Theoretical Analysis of a Mathematical Relation between Driving Pressures in Membrane-Based Desalting Processes

Osmotic and hydraulic pressures are both indispensable for operating membrane-based desalting processes, such as forward osmosis (FO), pressure-retarded osmosis (PRO), and reverse osmosis (RO). However, a clear relation between these driving pressures has not thus far been identified; hence, the effect of change in driving pressures on systems has not yet been sufficiently analyzed. In this context, this study formulates an actual mathematical relation between the driving pressures of membrane-based desalting processes by taking into consideration the presence of energy loss in each driving pressure. To do so, this study defines the pseudo-driving pressures representing the water transport direction of a system and the similarity coefficients that quantify the energy conservation rule. Consequently, this study finds three other theoretical constraints that are required to operate membrane-based desalting processes. Furthermore, along with the features of the similarity coefficients, this study diagnoses the commercial advantage of RO over FO/PRO and suggests desirable optimization sequences applicable to each process. Since this study provides researchers with guidelines regarding optimization sequences between membrane parameters and operational parameters for membrane-based desalting processes, it is expected that detailed optimization strategies for the processes could be established.