Kinetics analysis and model validation
The kinetic analysis of the changes in Mw of the hydrolyzed dextran was
modelled using eq. (1). The rate constant, k , is related to the
concentrations of substrate and enzyme 34, which could
be obtained by fitting with experimental data as presented inTable S1 . The simulated results in reasonable agreement with
the experimental data (Figure 3a ). The obtained value ofk decreased with increasing concentration of dextran substrate
(Figure 3b ). The curve-fitting results show that the values ofk follow an exponential relationship with dextran concentration
(cd ), with a correlation coefficient
R2>0.99 as shown in Figure 3b ,
and its values can be expressed with following equation:
\(k=0.0001e^{-0.017c_{d}}\) (38)
The Mw of dextran can be predicted when the dextranase concentration is
fixed as 0.05 g/L by combing eqs. (1) and (38).
To validate the developed model, the simulated permeate flux and the
oligodextran concentration in the permeate were compared with the
experimental data at different operating pressures as presented inFigure 4, where the simulated permeate flux can be seen to
agree well with the experimental data. Increasing operating pressure
enhanced the permeate flux as a result of higher driving force. It is
noteworthy that the permeate flux decreased significantly in the initial
stage but also gradually increased with prolonged operation time. This
was a result of the dextran being hydrolyzed into small molecules which
could penetrate through the membrane into the permeate and thus
alleviate concentration polarization. Similarly, the simulated permeate
concentration was in relatively good agreement with the experimental
results (Figure 4b ). The relatively large discrepancy in the
initial 30 min may have resulted from non-uniform distribution of
membrane pore size and the wider molecule weight distribution of dextran
substrate 35, which allowed some smaller dextran
molecules to penetrate through the large membrane pores into the
permeate in the initial filtration stage. The permeate concentration
increased as the operation proceeded due to generation of a large amount
of smaller oligodextran molecules following sufficient hydrolysis.
However, increasing operating pressure reduced the permeate
concentration because the denser fouling layer, the shorter the
retention time for dextran hydrolysis, and with enhanced water
convection transport at higher pressure, oligodextran rejection improved
and its concentration in the permeate fell 36. These
observations therefore indicate that the developed model is an efficient
tool for simulating the filtration characteristics of an EMR.
Figure 3 . Effect of dextran concentration on (a) the variation
of average Mw with reaction time and (b) the values of rate constant
(k )
in
a batch system with free enzyme. The simulated results are plotted as
curves, while the experimental results are presented as discrete
symbols.
Figure 4. Experimental (solid line) and simulated (discrete
symbols) profiles of (a) permeate flux and (b) permeate concentration
versus operation time with membrane pore size of 10 nm and membrane
porosity of 0.8. Substrate concentration: 50 g/L, enzyme concentration:
0.05 g/L, agitation speed: 160 rpm, and feeding mode: water feeding.