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 / Li ₂SiO ₃ crystallization

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The Author(s) 2025. This article is published with open access at link.springer.com and journal.hep.com.cn