Ind. Eng. Chem. Res. 2007, 46, 1277-1285
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Pilot Plant Investigation on the Kinetics of Dextrose Cooling Crystallization Mariapaola Parisi,* Alessandra Terranova, and Angelo Chianese Department of Chemical Engineering, Sapienza UniVersity of Rome, Via Eudossiana 18, 00184 Rome, Italy
This paper deals with an experimental study aimed at determining the kinetic expressions of both crystal growth and dextrose monohydrate nucleation from industrial aqueous solutions, containing polysaccharides as the main impurities. First, investigations at the bench scale were performed to evaluate the exponents of the kinetic power law expressions of both crystal growth and nucleation rates by specifically oriented experiments, and then, a pilot scale crystallizer was operated on an industrial site to determine the overall crystallization kinetics under industrial operating conditions. A simulation model was then implemented by using the gPROMS package both to interpret the experimental results and to obtain three kinetic coefficients of crystal growth and nucleation rates, adopted as adjusting parameters. The model allowed a satisfactory prediction of both the crystal size distributions (CSDs) and the dextrose concentration profiles. A weak correlation among the adjusting parameters was ascertained. 1. Introduction Dextrose monohydrate (DX) is one of the most widely used sugar compounds. It is mainly produced by crystallization of the syrup obtained from the hydrolysis of cornstarch. Since its solubility greatly decreases with temperature, cooling crystallization is generally adopted. The crystallizer residence time is very high due to slow crystal growth kinetics. The crystallization process can be performed either in batch or in continuous mode, always by seeding.1 The secondary nucleation by the catalytic mechanism is quite high, thus playing an important role in the crystal size distribution (CSD) of the final product.2 In spite of the great industrial importance of this product, very few experimental works on the crystal growth kinetics are present in the literature.2-7 Maltose and maltotriose, that is, the main impurities contained in the syrup, strongly affect crystal growth. This is a very important process factor, since the overall polysaccharides’ concentration greatly varies throughout a crystallization batch process, typically from a few mass percentages of up to 20%. No extensive work in the literature exists on DX nucleation; however, it is known that the metastable zone width is quite large.2,6 The mechanism of secondary nucleation was also studied by Elankovan and Berglund7 who investigated the nature and the behavior of contact nuclei for the DX-water system. They concluded that contact nuclei are produced by means of both breakage and catalytic mechanisms and that they exhibit growth rate dispersion. Finally, the tendency of fines crystals to stick over the coarse ones makes it more difficult to determine the CSD and to interpret the particles system behavior in terms of population balance. In conclusion, the prediction of the performance of an industrial DX crystallizer appears to be a difficult task on the basis of the literature, particularly if we consider the several, complex phenomena occurring simultaneously in a crystallizer, that is, different growth rates for the different crystal faces, nucleation by catalytic mechanism and by breakage, crystal agglomeration, etc. Moreover, it has to be pointed out that to study all of the above crystallization phenomena in detail takes too long with respect to the time available for an industrial research project. * To whom correspondence should Tel.: +39-06-44585158. Fax: E-mail:
[email protected].
be addressed. +39-06-4827453.
