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Growth behaviour of crystals formed by primary nucleation on different crystalliser scales
G.M. Westhoff*, B.K. Butler, H.J.M. Kramer, P.J. Jansens
Laboratory for Process Equipment, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, Netherlands
The growth behaviour of small ammonium sulphate crystals obtained from primary nucleation in different crystallisers were studied. The results revealed a broadening of the distribution upon growth of the crystals that is attributed to growth rate dispersion. This phenomena was somewhat more pronounced in experiments with the fines imported from a 11001 draft tube baffled crystalliser compared to those generated in a 21 cooling crystalliser. This small difference in the growth behaviour between the crystals originating from the two crystallisers, however, does not permit to reject the hypothesis that the outgrowth of the crystals originating from either primary and secondary nucleation is identical for a small and for a large-scale crystalliser. The growth behaviour of these crystals was simulated using a sizedependent growth . The simulation results revealed that the growth (Chem. Eng. Sci. 54 (1999) 1273,1283) is capable of simulating trends in the supersaturation and the median crystal size but was not able to describe the observed broadening of the crystal size distribution. r 2002 Published by Elsevier Science B.V.
Despite the fact that crystallisation is one of the oldest separation processes, the design of industrial crystallisers still poses a lot of problems. In order to achieve a predictive crystalliser , rigorous description of the crystallisation phenomena is needed taking into account the hydrodynamics and geometry of the crystalliser. In addition, a procedure is needed to derive kinetic information from laboratory scale experiments. In the ideal case the growth kinetics of the crystalline substance should be determined in a small scale laboratory crystalliser. In combination with a predictive crystallisation the crystallisation processes occurring in a large-scale crystalliser will be predicted.
One of the major hypothesis used in these crystallisation s is that the outgrowth of the crystals originating from either primary and secondary nucleation is identical for a small-scale and large-scale crystalliser under comparable operating conditions.
In this study the growth behaviour of primary nuclei of ammonium sulphate from different sources were studied. The primary nuclei were either obtained after minor outgrowth from a 11001 draft tube baffled (DTB) crystalliser and fed into a 21 batch cooling crystalliser for further outgrowth or the nuclei were directly formed in the
21 cooling crystalliser. Their growth behaviour was compared by ling of the development of the crystal size distribution with a size-dependent growth (SDG) .
The crystals, which are produced during the crystallisation process result from primary and/or secondary nucleation. Primary nucleation, can be either homogeneous or heterogeneous. In heterogeneous nucleation foreign particles, such as dust
particles, are used as substrate for nuclei. Except for precipitation processes, primary nucleation mainly occurs during the start-up phase of an unseeded crystalliser. Secondary nucleation results mainly from attrition of the parent crystals due to
external forces, such as collisions with the impeller blades [2,3]. Crystal fragments formed by secondary nucleation contain lattice strain, which is caused by the mechanical forces exerted on the crystals during the attrition process [4,5]. The presence of this lattice strain has been shown to result in growth rate dispersion (GRD), that is often mathematically described by a length-dependent growth rate function. During growth, healing occurs and the growth increases. It can easily be argued that the strain content of the fragments is related to the scale and the geometry of the crystalliser. Also primary nuclei, however, show GRD during their outgrowth. Their defect or mosaic structure could differ not only with the supersaturation during birth, but local turbulence might also play a role. It is therefore interesting to elucidate as to whether differences in scale could have an effect on their growth behaviour. The infuence of the strain in the crystal lattice on its solubility has been described by the following expression :
where Gs represents the lattice strain and L thelength of the crystal. The supersaturation Dc forthe crystal growth now equals
Note that this might even lead to dissolution of the small particles. The growth of the fines can then be described as a two-step process, consisting of a diffusion step from the bulk to the interface followed by a surface integration step. Growth defined by the increase in length L of the crystal then becomes
where kd is the mass transfer coefficient, kr thesurface integration rate constant and cs the molar concentration of the crystallising substance. There are two unknown parameters kr and Gs in the growth which must determined experimentally. The parameter (Gs) as derived by Gahn  should be a constant for a given substance.
