**4. Conclusions**

In the numerical study of the effect of dual gas injection using equal (50%:50%) and differentiated (75%:25%) flows and variable (slag) oil thickness compared with the experimental results obtained previously, the following conclusions can be made:


The anomaly in the observations is attributed to the insufficient capture of the hydrodynamic behavior near the water–oil (steel–slag) interface, probably caused by the emulsification of slag, which might also influence changes in the gas plumes, linked to the change in the mode of gas injection. This is coupled with the difficulty of accurately predicting the complex interaction between the gas plumes, especially in differentiated injection, which causes a variation in the predicted values of mixing time and slag eye area, although the effect of the variables (gas flow rate, slag height and injection mode) can be studied with an in-depth understanding of the mathematical model presented.

**Author Contributions:** Conceptualization, M.A.R.-A. and A.D.; methodology, L.E.J.-P.; software, L.E.J.-P. and A.D.; validation, L.E.J.-P. and C.G.-R.; formal analysis, C.G.-R.; investigation, L.E.J.-P. and C.G.-R.; resources, L.E.J.-P.; writing—original draft preparation, L.E.J.-P.; writing—review and editing, A.D. and C.G.-R.; supervision, A.D.; funding acquisition, M.A.R.-A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by [DGAPA UNAM] grant number [PAPIIT IN115619] and L.E.J.-P. received PhD scholarship by [CONACYT] grant number [CVU 624968].

**Conflicts of Interest:** The authors declare no conflict of interest.
