I n d . E n g . C h e m . Res. 1990,29, 1558-1562
1558
H = enthalpy, J / g P = pressure, Pa Pc = critical pressure, Pa R = gas constant T = temperature, K Tc = critical temperature, K V = volume, m3 V , = internal variables of the ADDS (n: number) cy = B W R constant ~r= Joule-Thomson coefficient (calculated), K/Pa = Joule-Thomson coefficient (experimental), K/Pa w = acentric factor y = B W R constant & = continuation line
Literature Cited Hearn, A. C. REDUCE user's manual; Rand Corp.: Santa Monica, CA, 1987. Dllay, G. W.; Heidemann, R. A. Ind. Eng. Chem. Fundam. 1986,25, 152.
Dymond, J. H.; Smith, E. B. The Virial coefficients of Pure Gases and Mixtures; Oxford University Press: New York, 1980. Iri, M. J p n . J . Appl. Math. 1984, I , 223. Miller, D. G. Ind. Eng. Chem. Fundam. 1970,9, 585. Miyazaki, T.; Hejmadi, A. V.; Powers, J. E. J . Chem. Thermodyn. 1980, 12, 105.
Perry, R. H.; Chilton, C. H. Chemical Engineers' Handbook, 6th ed.; McGraw-Hill: New York, 1984. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. T h e Properties of Gases and Liquids; McGraw-Hill: New York, 1977. Symbolics, Inc. V A X UNIX MACSYMA Reference Manual; Symbolics: 1985. Trebble, M. A.; Bishnoi, P. R. Fluid Phase Equilib. 1988, 39, 111. Walas, S. M. Phase Equilibria i n Chemical Engineering; Butterworths: London, 1985. Wengert, R. E. Commun. ACM 1964, 7, 463. Yoshida, T. Trans. Inf. Process. SOC.Jpn. 1989, 30, 799.
Yasuo Hirose,* Tsuyoshi Kitazawa Department of Industrial Chemistry Faculty of Engineering T o k y o Metropolitan University Tokyo, 158 J a p a n
Toshinobu Yoshida Department of Electrical and Electronics Engineering Faculty o f Engineering Chiba University Chiba, 260 J a p a n Received for review June 17, 1988 Revised manuscript received February 2, 1989 Accepted March 7, 1990
Growth Kinetics of (NH4)2S04 in the Ternary System (NH4)2S04-NHdN03-H20 T h e growth kinetics of ammonium sulfate crystals in the ternary system ammonium sulfate-ammonium nitrate-water were studied in a laboratory-scale fluidized bed crystallizer. T h e effects of supersaturation, temperature, crystal size, and solid voidage were investigated. T h e effect of the solute composition in the ternary system on the growth rate was also investigated. T h e order with respect to supersaturation was less than unity in the ternary system. It was observed that the growth rate of ammonium sulfate is dependent on the temperature, crystal size, solid voidage, and system composition. The determination and characterization of the kinetics in realistic environments is one of the important aspects of crystallization studies. Although a number of techniques have been proposed for growth rate measurements, fluidized bed experiments (Mullin and Gaska, 1969; Phillips and Epstein, 1974; Tavare and Chivate, 1978, 1979; Budz et al., 1984) are currently being emphasized for obtaining basic and reliable information for the design of classifying crystallizers. For crystallizer design, the independent effects of temperature, supersaturation, system voidage, and crystal size on the crystal growth rate should be known with reasonable precision. The object of the present study was to determine the crystal growth kinetics of ammonium sulfate under a variety of conditions in a fluidized bed crystallizer. The crystallization study of ammonium sulfate has received considerable attention, and some progress has been made in determining the applicable kinetic relationships (Mullin et al., 1970; Larson and Mullin, 1973; Klekar and Larson, 1973; Youngquist and Randolph, 1972;Bourne and Faubel, 1982; Tavare, 1985). However, all the results in the past were obtained in the binary system ammonium sulfatewater, and there are few publications that deal with the growth kinetics of ammonium sulfate in a fluidized bed crystallizer. In the present study the growth kinetics of ammonium sulfate in the ternary system ammonium sulfate-ammonium nitrate-water were obtained, and the effects of the variable operating conditions and solute 0888-5885/90/ 2629-1558$02.50/0
compositions in the system were discussed. Theoretical Section The overall growth may be represented by an empirical relationship of the form RG = k G ( C = kGACg (1) where kG is the overall growth rate constant and g is the "order" of the process with respect to supersaturation, Ac. In general the constant, k G , and exponent, g, are dependent on the temperature, the crystal size, the hydrodynamic situation, and the presence of impurities. The effect of temperature on the overall growth rate constant may be expressed by an Arrhenius type relation. The effect of crystal size may be expressed by a power law term as in the Bransom growth rate model. The effects of temperature and crystal size may be incorporated in eq 1 as RG = aLb exp(-E/RT)Acg
