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Advanced Membrane Fouling Characterization 111
Substituting Eq. (6) into Eq. (5) results in
Rf ¼ Rt R0: (6Þ
kf ¼ Rt R0
Ð t
0
:
v dt
(7Þ
The hydraulic resistances at the beginning and the end of fouling test are related to the
permeate fluxes with the basic membrane transport principle:
Dp
R0 ¼
Dp
; (8Þ
v0
Dp Dp
Rt ¼ ; (9Þ
where vt and v0 represent the measured permeate flux at the beginning and the end of the
fouling experiment, respectively, Dp is the osmotic pressure (Pa), and Dp is the driving
pressure (Pa). Unlike in most ultrafiltration and microfiltration processes, the permeate flux in
RO processes usually declines with time at a near constant rate. This is because the resistance
of fouling layer is much smaller than the resistance of RO membranes and nearly constant
permeate flux can be maintained during the fouling experiment. In this case, the integral term
in Eq. (7) can be well approximated to
ðt v dt ¼
0
t
2 ðv0 þ vtÞ: (10Þ
Substituting Eqs. (8)–(10) into Eq. (7) results in
kf ¼
2ðDp DpÞ
t
vt
ðv0 vtÞ
: (11Þ
v0vtðv0 þ vtÞ
Fouling potential in Eq. (11) can be easily determined since all the terms on the right-hand
side of the expression can be either measured from a crossflow RO test cell unit or
predetermined by the investigator.
3.3. Membrane Device for Fouling Potential Measurement
The RO membrane cell for fouling potential measurement is schematically shown in
Fig. 3.4. A small piece of RO membrane is housed in a stainless steel case that can sustain
high pressure. The membrane cell is operated under crossflow mode in order to simulate
fouling under similar hydraulic condition as in the full-scale RO processes. The feed water
under test is pumped into the cell at the testing crossflow velocity and pressure with a highpressure
pump. Permeate from the cell is collected in the glass container, weighed and
recorded at preset interval. The measurement usually last for a few hours, depending on the
fouling potential of the feed water. The duration is shorter for feed water with higher fouling
potential. The permeate fluxes at the beginning and the end of measurement are determined
and the fouling potential is calculated from Eq. (11).