Ind. Eng. Chem. Res. 1991,30, 1588-1593
1688
Nomenclature d = impeller diameter, mm D = vessel diameter, mm Em = Murphree stage efficiency of the extract phase Em = Murphree stage efficiency of the raffinate phase F = feed flow rate, g/min h = heavy phase dispersed phase holdup, g H = continuous phase holdup, g i = component K = distribution coefficient, y / x 1 = light phase n = impeller speed, s-l Np = power number Qh = flow rate of heavy phase, mL/min Q1= flow rate of light phase, mL/min rpm = revolutions/min R = raffinate, g (raffinate flow rate, g/min) RI = refractive index S = solvent flow rate, g/min T = residence time, min x = raffinate phase concentration, mass fraction x* = raffinate phase concentration in equilibrium with a certain extract phase concentration, mass fraction xo = feed concentration, mass fraction y = extract phase concentration, mass fraction y* = extract phase concentration in equilibrium with a certain raffinate phase concentration, mass fraction yo = solvent concentration, mass fraction a = solvent-to-feedratio 8 = extract-to-feed ratio y = activity coefficient 8 = coefficient defined by eq 2 p = viscosity, CP p = density, g/mL 4 = dispersed phase holdup, mass fraction Literature Cited Cheng, L. T. Commercial Liquid-Liquid Extraction Equipment. In Handbook Of Separation Techniques For Chemical Engineers; Schweitzer, P. A., Ed.; McGraw-Hill: New York, 1979;Section 1.10,pp 1-293. Eckert, R. E.; Laughlin, C. M.; Roushton, J. H. Liquid-Liquid Interfacial Areas Formed By Turbine Impliers in Baffled Cylindrical Mixing Tanks. AZChE J. 1985,31,1811-1820. Hooper, W. B.; Jacobs, L. J. Decantation. In Handbook Of Sepa-
ration Techniques For Chemical Engineers: Schweitzer, P. A., Ed.; McGraw-Hill: New York, 1979; Section 1.11, pp 1-345. Horvath, M.; Hartland, S. Mass-Transfer Efficiency and Entrainment. Znd. Eng. Chem. Proc. Des. Deo. 1985,24, 1220-1225. Karr, A. E. Reciprocating Plate Column As a Cocurrent Mixer. AZChE J. 1984,30,697-699. Laddha, G. S.; Degaleesan, T. E. Extraction Equipment Classification and Selection. In Transport Phenomena in Liquid Extraction; McGraw-Hill: New York, 1976;Chapter 8; p 215. Logsdail, D. H.; Lowes, L. Industrial Contacting Equipment. In Recent Advances in Liquid-Liquid Extraction; Hanson, C., Ed.; Pergamon: Oxford, 1971;Chapter 5; p 142. Nishikawa, M.; Mori, F.; Fujieda, S.; Kayama, T. Scale-up Of Liquid-Liquid Phase Mixing Vessel. J. Chem. Eng. Jpn. 1987,20, 454-459. O t h e r , D. F.; White, R. E.; Treuger, E. Liquid-Liquid Extraction Data. Ind. Eng. Chem. 1948,33,10-33. Prausnitz, J. M.; Anderson, T. F.; Grens, E. A.; Eckert, C. A.; Hsieh, R.; O'Connell, J. P. Calculation Of Equilibrium Separations in Multicomponent Systems. In Computer Calculations For Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria; Prentice-Hall: New Jersey, 1980;pp 116-129. Raman, R. Mass Transfer Operations. In Chemical Process Computation; Elsevier Applied Science Publishers: London, 1985;pp 165-167. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. Fluid Phase Equilibria in Multi Component Systems. In The Properties Of Gases and Liquids, 4th ed.; McGraw-Hill, New York, 1987;pp 365-368. Robbins, L. A. Liquid-Liquid Extraction. In Handbook Of Separation Techniques For Chemical Engineers; Schweitzer, P. A,, Ed.; McGraw-Hill: New York, 1979;Section 1.9,pp 1-268. Rocha, J. A,; Humphrey, J. L.; Fair, J. R. Mass Transfer Efficiency of Sieve-Tray Extractors. Ind. Eng. Chem. Process Des. Deu. 1986,25,862-871. Salem, A. S.; Sheirah, M. A. Dynamic Behavior Of Mixer-Settlers. Can. J. Chem. Eng. 1990,68,867-875. Shaw, K. G.; Long, R. S.Solvent Extraction of Uranium. Chem. Eng. 1957,64,251-256. Smith, B.D.Binary Distillation. In Design Of Equilibrium Stage Processes; McGraw-Hill; New York, 1963;pp 152-154. Treybal, R. E. Equipment For Stage-Wise Contact. In Liquid Extraction, 2nd ed.; McGraw-Hill New York, 1963;pp 285-289. Treybal, R. E. Versatile New Liquid Extractor. Chem. Eng. Prog. 1964,60,77-82. Woodman, R. M. The System Water-Acetic acid-Toluene: Triangular Diagram at 25 "C, with Densities and Viscosities of the Layers. J. Phys. Chem. 1926,30, 1283-1286. Received for review May 8, 1990 Revised manuscript received October 23, 1990 Accepted March 5,1991
