Multilayer Simulation of Heat Flow in a Submerged ARC Furnace Used in the Production of Ferroalloys

Abstract

A hierarchical simulation model consisting of four calculating levels for heat flow is developed for a submerged arc furnace. This model is part of an extensive simulation system designed for the stagewise optimization of production alternatives generated on the basis of design constraints. The present applications of the lower levels of the system are feasibility studies for the smelter, tools to aid pilot plant test runs and real time process operator assistance in smelters. The higher levels of the system are aimed at engineering design, dimensioning and scale-up purposes. The most detailed level of the models is applied to process study and development.In order to gradually increase the amount of detail in selected parts of the process, a decomposition procedure is used. On the first level, heat flow is combined with electrical flow by known specific energy consumption can be calculated on the basis of the energy balance. On the second level, the mass and energy balance is divided into several zone balances. On the third level, a descending burden element model corresponding to batch reactor calculations is used together with heat flow calculations in one-dimensional cases. On the fourth level the temperature distribution for selected zones is obtained by a transient scheme. The heat flow equation is strongly nonlinear, since the density, the specific heat, the thermal conductivity, the coefficient of the heat transfer and the heat generation are all functions of position, time and temperature. All these properties are iterated during the calculation.In process design applications a steady state solution is obtained in the calculations by a transient scheme based on the odd-even hopscotch method using finite difference approximations. Since the new temperatures are replacing the old ones, the memory requirement of the scheme is very small. The method is quite fast, and there is also an accelerated version which is applicable if the print-outs are not required for all temperatures. Time constants of the system must be estimated in order to insure the stability of the scheme. The boundary conditions are also important.The resulting temperature distribution agrees fairly well with published experimental data and the theoretical considerations. According to calculations, the present initial temperature distribution seems to correspond well with the optimum furnace conditions and is therefore quite useful in furnace design.