- Email: [email protected]
Melt Crystallization with Direct Contact Cooling Techniques
0263±8762/97/$07.00+ 0.00 Institution of Chemical Engineers
MELT CRYSTALLIZATION WITH DIRECT CONTACT COOLING TECHNIQUES KWANG-JOO KIM and A. MERSMANN* Chemical Engineering Division, Korea Research Institute of Chemical Technology, Korea *Department B of Chemical Engineering, Technical University of Munich, Germany
M
elt crystallization using direct contact cooling techniques has been examined for the separation of an n-decanol±n-dodecanol mixture. Additionally, the heat transfer of melt crystallization by direct contact of coolants has been investigated. Three coolants, i.e. air (as a gas), water (as a liquid) and butane (as a lique® ed gas) were employed. Volumetric heat transfer coe cients obtained by direct contact cooling in the melt crystallizer are in the range between 0.1 and 100 kW/(m3K) and increased roughly with the 1.5 to 1.8 power of the linear super® cial velocity of coolant. The volumetric production rate was found to be in the range between 0.01 and 0.2 kg/(m3s) for the coolant air, 0.05 to 1.4 kg/(m3s) for the coolant water and butane. The linear growth rate of crystals was proportional to the second power of subcooling. The quality of the crystals produced by this direct contact cooling technique was good, and the crystals are signi® cantly larger than those obtained using scraped-surface crystallizers. A comparison between the e ective distribution coe cient obtained before and after wiping has shown that the core of crystals is very pure and the impurity is concentrated in the outer layer of crystals. The described melt crystallization also shows the advantage of continuous operating, high thermal economy and no encrustation in spite of high mean temperature di erence. Keywords: melt crystallization; direct contact cooling; growth rate; purity; separation; n-dodecanol
INTRODUCTION
Furthermore, industrial cooling crystallizers using indirect cooling are prone to severe encrustation of the cooled surface which severely reduces the heat transfer e ciency and mass throughput. Another method of heat transfer is by direct contact applying an intimate contact between the melt and an inert coolant. Crystallization using the direct cooling technique has been mainly applied to the desalination of sea water7, 8, 9,10, 11 . This technique was also applied by French12 to the crystallization of benzene by impinging jets of benzene and cold brine inside a centrifuge which was subsequently used for the separation of the product. Another type of directly cooled crystallizer was used in the cocurrent ¯ ow of an immiscible organic coolant and an aqueous crystallizing solution was passed through the central tube of the unit, while the annular space served for ¯ ow and recirculation of the crystallizing solution13 . It is interesting to note that most of the earlier works on crystallization with direct contact cooling10, 11, 12, 13 were concerned with the development of equipment and processes. Kinetic studies, performance tests and heat transfer data of this technique were, however, not examined su ciently. In particular, this technique was not applied to melt crystallization for the separation of organics. The aim of this study, therefore, is to investigate the separation of an organic eutectic mixture by melt crystallization, its performance and direct contact heat transfer for three kinds of coolants such as gas, liquid and lique® ed
Melt crystallization is one of the separation techniques applied in the separation of organics (such as close boiling hydrocarbons), isomers, heat sensible materials and so on. The use of melt crystallization for separation of organic mixtures has increased rapidly in the chemical industry over the past few years. In melt crystallization the impurities are recovered in molten form and can be cycled, incinerated, or treated in some other fashion without an intermediate solvent removal step. From this point of view, melt crystallization is a clean technology for the separation of organics without using a solvent. There are two di erent types of melt crystallization method; one of these applies a cold surface on which a crystal layer is produced from the stable melt 1 and the other employs a simple stirred vessel in which a crystal suspension is produced by cooling the entire melt2 . For recovery of the crystals formed, the former uses a temperature gradient technique or a mechanical device, and the latter uses subsidiary equipment such as ® lters and centrifuges. In melt crystallization as well as industrial crystallization by cooling, the liquid phase is cooled in an indirect heat exchanger with metallic surfaces through which heat is extracted from the solution3, 4, 5,6 . The main problems of these methods are low product purity, low heat transfer e ciency and high energy consumption, associated with scale up problems. 176
MELT CRYSTALLIZATION WITH DIRECT CONTACT COOLING TECHNIQUES
177
Figure 1. Schematic diagram of the experimental apparatusfor gas as coolant. A. Reservoir; B. Data aquisition system; C. Thermostatic baths and circulators;D. Particle analysis sensor; E. Dilution tank; F. Temperature recorder; G. Crystallizer; H. Flowmeter; I. Refrigerator; J. Temperature programming controller; K. Heat exchanger.
gas. The system investigated in this study was the simple eutectic mixture of n-dodecanol±n-decanol. EXPERIMENTAL Apparatus The schematic diagram of the apparatus used in this study is shown in Figure 1. The components consisted of the crystallizer, storage vessels for the direct coolants and for mixtures, all thermostatically controlled, and systems for heat measurement and crystal size analysis. Details of the di erent types of crystallizers are shown in Figure 2. Experiments were performed for three kinds of direct contact coolants in batchwise and continuously operated crystallizers. The crystallizer using air as a coolant (see Figure 2a) was a 500ml glass bubble column with a 60 mm inner diameter, and was equipped with a distributor for gas bubbling, which had 250 holes with a hole diameter of 0.5 mm. In order to prevent fouling in the distributor, warm water with a temperature a little over the saturation temperature of the melt was circulated through the jacket outside distributor. The crystallizer for lique® ed gas and liquid as coolants (see Figure 2b) was a 500 ml vessel with a 100 mm diameter and was equipped with an agitator, a close clearance 6blade turbine type with 36 mm diameter at a speed in the range of about 400 to 700rpm. When the crystallizer was operated with water or butane as direct contact coolants, these liquids entered the vessel through an 1mm tube located 10 mm above the melt surface. When the crystallizer was operated with air as a direct contact coolant, the gas passed through the cooling chamber and then entered the distributor located at the bottom of the crystallizer. A double jacket was used to dissolve the solid organic by circulating the warm water through the clearance. No encrustation occurred. For continuous operation, the equipment was modi® ed to allow for the storage and introduction of feed solution, and for the removal of a mixed slurry. Slurry was withdrawn continuously through 10 mm tube. Measurements of the outlet temperature of the Trans IChemE, Vol 5, Part A, February 1997
crystallizer for calculation of the logarithm median temperature from the experiments were carried out by the ampli® ed trace of temperature signals from the thermocouple, which were monitored on the XY recorder. A crystal analysis system (PAMAS PMT 2100) and an image analysis system with a microscope were used so that the crystal size distribution could be measured continuously during continuous operation, as well as batchwise operation. Method and Analysis Three direct contact coolants, air as a gas, and water and a lique® ed gas butane as liquid have been investigated in this study. The melt crystallizer was operated
Figure 2. Experimental apparatus for batch and continuous experiments (a) gas coolant (b) liquid and lique® ed gas coolant.
