Page 218 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

P1: GAE/LSK P2: FLV Final Pages
Encyclopedia of Physical Science and Technology EN004D-ID159 June 8, 2001 15:47

Crystallization Processes 115

bothclear-liquoradvanceandfines-removalareenhancing
crystal size.
As an idealization of classified-fines removal, assume
that two streams are withdrawn from the crystallizer, one
corresponding to the product stream and the other a fines-
removal stream. Designate the flow rate of the clear so-
lution in the product stream to be V out and set the flow
rate of the clear solution in the fines-removal stream to be
(R − 1)V out . Also, assume that the device used to separate
fines from the larger crystals functions so that only crystals
below an arbitrary size L F are in the fines-removal stream
and that all crystals below size L F have an equal probabil-
ity of being withdrawn as fines. Under these conditions,
the crystal size distribution is characterized by two mean
residence times, one for the fines and the other for crystals
FIGURE 18 Population density plot for product from crystallizer
larger than L F , that are related by the equations:
with idealized classified-fines removal.
V T
τ = (for L > L F ) (68)
V out scale systems, by simply inserting a length of pipe or
tubing of appropriate diameter into the well-mixed crys-
V T τ tallizer chamber. The separation of crystals in the settling
τ F = = (for L ≤ L F ) (69) zone is based on the dependence of settling velocity on
RV out R
crystal size. Crystals entering the settling zone and hav-
where V T is the total volume of clear solution in the crys-
ing a settling velocity greater than the upward velocity of
tallizer.
the slurry remain in the crystallizer. As the cross-sectional
For systems following invariant growth, the crystal pop-
area of a settling zone is invariant, the flow rate of slurry
ulation density in each size range will decay exponentially
through the zone determines the cut-size L F , and it also
with the inverse of the product of growth rate and residence
determines the parameter R used in Eqs. (69) through (71).
time. For a continuous distribution, the population densi-
In a crystallizer equipped with classified-product re-
ties of the classified fines and the product crystals must be
moval, crystals above some coarse size L C are removed
the same at L = L F . Accordingly, the population density
at a rate Z times the removal rate of smaller crystals. This
for a crystallizer operating with classified-fines removal
can be accomplished by using an elutriation leg, a hydro-
is given by:
cyclone, or a screen to separate larger crystals for removal
RL from the system. Using the analysis of classified-fines re-

◦
n = n exp − (for L ≤ L F ) (70)
Gτ moval as a guide, it can be shown that the crystal popula-
tion density is given by the equations:

(R − 1)L F L L
◦
◦
n = n exp − exp − (for L > L F ) n = n exp − (for L ≤ L C ) (72)
Gτ Gτ Gτ
(71)
(Z − 1)L C ZL
n = n exp exp − (for L > L C )
◦
Figure 18 shows how the population density function Gτ Gτ
changes with the addition of classified-fines removal. The (73)
lines drawn are for a hypothetical system, but they illus-
trate qualitatively what can be demonstrated analytically; whereτ isdefinedastheresidencetime V T /V out .Figure 19
that is, fines removal increases the dominant crystal size, shows the effects of classified-product removal on crys-
but it also increases the spread of the distribution. tal size distribution; the dominant crystal size is reduced
A simple method for implementation of classified-fines and the spread of the distribution becomes narrower. Note
removal is to remove slurry from a settling zone in the that it is impossible for crystals smaller than L C to leave
crystallizer. The settling zone can be created by construct- the idealized classified-product crystallizer illustrated in
ing a baffle that separates the zone from the well-mixed Fig. 17c. Accordingly, the population densities shown on
portion of the vessel—recall, for example, the draft-tube- Fig. 19 for the classified-product crystallizer represent
baffle crystallizer described in Section V—or, in small- conditions inside the perfectly mixed region of the unit.