Population balance modeling of crystallization for monitoring and optimal control

Abstract

The Population Balance Equation (PBE) describe the change in the particle size distribution occasioned by a variety of mechanisms. This study evaluate the PBE with nucleation, growth and dissolution. The nucleation with growth process is known to be problematic due to the sharp profiles that it causes. The dissolution process requires the knowledge of the number of particles at the minimal stable size, such that unstable particles are removed from the particulate phase. These conditions require the use of specialized numerical method for mathematical modeling. In this thesis, an emphasis is given in the Moving Sectional Method, which combines the method of classes with the method of characteristics to mitigate numerical diffusion errors. The work focused on the PBE application for the enantioselective crystallization of racemic compounding forming systems. Initially, the conservation of the moments of the distribution was analyzed for the MSM with growth and nucleation mechanisms and methods were proposed for the addition of new elements of the particle size mesh. The estimation of kinetic parameters was approached for the dissolution of NaCl in solutions of monoethyleneglycol (MEG) from data of color patterns (RGB), which can be obtained by experimental apparatus of low cost. A method for determining the operating conditions for the batch crystallizer based on the ternary diagram is described. Subsequently, it is shown that the information obtained in the ternary diagram, such as the maximum yield obtained by the process due to thermodynamics, can be used to formulate constraints for a control method based on non-linear optimization to obtain the desired characteristics of the product.