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
!"#$ %&' )* +, 0,011 0 0,008 4 5 0,084 6 0,153 0,198 8 3 0,273 7 0,393 9 0,493 0,642 : 01 0,915 00 1,031 1,12 04 1,37 05 1,58 06 08 1,26 03 1,58 1,26 07 09 1,12 0: 1,2 41 0,99 0,86 40 Sandip Bankar 44 0,9
. )* +/123 1235 1235 1273 0213 0283 4245 4298 6208 8257 728: :26 0026 04244 05 05257 06267 08257 03204 03209 03237 07210
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 =
µ X
Y X
+
mO X 2
O2
O2 used for growth
µ
1 dX
substitute into above equation
=
X dt
OUR =
O2 used for maintenance
1
dX
Y X
dt
+
mO X 2
O2
To estimate
dX dt
: In exponential growth phase O2 for growth dominates, hence
OUR !
1
dX
Y X
dt O2
To estimate X: During stationary phase, cells aren't growing and O2 is needed for maintenance only
Sandip Bankar
OUR ! mO X 2
Calculate values for the yield(YX/O2) parameter from the data •
Calculate
!max (Plot
graph lnX Vs t (linear range 3-10h) and max. slope is =?)
•
In exponential growth phase
OUR !
1
Y X
dX dt
or
OUR
Y X
O2
•
Plot OUR Vs X graph and calculate slope =
µ X =
O2
µ
Y X
= ? gO2 /g.dw.hr
O2
•
Calculate
Y X O2
Y X
µ =
O2
slope
Sandip Bankar
