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Seeded batch crystallization of ammonium aluminum sulfate from aqueous solution
ARTICLE IN PRESS Journal of Crystal Growth 311 (2009) 4525–4529
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Seeded batch crystallization of ammonium aluminum sulfate from aqueous solution Noriaki Kubota , Masahiro Onosawa Department of Chemical Engineering, Iwate University, 4-3-5 Ueda, Morioka, 020-8551, 0041 Japan Tokyo, 191
a r t i c l e in fo
abstract
Article history: Received 29 June 2009 Received in revised form 2 August 2009 Accepted 19 August 2009 Communicated by K. Sato Available online 26 August 2009
Seed crystals of ammonium aluminum sulfate ((NH4)Al(SO4)2? 12H2O) were grown in aqueous solution by cooling. The temperature of a crystallizer was lowered with no control by circulating cooling water through the jacket. It fell in an exponential manner. The effects of seed amount and size on the product crystal size distribution were examined. The product crystals obtained were of narrow and unimodal size distribution with suppressed secondary nucleation if seed crystals were loaded more than a critical value. The critical value was determined and well compared with previously reported values for other material systems. This crystallization technique does not need any prior knowledge of the kinetics of crystal growth and nucleation. It is simple and robust, and can be easily applied to an existing crystallizer without installing any additional control systems. & 2009 Elsevier B.V. All rights reserved.
PACS: 87.15.nt Keywords: A2. Industrial crystallization A2. Seed crystals A2. Batch crystallization A2. Crystal size distribution
1. Introduction Batch crystallization is widely used in the pharmaceutical and chemical industries for the production of crystalline materials and for the purpose of purification. Control of crystal size distribution is a main issue in batch crystallization, because it decides the powder characteristics and quality of the product and it has a significant effect on the ease of down-stream processing such as centrifugal separation and drying. Griffiths [1] stated in his pioneering work in 1925 that the rate of cooling or evaporation should be adjusted to keep supersaturation within the metastable zone, and the surface area (or mass) of seed crystals should be maximum; to obtain the product of controlled size with suppressed secondary nucleation. Approximately 40 years later, Mullin and Nyvlt [2] proposed the programmed cooling policy as a practical answer to Griffiths’ remarks. Following this, many research papers have been published on cooling policy or optimal temperature profile. However, none of those ‘‘optimal’’ cooling profiles proposed seem to be effective as expected. Optimal cooling/supersaturation profile can be even said to be essentially a compromise [3], since the rate processes of growth and nucleation proceed simultaneously at any time in optimal cooling.
Seeding has not been not paid much attention until recently compared to the cooling policy. It is even said to be mysterious. In the last decade, however, research papers dealing with seeding effects in batch crystallization were published by Jagadesh et al. [4,5], Kubota et al. [6], Doki et al. [7–12], Serrena et al. [13], Lung-Sommariba et al. [14], Hojjati and Rohani [15] and Warstat and Ulrich [16]. One of the most important results obtained by these studies is a finding of the existence of a critical loading of seed crystals. If seeds are added sufficiently more than a critical seed loading, secondary nucleation can be suppressed, and hence only the added seed crystals grow without generation of fine particles (secondary nuclei), leading to product crystals with narrow size distribution. This was first found experimentally by the group of the present authors [4–12] and then confirmed by the another group [15]. Another important finding on seeding is that it has stronger effect on the size distribution of product crystals than cooling mode (supersaturation profile). This stronger effect on crystal size distribution was demonstrated experimentally [4,6,8,17] and by simulation [13]. In this study, we applied the seeding technique to batch cooling crystallization of ammonium aluminum sulfate from aqueous solution. It crystallizes as a hydrate of the form (NH4)Al(SO4)2 12H2O.
