CP504 – Lecture 5
Enzyme kinetics and associated reactor design:
Immobilized enzymes
enzyme mobility gets restricted in a fixed space
Prof. R. Shanthini
30 Sept 2011
1
Immobilized enzyme reactor (example)
Recycle packed column reactor
Prof. R. Shanthini
30 Sept 2011
2
Advantages of immobilized enzymes:
- Easy separation from reaction mixture, providing the
ability to control reaction times and minimize the
enzymes lost in the product
- Re-use of enzymes for many reaction cycles, lowering the
total production cost of enzyme mediated reactions
- Ability of enzymes to provide pure products
- Possible provision of a better environment for enzyme
activity
Prof. R. Shanthini
30 Sept 2011
3
Disadvantages of immobilized enzymes:
- Problem in diffusional mass transfer
- Enzyme leakage into solution
- Reduced enzyme activity and stability
- Lack of controls on micro environmental conditions
Prof. R. Shanthini
30 Sept 2011
4
Methods of immobilization
1) Entrapment Immobilization
2) Surface Immobilization
3) Cross-linking
Prof. R. Shanthini
30 Sept 2011
5
1) Entrapment Immobilization
It is the physical enclosure of enzymes in a small space.
- Matrix entrapment (matrices used are polysaccharides,
proteins, polymeric materials, activated carbon, porous
ceramic and so on)
- Membrane entrapment (microcapsulation or trapped
between thin, semi-permeable membranes)
Prof. R. Shanthini
30 Sept 2011
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1) Entrapment Immobilization
Advantage is enzyme is retained.
Disadvantages are
- substrate need to diffuse in to access enzyme and
product need to diffuse out
- reduced enzyme activity and enzyme stability owing
to the lack of control of micro environmental
conditions
Prof. R. Shanthini
30 Sept 2011
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2) Surface Immobilization
- Physical adsorption (Carriers are silica,
carbon nanotube, cellulose, and so on; easily
desorbed; simple and cheap; enzyme activity
unaffected )
- Ionic binding (Carriers are polysaccharides
and synthetic polymers having ion-exchange
centers)
- Covalent binding (Carriers are polymers
containing amino, carboxyl, hydroxyl, or
phenolic groups; loss of enzyme activity;
strong binding of enzymes)
Prof. R. Shanthini
30 Sept 2011
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Methods of immobilization
Prof. R. Shanthini
30 Sept 2011
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3) Cross linking
is to cross link enzyme molecules with each other
using agents such as glutaraldehyde.
Prof. R. Shanthini
30 Sept 2011
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Comparison between the methods
Adsorption
Covalent
coupling
Entrapment
Membrane
confinement
Simple
Difficult
Difficult
Simple
Low
High
Moderate
High
Variable
Strong
Weak
Strong
Yes
No
Yes
No
Applicability
Wide
Selective
Wide
Very wide
Running problems
High
Low
High
High
Matrix effects
Yes
Yes
Yes
No
Large diffusional
barriers
No
No
Yes
Yes
Microbial protection
No
No
Yes
Yes
Characteristics
Preparation
Cost
Binding force
Enzyme leakage
Prof. R. Shanthini
30 Sept 2011
11
Immobilized enzyme reactor (example)
Recycle packed column reactor
- Allow the reactor to
operate at high fluid
velocities
Prof. R. Shanthini
30 Sept 2011
12
Immobilized enzyme reactor (example)
Fluidized bed reactor
- A high viscosity substrate
solution
- A gaseous substrate or
product in a continuous
reaction system
- Care must be taken to avoid
the destruction and
decomposition of immobilized
enzymes
Prof. R. Shanthini
30 Sept 2011
13
Immobilized enzyme reactor (example)
- An immobilized enzyme
tends to decompose upon
physical stirring.
Continuous stirred
tank reactor
- The batch system is
generally suitable for the
production of rather small
amounts of chemicals.
Prof. R. Shanthini
30 Sept 2011
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Effect of mass-transfer resistance in immobilized
enzyme systems:
Mass transfer resistance is present
- due to the large particle size of the immobilized enzymes
- due to the inclusion of enzymes in polymeric matrix
Prof. R. Shanthini
30 Sept 2011
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Effect of mass-transfer resistance in immobilized
enzyme systems:
Mass transfer resistance are divided into the following:
- External mass transfer resistance
(during transfer of substrate from the bulk liquid to
the relatively unmixed liquid film surrounding the
immobilized enzyme and
during diffusion through the relatively unmixed
liquid film)
- Intra-particle mass transfer resistance
(during diffusion from the surface of the particle to
the active site of the enzyme in an inert support)
Prof. R. Shanthini
30 Sept 2011
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External mass-transfer resistance:
Assumption:
- Enzymes are evenly distributed on
the surface of a nonporous support
material.
- All enzyme molecules are equally
active.
- Substrate diffuses through a thin
liquid film surrounding the support
surface to reach the reactive surface.
- The process of immobilization has
not altered the enzyme structure and
the M-M kinetic parameters (rmax, KM)
are unaltered.
