Modified Solution–Diffusion Model Incorporating Rotational Kinetic Energy in Pressure Retarded Osmosis

Pressure-retarded osmosis (PRO) is a process that allows the production of mechanical energy from the chemical potential difference between two solutions of different concentrations separated by a semi-permeable membrane. One of the main obstacles for this technology to be commercially competitive is the difference between the theoretical power density and the experimental power density due to negative factors like ICP. Analytical models facilitate the analysis of the relationships between system parameters and thus facilitate the optimization of components. In general, PRO has traditionally been explained through the solution–diffusion model, where the flow of water through the membrane depends on a diffusivity factor, the concentration gradient, and the hydraulic pressure gradient. This paper focuses on developing a modified solution–diffusion model that includes means to control the ICP through rotational kinetic energy. An energy balance method for obtaining a solution diffusion-based model is explained, and an analytical model is obtained. Finally, said model is verified through simulations with parameters reported in the literature to obtain insight on the required dimensions for a prototype. It was found that a turning radius of 0.5 m and an angular speed of less than 3000 rev/min could generate enough kinetic energy to compensate for ICP losses in a PRO scenario. Also, the results suggest that bigger concentration differences could benefit more of this technology, as they require almost the same energy as smaller concentration differences but allow for more energy extraction.