Abstract
A mathematical model for spiral-wound reverse osmosis systems has been established using a porous media approach. Transport processes through membranes were investigated, fully taking account of concentration polarization associated with spiral-wound reverse osmosis desalination systems. A set of the governing equations, namely, the continuity, momentum, and concentration equations, have been derived for three distinctive phases, namely, brine, permeate, and membrane phases, following the procedure previously proposed by Nakayama and Sano for the analysis of hollow-fiber desalination modules. The first-order differential equations in terms of the average velocity, pressure, and salt concentration for the brine phase are integrated with an algebraic equation for the permeate flow rate per unit volume in order to estimate the permeate salinity, flow rate, and pressure drop in spiral-wound reverse osmosis modules. The present analytical results agree fairly well with available experiment data reported by Avlonitis et al. [Desalination, 81:191,1991; 86:273,1992; 89:227,1993; 203:218,2007; Sep. Sci. Technol., 40:2663,2005], substantiating the validity of the governing equations based on the porous media approach for spiral-wound reverse osmosis systems. The present analysis reveals that there exists an optimal brine pressure for attaining the maximum permeate flow rate for a given pumping power. The present model can be used to design spiral-wound reverse osmosis desalination systems without resorting to extensive finite difference calculations.
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