Models, crystallization process crystal size distribution

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... 

This misconception is particularly common in crystallization. The hypothesis of a perfectly mixed system is, for crystallization and precipitation processes, labeled as mixed-suspension, mixed-product removal (MSMPR). With diis model the crystalUzer is modeled with a spatially homogeneous NDF, generally called the crystal-size distribution (CSD). However, the fact that the CSD is constant through the vessel does not mean that the rates of crystal nucleation, molecular growth, aggregation, and breakage are constant. 

Aamir, E., Nagy, Z. K., Rielly, C. D., Kleinert, T. Judat, B. 2009 Combined quadrature method of moments and method of characteristics approach for efficient solution of population balance models for dynamic modeling and crystal size distribution control of crystallization processes. Industrial Engineering Chemistry Research 48, 8575-8584. 

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. 

Continuous MSMPR Precipitator. The population balance, which was put forward by Randolph and Larson (1962) and Hulbert and Katz (1964), provides the basis for modeling the crystal size distribution (CSD) in precipitation processes. For a continuous mixed-suspension, mixed-product-removal (CMSMPR) precipitator with no suspended solids in the feed streams, the population balance equation (PBE) can be written as (Randolph and Larson 1988)... 

The process dynamic model of a batch crystalliser is straightforward, fully described by the energy, mass and population balances. However, the dynamic of the crystal size distribution can be ignored if a batch is initially fed with seeds closely sized between two adjacent sieve sizes. General equations and constraints are developed for anhydrous salts. Additional equations are required to describe other transformations as in the case of hydrates and organic compounds. The subscript f and the superscript in the following equations denotes feed and saturation, respectively. The rate change in ... 

Particulate processes are characterized by properties like the paxticle shape, size, surface area, mass, and product purity. In crystallization the particle size and total number of crystals vary with time. Thus, determining particle size distribution (PSD) is important in crystallization. A population balance formulation describes the process of crystal size distribution with time most effectively. Thus, modeling of a batch crystallizer involves use of population balances to model the crystal size... 

Since crystallization is a particulate process, the model representing size distribution is written in terms of functions. Evans (1989) and Hounslow and... 

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. 

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