Dynamic modeling of mass transfer through a nanofiltration membrane using calcium salt in drinking water

Mechanism specificity of ion separations in drinking water is necessary for the study of modeling transfer of calcium salt through nanofiltration membrane. In the present work, we have investigated a mathematical model which can specify the transfer phenomena of solute through a nanofiltration membrane and to predict its reject. The proposed model is based on the extended equation of Nernst-Planck. It is characterized by constants called transfer parameters, which have been determined according to the composition of the initial solution as a binary or a ternary mixture. The established model permitted us to predict the retention of calcium salt. The result of the application of the model has shown that there is a good agreement between the theoretical and experimental curves.

In this study, we have established a model which presents better the behavior of the ion Ca2+ with respect to the membrane and predicts its retention without knowing information concerning the details about the structure and the surface charge of the membrane. We have used the modified Nernst-Planck equation which can be better adapted to this kind of study for binary solutions, then for ternary solutions. The results of the application of the model show that there was a good agreement between the theoretical and experimental curves. It will be necessary to continue the work by introducing another term into the Nernst-Planck equation, other than the concentration polarization, for the prediction of the retention of salt beyond the saturated pressure.