Mathematical model of flat sheet membrane modules for FO process: Plate-and-frame module and spiral-wound module

The forward osmosis process is considered a promising desalination method due to its low energy requirement compared to other methods. In this study, modelling and simulations for a plate-and-frame and a modified spiral-wound module are carried out for the FO process. The mathematical models consist of mass balance, a permeate flux model, and concentration polarization equations. The plate-and-frame model is formulated with consideration of flow directions, and the modified spiral-wound model is formulated with consideration of its geometric characteristics. These two sets of model equations are numerically and iteratively integrated since they are implicit and highly non-linear. The simulation for both modules was conducted by varying 4 types of operating conditions: volumetric flow rate of the feed and the draw solution, the concentration of the draw solution, flow direction, and the membrane orientation. The results for various conditions are also compared. In future research, the developed model could be applied for designing FO modules and finding optimal operating conditions.