Reactor-scale Modelling and Analysis of Heat and Mass Transfer in Silicon Carbide Rotary Kilns

Silicon carbide is a widely used material due to its unique combination of physical and chemical properties. However, existing Acheson furnaces, which cause direct CO_2 emissions, are expensive and energy inefficient. Rotary kilns are a promising alternative, but their use for silicon carbide production is still under development. In this article, we present a mathematical model for the consumption of quartz and carbon, and the formation of silicon carbide in a rotary kiln. We focus on the interplay between reaction kinetics, solid and gas transport, and thermal effects. Assuming radial mixing within the bed, we derive a simplified one-dimensional model that captures the dominant physics of the system. The model tracks the evolution of quartz, carbon, and silicon carbide, as well as gas-phase species and temperature, down the length of the kiln. We nondimensionalise the model and identify key parameter groupings—relating supplied heat to kiln fill level, initial carbon particle size, and the relative speed of the two chemical reactions we consider. Then, we examine the model’s behaviour via asymptotic analysis, before presenting numerical simulations. Our analysis shows that there is only one dimensionless parameter group that strongly influences reactor performance, with silicon carbide yield increasing monotonically with the value of this parameter. These findings offer broad-stroke insights into design principles and parameter operating regimes that favour efficient silicon carbide reactors.