Page 219 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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116 Crystallization Processes

surfaces or blinding of screens. In addition, classified-
product removal can lead to cycling of the crystal size dis-
tribution. Often such behavior can be minimized or even
eliminated by increasing the fines-removal rate.
Moments of the population density function given by
Eqs. (74) through (76) can be evaluated in piecewise
fashion:

L F L C ∞
i i i
m i = L ndL + L ndL + L ndL (77)
0 L F L C
Equation (77) is used to estimate the moments of the
population density function within the crystallizer, not
of the product distribution. (Recall that moments of the
distribution within the crystallizer are often required for
kinetic equations.) Assuming perfect classification, mo-
FIGURE 19 Population density plot for crystals in crystallizer with
ments of the product distribution can be obtained from the
idealized classified-product removal.
expression:
∞ i

If both fines and product are removed on a classified ba- m i,prod = L ndL (78)
sis, the population density will be given by the equations: L C
Moments can be used to characterize the material pro-

RL
◦ duced from or contained in a crystallizer with classified-
n = n exp − (for L ≤ L F ) (74)
Gτ fines or classified-product removal or to evaluate the effect

of these selective removal functions on product character-
(R − 1)L F L
◦
n = n exp − exp − istics. All that is required is theuse of the equationsderived
Gτ Gτ
earlier to relate special properties, such as coefficient of
(for L F < L < L C ) (75) variation to the operational parameters R and Z.

(R − 1)L F (Z − 1)L C
◦
n = n exp − exp
Gτ Gτ C. Batch Crystallization

ZL As with continuous crystallizers, the mode by which su-
× exp − (for L ≥ L C ) (76)
Gτ persaturation is generated affects the crystal yield and size
Selection of a crystallizer that has both classified-fines distribution; however, it is the rate at which such super-
and classified-product removal is done to combine the saturation is generated that is most important in determin-
best features of each: increased dominant size and nar- ing product characteristics. Furthermore, there are infinite
rower distribution. Figure 20 illustrates the effects of
both removal functions on population density. Note that
this plot of population density results from sampling the
magma within a crystallizer, not from sampling the prod-
uct stream, which for the ideal classification devices con-
sidered here can only have crystals larger than L C .As
discussed earlier for the classified-product crystallizer,
the population densities shown in Fig. 20 represent those
found in the crystallizer.
The model of the crystallizer and selective removal de-
vices that led to Eqs. (74) through (76) is referred to as
the R-Z crystallizer. It is an obvious idealization of actual
crystallizers because of the perfect cuts assumed at L F and
L C . However, it is a useful approximation to many systems
and it allows qualitative analyses of complex operations.
Although many commercial crystallizers operate with
some form of selective crystal removal, such devices can FIGURE 20 Population density plot for crystals in crystallizer with
bedifficulttooperatebecauseoffoulingofheat-exchanger idealized classifiedfines and classified-product removal.