Analysis of modified surface force pore flow model with concentration polarization and comparison with Spiegler–Kedem model in reverse osmosis systems

The Modified Surface Force Pore Flow (MD-SF-PF) model is used for predicting the performance of the sodium chloride–water and sodium sulphate–water reverse osmosis systems. Unlike the previous analysis available in literature on this model, the present work takes concentration polarization into account explicitly. The required mass transfer coefficient is estimated by relating it to the feed flow rate through two additional parameters. The model equations being non-linear are solved using the orthogonal collocation technique. The model solution code is validated by comparing results with those available in literature. Simulation studies indicate observed rejection versus flux has a similar trend to that predicted by the Spiegler–Kedem model. From some of the experimental observations of Murthy [Studies on membrane transport models, Ph.D. thesis, I.I.T. Delhi, July 1996], model solution and mass transfer parameters are estimated through a combination of the Downhill Simplex method and Monte Carlo search. Simulated results using above parameters are found to be in very good agreement with the remaining experimental observations. Prediction of the membrane performance and mass transfer coefficient are also found to be very close to those estimated through the Spiegler–Kedem model. The membrane specific parameters such as the membrane thickness and pore radius are calculated from experimental data for the two different systems on a similar cellulose acetate membrane. The closeness of these parameter values again shows the validity of MD-SF-PF model.