Controlled Cooling Crystallization of (NH4)#04 in the Ternary System (NH4)2SO4-NH4NOs-H20 Cheong-Song Choi* and Ik-SooKim Department of Chemical Engineering, Sogang University,
C.P.O.Box 1142, Seoul, Korea
The maximum allowable undercoolings of ammonium sulfate in the ternary system ammonium sulfateammonium nitratewater were measured. The nucleation parameters, which may be obtained from maximum allowable undercooling measurements, are shown to be dependent on the saturation temperature of the solution in the ternary system. These data were employed along with a supersaturation balance to calculate the optimum cooling curves in a batch cooling crystallizer. The results show that controlled cooling that takes into account the effect of the cooling rate on the maximum allowable undercooling improves the product crystal size distribution. Introduction Bakh-owrabd cooling crysuizers are widely used in the industry, because they me and flexible,
* Author to whom correspondence should be addressed.
require less investment, and generally involve less process development. Such systems are useful in small-scale operations, especially when working with chemical systems that are difficult to handle due perhaps to their toxic or highly viscous properties. However, batch crystallizers generally yield a poor quality nonuniform product. This
0888-5885/91/2630-1588$02.50/0Q 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991 1689 is mainly due to the use of a high cooling rate in the initial stages of the process, resulting in the formation of large numbers of crystal nuclei that cannot grow to the desired size. This demerit can be overcome by the application of an appropriate temperature control. One of the earliest studies of batch cooling crystallization was made by Griffiths (19251, who proposed that if the supersaturation could be maintained a t a level within the metastable limit throughout the cooling operation, an improved product crystal size would be obtained since nucleation would be negligible. This mode of operation was termed “controlled cooling”. The effect of controlled cooling on the crystal size distribution (CSD) in batch crystallizers was examined by Mullin and Nyvlt (1971), Jones and Mullin (1974), and Myeraon et al. (1986). They demonstrated that controlled cooling would keep the supersaturation level within the metastable limits, thus decreasing the rate of nuclei formation and improving the CSD. Cooling curves were calculated in a number of different situations by employing the supersaturation balance. The computed controlled cooling curves were qualitatively the reverse of natural cooling, i.e., a slow initial cooling rate and a high final cooling rate. In general the maximum allowable undercooling, Le., the boundary of the metastable region in which new crystals are not formed but the crystals already present grow, increases with increasing the rate of cooling. Therefore, in the controlled cooling operation, the maximum allowable undercooling is narrow when operating with a low cooling rate in the initial stages, whereas it is increasingly wide as the cooling rate increases with continuing the operation. Moreover, as the cumulative crystal surface area increases with time, due to crystal growth, the cooling rate may be increased since more solute will be assimilated by growth. That is, to maintain the supersaturation level within the maximum allowable supersaturation, the working supersaturation level must be low in the initial stages of the operation and can be increased as time passes. The cooling curves reported in the past did not consider this effect of the cooling rate on the maximum allowable undercooling. In this work, the controlled cooling crystallization of ammonium sulfate in the ternary system ammonium sulfata-ammonium nitrate-water considering the effect of the cooling rate was studied on the basis of the experimental nucleation and growth kinetics. For this, the solubility of ammonium sulfate in the ternary system ammonium sulfate-ammonium nitratewater was determined, and the maximum allowable undercooling was measured with the varations of the cooling rate and saturation temperature of the solution.
