Problem
(Shuler and Kargi, pp 202)
A biochemical engineer has determined in her laboratory that the
optimal productivity of a valuable antibiotic is achieved when the
carbon nutrient (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
to measure the growth rate (dX/dt) or biomass concentration (X)
during the course of fermentation. It is suggested that an oxygen
analyzer be installed on the plant fermenters so that the OUR
(oxygen uptake rate, g/l-h) may be measured.
1. Derive expressions that may be used to estimate X and
dX/dt from OUR and time data, assuming that a simple
yield and maintenance model may be used to describe the
rate of oxygen consumption by the culture.
2. Calculate values for the yield(YX/O2) parameter from the
data
Time
OUR (g/h)
1
0,011
2
0,008
3
0,084
4
0,153
5
0,198
6
0,273
7
0,393
8
0,493
9
0,642
10
0,915
11
1,031
12
1,12
13
1,37
14
1,58
15
1,26
16
1,58
17
1,26
18
1,12
19
1,2
20
0,99
21
0,86
22Sandip Bankar 0,9
X (g/l)
0,6
0,63
0,63
0,76
1,06
1,56
2,23
2,85
4,15
5,37
7,59
9,4
11,4
12,22
13
13,37
14,47
15,37
16,12
16,18
16,67
17,01
Derive expressions that may be used to estimate X and dX/dt from OUR and time data, assuming that a
simple yield and maintenance model may be used to describe the rate of oxygen consumption by the culture.
OUR =
µX
+ mO2 X
YX
O2
O2 used for growth
µ=
1 dX
X dt
OUR =
O2 used for maintenance
substitute into above equation
1 dX
+ mO2 X
YX dt
O2
To estimate
dX
dt
: In exponential growth phase O2 for growth dominates, hence
OUR ≅
1 dX
YX dt
O2
To estimate X: During stationary phase, cells aren't growing and O2 is needed for maintenance only OUR ≅ mO X
2
Sandip Bankar
Calculate values for the yield(YX/O2) parameter from the data
•
Calculate μmax (Plot graph lnX Vs t (linear range 3-10h) and max. slope is =?)
•
In exponential growth phase
OUR ≅
1 dX
YX dt
or
OUR =
O2
•
•
Plot OUR Vs X graph and calculate slope =
Calculate YX
O2
YX
O2
=
µX
YX
O2
µ
YX
= ? gO2/g.dw.hr
O2
µ
slope
Sandip Bankar