Both hypotheses require enzyme to be retained in the pores of the membrane. In each
series of reactors there is a distribution of cutinase on membrane surface and in the pores
accounting for the conversions detected in the recirculate and in the permeate. The
prediction of these amounts is based on Equations 55 and 57 (Carvalho et al., 2001b).
The estimated enzyme quantities for each case, considering Xin=0 and Xout=0.6 for
each relation are given in Table 7.5. These values were used to model the different
reactor series and the results are plotted in Figure 7.9. At low residence times the
substrate remained at higher concentrations, causing the overlapping of the different
models.
The two CSTRs model describe the results very well (Carvalho et al., 2001b). When
the flow rate is low, recirculation decreases, but by maintaining high recirculating flow
rates, the MBR acts as a CSTR 1 on the hollow membrane side. The flux through the
membrane pores is significantly lower, and the residence times become significantly
different (by a 5000 fold factor), causing a deviation from CSTR 1 characteristics.
Therefore, the inside (matrix) of the membrane is classified as a second CSTR 2.
Besides this reactor sequence being a good model for the experimental behavior of
MBR, it also upholds the fact that two CSTRs are more efficient than a unique CSTR.
Table 7.5 Parameters used to model the conversion
in MBR. (From Carvalho et al., 2001b)
Reactor series Xe Kcat/Km Enzyme distribution (g)
PFR 0.836 18.27 0.008175
CSTR 0.836 27.60 0.008175
CSTR+ PFR 0.836 22.16 0.005925+0.00225
CSTR 1 +CSTR 2 0.836 22.39 0.005494+0.002681
Reversed micellar bioreaction systems 225