The main aim of this work is to describe a two-stage investigation carried out to determine the kinetic data useful for predicting crystallizer behavior in a reasonable period of time. The proposed approach8,9 is based on the consideration that when a power law is adopted to express the crystal growth and nucleation rates as functions of relative supersaturation, the exponents are dependent only on the involved kinetic mechanisms regardless of the apparatus geometry and scale, whereas the kinetic coefficients are affected by both the operating conditions and the crystallizer configuration. Accordingly, the two-stage research work was planned as follows. First, nucleation and mass growth rates were separately investigated at the bench scale to obtain the nucleation and growth rate exponents. Then, a pilot scale crystallizer, with a similar geometry with respect to the column industrial crystallizer, was operated in batch mode on the industrial site and by using the industrial feed stream slurry in order to determine kinetic coefficients which can be applied at the industrial scale. The results obtained from the pilot crystallizer were interpreted by means of a simulation model to evaluate the relative importance of the different crystallization phenomena and to determine the kinetic coefficients, adopted as adjusting parameters. In this paper, the investigations on the kinetic studies at the bench scale are briefly reported, by referring to previous papers for the details, whereas the research work on the pilot crystallizer and the modeling approach to determine the crystallization kinetics are carefully described. 2. Part I: Fundamental Investigations 2.1. Solubility Measurements. The solubility data of DX in pure aqueous solutions are reported in the literature by some authors.3,10 In this work, the effect of maltose and maltotriose on the DX solubility was investigated. The solubility point was detected by the technique based on the last crystal dissolution at a fixed temperature. In particular, the following procedure was applied. Fixed amounts of DX crystals and water were put in contact and heated initially at a relatively high rate and, then, progressively more slowly. The temperature corresponding to the disappearance of the crystals gave a rough estimation of the solubility point. The solution temperature was then increased by 5 °C, and the solution was maintained at such a temperature for a couple of hours to ensure
10.1021/ie060425f CCC: $37.00 © 2007 American Chemical Society Published on Web 01/24/2007
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Figure 2. Induction time vs supersaturation. Figure 1. DX solubility in the presence of impurities.
the complete dissolution of crystals and to stabilize the solution. Finally, the solution was cooled down to 2 °C below the estimated solubility point and a few dextrose crystals were seeded. To carefully determine the solubility, the temperature was again raised at a very low rate, equal to 0.01 °C/min, until the last crystal was dissolved. The solid disappearance was detected by sight. Solubility was measured in the DX concentration range between 45 and 70% by weight (bw) and at the overall polysaccharides’ impurity content in the range 0.4-12.9% bw of dry substance. By HPLC analysis, a ratio between maltose and maltotriose of around 3 was measured; however, it was proven that this ratio does not significantly affect the DX solubility in the investigated range. In particular, the behaviors of the industrial solution and the synthetic mixture were compared and no meaningful difference was detected for an overall impurity level equal to 7%. The DX solubility in the presence of such polysaccharides as impurities was well fitted by the equation:
wDX eq ) 0.00650‚T[°C] + 0.343 - 0.466
(
wi wi + wDX
)
according to van der Leeden et al.,12 the nucleation of DX crystals generated by the growth of the crystallites swept away from the seeded crystal surface into the solution. Since the induction time is inversely proportional to the nucleation rate, the nucleation exponent for the catalytic mechanism was assumed to be equal to 3, that is
(1) B ) knσ3
where wDX and wi are the mass fractions of dextrose and impurities in solution, respectively. The solubility experimental data obtained for the synthetic mixtures and the industrial solution and the fitting curves are compared in Figure 1. 2.2. Nucleation. As mentioned above, the DX crystallization is industrially operated by using a feed stream slurry; thus, primary nucleation was not investigated. In the preliminary work at the bench scale, only the kinetic rate of secondary nucleation by the catalytic mechanism was considered. In order to determine the nucleation rate exponent, induction time experiments were carried out by seeding 3-4 large crystals in a supersaturated solution and by detecting the elapsed time at which nucleation took place2 by sight or by nephelometry. Since DX crystals are quite fragile and prone to breakage,11 the presence in the examined solutions of fragments generated by the seeded crystals was carefully checked. During some test runs, several samples of solution were withdrawn and observed under a microscope and the absence of fragments, among the generated crystals, was ascertained. In Figure 2, the log-log plot of the observed induction times against the applied supersaturation is shown. The best fitting of the data (correlation index 0.990) was given by the following relationship:
tind[s] ) 39.2‚σ-3
Figure 3. Mass increases per unit surface and per unit supersaturation at different impurities contents.
