Ind. Eng. Chem. Res. 1999, 38, 2803-2808
2803
Crystallization Kinetics of Calcium Lactate in a Mixed-Suspension-Mixed-Product Removal Crystallizer Z. Chemaly,† H. Muhr,‡ and M. Fick*,† Laboratoire des Sciences du Ge´ nie Chimique, CNRS, ENSAIA, 2 avenue de la Foreˆ t de Haye, 54505 Vandoeuvre Cedex, France, and ENSIC, 1 rue Grandville, 54001 Nancy Cedex, France
Continuous crystallization of calcium lactate pentahydrate was investigated in a mixedsuspension-mixed-product removal crystallizer. Wide ranges of the mean residence time, relative supersaturation, and magma density were covered (40-215 min, 0.01-1.12, and 2-65 kg/m3, respectively). Crystal growth was found to be dependent on crystal size. The Abegg, Stevens, and Larson model and the Mydlarz and Jones model were tested for the determination of the kinetics parameters from experimental results. Zero-size and larger size crystal growth rate values were found to be on the order of 10-13 and 10-8 m/s, respectively. A first-order growth kinetics resulted for both large and small crystals. Nucleation rate values were very high (≈10131015 no./m3‚s). Nucleation kinetics could not be described by a unique power law equation because two different nucleation mechanisms appeared to control crystallization at low and high residence times, respectively. Introduction Lactic acid is the most widespread occurring hydroxy acid. It is used in a very large range of applications in industrial, food, cosmetic, medical, and pharmaceutical fields.1,2 An important expansion opportunity for this acid is as an intermediate for lactic acid polymers manufacturing. These polymers, called PLA [poly(lactic acid)], are biodegradable thermoplastics, and they are becoming of great worldwide importance with the increasing interest for environmental-preserving products.3-5 Lactic acid is often produced in its salt form. One of the most widely used salts is calcium lactate. It is prepared by neutralization of lactic acid with calcium carbonate or calcium hydroxide. In pharmaceutical applications, it is mainly used in calcium deficiency therapies in humans and animals for bone mineralization and growth6 and as an antitartar agent in toothpastes. In food industry, calcium lactate is generally recognized as safe (GRAS) as a food ingredient. It is used as a firming agent, flavor enhancer, flavoring agent or adjuvant, leavening agent, nutrient supplement, and stabilizer and thickener.7 It is also used as an antibacterial agent.8 Calcium lactate recovery and purification by crystallization could be an economical and efficient process, provided optimal design and operation are determined. This could be achieved by use of the mixed-suspension-mixed-product removal (MSMPR) crystallization concept developed by Randolph and Larson in 1971. This method allows simultaneous determination of crystallization kinetics, i.e., nucleation and growth rates from a continuous crystallizer through the analysis of crystal size distribution (CSD). MSMPR crystallization of calcium lactate does not appear in the literature. This could have two explanations: * To whom correspondence should be addressed. E-mail:
[email protected]. Tel: (33) 3 83 59 58 01. Fax: (33) 3 83 59 58 04. † ENSAIA. ‡ ENSIC.
(1) Continuous calcium lactate crystallization is not performed at industrial scale. (2) More generally, academic crystallization studies mostly deal with inorganic compounds, for which crystallization is more easily performed than with organic compounds.9 The aim of the present study is to investigate the crystallization kinetics of pure calcium lactate pentahydrate in a continuous MSMPR crystallizer. The mean residence time of the crystallizer was varied, covering a wide range. Because calcium lactate pentahydrate presented “size-dependent” growth, estimation of kinetics was effected using two different size-dependent growth models. Theory The population balance equation in an MSMPR crystallizer operating at steady-state without crystal attrition nor agglomeration is
d(Gn) n )dL τ
(1)
G is the linear growth rate, τ is the residence time, and n0 is the population density at zero size. Integration of eq 1 for size-independent growth (G(L) ) constant) gives
(
n ) n0 exp -
L Gτ
)
(2)
In this case, graphical determination of n0 and G is an easy task by plotting log n vs L. When the growth is size-dependent, the semilog n vs L plot shows a curve instead of a straight line, i.e., violates McCabe’s ∆L law. This curve sometimes occurs only at the small sizes and sometimes at the overall size range. Many systems were found to exhibit such an anomalous growth: potassium sulfate,10-12 potassium alum,13 potassium carbonate,14 glutamic acid,15 and others. Note that the curvature occurrence is not restricted to size-dependent growth
10.1021/ie9806904 CCC: $18.00 © 1999 American Chemical Society Published on Web 05/29/1999
2804 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999
and may result from other processes such as growth dispersion, crystal attrition, agglomeration, etc. A number of empirical crystal growth correlations have been developed to characterize size-dependent growth. They are mentioned by Mydlarz and Jones.16,17 Two of these models are retained here and compared: a power-law function model developed by Abegg, Stevens and Larson, called the ASL model,18-20 and an exponential-law function model developed by Mydlarz and Jones in 1993, called the MJ3 model by the authors.21-23 It is called the MJ model in this paper. These models comprise summary mechanisms rather than a single one, including size-dependent growth, growth dispersion, and agglomeration.24 The two models are described herein. ASL Model. The growth rate expression of this model is
(
G ) G0 1 +
)
L G0τ
b
b 0, c * 0 (5)
where Gm is the growth rate of the largest crystals and a and c are empirical parameters. The crystal size distribution is then derived to be
n ) K exp(aL)[A exp(aL) - 1](-1-b)/b
(6)
with
K ) n0(A - 1)(1+b)/b A ) exp(ac) b ) aτGm In this model, G0 can be obtained by setting L ) 0 in eq 5. Determination of G0 by either model allows the calculation of the zero-size nucleation rate from the equation
B0 ) n0G0
Figure 1. Experimental setup.
