Solution-diffusion-electromigration approximation model (SDE-A) for strongly charged, weakly charged and effectively uncharged reverse osmosis membranes

The solution-diffusion-electromigration approximation model (SDE-A) was formulated to describe the salt permeability of effectively uncharged, weakly charged and strongly charged reverse osmosis (RO) membranes. The model uses three of fewer parameters, depending on the type of charge behavior that a particular membrane exhibits under the allowable experimental conditions regarding feedwater salinity and acidity. The resulting algebraic equation is an approximation of an analytical solution of the Nernst-Planck equations for a 1:1 salt where the membrane charge depends on the feedwater conditions. The SDE-A model was compared to the more complex solution-friction (SF) model, by converting SF parameters to SDE-A parameters, resulting in a typical difference in computed salt permeability of less than 20%. Furthermore, the SDE-A model was applied to datasets from literature, corresponding to strongly charged, weakly charged and uncharged membranes. The SDE-A model can describe the effect of salinity and pH in these datasets comparably to the SF model. Because the model parameters can be easily determined experimentally and the algebraic model equation does not require elaborate solvers, the model is suitable for process design and optimization.