This work was carried out within the Qatar Carbonates and Carbon Storage Research Centre to improve the characterisation of carbonate reservoirs. 3D images obtained using X-ray micro-tomography were used to characterise heterogeneity in surface area in one sandstone and five carbonate rocks. Surface area measured from X-ray imagery were 1 to 2 orders of magnitude lower than nitrogen BET measurements. Roughness factor, i.e. the ratio of BET surface area to X-ray based surface area, was correlated to the presence of clay or microporosity. Comparing statistical distributions of surface area to those in published modelling studies showed that the common practice of leaving surface area and pore volume uncorrelated in a pore led to unrealistic combinations of surface area and pore volume. In Berea sandstone, constraining ratios of surface area to pore volume to a range of values between that of quartz-lined and five times that of clay-lined spheres appeared sufficient. Statistical analysis suggest that at 600 micrometre, the observations do not yet form a representative elementary volume. The development of dual-energy CT for phase identification is presented. Kaolinite, plagioclase, biotite, quartz, orthoclase, albite, dolomite, calcite, pyrite, magnetite, and hematite were scanned. The pairs: plagioclase-orthoclase, albite-quartz, biotite-orthoclase, and hematite-magnetite were not distinguished. Discrimination was possible for all other combinations. In Berea sandstone, kaolinite-smectite, quartz-albite, alkali feldspar-plagioclase, and pyrite-rutile were identified separately. Dual-energy CT has better contrast or capacity for larger samples than single-energy CT. Finally, an adsorption isotherm was measured from batch experiments with quartz and aqueous caesium chloride. 0.755 M of caesium remained in solution while 0.995 mole of caesium was adsorbed per square metre of quartz. Adsorption was expected to increase average attenuation seven-fold and contribute to 86% of the average attenuation in the image. CT images were collected of an equivalent column experiment with quartz powder and aqueous caesium chloride. However, adsorbed caesium was measured to contribute less than 1% of the average attenuation. This work has provided new capabilities to characterise pore-scale mineral and surface area heterogeneity and improve our understanding of CO2 storage in carbonates.