Predicting Water Flux in Forward Osmosis with Unknown Feed Solution Composition: An Empirical Approach Based on Thermodynamical Properties

This study investigated the predictability of forward osmosis (FO) performance with an unknown feed solution composition, which is important in industrial applications where process solutions are concentrated but their composition is unknown. A fit function of the unknown solution’s osmotic pressure was created, correlating it with the recovery rate, limited by solubility. The osmotic concentration was derived and used in the subsequent simulation of the permeate flux in the considered FO membrane. For comparison, magnesium chloride and magnesium sulfate solutions were used since these show a particularly strong deviation from the ideal osmotic pressure according to Van’t Hoff and are, thus, characterized by an osmotic coefficient unequal to 1. The simulation is based on the solution–diffusion model with consideration of external and internal concentration polarization phenomena. Here, a membrane module was subdivided into 25 segments of equal membrane area, and the module performance was solved by a numerical differential. Experiments in a laboratory scale for validation confirmed that the simulation gave satisfactory results. The recovery rate in the experimental run could be described for both solutions with a relative error of less than 5%, while the calculated water flux as a mathematical derivative of the recovery rate showed a bigger deviation.