Mathematical modelling of a silicon carbide (SiC) pilot furnace

This report proposes a one-dimensional mathematical model of a novel silicon carbide furnace designed by Elkem ASA. The model consists of balance equations for volume fractions of three solids -- silicon dioxide, carbon, and silicon carbide -- and molar concentrations of two gases -- silicon monoxide and carbon monoxide -- within the furnace, which are coupled by reaction rate functions. Preliminary numerical results for steady-state solutions of these equations are presented. A simplified model involving two gas species is considered; the reaction rate for silicon monoxide formation is constant in places within the furnace where the temperature exceeds the minimum temperature for the reaction to proceed, and the presented solution can deal with the known carbon concentrations. The two-gas model is utilized to identify the residence time for the gas to vent from the top of the furnace.