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The programs WYK_Stal and Bi-Growth, developed at AGH-UST, Kraków, Poland, were used for simulating the refining process, the formation of non-metallic inclusions, and their growth. The Fe-Y-Al-O-S-Ca system in pre-oxidized steel was analyzed, where yttrium formed precipitates from both O and S. When first Al and second Y were added to steel, the proportion of Al2O3 inclusions remained constant. This resulted in higher yttrium losses for oxide formation, whereas the sulfur content promoted sulfide phase formation. The introduction of yttrium at the end of refining contributed to reducing the consumption of this element in the non-metallic phase formation. The addition of aluminum and then calcium were sufficient to achieve a high degree of deoxidation and desulfurization. Calculations performed with WYK_Stal for both (a) and (c) versions of the model showed that the sulfide phase was constituted by CaS and FeS (model c) and CaS (model (a)). The participation of the calcium sulfide phase turned out to be dominant in the inclusions. Their presence was also identified in the slag phase. Simulations of the growth of complex oxide and oxo-sulfide inclusions using the Bi_Growth program showed that the yttrium content of the steel has a decisive role in the formation of complex oxide inclusions and the final oxygen content of the steel. In contrast, for the growth of oxide-sulfide inclusions, the character of growth is determined by the sulfur content of steel.

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The research focused on the influence of cerium on the chemical composition and morphology of non-metallic inclusions in pre-oxidised steel to which Al, Ca, and Ce was added in different amount and order. Calculations were carried out using our own computer program. The simulation results obtained according to two calculation models helped identify precipitates from the Ce–O–S system. The possibility of CeN formation was also identified. The trace amounts of these inclusions were also found in the results. Consideration of the physicochemical phenomena at the boundary, as well as the interfacial partitioning and the sulfur partition coefficient, influences the favourable chemical composition of the inclusions, limiting it mainly to compounds from the Al2O3, Ce2O3, and CaS systems. It was found that the addition of Ce before Ca causes the elimination of MnS precipitates and Ca-containing inclusions in the steel.

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