3D concentration polarization modelling: diffusion/convection/electromigration/ion-pairing

Concentration polarization increases the ion concentration on the feed side of the membrane. It affects the membrane separation processes, such as UF and NF, by increasing the transmembrane pressure and the potential for salt precipitation on the membrane. Usually, Concentration polarization is calculated by a one-dimensional diffusion-convection balance. The 1-D model has numerous drawbacks: it accounts for a fixed boundary layer thickness, and the same value for all the ions, avoiding the hydrodynamics effects. Also, the 1-D model does not consider the effect of spacer geometries on the formation of stagnant zones. Finally, the traditional approach for solving the mass balance in the 1-D approach does not consider other mass transport mechanisms such as electromigration and the interaction between the components through chemical speciation.

We developed a 3-D numerical model considering the transport of ions by diffusion, convection and electromigration, while including fluid dynamics in a real spacer geometry taken from a CT-scan along with the chemical speciation considering equilibrium reactions. First, we compared the 3-D model results with the 1-D approach, finding that the conditions imposed on the boundary layer in the 1-D model do not match with those obtained when the hydrodynamics is considered in practical operation of the RO modules. Second, we verified the significant influence of the chosen speciation system on the formation of different concentration polarization layer thicknesses. Third, we confirmed that the formation of stagnant zones, due to the presence of spacers, enhances the precipitation potential by increasing the trace ion concentrations. Results suggest that electromigration, locally, influence the distribution of specie due to the mobility of the dominant ions, but globally, the ion-pairing is the phenomenon that influences the most the development of the concentration polarization.

In conclusion, although more computationally intensive than the 1-D approach, the developed 3-D model allows analyzing more realistic operating scenarios, and helps explaining the performance of practical processes as applied in industry.