An application of the Sano-Nakayama membrane transport model in hollow fiber reverse osmosis desalination systems

The Sano-Nakayama membrane transport model recently proposed for the analysis of a countercurrent dialyzer system has been extended to describe the concentration polarization phenomena associated with hollow fiber reverse osmosis desalination systems. A set of the governing equations, namely, the continuity, momentum and concentration equations, is derived for three distinctive phases, namely, brine, permeate and membrane phases, exploiting a volume averaging approach. These equations based on the Sano-Nakayama model are coupled and subsequently reduced to three distinctive first-order ordinary equations in terms of the average velocity, pressure and salt concentration of the brine phase. These equations along with an algebraic equation for the permeate flow rate per unit volume can readily be solved to estimate permeate salinity, permeate flow rate and pressure drop in a hollow fiber reverse osmosis desalination system. Available experimental data and numerical results based on finite difference methods are found to agree well with the present analytical estimates based on the Sano-Nakayama model.