Considerations on the crystallization modeling: Population balance solution

In crystallization processes, the need to improve the product quality and to minimize production cost requires understanding and optimization on how to obtain an appropriate particle-size distribution. In order to achieve this goal, a model of the process is necessary and the distribution of particles must be represented, which is made through the population balance. This latter constitutes a strongly nonlinear hyperbolic partial differential equation and, in most cases, an analytical solution is not possible, requiring the development and adaptation of numerical techniques. In the present work, it is proposed to analyze the positive and negative aspects of some methods chosen as a tool in the treatment of the population balance equation in crystallization processes. Numerical problems arising from transformation of the partial differential equation, computational effort, as well as the incorrect prediction of the total number of particles and/or no mass conservation of the dispersed phase are discussed.