Page 73 - Subyek Encyclopedia - Encyclopedia of Separation Science

68 I / CRYSTALLIZATION/ Derivatization

The enthalpy balance with the production rate or into the condensor. For the design of the heat ex-
solids production, P, is given by: changer see Sinnott (1998).
dH Cooling Crystallizers
" H,feed ! H,prod ! H,vapour #Q heat #P H cr
dt
In cooling crystallization the warm feed stream is
[19] cooled to the process temperature. In principle the
same set of mass and heat balance equations can be
The total enthalpy and the enthalpy of the streams are used, except that no vapour Sow exists. Furthermore,
deRned as: the process temperature cannot freely be chosen, be-
cause it is determined for a given production rate,
H"V( liquid C p,liquid #(1! ) crystal C p,crystal )T
crystal free fraction, , residence time, and liquid
mass fraction, w liquid,1 . This latter liquid mass fraction
H,feed " v,feed ( feed feed,liquid C p,liquid
of the main component will depend on the process
temperature, so a temperature-dependent equation
#(1! feed ) crystal C p,crystal )T feed
for w liquid,1 must be added. The degrees of freedom for
H,prod " v,prod ( liquid C p,liquid #(1! ) crystal C p,crystal )T the crystallizer design are therefore more limited.

H,vapour " v,vapour ( vapour C p,vapour T# vapour H evap )
The Population Balance
[20]
The Crystal Length-based Population Balance
The crystal free volume fraction should be as low as Equation
possible to reduce the crystallizer volume. In crystallization as a separation process, the separ-
The liquid mass fraction w liquid,1 of the main com- ability of the particles from the mother liquor by, for
ponent must be determined or can be approximated example, Rltration are of utmost importance, as well
by the saturation concentration, especially for soluble as their washability and drying. The efRciency of
compounds with a low value. these processes is directly related to the crystal size
With the production rate, P, as a design parameter,
the volumetric product Sow rate can be deduced for distribution (CSD) of the solid, and as soon as the
CSD of the solid phase becomes an interesting prod-
the chosen value from:
uct speciRcation, the population balance equation
[21] (PBE) must be introduced. The PBE describes how the
P" v,prod (1! ) crystal " v,prod M T
size distribution develops in time as a result of various
From the product Sow rate so obtained and the mean kinetic processes. The concept of the PBE was intro-
residence time that is needed to grow sufRciently duced to crystallization by Randolph. A general form
large crystals, the necessary suspension volume for of the PBE is as follows:
the crystallizer can be calculated from:

(n(L)V) "!V
(G L (L)n(L)) #B(L)V!D(L)V
v,prod " V [22]
t
L

m n
" L mean [23] # v,in,j n in,j (L)! v,out,k h out,k (L)n(L)
j"1
k"1
4G mean
[24]
Here, for the desired L mean , a reasonable value must
be chosen, that is related to its solubility and the mean where the amount and the size of the crystals (or
growth rate, G mean , can be estimated from a correla- particles) are expressed in terms of number density
3
tion (Mersmann, 1988; Kind and Mersmann 1990) or n(L)( /(m m)) and crystal (or particle) length L (m)
determined by laboratory experiments. respectively (Figure 2A).
From the crystallizer suspension volume, V, the All the variables in this equation are in principle
needed vapour head, the process streams and the heat also time-dependent. For the sake of simplicity, the
duty that has to be accommodated, the crystallizer t dependence is omitted here.
dimensions can now be determined. Constraints for In other representations of the PBE, the amount of
the design are a height/diameter ratio of about 3 : 2, particles may also be expressed in terms of volume
3
1
3
and a cross-sectional area for evaporation that is density v(L)(m /(m m )) or mass density m(L)
3
1
large enough to avoid entrainment of liquid droplets (kg/(m m ), where the size is represented by the