Optimal control of univariate and multivariate population balance systems involving external fines removal

Abstract

We propose an algorithm for optimal control of univariate and multivariate population balance systems governed by a class of first-order linear partial differential equation of hyperbolic type involving size dependent particle growth and filtering. In particular, we investigate the impact of filtering on the optimal control outcomes. To this end, we apply a recently developed polynomial method of moments and a standard steepest descent gradient-based optimization scheme to batch crystallization benchmark problems involving external fines removal. Numerical evaluations for various case-studies aiming at minimizing the mass of grown nuclei in the context of crystal shape manipulation demonstrate the effectiveness of fines dissolution. We also validate the accuracy of the proposed method of moments by utilizing a known numerical moving grid discretization method as a reference. Our results are of interest for the control of a wide range of population balance systems in various applications such as pharmaceutics, chemical engineering, particle shape engineering.