The data presented herein comprises raw and upscaled medical X-Ray CT data, MATLAB processing files and MATLAB analytical model files for the paper ‘Rate dependency of capillary heterogeneity trapping for CO2 storage’. The medical X-ray CT data is organised as three repeat experiments, each at a different flow rate. Full core scans capture the steady state core flood experiments. The core is a heterogenous Bentheimer outcrop (39 mm diameter, 15 cm length). Experimental MATLAB processing files upscale the saturation values in 3D. Post-processing MATLAB files are used to produce figures in the paper. The MATLAB analytical model files contain input parameters and code needed to run the analytical model and compare with experimental results.