Page 204 - Membranes for Industrial Wastewater Recovery and Re-Use

System design aids 173

Concentration polarisation (CP) can be quantified from film theory (Section
2.3.2, Equations (2.14)-(2.18)), and its effect on osmotic pressure and scale
formation respectively determined from the van’t Hoff equation (or the above
modifications thereof) and equilibrium thermodynamics expressions for
precipitation (Section 2.4.3). Whilst the effect on osmotic pressure can be
calculated with reasonable accuracy, the actual scale deposition rate cannot.
This is because the simple expressions outlined in Section 2.4.3 are derived from
equilibrium thermodynamics and cannot account for the very wide variations in
the scaling kinetics that exist. Indeed, it is quite common for some scalants to
remain dissolved at concentrations well beyond the theoretical saturation limit
determined from the solubility constant K, (Table 2.14), in a supersaturated
state, even without the addition of threshold inhibitors (Table 2.15) to suppress
nucleation.
In principle, film theory also permits the optimisation of both the retentate
flow rate and the design of the spacer material in the spiral-wound RO element.
However, in practice the choice of RO spacer material is dictated to a large extent
by cost and, in any case, is not one that can be made by the RO process designer
but by the membrane supplier. Similarly, although turbulence, and hence mass
transfer, is promoted by a high cross-flow velocity, a practical limit is placed on
the retentate flow rate by the construction of the spiral-wound element, which
can only withstand a certain maximum hydraulic loading without risk of failure.
Failure can be manifested through a phenomenon known as “telescoping”,
where the centre of the element is pushed axially outwards by the force of the
flow. Since the specific resistance (i.e. the hydraulic resistance per unit length)
offered by the membrane channel is constant along the length of the membrane
element, the limit on retentate flow rate implies a limit on both the inlet pressure
and the pressure drop across the element. For large elements, 1 m long, the
maximum pressure drop is normally much less than 1 bar.
Most RO filtration systems are based on the spiral-wound configuration, a
noteworthy exception being the Monsanto Prisma hollow fibre membrane. The
largest of the spiral-wound elements are 8 inch (about 0.2 m) in outer diameter
and 40 inch (about 1 m) in length, with newer membrane elements being 1.5 m
long, Membrane elements are mounted inside pressure vessels in which they are
connected sequentially to give a module length of up to 8 m or more for an 8-
element module. These modules can then be arranged in parallel and/or in series
to produce a matrix, or array (Section 2.4.1), of membranes with a sufficient
total membrane surface area to obtain a specified total permeate flow and
permeate quality at an acceptable cost.
Both the appropriate number of elements in the module and the arrangement
of modules in the array to obtain volumetric flow information can be arrived at
through a simple mass balance (Section 4.3.2) provided the conversion 0 per
membrane element can be assumed constant. However, since (a) 0 must
necessarily be a function of both the transmembrane pressure (TMP) and the
osmotic pressure n, and so of the solute concentration, and (b) the solute flux
through the membrane and the fouling propensity are both critically important,
a simple water balance is normally insufficient. To obtain water quality