The MBR Book: Principles and Applications of Membrane

130 The MBR Book
constant pressure to constant volume and takes a value of 1.4 for air, T K,1 is the inlet
temperature (K), and Q A is the volumetric flow rate of air. The blower efficiency (�)
varies significantly according to the type of blower and its mechanical design, the rotational
speed, and the blower rating for the task. As with pumping operations more
accurate data can be found from manufacturers’ data sheets. If Equation (3.15) is
divided by the total membrane module area A m to which the flow rate Q A applies,
then one obtains an expression in kW/m 2 for power per unit membrane area:
W
(3.15b)
where k is therefore a function of pressure, and thus the hydrostatic head �P h determined
by the depth at which the aerator is placed in the tank, as well as temperature.
If Equation (3.15) is divided by the permeate flow rate Q P, that is J netA m, where J net is the
net flux (m 3 /(m 2 h)), then one obtains an expression for specific energy demand in
kWh/m 3 :
W
b,m
b,V
⎡
PA,1 Tk,1l ⎢⎛
P
�
⎢ ⎜
2.73 �105 jl ( �1)
⎢⎜
⎝⎜
⎢
P
⎣
kQ
�
JA
A
m
(3.16)
Hence, whilst the hydrostatic head wholly or partly determines the flux, depending
on whether suction is applied, its main contribution to energy demand does not
relate to membrane permeation directly but to its impact on aeration energy. If the
flux and flow are normalised to 20°C and 101.3 kPa (i.e.J� net and Q� A respectively),
then k in Equation (3.15b) simplifies to:
⎡
108.748l
⎢⎛
P ⎞
A,2
k � ⎢ ⎜
jl ( � 1) ⎢⎝⎜
101.325⎠⎟
⎣⎢
1� 1
l
(3.17)
As already stated in most hollow fibre (HF) MBR technologies the membrane aeration
is carried out separately from the bioreactor aeration and does not necessarily
employ the same type of aerator. Some of the oxygen transfer is achieved by the
membrane aeration, and the extent to which this occurs depends mainly on the type
of membrane aerator employed.
3.1.4 Design calculation: summary
A,2
A,1
⎞
⎠⎟
⎤
⎥
� 1 ⎥
⎦⎥
1 1 �
l
⎤
⎥ Q
⎥ A kQ
�1� ⎥
Am
A
⎦
Inter-relationships within an MBR process are complex (Fig. 2.26), but the most crucial
relationships with respect to operating costs are those associated with aeration
since this provides the largest component of the process operating cost. The impacts of
aeration on the various operating parameters have already been discussed and depicted
in Fig. 2.18, and biological and physical parameters used for the determination
of operating costs are listed in Tables 3.2 and 3.3 respectively. Note that it is most
consistent to normalise against permeate product volume to produce specific energy
A
m