This dataset consists of multi-resolution X-Ray micro-tomography images of two Bentheimer sandstone rock cores. The rock cores were first used experimentally in [1] with further modelling in [2]. This new dataset is used directly in the publication [3] - preprint available at https://arxiv.org/abs/2111.01270. The original dataset from [1] (of the same rock cores) is hosted on the BGS National Geoscience Data Centre, ID #130625 at dx.doi.org/10.5285/5f899de8-4085-4370-a45e-e613f27e8f1d and there is also a subvolume image dataset, for easier download available on the Digital Rocks Portal, project 229, DOI:10.17612/KT0B-SZ28 at digitalrocksportal.org/projects/229. The images provided herein are from two distinct Bentheimer rock cores -- core 1 and core 2. The cores have diameter, 12.35mm, lengths 73.2mm and 64.7mm, core-averaged porosities of 0.203 and 0.223 and permeabilities of 1.636D and 0.681D for core 1 and 2, respectively. Core 2 has a clear low permeability lamination occurring at 2/3 of the total core length, whereas core 1 has a general fining towards the outlet of the core creating a reduction in porosity [1]. The images were acquired with a Zeiss Versa 510 X-Ray CT scanner. We acquired images of two sub volumes from each core, at locations 1/3rd (subvolume 1) and 2/3rds (subvolume 2) of the way along the core length, at resolutions of 2, 6 and 18 microns. We refer to the 2 micron images as high-resolution (HR), the 6 micron images as low-resolution (LR) and the 18 micron images as very-low-resolution (VLR). There are also super-resolution (SR) images created at 2 micron resolution from the LR images, using a deep-learning algorithm. There are also cubic interpolation images created from the LR image - these are labels bicubic. These have a resolution of 2 microns, and size equal to the HR and SR images. Details of the SR and LR Bicubic generation are found in [3]. The following scanning protocols were used for the direct imaging: 2 micron images: --We use a 4x microscope objective, an exposure time of 8s, 2x averaged binning, 9001 projections, a scan voltage of 80kV and a power of 7W. Each scan takes approximately 24 hours. 6 micron images: --We use a flat panel detector, an exposure time of 0.7s, 10x repeat frames, 1x averaged binning, 2401 projections, a scan voltage of 80kV and a power of 7W. The cone angle is 14.46 degrees and the fan angle is 22.2 degrees. Each scan takes approximately 1 hour. 18 micron images: --We use a 0.4x microscope objective, an exposure time of 1s, 10x repeat frames, 1x averaged binning, 2401 projections, a scan voltage of 80kV and a power of 7W. The cone angle is 12.65 degrees and the fan angle is 12.65 degrees. Each scan takes approximately 2 hours. We present 4 sets of the images with different levels of processing. All images are mutual registered to each other. Each image filename has a Core#_Subvol#_resolution identifier, either with the actual resolution (e.g. 6) or the short form (e.g. LR). The following name endings are used (1) - '_16bit_LE.raw'. These are the .raw images of little-endian format. Preceding this filename is also the cubic image side length in voxels, e.g. _75cube. 12 images in total. (2) - '_16bit_LE_normalised.raw'. These are the .raw images of little-endian format with normalised greyscale values following the procedure in [1]. Preceding this filename is also the cubic image side length in voxels, e.g. _75cube. 12 images in total. (3) - 'Core1_Subvol1_HR' etc. These are the .tiff images of (2) above, which have been converted to 8 bit. Includes bicubic interpolation images and SR images, but no 16 micron images, since these were not used in the analysis of [3]. 16 images in total. (4) - 'Core1_Subvol1_HR_filtered' etc. These are the .tiff images from (3) above, which have filtered using non-local means filtering. More details are found in [3]. Note there are no SR images here since they are already essentially filtered, and included in (3) above. 12 images in total. References [1] Jackson, S.J., Lin, Q. and Krevor, S. 2020. Representative Elementary Volumes, Hysteresis, and Heterogeneity in Multiphase Flow from the Pore to Continuum Scale. Water Resources Research, 56(6), e2019WR026396 [2] Zahasky, C., Jackson, S.J., Lin, Q., and Krevor, S. 2020. Pore network model predictions of Darcy���scale multiphase flow heterogeneity validated by experiments. Water Resources Research, 56(6), e e2019WR026708. [3] Jackson, S.J, Niu, Y., Manoorkar, S., Mostaghimi, P. and Armstrong, R.T. 2021. Deep learning of multi-resolution X-Ray micro-CT images for multi-scale modelling. Under review, preprint available at https://arxiv.org/abs/2111.01270