Chemical Engineering July 2020 - 41

Water
Evaporator(s)
Increase of CF
Increase of natural slurry density
FIGURE 3. Water evaporation is the driving force behind the relationship
between natural slurry density and concentration factor (CF)
However, in practice, slurry density is typically determined
as g%, using a glass (or plastic) measuring cylinder,
as illustrated in Figure 4. To determine slurry density
in g%, a crystal slurry is poured into a cylinder and subsequently
allowed to settle freely, which lasts ordinarily
only a few seconds. Then, g% is calculated as the height
of the settled crystal slurry divided by the height of the
mother liquor (both measured from the bottom of the
cylinder) times 100. Equations (10) and (11) below give
the conversion between g% and wt.% units.
100 ✕ wt.%/ρwb
g% =
_____________________________________
(100 - wt.%)/ρb + wt.%/ρs
100 ✕ g%/ρb
wt.% =
_________________________________________
100 / ρwb + g%/ρb - g%/ρs
In Equations (10) and (11), ρs is the crystal density
and ρb is the density of the mother liquor. The wet bulk
density (ρwb) reflects the mass of only the crystals at
100 g% slurry density, depending on the specific shape
of the crystals, among other parameters. For simple,
equally sized, cubic crystals at the closest packing density,
ρwb is equal to π/6 ≈ 0.5236 ✕
ρs [2].
However, in practice, determination of ρwb is essential,
because crystallization almost always results in a
specific particle-size distribution (PSD) of the crystals
and the closest packing is not reached. The ρwb at 100
g% actually reflects the loose bulk density - as if no
mother liquor is surrounding the submerged crystals.
Changing slurry density
Usually, operational considerations (like clogging) demand
that slurry density does not exceed about 30-40
g%, except for elutriation or washing legs, or exits of
hydro-cyclones just upstream of centrifuges.
An excessively low slurry density may lead to fine crystals
that hamper centrifuging. This shows that slurry density
has a profound influence on crystallization, because
slurry density determines the crystal surface available for
growth (assuming constant PSD). If insufficient crystal
surface area is available for growth, supersaturation increases
(as evaporation is imposed on the crystallizers)
until nucleation occurs.
The effect of slurry density on crystallization is temperature-dependent,
because kinetics are much faster
at higher temperatures. Consequently, at higher
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