This study reveals the pore-scale details of oil mobilisation and recovery from a carbonate rock upon injection of aqueous nanoparticle (NP) suspensions. X-ray computed micro-tomography (μCT), which is a non-destructive imaging technique, was used to acquire a dataset which includes: (i) 3D images of the sample collected at the end of fluid injection steps, and (ii) 2D radiogram series collected during fluid injections. The latter allows monitoring fluid flow dynamics at time resolutions down to a few seconds using a laboratory-based μCT scanner. By making this dataset publicly available we enable (i) new image reconstruction algorithms to be tested on large images, (ii) further development of image segmentation algorithms based on machine learning, and (iii) new models for multi-phase fluid displacements in porous media to be evaluated using images of a dynamic process in a naturally occurring and complex material. This dataset is comprehensive in that it offers a series of images that were captured before/during/and after the immiscible fluid injections.