We developed a conduit model of magma ascent to the surface, to understand the influence of input parameters like temperature, crystallinity, water content and depth of reservoir on the eruption rate and style of volcanic eruptions. The main novelty of this model over previous ones is that conduit radius, initial overpressure at the conduit inlet and initial bubble number density are not free parameters chosen by the user but are calculated by the code based on the previously mentioned inputs. We also introduce a simplified model of bubble coalescence to include in the analysis the ascent dynamics of low viscosity magmas. Our test results indicate that high crystal content and low- and high-end water contents favor effusive eruptions. Water content has a limited effect on eruption rate of explosive eruptions as the higher content of volatiles is compensated by a lower viscosity that promotes a smaller stable conduit radius. We tested the model with historical eruptions, ranging from low viscosity basaltic andesites to rhyolites, in order to assess the capability of the model to reproduce the eruption style and eruption rate. The model can predict the occurrence of explosive eruptions (Plinian, sub-Plinian, Strombolian and paroxysmal Hawaiian styles) and effusive eruptions and the order of magnitude of their eruption rates, giving new insights into the main controlling factors of volcanic activity.