Applications, Equipment, and Models for Reverse Osmosis

In many commercial units operating pressures in reverse osmosis range from about 1035 up to 10 350 kPa (150 up to 1500 psi). Comparison of Eq. (13.9-2) for solvent flux and Eq. (13.9-5) for solute flux shows that the solvent flux N depends only on the net pressure difference, while the solute flux N, depends only on the concentration difference. Hence, as the feed pressure is increased, solvent or water flow through the membrane increases and the solute flow remains approximately constant, giving lower solute concentration in the product solution. 

At a constant applied pressure, increasing the feed solute concentration increases the product solute concentration. This is caused by the increase in the feed osmotic pressure, since as more solvent is extracted from the feed solution (as water recovery increases), the solute concentration becomes higher and the water flux decreases. Also, the amount of solute present in the product solution increases because of the higher feed concentration. 

If a reverse-osmosis unit has a large membrane area (as in a commercial unit), and the path between the feed inlet and outlet is long, the outlet feed concentration can be considerably higher than the inlet feed Ci- Then the salt flux will be greater at the outlet feed cornpared to the inlet (K2). Many manufacturers use the feed solute or salt concentration average between inlet and outlet to calculate the solute or salt rejection R in Eq. (13.9-8). 

EXAMPLE 13.10-1. Prediction of Performance in a Reverse-Osmosis Unit 

A reverse-osmosis membrane to be used at 25°C for a NaCl feed solution containing 2.5 g NaCl/L (2.5 kg NaCl/m, p = 999 kg/m ) has a water permeability constant A = 4.81 x lO kg/s m atm and a solute (NaCl) permeability constant = 4.42 x 10 m/s (Al). Calculate the water flux and solute flux through the membrane using a AP = 27.20 atm and the solute rejection R. Also calculate Cj of the product solution. 

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