Optimization and Feedback Control of the Size and Shape Evolution of Elongated Crystals in Suspension

Abstract

The purification and the solidification of substances is of interest in a large number of applications in the fine chemical, pharmaceutical, and food industries. Batch crystallization from solution is often applied to fulfill this task. The macroscopic shapes of the crystals obtained in this way are governed by the principles of crystallography, and thus they exhibit a compound-specific diversity. Still, the shape and also the size of these solids can be influenced by the choice of the process operating conditions, for instance, by varying the driving force or by applying mechanical action. Since the particle size and shape distribution (PSSD) is widely accepted to be a central attribute of the obtained solid powder, the ability to engineer crystalline particles to a desirable size and shape is of great interest regardless of the application. The main purpose of this thesis is to develop, to implement, and to evaluate---both in simulation and in experiments---optimization and feedback control algorithms aimed at the manipulation of particle size and shape during batch crystallization processes. The presented methodologies are mainly concerned with elongated (or needle-like) crystals, since particles of this type often cause problems in the pharmaceutical industry. The main challenges encountered during the development of these methodologies are their high requirements with respect to online size and shape monitoring abilities, the limited predictive capabilities of currently available crystal shape evolution models, and the often encountered lack of physical actuators to alter the crystal shape. In particular, the following results have been achieved: - Model-based path planning methodologies have been developed for studying computationally the possible size and shape transitions of single crystals undergoing temperature cycling. - Feedback control laws for driving the average particle dimensions of ensembles of elongated crystals to target regions during growth-dominated batch cooling crystallization have been conceived and successfully validated. - A feedback controller for the targeted length reduction of elongated particles using wet milling has been designed and tested. - A multidimensional kinetic model for the dissolution of an elongated organic compound has been identified from experimental data. Furthermore, a simple feedback law for the controlled operation of dissolution stages has been implemented. - The feedback controllers developed for wet milling and dissolution have been integrated and combined with a simple controlled growth stage to operate a multistage process for the systematic PSSD modification in a fully automated, controlled, and thus robust manner. In particular, a significant and repeatable shape transformation from elongated to more equant particles has been realized in lab-scale experiments. From a control systems engineering point of view, the results collected in this thesis simply represent yet another example of the potential of feedback control. From a crystallization perspective, however, the developed control and operating strategies represent a novel and robust approach to crystallizing compounds that form elongated particles. The key benefits of these strategies are that most of them do not require kinetic models to operate the process and that they can mitigate considerably undesirable batch-to-batch variations in terms of selected properties of the product PSSD.