An assessment of the Silt Density Index based on RO membrane ...

S.G. Yiantsios, A.J. Karabelas / Desalination 151 (2002) 229-238 235
feed waters is considered to be <strong>the</strong> oxidation <strong>of</strong>
<strong>the</strong> soluble ferrous ion to ferric. Thus, precipitation
kinetics is assumed here to be fast relative
to <strong>the</strong> iron residence times in <strong>the</strong> present
experiments.
Regarding <strong>the</strong> effects <strong>of</strong> aggregation on
deposition rates and deposit structure, an indirect
piece <strong>of</strong> evidence is presented below. Considering
a cake filtration mechanism, an estimate <strong>of</strong>
<strong>the</strong> characteristic particle size, a, may be
obtained as follows. Membrane flux as a function
<strong>of</strong> time is given by
J- -- A’
where AP is <strong>the</strong> applied pressure, R, <strong>the</strong> membrane
resistance and R, <strong>the</strong> fouling cake resistance.
The latter is given by
R, = R’, H (W
where
R’ = 2 (pap
c
and
2 a2(l-cp,Y
t
H = s
J(p,lcp,dt
0
(3b)
(3c)
Here, R, is <strong>the</strong> specific cake resistance, H <strong>the</strong>
cake thickness, qc <strong>the</strong> cake volume fraction, (Pi
<strong>the</strong> foulant bulk volume fraction, and p <strong>the</strong> water
viscosity. Combining <strong>the</strong> above equations and
differentiating with respect to time, we find that
<strong>the</strong> initial rate <strong>of</strong> flux decline is given by
q/Jo)
= _ R’c Jo % = _ %AJc~Jo
dt t=O %% 2~2%(1-%~ ,.\
(4)
where Jo is <strong>the</strong> initial membrane flux. The
parameters Jo and R,,, in <strong>the</strong> above equation can
be determined from <strong>the</strong> experimental measurements.
The initial decline rate found in Fig. 4 is
used. A typical value <strong>of</strong> 0.64 is used for cp=,
whereas (Pi is estimated from <strong>the</strong> iron concentration
assuming a density <strong>of</strong> 4 g/cm3 for <strong>the</strong> iron
oxide particles. Then, Eq. (4) can be solved for a
to obtain an estimate <strong>of</strong> 3 nm for <strong>the</strong> characteristic
particle radius. Such a size may be
expected to be characteristic <strong>of</strong> primary precipitated
crystallites ra<strong>the</strong>r than aggregates since
values <strong>of</strong> <strong>the</strong> same order <strong>of</strong> magnitude have been
obtained by low-angle x-ray scattering measurements
[ 141. It must be emphasized that <strong>the</strong> above
exercise is performed to provide only an order <strong>of</strong>
magnitude size estimate since several assumptions
have been made. In addition, iron oxide
crystallites resemble elongated ellipsoids ra<strong>the</strong>r
than spheres considered here. This size estimate
for <strong>the</strong> particles forming <strong>the</strong> fouling deposit does
not necessarily mean that aggregation effects are
absent. Indeed, it was observed by <strong>the</strong> naked eye
that settleable floes were formed at an iron
concentration <strong>of</strong> 10 ppm within a period <strong>of</strong> 1 h.
Ra<strong>the</strong>r, it suggests two things. First, that porosity
<strong>of</strong> <strong>the</strong> deposits does not dramatically change by
aggregation effects or that it is controlled by
pressure and cake consolidation. Second, that any
effects <strong>of</strong> reduced deposition efficiency <strong>of</strong> large
size aggregates or any particle detachment effects
are not significant.
Efforts to obtain more precise information on
aggregation kinetics by a dynamic light scattering
technique were not successful due to <strong>the</strong> small
scattering intensity <strong>of</strong> <strong>the</strong> colloidal dispersions in
<strong>the</strong> range <strong>of</strong> iron concentrations used in <strong>the</strong>
fouling experiments. In general, such measurements
are difficult with very small particles due
to <strong>the</strong> conflicting requirements <strong>of</strong> <strong>the</strong> technique
such as sufficient scattering and sufficiently slow
aggregation kinetics compared to <strong>the</strong> time
required for a particle size distribution measurement,
which is roughly 1 min.