Theoretical Section The supersaturation balance (Mullin and Nyvlt (1971), Jones and Mullin (19741, Jones (1974)) for a batch crystallizer may be written as -dAc/dt = (dc*/dt) + kp(t)Ac@(t)+ k,Acm(t) (1) The first term on the right-hand side represents the eupersaturation created by cooling, the second term the desupersaturation due to crystal growth, and the third term the desupersaturation due to nucleation. If the eupereaturation level, Ac, is always well within the metastable limit beyond which massive nucleation occur, growth then occurs only on the added seed crystals; thus the third term on the righbhand side can be neglected, and eq 1 become8 -dAc/dt = (dc*/dt) + k#) Ac@(t) (2)
Figure 1. Experimental crystallizer: (1)draft-tube baffled cryetallizer; (2)hollow draft tube; (3) vertical wall baffles; (4) cooling water jacket; (5) three-blade screw; (6) bath reservoir; (7) temperature controller; (8)temperature programmer; (9) remote seneor; (10) recorder; (11)pump; (12)agitation speed controller.
For a cooling process the saturation rate, s, due to cooling may be written as s = - dc* dt
-d8 -dc*
dc* (3) dt d8 - bdB where b is the transient cooling rate and dc*/d8 is the temperature dependence of solubility. Eliminating dc*/dt between eqs 2 and 3 gives dc* -dAc/dt = b+ k&(t) Acg(t) (4) d8 The solution of this equation depends on the cooling mode employed, the evaluation of the area term A(t), the crystallization kinetics, and solubility. If the transient supersaturation is known, it may be solved for the corresponding cooling curve, e.g., for controlled cooling. The crystal surface area present at any time, A(t) is given by A(t) = fBW,,L,2(t)
(5)
The overall linear growth rate, G,is related to the mass growth rate coefficient, k,, by the expression G=
k,(8&,4 f@ 3fA
(6)
Eliminating @Ace between eqs 4 and 6 gives
Solving for the cooling rate, b, gives
This equation indicates the dependence of the temperature, 8, on the cryetallization time, t. In other words, it represents the cooling curve based on the growth rate in a seeded solution and negligible nucleation.
Experimental Section Batch crystallization experiments were performed in a draft-tube baffled cooling crystallizer. The experimental apparatus is shown in Figure 1. The cryetallizer was a cylindrical glass vessel with a volume of about 2 L. It was equipped with a hollow draft tube and jacket through both of which the cooling water can be circulated. The agitation was provided by a propeller stirrer located on the center
1590 Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991
55 50 45 4 0
es
( O c )
55 50
45
55
40
es 1
I
1
1
5 x
Figure 2. Cooling rate b vs AO-
1
I
I
1
I
IO
1
1
,
1
5
1
1
1
IO
5
1
LOCI
'kax
40
es( O C )
( O c )
1
50 45
LOCI
perax
0
[OCI
for seeded solutions of ammonium sulfate in the ternary system (average wt % of NH4NOB:(a) 16,(b)28,
(c) 40).
line of the draft tube. The temperature was controlled by using a Neslab RTE 210 circulator and an MTP-5 controller programmer. The programmer was used to control the rate of cooling. Controlled cooling curves were approximated as a series of linear steps, up to 99 being allowed in the programmer. Seed crystals were prepared from the reagent-grade ammonium sulfate by recrystallization in a stirred tank cooling crystallizer and sieving the product in the desired size range. In the experimental procedure used, a hot, filtered solution of reagent-grade ammonium sulfate and ammonium nitrate in distilled water of known concentration was charged to the crystallizer. Before each run the solution was maintained at 10 "C above the saturation temperature for 1 h. The temperature was adjusted to the desired initial value, a weighed quantity of seed cryatah was added, and the solution cooled according to the predetermined cooling curve. During each run the crystals were maintained essentially within the annular growth zone (between the draft-tube and the crystallizer wall) by control the agitation rate in order to achieve similar condition in the liquid fluidized bed crystallizer. At the end of each run a crystal size analysis was performed by hand sieving. Solubility In the present study, ternary systems with average concentrations of ammonium nitrate in solution about 16, 28,and 40 w t %, respectively, were the scope of the investigation. The solubility of ammonium sulfate in the ternary system ammonium sulfate-ammonium nitratewater over the temperature rage 35-70 "C was expressed as the linear relation c+ = CY + ge (9) where c* is the solubility (in kg of (NHd2S04/kg of (NH4N03+ H20)) at temperature B (in OC) and the values of the constants CY and B are shown in Table I. Additional