2. Critical seed loading and seed chart Corresponding author. Present address: (home) 2-2-4 Hino, Tokyo 191-0041,
Japan. Tel./fax: +81 42 599 5981. E-mail address: [email protected] (N. Kubota). 0022-0248/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2009.08.014
According to our previous studies [4–12,18], secondary nucleation can be suppressed and, therefore, the added seed
ARTICLE IN PRESS 4526
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li Lp
Nomenclature initial concentration of solution, kg-hydrate/kg-free water final concentration of solution, kg-hydrate/kg-free water seed loading ratio, defined by Eq. (2) coefficient of variation, % critical seed loading ratio volume (or volume-weighted) mean size of particles, defined by Eq. (3), mm
Ci Cf Cs CV C*s L
crystals can be grown safely if the following condition is satisfied, Cs ZCs
ð1Þ
where Cs is the seed loading ratio defined by the following equation. C*s is its critical value. The seed loading ratio Cs is defined by Cs ¼
Ws Wth
ð2Þ
It is the mass ratio of the added seeds Ws (kg) to the theoretical crystal yield Wth (kg). The value of Wth can be determined experimentally or calculated with w(CiCf), where Ci is the initial solution concentrations (kg-hydrate/kg-free water), Cf the final concentration (kg-hydrate/kg-free water) and w the mass of free solvent water (kg). The seeding effect on the mean size of product crystals can be illustrated on the seed chart, in which the volume mean size of product crystals normalized with the size of seed crystals Lp/Ls is plotted as a function of the seed loading ratio Cs with the seed size Ls (mm) as a parameter. The volume mean size was calculated by the following equation from sieve data (see Appendix). PN PN ni l4i wi li ¼ Pi¼1 ð3Þ L ¼ Pi¼1 N N 3 i¼1 wi i¼1 ni li where wi and ni are the mass and number of crystals, respectively, in the i-th sieve fraction with an average aperture size of li and N the total number of sieve fractions. Fig. 1 is a typical example of the seed chart, which was obtained for the potassium alum–water system in a previous study [9]. In Fig. 1, the ideal growth line is also drawn. It is a theoretical relation between Lp/Ls and Cs obtained for the mono-dispersed (ideal) seed crystals by assuming ideal growth, i.e., no change in the number of crystals with no generation of new crystals (secondary nuclei) and no change in the crystal shape. The following equation can be obtained under these conditions, Ws
arc L3s
¼
Wth þ Ws arc L3p
Ls N
ni wi Ws Wth
a r
average size of the two successive sieve apertures volume (or volume-weighted) mean size of product crystals, mm size of seed crystals, mm total number of sieve fractions the number of particles in the i-th sieve fraction mass of particles in the i-th sieve fraction mass of seed crystals, kg crystal yield of a batch, kg volume shape factor density of crystal, kg/m3
The seed loading ratio just at the point of coincidence is the critical seed loading ratio C*s mentioned above. All the data points in the range CsZC*s (Eq. (1)) lie on the ideal growth line. This means that no secondary nuclei are generated at CsZC*s. The critical seed loading plays a key role in seeded batch crystallization, because the condition of Eq. (1) guarantees the added seed crystals to grow safely with virtually no generation of secondary nucleation. In industrial situations, it is desirable to know the value of critical seed loading ratio C*s a priori. However, it is difficult to do it theoretically, since batch crystallization proceeds in a complicated unsteady state manner and it must be affected by many factors concerning secondary nucleation and crystal growth. From a practical point of view, it must be helpful if an estimate can be made, even though it is rough and empirical. In a previous paper [9], C*s was determined on the seed chart as the point that the experimental Lp/Ls coincides with the ideal growth line (see Fig. 1). The critical seed loading ratio C*s, thus determined, was correlated with seed size Ls by a simple experimental equation as [9]. Cs ¼ 2:17 106 L2s
ð6Þ
Eq. (6) is just an experimental equation, which has no theoretical basis. However, it is useful. It can be used to make a rough estimate of C*s. It is noted that the unit of Ls is micro-meter
ð4Þ
where a () and rc (kg/m3) are the volume shape factor and the density of crystal, respectively. Wth+Ws is the mass of the product (grown seeds). Substituting Eq. (2) (the definition of seed loading ratio) into Eq. (4) gives the equation of ideal growth Lp 1 þ Cs 1=3 ¼ ð5Þ Ls Cs , which gives a straight If Cso0.1, Eq. (5) reduces to Lp/Ls ¼ C1/3 s line with a slope of 1/3 on the logarithmic paper. The seeding effect on the product crystal size is clearly seen on the seed chart. The measured value of Lp/Ls increases as the seed loading ratio Cs is increased, passing through the maximum and then decreasing. Finally, it coincides with the ideal growth line. Such trend does not depend on the size of the seed crystals used.
Fig. 1. Seed chart for cooling crystallization of KAl(SO4)2.12H2O from aqueous solution (K: data for the solutions saturated at 28 1C, J: data for the solutions saturated at 35 1C).
ARTICLE IN PRESS N. Kubota, M. Onosawa / Journal of Crystal Growth 311 (2009) 4525–4529
and, therefore, the unit of the constant 2.17 106 is squared micro-meter. It would be very useful, from an industrial point of view, if Eq. (6), obtained for a specific material system, was applied to other material systems. One of the objectives of the present study is to explore such a possibility.