178
KIM and MERSMANN
batchwise or continuously. The typical procedure of the experiments is as follows. For batchwise operation, a homogeneous mixture of n-dodecanol and n-decanol was prepared and a total of about 400 ml charged into the feed. The fed solution was heated to 5 K above its saturation temperature. The crystallizer vessel was ® lled with the melt and then the chosen coolant was added to the melt. Crystal slurry was withdrawn from the crystallizer to the crystal analysis system to measure crystal size and crystal size distribution (CSD). At the same time, samples were taken to analyse the purity and yield. The slurry was separated into crystals and residual melt by vacuum ® ltration. For continuous operation, the equipment was modi® ed to allow for the storage and introduction of feed solution and for the removal of mixed slurry. After the operation of approximately ten residence times of the crystallizer, the run was terminated and the crystals and residual melt were separated. Suspended crystals and residual melt were sampled from the crystallizer every 2 minutes, and their amounts, their compositions and the size distributions of the sampled crystals were observed by mass balance, gas chromatography and the particle analysis system, respectively. The crystals from the crystallizer were examined by the crystal analysis system described earlier. The analysis of CSD was carried out by crystal analysis systems using a light scattering sensor and image analysis system with microscope. The former was achieved by rapidly treating a sample of the product slurry and feeding the crystals into the particle analysis sensor with the dilution liquor circulated, which had been in equilibrium with solid n-dodecanol at the equilibrium temperature. By this means, n-dodecanol crystals were brought into equilibrium with the mixture liquor. The fact that the ® ltered crystals were composed of easily separable, discrete crystals suggests that little or no freezing of the dilutent had taken place on the crystals. The latter was achieved by treating the crystals after ® ltration. RESULTS AND DISCUSSION Heat Transfer Coe cient Figure 3 shows heat transfer data taken at various super® cial velocities for three kinds of coolants in batchwise operation. The super® cial velocity is equal to the volumetric ¯ ow rate of coolant based on the cross sectional area of the column. The volumetric heat transfer coe cient Uv was calculated by LMTD (logarithm mean temperature di erence), crystallizer volume V and the average of heat ¯ ow transferred by the coolant and that given up by the melt. Uv =
(Qc + Qt )/ 2V
(1) LMTD Here LMTD is (D T i - D T o )/ ln(D T i / D T o ), D T i and D T o are the mean di erences of the temperatures of coolant and melt at the inlet side and outlet side of the crystallizer, respectively. Both the heat ¯ ow transferred from the melt to the coolant, Qc, as well as the heat ¯ ow removed from the melt, Qt , have been measured. Since Qc = Qt , the mean value is used in equation (1) in order to reduce the measuring error. Plots of the volumetric
Figure 3. Volumetricheat transfer coe cient as a function of super® cial velocity of coolants.
heat transfer coe cient versus super® cial linear velocity on log-log paper were found to give a straight line. The slope of the least square lines for the points on this plot is from 1.5 to 1.8. This agrees with previous results that the volumetric heat transfer coe cient is roughly proportional to the 1.6 power of the linear velocity valid for liquid-liquid contact in a pipe14. The exponent found for the gas coolant may be ascribed to the high degree of turbulence accompanied by more intimate mixing compared with water as a liquid coolant. Volumetric heat transfer coe cients obtained in this study are in the range of 0.1 and 100kW/(m3 K), which depend on the super® cial velocity and the type of coolant. The values of volumetric heat transfer coe cient for water as a liquid coolant and butane as a lique® ed gas coolant appear to be almost the same. Therefore, the mechanism of heat transfer between a lique® ed gas such as butane and the melt of organics seems to be similar to that between a liquid coolant such as water and a melt, where no phase change takes place. EŒect of Subcooling on Growth Rate Figure 4 shows the relationship between the growth rate G and the subcooling D T for continuous and batchwise test for a feed of 95 weight percent of ndodecanol. The subcooling means the di erence between the saturation and bulk temperature of the melt. In batchwise operation mode, the crystal growth rate was calculated from the slope in plots of measured mean crystal size against time15, 16. In continuous operation it was measured from crystal size distributions for the continuous crystallizer by using the population balance theory16. The kinetics of melt crystallization using direct contact cooling will be reported later elsewhere17 . In both continuous and batchwise tests the crystal growth rate for the mixture of n-dodecanol and n-decanol was proportional to the second power of subcooling D T . As a rule for a eutectic system, the dependence of supersaturation on growth rate is of the ® rst power in the case of a pure compound and ® rst to second for impure mixtures18,19. Therefore, the data obtained seem to be reasonable. The crystal growth rate for continuous crystallization is larger than that obtained in batchwise experiments with air as coolant. The limitation of heat transfer as the controlling step in melt crystallization can Trans IChemE, Vol 75, Part A, February 1997
MELT CRYSTALLIZATION WITH DIRECT CONTACT COOLING TECHNIQUES
179
Figure 4. Correlation between the growth rate G and degree of subcooling D T for continuous and batchwise test.
Figure 5. E ect of supersaturationon median crystal size for batchwise test.
be reduced by the use of a liquid or a lique® ed gas which results in a higher heat transfer.
increasing supersaturation and holdup of the coolants. The average crystal size is in the range of 0.1 to 1.4 mm for continuous tests and depends on supersaturation and holdup of the coolant. Our experiments have shown that the crystals are, as a rule, considerably larger than those obtained in a conventional industrial crystallizer. In industrial crystallization, an average crystal size of 0.05 to 0.2 mm is only obtained for organic systems in suspension crystallization22,23. The residence time in conventional melt crystallization processes is about one hour. Contrary to this, the crystals produced by direct contact cooling are larger despite a reduction of residence time only 10 minutes in the direct contact cooling process. The mean crystal size obtained for continuous operation is larger than that for batch tests. Our newresults suggest that the temperature drop is very large and fast which leads to higher growth rates and larger crystal sizes. However, further work is necessaryto prove these results.
