Biomedical Engineering Reference
In-Depth Information
The shrinking core model is applicable in areas ranging from pharmacokinetics (e.g. disso-
lution of pills in the stomach), to biomass gasification (solid to gas phase), to biomass extrac-
tion (solid to liquid phase), to porous catalyst regeneration (solid to gas phase), to coal
particle combustion (solid to gas phase), to pulping and bleaching of fibers (solid to liquid
phase), to pyrolysis. Mass transfer, especially diffusion in the solid matrix is often the rate-
limiting step in biomass conversion processes.
Further Reading
Aris, R., 1975. The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Oxford, England:
Clarendon Press.
Blanch, H.W., Clark, D.S., 1996. Biochemical Engineering, New York: Marcel Dekker, Inc.
Doran, P.M., 1995. Bioprocess Engineering Principles, New York: Academic Press.
Fogler, H.S., 1999. Elements of Chemical Reaction Engineering, 3rd ed. Upper Saddle River, NJ: Prentice Hall.
Frank-Kamenetskii, D.A., 1969. Diffusion and Heat Transfer in Chemical Kinetics, 2nd ed. New York: Plenum Press.
Nielsen, J., Villadsen, J., Lid
´
n, G., 2003. Bioreaction Engineering Principles, 2nd ed. New York: Kluwer Academic/
Plenum Publishers.
Satterfield, C.N., 1970. Mass Transfer in Heterogeneous Catalysis. Cambridge, MA: MIT Press.
vant't Riet, K., Tramper, J., 1991. Basic Bioreactor Design, New York: Marcel Dekker, Inc.
PROBLEMS
17.1.
Glucose oxidase catalyzes the oxidation of glucose. When glucose is present in excess,
oxygen can be considered the limiting substrate. Michaelis
e
Menten kinetics may be
applied to describe the oxygen-limited reaction rate. The enzyme is immobilized on the
surface of nonporous glass beads. The particles are of
d
p
¼
2762 kg
$
m
3
.
0.12 mm,
r
s
¼
1000 kg
$
m
3
,
C
O
2
b
¼
0.18 mol
$
m
3
.The
Themediumproperties are:
m
¼
0.001 Pa,
r
L
¼
10
9
m
2
/s, and the catalyst loading is
diffusivity of oxygen in the medium is
D
AB
¼
2.1
10
8
g per glass bead. The volume fraction of beads is 0.4 in the reactor. The
kinetic constants are:
r
max
¼
[E]
0
¼
2
0.1 mol
$
m
3
.
Calculate the effectiveness factor and the effective rate of reaction assuming
(a)
no agitation (i.e. diffusion mass transfer);
(b)
effective medium flow velocity is 0.5 m/s.
17.2.
Consider a system where a flat sheet of polymer coated with enzyme is placed in
a stirred beaker. Michaelis
e
Menten kinetics is applicable to this enzyme. The intrinsic
maximum reaction rate
r
max
of the enzyme is 5
10
2
mol-O
2
/(s
$
g-enzyme), and
K
m
¼
5.8
10
3
mol/(s
$
g-enzyme). The enzyme
loading on the surface has been determined as 1.2
10
5
g-enzyme/m
2
-support. In
solution, the value of saturation constant
K
m
has been determined to be 2
10
3
mol/L.
10
4
m/s. What is the
The mass transfer coefficient has been estimated as
k
L
¼
5.8
10
3
mol/L; b) the bulk
effective reaction rate if a) the bulk concentration is 5
concentration is 0.2 mol/L.
17.3.
Assume that for an enzyme immobilized on the surface of a nonporous support
material the external mass transfer resistance for substrate is not negligible as
compared to the reaction rate. The enzyme is subject to substrate inhibition.
(a)
Are multiple states possible?
(b)
Could the effectiveness factor be greater than one?
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