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    This dataset contains digital models of three carbonate (Indiana limestone, Estaillades limestone and Edwards Brown Dolomite) and two sandstone (Bentheimer and Bunter) cores with varying degrees of heterogeneity types and length scales. The models define the spatial distribution of porosity and capillary heterogeneity, and can simulate core floods. To build these models, the workflow by Jackson et al. (2018) was followed. It combines observations from coreflood experiments with a numerical optimisation scheme to characterise the capillary heterogeneity within a rock sample. The data presented here contains the experimental X-ray CT dataset used for the paper "History Matching Core Floods in Heterogeneous Sandstone and Carbonate Rocks" by Wenck et al. (Under Review) along with CMG IMEX modelling files. Funding source: EPSRC iCase studentship with BP