Module-scale analysis of pressure retarded osmosis: performance limitations and implications for full-scale operation.

We investigate the performance of pressure retarded osmosis (PRO) at the module scale, accounting for the detrimental effects of reverse salt flux, internal concentration polarization, and external concentration polarization. Our analysis offers insights on optimization of three critical operation and design parameters--applied hydraulic pressure, initial feed flow rate fraction, and membrane area--to maximize the specific energy and power density extractable in the system. For co- and counter-current flow modules, we determine that appropriate selection of the membrane area is critical to obtain a high specific energy. Furthermore, we find that the optimal operating conditions in a realistic module can be reasonably approximated using established optima for an ideal system (i.e., an applied hydraulic pressure equal to approximately half the osmotic pressure difference and an initial feed flow rate fraction that provides equal amounts of feed and draw solutions). For a system in counter-current operation with a river water (0.015 M NaCl) and seawater (0.6 M NaCl) solution pairing, the maximum specific energy obtainable using performance properties of commercially available membranes was determined to be 0.147 kWh per m(3) of total mixed solution, which is 57% of the Gibbs free energy of mixing. Operating to obtain a high specific energy, however, results in very low power densities (less than 2 W/m(2)), indicating that the trade-off between power density and specific energy is an inherent challenge to full-scale PRO systems. Finally, we quantify additional losses and energetic costs in the PRO system, which further reduce the net specific energy and indicate serious challenges in extracting net energy in PRO with river water and seawater solution pairings.