Basalt formations could enable secure long-term carbon storage by trapping injected CO2 as stable carbonates. Here, a predictive modeling framework was designed to evaluate the roles of transport limitations and mineral spatial distributions on mineral dissolution and carbonation reactions in fractured basalts exposed to CO2-acidified fluids. Reactive transport models were developed in CrunchTope based on data from high-temperature, high-pressure flow-through experiments. Models isolating the effect of transport compared nine flow conditions under the same mineralogy. Heterogeneities were incorporated by segmenting an actual reacted basalt sample, and these results were compared to equivalent flow conditions through randomly generated mineral distributions with the same bulk composition. While pure advective flow with shorter retention times promotes rapid initial carbonation, pure diffusion sustains mineral reactions for longer time frames and generates greater net carbonate volumes. For the same transport conditions and bulk composition, exact mineral spatial distributions do not impact the amount of carbonation but could determine the location by controlling local solution saturation with respect to secondary carbonates. In combination, the results indicate that bulk mineralogy will be more significant than small-scale heterogeneities in controlling the rate and extent of CO2 mineralization, which will likely occur in diffusive zones adjacent to flow paths or in dead-end fractures.