Short cut design methods for reverse osmosis separation with tubular modules

The basis for obtaining explicit flux expressions in reverse osmosis separations with concentration polarization has been illustrated for tubular modules with turbulent flow. Various analytical equations developed thereby to predict the required number of tubes and the permeate solute concentrations are described and compared with one another as well as with the currently used numerical methods. The utility of such simple design procedures are pointed out. The possibilities and difficulties of adopting these procedures for designing spiral-wound modules have been discussed. The analytical equations can be adopted to "tapered-flow" reverse osmosis without much difficulty.