Metastable zone determination

The shape of the equilibrium line, or solubility curve, is important in determining the mode of crystallization to be employed in order to crystallize a particular substance. If the curve is steep, i.e. the substance exhibits a strong temperature dependence of solubility (e.g. many salts and organic substances), then a cooling crystallization might be suitable. But if the metastable zone is wide (e.g. sucrose solutions), addition of seed crystal might be necessary. This can be desirable, particularly if a uniformly sized product is required. If on the other hand, the equilibrium line is relatively flat (e.g. for aqueous common salt... 

The most frequent site for erystal enerustation is on a eompatible solid surfaee within a zone of high supersaturation and low agitation. Seleetion of a less eompatible material having a smooth surfaee ean avoid the major exeesses of enerustation. Dunean and Phillips (1979) and Shoek (1983), respeetively, reveal a eonneetion between the metastable zone width of erystallizing solutions and their propensity to enerust. It is well known that judieious erystal seeding ean also help minimize enerustation. Simple laboratory tests are reeommended to determine all these issues before the plant is built. 

Sohnel, O. and Mullin, J.W., 1988. The role of time in metastable zone width determinations. Chemical Engineering Research and Design, 66, 537-540. 

The measurement of the width of the metastable zone is discussed in Section 15.2.4, and typical data are shown in Table 15.2. Provided the actual solution concentration and the corresponding equilibrium saturation concentration at a given temperature are known, the supersaturation may be calculated from equations 15.1-15.3. Data on the solubility for two- and three-component systems have been presented by Seidell and Linkiv22 , Stephen et alS23, > and Broul et a/. 24. Supersaturation concentrations may be determined by measuring a concentration-dependent property of the system such as density or refractive index, preferably in situ on the plant. On industrial plant, both temperature and feedstock concentration can fluctuate, making the assessment of supersaturation difficult. Under these conditions, the use of a mass balance based on feedstock and exit-liquor concentrations and crystal production rates, averaged over a period of time, is usually an adequate approach. 

Nucleation kinetics are experimentally determined from measurements of the nucleation rates, induction times, and metastability zone widths (the supersaturation or undercooling necessary for spontaneous nucleation) as a function of initial supersaturation. The nucleation rate will increase by increasing the supersaturation, while all other variables are constant. However, at constant supersaturation the nucleation rate will increase with increasing solubility. Solubility affects the preexponential factor and the probability of intermolecular collisions. Furthermore, when changes in solvent or solution composition lead to increases in solubility, the interfacial energy decreases as the affinity between crystallizing medium and crystal increases. Consequently, the supersaturation required for spontaneous nucleation decreases with increasing solubility, ° as shown in Fig. 7. 

Determination of metastable zone is usually the first step in the development of a batch crystallization process. Recent advances in in-process sensor technology enabled the determination of metastable zone to be carried out in an automated A typical... 

Fig. 9 Steps for automated determination of metastable zone using ATR-FTIR and FBRM. While automatically collecting the IR spectra for calibration, the metastable limit is determined using FBRM. Then the model for relating the IR spectra to solution concentration is constructed using multivariate analysis such as principal component regression (PCR) or partial least squares (PLS). Using this model, the solubility curve can be obtained from the IR spectra of saturated slurry.

The use of ATR-FTIR spectroscopy is not a requirement for the determination of the metastable zone. If the goal is the determination of metastable zone or solubility curve alone, then there are less technically complicated methods, such as the gravimetric method for solubility measurement and observation by eye for detection of the metastable limit. Even for the automation of the system, ATR-FTIR spectroscopy is not a requirement. Automated determination... 

Reliable determination of metastable zone width and induction time-generally is more time-consuming and difficult than the determination of supersaturation. This is because metastable zone width and induction time are affected by various factors. Therefore, the... 

Since the inherent growth rate of many organic compounds is relatively slow, addition times may be long in order to achieve supersaturation control within the metastable zone. Higher addition rates can result in nucleation and the creation of a bimodal distribution. Experimentation to determine acceptable addition rates can be evaluated by focused beam reflectance measurement (FBRM) and other in-sim, online methods (Chapter 2) or microscopic observation of the crystal slurry which could reveal the presence of fines. These issues are highhghted in the examples below. 

In this section we have described two methods to determine the kinetics governing the nucleation process. The first method, which utilizes the width of the metastable zone, is easy to use and gives an apparent order of nucleation. The second method uses the induction time to predict the mechanism and order of nucleation processes. A third method, which employs population balance techniques and an MSMPR crystallizer, will be described in Chapter 4 of this volume. 

