DeepAngle: Fast calculation of contact angles in tomography images using deep learning

DeepAngle is a machine learning-based method to determine the contact angles of different phases in the tomography images of porous materials. Measurement of angles in 3--D needs to be done within the surface perpendicular to the angle planes, and it could become inaccurate when dealing with the discretized space of the image voxels. A computationally intensive solution is to correlate and vectorize all surfaces using an adaptable grid, and then measure the angles within the desired planes. On the contrary, the present study provides a rapid and low-cost technique powered by deep learning to estimate the interfacial angles directly from images. DeepAngle is tested on both synthetic and realistic images against the direct measurement technique and found to improve the r-squared by 5 to 16% while lowering the computational cost 20 times. This rapid method is especially applicable for processing large tomography data and time-resolved images, which is computationally intensive. The developed code and the dataset are available at an open repository on GitHub (https://www.github.com/ArashRabbani/DeepAngle).

A comparative study of paired versus unpaired deep learning methods for physically enhancing digital rock image resolution

X-ray micro-computed tomography (micro-CT) has been widely leveraged to characterise pore-scale geometry in subsurface porous rock. Recent developments in super resolution (SR) methods using deep learning allow the digital enhancement of low resolution (LR) images over large spatial scales, creating SR images comparable to the high resolution (HR) ground truth. This circumvents traditional resolution and field-of-view trade-offs. An outstanding issue is the use of paired (registered) LR and HR data, which is often required in the training step of such methods but is difficult to obtain. In this work, we rigorously compare two different state-of-the-art SR deep learning techniques, using both paired and unpaired data, with like-for-like ground truth data. The first approach requires paired images to train a convolutional neural network (CNN) while the second approach uses unpaired images to train a generative adversarial network (GAN). The two approaches are compared using a micro-CT carbonate rock sample with complicated micro-porous textures. We implemented various image based and numerical verifications and experimental validation to quantitatively evaluate the physical accuracy and sensitivities of the two methods. Our quantitative results show that unpaired GAN approach can reconstruct super-resolution images as precise as paired CNN method, with comparable training times and dataset requirement. This unlocks new applications for micro-CT image enhancement using unpaired deep learning methods; image registration is no longer needed during the data processing stage. Decoupled images from data storage platforms can be exploited more efficiently to train networks for SR digital rock applications. This opens up a new pathway for various applications of multi-scale flow simulation in heterogeneous porous media.

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.

ML-LBM: Machine Learning Aided Flow Simulation in Porous Media

Simulation of fluid flow in porous media has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater, hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of flow in porous media requires significant computational resources to solve within reasonable timeframes. An integrated method combining predictions of fluid flow (fast, limited accuracy) with direct flow simulation (slow, high accuracy) is outlined. In the tortuous flow paths of porous media, Deep Learning techniques based on Convolutional Neural Networks (CNNs) are shown to give an accurate estimate of the steady state velocity fields (in all axes), and by extension, the macro-scale permeability. This estimate can be used as-is, or as initial conditions in direct simulation to reach a fully accurate result in a fraction of the compute time. A Gated U-Net Convolutional Neural Network is trained on a datasets of 2D and 3D porous media generated by correlated fields, with their steady state velocity fields calculated from direct LBM simulation. Sensitivity analysis indicates that network accuracy is dependent on (1) the tortuosity of the domain, (2) the size of convolution filters, (3) the use of distance maps as input, (4) the use of mass conservation loss functions. Permeability estimation from these predicted fields reaches over 90\% accuracy for 80\% of cases. It is further shown that these velocity fields are error prone when used for solute transport simulation. Using the predicted velocity fields as initial conditions is shown to accelerate direct flow simulation to physically true steady state conditions an order of magnitude less compute time. Using Deep Learning predictions (or potentially any other approximation method) to accelerate flow simulation to steady state in complex pore structures shows promise as a technique push the boundaries fluid flow modelling.

