Deep learning of multi-resolution X-Ray micro-CT images for multi-scale modelling

There are inherent field-of-view and resolution trade-offs in X-Ray micro-computed tomography imaging, which limit the characterization, analysis and model development of multi-scale porous systems. In this paper, we overcome these tradeoffs by developing a 3D Enhanced Deep Super Resolution (EDSR) convolutional neural network to create enhanced, high-resolution data over large spatial scales from low-resolution data. Paired high-resolution (HR, 2$\mu$m) and low resolution (LR, 6$\mu$m) image data from a Bentheimer rock sample are used to train the network. Unseen LR and HR data from the training sample, and another sample with a distinct micro-structure, are used to validate the network with various metrics: textual analysis, segmentation behaviour and pore-network model (PNM) multiphase flow simulations. The validated EDSR network is used to generate ~1000 high-resolution REV subvolume images for each full core sample of length 6-7cm (total image sizes are ~6000x6000x32000 voxels). Each subvolume has distinct petrophysical properties predicted from PNMs, which are combined to create a 3D continuum-scale model of each sample. Drainage immiscible flow at low capillary number is simulated across a range of fractional flows and compared directly to experimental pressures and 3D saturations on a 1:1 basis. The EDSR generated model is more accurate than the base LR model at predicting experimental behaviour in the presence of heterogeneities, especially in flow regimes where a wide distribution of pore-sizes are encountered. The models are generally accurate at predicting saturations to within the experimental repeatability and relative permeability across three orders of magnitude. The demonstrated workflow is a fully predictive, without calibration, and opens up the possibility to image, simulate and analyse flow in truly multi-scale heterogeneous systems that are otherwise intractable.