prof. r. shanthini 30 sept 2011 1 enzyme kinetics and associated reactor design: immobilized enzymes...

Prof. R. Shanthini 30 Sept 2011

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Enzyme kinetics and associated reactor design:

Immobilized enzymes

CP504 – Lecture 5

enzyme mobility gets restricted in a fixed space


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Immobilized enzyme reactor (example)

Recycle packed column reactor


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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


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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


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Methods of immobilization

1) Entrapment Immobilization

2) Surface Immobilization

3) Cross-linking


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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)


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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


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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)


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Methods of immobilization


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3) Cross linking

is to cross link enzyme molecules with each other using agents such as glutaraldehyde.


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Comparison between the methodsCharacteristics Adsorption Covalent

couplingEntrapment Membrane

confinement

Preparation Simple Difficult Difficult Simple

Cost Low High Moderate High

Binding force Variable Strong Weak Strong

Enzyme leakage 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


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Recycle packed column reactor

- Allow the reactor to operate at high fluid velocities


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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


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- An immobilized enzyme tends to decompose upon physical stirring.

- The batch system is generally suitable for the production of rather small amounts of chemicals.

Continuous stirred tank reactor


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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


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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)


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External mass-transfer resistance:

Enzyme

Ss

Sb

Liquid Film Thickness, L

Enzyme

Liquid film thickness, L

CSs

CSb

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.


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Enzyme

Ss

Sb


Enzyme


CSs

CSb

Diffusional mass transfer across the liquid film:

liquid mass transfer coefficient (cm/s)

substrate concentration in the bulk solution (mol/cm3)

kL

CSb

JS = kL (CSb – CSs)

substrate concentration at the immobilized enzyme surface (mol/cm3)

CSs


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Enzyme

Ss

Sb


Enzyme


CSs

CSb

At steady state, the reaction rate is equal to the mass-transfer rate:

JS = kL (CSb – CSs) = rmax CSs

KM + CSs

maximum reaction rate per unit of external surface area (e.g. mol/cm2.s)

rmax

is the M-M kinetic constant (e.g. mol/cm3)

KM


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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?


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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

where CSs should be solved for, which can then be used to calculate JS.

Equation to be solved:

JS = kL (CSb – CSs) + rmax CSs

KM + CSs


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Solution to Example 3.4 in Shuler & Kargi:

0.E+00

1.E-10

2.E-10

3.E-10

4.E-10

5.E-10

6.E-10

0 0.002 0.004 0.006 0.008 0.01

C_Ss (mol/l)

J_S

or

r_S

(m

ol/

s.cm

2)

J_S for part (a)J_S for part (b)r_S


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Non dimensionalizing the above equation, we get

JS = kL (CSb – CSs) = rmax CSs

KM + CSs

where

= β C’Ss

1 + β C’Ss

1 - C’Ss

NDa

rmax / (kL CSb )

C’Ss =

=

CSs / CSb

NDa

β = CSb / KM

is the Damköhler number

is the dimensionless substrate concentration


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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

If NDa << 1, rate of reaction is slow and therefore the limitingmechanism

If NDa = 1, rates of diffusion and reaction are comparable.

rp = JS = kL (CSb – CSs)

rp = rmax CSs

KM + CSs


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Effectiveness factor (η)

η = actual reaction rate

rate if not slowed by diffusion

η =

rmax CSs

KM + CSs

rmax CSb

KM + CSb

=

β C’Ss

1 + β C’Ss

β

1 + β

Effectiveness factor is a function of β and C’Ss


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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

CSs

CSr2


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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:

rS = η rmax’ CSs

KM + CSs

maximum reaction rate per volume of the support

M-M constant

substrate concentration on the surface of the support

rmax’

KM

CSs

η effectiveness factor


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η Definition of the effectiveness factor

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


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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.

β


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Relationship of effectiveness factor (η) with the size of immobilized enzyme particle and enzyme loading

prof. r. shanthini 30 sept 2011 1 enzyme kinetics and associated reactor design: immobilized enzymes...

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