A mathematical model entitled varying-bubble model (V-BM) was adapted to simulate a slurry bubble-column reactor, operating in a churn-turbulent regime, based on an axial-dispersion model. This model was theoretically able to estimate the size of forming bubbles at the sparger, variations of each chemical species and catalyst concentration, pressure drop in both gas and liquid phases, change in size and rising velocity of bubbles, as well as gas holdup and specific gas-liquid interfacial area along the reactor axis. A comparison between the V-BM and single-bubble model (S-BM) indicates that the V-BM is better compatible with the experimental data. The results demonstrate that the contribution of mass transfer is much more than the pressure drop in increasing the size of the bubble along the reactor.