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Numerical Approximations of a Population Balance Model for Coupled Batch Preferential Crystallizers

by Qamar, S., Angelov, I., Elsner, M. P., Ashfaq, A., Seidel-Morgenstern, A., Warnecke, G..

Series: 2006-57, Preprints

35L65 Conservation laws
35L45 Initial value problems for first-order hyperbolic systems
35L67 Shocks and singularities

This article is concerned with the numerical approximations of population balance equations for modeling coupled batch preferential crystallization processes. The current setup consists of two batch crystallizers interconnected with two fines dissolution pipes. The crystallization of both enantiomers is assumed to take place in separate crystallizers after seeding with their corresponding crystals. The withdrawn fines are assumed to be dissolved in the dissolution unit after heating. To avoid negative effect on the particles of the crystallizer, the liquid in the pip is cooled down back to the crystallizer temperature before entering to the opposite crystallizer. Two types of numerical methods are proposed for the simulation of this process. The first method uses high resolution finite volume
schemes, while the second method is the so-called method of characteristics. On the one hand, the finite volume schemes
which were derived for general system in divergence form, are computationally efficient, gives desired accuracy on coarse grids, and are robust. On the other hand, the method of characteristics is in general a powerful tool for solving growth processes, has capability to overcome numerical diffusion and dispersion, gives highly resolved solutions, as well as being computationally efficient. A numerical test problem with both isothermal and non-isothermal conditions is considered here.
The numerical results show clear advantages of the proposed schemes

Population balance models, preferential crystallization of enant