Biomedical Engineering Reference
In-Depth Information
TABLE 17.13-2
S
b
, mg/L
10
25
50
100
200
250
r
, mg/(L
$
h)
10
20
30
40
45
46
Assuming negligible liquid film and Ca-alginate shell resistances, calculate
r
max
and
K
m
for the enzyme. Assume no substrate or product inhibition.
17.14.
Urea dissolved in aqueous solution is degraded to ammonia and CO
2
by the enzyme
urease immobilized on surfaces of nonporous polymeric beads. Conversion rate is
controlled by transfer of urea to the surface of the beads through liquid film, and the
conversion takes place on the surfaces of the beads. The following parameters are
given for the system:
k
L
¼
0.2 cm/s;
K
m
¼
0.2 g/L
0.01 g-urea/m
2
-support surface
r
max
¼
1 g-urea/L
(a)
Determine the surface concentration of urea.
(b)
Determine the rate of urea degradation under mass transfer-controlled conditions.
17.15.
The bioconversion of glucose to ethanol is carried out in a packed-bed, immobilized-
cell bioreactor containing yeast cells entrapped in Ca-alginate beads. The diffusivity
of glucose inside the alginate beads is 10
10
m
2
/s. The rate-limiting substrate is
glucose, and its concentration in the feed bulk liquid phase is
S
0
¼
S
b
¼
5 g/L. The nutrient
flow rate is
Q
¼
2 L/min. The particle size of Ca-alginate beads is
d
p
¼
5 mm. The
Michaelis
e
Menten rate constants for this conversion are:
r
max
¼
100 g-S/(L
$
h) and
10
3
g/L. The surface area of the alginate beads per unit volume of the reactor is
K
m
¼
2500 m
2
/m
3
, and the cross-sectional area of the bed is 0.01 m
2
. The external mass
transfer resistance and the diffusional resistance through the alginate shell are
negligible. Determine the required height for 80% conversion of glucose to ethanol at
the exit stream.
17.16.
A effectively first-order (i.e.
K
A
/
N
a
c
¼
, due to the low coverage of A on the catalyst)
heterogeneous irreversible reaction is taking place within a spherical catalyst pellet
that is plated with platinum throughout the pellet. The reactant concentration
halfway between the external surface and the center of the pellet (i.e.
r
R
/2) is equal
to one-tenth the concentration of the pellet's external surface. The concentration at the
external surface is 0.001 mol/L, the pellet diameter is 2.0
¼
10
5
m, and the diffusion
coefficient is 0.1 cm
2
/s.
A
/
B
10
6
m inward from the
(a)
What is the concentration of reactant at a distance of 3
external pellet surface?
(b)
Towhat diameter should the pellet be reduced if the effectiveness factor is to be 0.8?
(c)
If the catalyst support were not yet plated with platinum, how would you suggest
that the catalyst support be plated
after
it had been reduced by grinding?
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