Bubble-size distributions and flow fields in bubble columns are calculated numerically. The population balance is simplified and reduced to a balance equation for the average bubble volume. Models developed predict the rate of bubble breakup and coalescence based on physical principles. The flow fields are numerically calculated for bubble columns with cylindrical cross sections using the Euler-Euler method. The newly derived balance equations for the average bubble volumes are implemented into a commercial CFD code. The solutions of the balance equation for high superficial gas velocities result mainly in two fractions: one for the fraction with small and the other for the fraction with large bubble diameters. Both are considered pseudocontinuous phases, in addition to the liquid phase. The calculated flow fields are characterized by several large-scale vortices. The local volume fractions of gas and liquid are locally inhomogeneous and highly time-dependent. The time-averaged flow field is axisymmetric and stationary. The calculated volume fractions, velocities, and bubble-size distributions agree well with existing and previously published experimental results for bubble columns up to 0.3 m in diameter.