Kohl et al. [8] studied seeding in batch crystallization. The system studied was an aqueous j3-cyclodextrin solution that had a wide metastable zone. They determined a critical size for the seed crystals in this system. When the size of the seeds used was larger than the critical size, secondary nucleation took place. 

Experimental techniques for determining the metastable zone width, the amount of undercooling that a solution will tolerate before nucleating, are described in section 5.3. The significance of the metastable zone and the interpretation of metastable zone width measurements are somewhat contentious subjects. Experimental values depend very strongly on the method of detection of the onset of nucleation, but it is still possible to extract kinetic information on the nucleation process as well as on the growth behaviour of very small crystals. These topics are discussed in some detail in section 5.3. 

The simple apparatus shown in Figure 5.10 (Mullin, Chakraborty and Mehta, 1970), based on an earlier one devised by Njwlt (1968), can be used to determine equilibrium solubilities (section 3.9) as well as metastable zone widths (seetion 3.12). About 40 mL of nearly saturated solution of known concentration is plaeed in the 50-mL flask and rapidly eooled until nueleation commenees. The contents of the flask are then slowly heated. The cooling and heating sequences may be effeeted by means of the water jacket, as shown, or by an externally operated cold/hot air blower. On approaching the saturation temperature the heating rate is reduced to about 0.2 °C/min. The temperature at whieh the last crystalline particle disappears is taken as the saturation temperature, 0. ... 

The precipitation boundary may or may not coincide with the solubility curve since its position in the diagram depends on the time and method of detection of the onset of precipitation. In effect, it establishes the metastable zone for the given system. If a stable precipitate is formed at low levels of supersaturation the precipitation boundary and solubility curve may be assumed to be virtually coincident. In cases where they do not coincide, the composition of the critical nuclei may be determined from the slopes of the precipitation boundary while the compositions of the corresponding bulk equilibrium solid phases may be obtained from the solubility curve. Hence, comparison of the two curves can yield information as to whether the composition of both nuclei and precipitate is the same or if the bulk solid phase is formed by a solid-state transformation from a metastable precursor. A useful account of the significance of the zones on a precipitation diagram has also been given by Nielsen (1979). 

The choice of the working level of supersaturation should be based on reliable measurements of the metastable limits of the system which may be made in the laboratory under carefully controlled conditions. Metastable zone widths depend on many factors including the temperature, cooling rate, agitation, presence of impurities, etc., but the most important requirement is that they must be determined in the presence of the crystalline phase and, if possible, with the actual liquor to be processed. 

Polythermal methods have in common that a suspension containing known amounts of solvent and solute in excess is heated and the temperature where last particles dissolve is detected. For detection, visual observation (e.g., under a microscope), turbidity measurements, particle-detecting inline probes (e.g., FBRM probe (Lasentec , Mettler Toledo GmbH)), or calorimetry may be used. Since it is a dynamic method, the results depend on dissolution kinetics of the particular system. In general, polythermal measurements are easier to automate since just a temperature has to be followed and no special analytical technique is required. The above-mentioned Crystall6 multiple reactor system can also be used to perform such kind of measurements. To detect both the dissolution process for derivation of saturation temperatures (clear points) and the formation of particles (cloud points) for determination of the metastable zone width, the... 

The supersaturation before the addition of seeds should be adjusted according to the solubility curve and the supersolubility curve (cf. Figure 10.2). Typically, seeding at 4—5 K below saturation temperature is fine. Of course, the metastable zone width has to be considered here and the seeding point should be closer to the solubility curve than to the supersolubility curve. It should be kept in mind that the metastable zone width is not thermodynamically determined, but strongly depends on plant properties and process parameters, such as cooling rate. If the metastable zone width is very narrow, for the sake of process robustness temperature control has to be improved or even an inline measurement of the supersaturation (e.g., by NIR) may have to be used to detect supersaturation close to the solubility curve and to avoid spontaneous nudeation or unwanted dissolving of the seed crystals. In such cases, special care has to be taken that no crystals are present in the crystallizer from the previous batch. 

In this example, it is assumed that desupersaturation is complete when point 0 is again reached. For this case, it is dear that the level of the supersaturation produced at the level of the solution depends on the redrculation flow rate. High recirculation flow rates reduce the supersaturation produced there (dilution), while low redrculation flow rates increase it. The redrculation flow rate, adjusted to the production output, is therefore the most important design parameter in industrial crystallizers. Where the production outputs are the same, this parameter is equal for all crystallizer designs. The required recirculation flow rate depends on the metastable zone width. If this is not known, it has to be determined beforehand by means of measurements. In practice, half of the metastable zone width is used for determining the required redrculation flow rate. Therefore,... 

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