The evolution of bubble size distribution is an important consideration in vertical gas-liquid flow, especially in determining the appropriate mass, momentum, and heat transfer between two phases. In order to adequately capture the distribution and to account for its effect on the local hydrodynamics, which generally represents the dominant flow characteristic in such a practical system, a numerical assessment has been performed to understand the six widely adopted different bubble coalescence and bubble breakage kernels. Three different breakage kernels have been selected where each kernel considers a different shape of the daughter size distribution of the bubbles, such as the U-shape, bell-shape, and M-shape. These are combined with different coalescence kernels. The bubble size distribution, void fraction, interfacial area concentration, and gas velocity profiles are compared against the experimental data. Numerical results reveal that the effect on the two-phase flow structure is mainly due to the application of the different breakage kernels. Moreover, the predicted results also show that the bell-shape daughter size distribution favours equal breakage of bubbles, which could lead to the over-prediction of large bubbles. A more sophisticated model for handling bubble induced turbulence should nonetheless be applied in future investigations of vertical gas-liquid flow.