Vibration of gas gives an improvement on bubble formation process in bubble column performance. The paper studies the simulation of the bubble size distribution (BSD) in an oscillating bubble column for the air-water system starting from the Population balance equation for water with AL2O3 nanoparticles. Two different coalescence models (Prince & Blanch model and Luo model were studied with one breakup model (Martinez-Bazan Breakup) to get the BSD simulation and the Sauter mean diameter at different heights of the column. To get the best coalescence model that would be suitable for the simulation when compared with the experiment and simulation done by Waghmare [18]. Prince and Blanch coalescence model gives very good results when compared with Waghmare [18]. Prince and Blanch model was the best model because it was stable in all frequencies simulations and is recommended for a more complicated vibration model in the future. Then the simulation was done with Prince and Blanch coalescence model, with the same input data, with different percentages of AL2O3 nanoparticles in water to investigate the effect of nanoparticles percentage on bubble formation.