Chemical Engineering Science, Vol.80, 253-269, 2012
Solutions to inversion problems in preferential crystallization of enantiomers-part I: Batch crystallization in a single vessel
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. (C) 2012 Elsevier Ltd. All rights reserved.
Keywords:Enantiomers;Preferential crystallization;Population balance;Moment model;Dynamic inversion;Orbital flatness