3. Experimental method The experimental method is basically the same as that used in a previous study [9], except for the size of the crystallizer used. A smaller crystallizer was used. It is a jacketed non-baffled crystallizer with a working volume of 2.3 L, equipped with a marine propeller stirrer. An ammonium aluminum sulfate aqueous solution, saturated at 50 1C, was introduced and cooled from above 50 1C to a termination temperature of 20 1C. Cooling was achieved by circulating a cooling water of 20 1C through the jacket. No temperature control was made so that it fell naturally in an exponential manner to the cooling water temperature. The stirrer speed was fixed at 350 rpm throughout all the experiments. Seed crystals were prepared by sieving crystals precipitated from aqueous solution by cooling. Seed crystal sizes Ls examined were 41.5, 165, and 328 and 550 mm. The seed size is an arithmetic mean of the two successive sieve openings used for seed classification. The seed crystals were introduced as dried directly into the solution just at the moment the solution temperature passed the saturation point of 50 1C. The batch time, the period from the moment of seeding to the termination, was fixed at 180 min. Seed loading ratios Cs examined are shown in Table 1. The temperature was measured on-line. Crystal size distributions of product were measured by sieving with a Sonic Shifter L-200P (Seishin Enterprise, Japan) equipped with Japanese Industrial Standards (JIS) sieves. For the arrangement of the seeds, the same shifter and sieves were used. Table 1 Seeding condition. Seed size Ls (mm) 41.5 165 328 550 a
0.0051 0.051 0.051 0.525
0.0085 0.076 0.102
0.017a 203
The above experiments are all single-stage cooling crystallization, where the temperature was lowered in single-stage from above 50 to 20 1C. As an additional experiment, a 2-stage cooling experiment was conducted for the seed crystals of 41.5 mm to examine the effect of cooling profile on the crystal size distribution. In Fig. 2, the temperature profiles in the single- and 2-stage cooling experiments are shown.
4. Results and discussion 4.1. Typical seeding effect on crystal size distribution Fig. 3 shows product crystal size distributions obtained for a seed size of 328 mm. The effect of the amount of seed crystals on crystal size distribution is clearly seen: a uni-modal size distribution with Lp ¼ 537 mm and CV (coefficient of variation) ¼ 26.6% was obtained for Cs ¼ 0.305, while a bi-modal distribution with Lp ¼ 530 mm and CV ¼ 56.0% for Cs ¼ 0.025. In the bi-modal distribution, the particles in the small size range can be assigned to the crystals generated by secondary nucleation, while the particles in the large size range can be of grown seed crystals. The similar results were obtained for seed crystals of the other sizes examined. 4.2. Reproducibility of the experiments In Fig. 4, two crystal size distributions, obtained under the identical seeding condition of Cs ¼ 0.0017 for the seed crystals of 41.5 mm, are compared. The two distributions are almost the same. This means that good reproducibility of the experiments is guaranteed in the present study. 4.3. Seed chart for the (NH4)Al(SO4)2–H2O system All the data of volume mean size normalized with seed size Lp/Ls, obtained in this study for the (NH4)Al(SO4)2–H2O system, are plotted in Fig. 5 on a seed chart as a function of seed loading ratio Cs. The solid line is the ideal growth line (Eq. (5)). The dotted
Seed loading ratio Sa 0.0025 0.025 0.025 0.465
4527
0.254
0.305
Duplicate experiments.
Fig. 2. Temperature profiles of single- and 2-stage coolings.
Fig. 3. The effect of seed loading ratio on product crystal size distribution.
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probably due to the decrease in the number of seed crystals caused by agglomeration among seed crystals. Small crystals tend to agglomerate in supersaturated solution [19]. This kind of shift is also seen, though slightly, for the 41.5 mm seeds of the KAl(SO4)2– H2O system (Fig. 1) when the solution concentration is higher (the corresponding data are indicated with open circles). The agglomeration occurred more dominantly for the (NH4)Al(SO4)2–H2O system. It is probably because a high supersaturation peak was established during the batch when the solution, saturated at 50 1C, was cooled to 20 1C. It is known that small crystals tend to agglomerate easier at higher supersaturations [20]. 4.4. Relation between the critical seed loading ratio and seed size
Fig. 4. Reproducibility of product crystal size distribution.
The critical seed loading ratio for the KAl(SO4)2–H2O system, which was obtained for the solutions of a relatively low concentration, was correlated with the seed size in the previous paper [9] as cited above as Eq. (6). As mentioned above, this equation would be very useful if it was applied to other material systems. In order to explore such a possibility, Eq. (6) was compared, in Fig. 6, with the data obtained for the (NH4)Al(SO4)2– H2O system in this study and literature data for the KAl(SO4)2– H2O system obtained different experimental conditions [9] and for another system ((NH4)2SO4–H2O system) [15]. Although a large scatter can be seen, all the data lie roughly on the line of Eq. (6). Therefore, Eq. (6) can be used as a rule of thumb for determining the seed amount when there is no information available on seeding. Some of the data for a seed size of 41.5 mm are seen, in Fig. 6, to deviate below the line of Eq. (6). This is probably due to the decrease in the number of seed crystals caused by agglomeration among them. 4.5. Effect of temperature profile—a typical result of 2-stage cooling experiment The effect of temperature profile is examined in an additional experiment. The temperature was lowered in two stages (see Fig. 2). The size distribution is compared with that obtained for
Fig. 5. Seed chart for cooling crystallization of (NH4)Al(SO4)2.12H2O from aqueous solution. Data are compared with those of the KAl(SO4)2–H2O system. (K: 2-stage cooling).
