In the present work, steel, slag and refractory samples were taken from the ladle at OVAKO Steel in Hofors, Sweden. The steel samples were analysed in LOM, SEM and OES PDA. The chemical compositions of the inclusions were determined by EDS. According to the morphologies and compositions, the inclusions were classified into 5 different types, namely, (1) type-1, alumina inclusions, (2) type-2, calcium aluminate, (3) type-3, splnel-calclum aluminate, (4) type-4, calcium aluminate surrounded by a CaS shell, and (5) spinel-calcium aluminate surrounded by a CaS shell. Ladle glaze was found to be a major supplier of the inclusions, while the inclusions brought over from EAF could be another important source. The results of OES PDA showed that removal of inclusions took place mostly during the vacuum degassing period.The characteristics of the non-equilibrium decarburization process during the vacuum circulation (RH) refining of molten steel have been considered and analysed. On the basis of the fundamentals of metallurgical reaction engineering and non-equilibrium thermodynamics, as well as the two-fluid model for gas-liquid two-phase flow and a modified k-s model for turbulent flow, a novel three-dimensional mathematical model for the process has been proposed and developed. The details of the model, including the establishment of the governing equations and the especially modified two-equation k-s model, the determination of the appropriate source terms and boundary conditions and others, have been presented. The related parameters of the model have been discussed and determined for the decarburization refining process of molten steel in a 90-t multifunction RH degasser under RH and RH-KTB operating conditions.