(2)
The power law dependence of the nucleation induction time on supersaturation was justified by Parisi et al.,2 which considered,
(3)
2.3. Crystal Growth. The mass growth rate of DX crystals in the presence of impurities was investigated. The adopted method was to measure the increase of crystal mass by operating a stirred tank cooling crystallizer, 1 L in capacity, in batch mode. Batch crystallization runs were performed by seeding crystals in a close size range. The impurities content was in the range 0.6-20.0% bw of dry substance. The experimental procedure is described in detail elsewhere.5 The main achieved results may be summarized as follows: • In the investigated size range, i.e., for the second crystal dimension between 106 and 250 µm, the average value of the growth rate does not significantly depend on crystal size. • The mass DX crystal growth is proportional to supersaturation, according to experimental results recently reported by Srisa-nga et al.6 • The resistance of the growth surface integration step is 1 order of magnitude higher than that of the diffusion step of DX from the solution bulk toward the crystal surface at a gentle stirring rate applied either at the bench or pilot scale. • The examined impurities decrease the DX growth rate. In Figure 3, the mass increases per unit surface and per unit supersaturation is plotted for 3 series of runs carried out at 35 °C for impurity mass percentages of 0.6, 10, and 20%. In particular, the presence of 20% impurities reduces the growth rate 2-3 times with respect to the value in pure solution. • A series of runs was performed to make a comparison between the behavior of the adopted synthetic solutions and
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Figure 4. Determination of the activation energy from runs at different temperatures.
the industrial one, at an overall impurity content of 7% bw. The same growth rate coefficient was measured in both cases. In the simulation model, the linear growth rate with respect to the second dimension was adopted. To evaluate the linear crystal growth G, from the mass growth rate RG, in terms of the mass of crystals per unit crystal surface and unit time, the following well-known equation was used:
Figure 5. Adopted pilot scale apparatus.
component
% bw
RGkS G) 3kvFcryst
dextrose maltose maltotriose higher oligomers others (fructose)
92.90 3.50 1.15 1.95 0.45
(4)
The volume and surface shape factors of the DX crystals, kv and ks, respectively, were derived from image analysis, and their relationships as a function of the second crystal dimension, L, were determined. In eq 4, both the shape factors ks and kv depend on the second crystal dimension; however, since their ratio is a very weak function of L, the linear growth rate is almost proportional to the mass growth rate. A growth rate exponent equal to one was also adopted for the linear growth kinetics, that is:
( )
G ) kG exp -
Ea σ RT
(5)
where T is the temperature in kelvin, R is the gas constant, and Ea is the energy of activation. From a series of experimental runs carried out in the temperature range of interest for the industrial crystallization, i.e., 30-45 °C, an activation energy equal to 30 500 J/mol was determined (see Figure 4). For the sake of simplicity, an average value of the growth rate was always considered, regardless of the significant DX crystals growth rate dispersion. Finally, the effect of the polysaccharides as impurities on the growth rate coefficient was expressed as a function of the polysaccharide fraction of the overall dry substance in solution, i.e., wi/(wi + wDX): this ratio is the measurement of the polysaccharides content given by HPLC analysis. To account for the impurities effect, the following empirical equation was chosen:
(
kG ) kpure 1 - knd
wi wi + wDX
)
(6)
The product of the polysaccharides fraction and the coefficient knd must always be lower than 1 to give a physical meaning to eq 6. In the present work, an impurity content up to 20% is considered, and thus, the value of the empirical coefficient knd must be lower than 5. However, it is important to stress the
Table 1. Dry Substance Composition of the Feed Solution