EŒect of Supersaturation on Crystals The subcooling strongly a ects supersaturation and the crystal growth rate (see Figure 4.). Increasing subcooling creates increasing supersaturation and eventually the production of crystals. The mean size and size distribution of crystals are important parameters in the separation of crystals from the mother liquor because they determine both the surface area to be washed and the rate of ® ltration. They are complex functions of nucleation and growth, which are functions of process variables such as agitation rate, feed composition, and production rate. These functions are therefore related to the degree of supersaturation. The e ect of supersaturation on crystal size was studied for the same feed concentration in both batchwise and continuous tests. Figure 5 shows the e ect of supersaturation on the crystal size for two di erent coolants, such as air as the gas and water as the liquid for batchwise tests. Supersaturation is de® ned as D w = w - w* which is the di erence between the bulk concentration, w, and the saturation concentration, w* . The particle size increases with increasing supersaturation. This also suggests that dependence of supersaturation on particle size is almost the same irrespective of the type of coolant. The median particle size is in the range between 0.2 and 0.7 mm for batchwise tests. In a column crystallizer with scraped walls, average crystal sizes of 0.1 to 0.3 mm were obtained for the condition of a partial re¯ ux ratio20, 21 . It can be expected that with respect to the improved quality of crystals produced by direct contact cooling, the product will be easier to ® lter and wash than that produced via the scraped surface chiller route. Figure 6 shows the e ect of supersaturation on the median crystal size for continuous tests, in which water was used as the coolant. The residence time was in the range between 200 to 800 seconds and the holdup of the coolant was 0.20 to 0.86. The particle size increases with Trans IChemE, Vol 5, Part A, February 1997
Production Rate The production rate depends mainly on the supersaturation that results from the degree of subcooling of
Figure 6. E ect of supersaturation on median crystal size for continuoustest.
180
KIM and MERSMANN
the melt. The volumetric crystallization rate Pv was calculated from a heat balance, and correlated with the volumetric heat transfer coe cient Uv and temperature di erence LMTD according to U LMTD mfCpm (T mi - T ms ) (2) Pv = v D hs D hsV The second term of the right side in equation (2) is neglected because latent heats are much larger than sensible heats in melt crystallization. Figure 7 shows the correlation between the volumetric production rate and the volumetric heat transfer according to equation (2). In a plot of the volumetric production rate versus the LMTD based on the heat of crystallization, the slope is equal to the heat transfer coe cient Uv . For three kinds of coolants, two regions can be clearly de® ned. For gas, the volumetric production rate increases from 0.01 to 0.2 kg/(m3s) as Uv increases from 0.1 to 1 kW/(m3K). For water and butane, the volumetric production rate is in the range between 0.05 and 1.4kg/(m3 s) as Uv increases from 4 to 40 kW/(m3K). In conventional melt crystallizers15 the volumetric production rate is about 0.1kg/(m3 s). Therefore, the major advantage of crystallizers with direct contact cooling is a larger production rate for a given volume in comparison to the conventional melt crystallizers. In spite of the high LMTD investigated in this study, the crystallizer surface is always free of encrustation. This means that a long operation time is possible at high heat transfer with the absence of encrustation. EŒect of Crystal Size on Purity Figure 8 presents a comparison of the purities of crude crystals and wiped crystals. The purity is plotted against the mean crystal size for the feed concentration of 95 wt.% n-dodecanol. Wiping means that the crystals have been spread on soft paper in order to transfer the adhering melt into the dry paper material. Therefore, only the impurity of the adhering outer melt can be removed to a certain degree. The purity of n-dodecanol crystal decreased from 98 to 97.2wt% with an increase of the mean crystal size from 0.1 to 1.4 mm. It is supposed that the impurity is dependent, via supersaturation, on
Figure 7. Volumetric production rate versus LMTD/ D hs for melt crystallization with direct contact coolants, air, water and n-butane.
Figure 8. Comparison of purities between crude crystals and wiped crystals against crystal size.
the rates of nucleation and growth, and on hydrodynamic conditions. Since the heat transfer by the direct coolant system is high, the growth rate is high, too. This means that the impurity is easily included in crystals at the high subcooling. According to the latest results of various investigators24, 25 , the growth rate for small crystals is smaller than that of large crystals. They suggested that large crystals result from a high growth rate of the crystals. In addition, the di usion boundary layer for tiny crystals is smaller than that for large crystals on account of di erent ¯ ow conditions. According to Wintermantel4 , the purity of crystals is the function of the crystal growth rate G and mass transfer coe cient k d and decreases with increasing growth rate G but increases with increasing mass transfer coe cient k d . Therefore, it can be expected that small crystals are purer due to smaller crystal growth rates and higher mass transfer coe cient: (q l - cl) k d q l (3) Purity = f cI G q s In Figure 8, the purities are almost 99.7 weight percent for crystals of a mean size smaller than 0.5 mm. However, for crystals above 0.5 mm, the purity decreases to only 98.8 weight percent for crystals with 0.8 mm in mean size. In particular, the purity of crystals obtained by gas cooling was 99.6 weight percent after wiping compared with 98.6 weight percent before wiping. It can be expected that crystals smaller than 0.8 mm are homogeneous inside.
(
)
Comparison of Distribution Coe cients To characterize the e ciency of a crystallization process, the e ective distribution coe cient k eff is de® ned as the ratio of the impurity concentration in the crystal phase to the impurity concentration in the melt phase: x (4) k eff = c xr A coe cient k eff close to 1 means that there is almost no separation, and k eff ® 0 means perfect separation. Figure 9 shows that dependence of e ective distribution Trans IChemE, Vol 75, Part A, February 1997
MELT CRYSTALLIZATION WITH DIRECT CONTACT COOLING TECHNIQUES
181
increasing particle size, growth rate and yield of crystal. The outer layer of crystals is less pure than the inner core of crystals. Therefore, washing in a hydrocyclone, sweating and/or partial melting can be applied for upgrading in order to obtain a high purity product. NOMENCLATURE
Figure 9. Distribution coe cient versus crystal growth rate for ndodecanol±n-decanol system.
