Mathematical Modeling of a Hollow Fiber Module Used in Pressure-Retarded Osmosis Process

Abstract

   Pressure retarded osmosis (PRO) can be considered as one of the methods for utilizing osmotic power, which is a membrane-based technology. Mathematical modeling plays an essential part in the development and optimization of PRO energy-generating systems. In this research, a mathematical model was developed for the hollow fiber module to predict the power density and the permeate water flux theoretically. Sodium chloride solution was employed as the feed and draw solution. Different operating parameters, draw solution concentration (1 and 2 M), the flow rate of draw solution (2, 3, and 4 L/min), and applied hydraulic pressure difference (0 - 90 bar) was used to evaluate the performance of PRO process of a hollow fiber module. The effect of these operational parameters was investigated on the theoretical permeate water flux and power density. According to the theoretical results, the permeate water flux and the power density increased with increasing the concentration of draw solution and the flow rate of the draw solution. While decreased with increasing the feed solution concentration. By increasing the applied hydraulic pressure on the draw solution, the water flux decreased and the produced power density increased. The maximum power density and the corresponding permeate water flux of 2 M NaCl draw solution was approximately 16.414 W/m2 and 11.818 LMH respectively, which occurs at an applied hydraulic pressure of 50 bar.