Integrating Calphad and finite volume method for predicting non-equilibrium solidification of lithium metasilicate

Abstract

Efficient recycling of lithium metasilicate (Li₂SiO₃) from lithium-containing slag via a pyrometallurgical route demands a comprehensive understanding of its solidification process in the slag reactor. A simulation framework is developed to predict the heterogeneous phase distribution of Li₂SiO₃, the temperature and velocity fields considering density changes in the solidifying melt, on the apparatus scale. This framework integrates thermodynamic models via calculation of phase diagrams with the enthalpy-porosity technique and the volume of fluid method within a finite volume approach, ensuring thermodynamic consistency and adherence to mass balance. Thus, the formation of Li₂SiO₃ from the liquid slag composed of Li₂O-SiO₂ is described in space and temporal fields. Thereby, the interrelationship between the temperature field, enthalpy field, velocity field, and phase distribution of Li₂SiO₃ is revealed. It is shown that the lower temperature on reactor boundaries prompts the earlier formation of Li₂SiO₃ in the vicinity of the boundaries, which subsequently induces a downward flow due to the higher density of Li₂SiO₃. The predicted global mass fraction of Li₂SiO₃ under non-equilibrium conditions is 11.5 wt % lower than that calculated using the global equilibrium assumption. This demonstrates the global non-equilibrium behavior on the process scale and its consequences on slag solidification.

Graphical abstract

Keywords

solidification / thermodynamic modeling / volume of fluid / finite volume method / process simulation / Li₂SiO₃ crystallization

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Competing interests

The authors declare that they have no competing interests.

Acknowledgements

The project on which this publication is based was funded by the German Federal Ministry of Education and Research within the Competence Cluster Recycling & Green Battery (greenBatt) under the grant number 03XP0336A. The authors are responsible for the contents of this publication.

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Open access funding enabled and organized by Projekt DEAL.

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