empirical nature of the proposed correlation, which can be applied only in the range of the examined polysaccharides percentages. 3. Part II: Investigation on the Pilot Scale Crystallizer 3.1. Experimental Apparatus and Procedures. The adopted experimental apparatus, shown in Figure 5, was a 200-L cooling batch crystallizer, approximately 1 m in height and 600 mm in diameter. It was built on the site of an industrial DX plant. The pilot crystallizer was provided with an internal cooling coil connected to a thermostatic bath: the cooling water was maintained at a constant flow rate, while its temperature was continuously adjusted according to the required cooling curve. Three impellers gently stirred the slurry inside the crystallizer, at a rotation speed, equal to 6 rpm. In order to enhance the mixing and to avoid crystal segregation an external loop was adopted. To recirculate the slurry stream at a constant flow rate of 1.5 L/min a Mohno pump was used. Both the crystallizer and the external loop pipe were thermally insulated. The temperature of the slurry in the upper section of the crystallizer and in the external loop was measured by two thermocouples, whereas the brix number, that is, the mass ratio of dissolved sugar to water, in the mother liquor was continuously measured by a K-Patent refractometer. The signals from the thermocouples and the refractometer were continuously recorded. At the run start, the crystallizer was filled by using the slurry feed stream of the industrial crystallizer. The DX concentrations of the feed stream ranged between 63 and 65% bw. The other components were mainly maltose, maltotriose, and higher oligomers, and their overall concentration, in terms of percentage of dry substance, was between 7 and 9% bw. A typical dry substance composition, measured by HPLC analysis, is reported in Table 1. In the sugar industry, the overall concentration of dry substance in solution is generally inferred from the brix measurement by means of a correlation that depends on the
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Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007 Table 2. Main Operating Conditions and Results of the Preliminary Runsa check reproducibility breakage aRun
Figure 6. Image of a DX crystal sample under microscope.
sugar composition: since the composition of the dry substance in solution changes as the crystallization proceeds, in a preliminary investigation, it was ascertained that the influence of the impurity content on the refractometric measurement is negligible under 20% bw of polysaccharides, that is, in the whole range of interest for this investigation. The adopted experimental procedure was as follows. Before each run, the crystallizer was filled with water and preheated for a couple of hours at the fixed value of the initial run temperature. The water was then discharged, the crystallizer was filled with the slurry feed stream coming from the industrial crystallizer, and the run started. The thermostatic bath was controlled to provide a linear cooling of the crystallization process. At the beginning, and throughout each run, several samples of the slurry were withdrawn from the external loop pipe at fixed intervals of time. Each slurry sample was filtered; the collected crystals were washed with saturated ethanol and airdried, and their size distribution was measured. Several CSD measurement techniques were attempted. Sieving measurements on the dry product did not give satisfactory results because of the agglomeration of fines during the sieving operation, in spite of an upward air flow stream through the sieves. The size distribution measurement based on the laser light diffraction was also unsatisfactory. In fact, this instrument measures the size distribution of the diameter of a spherical particle with the same projected area of the examined crystals. In this case, due to the quite elongated crystal shape, the measured dimension differs quite a lot from both the first and second crystal dimensions. Moreover the measurements are affected by a remarkable error due to the fragmentation of the crystals in the measurement cell.12 Therefore, in this work, the measurements of the CSDs were carried out by the image analysis of up to 1000 crystals for each sample, by using the Quantimet analyzer supplied by LEICA. The obtained DX crystals, shown in Figure 6, exhibit a prismatic habit, with an average ratio between the first and second dimension between 3 and 4. The following procedure was applied to characterize each class of crystals. The volume shape factor kv(L) was determined, as usual, by weighing a fixed number of crystals. First of all, a sample of crystals was sieved in a close size range, washed to remove the dust adhering over the crystal surface, and then dried.
MT,0 (kg/kg)
T0 (°C)
wDX 0 (kg/kg)
MT,fin (kg/kg)
Tfin (°C)
wDX fin (kg/kg)
0.06 0.07 0.46
44.9 44.3 29.1
0.649 0.645 0.462
0.45 0.44 0.47
30.1 30.0 28.2
0.465 0.470 0.449
time: 24 h.
