## Influent And Effluent Quality

3500 and 500 ppm TDS are typical values, respectively. MINIMUM {THERMODYNAMIC) ENERGY REQUIREMENT 3.8 kWh per 1000 gal of effluent water

While seldom practiced, wastewater treatment facilities can use reverse osmosis for wastewater dewatering and to recover valuable materials from the water. The flow of water across the membrane depends on the net pressure differential as expressed by the following equation:

where:

FIG. 7.37.12 Hydrate process.

W = Water flow rate kw = Membrane water permeation constant AP = Applied pressure differential t = Osmotic pressure differential

A small amount of salt permeates across the membranes. This salt flux is determined by the salt concentration on the feed and product water sides and is independent of the applied pressure.

The total energy requirement for reverse osmosis includes the minimum thermodynamic energy, which is about 3.8 kWh per 1000 gal for sea water at 25°C. In addition, power is required to overcome the irreversible losses, including pressure losses due to friction and concentration polarization. Concentration polarization is caused by a build up of solute ions at the surface of the membrane. Concentration polarization occurs because the water preferentially permeates the membrane, whereas the solute can only move from the membrane surface by back diffusion. This process depletes some pressure energy and is a major cause of inefficiency.

The following equation gives the salt permeation rate:

where:

S = Salt flow rate

Ks = Salt permeation constant

Cf = Concentration of salt in the influent solution

Cp = Concentration of salt in the effluent solution

Equations 7.37(6) and 7.37(7) show that the water effluent produced per unit of membrane surface increases with the pressure differential across the membrane, whereas the salt flux remains constant. Thus, an increase in operating pressure increases the ratio of water to salt and improves the efficiency of demineralization.

FIG. 7.37.13 Reverse osmosis.

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