Utilization of renewable energy sources, as an approach to reduce greenhouse gas (GHG) emissions, have been globally popular in the last few decades. Among renewable energy sources, pressure retarded osmosis (PRO) has been scrutinized by scientists since the mid 70's. However, even today, the existing river-sea PRO systems can only marginally meet the generally approved criterion of 5 W/m² power density, a threshold for an economically feasible PRO system. As an approach to increase the performance of PRO systems, multi-staging of PRO modules are investigated.

A mathematical model of the scaled up PRO process is proposed with consideration for internal and external concentration polarization, reverse salt flux, and spatial variations along the membrane. A thermodynamic model is also developed with consideration for entropy generation and losses in the process. It predicts the percentile of each work loss source compared to the net work in the system. Several confi gurations of dual stage PRO system are presented and compared to single stage PRO. The comparison is based on three proposed target functions of power density (PD), specific energy (SE), and work per drawn freshwater (W_drawn). Applied hydraulic pressures and flow rates of draw and feed solutions are optimized for maximizing the target functions. The results indicate that overall performance of the system could be improved by up to 8 % with a dual stage PRO in the case of SE. The system performance is not improved by depressurizing the draw solution before the second module in cases of SE and W_drawn. The thermodynamic analysis demonstrate the contribution of each work loss and justify the reason of diminishing the net work over the losses. The effect of membrane area and membrane characteristics on the SE target function is also investigated. The distribution of membrane area in each module depends on the selected con figuration and inlet draw solution. In the dual stage systems, the SE value increases up to 14% by improving the membrane characteristics. Reducing the salt rejection coefficient (B) is the most e ective membrane characteristic in our con figurations. Replacing seawater with RO brine in draw solution results in a signifi cant improvement in SE values.