## Design of the Reverse Osmosis Unit

A reverse osmosis plant consists of a series of modules arranged in parallel. The design data include recovery, pressure, brine, flow rates, product water quality and flux maintenance procedure.

To be able to design a reverse osmosis unit one must know the feed water composition, its temperature and osmotic pressure. The capacity requirements of a plant are usually based on a certain reject flow rate at a given temperature or, in the case of waste water treatment, on the feed flow rate.

Based on mass balance for the water as well as the solute, the following equations can be set up:

where

Qf = flow rate of feed stream

Qr = flow rate of reject

Qp = flow rate of permeate

Cit = concentration of i in the feed stream

Ci = concentration of i in the reject

Cip = concentration of i in the permeate

The mean concentration of i, Cia, on the one side of the membrane is given by:

The water quality in the permeate (product) can be expressed by means of Cia and the average rejection ratio, Rav:

The average salt rejection is given by:

This equation can be solved most easily by an iteration. If we assume Cip = 0, we have:

where

Cip is then estimated:

A better approximation can be obtained by utilizing the value given by equation (10.22) as next Cip-value, etc.

The minimum free energy requirement is determined (Johnson et al., 1966) by means of:

o where aw = the chemical activity of water nw = number of moles of water recovered aw can be calculated from:

where cp Is a coefficient.

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