Geological carbon storage provides an efficient technology for the large-scale reduction of atmospheric carbon, and the drive for net-zero emissions may necessitate the future usage of oil reservoirs for CO2 projects (without oil production), hence, dynamic modeling of an oil reservoir for CO2 storage in the Bredasdorp basin, South Africa, was therefore conducted. Injection into the reservoir was for 20 years (2030–2050), and 100 years (2050–2150) to study the CO2–brine–oil interactions, with sensitivities carried out on reservoir boundary conditions. The closed boundary scenario experienced pressure buildup with a target injection rate of 0.5 Mt/year, and a cutback on injection rate progressively until 2050 to not exceed the fracture pressure of the reservoir. The CO2 plume migration was not rapid due to the reduced volume of CO2 injected and the confining pressure. The system was gravity dominated, and gravity stability was not attained at the end of the simulation as fluid interfaces were not yet flat. The open boundary reservoir did not experience a pressure buildup because all boundaries were open, the target injection rate was achieved, and it was a viscous-dominated system. In both cases, the dissolution of CO2 in oil and brine was active, and there was a growing increase of CO2 fraction dissolved in water and oil, a decline in gaseous mobile CO2 phase between 2050 and 2150, and active trapping mechanisms were structural trapping, dissolution in oil and water, and residual trapping. The study showed that boundary condition was very crucial to the success of the project, with direct impacts on injection rate and pressure. This pioneering study has opened a vista on the injection of CO2 into an oil reservoir, and CO2–brine–oil interactions, with sensitivities carried out on reservoir boundary conditions in a closed and an open hydrocarbon system in South Africa.