lines drawn in this figure are the corresponding values obtained for the KAl(SO4)2–H2O system previously [9] (the original data shown already in Fig. 1). The data obtained for the (NH4)Al(SO4)2–H2O system are seen to be close to the dotted line for each corresponding seed size. The critical seed loading ratio C*s does not seem basically to depend on the material and also the crystallizer used (except for the data of 41.5 mm seeds). The reason for this is not clear at the present time. However, it could be explained as follows. Crystallization proceeds in growth-dominant mode around the critical seed loading ratio C*s due to lowered supersaturation caused by the growth of enough seeds. Crystal growth is not affected significantly by the geometry of crystallizer and stirrer speed, compared to secondary nucleation. The ideal growth line is the general relation that does not depend C*s may be considered to behave similarly. As for the case of 41.5 mm seeds, the values of Lp/Ls are shifted to above the ideal growth line at higher seed loading ratios. This is
Fig. 6. The relation between the critical seed loading ratio C*s and seed size Ls. Data for the KAl(SO4)2–H2O system [9] include those from different volume crystallizers and different cooling conditions. Data of the (NH4)Al(SO4)2–H2O system (this study) are obtained with a crystallizer of 2.3 L and those of the (NH4)2SO4–H2O system [15] with a crystallizer of 1.5 L.
ARTICLE IN PRESS N. Kubota, M. Onosawa / Journal of Crystal Growth 311 (2009) 4525–4529
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of JGC corporation, Japan, is acknowledged for his comments on the manuscript.
Appendix. Remarks on our previous papers During preparing the manuscript of the present paper, we realized that there are mistakes (or contradictions) in our previous papers [5–12,18]. In the texts of the previous papers, the word of ‘‘mean mass size’’ appears many times. However, all the average sizes calculated actually were recognized, during checking the related raw data, to be volume mean size (see the text of the present paper for definition). In addition, the equation of the ideal growth line was defined previously for the polydispersed seed crystals with a mean volume size Ls. Instead, in this paper it was newly defined for the mono-dispersed seed crystals of size Ls. This alteration does not bring any change in the form of the equation of ideal growth.
Fig. 7. Comparison of crystal size distributions obtained from single- and 2-stage cooling experiments.
the single-stage cooling in Fig. 7. The crystal size distribution is narrower than that obtained with the single-stage cooling. The position of the peak is nearly the same. The volume mean size of the product was smaller as already shown in Fig. 5 on the seed chart (K). A reason for the decreased volume mean size is probably less agglomeration of the seed crystals. A reason for the narrowed size distribution is less generation of secondary nuclei. Less agglomeration and less secondary nucleation are both caused by lower transient supersaturation. Although the transient supersaturation was not measured in this study, it is expected to have been lowered with multi-stage cooling as observed in a previous study [18] for the KAl(SO4)2–H2O system. Acknowledgements Dr. N. Doki, associate professor at Department of Chemical Engineering, Iwate University, is greatly appreciated for his support for the experimental work in this study. Mr. M. Kobari
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
H. Griffiths, J. Soc. Chem. Ind. 44 (1925) 7T. J.W. Mullin, J. Nyvlt, Chem. Eng. Sci. 26 (1971) 369. D. Sarkar, S. Rohani, A. Jutan, Chem. Eng. Sci. 61 (2006) 5282. D. Jagadesh, N. Kubota, M. Yokota, A. Sato, N. Tavare, J. Chem. Eng. Jpn. 29 (1996) 865. D. Jagadesh, N. Kubota, M. Yokota, N. Doki, A. Sato, N. Tavare, J. Chem. Eng. Jpn. 32 (1999) 514. N. Kubota, N. Doki, M. Yokota, A. Sato, Powder Technol. 121 (2001) 31. N. Doki, N. Kubota, M. Yokota, O. Hamada, F. Masumi, AIChE J. 45 (1999) 2527. N. Doki, N. Kubota, A. Sato, M. Yokota, Chem. Eng. J. 81 (2001) 313. N. Doki, N. Kubota, M. Yokota, A. Chianese, J. Chem. Eng. Jpn. 35 (2002) 670. N. Doki, N. Kubota, M. Yokota, S. Kimura, S. Sasaki, J. Chem. Eng. Jpn. 35 (2002) 1099. N. Doki, M. Yokota, H. Nakamura, S. Sasaki, N. Kubota, J. Chem. Eng. Jpn. 36 (2003) 1001. N. Doki, M. Yokota, H.S. Sasaki, N. Kubota, J. Chem. Eng. Jpn. 37 (2004) 436. H.C. Serrena, D.L. Ma, R.D. Braatz, Can. J. Chem. Eng. 77 (1999) 590. L.M. Lung-Somarriba, M. Moscossa-Santillan, C. Porte, A. Delacroix, J. Cryst. Growth 270 (2004) 624. H. Hojjati, S. Rohani, Chem. Eng. Process. 44 (2005) 949. A. Warstat, J. Ulrich, Chem. Eng. Technol. 29 (2006) 187. J.W. Chew, S.N. Black, P.S. Chow, R.B.H. Tan, Ind. Eng. Chem. Res. 46 (2006) 830. N. Kubota, N. Doki, M. Yokota, D. Jagadesh, J. Chem. Eng. Jpn. 35 (2002) 1063. N. Kubota, J.W. Mullin, J. Cryst. Growth 66 (1984) 676. ¨ L. Vicum, M. Mazzotti, J. Brozio, Cryst. Growth Des. 8 C. Lindenberg, J. Scholl, (2008) 224.
