Inverse populations balance problems: heuristics for aggregation/breakage of solid clusters in liquid metals

Jean-Marc Auger (1) , Sylvain Martin (2, 3) , Frédéric Gruy (2, 3)

1 InESS - Institut d'Electronique du Solide et des Systèmes
2 LGF-ENSMSE - Laboratoire Georges Friedel
3 PMMG-ENSMSE - Département Procédés de Mise en oeuvre des Milieux Granulaires

Populations balance models have been applied to the simultaneous aggregation and breakage of solid clusters in agitated liquid metal. Challenges for these systems lie in kinetics constants determination (kernels) from experimental clusters concentrations measurements. However, due to difficulties inherent to molten metals experimentation (severely limiting available data points and replication), and lack of literature information concerning the physical phenomena involved, more advanced inverse methods were needed. Taking into account physical characteristics, theoretical approaches using reactions networks proved the existence of at least one stable positive equilibrium state. This result allowed the construction of two distinct fitting algorithms, aimed at solving the corresponding inverse problem (kernels determination from experimental data). The first of these heuristic methods accurately identifies kernels parameters from perfect steady state data, while the second, based on transitory states, reliably leads to correct results with as few data points as 2, and measurements errors as high as 5%.

Mots clés: breakage; inverse methods; reaction networks; kernels; heuristics; populations balance; aggregation

Domaines: Génie des procédés

Jean-Marc Auger, Sylvain Martin, Frédéric Gruy. Inverse populations balance problems: heuristics for aggregation/breakage of solid clusters in liquid metals. Industrial and engineering chemistry research, 2020, 59 (22), pp.10363-10378. ⟨10.1021/acs.iecr.0c00859⟩. ⟨hal-02572811⟩