Mathematical model for the removal of trace metal by complexation-ultrafiltration

Complexation-ultrafiltration is emerging as the potential method for the removal of dissolved trace contaminant species from water in an energy efficient manner. The study incorporates the pore-size distribution of the membrane and the molecular weight distribution of the complexing ligand into the irreversible thermodynamic model by modifying the coefficients σ and ω to predict the rejection behavior of trace elements in the presence of complexing ligand necessitated due to the fact that the rejection behavior at trace concentrations is more dependent on probability with reference to a particular pore (related to pore diameter) and the size of the complexed species (mw of the particular species). A set of transport equations have been derived from Kedem Katachalsky’s irreversible thermodynamic model, by incorporating pore-size distribution of the membrane and molecular weight distribution (derived from size distribution) of ligand (polyethyleneimine). The validation of model has been done through the experimental data with copper–polyethyleneimine system using commercially available 6, 20, and 100 KD molecular wt. cutoff hollow fiber ultrafiltration membrane in-bench scale systems. The model developed is in good agreement with the experimental results as long as the stoichiometric concentration of ligand is equal or excess compared with the heavy metal species. Further, the studies also have underlined the importance of considering the pore-size distribution for predicting the performance characteristics. The model was not found suitable when the metal species is in excess, a situation we may not normally encounter in the removal trace metal species.