A discrete bubble model (DBM) has been used to study the overall gas holdup and the phase mixing in bubble column reactors. The Eulerian–Lagrangian approach has the advantage that it is possible to study the overall gas holdup and the gas phase mixing in a direct way. Furthermore, by introducing tracer particles, also the liquid phase mixing can be studied in a Lagrangian manner. Comparisons suggest that the overall gas holdups obtained from the discrete bubble model agree very well with the correlations of Kumar et al., Heijnen and Van’t Riet, and Ruzicka et al. within the applied range of the superficial gas velocity. The gas phase dispersion coefficients from the simulation results agree pretty well with Wachi and Nojima’s correlation, which is derived on the basis of the recirculation theory. In addition, the turbulent diffusion coefficient calculated from the tracer particles velocities are very close to those from the literature within the applied range of the superficial gas velocity.