New inversion methods for the single/multi-shape CLD-to-PSD problem with spheroid particles. (January 2022)

• Record Type: Journal Article
• Authors: Brivadis, Lucas; Sacchelli, Ludovic
• Is Part Of: Journal of process control. Volume 109(2022)
• Page Start: 1
• Page End: 12
• Publication Date: 2022-01
• Subjects: Particle Size Distribution -- Chord Length Distribution -- Spheroid particles -- Tikhonov regularization -- Back and Forth Nudging; Process control -- Periodicals; Fabrication -- Contrôle -- Périodiques; Process control; Periodicals; Electronic journals; 660.281
• DOI: 10.1016/j.jprocont.2021.11.008
• Languages: English
• ISSNs: 0959-1524

Abstract

Abstract: In this paper, we express the Chord Length Distribution (CLD) measure associated to a given Particle Size Distribution (PSD) when particles are modeled as suspended spheroids in a reactor. Using this approach, we propose two methods to reconstruct the unknown PSD from its CLD. In the single-shape case where all spheroids have the same shape, a Tikhonov regularization procedure is implemented. In the multi-shape case, the measured CLD mixes the contribution of the PSD associated to each shape. Then, an evolution model for a batch crystallization process allows to introduce a Back and Forth Nudging (BFN) algorithm, based on dynamical observers. We prove the convergence of this method when crystals are split into two clusters: spheres and elongated spheroids. These methods are illustrated with numerical simulations.