The MBR Book: Principles and Applications of Membrane

L being the internal module length and N being the number of fibres per element.
The total cross-sectional area associated with each fibre is thus given by:
X
Substituting Equation (C.3) into Equation (C.4) yields:
X
(C.4)
(C.5)
where � is the fibre surface area per unit module volume (A f/V f). So, combining
Equation (C.1) and Equation (C.5) yields:
D �
The separation, � is thus given by:
d �1.95 �
f
d
d
(C.6)
(C.7)
In fact, this separation differs by only 2.5% from the value calculated on the basis
of ignoring the excluded area, for which the coefficient in the above equation
becomes 2.
C.2 Free area Ax The total free area can be obtained by subtracting the cross-sectional area of the
fibres from that of the module:
A
Substituting for V and N with � and A f, from Equation (C.3), produces:
A
f
f
x
x
Vf
�
LN
pdVf pd
� �
A f
f
4(1� 0.046) d
f
V d2N � �
L 4
p
Af
Ad f � �
fL
4L
Appendix C: Hollow fibre module parameters 283
(C.8)
(C.9)