The datasets contain 5 stitched X-ray micro-tomographic images (grey-scale, doped, difference, segmented porespace and segmented micro-porespace with porespace) and 3 X-ray nano-tomographic images of a region of microporous porespace in Estaillades Limestone. The x-ray tomographic images were acquired at a voxel-resolution of 3.9676 µm using a Zeiss Versa XRM-510 flat-panel detector at 70 kV, 6W, and 85 µA with an exposure time of 0.037s and 64 frames. The X-ray nano-tomographic images were reconstructed using a proprietary filtered back projection algorithm from a set of 1601 projections, collected with the Zeiss Ultra 810 with 32nm voxel size using a 5.4keV energy quasi-monochromatic beam with an exposure time of 90s. The data was collected at Imperial College London and Zeiss Labs with the aim of investigating pore-scale microporosity in carbonates with a heterogenous pore structure. Understanding the effect of microporosity on flow is important in many natural and industrial processes such as contaminant transport, and geo-sequestration of supercritical CO2 to address global warming. These tomographic images can be used for validating various pore-scale flow models such as direct simulations, pore-network and neural network models for upscaling flow across scales.