Chemical Engineering July 2020 - 40

100
B
temperatures, lower slurry density
can be tolerated without detrimental
decrease of PSD due to excessive
nucleation. Clearly, control of
slurry density is essential for any
crystallization process. In principle,
there are two main methods to demother
liquor
crease slurry density:
* Crystal removal (for example,
A
crystal slurry
g% = (A / B) ✕ 100
FIGURE 4. To determine
the natural slurry density
in glass percentage (g%),
crystal slurry is poured
into a measuring cylinder
and allowed to settle
freely. Once settled, the
crystal slurry and mother
liquor heights are used
to determine the glass
percentage
SD = 100 ✕
via a washing leg)
* Mother liquor recycle (for instance,
mother liquor recycled
from a cyclone or centrifuge)
Conversely, there are also two main
methods to increase slurry density:
* Crystal recycle (for instance, a
more concentrated crystal slurry recycled
from a thickener or separator)
* Mother liquor removal via an
annular zone
Slurry density revisited
By definition, the actual slurry density
(SD, wt.%), including mother
liquor removal (or
recycle) or
crystal recycle (or removal) at the
crystallization process is given in
Equation (12):
(crystal + cR) / (crystal + cR + ML - MLR) (12)
In this equation, both crystal recycle (cR) and mother
liquor removal (MLR) are defined as positive mass flowrates,
similar to crystal and ML in Table 1. Conversely,
crystal removal is defined as negative crystal-recycle
mass flowrate, whereas mother-liquor recycle is defined
as negative MLR mass flowrate.
The SD equation above can mathematically be converted
by substitution using the set of seven equations
given before, and rearrangement, giving Equation (13):
100 ✕ (C ✕
CF - S) ✕
CF - S) ✕
(1 + cR#)
SD = _______________________________________________
(C ✕
(1 + cR#) + 100 ✕
(1 - MLR#)
Where:
cR# = crystal recycle fraction (cR/crystal)
MLR# = mother-liquor removal fraction (MLR/ML)
This last equation shows that the actual slurry density
is independent of mass flowrates and can simply be calculated
from easily accessible parameters, such as C,
S, CF, cR# and MLR#. Using the values given in Table
1, we see that cR# = 0.2 (logged as 20%), and MLR# =
0.3 (logged as 30%).
Crystal recycle is typically more effective compared
to mother liquor removal, since the crystal/ML ratio is
most frequently less than 1. The slurry density can be
increased, maintaining the same production level, because
this production level is determined by the evaporation
of water. The slurry density merely reflects the
hold-up of crystals in the evaporator, so a slurry den40
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sity increase prolongs the mean residence time of the
crystals. Finally, a crystal recycle fraction larger than 1
(where crystal recycle is greater than 100%) is not an
exceptional condition.
Other crystallization processes
The methodology described in this article is presented for
a continuous evaporative crystallization process, but it is
equally applicable for a batch evaporative crystallization
process by using mass instead of mass flowrate. Furthermore,
the method can be applied for cooling, antisolvent
and reaction crystallization processes. Because
no solvent is removed (W = 0) in these three crystallization
methods, CF is no longer a free variable and now equals
(100 - S)/(100 - C), provided that the following statements
are true:
* In anti-solvent crystallization, the concentration in the
feed, C, must be based on the total mass (or flowrates),
so the added anti-solvent mass (or flowrates)
should be included
* In
reaction crystallization, the concentration in the
feed, C, is the calculated concentration of the crystallizing
component, based on the total mass (or flowrates)
of all reactants, after complete conversion due
to reaction
Now, the formulas for NSD and SD can be shortened into
Equations (14) and (15), respectively:
NSD = 100 ✕ (C - S) / (100 - S)
100 ✕ (C - S) ✕
(1 + cR#)
SD = _______________________________________________
(C - S) ✕
(1 + cR#) + (100 - C) ✕
(1 - MLR#)
From this simple mass-balance approach, assessment
of just one mass flow can unlock the mass balance for the
entire crystallization process. Furthermore, this approach
clarifies that natural slurry density is fixed by concentration
factor, solubility in the mother liquor and solute concentration
in the feed - not by mass flowrate. Similarly, slurry
density is fixed by concentration factor, solubility in the
mother liquor and solute concentration of the feed, plus
crystal recycle and ML removal, and not by mass flowrate.
Beyond evaporative crystallization, the methodology presented
here is also applicable for cooling, anti-solvent and
reaction crystallization processes.
■
Edited by Mary Page Bailey
References
1. Lewis, A.E., Seckler, M.M., Kramer, H.J.M., van Rosmalen, G.M., " Industrial Crystallization:
Fundamentals and Applications, " Chapter 2, Cambridge University Press, 2015.
2. Sphere Packing, Wolfram MathWorld, https://mathworld.wolfram.com/spherepacking.html
Author
Johannes (Jan) Albertus Maria Meijer (jam.meijer@ziggo.nl;
Schalkhaar, the Netherlands) is a senior expert crystallization and
chemical technologist. Now retired, he worked for 32 years at
AkzoNobel Industrial Chemicals B.V., and led the salt and crystallization
R&D group for the final 26 years of his career. He holds an
M.Sc. with distinction in chemical technology and a Ph.D. in technical
sciences, both from the Delft University of Technology. Meijer
has designed 12 major crystallization processes and holds
eight patents. He has authored or co-authored 27 publications
related to salt technology and crystallization.
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