How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 603

11.5. The production of glycerol from corn amylum/asylum is to be carried out by
fermentation using yeast cells. The specific growth rate is given by

1 exp

K PI P

m max S
K S þ S þ S 2

X
X N

m G ¼

=K I

with YF P/S ¼ 1.33 g-P/g-S, m max ¼ 0.25/s, K S ¼ 0.018 g/L, K I ¼ 11.8 g/L, X

N ¼

32.4 g/L,

K PI ¼ 0.06 L/g. The product generation is growth associated, m P ¼ am G þ b , here

0.147/s.
Plot the concentration of cells, substrate, and product as a function of time for an
initial concentration of cells of 10 8 g/L and a substrate concentration of 50 g/L.
11.6. The production of L -malic acid (used in medicines and food additives) was produced
over immobilized cells of Bacillus flavum MA-3.

a ¼ 34.5 and b¼

fumarase HOOCCH 2 CH

HOOCCH ] CHCOOH þ H 2 O ð OH Þ COOH

!

The following rate law was obtained for the rate of formation of product:

1

r max S
K S þ S

P
P N

r P ¼

76 mol $ L 1 $ day 1 , K S ¼ 1.69 mol/L. Design

a batch reactor to process 10 m 3 /day of 1.5 mol/L of fumaric acid (S). The required
conversion of fumaric acid is 99%. The total preparation time (loading, unloading,
and cleaning) is 3 h for each batch.
11.7. Abiochemical engineer has determined inher laboratory that the optimal productivityof
a valuable antibiotic is achieved when the carbon nutrient, in this case molasses, is
metered into the fermenter at a rate proportional to the growth rate. However, she cannot
implement her discovery in the antibiotic plant, since there is no reliable way tomeasure
the growth rate r X or biomass concentration (X) during the course of the fermentation. It
is suggested that anoxygenanalyzer be installedon the plant fermenters so that theOUR,
g/L-h, may be measured.
(a) Derive expressions that may be used to estimate X and r X fromOUR and time data,
assuming that a simple yield and maintenance model may be used to describe the
rate of oxygen consumption by the culture.
(b) Calculate values for the yield ( YF X =O 2 ) and maintenance ( m O 2 ) parameters from the
data in Table P11.7 :

where r max ¼ 0.048 mol/L, and P

N ¼

TABLE P11.7

Time OUR, g/h X , g/L Time OUR, g/h X , g/L

0 0.011 0.60 11 1.12 9.40

1 0.008 0.63 12 1.37 11.40

2 0.084 0.63 13 1.58 12.22

(Continued)