For each sieving class, 200 crystals were weighed by means of an analytical balance with an accuracy of (1 × 10-4 mg, that is, less than 0.2% of the measured weight. In this way, it was possible to measure the average volume of the crystals. Then, the average first and second dimensions (i.e., width and length) of the 200 crystals were measured by an image analyzer. Finally, the average value of the third dimension was estimated from the determined average volume by assuming a prismatic crystal shape: it was found that the third dimension is quite lower than the second, i.e., the ratio between the two dimensions ranged from 0.2 to 0.5. The evaluation of the three crystals dimensions allowed the estimation of the surface factor ks(L). 3.2. Experimental Results. Some preliminary runs of the pilot scale crystallizer were devoted to assessing the reproducibility of the results and to evaluating the importance of crystal breakage, respectively. Table 2 shows the operating conditions and the main results of these runs. The reproducibility was tested by adopting very close operating conditions for two runs (see Table 2). Both runs were operated by decreasing the cooling water temperature from 44 down to 30 °C in 24 h. The obtained results showed a satisfactory reproducibility. The extent of the breakage phenomena was experimentally investigated by means of a 24-h run. The adopted feed had a very high magma density, i.e., 0.46, and a very low supersaturation, equal to 0.05, in order to maximize the number of collisions between crystals and to minimize crystal growth and nucleation by the catalytic mechanism. The operating temperature was maintained between 28 and 29 °C throughout the whole run. The fines content was monitored by using a turbidimeter developed at the University of Rome,13 which measured the magma density of crystals whose second dimension is lower than 125 µm. The instrument was previously calibrated on DX slurries with an overall magma density of up to 50%. The calibration slurries were prepared with two different DX samples, containing 6 and 70% of crystals under 125 µm, respectively. The reproducibility of the measurements was also tested. A precision of (3% was reached. In Figure 7 the measured fines contents throughout the run are shown: the deviations from the initial value are negligible since they are of the same order of magnitude as the measurement error. In conclusion, since during the run the fines content did not significantly increase due to collision mechanisms, despite the high magma density, a negligible extent of breakage was considered for the adopted apparatus. Therefore it can be concluded that the dominant nucleation mechanism in the pilot scale crystallizer is the catalytic one, thus the same mechanism investigated at lab scale. After the preliminary investigation, a series of four experimental runs were performed by changing the run time, the initial magma density and the cooling rate. The main operating conditions and the obtained results are reported in Table 3. The obtained results show that the process productivity, that is the crystal mass increase, is strongly dependent on the run
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be considered, i.e., the overall mass balance and the two partial mass balances concerning DX and the impurities. Since the crystallizer works in batch mode, the mass of slurry is constant throughout each run and the overall mass balance reduces to the following:
dM )0 dt
(7)
The slurry magma density, MT, is defined as the mass fraction of solid in the slurry; thus, the mass of solution per unit mass of slurry is equal to 1 - MT. By taking into account that the crystals of DX contain 9% bw water, the mass balance of DX can be written as follows: Figure 7. Fines measurements (up to 125 µm) during the breakage preliminary run.
(1 - MT)wDX + MT‚0.91 ) (1 - MT,0)wDX 0 + MT,0‚0.91 (8) where the index “0” refers to the initial conditions. The impurities weight fraction in the crystals is very low, i.e., 0.6% bw, and it can be neglected, as a first approximation, in the impurities mass balance, which can be written as follows:
(1 - MT)wi ) (1 - MT,0)wi0
Figure 8. Relative supersaturation vs time for the four runs.
