Mathematical modeling of multiple solutes system for reverse osmosis process in palm oil mill effluent (POME) treatment

Abstract

Abstract A membrane transport model suitable for the multiple solutes system in reverse osmosis is developed for unsteady-state simulation and prediction of membrane filtration dynamics in terms of permeate flux and concentration of each solute. This model is based on coupling the concentration polarization model using unsteady-state differential material balance and extended Spiegler-Kedem model. This model is characterized by the parameters solute diffusivity in the concentration polarization layer (Dbi), reflection coefficient (σi), osmotic constant (ai), hydraulic permeability constant (Lp), mass transfer coefficient (ki) and solute permeability coefficient (Pii). These parameters are estimated by using the Levenberg–Marquardt method coupled with the Gauss–Newton algorithm using the experimental data. The experimental data were obtained from the treatment of pretreated palm oil mill effluent (POME) as a feed in the pilot plant scale reverse osmosis system. The pretreated POME composed of a ternary system with the solutes of carbohydrate constituents, protein and ammoniacal nitrogen. The simulation results show a good agreement with the experimental data. The proposed model is suitable for predicting the performance of multiple solutes in a reverse osmosis process. The concentration of each solute present is correlated with the COD of the permeate stream.