Mathematical modeling and simulation of the multiple solutes system for nanofiltration process

A.L. Ahmad, M.F. Chong, S. Bhatia
2005 Journal of Membrane Science  
A one-dimensional model for the multiple solutes filtration system is developed by extending the Spiegler-Kedem model by incorporating the solute-solute interactions. This extended Spiegler-Kedem model is suitable for predicting the performance of multiple solutes system in nanofiltration. The model is characterized by the parameters of L p , σ s , P si , P ss and k s . The parameters were estimated using the Levenberg-Marquardt method coupled with Gauss-Newton algorithm based on the
more » ... l data obtained from the literature. The simulation results obtained from the proposed model were also compared with the simulation results obtained from the Spiegler-Kedem model and extended Nerst-Plank model, respectively. The simulation results indicate that the flux behavior and the predicted permeate concentrations were in good agreement with that predicted by the two existing models and the experimental data. The extended Spiegler-Kedem model developed is suitable for predicting the performance of multiple solutes for nanofiltration system. .my (A.L. Ahmad). been widely used in predicting the performance of different systems especially for the desalination system [1,3]. However, this model is only applicable for the system with single solute where the rejection is close to unity. The extended Nerst-Plank model is the most elaborate model for transport of multiple ions through the charged nanofiltration membrane. This model describes the three important mechanisms of ionic transport in the membranes: (a) diffusion and (b) electromigration, as a result of concentration and electrical potential gradients, respectively, and (c) convection caused by the pressure difference across the membrane [4] . The models derived from the irreversible thermodynamics are the Kedem-Katchalsky model and Spiegler-Kedem Model [5] . In these models, the membrane is treated as a black box in which relatively slow processes proceed near the equilibrium without specific transport mechanisms and structure of the membrane. The model simply considers that the fluxes of solute and solvent are directly related to the chemical potential differences between the two sides of the 0376-7388/$ -see front matter
doi:10.1016/j.memsci.2005.01.005 fatcat:h3vpyyrlefacvhbyogxfoi6j3y