SOME GENERAL EQUATIONS FOR REVERSE OSMOSIS PROCESS DESIGN

A generalized approach to reverse osmosis process design is presented for solution‐membrane‐operating systems characterized by the dimensionless parameters γ, θ, and λ defined in terms of the pure water permeability constant A, solute transport parameter (DAM/Kδ), mass transfer coefficient k on the high pressure side of the membrane, and the properties of the solution. Analytical expressions are derived, in terms of dimensionless quantities, for the change of volume of solution, concentration of the bulk solution and that of the concentrated boundary solution on the high pressure side of the membrane, the change in the permeating velocity of solvent water through the membrane, solute separation, and the other related quantities, at any instance, as a function of concentration of the product solution on the atmospheric pressure side of the membrane, or time from the start of the operation for reverse osmosis systems specified by γ, θ, and λ. The equations are applicable to membranes for which (DAM/Kδ) is independent of solute concentration and feed flow rate, and for aqueous feed solutions whose molar density can be assumed constant and whose osmatic pressure is proportional to mole fraction. The equations are developed first for the case of batch‐by‐batch operation, and their applicability to the flow case is then indicated. Copyright © 1969 American Institute of Chemical Engineers