time. In fact for run B, operated over a period of 8 h, a relatively small crystal mass was produced in spite of a temperature cooling range comparable with those of the other runs and the high supersaturation attained, as shown in Figure 8. The reason why is the rather low rates of both nucleation and growth phenomena, which require a long residence time to significantly affect the produced crystal mass. As expected, the sharp increase in supersaturation during the last 3 h of run B produced a considerable amount of new nuclei: nevertheless, they did not have time to reach a significant size, and they did not affect the cumulative weight distribution. It is interesting to notice the peculiar shape of the run C supersaturation profile. The initial magma density of this run was quite low, i.e., 5%; thus during the first hours, the overall crystal surface was small and the crystal mass increase was slow. In this condition, the cooling caused an initial increase in the supersaturation, while in runs A and D, where the mass of seeds was greater and the initial crystals growth faster, the cooling was not fast enough to let the supersaturation increase. For this reason, the run C supersaturation profile exhibited a peak, while during runs A and D the supersaturation decreased from the beginning. In Figure 9A-D, the initial and final CSD for the four runs are reported. Despite the magma density increase along each run, the size distribution of the crystal products did not significantly change with respect to that of the seeding. This means that the produced mass is due more to the generated new crystals and their subsequent growth rather than to the seeded crystals growth. 3.3. Simulation Model. The model is based on the mass and the crystal population balance equations. The temperature inside the crystallizer was recorded during each run, and thus, the heat balance was substituted by the measured temperature profile.14 3.3.1. Mass Balances. The considered system is described by means of three components; thus, three mass balances can
(9)
3.3.2. Population Balance. As mentioned above, breakage plays a negligible role and the secondary nucleation by catalytic mechanism is the only significant nucleation phenomenon for the examined process. Since the agglomeration was also neglected and crystal growth is independent of crystal size, the population balance equation can be written as
∂n(L) ∂(n(L)G) )∂t ∂L
(10)
with the initial condition
n(L) ) nseed(L) for t ) 0
(11)
and the boundary condition
n(L) )
B for L ) 0 G
(12)
3.3.3. Implementation of the Model. As usual, the magma density can be calculated from the population density of the crystals, n(L), by the equation:
MT )
Fcryst Fslurry
∫0L
n(L)kv(L)L3 dL
max
(13)
where Fcryst and Fslurry are the density of the crystals and of the slurry, respectively. The DX and impurity concentrations in solution are calculated from eqs 8 and 9, respectively. The DX equilibrium concentration is calculated by means of eq 1: then, the relative supersaturation is calculated in order to determine the growth and nucleation rates. The numerical solution of the above-reported differential algebraic equation set was made by using the gPROMS solver, which is a powerful general-purpose process modeling and optimization environment, provided by Process System Enterprise Lymited.15 The population balance equations were numerically integrated by adopting a not uniform size step, increasing from 4.7 to 85.5 µm as long as the crystal size increases to reduce the computing time.
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Table 3. Operating Conditions and Results of the Experimental Runs ID
run time (h)
T0 (°C)
wDX 0 (kg/kg)
MT,0 (kg/kg)
L50,0 (µm)
Tfin (°C)
wDX fin (kg/kg)
MT,fin (kg/kg)
L50,fin (µm)
∆MT,fin (kg/kg)
A B C D
24 8 24 24
43.6 41.5 44.9 42.1
0.637 0.629 0.649 0.639
0.139 0.090 0.050 0.118
130 158 103 133
30.6 32.5 28.9 31.8
0.472 0.574 0.467 0.496
0.463 0.239 0.441 0.421
133 168 102 136
0.324 0.149 0.391 0.303
3.3.4. Identification Procedure. For each of the 4 runs, the measurements of the initial conditionsthe magma density, the dextrose and impurities concentrations in the solution, the CSD of the seedssthe overall run time and the temperature profile during the run constitute the input set. The unknown kinetic coefficients kpure, knd, and kn (see eqs 3 and 6) were assumed as adjusting parameters of the model. The optimization was performed by using the gPROMS package, which has a specific tool for the determination of the parameter set that provides the best accordance between the experimental measurements and the correspondening predicted values. The gPROMS tool determines the optimal parameter set by minimizing an objective function that takes into account the differences between the experimental and predicted values of all the available measurements: since different physical quantities may be measured and simultaneously considered in the objective function, each difference is divided by the standard deviation of the measure in order to make them all dimensionless and commensurable. When the standard deviation is the same for all the measured values, the gPROMS objective function minimization corresponds to the least-squares technique. The optimization is performed by means of the gradient method.16 The optimal set of parameters was determined by taking into account the deviations between the experimental and the simulated values of both the DX concentrations and the CSDs for the four experimental runs.