Table I. Values of Constants in Ea 9 av wt % of NH4N03 16 28 40 a 0.3714 0.2568 0.1576 0.001821 0.001856 B 0.003045
details may be found in Choi and Kim (1990). Maximum Allowable Undercooling Measurement of the maximum allowable undercooling of seeded solutions provides a rapid method for determining secondary nucleation kinetics described by
R, = k,Acmm
(10)
The relationship between the maximum allowable undercooling, AB-, and the cooling rate, b (=dB/dt), is (Mullin (1972)) log b = (m- 1) log (dc*/dB) + log k , + m log AB,, (11) This equation indicates that the dependence of log b on log AB, is linear, and the slope of the line is the order of the nucleation process, m. The maximum allowable undercoolings in the presence of crystalline material were determined experimentally by the visual method (Nyvlt (1968);Nyvlt et al. (1970)) a t a number of different cooling rates and saturation temperatures. The variation of the maximum allowable undercooling, AB-, with the cooling rate, b, is shown in Figure 2. The maximum allowable undercooling is independent of the saturation temperature of the solution in the binary system ammonium sulfatewater (Nyvlt et al. (1970), Mullin et al. (1970)) but does depend on the saturation temperature in the ternary system ammonium sulfateammonium nitratewater studied in preaent work as shown in Figure 2. The maximum allowable undercooling increases with decreasing saturation temperature. This may
Ind. Eng. Chem. Res., Vol. 30,No. 7, 1991 1191 Table 11. Valuer of the Nucleation Parameterr in the Pmrence of C ~ r t a l r av wt W of NH,NOn e., O C k. m 4.61 X 10' 2.16 16 40 4.03 X 10' 2.08 45 1.98 3.21 X 10' 50 1.86 x lol 1.82 55 4.46 2.07 X 1@ 28 40 3.27 2.51 X lo' 45 3.00 1.18x 104 50 2.40 1.81 x 109 55 4.90 5.80 X 10' 40 40 3.70 7.44 x 106 45 3.14 8.14 X lo' 50 2.50 9.81 x 109 55
/
Table 111. Values of Conrtants in Ea 1S av wt W of NH4N03 16 28 40 ho 6.25 X 10' 109 104 3.692 X lo-' h, 6.055 X 10-1 3.652 X lo-' 3.924 X lo-' Hz 2.417 X lo-' 3.861 X lo-'
be considered due to the contribution of ammonium nitrate as an inhibitor for nucleation. The values of the nucleation rate order, m,and the nucleation rate constant, k,, were evaluated by Figure 2 and eq 11 and are shown in Table 11. If the nucleation rate, R,, is assumed to be independent of the saturation temperature, i.e. k,(dt)[Ac,(Bt)]m
= constant
(12)
Thus, after rearranging, the maximum allowable supersaturation is
If the cooling rate is constant, Ac, can be calculated from eq 13 and the values in Table 11. The computed results showed that Ac, depends linearly on the temperature. Therefore, Ac- could be expressed as the linear relation AC" = H~ ~ ~ ( e -, ,e,) (14) where H1and H2 are constants dependent on the rate of cooling. Mullin and Nyvlt (1971) expressed Ac, as in eq 14, but this equation expressed Ac- as a function of only temperature not considering the variation of Ac, with the cooling rate. The maximum allowable undercooling (i.e., maximum allowable Supersaturation) varies with the cooling rate. Since the rates of cooling vary with time incoperating the batch cooling crystallizer, the variation of Ac- with cooling rate must be considered. Using the values of AB, shown in Figure 2, the constants Hl and H2are calculated as a function of the cooling rate, and the results are shown in Figure 3. HIvaries largely with the variation of the cooling rate, whereas H2 remains reasonably constant. Therefore, H2 could be considered as a constant and H1 was expressed as a function of cooling rate as in eq 15. The values of the Ac, = hobhi + H2(B0- eJ (15)
+
constants in eq 15 are shown in Table 111, where b is the cooling rate in OC/h. To obtain an improved uniform product in a batch cooling crystallizer, the cooling rate must be slow at initial stage to avoid nucleation and can be increased with time. Equation 15 expresses the maximum allowable supersaturation in which the variation of the cooling rate in such a cooling crystallizer considered.
4 10 C001lnQ
YO
ra1e.b
3 (OC/hr)
u 1
rO-o-o-
I O
c o o 1 ~ n gr a 1 m . b
lDC/hr)
Figure 3. Plots of Hland Hzva b (average wt 46 of NH4NOa: 0 = 16,0 = 28,0 = 40).
