Models, crystallization process

Both growth rate dispersion and size-dependent growth affect the crystal size distribution obtained from laboratory and industrial crystallizers. They must, therefore, be taken into account when analyzing the modeling crystallization processes. More information on this topic can be found in Chapter 4 of this volume. 

Advanced control strategies require a model that accurately represents the behavior of the process. Model identification involves determining an appropriate model structure, performing experiments, collecting data that allow identification of model parameters, and estimating the parameters. There are several ways to model crystallization processes, but a review of parameter estimation is beyond the scope of this chapter. A discussion of the most relevant methods of model identification for continuous crystallizers is given below. 

In spite of these obstacles, crystallization does occur and the rate at which it develops can be measured. The following derivation will illustrate how the rates of nucleation and growth combine to give the net rate of crystallization. The theory we shall develop assumes a specific picture of the crystallization process. The assumptions of the model and some comments on their applicability follow ... 

In some cases, whole parts of the protein are missing from the experimentally determined structure. At times, these omissions reflect flexible parts of the molecule that do not have a well-defined structure (such as loops). At other times, they reflect parts of the molecule (e.g., terminal sequences) that were intentionally removed to facilitate the crystallization process. In both cases, structural models may be used to fill in the gaps. 

Several reported chemical systems of gas-liquid precipitation are first reviewed from the viewpoints of both experimental study and industrial application. The characteristic feature of gas-liquid mass transfer in terms of its effects on the crystallization process is then discussed theoretically together with a summary of experimental results. The secondary processes of particle agglomeration and disruption are then modelled and discussed in respect of the effect of reactor fluid dynamics. Finally, different types of gas-liquid contacting reactor and their respective design considerations are overviewed for application to controlled precipitate particle formation. 

Gertlauer, A., Mitrovic, A., Motz, S. and Gilles, E.-D., 2001. A population balance model for crystallization processes using two independent particles properties. Chemical Engineering Science, 56(7), 2553-2565. 

Rawlings, J.B., Miller, S.M. and Witkowski, W.R., 1993. Model identification and control of solution crystallization processes A review. Industrial and Engineering Chemistry Research, 32, 1275-1296. 

A mechanistic model for the kinetics of gas hydrate formation was proposed by Englezos et al. (1987). The model contains one adjustable parameter for each gas hydrate forming substance. The parameters for methane and ethane were determined from experimental data in a semi-batch agitated gas-liquid vessel. During a typical experiment in such a vessel one monitors the rate of methane or ethane gas consumption, the temperature and the pressure. Gas hydrate formation is a crystallization process but the fact that it occurs from a gas-liquid system under pressure makes it difficult to measure and monitor in situ the particle size and particle size distribution as well as the concentration of the methane or ethane in the water phase. 

Cairns-Smith is careful enough to concede that the first hypothetical informationcarrying material was not of necessity a clay mineral however, the basic features of the model can best be demonstrated using different clay species. Thus, for example, clays could have crystallized out in sandstone pores from solutions containing products derived from weathering. The result would have been clay layers, which could have been separated and transported further by external influences replication under similar conditions would have followed. Such crystallization processes would have also involved errors, such as defects, vacancies, and the incorporation of other ions or atoms these inorganic mutations would have been passed on, i.e., they would have been incorporated into the next sheet to be formed. 

The ideal solubility equation (Eq. 2) is the simplest form of model that is applicable to solvent based crystallization process design. Even though the equation excludes non-ideal interactions in the liquid phase, it is still a useful tool in certain circumstances. 

The non-random two-liquid segment activity coefficient model is a recent development of Chen and Song at Aspen Technology, Inc., [1], It is derived from the polymer NRTL model of Chen [26], which in turn is developed from the original NRTL model of Renon and Prausznitz [27]. The NRTL-SAC model is proposed in support of pharmaceutical and fine chemicals process and product design, for the qualitative tasks of solvent selection and the first approximation of phase equilibrium behavior in vapour liquid and liquid systems, where dissolved or solid phase pharmaceutical solutes are present. The application of NRTL-SAC is demonstrated here with a case study on the active pharmaceutical intermediate Cimetidine, and the design of a suitable crystallization process. 

Case Study - Solubility Modelling and Crystallization Process Design for Cimetidine... 

Solubility modelling with activity coefficient methods is an under-utilized tool in the pharmaceutical sector. Within the last few years there have been several new developments that have increased the capabilities of these techniques. The NRTL-SAC model is a flexible new addition to the predictive armory and new software that facilitates local fitting of UNIFAC groups for Pharmaceutical molecules offers an interesting alternative. Quantum chemistry approaches like COSMO-RS [25] and COSMO-SAC [26] may allow realistic ab-initio calculations to be performed, although computational requirements are still restrictive in many corporate environments. Solubility modelling has an important role to play in the efficient development and fundamental understanding of pharmaceutical crystallization processes. The application of these methods to industrially relevant problems, and the development of new... 

NRTL-SAC has been demonstrated through the case study on Cimetidine as a valuable aid to solubility data assessment and targeted solvent selection for crystallization process design. The average model error is typically 0.5 Ln (x) [1] and is sufficient as a solvent screening tool. Methods that can deliver greater accuracy would increase the value and utility of these techniques. It is impressive in the case of Cimetidine that the NRTL-SAC correlation is capable of reasonable accuracy and predictive capability on the basis of just 2 fitted parameters. Further work to extend the solvent database and optimize the descriptive parameters will be beneficial, and are planned by the developers. 

One surface feature that we see in our model of the NCP may have biological implications, or may be an artifact of the crystallization process. This is the presence of a cacodylate ion that serves as an interparticle contact in the crystal (Fig. 16). This interaction occurs within a pocket formed by side chains of Gin 76 and Asp 77 of 2H3 and the main chain carbonyl of Leu 22 of 2H4 on the NCP and by side chains of Glu 64 of 1H2A and His 49 of 2H2B as well as the main chain carbonyl of Val 48 of 1H2B on the symmetry neighbor. The possibility of cacodylate ion mediating an interaction between chromatin elements could be a clue... 

Albarede and Bottinga, 1972), where t is time since the beginning of the process (at constant accretion or dissolution rates), is the trace element concentration measured at distance x from the interface and at time t, and L (in the case of fractional crystallization) is half the mean distance between centers of accreting crystals less half the mean thickness of the crystals. We will see later the effects of erroneous evaluation of and K when modeling fractional crystallization processes. 

The observed transients of the crystal size distribution (CSD) of industrial crystallizers are either caused by process disturbances or by instabilities in the crystallization process itself (1 ). Due to the introduction of an on-line CSD measurement technique (2), the control of CSD s in crystallization processes comes into sight. Another requirement to reach this goal is a dynamic model for the CSD in Industrial crystallizers. The dynamic model for a continuous crystallization process consists of a nonlinear partial difference equation coupled to one or two ordinary differential equations (2..iU and is completed by a set of algebraic relations for the growth and nucleatlon kinetics. The kinetic relations are empirical and contain a number of parameters which have to be estimated from the experimental data. Simulation of the experimental data in combination with a nonlinear parameter estimation is a powerful 1 technique to determine the kinetic parameters from the experimental... 

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