(2) and eq 2 has been used by many investigators (Tavare and Chivate, 1978, 1979; Jones and Mullin, 1973). Although the effects of the system voidage are usually neglected for simplicity in such growth models, the system voidage may influence the characteristic turbulence of the suspension and relative crystal/solution velocity in particular fluidized beds. The solid voidage may have some influence on the overall growth rate. To account for the effect of solid voidage on the overall growth rates, a simple empirical 0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1559
n
A' 9
5
n o
t
0.1
0.2
0.3
0.4
0.s
INHA J2SOA
Figure 2. Solubility diagram for (NH,)2S0,-NH4NOS-H20 system.
Figure 1. Fluidized bed crystallizer: 1, growth zone; 2, calming zone; 3, packing of glass beads; 4, dissolver; 5, pump; 6, rotameter; 7, heat exchanger; 8, thermometer; 9, condenser; 10, basketlike device for removal of crystals; 11, magnetic stirrer; 12, product remover.
power law term of the ratio of the solid voidage to the solid fraction may be incorporated in eq 2 as RG = aL*[t/(l - t)Ie exp(-E/RT)Acg
(3)
In the differential method of analysis a small quantity of closely sized and weighed crystals is suspended by an upward flowing stream of the supersaturated solution in the growth zones of the fluidized bed crystallizer. In this type of operation, solution concentration changes are relatively small, but at the same time measurable solid deposition is achieved. Direct measurement of the crystal weight change allows us to determine the overall growth rate as RG =
AW A At
(4)
at a particular temperature, crystal size, system voidage, and supersaturation level assuming negligible mass deposition as nuclei. The averge size and surface area of crystals may be evaluated from the corresponding values of the initial seed and the final product. The surface area of the seed crystals may be calculated as W0.F A, = -
(5)
P J O
where F is the overall shape factor. Under the assumptions of constant shape factors, negligible nucleation, breakage, and agglomeration,the average size and surface area of the product crystals may be determined as
A = A,( Wp/ WJ2I3
(6)
L = Lo(wp/ W,)'/3
(7)
Experimental Section The schematic diagram of the crystallizer used is shown in Figure 1. It was constructed mainly of glass with a diameter of 2.5 cm and a height of 28 cm. I t consists of two zones: one for the growth zone (l),the other for the calming zone (2) within which the entrained crystals return to the growth zone. To avoid the dispersion of the solution
velocity within a growth zone, the bottom of the crystallizer was provided with a velocity profile equallizer (3) by packing the l-mm glass beads to 5-cm height. A solution of known concentration was prepared in the dissolver (4) and was circulated by a pump (5). The circulation rates were measured by means of the rotameter (6) and controlled so that the seed crystals were uniformly fluidized. In order to dissolve the nuclei which could be created in the crystallizer and to be able to neglect the change of concentration of the circulating solution due to the crystal growth, the volume of the dissolver was 0.01 m3and the temperature of the solution in the dissolver was maintained 10 "C higher than in the crystallizer. The temperature of the solution entering the crystallizer was controlled by means of the heat exchanger (7). The temperature in the growth zone was measured by a thermometer graduated to 0.05 "C and was controlled precisely within f0.05 "C during the run. Seed crystals were carefully prepared from the reagent-grade ammonium sulfate by recrystallization in a stirred tank cooling crystallizer and sieving the product in the desired size range. It was observed that the prepared ammonium sulfate seed crystals formed orthorhombic crystals. In the experimental procedure used, a hot, filtered solution of reagent-grade ammonium sulfate and ammonium nitrate in distilled water of exactly known concentration was charged to the dissolver. The solution was circulated and maintained at 15 "C above the saturation temperature. After circulating for 1 h, the solution entering the crystallizer was then cooled to the desired operating temperature. When the desired operating temperature