(7)
Experimental Section Calcium lactate used for the feed preparation is a pharmaceutical-grade white powder (Sigma) with a purity content of 99.5%. Solutions were prepared by dissolving the powder in pure water. The experimental setup is shown in Figure 1. It consisted of a small jacketed glass MSMPR crystallizer. Its internal diameter was 80 mm and its height 100 mm. The active volume was fixed at 300 mL. Cooling was controlled by circulating water from a thermostated bath into the crystallizer jacket. The bath temperature was kept within (0.1 °C. Agitation was provided by a three-blade
Figure 2. Typical experimental population density plot.
marine-type propeller (diameter 40 mm). A peristaltic pump was used to carry the feed into the crystallizer. The feed piping was wrapped in a heating ribbon to avoid crystallization in the feed line. Withdrawal was carried out through a peristaltic pump working intermittently at high flow rate. The crystallizer was operated to reach steady state, which was found to be assured after at least 20 residence times (τ). This period exceeds what is normally seen in the literature for other systems (usually 10-15 τ). This is probably due to a very low-rate crystallization system. Sample volumes of slurry were taken rapidly within the crystallizer to avoid crystal classification. They were then filtered. The crystal mass was washed with ethanol and air-dried to determine the suspension density. The crystal size distribution was obtained by laser light diffraction analysis (Malvern laser granulometer). The minimum size down to which the CSD was measured is 1.20 µm. The volume distribution was then transformed to population density. Solution concentrations were determined by using a high-performance liquid chromatograph (Waters). Crystallizer was seeded with calcium lactate crystals. Seed crystals were prepared by cooling the calcium lactate solution in flasks for several days. The operating conditions were carried out over the following ranges: crystallization volume (mL) residence time (min) relative supersaturation σ magma density (kg/m3) temperature (°C) agitation speed (rpm)
300 40-215 0.01-1.12 2-65 15 400
Results and Discussion Crystal Size Distributions. A typical experimental population density plot is given in Figure 2. The plot deviates from the ideal MSMPR theory especially at the smaller sizes. This indicates that the crystal growth rate is not constant. For all runs, the population density plot shows a considerable curvature followed by a quasilinear decrease.
Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2805 Table 1. Kinetics Parameters Obtained by the Two Models Abegg, Stevens, and Larson model τ (min) 40 43 50 55 60 66 70 85 105 150 188 215
Mydlarz and Jones model
b
G0 (m/s)
n0 (no./m3‚m)
B0 (no./m3‚s)
0.87 0.85 0.88 0.86 0.89 0.91 0.88 0.87 0.89 0.87 0.90 0.87
5.58 × 3.11 × 10-11 2.69 × 10-11 3.99 × 10-11 2.22 × 10-11 1.19 × 10-11 1.87 × 10-11 1.75 × 10-11 2.63 × 10-12 3.89 × 10-12 1.38 × 10-12 9.84 × 10-13
5.34 × 1.44 × 1023 6.58 × 1022 4.33 × 1021 6.93 × 1021 1.89 × 1022 1.88 × 1022 3.62 × 1022 3.80 × 1023 6.68 × 1023 2.10 × 1024 3.96 × 1024
2.98 × 4.47 × 1012 1.77 × 1012 1.73 × 1011 1.54 × 1011 2.25 × 1011 3.53 × 1011 6.33 × 1011 1.00 × 1012 2.60 × 1012 2.94 × 1012 3.90 × 1012
10-11
1022
1012
a (m-1) 3248 3247 3402 2759 2719 2760 2633 2819 3200 3209 3217 3103
b
c (m)
G0 (m/s)
Gm (m/s)
n0 (no./m3‚m)
B0 (no./m3‚s)
0.52 0.47 0.54 0.49 0.51 0.59 0.50 0.49 0.50 0.52 0.50 0.46
3.08 × 3.08 × 10-9 2.94 × 10-9 3.62 × 10-9 3.67 × 10-9 3.62 × 10-9 3.80 × 10-9 3.55 × 10-9 3.12 × 10-9 3.11 × 10-9 3.11 × 10-9 3.22 × 10-9
6.67 × 5.61 × 10-13 5.29 × 10-13 5.38 × 10-13 5.21 × 10-13 5.34 × 10-13 4.52 × 10-13 3.38 × 10-13 2.48 × 10-13 1.80 × 10-13 1.38 × 10-13 1.16 × 10-13
6.66 × 5.60 × 10-8 5.29 × 10-8 5.38 × 10-8 5.21 × 10-8 5.34 × 10-8 4.52 × 10-8 3.38 × 10-8 2.48 × 10-8 1.80 × 10-8 1.38 × 10-8 1.16 × 10-8
2.77 × 3.40 × 1027 1.48 × 1027 3.19 × 1026 2.94 × 1026 2.43 × 1026 4.20 × 1026 1.25 × 1027 4.60 × 1027 1.12 × 1028 1.52 × 1028 3.06 × 1028
1.85 × 1015 1.91 × 1015 7.82 × 1014 1.72 × 1014 1.53 × 1014 1.31 × 1014 1.90 × 1014 4.23 × 1014 1.14 × 1015 2.02 × 1015 2.10 × 1015 3.56 × 1015
10-9
10-13
10-8
1027
Table 2. Sum of Least-Squares Values τ (min) 40
43
50
ASL MJ
10.94 4.51
6.49 1.24
1.6 1.41
ASL MJ
15 8.11
10.83 3.55
25.16 6.39
55
60
105
150
188
215
Sum of Least-Squares Values for Small Sizes ( 1) and sharply decreases with decreasing σ. High kinetic orders generally occur in precipitation and salting out systems where primary nucleation is dominating.9 However, secondary nucleation was found to be also strongly dependent on supersaturation in some systems as magnesium sulfate heptahydrate34 and citric acid.35 Wang et al. experimentally excluded the occurrence of primary nucleation in their crystallization. They (and others) also demonstrated that a high supersaturation was needed for nuclei survival. It is obvious that the negative exponent in eq 12 is suspect because the nucleation rate is expected to increase with increasing supersaturation. A negative value can be expected when the mechanism of contact microabrasion is controlling nucleation. In this case, the nucleation rate does not depend on the supersaturation anymore but mainly on the suspension concentration (first to second power) and on the mean residence time.34 As the residence time increases, however, the supersaturation decreases. Depending on the relative influ-
(13)
The exponent of 1.70 on the suspension density points toward crystal-crystal collisions rather than crystalstirrer or crystal-crystallizer collisions (j ) 1) as the source of nucleation.38,39 In most systems, a first-order dependence of the nucleation rate on the magma density is found.9,15,40 In dilute suspensions, crystal-crystal collisions appear to have no effect on nucleation,41 but this mechanism probably predominates at high magma densities because it is proportional to the crystal concentration.42 This is in accordance with the present results where fragmentation appears only after reaching a relatively high magma density. Conclusions Cooling crystallization of calcium lactate pentahydrate was performed in a MSMPR crystallizer over a wide range of supersaturation. The high mean residence time values as well as the time needed to reach steady state within the crystallizer indicated a very slow crystallization process. It was found that LaCa‚5H2O shows a size-dependent growth rate for small crystal size (up to nearly 50 µm) followed by a quasi-independence. Two models have been investigated for the estimation of crystallization kinetics. For the present work, the MJ model was found to better fit experimental results than the ASL model. A first-order growth kinetics resulted for both small and large crystals. At low residence times, the nucleation rate was strongly dependent on supersaturation, while