Table 4. Optimal Set of the Adjusting Parameters parameter
values
units
kpure knd kn
1.89 × 10-3 4.05 7.97 × 106
m/s # #/(m3s)
3.4. Simulation Results and Discussion. The obtained optimal values of the adjusting parameters are reported in Table 4. Since no data on the DX nucleation rate are available in the literature, the obtained nucleation rate expression could not be verified. On the contrary, the obtained growth rate expression was compared with the one proposed by Perelygin et al.4 These authors reported a mass growth rate obtained from a lab scale investigation on DX crystal growth. The mass growth rate of very large DX crystals, i.e., 500-1500 mm, was measured in the temperature range 20-45 °C. Under the operating conditions applied for the starting point of run A, i.e., σ ) 0.10 and T ) 43.6 °C, a linear growth rate equal to 1.04 × 10-9 m/s is predicted by means of eq 5, which corresponds to a mass growth rate equal to 6.4 × 10-7 (kg m2)/s. The equation proposed by Perelygin et al. predicted a 20% lower growth rate value. At lower temperatures, this underestimation is reduced, since the value of the activation energy measured by these authors, i.e., 19 950 J/mol, is considerably lower than the values measured in the present work, 30 500 J/mol, and by Srisa-nga et al.,6 50 000 J/mol. The quality of the adopted growth rate expression can also be checked in the light of the experimental results on
Figure 9. Initial and final CSD of the four runs. CSDs are measured on a weight basis.
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Figure 10. Comparison between experimental and simulated DX concentration trends.
Figure 11. Comparison between experimental and simulated final CSDs (on a weight basis).
mass growth rate reported in Figure 2. It must be taken into account that the seeds adopted in the growth mass experiments were produced in the absence of impurities, whereas the proposed expression represents the average growth rate of crystals born and grown in the presence of a high impurity
content. Since the impurities partially deactivate the crystal surfaces, the predicted growth rate should be of the same order of magnitude but lower than the one measured in the mass growth experiments. As expected, the prediction slightly underestimates the experimental value: for instance, for an
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Figure 12. 95% confidence ellipsoids of the adjusting parameters.
impurity content equal to 10%, the deviation is approximately 20%. Figure 10A-D shows the comparison between the experimental and calculated DX solute concentration profiles throughout the four runs. A very good agreement can be noticed during all the run time: the deviation between simulation and experimental concentration never exceeded 0.7%. Except for run A, the maximum deviation took place at the end of each run. The comparison between the predicted and experimental CSD profiles at the end of each run are reported in Figure 11A-D. A satisfactory comparison can be observed between the experimental measurements and the predicted distributions for all the crystal sizes. The largest deviations occur for run B: however, within the size range 50-350 µm, the deviation between experimental and predicted values never exceeds 20 µm. The sensitivity of the developed model with respect to both the kinetics parameters and the modeled operating conditions was checked. When a 20% variation is assumed for each of the 3 kinetics parameters, the model is still able to provide an acceptable estimation of both the magma densities, i.e., less than 3% deviation, and the CSDs, i.e., less than 2% deviation, of the fines content. As expected, the nucleation parameters mainly affect the CSD, while the magma density is more sensible to the variations of the growth rate parameters. Concerning the operating conditions, the amount of produced crystals is very sensitive to the variations of the initial concentration and the temperature profile: on the contrary it is only slightly affected by the variation of the initial magma densities, that mainly affect the supersaturation profile during the first hours of the run. When the supersaturation is very high, i.e., more than 0.2 at the beginning of the run, a bimodal final CSD is obtained due to the high nucleation rate, as expected. Finally, a statistical analysis on the adjusting parameters