Membrane and Desalination Technologies - TCE Moodle Website

Membrane Separation: Basics and Applications 309
Combining Eq. (32), Eq. (33) and Eq. (37) yields
R ¼
BðDP DPÞ
; (38)
BðDP DPÞþ1
B ¼ Aw
:
Ascw2
Noted that the newly combined parameter B has a unit of atm
(39)
1 .
During membrane operations, localized concentration of salt builds up at the boundary
layer of membrane. This is called the concentration polarization (40, 49). The concentration
polarization can be reduced by increasing turbulence.
Owing to the presence of concentration polarization, Eq. (33) and Eq. (35) will have to be
revised as
Ns ¼ Asðbc1 c2Þ; (40)
DP ¼ bP1 P2; (41)
where b is the concentration polarization, which normally ranges from 1.2 to 2.0. When the
feed solution is well mixed and the salt concentration is about 1%, the RO membrane
filtration unit can be treated as a continuously stirred tank reactor (27).
Example 3
An RO membrane system is used for the desalination of a feed water that contains 2.5 g
NaCl/L. The temperature is 25 C and the density of the feed is 999 kg/m 3 . The applied
pressure (DP) is 27.6 atm. The water permeability constant (Aw) and the NaCl permeability
constant (As) are 4.8 10 4 kg/s m 2 atm and 4.4 10 7 m/s, respectively:
(a) Assume that the concentration polarization can be neglected. Calculate the salt rejection, the
water flux and the salt flux through the membrane, and the salt concentration in the permeate.
(b) Owing to the incomplete mixing in the RO module, the concentration polarization can be
assumed to be 2.0. What are the salt rejection, the water flux, the salt flux and the salt
concentration in the permeate? Also comment on the applied pressure (DP) if the quality of
the product water remains the same as in (a).
Solution
(a) According to Eq. (10a), the osmotic pressure in the feed can be determined by
X Mi ¼ 2 2:5=58:45 ¼ 0:0856 M;
P1 ¼ RT X Mi ¼ 0:08206 ð273 þ 25Þ 0:0856 ¼ 2:09 atm:
Assume that the salt concentration in the permeate is very low. Therefore, we have
Nw ¼ AwðDp DPÞ ¼4:8 10 4
P2 ¼ 0;
ð27:6 2:09Þ ¼0:01224 kg water=sm 2 :