In ladle metallurgy, the role of argon gas purging in liquid steel is well recognized. One key aspect of this process is the prediction of gas volume fraction and gas bubble diameter. Calculation of bubble size is important as it is significantly modified by the injection system and gas flow rate, and it also directly determines the buoyancy which influences the physical mixing process and surface reactions. In this study, a porous plug was used for gas injection as the common practice in the steel industry and a one-third scale water model was established. Then a numerical model based on the Eulerian multiphase model was established and the population balance model (PBM) was used to calculate the gas bubble size distribution. The bubble coalescence and breakage were included and the phase interactions were coupled with the PBM to consider the effect of bubble diameter on the fluid flow. A user defined scalar (UDS) transport equation was added to simulate the solute transport in ladle to study the mixing efficiency. The mixing time, wall shear stress and slag entrapment probability were taken into consideration to find a suitable plug position to balance the mixing efficiency and steel cleanness. The results show that the mixing time decreases with increasing the plug radial distance and the maximum wall shear stress appears when plug radial distance is 0.67 R.