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Hydrolysis of Oils by Using Immobilized Lipase Enzyme: A Review

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64 Biotechnol. Bioprocess Eng. 2002, Vol. 7, No. 2<br />

<br />

<strong>of</strong> internal diffusion, but they increase the magnitude Where, η is independent <strong>of</strong> S for the first-order reaction.<br />

<strong>of</strong> any pressure drop. Regular-shaped particles are much In packed bed reactor Equation (14) becomes<br />

better at reducing the problem <strong>of</strong> high-pressure drop in<br />

2<br />

packed beds and <strong>of</strong> irregular flow pattern, as observed V R ln[1 − x]<br />

= <br />

(21)<br />

<strong>by</strong> O’Neill et al. [27]. In general, the size <strong>of</strong> the particle, F ( 1− ε)<br />

De ϕ<br />

cothϕ1<br />

− 1]<br />

which shows essentially no internal diffusional limitations,<br />

is so small that the pressure drops incurred become<br />

prohibitive.<br />

Continuous Stirred Tank Reactors (CSTR’S)<br />

Based on the pseudo-steady state assumption the<br />

design equation for immobilized packed bed reactor can<br />

be expressed as follows:<br />

S<br />

V 1<br />

out<br />

dS<br />

= − ∫<br />

F 1−ε<br />

η − r<br />

S<br />

in<br />

( )<br />

s<br />

(14)<br />

The volumetric rate (-r s<br />

) can be separated into two<br />

terms for any enzymatic reaction whether it is onesubstrate<br />

irreversible or multi substrate reversible [18].<br />

(-r s<br />

) = Ef(S,P) (15)<br />

the simplest expression <strong>of</strong> f(S,P) is a hyperbolic function<br />

<strong>of</strong> S as typically shown <strong>by</strong> the Michaelis-Menten equation.<br />

The different CSTR configurations have been employed<br />

<strong>by</strong> a number investigators [2]. CSTR’S posses<br />

some particular advantages over fixed bed reactors, e.g.,<br />

lower construction costs and efficient stirring that<br />

eliminates the presence <strong>of</strong> concentration and/or temperature<br />

gradient. In general, however, a CSTR must be<br />

larger than a packed bed reactor to achieve the same<br />

extent <strong>of</strong> reaction. In order to prevent the immobilized<br />

lipase from leaving the CSTR, a micr<strong>of</strong>ilter or a screen<br />

must be provided at the reactor outlet.<br />

Based on the pseudo-steady state assumption the<br />

design equation for CSTR can be expressed as follows:<br />

V S<br />

x<br />

=<br />

F −<br />

ε)η( −r<br />

<br />

<br />

(22)<br />

f(S) = kS/K m<br />

+S (16)<br />

Equation (16) has two extremities: (i) first order kinetics,<br />

(-r s<br />

) = (kE/K m<br />

)S. where S > K m<br />

.<br />

X = (S in<br />

-S out<br />

)/S in<br />

(17)<br />

Equation (14) is modified into following forms, depending<br />

on the intra particle and film diffusion.<br />

(a) No limitation <strong>of</strong> diffusion (η=1.0): when the reaction<br />

rate <strong>of</strong> the immobilized enzyme particle is not<br />

influenced <strong>by</strong> intraparticle and boundary layer diffusion,<br />

eqn(14) for packed bed reactor becomes<br />

S<br />

V 1 out<br />

= − ∫<br />

F 1−ε<br />

S<br />

in<br />

dS<br />

r<br />

( − )<br />

(18)<br />

(b) Diffusion-influenced first-order kinetics (η

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