was attained, accurately weighed and closely sized seeds were introduced into the crystallizer. The solution velocity was adjusted in such a way that the crystals were uniformly suspended within the growth zone. The average size of the seed crystals was increased to less than 10% of the initial size so as to enable neglecting the change of the upward solution velocity in the liquid fluidized bed crystallizer and the values of shape factors of seed crystals due to the habit modification during the run. The crystals grown for a definite time were removed from the crystallizer by using a basketlike device (10) made of the fine stainless steel grid, were dried, and were carefully weighed. Solubility. The solubility of ammonium sulfate in the ternary system ammonium sulfate-ammonium nitrate-
1560 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 Table I. Values of Constants in Equation 8 av wt 70 of NH,NO, n
13
16 0.371 4 0.003 045
28
40
0.256 8 0.001 821
0.1576 0.001 856
water over the temperature range 40-70 O C was determined from the phase diagram shown in Figure 2. The isotherms in Figure 2 were plotted from the equilibrium data by Linke and Seidell(1965) and experimental data. In the region below each isotherm, only ammonium sulfate crystallizes out, and this region is called the ^TYPE I subsystem" (Fitch, 1970). In the present study, ternary systems with the average ammonium nitrate concentrations of 16,28, and 40 wt % were the scope of the investigation. The equilibrium data corresponding to each particular composition were determined by the polythermal method (Nyvlt, 1977). The flask containing about 50 mL of the solution of known concentration was placed in the Perspex water jacket supplied with water. The flask was first cooled by supplying the cold water through the jacket until ammonium sulfate nuclei appeared and then slowly heated (at 0.5 "C/h) while the sample was stirred constantly. A visual check was occasionally made so as to ascertain whether the solid phase was still present. When only a few crystals remained, the temperature was maintained constant for a sufficient time to ensure that these crystals do not dissolve. Then the temperature was increased minutely and the process was repeated until the exact temperature at which the last of the solid phase was dissolved was determined. The same procedure was followed for a number of systems with different compositions. By interpolation, a number of points corresponding to the given isotherm are obtained. The method was comparatively quick, and the measurements were reproducible to f O . l "C. Since only ammonium sulfate crystallized out from the ternary solution over the experimental range, both ammonium nitrate and water could be considered as the free solvent. The solubility of ammonium sulfate in the ternary system over the experimental temperature range was expressed as the linear relation e, = a + pe (8) where c, is the solubility (in kilograms of (NH4&304/kilograms of (NH4N03 H20))at temperature '6 (in "C) and the values of the constants, a and 0,for each case are shown in Table I. Crystal Shape Factors. A value of the overall shape factor, F , is needed for calculating the mean total crystal surface area from eqs 5 and 6, but as the crystal size in the present study ranged from about 300 to 700 pm, it was necessary to see if F was size-dependent. Accordingly, ammonium sulfate crystals were carefully separated into five size fractions between 300-and 700-pm sieves, and their volume and surface shape factors were determined separately. The volume shape factor, f,, was determined by weighing 1000 crystals from each sieve fraction and then applying eq 9, taking the arithmetic mean aperture size as the characteristic dimension, L, of each sieve fraction.
+
M = NpfJ3 (9) Within the limits of experimental error, f, remained constant a t 0.64 f 0.02. This value coincides with the value reported by Bourne and Faubel (1982). The surface shape factor, f,, for the crystals in each sieve fractions was determined with the aid of a microscope
Table 11. Values of Growth Rate Parameters in Equation 3 av wt 70 of NH,NO, parameter 16 28 40 coeff, a 6.25 x io* 3.90 x 103 1.38 x 104 exponent of size, b 0.90 0.94 0.89 activation energy, E, kJ/mol 17.11 23.24 29.84 order with respect to Ac, g 0.85 0.80 0.65 0.21 exponent of the ratio of 0.32 0.29 slurry voidage to the solid fraction, e multiple correlation coeff 0.94 0.94 0.93
c
d
Figure 3. Growth rate correlation (eq 3); average wt % of NH4N0s = 16.
