Three-dimensional concentration-polarization modeling of trace-ions in reverse osmosis

Concentration polarization (CP) is mostly evaluated through one-dimensional (1D) film models considering convective and diffusive transport of solutes. However, in multicomponent ionic solutions, electromigration and chemical speciation may also play a role in the solute transport within the CP layer, thus affecting the process performance. We developed a three-dimensional (3D) numerical model for evaluating the CP in spacer-filled feed reverse osmosis (RO) channels by coupling hydrodynamics with the transport of solutes by convection, diffusion and electromigration, and chemical speciation by several ion-pairing equilibria. A realistic spacer geometry was obtained by CT-scans of commercial RO spacers. The model revealed highly non-uniform distributions of CP, mass transfer coefficients and precipitation potential on the membrane. While electromigration tends to equalize the fluxes of dominant ions, increases locally the CP of anions and decreases that of cations, it was found not to significantly affect the boundary layer thickness. However, the chemical speciation strongly affected the CP of trace ions binding with dominant ions. Finally, the 3D results were compared with those obtained from simpler 1D models. While 1D approaches help explaining qualitatively the effects of electromigration and speciation, and serve as a reasonable first approximation, they do not capture the non-uniform distribution of concentrations, mass transfer rates or saturation indices. The model will be used to study the full length of an RO membrane module and thus provide better indicators of the overall performance of the separation process.