Abstract
A thermodynamically oriented method is developed to identify the theoretical and practical limits of pressure-retarded osmosis (PRO) on converting salinity gradient power to mechanical energy under constant operating pressure with infinite and finite mass exchange area, respectively. It is proved that pinch analysis can be used to find the mass exchange limit of PRO, and according to which draw and feed streams can be plotted on a graph of net osmotic pressure - water exchange. Based on the graphical method, an expression of optimal pressure change is derived that achieves the maximum work extraction of a PRO process with single draw/feed stream. Moreover, problem table method is presented that serves as an analytical procedure to determine the maximum extractable work of the conceptualized multi-stream PRO process. Examples of both a PRO process with a draw stream (0.6 M NaCl seawater) and a feed stream feed (0.015 M NaCl river water) and a multi-stream PRO are included to illustrate the proposed methods. Results of the former example show that the counter-current design achieves 30.85% and 31.49% increase, respectively, in the maximum theoretical and practical work output, compared with the co-current design. The latter example shows that the problem table method produces a 20.47% increase in the work output, compared with the standalone design.
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