Integrating numerical modelling and experimental observations is essential to characterising small-scale heterogeneity for subsurface flow • Capillary heterogeneity characterisation in carbonates was only successful when 10 key features were resolved in X-ray imagery 11 • Isotropic capillary heterogeneity in carbonates results in a non-monotonic rate-12 dependant relative permeability

The scaleup of CO 2 storage underground to mitigate climate change will require accurate forecasts of the flow behavior of CO 2 in subsurface reservoirs (Boot-Handford et al., 2014;Edenhofer et al., 2014). Flow in the subsurface is often controlled by geological heterogeneity with length scales ranging from micrometers to kilometers. This is particularly the case for carbonate reservoirs which hold more than half of the world's hydrocarbon reserves and have significant storage potential (Sayers, 2008). Reservoir heterogeneity poses challenges to modeling of the fluid flow and is considered a leading cause of difficulties in simulating observed plume migration at a number of industrial and pilot CO 2 storage projects (Cavanagh & Nazari-

The flow of a suspension through a bifurcating channel is studied experimentally and by computational methods. The geometry considered is an ‘asymmetric T’, as flow in the entering branch divides to either continue straight or to make a right angle turn. All branches are of the same square cross-section of side length $D$, with inlet and outlet section lengths $L$ yielding $L/D=58$ in the experiments. The suspensions are composed of neutrally buoyant spherical particles in a Newtonian liquid, with mean particle diameters of $d=250~\unicode[STIX]{x03BC}\text{m}$ and $480~\unicode[STIX]{x03BC}\text{m}$ resulting in $d/D\approx 0.1$ to $d/D\approx 0.2$ for $D=2.4~\text{mm}$. The flow rate ratio $\unicode[STIX]{x1D6FD}=Q_{\Vert }/Q_{0}$, defined for the bulk, fluid and particles, is used to characterize the flow behaviour; here $Q_{\Vert }$ and $Q_{0}$ are volumetric flow rates in the straight outlet branch and inlet branch, respectively. The channel Reynolds number $Re=(\unicode[STIX]{x1D70C}DU)/\unicode[STIX]{x1D702}$ was varied over $0<Re<900$, with $\unicode[STIX]{x1D70C}$ and $\unicode[STIX]{x1D702}$ the fluid density and viscosity, respectively, and $U$ the mean velocity in the inlet channel; the inlet particle volume fraction was $0.05\leqslant \unicode[STIX]{x1D719}_{0}\leqslant 0.30$. Experimental and numerical results for single-phase Newtonian fluid both show $\unicode[STIX]{x1D6FD}$ increasing with $Re$, implying more material tending toward the straight branch as the inertia of the flow increases. In suspension flow at small $\unicode[STIX]{x1D719}_{0}$, inertial migration of particles in the inlet branch affects the flow rate ratio for particles ($\unicode[STIX]{x1D6FD}_{\mathit{particle}}$) and suspension ($\unicode[STIX]{x1D6FD}_{\mathit{suspension}}$). The flow split for the bulk suspension satisfies $\unicode[STIX]{x1D6FD}>0.5$ for $\unicode[STIX]{x1D719}_{0}<0.16$ while $\unicode[STIX]{x1D719}_{0}=0.16$ crosses from $\unicode[STIX]{x1D6FD}\approx 0.5$ to $\unicode[STIX]{x1D6FD}>0.5$ at $Re\approx 100$. For $\unicode[STIX]{x1D719}_{0}\geqslant 0.2$, $\unicode[STIX]{x1D6FD}<0.5$ at all $Re$ studied. A complex dependence of the mean solid fraction in the downstream branches upon inlet fraction $\unicode[STIX]{x1D719}_{0}$ and $Re$ is observed: for $\unicode[STIX]{x1D719}_{0}<0.1$, the solid fraction in the straight downstream branch initially decreases with $Re$, before increasing to surpass the inlet fraction at large $Re$ ($Re\approx 500$ for $\unicode[STIX]{x1D719}_{0}=0.05$). At $\unicode[STIX]{x1D719}_{0}>0.1$, the solid fraction in the straight branch satisfies $\unicode[STIX]{x1D719}_{\Vert }/\unicode[STIX]{x1D719}_{0}>1$, and this ratio grows with $Re$. Discrete-particle simulations employing immersed boundary and lattice-Boltzmann techniques are used to analyse these phenomena, allowing rationalization of aspects of this complex behaviour as being due to particle migration in the inlet branch.

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There are inherent field-of-view and resolution trade-offs in X-Ray micro-computed tomography (micro-CT) 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, 2µm) and low resolution (LR, 6µm) 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 porenetwork model (PNM) multiphase flow simulations. The validated EDSR network is then used to generate ≈1000 high-resolution REV subvolume images for each full core sample of length 6-7cm (total image sizes are ≈6000×6000×32000 voxels). Each subvolume has distinct petrophysical properties predicted from PNM simulations, which are combined to create a 3D continuum-scale model of each sample. Drainage immiscible flow at low capillary number is simulated with the models across a range of fractional flows and flow rates and compared directly to experimental pressures and 3D saturations on a 1:1 basis. The EDSR generated model is found to be 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 modelling approach, without calibration, and opens up the possibility to image, simulate and analyse flow in truly multiscale heterogeneous systems that are otherwise intractable.