cl Cp G k eff kd LMTD mf Pv Qt Qc Uv V w w* xc xr D hs DT Dw
coe cient on the crystal growth rate for various feed compositions of crude and wiped crystals. A comparison between distribution coe cients of layer crystallization26 and crystallization with direct contact cooling is also depicted. As can be seen, the distribution coe cient in layer crystallization is 0.56 for a crystal growth rate of 0.5 ´ 10- 6 m s- 1 . Compared with direct contact crystallization under the same conditions, the distribution coe cient is only 0.41 for crude crystals and 0.10 for wiped crystals. This means that the quality of crystals from crystallization by direct contact cooling is better than that of layer crystallization. The distribution coe cient increases with increasing cooling rate. In a batch system the cooling rate is proportional to the rate of crystal growth. Therefore, the distribution coe cient depends on the rate of crystal growth. This means that the rate of inclusion of residual melt in crystals increases with increasing cooling rates. These phenomena also suggest that higher cooling rates induce high crystal growth rate. In addition, e ective distribution coe cient increases with increasing subcooling, because high subcooling induces the high crystal growth rate in batch operation. Also, for a high impurity concentration a distinct enhancement of the distribution coe cient is observable. CONCLUSION Application of melt crystallization by direct contact cooling techniques for the separation of organics is possible if the coolant is inert with respect to the melt. Since a variety of inert coolants such as (pressurized) gas, lique® ed gases and inorganic solutions is available, a suitable contact medium can be found in most cases. The process should be taken into consideration for melt crystallization. The advantages are no cooled surfaces, high yields, high purity, large size of crystals, short residence time, batchwise and continuous operation, maximum heat e ciency. With regard to conventional melt crystallization, the process by direct contact cooling is suitable for continuous operation without encrustation, and scale-up of the crystallizer is no problem. The amount of impurities in the crystal increases with Trans IChemE, Vol 5, Part A, February 1997
q
concentration of melt, kgm- 3 heat capacity, J kg- 1 K- 1 growth rate of crystals, m s- 1 e ective distribution coe cient de® ned in equation (4) mass transfer coe cient, m s- 1 logarithm mean temperature di erence, K ¯ ow rate of feed melt, kgs- 1 volumetric production rate, kgm- 3 s- 1 ¯ ow of heat exchanged with the crystallizer kW ¯ ow of heat produced by crystals kW Volumetric heat transfer coe cient, kWm- 3 K- 1 crystallizer volume, m3 concentration, kgkg- 1 saturation concetration, kgkg- 1 concentration of impuity in the crystal, wt% concentration of impuirty in residual melt, wt% latent heat of crystal, J kg- 1 temperature di erence, K supersaturation, kgkg- 1 density kgm- 3
Subscripts i inlet o outlet s solid phase c coolant phase m melt phase
REFERENCES 1. Wynn, N. P., 1992, Separation organics by melt crystallization, Chem Eng Prog, 52±60. 2. Yamazaki, Y., Watanuma, Y. and Toyokura, K., 1986, Formation of benzene crystals in benzene-cyclohexane in the batch agitation systems, Kagaku Kogaku Ronbunshu, 12 (5): 610±613. 3. Player, M. R., 1969, Mathematical analysis of column crystallization, Ind Eng Chem Proc Des Dev, 8 (2): 210±217. 4. Wintermantel,K. and Wellingho , G., 1994, Melt crystallizationÐ theoretical premises and technical limitation, Inter Chem Eng, 34 (1): 17±27. 5. Jancic, S. J., 1986, The Sulzer MWB Fractional Crystallization Systems, Technical Review (Sulzer, Winterthur, Switzerland). 6. Sakuma, K., Taketou, T., Nakagaki, H., Ikeda, J. and Yamamoto, A., 1993, Development of column crystallization,Kagaku Kogaku, 57 (6): 413±419. 7. Barduhn, A. J., 1975, The status of freeze-desalination, Chem Eng Prog, 71 (11): 80±87. 8. Wiegandt, H. F., Madani, A. and Hariott, P., 1987, Ice crystallization development for the butane direct contact process, Desalination, 67: 107±115. 9. Nagashima Y. and Maeda, S., 1979, The characteristicsof a direct contact type crystalizer agitation by the buoyancy force of a secondary refrigerant in a desalination plant, Ind Cryst, 78, E. J. dejong and S. J. Jancic, 425±435. 10. Lathan, R., 1973, A direct contact cooled crystallization, Ind Eng Chem Proc Des Dev, 12 (3): 300±305. 11. Casper, C., 1981, Investigation of evaporative freeze crystallization, Ger Chem Eng, 4: 219±225. 12. French, K. H. W., 1963, The production of pure benzene, Ind Chem, 39: 9±12. 13. Cerny, J., 1963, Continuous crystallization of calcium nitrate tetrahydrate, British Patent 932, 215. 14. Levich, V. G., 1962, Physicochemical Hydrodynamics, ( PrenticeHall, Englewood CliŒs, N. J.).
182
KIM and MERSMANN
15. Mersmann, A. 1994, Crystallization Technology Handbook, (Marcel Dekker, Inc., N.Y.). 16. Garside, J., Mersmann, A. and Nyvlt, J., 1990, Measurement of crystal growth rates, EFCE, Working Party on Crystallization, (Druckhaus Deutsch, Munich). 17. Kim, K. J. and Mersmann, A., 1996, Kinetic study on melt crystallization by direct contact cooling, (to be submitted). 18. Toyokura, K., Murata, H. and Akiya, T., 1976, Crystallization of naphthalene-benzoicacid mxitrues,AlChE Symp Ser, 72 (153): 87±95. 19. Singh, D. P. and Singh, N. B., 1980, Solidi® cation behaviour of eutectics naphthalene-p-chloroaniline and benzoic acid-connamic acid system, Bulle tin De La Socie teÂChemique De France, 3: 113±116. 20. Tavare, N. S., Matsuoka, M., Garside, J., 1990, Modeling a Continuous Column Crystallizer, J of Crystal Growth, 99: 1151± 1155. 21. Albertines, R., 1967, Experimental and theoretical investigation of separation in a column crystallizer, PhD Diss, (University of Michigan, Ann Arbor, USA). 22. Power, J. M. and Bennet, R. B., 1955, p-xylene from petrolum, Ind Eng Chem, 47: 1096±1110.
23. Toyokura, K., Hirawa, I., Imada, S. and Irie, Y., 1992, Purity of benzene crystals obtained from a benzene-cyclohexane melt by a batch coolingcrystallization,Develop in Cryst Eng, (Waseda Univ., Tokyo). 24. Wang, S. and Mersmann, A., 1992, The initial size dependent growth rate dispersion of attrition fragments and secondarynuclei, Chem Eng Sci, 47 (6): 1365±1371. 25. Zacher, U. and Mersmann, A., 1995, The in¯ uence of internal crystal perfection on growth rate dispersion in a continuous suspension crystallizer, J Crystal Growth 147: 172±180. 26. Ozoguz, M. Y., 1992, Melt crystallization and melt crystallization process, PhD Diss (University of Bremen, Germany) VDIFortschritt-Berichte, Series 3, no. 271, VDI-Verlag, Dusseldorf.
ADDRESS Correspondenceconcerningthis paper should be addressed to Dr A. Mersmann, LehrstuhlB fuÈr Verfahrenstechnik,TechnicalUniversityof Munich, Arcisstrasse 21, 8000 Munich 2, Germany.
