Developing a Unidimensional Simulation Model for Producing Silicon in an Electric Furnace

Summary

Within Elkem a/s two different approaches were followed in the early stages of developing a model for the Si-process. In Kristiansand, Norway, we chose to keep close to a rather fundamental formulation. Serious numerical difficulties occurred, however, during implementation, and the model was not finished. In Niagara Falls, USA, a simple and direct approach was followed, leading to a complete simple model. The model was then significantly improved by implementing time integration, reaction rate formulations etc based on the more fundamental formulations developed in Kristiansand.

In the final model difficult gas dynamic computations have been avoided at the cost of solving a nonlinear equation (with one unknown) for each segment in the model. Fast, irreversible chemical reactions rates caused serious numerical convergence problems also for this model, but in this case the problem could be solved by implementing discontinuity handling for the time integration procedure. For the original Kristiansand model the numerical problems remain open, implying that academic research is wanted.