Retention modelling of the bivalent cations in crossflow nanofiltration investigation in the porous models

Our work concerns the feasibility of certain models based on approach of a capillary type, and applied before in ultrafiltration process, for the prediction of the divalent salts retention by a nanofiltration membrane. The model solutions that we chose are those of cadmium and copper salts – whose cations constitute toxic elements introduced into the environment by the effluents coming from industries like those of surface treatment – calcium salt solutions, used within the framework of the nanofiltration softening of the aqueous solutions. The study of the bibliography on the salts retention through a membrane enabled us to formulate some observations: The flow of solvent depends on the membrane permeability; the aqueous solution flow depends on the solvent nature and membrane structure. On this basis, we also could highlight the existence of two mechanisms observed during the filtration of salts: the first, of type solubilization diffusion with the Donnan effect which does not take account of the membrane porosity; the second, electrokinetic who takes account of the membrane porosity. The mathematical models chosen, which seem quite suitable and which derive from this second type of mechanism are: TREMBLAY model; VERNIORY model; NAKAO model. The application of these mathematical models (for the study of the retention evolution of bivalent salts according to volumic flow) requires the development of a data-processing program which finally led to software simulation. We confronted this modeling with experimental results allowing to estimate the principal parameters of transport: the optimal pore radius, reflection coefficient σ and membrane permeability for solute PS. Apparently, the comparison carried out between the experimental results and numerically results obtained (VERNIORY model in particular) gave a good correspondence for a pore radius close to that evaluated by porosimetry method [1]. Moreover, this confrontation authorized us to underline the essential role of certain parameters influencing the retention such as: pH, transmembrane pressure, temperature, concentration of solution treatment and components nature in the solution.