Population balance modeling in a gas-liquid two-phase bubbly flow allows us to predict the bubble size distribution. The prediction of bubble size distribution is of utmost importance as it prevails the heat, mass, and momentum transport mechanisms. In the present work, numerical simulations of gas-liquid two-phase flow in a vertical pipe have been performed using population balance modeling. The effects of different coalescence and breakage models have been studied. The wall peak and core peak case in the bubbly flow regime is considered for the prediction of the radial distribution of the gas void fraction, interfacial area concentration, bubble size distribution, Sauter mean diameter, and gas and liquid velocities. Numerical simulations were performed with the Euler-Euler two-fluid model and the k-omega SST turbulence model. The population balance equation is solved using the traditional class method. The combination of Brownian coalescence and Ghadiri breakage model is recommended for the prediction of the wall peak case, whereas the combination of Luo coalescence and Ghadiri breakage model is recommended for the prediction of the core peak case.