Concentration polarization in a reverse osmosis/nanofiltration plate-and-frame membrane module

Abstract

The flow structure and solute concentration distribution in a nanofiltration/reverse osmosis plate-and-frame module with radial thin feed channels that have considerable entrance and outlet effects was determined by computational fluid dynamics (CFD). Simulations were performed for binary aqueous solutions, Reynolds ( Re) numbers in the range of 64–570 (based on the channel height) and Schmidt ( Sc) numbers between 450 and 8900. The CFD simulations showed that both the velocity field and the solute concentration distribution exhibit important 3D effects and, at rather low Reynolds numbers ( Re ≥ 118), flow instabilities start to appear in the entrance/outlet regions. However, those instabilities do not affect significantly the average concentration polarization on the membranes surface up to the maximum Reynolds number simulated ( Re = 570). The friction factors predicted by CFD were in agreement with the corresponding experimental values for the range of Re numbers investigated. The simulations allowed the determination of a mass-transfer correlation at vanishing mass-transfer rates and a correlation for mass-transfer correction factor. The obtained mass-transfer correlation at vanishing mass-transfer rates was compared with the ones available in the literature as well as with the Sherwood numbers determined by the velocity variation method, using diluted aqueous solutions of glycerol. It was also found that a generalized mass-transfer correction factor correlation for high mass-transfer rates, previously developed for membrane modules with 2D configurations, is still valid to predict the average concentration polarization in the module investigated.