New inversion methods for the single/multi-shape CLD-to-PSD problem with spheroid particles

Lucas Brivadis (1) , Ludovic Sacchelli (1)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique

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.

Mots clés: Particle Size Distribution; Chord Length Distribution; spheroid particles; Tikhonov regularization; Back and Forth Nudging

Domaines: Automatique / Robotique; Génie des procédés; Optimisation et contrôle [math.OC]

Lucas Brivadis, Ludovic Sacchelli. New inversion methods for the single/multi-shape CLD-to-PSD problem with spheroid particles. Journal of Process Control, 2022, 109, pp.1-12. ⟨10.1016/j.jprocont.2021.11.008⟩. ⟨hal-03053999⟩