Theoretical Model for the Prediction of Water Flux during the Concentration of an Olive Mill Wastewater Model Solution by Means of Forward Osmosis

Currently, understanding the dynamics of the interaction between the agents in a process is one of the most important factors regarding its operation and design. Membrane processes for industrial wastewater management are not strangers to this topic. One such example is the concentration of compounds with high added value, such as the phenolic compounds present in olive mill wastewater (OMW). This process is a viable option, thanks to the forward osmosis (FO) process, osmotically driven by a saline stream. In this context, the transport of the solute and the solvent through the FO membranes, although essential to the process, remains problematic. This paper presents a study to predict, by means of a theoretical model, the water flux for two membranes (a cellulose triacetate flat sheet and a polyamide hollow fiber with integrated aquaporin proteins) with different characteristics using a sodium chloride solution as the draw solution (DS). The novelty of this model is the consideration of the contribution of organic compounds (in addition to the inorganic salts) to the osmotic pressure in the feed side. Moreover, the geometry of the modules and the characteristics of the membranes were also considered. The model was developed with the ability to run under different conditions, with or without tyrosol (the compound chosen as representative of OMW phenolic compounds) in the feed solution (FS), and was fitted and evaluated using experimental data. The results presented a variability in the model prediction, which was a function of both the membrane used and the FS and DS, with a greater influence of tyrosol observed on the permeate flux in the flat cellulose triacetate membrane.