LAUSR

This study presents an integrated analytical model for the hydrodynamic behavior of the spiral-wound membrane element considering the curvature of the flow feed and permeate channels. The new model introduces a set of closed-form expressions for the output parameters of the permeate flow rate, fluid recovery fraction, and the permeation flux, which can be a necessary tool for optimization and evaluation of the parameters involved in the problem. Accordingly, the results were set forth for a reverse osmosis water treatment SWM element. The difference in the output parameters for the solutions with flat and curved membranes was investigated, and the consequences of the common assumption of the flat-sheet membrane were examined mathematically. It was found that neglecting the membrane curvature implements a significant impact/error on the prediction of the permeate channel pressure and membrane width with maximum permeation rate, whereas its impacts on feed channel pressure and output parameters are insignificant, especially for the considered reverse osmosis case study. Also, the curvature effect on the solution can be magnified by three parameters of the membrane width: permeate channel permeability, and membrane resistance.