The MBR Book: Principles and Applications of Membrane

204 The MBR Book
where A x is the open cross-sectional area and Q A is the aeration rate. For an HF module,
A x can be determined from the same trigonometric approach as that yielding
Equation (4.1) as being:
A
(4.3)
where A f is the module or element membrane area. The area associated with each
filament is given by (Appendix C):
A
x
Fibre separation (mm)
A ⎛
f 1 d ⎞
� ⎜ �
L ⎝⎜
f 4 ⎠⎟
x,filament
3.50
3.00
2.50
2.00
1.50
1.00
0.50
(4.4)
This compares with the more straightforward case of the FS module, where A x is
simply the total cross-sectional area provided by the channels and each panel crosssectional
area is given by:
Ax,panel dw �
HF data
FS & MTline
0.00
0.00 0.50 1.00 1.50 2.00 2.50 3.00
p ⎛ 4d
⎞
� ⎜ � d 2
⎜
4 ⎝⎜
f ⎠⎟
Fibre diameter (mm)
Figure 4.49 Membrane separation vs. filament diameter for HF membrane modules
(4.5)
where w is the panel width.
According to Equations (4.2) and (4.4), for a fixed aeration rate shear increases
both with increasing packing density and with decreasing filament diameter in the
case of an HF module. For an FS module it increases with decreasing channel width
(Equation (4.5)). However, a number of important parameters mitigate against
small filaments and high packing densities:
(a) the bubble rise velocity decreases with bubble size, and thus decreasing �,
with correspondingly increasing downward drag force;
(b) clogging, the risk of which increases with decreasing �;