at high residence times, the nucleation rate appeared to be controlled by a contact microabrasion mechanism due to crystalcrystal collisions. This leads to the conclusion that the nucleation process should be treated with extreme caution: a global interpretation is not always judicious, and extrapolation of the power law could lead to erroneous results when several consecutive mechanisms occur during crystallization operation. Nomenclature a, b, c ) parameters of size-dependent growth models K, A ) parameters of the MJ growth model (eq 6) B0 ) zero-size nucleation rate or nucleation rate of nuclei (no./m3‚s) c ) bulk concentration of solute (kg/m3) c* ) saturation concentration (kg/m3) G ) linear growth rate (m/s) G0 ) zero-size growth rate or growth rate of nuclei (m/s) Gm ) largest crystal growth rate (m/s) k ) empirical constant L ) crystal size (m) L50 ) volumic crystal mean size (m) M ) magma density (kg/m3) n ) population density (no./m3‚m) n0 ) zero-size population density or population density of nuclei (no./m3‚m)
2808 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 τ ) mean residence time (min) σ ) relative supersaturation c/c* - 1
Literature Cited (1) Vickroy, T. B. Lactic Acid. In Comprehensive Biotechnology; Moo Young, M., Ed.; Pergamon Press: Oxford, U.K., 1985; Vol. 3, p 761. (2) Litchfield, J. H. Microbiological Production of Lactic Acid. Adv. Appl. Microbiol. 1996, 42, 45. (3) Lipinsky, E. S.; Sinclair, R. G. Is Lactic Acid a Commodity Chemical? Chem. Eng. Prog. 1986, Aug, 26. (4) Andreopoulos, A. G.; Theophanides, T. Degradable Plastics: A Smart Approach to Various Applications. J. Elastomers Plast. 1994, 26, 308. (5) Datta, R.; Tsai, S.-P.; Bonsignore, P.; Moon, S.-H.; Frank, J. R. Technological and Economic Potential of Poly(Lactic Acid) and Lactic Acid Derivatives. FEMS Microbiol. Rev. 1995, 16, 221. (6) Tsugawa, N.; Okano, T.; Higashino, R.; Kimura, T.; Oshio, Y.; Teraoka, Y.; Igarashi, C.; Ezawa, I.; Kobayashi, T. Bioavailability of Calcium Carbonate, DL-Calcium Lactate, L-Calcium Lactate, and Powdered Oyster Shell Calcium in Vitamin DDeficient or -Replete Rats. Biol. Pharm. Bull. 1995, 5, 677. (7) Code of Federal Regulations, Food and Drugs Administration. Calcium Lactate; Title 21, 184.1207; U.S. Government Printing Office: Washington, DC, 1997. (8) Shelef, L. A.; Potluri, V. Behaviour of Foodborne Pathogens in Cooked Liver Sausage Containing Lactates. Food Microbiol. 1995, 12, 221. (9) Garside, J.; Shah, M. B. Crystallization Kinetics from MSMPR Crystallizers. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 509. (10) Randolph, A. D.; Cise, M. D. Nucleation kinetics of the Potassium Sulfate-Water System. AIChE J. 1972, 18, 798. (11) Garside, J.; Mullin, J. W.; Das, S. N. Growth and Dissolution of Potassium Sulfate in an Agitated Vessel. Ind. Eng. Chem. Fundam. 1974, 13, 299. (12) White, E. T.; Bendig, L. L.; Larson, M. A. The Effect of Size on the Growth Rate of Potassium Sulfate Crystals. AIChE Symp. Ser. No. 153 1976, 72, 41. (13) Rousseau, R. W.; Woo, R. Effects of Operating Variables on Potassium Alum Crystal Size Distribution. AIChE Symp. Ser. No. 193 1980, 76, 27. (14) Skrtic, D.; Sangl, R.; Kind, M.; Mersmann, A. Continuous Crystallization of Potassium Carbonate. Chem. Eng. Technol. 1989, 12, 345. (15) Tai, C. Y.; Shei, W.-L. Crystallization Kinetics and Product Purity of R-Glutamic Acid Crystal. Chem. Eng. Commun. 1993, 120, 139. (16) Mydlarz, J.; Jones, A. G. On Numerical Computation Of Size-Dependent Crystal Growth Rates. Comput. Chem. Eng. 1989, 13 (8), 959. (17) Mydlarz, J.; Jones, A. G. On Modelling The Size-Dependent Growth Rate Of Potassium Sulphate in an MSMPR Crystallizer. Chem. Eng. Commun. 1990, 90, 47. (18) Abegg, C. F.; Stevens, J. D.; Larson, M. A. Crystal Size Distributions in Continuous Crystallizers when Growth Rate is Size Dependent. AIChE J. 1968, 14, 118. (19) O’Dell, F. P.; Rousseau, R. W. Magma Density and Dominant Size for Size Dependent Crystal Growth. AIChE J. 1978, 24, 738. (20) Rousseau, R. W.; O’Dell, F. P. Moments of Crystal Size Distributions in Systems with Selective Crystal Removal or Size Dependent Crystal Growth. Chem. Eng. Commun. 1980, 6, 293. (21) Mydlarz, J.; Jones, A. G. On The Estimation of SizeDependent Crystal Growth Rate Functions in MSMPR Crystallizers. Chem. Eng. J. 1993, 53, 125.
