The MBR Book: Principles and Applications of Membrane

of the particularly large-diameter Berghof HyPerm-AE module, all of the commercial
MBR membrane elements identified which are of specific surface area (�) below
170/m are FS in geometry, and only one FS technology is above 130/m.
Perhaps the most pertinent parameter for comparison of the various systems is the
membrane separation itself. For an FS system, this is simply given by the thickness of
the flow channel. For HF elements, the mean minimum separation can be determined
from trigonometry (Appendix C) as being related to filament ID and � by:
d
1/packing density
0.012
0.01
0.008
0.006
0.004
0.002
0
� 1.95 �
f
d
d
(4.1)
Values for � are included in parenthesis in Table 4.5. As might be expected, the
largest separations arise with the largest diameter filaments, but even the largest HF
� values are half those of the FS modules, as is inevitable from the packing densities.
There appears to be a roughly inverse relationship between � and � (Fig. 4.48), with
the coefficient or proportionality being around 10 �3 , regardless of the configuration.
Outliers arise mainly from the high packing densities attainable with some of the
MT products. On the other hand, HF configurations generally provide a higher minimum
separation distance, relative to the filament size (hence d/�), than the FS and
MT counterparts, where d � � (Fig. 4.49).
The deliberation over the optimum membrane configuration may proceed firstly
through a consideration of shear, which is given by the ratio of the velocity to channel
thickness (Equation (2.31)). If shear can be assumed to relate to the aeration velocity,
it follows that shear rate can be represented by:
U Q
G A,m
g � �
d A d
x
HF
FS
MT
0 2 4 6 8 10 12
Membrane separation (mm)
Commercial technologies 203
Figure 4.48 Inverse packing density (1/�) vs. membrane separation for the three module configurations,
data from Table 4.5
(4.2)