correlation was made by means of the gPROMS package. Figure 12 shows the confidence ellipsoids for the three estimated parameter couples evaluated at a confidence level equal to 95%. The only significant correlation exists for the two growth rate parameter couples, kpure and knd; however, in this case, the ellipsoid is very small. The absence of cross correlation between parameters that describe different physical phenomena is one of the most important indicators of the good quality of the model description. In conclusion, the determined kinetic parameters, in spite of their semiempirical nature, appear rather robust. Conclusion This work reports a kinetic study carried out on the crystallization of dextrose monohydrate. The kinetic relationships refer to an aqueous solution used in an industrial crystallizer; thus, they can be used in a model implemented to simulate the industrial crystallizer itself. This result was achieved by applying a double stage experimental work. First, an experimental
investigation was carried out at the bench scale in the presence of impurities to evaluate the order of both the crystal growth rate and the nucleation rate, and then, the experiments performed by using a pilot batch crystallizer allowed the determination of the kinetic coefficients of the crystallization process. This procedure seems to be suitable for obtaining in a reasonable period of time robust kinetic data on a crystallization system which can be applied at the industrial scale. Acknowledgment This work was done in the framework of the European Project Sinc-Pro (contract no. G1RD-CT-2002-00756). The authors gratefully acknowledge the grant received by the European Community. List of Symbols B ) secondary nucleation rate, #/m3 s Ea ) energy of activation, J/mol G ) linear crystal growth rate with respect to the second dimension, m/s kG ) growth rate coefficient, m/s kpure ) growth rate coefficient for pure dextrose, m/s kn ) nucleation rate coefficient, #/m3s knd ) crystal growth rate parameter ks ) surface shape factor with respect to the second dimension kv ) volume shape factor with respect to the second dimension L ) crystal second dimension, m M ) overall mass in the crystallizer, kg MT ) magma density, kg of solid/kg of slurry n ) population density function, #/(m3 of slurry m) RG ) mass growth rate, kg/(m2 of crystal surface s) t ) time, s tind ) induction time, s T ) temperature, K w ) weight fraction Fcryst ) crystals density, kg /m3 Fslurry ) density of slurry, kg /m3 σ ) relative supersaturation Additional Superscripts DX ) dextrose i ) impurities Additional Subscripts 0 ) initial fin ) final Literature Cited (1) Kirk-Othmer Encyclopedia of Chemistry and Technology, IVth edition; Wiley: New York, 1997.
Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007 1285 (2) Parisi, M.; Rivallin, M.; Chianese, A. Prediction of the Dextrose Nucleation Kinetics by the Growth Rate of Crystallites. Chem. Eng. Technol. 2006, 29 (2), 265. (3) van Hook, A. Crystallization: Theory and Practice; Reinhold: New York, 1961. (4) Perelygin, V. M.; Kryl’skii, D. V. Kinetics of crystallization of dextrose monohydrate from aqueous solutions (in Russian). IzV. Vyssh. Uchebn. ZaVed., PishcheVaya Tekhnol. 1990, 2-3, 26. (5) Chianese, A.; Parisi, M.; Terranova, A. On the Influence of Polysaccharides on Dextrose Crystallization. AIDIC Conf. Ser. 2005, 7, 49. (6) Srisa-nga, S.; Flood, A.; White, E. T. Secondary Nucleation Threshold and Crystal Growth of R-Glucose Monohydrate in Aqueous Solutions. 12th Cryst. Growth Des. 2006, 6 (3), 795. (7) Elankovan, P.; Berglund, K. A. Contact Nucleation from Aqueous Dextrose Solutions. AIChE J. 1987, 33 (11), 1844. (8) Bermingham, S. K.; Landlust, J.; Mesˇic´, S.; Tijl, P.; Kilpio, T.; Parisi, M.; Chianese, A.; Raccoli, F.; Kramer, H. J. M. Development and validation of models for optimisation and control of batch and continuous crystallization processes. Proceddings of the 2nd International Symposium on Industrial Crystallization Inspiring Powder Technology (ISICIPT), Tokyo, Nov 10, 2004; p 38. (9) Terranova, A.; Parisi, M.; Chianese, A.; Bonadonna, G.; Bermingham, S. K. Modeling and Optimal Kinetics Parameter Set Estimation for a
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ReceiVed for reView April 5, 2006 ReVised manuscript receiVed October 27, 2006 Accepted December 19, 2006 IE060425F
