Generalized mass-transfer correction factor for nanofiltration and reverse osmosis

The assessment of the concentration polarization in pressure-driven membrane modules is fundamental for their design and optimization. To account for the suction effect in nanofiltration (NF)/reverse osmosis (RO) membrane modules, a correction factor for conventional mass-transfer coefficients at vanishing mass-transfer rates was obtained through computational fluid dynamics (CFD) simulations of a symmetrical NF/RO rectangular channel with fully developed laminar flow, for a wide range of operating conditions. The correction factor is defined as Xi = Sh/Sh(0) where Sh is the Sherwood number with suction and Sh(0) is the Sherwood number for impermeable walls and low mass-transfer rates. For the range of dimensionless numbers assigned in the simulations, it was found by fitting of CFD data that Xi depends only on phi = Pe/Sh(0), through the correlation Xi = phi + (1 + 0.260(1.4))(-1.7), where Pe is the permeation Peclet number. This correlation can be used to predict the average concentration polarization index, Gamma = R/(Xi - R), where R is the intrinsic rejection, with an average relative error of 3.2%. The correlation obtained appears to be suitable to determine mass-transfer coefficients at high mass-transfer rates, independently of the membrane module geometry and the flow regime. Moreover, unlike the correction factor correlations available in the literature, the generalized correlation accurately predicts the concentration polarization index for phi < 20. (c) 2006 American Institute of Chemical Engineers.