This work presents a systematic method for analysis and optimization of specific energy production (SEP) of PRO systems employing single-stage configuration as well as multi-stage design with inter-stage hydro-turbines. It is shown that the SEP normalized by the draw solution feed osmotic pressure increases with the number of stages as well as a dimensionless parameter Υ
total = A
totalL
pÏ
0/Q
0. As compared to the single-stage PRO, the multi-stage arrangement not only increases flux and volume gain, but also allows a stage-dependent, progressively decreasing hydraulic pressure, both of which contribute to enhanced SEP and power density. At the thermodynamic limit where Υ
total goes to infinity, the theoretical maximum SEP that can be recovered by an N-stage PRO system is derived analytically. For single-stage PRO, it is no more than Ï
0. For infinite number of stages, the theoretical limit becomes ln(q
total)Ï
0, where q
totalis the dilution ratio. The gap between SEP under practical conditions and its theoretical value is discussed.
Reference:
[1] M. Li. Theoretical Investigation of Power Generation by Pressure Retarded Osmosis. Under Review, 2017.