Fed-Batch Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 692

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

(c) the concentration and total amount of cells when t ¼

m P ¼ 0.05 g-product/

0.1 g/L.
13.2. Lactobacillus casi is propagated under essentially anaerobic conditions to provide
a starter culture for manufacture of Swiss cheese. The culture produces lactic acid
as a by-product of endogenous metabolism. The growth parameters are given by
YF X/S ¼

(g-cells h) and P 0 ¼

0.03 h 1 . A stirred tank
fermentor is operated in fed-batch mode at pseudo-steady state with a feed flow of
4000 L/h and feed substrate concentration of 80 g/L. The feed is started such that
pseudo-steady state is reached from time zero. After 8 h, the liquid volume is
40,000 L.
(a) What was the initial culture volume?
(b) What is the concentration of cell biomass at pseudo-steady state?
(c) What is the mass of cells produced after 8 h fed-batch operation?
(d) What is the substrate concentration in the reactor after 8 h fed-batch operation?
13.3. In a fed-batch culture operating with the intermittent addition of glucose solution, the
initial culture volume is V 0 ¼

0.33 h 1 , k d ¼

0.23 g-X/g-S, K S ¼ 0.15 g/L, m max ¼

1 L, and glucose-containing nutrient solution is added
exponentially with a flow rate of Q 0.2 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,

0.3 h 1 ,

and X 0 ¼ 50 g/L. The kinetic and yield factors of the organism are m max ¼

K S ¼ 0.5 g-dw/g-glucose. Using the pseudo-steady state

approximation, determine:
(a) the culture volume at t

0.1 g/L, and YF X/S ¼

48 h;
(b) the concentration of glucose at t

¼

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

¼

48 h;
(d) the product (penicillin) concentration in the vessel at 48 h, if

¼

m P ¼ 0.1 g-product/

(g-cells h) and P 0 ¼

0 g/L.
13.4. In a fed-batch culture operating with the intermittent addition of glucose solution, the
initial culture volume is V 0 ¼

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

0.1 exp(0.2 h 1

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

¼

300 g/L,

S 0 ¼ 0.1 g/L, and X 0 ¼ 100 g/L. The kinetic and yield factors of the organism are

0.3 h 1 , K S ¼

m max ¼ 0.1 g/L, k d ¼ 0.001/h, and YF X/S ¼ 0.5 g-dw/g-glucose. Using the

pseudo-steady state approximation, determine:
(a) the culture volume at t 36 h;

(b) the concentration of glucose at t

¼

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

¼

36 h;
(d) the product (penicillin) concentration in the vessel at 36 h, if

¼

m P ¼ 0.02 g-product/

0 g/L.
13.5. A solution containing bacteria at a concentration of 0.001 g/L was fed to a semibatch
reactor. The nutrient was in excess. The reactor was empty at the start of the experiment.
If the concentration of bacteria in the reactor at the end of 2 h is 0.025 g/L, what is the
net specific growth rate

(g-cells h) and P 0 ¼

m net in min 1 ?