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Seeded batch crystallization of ammonium aluminum sulfate from aqueous solution Noriaki Kubota , Masahiro Onosawa Department of Chemical Engineering, Iwate University, 4-3-5 Ueda, Morioka, 020-8551, 0041 Japan Tokyo, 191
a r t i c l e in fo
abstract
Article history: Received 29 June 2009 Received in revised form 2 August 2009 Accepted 19 August 2009 Communicated by K. Sato Available online 26 August 2009
Seed crystals of ammonium aluminum sulfate ((NH4)Al(SO4)2? 12H2O) were grown in aqueous solution by cooling. The temperature of a crystallizer was lowered with no control by circulating cooling water through the jacket. It fell in an exponential manner. The effects of seed amount and size on the product crystal size distribution were examined. The product crystals obtained were of narrow and unimodal size distribution with suppressed secondary nucleation if seed crystals were loaded more than a critical value. The critical value was determined and well compared with previously reported values for other material systems. This crystallization technique does not need any prior knowledge of the kinetics of crystal growth and nucleation. It is simple and robust, and can be easily applied to an existing crystallizer without installing any additional control systems. & 2009 Elsevier B.V. All rights reserved.
PACS: 87.15.nt Keywords: A2. Industrial crystallization A2. Seed crystals A2. Batch crystallization A2. Crystal size distribution
1. Introduction Batch crystallization is widely used in the pharmaceutical and chemical industries for the production of crystalline materials and for the purpose of purification. Control of crystal size distribution is a main issue in batch crystallization, because it decides the powder characteristics and quality of the product and it has a significant effect on the ease of down-stream processing such as centrifugal separation and drying. Griffiths [1] stated in his pioneering work in 1925 that the rate of cooling or evaporation should be adjusted to keep supersaturation within the metastable zone, and the surface area (or mass) of seed crystals should be maximum; to obtain the product of controlled size with suppressed secondary nucleation. Approximately 40 years later, Mullin and Nyvlt [2] proposed the programmed cooling policy as a practical answer to Griffiths’ remarks. Following this, many research papers have been published on cooling policy or optimal temperature profile. However, none of those ‘‘optimal’’ cooling profiles proposed seem to be effective as expected. Optimal cooling/supersaturation profile can be even said to be essentially a compromise [3], since the rate processes of growth and nucleation proceed simultaneously at any time in optimal cooling.
Seeding has not been not paid much attention until recently compared to the cooling policy. It is even said to be mysterious. In the last decade, however, research papers dealing with seeding effects in batch crystallization were published by Jagadesh et al. [4,5], Kubota et al. [6], Doki et al. [7–12], Serrena et al. [13], Lung-Sommariba et al. [14], Hojjati and Rohani [15] and Warstat and Ulrich [16]. One of the most important results obtained by these studies is a finding of the existence of a critical loading of seed crystals. If seeds are added sufficiently more than a critical seed loading, secondary nucleation can be suppressed, and hence only the added seed crystals grow without generation of fine particles (secondary nuclei), leading to product crystals with narrow size distribution. This was first found experimentally by the group of the present authors [4–12] and then confirmed by the another group [15]. Another important finding on seeding is that it has stronger effect on the size distribution of product crystals than cooling mode (supersaturation profile). This stronger effect on crystal size distribution was demonstrated experimentally [4,6,8,17] and by simulation [13]. In this study, we applied the seeding technique to batch cooling crystallization of ammonium aluminum sulfate from aqueous solution. It crystallizes as a hydrate of the form (NH4)Al(SO4)2 12H2O.
