Modeling and monitoring of shape evolution of particles in batch crystallization processes

Abstract

Crystallization is an important process in the chemical and pharmaceutical industry. Process performance can strongly depend on product properties like crystal size and shape. Particularly in recent years, crystal shape therefore became the topic of scientific research. The main goals of this work are to understand the mechanisms leading to specific morphologies and, more importantly, to study how the shape of crystals can be altered. The focus of this work was to investigate with simulations and experiments the evolution of particle shape in batch cooling crystallization processes. To that aim different models for the prediction of crystal morphology were studied. A simplified particle description using two independent characteristic crystal dimensions was incorporated in a process model leading to a two dimensional particle size distribution (PSD). The corresponding two dimensional population balance was analyzed with the method of characteristics. The evolution of crystal shape was then described by a time dependent ratio of growth rates. This result allowed for a detailed analysis of the parameters in the growth kinetics yielding a qualitative understanding of the relationship between operating conditions and particle shape. Another important aspect was the appropriate monitoring of crystallization processes. For the on–line measurement of the solute concentration ATR–FTIR was successfully used. In–situ monitoring tools for particle size and shape and also some ex–situ size and shape characterization tools suffer from a common problem: they have a two dimensional perspective on the particles that can float freely in front of the probe and adopt any orientation in space. Thus, the desired properties, i.e. size and shape, cannot be measured directly and the relation between the obtained measurement data and the desired ones is not straightforward. A Monte–Carlo approach was used to simulate such measurements and it allows for the computation of the expected measurements for a given particle population. An optimization algorithm is introduced to solve the inverse problem, namely the restoration of a two dimensional PSD based on the measured data. The algorithm was tested in simulations and applied in real crystallization experiments.