Carbon dioxide is a commonly used fluid in Enhanced Oil Recovery (EOR). CO2 EOR process can contribute to the minimisation of the impact of greenhouse gas emission by keeping CO2 out of the atmosphere, as much of it is exchanged with the displaced oil in the pores, and remains trapped in the deep rock formations. We propose to utilise neutron scattering in order to monitor, for first time, the CO2 EOR process by the injection of supercritical CO2 at carbonate samples saturated with crude oil. Mapping the phase behavior of the confined mixture during CO2 injection and the displacement of oil from the pores will shed light about the process at the nanoscale level as it will be linked to the molecular order of the confined fluid mixture. The obtained information will be valuable for the optimization of the oil recovery and the development of appropriate additives for further improvement.