MODELING A CASCADE OF CONTINUOUS MSMPR CRYSTALLIZERS WITH AGGLOMERATION

Cascade models have been used to account for real flow patterns in crystallizers that are not well-mixed and to better control the characteristics of the crystal size distribution (CSD). Such models have been solved under two different sets of boundary conditions describing nucleation in each stage. In this article, we have solved (numerically and analytically) population balance equations that include the mechanism of agglomeration in each stage of the cascade without considering classification or recycle, and have derived expressions for the moments of the CSD in closed forms. We then obtained analytic solutions to our model equations for two stages in the cascade under two different sets of boundary conditions. When there were more than two stages in the cascade, we found out that it was necessary and also efficient (computing timewise) to use numerical schemes to solve and analyze our model equations. Our results show that the agglomeration kernel has a significant influence on the coefficient of variation of the CSD, and hence it should be considered in applying the cascade models to describe the mixing and performance of crystallizers with significant particle agglomeration.