Batch crystallization analysis

The analysis of batch crystallization processes is generally more difficult than that of continuous crystallization processes. This is mainly due to the complexity of problems encountered in the batch systems the mass and surface area of the crystals increase during the run, and the supersaturation varies in a complex way as a function of time. Thus, in the development of a descriptive model, one needs to consider the time-dependent batch conservation 

---

A theoretical analysis of an idealized seeded batch crystallization by McCabe (1929a) lead to what is now known as the AL law . The analysis was based on the following assumptions (a) all crystals have the same shape (b) they grown invariantly, i.e. the growth rate is independent of crystal size (c) supersaturation is constant throughout the crystallizer (d) no nucleation occurs (e) no size classification occurs and (f) the relative velocity between crystals and liquor remains constant. 

Tavare and Garside ( ) developed a method to employ the time evolution of the CSD in a seeded isothermal batch crystallizer to estimate both growth and nucleation kinetics. In this method, a distinction is made between the seed (S) crystals and those which have nucleated (N crystals). The moment transformation of the population balance model is used to represent the N crystals. A supersaturation balance is written in terms of both the N and S crystals. Experimental size distribution data is used along with a parameter estimation technique to obtain the kinetic constants. The parameter estimation involves a Laplace transform of the experimentally determined size distribution data followed a linear least square analysis. Depending on the form of the nucleation equation employed four, six or eight parameters will be estimated. A nonlinear method of parameter estimation employing desupersaturation curve data has been developed by Witkowki et al (S5). 

The dynamic model used in predicting the transient behavior of isothermal batch crystallizers is well developed. Randolph and Larson (5) and Hulburt and Katz (6) offer a complete discussion of the theoretical development of the population balance approach. A summary of the set of equations used in this analysis is given below. 

An alternative scheme, proposed by Garside et al. (16,17), uses the dynamic desupersaturation data from a batch crystallization experiment. After formulating a solute mass balance, where mass deposition due to nucleation was negligible, expressions are derived to calculate g and kg in Equation 3 explicitly. Estimates of the first and second derivatives of the transient desupersaturation curve at time zero are required. The disadvantages of this scheme are that numerical differentiation of experimental data is quite inaccurate due to measurement noise, the nucleation parameters are not estimated, and the analysis is invalid if nucleation rates are significant. Other drawbacks of both methods are that they are limited to specific model formulations, i.e., growth and nucleation rate forms and crystallizer configurations. 

The Investigation was carried out using a seeded, batch crystallization In the absence of nucleatlon. Supersaturated solutions were prepared, seeded and maintained at a constant temperature while crystallization proceeded. Samples were taken periodically to give a solution for analysis and crystals for size analysis and crystal content determination. 

The first-principle method used in the present study will be outlined below. Population balance analysis on a perfectly mixed batch crystallizer with negligible crystal breakage and agglomeration yields the familiar nucleation rate equation used by Misra and White (5)... 

It is assumed in this analysis that there is no secondary nucleation during the batch crystallization process. Secondary nucleation will tend to increase the number of crystals and thereby... 

Deductions from a Differential Distribution Obtained at a Known Residence Time 533 Batch Crystallization with Seeded Liquor 534 Analysis of Size Distribution Data Obtained in a CSTC 537... 

PuEL, F., Fevotte, G. Klein, J. P. 2003b Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. Part 2 a study of semi-batch crystalization. Chemical Engineering Science 58, 3729-3740. 

Perhaps the most troublesome aspect of batch crystallizers is the difficulty associate ciystal size distributions in going from one batch to the next. This may be overcome and control of mixing conditions. In general, however, the development of methods for design and analysis of batch crystallizers lags those for cortinuous systems. 

Several experimental techniques and data analysis methods can be employed to study the nucleation/growth kinetics and CSD in batch crystallizers. 

The analysis of batch crystallizers normally requires the consideration of the time-dependent, batch conservation equations (e.g., population, mass, and energy balances), together with appropriate nucleation and growth kinetic equations. The solution of these nonlinear partial differential equations is relatively difficult. Under certain conditions, these batch conservation equations can be solved numerically by a moment technique. Several simple and useful techniques to study crystallization kinetics and CSDs are discussed. These include the thermal response technique, the desupersaturation curve technique, the cumulative CSD method, and the characterization of CSD maximum. 

Tavare, N.S., Garside, J. and Chivate, M.R. (1980) Analysis of batch crystallizers. Industrial and Engineering Chemistry Process Design and Development, 19, 653-665. 

Crystallization analysis fractionation (Crystaf) fractionates polymer chains according to differences in crystallizability. Crystaf can be used to fractionate polymers due to differences in chemical composition, comonomer sequence length, and tacticity. It may also respond to long-chain branching, provided that the polymer is branched enough to affect its crystallinity. The fractionation principle operative in Crystaf was discussed in the section on batch fractionation for the case of slowly cooling (or warming) solutions of semicrystalline polymers. 

In principle, SEC can be calibrated with standards of narrow molecular weight distribution of the polymer that one wishes to analyze. In this way, a calibration curve relating molecular weight to elution volume is obtained, in a fashion similar to what is done for the calibration of TREF or crystallization analysis fractionation. This approach, however, suffers from the limitation that the calibration curve is only applicable to one specific polymer. Additionally, narrow standards are not available for many different types of polymers. In principle, the batch fractionation techniques discussed above could be used to obtain such narrow standards, but these processes are time-consuming and, as explained, do not permit the isolation of samples with very narrow molecular weight distributions. 

The installation of a new heat exchanger is proposed for the batch crystallization step in an existing pharmaceutical manufacturing process. The heat exchanger costs 49,600 (installed) and saves 8000/yr in operating costs. Is this a good investment based on a before-tax analysis ... 

Monnier, O., Fevotte, G., Hoff, C. and Klein, J.P., 1997. Model identification of batch cooling crystallizations through calorimetry and image analysis. Chemical Engineering Science, 52, 1125-1139. 

Figure 4.41. Trend analysis over 12 batches of a bulk chemical. The sieve analysis shows that over time crystals larger than 250 /urn were reduced from a weight contribution in the range of a few percent of the total to about 1% in favor of smaller sizes. Impurity C appears to follow the trend given by the lead compound for the competing side reaction 1. The very low moisture found for sample 3 could be due to a laboratory error because during drying one would expect ethanol to be driven off before water. Methanol is always below the detection limit.

The crystallization step is generally studied quite exhaustively at the laboratory scale and often at the pilot scale. The reaction chemistry should be properly understood to access effects, if any, of the synthesis step on the impurity profile. In batch cooling crystallizers attempts have been made to create optimum conditions by on-line turbidity analysis (Moscosa-Santillan et al., 2000). Physicochemical characterization of the products should be done rigorously (Tanguy and Marchal, 1996). 

---