## 2 Description of the Integrated ABE Fermentation-Membrane Pervaporation Process
Mass balances for the main species of the fermentation broth, namely acetone, acetic acid, butanol, butyric acid, ethanol, microorganism, glucose, and water, were considered in this work. The detailed set of mass balances and process equations can be found in [10]. In this process, a solution of glucose is continuously fed to a 400 m\({}^{3}\) fermenter with a constant flow rate and sugar concentration. Initial species concentrations in the fermenter are assumed. The set of kinetic reactions as described by [PERSON] and [PERSON] [11], accounting for the production of solvents (acetone, butanol, and ethanol), intermediate products (acetic acid and butyric acid), and microbial cells as well as the consumption of glucose in the fermentation broth was used. This model is still the most commonly used in the literature, because it accounts for the carbon substrate limitation in addition to the inhibition of butanol and butyric acid. Other models were recently proposed in  
Figure 1: Schematic diagram of the butanol fermentation system integrated with a membrane pervaporation separation unit. Numbers correspond to process streams. the literature and were tested in this investigation. [PERSON] et al. [12] presented a kinetic model that considers numerous intermediates in the metabolic pathway as well as product and glucose inhibition. However, this model could not be used, as it leads to unrealistically high butanol concentration, far beyond the inhibitory concentration levels. The dynamic model of [PERSON] and [PERSON] [13] initially seemed interesting, as it accounts for the pH of the fermentation broth, but some dynamic model constants are extremely high, therefore the system of ordinary differential equations cannot be solved with a practical step size in terms of time. To achieve steady state for a set of input conditions, the overall mass balance is satisfied by removing the same quantity of material through Streams 5, 8, 10 and 12 as the one entering into the process in Stream 1. In a continuous operation, Stream 2 is sent to the microfiltration membrane unit to give the permeate cell-free Stream 3 and the retentate Stream 7 containing all the microbial cells of Stream 2. A large proportion of Stream 7 is returned to the fermenter through Stream 9. Stream 8 is purged and sent to the separation train. Purge Stream 8 is adjusted to maintain an optimal steady-state concentration of microbial cells in the fermenter and provides an exit for other metabolites [14]. Stream 3 flows through the membrane pervaporation unit, where a fraction permeates through the membrane and is subsequently cooled in the condenser to form Stream 4. The permeate side of the membrane is maintained under high vacuum. The rate of permeation depends on the membrane area and permeability as well as stream temperature and composition [10]. Stream 4 is separated to give Streams 5 and 10, assumed to be 99% and 1% of Stream 4, respectively. Stream 5, which has a much higher concentration of ABE solvents than Stream 3, is sent to the separation train. Retentate Stream 6 is split into Streams 11 and 12. Purge Stream 12, used to maintain steady-state operation along with other exiting streams, is sent to the separation train, whereas Stream 11, depleted of ABE solvents, is recycled back to the fermenter.