Biomedical Engineering Reference
In-Depth Information
R
= 0 . 5,
C R = 2,
k d = 0
2.0
R
= 0.5,
C R = 2,
k d = 0.05
µ max
1.5
R = 0, k d = 0
1.0
R
= 0,
k d = 0.05
µ max
0.5
0.0
0.0
0.5
1.0
1.5
2.0
D/ µ max
FIGURE 12.10 Comparison of biomass concentrations in steady states of chemostat cultures with and without
recycle. The saturation parameter is K S ¼
0.01 S 0 .
under glucose limitation, and the yield factor, YF X/S , is 0.5 g-cells/g-substrate. Glucose
concentration in the feed is S 0 ¼
50 g glucose/L. The kinetic constants of the organisms are
0.2 h 1 , K S ¼
m max ¼
1 g glucose/L. The value of C R is 2.5, and the recycle ratio is R
¼
0.25.
The system is at steady state.
(a) Find the substrate concentration in the recycle stream ( S ).
(b) Find the specific growth rate (
m net ) of the organisms.
(c) Find the cell (biomass) concentration in the recycle stream.
(d) Find the cell concentration in the centrifuge effluent ( X e ).
Solution. In this solution, we will use the derivations already shown in the proceeding
section. For students, you are expected to follow the steps from the beginning with mass
balances. Using Eqn (12.32) , we determine
m net .
min 1
min 1
m net ¼ð1 þ R RC R ÞD ¼ð1 þ 0:25 0:25 2:5Þ1=1000
¼ 0:000625
h 1
¼ 0:0375
Since the endogenous maintenance is negligible, we have
m net ¼ m G ¼ m max S
K S þ S
which can be rearranged to give
K S m net
1 0:0375
0:2 0:0375
S ¼
m max m net ¼
g
=
L
¼ 0:23077
g
=
L
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