Multiphase Bioreactor Design

(61)

where E is the effective enzyme activity in the reactor at time t and kd is the first-order
decay constant.
Substituing this model in the reactor performance equation for Michaelis kinetics, the
following equations can be obtained for the three main types of reactors:

(62)

and;

(63)

where Xo and Xt are the degrees of substrate conversion at t=0 and when the reactor has
been operating for time t.
From these equations it can be seen that the immobilised biocatalyst deactivates
slower in a CSTR than in a BSTR or a PFR.
Other models of enzyme inactivation have also been proposed:

(a) substrate-dependent enzyme decay

(64)

(b) product-dependent enzyme decay

(65)

(c) inverted linear model:

(66)

(d) time-dependent enzyme decay:

(67)

With these models similar equations to (62) and (63) can be obtained.

Modelling of immobilised viable cell reactors

Design and modelling of immobilised biocatalytic reactors 119