Page 72 - Subyek Encyclopedia - Encyclopedia of Separation Science

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I / CRYSTALLIZATION 67

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Here c can be expressed by kg solute per kg or m of content of the crystallizer. The volume, V, of the
the solvent or solution, but an expression in kg solute crystallizer is often assumed to be constant in
3
per m solution ("liquid) phase is generally used in eqns [12}19], However, by making V and the feed
mass balances ("mass fraction, w). streams time-dependent, dynamic effects can be
For evaporative crystallization, eqn [1] can be taken into account, and thus also batch processes.
transformed into: The mass balance is given by:

c
a
"RT ln a eq "RT ln eq cH [8] dM total " v,feed ( feed feed,liquid #(1! feed ) crystal )
dt
! v,prod ( liquid #(1! ) crys )! v,vapour vapour
Given the relatively low supersaturations, , that
often lie between 0.001 and 0.01 with more easily [12]
soluble substances, eqn [8] simpliRes into: The component balances are given by:

c dM i feed feed,liquid w feed,liquid,i
"RT "RT [9] " v,feed #(1! feed ) crystal w feed,crystal,i
cH dt
! v,prod ( liquid w liquid,i #(1! ) crystal w crystal,i )
For two or more A and B ions in solution that react to
form crystal c, the expression for becomes:
(i"1, N comp ) [13]
v i
i
a i
"RT ln [10] with:
K sp
M i "V( liquid w liquid,i #(1! ) crystal w crystal,i ) [14]
and for stoichiometric solutions equals:
"RTv ln S+RT [11] where component i"1 is the main compound to be
crystallized, and components i"2, 3, 2 N comp are
the impurities present.
In practice the supersaturation is often indicated by The distribution coefRcients relate the impurity
eqn [5]. uptake by the solid and the concentration of the
For Sash cooling or evaporation two terms contri-
bute to the driving force ( T and c). impurity in the liquid phase:
For precipitation, no simpliRcations are allowed,
owing to the high supersaturation values ( 1), and k distr,i " w crystal,i (i"2, 2 N comp ) [15]
either eqn [8] or eqn [10] is used. For antisolvent w liquid,i
precipitation the value of c depends on the actual
concentration of the solute in the original solvent Instead of substituting all component balances into
and, like cH, on the degree of dilution by the anti- the total mass balance given by eqn [12] to solve the
solvent. mass balance of the total system, it is more conve-
nient to combine the solvent mass balance together
with the component balances:
Mass and Heat Balances

Traditional design of an industrial crystallizer is dV liquid w liquid,solvent " v,feed ( feed feed,liquid w feed,solvent )
based on only mass and enthalpy balances. The pro- dt
duction rate determines to a large extent the dimen-
! v,prod ( liquid w liquid,solvent )
sions of the crystallizer as well as the energy con-
sumption. It also determines the mode of operation, ! v,vapour vapour [16]
which means batchwise or continuous, single or
multistage operation. In the next section the balance Finally, the sum of the mass fractions in both the
equations are given for an evaporative and for a cool- liquid and the solid phase must equal one:
ing crystallizer.
w liquid,solvent # w liquid,i "1 [17]
Evaporative Crystallizers i
Consider an ideally mixed vessel. The composition w crystal,i "1 [18]
of the product stream is kept similar to that of the i