Prof. R. Shanthini
30 Sept 2011
Ss
C
Ss
Sb
CSb
Enzyme
Enzyme
Liquid
Filmfilm
Thickness,
L
Liquid
thickness,
17
L
External mass-transfer resistance:
Diffusional mass transfer across
the liquid film:
Ss
C
Ss
JS = kL (CSb – CSs)
kL
Sb
CSb
liquid mass transfer
coefficient (cm/s)
CSb
substrate concentration in
the bulk solution (mol/cm3)
CSs
substrate concentration at
the immobilized enzyme
surface (mol/cm3)
Prof. R. Shanthini
30 Sept 2011
Enzyme
Enzyme
Liquid
Filmfilm
Thickness,
L
Liquid
thickness,
18
L
External mass-transfer resistance:
At steady state, the reaction rate is
equal to the mass-transfer rate:
JS = kL (CSb – CSs) =
Sb
CSb
rmax CSs
KM + CSs
rmax
maximum reaction rate per
unit of external surface area
(e.g. mol/cm2.s)
KM
is the M-M kinetic constant
(e.g. mol/cm3)
Prof. R. Shanthini
30 Sept 2011
Ss
C
Ss
Enzyme
Enzyme
Liquid
Filmfilm
Thickness,
L
Liquid
thickness,
19
L
Example 3.4 in Shuler & Kargi:
Consider a system where a flat sheet of polymer coated with
enzyme is placed in a stirred beaker. The intrinsic maximum
reaction rate of the enzyme is 6 x 10-6 mols/s.mg enzyme. The
amount of enzyme bound to the surface has been determined
to be maximum 1 x 10-4 mg enzyme/cm2 of support. In
solution, the value of KM has been determined to be 2 x 10-3
mol/l. The mass-transfer coefficient can be estimated from
standard correlations for stirred vessels. We assume in this
case a very poorly mixed system where kL = 4.3 x 10-5 cm/s.
What is the reaction rate, when the bulk concentration of the
substrate (CSb) is (a) 7 x 10-3 mol/l and (b) 1 x 10-2 mol/l?
Prof. R. Shanthini
30 Sept 2011
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Solution to Example 3.4 in Shuler & Kargi:
Data provided:
rmax = 6 x 10-6 x 1 x 10-4 mols/s.cm2
= 6 x 10-10 mols/s.cm2
KM
= 2 x 10-3 mol/l
= 2 x 10-6 mol/cm3
kL
= 4.3 x 10-5 cm/s
CSb = 7 x 10-3 mol/l OR 1 x 10-2 mol/l
= 7 x 10-6 mol/cm3 OR 1 x 10-5 mol/cm3
Equation to be solved:
JS = kL (CSb – CSs) +
rmax CSs
KM + CSs
where CSs should be solved for, which can then be used to
calculate JS.
Prof. R. Shanthini
30 Sept 2011
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Solution to Example 3.4 in Shuler & Kargi:
J_S for part (a)
J_S for part (b)
r_S
2
J_S or r_S (mol/s.cm )
6.E-10
5.E-10
4.E-10
3.E-10
2.E-10
1.E-10
0.E+00
0
Prof. R. Shanthini
30 Sept 2011
0.002
0.004
0.006
C_Ss (mol/l)
0.008
0.01
22
External mass-transfer resistance:
JS = kL (CSb – CSs) =
rmax CSs
KM + CSs
Non dimensionalizing the above equation, we get
1 - C’Ss
NDa
=
β C’Ss
1 + β C’Ss
where
C’Ss = CSs / CSb
NDa
β
Prof. R. Shanthini
30 Sept 2011
= rmax / (kL CSb )
= CSb / KM
is the Damköhler number
is the dimensionless substrate
concentration
23
Damköhler number (NDa)
NDa =
Maximum rate of reaction
Maximum rate of diffusion
=
rmax
kL CSb
If NDa >> 1, rate of diffusion is slow and therefore the limiting
mechanism
rp = JS = kL (CSb – CSs)
If NDa << 1, rate of reaction is slow and therefore the limiting
mechanism
rmax CSs
rp =
KM + CSs
If NDa = 1, rates of diffusion and reaction are comparable.
Prof. R. Shanthini
30 Sept 2011
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Effectiveness factor (η)
η=
actual reaction rate
rate if not slowed by diffusion
β C’Ss
rmax CSs
η=
KM + CSs
rmax CSb
KM + CSb
=
1 + β C’Ss
β
1+β
Effectiveness factor is a function of β and C’Ss
Prof. R. Shanthini
30 Sept 2011
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Internal mass transfer resistance:
Assumption:
- Enzyme are uniformly distributed
in spherical support particle.
- Substrate diffuses through the
tortuous pathway among pores to
reach the enzyme
- Substrate reacts with enzyme on
the pore surface
-Diffusion and reaction are
simultaneous
- Reaction kinetics are M-M kinetics
Prof. R. Shanthini
30 Sept 2011
CSs
CSr2
26
Diffusion effects in enzymes immobilized in a
porous matrix:
Under internal diffusion limitations, the rate per unit volume is
expressed in terms of the effectiveness factor as follows:
rmax’ CSs
rS = η
KM + CSs
rmax’
KM
CSs
η
maximum reaction rate per volume of the support
M-M constant
substrate concentration on the surface of the support
effectiveness factor
Prof. R. Shanthini
30 Sept 2011
27
Diffusion effects in enzymes immobilized in a
porous matrix:
Definition of the effectiveness factor η
η=
reaction rate with intra-particle diffusion limitation
reaction rate without diffusion limitation
For η < 1, the conversion is diffusion limited
For η = 1, the conversion is limited by the reaction rate
Effectiveness factor is a function of β and C’Ss
Prof. R. Shanthini
30 Sept 2011
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Diffusion effects in enzymes immobilized in a
porous matrix:
β
η
φ
Theoretical relationship between the effectiveness factor (η) and
first-order Thiele’s modulus (φ) for a spherical porous immobilized
particle for various values of β, where β is the substrate
concentration at the surface divided by M-M constant.
Prof. R. Shanthini
30 Sept 2011
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Diffusion effects in enzymes immobilized in a
porous matrix:
Relationship of
effectiveness
factor (η) with the
size of
immobilized
enzyme particle
and enzyme
loading
Prof. R. Shanthini
30 Sept 2011
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