Table IV. Values of Growth Rate Parameters for Eq 17 av wt W of NH4NOB 16 28 40 3.90 X 109 1.38 X 104 a 6.25 X 10' 0.94 0.89 d 0.90 0.29 0.21 e 0.32 29.84 17.11 23.24 E , kJ/mol 0.80 0.65 0.85 g
Growth Kinetics Experiments to determine the kinetics of ammonium sulfate crystal growth were performed by employing a liquid fluidized bed crystallizer. Full details of the crystallizer and the experimental procedure are reported elsewhere (Choi and Kim (1990)). The overall growth rate may be represented by an empirical relationship of the form (16) R, = k,(c - ,*)a = k,A@ where k, is the overall growth rate constant and g is the order of the process with respect to supersaturtion, Ac. In general the constant, k,, and exponent, g, are dependent on temperature, crystal size, hydrodynamic situation, and the presence of impurities. The effect of temperature on overall growth rate constant may be expressed by an Arrhenius type relation. Size-dependent overall growth rate may be observed because of the size dependence of the relative crystal/solution velocity in suspension. The effect of crystal size may be expressed by a power law term as in the Bransom growth rate model. The solid voidage may have some influence on the overall growth rate. To account for the effect of solid voidage on overall growth rates, simple empirical power law term of the ratio of the solid voidage to the solid fraction may be incorporated. The effects of temperature, crystal size, and solid voidage may be incorporated in eq 16 as R, = aLd(e/(l - exp(-E/RT)A@ (17) The parameter values in eq 17 were estimated from the experimental data, and the results are presented in Table IV. Cooling Curve The theoretical cooling curves were computed from the eq 8 and the empirical expressions for the kinetics of crystal growth by using the values in Table IV. The working supersaturation level, Ac, was chosen as 50% of the maximum supersaturation, Ac-. The typical reaulta of these calculations are shown in Figure 4. The solid line
1592 Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991
l a ) Ac,,,=
hob
hl
+ Hz(8 -8,J
MEDIAN S I Z E
0
IO0
200 Time.t
9 5 0 um
300
ri
(mln)
Figure 4. Cooling curves for batch cooling crystallization: L = 0.55 mm, W, = 5.4 kg/kg of solvent; (-) Ac- = hobh' + Hz80- 04; (---) Ac, = HI+ Hz(B0 - 0J.
(i) represents the cooling curve using Ac- expressed in eq 15,and the dotted line (ii) the cooling curve using Ac, at a constant cooling rate 5 OC/h (eq 14). Since the values of Ac used in calculating curve (ii) are larger than those of Ac in curve (i) which are small in the initial stages because of the slow cooling rate, curve (ii) shows higher cooling rate than curve (i) in the initial stages. As time passea the cooling rate increases, and this causes to increase the maximum allowable undercooling (Le., Ac). This results in higher cooling rates in curve (i) with time. Therefore, curve (i), which considers the effect of the cooling rate, shows a very slow rate of cooling in the initial stages thus decreasing the rate of nucleation, whereas a higher rate of cooling in the final stages can reduce the operating time.
Product Size Distribution Batch crystallization experiments were conducted for ammonium sulfate crystals in the ternary solution of ammonium sulfate-ammonium nitratewater system. Seed crystals, of mean size 0.55 mm, were added to the crystallizer and were to grow to the desired size (1 mm). A typical experimental distribution is shown in Figure 5. The frequency histograms are plotted as a percentage by weight of the fraction retained between two sieves. Figure 5a is the distribution by the cooling curve (i) in Figure 4,and Figure 5b by the curve (ii) in Figure 4. The product mean size of (a) is higher than in (b). Although the nucleation is not negligible, fine crystals are lese in (a). These demonstrate that controlled cooling by using Ac which considers the effect of cooling rate, keeps the supersaturtion level well within the desired working supersaturation and thus improves the product size distribution. Similar experiments were conducted for different seed weights, and the results are shown in Table V. As shown in Table V, the coefficient of variation (CV) values are about 20% showing uniform product distribution in both cams, but the CV values in case (a) are lower than in case (b) as a whole. Also the mean crystal sizes in case (a) are larger than in case (b). Therefore it was demonstrated that the cooling curves in the ternary system should be calculated from the supersaturation level considering the effect of the variation of the cooling rate. Conclurione The maximum allowable undercooling of ammonium sulfate in the ternary system ammonium sulfate-ammonium nitratewater was dependent on the saturation tem-
( b ) AcmaX=HI + H 2 ( e o - e t J
MEDIAN S I Z E
910
um
500
200
1000
crystal size,L
1500
[pml
Figure 5. Experimental product size distribution: L, = 0.55 mm, W, = 5.4 kg/kg of solvent.
