STAGEWISE REVERSE OSMOSIS PROCESS DESIGN

Reverse osmosis is treated as a general separation process which can be operated in stages, if necessary. Equations developed for stagewise reverse osmosis process design are based on the Kimura-Sourirajan analysis of the reverse osmosis data for water and solute transport through the Loeb-Sourirajan type porous cellulose acetate membranes. The analysis involves the specification of the membrane in terms of the pure water permeability constant, A, and the solute transport parameter, (DAM/Kδ). Expressions connecting the concentrations of the feed solution entering and leaving the unit stage on the high pressure side of the membrane, and of the membrane-permeated product solution leaving the atmospheric side of the membrane are derived as functions of A, (DAM/Kδ), operating pressure, molar density of the solution, average mass transfer coefficient, and volumetric fraction of product recovery. Following the formalism of the multistage distillation process, the cascade theory is applied to the multistage reverse osmosis process, and expressions for the minimum number of stages and minimum reflux ratio are derived. The ideal cascade theory is then used to establish a practical criterion for multistage reverse osmosis process design. To minimize concentration polarization effects on product concentration, membrane area per unit product rate, and power consumption due to frictional pressure drop, a unit stage is considered as a combination of several inner stages connected in series. Assuming complete mixing of the feed solution between adjacent inner stages, equations are developed for unit-stage and two-stage reverse osmosis process design. Application of the design equations is illustrated by a set of calculations with particular reference to saline water conversion. © 1969, American Chemical Society. All rights reserved.