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A mathematical model for industrial refining of silicon alloys has been developed for the so-called oxidative ladle refining process. It is a lumped (zero-dimensional) model, based on the mass balances of metal, slag, and gas in the ladle, developed to operate with relatively short computational times for the sake of industrial relevance. The model accounts for a semi-continuous process which includes both the tapping and post-tapping refining stages. It predicts the concentrations of Ca, Al, and trace elements, most notably the alkaline metals, alkaline earth metal, and rare earth metals. The predictive power of the model depends on the quality of the model coefficients, the kinetic coefficient,  and the equilibrium partition coefficient,  for a given element. A sensitivity analysis indicates that the model results are most sensitive to . The model has been compared to industrial measurement data and found to be able to qualitatively, and to some extent quantitatively, predict the data. The model is very well suited for alkaline and alkaline earth metals which respond relatively fast to the refining process. The model is less well suited for elements such as the lanthanides and Al, which are refined more slowly. A major challenge for the prediction of the behavior of the rare earth metals is that reliable thermodynamic data for true equilibrium conditions relevant to the industrial process is not typically available in literature.

Model of Silicon Refining During Tapping: Removal of Ca, Al, and Other Selected Element Groups