Membrane and Desalination Technologies - TCE Moodle Website

Potable Water Biotechnology, Membrane Filtration and Biofiltration 515
where Qf is the feed flow to the membrane unit (m 3 /h), Qc is the concentrate flow from the
membrane unit (m 3 /h), Qp is the filtrate flow produced by the membrane unit (m 3 /h).
For the system operating without a concentration waste or “bleed” stream mode or crossflow
systems in which 100% of the concentrate is recirculated, the concentrate (i.e., bleed or
reject) flow, Qc, is zero. For the purpose of sizing a membrane filtration system, it may be
desirable to account for the additional filtered water used for both backwashing and chemical
cleaning in the determination of the filtrate flow, Qp. Similarly, an estimate of the total
required feed flow Qf to the system should incorporate any raw water that may be used in
these routine maintenance processes.
For the most widely used configuration as fiber membrane, the feed solution passes across
the fibers or flows parallel to the fibers and the product water is collected at one or both ends
of the bundle. The water flux can be determined from Eq. (9):
J ¼ VavgD
; (9Þ
4L
where J is the water flux (m 3 /m 2 -h), Vavg is the average water velocity (m/h), D is the tube
diameter (m), L is the fiber length (m).
If the water velocity was constant at the exit value, the pressure drop could be calculated
using Eq. (10):
Dp ¼ 1 mLVavg
2 D2 ; (10Þ
where Dp is the pressure drop (Pa), m is the viscosity (Pa·s), V avg is the average water velocity
(m/s), L is the fiber length (m), D is the tube diameter (m).
Example 1
A hollow-fiber permeator with inside diameter 0.02 cm with a water flux of 8 10 6 m/s. The fiber
length is 2 m.
(a) Determine the exit velocity of water
(b) Calculate the pressure drop
Solution
(a) Determine the exit velocity of water
Using Eq. (9) to determine the exit velocity of water
The exit velocity of water is 0.32 m/s.
J ¼ VavgD
4L ;
Vavg ¼ 4JL
D ;
Vavg ¼ 4 ð8 10 6m=sÞ ð2mÞ
ð0:02 10 2 ;
mÞ
Vavg ¼ 0:32 m=s: