Batch Cooling Crystallization of Plate-like Crystals: A Simulation Study

Botond Szilágyi, Béla Lakatos
2015 Periodica Polytechnica: Chemical Engineering  
In the paper, batch cooling crystallization of plate-like crystals is investigated by numerical experimentation. The population balance approach is used to describe a seeded crystallization process, developing a bivariate morphological population balance model including nucleation and size dependent crystal growth. The population balance equation is reduced to a system of equations for the bivariate mixed moments of internal variables, which are solved by means of the quadrature method of
more » ... s. A sensitivity analyses is carried out to investigate the effects of the process parameters on dynamic evolution of particulate properties including the characteristic mean particle size and shape. Introduction From practical point of view, crystal shape and size define properties like specific surface area and dissolution rate. They affect also some biological properties and have major influence on the downstream operations during the manufacturing like filtering, washing or drying. As a consequence, one of the recent challenges in particulate science is the simultaneous shape and size manipulation of the crystals during the crystallization process [1]. The shape often differs from the simple geometries like cube or sphere because of the different growth rates of specific crystal faces [2] . The growth rate in each direction can be an individual function of temperature, supersaturation and even the size of the growing face. In this context, the shape and size of an individual crystal is continuously changing during the crystallization process. Moreover, nucleation occurs simultaneously with the crystal growth that beside of the material specific properties depend on the temperature, supersaturation, concentrations, surface of the existing particles, and even on the stirring energy [3] . The time evolution of crystal size distribution is sensitive to the initial supersaturation, temperature and the seed properties, i.e. to the quantity and size distribution of seeds. Although some advanced techniques exist for in situ measurement of the particulate properties which undoubtedly eases the data gathering and the development of on-line control strategies [4], currently these would be too expensive for a detailed system investigation. Therefore, mathematical modelling appears to be a useful tool for analysing these processes. In the last decade, the population balances were extended to multivariate cases, making possible to model not only the size but the shape evolution in time of the crystal populations. These types of population balances are the so called morphological population balances and are typically able to reconstruct the particle shape at each moment of simulation. They are useful for kinetic estimations followed by solving shape optimization and/or control problems and are especially handful for the investigation of the crystallization process itself. The morphological population balances were often applied to model and simulate crystallization of rod-like or needleshape crystals [4, 5] , but only several studies were reported
doi:10.3311/ppch.7581 fatcat:7eowlijnmveaboe5hy773gc7mm