Effectiveness-mass transfer units (ε-MTU) model of a reverse osmosis membrane mass exchanger

A strong analogy exists between heat exchangers and osmotic mass exchangers. The effectiveness-number of transfer units (ε-NTU) method is well-known for the sizing and rating of heat exchangers. A similar method, called the effectiveness-mass transfer units (ε-MTU) method, is developed for reverse osmosis (RO) mass exchangers. Governing equations for an RO mass exchanger are nondimensionalized assuming ideal membrane characteristics and a linearized form of the osmotic pressure function for seawater. A closed form solution is found which relates three dimensionless groups: the number of mass transfer units, which is an effective size of the exchanger; a pressure ratio, which relates osmotic and hydraulic pressures; and the recovery ratio, which is the ratio of permeate to inlet feed flow rates. A novel performance parameter, the effectiveness of an RO exchanger, is defined as a ratio of the recovery ratio to the maximum recovery ratio. A one-dimensional numerical model is developed to correct for the effects of feed-side external concentration polarization and nonlinearities in osmotic pressure as a function of salinity. A comparison of model results to experimental data found in the literature resulted in an average error of less than 7.8%. The analytical ε-MTU model can be used for design or performance evaluation of RO membrane mass exchangers.