2. Critical seed loading and seed chart Corresponding author. Present address: (home) 2-2-4 Hino, Tokyo 191-0041,
Japan. Tel./fax: +81 42 599 5981. E-mail address: [email protected] (N. Kubota). 0022-0248/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2009.08.014
According to our previous studies [4–12,18], secondary nucleation can be suppressed and, therefore, the added seed
ARTICLE IN PRESS 4526
N. Kubota, M. Onosawa / Journal of Crystal Growth 311 (2009) 4525–4529
li Lp
Nomenclature initial concentration of solution, kg-hydrate/kg-free water final concentration of solution, kg-hydrate/kg-free water seed loading ratio, defined by Eq. (2) coefficient of variation, % critical seed loading ratio volume (or volume-weighted) mean size of particles, defined by Eq. (3), mm
Ci Cf Cs CV C*s L
crystals can be grown safely if the following condition is satisfied, Cs ZCs
ð1Þ
where Cs is the seed loading ratio defined by the following equation. C*s is its critical value. The seed loading ratio Cs is defined by Cs ¼
Ws Wth
ð2Þ
It is the mass ratio of the added seeds Ws (kg) to the theoretical crystal yield Wth (kg). The value of Wth can be determined experimentally or calculated with w(CiCf), where Ci is the initial solution concentrations (kg-hydrate/kg-free water), Cf the final concentration (kg-hydrate/kg-free water) and w the mass of free solvent water (kg). The seeding effect on the mean size of product crystals can be illustrated on the seed chart, in which the volume mean size of product crystals normalized with the size of seed crystals Lp/Ls is plotted as a function of the seed loading ratio Cs with the seed size Ls (mm) as a parameter. The volume mean size was calculated by the following equation from sieve data (see Appendix). PN PN ni l4i wi li ¼ Pi¼1 ð3Þ L ¼ Pi¼1 N N 3 i¼1 wi i¼1 ni li where wi and ni are the mass and number of crystals, respectively, in the i-th sieve fraction with an average aperture size of li and N the total number of sieve fractions. Fig. 1 is a typical example of the seed chart, which was obtained for the potassium alum–water system in a previous study [9]. In Fig. 1, the ideal growth line is also drawn. It is a theoretical relation between Lp/Ls and Cs obtained for the mono-dispersed (ideal) seed crystals by assuming ideal growth, i.e., no change in the number of crystals with no generation of new crystals (secondary nuclei) and no change in the crystal shape. The following equation can be obtained under these conditions, Ws
arc L3s
¼
Wth þ Ws arc L3p
Ls N
ni wi Ws Wth
a r
average size of the two successive sieve apertures volume (or volume-weighted) mean size of product crystals, mm size of seed crystals, mm total number of sieve fractions the number of particles in the i-th sieve fraction mass of particles in the i-th sieve fraction mass of seed crystals, kg crystal yield of a batch, kg volume shape factor density of crystal, kg/m3
The seed loading ratio just at the point of coincidence is the critical seed loading ratio C*s mentioned above. All the data points in the range CsZC*s (Eq. (1)) lie on the ideal growth line. This means that no secondary nuclei are generated at CsZC*s. The critical seed loading plays a key role in seeded batch crystallization, because the condition of Eq. (1) guarantees the added seed crystals to grow safely with virtually no generation of secondary nucleation. In industrial situations, it is desirable to know the value of critical seed loading ratio C*s a priori. However, it is difficult to do it theoretically, since batch crystallization proceeds in a complicated unsteady state manner and it must be affected by many factors concerning secondary nucleation and crystal growth. From a practical point of view, it must be helpful if an estimate can be made, even though it is rough and empirical. In a previous paper [9], C*s was determined on the seed chart as the point that the experimental Lp/Ls coincides with the ideal growth line (see Fig. 1). The critical seed loading ratio C*s, thus determined, was correlated with seed size Ls by a simple experimental equation as [9]. Cs ¼ 2:17 106 L2s
ð6Þ
Eq. (6) is just an experimental equation, which has no theoretical basis. However, it is useful. It can be used to make a rough estimate of C*s. It is noted that the unit of Ls is micro-meter
ð4Þ
where a () and rc (kg/m3) are the volume shape factor and the density of crystal, respectively. Wth+Ws is the mass of the product (grown seeds). Substituting Eq. (2) (the definition of seed loading ratio) into Eq. (4) gives the equation of ideal growth Lp 1 þ Cs 1=3 ¼ ð5Þ Ls Cs , which gives a straight If Cso0.1, Eq. (5) reduces to Lp/Ls ¼ C1/3 s line with a slope of 1/3 on the logarithmic paper. The seeding effect on the product crystal size is clearly seen on the seed chart. The measured value of Lp/Ls increases as the seed loading ratio Cs is increased, passing through the maximum and then decreasing. Finally, it coincides with the ideal growth line. Such trend does not depend on the size of the seed crystals used.
