Multiphase Bioreactor Design

This equation can be integrated for a particular kinetic expression. For the Michaelis-
Menten kinetics,

(49)

equation (48) is:

(50)

where k2i is the reaction rate constant, Kmi the Michaelis constant for the immobilised
system, and ET is the total enzyme activity in the reactor (ET=EW WIME with EW the
enzyme activity per unit weight of solid support).
The term ETt/V is defined as the normalised residence time, τ. This is an important
reactor parameter which allows the comparison of the different types of reactors.
When the enzymes are subjected to inhibition by substrate and/or product the reactor
performance is significantly modified. Table 4.4 summarises the BSTR performance
equations for Michaelis-Menten, substrate-inhibition and product-inhibition (competitive
and non-competitive) and reversible equilibrium reactions kinetics.

Plug flow reactors

A plug flow reactor is characterised by a variation of component concentrations from the
entrance to the exit. The substrate concentration decreases and the product concentration
increases with the length of the reactor. Plug flow assumes radial mixing but no axial
mixing. Making a mass balance to a fluid element, the following equation can be
obtained:

(51)

The equations for the design of plug flow immobilised enzyme reactors are shown in
Table 4.4.
For continuous reactors it can be seen that the normalised residence time can be given

by

Continuous stirred tank reactors

In a continuous stirred tank reactor, assuming complete mixing, the component
concentration in the reactor is the same as in the outlet stream. The composition of the
liquid phase is independent of the position in the reactor.
The general design equation for an immobilised enzyme system is:

(52)

where Xf and Xi are the final and initial conversion degrees, respectively.
Table 4.4 also shows the design equations for several kinetic types.

Design and modelling of immobilised biocatalytic reactors 115