Page 203 - Membranes for Industrial Wastewater Recovery and Re-Use

172 Membranes for lndustrial Wastewater Recovery and Re-use

4.1 Computer-aided design for reverse osmosis plant

4.1.1 Introduction
It has already been pointed out (Section 2.3.2) that modelling of filtration
processes is not feasible on a universal basis, and that only reverse osmosis can
be modelled on the basis of solution-diffusion. In such a case, modelling is
possible using simple analytical expressions provided the water can be treated as
a continuum essentially free of the more complex interactions introduced by the
presence of dispersed particles, solute precipitation effects (gel layer formation)
and/or biological activity at the membrane-solution interface. As a result of
these complicating factors, which relate largely to porous membrane processes,
computer-aided design (CAD) software is currently available only for reverse
osmosis membranes and modules. The software packages are based on a series of
calculations that enable the estimation of the RO array design and operation. It is
instructive to review these CAD packages, which are produced by RO membrane
manufacturers and suppliers based on their own products, with a view to
ascertaining their general usefulness and limitations (Brauns, 200 1).

4.1.2 Key elements of the reverse osmosis process
Modelling of the reverse osmosis process relies on accurate mathematical
representation of

0 the osmotic pressure,
0 concentration polarisation, and
0 the hydraulic resistance offered by the membrane and the membrane
channels.

As already discussed (Section 2.3.1), the pressure required to drive a reverse
osmosis process relates both to the permeability of the membrane and the
osmotic pressure. The osmotic pressure is solute concentration related, and can
be very high for highly saline solutions: the osmotic pressure for seawater (3 5 g lF1
NaCl) is around 27 bar. No flow of water takes place unless this pressure is
exceeded. At moderate concentration values, osmotic pressure varies almost
linearly with concentration for many univalent salts, including sodium chloride,
according to the van't Hoff equation (Chapter 2, Equation (2.9)). In this equation
y depends on the degree of dissociation of the salt. Non-linear correlations of
ll with C have been fitted to Taylor series and power relationships:

" = RT(YlC1 + y2c2 + . . .)
n = yRTC"
Any one of the above relationships may be employed in existing RO design
sortware.