3. Materials and method
3.1. Description of 2 l-batch cooling crystalliser
The outgrowth of ammonium sulphate fines either directly created or fed from the fines loop of the 1100 l crystalliser (see Section 3.2) was studied in a 2 l-batch cooling crystalliser. The crystalliser was equipped with a three-blade marine impeller. The stirring rate during the experiments was 500 r.p.m. The temperature of the crystalliser was controlled by a Lauda UKS 1000 thermostat water bath. The solution density was measured every 240 s with an Anton Paar mPDS 2000 density meter. The solution was .ltered over a 5 mm Millipore .lter prior to the density measurement and recirculated to the crystalliser. The density meter was kept at a temperature of 601C to prevent crystallisation during measurement. The solution concentration followed from a calibration curve. The experimental error of 10_5 kg l_1 in the density measurements gives an experimental error 0.1% in the concentration.
The temperature in the crystalliser was measured every 10 s with an F250 MK II precision thermometer. The crystalliser temperature determines the saturation concentration c_ in the crystalliser. The 0.011C accuracy of the precision thermometer gives an experimental error in the saturation concentration below 1%. The suspension was circulated through a llow cell of a Malvern (size range: 0–754.7 mm) with a hose pump (Watson– Marlow) to measure the total crystal content and the crystal size distribution on-line with a time interval of 30 s. The temperature of the solution in
the crystalliser and in the density meter, the solution density, the obscuration and the crystal size distribution were recorded.
3.2. Experimental method
The fines were either directly created in the 21 cooling crystalliser or fed into this crystalliser from the fines removal system of an evaporative 11001 continuous DTBcryst alliser shortly after the startup (process conditions: P ¼ 71 _ 104 Pa and T ¼ 501C). The system consisted of (NH4)2SO4 (DSM Technical Pure) dissolved in water. The crystalliser is described in detail by Neumann . The sampled fines were pumped directly into the 2 l cooling crystalliser, which was maintained at a temperature of 501C, and cooled with a cooling rate of 0.251Cmin_1 for 40 min. For the experiment with direct primary nucleation in the 2 l cooling crystalliser the vessel was filled with a crystal-free saturated solution (NH4)2SO4 (DSM Technical Pure) in water, saturated at 501C). A cooling profile of 0.251Cmin_1 was applied for 40 min. Primarynucleation was induced by local cooling. The crystal content during the experiments was maximal 71% (v/v) and the maximal crystal was kept below 600 mm to avoid secondary nucleation by attrition. This was checked by visible inspection of the crystals and by studying the effect of the increase of the stirring rate on the experimental results (not shown).
For the evaluation of growth rate behaviour of the fines a crystallisation  was used that was implemented in a generic crystalliser based on a compartmental approach . This crystalliser was built in gPROMS, a dynamic fow-sheeting program. The population balance is solved using a .nite volume method. The 2 l batch crystalliser was assumed to be ideally mixed, and was treated as a single compartment.
4. Results and discussion
Fig. 1 shows the development of the volume density distribution during the growth of the crystals fed from the 1100 l crystalliser. The distributions show a broadening, indicating growth rate dispersion. This can be seen more clearly in Fig. 2, which shows experimental trends of the L10; L50 and L90 for this experiment. Until t ¼ 500 s the crystals grow relatively fast, due to the high supersaturation in the beginning of the experiment, as follows from the fast increase of the quantiles. The coef.cient of variation
(CV ¼ ln (L90=L10)) of the crystal size distribution at the end of the experiment is 0.83. The measured trend in the supersaturation for this experiment is plotted in Fig. 3.
ARTICLE IN PRESS
Fig. 1. The development of the volume density distribution
during growth of .nes imported from 1100 l DTBcrystalliser.
