Modeling concentration-polarization in reverse osmosis spiral-wound elements

The effect of feed water flow rate on the concentration-polarization of magnesium sulfate, sodium chloride, and sodium selenate in reverse osmosis (RO) spiral-wound elements was investigated and modeled. Experiments were performed with 40 in. long and 2.5 in. in diameter spiral-wound elements tested with feed solutions of the single electrolyte magnesium sulfate, and a mixture of sodium chloride and sodium selenate as major and trace components, respectively. The feed flow rates investigated ranged from 1.12 to 13.5 L/min, corresponding to Reynolds numbers from 25 to 300. The element was modeled by dividing it into n identical subelements, each separated into two compartments, feed channel and product water carrier, by the RO membrane. The feed channel compartment of each subelement was assumed to be an ideal continuous-flow stirred tank reactor (CSTR). Model predictions correlated generally well with experimental observations. Predicted product water flow rates and solute concentrations were within 12 and 24%, respectively, of corresponding experimental values.