Estimation of mass transfer coefficient using a combined nonlinear membrane transport and film theory model

Abstract

The problem of estimating mass transfer coefficient ( k) in reverse osmosis is very important as can be seen from a number of studies reported in the literature. The methods employed are (a) direct measurements, using optical or microelectrode measurements; (b) indirect measurements, in which the true rejection is calculated by extrapolation to infinite feed circulation; and (c) indirect measurements, in which a concentration polarization model combined with a membrane transport model is used for mass transfer coefficient calculation. In the present work, the reverse osmosis experiments were conducted in a flat disk cell to get separation data using a NaCl-water system and cellulose acetate membrane. To analyze data, method (c) is used with two membrane transport models, the nonlinear Spiegler-Kedem model and the solution-diffusion model, to estimate the membrane transport parameters and k, simultaneously. The nonlinear equation obtained is solved numerically using the Box-Kanemasu method to determine various parameters. The k values estimated from two models show a marked variation that may be attributed to the presence of reflection coefficient in the Spiegler-Kedem model. It is suggested that the combined Spiegler-Kedem/film theory model may be the best method for establishing the mass transfer correlation for a given membrane cell of reverse osmosis and nanofiltration. Finally, a relation in the standard form Sh= a( Sc) b( Re) c is obtained for our reverse osmosis cell using the k values estimated from combined Spiegler-Kedem/film theory model. The relation is in good agreement with the experimental values.