Trans IChemE, Vol 75, Part A, February 1997
0263±8762/97/$07.00+ 0.00 Institution of Chemical Engineers
MELT CRYSTALLIZATION WITH DIRECT CONTACT COOLING TECHNIQUES KWANG-JOO KIM and A. MERSMANN* Chemical Engineering Division, Korea Research Institute of Chemical Technology, Korea *Department B of Chemical Engineering, Technical University of Munich, Germany
M
elt crystallization using direct contact cooling techniques has been examined for the separation of an n-decanol±n-dodecanol mixture. Additionally, the heat transfer of melt crystallization by direct contact of coolants has been investigated. Three coolants, i.e. air (as a gas), water (as a liquid) and butane (as a lique® ed gas) were employed. Volumetric heat transfer coe cients obtained by direct contact cooling in the melt crystallizer are in the range between 0.1 and 100 kW/(m3K) and increased roughly with the 1.5 to 1.8 power of the linear super® cial velocity of coolant. The volumetric production rate was found to be in the range between 0.01 and 0.2 kg/(m3s) for the coolant air, 0.05 to 1.4 kg/(m3s) for the coolant water and butane. The linear growth rate of crystals was proportional to the second power of subcooling. The quality of the crystals produced by this direct contact cooling technique was good, and the crystals are signi® cantly larger than those obtained using scraped-surface crystallizers. A comparison between the e ective distribution coe cient obtained before and after wiping has shown that the core of crystals is very pure and the impurity is concentrated in the outer layer of crystals. The described melt crystallization also shows the advantage of continuous operating, high thermal economy and no encrustation in spite of high mean temperature di erence. Keywords: melt crystallization; direct contact cooling; growth rate; purity; separation; n-dodecanol
INTRODUCTION
Furthermore, industrial cooling crystallizers using indirect cooling are prone to severe encrustation of the cooled surface which severely reduces the heat transfer e ciency and mass throughput. Another method of heat transfer is by direct contact applying an intimate contact between the melt and an inert coolant. Crystallization using the direct cooling technique has been mainly applied to the desalination of sea water7, 8, 9,10, 11 . This technique was also applied by French12 to the crystallization of benzene by impinging jets of benzene and cold brine inside a centrifuge which was subsequently used for the separation of the product. Another type of directly cooled crystallizer was used in the cocurrent ¯ ow of an immiscible organic coolant and an aqueous crystallizing solution was passed through the central tube of the unit, while the annular space served for ¯ ow and recirculation of the crystallizing solution13 . It is interesting to note that most of the earlier works on crystallization with direct contact cooling10, 11, 12, 13 were concerned with the development of equipment and processes. Kinetic studies, performance tests and heat transfer data of this technique were, however, not examined su ciently. In particular, this technique was not applied to melt crystallization for the separation of organics. The aim of this study, therefore, is to investigate the separation of an organic eutectic mixture by melt crystallization, its performance and direct contact heat transfer for three kinds of coolants such as gas, liquid and lique® ed
Melt crystallization is one of the separation techniques applied in the separation of organics (such as close boiling hydrocarbons), isomers, heat sensible materials and so on. The use of melt crystallization for separation of organic mixtures has increased rapidly in the chemical industry over the past few years. In melt crystallization the impurities are recovered in molten form and can be cycled, incinerated, or treated in some other fashion without an intermediate solvent removal step. From this point of view, melt crystallization is a clean technology for the separation of organics without using a solvent. There are two di erent types of melt crystallization method; one of these applies a cold surface on which a crystal layer is produced from the stable melt 1 and the other employs a simple stirred vessel in which a crystal suspension is produced by cooling the entire melt2 . For recovery of the crystals formed, the former uses a temperature gradient technique or a mechanical device, and the latter uses subsidiary equipment such as ® lters and centrifuges. In melt crystallization as well as industrial crystallization by cooling, the liquid phase is cooled in an indirect heat exchanger with metallic surfaces through which heat is extracted from the solution3, 4, 5,6 . The main problems of these methods are low product purity, low heat transfer e ciency and high energy consumption, associated with scale up problems. 176
MELT CRYSTALLIZATION WITH DIRECT CONTACT COOLING TECHNIQUES
177
Figure 1. Schematic diagram of the experimental apparatusfor gas as coolant. A. Reservoir; B. Data aquisition system; C. Thermostatic baths and circulators;D. Particle analysis sensor; E. Dilution tank; F. Temperature recorder; G. Crystallizer; H. Flowmeter; I. Refrigerator; J. Temperature programming controller; K. Heat exchanger.
gas. The system investigated in this study was the simple eutectic mixture of n-dodecanol±n-decanol. EXPERIMENTAL Apparatus The schematic diagram of the apparatus used in this study is shown in Figure 1. The components consisted of the crystallizer, storage vessels for the direct coolants and for mixtures, all thermostatically controlled, and systems for heat measurement and crystal size analysis. Details of the di erent types of crystallizers are shown in Figure 2. Experiments were performed for three kinds of direct contact coolants in batchwise and continuously operated crystallizers. The crystallizer using air as a coolant (see Figure 2a) was a 500ml glass bubble column with a 60 mm inner diameter, and was equipped with a distributor for gas bubbling, which had 250 holes with a hole diameter of 0.5 mm. In order to prevent fouling in the distributor, warm water with a temperature a little over the saturation temperature of the melt was circulated through the jacket outside distributor. The crystallizer for lique® ed gas and liquid as coolants (see Figure 2b) was a 500 ml vessel with a 100 mm diameter and was equipped with an agitator, a close clearance 6blade turbine type with 36 mm diameter at a speed in the range of about 400 to 700rpm. When the crystallizer was operated with water or butane as direct contact coolants, these liquids entered the vessel through an 1mm tube located 10 mm above the melt surface. When the crystallizer was operated with air as a direct contact coolant, the gas passed through the cooling chamber and then entered the distributor located at the bottom of the crystallizer. A double jacket was used to dissolve the solid organic by circulating the warm water through the clearance. No encrustation occurred. For continuous operation, the equipment was modi® ed to allow for the storage and introduction of feed solution, and for the removal of a mixed slurry. Slurry was withdrawn continuously through 10 mm tube. Measurements of the outlet temperature of the Trans IChemE, Vol 5, Part A, February 1997
crystallizer for calculation of the logarithm median temperature from the experiments were carried out by the ampli® ed trace of temperature signals from the thermocouple, which were monitored on the XY recorder. A crystal analysis system (PAMAS PMT 2100) and an image analysis system with a microscope were used so that the crystal size distribution could be measured continuously during continuous operation, as well as batchwise operation. Method and Analysis Three direct contact coolants, air as a gas, and water and a lique® ed gas butane as liquid have been investigated in this study. The melt crystallizer was operated
Figure 2. Experimental apparatus for batch and continuous experiments (a) gas coolant (b) liquid and lique® ed gas coolant.
