Vacuum degassers are critical in modern steelmakingSteelmaking processes, as they facilitate the reduction of undesirable elements, particularly dissolved gases, which can significantly impair the quality of the final steel product. In this study, a detailed mathematical modeling approach was employed to investigate the fluid dynamics behavior of molten steel within the RH reactor variant, also known as the Single Snorkel Refining Furnace (SSRFSingle Snorkel Refining Furnace (SSRF)). The study included a comparative analysis of different mathematical modelsMathematical model to accurately predict the behavior of the steel during the degassing process. Specifically, the investigation focused on two approaches: utilizing only the Volume of Fluid (VOF) multiphase model and a combination of the VOF modelVOF model with the Discrete Phase Model (DPM). Additionally, an extra injection was added to the snorkel wall without considering the DPM modelDPM model. It was shown that even with the extra injection, the VOF modelVOF model exhibited a lower mass flow compared to the case where the DPM modelDPM model was used. The results demonstrated that the VOF + DPM coupling provided a more robust prediction, leading to a higher recirculation rate, thereby enhancing the efficiency of the steel refining process. It was concluded that a dedicated study is required to optimize the nozzle injection parameters, including the angles and diameters, to achieve maximum efficiency in this reactor design.