fitted with a calibrated eyepiece. Assuming that the ammonium sulfate crystals were parallelepiped, the length, x , breadth, y, and thickness, z, of 100 crystals in each sieve fraction were measured. The surface shape factor of a crystal, characterized by its mean sieve aperture size, L, is given by f, = 2(xy
+ yz + zx)/L2
(10)
Over the size range studied, the surface shape factor remained reasonably constant a t f, = 4.89 f 0.02. Consequently, a constant overall shape factor F = f,/f, = 7.7 f 0.3 was used when calculating the average surface area of crystals from eqs 5 and 6.
Results and Discussion The overall growth rate was evaluated by eq 4 using arithmetic mean values of crystal surface area. Arithmetic mean values of crystal size and solid voidage were also calculated from the initial and final values. The values of the model parameters in eq 3 were estimated by least-squares multiple linear regression analysis of the experimental data. The parameters estimated are reported in Table 11. A typical presentation of the growth rate correlation represented by eq 3 is shown in Figure 3. The ranges of the variables studied are also given in Table 111. Effect of Supersaturation. Supersaturation is the most important variable in determining the overall growth rates. Growth rate measurements were made for different
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1561 Table 111. Range of Variables in the Growth Rate Experiments variable range units supersaturation, Ac (0.5-1.6)X kg (NHJ2SO,/kg (NHdN03 + H2O) crystal size, L (3.3-6.6) X lo-' m solid voidage, c 95-100 70 temp, 8 30-70 "C
temperatures, initial crystal sizes, and solid voidages. The order with respect to supersaturation is 0.85,0.80, and 0.65 for the case of solution with the average ammonium nitrate concentration of 16,28, and 40 wt 70,respectively. These values are lower than those reported by Mullin and Nyvlt (1971), 1.0, Larson and Mullin (1973), 1.5, and Tavare (1985), 0.91, all of which were investigated in the binary system ammonium sulfate-water. This difference may be due to contributions of the second solute, ammonium nitrate, as an inhibitor for the ammonium sulfate crystals growth in the ternary system. As the concentration of ammonium nitrate decreases, i.e., as the ternary system approaches closely to the binary system by decreasing the concentration of ammonium nitrate, the value of the order approaches unity, whereas as the concentration of ammonium nitrate increases, the effect of ammonium nitrate as an inhibitor increases and the value of the order decreases. Effect of Crystal Size. The effect of crystal size on the growth rate of ammonium sulfate crystals was investigated for five different sizes of seeds in the range 3W700 pm. The solution velocity was fixed so that the seeds were reasonably uniformly suspended within the growth zone of the crystallizer. The growth rate of ammonium sulfate in the ternary system is size (Le., velocity) dependent, and the exponents on the crystal size dependence of the growth rate are 0.90, 0.94, and 0.89 for each case. In a liquid fluidized bed crystallizer, as the crystal grows the terminal velocity of it increases; therefore, it is necessary to increase the solution velocity in order to maintain the corresponding fluidizing condition. As the relative crystal/solution velocity in suspension increases, the diffusion rate of ammonium sulfate a t the crystal/solution interface increases; consequently, the growth rate of ammonium sulfate is size-dependen t. Effect of Temperature. The temperature dependence is incorporated by the Arrhenius type of relationship in the rate models. The activation energy values for overall growth are 17, 23, and 30 kJ/mol for each case, which shows that the activation energy for crystal growth increases as the concentration of ammonium nitrate increases. This variation in the activation energy is also attributed to the contribution of ammonium nitrate as an inhibitor in the ternary system. Effect of Solid Voidage. To study the influence of the system voidage on the growth rate, a simple power law term is included in the model, eq 3. In the present study, when the power law term of the ratio of the solid voidage to the solid fraction is incorporated, the exponents are 0.37, 0.32, and 0.25. The hydrodynamic flow regime in a particular fluidized bed is relatively well-defined. However, over a range of voidage, the hydrodynamic flow regime might have changed during the run. Furthermore, since the consuming rate of solute for the given crystal seeds increases with increasing system voidage, the growth rate of crystals increases with system voidage. Effect of NH4N03on the Growth of (NH4)2S04in the Ternary System. Ammonium sulfate, which crystallizes from aqueous solution (i.e., ammonium sulfatewater) in an anhydrous form, belongs to the orthorhombic
Figure 4. Habit change of (NH4)804 crystals in the ternary system from (a) orthorhombic to (b) hexagonal.
