrations in the reactor are S F ¼

¼

200 g/L, S 0 ¼ 1 g/L,

and X 0 ¼ 50 g/L. The growth kinetics is governed by

m max S
K S þ Sð1 þ S=K I Þ

m G ¼

1.5 h 1 , K S ¼

with m max ¼ 1 g/L, K I ¼ 50 g/L. The yield factor YF X/S ¼ 0.5 g-dw/

g-glucose. Using the pseudo-steady state approximation, determine:
(a) the culture volume at t 24 h;

(b) the concentration of glucose at t

¼

24 h;
(c) the concentration and total amount of cells when t

¼

24 h;
(d) the product (penicillin) concentration in the vessel at 24 h, if

¼

m P ¼ 0.1 g-product/

0 g/L.
13.8. Nicotiana tabacum cells are cultivated to high density for production of polysaccharide
gum. The reactor used is a stirred tank, with an initial medium volume of 15 L. The
maximum specific growth rate of the culture is 0.01 h 1 , the saturation constant is
0.1 g/L and the biomass yield factor is YF X/S ¼

(g-cells h) and P 0 ¼

0.5 g-X/g-S. The concentration of
growth-limiting substrate in the medium is 3% (w/v), for both the initial medium in the
reactor and the feed. The reactor is inoculated with 1.0 g/L cells and operated in batch
until the substrate is virtually consumed ( S

0.5 mg/L); medium flow is then started at
a constant rate of 0.2 L/h. Assume that fed-batch operation reaches pseudo-steady
conditions rapidly.
(a) Estimate the batch culture time and final biomass concentration.
(b) Fed-batch operation is carried out for 1000 h. What is the final mass of cells in the
reactor?
(c) The fermentor is available 300 days per year with a downtime between runs of 24 h.
How much plant cell biomass is produced annually?

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