Page 246 - Membranes for Industrial Wastewater Recovery and Re-Use

System design aids 2 1 5

than the flows of up to 1.6 m3/h attainable in practice for elements of this size,
suggesting that mass transfer promotion is greater in real systems. This is partly
accounted for by the higher cross-flows at the element inlet, but is most likely to
be due to assumptions made about the respective vales of the spacer mesh width
and the diffusion coefficient. The calculation is extremely sensitive to both these
values.
The feed pressure can be estimated from resistance theory, whereby:

0 the hydraulic losses across the retentate side, and
0 the transmembrane pressure

are calculated from the retentate channel hydraulic resistance and the
membrane resistance R, (Equation (2.5)). The feed pressure is further increased
by the effect of concentration polarisation, since:
TMP = J x R,, x /J + An*,

where
]Rmp = 5.83 x 10-' x 8.5 x 1013 x 1.15 x = 5.70 x 10' Pa
= 5.7 bar

and

where All is the maximum osmotic pressure difference across the membrane
(from Equation (2.9)) modified for concentration polarisation and conversion.
so:
An = 1.14 x 0.9 x 8.314 x (273 + 15) x 2 x 0.98 X (850/58.5)
= 69 960 Pa

Thus

An* = 1.14 x 69 960 = 7.98 x lo4 Pa

And so

AII- 7.98 x 104
-- - = 9.24 x lo4 Pa = 0.924 bar
(1 - 0) (1 - 0.136)
Therefore

TMP = (5.70 + 0.92) = 6.62 bar