We present and discuss numerical results from simulations of the air-water flow in an annular gap bubble column of 0.24 m internal diameter, at air superficial velocities ranging from 0.004 m/s to 0.225 m/s, covering the homogeneous and heterogeneous flow regimes. A bi-dispersed Eulerian model is implemented to account for both the stabilizing and destabilizing effects of small and large bubbles. Sensitivity studies on the mesh element size, time step size and number of outer iterations per time step are performed and most appropriate simulation parameters and mesh are used to predict the gas holdup curve. Comparison with two mono-dispersed models is provided to emphasize the necessity of a bi-dispersed approach for the accurate prediction of the homogeneous flow regime, given the poly dispersed nature of the flow investigated. Two different approaches for the characterization of the small and large bubbles groups are also discussed. We found that the relative amount of small bubbles is an important input parameter for the present model and can be provided using available empirical correlations or experimental data. The results obtained from the simulations also demonstrated the necessity of a population balance model able to capture the bubbles coalescence and breakup phenomena for the correct prediction of the heterogeneous flow regime. (C) 2016 Elsevier Ltd. All rights reserved.