Modeling of a radial flow hollow fiber module and estimation of model parameters for aqueous multi-component mixture using numerical techniques

A mathematical model is developed for the separation of two solutes from aqueous solutions in a hollow fibre module. The model combines the extended Spiegler–Kedem model with the film theory model and takes into account the pressure drops in both feed side and permeate side streams. This model is then used for the simulation of the separation of phenol and NaCl in an aqueous solution at different operating conditions and the role of the solute–solute interaction parameter appearing in the extended Spiegler–Kedem model is further investigated. To validate this model, the separation data for a ternary NaCl–KBr aqueous solution are obtained in a hollow fiber reverse osmosis (HFRO) module. Using part of the experimental results for the binary and ternary systems separation, the six unknown membrane parameters of the model, namely the pure water hydrodynamic permeability, the two solute permeabilties, two reflection coefficients and the solute–solute interaction parameter were determined by using an optimization technique—the simplex search. These values are then used to predict and compare the performances at other operating conditions. The theoretically predicted and the experimental values are found to be in excellent agreement.