Modeling of forward osmosis for microalgae harvesting

In this study, a transport-based model capable of predicting water flux in microalgae harvesting in forward osmosis (FO) system was developed. Based on Carman-Kozeny resistance model, steady state hydraulic resistance of cake layer comprised of microalgae cells was calculated; by means of control volume approach growth rate of the cake layer was also quantitatively obtained at transient state. Cake-enhanced concentration polarization (CECP), which arises from cells, along with dissolved compounds, deposited on membrane surface and acts to degrade FO performance, was estimated in real time. Model parameters related to a feed solution of microalgae cells were evaluated on the basis of empirical and theoretical data. It was found that deposition rate constant of microalgal cells was at least two orders of magnitude higher than diffusion rate constant under the experimental condition. Among microalgae related parameters, the porosity and thickness of cake layer were found to be the most influential on the water flux according to sensitivity analysis; and therefore they were calibrated by a statistical technique to improve model accuracy. Based on the estimated parameters, the developed model was validated through batch FO operations, and it was in good alignment with quasi-steady state data. There have been quite a few FO modeling studies thus far; and yet to the best of our knowledge, this study is the first one that elucidates actual fouling phenomenon with an actual feed solution, which may offer both theoretical and practical understandings needed for the development of FO-based microalgae harvesting process.