178
KIM and MERSMANN
batchwise or continuously. The typical procedure of the experiments is as follows. For batchwise operation, a homogeneous mixture of n-dodecanol and n-decanol was prepared and a total of about 400 ml charged into the feed. The fed solution was heated to 5 K above its saturation temperature. The crystallizer vessel was ® lled with the melt and then the chosen coolant was added to the melt. Crystal slurry was withdrawn from the crystallizer to the crystal analysis system to measure crystal size and crystal size distribution (CSD). At the same time, samples were taken to analyse the purity and yield. The slurry was separated into crystals and residual melt by vacuum ® ltration. For continuous operation, the equipment was modi® ed to allow for the storage and introduction of feed solution and for the removal of mixed slurry. After the operation of approximately ten residence times of the crystallizer, the run was terminated and the crystals and residual melt were separated. Suspended crystals and residual melt were sampled from the crystallizer every 2 minutes, and their amounts, their compositions and the size distributions of the sampled crystals were observed by mass balance, gas chromatography and the particle analysis system, respectively. The crystals from the crystallizer were examined by the crystal analysis system described earlier. The analysis of CSD was carried out by crystal analysis systems using a light scattering sensor and image analysis system with microscope. The former was achieved by rapidly treating a sample of the product slurry and feeding the crystals into the particle analysis sensor with the dilution liquor circulated, which had been in equilibrium with solid n-dodecanol at the equilibrium temperature. By this means, n-dodecanol crystals were brought into equilibrium with the mixture liquor. The fact that the ® ltered crystals were composed of easily separable, discrete crystals suggests that little or no freezing of the dilutent had taken place on the crystals. The latter was achieved by treating the crystals after ® ltration. RESULTS AND DISCUSSION Heat Transfer Coe cient Figure 3 shows heat transfer data taken at various super® cial velocities for three kinds of coolants in batchwise operation. The super® cial velocity is equal to the volumetric ¯ ow rate of coolant based on the cross sectional area of the column. The volumetric heat transfer coe cient Uv was calculated by LMTD (logarithm mean temperature di erence), crystallizer volume V and the average of heat ¯ ow transferred by the coolant and that given up by the melt. Uv =
(Qc + Qt )/ 2V
(1) LMTD Here LMTD is (D T i - D T o )/ ln(D T i / D T o ), D T i and D T o are the mean di erences of the temperatures of coolant and melt at the inlet side and outlet side of the crystallizer, respectively. Both the heat ¯ ow transferred from the melt to the coolant, Qc, as well as the heat ¯ ow removed from the melt, Qt , have been measured. Since Qc = Qt , the mean value is used in equation (1) in order to reduce the measuring error. Plots of the volumetric
Figure 3. Volumetricheat transfer coe cient as a function of super® cial velocity of coolants.
heat transfer coe cient versus super® cial linear velocity on log-log paper were found to give a straight line. The slope of the least square lines for the points on this plot is from 1.5 to 1.8. This agrees with previous results that the volumetric heat transfer coe cient is roughly proportional to the 1.6 power of the linear velocity valid for liquid-liquid contact in a pipe14. The exponent found for the gas coolant may be ascribed to the high degree of turbulence accompanied by more intimate mixing compared with water as a liquid coolant. Volumetric heat transfer coe cients obtained in this study are in the range of 0.1 and 100kW/(m3 K), which depend on the super® cial velocity and the type of coolant. The values of volumetric heat transfer coe cient for water as a liquid coolant and butane as a lique® ed gas coolant appear to be almost the same. Therefore, the mechanism of heat transfer between a lique® ed gas such as butane and the melt of organics seems to be similar to that between a liquid coolant such as water and a melt, where no phase change takes place. EŒect of Subcooling on Growth Rate Figure 4 shows the relationship between the growth rate G and the subcooling D T for continuous and batchwise test for a feed of 95 weight percent of ndodecanol. The subcooling means the di erence between the saturation and bulk temperature of the melt. In batchwise operation mode, the crystal growth rate was calculated from the slope in plots of measured mean crystal size against time15, 16. In continuous operation it was measured from crystal size distributions for the continuous crystallizer by using the population balance theory16. The kinetics of melt crystallization using direct contact cooling will be reported later elsewhere17 . In both continuous and batchwise tests the crystal growth rate for the mixture of n-dodecanol and n-decanol was proportional to the second power of subcooling D T . As a rule for a eutectic system, the dependence of supersaturation on growth rate is of the ® rst power in the case of a pure compound and ® rst to second for impure mixtures18,19. Therefore, the data obtained seem to be reasonable. The crystal growth rate for continuous crystallization is larger than that obtained in batchwise experiments with air as coolant. The limitation of heat transfer as the controlling step in melt crystallization can Trans IChemE, Vol 75, Part A, February 1997
MELT CRYSTALLIZATION WITH DIRECT CONTACT COOLING TECHNIQUES
179
Figure 4. Correlation between the growth rate G and degree of subcooling D T for continuous and batchwise test.
Figure 5. E ect of supersaturationon median crystal size for batchwise test.
be reduced by the use of a liquid or a lique® ed gas which results in a higher heat transfer.
increasing supersaturation and holdup of the coolants. The average crystal size is in the range of 0.1 to 1.4 mm for continuous tests and depends on supersaturation and holdup of the coolant. Our experiments have shown that the crystals are, as a rule, considerably larger than those obtained in a conventional industrial crystallizer. In industrial crystallization, an average crystal size of 0.05 to 0.2 mm is only obtained for organic systems in suspension crystallization22,23. The residence time in conventional melt crystallization processes is about one hour. Contrary to this, the crystals produced by direct contact cooling are larger despite a reduction of residence time only 10 minutes in the direct contact cooling process. The mean crystal size obtained for continuous operation is larger than that for batch tests. Our newresults suggest that the temperature drop is very large and fast which leads to higher growth rates and larger crystal sizes. However, further work is necessaryto prove these results.
