Over the last decade, there has been an irreversible shift from hydrocarbon exploration towards carbon storage, low-carbon energy generation and hydrogen exploration. Whilst basin modelling techniques may be used to predict the migration of hydrocarbons through sedimentary basins on geological timescales, there remains little understanding of how fluids behave at the basin scale on present-day timescales. Maximum vertical fluid velocity, vmax, may be calculated as the product of mobility and buoyancy. We present am algorithm to determine the basin-scale mobilities of CO2 and methane with depth for sandstone and carbonate. CO2 and methane mobility and buoyancy increase by an order of magnitude at gas phase transitions and are significantly greater in sandstone than in carbonate. Critical properties of CO2 cause fluid mobility and buoyancy to be sensitive to changes in surface temperature. vmax for CO2 and methane are on scales of m/year. Our results indicate an optimal depth for CO2 storage of below 0.59 km and 1.24 km when surface temperature > 20oC and 0oC, respectively. vmax for hydrogen is approximately 2-10 times greater than other hydrocarbon fluids and this will have important consequences for the future use of basin modelling software for determining hydrogen migration for exploration and storage.