Fig. 1. Seed chart for cooling crystallization of KAl(SO4)2.12H2O from aqueous solution (K: data for the solutions saturated at 28 1C, J: data for the solutions saturated at 35 1C).
ARTICLE IN PRESS N. Kubota, M. Onosawa / Journal of Crystal Growth 311 (2009) 4525–4529
and, therefore, the unit of the constant 2.17 106 is squared micro-meter. It would be very useful, from an industrial point of view, if Eq. (6), obtained for a specific material system, was applied to other material systems. One of the objectives of the present study is to explore such a possibility.
3. Experimental method The experimental method is basically the same as that used in a previous study [9], except for the size of the crystallizer used. A smaller crystallizer was used. It is a jacketed non-baffled crystallizer with a working volume of 2.3 L, equipped with a marine propeller stirrer. An ammonium aluminum sulfate aqueous solution, saturated at 50 1C, was introduced and cooled from above 50 1C to a termination temperature of 20 1C. Cooling was achieved by circulating a cooling water of 20 1C through the jacket. No temperature control was made so that it fell naturally in an exponential manner to the cooling water temperature. The stirrer speed was fixed at 350 rpm throughout all the experiments. Seed crystals were prepared by sieving crystals precipitated from aqueous solution by cooling. Seed crystal sizes Ls examined were 41.5, 165, and 328 and 550 mm. The seed size is an arithmetic mean of the two successive sieve openings used for seed classification. The seed crystals were introduced as dried directly into the solution just at the moment the solution temperature passed the saturation point of 50 1C. The batch time, the period from the moment of seeding to the termination, was fixed at 180 min. Seed loading ratios Cs examined are shown in Table 1. The temperature was measured on-line. Crystal size distributions of product were measured by sieving with a Sonic Shifter L-200P (Seishin Enterprise, Japan) equipped with Japanese Industrial Standards (JIS) sieves. For the arrangement of the seeds, the same shifter and sieves were used. Table 1 Seeding condition. Seed size Ls (mm) 41.5 165 328 550 a
0.0051 0.051 0.051 0.525
0.0085 0.076 0.102
0.017a 203
The above experiments are all single-stage cooling crystallization, where the temperature was lowered in single-stage from above 50 to 20 1C. As an additional experiment, a 2-stage cooling experiment was conducted for the seed crystals of 41.5 mm to examine the effect of cooling profile on the crystal size distribution. In Fig. 2, the temperature profiles in the single- and 2-stage cooling experiments are shown.
4. Results and discussion 4.1. Typical seeding effect on crystal size distribution Fig. 3 shows product crystal size distributions obtained for a seed size of 328 mm. The effect of the amount of seed crystals on crystal size distribution is clearly seen: a uni-modal size distribution with Lp ¼ 537 mm and CV (coefficient of variation) ¼ 26.6% was obtained for Cs ¼ 0.305, while a bi-modal distribution with Lp ¼ 530 mm and CV ¼ 56.0% for Cs ¼ 0.025. In the bi-modal distribution, the particles in the small size range can be assigned to the crystals generated by secondary nucleation, while the particles in the large size range can be of grown seed crystals. The similar results were obtained for seed crystals of the other sizes examined. 4.2. Reproducibility of the experiments In Fig. 4, two crystal size distributions, obtained under the identical seeding condition of Cs ¼ 0.0017 for the seed crystals of 41.5 mm, are compared. The two distributions are almost the same. This means that good reproducibility of the experiments is guaranteed in the present study. 4.3. Seed chart for the (NH4)Al(SO4)2–H2O system All the data of volume mean size normalized with seed size Lp/Ls, obtained in this study for the (NH4)Al(SO4)2–H2O system, are plotted in Fig. 5 on a seed chart as a function of seed loading ratio Cs. The solid line is the ideal growth line (Eq. (5)). The dotted
Seed loading ratio Sa 0.0025 0.025 0.025 0.465
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0.254
0.305
Duplicate experiments.
Fig. 2. Temperature profiles of single- and 2-stage coolings.
Fig. 3. The effect of seed loading ratio on product crystal size distribution.
