(41)
(42)
Equation 42 establishes the influence of the recirculation rate on the conversion degree. A
recirculation rate, R, higher than 100, leads to differences between Xl and Xr that
represent less than 1 % conversion, which is characteristic of a differential reactor. In
addition, if Xl and Xr have a similar value, that suggests the reaction rate (v) is
approximately constant over the reactor.
For the start-up of the reaction it could be inferred that and by
substitution in Equation 40:
(43)
Thus,
(44)Replacing in Equation 36:
(45)
Since the MBR acts like a tubular reactor with partial recirculation, assuming that the
enzyme is all located in the membrane, Xl and Xr could be undertaken as the integration
limits,
(46)Taking into account Equation 42, then;
(47)
If the two extreme cases of very high recirculation rate (A) and very low recirculation
rate (B) are considered, the following equations are obtained:
(A) R→then the reaction rate will be approximately constant in the reactor
and:
(48)
which leads to;
Reversed micellar bioreaction systems 219