Mathematical model of blast furnace hearth filling

The article presents a mathematical model for estimating the filling and emptying of a blast furnace hearth with liquid smelting products, namely iron and slag. The developed algorithm is based on integration of material balance data, chemical composition of charge materials, and history of discharges. This ensures high accuracy of calculations both in real time and when analyzing historical data. The model is applied to a blast furnace with a volume of 2000 m³, with the hearth geometric parameters being taken into account. In this study, physical properties of the materials in question are considered, incorporating such metrics as hot iron density, apparent density of foamed slag, and porosity of coke charge. The algorithm comprises multiple stages, including the request of data on the last six discharges, the processing of missing values by means of imputation with averages, validation of time intervals, and calculation of the dynamics of furnace filling and emptying. The calculation was performed with a 5-minute sampling interval using a one-dimensional model that takes into account the supply of iron with ore and coke ash, as well as the volumes of products tapped. It is imperative to emphasize the meticulous attention devoted to the results rectification with consideration for the stipulated filling limits and the temporal allowance prior to the initiation of slag discharge. The model enables the calculation of the levels of hot iron and slag at any given moment in time, thus constituting a useful tool for technologists. The results are presented as three-dimensional profiles illustrating the furnace filling process. The developed system contributes to improving the safety, stability, and efficiency of the blast furnace process by preventing furnace overflow and optimizing the tapping mode. The model can be integrated into digital twins of blast furnaces.

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