A new mathematical model considering the process of bubbles interaction has been developed to simulate the transient fluid flow, dispersed bubbles motion and transport process in the slab continuous casting mold. Rather than prescribing a constant bubbles size in previous work, this model allow us to calculate the constantly changed daughter particles size distribution after the process of bubbles collision and breakup. In this paper, using the new model to study the effect of some parameters such as gas flow, casting speed, and the depth of submerged entry nozzle (SEN) on the fluid flow pattern, the gas volume fraction, the distribution of bubbles and so on. The predictions of gas bubble distribution and fluid flow pattern are in good agreement with the water model experimental observations. Meanwhile, the model has successfully reproduced many known phenomena and other new predictions, including the process of bubbles collision and breakup. The simulation results show that the important factors that influence the size and quantity distribution range of bubbles are casting speed and argon gas flow rate and depth of SEN. Through the statistical analysis of bubbles behavior, the effects of blowing argon on porosity defects under different operating conditions can be obtained.