EŒect of Supersaturation on Crystals The subcooling strongly a ects supersaturation and the crystal growth rate (see Figure 4.). Increasing subcooling creates increasing supersaturation and eventually the production of crystals. The mean size and size distribution of crystals are important parameters in the separation of crystals from the mother liquor because they determine both the surface area to be washed and the rate of ® ltration. They are complex functions of nucleation and growth, which are functions of process variables such as agitation rate, feed composition, and production rate. These functions are therefore related to the degree of supersaturation. The e ect of supersaturation on crystal size was studied for the same feed concentration in both batchwise and continuous tests. Figure 5 shows the e ect of supersaturation on the crystal size for two di erent coolants, such as air as the gas and water as the liquid for batchwise tests. Supersaturation is de® ned as D w = w - w* which is the di erence between the bulk concentration, w, and the saturation concentration, w* . The particle size increases with increasing supersaturation. This also suggests that dependence of supersaturation on particle size is almost the same irrespective of the type of coolant. The median particle size is in the range between 0.2 and 0.7 mm for batchwise tests. In a column crystallizer with scraped walls, average crystal sizes of 0.1 to 0.3 mm were obtained for the condition of a partial re¯ ux ratio20, 21 . It can be expected that with respect to the improved quality of crystals produced by direct contact cooling, the product will be easier to ® lter and wash than that produced via the scraped surface chiller route. Figure 6 shows the e ect of supersaturation on the median crystal size for continuous tests, in which water was used as the coolant. The residence time was in the range between 200 to 800 seconds and the holdup of the coolant was 0.20 to 0.86. The particle size increases with Trans IChemE, Vol 5, Part A, February 1997
Production Rate The production rate depends mainly on the supersaturation that results from the degree of subcooling of
Figure 6. E ect of supersaturation on median crystal size for continuoustest.
180
KIM and MERSMANN
the melt. The volumetric crystallization rate Pv was calculated from a heat balance, and correlated with the volumetric heat transfer coe cient Uv and temperature di erence LMTD according to U LMTD mfCpm (T mi - T ms ) (2) Pv = v D hs D hsV The second term of the right side in equation (2) is neglected because latent heats are much larger than sensible heats in melt crystallization. Figure 7 shows the correlation between the volumetric production rate and the volumetric heat transfer according to equation (2). In a plot of the volumetric production rate versus the LMTD based on the heat of crystallization, the slope is equal to the heat transfer coe cient Uv . For three kinds of coolants, two regions can be clearly de® ned. For gas, the volumetric production rate increases from 0.01 to 0.2 kg/(m3s) as Uv increases from 0.1 to 1 kW/(m3K). For water and butane, the volumetric production rate is in the range between 0.05 and 1.4kg/(m3 s) as Uv increases from 4 to 40 kW/(m3K). In conventional melt crystallizers15 the volumetric production rate is about 0.1kg/(m3 s). Therefore, the major advantage of crystallizers with direct contact cooling is a larger production rate for a given volume in comparison to the conventional melt crystallizers. In spite of the high LMTD investigated in this study, the crystallizer surface is always free of encrustation. This means that a long operation time is possible at high heat transfer with the absence of encrustation. EŒect of Crystal Size on Purity Figure 8 presents a comparison of the purities of crude crystals and wiped crystals. The purity is plotted against the mean crystal size for the feed concentration of 95 wt.% n-dodecanol. Wiping means that the crystals have been spread on soft paper in order to transfer the adhering melt into the dry paper material. Therefore, only the impurity of the adhering outer melt can be removed to a certain degree. The purity of n-dodecanol crystal decreased from 98 to 97.2wt% with an increase of the mean crystal size from 0.1 to 1.4 mm. It is supposed that the impurity is dependent, via supersaturation, on
Figure 7. Volumetric production rate versus LMTD/ D hs for melt crystallization with direct contact coolants, air, water and n-butane.
Figure 8. Comparison of purities between crude crystals and wiped crystals against crystal size.
the rates of nucleation and growth, and on hydrodynamic conditions. Since the heat transfer by the direct coolant system is high, the growth rate is high, too. This means that the impurity is easily included in crystals at the high subcooling. According to the latest results of various investigators24, 25 , the growth rate for small crystals is smaller than that of large crystals. They suggested that large crystals result from a high growth rate of the crystals. In addition, the di usion boundary layer for tiny crystals is smaller than that for large crystals on account of di erent ¯ ow conditions. According to Wintermantel4 , the purity of crystals is the function of the crystal growth rate G and mass transfer coe cient k d and decreases with increasing growth rate G but increases with increasing mass transfer coe cient k d . Therefore, it can be expected that small crystals are purer due to smaller crystal growth rates and higher mass transfer coe cient: (q l - cl) k d q l (3) Purity = f cI G q s In Figure 8, the purities are almost 99.7 weight percent for crystals of a mean size smaller than 0.5 mm. However, for crystals above 0.5 mm, the purity decreases to only 98.8 weight percent for crystals with 0.8 mm in mean size. In particular, the purity of crystals obtained by gas cooling was 99.6 weight percent after wiping compared with 98.6 weight percent before wiping. It can be expected that crystals smaller than 0.8 mm are homogeneous inside.
(
)
Comparison of Distribution Coe cients To characterize the e ciency of a crystallization process, the e ective distribution coe cient k eff is de® ned as the ratio of the impurity concentration in the crystal phase to the impurity concentration in the melt phase: x (4) k eff = c xr A coe cient k eff close to 1 means that there is almost no separation, and k eff ® 0 means perfect separation. Figure 9 shows that dependence of e ective distribution Trans IChemE, Vol 75, Part A, February 1997
MELT CRYSTALLIZATION WITH DIRECT CONTACT COOLING TECHNIQUES
181
increasing particle size, growth rate and yield of crystal. The outer layer of crystals is less pure than the inner core of crystals. Therefore, washing in a hydrocyclone, sweating and/or partial melting can be applied for upgrading in order to obtain a high purity product. NOMENCLATURE
Figure 9. Distribution coe cient versus crystal growth rate for ndodecanol±n-decanol system.
