Limiting extractable energy from pressure retarded osmosis with different pretreatment costs for feed and draw solutions

Pressure retarded osmosis (PRO) is technically feasible to extract salinity gradient energy, which represents a potential source of clean and renewable energy of enormous amount. Specific energy used in the assessment of economic viability of a pressure retarded osmosis (PRO) is commonly determined by normalization of the total energy with the combined volume of feed and draw waters indiscriminately. Such a specific energy may not be appropriate to serve this purpose because it does not reflect the enormous impact of the different pretreatment costs for feed and draw waters. In this article, expression for maximum available salinity gradient energy is derived by construction of a reversible PRO process. By introduction of a new concept of equivalent volume, the specific energy from salinity gradients can be rigorously analyzed for PRO process with different costs in pretreatment of low and high salinity waters. The feed fraction to maximize the specific energy in PRO is analytically determined to be 1-1/e (≈ 0.632) when the cost for pretreatment of feed and draw waters are equal. Furthermore, higher peak specific energy occurs at lower feed fraction as the cost for draw water pretreatment decreases.