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114 Crystallization Processes

have the same residence time distributions, and it is the Clear-liquor advance is used for two purposes: (1) to
crystal residence time distribution that gives the popula- reduce the quantity of liquor that must be processed by
tion density function the characteristic exponential form the solid–liquid separation equipment (e.g., filter or cen-
in Eq. (54). Nucleation and growth kinetics can influence trifuge) that follows the crystallizer, and (2) to separate
the population density function, but they cannot alter the the residence time distributions of crystals and liquor. The
form of the functional dependence of n on L. reduction in liquor flow through the separation equipment
Crystallizers are made more flexible by the introduc- can allow the use of smaller equipment for a fixed produc-
tion of selective removal devices that alter the residence tion rate or increased production through fixed equipment.
time distributions of materials flowing from the crys- Separating the residence time distributions of crystals and
tallizer. Three removal functions—clear-liquor advance, liquor means that crystals will have an average residence
classified-finesremoval,andclassified-productremoval— time longer than that of the liquor. This should, in princi-
and their idealized removal devices will be used here to ple, lead to the production of larger crystals, but because
illustrate how design and operating variables can be ma- the crystallizer is otherwise well mixed, the crystal pop-
nipulatedtoaltercrystalsizedistributions.Idealizedrepre- ulation density will have the same form as that for the
sentations of the three classification devices are illustrated MSMPR crystallizer (Eq. (54)).
in Fig. 17. The analysis goes as follows: Let V in , V CL , and V out
Clear-liquor advancefromwhatis called adoubledraw- represent volumetric flow rates of clear liquor fed to the
off crystallizer is simply the removal of mother liquor crystallizer, of clear-liquor advance, and of output slurry
without simultaneous removal of crystals. The primary ac- respectively. The population density function is given by
tion in classified-fines removal is preferential withdrawal the expression:
from the crystallizer of crystals of a size below some spec-

ified value; this may be coupled with the dissolution of the L
◦
n = n exp − (67)
crystals removed as fines and the return of the resulting Gτ prod
solution to the crystallizer. Classified-product removal is
carried out to remove preferentially those crystals of a where τ prod = V T /V out . Increasing V CL decreases V out and
size larger than some specified value. In the following thereby increases the residence time of the crystals in the
discussion, the effects of each of these selective removal crystallizer. Unless the increase in magma density results
functions on crystal size distributions will be described in in significant increases in nucleation, the utilization of
terms of the population density function n. Only the ideal clear-liquor advance will produce an increase in the dom-
solid–liquid classification devices will be examined. It is inant crystal size. Often the increase is much greater than
convenient in the analyses to define flow rates in terms that predicted from theory, and it is suspected that this is
of clear liquor. Necessarily, then, the population density because the stream being removed as clear liquor actu-
function is defined on a clear-liquor basis. ally contains varying amounts of fines. If this is the case,

FIGURE 17 Schematic representations of idealized removal functions. (a) Clear-liquor advance, (b) classified-fines removal, (c) classified-
product removal.