Table V. Experimental Product CSDm: Bo = 55 O C , L, = 0.55 mm a b initial product product median median av w t % of seed wt, NH,NO, kg/kg size, mm CV, 9% size, mm CV, W 16 28 40
a
Ac,
1.0 5.4 10.0 1.0 5.4 10.0 1.0 5.4 10.0
= hobh'
0.93 0.97 0.90 0.93 0.95 0.96 0.89 0.91 0.90
+ Ha(Oo- et).
18.3 16.8 19.6 17.8 18.2 20.5 19.2 19.4 20.4
,cA
0.88 0.91 0.89 0.94 0.92 0.94 0.87 0.90 0.84
Hi + H&
20.3 18.8 18.4 20.4 19.5 19.8 21.3 21.7 22.6
- OS.
perature of the solution. From this the nucleation parameters were obtained, and the maximum allowable supersaturation could be expressed as a function of the cooling rate and temperature.
Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991 1593 On the basis of this supersaturation level and the experimental kinetic results, the optimum cooling curves in a batch cooling crystallizer were calculated along with a supersaturation balance. The results showed that controlled cooling which considered the effect of the cooling rate on the maximum allowable undercooling brought about an improvement in the quality of crystals from a batch crystallizer. Acknowledgment We are grateful to the Korean Science and Engineering Foundation and Sogang University for financial support. Nomenclature a = coefficient (eq 17) A = surface area of crystals, m2/kg of solvent b = cooling rate, OC/s c = solution concentration, kg of solute/kg of solvent c* = saturation concentration, kg of solute/kg of solvent At = supersaturation, kg of solute/kg of solvent d = exponent of size (eq 17) e = exponent of ratio slurry voidage to solid fraction (eq 17) E = activation energy, kJ/mol f, = surface shape factor f, = volume shape factor g = crystal growth rate order G = overall linear crystal growth rate, m/s ho, hl = constanta defined by eq 15 HI, H2 = constanta defined by eq 14 k, = growth rate constant, [kg/m2 s][(Ac)-g] k, = nucleation rate constant, [kg/~][(Ac)-~] L = size of crystal, m m = nucleation rate order N = number of crystals, number/kg of solvent R = universal gas constant, 8.314 J/mol K R, = overall growth rate, kg/m2 s per kg of solvent R, = nucleation rate, kg/s per kg of solvent s = supersaturation rate, kg/s per kg of solvent t = time, s T = absolute temperature, K W = weight of crystals, kg per kg of solvent
(solvent = NH4N03+ H2O) Greek Letters a,0 = constants
(eq 9)
e = fractional slurry voidage 8 = temperature, OC Os = saturation temperature, O C AO- = maximum allowable undercooling, O C pc = density of crystal, kg/m3
Subscripts 0 = initial s = seeds t = at any time t Registry No. (NH4)2SOI,7783-20-2; NH,N03, 6484-52-2.
Literature Cited Choi, C. S.; Kim, I. S. Growth kinetics of (NH,)aO, in the Ternary System (NH4)2S04-NH4NOs-H20. Znd. Eng. Chem. Res. 1990, 29,1558-1562.
Griffiths, H. J. SOC.Chem. Znd. 1925,44, T.7. Cited in Jones and Mullin (1974). Jones, A. G. Optimal Operation of a batch Cooling Crystallizer. Chem. Eng. Sci. 1974,29,1075-1087. Jones, A. G.; Mullin, J. W. Programmed Cooling Crystallization of Potassium Sulfata Solutione. Chem. Eng. Sci. 1974,29,106118. Mullin, J. W. Heterogeneous Nucleation. In Crystallization; Butterworths: London, 1972; 178-180. Mullin, J. W.; Nyvlt, J. Programmed Cooling of Batch Cryatallizers. Chem. Eng. Sci. 1971,26,369-377. Mullin, J. W.; Chakraborty, M.; Mehta, K. Nucleation and Growth of Ammonium Sulphate Crystale from Aqueous Solution. J. Appl. Chem. 1970,20,367-371. Myerson, A. S.; Decker, S. E.; Weiping, F. Solvent Selection and Batch Crystallization. Znd. Eng. Chem. Process Des. Dev. 1986, 25,925-929.
Nyvlt, J. Kinetica of Nucleation in Solutions. J. Cryst. Growth 1986, 3,377-383.
Nyvlt, J.; Rychly, R.; Gottfried, J.; Wurzelova, J. Metestable ZoneWidth of Some Aqueous Solutions. J. Cryst. Growth 1970, 6, 151-162.
Received for review April 5, 1990 Revised manuscript receiued December 10, 1990 Accepted January 2,1991
