Rapid implementation of global scale carbon capture and storage is required to limit temperature rises to 1.5 °C this century. Depleted oilfields provide an immediate option for storage, since injection infrastructure is in place and there is an economic benefit from enhanced oil recovery. To design secure storage, we need to understand how the fluids are configured in the microscopic pore spaces of the reservoir rock. We use high-resolution X-ray imaging to study the flow of oil, water and CO2 in an oil-wet rock at subsurface conditions of high temperature and pressure. We show that contrary to conventional understanding, CO2 does not reside in the largest pores, which would facilitate its escape, but instead occupies smaller pores or is present in layers in the corners of the pore space. The CO2 flow is restricted by a factor of ten, compared to if it occupied the larger pores. This shows that CO2 injection in oilfields provides secure storage with limited recycling of gas; the injection of large amounts of water to capillary trap the CO2 is unnecessary.