CFD simulations of bubble columns have received much attention, and several multiphase models have been developed, tested, and validated through comparison with experimental data. It is well-known that bubble coalescence and breakup can lead to significant variations in the bubble size distribution and that, to model the evolution of the dispersed gas phase, the population balance equation has to be solved. In this work, a classes method (CM) and a method of moments (MOM) are investigated and compared. The MOM represents an attractive alternative in which, instead of tracking the entire bubble distribution, only the lower-order moments of the distribution are tracked. The above two approaches have been implemented in the commercial CFD code FLUENT, version 6.0, in conjunction with the Eulerian multiphase model.