Modeling of a spiral-wound module and estimation of model parameters using numerical techniques

A model for a spiral-wound reverse osmosis system using the three-parameter membrane transport model by Spiegler–Kedem is presented. The pressure drops in the permeate channel, feed channel and also the variation of the mass transfer coefficient along the feed channel were taken into account. An analytical solution was not possible due to the large number of nonlinear model equations; therefore, a computer solution utilizing finite differences was employed. The data generated by the simulation of the proposed model clearly indicate that neglecting the variation in the mass transfer coefficient and pressure drop along the flow channels can lead to errors in permeate concentration, though the effect on permeate flow rate may not be significant. The significance of the reflection coefficient in the membrane transport model was also investigated. A method for estimation of the model parameters is also presented; previously reported experimental data were analyzed. Using this parameter-estimation program, a correlation for the mass transfer coefficient in the feed channel is proposed and compared with the correlation available in the literature.

It was found that for lower values of the reflection coefficient, the overall permeate produced is much higher and the permeate concentration differs substantially from that obtained for F = 1 where the SK model mathematically is reduced to the solution–diffusion model. Since the SK model is known to be the most accurate membrane transport model, the present model for spiral-wound modules may provide more accurate results for design and analysis for reverse osmosis systems. The data generated also show that the pressure drop in the flow channels as well as the mass transfer coefficient variation cannot be neglected. Disregarding the above can lead to considerable errors in the predicted results. The membrane performance parameters have been estimated for the experimental data of Taniguchi [2] and Boudinar et al. [4], and the results clearly show that the present model predicts data very well, and the estimated membrane parameters remain constant for a variety of operating conditions. The mass transfer correlations were found for the both Roga and FilmTech spiral-wound modules, and these correlations compare very well with correlations available in the literature.