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The following discussion of flux models will be limited to the phenomenological description of the solvent flux. Models also exist for the solute flux, which can be used to provide greater detail in process design, but are beyond the scope of this particular presentation. 11.2.1 Reverse Osmosis. -Permeation of water through the membrane, J,, in reverse osmosis is given by the following equation: J, = 2 (AP - Arc) m This case assumes that no gel layer with thickness tg is present; therefore C, = CWi. The intrinsic rejection of salt, R”, is less than 1. The concentrations refer to the solute (salt) concentration. where: P, = specific water permeability 4n = membrane thickness AP = applied transmembrane mechanical pressure (at a specific point) AK = actual osmotic pressure gradient based on C, and Cp (at a specific point) The term P,lt, is often referred to as the coefficient of water transport, which can be determined from experimental data by dividing the observed water flux per unit area of membrane by the net applied pressure (AP - AZ). 11.2.2 Nmofiltration, ultrafiltration, and microfiltration. -The most general form for water permeation in nanofiltration, ultrafiltration, and microfiltration is: where: pv = specific water permeability = membrane thickness t,” = thickness of: - effective adsorption - effective gel layer, and/or - effective fouling layer,and/or - effective cake layer J, = AP - AK 2 = specific permeability of clean membrane of the ‘g’ layer layer, and/or AZ’ = applied, transmembrane, mechanical pressure (at a specific point)PDF Image | DESALTING AND WATER TREATMENT MEMBRANE
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