system, and a common habit is shown in Figure 4a. This orthorhombic crystal of ammonium sulfate grows invariantly in the binary solution but transforms into the hexagonal crystal through the habit modification during the growth in the ternary solution used in this study. The hexagonal crystal of ammonium sulfate shown in Figure 4b is obtained by growing the orthorhombic crystal shown in Figure 4a in the static ternary solution a t the supersaturation level, Ac = 0.005 kg of (NH4),S04/kg of (NH4N03 + H20), for about 10 h. The habit modification of ammonium sulfate crystals is due to the presence of ammonium nitrate in the ternary system. Although the mechanism of the habit modification is not clear, it seems reasonable that the variation of the interfacial energy of each face in the presence of ammonium nitrate is a significant factor. In the experimental observations, the development of the habit modification from orthorhombic to hexagonal shows that the growth rate of the (110) face of the orthorhombic crystal is faster than that of the (100) and (010) faces. So, (110) faces, which grow faster than the other faces, gradually disappear from the pattern of orthorhombic.
Conclusion In the present study, the growth rate characteristics of ammonium sulfate crystals in the ternary system ammonium sulfate-ammonium nitrate-water in a fluidized bed crystallizer were investigated by a differential method. Over the range of variables investigated, the orders with respect to supersaturation were 0.85,0.80, and 0.65, and the activation energies were about 17,23, and 30 kJ/mol for the ternary solutions with average ammonium nitrate concentrations of 16,28, and 40 wt %, respectively. The growth rate correlation in eq 3 shows a positive dependence of the crystal size and the ratio of the slurry voidage to solid fraction for each case. The results show that the growth rate of ammonium sulfate crystals in the ternary system ammonium sulfate-ammonium nitrate-water is dependent on the composition of the system. As the concentration of ammonium nitrate in the system increases, the growth rate of ammonium sulfate crystals decreases.
Ind. E n g . Chem. Res. 1990, 29, 1562-1565
1562
Acknowledgment We are grateful to the Korean Science and Engineering Foundation and Sogang University for financial support. Nomenclature a = coefficient (eq 3) A = area of crystals, m2 A = mean total surface area, m2 b = exponent of size (eq 3)
c = solution concentration, kg of solute/kg of solvent c, = saturation concentration, kg of solute/kg of solvent Ac = supersaturation, kg of solute/kg of solvent e = exponent of ratio slurry voidage to solid fraction (eq 3) E = activation energy, kJ/mol f, = surface shape factor f, = volume shape factor F = overall shape factor g = order of growth kG = overall growth rate constant, [kg/m*/s]/[(kg of solute/kg of solvent)#] L = crystal size, m M = mass of crystals, kg N = number of crystals R = universal gas constant (8.314 kJ/mol/K) RG = overall growth rate, kg/m2/s At = run time, s T = absolute temperature, K W = weight of crystals, kg AW = weight difference of product and seed crystals, kg x, y, z = length, breadth, thickness of a crystal, m Greek Letters
a , @ = constants (eq 8) t
= fractional slurry voidage
0 = temperature, "C pc = density of crystal, kg/m3 Subscripts o = seed quantities p = product quantities Registry No. (NH4),SO4, 7783-20-2; NH4N03,6484-52-2.
Literature Cited Bourne, J. R.; Faubel, A. Influence of Agitation on the Nucleation of Ammonium Sulphate. In Industrial Crystallization 81, Symposium Proceedings; Jancic, S.J., de Jong, E. J., Eds.; Elsevier: Amsterdam, 1982.