Physical Accuracy of Deep Neural Networks for 2D and 3D Multi-Mineral Segmentation of Rock micro-CT Images

Segmentation of 3D micro-Computed Tomographic uCT) images of rock samples is essential for further Digital Rock Physics (DRP) analysis, however, conventional methods such as thresholding, watershed segmentation, and converging active contours are susceptible to user-bias. Deep Convolutional Neural Networks (CNNs) have produced accurate pixelwise semantic segmentation results with natural images and $\mu$CT rock images, however, physical accuracy is not well documented. The performance of 4 CNN architectures is tested for 2D and 3D cases in 10 configurations. Manually segmented uCT images of Mt. Simon Sandstone are treated as ground truth and used as training and validation data, with a high voxelwise accuracy (over 99%) achieved. Downstream analysis is then used to validate physical accuracy. The topology of each segmented phase is calculated, and the absolute permeability and multiphase flow is modelled with direct simulation in single and mixed wetting cases. These physical measures of connectivity, and flow characteristics show high variance and uncertainty, with models that achieve 95\%+ in voxelwise accuracy possessing permeabilities and connectivities orders of magnitude off. A new network architecture is also introduced as a hybrid fusion of U-net and ResNet, combining short and long skip connections in a Network-in-Network configuration. The 3D implementation outperforms all other tested models in voxelwise and physical accuracy measures. The network architecture and the volume fraction in the dataset (and associated weighting), are factors that not only influence the accuracy trade-off in the voxelwise case, but is especially important in training a physically accurate model for segmentation.

Boosting Resolution and Recovering Texture of micro-CT Images with Deep Learning

Digital Rock Imaging is constrained by detector hardware, and a trade-off between the image field of view (FOV) and the image resolution must be made. This can be compensated for with super resolution (SR) techniques that take a wide FOV, low resolution (LR) image, and super resolve a high resolution (HR), high FOV image. The Enhanced Deep Super Resolution Generative Adversarial Network (EDSRGAN) is trained on the Deep Learning Digital Rock Super Resolution Dataset, a diverse compilation 12000 of raw and processed uCT images. The network shows comparable performance of 50% to 70% reduction in relative error over bicubic interpolation. GAN performance in recovering texture shows superior visual similarity compared to SRCNN and other methods. Difference maps indicate that the SRCNN section of the SRGAN network recovers large scale edge (grain boundaries) features while the GAN network regenerates perceptually indistinguishable high frequency texture. Network performance is generalised with augmentation, showing high adaptability to noise and blur. HR images are fed into the network, generating HR-SR images to extrapolate network performance to sub-resolution features present in the HR images themselves. Results show that under-resolution features such as dissolved minerals and thin fractures are regenerated despite the network operating outside of trained specifications. Comparison with Scanning Electron Microscope images shows details are consistent with the underlying geometry of the sample. Recovery of textures benefits the characterisation of digital rocks with a high proportion of under-resolution micro-porous features, such as carbonate and coal samples. Images that are normally constrained by the mineralogy of the rock (coal), by fast transient imaging (waterflooding), or by the energy of the source (microporosity), can be super resolved accurately for further analysis downstream.

Super Resolution Convolutional Neural Network Models for Enhancing Resolution of Rock Micro-CT Images

Single Image Super Resolution (SISR) techniques based on Super Resolution Convolutional Neural Networks (SRCNN) are applied to micro-computed tomography ({\mu}CT) images of sandstone and carbonate rocks. Digital rock imaging is limited by the capability of the scanning device resulting in trade-offs between resolution and field of view, and super resolution methods tested in this study aim to compensate for these limits. SRCNN models SR-Resnet, Enhanced Deep SR (EDSR), and Wide-Activation Deep SR (WDSR) are used on the Digital Rock Super Resolution 1 (DRSRD1) Dataset of 4x downsampled images, comprising of 2000 high resolution (800x800) raw micro-CT images of Bentheimer sandstone and Estaillades carbonate. The trained models are applied to the validation and test data within the dataset and show a 3-5 dB rise in image quality compared to bicubic interpolation, with all tested models performing within a 0.1 dB range. Difference maps indicate that edge sharpness is completely recovered in images within the scope of the trained model, with only high frequency noise related detail loss. We find that aside from generation of high-resolution images, a beneficial side effect of super resolution methods applied to synthetically downgraded images is the removal of image noise while recovering edgewise sharpness which is beneficial for the segmentation process. The model is also tested against real low-resolution images of Bentheimer rock with image augmentation to account for natural noise and blur. The SRCNN method is shown to act as a preconditioner for image segmentation under these circumstances which naturally leads to further future development and training of models that segment an image directly. Image restoration by SRCNN on the rock images is of significantly higher quality than traditional methods and suggests SRCNN methods are a viable processing step in a digital rock workflow.