Adsorption-transport modeling of anions through PVD membrane in the presence of the screen phenomenon

A mathematical model for transport and adsorption of chloride and sulphate ions through PVD membrane is presented at two pressures; 8 and 15 bar and 40 °C. The PVD membrane is negatively charged. Saturated brine containing NaCl with the concentration higher than 97% was challenged with the membrane as the feed. Other available ions in the solution were Fe2+, Ca2+, Mg2+ and SO42−. The screen effect of the cations on the membrane surface charge facilitates the passage of the anions through the membrane without any noticeable electrostatic repulsion. Hermia blocking laws combined with experimental results indicate that the internal pore closure of the membrane by anions and cake deposition on the membrane surface by cations are the separation mechanisms. The transmission of anions through the membrane may be predicted with a simple transport equation (convection and diffusion) combined with an adsorption isotherm. Both Langmuir and Freundlich adsorption isotherms were employed due to the simplicity and validity in liquid systems. The isotherm’s parameters were determined at 10 bar during the unsteady state filtration. Under this condition, the permeate flux and concentration varied sharply due to adsorption. Finally, the model was compared with the experimental rejection data. An acceptable agreement around 95% at 8 bar and 92% at 15 bar was observed between theoretical model and experimental data.