Budz, J.; Karpinski, P. H.; Nuruc, Z. Influence of Hydrodynamic on Crvstal Growth and Dissolution in a Fluidized Bed. AIChE J . 1984, 30, 710-717. Fitch, B. How to Design Fractional Crystallization Processes. Ind. Ena. Chem. Process Des. Deu. 1970. 62. 6-33. KlekG, S. A.; Larson, M. A. In Situ Measurement of Supersaturation in Crystallization from Solution. 66th Annual Meeting of AIChE, Philadelphia, 1973. Jones, A. G.; Mullin, J. W. Crystallization Kinetics of Potassium Sulphate in a Draft-Tube Agitated Vessel. Trans. Inst. Chem. Eng. 1973, 51, 302-308. Larson, M. A.; Mullin, J. W. Crystallization Kinetics of Ammonium Sulphate. J . Cryst. Growth 1973, 20, 183-191. Linke, W. F.; Seidell, A. Solubilities of Inorganic and Organic Compounds;American Chemical Society: Washington, DC, 1965; Vol. 11. Mullin, J. W.; Gaska, C. The Growth and Dissolution of Potassium Sulphate Crystals in a Fluidized Bed Crystallizer. Can. J . Chem. Eng. 1969, 47, 483-489. Mullin, J. W.; Nyvlt, J. Programmed Cooling of Batch Crystallizers. Chem. Eng. Sci. 1971,26, 369-377. Mullin, J. W.; Chakraborty, M.; Mehta, K. Nucleation and Growth of Ammonium Sulphate Crystals from Aqueous Solution. J . Appl. Chem. 1970,20, 367-371. Nyvlt, J. Measurement of Phase Equilibria in Condensed Systems. Solid-Liquid Phase Equilibria; Elsevier: Amsterdam, 1977. Phillips, V. R.; Epstein, N. Growth of Nickel Sulphate in Laboratory-Scale Fluidized-Bed Crystallizer. AIChE J . 1974,20,678-687. Tavare, N. S. Growth Kinetics of Ammonium Sulfate in a Batch Cooling Crystallizer Using Initial Derivatives. AIChE J. 1985,31, 1733-1735. Tavare, N. S.;Chivate, M. R. Growth Rate Correlation for Potassium Sulphate Crystals in a Fluidized Bed Crystallizer. Chem. Eng. Sci. 1978, 33, 1290-1292. Tavare, N. S.;Chivate, M. R. Growth and Dissolution Kinetics of Potassium Sulphate Crystals in a Fluidized Bed Crystallizer. Trans. Inst. Chem. Eng. 1979,57, 35-42. Youngquist, G. R.; Randolph, A. D. Secondary Nucleation in a Class I1 System: Ammonium Sulfate-Water. AIChE J . 1972, 28, 421-429. *Author to whom all correspondence should be addressed.
Cheong-Song Choi,* ik-Soo Kim Department of Chemical Engineering Sogang Unitiersity C.P.O. Box 1142 Seoul, Korea Received for review J u n e 19, 1989 Revised manuscript receitied January 8, 1990 Accepted March 19, 1990
A Distillation Method of Aromatic Nitration Using Azeotropic Nitric Acid The possibility of using a nitric acid-water azeotrope for the nitration of chlorobenzene has been investigated. When the reaction is carried out under continuous distillation to remove the water produced as it is formed, yields of nitrochlorobenzene in excess of 80% theoretical are obtained. T h e isomer proportions in the nitro product are 39% 2-nitro-, 1% 3-nitro-, and 60% 4-nitrochlorobenzene. However, at room temperature, part of the nitro product is liquid. The phase diagram for mixtures of the 2- and 4-nitroisomers shows a eutectic mixture containing 67% 2-nitro- and 33% 4-nitrochlorobenzene, having a freezing point of ca. 16 "C. The fraction of the nitro products that is liquid a t room temperature has a composition close to this. Methods of obtaining pure 4-nitrochlorobenzene from the products have been demonstrated. Introduction The use of nitric acid alone for nitration reactions is economically attractive, not just because sulfuric acid is eliminated from the process but also because the problem of disposal of spent acid is obviated. Nevertheless, little 0888-5885/90/2629-1562$02.50/0
work has been published on the subject. In the first reported applications of nitric acid as a nitrating agent ( O t h e r et al., 1942) and in more recent work (Kanhere and Chandalia, 1981), either azeotropic or fuming nitric acid was used, with the aromatic substrate in 0 1990 American Chemical Society
