We model carbon dioxide (CO2) storage into a deep North Sea aquifer using streamline-based simulation. We assume incompressible flow of liquid-like CO2 and aqueous phases. We simulate dissolution of CO2 and a rate-limited precipitation reaction. Advective transport and reactions are solved along streamlines, while dispersion and flow due to gravity segregation of the phases are solved on the underlying grid. Geological storage is modeled on a one million cell model. The distribution of CO2 after injection is dominated by advective transport due to multiphase flow, and CO2 moves preferentially through high-permeability channels. Without reaction the regional groundwater flow causes the CO2 to continue to migrate until it reaches residual saturation, where it continues, slowly, to dissolve. Precipitation leads to a decrease in porosity and permeability, while CO2 is stored in the solid phase. The storage efficiency is low, around 2%, because of aquifer heterogeneity.