We imaged the steady-state flow of brine and decane (oil) at different fractional flows during dual injection in a micro-porous limestone, Estaillades, using X-ray micro-tomography. We applied differential imaging to: (a) distinguish micro-porous regions from macro-pores, and (b) determine fluid pore occupancy in both regions, and relative permeability at a capillary number, Ca = 7.3 × 10 −6 . The sample porosity was approximately 28%, with 7% in macro-pores and 21% in pores that could not be directly resolved (micro-porosity). Fluid occupancy in micro-porosity was classified into three sub-phases: micro-pore space with oil, micro-pore space with brine, and micro-pores partially filled with oil and brine. Our method indicated an initially higher oil recovery from micro-porosity, consistent with waterflooding in a water-wet rock. The fractional flow and relative permeabilities of the two fluids were obtained from measurements of the pressure differential across the sample and the saturation calculated from the images. The brine saturation and relative permeabilities are impacted by the presence of water-wet micro-porosity which provides additional connectivity to the phases. Furthermore, we find that in addition to brine and decane, a fraction of the macroscopic pore space contains an intermittent phase, which is occupied either by brine or decane during the hour-long scan time. Pore and throat occupancy of oil, brine and intermittent phase were obtained from images at different fractional flows using the generalized pore network extracted from the image of macro-pores. The intermittent phase, where the occupancy fluctuated between oil-filled and brine-filled, was predominantly located in the small and intermediate size pores and throats. Overall, we establish a new experimental methodology to: (i) quantify initial and recovered oil in micro-pores, (ii) characterise intermittent flow, and (iii) measure steady-state relative permeability in carbonates, which is shown to be greatly influenced by micro-porosity.