Crystal Population Balance Formulation and Solution Methods: A Review

Crystallization is an important part of many chemical industries. Efforts are being invested to improve the performance of the crystallization process by designing novel crystallizers. An important aspect in the development of new crystallizers is the ability to describe the behavior of such units in terms of rigorous dynamic mathematical models and solving the resulting models efficiently. The current bottleneck in modeling crystallization systems is the complexities associated with the crystal birth, growth, and death processes using population balance equations. In this article, various crystal birth, death, and growth models are introduced and reviewed. Population balance models as well as solution methods (e.g.,analytical, moment methods, discretization (classes/sectional) methods and Monte Carlo methods) are also reviewed, and new advances in solution methods are described. Population balance equations are used in other fields, and developments from other fields that can be extended to crystal population balance equations are included in this review.