Solutions to inversion problems in preferential crystallization of enantiomers—part I: Batch crystallization in a single vessel

Abstract

In this series of two papers, we investigate inversion techniques for models describing the crystallization of conglomerate forming enantiomers, with application for preferential crystallization. Here, in Part I, a simple batch process in one vessel is considered. In Part II, the results will be extended to a technically important setup consisting of two coupled crystallizers. The research presented here builds on prior work on the use of orbital flatness concepts for trajectory planning and control of single-substance crystallization. Based on a known necessary condition for flatness, we show that moment models for crystallization of enantiomers typically do not exhibit the orbital flatness property. However, we show that a scaling of time introduced in our prior work is still useful. We present inversion results for the realization of prescribed final-time crystal size distributions (CSDs). Due to the lack of orbital flatness, these results involve integration of a zero dynamics. A number of idealizations of the process model are investigated and shown to be suitable for appropriate problem settings. We present a numerical example which demonstrates the exact as well as the simplified inversion procedures, and also justifies application of the simplified techniques.