cl Cp G k eff kd LMTD mf Pv Qt Qc Uv V w w* xc xr D hs DT Dw
coe cient on the crystal growth rate for various feed compositions of crude and wiped crystals. A comparison between distribution coe cients of layer crystallization26 and crystallization with direct contact cooling is also depicted. As can be seen, the distribution coe cient in layer crystallization is 0.56 for a crystal growth rate of 0.5 ´ 10- 6 m s- 1 . Compared with direct contact crystallization under the same conditions, the distribution coe cient is only 0.41 for crude crystals and 0.10 for wiped crystals. This means that the quality of crystals from crystallization by direct contact cooling is better than that of layer crystallization. The distribution coe cient increases with increasing cooling rate. In a batch system the cooling rate is proportional to the rate of crystal growth. Therefore, the distribution coe cient depends on the rate of crystal growth. This means that the rate of inclusion of residual melt in crystals increases with increasing cooling rates. These phenomena also suggest that higher cooling rates induce high crystal growth rate. In addition, e ective distribution coe cient increases with increasing subcooling, because high subcooling induces the high crystal growth rate in batch operation. Also, for a high impurity concentration a distinct enhancement of the distribution coe cient is observable. CONCLUSION Application of melt crystallization by direct contact cooling techniques for the separation of organics is possible if the coolant is inert with respect to the melt. Since a variety of inert coolants such as (pressurized) gas, lique® ed gases and inorganic solutions is available, a suitable contact medium can be found in most cases. The process should be taken into consideration for melt crystallization. The advantages are no cooled surfaces, high yields, high purity, large size of crystals, short residence time, batchwise and continuous operation, maximum heat e ciency. With regard to conventional melt crystallization, the process by direct contact cooling is suitable for continuous operation without encrustation, and scale-up of the crystallizer is no problem. The amount of impurities in the crystal increases with Trans IChemE, Vol 5, Part A, February 1997
q
concentration of melt, kgm- 3 heat capacity, J kg- 1 K- 1 growth rate of crystals, m s- 1 e ective distribution coe cient de® ned in equation (4) mass transfer coe cient, m s- 1 logarithm mean temperature di erence, K ¯ ow rate of feed melt, kgs- 1 volumetric production rate, kgm- 3 s- 1 ¯ ow of heat exchanged with the crystallizer kW ¯ ow of heat produced by crystals kW Volumetric heat transfer coe cient, kWm- 3 K- 1 crystallizer volume, m3 concentration, kgkg- 1 saturation concetration, kgkg- 1 concentration of impuity in the crystal, wt% concentration of impuirty in residual melt, wt% latent heat of crystal, J kg- 1 temperature di erence, K supersaturation, kgkg- 1 density kgm- 3
Subscripts i inlet o outlet s solid phase c coolant phase m melt phase
REFERENCES 1. Wynn, N. P., 1992, Separation organics by melt crystallization, Chem Eng Prog, 52±60. 2. Yamazaki, Y., Watanuma, Y. and Toyokura, K., 1986, Formation of benzene crystals in benzene-cyclohexane in the batch agitation systems, Kagaku Kogaku Ronbunshu, 12 (5): 610±613. 3. Player, M. R., 1969, Mathematical analysis of column crystallization, Ind Eng Chem Proc Des Dev, 8 (2): 210±217. 4. Wintermantel,K. and Wellingho , G., 1994, Melt crystallizationÐ theoretical premises and technical limitation, Inter Chem Eng, 34 (1): 17±27. 5. Jancic, S. J., 1986, The Sulzer MWB Fractional Crystallization Systems, Technical Review (Sulzer, Winterthur, Switzerland). 6. Sakuma, K., Taketou, T., Nakagaki, H., Ikeda, J. and Yamamoto, A., 1993, Development of column crystallization,Kagaku Kogaku, 57 (6): 413±419. 7. Barduhn, A. J., 1975, The status of freeze-desalination, Chem Eng Prog, 71 (11): 80±87. 8. Wiegandt, H. F., Madani, A. and Hariott, P., 1987, Ice crystallization development for the butane direct contact process, Desalination, 67: 107±115. 9. Nagashima Y. and Maeda, S., 1979, The characteristicsof a direct contact type crystalizer agitation by the buoyancy force of a secondary refrigerant in a desalination plant, Ind Cryst, 78, E. J. dejong and S. J. Jancic, 425±435. 10. Lathan, R., 1973, A direct contact cooled crystallization, Ind Eng Chem Proc Des Dev, 12 (3): 300±305. 11. Casper, C., 1981, Investigation of evaporative freeze crystallization, Ger Chem Eng, 4: 219±225. 12. French, K. H. W., 1963, The production of pure benzene, Ind Chem, 39: 9±12. 13. Cerny, J., 1963, Continuous crystallization of calcium nitrate tetrahydrate, British Patent 932, 215. 14. Levich, V. G., 1962, Physicochemical Hydrodynamics, ( PrenticeHall, Englewood CliŒs, N. J.).
182
KIM and MERSMANN
15. Mersmann, A. 1994, Crystallization Technology Handbook, (Marcel Dekker, Inc., N.Y.). 16. Garside, J., Mersmann, A. and Nyvlt, J., 1990, Measurement of crystal growth rates, EFCE, Working Party on Crystallization, (Druckhaus Deutsch, Munich). 17. Kim, K. J. and Mersmann, A., 1996, Kinetic study on melt crystallization by direct contact cooling, (to be submitted). 18. Toyokura, K., Murata, H. and Akiya, T., 1976, Crystallization of naphthalene-benzoicacid mxitrues,AlChE Symp Ser, 72 (153): 87±95. 19. Singh, D. P. and Singh, N. B., 1980, Solidi® cation behaviour of eutectics naphthalene-p-chloroaniline and benzoic acid-connamic acid system, Bulle tin De La Socie teÂChemique De France, 3: 113±116. 20. Tavare, N. S., Matsuoka, M., Garside, J., 1990, Modeling a Continuous Column Crystallizer, J of Crystal Growth, 99: 1151± 1155. 21. Albertines, R., 1967, Experimental and theoretical investigation of separation in a column crystallizer, PhD Diss, (University of Michigan, Ann Arbor, USA). 22. Power, J. M. and Bennet, R. B., 1955, p-xylene from petrolum, Ind Eng Chem, 47: 1096±1110.
23. Toyokura, K., Hirawa, I., Imada, S. and Irie, Y., 1992, Purity of benzene crystals obtained from a benzene-cyclohexane melt by a batch coolingcrystallization,Develop in Cryst Eng, (Waseda Univ., Tokyo). 24. Wang, S. and Mersmann, A., 1992, The initial size dependent growth rate dispersion of attrition fragments and secondarynuclei, Chem Eng Sci, 47 (6): 1365±1371. 25. Zacher, U. and Mersmann, A., 1995, The in¯ uence of internal crystal perfection on growth rate dispersion in a continuous suspension crystallizer, J Crystal Growth 147: 172±180. 26. Ozoguz, M. Y., 1992, Melt crystallization and melt crystallization process, PhD Diss (University of Bremen, Germany) VDIFortschritt-Berichte, Series 3, no. 271, VDI-Verlag, Dusseldorf.
ADDRESS Correspondenceconcerningthis paper should be addressed to Dr A. Mersmann, LehrstuhlB fuÈr Verfahrenstechnik,TechnicalUniversityof Munich, Arcisstrasse 21, 8000 Munich 2, Germany.
Trans IChemE, Vol 75, Part A, February 1997