A reservoir carbonate core plug has been imaged in 3D across a range of length scales using high resolution X-ray microtomography (μ-CT). Data from the original 40-mm diameter plug was obtained at the vug scale (42 μm resolution) and allows the size, shape and spatial distribution of the disconnected vuggy porosity, ϕvug = 3.5% to be measured. Within the imaged volume over 32,000 separate vugs are identified and a broad vug size distribution is measured. Higher resolution images, down to 1.1 μm resolution, on subsets of the plug exhibit interconnected porosity and allow one to measure characteristic, intergranular pore size. Pore scale structure and petrophysical properties (permeability, drainage capillary pressure, formation factor, and NMR response) are derived directly on the highest resolution tomographic dataset. We show that data over a range of porosity can be computed from a single plug fragment. Data for the carbonate core is compared to results derived from 3D images of clastic cores and strong differences noted. Computations of permeability are compared to conventional laboratory measurements on the same core material with good agreement. This demonstrates the feasibility of combining digitized images with numerical calculations to predict properties and derive cross-correlations for carbonate lithologies.