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Keywords:

  • Monte Carlo;
  • stochastic modeling;
  • population balance;
  • crystallization;
  • aggregation;
  • agglomeration;
  • agglomerate structure

Abstract

Modeling of crystallization processes is usually based on deterministic population balances. Although conceptually there is no such limitation, population balance modeling is used only up to a few internal dimensions because of the computational effort. Alternatively, Monte Carlo methods are increasingly used for the simulation of particulate systems. There, the characterization of particles is also often limited to a few size and shape parameters similar to those of deterministic population balance modeling. A major advantage of Monte Carlo methods, however, is its simple extensibility to more complex particle characterizations. However, actually considering the full three-dimensional shape of a complex agglomerate may lead to a prohibitive computational effort. To overcome this bottleneck a hierarchical particle characterization is proposed. This characterization allows the realistic representation of the agglomerates, without the need for detailed geometric computations for each particle. Instead of the full geometry, substitution systems are introduced that can be used to perform aggregation events or to identify crystal faces that are available for growth. The substitution systems consist of point mass systems, which preserve certain characteristics of the original agglomerate such as the moment of inertia. Numerical studies show the applicability of the approach. Based on this characterization, modeling of rate processes can be performed on a much higher level of detail than is allowed by standard one- or two-dimensional particle characterizations. © 2006 American Institute of Chemical Engineers AIChE J, 2006