Page 245 - Membranes for Industrial Wastewater Recovery and Re-Use

2 14 Membranes for Industrical Wastewater Recover9 and Re-use

According to the expression derived for filled channels by Chiolle et al. (1978),
Table 2.11 and Equation (2.15). the Sherwood number correlates to the
Reynolds and Schmidt numbers Re and Sc respectively according to:

Sh = 1.065Re".sS~o-33 [d/( 6Lrn)]0.5

and from Equations (2.1 7) and (2.18):
Re = pUd/p lo3 x U x 1.6 x 10-3/(1.15 x lop3) = 1391U

=
sC = w/p~ 1.15 m3/(103 8 x = 1438

The Reynolds number can then be calculated as:

It follows that the (retentate) cross-flow approach velocity is:
U = 129/1391 = 0.0927 m/s

The volumetric flow Q at this flow velocity relates to the channel cross-sectional
area, given by d x A/(2L):

Q = U x d x A/(2L) = 0.0927 x 0.8 x x (36/2 x 1) x 60 x 60
= 4.81 m3/h
If this is assumed to relate to the flow at the retentate outlet, where
concentration polarisation is greatest, then the feed flow will higher than this
due to conversion. The total volumetric flow of permeate is given by:
Qpermeate =I > xarea = (21/1000) x 36 = 0.76 m3/h

The feed flow is then given by:

Qfeed = 4.81 + 0.76 = 5.57 m3/h

and the conversion is thus:

0 = 100 x 0.76/5.57 = 13.6%

This is within the normal range of 7-1 7% quoted for a typical brackish water
40-inch membrane element. However. the production rate is considerably lower