Predicting influence of operating conditions on filtration performance
We systematically investigated the influence of agitation speed, operating pressure and feeding mode on the filtration performance of an EMR. As expected, the permeate flux increases at high agitation speed (Figure 7a ). This positive phenomenon is attributed to a thinner concentration polarization layer at higher agitation (a strong shear force on the membrane surface) 36. There were no changes of the permeate flux when agitation speed is less than 1000 rpm because the shear force generated by lower agitation is not enough to mitigate concentration polarization (Figure S1 ). The increased concentration polarization caused higher solute flux (Figure 7b ). A similar trend is observed with the permeate flux with increasing operating pressure, which is attributed to a greater driving force at higher operating pressure (Figure 8a ). The intensified driving force could accelerate the penetration of oligodextran products through the membrane and thus result in higher solute flux (Figure 8b ). However, increasing the agitation speed and operating pressure decreases the permeate concentration due to a dilution effect at higher permeate flux under the water feeding mode (Figure 7c and 8c ).
The substrate feeding mode is an alternative for enhancing the concentration of oligodextran in the permeate. Unlike the water feeding mode where pure water is continuously fed into the system, in the substrate feeding mode the dextran at constant concentration is continuously fed into the reaction system to maintain a constant feed volume. The simulations on the influence of feeding mode are summarized in Figure 9 . It is no doubt that the membrane suffers from more severe fouling under the substrate feeding mode 10, which thus leads to an obvious decrease of permeate flux (Figure 9a ). The decreased permeate flux under the substrate feeding mode reduced the oligodextran passing through the membrane, as is evidenced by the lower solute flux (Figure 9b ). The solute flux increases monotonically with prolonged operation duration under the substrate feeding mode, while the solute flux gradually decreases in the later stages under the water feeding mode owing to reduced substrate concentration in the EMR (Figure 9b ). This phenomenon is more prominent in the variation of permeate concentration with operation time (Figure 9c ). The increased permeate concentration is beneficial in terms of decrease in energy consumption (based on eq. (35)). This analysis was confirmed by the finding that the substrate feeding mode exhibits a lower specific energy consumption (2.4 kWh/kg) compared to the water feeding mode (3.5 kWh/kg) (Figure 9d ). However, the oligodextran yield obtained under the substrate feeding mode (28.2 %) is obviously lower than that obtained under the water feeding mode (89.6 %) (Figure 9d ), which is attributed to the higher substrate concentration in the feed of the former mode so that the enzyme is not enough to achieve a high conversation rate 39. The lower permeate flux under the substrate feeding mode causes a smaller permeate volume, and even with a higher permeate concentration, the mass of product is still smaller. Therefore optimization of system operating conditions is of great significance for the stable and efficient operation of an EMR system.
Figure 7. Simulation investigation of the effect of agitation speed on (a) permeate flux, (b) solute flux, and (c) permeate concentration with membrane pore size of 10 nm and membrane porosity of 0.8. Substrate concentration: 50 g/L, enzyme concentration: 0.05 g/L, operating pressure: 1 bar, and feeding mode: water feeding.
Figure 8. Simulation investigation of the effect of operating pressure on (a) permeate flux, (b) solute flux, and (c) permeate concentration 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: 1000 rpm, and feeding mode: water feeding.
Figure 9. Simulation investigation of the effect of feeding mode on (a) permeate flux, (b) solute flux, (c) permeate concentration, and (d) yield and specific energy consumption 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: 1000 rpm, and operating pressure: 3 bar.