Abstract
Mass transfer model equations are derived for the process of oxidative ladle refining of silicon melt containing Al and Ca as impurities. Derivations are based on the theoretical development of interfacial mass transfer model equations for the multiphase reactive systems which is also performed in this report. The application of these models is either in Eulerian / Lagrangian CFD calculations, or in any simplified semi-batch reactor model developed for estimating the overall refining efficiency. The flux of species across the interfaces is expressed in terms of concentration gradients multiplied by a mass transfer coefficient which is often enhanced by an enhancement factor due to chemical reactions. The challenge is in modelling mass transfer by chemical reactions in which the product is not in either of the reactant phases. This situation occurs in the reaction between silicon melt and oxygen bubbles, where the product (silica) is in a separate phase (slag). Understanding the morphology of the created slag is important in order to model the mass transfer between air bubbles and the silicon melt. For this reason, the spreading coefficient is introduced and calculated by means of computational thermodynamics techniques. It is found out that the produced slag at the gas-melt interface does not wet the interface and therefore it is assumed that it precipitates from the interface into the melt phase, in form of tiny droplets. Further modelling of the precipitation process including estimations for slag droplet size is not included at this stage of research. Model equations for the main refining reactions are derived in which information for equilibrium concentrations at the slag-metal interface which are provided by computational thermodynamics are included.