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probably due to the decrease in the number of seed crystals caused by agglomeration among seed crystals. Small crystals tend to agglomerate in supersaturated solution [19]. This kind of shift is also seen, though slightly, for the 41.5 mm seeds of the KAl(SO4)2– H2O system (Fig. 1) when the solution concentration is higher (the corresponding data are indicated with open circles). The agglomeration occurred more dominantly for the (NH4)Al(SO4)2–H2O system. It is probably because a high supersaturation peak was established during the batch when the solution, saturated at 50 1C, was cooled to 20 1C. It is known that small crystals tend to agglomerate easier at higher supersaturations [20]. 4.4. Relation between the critical seed loading ratio and seed size
Fig. 4. Reproducibility of product crystal size distribution.
The critical seed loading ratio for the KAl(SO4)2–H2O system, which was obtained for the solutions of a relatively low concentration, was correlated with the seed size in the previous paper [9] as cited above as Eq. (6). As mentioned above, this equation would be very useful if it was applied to other material systems. In order to explore such a possibility, Eq. (6) was compared, in Fig. 6, with the data obtained for the (NH4)Al(SO4)2– H2O system in this study and literature data for the KAl(SO4)2– H2O system obtained different experimental conditions [9] and for another system ((NH4)2SO4–H2O system) [15]. Although a large scatter can be seen, all the data lie roughly on the line of Eq. (6). Therefore, Eq. (6) can be used as a rule of thumb for determining the seed amount when there is no information available on seeding. Some of the data for a seed size of 41.5 mm are seen, in Fig. 6, to deviate below the line of Eq. (6). This is probably due to the decrease in the number of seed crystals caused by agglomeration among them. 4.5. Effect of temperature profile—a typical result of 2-stage cooling experiment The effect of temperature profile is examined in an additional experiment. The temperature was lowered in two stages (see Fig. 2). The size distribution is compared with that obtained for
Fig. 5. Seed chart for cooling crystallization of (NH4)Al(SO4)2.12H2O from aqueous solution. Data are compared with those of the KAl(SO4)2–H2O system. (K: 2-stage cooling).
lines drawn in this figure are the corresponding values obtained for the KAl(SO4)2–H2O system previously [9] (the original data shown already in Fig. 1). The data obtained for the (NH4)Al(SO4)2–H2O system are seen to be close to the dotted line for each corresponding seed size. The critical seed loading ratio C*s does not seem basically to depend on the material and also the crystallizer used (except for the data of 41.5 mm seeds). The reason for this is not clear at the present time. However, it could be explained as follows. Crystallization proceeds in growth-dominant mode around the critical seed loading ratio C*s due to lowered supersaturation caused by the growth of enough seeds. Crystal growth is not affected significantly by the geometry of crystallizer and stirrer speed, compared to secondary nucleation. The ideal growth line is the general relation that does not depend C*s may be considered to behave similarly. As for the case of 41.5 mm seeds, the values of Lp/Ls are shifted to above the ideal growth line at higher seed loading ratios. This is
Fig. 6. The relation between the critical seed loading ratio C*s and seed size Ls. Data for the KAl(SO4)2–H2O system [9] include those from different volume crystallizers and different cooling conditions. Data of the (NH4)Al(SO4)2–H2O system (this study) are obtained with a crystallizer of 2.3 L and those of the (NH4)2SO4–H2O system [15] with a crystallizer of 1.5 L.
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of JGC corporation, Japan, is acknowledged for his comments on the manuscript.
Appendix. Remarks on our previous papers During preparing the manuscript of the present paper, we realized that there are mistakes (or contradictions) in our previous papers [5–12,18]. In the texts of the previous papers, the word of ‘‘mean mass size’’ appears many times. However, all the average sizes calculated actually were recognized, during checking the related raw data, to be volume mean size (see the text of the present paper for definition). In addition, the equation of the ideal growth line was defined previously for the polydispersed seed crystals with a mean volume size Ls. Instead, in this paper it was newly defined for the mono-dispersed seed crystals of size Ls. This alteration does not bring any change in the form of the equation of ideal growth.
Fig. 7. Comparison of crystal size distributions obtained from single- and 2-stage cooling experiments.
the single-stage cooling in Fig. 7. The crystal size distribution is narrower than that obtained with the single-stage cooling. The position of the peak is nearly the same. The volume mean size of the product was smaller as already shown in Fig. 5 on the seed chart (K). A reason for the decreased volume mean size is probably less agglomeration of the seed crystals. A reason for the narrowed size distribution is less generation of secondary nuclei. Less agglomeration and less secondary nucleation are both caused by lower transient supersaturation. Although the transient supersaturation was not measured in this study, it is expected to have been lowered with multi-stage cooling as observed in a previous study [18] for the KAl(SO4)2–H2O system. Acknowledgements Dr. N. Doki, associate professor at Department of Chemical Engineering, Iwate University, is greatly appreciated for his support for the experimental work in this study. Mr. M. Kobari
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