G.M. Westhoff et al. / Journal of Crystal Growth ]
In Fig. 4 the measured trends of the L10; L50 and L90 during the outgrowth of the primary nuclei directly nucleated in the 2 l crystalliser are shown. Also here the L90_L10; which is a measure of the width of the distribution increases during the experiment. The CV at the end of this experiment is 0.81. The measured supersaturation is given in Fig. 5. The supersaturation shows a slight increase at t ¼ 7300 s, before the supersaturation decreases again. Comparison of the results of both experiments, reveals that the growth behaviour (rate of broadening of the crystal size distribution) seems to be quite similar. In both experiments a considerable broadening is observed.
Fig. 2. Measured and simulated quantiles of the crystal size
distribution during the growth of fines fed from the 1100 l DTB
Fig. 4. Measured and simulated quantiles of the crystal size
distribution during the growth of fines nucleated in the 2 l
Fig. 3. Measured and simulated supersaturation during the
growth of fines imported form the 1100 l DTB
Fig. 5. Measured and simulated supersaturation during the
growth of .nes nucleated in the 2 l cooling crystalliser
4.1. Simulation results
The two kinetic parameters (kr; Gs) were determined by using a least-squares objective
function for minimising the deviation between the predicted and measured values of the supersaturation, the quantiles L10; L50 and L90 (dynamic parameter estimation). The initial conditions of the simulation are the initial crystal size distribution, crystal density and supersaturation. The initial crystal size distribution used for the simulations was fitted from the experimental one using two log normal distributions. The simulated quantiles of the crystal size distribution during the growth of fines from the 1100 l crystalliser are given in Fig. 2. The results show a good .t of the median crystal size, whereas the simulated quantiles L10 and L90 are too high or too low, respectively. The CV at t ¼ 2500 s is in this simulation =0.43. The simulated supersaturation during this experiment is given in Fig. 3 and shows a good agreement with the experimental
results. The simulation results for the second experiments are given in Figs. 4 and 5. Again a good description of the experimental median crystal sizeis obtained. On the other side, the broadening of the distribution is again underestimated resulting in higher values for the L10 and lower values for the L90 compared to the measured quantiles. The CV at t ¼ 2500 s is in this simulation =0.46. The measured and simulated supersaturation given in Fig. 5 are also in reasonable agreement. Possible explanations for the discrepancy between the simulated and measured quantiles L10 and L90 in both experiments are growth rate dispersion or underestimation of the (secondary) nucleation. The measurements of the first size distributions are characterised by a high uncertainty due to the low crystal concentration. An error in the initial distribution can affect the simulation of the broadness of the distribution but cannot explain the deviation in the simulated and experimental results. The initial values for the crystal density and the supersaturation had only a minor effect on the simulation results.
The obtained kr values for both simulations imply that the growth of (NH4)2SO4 in the range 401CoTo501C is diffusion controlled, which is in agreement with the literature . The optimal fit for both simulations give each a somewhat different value for the parameter Gs: The determined values for Gs are slightly different from values determined for a secondary nucleation ted crystallisation process performed in a 22 l DT crystalliser . They reported values for Gs equal from 2.2_10_4 to 7.6_10_5m4 mol_1 s_1.
Growth rate experiments have been performed with fine crystals obtained from primary nucleation in a DTBevaporat ive and a 2 l cooling crystalliser. The results show a broadening of the crystal size distribution upon growth of the crystals. The broadening of the distribution that is attributed to growth rate dispersion is somewhat more pronounced in the experiment with the fines imported from the 1100 l DTBcrystall iser. The small differences in the growth behaviour between the crystals originating from the two crystallisers does not allow one to reject the hypothesis that the outgrowth of the crystals originating from primary nucleation is identical for a small and large-scale crystalliser. The size-dependent growth rate  that has been used to simulate the experiments gives a good description of trends in the median crystal size and the supersaturation, but gives no satisfactory description of the broadening of the
distribution. Acknowledgements The authors would like to acknowledge Akzo- Nobel, BASF, Bayer, Dow Chemicals, DSM, Dupont de Nemours, Purac BioChem and the
Dutch Technology Foundation for their financialsupport.
ARTICLE IN PRESS
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