(22) Mydlarz, J.; Jones, A. G. An Assessment of MSMPR Crystallization Kinetics Data for Systems Modelled by SizeDependent Crystal Growth Functions. Chem. Eng. J. 1994, 55, 69. (23) Mydlarz, J.; Briedis, D. Modeling of Crystal Size Distribution in a Mixed Suspension Mixed Product Removal Crystallizer when Growth is Size Dependent. Sep. Technol. 1993, 3, Oct, 212. (24) Mersmann, A. Crystallization Technology Handbook; Marcel Dekker: New York, 1995. (25) Randolph, A. D.; Larson, M. A. Theory of Particulate Processes, 2nd ed.; Academic Press: New York, 1988. (26) Qian, R. Y.; Fang, X. S.; Wang, Z. K. Supersaturation and Crystallization Kinetics of Potassium Chloride. Ind. Eng. Chem. Res. 1989, 28, 844. (27) Kirwan, D. J.; Feins, I. B.; Mahajan, A. J. Crystal Growth Kinetics of Complex Organic Compounds. In Crystal Growth of Organic Materials Proceedings; Myerson, A. S., Green, D. A., Meenan, P., Eds.; American Chemical Society: Washington, DC, 1996. (28) Canning, T. F. Interpreting Population Density Data From Crystallizers. Chem. Eng. Prog. Symp. Ser. No. 110 1971, 67, 74. (29) Garside, J.; Jancic, S. J. Growth and Dissolution of Potash Alum Crystals in the Subsieve Range. AIChE J. 1976, 22, 887. (30) Bravi, M.; Mazzarotta, B. Size Dependency of Citric Acid Monohydrate Kinetics. Chem. Eng. J. 1998, 70, 203. (31) Garside, J.; Phillips, V. R.; Shah, M. B. On Size-Dependent Crystal Growth. Ind. Eng. Chem. Fundam. 1976, 15 (3), 230. (32) Liu, S. T.; Nancollas, G. H. The Kinetics of Crystallization and Dissolution of Barium Oxalate Dihydrate and Cadmium Oxalate Trihydrate. J. Inorg. Nucl. Chem. 1976, 38, 515. (33) Nyvlt, J.; So¨hnel, O.; Matuchova`, M.; Broul, M. The Kinetics of Industrial Crystallization; Elsevier: Amsterdam, The Netherlands, 1985. (34) Sung, C. Y.; Estrin, J.; Youngquist, G. R. Secondary Nucleation of Magnesium Sulfate by Fluid Shear. AIChE J. 1973, 19, 957. (35) Wang, M.-L.; Huang, H.-T.; Estrin, J. Secondary Nucleation of Citric Acid due to Fluid Forces in a Couette Flow Crystallizer. AIChE J. 1981, 27, 315. (36) Bennett, R. C.; Van Buren, M. Commercial Urea Crystallization. Chem. Eng. Prog. Symp. Ser. No. 95 1969, 65, 44. (37) Lodaya, K.; Lahti, L. E.; Jones, M. L. An Investigation into the Nucleation Kinetics of Urea Crystallization in Water by Means of Crystal-Size Distribution Analysis. Ind. Eng. Process Des. Dev. 1977, 16 (3), 294. (38) Ottens, E. P. K.; de Jong, E. A Model For Secondary Nucleation in a Stirred Vessel Cooling Crystallizer. Ind. Eng. Chem. Fundam. 1973, 12 (2), 179. (39) Evans, T. W.; Sarofim, A. F.; Margolis, G. Models of Secondary Nucleation Attribuable to Crystal-Crystallizer and Crystal-Crystal Collisions. AIChE J. 1974, 20, 959. (40) Jones, A. G.; Budz, J.; Mullin, J. W. Crystallization Kinetics of Potassium Sulfate in an MSMPR Agitated Vessel. AIChE J. 1986, 32, 2002. (41) Synowiec, P.; Jones, A. G.; Ayazi Shamlou, P. Crystal Break-Up in Dilute Turbulently Agitated Suspensions. Chem. Eng. Sci. 1993, 48, 3485. (42) Pohlish, J.; Mersmann, A. The Influence of Stress and Attrition on Crystal Size Distributions. Chem. Eng. Technol. 1988, 11, 40.
Received for review November 2, 1998 Revised manuscript received April 7, 1999 Accepted April 13, 1999 IE9806904
