Desalination, Vol.201, No.1-3, 297-305, 2006
Shortcut design method for reverse osmosis tubular module: the effect of varying transmembrane pressure and concentration polarization
A good shortcut design method of tubular membrane modules provides a more accurate estimate of the size or area of the module required for a given separation duty and hence its cost. A previous shortcut design method based on the cross-flow nature of the membrane developed by the author considered only a constant trans-membrane pressure and a constant polarization. The pressure drop along the tube due to friction decreases the transmembrane pressure along the tube that is available to drive the flux resulting in a decrease in the flux across the membrane further down the tube. Concentration polarization along the tube would also lead to a decrease in flux. Both tends to decrease the overall size of the membrane area. This paper proposes to extend the cross-flow design method to include the effect of trans-membrane pressure drop and concentration polarization along the tube. The number of transfer unit (NTU) for reverse osmosis is found to depend on four parameters: the rejection, R, the recovery, S, the dimensionless applied transmembrane pressure, psi, the polarization represented by Peclet number, Pe, and the pressure drop ratio, Delta P-f/Delta P-T, It was found that the pressure drop along the membrane tubes does not generally affect the NTU and hence the area of the membrane required for the separation. It only increases slightly the NTU and hence the area at lower transmembrane pressure, low recovery and high rejection. At high rejection, the NTU and hence the area increase slightly with higher polarization but decrease slightly at low rejection.